Properties

Label 531.2.i.c.46.2
Level $531$
Weight $2$
Character 531.46
Analytic conductor $4.240$
Analytic rank $0$
Dimension $140$
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] = [531,2,Mod(19,531)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(531, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([0, 38]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("531.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 531.i (of order \(29\), degree \(28\), 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: \(4.24005634733\)
Analytic rank: \(0\)
Dimension: \(140\)
Relative dimension: \(5\) over \(\Q(\zeta_{29})\)
Twist minimal: no (minimal twist has level 177)
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 46.2
Character \(\chi\) \(=\) 531.46
Dual form 531.2.i.c.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15330 - 1.35777i) q^{2} +(-0.189873 + 1.15817i) q^{4} +(1.46043 - 2.75467i) q^{5} +(1.72018 - 0.187081i) q^{7} +(-1.26142 + 0.758972i) q^{8} +O(q^{10})\) \(q+(-1.15330 - 1.35777i) q^{2} +(-0.189873 + 1.15817i) q^{4} +(1.46043 - 2.75467i) q^{5} +(1.72018 - 0.187081i) q^{7} +(-1.26142 + 0.758972i) q^{8} +(-5.42452 + 1.19403i) q^{10} +(3.50223 - 1.18004i) q^{11} +(-0.873623 - 3.14651i) q^{13} +(-2.23789 - 2.11985i) q^{14} +(4.70970 + 1.58688i) q^{16} +(-1.83403 - 0.199462i) q^{17} +(-0.157535 - 2.90556i) q^{19} +(2.91308 + 2.21447i) q^{20} +(-5.64134 - 3.39428i) q^{22} +(7.49743 + 3.46868i) q^{23} +(-2.64941 - 3.90759i) q^{25} +(-3.26468 + 4.81504i) q^{26} +(-0.109943 + 2.02779i) q^{28} +(-1.36377 + 1.60555i) q^{29} +(-0.0823814 + 1.51944i) q^{31} +(-2.18727 - 5.48964i) q^{32} +(1.84436 + 2.72022i) q^{34} +(1.99686 - 5.01175i) q^{35} +(-1.78180 - 1.07207i) q^{37} +(-3.76339 + 3.56487i) q^{38} +(0.248496 + 4.58323i) q^{40} +(-5.46309 + 2.52749i) q^{41} +(-6.73289 - 2.26858i) q^{43} +(0.701710 + 4.28024i) q^{44} +(-3.93711 - 14.1802i) q^{46} +(-6.21469 - 11.7222i) q^{47} +(-3.91232 + 0.861167i) q^{49} +(-2.25004 + 8.10390i) q^{50} +(3.81007 - 0.414370i) q^{52} +(-1.87607 - 0.412954i) q^{53} +(1.86416 - 11.3709i) q^{55} +(-2.02788 + 1.54156i) q^{56} +3.75280 q^{58} +(4.93927 + 5.88249i) q^{59} +(8.38208 + 9.86815i) q^{61} +(2.15805 - 1.64051i) q^{62} +(-0.275238 + 0.519153i) q^{64} +(-9.94346 - 2.18872i) q^{65} +(-9.28244 + 5.58506i) q^{67} +(0.579243 - 2.08624i) q^{68} +(-9.10778 + 3.06877i) q^{70} +(-5.63672 - 10.6320i) q^{71} +(8.12186 + 7.69344i) q^{73} +(0.599321 + 3.65570i) q^{74} +(3.39505 + 0.369234i) q^{76} +(5.80371 - 2.68508i) q^{77} +(3.62730 + 2.75740i) q^{79} +(11.2495 - 10.6561i) q^{80} +(9.73232 + 4.50265i) q^{82} +(-5.51813 + 13.8495i) q^{83} +(-3.22793 + 4.76084i) q^{85} +(4.68484 + 11.7581i) q^{86} +(-3.52217 + 4.14662i) q^{88} +(7.04180 - 8.29025i) q^{89} +(-2.09144 - 5.24912i) q^{91} +(-5.44088 + 8.02470i) q^{92} +(-8.74857 + 21.9573i) q^{94} +(-8.23393 - 3.80942i) q^{95} +(4.83488 - 4.57985i) q^{97} +(5.68134 + 4.31884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).

\(n\) \(119\) \(415\)
\(\chi(n)\) \(1\) \(e\left(\frac{8}{29}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15330 1.35777i −0.815505 0.960087i 0.184235 0.982882i \(-0.441019\pi\)
−0.999740 + 0.0227952i \(0.992743\pi\)
\(3\) 0 0
\(4\) −0.189873 + 1.15817i −0.0949363 + 0.579086i
\(5\) 1.46043 2.75467i 0.653126 1.23193i −0.306827 0.951765i \(-0.599267\pi\)
0.959953 0.280161i \(-0.0903879\pi\)
\(6\) 0 0
\(7\) 1.72018 0.187081i 0.650167 0.0707099i 0.222908 0.974839i \(-0.428445\pi\)
0.427259 + 0.904129i \(0.359479\pi\)
\(8\) −1.26142 + 0.758972i −0.445980 + 0.268337i
\(9\) 0 0
\(10\) −5.42452 + 1.19403i −1.71538 + 0.377585i
\(11\) 3.50223 1.18004i 1.05596 0.355795i 0.262829 0.964842i \(-0.415345\pi\)
0.793134 + 0.609047i \(0.208448\pi\)
\(12\) 0 0
\(13\) −0.873623 3.14651i −0.242300 0.872684i −0.980239 0.197817i \(-0.936615\pi\)
0.737939 0.674867i \(-0.235799\pi\)
\(14\) −2.23789 2.11985i −0.598102 0.566553i
\(15\) 0 0
\(16\) 4.70970 + 1.58688i 1.17742 + 0.396720i
\(17\) −1.83403 0.199462i −0.444817 0.0483767i −0.117030 0.993128i \(-0.537337\pi\)
−0.327787 + 0.944752i \(0.606303\pi\)
\(18\) 0 0
\(19\) −0.157535 2.90556i −0.0361410 0.666581i −0.959339 0.282257i \(-0.908917\pi\)
0.923198 0.384325i \(-0.125566\pi\)
\(20\) 2.91308 + 2.21447i 0.651386 + 0.495170i
\(21\) 0 0
\(22\) −5.64134 3.39428i −1.20274 0.723663i
\(23\) 7.49743 + 3.46868i 1.56332 + 0.723270i 0.995032 0.0995574i \(-0.0317427\pi\)
0.568291 + 0.822828i \(0.307605\pi\)
\(24\) 0 0
\(25\) −2.64941 3.90759i −0.529882 0.781517i
\(26\) −3.26468 + 4.81504i −0.640256 + 0.944307i
\(27\) 0 0
\(28\) −0.109943 + 2.02779i −0.0207773 + 0.383215i
\(29\) −1.36377 + 1.60555i −0.253245 + 0.298143i −0.874064 0.485811i \(-0.838524\pi\)
0.620819 + 0.783954i \(0.286800\pi\)
\(30\) 0 0
\(31\) −0.0823814 + 1.51944i −0.0147961 + 0.272899i 0.981769 + 0.190080i \(0.0608749\pi\)
−0.996565 + 0.0828183i \(0.973608\pi\)
\(32\) −2.18727 5.48964i −0.386659 0.970440i
\(33\) 0 0
\(34\) 1.84436 + 2.72022i 0.316304 + 0.466514i
\(35\) 1.99686 5.01175i 0.337532 0.847141i
\(36\) 0 0
\(37\) −1.78180 1.07207i −0.292926 0.176248i 0.361503 0.932371i \(-0.382264\pi\)
−0.654430 + 0.756123i \(0.727091\pi\)
\(38\) −3.76339 + 3.56487i −0.610503 + 0.578299i
\(39\) 0 0
\(40\) 0.248496 + 4.58323i 0.0392906 + 0.724672i
\(41\) −5.46309 + 2.52749i −0.853191 + 0.394728i −0.797209 0.603704i \(-0.793691\pi\)
−0.0559819 + 0.998432i \(0.517829\pi\)
\(42\) 0 0
\(43\) −6.73289 2.26858i −1.02676 0.345955i −0.244990 0.969526i \(-0.578785\pi\)
−0.781767 + 0.623571i \(0.785681\pi\)
\(44\) 0.701710 + 4.28024i 0.105787 + 0.645271i
\(45\) 0 0
\(46\) −3.93711 14.1802i −0.580496 2.09076i
\(47\) −6.21469 11.7222i −0.906506 1.70985i −0.676177 0.736739i \(-0.736365\pi\)
−0.230329 0.973113i \(-0.573980\pi\)
\(48\) 0 0
\(49\) −3.91232 + 0.861167i −0.558903 + 0.123024i
\(50\) −2.25004 + 8.10390i −0.318203 + 1.14606i
\(51\) 0 0
\(52\) 3.81007 0.414370i 0.528362 0.0574628i
\(53\) −1.87607 0.412954i −0.257698 0.0567235i 0.0842425 0.996445i \(-0.473153\pi\)
−0.341940 + 0.939722i \(0.611084\pi\)
\(54\) 0 0
\(55\) 1.86416 11.3709i 0.251363 1.53325i
\(56\) −2.02788 + 1.54156i −0.270987 + 0.205999i
\(57\) 0 0
\(58\) 3.75280 0.492767
\(59\) 4.93927 + 5.88249i 0.643038 + 0.765834i
\(60\) 0 0
\(61\) 8.38208 + 9.86815i 1.07322 + 1.26349i 0.962977 + 0.269582i \(0.0868855\pi\)
0.110238 + 0.993905i \(0.464839\pi\)
\(62\) 2.15805 1.64051i 0.274073 0.208345i
\(63\) 0 0
\(64\) −0.275238 + 0.519153i −0.0344047 + 0.0648942i
\(65\) −9.94346 2.18872i −1.23333 0.271477i
\(66\) 0 0
\(67\) −9.28244 + 5.58506i −1.13403 + 0.682323i −0.953544 0.301254i \(-0.902595\pi\)
−0.180486 + 0.983578i \(0.557767\pi\)
\(68\) 0.579243 2.08624i 0.0702435 0.252994i
\(69\) 0 0
\(70\) −9.10778 + 3.06877i −1.08859 + 0.366788i
\(71\) −5.63672 10.6320i −0.668956 1.26178i −0.952999 0.302973i \(-0.902021\pi\)
0.284043 0.958812i \(-0.408324\pi\)
\(72\) 0 0
\(73\) 8.12186 + 7.69344i 0.950592 + 0.900449i 0.995131 0.0985588i \(-0.0314232\pi\)
−0.0445389 + 0.999008i \(0.514182\pi\)
\(74\) 0.599321 + 3.65570i 0.0696697 + 0.424966i
\(75\) 0 0
\(76\) 3.39505 + 0.369234i 0.389439 + 0.0423540i
\(77\) 5.80371 2.68508i 0.661394 0.305993i
\(78\) 0 0
\(79\) 3.62730 + 2.75740i 0.408103 + 0.310232i 0.789009 0.614382i \(-0.210595\pi\)
−0.380905 + 0.924614i \(0.624388\pi\)
\(80\) 11.2495 10.6561i 1.25774 1.19139i
\(81\) 0 0
\(82\) 9.73232 + 4.50265i 1.07475 + 0.497234i
\(83\) −5.51813 + 13.8495i −0.605694 + 1.52018i 0.231254 + 0.972893i \(0.425717\pi\)
−0.836947 + 0.547283i \(0.815662\pi\)
\(84\) 0 0
\(85\) −3.22793 + 4.76084i −0.350118 + 0.516385i
\(86\) 4.68484 + 11.7581i 0.505179 + 1.26790i
\(87\) 0 0
\(88\) −3.52217 + 4.14662i −0.375465 + 0.442032i
\(89\) 7.04180 8.29025i 0.746430 0.878765i −0.249548 0.968362i \(-0.580282\pi\)
0.995978 + 0.0895974i \(0.0285580\pi\)
\(90\) 0 0
\(91\) −2.09144 5.24912i −0.219243 0.550258i
\(92\) −5.44088 + 8.02470i −0.567251 + 0.836633i
\(93\) 0 0
\(94\) −8.74857 + 21.9573i −0.902346 + 2.26472i
\(95\) −8.23393 3.80942i −0.844784 0.390839i
\(96\) 0 0
\(97\) 4.83488 4.57985i 0.490908 0.465013i −0.401749 0.915750i \(-0.631597\pi\)
0.892657 + 0.450737i \(0.148839\pi\)
\(98\) 5.68134 + 4.31884i 0.573902 + 0.436269i
\(99\) 0 0
\(100\) 5.02871 2.32653i 0.502871 0.232653i
\(101\) 15.2319 + 1.65657i 1.51563 + 0.164834i 0.827793 0.561033i \(-0.189596\pi\)
0.687835 + 0.725868i \(0.258561\pi\)
\(102\) 0 0
\(103\) 0.0496378 + 0.302777i 0.00489096 + 0.0298335i 0.989159 0.146847i \(-0.0469124\pi\)
−0.984268 + 0.176680i \(0.943464\pi\)
\(104\) 3.49012 + 3.30602i 0.342234 + 0.324181i
\(105\) 0 0
\(106\) 1.60297 + 3.02352i 0.155694 + 0.293671i
\(107\) 8.94857 3.01513i 0.865091 0.291483i 0.148446 0.988921i \(-0.452573\pi\)
0.716646 + 0.697437i \(0.245676\pi\)
\(108\) 0 0
\(109\) −2.19974 + 7.92274i −0.210697 + 0.758861i 0.780350 + 0.625343i \(0.215041\pi\)
−0.991046 + 0.133518i \(0.957373\pi\)
\(110\) −17.5889 + 10.5829i −1.67704 + 1.00904i
\(111\) 0 0
\(112\) 8.39840 + 1.84863i 0.793574 + 0.174679i
\(113\) 5.07446 9.57144i 0.477365 0.900405i −0.521522 0.853238i \(-0.674636\pi\)
0.998887 0.0471676i \(-0.0150195\pi\)
\(114\) 0 0
\(115\) 20.5046 15.5872i 1.91206 1.45351i
\(116\) −1.60056 1.88433i −0.148608 0.174955i
\(117\) 0 0
\(118\) 2.29060 13.4906i 0.210867 1.24191i
\(119\) −3.19217 −0.292626
\(120\) 0 0
\(121\) 2.11611 1.60863i 0.192374 0.146239i
\(122\) 3.73162 22.7618i 0.337845 2.06076i
\(123\) 0 0
\(124\) −1.74412 0.383911i −0.156627 0.0344762i
\(125\) 0.864532 0.0940235i 0.0773261 0.00840972i
\(126\) 0 0
\(127\) 4.44261 16.0008i 0.394217 1.41984i −0.454382 0.890807i \(-0.650140\pi\)
0.848599 0.529036i \(-0.177446\pi\)
\(128\) −10.5200 + 2.31564i −0.929849 + 0.204675i
\(129\) 0 0
\(130\) 8.49600 + 16.0252i 0.745149 + 1.40550i
\(131\) 2.36612 + 8.52199i 0.206729 + 0.744570i 0.992090 + 0.125532i \(0.0400636\pi\)
−0.785361 + 0.619038i \(0.787523\pi\)
\(132\) 0 0
\(133\) −0.814563 4.96862i −0.0706316 0.430834i
\(134\) 18.2886 + 6.16216i 1.57990 + 0.532329i
\(135\) 0 0
\(136\) 2.46487 1.14037i 0.211360 0.0977858i
\(137\) 0.215073 + 3.96678i 0.0183749 + 0.338905i 0.993238 + 0.116099i \(0.0370390\pi\)
−0.974863 + 0.222806i \(0.928478\pi\)
\(138\) 0 0
\(139\) 10.0470 9.51705i 0.852178 0.807226i −0.130712 0.991420i \(-0.541726\pi\)
0.982890 + 0.184195i \(0.0589677\pi\)
\(140\) 5.42532 + 3.26430i 0.458523 + 0.275884i
\(141\) 0 0
\(142\) −7.93495 + 19.9152i −0.665886 + 1.67125i
\(143\) −6.77263 9.98889i −0.566356 0.835313i
\(144\) 0 0
\(145\) 2.43107 + 6.10153i 0.201890 + 0.506705i
\(146\) 1.07897 19.9004i 0.0892962 1.64697i
\(147\) 0 0
\(148\) 1.57996 1.86007i 0.129872 0.152897i
\(149\) −0.0906432 + 1.67182i −0.00742578 + 0.136960i 0.992470 + 0.122492i \(0.0390885\pi\)
−0.999895 + 0.0144688i \(0.995394\pi\)
\(150\) 0 0
\(151\) 3.60975 5.32399i 0.293758 0.433260i −0.651958 0.758255i \(-0.726052\pi\)
0.945716 + 0.324995i \(0.105363\pi\)
\(152\) 2.40396 + 3.54557i 0.194987 + 0.287584i
\(153\) 0 0
\(154\) −10.3391 4.78339i −0.833151 0.385457i
\(155\) 4.06523 + 2.44597i 0.326527 + 0.196465i
\(156\) 0 0
\(157\) 17.6957 + 13.4519i 1.41227 + 1.07358i 0.985585 + 0.169182i \(0.0541126\pi\)
0.426687 + 0.904399i \(0.359680\pi\)
\(158\) −0.439448 8.10515i −0.0349606 0.644811i
\(159\) 0 0
\(160\) −18.3165 1.99204i −1.44805 0.157485i
\(161\) 13.5459 + 4.56413i 1.06756 + 0.359704i
\(162\) 0 0
\(163\) −7.99829 7.57638i −0.626474 0.593428i 0.307159 0.951658i \(-0.400622\pi\)
−0.933633 + 0.358230i \(0.883380\pi\)
\(164\) −1.88998 6.80709i −0.147583 0.531544i
\(165\) 0 0
\(166\) 25.1684 8.48023i 1.95345 0.658193i
\(167\) −10.9883 + 2.41870i −0.850298 + 0.187165i −0.618681 0.785642i \(-0.712333\pi\)
−0.231617 + 0.972807i \(0.574402\pi\)
\(168\) 0 0
\(169\) 2.00185 1.20448i 0.153989 0.0926520i
\(170\) 10.1869 1.10789i 0.781298 0.0849712i
\(171\) 0 0
\(172\) 3.90579 7.36710i 0.297814 0.561736i
\(173\) −3.42431 + 20.8874i −0.260345 + 1.58804i 0.455798 + 0.890083i \(0.349354\pi\)
−0.716143 + 0.697954i \(0.754094\pi\)
\(174\) 0 0
\(175\) −5.28850 6.22610i −0.399773 0.470649i
\(176\) 18.3670 1.38447
\(177\) 0 0
\(178\) −19.3775 −1.45241
\(179\) 4.10258 + 4.82993i 0.306641 + 0.361006i 0.893800 0.448466i \(-0.148029\pi\)
−0.587159 + 0.809472i \(0.699754\pi\)
\(180\) 0 0
\(181\) −0.567860 + 3.46379i −0.0422087 + 0.257462i −0.999498 0.0316687i \(-0.989918\pi\)
0.957290 + 0.289130i \(0.0933661\pi\)
\(182\) −4.71503 + 8.89350i −0.349502 + 0.659230i
\(183\) 0 0
\(184\) −12.0901 + 1.31487i −0.891291 + 0.0969337i
\(185\) −5.55542 + 3.34258i −0.408443 + 0.245752i
\(186\) 0 0
\(187\) −6.65856 + 1.46566i −0.486922 + 0.107180i
\(188\) 14.7563 4.97196i 1.07621 0.362618i
\(189\) 0 0
\(190\) 4.32387 + 15.5732i 0.313687 + 1.12980i
\(191\) 18.7660 + 17.7761i 1.35786 + 1.28623i 0.922513 + 0.385966i \(0.126132\pi\)
0.435344 + 0.900264i \(0.356627\pi\)
\(192\) 0 0
\(193\) −6.71264 2.26175i −0.483186 0.162804i 0.0671579 0.997742i \(-0.478607\pi\)
−0.550344 + 0.834938i \(0.685503\pi\)
\(194\) −11.7944 1.28272i −0.846791 0.0920941i
\(195\) 0 0
\(196\) −0.254537 4.69465i −0.0181812 0.335332i
\(197\) −16.8902 12.8396i −1.20338 0.914783i −0.205420 0.978674i \(-0.565856\pi\)
−0.997957 + 0.0638904i \(0.979649\pi\)
\(198\) 0 0
\(199\) 6.65262 + 4.00275i 0.471592 + 0.283748i 0.731445 0.681901i \(-0.238846\pi\)
−0.259853 + 0.965648i \(0.583674\pi\)
\(200\) 6.30777 + 2.91829i 0.446027 + 0.206354i
\(201\) 0 0
\(202\) −15.3177 22.5919i −1.07775 1.58956i
\(203\) −2.04556 + 3.01697i −0.143570 + 0.211750i
\(204\) 0 0
\(205\) −1.01607 + 18.7402i −0.0709652 + 1.30888i
\(206\) 0.353854 0.416589i 0.0246542 0.0290252i
\(207\) 0 0
\(208\) 0.878633 16.2054i 0.0609222 1.12364i
\(209\) −3.98040 9.99005i −0.275330 0.691026i
\(210\) 0 0
\(211\) 0.0947909 + 0.139806i 0.00652567 + 0.00962465i 0.830938 0.556365i \(-0.187804\pi\)
−0.824412 + 0.565990i \(0.808494\pi\)
\(212\) 0.834485 2.09440i 0.0573126 0.143844i
\(213\) 0 0
\(214\) −14.4142 8.67275i −0.985336 0.592857i
\(215\) −16.0821 + 15.2338i −1.09679 + 1.03894i
\(216\) 0 0
\(217\) 0.142547 + 2.62912i 0.00967669 + 0.178476i
\(218\) 13.2942 6.15055i 0.900397 0.416568i
\(219\) 0 0
\(220\) 12.8155 + 4.31803i 0.864018 + 0.291122i
\(221\) 0.974638 + 5.94503i 0.0655612 + 0.399906i
\(222\) 0 0
\(223\) 3.40355 + 12.2585i 0.227918 + 0.820888i 0.985719 + 0.168401i \(0.0538603\pi\)
−0.757800 + 0.652487i \(0.773726\pi\)
\(224\) −4.78951 9.03397i −0.320013 0.603608i
\(225\) 0 0
\(226\) −18.8482 + 4.14879i −1.25376 + 0.275974i
\(227\) −0.166243 + 0.598754i −0.0110339 + 0.0397407i −0.968862 0.247601i \(-0.920358\pi\)
0.957828 + 0.287342i \(0.0927716\pi\)
\(228\) 0 0
\(229\) 6.28906 0.683976i 0.415593 0.0451984i 0.102065 0.994778i \(-0.467455\pi\)
0.313527 + 0.949579i \(0.398489\pi\)
\(230\) −44.8117 9.86380i −2.95480 0.650400i
\(231\) 0 0
\(232\) 0.501717 3.06034i 0.0329393 0.200921i
\(233\) −17.6167 + 13.3918i −1.15411 + 0.877329i −0.993958 0.109764i \(-0.964990\pi\)
−0.160148 + 0.987093i \(0.551197\pi\)
\(234\) 0 0
\(235\) −41.3668 −2.69847
\(236\) −7.75076 + 4.60359i −0.504531 + 0.299668i
\(237\) 0 0
\(238\) 3.68153 + 4.33423i 0.238638 + 0.280946i
\(239\) 2.69488 2.04859i 0.174317 0.132512i −0.514378 0.857564i \(-0.671977\pi\)
0.688695 + 0.725051i \(0.258184\pi\)
\(240\) 0 0
\(241\) 2.38613 4.50071i 0.153704 0.289916i −0.794687 0.607019i \(-0.792365\pi\)
0.948391 + 0.317103i \(0.102710\pi\)
\(242\) −4.62466 1.01796i −0.297284 0.0654372i
\(243\) 0 0
\(244\) −13.0205 + 7.83420i −0.833554 + 0.501533i
\(245\) −3.34146 + 12.0348i −0.213478 + 0.768878i
\(246\) 0 0
\(247\) −9.00474 + 3.03405i −0.572958 + 0.193052i
\(248\) −1.04929 1.97917i −0.0666301 0.125678i
\(249\) 0 0
\(250\) −1.12473 1.06540i −0.0711339 0.0673816i
\(251\) −1.31480 8.01990i −0.0829891 0.506211i −0.995310 0.0967356i \(-0.969160\pi\)
0.912321 0.409476i \(-0.134288\pi\)
\(252\) 0 0
\(253\) 30.3509 + 3.30086i 1.90815 + 0.207523i
\(254\) −26.8491 + 12.4217i −1.68466 + 0.779406i
\(255\) 0 0
\(256\) 16.2124 + 12.3244i 1.01328 + 0.770273i
\(257\) 6.33161 5.99762i 0.394955 0.374121i −0.464292 0.885682i \(-0.653691\pi\)
0.859247 + 0.511561i \(0.170933\pi\)
\(258\) 0 0
\(259\) −3.26559 1.51082i −0.202914 0.0938779i
\(260\) 4.42290 11.1007i 0.274297 0.688433i
\(261\) 0 0
\(262\) 8.84205 13.0410i 0.546263 0.805678i
\(263\) −5.60169 14.0592i −0.345415 0.866927i −0.994357 0.106089i \(-0.966167\pi\)
0.648941 0.760838i \(-0.275212\pi\)
\(264\) 0 0
\(265\) −3.87742 + 4.56486i −0.238188 + 0.280417i
\(266\) −5.80680 + 6.83629i −0.356037 + 0.419160i
\(267\) 0 0
\(268\) −4.70597 11.8111i −0.287463 0.721478i
\(269\) 8.52087 12.5673i 0.519526 0.766244i −0.473917 0.880570i \(-0.657160\pi\)
0.993443 + 0.114325i \(0.0364707\pi\)
\(270\) 0 0
\(271\) −3.13725 + 7.87391i −0.190574 + 0.478306i −0.992953 0.118510i \(-0.962188\pi\)
0.802378 + 0.596816i \(0.203568\pi\)
\(272\) −8.32118 3.84979i −0.504546 0.233428i
\(273\) 0 0
\(274\) 5.13793 4.86691i 0.310394 0.294021i
\(275\) −13.8900 10.5589i −0.837596 0.636724i
\(276\) 0 0
\(277\) 6.53504 3.02343i 0.392653 0.181660i −0.213621 0.976917i \(-0.568526\pi\)
0.606274 + 0.795256i \(0.292664\pi\)
\(278\) −24.5092 2.66553i −1.46996 0.159868i
\(279\) 0 0
\(280\) 1.28489 + 7.83749i 0.0767870 + 0.468380i
\(281\) 11.2470 + 10.6538i 0.670942 + 0.635550i 0.945348 0.326064i \(-0.105723\pi\)
−0.274406 + 0.961614i \(0.588481\pi\)
\(282\) 0 0
\(283\) 8.44984 + 15.9381i 0.502291 + 0.947421i 0.996928 + 0.0783212i \(0.0249560\pi\)
−0.494638 + 0.869099i \(0.664699\pi\)
\(284\) 13.3839 4.50957i 0.794190 0.267594i
\(285\) 0 0
\(286\) −5.75172 + 20.7158i −0.340107 + 1.22495i
\(287\) −8.92465 + 5.36978i −0.526805 + 0.316968i
\(288\) 0 0
\(289\) −13.2787 2.92286i −0.781099 0.171933i
\(290\) 5.48072 10.3377i 0.321839 0.607052i
\(291\) 0 0
\(292\) −10.4524 + 7.94574i −0.611683 + 0.464989i
\(293\) 8.37900 + 9.86452i 0.489506 + 0.576291i 0.950347 0.311191i \(-0.100728\pi\)
−0.460841 + 0.887483i \(0.652452\pi\)
\(294\) 0 0
\(295\) 23.4178 5.01507i 1.36344 0.291989i
\(296\) 3.06128 0.177933
\(297\) 0 0
\(298\) 2.37448 1.80503i 0.137550 0.104563i
\(299\) 4.36430 26.6210i 0.252394 1.53954i
\(300\) 0 0
\(301\) −12.0062 2.64277i −0.692026 0.152326i
\(302\) −11.3919 + 1.23894i −0.655528 + 0.0712930i
\(303\) 0 0
\(304\) 3.86884 13.9343i 0.221893 0.799187i
\(305\) 39.4250 8.67810i 2.25747 0.496906i
\(306\) 0 0
\(307\) −14.9524 28.2031i −0.853376 1.60964i −0.791187 0.611574i \(-0.790537\pi\)
−0.0621893 0.998064i \(-0.519808\pi\)
\(308\) 2.00782 + 7.23151i 0.114406 + 0.412054i
\(309\) 0 0
\(310\) −1.36737 8.34058i −0.0776613 0.473713i
\(311\) 13.3291 + 4.49111i 0.755826 + 0.254668i 0.670726 0.741705i \(-0.265983\pi\)
0.0850999 + 0.996372i \(0.472879\pi\)
\(312\) 0 0
\(313\) 16.5100 7.63833i 0.933200 0.431744i 0.106452 0.994318i \(-0.466051\pi\)
0.826747 + 0.562574i \(0.190189\pi\)
\(314\) −2.14384 39.5408i −0.120984 2.23142i
\(315\) 0 0
\(316\) −3.88227 + 3.67748i −0.218395 + 0.206875i
\(317\) −8.74979 5.26457i −0.491437 0.295688i 0.248182 0.968713i \(-0.420167\pi\)
−0.739619 + 0.673026i \(0.764994\pi\)
\(318\) 0 0
\(319\) −2.88162 + 7.23231i −0.161340 + 0.404932i
\(320\) 1.02813 + 1.51638i 0.0574742 + 0.0847681i
\(321\) 0 0
\(322\) −9.42539 23.6560i −0.525257 1.31829i
\(323\) −0.290627 + 5.36029i −0.0161709 + 0.298255i
\(324\) 0 0
\(325\) −9.98066 + 11.7501i −0.553628 + 0.651781i
\(326\) −1.06255 + 19.5976i −0.0588494 + 1.08541i
\(327\) 0 0
\(328\) 4.97296 7.33456i 0.274586 0.404983i
\(329\) −12.8834 19.0016i −0.710284 1.04759i
\(330\) 0 0
\(331\) −17.3630 8.03298i −0.954357 0.441533i −0.120011 0.992773i \(-0.538293\pi\)
−0.834347 + 0.551240i \(0.814155\pi\)
\(332\) −14.9923 9.02058i −0.822810 0.495068i
\(333\) 0 0
\(334\) 15.9568 + 12.1300i 0.873117 + 0.663726i
\(335\) 1.82861 + 33.7267i 0.0999075 + 1.84268i
\(336\) 0 0
\(337\) −29.7222 3.23249i −1.61907 0.176085i −0.746782 0.665069i \(-0.768402\pi\)
−0.872292 + 0.488984i \(0.837367\pi\)
\(338\) −3.94414 1.32893i −0.214533 0.0722845i
\(339\) 0 0
\(340\) −4.90097 4.64244i −0.265792 0.251772i
\(341\) 1.50448 + 5.41863i 0.0814719 + 0.293435i
\(342\) 0 0
\(343\) −18.0470 + 6.08075i −0.974448 + 0.328330i
\(344\) 10.2148 2.24845i 0.550745 0.121228i
\(345\) 0 0
\(346\) 32.3095 19.4400i 1.73697 1.04510i
\(347\) 13.1544 1.43062i 0.706163 0.0767999i 0.252011 0.967724i \(-0.418908\pi\)
0.454152 + 0.890924i \(0.349942\pi\)
\(348\) 0 0
\(349\) −9.17190 + 17.3000i −0.490961 + 0.926050i 0.506983 + 0.861956i \(0.330761\pi\)
−0.997944 + 0.0640939i \(0.979584\pi\)
\(350\) −2.35438 + 14.3611i −0.125847 + 0.767634i
\(351\) 0 0
\(352\) −14.1383 16.6449i −0.753575 0.887177i
\(353\) −28.2752 −1.50494 −0.752468 0.658629i \(-0.771137\pi\)
−0.752468 + 0.658629i \(0.771137\pi\)
\(354\) 0 0
\(355\) −37.5197 −1.99134
\(356\) 8.26449 + 9.72971i 0.438017 + 0.515673i
\(357\) 0 0
\(358\) 1.82642 11.1407i 0.0965295 0.588804i
\(359\) 2.76101 5.20781i 0.145720 0.274858i −0.799898 0.600136i \(-0.795113\pi\)
0.945618 + 0.325278i \(0.105458\pi\)
\(360\) 0 0
\(361\) 10.4712 1.13881i 0.551113 0.0599372i
\(362\) 5.35794 3.22376i 0.281607 0.169437i
\(363\) 0 0
\(364\) 6.47649 1.42558i 0.339460 0.0747209i
\(365\) 33.0543 11.1373i 1.73014 0.582953i
\(366\) 0 0
\(367\) −5.51147 19.8505i −0.287696 1.03619i −0.956256 0.292530i \(-0.905503\pi\)
0.668560 0.743658i \(-0.266911\pi\)
\(368\) 29.8062 + 28.2340i 1.55376 + 1.47180i
\(369\) 0 0
\(370\) 10.9455 + 3.68797i 0.569030 + 0.191729i
\(371\) −3.30443 0.359378i −0.171557 0.0186580i
\(372\) 0 0
\(373\) 0.828051 + 15.2725i 0.0428749 + 0.790780i 0.938354 + 0.345676i \(0.112351\pi\)
−0.895479 + 0.445104i \(0.853167\pi\)
\(374\) 9.66933 + 7.35043i 0.499989 + 0.380082i
\(375\) 0 0
\(376\) 16.7361 + 10.0698i 0.863100 + 0.519310i
\(377\) 6.24330 + 2.88846i 0.321546 + 0.148763i
\(378\) 0 0
\(379\) 9.60702 + 14.1693i 0.493479 + 0.727828i 0.990134 0.140120i \(-0.0447489\pi\)
−0.496655 + 0.867948i \(0.665439\pi\)
\(380\) 5.97536 8.81300i 0.306530 0.452097i
\(381\) 0 0
\(382\) 2.49301 45.9809i 0.127554 2.35259i
\(383\) −20.9952 + 24.7175i −1.07280 + 1.26300i −0.109674 + 0.993968i \(0.534981\pi\)
−0.963130 + 0.269035i \(0.913295\pi\)
\(384\) 0 0
\(385\) 1.07942 19.9087i 0.0550122 1.01464i
\(386\) 4.67074 + 11.7227i 0.237735 + 0.596669i
\(387\) 0 0
\(388\) 4.38623 + 6.46921i 0.222677 + 0.328424i
\(389\) −2.50229 + 6.28027i −0.126871 + 0.318422i −0.978668 0.205451i \(-0.934134\pi\)
0.851796 + 0.523873i \(0.175513\pi\)
\(390\) 0 0
\(391\) −13.0586 7.85711i −0.660402 0.397351i
\(392\) 4.28148 4.05564i 0.216248 0.204841i
\(393\) 0 0
\(394\) 2.04625 + 37.7409i 0.103089 + 1.90136i
\(395\) 12.8932 5.96502i 0.648726 0.300133i
\(396\) 0 0
\(397\) 31.5449 + 10.6287i 1.58319 + 0.533439i 0.967135 0.254263i \(-0.0818329\pi\)
0.616056 + 0.787702i \(0.288729\pi\)
\(398\) −2.23765 13.6491i −0.112163 0.684167i
\(399\) 0 0
\(400\) −6.27704 22.6078i −0.313852 1.13039i
\(401\) 0.971028 + 1.83155i 0.0484908 + 0.0914634i 0.906573 0.422049i \(-0.138689\pi\)
−0.858082 + 0.513512i \(0.828344\pi\)
\(402\) 0 0
\(403\) 4.85289 1.06820i 0.241739 0.0532109i
\(404\) −4.81070 + 17.3266i −0.239341 + 0.862030i
\(405\) 0 0
\(406\) 6.45549 0.702077i 0.320381 0.0348435i
\(407\) −7.50538 1.65206i −0.372028 0.0818895i
\(408\) 0 0
\(409\) −2.05729 + 12.5489i −0.101726 + 0.620503i 0.885924 + 0.463830i \(0.153525\pi\)
−0.987651 + 0.156673i \(0.949923\pi\)
\(410\) 26.6167 20.2335i 1.31451 0.999262i
\(411\) 0 0
\(412\) −0.360093 −0.0177405
\(413\) 9.59693 + 9.19490i 0.472234 + 0.452451i
\(414\) 0 0
\(415\) 30.0919 + 35.4269i 1.47715 + 1.73904i
\(416\) −15.3623 + 11.6781i −0.753200 + 0.572568i
\(417\) 0 0
\(418\) −8.97358 + 16.9260i −0.438912 + 0.827876i
\(419\) 4.21147 + 0.927016i 0.205744 + 0.0452877i 0.316647 0.948544i \(-0.397443\pi\)
−0.110903 + 0.993831i \(0.535374\pi\)
\(420\) 0 0
\(421\) −19.0210 + 11.4445i −0.927025 + 0.557772i −0.897123 0.441780i \(-0.854347\pi\)
−0.0299017 + 0.999553i \(0.509519\pi\)
\(422\) 0.0805021 0.289942i 0.00391878 0.0141142i
\(423\) 0 0
\(424\) 2.67993 0.902974i 0.130149 0.0438523i
\(425\) 4.07967 + 7.69507i 0.197893 + 0.373266i
\(426\) 0 0
\(427\) 16.2648 + 15.4069i 0.787111 + 0.745591i
\(428\) 1.79294 + 10.9365i 0.0866652 + 0.528634i
\(429\) 0 0
\(430\) 39.2315 + 4.26668i 1.89191 + 0.205758i
\(431\) −1.61486 + 0.747115i −0.0777852 + 0.0359873i −0.458396 0.888748i \(-0.651576\pi\)
0.380611 + 0.924735i \(0.375714\pi\)
\(432\) 0 0
\(433\) 22.9317 + 17.4322i 1.10203 + 0.837740i 0.987802 0.155715i \(-0.0497681\pi\)
0.114226 + 0.993455i \(0.463561\pi\)
\(434\) 3.40533 3.22570i 0.163461 0.154839i
\(435\) 0 0
\(436\) −8.75822 4.05199i −0.419443 0.194055i
\(437\) 8.89736 22.3307i 0.425618 1.06822i
\(438\) 0 0
\(439\) −3.43005 + 5.05895i −0.163707 + 0.241450i −0.900691 0.434460i \(-0.856939\pi\)
0.736984 + 0.675911i \(0.236250\pi\)
\(440\) 6.27868 + 15.7583i 0.299324 + 0.751248i
\(441\) 0 0
\(442\) 6.94792 8.17973i 0.330479 0.389070i
\(443\) 24.7776 29.1705i 1.17722 1.38593i 0.271296 0.962496i \(-0.412548\pi\)
0.905926 0.423436i \(-0.139176\pi\)
\(444\) 0 0
\(445\) −12.5528 31.5052i −0.595061 1.49349i
\(446\) 12.7188 18.7589i 0.602255 0.888260i
\(447\) 0 0
\(448\) −0.376335 + 0.944529i −0.0177801 + 0.0446248i
\(449\) −12.0082 5.55557i −0.566701 0.262184i 0.115550 0.993302i \(-0.463137\pi\)
−0.682251 + 0.731118i \(0.738999\pi\)
\(450\) 0 0
\(451\) −16.1505 + 15.2985i −0.760495 + 0.720379i
\(452\) 10.1219 + 7.69444i 0.476093 + 0.361916i
\(453\) 0 0
\(454\) 1.00470 0.464822i 0.0471528 0.0218152i
\(455\) −17.5140 1.90476i −0.821070 0.0892967i
\(456\) 0 0
\(457\) −1.47951 9.02461i −0.0692086 0.422154i −0.998592 0.0530389i \(-0.983109\pi\)
0.929384 0.369115i \(-0.120339\pi\)
\(458\) −8.18184 7.75025i −0.382312 0.362145i
\(459\) 0 0
\(460\) 14.1594 + 26.7074i 0.660184 + 1.24524i
\(461\) −36.7671 + 12.3883i −1.71242 + 0.576980i −0.993054 0.117657i \(-0.962462\pi\)
−0.719361 + 0.694637i \(0.755565\pi\)
\(462\) 0 0
\(463\) 10.4668 37.6980i 0.486434 1.75198i −0.158123 0.987419i \(-0.550544\pi\)
0.644556 0.764557i \(-0.277042\pi\)
\(464\) −8.97075 + 5.39752i −0.416457 + 0.250574i
\(465\) 0 0
\(466\) 38.5003 + 8.47455i 1.78349 + 0.392576i
\(467\) −1.48278 + 2.79682i −0.0686148 + 0.129421i −0.915446 0.402440i \(-0.868162\pi\)
0.846832 + 0.531861i \(0.178507\pi\)
\(468\) 0 0
\(469\) −14.9226 + 11.3439i −0.689062 + 0.523811i
\(470\) 47.7083 + 56.1666i 2.20062 + 2.59077i
\(471\) 0 0
\(472\) −10.6951 3.67153i −0.492284 0.168996i
\(473\) −26.2572 −1.20731
\(474\) 0 0
\(475\) −10.9364 + 8.31360i −0.501794 + 0.381454i
\(476\) 0.606106 3.69708i 0.0277808 0.169455i
\(477\) 0 0
\(478\) −5.88951 1.29638i −0.269380 0.0592951i
\(479\) −21.1071 + 2.29554i −0.964410 + 0.104886i −0.576754 0.816918i \(-0.695681\pi\)
−0.387656 + 0.921804i \(0.626715\pi\)
\(480\) 0 0
\(481\) −1.81667 + 6.54304i −0.0828329 + 0.298337i
\(482\) −8.86284 + 1.95086i −0.403691 + 0.0888592i
\(483\) 0 0
\(484\) 1.46128 + 2.75626i 0.0664216 + 0.125284i
\(485\) −5.55494 20.0071i −0.252237 0.908475i
\(486\) 0 0
\(487\) −3.14184 19.1644i −0.142371 0.868422i −0.957350 0.288932i \(-0.906700\pi\)
0.814979 0.579490i \(-0.196748\pi\)
\(488\) −18.0630 6.08613i −0.817673 0.275506i
\(489\) 0 0
\(490\) 20.1942 9.34284i 0.912282 0.422066i
\(491\) 0.259992 + 4.79528i 0.0117333 + 0.216408i 0.998520 + 0.0543838i \(0.0173194\pi\)
−0.986787 + 0.162024i \(0.948198\pi\)
\(492\) 0 0
\(493\) 2.82143 2.67260i 0.127071 0.120368i
\(494\) 14.5047 + 8.72718i 0.652597 + 0.392655i
\(495\) 0 0
\(496\) −2.79916 + 7.02535i −0.125686 + 0.315448i
\(497\) −11.6852 17.2344i −0.524154 0.773069i
\(498\) 0 0
\(499\) 5.01934 + 12.5976i 0.224696 + 0.563946i 0.997497 0.0707029i \(-0.0225242\pi\)
−0.772801 + 0.634648i \(0.781145\pi\)
\(500\) −0.0552555 + 1.01913i −0.00247110 + 0.0455768i
\(501\) 0 0
\(502\) −9.37281 + 11.0345i −0.418329 + 0.492495i
\(503\) 1.93924 35.7671i 0.0864663 1.59478i −0.557800 0.829975i \(-0.688354\pi\)
0.644266 0.764801i \(-0.277163\pi\)
\(504\) 0 0
\(505\) 26.8084 39.5395i 1.19296 1.75948i
\(506\) −30.5219 45.0164i −1.35686 2.00122i
\(507\) 0 0
\(508\) 17.6882 + 8.18341i 0.784785 + 0.363080i
\(509\) 29.9505 + 18.0206i 1.32753 + 0.798749i 0.989796 0.142492i \(-0.0455116\pi\)
0.337735 + 0.941241i \(0.390339\pi\)
\(510\) 0 0
\(511\) 15.4104 + 11.7147i 0.681715 + 0.518226i
\(512\) −0.797781 14.7142i −0.0352573 0.650282i
\(513\) 0 0
\(514\) −15.4456 1.67981i −0.681277 0.0740933i
\(515\) 0.906545 + 0.305450i 0.0399471 + 0.0134598i
\(516\) 0 0
\(517\) −35.5979 33.7201i −1.56559 1.48301i
\(518\) 1.71485 + 6.17634i 0.0753463 + 0.271373i
\(519\) 0 0
\(520\) 14.2041 4.78591i 0.622890 0.209876i
\(521\) 27.3778 6.02630i 1.19944 0.264017i 0.430056 0.902802i \(-0.358494\pi\)
0.769385 + 0.638785i \(0.220563\pi\)
\(522\) 0 0
\(523\) −21.7043 + 13.0590i −0.949061 + 0.571031i −0.903805 0.427944i \(-0.859238\pi\)
−0.0452559 + 0.998975i \(0.514410\pi\)
\(524\) −10.3192 + 1.12228i −0.450796 + 0.0490270i
\(525\) 0 0
\(526\) −12.6287 + 23.8203i −0.550637 + 1.03861i
\(527\) 0.454160 2.77025i 0.0197835 0.120674i
\(528\) 0 0
\(529\) 29.2899 + 34.4827i 1.27347 + 1.49925i
\(530\) 10.6698 0.463468
\(531\) 0 0
\(532\) 5.90917 0.256195
\(533\) 12.7255 + 14.9816i 0.551201 + 0.648923i
\(534\) 0 0
\(535\) 4.76312 29.0538i 0.205928 1.25610i
\(536\) 7.47016 14.0902i 0.322662 0.608605i
\(537\) 0 0
\(538\) −26.8906 + 2.92453i −1.15934 + 0.126086i
\(539\) −12.6856 + 7.63270i −0.546410 + 0.328764i
\(540\) 0 0
\(541\) −10.8443 + 2.38700i −0.466231 + 0.102625i −0.441872 0.897078i \(-0.645686\pi\)
−0.0243590 + 0.999703i \(0.507754\pi\)
\(542\) 14.3091 4.82131i 0.614630 0.207093i
\(543\) 0 0
\(544\) 2.91654 + 10.5044i 0.125045 + 0.450373i
\(545\) 18.6120 + 17.6302i 0.797250 + 0.755195i
\(546\) 0 0
\(547\) 27.4694 + 9.25551i 1.17451 + 0.395737i 0.837855 0.545892i \(-0.183809\pi\)
0.336651 + 0.941630i \(0.390706\pi\)
\(548\) −4.63505 0.504092i −0.198000 0.0215338i
\(549\) 0 0
\(550\) 1.68277 + 31.0369i 0.0717536 + 1.32342i
\(551\) 4.87987 + 3.70958i 0.207889 + 0.158033i
\(552\) 0 0
\(553\) 6.75547 + 4.06463i 0.287272 + 0.172846i
\(554\) −11.6420 5.38615i −0.494620 0.228836i
\(555\) 0 0
\(556\) 9.11472 + 13.4432i 0.386550 + 0.570119i
\(557\) −26.0304 + 38.3920i −1.10295 + 1.62672i −0.398136 + 0.917326i \(0.630343\pi\)
−0.704810 + 0.709396i \(0.748968\pi\)
\(558\) 0 0
\(559\) −1.25608 + 23.1670i −0.0531264 + 0.979859i
\(560\) 17.3577 20.4350i 0.733496 0.863538i
\(561\) 0 0
\(562\) 1.49414 27.5578i 0.0630266 1.16246i
\(563\) 2.05673 + 5.16200i 0.0866808 + 0.217552i 0.965927 0.258816i \(-0.0833323\pi\)
−0.879246 + 0.476368i \(0.841953\pi\)
\(564\) 0 0
\(565\) −18.9553 27.9569i −0.797454 1.17616i
\(566\) 11.8950 29.8543i 0.499986 1.25487i
\(567\) 0 0
\(568\) 15.1797 + 9.13330i 0.636925 + 0.383225i
\(569\) 9.16401 8.68061i 0.384175 0.363910i −0.471104 0.882078i \(-0.656144\pi\)
0.855279 + 0.518168i \(0.173386\pi\)
\(570\) 0 0
\(571\) 1.17732 + 21.7144i 0.0492693 + 0.908719i 0.913806 + 0.406150i \(0.133129\pi\)
−0.864537 + 0.502569i \(0.832388\pi\)
\(572\) 12.8548 5.94725i 0.537485 0.248667i
\(573\) 0 0
\(574\) 17.5837 + 5.92464i 0.733930 + 0.247290i
\(575\) −6.30960 38.4868i −0.263128 1.60501i
\(576\) 0 0
\(577\) −2.42464 8.73276i −0.100939 0.363550i 0.895779 0.444499i \(-0.146618\pi\)
−0.996718 + 0.0809498i \(0.974205\pi\)
\(578\) 11.3457 + 21.4003i 0.471920 + 0.890135i
\(579\) 0 0
\(580\) −7.52822 + 1.65709i −0.312592 + 0.0688067i
\(581\) −6.90121 + 24.8559i −0.286311 + 1.03120i
\(582\) 0 0
\(583\) −7.05772 + 0.767574i −0.292301 + 0.0317897i
\(584\) −16.0842 3.54040i −0.665569 0.146503i
\(585\) 0 0
\(586\) 3.73024 22.7535i 0.154095 0.939937i
\(587\) −9.50150 + 7.22285i −0.392169 + 0.298119i −0.782614 0.622507i \(-0.786114\pi\)
0.390445 + 0.920626i \(0.372321\pi\)
\(588\) 0 0
\(589\) 4.42779 0.182444
\(590\) −33.8170 26.0121i −1.39222 1.07090i
\(591\) 0 0
\(592\) −6.69049 7.87666i −0.274977 0.323729i
\(593\) −0.601740 + 0.457431i −0.0247105 + 0.0187844i −0.617457 0.786605i \(-0.711837\pi\)
0.592746 + 0.805389i \(0.298044\pi\)
\(594\) 0 0
\(595\) −4.66196 + 8.79338i −0.191122 + 0.360493i
\(596\) −1.91904 0.422412i −0.0786069 0.0173027i
\(597\) 0 0
\(598\) −41.1786 + 24.7763i −1.68392 + 1.01318i
\(599\) −6.38483 + 22.9961i −0.260877 + 0.939594i 0.710822 + 0.703372i \(0.248323\pi\)
−0.971699 + 0.236222i \(0.924091\pi\)
\(600\) 0 0
\(601\) −10.1760 + 3.42870i −0.415088 + 0.139860i −0.519094 0.854717i \(-0.673731\pi\)
0.104006 + 0.994577i \(0.466834\pi\)
\(602\) 10.2585 + 19.3495i 0.418104 + 0.788628i
\(603\) 0 0
\(604\) 5.48070 + 5.19159i 0.223006 + 0.211243i
\(605\) −1.34080 8.17850i −0.0545111 0.332503i
\(606\) 0 0
\(607\) −19.4890 2.11956i −0.791035 0.0860303i −0.296324 0.955088i \(-0.595761\pi\)
−0.494711 + 0.869057i \(0.664726\pi\)
\(608\) −15.6059 + 7.22006i −0.632903 + 0.292812i
\(609\) 0 0
\(610\) −57.2516 43.5216i −2.31805 1.76214i
\(611\) −31.4545 + 29.7953i −1.27251 + 1.20539i
\(612\) 0 0
\(613\) 24.9841 + 11.5589i 1.00910 + 0.466858i 0.853573 0.520974i \(-0.174431\pi\)
0.155525 + 0.987832i \(0.450293\pi\)
\(614\) −21.0488 + 52.8285i −0.849460 + 2.13198i
\(615\) 0 0
\(616\) −5.28302 + 7.79187i −0.212859 + 0.313944i
\(617\) 2.40077 + 6.02547i 0.0966512 + 0.242576i 0.969351 0.245682i \(-0.0790118\pi\)
−0.872699 + 0.488258i \(0.837633\pi\)
\(618\) 0 0
\(619\) 25.2182 29.6892i 1.01360 1.19331i 0.0325715 0.999469i \(-0.489630\pi\)
0.981033 0.193839i \(-0.0620938\pi\)
\(620\) −3.60473 + 4.24381i −0.144769 + 0.170436i
\(621\) 0 0
\(622\) −9.27459 23.2775i −0.371877 0.933342i
\(623\) 10.5622 15.5781i 0.423167 0.624124i
\(624\) 0 0
\(625\) 9.74085 24.4477i 0.389634 0.977908i
\(626\) −29.4120 13.6075i −1.17554 0.543863i
\(627\) 0 0
\(628\) −18.9396 + 17.9405i −0.755771 + 0.715905i
\(629\) 3.05403 + 2.32161i 0.121772 + 0.0925689i
\(630\) 0 0
\(631\) −8.75573 + 4.05083i −0.348560 + 0.161261i −0.586355 0.810054i \(-0.699438\pi\)
0.237795 + 0.971315i \(0.423575\pi\)
\(632\) −6.66835 0.725227i −0.265253 0.0288480i
\(633\) 0 0
\(634\) 2.94305 + 17.9518i 0.116883 + 0.712957i
\(635\) −37.5889 35.6061i −1.49167 1.41298i
\(636\) 0 0
\(637\) 6.12756 + 11.5578i 0.242783 + 0.457937i
\(638\) 13.1432 4.42845i 0.520343 0.175324i
\(639\) 0 0
\(640\) −8.98501 + 32.3611i −0.355164 + 1.27918i
\(641\) −3.97894 + 2.39405i −0.157159 + 0.0945592i −0.591961 0.805967i \(-0.701646\pi\)
0.434802 + 0.900526i \(0.356818\pi\)
\(642\) 0 0
\(643\) 26.2753 + 5.78364i 1.03620 + 0.228084i 0.700326 0.713823i \(-0.253038\pi\)
0.335872 + 0.941908i \(0.390969\pi\)
\(644\) −7.85803 + 14.8218i −0.309650 + 0.584062i
\(645\) 0 0
\(646\) 7.61322 5.78742i 0.299538 0.227703i
\(647\) −2.77715 3.26951i −0.109181 0.128538i 0.704857 0.709349i \(-0.251011\pi\)
−0.814038 + 0.580812i \(0.802735\pi\)
\(648\) 0 0
\(649\) 24.2400 + 14.7733i 0.951504 + 0.579903i
\(650\) 27.4647 1.07725
\(651\) 0 0
\(652\) 10.2934 7.82484i 0.403121 0.306444i
\(653\) −3.71514 + 22.6614i −0.145385 + 0.886808i 0.808908 + 0.587935i \(0.200059\pi\)
−0.954293 + 0.298873i \(0.903389\pi\)
\(654\) 0 0
\(655\) 26.9308 + 5.92793i 1.05228 + 0.231623i
\(656\) −29.7403 + 3.23445i −1.16116 + 0.126284i
\(657\) 0 0
\(658\) −10.9413 + 39.4071i −0.426538 + 1.53625i
\(659\) 0.844507 0.185890i 0.0328973 0.00724125i −0.198491 0.980103i \(-0.563604\pi\)
0.231389 + 0.972861i \(0.425673\pi\)
\(660\) 0 0
\(661\) −10.8932 20.5467i −0.423696 0.799176i 0.576139 0.817352i \(-0.304559\pi\)
−0.999835 + 0.0181762i \(0.994214\pi\)
\(662\) 9.11781 + 32.8394i 0.354374 + 1.27634i
\(663\) 0 0
\(664\) −3.55067 21.6581i −0.137793 0.840498i
\(665\) −14.8765 5.01248i −0.576887 0.194376i
\(666\) 0 0
\(667\) −15.7939 + 7.30704i −0.611542 + 0.282930i
\(668\) −0.714899 13.1855i −0.0276603 0.510164i
\(669\) 0 0
\(670\) 43.6841 41.3797i 1.68766 1.59864i
\(671\) 41.0008 + 24.6694i 1.58282 + 0.952350i
\(672\) 0 0
\(673\) −5.44051 + 13.6546i −0.209716 + 0.526348i −0.995777 0.0918009i \(-0.970738\pi\)
0.786061 + 0.618149i \(0.212117\pi\)
\(674\) 29.8897 + 44.0839i 1.15131 + 1.69805i
\(675\) 0 0
\(676\) 1.01489 + 2.54719i 0.0390343 + 0.0979687i
\(677\) 1.53807 28.3681i 0.0591129 1.09027i −0.807041 0.590496i \(-0.798932\pi\)
0.866154 0.499778i \(-0.166585\pi\)
\(678\) 0 0
\(679\) 7.46007 8.78268i 0.286291 0.337048i
\(680\) 0.458434 8.45533i 0.0175802 0.324247i
\(681\) 0 0
\(682\) 5.62213 8.29203i 0.215283 0.317518i
\(683\) −13.4373 19.8185i −0.514162 0.758333i 0.478651 0.878005i \(-0.341126\pi\)
−0.992813 + 0.119672i \(0.961816\pi\)
\(684\) 0 0
\(685\) 11.2413 + 5.20077i 0.429508 + 0.198711i
\(686\) 29.0699 + 17.4907i 1.10989 + 0.667800i
\(687\) 0 0
\(688\) −28.1099 21.3686i −1.07168 0.814671i
\(689\) 0.339615 + 6.26382i 0.0129383 + 0.238633i
\(690\) 0 0
\(691\) −41.9640 4.56386i −1.59639 0.173618i −0.733742 0.679428i \(-0.762228\pi\)
−0.862645 + 0.505810i \(0.831194\pi\)
\(692\) −23.5410 7.93187i −0.894893 0.301525i
\(693\) 0 0
\(694\) −17.1134 16.2106i −0.649614 0.615347i
\(695\) −11.5433 41.5753i −0.437863 1.57704i
\(696\) 0 0
\(697\) 10.5236 3.54581i 0.398609 0.134307i
\(698\) 34.0674 7.49880i 1.28947 0.283834i
\(699\) 0 0
\(700\) 8.21503 4.94282i 0.310499 0.186821i
\(701\) −16.6595 + 1.81183i −0.629222 + 0.0684320i −0.417173 0.908827i \(-0.636979\pi\)
−0.212049 + 0.977259i \(0.568014\pi\)
\(702\) 0 0
\(703\) −2.83428 + 5.34602i −0.106897 + 0.201629i
\(704\) −0.351325 + 2.14299i −0.0132411 + 0.0807668i
\(705\) 0 0
\(706\) 32.6097 + 38.3911i 1.22728 + 1.44487i
\(707\) 26.5115 0.997067
\(708\) 0 0
\(709\) −2.37408 −0.0891603 −0.0445801 0.999006i \(-0.514195\pi\)
−0.0445801 + 0.999006i \(0.514195\pi\)
\(710\) 43.2714 + 50.9430i 1.62395 + 1.91186i
\(711\) 0 0
\(712\) −2.59061 + 15.8020i −0.0970873 + 0.592206i
\(713\) −5.88809 + 11.1061i −0.220511 + 0.415927i
\(714\) 0 0
\(715\) −37.4071 + 4.06827i −1.39895 + 0.152145i
\(716\) −6.37285 + 3.83442i −0.238165 + 0.143299i
\(717\) 0 0
\(718\) −10.2553 + 2.25736i −0.382723 + 0.0842438i
\(719\) 14.8939 5.01835i 0.555450 0.187153i −0.0275566 0.999620i \(-0.508773\pi\)
0.583007 + 0.812467i \(0.301876\pi\)
\(720\) 0 0
\(721\) 0.142030 + 0.511545i 0.00528947 + 0.0190509i
\(722\) −13.6226 12.9040i −0.506981 0.480238i
\(723\) 0 0
\(724\) −3.90384 1.31536i −0.145085 0.0488849i
\(725\) 9.88701 + 1.07528i 0.367194 + 0.0399348i
\(726\) 0 0
\(727\) 0.487739 + 8.99582i 0.0180892 + 0.333636i 0.993545 + 0.113440i \(0.0361870\pi\)
−0.975456 + 0.220196i \(0.929330\pi\)
\(728\) 6.62213 + 5.03401i 0.245432 + 0.186573i
\(729\) 0 0
\(730\) −53.2434 32.0355i −1.97063 1.18569i
\(731\) 11.8958 + 5.50359i 0.439982 + 0.203557i
\(732\) 0 0
\(733\) 5.36054 + 7.90620i 0.197996 + 0.292022i 0.913706 0.406375i \(-0.133207\pi\)
−0.715710 + 0.698397i \(0.753897\pi\)
\(734\) −20.5960 + 30.3769i −0.760213 + 1.12123i
\(735\) 0 0
\(736\) 2.64289 48.7452i 0.0974180 1.79677i
\(737\) −25.9187 + 30.5138i −0.954726 + 1.12399i
\(738\) 0 0
\(739\) 1.44613 26.6724i 0.0531969 0.981160i −0.843114 0.537734i \(-0.819280\pi\)
0.896311 0.443425i \(-0.146237\pi\)
\(740\) −2.81646 7.06879i −0.103535 0.259854i
\(741\) 0 0
\(742\) 3.32304 + 4.90112i 0.121993 + 0.179926i
\(743\) 8.84838 22.2078i 0.324616 0.814724i −0.672590 0.740016i \(-0.734818\pi\)
0.997205 0.0747083i \(-0.0238026\pi\)
\(744\) 0 0
\(745\) 4.47292 + 2.69127i 0.163875 + 0.0986005i
\(746\) 19.7815 18.7381i 0.724253 0.686049i
\(747\) 0 0
\(748\) −0.433207 7.99004i −0.0158396 0.292145i
\(749\) 14.8291 6.86067i 0.541843 0.250683i
\(750\) 0 0
\(751\) −17.1214 5.76888i −0.624769 0.210509i −0.0109300 0.999940i \(-0.503479\pi\)
−0.613839 + 0.789431i \(0.710376\pi\)
\(752\) −10.6676 65.0698i −0.389009 2.37285i
\(753\) 0 0
\(754\) −3.27853 11.8082i −0.119397 0.430030i
\(755\) −9.39403 17.7190i −0.341884 0.644861i
\(756\) 0 0
\(757\) −19.9915 + 4.40046i −0.726602 + 0.159937i −0.562844 0.826563i \(-0.690293\pi\)
−0.163758 + 0.986500i \(0.552362\pi\)
\(758\) 8.15885 29.3855i 0.296343 1.06733i
\(759\) 0 0
\(760\) 13.2777 1.44404i 0.481633 0.0523807i
\(761\) 20.1615 + 4.43789i 0.730855 + 0.160873i 0.564782 0.825240i \(-0.308960\pi\)
0.166073 + 0.986114i \(0.446891\pi\)
\(762\) 0 0
\(763\) −2.30175 + 14.0401i −0.0833291 + 0.508285i
\(764\) −24.1509 + 18.3590i −0.873747 + 0.664206i
\(765\) 0 0
\(766\) 57.7743 2.08747
\(767\) 14.1942 20.6805i 0.512524 0.746730i
\(768\) 0 0
\(769\) −20.2459 23.8353i −0.730086 0.859523i 0.264398 0.964414i \(-0.414827\pi\)
−0.994484 + 0.104890i \(0.966551\pi\)
\(770\) −28.2763 + 21.4951i −1.01901 + 0.774629i
\(771\) 0 0
\(772\) 3.89404 7.34494i 0.140150 0.264350i
\(773\) 1.07943 + 0.237601i 0.0388245 + 0.00854593i 0.234340 0.972155i \(-0.424707\pi\)
−0.195516 + 0.980701i \(0.562638\pi\)
\(774\) 0 0
\(775\) 6.15559 3.70370i 0.221115 0.133041i
\(776\) −2.62285 + 9.44666i −0.0941549 + 0.339115i
\(777\) 0 0
\(778\) 11.4130 3.84550i 0.409177 0.137868i
\(779\) 8.20441 + 15.4752i 0.293953 + 0.554455i
\(780\) 0 0
\(781\) −32.2873 30.5841i −1.15533 1.09439i
\(782\) 4.39235 + 26.7922i 0.157070 + 0.958086i
\(783\) 0 0
\(784\) −19.7924 2.15255i −0.706872 0.0768770i
\(785\) 62.8991 29.1002i 2.24496 1.03863i
\(786\) 0 0
\(787\) 9.52622 + 7.24164i 0.339573 + 0.258137i 0.761037 0.648708i \(-0.224691\pi\)
−0.421464 + 0.906845i \(0.638484\pi\)
\(788\) 18.0774 17.1239i 0.643982 0.610012i
\(789\) 0 0
\(790\) −22.9688 10.6265i −0.817193 0.378074i
\(791\) 6.93835 17.4139i 0.246699 0.619168i
\(792\) 0 0
\(793\) 23.7274 34.9953i 0.842585 1.24272i
\(794\) −21.9493 55.0887i −0.778953 1.95502i
\(795\) 0 0
\(796\) −5.89902 + 6.94487i −0.209085 + 0.246154i
\(797\) −10.6846 + 12.5789i −0.378469 + 0.445568i −0.918109 0.396328i \(-0.870284\pi\)
0.539640 + 0.841896i \(0.318560\pi\)
\(798\) 0 0
\(799\) 9.05978 + 22.7383i 0.320512 + 0.804424i
\(800\) −15.6563 + 23.0913i −0.553532 + 0.816399i
\(801\) 0 0
\(802\) 1.36694 3.43076i 0.0482683 0.121144i
\(803\) 37.5232 + 17.3601i 1.32417 + 0.612624i
\(804\) 0 0
\(805\) 32.3555 30.6488i 1.14038 1.08023i
\(806\) −7.04720 5.35714i −0.248227 0.188697i
\(807\) 0 0
\(808\) −20.4711 + 9.47094i −0.720171 + 0.333186i
\(809\) −34.3244 3.73300i −1.20678 0.131245i −0.517464 0.855705i \(-0.673124\pi\)
−0.689317 + 0.724460i \(0.742089\pi\)
\(810\) 0 0
\(811\) −8.42719 51.4036i −0.295919 1.80502i −0.547082 0.837079i \(-0.684261\pi\)
0.251163 0.967945i \(-0.419187\pi\)
\(812\) −3.10578 2.94195i −0.108991 0.103242i
\(813\) 0 0
\(814\) 6.41283 + 12.0959i 0.224770 + 0.423960i
\(815\) −32.5514 + 10.9678i −1.14023 + 0.384187i
\(816\) 0 0
\(817\) −5.53082 + 19.9202i −0.193499 + 0.696920i
\(818\) 19.4112 11.6793i 0.678695 0.408357i
\(819\) 0 0
\(820\) −21.5115 4.73504i −0.751214 0.165355i
\(821\) −6.90184 + 13.0182i −0.240876 + 0.454340i −0.974245 0.225490i \(-0.927602\pi\)
0.733370 + 0.679830i \(0.237946\pi\)
\(822\) 0 0
\(823\) 6.30790 4.79514i 0.219880 0.167148i −0.489436 0.872039i \(-0.662797\pi\)
0.709315 + 0.704891i \(0.249004\pi\)
\(824\) −0.292414 0.344256i −0.0101867 0.0119927i
\(825\) 0 0
\(826\) 1.41641 23.6349i 0.0492831 0.822362i
\(827\) 6.80483 0.236627 0.118314 0.992976i \(-0.462251\pi\)
0.118314 + 0.992976i \(0.462251\pi\)
\(828\) 0 0
\(829\) −38.7142 + 29.4298i −1.34460 + 1.02214i −0.348196 + 0.937422i \(0.613206\pi\)
−0.996405 + 0.0847171i \(0.973001\pi\)
\(830\) 13.3966 81.7155i 0.465002 2.83639i
\(831\) 0 0
\(832\) 1.87397 + 0.412493i 0.0649683 + 0.0143006i
\(833\) 7.34707 0.799042i 0.254561 0.0276852i
\(834\) 0 0
\(835\) −9.38492 + 33.8014i −0.324779 + 1.16975i
\(836\) 12.3260 2.71315i 0.426302 0.0938362i
\(837\) 0 0
\(838\) −3.59842 6.78733i −0.124305 0.234464i
\(839\) −2.96406 10.6756i −0.102331 0.368562i 0.894598 0.446871i \(-0.147462\pi\)
−0.996929 + 0.0783091i \(0.975048\pi\)
\(840\) 0 0
\(841\) 3.97374 + 24.2388i 0.137026 + 0.835820i
\(842\) 37.4759 + 12.6271i 1.29150 + 0.435158i
\(843\) 0 0
\(844\) −0.179918 + 0.0832388i −0.00619302 + 0.00286520i
\(845\) −0.394358 7.27351i −0.0135663 0.250216i
\(846\) 0 0
\(847\) 3.33916 3.16302i 0.114735 0.108683i
\(848\) −8.18040 4.92198i −0.280916 0.169022i
\(849\) 0 0
\(850\) 5.74305 14.4140i 0.196985 0.494395i
\(851\) −9.64026 14.2183i −0.330464 0.487398i
\(852\) 0 0
\(853\) 8.27273 + 20.7630i 0.283253 + 0.710911i 0.999909 + 0.0134845i \(0.00429237\pi\)
−0.716656 + 0.697427i \(0.754328\pi\)
\(854\) 2.16075 39.8526i 0.0739392 1.36373i
\(855\) 0 0
\(856\) −8.99953 + 10.5951i −0.307597 + 0.362132i
\(857\) −0.924110 + 17.0442i −0.0315670 + 0.582219i 0.939373 + 0.342897i \(0.111408\pi\)
−0.970940 + 0.239323i \(0.923075\pi\)
\(858\) 0 0
\(859\) 8.39693 12.3845i 0.286500 0.422555i −0.657019 0.753874i \(-0.728183\pi\)
0.943519 + 0.331318i \(0.107493\pi\)
\(860\) −14.5898 21.5183i −0.497508 0.733769i
\(861\) 0 0
\(862\) 2.87683 + 1.33096i 0.0979851 + 0.0453328i
\(863\) −38.5761 23.2105i −1.31315 0.790094i −0.325312 0.945607i \(-0.605469\pi\)
−0.987834 + 0.155513i \(0.950297\pi\)
\(864\) 0 0
\(865\) 52.5368 + 39.9375i 1.78631 + 1.35791i
\(866\) −2.77818 51.2405i −0.0944064 1.74122i
\(867\) 0 0
\(868\) −3.07203 0.334104i −0.104272 0.0113402i
\(869\) 15.9575 + 5.37671i 0.541321 + 0.182392i
\(870\) 0 0
\(871\) 25.6828 + 24.3280i 0.870228 + 0.824323i
\(872\) −3.23834 11.6635i −0.109664 0.394975i
\(873\) 0 0
\(874\) −40.5812 + 13.6734i −1.37268 + 0.462510i
\(875\) 1.46956 0.323475i 0.0496802 0.0109354i
\(876\) 0 0
\(877\) −24.6271 + 14.8176i −0.831598 + 0.500356i −0.866584 0.499032i \(-0.833689\pi\)
0.0349855 + 0.999388i \(0.488862\pi\)
\(878\) 10.8248 1.17726i 0.365318 0.0397307i
\(879\) 0 0
\(880\) 26.8238 50.5951i 0.904232 1.70556i
\(881\) 3.72232 22.7051i 0.125408 0.764955i −0.846987 0.531614i \(-0.821586\pi\)
0.972395 0.233341i \(-0.0749660\pi\)
\(882\) 0 0
\(883\) −28.9648 34.1000i −0.974742 1.14756i −0.989039 0.147658i \(-0.952827\pi\)
0.0142962 0.999898i \(-0.495449\pi\)
\(884\) −7.07042 −0.237804
\(885\) 0 0
\(886\) −68.1828 −2.29065
\(887\) −8.47439 9.97683i −0.284542 0.334989i 0.601259 0.799054i \(-0.294666\pi\)
−0.885801 + 0.464065i \(0.846390\pi\)
\(888\) 0 0
\(889\) 4.64864 28.3554i 0.155910 0.951010i
\(890\) −28.2996 + 53.3788i −0.948606 + 1.78926i
\(891\) 0 0
\(892\) −14.8436 + 1.61434i −0.497002 + 0.0540522i
\(893\) −33.0804 + 19.9038i −1.10699 + 0.666056i
\(894\) 0 0
\(895\) 19.2964 4.24746i 0.645008 0.141977i
\(896\) −17.6632 + 5.95141i −0.590085 + 0.198823i
\(897\) 0 0
\(898\) 6.30583 + 22.7115i 0.210428 + 0.757894i
\(899\) −2.32718 2.20443i −0.0776159 0.0735217i
\(900\) 0 0
\(901\) 3.35839 + 1.13157i 0.111884 + 0.0376981i
\(902\) 39.3981 + 4.28481i 1.31181 + 0.142668i
\(903\) 0 0
\(904\) 0.863428 + 15.9250i 0.0287172 + 0.529657i
\(905\) 8.71229 + 6.62291i 0.289606 + 0.220153i
\(906\) 0 0
\(907\) −8.67619 5.22029i −0.288088 0.173337i 0.364173 0.931331i \(-0.381352\pi\)
−0.652261 + 0.757994i \(0.726179\pi\)
\(908\) −0.661894 0.306225i −0.0219657 0.0101624i
\(909\) 0 0
\(910\) 17.6127 + 25.9767i 0.583854 + 0.861120i
\(911\) 0.616734 0.909615i 0.0204333 0.0301369i −0.817335 0.576163i \(-0.804550\pi\)
0.837768 + 0.546026i \(0.183860\pi\)
\(912\) 0 0
\(913\) −2.98286 + 55.0157i −0.0987184 + 1.82075i
\(914\) −10.5470 + 12.4169i −0.348864 + 0.410715i
\(915\) 0 0
\(916\) −0.401958 + 7.41367i −0.0132811 + 0.244955i
\(917\) 5.66445 + 14.2167i 0.187057 + 0.469477i
\(918\) 0 0
\(919\) −15.6792 23.1251i −0.517208 0.762825i 0.475966 0.879464i \(-0.342099\pi\)
−0.993174 + 0.116638i \(0.962788\pi\)
\(920\) −14.0347 + 35.2244i −0.462710 + 1.16131i
\(921\) 0 0
\(922\) 59.2239 + 35.6338i 1.95043 + 1.17354i
\(923\) −28.5293 + 27.0243i −0.939052 + 0.889517i
\(924\) 0 0
\(925\) 0.531499 + 9.80291i 0.0174756 + 0.322318i
\(926\) −63.2565 + 29.2656i −2.07874 + 0.961727i
\(927\) 0 0
\(928\) 11.7968 + 3.97481i 0.387250 + 0.130480i
\(929\) 2.36556 + 14.4293i 0.0776115 + 0.473409i 0.996823 + 0.0796457i \(0.0253789\pi\)
−0.919212 + 0.393764i \(0.871173\pi\)
\(930\) 0 0
\(931\) 3.11850 + 11.2318i 0.102205 + 0.368108i
\(932\) −12.1651 22.9459i −0.398482 0.751617i
\(933\) 0 0
\(934\) 5.50752 1.21230i 0.180211 0.0396675i
\(935\) −5.68698 + 20.4826i −0.185984 + 0.669854i
\(936\) 0 0
\(937\) 1.20229 0.130757i 0.0392771 0.00427164i −0.0884594 0.996080i \(-0.528194\pi\)
0.127736 + 0.991808i \(0.459229\pi\)
\(938\) 32.6126 + 7.17857i 1.06484 + 0.234389i
\(939\) 0 0
\(940\) 7.85442 47.9099i 0.256183 1.56265i
\(941\) 15.1590 11.5235i 0.494168 0.375657i −0.328204 0.944607i \(-0.606443\pi\)
0.822372 + 0.568950i \(0.192650\pi\)
\(942\) 0 0
\(943\) −49.7262 −1.61931
\(944\) 13.9276 + 35.5428i 0.453306 + 1.15682i
\(945\) 0 0
\(946\) 30.2824 + 35.6512i 0.984564 + 1.15912i
\(947\) 11.2456 8.54871i 0.365434 0.277796i −0.406302 0.913739i \(-0.633182\pi\)
0.771736 + 0.635943i \(0.219389\pi\)
\(948\) 0 0
\(949\) 17.1120 32.2767i 0.555479 1.04775i
\(950\) 23.9008 + 5.26097i 0.775445 + 0.170688i
\(951\) 0 0
\(952\) 4.02667 2.42277i 0.130505 0.0785224i
\(953\) −2.25299 + 8.11454i −0.0729815 + 0.262856i −0.991035 0.133600i \(-0.957346\pi\)
0.918054 + 0.396456i \(0.129760\pi\)
\(954\) 0 0
\(955\) 76.3736 25.7333i 2.47139 0.832709i
\(956\) 1.86094 + 3.51010i 0.0601871 + 0.113525i
\(957\) 0 0
\(958\) 27.4597 + 26.0112i 0.887181 + 0.840383i
\(959\) 1.11207 + 6.78335i 0.0359107 + 0.219046i
\(960\) 0 0
\(961\) 28.5164 + 3.10134i 0.919883 + 0.100043i
\(962\) 10.9791 5.07947i 0.353980 0.163769i
\(963\) 0 0
\(964\) 4.75954 + 3.61811i 0.153294 + 0.116531i
\(965\) −16.0337 + 15.1880i −0.516144 + 0.488918i
\(966\) 0 0
\(967\) 37.3528 + 17.2812i 1.20118 + 0.555727i 0.915392 0.402564i \(-0.131881\pi\)
0.285793 + 0.958291i \(0.407743\pi\)
\(968\) −1.44841 + 3.63523i −0.0465536 + 0.116841i
\(969\) 0 0
\(970\) −20.7585 + 30.6165i −0.666514 + 0.983035i
\(971\) −3.46977 8.70848i −0.111350 0.279468i 0.862732 0.505661i \(-0.168751\pi\)
−0.974083 + 0.226193i \(0.927372\pi\)
\(972\) 0 0
\(973\) 15.5022 18.2507i 0.496979 0.585089i
\(974\) −22.3973 + 26.3682i −0.717657 + 0.844891i
\(975\) 0 0
\(976\) 23.8175 + 59.7774i 0.762379 + 1.91343i
\(977\) −26.3924 + 38.9258i −0.844366 + 1.24535i 0.123112 + 0.992393i \(0.460713\pi\)
−0.967478 + 0.252954i \(0.918598\pi\)
\(978\) 0 0
\(979\) 14.8792 37.3440i 0.475542 1.19352i
\(980\) −13.3040 6.15506i −0.424979 0.196616i
\(981\) 0 0
\(982\) 6.21103 5.88340i 0.198202 0.187747i
\(983\) 42.2632 + 32.1277i 1.34799 + 1.02471i 0.996060 + 0.0886860i \(0.0282668\pi\)
0.351928 + 0.936027i \(0.385526\pi\)
\(984\) 0 0
\(985\) −60.0359 + 27.7756i −1.91290 + 0.885003i
\(986\) −6.88273 0.748542i −0.219191 0.0238384i
\(987\) 0 0
\(988\) −1.80420 11.0051i −0.0573991 0.350119i
\(989\) −42.6105 40.3628i −1.35493 1.28346i
\(990\) 0 0
\(991\) −6.48933 12.2402i −0.206140 0.388822i 0.758787 0.651339i \(-0.225792\pi\)
−0.964927 + 0.262517i \(0.915447\pi\)
\(992\) 8.52135 2.87118i 0.270553 0.0911599i
\(993\) 0 0
\(994\) −9.92379 + 35.7423i −0.314763 + 1.13368i
\(995\) 20.7420 12.4800i 0.657565 0.395644i
\(996\) 0 0
\(997\) 7.39924 + 1.62870i 0.234336 + 0.0515813i 0.330586 0.943776i \(-0.392754\pi\)
−0.0962495 + 0.995357i \(0.530685\pi\)
\(998\) 11.3158 21.3439i 0.358196 0.675629i
\(999\) 0 0
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 531.2.i.c.46.2 140
3.2 odd 2 177.2.e.a.46.4 140
59.9 even 29 inner 531.2.i.c.127.2 140
177.68 odd 58 177.2.e.a.127.4 yes 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.2.e.a.46.4 140 3.2 odd 2
177.2.e.a.127.4 yes 140 177.68 odd 58
531.2.i.c.46.2 140 1.1 even 1 trivial
531.2.i.c.127.2 140 59.9 even 29 inner