Properties

Label 19.5.d.a.8.3
Level $19$
Weight $5$
Character 19.8
Analytic conductor $1.964$
Analytic rank $0$
Dimension $10$
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] = [19,5,Mod(8,19)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(19, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("19.8");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 19.d (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.96402929859\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 8.3
Root \(0.625165i\) of defining polynomial
Character \(\chi\) \(=\) 19.8
Dual form 19.5.d.a.12.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.541408 - 0.312582i) q^{2} +(-8.70876 - 5.02800i) q^{3} +(-7.80458 - 13.5179i) q^{4} +(4.61985 - 8.00181i) q^{5} +(3.14333 + 5.44441i) q^{6} +0.274467 q^{7} +19.7609i q^{8} +(10.0617 + 17.4273i) q^{9} +O(q^{10})\) \(q+(-0.541408 - 0.312582i) q^{2} +(-8.70876 - 5.02800i) q^{3} +(-7.80458 - 13.5179i) q^{4} +(4.61985 - 8.00181i) q^{5} +(3.14333 + 5.44441i) q^{6} +0.274467 q^{7} +19.7609i q^{8} +(10.0617 + 17.4273i) q^{9} +(-5.00245 + 2.88816i) q^{10} +45.5269 q^{11} +156.966i q^{12} +(111.271 - 64.2421i) q^{13} +(-0.148599 - 0.0857934i) q^{14} +(-80.4663 + 46.4572i) q^{15} +(-118.696 + 205.588i) q^{16} +(212.040 - 367.264i) q^{17} -12.5804i q^{18} +(-280.252 - 227.552i) q^{19} -144.224 q^{20} +(-2.39026 - 1.38002i) q^{21} +(-24.6486 - 14.2309i) q^{22} +(-286.876 - 496.884i) q^{23} +(99.3581 - 172.093i) q^{24} +(269.814 + 467.332i) q^{25} -80.3238 q^{26} +612.176i q^{27} +(-2.14210 - 3.71022i) q^{28} +(763.678 - 440.909i) q^{29} +58.0868 q^{30} +1531.33i q^{31} +(402.342 - 232.292i) q^{32} +(-396.483 - 228.909i) q^{33} +(-229.600 + 132.560i) q^{34} +(1.26799 - 2.19623i) q^{35} +(157.054 - 272.026i) q^{36} -71.9344i q^{37} +(80.6022 + 210.800i) q^{38} -1292.04 q^{39} +(158.123 + 91.2925i) q^{40} +(1112.58 + 642.350i) q^{41} +(0.862740 + 1.49431i) q^{42} +(603.976 - 1046.12i) q^{43} +(-355.318 - 615.429i) q^{44} +185.933 q^{45} +358.690i q^{46} +(-1347.59 - 2334.09i) q^{47} +(2067.40 - 1193.61i) q^{48} -2400.92 q^{49} -337.356i q^{50} +(-3693.21 + 2132.27i) q^{51} +(-1736.84 - 1002.77i) q^{52} +(1834.78 - 1059.31i) q^{53} +(191.356 - 331.437i) q^{54} +(210.327 - 364.297i) q^{55} +5.42372i q^{56} +(1296.52 + 3390.80i) q^{57} -551.282 q^{58} +(4850.33 + 2800.34i) q^{59} +(1256.01 + 725.158i) q^{60} +(1240.48 + 2148.57i) q^{61} +(478.666 - 829.075i) q^{62} +(2.76159 + 4.78322i) q^{63} +3507.84 q^{64} -1187.16i q^{65} +(143.106 + 247.867i) q^{66} +(-656.457 + 379.006i) q^{67} -6619.53 q^{68} +5769.66i q^{69} +(-1.37300 + 0.792705i) q^{70} +(-5268.29 - 3041.65i) q^{71} +(-344.380 + 198.828i) q^{72} +(3512.83 - 6084.39i) q^{73} +(-22.4854 + 38.9459i) q^{74} -5426.51i q^{75} +(-888.778 + 5564.38i) q^{76} +12.4956 q^{77} +(699.521 + 403.869i) q^{78} +(-2796.99 - 1614.84i) q^{79} +(1096.72 + 1899.57i) q^{80} +(3893.02 - 6742.91i) q^{81} +(-401.574 - 695.547i) q^{82} +5586.78 q^{83} +43.0819i q^{84} +(-1959.18 - 3393.40i) q^{85} +(-653.995 + 377.584i) q^{86} -8867.58 q^{87} +899.653i q^{88} +(-4918.49 + 2839.69i) q^{89} +(-100.666 - 58.1195i) q^{90} +(30.5401 - 17.6323i) q^{91} +(-4477.90 + 7755.95i) q^{92} +(7699.53 - 13336.0i) q^{93} +1684.93i q^{94} +(-3115.55 + 1191.27i) q^{95} -4671.87 q^{96} +(10277.2 + 5933.52i) q^{97} +(1299.88 + 750.487i) q^{98} +(458.076 + 793.411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9} + 144 q^{10} + 50 q^{11} - 624 q^{13} - 474 q^{14} + 504 q^{15} + 285 q^{16} - 292 q^{17} + 305 q^{19} - 652 q^{20} + 1158 q^{21} + 1629 q^{22} + 98 q^{23} + 505 q^{24} - 681 q^{25} + 1524 q^{26} - 1472 q^{28} + 2598 q^{29} - 6656 q^{30} - 2745 q^{32} - 3441 q^{33} + 486 q^{34} + 694 q^{35} + 3402 q^{36} - 342 q^{38} - 5552 q^{39} + 8784 q^{40} - 1407 q^{41} + 292 q^{42} + 5424 q^{43} + 4151 q^{44} + 9572 q^{45} - 2416 q^{47} + 11481 q^{48} - 17826 q^{49} - 3342 q^{51} - 19962 q^{52} + 1122 q^{53} - 1039 q^{54} + 11424 q^{55} - 7906 q^{57} - 20236 q^{58} + 15387 q^{59} + 8886 q^{60} + 860 q^{61} + 21636 q^{62} + 5318 q^{63} + 19710 q^{64} - 13921 q^{66} + 14763 q^{67} - 48844 q^{68} - 20334 q^{70} - 27264 q^{71} + 354 q^{72} + 1561 q^{73} + 17094 q^{74} + 1955 q^{76} - 18392 q^{77} + 40266 q^{78} + 24750 q^{79} - 2002 q^{80} + 14311 q^{81} + 14479 q^{82} + 6002 q^{83} - 14944 q^{85} + 59946 q^{86} - 31996 q^{87} - 22566 q^{89} - 60630 q^{90} + 8724 q^{91} + 9572 q^{92} + 12476 q^{93} - 7312 q^{95} - 41850 q^{96} + 46287 q^{97} + 25515 q^{98} - 2048 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.541408 0.312582i −0.135352 0.0781456i 0.430795 0.902450i \(-0.358233\pi\)
−0.566147 + 0.824304i \(0.691567\pi\)
\(3\) −8.70876 5.02800i −0.967640 0.558667i −0.0691240 0.997608i \(-0.522020\pi\)
−0.898516 + 0.438941i \(0.855354\pi\)
\(4\) −7.80458 13.5179i −0.487787 0.844871i
\(5\) 4.61985 8.00181i 0.184794 0.320072i −0.758713 0.651425i \(-0.774172\pi\)
0.943507 + 0.331353i \(0.107505\pi\)
\(6\) 3.14333 + 5.44441i 0.0873147 + 0.151234i
\(7\) 0.274467 0.00560136 0.00280068 0.999996i \(-0.499109\pi\)
0.00280068 + 0.999996i \(0.499109\pi\)
\(8\) 19.7609i 0.308765i
\(9\) 10.0617 + 17.4273i 0.124218 + 0.215152i
\(10\) −5.00245 + 2.88816i −0.0500245 + 0.0288816i
\(11\) 45.5269 0.376255 0.188128 0.982145i \(-0.439758\pi\)
0.188128 + 0.982145i \(0.439758\pi\)
\(12\) 156.966i 1.09004i
\(13\) 111.271 64.2421i 0.658406 0.380131i −0.133263 0.991081i \(-0.542546\pi\)
0.791669 + 0.610950i \(0.209212\pi\)
\(14\) −0.148599 0.0857934i −0.000758156 0.000437722i
\(15\) −80.4663 + 46.4572i −0.357628 + 0.206476i
\(16\) −118.696 + 205.588i −0.463658 + 0.803079i
\(17\) 212.040 367.264i 0.733702 1.27081i −0.221589 0.975140i \(-0.571124\pi\)
0.955291 0.295669i \(-0.0955425\pi\)
\(18\) 12.5804i 0.0388284i
\(19\) −280.252 227.552i −0.776322 0.630337i
\(20\) −144.224 −0.360560
\(21\) −2.39026 1.38002i −0.00542010 0.00312930i
\(22\) −24.6486 14.2309i −0.0509269 0.0294027i
\(23\) −286.876 496.884i −0.542299 0.939289i −0.998772 0.0495518i \(-0.984221\pi\)
0.456473 0.889737i \(-0.349113\pi\)
\(24\) 99.3581 172.093i 0.172497 0.298773i
\(25\) 269.814 + 467.332i 0.431702 + 0.747731i
\(26\) −80.3238 −0.118822
\(27\) 612.176i 0.839748i
\(28\) −2.14210 3.71022i −0.00273227 0.00473243i
\(29\) 763.678 440.909i 0.908059 0.524268i 0.0282529 0.999601i \(-0.491006\pi\)
0.879806 + 0.475333i \(0.157672\pi\)
\(30\) 58.0868 0.0645409
\(31\) 1531.33i 1.59348i 0.604326 + 0.796738i \(0.293443\pi\)
−0.604326 + 0.796738i \(0.706557\pi\)
\(32\) 402.342 232.292i 0.392912 0.226848i
\(33\) −396.483 228.909i −0.364079 0.210201i
\(34\) −229.600 + 132.560i −0.198616 + 0.114671i
\(35\) 1.26799 2.19623i 0.00103510 0.00179284i
\(36\) 157.054 272.026i 0.121184 0.209897i
\(37\) 71.9344i 0.0525452i −0.999655 0.0262726i \(-0.991636\pi\)
0.999655 0.0262726i \(-0.00836380\pi\)
\(38\) 80.6022 + 210.800i 0.0558187 + 0.145984i
\(39\) −1292.04 −0.849467
\(40\) 158.123 + 91.2925i 0.0988270 + 0.0570578i
\(41\) 1112.58 + 642.350i 0.661857 + 0.382123i 0.792984 0.609242i \(-0.208526\pi\)
−0.131127 + 0.991366i \(0.541860\pi\)
\(42\) 0.862740 + 1.49431i 0.000489081 + 0.000847114i
\(43\) 603.976 1046.12i 0.326650 0.565775i −0.655195 0.755460i \(-0.727413\pi\)
0.981845 + 0.189685i \(0.0607468\pi\)
\(44\) −355.318 615.429i −0.183532 0.317887i
\(45\) 185.933 0.0918189
\(46\) 358.690i 0.169513i
\(47\) −1347.59 2334.09i −0.610045 1.05663i −0.991232 0.132131i \(-0.957818\pi\)
0.381187 0.924498i \(-0.375515\pi\)
\(48\) 2067.40 1193.61i 0.897308 0.518061i
\(49\) −2400.92 −0.999969
\(50\) 337.356i 0.134943i
\(51\) −3693.21 + 2132.27i −1.41992 + 0.819790i
\(52\) −1736.84 1002.77i −0.642323 0.370846i
\(53\) 1834.78 1059.31i 0.653177 0.377112i −0.136495 0.990641i \(-0.543584\pi\)
0.789673 + 0.613529i \(0.210250\pi\)
\(54\) 191.356 331.437i 0.0656226 0.113662i
\(55\) 210.327 364.297i 0.0695296 0.120429i
\(56\) 5.42372i 0.00172950i
\(57\) 1296.52 + 3390.80i 0.399051 + 1.04364i
\(58\) −551.282 −0.163877
\(59\) 4850.33 + 2800.34i 1.39337 + 0.804465i 0.993687 0.112187i \(-0.0357857\pi\)
0.399686 + 0.916652i \(0.369119\pi\)
\(60\) 1256.01 + 725.158i 0.348892 + 0.201433i
\(61\) 1240.48 + 2148.57i 0.333372 + 0.577417i 0.983171 0.182689i \(-0.0584803\pi\)
−0.649799 + 0.760106i \(0.725147\pi\)
\(62\) 478.666 829.075i 0.124523 0.215680i
\(63\) 2.76159 + 4.78322i 0.000695790 + 0.00120514i
\(64\) 3507.84 0.856407
\(65\) 1187.16i 0.280983i
\(66\) 143.106 + 247.867i 0.0328526 + 0.0569024i
\(67\) −656.457 + 379.006i −0.146237 + 0.0844298i −0.571333 0.820718i \(-0.693574\pi\)
0.425096 + 0.905148i \(0.360240\pi\)
\(68\) −6619.53 −1.43156
\(69\) 5769.66i 1.21186i
\(70\) −1.37300 + 0.792705i −0.000280205 + 0.000161776i
\(71\) −5268.29 3041.65i −1.04509 0.603381i −0.123817 0.992305i \(-0.539514\pi\)
−0.921270 + 0.388924i \(0.872847\pi\)
\(72\) −344.380 + 198.828i −0.0664313 + 0.0383541i
\(73\) 3512.83 6084.39i 0.659191 1.14175i −0.321635 0.946864i \(-0.604232\pi\)
0.980826 0.194888i \(-0.0624343\pi\)
\(74\) −22.4854 + 38.9459i −0.00410618 + 0.00711211i
\(75\) 5426.51i 0.964712i
\(76\) −888.778 + 5564.38i −0.153874 + 0.963362i
\(77\) 12.4956 0.00210754
\(78\) 699.521 + 403.869i 0.114977 + 0.0663821i
\(79\) −2796.99 1614.84i −0.448164 0.258747i 0.258891 0.965907i \(-0.416643\pi\)
−0.707054 + 0.707159i \(0.749976\pi\)
\(80\) 1096.72 + 1899.57i 0.171362 + 0.296808i
\(81\) 3893.02 6742.91i 0.593358 1.02773i
\(82\) −401.574 695.547i −0.0597225 0.103442i
\(83\) 5586.78 0.810971 0.405485 0.914102i \(-0.367103\pi\)
0.405485 + 0.914102i \(0.367103\pi\)
\(84\) 43.0819i 0.00610572i
\(85\) −1959.18 3393.40i −0.271167 0.469675i
\(86\) −653.995 + 377.584i −0.0884256 + 0.0510525i
\(87\) −8867.58 −1.17157
\(88\) 899.653i 0.116174i
\(89\) −4918.49 + 2839.69i −0.620943 + 0.358502i −0.777236 0.629209i \(-0.783379\pi\)
0.156293 + 0.987711i \(0.450046\pi\)
\(90\) −100.666 58.1195i −0.0124279 0.00717524i
\(91\) 30.5401 17.6323i 0.00368797 0.00212925i
\(92\) −4477.90 + 7755.95i −0.529052 + 0.916345i
\(93\) 7699.53 13336.0i 0.890222 1.54191i
\(94\) 1684.93i 0.190689i
\(95\) −3115.55 + 1191.27i −0.345213 + 0.131997i
\(96\) −4671.87 −0.506930
\(97\) 10277.2 + 5933.52i 1.09227 + 0.630622i 0.934180 0.356803i \(-0.116133\pi\)
0.158089 + 0.987425i \(0.449467\pi\)
\(98\) 1299.88 + 750.487i 0.135348 + 0.0781431i
\(99\) 458.076 + 793.411i 0.0467377 + 0.0809520i
\(100\) 4211.57 7294.66i 0.421157 0.729466i
\(101\) 7781.01 + 13477.1i 0.762769 + 1.32116i 0.941418 + 0.337242i \(0.109494\pi\)
−0.178649 + 0.983913i \(0.557173\pi\)
\(102\) 2666.05 0.256252
\(103\) 1961.40i 0.184881i 0.995718 + 0.0924403i \(0.0294667\pi\)
−0.995718 + 0.0924403i \(0.970533\pi\)
\(104\) 1269.48 + 2198.81i 0.117371 + 0.203293i
\(105\) −22.0853 + 12.7510i −0.00200320 + 0.00115655i
\(106\) −1324.48 −0.117879
\(107\) 18401.5i 1.60726i 0.595128 + 0.803631i \(0.297102\pi\)
−0.595128 + 0.803631i \(0.702898\pi\)
\(108\) 8275.36 4777.78i 0.709479 0.409618i
\(109\) −6715.47 3877.18i −0.565228 0.326334i 0.190013 0.981782i \(-0.439147\pi\)
−0.755241 + 0.655447i \(0.772480\pi\)
\(110\) −227.746 + 131.489i −0.0188220 + 0.0108669i
\(111\) −361.687 + 626.460i −0.0293553 + 0.0508449i
\(112\) −32.5782 + 56.4271i −0.00259712 + 0.00449834i
\(113\) 4465.17i 0.349688i −0.984596 0.174844i \(-0.944058\pi\)
0.984596 0.174844i \(-0.0559421\pi\)
\(114\) 357.959 2241.08i 0.0275438 0.172444i
\(115\) −5301.29 −0.400854
\(116\) −11920.4 6882.23i −0.885878 0.511462i
\(117\) 2239.14 + 1292.77i 0.163572 + 0.0944383i
\(118\) −1750.67 3032.26i −0.125731 0.217772i
\(119\) 58.1979 100.802i 0.00410973 0.00711826i
\(120\) −918.038 1590.09i −0.0637526 0.110423i
\(121\) −12568.3 −0.858432
\(122\) 1551.00i 0.104206i
\(123\) −6459.47 11188.1i −0.426960 0.739516i
\(124\) 20700.4 11951.4i 1.34628 0.777276i
\(125\) 10760.8 0.688691
\(126\) 3.45290i 0.000217492i
\(127\) −355.004 + 204.962i −0.0220103 + 0.0127076i −0.510965 0.859602i \(-0.670712\pi\)
0.488954 + 0.872309i \(0.337378\pi\)
\(128\) −8336.65 4813.17i −0.508829 0.293772i
\(129\) −10519.8 + 6073.59i −0.632159 + 0.364977i
\(130\) −371.084 + 642.736i −0.0219576 + 0.0380317i
\(131\) −1477.71 + 2559.46i −0.0861084 + 0.149144i −0.905863 0.423571i \(-0.860776\pi\)
0.819755 + 0.572715i \(0.194110\pi\)
\(132\) 7146.17i 0.410134i
\(133\) −76.9199 62.4554i −0.00434846 0.00353075i
\(134\) 473.882 0.0263913
\(135\) 4898.52 + 2828.16i 0.268780 + 0.155180i
\(136\) 7257.48 + 4190.11i 0.392381 + 0.226541i
\(137\) −13132.3 22745.8i −0.699679 1.21188i −0.968578 0.248711i \(-0.919993\pi\)
0.268899 0.963168i \(-0.413340\pi\)
\(138\) 1803.49 3123.74i 0.0947014 0.164028i
\(139\) −2168.28 3755.57i −0.112224 0.194378i 0.804443 0.594030i \(-0.202464\pi\)
−0.916667 + 0.399653i \(0.869131\pi\)
\(140\) −39.5847 −0.00201963
\(141\) 27102.7i 1.36325i
\(142\) 1901.53 + 3293.55i 0.0943032 + 0.163338i
\(143\) 5065.80 2924.74i 0.247729 0.143026i
\(144\) −4777.13 −0.230379
\(145\) 8147.73i 0.387526i
\(146\) −3803.75 + 2196.09i −0.178446 + 0.103026i
\(147\) 20909.1 + 12071.9i 0.967610 + 0.558650i
\(148\) −972.405 + 561.418i −0.0443939 + 0.0256309i
\(149\) −1635.85 + 2833.37i −0.0736835 + 0.127623i −0.900513 0.434829i \(-0.856809\pi\)
0.826830 + 0.562453i \(0.190142\pi\)
\(150\) −1696.23 + 2937.96i −0.0753880 + 0.130576i
\(151\) 3278.86i 0.143803i −0.997412 0.0719016i \(-0.977093\pi\)
0.997412 0.0719016i \(-0.0229068\pi\)
\(152\) 4496.63 5538.04i 0.194626 0.239701i
\(153\) 8533.90 0.364556
\(154\) −6.76523 3.90591i −0.000285260 0.000164695i
\(155\) 12253.4 + 7074.51i 0.510027 + 0.294464i
\(156\) 10083.8 + 17465.7i 0.414359 + 0.717690i
\(157\) −15632.5 + 27076.3i −0.634204 + 1.09847i 0.352479 + 0.935820i \(0.385339\pi\)
−0.986683 + 0.162654i \(0.947995\pi\)
\(158\) 1009.54 + 1748.58i 0.0404399 + 0.0700440i
\(159\) −21304.8 −0.842721
\(160\) 4292.62i 0.167680i
\(161\) −78.7379 136.378i −0.00303761 0.00526130i
\(162\) −4215.43 + 2433.78i −0.160624 + 0.0927366i
\(163\) 32759.0 1.23298 0.616489 0.787363i \(-0.288554\pi\)
0.616489 + 0.787363i \(0.288554\pi\)
\(164\) 20053.1i 0.745579i
\(165\) −3663.38 + 2115.05i −0.134559 + 0.0776878i
\(166\) −3024.73 1746.33i −0.109767 0.0633738i
\(167\) 22419.2 12943.7i 0.803872 0.464116i −0.0409511 0.999161i \(-0.513039\pi\)
0.844823 + 0.535045i \(0.179705\pi\)
\(168\) 27.2705 47.2339i 0.000966216 0.00167354i
\(169\) −6026.39 + 10438.0i −0.211001 + 0.365464i
\(170\) 2449.62i 0.0847621i
\(171\) 1145.81 7173.59i 0.0391851 0.245326i
\(172\) −18855.1 −0.637342
\(173\) −3010.79 1738.28i −0.100598 0.0580802i 0.448857 0.893604i \(-0.351831\pi\)
−0.549455 + 0.835523i \(0.685165\pi\)
\(174\) 4800.98 + 2771.85i 0.158574 + 0.0915527i
\(175\) 74.0550 + 128.267i 0.00241812 + 0.00418831i
\(176\) −5403.88 + 9359.79i −0.174454 + 0.302163i
\(177\) −28160.3 48775.0i −0.898856 1.55686i
\(178\) 3550.55 0.112061
\(179\) 40116.5i 1.25204i −0.779809 0.626018i \(-0.784684\pi\)
0.779809 0.626018i \(-0.215316\pi\)
\(180\) −1451.13 2513.44i −0.0447880 0.0775752i
\(181\) −43406.5 + 25060.8i −1.32494 + 0.764957i −0.984513 0.175313i \(-0.943906\pi\)
−0.340431 + 0.940269i \(0.610573\pi\)
\(182\) −22.0462 −0.000665566
\(183\) 24948.5i 0.744975i
\(184\) 9818.89 5668.94i 0.290019 0.167443i
\(185\) −575.605 332.326i −0.0168183 0.00971003i
\(186\) −8337.18 + 4813.47i −0.240987 + 0.139134i
\(187\) 9653.51 16720.4i 0.276059 0.478148i
\(188\) −21034.7 + 36433.2i −0.595143 + 1.03082i
\(189\) 168.022i 0.00470373i
\(190\) 2059.15 + 328.901i 0.0570402 + 0.00911083i
\(191\) 65019.2 1.78227 0.891137 0.453734i \(-0.149908\pi\)
0.891137 + 0.453734i \(0.149908\pi\)
\(192\) −30549.0 17637.5i −0.828694 0.478447i
\(193\) −57399.9 33139.8i −1.54098 0.889684i −0.998777 0.0494353i \(-0.984258\pi\)
−0.542201 0.840249i \(-0.682409\pi\)
\(194\) −3709.43 6424.91i −0.0985606 0.170712i
\(195\) −5969.02 + 10338.6i −0.156976 + 0.271891i
\(196\) 18738.2 + 32455.5i 0.487771 + 0.844845i
\(197\) 44015.7 1.13416 0.567081 0.823662i \(-0.308073\pi\)
0.567081 + 0.823662i \(0.308073\pi\)
\(198\) 572.746i 0.0146094i
\(199\) 35353.3 + 61233.7i 0.892738 + 1.54627i 0.836580 + 0.547845i \(0.184552\pi\)
0.0561582 + 0.998422i \(0.482115\pi\)
\(200\) −9234.91 + 5331.78i −0.230873 + 0.133294i
\(201\) 7622.57 0.188673
\(202\) 9728.82i 0.238428i
\(203\) 209.604 121.015i 0.00508637 0.00293661i
\(204\) 57647.9 + 33283.0i 1.38523 + 0.799765i
\(205\) 10279.9 5935.11i 0.244614 0.141228i
\(206\) 613.098 1061.92i 0.0144476 0.0250240i
\(207\) 5772.90 9998.96i 0.134727 0.233353i
\(208\) 30501.3i 0.705003i
\(209\) −12759.0 10359.7i −0.292095 0.237168i
\(210\) 15.9429 0.000361517
\(211\) −15047.0 8687.41i −0.337976 0.195131i 0.321400 0.946943i \(-0.395846\pi\)
−0.659377 + 0.751813i \(0.729180\pi\)
\(212\) −28639.3 16534.9i −0.637222 0.367900i
\(213\) 30586.8 + 52977.9i 0.674179 + 1.16771i
\(214\) 5752.00 9962.75i 0.125600 0.217546i
\(215\) −5580.55 9665.80i −0.120726 0.209103i
\(216\) −12097.2 −0.259284
\(217\) 420.299i 0.00892563i
\(218\) 2423.88 + 4198.27i 0.0510032 + 0.0883401i
\(219\) −61184.7 + 35325.0i −1.27572 + 0.736536i
\(220\) −6566.06 −0.135662
\(221\) 54487.6i 1.11561i
\(222\) 391.640 226.114i 0.00794660 0.00458797i
\(223\) 21863.6 + 12622.9i 0.439654 + 0.253835i 0.703451 0.710744i \(-0.251641\pi\)
−0.263797 + 0.964578i \(0.584975\pi\)
\(224\) 110.429 63.7565i 0.00220084 0.00127066i
\(225\) −5429.56 + 9404.27i −0.107250 + 0.185763i
\(226\) −1395.73 + 2417.48i −0.0273266 + 0.0473310i
\(227\) 916.210i 0.0177805i 0.999960 + 0.00889024i \(0.00282989\pi\)
−0.999960 + 0.00889024i \(0.997170\pi\)
\(228\) 35717.9 43990.0i 0.687093 0.846223i
\(229\) −4664.33 −0.0889443 −0.0444721 0.999011i \(-0.514161\pi\)
−0.0444721 + 0.999011i \(0.514161\pi\)
\(230\) 2870.16 + 1657.09i 0.0542564 + 0.0313250i
\(231\) −108.821 62.8280i −0.00203934 0.00117741i
\(232\) 8712.78 + 15091.0i 0.161875 + 0.280376i
\(233\) −33186.8 + 57481.2i −0.611299 + 1.05880i 0.379723 + 0.925100i \(0.376019\pi\)
−0.991022 + 0.133701i \(0.957314\pi\)
\(234\) −808.191 1399.83i −0.0147599 0.0255648i
\(235\) −24902.6 −0.450930
\(236\) 87422.0i 1.56963i
\(237\) 16238.9 + 28126.6i 0.289107 + 0.500749i
\(238\) −63.0176 + 36.3833i −0.00111252 + 0.000642314i
\(239\) 32277.5 0.565073 0.282537 0.959257i \(-0.408824\pi\)
0.282537 + 0.959257i \(0.408824\pi\)
\(240\) 22057.2i 0.382938i
\(241\) 71795.8 41451.3i 1.23613 0.713681i 0.267830 0.963466i \(-0.413693\pi\)
0.968301 + 0.249785i \(0.0803600\pi\)
\(242\) 6804.59 + 3928.63i 0.116191 + 0.0670827i
\(243\) −24863.8 + 14355.1i −0.421070 + 0.243105i
\(244\) 19362.8 33537.3i 0.325228 0.563312i
\(245\) −11091.9 + 19211.7i −0.184788 + 0.320062i
\(246\) 8076.47i 0.133460i
\(247\) −45802.2 7315.83i −0.750746 0.119914i
\(248\) −30260.5 −0.492009
\(249\) −48653.9 28090.3i −0.784728 0.453063i
\(250\) −5825.99 3363.64i −0.0932158 0.0538182i
\(251\) −32836.9 56875.1i −0.521212 0.902766i −0.999696 0.0246692i \(-0.992147\pi\)
0.478484 0.878096i \(-0.341187\pi\)
\(252\) 43.1061 74.6620i 0.000678794 0.00117571i
\(253\) −13060.6 22621.6i −0.204043 0.353412i
\(254\) 256.270 0.00397219
\(255\) 39403.1i 0.605969i
\(256\) −25053.7 43394.3i −0.382290 0.662145i
\(257\) −7843.69 + 4528.55i −0.118756 + 0.0685635i −0.558201 0.829706i \(-0.688508\pi\)
0.439446 + 0.898269i \(0.355175\pi\)
\(258\) 7593.99 0.114085
\(259\) 19.7436i 0.000294325i
\(260\) −16047.9 + 9265.25i −0.237395 + 0.137060i
\(261\) 15367.7 + 8872.57i 0.225595 + 0.130247i
\(262\) 1600.08 923.809i 0.0233099 0.0134580i
\(263\) −46299.9 + 80193.7i −0.669373 + 1.15939i 0.308707 + 0.951157i \(0.400104\pi\)
−0.978080 + 0.208231i \(0.933230\pi\)
\(264\) 4523.46 7834.87i 0.0649027 0.112415i
\(265\) 19575.4i 0.278752i
\(266\) 22.1226 + 57.8576i 0.000312661 + 0.000817707i
\(267\) 57111.9 0.801132
\(268\) 10246.7 + 5915.96i 0.142665 + 0.0823675i
\(269\) 43611.5 + 25179.1i 0.602693 + 0.347965i 0.770100 0.637923i \(-0.220206\pi\)
−0.167407 + 0.985888i \(0.553540\pi\)
\(270\) −1768.07 3062.38i −0.0242533 0.0420080i
\(271\) −3028.20 + 5245.00i −0.0412331 + 0.0714179i −0.885905 0.463866i \(-0.846462\pi\)
0.844672 + 0.535284i \(0.179795\pi\)
\(272\) 50336.8 + 87185.8i 0.680373 + 1.17844i
\(273\) −354.622 −0.00475817
\(274\) 16419.7i 0.218707i
\(275\) 12283.8 + 21276.1i 0.162430 + 0.281337i
\(276\) 77993.9 45029.8i 1.02386 0.591128i
\(277\) 94487.4 1.23144 0.615721 0.787964i \(-0.288865\pi\)
0.615721 + 0.787964i \(0.288865\pi\)
\(278\) 2711.06i 0.0350792i
\(279\) −26687.0 + 15407.7i −0.342839 + 0.197938i
\(280\) 43.3995 + 25.0567i 0.000553566 + 0.000319601i
\(281\) 25206.5 14553.0i 0.319227 0.184306i −0.331821 0.943342i \(-0.607663\pi\)
0.651048 + 0.759036i \(0.274330\pi\)
\(282\) 8471.84 14673.6i 0.106532 0.184518i
\(283\) −34326.4 + 59455.1i −0.428603 + 0.742363i −0.996749 0.0805650i \(-0.974328\pi\)
0.568146 + 0.822928i \(0.307661\pi\)
\(284\) 94955.1i 1.17729i
\(285\) 33122.3 + 5290.50i 0.407784 + 0.0651339i
\(286\) −3656.89 −0.0447075
\(287\) 305.367 + 176.304i 0.00370730 + 0.00214041i
\(288\) 8096.46 + 4674.49i 0.0976136 + 0.0563572i
\(289\) −48161.3 83417.8i −0.576637 0.998765i
\(290\) −2546.84 + 4411.25i −0.0302834 + 0.0524525i
\(291\) −59667.5 103347.i −0.704615 1.22043i
\(292\) −109665. −1.28618
\(293\) 155003.i 1.80553i 0.430132 + 0.902766i \(0.358467\pi\)
−0.430132 + 0.902766i \(0.641533\pi\)
\(294\) −7546.90 13071.6i −0.0873120 0.151229i
\(295\) 44815.6 25874.3i 0.514974 0.297320i
\(296\) 1421.49 0.0162241
\(297\) 27870.5i 0.315960i
\(298\) 1771.32 1022.67i 0.0199464 0.0115161i
\(299\) −63841.8 36859.1i −0.714106 0.412289i
\(300\) −73355.2 + 42351.6i −0.815057 + 0.470574i
\(301\) 165.771 287.124i 0.00182969 0.00316911i
\(302\) −1024.91 + 1775.20i −0.0112376 + 0.0194641i
\(303\) 156492.i 1.70454i
\(304\) 80046.9 30607.0i 0.866158 0.331187i
\(305\) 22923.2 0.246420
\(306\) −4620.32 2667.54i −0.0493434 0.0284885i
\(307\) 86829.3 + 50130.9i 0.921275 + 0.531899i 0.884042 0.467408i \(-0.154812\pi\)
0.0372337 + 0.999307i \(0.488145\pi\)
\(308\) −97.5230 168.915i −0.00102803 0.00178060i
\(309\) 9861.92 17081.3i 0.103287 0.178898i
\(310\) −4422.73 7660.39i −0.0460222 0.0797127i
\(311\) −43558.3 −0.450350 −0.225175 0.974318i \(-0.572295\pi\)
−0.225175 + 0.974318i \(0.572295\pi\)
\(312\) 25531.9i 0.262285i
\(313\) −33606.5 58208.2i −0.343032 0.594149i 0.641962 0.766736i \(-0.278121\pi\)
−0.984994 + 0.172587i \(0.944787\pi\)
\(314\) 16927.1 9772.88i 0.171682 0.0991205i
\(315\) 51.0325 0.000514311
\(316\) 50412.7i 0.504854i
\(317\) −20383.1 + 11768.2i −0.202839 + 0.117109i −0.597979 0.801512i \(-0.704029\pi\)
0.395140 + 0.918621i \(0.370696\pi\)
\(318\) 11534.6 + 6659.51i 0.114064 + 0.0658549i
\(319\) 34767.8 20073.2i 0.341662 0.197259i
\(320\) 16205.7 28069.1i 0.158259 0.274112i
\(321\) 92523.1 160255.i 0.897925 1.55525i
\(322\) 98.4483i 0.000949504i
\(323\) −142996. + 54676.4i −1.37063 + 0.524077i
\(324\) −121534. −1.15773
\(325\) 60044.8 + 34666.9i 0.568471 + 0.328207i
\(326\) −17736.0 10239.9i −0.166886 0.0963518i
\(327\) 38988.9 + 67530.8i 0.364625 + 0.631548i
\(328\) −12693.4 + 21985.7i −0.117986 + 0.204358i
\(329\) −369.868 640.631i −0.00341708 0.00591856i
\(330\) 2644.51 0.0242838
\(331\) 23677.2i 0.216110i −0.994145 0.108055i \(-0.965538\pi\)
0.994145 0.108055i \(-0.0344622\pi\)
\(332\) −43602.5 75521.7i −0.395581 0.685166i
\(333\) 1253.62 723.780i 0.0113052 0.00652707i
\(334\) −16183.9 −0.145074
\(335\) 7003.79i 0.0624085i
\(336\) 567.432 327.607i 0.00502615 0.00290185i
\(337\) −135878. 78449.2i −1.19644 0.690763i −0.236677 0.971588i \(-0.576058\pi\)
−0.959759 + 0.280825i \(0.909392\pi\)
\(338\) 6525.48 3767.49i 0.0571188 0.0329776i
\(339\) −22450.9 + 38886.1i −0.195359 + 0.338372i
\(340\) −30581.2 + 52968.2i −0.264543 + 0.458203i
\(341\) 69716.6i 0.599553i
\(342\) −2862.69 + 3525.68i −0.0244750 + 0.0301433i
\(343\) −1317.97 −0.0112025
\(344\) 20672.3 + 11935.1i 0.174691 + 0.100858i
\(345\) 46167.7 + 26654.9i 0.387882 + 0.223944i
\(346\) 1086.71 + 1882.24i 0.00907742 + 0.0157225i
\(347\) 102854. 178148.i 0.854204 1.47953i −0.0231772 0.999731i \(-0.507378\pi\)
0.877381 0.479794i \(-0.159288\pi\)
\(348\) 69207.8 + 119871.i 0.571474 + 0.989822i
\(349\) 147121. 1.20788 0.603939 0.797031i \(-0.293597\pi\)
0.603939 + 0.797031i \(0.293597\pi\)
\(350\) 92.5931i 0.000755862i
\(351\) 39327.5 + 68117.3i 0.319214 + 0.552895i
\(352\) 18317.4 10575.5i 0.147835 0.0853527i
\(353\) −75142.1 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(354\) 35209.6i 0.280966i
\(355\) −48677.3 + 28103.9i −0.386251 + 0.223002i
\(356\) 76773.5 + 44325.2i 0.605775 + 0.349745i
\(357\) −1013.66 + 585.238i −0.00795348 + 0.00459194i
\(358\) −12539.7 + 21719.4i −0.0978410 + 0.169466i
\(359\) 9387.33 16259.3i 0.0728372 0.126158i −0.827307 0.561751i \(-0.810128\pi\)
0.900144 + 0.435593i \(0.143461\pi\)
\(360\) 3674.22i 0.0283504i
\(361\) 26761.5 + 127544.i 0.205350 + 0.978688i
\(362\) 31334.2 0.239112
\(363\) 109454. + 63193.5i 0.830653 + 0.479578i
\(364\) −476.705 275.226i −0.00359789 0.00207724i
\(365\) −32457.4 56217.9i −0.243629 0.421977i
\(366\) −7798.45 + 13507.3i −0.0582165 + 0.100834i
\(367\) 22404.8 + 38806.3i 0.166345 + 0.288118i 0.937132 0.348975i \(-0.113470\pi\)
−0.770787 + 0.637093i \(0.780137\pi\)
\(368\) 136205. 1.00576
\(369\) 25852.4i 0.189867i
\(370\) 207.758 + 359.848i 0.00151759 + 0.00262855i
\(371\) 503.585 290.745i 0.00365868 0.00211234i
\(372\) −240367. −1.73695
\(373\) 163639.i 1.17617i 0.808799 + 0.588085i \(0.200118\pi\)
−0.808799 + 0.588085i \(0.799882\pi\)
\(374\) −10453.0 + 6035.03i −0.0747304 + 0.0431456i
\(375\) −93713.3 54105.4i −0.666405 0.384749i
\(376\) 46123.8 26629.6i 0.326249 0.188360i
\(377\) 56649.9 98120.6i 0.398581 0.690363i
\(378\) 52.5207 90.9685i 0.000367576 0.000636660i
\(379\) 132155.i 0.920039i −0.887909 0.460019i \(-0.847842\pi\)
0.887909 0.460019i \(-0.152158\pi\)
\(380\) 40419.1 + 32818.4i 0.279910 + 0.227274i
\(381\) 4122.19 0.0283974
\(382\) −35201.9 20323.8i −0.241235 0.139277i
\(383\) −200322. 115656.i −1.36562 0.788442i −0.375256 0.926921i \(-0.622445\pi\)
−0.990365 + 0.138479i \(0.955779\pi\)
\(384\) 48401.2 + 83833.4i 0.328242 + 0.568532i
\(385\) 57.7278 99.9875i 0.000389461 0.000674565i
\(386\) 20717.9 + 35884.4i 0.139050 + 0.240841i
\(387\) 24308.0 0.162303
\(388\) 185235.i 1.23043i
\(389\) −826.840 1432.13i −0.00546414 0.00946418i 0.863280 0.504725i \(-0.168406\pi\)
−0.868745 + 0.495260i \(0.835073\pi\)
\(390\) 6463.36 3731.62i 0.0424941 0.0245340i
\(391\) −243317. −1.59154
\(392\) 47444.5i 0.308755i
\(393\) 25738.0 14859.8i 0.166644 0.0962118i
\(394\) −23830.5 13758.5i −0.153511 0.0886297i
\(395\) −25843.3 + 14920.6i −0.165636 + 0.0956299i
\(396\) 7150.19 12384.5i 0.0455960 0.0789746i
\(397\) 102128. 176890.i 0.647981 1.12234i −0.335623 0.941996i \(-0.608947\pi\)
0.983604 0.180340i \(-0.0577198\pi\)
\(398\) 44203.3i 0.279054i
\(399\) 355.851 + 930.662i 0.00223523 + 0.00584583i
\(400\) −128104. −0.800649
\(401\) 56182.7 + 32437.1i 0.349393 + 0.201722i 0.664418 0.747361i \(-0.268680\pi\)
−0.315025 + 0.949083i \(0.602013\pi\)
\(402\) −4126.92 2382.68i −0.0255373 0.0147439i
\(403\) 98375.9 + 170392.i 0.605729 + 1.04915i
\(404\) 121455. 210366.i 0.744137 1.28888i
\(405\) −35970.3 62302.4i −0.219298 0.379835i
\(406\) −151.309 −0.000917934
\(407\) 3274.95i 0.0197704i
\(408\) −42135.7 72981.2i −0.253122 0.438421i
\(409\) −219413. + 126678.i −1.31164 + 0.757276i −0.982368 0.186958i \(-0.940137\pi\)
−0.329273 + 0.944235i \(0.606804\pi\)
\(410\) −7420.84 −0.0441454
\(411\) 264117.i 1.56355i
\(412\) 26514.1 15307.9i 0.156200 0.0901823i
\(413\) 1331.25 + 768.600i 0.00780479 + 0.00450610i
\(414\) −6251.00 + 3609.01i −0.0364711 + 0.0210566i
\(415\) 25810.0 44704.3i 0.149862 0.259569i
\(416\) 29845.9 51694.6i 0.172464 0.298716i
\(417\) 43608.5i 0.250783i
\(418\) 3669.57 + 9597.07i 0.0210021 + 0.0549271i
\(419\) −46712.5 −0.266076 −0.133038 0.991111i \(-0.542473\pi\)
−0.133038 + 0.991111i \(0.542473\pi\)
\(420\) 344.733 + 199.032i 0.00195427 + 0.00112830i
\(421\) 19528.3 + 11274.7i 0.110179 + 0.0636121i 0.554077 0.832465i \(-0.313071\pi\)
−0.443898 + 0.896078i \(0.646405\pi\)
\(422\) 5431.06 + 9406.88i 0.0304972 + 0.0528227i
\(423\) 27118.0 46969.7i 0.151557 0.262505i
\(424\) 20932.9 + 36256.9i 0.116439 + 0.201678i
\(425\) 228845. 1.26696
\(426\) 38243.6i 0.210736i
\(427\) 340.469 + 589.710i 0.00186733 + 0.00323432i
\(428\) 248751. 143616.i 1.35793 0.784001i
\(429\) −58822.5 −0.319616
\(430\) 6977.53i 0.0377368i
\(431\) −215793. + 124588.i −1.16167 + 0.670690i −0.951704 0.307018i \(-0.900669\pi\)
−0.209966 + 0.977709i \(0.567335\pi\)
\(432\) −125856. 72663.2i −0.674384 0.389356i
\(433\) 38427.2 22186.0i 0.204957 0.118332i −0.394008 0.919107i \(-0.628912\pi\)
0.598966 + 0.800775i \(0.295579\pi\)
\(434\) 131.378 227.553i 0.000697498 0.00120810i
\(435\) −40966.8 + 70956.7i −0.216498 + 0.374986i
\(436\) 121039.i 0.636726i
\(437\) −32669.1 + 204532.i −0.171070 + 1.07102i
\(438\) 44167.9 0.230228
\(439\) 211594. + 122164.i 1.09793 + 0.633888i 0.935676 0.352861i \(-0.114791\pi\)
0.162251 + 0.986749i \(0.448125\pi\)
\(440\) 7198.85 + 4156.26i 0.0371842 + 0.0214683i
\(441\) −24157.3 41841.7i −0.124214 0.215145i
\(442\) −17031.9 + 29500.0i −0.0871801 + 0.151000i
\(443\) −29784.6 51588.5i −0.151770 0.262873i 0.780108 0.625644i \(-0.215164\pi\)
−0.931878 + 0.362772i \(0.881831\pi\)
\(444\) 11291.3 0.0572765
\(445\) 52475.7i 0.264996i
\(446\) −7891.41 13668.3i −0.0396721 0.0687141i
\(447\) 28492.4 16450.1i 0.142598 0.0823291i
\(448\) 962.786 0.00479705
\(449\) 181264.i 0.899122i −0.893250 0.449561i \(-0.851580\pi\)
0.893250 0.449561i \(-0.148420\pi\)
\(450\) 5879.22 3394.37i 0.0290332 0.0167623i
\(451\) 50652.4 + 29244.2i 0.249027 + 0.143776i
\(452\) −60359.9 + 34848.8i −0.295441 + 0.170573i
\(453\) −16486.1 + 28554.8i −0.0803381 + 0.139150i
\(454\) 286.391 496.044i 0.00138947 0.00240662i
\(455\) 325.835i 0.00157389i
\(456\) −67005.4 + 25620.4i −0.322241 + 0.123213i
\(457\) −51325.5 −0.245754 −0.122877 0.992422i \(-0.539212\pi\)
−0.122877 + 0.992422i \(0.539212\pi\)
\(458\) 2525.31 + 1457.99i 0.0120388 + 0.00695060i
\(459\) 224830. + 129806.i 1.06716 + 0.616125i
\(460\) 41374.4 + 71662.6i 0.195531 + 0.338670i
\(461\) −66811.0 + 115720.i −0.314373 + 0.544511i −0.979304 0.202394i \(-0.935128\pi\)
0.664931 + 0.746905i \(0.268461\pi\)
\(462\) 39.2778 + 68.0312i 0.000184019 + 0.000318731i
\(463\) −171665. −0.800792 −0.400396 0.916342i \(-0.631127\pi\)
−0.400396 + 0.916342i \(0.631127\pi\)
\(464\) 209338.i 0.972324i
\(465\) −71141.3 123220.i −0.329015 0.569871i
\(466\) 35935.2 20747.2i 0.165481 0.0955406i
\(467\) 143069. 0.656012 0.328006 0.944676i \(-0.393623\pi\)
0.328006 + 0.944676i \(0.393623\pi\)
\(468\) 40358.0i 0.184263i
\(469\) −180.176 + 104.024i −0.000819125 + 0.000472922i
\(470\) 13482.5 + 7784.12i 0.0610343 + 0.0352382i
\(471\) 272279. 157201.i 1.22736 0.708618i
\(472\) −55337.4 + 95847.1i −0.248390 + 0.430224i
\(473\) 27497.1 47626.4i 0.122904 0.212876i
\(474\) 20303.9i 0.0903699i
\(475\) 30726.1 192367.i 0.136182 0.852598i
\(476\) −1816.84 −0.00801868
\(477\) 36921.8 + 21316.8i 0.162273 + 0.0936883i
\(478\) −17475.3 10089.4i −0.0764838 0.0441580i
\(479\) −202937. 351498.i −0.884485 1.53197i −0.846302 0.532703i \(-0.821176\pi\)
−0.0381829 0.999271i \(-0.512157\pi\)
\(480\) −21583.3 + 37383.4i −0.0936775 + 0.162254i
\(481\) −4621.22 8004.19i −0.0199741 0.0345961i
\(482\) −51827.8 −0.223084
\(483\) 1583.58i 0.00678806i
\(484\) 98090.4 + 169898.i 0.418732 + 0.725264i
\(485\) 94957.7 54823.9i 0.403689 0.233070i
\(486\) 17948.6 0.0759903
\(487\) 252587.i 1.06501i 0.846428 + 0.532503i \(0.178749\pi\)
−0.846428 + 0.532503i \(0.821251\pi\)
\(488\) −42457.7 + 24513.0i −0.178286 + 0.102933i
\(489\) −285290. 164712.i −1.19308 0.688825i
\(490\) 12010.5 6934.26i 0.0500229 0.0288807i
\(491\) 82201.6 142377.i 0.340971 0.590579i −0.643642 0.765326i \(-0.722578\pi\)
0.984613 + 0.174747i \(0.0559109\pi\)
\(492\) −100827. + 174637.i −0.416530 + 0.721452i
\(493\) 373962.i 1.53863i
\(494\) 22510.9 + 18277.8i 0.0922443 + 0.0748980i
\(495\) 8464.96 0.0345473
\(496\) −314823. 181763.i −1.27969 0.738827i
\(497\) −1445.97 834.831i −0.00585391 0.00337976i
\(498\) 17561.1 + 30416.7i 0.0708097 + 0.122646i
\(499\) 32862.8 56920.1i 0.131979 0.228594i −0.792461 0.609923i \(-0.791200\pi\)
0.924439 + 0.381329i \(0.124534\pi\)
\(500\) −83983.6 145464.i −0.335934 0.581855i
\(501\) −260325. −1.03715
\(502\) 41056.9i 0.162922i
\(503\) −92338.3 159935.i −0.364961 0.632130i 0.623809 0.781577i \(-0.285584\pi\)
−0.988770 + 0.149446i \(0.952251\pi\)
\(504\) −94.5208 + 54.5716i −0.000372106 + 0.000214835i
\(505\) 143788. 0.563820
\(506\) 16330.0i 0.0637801i
\(507\) 104965. 60601.5i 0.408346 0.235758i
\(508\) 5541.32 + 3199.28i 0.0214726 + 0.0123972i
\(509\) −395925. + 228587.i −1.52819 + 0.882301i −0.528752 + 0.848777i \(0.677340\pi\)
−0.999438 + 0.0335240i \(0.989327\pi\)
\(510\) 12316.7 21333.2i 0.0473538 0.0820192i
\(511\) 964.154 1669.96i 0.00369236 0.00639536i
\(512\) 185347.i 0.707042i
\(513\) 139302. 171564.i 0.529324 0.651915i
\(514\) 5662.18 0.0214318
\(515\) 15694.7 + 9061.36i 0.0591752 + 0.0341648i
\(516\) 164205. + 94803.7i 0.616718 + 0.356062i
\(517\) −61351.5 106264.i −0.229532 0.397562i
\(518\) −6.17150 + 10.6894i −2.30002e−5 + 3.98375e-5i
\(519\) 17480.2 + 30276.5i 0.0648950 + 0.112401i
\(520\) 23459.3 0.0867577
\(521\) 301070.i 1.10916i 0.832132 + 0.554578i \(0.187120\pi\)
−0.832132 + 0.554578i \(0.812880\pi\)
\(522\) −5546.81 9607.36i −0.0203565 0.0352584i
\(523\) 142864. 82482.4i 0.522298 0.301549i −0.215576 0.976487i \(-0.569163\pi\)
0.737874 + 0.674938i \(0.235830\pi\)
\(524\) 46131.5 0.168010
\(525\) 1489.39i 0.00540370i
\(526\) 50134.3 28945.0i 0.181202 0.104617i
\(527\) 562402. + 324703.i 2.02500 + 1.16914i
\(528\) 94122.1 54341.4i 0.337617 0.194923i
\(529\) −24675.3 + 42738.9i −0.0881762 + 0.152726i
\(530\) −6118.91 + 10598.3i −0.0217832 + 0.0377297i
\(531\) 112704.i 0.399716i
\(532\) −243.940 + 1527.24i −0.000861905 + 0.00539614i
\(533\) 165064. 0.581028
\(534\) −30920.9 17852.2i −0.108435 0.0626050i
\(535\) 147246. + 85012.3i 0.514440 + 0.297012i
\(536\) −7489.50 12972.2i −0.0260689 0.0451527i
\(537\) −201706. + 349365.i −0.699471 + 1.21152i
\(538\) −15741.1 27264.3i −0.0543838 0.0941955i
\(539\) −109307. −0.376243
\(540\) 88290.5i 0.302779i
\(541\) −23100.4 40011.0i −0.0789268 0.136705i 0.823860 0.566793i \(-0.191816\pi\)
−0.902787 + 0.430088i \(0.858483\pi\)
\(542\) 3278.99 1893.13i 0.0111620 0.00644438i
\(543\) 504022. 1.70943
\(544\) 197021.i 0.665755i
\(545\) −62048.9 + 35823.9i −0.208901 + 0.120609i
\(546\) 191.995 + 110.848i 0.000644028 + 0.000371830i
\(547\) −75590.9 + 43642.4i −0.252636 + 0.145859i −0.620971 0.783834i \(-0.713261\pi\)
0.368335 + 0.929693i \(0.379928\pi\)
\(548\) −204984. + 355043.i −0.682588 + 1.18228i
\(549\) −24962.5 + 43236.3i −0.0828216 + 0.143451i
\(550\) 15358.8i 0.0507728i
\(551\) −314352. 50210.3i −1.03541 0.165383i
\(552\) −114014. −0.374179
\(553\) −767.681 443.221i −0.00251033 0.00144934i
\(554\) −51156.3 29535.1i −0.166678 0.0962318i
\(555\) 3341.87 + 5788.29i 0.0108494 + 0.0187916i
\(556\) −33845.0 + 58621.3i −0.109483 + 0.189630i
\(557\) 95840.4 + 166000.i 0.308914 + 0.535055i 0.978125 0.208017i \(-0.0667010\pi\)
−0.669211 + 0.743073i \(0.733368\pi\)
\(558\) 19264.7 0.0618720
\(559\) 155203.i 0.496679i
\(560\) 301.013 + 521.369i 0.000959862 + 0.00166253i
\(561\) −168140. + 97075.8i −0.534252 + 0.308450i
\(562\) −18196.0 −0.0576108
\(563\) 488949.i 1.54258i −0.636486 0.771288i \(-0.719613\pi\)
0.636486 0.771288i \(-0.280387\pi\)
\(564\) 366373. 211526.i 1.15177 0.664974i
\(565\) −35729.4 20628.4i −0.111926 0.0646202i
\(566\) 37169.2 21459.7i 0.116025 0.0669869i
\(567\) 1068.50 1850.70i 0.00332361 0.00575666i
\(568\) 60105.8 104106.i 0.186303 0.322686i
\(569\) 606639.i 1.87372i 0.349699 + 0.936862i \(0.386284\pi\)
−0.349699 + 0.936862i \(0.613716\pi\)
\(570\) −16278.9 13217.7i −0.0501045 0.0406825i
\(571\) 92670.7 0.284230 0.142115 0.989850i \(-0.454610\pi\)
0.142115 + 0.989850i \(0.454610\pi\)
\(572\) −79073.0 45652.8i −0.241677 0.139533i
\(573\) −566236. 326917.i −1.72460 0.995698i
\(574\) −110.219 190.904i −0.000334527 0.000579418i
\(575\) 154806. 268133.i 0.468224 0.810987i
\(576\) 35294.7 + 61132.3i 0.106381 + 0.184258i
\(577\) −117869. −0.354037 −0.177019 0.984208i \(-0.556645\pi\)
−0.177019 + 0.984208i \(0.556645\pi\)
\(578\) 60217.5i 0.180247i
\(579\) 333255. + 577214.i 0.994075 + 1.72179i
\(580\) −110141. + 63589.7i −0.327410 + 0.189030i
\(581\) 1533.38 0.00454254
\(582\) 74604.0i 0.220250i
\(583\) 83531.6 48227.0i 0.245761 0.141890i
\(584\) 120233. + 69416.7i 0.352532 + 0.203535i
\(585\) 20688.9 11944.8i 0.0604542 0.0349032i
\(586\) 48451.2 83920.0i 0.141094 0.244383i
\(587\) −35695.9 + 61827.1i −0.103596 + 0.179433i −0.913164 0.407593i \(-0.866368\pi\)
0.809568 + 0.587026i \(0.199701\pi\)
\(588\) 376863.i 1.09001i
\(589\) 348457. 429158.i 1.00443 1.23705i
\(590\) −32351.4 −0.0929370
\(591\) −383322. 221311.i −1.09746 0.633619i
\(592\) 14788.9 + 8538.36i 0.0421980 + 0.0243630i
\(593\) 70754.5 + 122550.i 0.201208 + 0.348502i 0.948918 0.315523i \(-0.102180\pi\)
−0.747710 + 0.664025i \(0.768847\pi\)
\(594\) 8711.82 15089.3i 0.0246908 0.0427658i
\(595\) −537.730 931.376i −0.00151891 0.00263082i
\(596\) 51068.4 0.143767
\(597\) 711026.i 1.99497i
\(598\) 23043.0 + 39911.6i 0.0644372 + 0.111608i
\(599\) −462882. + 267245.i −1.29008 + 0.744828i −0.978668 0.205447i \(-0.934135\pi\)
−0.311412 + 0.950275i \(0.600802\pi\)
\(600\) 107233. 0.297869
\(601\) 126491.i 0.350196i −0.984551 0.175098i \(-0.943976\pi\)
0.984551 0.175098i \(-0.0560243\pi\)
\(602\) −179.500 + 103.634i −0.000495304 + 0.000285964i
\(603\) −13210.1 7626.85i −0.0363305 0.0209754i
\(604\) −44323.4 + 25590.1i −0.121495 + 0.0701453i
\(605\) −58063.6 + 100569.i −0.158633 + 0.274760i
\(606\) −48916.6 + 84726.0i −0.133202 + 0.230713i
\(607\) 75673.3i 0.205383i −0.994713 0.102692i \(-0.967255\pi\)
0.994713 0.102692i \(-0.0327455\pi\)
\(608\) −165616. 26453.2i −0.448017 0.0715601i
\(609\) −2433.86 −0.00656236
\(610\) −12410.8 7165.39i −0.0333535 0.0192566i
\(611\) −299894. 173144.i −0.803315 0.463794i
\(612\) −66603.5 115361.i −0.177826 0.308003i
\(613\) −336906. + 583538.i −0.896577 + 1.55292i −0.0647358 + 0.997902i \(0.520620\pi\)
−0.831841 + 0.555014i \(0.812713\pi\)
\(614\) −31340.1 54282.6i −0.0831310 0.143987i
\(615\) −119367. −0.315598
\(616\) 246.925i 0.000650734i
\(617\) −75123.6 130118.i −0.197336 0.341796i 0.750328 0.661066i \(-0.229896\pi\)
−0.947664 + 0.319270i \(0.896562\pi\)
\(618\) −10678.7 + 6165.32i −0.0279602 + 0.0161428i
\(619\) −98758.2 −0.257746 −0.128873 0.991661i \(-0.541136\pi\)
−0.128873 + 0.991661i \(0.541136\pi\)
\(620\) 220854.i 0.574543i
\(621\) 304181. 175619.i 0.788766 0.455394i
\(622\) 23582.8 + 13615.5i 0.0609558 + 0.0351928i
\(623\) −1349.96 + 779.401i −0.00347813 + 0.00200810i
\(624\) 153360. 265628.i 0.393862 0.682189i
\(625\) −118921. + 205976.i −0.304437 + 0.527300i
\(626\) 42019.2i 0.107226i
\(627\) 59026.4 + 154373.i 0.150145 + 0.392677i
\(628\) 488021. 1.23742
\(629\) −26418.9 15253.0i −0.0667750 0.0385525i
\(630\) −27.6294 15.9519i −6.96131e−5 4.01911e-5i
\(631\) 338314. + 585977.i 0.849691 + 1.47171i 0.881484 + 0.472214i \(0.156545\pi\)
−0.0317927 + 0.999494i \(0.510122\pi\)
\(632\) 31910.8 55271.1i 0.0798920 0.138377i
\(633\) 87360.7 + 151313.i 0.218026 + 0.377632i
\(634\) 14714.1 0.0366063
\(635\) 3787.56i 0.00939318i
\(636\) 166275. + 287997.i 0.411068 + 0.711990i
\(637\) −267152. + 154241.i −0.658386 + 0.380119i
\(638\) −25098.1 −0.0616595
\(639\) 122416.i 0.299804i
\(640\) −77028.1 + 44472.2i −0.188057 + 0.108575i
\(641\) 615303. + 355245.i 1.49752 + 0.864594i 0.999996 0.00285662i \(-0.000909293\pi\)
0.497524 + 0.867450i \(0.334243\pi\)
\(642\) −100186. + 57842.2i −0.243072 + 0.140338i
\(643\) 70190.5 121574.i 0.169768 0.294047i −0.768570 0.639766i \(-0.779031\pi\)
0.938338 + 0.345718i \(0.112365\pi\)
\(644\) −1229.03 + 2128.75i −0.00296341 + 0.00513278i
\(645\) 112236.i 0.269782i
\(646\) 94510.2 + 15095.8i 0.226472 + 0.0361735i
\(647\) 439296. 1.04942 0.524710 0.851281i \(-0.324174\pi\)
0.524710 + 0.851281i \(0.324174\pi\)
\(648\) 133246. + 76929.7i 0.317325 + 0.183208i
\(649\) 220820. + 127491.i 0.524264 + 0.302684i
\(650\) −21672.5 37537.9i −0.0512958 0.0888470i
\(651\) 2113.27 3660.28i 0.00498646 0.00863680i
\(652\) −255670. 442834.i −0.601430 1.04171i
\(653\) 694597. 1.62894 0.814472 0.580203i \(-0.197027\pi\)
0.814472 + 0.580203i \(0.197027\pi\)
\(654\) 48749.0i 0.113975i
\(655\) 13653.5 + 23648.6i 0.0318246 + 0.0551218i
\(656\) −264119. + 152489.i −0.613751 + 0.354349i
\(657\) 141380. 0.327534
\(658\) 462.457i 0.00106812i
\(659\) −544541. + 314391.i −1.25389 + 0.723935i −0.971880 0.235476i \(-0.924335\pi\)
−0.282012 + 0.959411i \(0.591002\pi\)
\(660\) 57182.3 + 33014.2i 0.131272 + 0.0757902i
\(661\) −16257.2 + 9386.09i −0.0372085 + 0.0214823i −0.518489 0.855084i \(-0.673505\pi\)
0.481280 + 0.876567i \(0.340172\pi\)
\(662\) −7401.07 + 12819.0i −0.0168880 + 0.0292509i
\(663\) −273964. + 474519.i −0.623256 + 1.07951i
\(664\) 110400.i 0.250399i
\(665\) −855.114 + 326.964i −0.00193366 + 0.000739361i
\(666\) −904.963 −0.00204025
\(667\) −438162. 252973.i −0.984879 0.568620i
\(668\) −349945. 202041.i −0.784236 0.452779i
\(669\) −126936. 219860.i −0.283618 0.491241i
\(670\) 2189.26 3791.91i 0.00487694 0.00844712i
\(671\) 56475.0 + 97817.5i 0.125433 + 0.217256i
\(672\) −1282.27 −0.00283950
\(673\) 39754.5i 0.0877721i 0.999037 + 0.0438861i \(0.0139739\pi\)
−0.999037 + 0.0438861i \(0.986026\pi\)
\(674\) 49043.7 + 84946.2i 0.107960 + 0.186992i
\(675\) −286089. + 165174.i −0.627905 + 0.362521i
\(676\) 188134. 0.411693
\(677\) 739937.i 1.61442i −0.590262 0.807212i \(-0.700975\pi\)
0.590262 0.807212i \(-0.299025\pi\)
\(678\) 24310.2 14035.5i 0.0528846 0.0305329i
\(679\) 2820.74 + 1628.55i 0.00611819 + 0.00353234i
\(680\) 67056.8 38715.3i 0.145019 0.0837268i
\(681\) 4606.71 7979.05i 0.00993337 0.0172051i
\(682\) 21792.2 37745.2i 0.0468524 0.0811508i
\(683\) 244927.i 0.525043i −0.964926 0.262522i \(-0.915446\pi\)
0.964926 0.262522i \(-0.0845541\pi\)
\(684\) −105915. + 40497.9i −0.226383 + 0.0865606i
\(685\) −242676. −0.517185
\(686\) 713.559 + 411.974i 0.00151629 + 0.000875429i
\(687\) 40620.5 + 23452.3i 0.0860660 + 0.0496903i
\(688\) 143380. + 248341.i 0.302908 + 0.524652i
\(689\) 136104. 235740.i 0.286704 0.496586i
\(690\) −16663.7 28862.4i −0.0350005 0.0606226i
\(691\) −607326. −1.27194 −0.635969 0.771715i \(-0.719399\pi\)
−0.635969 + 0.771715i \(0.719399\pi\)
\(692\) 54266.3i 0.113323i
\(693\) 125.727 + 217.765i 0.000261795 + 0.000453442i
\(694\) −111372. + 64300.6i −0.231237 + 0.133505i
\(695\) −40068.5 −0.0829532
\(696\) 175232.i 0.361738i
\(697\) 471823. 272407.i 0.971212 0.560729i
\(698\) −79652.4 45987.3i −0.163489 0.0943903i
\(699\) 578032. 333727.i 1.18303 0.683025i
\(700\) 1155.94 2002.14i 0.00235905 0.00408600i
\(701\) 88390.8 153097.i 0.179875 0.311553i −0.761963 0.647621i \(-0.775764\pi\)
0.941838 + 0.336068i \(0.109097\pi\)
\(702\) 49172.3i 0.0997807i
\(703\) −16368.8 + 20159.8i −0.0331212 + 0.0407920i
\(704\) 159701. 0.322228
\(705\) 216871. + 125210.i 0.436338 + 0.251920i
\(706\) 40682.5 + 23488.1i 0.0816204 + 0.0471236i
\(707\) 2135.63 + 3699.02i 0.00427255 + 0.00740027i
\(708\) −439558. + 761337.i −0.876900 + 1.51883i
\(709\) −312672. 541564.i −0.622009 1.07735i −0.989111 0.147171i \(-0.952983\pi\)
0.367102 0.930181i \(-0.380350\pi\)
\(710\) 35139.1 0.0697066
\(711\) 64992.0i 0.128564i
\(712\) −56115.0 97194.0i −0.110693 0.191725i
\(713\) 760893. 439302.i 1.49673 0.864140i
\(714\) 731.741 0.00143536
\(715\) 54047.5i 0.105721i
\(716\) −542292. + 313092.i −1.05781 + 0.610726i
\(717\) −281097. 162292.i −0.546787 0.315688i
\(718\) −10164.8 + 5868.62i −0.0197173 + 0.0113838i
\(719\) 47265.5 81866.2i 0.0914295 0.158360i −0.816683 0.577086i \(-0.804190\pi\)
0.908113 + 0.418726i \(0.137523\pi\)
\(720\) −22069.6 + 38225.7i −0.0425726 + 0.0737379i
\(721\) 538.339i 0.00103558i
\(722\) 25379.0 77418.4i 0.0486856 0.148515i
\(723\) −833669. −1.59484
\(724\) 677539. + 391178.i 1.29258 + 0.746271i
\(725\) 412102. + 237927.i 0.784023 + 0.452656i
\(726\) −39506.3 68427.0i −0.0749538 0.129824i
\(727\) 4503.05 7799.52i 0.00851997 0.0147570i −0.861734 0.507360i \(-0.830621\pi\)
0.870254 + 0.492603i \(0.163955\pi\)
\(728\) 348.431 + 603.501i 0.000657437 + 0.00113871i
\(729\) −341959. −0.643456
\(730\) 40582.5i 0.0761540i
\(731\) −256134. 443637.i −0.479328 0.830220i
\(732\) −337252. + 194712.i −0.629408 + 0.363389i
\(733\) −234971. −0.437326 −0.218663 0.975800i \(-0.570170\pi\)
−0.218663 + 0.975800i \(0.570170\pi\)
\(734\) 28013.4i 0.0519965i
\(735\) 193193. 111540.i 0.357617 0.206470i
\(736\) −230845. 133278.i −0.426152 0.246039i
\(737\) −29886.4 + 17254.9i −0.0550223 + 0.0317672i
\(738\) 8081.01 13996.7i 0.0148372 0.0256988i
\(739\) −156095. + 270364.i −0.285825 + 0.495063i −0.972809 0.231609i \(-0.925601\pi\)
0.686984 + 0.726673i \(0.258934\pi\)
\(740\) 10374.7i 0.0189457i
\(741\) 362097. + 294006.i 0.659460 + 0.535450i
\(742\) −363.527 −0.000660281
\(743\) −424908. 245321.i −0.769693 0.444383i 0.0630720 0.998009i \(-0.479910\pi\)
−0.832765 + 0.553626i \(0.813244\pi\)
\(744\) 263531. + 152150.i 0.476087 + 0.274869i
\(745\) 15114.7 + 26179.5i 0.0272325 + 0.0471681i
\(746\) 51150.8 88595.7i 0.0919125 0.159197i
\(747\) 56212.3 + 97362.5i 0.100737 + 0.174482i
\(748\) −301367. −0.538632
\(749\) 5050.61i 0.00900286i
\(750\) 33824.8 + 58586.2i 0.0601329 + 0.104153i
\(751\) 695752. 401693.i 1.23360 0.712220i 0.265822 0.964022i \(-0.414357\pi\)
0.967779 + 0.251802i \(0.0810233\pi\)
\(752\) 639816. 1.13141
\(753\) 660416.i 1.16474i
\(754\) −61341.5 + 35415.5i −0.107898 + 0.0622947i
\(755\) −26236.8 15147.8i −0.0460274 0.0265739i
\(756\) 2271.31 1311.34i 0.00397405 0.00229442i
\(757\) 37763.2 65407.7i 0.0658987 0.114140i −0.831194 0.555983i \(-0.812342\pi\)
0.897092 + 0.441843i \(0.145675\pi\)
\(758\) −41309.4 + 71550.0i −0.0718970 + 0.124529i
\(759\) 262674.i 0.455968i
\(760\) −23540.6 61566.1i −0.0407559 0.106590i
\(761\) 854120. 1.47486 0.737428 0.675426i \(-0.236040\pi\)
0.737428 + 0.675426i \(0.236040\pi\)
\(762\) −2231.79 1288.52i −0.00384365 0.00221913i
\(763\) −1843.17 1064.16i −0.00316604 0.00182792i
\(764\) −507447. 878925.i −0.869369 1.50579i
\(765\) 39425.3 68286.6i 0.0673677 0.116684i
\(766\) 72303.9 + 125234.i 0.123226 + 0.213435i
\(767\) 719600. 1.22321
\(768\) 503881.i 0.854291i
\(769\) 268960. + 465853.i 0.454816 + 0.787764i 0.998678 0.0514105i \(-0.0163717\pi\)
−0.543862 + 0.839175i \(0.683038\pi\)
\(770\) −62.5086 + 36.0894i −0.000105429 + 6.08692e-5i
\(771\) 91078.4 0.153217
\(772\) 1.03457e6i 1.73590i
\(773\) −374936. + 216469.i −0.627477 + 0.362274i −0.779774 0.626061i \(-0.784666\pi\)
0.152297 + 0.988335i \(0.451333\pi\)
\(774\) −13160.6 7598.26i −0.0219681 0.0126833i
\(775\) −715639. + 413174.i −1.19149 + 0.687907i
\(776\) −117252. + 203086.i −0.194714 + 0.337254i
\(777\) −99.2709 + 171.942i −0.000164430 + 0.000284800i
\(778\) 1033.82i 0.00170799i
\(779\) −165636. 433190.i −0.272948 0.713844i
\(780\) 186343. 0.306284
\(781\) −239849. 138477.i −0.393219 0.227025i
\(782\) 131734. + 76056.5i 0.215419 + 0.124372i
\(783\) 269914. + 467505.i 0.440253 + 0.762541i
\(784\) 284981. 493602.i 0.463643 0.803054i
\(785\) 144439. + 250176.i 0.234394 + 0.405982i
\(786\) −18579.7 −0.0300741
\(787\) 451093.i 0.728311i 0.931338 + 0.364155i \(0.118642\pi\)
−0.931338 + 0.364155i \(0.881358\pi\)
\(788\) −343524. 595001.i −0.553229 0.958220i
\(789\) 806429. 465592.i 1.29542 0.747913i
\(790\) 18655.7 0.0298922
\(791\) 1225.54i 0.00195873i
\(792\) −15678.5 + 9052.01i −0.0249951 + 0.0144309i
\(793\) 276057. + 159382.i 0.438988 + 0.253450i
\(794\) −110586. + 63846.6i −0.175411 + 0.101274i
\(795\) −98425.0 + 170477.i −0.155730 + 0.269732i
\(796\) 551836. 955808.i 0.870931 1.50850i
\(797\) 698630.i 1.09984i 0.835216 + 0.549921i \(0.185342\pi\)
−0.835216 + 0.549921i \(0.814658\pi\)
\(798\) 98.2479 615.101i 0.000154283 0.000965919i
\(799\) −1.14297e6 −1.79036
\(800\) 217115. + 125351.i 0.339242 + 0.195862i
\(801\) −98976.4 57144.0i −0.154265 0.0890648i
\(802\) −20278.5 35123.4i −0.0315274 0.0546070i
\(803\) 159928. 277003.i 0.248024 0.429590i
\(804\) −59491.0 103041.i −0.0920320 0.159404i
\(805\) −1455.03 −0.00224533
\(806\) 123002.i 0.189340i
\(807\) −253201. 438557.i −0.388793 0.673409i
\(808\) −266320. + 153760.i −0.407926 + 0.235516i
\(809\) −1.25493e6 −1.91744 −0.958722 0.284345i \(-0.908224\pi\)
−0.958722 + 0.284345i \(0.908224\pi\)
\(810\) 44974.7i 0.0685486i
\(811\) 475389. 274466.i 0.722782 0.417298i −0.0929939 0.995667i \(-0.529644\pi\)
0.815776 + 0.578368i \(0.196310\pi\)
\(812\) −3271.75 1888.94i −0.00496212 0.00286488i
\(813\) 52743.8 30451.6i 0.0797977 0.0460712i
\(814\) −1023.69 + 1773.08i −0.00154497 + 0.00267597i
\(815\) 151342. 262131.i 0.227847 0.394642i
\(816\) 1.01237e6i 1.52041i
\(817\) −407311. + 155741.i −0.610214 + 0.233323i
\(818\) 158389. 0.236711
\(819\) 614.568 + 354.821i 0.000916225 + 0.000528983i
\(820\) −160461. 92642.2i −0.238639 0.137778i
\(821\) −488125. 845457.i −0.724177 1.25431i −0.959312 0.282348i \(-0.908887\pi\)
0.235135 0.971963i \(-0.424447\pi\)
\(822\) 82558.2 142995.i 0.122185 0.211630i
\(823\) 404279. + 700231.i 0.596872 + 1.03381i 0.993280 + 0.115738i \(0.0369233\pi\)
−0.396408 + 0.918074i \(0.629743\pi\)
\(824\) −38759.1 −0.0570846
\(825\) 247052.i 0.362978i
\(826\) −480.502 832.253i −0.000704263 0.00121982i
\(827\) 737136. 425586.i 1.07780 0.622266i 0.147495 0.989063i \(-0.452879\pi\)
0.930301 + 0.366797i \(0.119546\pi\)
\(828\) −180220. −0.262871
\(829\) 305115.i 0.443970i 0.975050 + 0.221985i \(0.0712537\pi\)
−0.975050 + 0.221985i \(0.928746\pi\)
\(830\) −27947.5 + 16135.5i −0.0405684 + 0.0234222i
\(831\) −822868. 475083.i −1.19159 0.687967i
\(832\) 390320. 225351.i 0.563864 0.325547i
\(833\) −509092. + 881773.i −0.733679 + 1.27077i
\(834\) 13631.2 23610.0i 0.0195976 0.0339441i
\(835\) 239192.i 0.343063i
\(836\) −40463.3 + 253329.i −0.0578960 + 0.362470i
\(837\) −937444. −1.33812
\(838\) 25290.6 + 14601.5i 0.0360139 + 0.0207927i
\(839\) 222988. + 128742.i 0.316781 + 0.182893i 0.649957 0.759971i \(-0.274787\pi\)
−0.333176 + 0.942865i \(0.608120\pi\)
\(840\) −251.971 436.426i −0.000357101 0.000618518i
\(841\) 35161.8 60902.1i 0.0497141 0.0861073i
\(842\) −7048.53 12208.4i −0.00994201 0.0172201i
\(843\) −292690. −0.411863
\(844\) 271207.i 0.380728i
\(845\) 55682.0 + 96444.1i 0.0779833 + 0.135071i
\(846\) −29363.8 + 16953.2i −0.0410272 + 0.0236870i
\(847\) −3449.58 −0.00480839
\(848\) 502944.i 0.699404i
\(849\) 597881. 345187.i 0.829467 0.478893i
\(850\) −123899. 71533.0i −0.171486 0.0990076i
\(851\) −35743.1 + 20636.3i −0.0493552 + 0.0284952i
\(852\) 477435. 826941.i 0.657711 1.13919i
\(853\) 349883. 606015.i 0.480866 0.832885i −0.518893 0.854839i \(-0.673656\pi\)
0.999759 + 0.0219545i \(0.00698891\pi\)
\(854\) 425.699i 0.000583696i
\(855\) −52108.2 42309.4i −0.0712810 0.0578769i
\(856\) −363632. −0.496266
\(857\) 402851. + 232586.i 0.548508 + 0.316681i 0.748520 0.663112i \(-0.230765\pi\)
−0.200012 + 0.979793i \(0.564098\pi\)
\(858\) 31847.0 + 18386.9i 0.0432607 + 0.0249766i
\(859\) 359632. + 622900.i 0.487384 + 0.844174i 0.999895 0.0145066i \(-0.00461777\pi\)
−0.512511 + 0.858681i \(0.671284\pi\)
\(860\) −87107.8 + 150875.i −0.117777 + 0.203996i
\(861\) −1772.91 3070.77i −0.00239156 0.00414230i
\(862\) 155776. 0.209646
\(863\) 380009.i 0.510237i 0.966910 + 0.255118i \(0.0821145\pi\)
−0.966910 + 0.255118i \(0.917886\pi\)
\(864\) 142204. + 246304.i 0.190495 + 0.329947i
\(865\) −27818.8 + 16061.2i −0.0371797 + 0.0214657i
\(866\) −27739.8 −0.0369885
\(867\) 968621.i 1.28859i
\(868\) 5681.57 3280.26i 0.00754101 0.00435380i
\(869\) −127338. 73518.7i −0.168624 0.0973550i
\(870\) 44359.6 25611.0i 0.0586069 0.0338367i
\(871\) −48696.3 + 84344.4i −0.0641888 + 0.111178i
\(872\) 76616.7 132704.i 0.100761 0.174522i
\(873\) 238804.i 0.313338i
\(874\) 81620.4 100524.i 0.106850 0.131597i
\(875\) 2953.48 0.00385761
\(876\) 955043. + 551394.i 1.24456 + 0.718545i
\(877\) −7312.18 4221.69i −0.00950710 0.00548892i 0.495239 0.868757i \(-0.335081\pi\)
−0.504746 + 0.863268i \(0.668414\pi\)
\(878\) −76372.4 132281.i −0.0990711 0.171596i
\(879\) 779357. 1.34989e6i 1.00869 1.74711i
\(880\) 49930.2 + 86481.6i 0.0644759 + 0.111676i
\(881\) 631669. 0.813838 0.406919 0.913464i \(-0.366603\pi\)
0.406919 + 0.913464i \(0.366603\pi\)
\(882\) 30204.6i 0.0388272i
\(883\) −31430.2 54438.8i −0.0403113 0.0698211i 0.845166 0.534504i \(-0.179502\pi\)
−0.885477 + 0.464683i \(0.846168\pi\)
\(884\) −736560. + 425253.i −0.942548 + 0.544180i
\(885\) −520384. −0.664412
\(886\) 37240.6i 0.0474405i
\(887\) −770362. + 444769.i −0.979146 + 0.565310i −0.902012 0.431711i \(-0.857910\pi\)
−0.0771338 + 0.997021i \(0.524577\pi\)
\(888\) −12379.4 7147.26i −0.0156991 0.00906388i
\(889\) −97.4368 + 56.2551i −0.000123288 + 7.11801e-5i
\(890\) 16403.0 28410.8i 0.0207082 0.0358677i
\(891\) 177237. 306984.i 0.223254 0.386687i
\(892\) 394067.i 0.495268i
\(893\) −153462. + 960780.i −0.192441 + 1.20482i
\(894\) −20568.0 −0.0257346
\(895\) −321004. 185332.i −0.400742 0.231368i
\(896\) −2288.13 1321.05i −0.00285013 0.00164553i
\(897\) 370655. + 641994.i 0.460665 + 0.797895i
\(898\) −56659.9 + 98137.8i −0.0702624 + 0.121698i
\(899\) 675178. + 1.16944e6i 0.835408 + 1.44697i
\(900\) 169502. 0.209261
\(901\) 898462.i 1.10675i
\(902\) −18282.4 31666.1i −0.0224709 0.0389207i
\(903\) −2887.33 + 1667.00i −0.00354095 + 0.00204437i
\(904\) 88235.9 0.107971
\(905\) 463107.i 0.565437i
\(906\) 17851.4 10306.5i 0.0217479 0.0125561i
\(907\) −408359. 235766.i −0.496396 0.286594i 0.230828 0.972995i \(-0.425856\pi\)
−0.727224 + 0.686400i \(0.759190\pi\)
\(908\) 12385.3 7150.64i 0.0150222 0.00867308i
\(909\) −156580. + 271204.i −0.189499 + 0.328223i
\(910\) −101.850 + 176.410i −0.000122993 + 0.000213029i
\(911\) 227945.i 0.274659i 0.990525 + 0.137329i \(0.0438518\pi\)
−0.990525 + 0.137329i \(0.956148\pi\)
\(912\) −851001. 135927.i −1.02315 0.163424i
\(913\) 254348. 0.305132
\(914\) 27788.1 + 16043.4i 0.0332633 + 0.0192046i
\(915\) −199633. 115258.i −0.238446 0.137667i
\(916\) 36403.1 + 63052.1i 0.0433858 + 0.0751464i
\(917\) −405.581 + 702.487i −0.000482324 + 0.000835410i
\(918\) −81150.0 140556.i −0.0962949 0.166788i
\(919\) 1.19281e6 1.41235 0.706173 0.708040i \(-0.250420\pi\)
0.706173 + 0.708040i \(0.250420\pi\)
\(920\) 104759.i 0.123770i
\(921\) −504117. 873156.i −0.594309 1.02937i
\(922\) 72344.0 41767.8i 0.0851022 0.0491338i
\(923\) −781607. −0.917456
\(924\) 1961.39i 0.00229731i
\(925\) 33617.2 19408.9i 0.0392897 0.0226839i
\(926\) 92940.9 + 53659.4i 0.108389 + 0.0625784i
\(927\) −34181.9 + 19734.9i −0.0397774 + 0.0229655i
\(928\) 204840. 354793.i 0.237858 0.411983i
\(929\) −146300. + 253398.i −0.169516 + 0.293611i −0.938250 0.345958i \(-0.887554\pi\)
0.768734 + 0.639569i \(0.220887\pi\)
\(930\) 88950.0i 0.102844i
\(931\) 672864. + 546334.i 0.776297 + 0.630317i
\(932\) 1.03604e6 1.19273
\(933\) 379338. + 219011.i 0.435776 + 0.251596i
\(934\) −77458.8 44720.9i −0.0887926 0.0512645i
\(935\) −89195.5 154491.i −0.102028 0.176718i
\(936\) −25546.3 + 44247.4i −0.0291592 + 0.0505052i
\(937\) −580745. 1.00588e6i −0.661464 1.14569i −0.980231 0.197857i \(-0.936602\pi\)
0.318767 0.947833i \(-0.396731\pi\)
\(938\) 130.065 0.000147827
\(939\) 675895.i 0.766564i
\(940\) 194355. + 336632.i 0.219958 + 0.380978i
\(941\) 494228. 285343.i 0.558147 0.322246i −0.194254 0.980951i \(-0.562229\pi\)
0.752401 + 0.658705i \(0.228895\pi\)
\(942\) −196552. −0.221501
\(943\) 737099.i 0.828900i
\(944\) −1.15143e6 + 664781.i −1.29210 + 0.745993i
\(945\) 1344.48 + 776.236i 0.00150553 + 0.000869221i
\(946\) −29774.4 + 17190.2i −0.0332706 + 0.0192088i
\(947\) 443648. 768420.i 0.494696 0.856838i −0.505285 0.862952i \(-0.668613\pi\)
0.999981 + 0.00611394i \(0.00194614\pi\)
\(948\) 253475. 439032.i 0.282045 0.488517i
\(949\) 902686.i 1.00232i
\(950\) −76766.0 + 94544.8i −0.0850593 + 0.104759i
\(951\) 236682. 0.261700
\(952\) 1991.94 + 1150.04i 0.00219787 + 0.00126894i
\(953\) −323576. 186816.i −0.356279 0.205698i 0.311168 0.950355i \(-0.399280\pi\)
−0.667447 + 0.744657i \(0.732613\pi\)
\(954\) −13326.5 23082.2i −0.0146426 0.0253618i
\(955\) 300378. 520271.i 0.329353 0.570457i
\(956\) −251913. 436326.i −0.275635 0.477414i
\(957\) −403713. −0.440808
\(958\) 253738.i 0.276474i
\(959\) −3604.37 6242.96i −0.00391915 0.00678818i
\(960\) −282263. + 162965.i −0.306275 + 0.176828i
\(961\) −1.42145e6 −1.53916
\(962\) 5778.05i 0.00624354i
\(963\) −320690. + 185150.i −0.345806 + 0.199651i
\(964\) −1.12067e6 647020.i −1.20594 0.696248i
\(965\) −530357. + 306202.i −0.569527 + 0.328816i
\(966\) 494.999 857.363i 0.000530457 0.000918778i
\(967\) −426457. + 738645.i −0.456060 + 0.789919i −0.998748 0.0500149i \(-0.984073\pi\)
0.542688 + 0.839934i \(0.317406\pi\)
\(968\) 248361.i 0.265053i
\(969\) 1.52023e6 + 242821.i 1.61906 + 0.258606i
\(970\) −68547.9 −0.0728535
\(971\) −75186.2 43408.8i −0.0797443 0.0460404i 0.459598 0.888127i \(-0.347994\pi\)
−0.539342 + 0.842087i \(0.681327\pi\)
\(972\) 388103. + 224071.i 0.410785 + 0.237167i
\(973\) −595.121 1030.78i −0.000628607 0.00108878i
\(974\) 78954.1 136752.i 0.0832255 0.144151i
\(975\) −348610. 603811.i −0.366717 0.635172i
\(976\) −588960. −0.618282
\(977\) 1.54915e6i 1.62295i −0.584387 0.811475i \(-0.698665\pi\)
0.584387 0.811475i \(-0.301335\pi\)
\(978\) 102972. + 178353.i 0.107657 + 0.186468i
\(979\) −223923. + 129282.i −0.233633 + 0.134888i
\(980\) 346271. 0.360548
\(981\) 156043.i 0.162147i
\(982\) −89009.3 + 51389.6i −0.0923023 + 0.0532908i
\(983\) −420874. 242992.i −0.435557 0.251469i 0.266154 0.963930i \(-0.414247\pi\)
−0.701711 + 0.712462i \(0.747580\pi\)
\(984\) 221088. 127645.i 0.228336 0.131830i
\(985\) 203346. 352205.i 0.209586 0.363014i
\(986\) −116894. + 202466.i −0.120237 + 0.208256i
\(987\) 7438.80i 0.00763604i
\(988\) 258573. + 676249.i 0.264892 + 0.692776i
\(989\) −693065. −0.708568
\(990\) −4583.00 2646.00i −0.00467606 0.00269972i
\(991\) 664833. + 383842.i 0.676964 + 0.390845i 0.798710 0.601716i \(-0.205516\pi\)
−0.121746 + 0.992561i \(0.538849\pi\)
\(992\) 355716. + 616118.i 0.361477 + 0.626096i
\(993\) −119049. + 206199.i −0.120733 + 0.209116i
\(994\) 521.906 + 903.969i 0.000528226 + 0.000914915i
\(995\) 653307. 0.659890
\(996\) 876934.i 0.883991i
\(997\) −165150. 286047.i −0.166145 0.287772i 0.770916 0.636936i \(-0.219799\pi\)
−0.937061 + 0.349165i \(0.886465\pi\)
\(998\) −35584.4 + 20544.7i −0.0357272 + 0.0206271i
\(999\) 44036.6 0.0441248
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 19.5.d.a.8.3 10
3.2 odd 2 171.5.p.a.46.3 10
4.3 odd 2 304.5.r.a.65.5 10
19.12 odd 6 inner 19.5.d.a.12.3 yes 10
57.50 even 6 171.5.p.a.145.3 10
76.31 even 6 304.5.r.a.145.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.5.d.a.8.3 10 1.1 even 1 trivial
19.5.d.a.12.3 yes 10 19.12 odd 6 inner
171.5.p.a.46.3 10 3.2 odd 2
171.5.p.a.145.3 10 57.50 even 6
304.5.r.a.65.5 10 4.3 odd 2
304.5.r.a.145.5 10 76.31 even 6