Properties

Label 13.5.f.a.6.4
Level $13$
Weight $5$
Character 13.6
Analytic conductor $1.344$
Analytic rank $0$
Dimension $16$
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] = [13,5,Mod(2,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(12))
 
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("13.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 13.f (of order \(12\), degree \(4\), 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: \(1.34380952009\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + 100636992 x^{2} + 3779136 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2}\cdot 13^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 6.4
Root \(-0.200628i\) of defining polynomial
Character \(\chi\) \(=\) 13.6
Dual form 13.5.f.a.11.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.59772 + 5.96275i) q^{2} +(2.76012 - 4.78067i) q^{3} +(-19.1453 + 11.0536i) q^{4} +(-5.37551 + 5.37551i) q^{5} +(32.9158 + 8.81977i) q^{6} +(23.3974 - 87.3205i) q^{7} +(-26.6579 - 26.6579i) q^{8} +(25.2635 + 43.7576i) q^{9} +O(q^{10})\) \(q+(1.59772 + 5.96275i) q^{2} +(2.76012 - 4.78067i) q^{3} +(-19.1453 + 11.0536i) q^{4} +(-5.37551 + 5.37551i) q^{5} +(32.9158 + 8.81977i) q^{6} +(23.3974 - 87.3205i) q^{7} +(-26.6579 - 26.6579i) q^{8} +(25.2635 + 43.7576i) q^{9} +(-40.6414 - 23.4643i) q^{10} +(-131.169 + 35.1465i) q^{11} +122.037i q^{12} +(-164.495 - 38.7617i) q^{13} +558.053 q^{14} +(10.8615 + 40.5356i) q^{15} +(-60.4944 + 104.779i) q^{16} +(97.4284 - 56.2503i) q^{17} +(-220.552 + 220.552i) q^{18} +(-27.6068 - 7.39723i) q^{19} +(43.4974 - 162.335i) q^{20} +(-352.871 - 352.871i) q^{21} +(-419.140 - 725.972i) q^{22} +(382.304 + 220.723i) q^{23} +(-201.021 + 53.8635i) q^{24} +567.208i q^{25} +(-31.6895 - 1042.77i) q^{26} +726.060 q^{27} +(517.250 + 1930.41i) q^{28} +(141.434 - 244.970i) q^{29} +(-224.350 + 129.529i) q^{30} +(596.807 - 596.807i) q^{31} +(-1304.07 - 349.425i) q^{32} +(-194.017 + 724.082i) q^{33} +(491.070 + 491.070i) q^{34} +(343.619 + 595.166i) q^{35} +(-967.355 - 558.503i) q^{36} +(-358.208 + 95.9816i) q^{37} -176.431i q^{38} +(-639.332 + 679.408i) q^{39} +286.599 q^{40} +(-339.191 - 1265.88i) q^{41} +(1540.29 - 2667.87i) q^{42} +(-37.5303 + 21.6682i) q^{43} +(2122.77 - 2122.77i) q^{44} +(-371.024 - 99.4155i) q^{45} +(-705.305 + 2632.24i) q^{46} +(2361.67 + 2361.67i) q^{47} +(333.944 + 578.408i) q^{48} +(-4998.10 - 2885.65i) q^{49} +(-3382.12 + 906.236i) q^{50} -621.031i q^{51} +(3577.76 - 1076.15i) q^{52} -150.315 q^{53} +(1160.04 + 4329.32i) q^{54} +(516.168 - 894.029i) q^{55} +(-2951.50 + 1704.05i) q^{56} +(-111.562 + 111.562i) q^{57} +(1686.67 + 451.941i) q^{58} +(-447.938 + 1671.73i) q^{59} +(-656.010 - 656.010i) q^{60} +(1068.49 + 1850.67i) q^{61} +(4512.14 + 2605.09i) q^{62} +(4412.04 - 1182.20i) q^{63} -6398.32i q^{64} +(1092.61 - 675.880i) q^{65} -4627.51 q^{66} +(-1444.15 - 5389.66i) q^{67} +(-1243.53 + 2153.86i) q^{68} +(2110.41 - 1218.45i) q^{69} +(-2999.82 + 2999.82i) q^{70} +(-6954.13 - 1863.35i) q^{71} +(493.014 - 1839.95i) q^{72} +(-3856.78 - 3856.78i) q^{73} +(-1144.63 - 1982.56i) q^{74} +(2711.63 + 1565.56i) q^{75} +(610.308 - 163.531i) q^{76} +12276.0i q^{77} +(-5072.62 - 2726.68i) q^{78} +9010.15 q^{79} +(-238.055 - 888.432i) q^{80} +(-42.3260 + 73.3108i) q^{81} +(7006.20 - 4045.03i) q^{82} +(-2184.19 + 2184.19i) q^{83} +(10656.3 + 2855.35i) q^{84} +(-221.353 + 826.102i) q^{85} +(-189.165 - 189.165i) q^{86} +(-780.747 - 1352.29i) q^{87} +(4433.61 + 2559.74i) q^{88} +(1348.94 - 361.446i) q^{89} -2371.16i q^{90} +(-7233.45 + 13456.8i) q^{91} -9759.11 q^{92} +(-1205.88 - 4500.40i) q^{93} +(-10308.8 + 17855.4i) q^{94} +(188.165 - 108.637i) q^{95} +(-5269.88 + 5269.88i) q^{96} +(6839.94 + 1832.76i) q^{97} +(9220.90 - 34412.9i) q^{98} +(-4851.70 - 4851.70i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.59772 + 5.96275i 0.399429 + 1.49069i 0.814104 + 0.580719i \(0.197229\pi\)
−0.414675 + 0.909969i \(0.636105\pi\)
\(3\) 2.76012 4.78067i 0.306680 0.531186i −0.670954 0.741499i \(-0.734115\pi\)
0.977634 + 0.210314i \(0.0674485\pi\)
\(4\) −19.1453 + 11.0536i −1.19658 + 0.690848i
\(5\) −5.37551 + 5.37551i −0.215021 + 0.215021i −0.806396 0.591376i \(-0.798585\pi\)
0.591376 + 0.806396i \(0.298585\pi\)
\(6\) 32.9158 + 8.81977i 0.914329 + 0.244994i
\(7\) 23.3974 87.3205i 0.477499 1.78205i −0.134194 0.990955i \(-0.542845\pi\)
0.611693 0.791095i \(-0.290489\pi\)
\(8\) −26.6579 26.6579i −0.416529 0.416529i
\(9\) 25.2635 + 43.7576i 0.311895 + 0.540217i
\(10\) −40.6414 23.4643i −0.406414 0.234643i
\(11\) −131.169 + 35.1465i −1.08404 + 0.290467i −0.756249 0.654284i \(-0.772970\pi\)
−0.327789 + 0.944751i \(0.606304\pi\)
\(12\) 122.037i 0.847477i
\(13\) −164.495 38.7617i −0.973342 0.229359i
\(14\) 558.053 2.84721
\(15\) 10.8615 + 40.5356i 0.0482733 + 0.180158i
\(16\) −60.4944 + 104.779i −0.236306 + 0.409295i
\(17\) 97.4284 56.2503i 0.337122 0.194638i −0.321876 0.946782i \(-0.604314\pi\)
0.658999 + 0.752144i \(0.270980\pi\)
\(18\) −220.552 + 220.552i −0.680716 + 0.680716i
\(19\) −27.6068 7.39723i −0.0764732 0.0204909i 0.220380 0.975414i \(-0.429270\pi\)
−0.296853 + 0.954923i \(0.595937\pi\)
\(20\) 43.4974 162.335i 0.108744 0.405837i
\(21\) −352.871 352.871i −0.800160 0.800160i
\(22\) −419.140 725.972i −0.865992 1.49994i
\(23\) 382.304 + 220.723i 0.722691 + 0.417246i 0.815742 0.578415i \(-0.196329\pi\)
−0.0930512 + 0.995661i \(0.529662\pi\)
\(24\) −201.021 + 53.8635i −0.348995 + 0.0935131i
\(25\) 567.208i 0.907532i
\(26\) −31.6895 1042.77i −0.0468779 1.54256i
\(27\) 726.060 0.995968
\(28\) 517.250 + 1930.41i 0.659758 + 2.46225i
\(29\) 141.434 244.970i 0.168173 0.291284i −0.769604 0.638521i \(-0.779547\pi\)
0.937778 + 0.347237i \(0.112880\pi\)
\(30\) −224.350 + 129.529i −0.249278 + 0.143921i
\(31\) 596.807 596.807i 0.621027 0.621027i −0.324767 0.945794i \(-0.605286\pi\)
0.945794 + 0.324767i \(0.105286\pi\)
\(32\) −1304.07 349.425i −1.27351 0.341235i
\(33\) −194.017 + 724.082i −0.178161 + 0.664906i
\(34\) 491.070 + 491.070i 0.424801 + 0.424801i
\(35\) 343.619 + 595.166i 0.280505 + 0.485850i
\(36\) −967.355 558.503i −0.746416 0.430943i
\(37\) −358.208 + 95.9816i −0.261657 + 0.0701107i −0.387262 0.921970i \(-0.626579\pi\)
0.125606 + 0.992080i \(0.459913\pi\)
\(38\) 176.431i 0.122182i
\(39\) −639.332 + 679.408i −0.420337 + 0.446685i
\(40\) 286.599 0.179125
\(41\) −339.191 1265.88i −0.201780 0.753051i −0.990407 0.138180i \(-0.955875\pi\)
0.788628 0.614871i \(-0.210792\pi\)
\(42\) 1540.29 2667.87i 0.873182 1.51240i
\(43\) −37.5303 + 21.6682i −0.0202976 + 0.0117189i −0.510114 0.860107i \(-0.670397\pi\)
0.489817 + 0.871825i \(0.337064\pi\)
\(44\) 2122.77 2122.77i 1.09647 1.09647i
\(45\) −371.024 99.4155i −0.183222 0.0490941i
\(46\) −705.305 + 2632.24i −0.333320 + 1.24397i
\(47\) 2361.67 + 2361.67i 1.06911 + 1.06911i 0.997427 + 0.0716878i \(0.0228385\pi\)
0.0716878 + 0.997427i \(0.477161\pi\)
\(48\) 333.944 + 578.408i 0.144941 + 0.251045i
\(49\) −4998.10 2885.65i −2.08167 1.20185i
\(50\) −3382.12 + 906.236i −1.35285 + 0.362495i
\(51\) 621.031i 0.238766i
\(52\) 3577.76 1076.15i 1.32314 0.397984i
\(53\) −150.315 −0.0535120 −0.0267560 0.999642i \(-0.508518\pi\)
−0.0267560 + 0.999642i \(0.508518\pi\)
\(54\) 1160.04 + 4329.32i 0.397818 + 1.48468i
\(55\) 516.168 894.029i 0.170634 0.295547i
\(56\) −2951.50 + 1704.05i −0.941168 + 0.543384i
\(57\) −111.562 + 111.562i −0.0343373 + 0.0343373i
\(58\) 1686.67 + 451.941i 0.501387 + 0.134346i
\(59\) −447.938 + 1671.73i −0.128681 + 0.480244i −0.999944 0.0105725i \(-0.996635\pi\)
0.871263 + 0.490816i \(0.163301\pi\)
\(60\) −656.010 656.010i −0.182225 0.182225i
\(61\) 1068.49 + 1850.67i 0.287150 + 0.497358i 0.973128 0.230264i \(-0.0739588\pi\)
−0.685978 + 0.727622i \(0.740626\pi\)
\(62\) 4512.14 + 2605.09i 1.17381 + 0.677702i
\(63\) 4412.04 1182.20i 1.11162 0.297859i
\(64\) 6398.32i 1.56209i
\(65\) 1092.61 675.880i 0.258605 0.159972i
\(66\) −4627.51 −1.06233
\(67\) −1444.15 5389.66i −0.321710 1.20064i −0.917578 0.397555i \(-0.869859\pi\)
0.595869 0.803082i \(-0.296808\pi\)
\(68\) −1243.53 + 2153.86i −0.268930 + 0.465801i
\(69\) 2110.41 1218.45i 0.443270 0.255922i
\(70\) −2999.82 + 2999.82i −0.612208 + 0.612208i
\(71\) −6954.13 1863.35i −1.37951 0.369640i −0.508570 0.861021i \(-0.669826\pi\)
−0.870945 + 0.491381i \(0.836492\pi\)
\(72\) 493.014 1839.95i 0.0951031 0.354930i
\(73\) −3856.78 3856.78i −0.723734 0.723734i 0.245630 0.969364i \(-0.421005\pi\)
−0.969364 + 0.245630i \(0.921005\pi\)
\(74\) −1144.63 1982.56i −0.209026 0.362045i
\(75\) 2711.63 + 1565.56i 0.482068 + 0.278322i
\(76\) 610.308 163.531i 0.105663 0.0283122i
\(77\) 12276.0i 2.07051i
\(78\) −5072.62 2726.68i −0.833763 0.448172i
\(79\) 9010.15 1.44370 0.721851 0.692048i \(-0.243291\pi\)
0.721851 + 0.692048i \(0.243291\pi\)
\(80\) −238.055 888.432i −0.0371960 0.138817i
\(81\) −42.3260 + 73.3108i −0.00645116 + 0.0111737i
\(82\) 7006.20 4045.03i 1.04197 0.601581i
\(83\) −2184.19 + 2184.19i −0.317055 + 0.317055i −0.847635 0.530580i \(-0.821974\pi\)
0.530580 + 0.847635i \(0.321974\pi\)
\(84\) 10656.3 + 2855.35i 1.51025 + 0.404669i
\(85\) −221.353 + 826.102i −0.0306371 + 0.114339i
\(86\) −189.165 189.165i −0.0255766 0.0255766i
\(87\) −780.747 1352.29i −0.103151 0.178662i
\(88\) 4433.61 + 2559.74i 0.572522 + 0.330545i
\(89\) 1348.94 361.446i 0.170299 0.0456314i −0.172662 0.984981i \(-0.555237\pi\)
0.342961 + 0.939350i \(0.388570\pi\)
\(90\) 2371.16i 0.292736i
\(91\) −7233.45 + 13456.8i −0.873499 + 1.62503i
\(92\) −9759.11 −1.15301
\(93\) −1205.88 4500.40i −0.139424 0.520338i
\(94\) −10308.8 + 17855.4i −1.16668 + 2.02075i
\(95\) 188.165 108.637i 0.0208493 0.0120373i
\(96\) −5269.88 + 5269.88i −0.571819 + 0.571819i
\(97\) 6839.94 + 1832.76i 0.726957 + 0.194788i 0.603274 0.797534i \(-0.293863\pi\)
0.123683 + 0.992322i \(0.460529\pi\)
\(98\) 9220.90 34412.9i 0.960110 3.58318i
\(99\) −4851.70 4851.70i −0.495021 0.495021i
\(100\) −6269.67 10859.4i −0.626967 1.08594i
\(101\) 3354.45 + 1936.69i 0.328835 + 0.189853i 0.655324 0.755348i \(-0.272532\pi\)
−0.326489 + 0.945201i \(0.605865\pi\)
\(102\) 3703.05 992.230i 0.355926 0.0953700i
\(103\) 3372.99i 0.317937i −0.987284 0.158968i \(-0.949183\pi\)
0.987284 0.158968i \(-0.0508168\pi\)
\(104\) 3351.78 + 5418.38i 0.309891 + 0.500960i
\(105\) 3793.72 0.344102
\(106\) −240.161 896.292i −0.0213742 0.0797697i
\(107\) 1930.57 3343.84i 0.168623 0.292064i −0.769313 0.638872i \(-0.779401\pi\)
0.937936 + 0.346808i \(0.112735\pi\)
\(108\) −13900.7 + 8025.56i −1.19176 + 0.688062i
\(109\) 8275.58 8275.58i 0.696539 0.696539i −0.267123 0.963662i \(-0.586073\pi\)
0.963662 + 0.267123i \(0.0860731\pi\)
\(110\) 6155.57 + 1649.38i 0.508724 + 0.136312i
\(111\) −529.842 + 1977.40i −0.0430031 + 0.160490i
\(112\) 7733.97 + 7733.97i 0.616548 + 0.616548i
\(113\) 4225.16 + 7318.19i 0.330892 + 0.573121i 0.982687 0.185274i \(-0.0593171\pi\)
−0.651795 + 0.758395i \(0.725984\pi\)
\(114\) −843.460 486.972i −0.0649015 0.0374709i
\(115\) −3241.58 + 868.578i −0.245110 + 0.0656770i
\(116\) 6253.38i 0.464728i
\(117\) −2459.59 8177.15i −0.179676 0.597352i
\(118\) −10683.8 −0.767292
\(119\) −2632.23 9823.60i −0.185879 0.693708i
\(120\) 791.049 1370.14i 0.0549340 0.0951484i
\(121\) 3290.45 1899.74i 0.224742 0.129755i
\(122\) −9327.96 + 9327.96i −0.626711 + 0.626711i
\(123\) −6987.96 1872.42i −0.461892 0.123764i
\(124\) −4829.23 + 18022.9i −0.314076 + 1.17215i
\(125\) −6408.73 6408.73i −0.410159 0.410159i
\(126\) 14098.4 + 24419.1i 0.888029 + 1.53811i
\(127\) 3336.63 + 1926.41i 0.206872 + 0.119437i 0.599857 0.800107i \(-0.295224\pi\)
−0.392985 + 0.919545i \(0.628558\pi\)
\(128\) 17286.5 4631.89i 1.05508 0.282708i
\(129\) 239.227i 0.0143758i
\(130\) 5775.78 + 5435.09i 0.341762 + 0.321603i
\(131\) −18579.1 −1.08264 −0.541318 0.840818i \(-0.682074\pi\)
−0.541318 + 0.840818i \(0.682074\pi\)
\(132\) −4289.17 16007.4i −0.246164 0.918698i
\(133\) −1291.86 + 2237.56i −0.0730318 + 0.126495i
\(134\) 29829.9 17222.3i 1.66128 0.959138i
\(135\) −3902.95 + 3902.95i −0.214154 + 0.214154i
\(136\) −4096.75 1097.72i −0.221494 0.0593490i
\(137\) −7754.09 + 28938.6i −0.413133 + 1.54183i 0.375414 + 0.926857i \(0.377500\pi\)
−0.788547 + 0.614975i \(0.789166\pi\)
\(138\) 10637.1 + 10637.1i 0.558555 + 0.558555i
\(139\) −7596.66 13157.8i −0.393182 0.681011i 0.599686 0.800236i \(-0.295292\pi\)
−0.992867 + 0.119225i \(0.961959\pi\)
\(140\) −13157.4 7596.43i −0.671296 0.387573i
\(141\) 17808.9 4771.88i 0.895775 0.240022i
\(142\) 44442.9i 2.20407i
\(143\) 22938.9 697.105i 1.12176 0.0340899i
\(144\) −6113.19 −0.294811
\(145\) 556.562 + 2077.12i 0.0264714 + 0.0987928i
\(146\) 16835.0 29159.1i 0.789782 1.36794i
\(147\) −27590.7 + 15929.5i −1.27682 + 0.737170i
\(148\) 5797.08 5797.08i 0.264658 0.264658i
\(149\) −21511.3 5763.93i −0.968933 0.259625i −0.260555 0.965459i \(-0.583906\pi\)
−0.708377 + 0.705834i \(0.750572\pi\)
\(150\) −5002.64 + 18670.1i −0.222340 + 0.829783i
\(151\) −10348.1 10348.1i −0.453845 0.453845i 0.442783 0.896629i \(-0.353991\pi\)
−0.896629 + 0.442783i \(0.853991\pi\)
\(152\) 538.745 + 933.133i 0.0233182 + 0.0403884i
\(153\) 4922.76 + 2842.15i 0.210293 + 0.121413i
\(154\) −73199.0 + 19613.6i −3.08648 + 0.827021i
\(155\) 6416.29i 0.267067i
\(156\) 4730.35 20074.4i 0.194377 0.824885i
\(157\) 22244.0 0.902431 0.451215 0.892415i \(-0.350991\pi\)
0.451215 + 0.892415i \(0.350991\pi\)
\(158\) 14395.6 + 53725.3i 0.576656 + 2.15211i
\(159\) −414.888 + 718.607i −0.0164111 + 0.0284248i
\(160\) 8888.40 5131.72i 0.347203 0.200458i
\(161\) 28218.6 28218.6i 1.08864 1.08864i
\(162\) −504.759 135.250i −0.0192333 0.00515355i
\(163\) −1844.86 + 6885.11i −0.0694365 + 0.259141i −0.991914 0.126910i \(-0.959494\pi\)
0.922478 + 0.386050i \(0.126161\pi\)
\(164\) 20486.4 + 20486.4i 0.761690 + 0.761690i
\(165\) −2849.37 4935.26i −0.104660 0.181277i
\(166\) −16513.5 9534.08i −0.599271 0.345989i
\(167\) 29795.5 7983.69i 1.06836 0.286267i 0.318542 0.947909i \(-0.396807\pi\)
0.749820 + 0.661642i \(0.230140\pi\)
\(168\) 18813.6i 0.666580i
\(169\) 25556.1 + 12752.2i 0.894789 + 0.446489i
\(170\) −5279.50 −0.182682
\(171\) −373.759 1394.89i −0.0127820 0.0477032i
\(172\) 479.021 829.688i 0.0161919 0.0280452i
\(173\) −47178.7 + 27238.7i −1.57636 + 0.910109i −0.580994 + 0.813908i \(0.697336\pi\)
−0.995362 + 0.0962012i \(0.969331\pi\)
\(174\) 6815.99 6815.99i 0.225128 0.225128i
\(175\) 49528.8 + 13271.2i 1.61727 + 0.433346i
\(176\) 4252.34 15869.9i 0.137278 0.512330i
\(177\) 6755.62 + 6755.62i 0.215635 + 0.215635i
\(178\) 4310.43 + 7465.88i 0.136044 + 0.235636i
\(179\) −12658.7 7308.50i −0.395078 0.228099i 0.289280 0.957245i \(-0.406584\pi\)
−0.684358 + 0.729146i \(0.739917\pi\)
\(180\) 8202.27 2197.79i 0.253156 0.0678331i
\(181\) 15636.6i 0.477292i 0.971107 + 0.238646i \(0.0767036\pi\)
−0.971107 + 0.238646i \(0.923296\pi\)
\(182\) −91796.8 21631.1i −2.77131 0.653033i
\(183\) 11796.6 0.352253
\(184\) −4307.39 16075.4i −0.127227 0.474817i
\(185\) 1409.60 2441.50i 0.0411863 0.0713368i
\(186\) 24908.1 14380.7i 0.719971 0.415676i
\(187\) −10802.5 + 10802.5i −0.308918 + 0.308918i
\(188\) −71320.0 19110.1i −2.01788 0.540690i
\(189\) 16988.0 63399.9i 0.475574 1.77486i
\(190\) 948.409 + 948.409i 0.0262717 + 0.0262717i
\(191\) −10415.6 18040.4i −0.285508 0.494514i 0.687224 0.726445i \(-0.258829\pi\)
−0.972732 + 0.231931i \(0.925496\pi\)
\(192\) −30588.3 17660.1i −0.829760 0.479062i
\(193\) −47365.6 + 12691.6i −1.27159 + 0.340722i −0.830641 0.556808i \(-0.812026\pi\)
−0.440952 + 0.897530i \(0.645359\pi\)
\(194\) 43713.1i 1.16147i
\(195\) −215.429 7088.91i −0.00566547 0.186428i
\(196\) 127587. 3.32119
\(197\) 16495.3 + 61561.3i 0.425038 + 1.58626i 0.763841 + 0.645405i \(0.223311\pi\)
−0.338803 + 0.940857i \(0.610022\pi\)
\(198\) 21177.9 36681.1i 0.540197 0.935648i
\(199\) 21392.2 12350.8i 0.540193 0.311881i −0.204964 0.978770i \(-0.565708\pi\)
0.745157 + 0.666889i \(0.232374\pi\)
\(200\) 15120.5 15120.5i 0.378014 0.378014i
\(201\) −29752.2 7972.08i −0.736423 0.197324i
\(202\) −6188.56 + 23096.0i −0.151666 + 0.566024i
\(203\) −18081.7 18081.7i −0.438781 0.438781i
\(204\) 6864.60 + 11889.8i 0.164951 + 0.285704i
\(205\) 8628.08 + 4981.42i 0.205308 + 0.118535i
\(206\) 20112.3 5389.08i 0.473945 0.126993i
\(207\) 22304.9i 0.520547i
\(208\) 14012.4 14890.8i 0.323882 0.344185i
\(209\) 3881.14 0.0888518
\(210\) 6061.28 + 22621.0i 0.137444 + 0.512948i
\(211\) −7684.22 + 13309.5i −0.172598 + 0.298948i −0.939327 0.343022i \(-0.888549\pi\)
0.766730 + 0.641970i \(0.221883\pi\)
\(212\) 2877.83 1661.52i 0.0640315 0.0369686i
\(213\) −28102.3 + 28102.3i −0.619417 + 0.619417i
\(214\) 23023.0 + 6168.99i 0.502729 + 0.134706i
\(215\) 85.2674 318.222i 0.00184462 0.00688420i
\(216\) −19355.2 19355.2i −0.414850 0.414850i
\(217\) −38149.7 66077.3i −0.810162 1.40324i
\(218\) 62567.3 + 36123.2i 1.31654 + 0.760105i
\(219\) −29083.2 + 7792.81i −0.606392 + 0.162482i
\(220\) 22822.0i 0.471529i
\(221\) −18206.8 + 5476.39i −0.372777 + 0.112127i
\(222\) −12637.3 −0.256417
\(223\) −360.162 1344.14i −0.00724250 0.0270294i 0.962210 0.272308i \(-0.0877871\pi\)
−0.969453 + 0.245279i \(0.921120\pi\)
\(224\) −61023.9 + 105697.i −1.21620 + 2.10652i
\(225\) −24819.7 + 14329.6i −0.490265 + 0.283054i
\(226\) −36886.0 + 36886.0i −0.722178 + 0.722178i
\(227\) 76619.8 + 20530.2i 1.48693 + 0.398420i 0.908698 0.417455i \(-0.137078\pi\)
0.578228 + 0.815876i \(0.303745\pi\)
\(228\) 902.733 3369.05i 0.0173656 0.0648093i
\(229\) −49114.8 49114.8i −0.936573 0.936573i 0.0615317 0.998105i \(-0.480401\pi\)
−0.998105 + 0.0615317i \(0.980401\pi\)
\(230\) −10358.2 17941.0i −0.195808 0.339149i
\(231\) 58687.7 + 33883.4i 1.09982 + 0.634984i
\(232\) −10300.7 + 2760.06i −0.191377 + 0.0512794i
\(233\) 90643.7i 1.66965i −0.550515 0.834826i \(-0.685568\pi\)
0.550515 0.834826i \(-0.314432\pi\)
\(234\) 44828.6 27730.7i 0.818698 0.506441i
\(235\) −25390.4 −0.459763
\(236\) −9902.63 36957.1i −0.177798 0.663551i
\(237\) 24869.1 43074.5i 0.442755 0.766874i
\(238\) 54370.2 31390.6i 0.959858 0.554174i
\(239\) 53610.9 53610.9i 0.938549 0.938549i −0.0596691 0.998218i \(-0.519005\pi\)
0.998218 + 0.0596691i \(0.0190045\pi\)
\(240\) −4904.36 1314.12i −0.0851451 0.0228146i
\(241\) −6713.31 + 25054.4i −0.115585 + 0.431370i −0.999330 0.0365992i \(-0.988348\pi\)
0.883745 + 0.467969i \(0.155014\pi\)
\(242\) 16584.9 + 16584.9i 0.283193 + 0.283193i
\(243\) 29639.1 + 51336.4i 0.501941 + 0.869387i
\(244\) −40913.0 23621.1i −0.687198 0.396754i
\(245\) 42379.2 11355.5i 0.706026 0.189179i
\(246\) 44659.1i 0.737972i
\(247\) 4254.45 + 2286.89i 0.0697348 + 0.0374845i
\(248\) −31819.2 −0.517352
\(249\) 4413.26 + 16470.5i 0.0711805 + 0.265649i
\(250\) 27974.4 48453.0i 0.447590 0.775248i
\(251\) −57981.5 + 33475.7i −0.920327 + 0.531351i −0.883739 0.467979i \(-0.844982\pi\)
−0.0365878 + 0.999330i \(0.511649\pi\)
\(252\) −71402.4 + 71402.4i −1.12438 + 1.12438i
\(253\) −57903.9 15515.3i −0.904621 0.242392i
\(254\) −6155.70 + 22973.4i −0.0954135 + 0.356088i
\(255\) 3338.36 + 3338.36i 0.0513396 + 0.0513396i
\(256\) 4051.12 + 7016.75i 0.0618152 + 0.107067i
\(257\) −32203.7 18592.8i −0.487573 0.281500i 0.235994 0.971754i \(-0.424165\pi\)
−0.723567 + 0.690254i \(0.757499\pi\)
\(258\) −1426.45 + 382.216i −0.0214298 + 0.00574209i
\(259\) 33524.6i 0.499763i
\(260\) −13447.5 + 25017.2i −0.198927 + 0.370076i
\(261\) 14292.4 0.209809
\(262\) −29684.1 110783.i −0.432436 1.61387i
\(263\) 10900.9 18881.0i 0.157598 0.272969i −0.776404 0.630236i \(-0.782958\pi\)
0.934002 + 0.357267i \(0.116291\pi\)
\(264\) 24474.6 14130.4i 0.351162 0.202743i
\(265\) 808.021 808.021i 0.0115062 0.0115062i
\(266\) −15406.1 4128.04i −0.217735 0.0583420i
\(267\) 1995.27 7446.45i 0.0279885 0.104454i
\(268\) 87223.8 + 87223.8i 1.21441 + 1.21441i
\(269\) 53948.9 + 93442.2i 0.745552 + 1.29133i 0.949936 + 0.312444i \(0.101148\pi\)
−0.204384 + 0.978891i \(0.565519\pi\)
\(270\) −29508.1 17036.5i −0.404775 0.233697i
\(271\) 42444.4 11372.9i 0.577939 0.154858i 0.0420036 0.999117i \(-0.486626\pi\)
0.535935 + 0.844259i \(0.319959\pi\)
\(272\) 13611.3i 0.183976i
\(273\) 44367.5 + 71723.2i 0.595305 + 0.962353i
\(274\) −184943. −2.46341
\(275\) −19935.4 74399.8i −0.263608 0.983800i
\(276\) −26936.3 + 46655.1i −0.353606 + 0.612464i
\(277\) −1084.76 + 626.285i −0.0141375 + 0.00816230i −0.507052 0.861915i \(-0.669265\pi\)
0.492915 + 0.870078i \(0.335932\pi\)
\(278\) 66319.5 66319.5i 0.858127 0.858127i
\(279\) 41192.3 + 11037.4i 0.529185 + 0.141795i
\(280\) 6705.70 25026.0i 0.0855318 0.319209i
\(281\) 74905.1 + 74905.1i 0.948634 + 0.948634i 0.998744 0.0501093i \(-0.0159570\pi\)
−0.0501093 + 0.998744i \(0.515957\pi\)
\(282\) 56907.1 + 98566.0i 0.715596 + 1.23945i
\(283\) −37049.3 21390.4i −0.462601 0.267083i 0.250536 0.968107i \(-0.419393\pi\)
−0.713137 + 0.701024i \(0.752726\pi\)
\(284\) 153736. 41193.4i 1.90607 0.510730i
\(285\) 1199.40i 0.0147664i
\(286\) 40806.5 + 135665.i 0.498881 + 1.65858i
\(287\) −118473. −1.43833
\(288\) −17655.4 65890.8i −0.212859 0.794400i
\(289\) −35432.3 + 61370.6i −0.424232 + 0.734792i
\(290\) −11496.1 + 6637.29i −0.136696 + 0.0789213i
\(291\) 27640.9 27640.9i 0.326412 0.326412i
\(292\) 116471. + 31208.2i 1.36600 + 0.366018i
\(293\) 8238.85 30747.8i 0.0959691 0.358162i −0.901195 0.433413i \(-0.857309\pi\)
0.997165 + 0.0752512i \(0.0239759\pi\)
\(294\) −139066. 139066.i −1.60889 1.60889i
\(295\) −6578.50 11394.3i −0.0755932 0.130931i
\(296\) 12107.7 + 6990.40i 0.138191 + 0.0797845i
\(297\) −95236.3 + 25518.5i −1.07967 + 0.289296i
\(298\) 137476.i 1.54808i
\(299\) −54331.4 51126.5i −0.607727 0.571879i
\(300\) −69220.2 −0.769113
\(301\) 1013.96 + 3784.15i 0.0111915 + 0.0417672i
\(302\) 45170.0 78236.7i 0.495263 0.857821i
\(303\) 18517.4 10691.0i 0.201694 0.116448i
\(304\) 2445.14 2445.14i 0.0264579 0.0264579i
\(305\) −15692.0 4204.65i −0.168685 0.0451991i
\(306\) −9081.91 + 33894.1i −0.0969916 + 0.361978i
\(307\) 84129.7 + 84129.7i 0.892632 + 0.892632i 0.994770 0.102138i \(-0.0325683\pi\)
−0.102138 + 0.994770i \(0.532568\pi\)
\(308\) −135694. 235029.i −1.43041 2.47754i
\(309\) −16125.2 9309.86i −0.168883 0.0975048i
\(310\) −38258.8 + 10251.4i −0.398114 + 0.106674i
\(311\) 13886.4i 0.143572i −0.997420 0.0717860i \(-0.977130\pi\)
0.997420 0.0717860i \(-0.0228699\pi\)
\(312\) 35154.8 1068.34i 0.361140 0.0109749i
\(313\) 63260.4 0.645718 0.322859 0.946447i \(-0.395356\pi\)
0.322859 + 0.946447i \(0.395356\pi\)
\(314\) 35539.6 + 132636.i 0.360457 + 1.34524i
\(315\) −17362.0 + 30071.9i −0.174976 + 0.303068i
\(316\) −172502. + 99594.3i −1.72751 + 0.997379i
\(317\) −10553.4 + 10553.4i −0.105020 + 0.105020i −0.757664 0.652644i \(-0.773660\pi\)
0.652644 + 0.757664i \(0.273660\pi\)
\(318\) −4947.75 1325.75i −0.0489275 0.0131101i
\(319\) −9941.79 + 37103.3i −0.0976975 + 0.364612i
\(320\) 34394.3 + 34394.3i 0.335881 + 0.335881i
\(321\) −10657.2 18458.8i −0.103427 0.179140i
\(322\) 213346. + 123175.i 2.05765 + 1.18799i
\(323\) −3105.78 + 832.192i −0.0297691 + 0.00797662i
\(324\) 1871.41i 0.0178271i
\(325\) 21985.9 93302.7i 0.208151 0.883339i
\(326\) −44001.8 −0.414033
\(327\) −16721.2 62404.4i −0.156377 0.583606i
\(328\) −24703.5 + 42787.8i −0.229621 + 0.397715i
\(329\) 261480. 150965.i 2.41572 1.39472i
\(330\) 24875.2 24875.2i 0.228423 0.228423i
\(331\) −45405.1 12166.3i −0.414428 0.111046i 0.0455795 0.998961i \(-0.485487\pi\)
−0.460007 + 0.887915i \(0.652153\pi\)
\(332\) 17674.0 65960.2i 0.160346 0.598419i
\(333\) −13249.5 13249.5i −0.119484 0.119484i
\(334\) 95209.6 + 164908.i 0.853469 + 1.47825i
\(335\) 36735.3 + 21209.1i 0.327336 + 0.188987i
\(336\) 58320.3 15626.9i 0.516584 0.138418i
\(337\) 8592.02i 0.0756546i 0.999284 + 0.0378273i \(0.0120437\pi\)
−0.999284 + 0.0378273i \(0.987956\pi\)
\(338\) −35206.8 + 172759.i −0.308172 + 1.51219i
\(339\) 46647.8 0.405912
\(340\) −4893.49 18262.7i −0.0423312 0.157982i
\(341\) −57306.7 + 99258.1i −0.492829 + 0.853605i
\(342\) 7720.21 4457.27i 0.0660051 0.0381080i
\(343\) −215440. + 215440.i −1.83121 + 1.83121i
\(344\) 1578.11 + 422.852i 0.0133358 + 0.00357332i
\(345\) −4794.76 + 17894.3i −0.0402837 + 0.150341i
\(346\) −237796. 237796.i −1.98633 1.98633i
\(347\) −86232.5 149359.i −0.716163 1.24043i −0.962509 0.271249i \(-0.912563\pi\)
0.246346 0.969182i \(-0.420770\pi\)
\(348\) 29895.3 + 17260.1i 0.246857 + 0.142523i
\(349\) 126776. 33969.6i 1.04085 0.278894i 0.302383 0.953186i \(-0.402218\pi\)
0.738465 + 0.674292i \(0.235551\pi\)
\(350\) 316532.i 2.58393i
\(351\) −119433. 28143.3i −0.969417 0.228434i
\(352\) 183334. 1.47965
\(353\) −11384.2 42486.4i −0.0913593 0.340958i 0.905083 0.425235i \(-0.139809\pi\)
−0.996442 + 0.0842773i \(0.973142\pi\)
\(354\) −29488.5 + 51075.6i −0.235313 + 0.407575i
\(355\) 47398.5 27365.6i 0.376104 0.217144i
\(356\) −21830.6 + 21830.6i −0.172252 + 0.172252i
\(357\) −54228.7 14530.5i −0.425493 0.114011i
\(358\) 23353.8 87157.6i 0.182218 0.680048i
\(359\) −15691.6 15691.6i −0.121753 0.121753i 0.643605 0.765358i \(-0.277438\pi\)
−0.765358 + 0.643605i \(0.777438\pi\)
\(360\) 7240.50 + 12540.9i 0.0558680 + 0.0967662i
\(361\) −112154. 64752.1i −0.860597 0.496866i
\(362\) −93237.1 + 24982.8i −0.711494 + 0.190644i
\(363\) 20974.1i 0.159173i
\(364\) −10259.3 337591.i −0.0774308 2.54793i
\(365\) 41464.3 0.311235
\(366\) 18847.6 + 70340.2i 0.140700 + 0.525099i
\(367\) 100985. 174910.i 0.749761 1.29862i −0.198175 0.980167i \(-0.563502\pi\)
0.947937 0.318458i \(-0.103165\pi\)
\(368\) −46254.5 + 26705.0i −0.341553 + 0.197196i
\(369\) 46822.7 46822.7i 0.343878 0.343878i
\(370\) 16810.2 + 4504.29i 0.122792 + 0.0329020i
\(371\) −3516.99 + 13125.6i −0.0255519 + 0.0953610i
\(372\) 72832.4 + 72832.4i 0.526307 + 0.526307i
\(373\) 124830. + 216212.i 0.897226 + 1.55404i 0.831025 + 0.556235i \(0.187755\pi\)
0.0662014 + 0.997806i \(0.478912\pi\)
\(374\) −81672.3 47153.5i −0.583891 0.337109i
\(375\) −48326.9 + 12949.1i −0.343658 + 0.0920828i
\(376\) 125914.i 0.890635i
\(377\) −32760.5 + 34814.1i −0.230499 + 0.244947i
\(378\) 405180. 2.83573
\(379\) 19032.3 + 71029.7i 0.132499 + 0.494494i 0.999996 0.00294932i \(-0.000938800\pi\)
−0.867496 + 0.497444i \(0.834272\pi\)
\(380\) −2401.65 + 4159.78i −0.0166319 + 0.0288074i
\(381\) 18419.0 10634.2i 0.126887 0.0732582i
\(382\) 90929.1 90929.1i 0.623127 0.623127i
\(383\) −97227.9 26052.1i −0.662817 0.177601i −0.0882998 0.996094i \(-0.528143\pi\)
−0.574517 + 0.818493i \(0.694810\pi\)
\(384\) 25569.2 95425.4i 0.173402 0.647145i
\(385\) −65990.0 65990.0i −0.445202 0.445202i
\(386\) −151353. 262152.i −1.01582 1.75946i
\(387\) −1896.29 1094.83i −0.0126615 0.00731009i
\(388\) −151211. + 40517.0i −1.00443 + 0.269137i
\(389\) 214008.i 1.41426i 0.707082 + 0.707131i \(0.250011\pi\)
−0.707082 + 0.707131i \(0.749989\pi\)
\(390\) 41925.2 12610.6i 0.275642 0.0829100i
\(391\) 49663.0 0.324847
\(392\) 56313.3 + 210164.i 0.366470 + 1.36768i
\(393\) −51280.6 + 88820.6i −0.332023 + 0.575080i
\(394\) −340720. + 196715.i −2.19485 + 1.26720i
\(395\) −48434.2 + 48434.2i −0.310426 + 0.310426i
\(396\) 146516. + 39258.9i 0.934318 + 0.250350i
\(397\) 35355.3 131948.i 0.224323 0.837184i −0.758352 0.651845i \(-0.773995\pi\)
0.982675 0.185339i \(-0.0593382\pi\)
\(398\) 107823. + 107823.i 0.680686 + 0.680686i
\(399\) 7131.37 + 12351.9i 0.0447948 + 0.0775868i
\(400\) −59431.7 34312.9i −0.371448 0.214456i
\(401\) −197833. + 53009.2i −1.23030 + 0.329657i −0.814695 0.579890i \(-0.803096\pi\)
−0.415602 + 0.909547i \(0.636429\pi\)
\(402\) 190142.i 1.17659i
\(403\) −121305. + 75038.4i −0.746910 + 0.462034i
\(404\) −85629.4 −0.524638
\(405\) −166.559 621.608i −0.00101545 0.00378971i
\(406\) 78927.4 136706.i 0.478824 0.829347i
\(407\) 43612.2 25179.5i 0.263281 0.152005i
\(408\) −16555.3 + 16555.3i −0.0994530 + 0.0994530i
\(409\) 152546. + 40874.6i 0.911916 + 0.244347i 0.684126 0.729363i \(-0.260184\pi\)
0.227789 + 0.973710i \(0.426850\pi\)
\(410\) −15917.8 + 59406.0i −0.0946924 + 0.353397i
\(411\) 116944. + 116944.i 0.692299 + 0.692299i
\(412\) 37283.6 + 64577.0i 0.219646 + 0.380438i
\(413\) 135495. + 78228.3i 0.794373 + 0.458632i
\(414\) −132999. + 35636.9i −0.775974 + 0.207922i
\(415\) 23482.3i 0.136347i
\(416\) 200969. + 108027.i 1.16129 + 0.624229i
\(417\) −83870.9 −0.482324
\(418\) 6200.95 + 23142.3i 0.0354900 + 0.132450i
\(419\) 98539.2 170675.i 0.561282 0.972168i −0.436103 0.899897i \(-0.643642\pi\)
0.997385 0.0722718i \(-0.0230249\pi\)
\(420\) −72632.1 + 41934.1i −0.411746 + 0.237722i
\(421\) 107929. 107929.i 0.608939 0.608939i −0.333729 0.942669i \(-0.608307\pi\)
0.942669 + 0.333729i \(0.108307\pi\)
\(422\) −91638.2 24554.4i −0.514579 0.137881i
\(423\) −43677.1 + 163005.i −0.244103 + 0.911006i
\(424\) 4007.08 + 4007.08i 0.0222893 + 0.0222893i
\(425\) 31905.6 + 55262.1i 0.176640 + 0.305949i
\(426\) −212467. 122668.i −1.17077 0.675945i
\(427\) 186601. 49999.7i 1.02343 0.274228i
\(428\) 85358.6i 0.465972i
\(429\) 59981.5 111587.i 0.325914 0.606318i
\(430\) 2033.71 0.0109990
\(431\) 32479.2 + 121214.i 0.174844 + 0.652528i 0.996578 + 0.0826563i \(0.0263404\pi\)
−0.821734 + 0.569871i \(0.806993\pi\)
\(432\) −43922.6 + 76076.2i −0.235353 + 0.407644i
\(433\) 228921. 132167.i 1.22098 0.704934i 0.255855 0.966715i \(-0.417643\pi\)
0.965127 + 0.261781i \(0.0843097\pi\)
\(434\) 333050. 333050.i 1.76819 1.76819i
\(435\) 11466.2 + 3072.36i 0.0605955 + 0.0162365i
\(436\) −66964.1 + 249913.i −0.352265 + 1.31467i
\(437\) −8921.45 8921.45i −0.0467168 0.0467168i
\(438\) −92933.2 160965.i −0.484421 0.839042i
\(439\) −207852. 120004.i −1.07851 0.622680i −0.148019 0.988985i \(-0.547290\pi\)
−0.930495 + 0.366304i \(0.880623\pi\)
\(440\) −37592.9 + 10073.0i −0.194178 + 0.0520298i
\(441\) 291606.i 1.49941i
\(442\) −61743.7 99813.0i −0.316044 0.510908i
\(443\) 56485.3 0.287825 0.143912 0.989590i \(-0.454032\pi\)
0.143912 + 0.989590i \(0.454032\pi\)
\(444\) −11713.3 43714.5i −0.0594172 0.221748i
\(445\) −5308.26 + 9194.18i −0.0268060 + 0.0464294i
\(446\) 7439.36 4295.12i 0.0373995 0.0215926i
\(447\) −86929.1 + 86929.1i −0.435061 + 0.435061i
\(448\) −558704. 149704.i −2.78372 0.745896i
\(449\) −34627.1 + 129230.i −0.171761 + 0.641020i 0.825320 + 0.564665i \(0.190995\pi\)
−0.997081 + 0.0763545i \(0.975672\pi\)
\(450\) −125099. 125099.i −0.617772 0.617772i
\(451\) 88982.5 + 154122.i 0.437473 + 0.757726i
\(452\) −161784. 93406.1i −0.791879 0.457192i
\(453\) −78033.0 + 20908.9i −0.380261 + 0.101891i
\(454\) 489666.i 2.37568i
\(455\) −33453.9 111221.i −0.161594 0.537234i
\(456\) 5948.00 0.0286050
\(457\) 46049.5 + 171859.i 0.220492 + 0.822886i 0.984161 + 0.177278i \(0.0567293\pi\)
−0.763669 + 0.645608i \(0.776604\pi\)
\(458\) 214388. 371331.i 1.02204 1.77023i
\(459\) 70738.9 40841.1i 0.335763 0.193853i
\(460\) 52460.2 52460.2i 0.247922 0.247922i
\(461\) −303818. 81407.7i −1.42959 0.383057i −0.540714 0.841207i \(-0.681846\pi\)
−0.888875 + 0.458149i \(0.848512\pi\)
\(462\) −108272. + 404076.i −0.507262 + 1.89313i
\(463\) 238507. + 238507.i 1.11260 + 1.11260i 0.992797 + 0.119805i \(0.0382269\pi\)
0.119805 + 0.992797i \(0.461773\pi\)
\(464\) 17111.9 + 29638.6i 0.0794807 + 0.137665i
\(465\) 30674.2 + 17709.7i 0.141862 + 0.0819042i
\(466\) 540486. 144823.i 2.48893 0.666907i
\(467\) 300948.i 1.37993i −0.723842 0.689965i \(-0.757626\pi\)
0.723842 0.689965i \(-0.242374\pi\)
\(468\) 137476. + 129367.i 0.627677 + 0.590653i
\(469\) −504417. −2.29321
\(470\) −40566.7 151397.i −0.183643 0.685364i
\(471\) 61396.2 106341.i 0.276758 0.479358i
\(472\) 56505.8 32623.6i 0.253635 0.146436i
\(473\) 4161.24 4161.24i 0.0185995 0.0185995i
\(474\) 296577. + 79467.5i 1.32002 + 0.353698i
\(475\) 4195.76 15658.8i 0.0185962 0.0694019i
\(476\) 158981. + 158981.i 0.701666 + 0.701666i
\(477\) −3797.48 6577.43i −0.0166901 0.0289081i
\(478\) 405323. + 234014.i 1.77397 + 1.02420i
\(479\) −206969. + 55457.3i −0.902059 + 0.241706i −0.679900 0.733304i \(-0.737977\pi\)
−0.222159 + 0.975010i \(0.571310\pi\)
\(480\) 56656.6i 0.245906i
\(481\) 62643.8 1903.72i 0.270762 0.00822836i
\(482\) −160119. −0.689206
\(483\) −57017.0 212790.i −0.244405 0.912132i
\(484\) −41997.8 + 72742.4i −0.179282 + 0.310525i
\(485\) −46620.2 + 26916.2i −0.198194 + 0.114427i
\(486\) −258752. + 258752.i −1.09550 + 1.09550i
\(487\) 55699.6 + 14924.7i 0.234852 + 0.0629283i 0.374325 0.927297i \(-0.377874\pi\)
−0.139474 + 0.990226i \(0.544541\pi\)
\(488\) 20851.4 77818.5i 0.0875579 0.326771i
\(489\) 27823.4 + 27823.4i 0.116357 + 0.116357i
\(490\) 135420. + 234554.i 0.564014 + 0.976901i
\(491\) 339332. + 195914.i 1.40754 + 0.812646i 0.995151 0.0983596i \(-0.0313595\pi\)
0.412394 + 0.911006i \(0.364693\pi\)
\(492\) 154484. 41393.8i 0.638194 0.171004i
\(493\) 31822.7i 0.130931i
\(494\) −6838.78 + 29022.0i −0.0280236 + 0.118925i
\(495\) 52160.8 0.212879
\(496\) 26429.6 + 98636.6i 0.107430 + 0.400936i
\(497\) −325418. + 563640.i −1.31743 + 2.28186i
\(498\) −91158.5 + 52630.4i −0.367569 + 0.212216i
\(499\) −49256.6 + 49256.6i −0.197817 + 0.197817i −0.799063 0.601247i \(-0.794671\pi\)
0.601247 + 0.799063i \(0.294671\pi\)
\(500\) 193537. + 51858.0i 0.774146 + 0.207432i
\(501\) 44071.9 164479.i 0.175585 0.655290i
\(502\) −292245. 292245.i −1.15968 1.15968i
\(503\) −207038. 358600.i −0.818302 1.41734i −0.906932 0.421276i \(-0.861582\pi\)
0.0886300 0.996065i \(-0.471751\pi\)
\(504\) −149130. 86100.5i −0.587091 0.338957i
\(505\) −28442.6 + 7621.17i −0.111529 + 0.0298840i
\(506\) 370056.i 1.44533i
\(507\) 131502. 86977.5i 0.511583 0.338369i
\(508\) −85174.6 −0.330052
\(509\) −32960.3 123010.i −0.127220 0.474792i 0.872689 0.488277i \(-0.162374\pi\)
−0.999909 + 0.0134846i \(0.995708\pi\)
\(510\) −14572.1 + 25239.6i −0.0560248 + 0.0970379i
\(511\) −427015. + 246537.i −1.63531 + 0.944149i
\(512\) 167106. 167106.i 0.637461 0.637461i
\(513\) −20044.2 5370.83i −0.0761648 0.0204083i
\(514\) 59412.0 221729.i 0.224879 0.839258i
\(515\) 18131.6 + 18131.6i 0.0683629 + 0.0683629i
\(516\) −2644.31 4580.08i −0.00993146 0.0172018i
\(517\) −392782. 226773.i −1.46950 0.848419i
\(518\) −199899. + 53562.8i −0.744991 + 0.199620i
\(519\) 300728.i 1.11645i
\(520\) −47144.1 11109.1i −0.174350 0.0410839i
\(521\) 288110. 1.06141 0.530705 0.847557i \(-0.321927\pi\)
0.530705 + 0.847557i \(0.321927\pi\)
\(522\) 22835.2 + 85222.1i 0.0838038 + 0.312760i
\(523\) 170871. 295958.i 0.624692 1.08200i −0.363909 0.931435i \(-0.618558\pi\)
0.988600 0.150563i \(-0.0481087\pi\)
\(524\) 355703. 205365.i 1.29546 0.747937i
\(525\) 200151. 200151.i 0.726171 0.726171i
\(526\) 129999. + 34833.2i 0.469861 + 0.125899i
\(527\) 24575.4 91716.6i 0.0884869 0.330238i
\(528\) −64132.0 64132.0i −0.230042 0.230042i
\(529\) −42483.1 73582.9i −0.151812 0.262945i
\(530\) 6109.02 + 3527.04i 0.0217480 + 0.0125562i
\(531\) −84467.3 + 22632.9i −0.299571 + 0.0802698i
\(532\) 57118.6i 0.201815i
\(533\) 6727.60 + 221378.i 0.0236813 + 0.779256i
\(534\) 47589.2 0.166888
\(535\) 7597.07 + 28352.7i 0.0265423 + 0.0990572i
\(536\) −105179. + 182175.i −0.366099 + 0.634102i
\(537\) −69879.1 + 40344.7i −0.242325 + 0.139907i
\(538\) −470978. + 470978.i −1.62718 + 1.62718i
\(539\) 757014. + 202841.i 2.60571 + 0.698198i
\(540\) 31581.8 117865.i 0.108305 0.404200i
\(541\) −195832. 195832.i −0.669096 0.669096i 0.288411 0.957507i \(-0.406873\pi\)
−0.957507 + 0.288411i \(0.906873\pi\)
\(542\) 135628. + 234915.i 0.461691 + 0.799672i
\(543\) 74753.3 + 43158.8i 0.253531 + 0.146376i
\(544\) −146709. + 39310.5i −0.495745 + 0.132835i
\(545\) 88971.0i 0.299540i
\(546\) −356781. + 379146.i −1.19679 + 1.27181i
\(547\) 232302. 0.776387 0.388194 0.921578i \(-0.373099\pi\)
0.388194 + 0.921578i \(0.373099\pi\)
\(548\) −171421. 639750.i −0.570824 2.13034i
\(549\) −53987.3 + 93508.7i −0.179121 + 0.310247i
\(550\) 411777. 237740.i 1.36125 0.785916i
\(551\) −5716.63 + 5716.63i −0.0188294 + 0.0188294i
\(552\) −88740.1 23777.8i −0.291234 0.0780359i
\(553\) 210814. 786770.i 0.689366 2.57275i
\(554\) −5467.52 5467.52i −0.0178144 0.0178144i
\(555\) −7781.35 13477.7i −0.0252621 0.0437552i
\(556\) 290881. + 167940.i 0.940950 + 0.543258i
\(557\) 379764. 101757.i 1.22406 0.327986i 0.411797 0.911276i \(-0.364901\pi\)
0.812264 + 0.583290i \(0.198235\pi\)
\(558\) 263254.i 0.845487i
\(559\) 7013.44 2109.56i 0.0224444 0.00675100i
\(560\) −83148.1 −0.265141
\(561\) 21827.1 + 81459.7i 0.0693537 + 0.258831i
\(562\) −326964. + 566318.i −1.03521 + 1.79303i
\(563\) −270897. + 156402.i −0.854648 + 0.493431i −0.862216 0.506540i \(-0.830924\pi\)
0.00756835 + 0.999971i \(0.497591\pi\)
\(564\) −288211. + 288211.i −0.906050 + 0.906050i
\(565\) −62051.4 16626.6i −0.194381 0.0520843i
\(566\) 68351.5 255091.i 0.213361 0.796275i
\(567\) 5411.22 + 5411.22i 0.0168317 + 0.0168317i
\(568\) 135709. + 235055.i 0.420642 + 0.728574i
\(569\) 121130. + 69934.3i 0.374133 + 0.216006i 0.675263 0.737577i \(-0.264030\pi\)
−0.301129 + 0.953583i \(0.597364\pi\)
\(570\) 7151.76 1916.31i 0.0220122 0.00589814i
\(571\) 53058.0i 0.162734i 0.996684 + 0.0813671i \(0.0259286\pi\)
−0.996684 + 0.0813671i \(0.974071\pi\)
\(572\) −431467. + 266903.i −1.31873 + 0.815758i
\(573\) −114993. −0.350238
\(574\) −189287. 706428.i −0.574508 2.14409i
\(575\) −125196. + 216846.i −0.378664 + 0.655866i
\(576\) 279975. 161644.i 0.843868 0.487207i
\(577\) −321525. + 321525.i −0.965748 + 0.965748i −0.999433 0.0336847i \(-0.989276\pi\)
0.0336847 + 0.999433i \(0.489276\pi\)
\(578\) −422548. 113221.i −1.26480 0.338901i
\(579\) −70060.5 + 261470.i −0.208986 + 0.779945i
\(580\) −33615.1 33615.1i −0.0999261 0.0999261i
\(581\) 139620. + 241829.i 0.413614 + 0.716401i
\(582\) 208978. + 120653.i 0.616956 + 0.356200i
\(583\) 19716.6 5283.05i 0.0580090 0.0155435i
\(584\) 205627.i 0.602913i
\(585\) 57178.0 + 30734.8i 0.167077 + 0.0898088i
\(586\) 196505. 0.572240
\(587\) 105377. + 393271.i 0.305822 + 1.14134i 0.932236 + 0.361852i \(0.117855\pi\)
−0.626414 + 0.779491i \(0.715478\pi\)
\(588\) 352156. 609951.i 1.01854 1.76417i
\(589\) −20890.7 + 12061.2i −0.0602174 + 0.0347665i
\(590\) 57430.8 57430.8i 0.164984 0.164984i
\(591\) 339833. + 91058.0i 0.972950 + 0.260701i
\(592\) 11612.7 43339.2i 0.0331352 0.123662i
\(593\) −65134.9 65134.9i −0.185227 0.185227i 0.608402 0.793629i \(-0.291811\pi\)
−0.793629 + 0.608402i \(0.791811\pi\)
\(594\) −304321. 527100.i −0.862500 1.49389i
\(595\) 66956.5 + 38657.3i 0.189129 + 0.109194i
\(596\) 475552. 127424.i 1.33877 0.358722i
\(597\) 136359.i 0.382591i
\(598\) 218049. 405650.i 0.609750 1.13436i
\(599\) −267881. −0.746600 −0.373300 0.927711i \(-0.621774\pi\)
−0.373300 + 0.927711i \(0.621774\pi\)
\(600\) −30551.8 114021.i −0.0848661 0.316725i
\(601\) 92557.9 160315.i 0.256250 0.443839i −0.708984 0.705225i \(-0.750846\pi\)
0.965234 + 0.261386i \(0.0841795\pi\)
\(602\) −20943.9 + 12092.0i −0.0577916 + 0.0333660i
\(603\) 199354. 199354.i 0.548265 0.548265i
\(604\) 312502. + 83734.7i 0.856602 + 0.229526i
\(605\) −7475.76 + 27899.9i −0.0204242 + 0.0762241i
\(606\) 93333.3 + 93333.3i 0.254151 + 0.254151i
\(607\) −159586. 276411.i −0.433129 0.750201i 0.564012 0.825766i \(-0.309257\pi\)
−0.997141 + 0.0755656i \(0.975924\pi\)
\(608\) 33416.5 + 19293.0i 0.0903970 + 0.0521907i
\(609\) −136350. + 36535.0i −0.367639 + 0.0985087i
\(610\) 100285.i 0.269511i
\(611\) −296941. 480026.i −0.795403 1.28583i
\(612\) −125664. −0.335511
\(613\) 152708. + 569912.i 0.406387 + 1.51666i 0.801484 + 0.598017i \(0.204044\pi\)
−0.395097 + 0.918640i \(0.629289\pi\)
\(614\) −367229. + 636060.i −0.974094 + 1.68718i
\(615\) 47629.1 27498.7i 0.125928 0.0727045i
\(616\) 327253. 327253.i 0.862427 0.862427i
\(617\) −473767. 126946.i −1.24450 0.333463i −0.424290 0.905526i \(-0.639476\pi\)
−0.820209 + 0.572063i \(0.806143\pi\)
\(618\) 29749.0 111025.i 0.0778925 0.290699i
\(619\) −241958. 241958.i −0.631478 0.631478i 0.316961 0.948439i \(-0.397338\pi\)
−0.948439 + 0.316961i \(0.897338\pi\)
\(620\) −70922.9 122842.i −0.184503 0.319568i
\(621\) 277576. + 160258.i 0.719777 + 0.415564i
\(622\) 82801.4 22186.6i 0.214021 0.0573468i
\(623\) 126247.i 0.325270i
\(624\) −32512.0 108089.i −0.0834976 0.277596i
\(625\) −285604. −0.731147
\(626\) 101072. + 377206.i 0.257918 + 0.962565i
\(627\) 10712.4 18554.4i 0.0272491 0.0471968i
\(628\) −425869. + 245876.i −1.07983 + 0.623442i
\(629\) −29500.6 + 29500.6i −0.0745642 + 0.0745642i
\(630\) −207051. 55479.1i −0.521670 0.139781i
\(631\) −79353.2 + 296150.i −0.199299 + 0.743795i 0.791813 + 0.610764i \(0.209138\pi\)
−0.991112 + 0.133031i \(0.957529\pi\)
\(632\) −240191. 240191.i −0.601344 0.601344i
\(633\) 42418.8 + 73471.4i 0.105865 + 0.183363i
\(634\) −79788.5 46065.9i −0.198501 0.114604i
\(635\) −28291.5 + 7580.70i −0.0701632 + 0.0188002i
\(636\) 18344.0i 0.0453502i
\(637\) 710308. + 668409.i 1.75052 + 1.64727i
\(638\) −237122. −0.582546
\(639\) −94149.6 351371.i −0.230577 0.860526i
\(640\) −68024.8 + 117822.i −0.166076 + 0.287652i
\(641\) 98429.5 56828.3i 0.239557 0.138308i −0.375416 0.926856i \(-0.622500\pi\)
0.614973 + 0.788548i \(0.289167\pi\)
\(642\) 93038.2 93038.2i 0.225731 0.225731i
\(643\) −14225.1 3811.61i −0.0344060 0.00921906i 0.241575 0.970382i \(-0.422336\pi\)
−0.275981 + 0.961163i \(0.589003\pi\)
\(644\) −228338. + 852170.i −0.550563 + 2.05473i
\(645\) −1285.97 1285.97i −0.00309108 0.00309108i
\(646\) −9924.32 17189.4i −0.0237813 0.0411904i
\(647\) −213468. 123246.i −0.509946 0.294417i 0.222866 0.974849i \(-0.428459\pi\)
−0.732811 + 0.680432i \(0.761792\pi\)
\(648\) 3082.63 825.989i 0.00734128 0.00196709i
\(649\) 235022.i 0.557980i
\(650\) 591468. 17974.5i 1.39993 0.0425432i
\(651\) −421191. −0.993843
\(652\) −40784.5 152210.i −0.0959401 0.358053i
\(653\) 114446. 198226.i 0.268394 0.464872i −0.700053 0.714091i \(-0.746840\pi\)
0.968447 + 0.249219i \(0.0801738\pi\)
\(654\) 345386. 199409.i 0.807513 0.466218i
\(655\) 99872.3 99872.3i 0.232789 0.232789i
\(656\) 153157. + 41038.4i 0.355902 + 0.0953636i
\(657\) 71327.8 266199.i 0.165245 0.616703i
\(658\) 1.31794e6 + 1.31794e6i 3.04399 + 3.04399i
\(659\) −139582. 241763.i −0.321409 0.556697i 0.659370 0.751819i \(-0.270823\pi\)
−0.980779 + 0.195122i \(0.937490\pi\)
\(660\) 109104. + 62991.4i 0.250469 + 0.144608i
\(661\) 85509.9 22912.3i 0.195710 0.0524404i −0.159632 0.987177i \(-0.551031\pi\)
0.355343 + 0.934736i \(0.384364\pi\)
\(662\) 290178.i 0.662138i
\(663\) −24072.2 + 102156.i −0.0547631 + 0.232401i
\(664\) 116452. 0.264125
\(665\) −5083.66 18972.5i −0.0114956 0.0429023i
\(666\) 57834.6 100172.i 0.130388 0.225839i
\(667\) 108141. 62435.3i 0.243074 0.140339i
\(668\) −482197. + 482197.i −1.08062 + 1.08062i
\(669\) −7420.00 1988.18i −0.0165787 0.00444226i
\(670\) −67772.2 + 252929.i −0.150974 + 0.563443i
\(671\) −205196. 205196.i −0.455748 0.455748i
\(672\) 336867. + 583470.i 0.745967 + 1.29205i
\(673\) 130883. + 75565.6i 0.288971 + 0.166838i 0.637478 0.770469i \(-0.279978\pi\)
−0.348507 + 0.937306i \(0.613311\pi\)
\(674\) −51232.1 + 13727.6i −0.112777 + 0.0302186i
\(675\) 411827.i 0.903873i
\(676\) −630237. + 38340.7i −1.37915 + 0.0839010i
\(677\) 752917. 1.64274 0.821372 0.570393i \(-0.193209\pi\)
0.821372 + 0.570393i \(0.193209\pi\)
\(678\) 74529.9 + 278149.i 0.162133 + 0.605088i
\(679\) 320074. 554385.i 0.694243 1.20246i
\(680\) 27922.9 16121.3i 0.0603869 0.0348644i
\(681\) 309628. 309628.i 0.667645 0.667645i
\(682\) −683411. 183120.i −1.46931 0.393700i
\(683\) −145592. + 543357.i −0.312102 + 1.16478i 0.614555 + 0.788874i \(0.289335\pi\)
−0.926657 + 0.375907i \(0.877331\pi\)
\(684\) 22574.2 + 22574.2i 0.0482504 + 0.0482504i
\(685\) −113878. 197242.i −0.242694 0.420358i
\(686\) −1.62883e6 940404.i −3.46120 1.99833i
\(687\) −370365. + 99238.9i −0.784723 + 0.210266i
\(688\) 5243.21i 0.0110770i
\(689\) 24726.1 + 5826.47i 0.0520854 + 0.0122735i
\(690\) −114360. −0.240202
\(691\) −103894. 387737.i −0.217588 0.812048i −0.985240 0.171181i \(-0.945242\pi\)
0.767652 0.640867i \(-0.221425\pi\)
\(692\) 602169. 1.04299e6i 1.25749 2.17804i
\(693\) −537170. + 310135.i −1.11852 + 0.645780i
\(694\) 752816. 752816.i 1.56304 1.56304i
\(695\) 111566. + 29894.0i 0.230973 + 0.0618892i
\(696\) −15236.2 + 56862.3i −0.0314528 + 0.117383i
\(697\) −104253. 104253.i −0.214597 0.214597i
\(698\) 405105. + 701662.i 0.831489 + 1.44018i
\(699\) −433338. 250188.i −0.886894 0.512049i
\(700\) −1.09494e6 + 293388.i −2.23457 + 0.598752i
\(701\) 465668.i 0.947634i −0.880623 0.473817i \(-0.842876\pi\)
0.880623 0.473817i \(-0.157124\pi\)
\(702\) −23008.5 757116.i −0.0466889 1.53634i
\(703\) 10599.0 0.0214464
\(704\) 224879. + 839259.i 0.453736 + 1.69336i
\(705\) −70080.7 + 121383.i −0.141000 + 0.244220i
\(706\) 235147. 135762.i 0.471770 0.272377i
\(707\) 247598. 247598.i 0.495346 0.495346i
\(708\) −204012. 54664.9i −0.406995 0.109054i
\(709\) −198348. + 740245.i −0.394581 + 1.47259i 0.427913 + 0.903820i \(0.359249\pi\)
−0.822493 + 0.568775i \(0.807418\pi\)
\(710\) 238903. + 238903.i 0.473921 + 0.473921i
\(711\) 227628. + 394262.i 0.450283 + 0.779913i
\(712\) −45595.1 26324.4i −0.0899412 0.0519276i
\(713\) 359891. 96432.5i 0.707932 0.189690i
\(714\) 346568.i 0.679817i
\(715\) −119561. + 127056.i −0.233872 + 0.248532i
\(716\) 323140. 0.630326
\(717\) −108323. 404268.i −0.210709 0.786378i
\(718\) 68494.5 118636.i 0.132864 0.230127i
\(719\) −579881. + 334794.i −1.12171 + 0.647620i −0.941837 0.336070i \(-0.890902\pi\)
−0.179874 + 0.983690i \(0.557569\pi\)
\(720\) 32861.6 32861.6i 0.0633904 0.0633904i
\(721\) −294531. 78919.4i −0.566579 0.151814i
\(722\) 206911. 772201.i 0.396925 1.48134i
\(723\) 101247. + 101247.i 0.193690 + 0.193690i
\(724\) −172840. 299368.i −0.329736 0.571120i
\(725\) 138949. + 80222.2i 0.264350 + 0.152622i
\(726\) 125063. 33510.6i 0.237277 0.0635783i
\(727\) 852719.i 1.61338i 0.590974 + 0.806690i \(0.298743\pi\)
−0.590974 + 0.806690i \(0.701257\pi\)
\(728\) 551559. 165902.i 1.04071 0.313033i
\(729\) 320373. 0.602839
\(730\) 66248.2 + 247242.i 0.124316 + 0.463955i
\(731\) −2437.68 + 4222.19i −0.00456186 + 0.00790137i
\(732\) −225850. + 130394.i −0.421500 + 0.243353i
\(733\) 195353. 195353.i 0.363590 0.363590i −0.501543 0.865133i \(-0.667234\pi\)
0.865133 + 0.501543i \(0.167234\pi\)
\(734\) 1.20429e6 + 322689.i 2.23532 + 0.598953i
\(735\) 62684.9 233943.i 0.116035 0.433048i
\(736\) −421425. 421425.i −0.777974 0.777974i
\(737\) 378855. + 656197.i 0.697491 + 1.20809i
\(738\) 354002. + 204383.i 0.649969 + 0.375260i
\(739\) 341809. 91587.4i 0.625885 0.167705i 0.0680832 0.997680i \(-0.478312\pi\)
0.557802 + 0.829974i \(0.311645\pi\)
\(740\) 62324.5i 0.113814i
\(741\) 22675.7 14027.0i 0.0412975 0.0255464i
\(742\) −83883.8 −0.152360
\(743\) −107468. 401075.i −0.194671 0.726520i −0.992352 0.123441i \(-0.960607\pi\)
0.797681 0.603079i \(-0.206060\pi\)
\(744\) −87824.9 + 152117.i −0.158662 + 0.274810i
\(745\) 146618. 84650.1i 0.264165 0.152516i
\(746\) −1.08978e6 + 1.08978e6i −1.95821 + 1.95821i
\(747\) −150755. 40394.7i −0.270166 0.0723908i
\(748\) 87411.7 326225.i 0.156231 0.583061i
\(749\) −246815. 246815.i −0.439955 0.439955i
\(750\) −154425. 267472.i −0.274534 0.475506i
\(751\) 163029. + 94124.8i 0.289058 + 0.166888i 0.637517 0.770436i \(-0.279962\pi\)
−0.348459 + 0.937324i \(0.613295\pi\)
\(752\) −390323. + 104587.i −0.690222 + 0.184944i
\(753\) 369587.i 0.651819i
\(754\) −259930. 139720.i −0.457208 0.245763i
\(755\) 111253. 0.195172
\(756\) 375555. + 1.40159e6i 0.657098 + 2.45232i
\(757\) −399242. + 691507.i −0.696698 + 1.20672i 0.272908 + 0.962040i \(0.412015\pi\)
−0.969605 + 0.244675i \(0.921319\pi\)
\(758\) −393124. + 226970.i −0.684213 + 0.395031i
\(759\) −233995. + 233995.i −0.406185 + 0.406185i
\(760\) −7912.10 2120.04i −0.0136982 0.00367043i
\(761\) 24628.2 91913.9i 0.0425269 0.158713i −0.941397 0.337300i \(-0.890486\pi\)
0.983924 + 0.178588i \(0.0571528\pi\)
\(762\) 92837.7 + 92837.7i 0.159887 + 0.159887i
\(763\) −529000. 916255.i −0.908671 1.57386i
\(764\) 398821. + 230259.i 0.683268 + 0.394485i
\(765\) −41740.4 + 11184.3i −0.0713237 + 0.0191111i
\(766\) 621370.i 1.05899i
\(767\) 138482. 257628.i 0.235399 0.437927i
\(768\) 44726.3 0.0758300
\(769\) 110548. + 412572.i 0.186939 + 0.697666i 0.994207 + 0.107481i \(0.0342784\pi\)
−0.807268 + 0.590185i \(0.799055\pi\)
\(770\) 288049. 498916.i 0.485831 0.841484i
\(771\) −177772. + 102637.i −0.299058 + 0.172661i
\(772\) 766543. 766543.i 1.28618 1.28618i
\(773\) −931158. 249503.i −1.55835 0.417558i −0.626208 0.779656i \(-0.715394\pi\)
−0.932140 + 0.362097i \(0.882061\pi\)
\(774\) 3498.44 13056.3i 0.00583972 0.0217941i
\(775\) 338514. + 338514.i 0.563602 + 0.563602i
\(776\) −133481. 231196.i −0.221664 0.383934i
\(777\) 160270. + 92532.0i 0.265467 + 0.153267i
\(778\) −1.27607e6 + 341923.i −2.10822 + 0.564897i
\(779\) 37456.0i 0.0617229i
\(780\) 82482.2 + 133338.i 0.135572 + 0.219162i
\(781\) 977654. 1.60281
\(782\) 79347.3 + 296128.i 0.129753 + 0.484246i
\(783\) 102689. 177863.i 0.167495 0.290110i
\(784\) 604714. 349132.i 0.983825 0.568012i
\(785\) −119573. + 119573.i −0.194041 + 0.194041i
\(786\) −611547. 163864.i −0.989885 0.265239i
\(787\) −179306. + 669180.i −0.289498 + 1.08042i 0.655991 + 0.754769i \(0.272251\pi\)
−0.945489 + 0.325653i \(0.894416\pi\)
\(788\) −996279. 996279.i −1.60446 1.60446i
\(789\) −60175.8 104227.i −0.0966646 0.167428i
\(790\) −366185. 211417.i −0.586741 0.338755i
\(791\) 737885. 197716.i 1.17933 0.316001i
\(792\) 258672.i 0.412381i
\(793\) −104025. 345842.i −0.165422 0.549960i
\(794\) 843260. 1.33758
\(795\) −1632.65 6093.12i −0.00258320 0.00964063i
\(796\) −273041. + 472920.i −0.430924 + 0.746383i
\(797\) 806320. 465529.i 1.26938 0.732875i 0.294507 0.955649i \(-0.404845\pi\)
0.974870 + 0.222774i \(0.0715112\pi\)
\(798\) −62257.4 + 62257.4i −0.0977655 + 0.0977655i
\(799\) 362939. + 97249.2i 0.568513 + 0.152333i
\(800\) 198197. 739680.i 0.309682 1.15575i
\(801\) 49894.8 + 49894.8i 0.0777661 + 0.0777661i
\(802\) −632161. 1.09494e6i −0.982832 1.70231i
\(803\) 641441. + 370336.i 0.994777 + 0.574334i
\(804\) 657736. 176240.i 1.01751 0.272642i
\(805\) 303379.i 0.468159i
\(806\) −641247. 603422.i −0.987086 0.928861i
\(807\) 595622. 0.914584
\(808\) −37794.4 141051.i −0.0578901 0.216049i
\(809\) 26946.9 46673.5i 0.0411730 0.0713137i −0.844705 0.535233i \(-0.820224\pi\)
0.885878 + 0.463919i \(0.153557\pi\)
\(810\) 3440.38 1986.30i 0.00524368 0.00302744i
\(811\) −867670. + 867670.i −1.31921 + 1.31921i −0.404803 + 0.914404i \(0.632660\pi\)
−0.914404 + 0.404803i \(0.867340\pi\)
\(812\) 546048. + 146313.i 0.828169 + 0.221907i
\(813\) 62781.4 234303.i 0.0949838 0.354485i
\(814\) 219819. + 219819.i 0.331755 + 0.331755i
\(815\) −27093.9 46928.0i −0.0407903 0.0706508i
\(816\) 65071.2 + 37568.9i 0.0977257 + 0.0564219i
\(817\) 1196.38 320.569i 0.00179236 0.000480260i
\(818\) 974901.i 1.45698i
\(819\) −771581. + 23448.1i −1.15031 + 0.0349574i
\(820\) −220250. −0.327558
\(821\) −277240. 1.03468e6i −0.411311 1.53503i −0.792112 0.610376i \(-0.791018\pi\)
0.380801 0.924657i \(-0.375648\pi\)
\(822\) −510465. + 884151.i −0.755478 + 1.30853i
\(823\) 948821. 547802.i 1.40083 0.808768i 0.406350 0.913718i \(-0.366801\pi\)
0.994478 + 0.104950i \(0.0334682\pi\)
\(824\) −89916.7 + 89916.7i −0.132430 + 0.132430i
\(825\) −410705. 110048.i −0.603424 0.161687i
\(826\) −249973. + 932913.i −0.366381 + 1.36735i
\(827\) −118484. 118484.i −0.173240 0.173240i 0.615161 0.788401i \(-0.289091\pi\)
−0.788401 + 0.615161i \(0.789091\pi\)
\(828\) −246549. 427035.i −0.359619 0.622878i
\(829\) −598258. 345405.i −0.870522 0.502596i −0.00300029 0.999995i \(-0.500955\pi\)
−0.867522 + 0.497399i \(0.834288\pi\)
\(830\) 140019. 37518.0i 0.203250 0.0544608i
\(831\) 6914.49i 0.0100129i
\(832\) −248010. + 1.05249e6i −0.358279 + 1.52045i
\(833\) −649275. −0.935705
\(834\) −134002. 500101.i −0.192654 0.718995i
\(835\) −117250. + 203083.i −0.168166 + 0.291273i
\(836\) −74305.7 + 42900.4i −0.106319 + 0.0613831i
\(837\) 433318. 433318.i 0.618523 0.618523i
\(838\) 1.17513e6 + 314875.i 1.67339 + 0.448384i
\(839\) 43984.2 164151.i 0.0624845 0.233195i −0.927620 0.373524i \(-0.878149\pi\)
0.990105 + 0.140329i \(0.0448160\pi\)
\(840\) −101132. 101132.i −0.143328 0.143328i
\(841\) 313634. + 543229.i 0.443436 + 0.768053i
\(842\) 815994. + 471114.i 1.15097 + 0.664511i
\(843\) 564844. 151349.i 0.794828 0.212974i
\(844\) 339752.i 0.476955i
\(845\) −205927. + 68827.4i −0.288402 + 0.0963936i
\(846\) −1.04174e6 −1.45553
\(847\) −88898.2 331773.i −0.123916 0.462459i
\(848\) 9093.23 15749.9i 0.0126452 0.0219022i
\(849\) −204521. + 118080.i −0.283741 + 0.163818i
\(850\) −278538. + 278538.i −0.385520 + 0.385520i
\(851\) −158130. 42370.7i −0.218350 0.0585068i
\(852\) 227398. 848660.i 0.313261 1.16911i
\(853\) −621614. 621614.i −0.854324 0.854324i 0.136338 0.990662i \(-0.456467\pi\)
−0.990662 + 0.136338i \(0.956467\pi\)
\(854\) 596271. + 1.03277e6i 0.817576 + 1.41608i
\(855\) 9507.39 + 5489.09i 0.0130056 + 0.00750876i
\(856\) −140604. + 37674.9i −0.191890 + 0.0514167i
\(857\) 433050.i 0.589626i 0.955555 + 0.294813i \(0.0952574\pi\)
−0.955555 + 0.294813i \(0.904743\pi\)
\(858\) 761201. + 179370.i 1.03401 + 0.243655i
\(859\) 264929. 0.359040 0.179520 0.983754i \(-0.442546\pi\)
0.179520 + 0.983754i \(0.442546\pi\)
\(860\) 1885.02 + 7034.98i 0.00254870 + 0.00951188i
\(861\) −327001. + 566382.i −0.441106 + 0.764017i
\(862\) −670878. + 387332.i −0.902878 + 0.521277i
\(863\) 344574. 344574.i 0.462659 0.462659i −0.436867 0.899526i \(-0.643912\pi\)
0.899526 + 0.436867i \(0.143912\pi\)
\(864\) −946835. 253704.i −1.26837 0.339859i
\(865\) 107188. 400032.i 0.143257 0.534641i
\(866\) 1.15383e6 + 1.15383e6i 1.53853 + 1.53853i
\(867\) 195595. + 338780.i 0.260207 + 0.450692i
\(868\) 1.46078e6 + 843381.i 1.93885 + 1.11940i
\(869\) −1.18185e6 + 316675.i −1.56503 + 0.419348i
\(870\) 73278.8i 0.0968144i
\(871\) 28643.7 + 942548.i 0.0377566 + 1.24242i
\(872\) −441219. −0.580258
\(873\) 92603.6 + 345601.i 0.121506 + 0.453468i
\(874\) 38942.5 67450.4i 0.0509801 0.0883002i
\(875\) −709561. + 409665.i −0.926774 + 0.535073i
\(876\) 470669. 470669.i 0.613348 0.613348i
\(877\) 910707. + 244023.i 1.18408 + 0.317272i 0.796542 0.604583i \(-0.206660\pi\)
0.387534 + 0.921855i \(0.373327\pi\)
\(878\) 383463. 1.43110e6i 0.497433 1.85644i
\(879\) −124255. 124255.i −0.160818 0.160818i
\(880\) 62450.6 + 108168.i 0.0806438 + 0.139679i
\(881\) −896268. 517461.i −1.15475 0.666692i −0.204706 0.978823i \(-0.565624\pi\)
−0.950039 + 0.312131i \(0.898957\pi\)
\(882\) 1.73878e6 465904.i 2.23515 0.598907i
\(883\) 200330.i 0.256936i −0.991714 0.128468i \(-0.958994\pi\)
0.991714 0.128468i \(-0.0410059\pi\)
\(884\) 288042. 306098.i 0.368596 0.391702i
\(885\) −72629.8 −0.0927317
\(886\) 90247.5 + 336808.i 0.114966 + 0.429057i
\(887\) 661285. 1.14538e6i 0.840507 1.45580i −0.0489590 0.998801i \(-0.515590\pi\)
0.889466 0.457001i \(-0.151076\pi\)
\(888\) 66837.6 38588.7i 0.0847608 0.0489366i
\(889\) 246283. 246283.i 0.311625 0.311625i
\(890\) −63303.7 16962.2i −0.0799189 0.0214142i
\(891\) 2975.23 11103.7i 0.00374770 0.0139866i
\(892\) 21753.0 + 21753.0i 0.0273394 + 0.0273394i
\(893\) −47728.5 82668.2i −0.0598515 0.103666i
\(894\) −657225. 379449.i −0.822317 0.474765i
\(895\) 107334. 28760.1i 0.133996 0.0359041i
\(896\) 1.61784e6i 2.01520i
\(897\) −394380. + 118625.i −0.490151 + 0.147432i
\(898\) −825892. −1.02417
\(899\) −61791.4 230609.i −0.0764554 0.285336i
\(900\) 316787. 548691.i 0.391095 0.677397i
\(901\) −14645.0 + 8455.27i −0.0180401 + 0.0104154i
\(902\) −776824. + 776824.i −0.954794 + 0.954794i
\(903\) 20889.4 + 5597.30i 0.0256183 + 0.00686441i
\(904\) 82453.6 307721.i 0.100896 0.376548i
\(905\) −84054.6 84054.6i −0.102628 0.102628i
\(906\) −249349. 431885.i −0.303775 0.526153i
\(907\) −1.13720e6 656563.i −1.38236 0.798108i −0.389925 0.920847i \(-0.627499\pi\)
−0.992439 + 0.122738i \(0.960832\pi\)
\(908\) −1.69384e6 + 453864.i −2.05448 + 0.550496i
\(909\) 195710.i 0.236857i
\(910\) 609733. 377177.i 0.736304 0.455473i
\(911\) −773793. −0.932370 −0.466185 0.884687i \(-0.654372\pi\)
−0.466185 + 0.884687i \(0.654372\pi\)
\(912\) −4940.52 18438.3i −0.00593995 0.0221682i
\(913\) 209731. 363264.i 0.251605 0.435793i
\(914\) −951179. + 549164.i −1.13860 + 0.657369i
\(915\) −63412.8 + 63412.8i −0.0757416 + 0.0757416i
\(916\) 1.48321e6 + 397426.i 1.76772 + 0.473659i
\(917\) −434704. + 1.62234e6i −0.516957 + 1.92931i
\(918\) 356546. + 356546.i 0.423088 + 0.423088i
\(919\) 6404.07 + 11092.2i 0.00758272 + 0.0131337i 0.869792 0.493419i \(-0.164253\pi\)
−0.862209 + 0.506552i \(0.830920\pi\)
\(920\) 109568. + 63259.1i 0.129452 + 0.0747390i
\(921\) 634404. 169988.i 0.747906 0.200401i
\(922\) 1.94166e6i 2.28408i
\(923\) 1.07169e6 + 576066.i 1.25796 + 0.676190i
\(924\) −1.49813e6 −1.75471
\(925\) −54441.5 203178.i −0.0636277 0.237462i
\(926\) −1.04109e6 + 1.80323e6i −1.21414 + 2.10295i
\(927\) 147594. 85213.4i 0.171755 0.0991627i
\(928\) −270038. + 270038.i −0.313566 + 0.313566i
\(929\) −552161. 147951.i −0.639786 0.171430i −0.0756793 0.997132i \(-0.524113\pi\)
−0.564106 + 0.825702i \(0.690779\pi\)
\(930\) −56590.2 + 211198.i −0.0654298 + 0.244187i
\(931\) 116636. + 116636.i 0.134565 + 0.134565i
\(932\) 1.00194e6 + 1.73540e6i 1.15347 + 1.99788i
\(933\) −66386.4 38328.2i −0.0762634 0.0440307i
\(934\) 1.79448e6 480829.i 2.05705 0.551184i
\(935\) 116138.i 0.132847i
\(936\) −152418. + 283553.i −0.173974 + 0.323655i
\(937\) −763773. −0.869931 −0.434966 0.900447i \(-0.643239\pi\)
−0.434966 + 0.900447i \(0.643239\pi\)
\(938\) −805915. 3.00771e6i −0.915975 3.41846i
\(939\) 174606. 302427.i 0.198029 0.342996i
\(940\) 486108. 280655.i 0.550145 0.317627i
\(941\) 408742. 408742.i 0.461604 0.461604i −0.437577 0.899181i \(-0.644163\pi\)
0.899181 + 0.437577i \(0.144163\pi\)
\(942\) 732181. + 196187.i 0.825119 + 0.221090i
\(943\) 149735. 558818.i 0.168383 0.628415i
\(944\) −148065. 148065.i −0.166153 0.166153i
\(945\) 249488. + 432126.i 0.279374 + 0.483890i
\(946\) 31460.9 + 18164.0i 0.0351552 + 0.0202969i
\(947\) 70724.2 18950.5i 0.0788620 0.0211310i −0.219172 0.975686i \(-0.570336\pi\)
0.298034 + 0.954555i \(0.403669\pi\)
\(948\) 1.09957e6i 1.22350i
\(949\) 484925. + 783915.i 0.538446 + 0.870436i
\(950\) 100073. 0.110884
\(951\) 21323.6 + 79580.8i 0.0235776 + 0.0879928i
\(952\) −191707. + 332046.i −0.211526 + 0.366374i
\(953\) 896707. 517714.i 0.987335 0.570038i 0.0828585 0.996561i \(-0.473595\pi\)
0.904477 + 0.426523i \(0.140262\pi\)
\(954\) 33152.3 33152.3i 0.0364265 0.0364265i
\(955\) 152966. + 40987.0i 0.167721 + 0.0449406i
\(956\) −433807. + 1.61899e6i −0.474658 + 1.77145i
\(957\) 149938. + 149938.i 0.163715 + 0.163715i
\(958\) −661356. 1.14550e6i −0.720617 1.24815i
\(959\) 2.34551e6 + 1.35418e6i 2.55035 + 1.47245i
\(960\) 259360. 69495.3i 0.281424 0.0754072i
\(961\) 211163.i 0.228650i
\(962\) 111438. + 370488.i 0.120416 + 0.400335i
\(963\) 195091. 0.210371
\(964\) −148412. 553881.i −0.159704 0.596022i
\(965\) 186391. 322838.i 0.200156 0.346681i
\(966\) 1.17772e6 679957.i 1.26208 0.728664i
\(967\) −191562. + 191562.i −0.204860 + 0.204860i −0.802078 0.597219i \(-0.796272\pi\)
0.597219 + 0.802078i \(0.296272\pi\)
\(968\) −138359. 37073.3i −0.147658 0.0395649i
\(969\) −4593.90 + 17144.7i −0.00489254 + 0.0182592i
\(970\) −234980. 234980.i −0.249740 0.249740i
\(971\) 544139. + 942477.i 0.577127 + 0.999614i 0.995807 + 0.0914796i \(0.0291596\pi\)
−0.418680 + 0.908134i \(0.637507\pi\)
\(972\) −1.13490e6 655235.i −1.20123 0.693529i
\(973\) −1.32669e6 + 355485.i −1.40134 + 0.375488i
\(974\) 355968.i 0.375226i
\(975\) −385366. 362634.i −0.405381 0.381469i
\(976\) −258550. −0.271421
\(977\) −1357.53 5066.37i −0.00142220 0.00530771i 0.965211 0.261472i \(-0.0842079\pi\)
−0.966633 + 0.256164i \(0.917541\pi\)
\(978\) −121450. + 210358.i −0.126976 + 0.219928i
\(979\) −164234. + 94820.8i −0.171356 + 0.0989323i
\(980\) −685846. + 685846.i −0.714125 + 0.714125i
\(981\) 571189. + 153050.i 0.593529 + 0.159036i
\(982\) −626028. + 2.33637e6i −0.649189 + 2.42280i
\(983\) 779317. + 779317.i 0.806505 + 0.806505i 0.984103 0.177598i \(-0.0568326\pi\)
−0.177598 + 0.984103i \(0.556833\pi\)
\(984\) 136369. + 236199.i 0.140840 + 0.243943i
\(985\) −419594. 242253.i −0.432471 0.249687i
\(986\) 189751. 50843.6i 0.195178 0.0522977i
\(987\) 1.66673e6i 1.71093i
\(988\) −106731. + 3243.52i −0.109340 + 0.00332279i
\(989\) −19130.7 −0.0195586
\(990\) 83338.1 + 311022.i 0.0850302 + 0.317337i
\(991\) −67246.2 + 116474.i −0.0684732 + 0.118599i −0.898229 0.439527i \(-0.855146\pi\)
0.829756 + 0.558126i \(0.188479\pi\)
\(992\) −986819. + 569740.i −1.00280 + 0.578967i
\(993\) −183487. + 183487.i −0.186083 + 0.186083i
\(994\) −3.88077e6 1.03985e6i −3.92777 1.05244i
\(995\) −48602.2 + 181386.i −0.0490919 + 0.183213i
\(996\) −266551. 266551.i −0.268697 0.268697i
\(997\) −949605. 1.64476e6i −0.955329 1.65468i −0.733614 0.679567i \(-0.762168\pi\)
−0.221715 0.975112i \(-0.571165\pi\)
\(998\) −372403. 215007.i −0.373897 0.215870i
\(999\) −260081. + 69688.4i −0.260602 + 0.0698280i
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 13.5.f.a.6.4 16
3.2 odd 2 117.5.bd.c.19.1 16
13.4 even 6 169.5.d.c.70.2 16
13.6 odd 12 169.5.d.c.99.2 16
13.7 odd 12 169.5.d.d.99.7 16
13.9 even 3 169.5.d.d.70.7 16
13.11 odd 12 inner 13.5.f.a.11.4 yes 16
39.11 even 12 117.5.bd.c.37.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.5.f.a.6.4 16 1.1 even 1 trivial
13.5.f.a.11.4 yes 16 13.11 odd 12 inner
117.5.bd.c.19.1 16 3.2 odd 2
117.5.bd.c.37.1 16 39.11 even 12
169.5.d.c.70.2 16 13.4 even 6
169.5.d.c.99.2 16 13.6 odd 12
169.5.d.d.70.7 16 13.9 even 3
169.5.d.d.99.7 16 13.7 odd 12