Properties

Label 48.4.j.a.13.10
Level $48$
Weight $4$
Character 48.13
Analytic conductor $2.832$
Analytic rank $0$
Dimension $24$
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] = [48,4,Mod(13,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.13");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 48.j (of order \(4\), 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: \(2.83209168028\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.10
Character \(\chi\) \(=\) 48.13
Dual form 48.4.j.a.37.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.07099 + 1.92640i) q^{2} +(2.12132 + 2.12132i) q^{3} +(0.577966 + 7.97909i) q^{4} +(0.644922 - 0.644922i) q^{5} +(0.306713 + 8.47974i) q^{6} -7.13926i q^{7} +(-14.1740 + 17.6380i) q^{8} +9.00000i q^{9} +O(q^{10})\) \(q+(2.07099 + 1.92640i) q^{2} +(2.12132 + 2.12132i) q^{3} +(0.577966 + 7.97909i) q^{4} +(0.644922 - 0.644922i) q^{5} +(0.306713 + 8.47974i) q^{6} -7.13926i q^{7} +(-14.1740 + 17.6380i) q^{8} +9.00000i q^{9} +(2.57800 - 0.0932465i) q^{10} +(25.4455 - 25.4455i) q^{11} +(-15.7002 + 18.1523i) q^{12} +(-14.6030 - 14.6030i) q^{13} +(13.7531 - 14.7853i) q^{14} +2.73617 q^{15} +(-63.3319 + 9.22328i) q^{16} +71.4024 q^{17} +(-17.3376 + 18.6389i) q^{18} +(-43.6238 - 43.6238i) q^{19} +(5.51863 + 4.77315i) q^{20} +(15.1447 - 15.1447i) q^{21} +(101.715 - 3.67906i) q^{22} -211.845i q^{23} +(-67.4834 + 7.34829i) q^{24} +124.168i q^{25} +(-2.11138 - 58.3737i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(56.9649 - 4.12625i) q^{28} +(5.84463 + 5.84463i) q^{29} +(5.66657 + 5.27096i) q^{30} -107.807 q^{31} +(-148.927 - 102.901i) q^{32} +107.956 q^{33} +(147.873 + 137.550i) q^{34} +(-4.60426 - 4.60426i) q^{35} +(-71.8119 + 5.20169i) q^{36} +(-184.865 + 184.865i) q^{37} +(-6.30739 - 174.381i) q^{38} -61.9551i q^{39} +(2.23402 + 20.5162i) q^{40} +360.146i q^{41} +(60.5391 - 2.18970i) q^{42} +(-312.475 + 312.475i) q^{43} +(217.739 + 188.325i) q^{44} +(5.80429 + 5.80429i) q^{45} +(408.099 - 438.729i) q^{46} +343.892 q^{47} +(-153.913 - 114.782i) q^{48} +292.031 q^{49} +(-239.198 + 257.150i) q^{50} +(151.467 + 151.467i) q^{51} +(108.078 - 124.958i) q^{52} +(-249.900 + 249.900i) q^{53} +(-76.3176 + 2.76042i) q^{54} -32.8207i q^{55} +(125.922 + 101.192i) q^{56} -185.080i q^{57} +(0.845051 + 23.3632i) q^{58} +(-152.755 + 152.755i) q^{59} +(1.58141 + 21.8322i) q^{60} +(-525.985 - 525.985i) q^{61} +(-223.267 - 207.680i) q^{62} +64.2534 q^{63} +(-110.197 - 500.001i) q^{64} -18.8355 q^{65} +(223.576 + 207.967i) q^{66} +(-35.3052 - 35.3052i) q^{67} +(41.2681 + 569.727i) q^{68} +(449.392 - 449.392i) q^{69} +(-0.665712 - 18.4050i) q^{70} -784.715i q^{71} +(-158.742 - 127.566i) q^{72} -800.215i q^{73} +(-738.977 + 26.7289i) q^{74} +(-263.400 + 263.400i) q^{75} +(322.866 - 373.292i) q^{76} +(-181.662 - 181.662i) q^{77} +(119.350 - 128.308i) q^{78} +548.062 q^{79} +(-34.8958 + 46.7924i) q^{80} -81.0000 q^{81} +(-693.784 + 745.856i) q^{82} +(464.431 + 464.431i) q^{83} +(129.594 + 112.088i) q^{84} +(46.0489 - 46.0489i) q^{85} +(-1249.08 + 45.1794i) q^{86} +24.7967i q^{87} +(88.1436 + 809.471i) q^{88} +302.977i q^{89} +(0.839219 + 23.2020i) q^{90} +(-104.254 + 104.254i) q^{91} +(1690.33 - 122.439i) q^{92} +(-228.693 - 228.693i) q^{93} +(712.195 + 662.473i) q^{94} -56.2679 q^{95} +(-97.6357 - 534.209i) q^{96} +1567.24 q^{97} +(604.792 + 562.568i) q^{98} +(229.009 + 229.009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.07099 + 1.92640i 0.732204 + 0.681085i
\(3\) 2.12132 + 2.12132i 0.408248 + 0.408248i
\(4\) 0.577966 + 7.97909i 0.0722457 + 0.997387i
\(5\) 0.644922 0.644922i 0.0576835 0.0576835i −0.677677 0.735360i \(-0.737013\pi\)
0.735360 + 0.677677i \(0.237013\pi\)
\(6\) 0.306713 + 8.47974i 0.0208692 + 0.576973i
\(7\) 7.13926i 0.385484i −0.981249 0.192742i \(-0.938262\pi\)
0.981249 0.192742i \(-0.0617380\pi\)
\(8\) −14.1740 + 17.6380i −0.626407 + 0.779496i
\(9\) 9.00000i 0.333333i
\(10\) 2.57800 0.0932465i 0.0815235 0.00294871i
\(11\) 25.4455 25.4455i 0.697464 0.697464i −0.266399 0.963863i \(-0.585834\pi\)
0.963863 + 0.266399i \(0.0858338\pi\)
\(12\) −15.7002 + 18.1523i −0.377687 + 0.436676i
\(13\) −14.6030 14.6030i −0.311549 0.311549i 0.533961 0.845509i \(-0.320703\pi\)
−0.845509 + 0.533961i \(0.820703\pi\)
\(14\) 13.7531 14.7853i 0.262547 0.282253i
\(15\) 2.73617 0.0470984
\(16\) −63.3319 + 9.22328i −0.989561 + 0.144114i
\(17\) 71.4024 1.01868 0.509342 0.860564i \(-0.329889\pi\)
0.509342 + 0.860564i \(0.329889\pi\)
\(18\) −17.3376 + 18.6389i −0.227028 + 0.244068i
\(19\) −43.6238 43.6238i −0.526736 0.526736i 0.392861 0.919598i \(-0.371485\pi\)
−0.919598 + 0.392861i \(0.871485\pi\)
\(20\) 5.51863 + 4.77315i 0.0617002 + 0.0533654i
\(21\) 15.1447 15.1447i 0.157373 0.157373i
\(22\) 101.715 3.67906i 0.985719 0.0356536i
\(23\) 211.845i 1.92056i −0.279045 0.960278i \(-0.590018\pi\)
0.279045 0.960278i \(-0.409982\pi\)
\(24\) −67.4834 + 7.34829i −0.573958 + 0.0624985i
\(25\) 124.168i 0.993345i
\(26\) −2.11138 58.3737i −0.0159260 0.440309i
\(27\) −19.0919 + 19.0919i −0.136083 + 0.136083i
\(28\) 56.9649 4.12625i 0.384477 0.0278496i
\(29\) 5.84463 + 5.84463i 0.0374248 + 0.0374248i 0.725572 0.688147i \(-0.241575\pi\)
−0.688147 + 0.725572i \(0.741575\pi\)
\(30\) 5.66657 + 5.27096i 0.0344856 + 0.0320780i
\(31\) −107.807 −0.624604 −0.312302 0.949983i \(-0.601100\pi\)
−0.312302 + 0.949983i \(0.601100\pi\)
\(32\) −148.927 102.901i −0.822715 0.568455i
\(33\) 107.956 0.569477
\(34\) 147.873 + 137.550i 0.745884 + 0.693811i
\(35\) −4.60426 4.60426i −0.0222361 0.0222361i
\(36\) −71.8119 + 5.20169i −0.332462 + 0.0240819i
\(37\) −184.865 + 184.865i −0.821395 + 0.821395i −0.986308 0.164913i \(-0.947266\pi\)
0.164913 + 0.986308i \(0.447266\pi\)
\(38\) −6.30739 174.381i −0.0269261 0.744431i
\(39\) 61.9551i 0.254379i
\(40\) 2.23402 + 20.5162i 0.00883073 + 0.0810975i
\(41\) 360.146i 1.37184i 0.727679 + 0.685918i \(0.240599\pi\)
−0.727679 + 0.685918i \(0.759401\pi\)
\(42\) 60.5391 2.18970i 0.222414 0.00804473i
\(43\) −312.475 + 312.475i −1.10818 + 1.10818i −0.114795 + 0.993389i \(0.536621\pi\)
−0.993389 + 0.114795i \(0.963379\pi\)
\(44\) 217.739 + 188.325i 0.746030 + 0.645253i
\(45\) 5.80429 + 5.80429i 0.0192278 + 0.0192278i
\(46\) 408.099 438.729i 1.30806 1.40624i
\(47\) 343.892 1.06727 0.533636 0.845715i \(-0.320825\pi\)
0.533636 + 0.845715i \(0.320825\pi\)
\(48\) −153.913 114.782i −0.462821 0.345152i
\(49\) 292.031 0.851402
\(50\) −239.198 + 257.150i −0.676553 + 0.727331i
\(51\) 151.467 + 151.467i 0.415876 + 0.415876i
\(52\) 108.078 124.958i 0.288227 0.333243i
\(53\) −249.900 + 249.900i −0.647667 + 0.647667i −0.952429 0.304762i \(-0.901423\pi\)
0.304762 + 0.952429i \(0.401423\pi\)
\(54\) −76.3176 + 2.76042i −0.192324 + 0.00695639i
\(55\) 32.8207i 0.0804644i
\(56\) 125.922 + 101.192i 0.300483 + 0.241470i
\(57\) 185.080i 0.430078i
\(58\) 0.845051 + 23.3632i 0.00191311 + 0.0528921i
\(59\) −152.755 + 152.755i −0.337067 + 0.337067i −0.855262 0.518195i \(-0.826604\pi\)
0.518195 + 0.855262i \(0.326604\pi\)
\(60\) 1.58141 + 21.8322i 0.00340266 + 0.0469753i
\(61\) −525.985 525.985i −1.10402 1.10402i −0.993920 0.110104i \(-0.964882\pi\)
−0.110104 0.993920i \(-0.535118\pi\)
\(62\) −223.267 207.680i −0.457338 0.425409i
\(63\) 64.2534 0.128495
\(64\) −110.197 500.001i −0.215229 0.976564i
\(65\) −18.8355 −0.0359425
\(66\) 223.576 + 207.967i 0.416973 + 0.387862i
\(67\) −35.3052 35.3052i −0.0643764 0.0643764i 0.674186 0.738562i \(-0.264495\pi\)
−0.738562 + 0.674186i \(0.764495\pi\)
\(68\) 41.2681 + 569.727i 0.0735955 + 1.01602i
\(69\) 449.392 449.392i 0.784064 0.784064i
\(70\) −0.665712 18.4050i −0.00113668 0.0314260i
\(71\) 784.715i 1.31167i −0.754905 0.655834i \(-0.772317\pi\)
0.754905 0.655834i \(-0.227683\pi\)
\(72\) −158.742 127.566i −0.259832 0.208802i
\(73\) 800.215i 1.28299i −0.767128 0.641494i \(-0.778315\pi\)
0.767128 0.641494i \(-0.221685\pi\)
\(74\) −738.977 + 26.7289i −1.16087 + 0.0419888i
\(75\) −263.400 + 263.400i −0.405531 + 0.405531i
\(76\) 322.866 373.292i 0.487306 0.563414i
\(77\) −181.662 181.662i −0.268861 0.268861i
\(78\) 119.350 128.308i 0.173253 0.186257i
\(79\) 548.062 0.780530 0.390265 0.920703i \(-0.372383\pi\)
0.390265 + 0.920703i \(0.372383\pi\)
\(80\) −34.8958 + 46.7924i −0.0487684 + 0.0653944i
\(81\) −81.0000 −0.111111
\(82\) −693.784 + 745.856i −0.934337 + 1.00446i
\(83\) 464.431 + 464.431i 0.614191 + 0.614191i 0.944035 0.329844i \(-0.106996\pi\)
−0.329844 + 0.944035i \(0.606996\pi\)
\(84\) 129.594 + 112.088i 0.168331 + 0.145592i
\(85\) 46.0489 46.0489i 0.0587613 0.0587613i
\(86\) −1249.08 + 45.1794i −1.56619 + 0.0566491i
\(87\) 24.7967i 0.0305573i
\(88\) 88.1436 + 809.471i 0.106774 + 0.980567i
\(89\) 302.977i 0.360849i 0.983589 + 0.180424i \(0.0577471\pi\)
−0.983589 + 0.180424i \(0.942253\pi\)
\(90\) 0.839219 + 23.2020i 0.000982905 + 0.0271745i
\(91\) −104.254 + 104.254i −0.120097 + 0.120097i
\(92\) 1690.33 122.439i 1.91554 0.138752i
\(93\) −228.693 228.693i −0.254994 0.254994i
\(94\) 712.195 + 662.473i 0.781460 + 0.726903i
\(95\) −56.2679 −0.0607680
\(96\) −97.6357 534.209i −0.103801 0.567942i
\(97\) 1567.24 1.64050 0.820252 0.572002i \(-0.193833\pi\)
0.820252 + 0.572002i \(0.193833\pi\)
\(98\) 604.792 + 562.568i 0.623400 + 0.579877i
\(99\) 229.009 + 229.009i 0.232488 + 0.232488i
\(100\) −990.749 + 71.7649i −0.990749 + 0.0717649i
\(101\) 59.6129 59.6129i 0.0587297 0.0587297i −0.677132 0.735862i \(-0.736777\pi\)
0.735862 + 0.677132i \(0.236777\pi\)
\(102\) 21.9000 + 605.474i 0.0212591 + 0.587753i
\(103\) 1762.59i 1.68615i 0.537795 + 0.843076i \(0.319257\pi\)
−0.537795 + 0.843076i \(0.680743\pi\)
\(104\) 464.549 50.5849i 0.438007 0.0476948i
\(105\) 19.5342i 0.0181557i
\(106\) −998.945 + 36.1319i −0.915341 + 0.0331080i
\(107\) 656.579 656.579i 0.593214 0.593214i −0.345284 0.938498i \(-0.612218\pi\)
0.938498 + 0.345284i \(0.112218\pi\)
\(108\) −163.370 141.301i −0.145559 0.125896i
\(109\) −327.776 327.776i −0.288030 0.288030i 0.548271 0.836301i \(-0.315286\pi\)
−0.836301 + 0.548271i \(0.815286\pi\)
\(110\) 63.2258 67.9712i 0.0548031 0.0589164i
\(111\) −784.316 −0.670667
\(112\) 65.8475 + 452.143i 0.0555536 + 0.381460i
\(113\) −1349.18 −1.12319 −0.561593 0.827414i \(-0.689811\pi\)
−0.561593 + 0.827414i \(0.689811\pi\)
\(114\) 356.539 383.299i 0.292920 0.314905i
\(115\) −136.624 136.624i −0.110784 0.110784i
\(116\) −43.2569 + 50.0128i −0.0346233 + 0.0400308i
\(117\) 131.427 131.427i 0.103850 0.103850i
\(118\) −610.620 + 22.0862i −0.476374 + 0.0172305i
\(119\) 509.761i 0.392686i
\(120\) −38.7824 + 48.2605i −0.0295028 + 0.0367130i
\(121\) 36.0534i 0.0270875i
\(122\) −76.0500 2102.56i −0.0564364 1.56031i
\(123\) −763.984 + 763.984i −0.560050 + 0.560050i
\(124\) −62.3088 860.203i −0.0451250 0.622972i
\(125\) 160.694 + 160.694i 0.114983 + 0.114983i
\(126\) 133.068 + 123.778i 0.0940843 + 0.0875158i
\(127\) 52.2111 0.0364802 0.0182401 0.999834i \(-0.494194\pi\)
0.0182401 + 0.999834i \(0.494194\pi\)
\(128\) 734.984 1247.78i 0.507532 0.861633i
\(129\) −1325.72 −0.904829
\(130\) −39.0081 36.2848i −0.0263172 0.0244799i
\(131\) −387.958 387.958i −0.258749 0.258749i 0.565796 0.824545i \(-0.308569\pi\)
−0.824545 + 0.565796i \(0.808569\pi\)
\(132\) 62.3949 + 861.392i 0.0411423 + 0.567989i
\(133\) −311.442 + 311.442i −0.203048 + 0.203048i
\(134\) −5.10463 141.128i −0.00329084 0.0909824i
\(135\) 24.6255i 0.0156995i
\(136\) −1012.06 + 1259.39i −0.638111 + 0.794060i
\(137\) 795.048i 0.495807i 0.968785 + 0.247903i \(0.0797415\pi\)
−0.968785 + 0.247903i \(0.920258\pi\)
\(138\) 1796.39 64.9757i 1.10811 0.0400804i
\(139\) 1708.70 1708.70i 1.04266 1.04266i 0.0436142 0.999048i \(-0.486113\pi\)
0.999048 0.0436142i \(-0.0138872\pi\)
\(140\) 34.0768 39.3990i 0.0205715 0.0237844i
\(141\) 729.504 + 729.504i 0.435712 + 0.435712i
\(142\) 1511.67 1625.13i 0.893358 0.960409i
\(143\) −743.160 −0.434588
\(144\) −83.0096 569.987i −0.0480379 0.329854i
\(145\) 7.53865 0.00431759
\(146\) 1541.53 1657.23i 0.873824 0.939409i
\(147\) 619.491 + 619.491i 0.347583 + 0.347583i
\(148\) −1581.90 1368.21i −0.878591 0.759907i
\(149\) −69.6301 + 69.6301i −0.0382840 + 0.0382840i −0.725990 0.687706i \(-0.758618\pi\)
0.687706 + 0.725990i \(0.258618\pi\)
\(150\) −1052.91 + 38.0840i −0.573133 + 0.0207303i
\(151\) 1567.48i 0.844768i 0.906417 + 0.422384i \(0.138807\pi\)
−0.906417 + 0.422384i \(0.861193\pi\)
\(152\) 1387.76 151.114i 0.740540 0.0806377i
\(153\) 642.622i 0.339561i
\(154\) −26.2658 726.174i −0.0137439 0.379979i
\(155\) −69.5271 + 69.5271i −0.0360294 + 0.0360294i
\(156\) 494.346 35.8079i 0.253714 0.0183778i
\(157\) 1738.35 + 1738.35i 0.883667 + 0.883667i 0.993905 0.110238i \(-0.0351614\pi\)
−0.110238 + 0.993905i \(0.535161\pi\)
\(158\) 1135.03 + 1055.79i 0.571507 + 0.531607i
\(159\) −1060.23 −0.528818
\(160\) −162.410 + 29.6831i −0.0802476 + 0.0146666i
\(161\) −1512.42 −0.740344
\(162\) −167.750 156.038i −0.0813560 0.0756761i
\(163\) −2685.71 2685.71i −1.29056 1.29056i −0.934442 0.356116i \(-0.884101\pi\)
−0.356116 0.934442i \(-0.615899\pi\)
\(164\) −2873.64 + 208.152i −1.36825 + 0.0991093i
\(165\) 69.6232 69.6232i 0.0328495 0.0328495i
\(166\) 67.1501 + 1856.51i 0.0313967 + 0.868030i
\(167\) 27.5126i 0.0127484i 0.999980 + 0.00637422i \(0.00202899\pi\)
−0.999980 + 0.00637422i \(0.997971\pi\)
\(168\) 52.4614 + 481.781i 0.0240922 + 0.221251i
\(169\) 1770.51i 0.805875i
\(170\) 184.075 6.65803i 0.0830467 0.00300381i
\(171\) 392.614 392.614i 0.175579 0.175579i
\(172\) −2673.86 2312.67i −1.18535 1.02523i
\(173\) 3044.87 + 3044.87i 1.33813 + 1.33813i 0.897867 + 0.440267i \(0.145116\pi\)
0.440267 + 0.897867i \(0.354884\pi\)
\(174\) −47.7683 + 51.3535i −0.0208121 + 0.0223741i
\(175\) 886.469 0.382919
\(176\) −1376.82 + 1846.20i −0.589669 + 0.790698i
\(177\) −648.083 −0.275214
\(178\) −583.656 + 627.462i −0.245769 + 0.264215i
\(179\) −365.808 365.808i −0.152747 0.152747i 0.626597 0.779344i \(-0.284447\pi\)
−0.779344 + 0.626597i \(0.784447\pi\)
\(180\) −42.9583 + 49.6677i −0.0177885 + 0.0205667i
\(181\) −1737.10 + 1737.10i −0.713359 + 0.713359i −0.967236 0.253877i \(-0.918294\pi\)
0.253877 + 0.967236i \(0.418294\pi\)
\(182\) −416.745 + 15.0737i −0.169732 + 0.00613922i
\(183\) 2231.56i 0.901432i
\(184\) 3736.52 + 3002.69i 1.49707 + 1.20305i
\(185\) 238.447i 0.0947620i
\(186\) −33.0658 914.176i −0.0130350 0.360380i
\(187\) 1816.87 1816.87i 0.710495 0.710495i
\(188\) 198.757 + 2743.94i 0.0771057 + 1.06448i
\(189\) 136.302 + 136.302i 0.0524577 + 0.0524577i
\(190\) −116.530 108.394i −0.0444946 0.0413882i
\(191\) −1709.44 −0.647595 −0.323798 0.946126i \(-0.604960\pi\)
−0.323798 + 0.946126i \(0.604960\pi\)
\(192\) 826.898 1294.42i 0.310814 0.486547i
\(193\) 2404.54 0.896800 0.448400 0.893833i \(-0.351994\pi\)
0.448400 + 0.893833i \(0.351994\pi\)
\(194\) 3245.73 + 3019.13i 1.20118 + 1.11732i
\(195\) −39.9562 39.9562i −0.0146735 0.0146735i
\(196\) 168.784 + 2330.14i 0.0615101 + 0.849177i
\(197\) 2772.54 2772.54i 1.00272 1.00272i 0.00271983 0.999996i \(-0.499134\pi\)
0.999996 0.00271983i \(-0.000865750\pi\)
\(198\) 33.1115 + 915.439i 0.0118845 + 0.328573i
\(199\) 1506.90i 0.536790i 0.963309 + 0.268395i \(0.0864932\pi\)
−0.963309 + 0.268395i \(0.913507\pi\)
\(200\) −2190.08 1759.96i −0.774309 0.622238i
\(201\) 149.787i 0.0525631i
\(202\) 238.296 8.61918i 0.0830021 0.00300219i
\(203\) 41.7263 41.7263i 0.0144267 0.0144267i
\(204\) −1121.03 + 1296.12i −0.384744 + 0.444834i
\(205\) 232.266 + 232.266i 0.0791324 + 0.0791324i
\(206\) −3395.46 + 3650.31i −1.14841 + 1.23461i
\(207\) 1906.61 0.640185
\(208\) 1059.52 + 790.147i 0.353195 + 0.263398i
\(209\) −2220.06 −0.734760
\(210\) 37.6308 40.4551i 0.0123656 0.0132937i
\(211\) −1965.22 1965.22i −0.641190 0.641190i 0.309658 0.950848i \(-0.399785\pi\)
−0.950848 + 0.309658i \(0.899785\pi\)
\(212\) −2138.41 1849.54i −0.692766 0.599183i
\(213\) 1664.63 1664.63i 0.535487 0.535487i
\(214\) 2624.60 94.9320i 0.838383 0.0303244i
\(215\) 403.043i 0.127848i
\(216\) −66.1346 607.350i −0.0208328 0.191319i
\(217\) 769.663i 0.240775i
\(218\) −47.3918 1310.25i −0.0147238 0.407070i
\(219\) 1697.51 1697.51i 0.523778 0.523778i
\(220\) 261.879 18.9692i 0.0802541 0.00581321i
\(221\) −1042.69 1042.69i −0.317370 0.317370i
\(222\) −1624.31 1510.91i −0.491065 0.456781i
\(223\) 85.7869 0.0257610 0.0128805 0.999917i \(-0.495900\pi\)
0.0128805 + 0.999917i \(0.495900\pi\)
\(224\) −734.640 + 1063.23i −0.219130 + 0.317143i
\(225\) −1117.51 −0.331115
\(226\) −2794.13 2599.06i −0.822402 0.764986i
\(227\) 2526.02 + 2526.02i 0.738582 + 0.738582i 0.972304 0.233722i \(-0.0750905\pi\)
−0.233722 + 0.972304i \(0.575090\pi\)
\(228\) 1476.77 106.970i 0.428955 0.0310713i
\(229\) −1116.65 + 1116.65i −0.322227 + 0.322227i −0.849621 0.527394i \(-0.823169\pi\)
0.527394 + 0.849621i \(0.323169\pi\)
\(230\) −19.7538 546.137i −0.00566317 0.156570i
\(231\) 770.727i 0.219524i
\(232\) −185.929 + 20.2459i −0.0526157 + 0.00572934i
\(233\) 5754.25i 1.61791i −0.587869 0.808956i \(-0.700033\pi\)
0.587869 0.808956i \(-0.299967\pi\)
\(234\) 525.363 19.0024i 0.146770 0.00530867i
\(235\) 221.783 221.783i 0.0615640 0.0615640i
\(236\) −1307.13 1130.56i −0.360538 0.311835i
\(237\) 1162.62 + 1162.62i 0.318650 + 0.318650i
\(238\) 982.003 1055.71i 0.267453 0.287527i
\(239\) −641.784 −0.173697 −0.0868484 0.996222i \(-0.527680\pi\)
−0.0868484 + 0.996222i \(0.527680\pi\)
\(240\) −173.287 + 25.2365i −0.0466068 + 0.00678753i
\(241\) −2887.45 −0.771771 −0.385885 0.922547i \(-0.626104\pi\)
−0.385885 + 0.922547i \(0.626104\pi\)
\(242\) −69.4533 + 74.6661i −0.0184489 + 0.0198335i
\(243\) −171.827 171.827i −0.0453609 0.0453609i
\(244\) 3892.88 4500.88i 1.02138 1.18090i
\(245\) 188.337 188.337i 0.0491119 0.0491119i
\(246\) −3053.94 + 110.461i −0.791512 + 0.0286291i
\(247\) 1274.07i 0.328208i
\(248\) 1528.05 1901.50i 0.391256 0.486877i
\(249\) 1970.41i 0.501485i
\(250\) 23.2341 + 642.356i 0.00587781 + 0.162505i
\(251\) −2367.55 + 2367.55i −0.595372 + 0.595372i −0.939077 0.343706i \(-0.888318\pi\)
0.343706 + 0.939077i \(0.388318\pi\)
\(252\) 37.1362 + 512.684i 0.00928319 + 0.128159i
\(253\) −5390.51 5390.51i −1.33952 1.33952i
\(254\) 108.129 + 100.580i 0.0267110 + 0.0248462i
\(255\) 195.369 0.0479784
\(256\) 3925.86 1168.26i 0.958462 0.285219i
\(257\) 5112.43 1.24087 0.620437 0.784256i \(-0.286955\pi\)
0.620437 + 0.784256i \(0.286955\pi\)
\(258\) −2745.54 2553.86i −0.662519 0.616266i
\(259\) 1319.80 + 1319.80i 0.316635 + 0.316635i
\(260\) −10.8863 150.291i −0.00259669 0.0358486i
\(261\) −52.6017 + 52.6017i −0.0124749 + 0.0124749i
\(262\) −56.0933 1550.82i −0.0132269 0.365687i
\(263\) 5496.36i 1.28867i 0.764744 + 0.644334i \(0.222866\pi\)
−0.764744 + 0.644334i \(0.777134\pi\)
\(264\) −1530.17 + 1904.13i −0.356724 + 0.443905i
\(265\) 322.331i 0.0747194i
\(266\) −1244.95 + 45.0301i −0.286966 + 0.0103796i
\(267\) −642.712 + 642.712i −0.147316 + 0.147316i
\(268\) 261.298 302.109i 0.0595572 0.0688591i
\(269\) −2474.35 2474.35i −0.560831 0.560831i 0.368712 0.929544i \(-0.379799\pi\)
−0.929544 + 0.368712i \(0.879799\pi\)
\(270\) −47.4386 + 50.9991i −0.0106927 + 0.0114952i
\(271\) −1718.58 −0.385226 −0.192613 0.981275i \(-0.561696\pi\)
−0.192613 + 0.981275i \(0.561696\pi\)
\(272\) −4522.05 + 658.565i −1.00805 + 0.146806i
\(273\) −442.314 −0.0980589
\(274\) −1531.58 + 1646.53i −0.337687 + 0.363032i
\(275\) 3159.52 + 3159.52i 0.692823 + 0.692823i
\(276\) 3845.47 + 3326.01i 0.838660 + 0.725370i
\(277\) −4722.69 + 4722.69i −1.02440 + 1.02440i −0.0247055 + 0.999695i \(0.507865\pi\)
−0.999695 + 0.0247055i \(0.992135\pi\)
\(278\) 6830.34 247.054i 1.47358 0.0532997i
\(279\) 970.264i 0.208201i
\(280\) 146.471 15.9492i 0.0312618 0.00340411i
\(281\) 2543.21i 0.539911i 0.962873 + 0.269955i \(0.0870090\pi\)
−0.962873 + 0.269955i \(0.912991\pi\)
\(282\) 105.476 + 2916.11i 0.0222731 + 0.615787i
\(283\) −3206.82 + 3206.82i −0.673589 + 0.673589i −0.958542 0.284952i \(-0.908022\pi\)
0.284952 + 0.958542i \(0.408022\pi\)
\(284\) 6261.31 453.538i 1.30824 0.0947624i
\(285\) −119.362 119.362i −0.0248084 0.0248084i
\(286\) −1539.07 1431.62i −0.318207 0.295992i
\(287\) 2571.17 0.528821
\(288\) 926.112 1340.35i 0.189485 0.274238i
\(289\) 185.302 0.0377167
\(290\) 15.6124 + 14.5225i 0.00316136 + 0.00294065i
\(291\) 3324.61 + 3324.61i 0.669733 + 0.669733i
\(292\) 6384.99 462.497i 1.27964 0.0926903i
\(293\) 5911.40 5911.40i 1.17866 1.17866i 0.198575 0.980086i \(-0.436369\pi\)
0.980086 0.198575i \(-0.0636313\pi\)
\(294\) 89.5697 + 2476.35i 0.0177681 + 0.491236i
\(295\) 197.030i 0.0388865i
\(296\) −640.376 5880.92i −0.125747 1.15480i
\(297\) 971.605i 0.189826i
\(298\) −278.338 + 10.0675i −0.0541064 + 0.00195703i
\(299\) −3093.57 + 3093.57i −0.598347 + 0.598347i
\(300\) −2253.93 1949.46i −0.433770 0.375174i
\(301\) 2230.84 + 2230.84i 0.427187 + 0.427187i
\(302\) −3019.60 + 3246.23i −0.575359 + 0.618542i
\(303\) 252.916 0.0479526
\(304\) 3165.14 + 2360.43i 0.597148 + 0.445328i
\(305\) −678.438 −0.127368
\(306\) −1237.95 + 1330.86i −0.231270 + 0.248628i
\(307\) 1162.25 + 1162.25i 0.216068 + 0.216068i 0.806839 0.590771i \(-0.201176\pi\)
−0.590771 + 0.806839i \(0.701176\pi\)
\(308\) 1344.50 1554.49i 0.248735 0.287583i
\(309\) −3739.03 + 3739.03i −0.688368 + 0.688368i
\(310\) −277.927 + 10.0526i −0.0509199 + 0.00184178i
\(311\) 2357.28i 0.429805i −0.976636 0.214902i \(-0.931057\pi\)
0.976636 0.214902i \(-0.0689433\pi\)
\(312\) 1092.76 + 878.150i 0.198287 + 0.159344i
\(313\) 3785.95i 0.683689i 0.939757 + 0.341844i \(0.111052\pi\)
−0.939757 + 0.341844i \(0.888948\pi\)
\(314\) 251.341 + 6948.87i 0.0451720 + 1.24888i
\(315\) 41.4384 41.4384i 0.00741203 0.00741203i
\(316\) 316.761 + 4373.04i 0.0563899 + 0.778490i
\(317\) −3135.51 3135.51i −0.555545 0.555545i 0.372491 0.928036i \(-0.378504\pi\)
−0.928036 + 0.372491i \(0.878504\pi\)
\(318\) −2195.73 2042.44i −0.387203 0.360170i
\(319\) 297.439 0.0522050
\(320\) −393.530 251.393i −0.0687468 0.0439165i
\(321\) 2785.63 0.484357
\(322\) −3132.20 2913.52i −0.542083 0.504237i
\(323\) −3114.85 3114.85i −0.536578 0.536578i
\(324\) −46.8152 646.307i −0.00802730 0.110821i
\(325\) 1813.22 1813.22i 0.309476 0.309476i
\(326\) −388.316 10735.8i −0.0659718 1.82393i
\(327\) 1390.64i 0.235176i
\(328\) −6352.24 5104.69i −1.06934 0.859328i
\(329\) 2455.13i 0.411416i
\(330\) 278.311 10.0665i 0.0464258 0.00167923i
\(331\) −1734.12 + 1734.12i −0.287963 + 0.287963i −0.836274 0.548312i \(-0.815271\pi\)
0.548312 + 0.836274i \(0.315271\pi\)
\(332\) −3437.31 + 3974.16i −0.568214 + 0.656959i
\(333\) −1663.79 1663.79i −0.273798 0.273798i
\(334\) −53.0003 + 56.9783i −0.00868278 + 0.00933446i
\(335\) −45.5382 −0.00742691
\(336\) −819.457 + 1098.82i −0.133051 + 0.178410i
\(337\) 5828.89 0.942196 0.471098 0.882081i \(-0.343858\pi\)
0.471098 + 0.882081i \(0.343858\pi\)
\(338\) 3410.70 3666.69i 0.548869 0.590065i
\(339\) −2862.04 2862.04i −0.458539 0.458539i
\(340\) 394.044 + 340.814i 0.0628530 + 0.0543625i
\(341\) −2743.21 + 2743.21i −0.435639 + 0.435639i
\(342\) 1569.43 56.7665i 0.248144 0.00897538i
\(343\) 4533.65i 0.713686i
\(344\) −1082.42 9940.43i −0.169651 1.55800i
\(345\) 579.645i 0.0904551i
\(346\) 440.245 + 12171.5i 0.0684038 + 1.89117i
\(347\) −716.234 + 716.234i −0.110805 + 0.110805i −0.760336 0.649530i \(-0.774966\pi\)
0.649530 + 0.760336i \(0.274966\pi\)
\(348\) −197.855 + 14.3316i −0.0304774 + 0.00220763i
\(349\) −4388.39 4388.39i −0.673081 0.673081i 0.285344 0.958425i \(-0.407892\pi\)
−0.958425 + 0.285344i \(0.907892\pi\)
\(350\) 1835.87 + 1707.69i 0.280375 + 0.260800i
\(351\) 557.596 0.0847928
\(352\) −6407.90 + 1171.15i −0.970291 + 0.177337i
\(353\) 9348.76 1.40959 0.704794 0.709412i \(-0.251040\pi\)
0.704794 + 0.709412i \(0.251040\pi\)
\(354\) −1342.17 1248.47i −0.201513 0.187444i
\(355\) −506.079 506.079i −0.0756617 0.0756617i
\(356\) −2417.49 + 175.110i −0.359906 + 0.0260698i
\(357\) 1081.37 1081.37i 0.160314 0.160314i
\(358\) −52.8906 1462.27i −0.00780826 0.215876i
\(359\) 12531.1i 1.84224i −0.389275 0.921122i \(-0.627274\pi\)
0.389275 0.921122i \(-0.372726\pi\)
\(360\) −184.646 + 20.1062i −0.0270325 + 0.00294358i
\(361\) 3052.92i 0.445097i
\(362\) −6943.88 + 251.161i −1.00818 + 0.0364661i
\(363\) −76.4808 + 76.4808i −0.0110584 + 0.0110584i
\(364\) −892.112 771.601i −0.128460 0.111107i
\(365\) −516.076 516.076i −0.0740073 0.0740073i
\(366\) 4298.89 4621.54i 0.613952 0.660032i
\(367\) 9276.83 1.31947 0.659736 0.751497i \(-0.270668\pi\)
0.659736 + 0.751497i \(0.270668\pi\)
\(368\) 1953.91 + 13416.6i 0.276779 + 1.90051i
\(369\) −3241.31 −0.457279
\(370\) −459.344 + 493.820i −0.0645410 + 0.0693851i
\(371\) 1784.10 + 1784.10i 0.249665 + 0.249665i
\(372\) 1692.59 1956.94i 0.235905 0.272749i
\(373\) 1765.32 1765.32i 0.245053 0.245053i −0.573884 0.818937i \(-0.694564\pi\)
0.818937 + 0.573884i \(0.194564\pi\)
\(374\) 7262.73 262.694i 1.00414 0.0363197i
\(375\) 681.766i 0.0938834i
\(376\) −4874.31 + 6065.55i −0.668546 + 0.831934i
\(377\) 170.698i 0.0233193i
\(378\) 19.7073 + 544.852i 0.00268158 + 0.0741380i
\(379\) 2909.05 2909.05i 0.394269 0.394269i −0.481937 0.876206i \(-0.660067\pi\)
0.876206 + 0.481937i \(0.160067\pi\)
\(380\) −32.5209 448.967i −0.00439023 0.0606092i
\(381\) 110.757 + 110.757i 0.0148930 + 0.0148930i
\(382\) −3540.22 3293.06i −0.474172 0.441067i
\(383\) 1520.26 0.202824 0.101412 0.994845i \(-0.467664\pi\)
0.101412 + 0.994845i \(0.467664\pi\)
\(384\) 4206.07 1087.80i 0.558959 0.144561i
\(385\) −234.316 −0.0310177
\(386\) 4979.77 + 4632.10i 0.656641 + 0.610798i
\(387\) −2812.27 2812.27i −0.369395 0.369395i
\(388\) 905.810 + 12505.1i 0.118519 + 1.63622i
\(389\) −8093.35 + 8093.35i −1.05488 + 1.05488i −0.0564785 + 0.998404i \(0.517987\pi\)
−0.998404 + 0.0564785i \(0.982013\pi\)
\(390\) −5.77710 159.720i −0.000750090 0.0207378i
\(391\) 15126.3i 1.95644i
\(392\) −4139.24 + 5150.84i −0.533324 + 0.663665i
\(393\) 1645.97i 0.211267i
\(394\) 11082.9 400.870i 1.41713 0.0512577i
\(395\) 353.457 353.457i 0.0450237 0.0450237i
\(396\) −1694.93 + 1959.65i −0.215084 + 0.248677i
\(397\) 8897.26 + 8897.26i 1.12479 + 1.12479i 0.991012 + 0.133776i \(0.0427101\pi\)
0.133776 + 0.991012i \(0.457290\pi\)
\(398\) −2902.89 + 3120.76i −0.365600 + 0.393040i
\(399\) −1321.34 −0.165788
\(400\) −1145.24 7863.81i −0.143155 0.982976i
\(401\) −4199.74 −0.523004 −0.261502 0.965203i \(-0.584218\pi\)
−0.261502 + 0.965203i \(0.584218\pi\)
\(402\) 288.550 310.207i 0.0357999 0.0384869i
\(403\) 1574.30 + 1574.30i 0.194595 + 0.194595i
\(404\) 510.111 + 441.203i 0.0628192 + 0.0543333i
\(405\) −52.2386 + 52.2386i −0.00640928 + 0.00640928i
\(406\) 166.796 6.03304i 0.0203891 0.000737475i
\(407\) 9407.97i 1.14579i
\(408\) −4818.47 + 524.685i −0.584681 + 0.0636662i
\(409\) 7881.87i 0.952894i 0.879203 + 0.476447i \(0.158076\pi\)
−0.879203 + 0.476447i \(0.841924\pi\)
\(410\) 33.5823 + 928.455i 0.00404515 + 0.111837i
\(411\) −1686.55 + 1686.55i −0.202412 + 0.202412i
\(412\) −14063.9 + 1018.72i −1.68174 + 0.121817i
\(413\) 1090.56 + 1090.56i 0.129934 + 0.129934i
\(414\) 3948.56 + 3672.89i 0.468746 + 0.436021i
\(415\) 599.043 0.0708575
\(416\) 672.115 + 3677.44i 0.0792143 + 0.433417i
\(417\) 7249.40 0.851331
\(418\) −4597.71 4276.72i −0.537994 0.500434i
\(419\) −5502.69 5502.69i −0.641585 0.641585i 0.309360 0.950945i \(-0.399885\pi\)
−0.950945 + 0.309360i \(0.899885\pi\)
\(420\) 155.866 11.2901i 0.0181082 0.00131167i
\(421\) 11302.2 11302.2i 1.30840 1.30840i 0.385823 0.922573i \(-0.373918\pi\)
0.922573 0.385823i \(-0.126082\pi\)
\(422\) −284.142 7855.73i −0.0327769 0.906187i
\(423\) 3095.02i 0.355757i
\(424\) −865.656 7949.79i −0.0991509 0.910557i
\(425\) 8865.90i 1.01190i
\(426\) 6654.17 240.682i 0.756798 0.0273734i
\(427\) −3755.14 + 3755.14i −0.425584 + 0.425584i
\(428\) 5618.38 + 4859.42i 0.634521 + 0.548806i
\(429\) −1576.48 1576.48i −0.177420 0.177420i
\(430\) −776.423 + 834.697i −0.0870754 + 0.0936108i
\(431\) −5428.20 −0.606652 −0.303326 0.952887i \(-0.598097\pi\)
−0.303326 + 0.952887i \(0.598097\pi\)
\(432\) 1033.04 1385.22i 0.115051 0.154274i
\(433\) −5143.78 −0.570888 −0.285444 0.958395i \(-0.592141\pi\)
−0.285444 + 0.958395i \(0.592141\pi\)
\(434\) −1482.68 + 1593.96i −0.163988 + 0.176296i
\(435\) 15.9919 + 15.9919i 0.00176265 + 0.00176265i
\(436\) 2425.92 2804.80i 0.266469 0.308086i
\(437\) −9241.50 + 9241.50i −1.01163 + 1.01163i
\(438\) 6785.61 245.436i 0.740249 0.0267749i
\(439\) 2183.50i 0.237386i −0.992931 0.118693i \(-0.962130\pi\)
0.992931 0.118693i \(-0.0378705\pi\)
\(440\) 578.891 + 465.200i 0.0627217 + 0.0504035i
\(441\) 2628.28i 0.283801i
\(442\) −150.758 4168.02i −0.0162236 0.448535i
\(443\) 561.821 561.821i 0.0602549 0.0602549i −0.676337 0.736592i \(-0.736434\pi\)
0.736592 + 0.676337i \(0.236434\pi\)
\(444\) −453.308 6258.13i −0.0484528 0.668914i
\(445\) 195.397 + 195.397i 0.0208150 + 0.0208150i
\(446\) 177.663 + 165.260i 0.0188623 + 0.0175455i
\(447\) −295.415 −0.0312588
\(448\) −3569.64 + 786.726i −0.376450 + 0.0829672i
\(449\) −2639.02 −0.277378 −0.138689 0.990336i \(-0.544289\pi\)
−0.138689 + 0.990336i \(0.544289\pi\)
\(450\) −2314.35 2152.78i −0.242444 0.225518i
\(451\) 9164.08 + 9164.08i 0.956807 + 0.956807i
\(452\) −779.779 10765.2i −0.0811454 1.12025i
\(453\) −3325.13 + 3325.13i −0.344875 + 0.344875i
\(454\) 365.227 + 10097.5i 0.0377554 + 1.04383i
\(455\) 134.472i 0.0138552i
\(456\) 3264.44 + 2623.32i 0.335245 + 0.269404i
\(457\) 5546.69i 0.567753i −0.958861 0.283876i \(-0.908379\pi\)
0.958861 0.283876i \(-0.0916205\pi\)
\(458\) −4463.66 + 161.451i −0.455400 + 0.0164719i
\(459\) −1363.21 + 1363.21i −0.138625 + 0.138625i
\(460\) 1011.17 1169.10i 0.102491 0.118499i
\(461\) 8475.23 + 8475.23i 0.856249 + 0.856249i 0.990894 0.134645i \(-0.0429894\pi\)
−0.134645 + 0.990894i \(0.542989\pi\)
\(462\) 1484.73 1596.16i 0.149515 0.160737i
\(463\) −16410.6 −1.64722 −0.823612 0.567154i \(-0.808044\pi\)
−0.823612 + 0.567154i \(0.808044\pi\)
\(464\) −424.058 316.245i −0.0424276 0.0316407i
\(465\) −294.979 −0.0294179
\(466\) 11085.0 11917.0i 1.10194 1.18464i
\(467\) −6689.53 6689.53i −0.662858 0.662858i 0.293195 0.956053i \(-0.405281\pi\)
−0.956053 + 0.293195i \(0.905281\pi\)
\(468\) 1124.63 + 972.706i 0.111081 + 0.0960755i
\(469\) −252.053 + 252.053i −0.0248161 + 0.0248161i
\(470\) 886.553 32.0667i 0.0870077 0.00314708i
\(471\) 7375.21i 0.721511i
\(472\) −529.145 4859.43i −0.0516014 0.473884i
\(473\) 15902.1i 1.54584i
\(474\) 168.098 + 4647.42i 0.0162890 + 0.450344i
\(475\) 5416.69 5416.69i 0.523231 0.523231i
\(476\) 4067.43 294.624i 0.391660 0.0283699i
\(477\) −2249.10 2249.10i −0.215889 0.215889i
\(478\) −1329.13 1236.33i −0.127182 0.118302i
\(479\) 7188.55 0.685707 0.342853 0.939389i \(-0.388607\pi\)
0.342853 + 0.939389i \(0.388607\pi\)
\(480\) −407.490 281.555i −0.0387485 0.0267733i
\(481\) 5399.16 0.511810
\(482\) −5979.86 5562.38i −0.565094 0.525642i
\(483\) −3208.33 3208.33i −0.302244 0.302244i
\(484\) −287.674 + 20.8376i −0.0270167 + 0.00195695i
\(485\) 1010.75 1010.75i 0.0946301 0.0946301i
\(486\) −24.8437 686.859i −0.00231880 0.0641081i
\(487\) 11181.6i 1.04042i 0.854038 + 0.520210i \(0.174146\pi\)
−0.854038 + 0.520210i \(0.825854\pi\)
\(488\) 16732.6 1822.02i 1.55215 0.169014i
\(489\) 11394.5i 1.05374i
\(490\) 752.856 27.2309i 0.0694093 0.00251054i
\(491\) 11679.8 11679.8i 1.07353 1.07353i 0.0764529 0.997073i \(-0.475641\pi\)
0.997073 0.0764529i \(-0.0243595\pi\)
\(492\) −6537.46 5654.35i −0.599048 0.518125i
\(493\) 417.321 + 417.321i 0.0381241 + 0.0381241i
\(494\) −2454.38 + 2638.59i −0.223538 + 0.240315i
\(495\) 295.386 0.0268215
\(496\) 6827.63 994.336i 0.618084 0.0900141i
\(497\) −5602.28 −0.505627
\(498\) −3795.80 + 4080.70i −0.341554 + 0.367189i
\(499\) −2094.26 2094.26i −0.187880 0.187880i 0.606899 0.794779i \(-0.292413\pi\)
−0.794779 + 0.606899i \(0.792413\pi\)
\(500\) −1189.32 + 1375.07i −0.106376 + 0.122990i
\(501\) −58.3631 + 58.3631i −0.00520453 + 0.00520453i
\(502\) −9464.00 + 342.314i −0.841433 + 0.0304347i
\(503\) 4293.63i 0.380604i 0.981726 + 0.190302i \(0.0609466\pi\)
−0.981726 + 0.190302i \(0.939053\pi\)
\(504\) −910.725 + 1133.30i −0.0804899 + 0.100161i
\(505\) 76.8912i 0.00677548i
\(506\) −779.391 21547.9i −0.0684746 1.89313i
\(507\) 3755.81 3755.81i 0.328997 0.328997i
\(508\) 30.1762 + 416.598i 0.00263554 + 0.0363849i
\(509\) −9115.13 9115.13i −0.793755 0.793755i 0.188348 0.982102i \(-0.439687\pi\)
−0.982102 + 0.188348i \(0.939687\pi\)
\(510\) 404.607 + 376.359i 0.0351300 + 0.0326774i
\(511\) −5712.95 −0.494571
\(512\) 10380.9 + 5143.34i 0.896048 + 0.443956i
\(513\) 1665.72 0.143359
\(514\) 10587.8 + 9848.59i 0.908574 + 0.845142i
\(515\) 1136.73 + 1136.73i 0.0972631 + 0.0972631i
\(516\) −766.219 10578.0i −0.0653700 0.902464i
\(517\) 8750.49 8750.49i 0.744383 0.744383i
\(518\) 190.825 + 5275.75i 0.0161860 + 0.447497i
\(519\) 12918.3i 1.09258i
\(520\) 266.974 332.221i 0.0225146 0.0280170i
\(521\) 23150.3i 1.94671i −0.229309 0.973354i \(-0.573647\pi\)
0.229309 0.973354i \(-0.426353\pi\)
\(522\) −210.269 + 7.60546i −0.0176307 + 0.000637705i
\(523\) −8510.52 + 8510.52i −0.711547 + 0.711547i −0.966859 0.255312i \(-0.917822\pi\)
0.255312 + 0.966859i \(0.417822\pi\)
\(524\) 2871.33 3319.78i 0.239379 0.276766i
\(525\) 1880.49 + 1880.49i 0.156326 + 0.156326i
\(526\) −10588.2 + 11382.9i −0.877693 + 0.943569i
\(527\) −7697.69 −0.636274
\(528\) −6837.07 + 995.710i −0.563532 + 0.0820695i
\(529\) −32711.4 −2.68854
\(530\) −620.939 + 667.543i −0.0508903 + 0.0547099i
\(531\) −1374.79 1374.79i −0.112356 0.112356i
\(532\) −2665.03 2305.02i −0.217187 0.187849i
\(533\) 5259.19 5259.19i 0.427394 0.427394i
\(534\) −2569.17 + 92.9271i −0.208200 + 0.00753061i
\(535\) 846.884i 0.0684373i
\(536\) 1123.13 122.298i 0.0905069 0.00985533i
\(537\) 1551.99i 0.124718i
\(538\) −357.756 9890.92i −0.0286690 0.792617i
\(539\) 7430.87 7430.87i 0.593822 0.593822i
\(540\) −196.489 + 14.2327i −0.0156584 + 0.00113422i
\(541\) 3403.84 + 3403.84i 0.270504 + 0.270504i 0.829303 0.558799i \(-0.188738\pi\)
−0.558799 + 0.829303i \(0.688738\pi\)
\(542\) −3559.15 3310.67i −0.282064 0.262372i
\(543\) −7369.91 −0.582455
\(544\) −10633.8 7347.40i −0.838086 0.579076i
\(545\) −422.780 −0.0332292
\(546\) −916.026 852.074i −0.0717991 0.0667864i
\(547\) 15672.4 + 15672.4i 1.22505 + 1.22505i 0.965814 + 0.259237i \(0.0834710\pi\)
0.259237 + 0.965814i \(0.416529\pi\)
\(548\) −6343.76 + 459.510i −0.494511 + 0.0358199i
\(549\) 4733.86 4733.86i 0.368008 0.368008i
\(550\) 456.822 + 12629.8i 0.0354163 + 0.979159i
\(551\) 509.930i 0.0394261i
\(552\) 1556.70 + 14296.0i 0.120032 + 1.10232i
\(553\) 3912.76i 0.300882i
\(554\) −18878.4 + 682.834i −1.44777 + 0.0523661i
\(555\) −505.822 + 505.822i −0.0386864 + 0.0386864i
\(556\) 14621.5 + 12646.3i 1.11527 + 0.964610i
\(557\) 6285.58 + 6285.58i 0.478149 + 0.478149i 0.904539 0.426391i \(-0.140215\pi\)
−0.426391 + 0.904539i \(0.640215\pi\)
\(558\) 1869.12 2009.40i 0.141803 0.152446i
\(559\) 9126.11 0.690507
\(560\) 334.063 + 249.130i 0.0252085 + 0.0187994i
\(561\) 7708.32 0.580117
\(562\) −4899.23 + 5266.94i −0.367725 + 0.395325i
\(563\) −1763.14 1763.14i −0.131985 0.131985i 0.638028 0.770013i \(-0.279750\pi\)
−0.770013 + 0.638028i \(0.779750\pi\)
\(564\) −5399.15 + 6242.41i −0.403095 + 0.466051i
\(565\) −870.114 + 870.114i −0.0647894 + 0.0647894i
\(566\) −12818.9 + 463.661i −0.951977 + 0.0344331i
\(567\) 578.280i 0.0428316i
\(568\) 13840.8 + 11122.5i 1.02244 + 0.821639i
\(569\) 1150.05i 0.0847323i 0.999102 + 0.0423662i \(0.0134896\pi\)
−0.999102 + 0.0423662i \(0.986510\pi\)
\(570\) −17.2581 477.137i −0.00126818 0.0350615i
\(571\) −4853.30 + 4853.30i −0.355699 + 0.355699i −0.862225 0.506526i \(-0.830930\pi\)
0.506526 + 0.862225i \(0.330930\pi\)
\(572\) −429.521 5929.74i −0.0313971 0.433453i
\(573\) −3626.27 3626.27i −0.264380 0.264380i
\(574\) 5324.87 + 4953.11i 0.387205 + 0.360172i
\(575\) 26304.4 1.90778
\(576\) 4500.01 991.774i 0.325521 0.0717429i
\(577\) −5152.84 −0.371777 −0.185889 0.982571i \(-0.559516\pi\)
−0.185889 + 0.982571i \(0.559516\pi\)
\(578\) 383.759 + 356.967i 0.0276164 + 0.0256883i
\(579\) 5100.80 + 5100.80i 0.366117 + 0.366117i
\(580\) 4.35708 + 60.1516i 0.000311928 + 0.00430631i
\(581\) 3315.69 3315.69i 0.236761 0.236761i
\(582\) 480.692 + 13289.8i 0.0342360 + 0.946527i
\(583\) 12717.6i 0.903449i
\(584\) 14114.2 + 11342.2i 1.00008 + 0.803672i
\(585\) 169.520i 0.0119808i
\(586\) 23630.1 854.705i 1.66579 0.0602517i
\(587\) 12549.2 12549.2i 0.882387 0.882387i −0.111390 0.993777i \(-0.535530\pi\)
0.993777 + 0.111390i \(0.0355302\pi\)
\(588\) −4584.93 + 5301.02i −0.321564 + 0.371787i
\(589\) 4702.96 + 4702.96i 0.329002 + 0.329002i
\(590\) −379.558 + 408.046i −0.0264850 + 0.0284728i
\(591\) 11762.9 0.818714
\(592\) 10002.8 13412.9i 0.694447 0.931195i
\(593\) −1116.75 −0.0773347 −0.0386674 0.999252i \(-0.512311\pi\)
−0.0386674 + 0.999252i \(0.512311\pi\)
\(594\) −1871.70 + 2012.18i −0.129287 + 0.138991i
\(595\) −328.756 328.756i −0.0226515 0.0226515i
\(596\) −595.829 515.341i −0.0409498 0.0354181i
\(597\) −3196.61 + 3196.61i −0.219143 + 0.219143i
\(598\) −12366.2 + 447.286i −0.845637 + 0.0305868i
\(599\) 15827.4i 1.07962i 0.841788 + 0.539808i \(0.181503\pi\)
−0.841788 + 0.539808i \(0.818497\pi\)
\(600\) −912.423 8379.28i −0.0620825 0.570138i
\(601\) 12216.9i 0.829180i −0.910008 0.414590i \(-0.863925\pi\)
0.910008 0.414590i \(-0.136075\pi\)
\(602\) 322.548 + 8917.52i 0.0218373 + 0.603739i
\(603\) 317.747 317.747i 0.0214588 0.0214588i
\(604\) −12507.1 + 905.951i −0.842560 + 0.0610308i
\(605\) 23.2516 + 23.2516i 0.00156250 + 0.00156250i
\(606\) 523.785 + 487.217i 0.0351111 + 0.0326598i
\(607\) −24175.5 −1.61656 −0.808282 0.588795i \(-0.799602\pi\)
−0.808282 + 0.588795i \(0.799602\pi\)
\(608\) 2007.83 + 10985.7i 0.133928 + 0.732780i
\(609\) 177.030 0.0117793
\(610\) −1405.04 1306.94i −0.0932594 0.0867485i
\(611\) −5021.84 5021.84i −0.332507 0.332507i
\(612\) −5127.54 + 371.413i −0.338674 + 0.0245318i
\(613\) 12893.7 12893.7i 0.849544 0.849544i −0.140532 0.990076i \(-0.544881\pi\)
0.990076 + 0.140532i \(0.0448812\pi\)
\(614\) 168.044 + 4645.95i 0.0110451 + 0.305367i
\(615\) 985.420i 0.0646113i
\(616\) 5779.03 629.280i 0.377993 0.0411598i
\(617\) 13762.7i 0.897998i −0.893532 0.448999i \(-0.851781\pi\)
0.893532 0.448999i \(-0.148219\pi\)
\(618\) −14946.3 + 540.610i −0.972864 + 0.0351886i
\(619\) −326.797 + 326.797i −0.0212199 + 0.0212199i −0.717637 0.696417i \(-0.754776\pi\)
0.696417 + 0.717637i \(0.254776\pi\)
\(620\) −594.948 514.579i −0.0385382 0.0333323i
\(621\) 4044.52 + 4044.52i 0.261355 + 0.261355i
\(622\) 4541.07 4881.90i 0.292734 0.314705i
\(623\) 2163.04 0.139101
\(624\) 571.430 + 3923.74i 0.0366595 + 0.251723i
\(625\) −15313.7 −0.980080
\(626\) −7293.25 + 7840.65i −0.465650 + 0.500600i
\(627\) −4709.46 4709.46i −0.299964 0.299964i
\(628\) −12865.8 + 14875.2i −0.817517 + 0.945199i
\(629\) −13199.8 + 13199.8i −0.836742 + 0.836742i
\(630\) 165.645 5.99140i 0.0104753 0.000378894i
\(631\) 12260.2i 0.773487i −0.922187 0.386744i \(-0.873600\pi\)
0.922187 0.386744i \(-0.126400\pi\)
\(632\) −7768.22 + 9666.72i −0.488929 + 0.608420i
\(633\) 8337.71i 0.523529i
\(634\) −453.350 12533.8i −0.0283988 0.785146i
\(635\) 33.6721 33.6721i 0.00210431 0.00210431i
\(636\) −612.779 8459.71i −0.0382048 0.527436i
\(637\) −4264.52 4264.52i −0.265253 0.265253i
\(638\) 615.992 + 572.986i 0.0382247 + 0.0355560i
\(639\) 7062.43 0.437223
\(640\) −330.712 1278.73i −0.0204258 0.0789783i
\(641\) 10329.4 0.636485 0.318242 0.948009i \(-0.396907\pi\)
0.318242 + 0.948009i \(0.396907\pi\)
\(642\) 5769.00 + 5366.23i 0.354648 + 0.329888i
\(643\) −19299.9 19299.9i −1.18369 1.18369i −0.978781 0.204911i \(-0.934309\pi\)
−0.204911 0.978781i \(-0.565691\pi\)
\(644\) −874.126 12067.7i −0.0534866 0.738409i
\(645\) −854.984 + 854.984i −0.0521937 + 0.0521937i
\(646\) −450.363 12451.2i −0.0274292 0.758340i
\(647\) 8657.07i 0.526035i −0.964791 0.263017i \(-0.915282\pi\)
0.964791 0.263017i \(-0.0847177\pi\)
\(648\) 1148.09 1428.68i 0.0696008 0.0866107i
\(649\) 7773.84i 0.470185i
\(650\) 7248.15 262.167i 0.437378 0.0158200i
\(651\) −1632.70 + 1632.70i −0.0982960 + 0.0982960i
\(652\) 19877.3 22981.8i 1.19395 1.38042i
\(653\) 5966.31 + 5966.31i 0.357549 + 0.357549i 0.862909 0.505360i \(-0.168640\pi\)
−0.505360 + 0.862909i \(0.668640\pi\)
\(654\) 2678.92 2879.99i 0.160175 0.172197i
\(655\) −500.405 −0.0298511
\(656\) −3321.72 22808.7i −0.197701 1.35752i
\(657\) 7201.94 0.427663
\(658\) 4729.57 5084.55i 0.280209 0.301240i
\(659\) 7127.52 + 7127.52i 0.421318 + 0.421318i 0.885657 0.464339i \(-0.153708\pi\)
−0.464339 + 0.885657i \(0.653708\pi\)
\(660\) 595.770 + 515.290i 0.0351368 + 0.0303904i
\(661\) 2386.19 2386.19i 0.140412 0.140412i −0.633407 0.773819i \(-0.718344\pi\)
0.773819 + 0.633407i \(0.218344\pi\)
\(662\) −6931.93 + 250.729i −0.406974 + 0.0147203i
\(663\) 4423.75i 0.259131i
\(664\) −14774.4 + 1608.80i −0.863494 + 0.0940261i
\(665\) 401.711i 0.0234251i
\(666\) −240.560 6650.79i −0.0139963 0.386956i
\(667\) 1238.16 1238.16i 0.0718765 0.0718765i
\(668\) −219.526 + 15.9013i −0.0127151 + 0.000921020i
\(669\) 181.981 + 181.981i 0.0105169 + 0.0105169i
\(670\) −94.3089 87.7247i −0.00543802 0.00505836i
\(671\) −26767.9 −1.54003
\(672\) −3813.86 + 697.047i −0.218933 + 0.0400137i
\(673\) −3709.39 −0.212461 −0.106231 0.994342i \(-0.533878\pi\)
−0.106231 + 0.994342i \(0.533878\pi\)
\(674\) 12071.6 + 11228.8i 0.689880 + 0.641716i
\(675\) −2370.60 2370.60i −0.135177 0.135177i
\(676\) 14127.0 1023.29i 0.803769 0.0582210i
\(677\) −1602.20 + 1602.20i −0.0909564 + 0.0909564i −0.751121 0.660165i \(-0.770487\pi\)
0.660165 + 0.751121i \(0.270487\pi\)
\(678\) −413.811 11440.7i −0.0234400 0.648048i
\(679\) 11188.9i 0.632388i
\(680\) 159.514 + 1464.91i 0.00899572 + 0.0826127i
\(681\) 10717.0i 0.603050i
\(682\) −10965.7 + 396.629i −0.615684 + 0.0222694i
\(683\) −15495.9 + 15495.9i −0.868130 + 0.868130i −0.992265 0.124135i \(-0.960384\pi\)
0.124135 + 0.992265i \(0.460384\pi\)
\(684\) 3359.63 + 2905.79i 0.187805 + 0.162435i
\(685\) 512.743 + 512.743i 0.0285999 + 0.0285999i
\(686\) 8733.63 9389.13i 0.486081 0.522564i
\(687\) −4737.52 −0.263097
\(688\) 16907.6 22671.7i 0.936912 1.25632i
\(689\) 7298.55 0.403560
\(690\) 1116.63 1200.44i 0.0616077 0.0662316i
\(691\) 6337.43 + 6337.43i 0.348896 + 0.348896i 0.859698 0.510802i \(-0.170652\pi\)
−0.510802 + 0.859698i \(0.670652\pi\)
\(692\) −22535.5 + 26055.1i −1.23796 + 1.43131i
\(693\) 1634.96 1634.96i 0.0896204 0.0896204i
\(694\) −2863.06 + 103.557i −0.156600 + 0.00566424i
\(695\) 2203.96i 0.120289i
\(696\) −437.363 351.467i −0.0238193 0.0191413i
\(697\) 25715.3i 1.39747i
\(698\) −634.499 17542.1i −0.0344071 0.951258i
\(699\) 12206.6 12206.6i 0.660510 0.660510i
\(700\) 512.349 + 7073.22i 0.0276642 + 0.381918i
\(701\) −952.656 952.656i −0.0513285 0.0513285i 0.680977 0.732305i \(-0.261556\pi\)
−0.732305 + 0.680977i \(0.761556\pi\)
\(702\) 1154.77 + 1074.15i 0.0620857 + 0.0577512i
\(703\) 16129.0 0.865318
\(704\) −15526.8 9918.74i −0.831233 0.531004i
\(705\) 940.946 0.0502668
\(706\) 19361.1 + 18009.5i 1.03211 + 0.960049i
\(707\) −425.592 425.592i −0.0226394 0.0226394i
\(708\) −374.570 5171.12i −0.0198830 0.274495i
\(709\) −20781.1 + 20781.1i −1.10078 + 1.10078i −0.106461 + 0.994317i \(0.533952\pi\)
−0.994317 + 0.106461i \(0.966048\pi\)
\(710\) −73.1719 2022.99i −0.00386774 0.106932i
\(711\) 4932.56i 0.260177i
\(712\) −5343.91 4294.39i −0.281280 0.226038i
\(713\) 22838.4i 1.19959i
\(714\) 4322.64 156.350i 0.226569 0.00819504i
\(715\) −479.280 + 479.280i −0.0250686 + 0.0250686i
\(716\) 2707.39 3130.24i 0.141313 0.163383i
\(717\) −1361.43 1361.43i −0.0709114 0.0709114i
\(718\) 24139.9 25951.7i 1.25472 1.34890i
\(719\) −1927.96 −0.100001 −0.0500006 0.998749i \(-0.515922\pi\)
−0.0500006 + 0.998749i \(0.515922\pi\)
\(720\) −421.132 314.062i −0.0217981 0.0162561i
\(721\) 12583.6 0.649984
\(722\) 5881.15 6322.56i 0.303149 0.325902i
\(723\) −6125.20 6125.20i −0.315074 0.315074i
\(724\) −14864.5 12856.5i −0.763032 0.659958i
\(725\) −725.717 + 725.717i −0.0371758 + 0.0371758i
\(726\) −305.723 + 11.0580i −0.0156287 + 0.000565293i
\(727\) 5482.27i 0.279678i −0.990174 0.139839i \(-0.955341\pi\)
0.990174 0.139839i \(-0.0446585\pi\)
\(728\) −361.139 3316.54i −0.0183856 0.168845i
\(729\) 729.000i 0.0370370i
\(730\) −74.6173 2062.95i −0.00378316 0.104594i
\(731\) −22311.4 + 22311.4i −1.12889 + 1.12889i
\(732\) 17805.9 1289.77i 0.899076 0.0651246i
\(733\) 15048.8 + 15048.8i 0.758311 + 0.758311i 0.976015 0.217704i \(-0.0698568\pi\)
−0.217704 + 0.976015i \(0.569857\pi\)
\(734\) 19212.2 + 17870.9i 0.966123 + 0.898673i
\(735\) 799.046 0.0400997
\(736\) −21799.2 + 31549.5i −1.09175 + 1.58007i
\(737\) −1796.72 −0.0898004
\(738\) −6712.71 6244.06i −0.334821 0.311446i
\(739\) 12622.3 + 12622.3i 0.628306 + 0.628306i 0.947642 0.319335i \(-0.103460\pi\)
−0.319335 + 0.947642i \(0.603460\pi\)
\(740\) −1902.59 + 137.814i −0.0945144 + 0.00684615i
\(741\) −2702.72 + 2702.72i −0.133990 + 0.133990i
\(742\) 257.956 + 7131.73i 0.0127626 + 0.352849i
\(743\) 2335.45i 0.115315i 0.998336 + 0.0576576i \(0.0183632\pi\)
−0.998336 + 0.0576576i \(0.981637\pi\)
\(744\) 7275.19 792.198i 0.358496 0.0390368i
\(745\) 89.8119i 0.00441672i
\(746\) 7056.67 255.241i 0.346331 0.0125268i
\(747\) −4179.88 + 4179.88i −0.204730 + 0.204730i
\(748\) 15547.1 + 13446.9i 0.759969 + 0.657309i
\(749\) −4687.49 4687.49i −0.228674 0.228674i
\(750\) −1313.36 + 1411.93i −0.0639426 + 0.0687418i
\(751\) −3513.73 −0.170729 −0.0853647 0.996350i \(-0.527206\pi\)
−0.0853647 + 0.996350i \(0.527206\pi\)
\(752\) −21779.3 + 3171.81i −1.05613 + 0.153809i
\(753\) −10044.7 −0.486119
\(754\) 328.832 353.513i 0.0158825 0.0170745i
\(755\) 1010.90 + 1010.90i 0.0487292 + 0.0487292i
\(756\) −1008.79 + 1166.34i −0.0485308 + 0.0561105i
\(757\) −10416.0 + 10416.0i −0.500102 + 0.500102i −0.911470 0.411368i \(-0.865051\pi\)
0.411368 + 0.911470i \(0.365051\pi\)
\(758\) 11628.6 420.607i 0.557215 0.0201545i
\(759\) 22870.0i 1.09371i
\(760\) 797.539 992.452i 0.0380655 0.0473685i
\(761\) 17937.9i 0.854464i 0.904142 + 0.427232i \(0.140511\pi\)
−0.904142 + 0.427232i \(0.859489\pi\)
\(762\) 16.0138 + 442.737i 0.000761312 + 0.0210481i
\(763\) −2340.08 + 2340.08i −0.111031 + 0.111031i
\(764\) −987.997 13639.8i −0.0467860 0.645903i
\(765\) 414.440 + 414.440i 0.0195871 + 0.0195871i
\(766\) 3148.43 + 2928.62i 0.148508 + 0.138140i
\(767\) 4461.34 0.210026
\(768\) 10806.3 + 5849.76i 0.507731 + 0.274851i
\(769\) 32224.0 1.51109 0.755544 0.655097i \(-0.227372\pi\)
0.755544 + 0.655097i \(0.227372\pi\)
\(770\) −485.264 451.386i −0.0227113 0.0211257i
\(771\) 10845.1 + 10845.1i 0.506585 + 0.506585i
\(772\) 1389.74 + 19186.0i 0.0647900 + 0.894457i
\(773\) 13719.5 13719.5i 0.638365 0.638365i −0.311787 0.950152i \(-0.600928\pi\)
0.950152 + 0.311787i \(0.100928\pi\)
\(774\) −406.615 11241.7i −0.0188830 0.522062i
\(775\) 13386.2i 0.620448i
\(776\) −22214.0 + 27642.9i −1.02762 + 1.27877i
\(777\) 5599.44i 0.258531i
\(778\) −32352.2 + 1170.18i −1.49085 + 0.0539243i
\(779\) 15710.9 15710.9i 0.722596 0.722596i
\(780\) 295.721 341.908i 0.0135750 0.0156952i
\(781\) −19967.5 19967.5i −0.914842 0.914842i
\(782\) 29139.2 31326.3i 1.33250 1.43251i
\(783\) −223.170 −0.0101858
\(784\) −18494.9 + 2693.48i −0.842514 + 0.122699i
\(785\) 2242.20 0.101946
\(786\) 3170.79 3408.77i 0.143891 0.154691i
\(787\) −9919.72 9919.72i −0.449301 0.449301i 0.445821 0.895122i \(-0.352912\pi\)
−0.895122 + 0.445821i \(0.852912\pi\)
\(788\) 23724.8 + 20519.9i 1.07254 + 0.927654i
\(789\) −11659.5 + 11659.5i −0.526097 + 0.526097i
\(790\) 1412.90 51.1049i 0.0636315 0.00230156i
\(791\) 9632.14i 0.432970i
\(792\) −7285.24 + 793.292i −0.326856 + 0.0355914i
\(793\) 15361.9i 0.687915i
\(794\) 1286.42 + 35565.8i 0.0574978 + 1.58965i
\(795\) −683.768 + 683.768i −0.0305041 + 0.0305041i
\(796\) −12023.7 + 870.935i −0.535387 + 0.0387807i
\(797\) −20018.0 20018.0i −0.889679 0.889679i 0.104813 0.994492i \(-0.466576\pi\)
−0.994492 + 0.104813i \(0.966576\pi\)
\(798\) −2736.47 2545.42i −0.121391 0.112916i
\(799\) 24554.7 1.08721
\(800\) 12777.1 18492.0i 0.564672 0.817240i
\(801\) −2726.80 −0.120283
\(802\) −8697.59 8090.37i −0.382946 0.356211i
\(803\) −20361.9 20361.9i −0.894838 0.894838i
\(804\) 1195.17 86.5719i 0.0524257 0.00379746i
\(805\) −975.392 + 975.392i −0.0427056 + 0.0427056i
\(806\) 227.622 + 6293.10i 0.00994745 + 0.275019i
\(807\) 10497.8i 0.457917i
\(808\) 206.500 + 1896.40i 0.00899089 + 0.0825683i
\(809\) 9967.99i 0.433196i −0.976261 0.216598i \(-0.930504\pi\)
0.976261 0.216598i \(-0.0694961\pi\)
\(810\) −208.818 + 7.55297i −0.00905817 + 0.000327635i
\(811\) 16080.2 16080.2i 0.696243 0.696243i −0.267355 0.963598i \(-0.586150\pi\)
0.963598 + 0.267355i \(0.0861498\pi\)
\(812\) 357.055 + 308.822i 0.0154312 + 0.0133467i
\(813\) −3645.66 3645.66i −0.157268 0.157268i
\(814\) −18123.5 + 19483.8i −0.780379 + 0.838950i
\(815\) −3464.14 −0.148888
\(816\) −10989.7 8195.69i −0.471468 0.351601i
\(817\) 27262.7 1.16744
\(818\) −15183.6 + 16323.3i −0.649002 + 0.697713i
\(819\) −938.290 938.290i −0.0400324 0.0400324i
\(820\) −1719.03 + 1987.51i −0.0732086 + 0.0846426i
\(821\) 8235.64 8235.64i 0.350092 0.350092i −0.510051 0.860144i \(-0.670374\pi\)
0.860144 + 0.510051i \(0.170374\pi\)
\(822\) −6741.79 + 243.851i −0.286067 + 0.0103471i
\(823\) 21762.8i 0.921752i −0.887464 0.460876i \(-0.847535\pi\)
0.887464 0.460876i \(-0.152465\pi\)
\(824\) −31088.6 24983.0i −1.31435 1.05622i
\(825\) 13404.7i 0.565687i
\(826\) 157.679 + 4359.37i 0.00664208 + 0.183634i
\(827\) −30211.4 + 30211.4i −1.27032 + 1.27032i −0.324396 + 0.945921i \(0.605161\pi\)
−0.945921 + 0.324396i \(0.894839\pi\)
\(828\) 1101.95 + 15213.0i 0.0462506 + 0.638512i
\(829\) −16821.1 16821.1i −0.704729 0.704729i 0.260692 0.965422i \(-0.416049\pi\)
−0.965422 + 0.260692i \(0.916049\pi\)
\(830\) 1240.61 + 1154.00i 0.0518821 + 0.0482600i
\(831\) −20036.7 −0.836419
\(832\) −5692.29 + 8910.70i −0.237193 + 0.371302i
\(833\) 20851.7 0.867310
\(834\) 15013.4 + 13965.3i 0.623348 + 0.579829i
\(835\) 17.7435 + 17.7435i 0.000735375 + 0.000735375i
\(836\) −1283.12 17714.1i −0.0530832 0.732840i
\(837\) 2058.24 2058.24i 0.0849979 0.0849979i
\(838\) −795.612 21996.4i −0.0327971 0.906746i
\(839\) 21686.9i 0.892389i −0.894936 0.446194i \(-0.852779\pi\)
0.894936 0.446194i \(-0.147221\pi\)
\(840\) 344.545 + 276.878i 0.0141523 + 0.0113728i
\(841\) 24320.7i 0.997199i
\(842\) 45179.2 1634.14i 1.84914 0.0668837i
\(843\) −5394.95 + 5394.95i −0.220418 + 0.220418i
\(844\) 14544.8 16816.5i 0.593191 0.685838i
\(845\) −1141.84 1141.84i −0.0464857 0.0464857i
\(846\) −5962.25 + 6409.75i −0.242301 + 0.260487i
\(847\) 257.395 0.0104418
\(848\) 13521.7 18131.5i 0.547568 0.734244i
\(849\) −13605.4 −0.549983
\(850\) −17079.3 + 18361.2i −0.689193 + 0.740921i
\(851\) 39162.8 + 39162.8i 1.57754 + 1.57754i
\(852\) 14244.3 + 12320.2i 0.572774 + 0.495401i
\(853\) 12612.5 12612.5i 0.506266 0.506266i −0.407112 0.913378i \(-0.633464\pi\)
0.913378 + 0.407112i \(0.133464\pi\)
\(854\) −15010.8 + 542.941i −0.601473 + 0.0217553i
\(855\) 506.411i 0.0202560i
\(856\) 2274.40 + 20887.1i 0.0908147 + 0.834001i
\(857\) 46080.3i 1.83672i −0.395741 0.918362i \(-0.629512\pi\)
0.395741 0.918362i \(-0.370488\pi\)
\(858\) −227.937 6301.80i −0.00906950 0.250746i
\(859\) 8935.85 8935.85i 0.354933 0.354933i −0.507008 0.861941i \(-0.669249\pi\)
0.861941 + 0.507008i \(0.169249\pi\)
\(860\) −3215.92 + 232.945i −0.127514 + 0.00923647i
\(861\) 5454.28 + 5454.28i 0.215890 + 0.215890i
\(862\) −11241.7 10456.9i −0.444193 0.413182i
\(863\) 19360.8 0.763674 0.381837 0.924230i \(-0.375292\pi\)
0.381837 + 0.924230i \(0.375292\pi\)
\(864\) 4807.88 878.722i 0.189314 0.0346004i
\(865\) 3927.40 0.154377
\(866\) −10652.7 9908.98i −0.418006 0.388823i
\(867\) 393.086 + 393.086i 0.0153978 + 0.0153978i
\(868\) −6141.22 + 444.839i −0.240146 + 0.0173950i
\(869\) 13945.7 13945.7i 0.544391 0.544391i
\(870\) 2.31220 + 63.9258i 9.01046e−5 + 0.00249114i
\(871\) 1031.12i 0.0401128i
\(872\) 10427.2 1135.42i 0.404943 0.0440943i
\(873\) 14105.1i 0.546835i
\(874\) −36941.8 + 1336.19i −1.42972 + 0.0517132i
\(875\) 1147.24 1147.24i 0.0443242 0.0443242i
\(876\) 14525.7 + 12563.5i 0.560250 + 0.484568i
\(877\) 19139.4 + 19139.4i 0.736933 + 0.736933i 0.971983 0.235050i \(-0.0755254\pi\)
−0.235050 + 0.971983i \(0.575525\pi\)
\(878\) 4206.29 4521.99i 0.161680 0.173815i
\(879\) 25079.9 0.962372
\(880\) 302.715 + 2078.60i 0.0115960 + 0.0796244i
\(881\) 4836.79 0.184967 0.0924833 0.995714i \(-0.470520\pi\)
0.0924833 + 0.995714i \(0.470520\pi\)
\(882\) −5063.12 + 5443.13i −0.193292 + 0.207800i
\(883\) −7730.89 7730.89i −0.294638 0.294638i 0.544271 0.838909i \(-0.316806\pi\)
−0.838909 + 0.544271i \(0.816806\pi\)
\(884\) 7717.06 8922.34i 0.293612 0.339469i
\(885\) −417.963 + 417.963i −0.0158753 + 0.0158753i
\(886\) 2245.81 81.2314i 0.0851576 0.00308016i
\(887\) 12163.5i 0.460442i −0.973138 0.230221i \(-0.926055\pi\)
0.973138 0.230221i \(-0.0739448\pi\)
\(888\) 11116.9 13833.8i 0.420110 0.522782i
\(889\) 372.749i 0.0140625i
\(890\) 28.2516 + 781.076i 0.00106404 + 0.0294177i
\(891\) −2061.09 + 2061.09i −0.0774960 + 0.0774960i
\(892\) 49.5818 + 684.501i 0.00186112 + 0.0256937i
\(893\) −15001.9 15001.9i −0.562171 0.562171i
\(894\) −611.801 569.088i −0.0228878 0.0212899i
\(895\) −471.835 −0.0176220
\(896\) −8908.22 5247.25i −0.332146 0.195645i
\(897\) −13124.9 −0.488548
\(898\) −5465.37 5083.80i −0.203098 0.188918i
\(899\) −630.093 630.093i −0.0233757 0.0233757i
\(900\) −645.884 8916.75i −0.0239216 0.330250i
\(901\) −17843.4 + 17843.4i −0.659768 + 0.659768i
\(902\) 1325.00 + 36632.4i 0.0489108 + 1.35224i
\(903\) 9464.65i 0.348797i
\(904\) 19123.2 23796.8i 0.703572 0.875519i
\(905\) 2240.59i 0.0822981i
\(906\) −13291.8 + 480.767i −0.487408 + 0.0176296i
\(907\) −8264.83 + 8264.83i −0.302568 + 0.302568i −0.842018 0.539450i \(-0.818632\pi\)
0.539450 + 0.842018i \(0.318632\pi\)
\(908\) −18695.4 + 21615.3i −0.683292 + 0.790011i
\(909\) 536.516 + 536.516i 0.0195766 + 0.0195766i
\(910\) −259.047 + 278.489i −0.00943661 + 0.0101449i
\(911\) −41364.8 −1.50437 −0.752183 0.658955i \(-0.770999\pi\)
−0.752183 + 0.658955i \(0.770999\pi\)
\(912\) 1707.05 + 11721.5i 0.0619803 + 0.425589i
\(913\) 23635.3 0.856753
\(914\) 10685.1 11487.1i 0.386688 0.415711i
\(915\) −1439.18 1439.18i −0.0519978 0.0519978i
\(916\) −9555.20 8264.44i −0.344665 0.298106i
\(917\) −2769.74 + 2769.74i −0.0997434 + 0.0997434i
\(918\) −5449.26 + 197.100i −0.195918 + 0.00708636i
\(919\) 36966.7i 1.32690i 0.748221 + 0.663449i \(0.230908\pi\)
−0.748221 + 0.663449i \(0.769092\pi\)
\(920\) 4346.26 473.266i 0.155752 0.0169599i
\(921\) 4930.99i 0.176419i
\(922\) 1225.40 + 33878.8i 0.0437704 + 1.21013i
\(923\) −11459.2 + 11459.2i −0.408649 + 0.408649i
\(924\) 6149.70 445.454i 0.218951 0.0158597i
\(925\) −22954.4 22954.4i −0.815929 0.815929i
\(926\) −33986.1 31613.3i −1.20610 1.12190i
\(927\) −15863.3 −0.562050
\(928\) −269.004 1471.84i −0.00951563 0.0520643i
\(929\) −18882.5 −0.666862 −0.333431 0.942774i \(-0.608206\pi\)
−0.333431 + 0.942774i \(0.608206\pi\)
\(930\) −610.897 568.247i −0.0215399 0.0200361i
\(931\) −12739.5 12739.5i −0.448464 0.448464i
\(932\) 45913.7 3325.76i 1.61368 0.116887i
\(933\) 5000.55 5000.55i 0.175467 0.175467i
\(934\) −967.211 26740.6i −0.0338845 0.936810i
\(935\) 2343.48i 0.0819678i
\(936\) 455.264 + 4180.94i 0.0158983 + 0.146002i
\(937\) 8581.23i 0.299185i −0.988748 0.149593i \(-0.952204\pi\)
0.988748 0.149593i \(-0.0477962\pi\)
\(938\) −1007.55 + 36.4433i −0.0350723 + 0.00126857i
\(939\) −8031.21 + 8031.21i −0.279115 + 0.279115i
\(940\) 1897.81 + 1641.45i 0.0658508 + 0.0569554i
\(941\) −5618.83 5618.83i −0.194653 0.194653i 0.603050 0.797703i \(-0.293952\pi\)
−0.797703 + 0.603050i \(0.793952\pi\)
\(942\) −14207.6 + 15274.0i −0.491411 + 0.528293i
\(943\) 76295.1 2.63469
\(944\) 8265.35 11083.1i 0.284973 0.382125i
\(945\) 175.808 0.00605189
\(946\) −30633.9 + 32933.1i −1.05285 + 1.13187i
\(947\) 18722.7 + 18722.7i 0.642456 + 0.642456i 0.951159 0.308702i \(-0.0998947\pi\)
−0.308702 + 0.951159i \(0.599895\pi\)
\(948\) −8604.67 + 9948.57i −0.294796 + 0.340838i
\(949\) −11685.5 + 11685.5i −0.399713 + 0.399713i
\(950\) 21652.6 783.177i 0.739477 0.0267470i
\(951\) 13302.8i 0.453600i
\(952\) 8991.15 + 7225.33i 0.306098 + 0.245981i
\(953\) 17197.8i 0.584565i −0.956332 0.292282i \(-0.905585\pi\)
0.956332 0.292282i \(-0.0944147\pi\)
\(954\) −325.188 8990.51i −0.0110360 0.305114i
\(955\) −1102.45 + 1102.45i −0.0373556 + 0.0373556i
\(956\) −370.929 5120.85i −0.0125488 0.173243i
\(957\) 630.963 + 630.963i 0.0213126 + 0.0213126i
\(958\) 14887.4 + 13848.0i 0.502077 + 0.467025i
\(959\) 5676.06 0.191126
\(960\) −301.518 1368.09i −0.0101369 0.0459946i
\(961\) −18168.6 −0.609870
\(962\) 11181.6 + 10400.9i 0.374749 + 0.348586i
\(963\) 5909.21 + 5909.21i 0.197738 + 0.197738i
\(964\) −1668.84 23039.2i −0.0557571 0.769754i
\(965\) 1550.74 1550.74i 0.0517306 0.0517306i
\(966\) −463.879 12824.9i −0.0154504 0.427158i
\(967\) 58259.3i 1.93743i 0.248182 + 0.968713i \(0.420167\pi\)
−0.248182 + 0.968713i \(0.579833\pi\)
\(968\) −635.909 511.020i −0.0211146 0.0169678i
\(969\) 13215.2i 0.438114i
\(970\) 4040.34 146.140i 0.133740 0.00483738i
\(971\) −19203.8 + 19203.8i −0.634685 + 0.634685i −0.949239 0.314555i \(-0.898145\pi\)
0.314555 + 0.949239i \(0.398145\pi\)
\(972\) 1271.71 1470.33i 0.0419653 0.0485195i
\(973\) −12198.9 12198.9i −0.401930 0.401930i
\(974\) −21540.2 + 23156.9i −0.708615 + 0.761800i
\(975\) 7692.86 0.252686
\(976\) 38162.9 + 28460.3i 1.25160 + 0.933394i
\(977\) −16691.4 −0.546578 −0.273289 0.961932i \(-0.588112\pi\)
−0.273289 + 0.961932i \(0.588112\pi\)
\(978\) 21950.4 23597.8i 0.717684 0.771550i
\(979\) 7709.41 + 7709.41i 0.251679 + 0.251679i
\(980\) 1611.61 + 1393.91i 0.0525317 + 0.0454354i
\(981\) 2949.99 2949.99i 0.0960101 0.0960101i
\(982\) 46688.6 1688.73i 1.51720 0.0548774i
\(983\) 36043.6i 1.16949i 0.811216 + 0.584747i \(0.198806\pi\)
−0.811216 + 0.584747i \(0.801194\pi\)
\(984\) −2646.45 24303.8i −0.0857376 0.787376i
\(985\) 3576.14i 0.115680i
\(986\) 60.3387 + 1668.19i 0.00194886 + 0.0538804i
\(987\) 5208.12 5208.12i 0.167960 0.167960i
\(988\) −10166.0 + 736.371i −0.327351 + 0.0237116i
\(989\) 66196.3 + 66196.3i 2.12833 + 2.12833i
\(990\) 611.741 + 569.032i 0.0196388 + 0.0182677i
\(991\) −48948.9 −1.56904 −0.784518 0.620107i \(-0.787089\pi\)
−0.784518 + 0.620107i \(0.787089\pi\)
\(992\) 16055.4 + 11093.5i 0.513871 + 0.355059i
\(993\) −7357.23 −0.235120
\(994\) −11602.3 10792.2i −0.370222 0.344375i
\(995\) 971.831 + 971.831i 0.0309639 + 0.0309639i
\(996\) −15722.1 + 1138.83i −0.500175 + 0.0362301i
\(997\) −22542.1 + 22542.1i −0.716062 + 0.716062i −0.967796 0.251734i \(-0.918999\pi\)
0.251734 + 0.967796i \(0.418999\pi\)
\(998\) −302.800 8371.56i −0.00960418 0.265528i
\(999\) 7058.84i 0.223556i
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 48.4.j.a.13.10 24
3.2 odd 2 144.4.k.b.109.3 24
4.3 odd 2 192.4.j.a.145.3 24
8.3 odd 2 384.4.j.a.289.9 24
8.5 even 2 384.4.j.b.289.4 24
12.11 even 2 576.4.k.b.145.7 24
16.3 odd 4 384.4.j.a.97.9 24
16.5 even 4 inner 48.4.j.a.37.10 yes 24
16.11 odd 4 192.4.j.a.49.3 24
16.13 even 4 384.4.j.b.97.4 24
48.5 odd 4 144.4.k.b.37.3 24
48.11 even 4 576.4.k.b.433.7 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.4.j.a.13.10 24 1.1 even 1 trivial
48.4.j.a.37.10 yes 24 16.5 even 4 inner
144.4.k.b.37.3 24 48.5 odd 4
144.4.k.b.109.3 24 3.2 odd 2
192.4.j.a.49.3 24 16.11 odd 4
192.4.j.a.145.3 24 4.3 odd 2
384.4.j.a.97.9 24 16.3 odd 4
384.4.j.a.289.9 24 8.3 odd 2
384.4.j.b.97.4 24 16.13 even 4
384.4.j.b.289.4 24 8.5 even 2
576.4.k.b.145.7 24 12.11 even 2
576.4.k.b.433.7 24 48.11 even 4