Properties

Label 42.5.g.a.31.2
Level $42$
Weight $5$
Character 42.31
Analytic conductor $4.342$
Analytic rank $0$
Dimension $4$
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] = [42,5,Mod(19,42)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("42.19");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 42.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.34153844952\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 42.31
Dual form 42.5.g.a.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.41421 + 2.44949i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-20.7426 + 11.9758i) q^{5} -14.6969i q^{6} +(-47.1985 + 13.1645i) q^{7} -22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +O(q^{10})\) \(q+(1.41421 + 2.44949i) q^{2} +(-4.50000 - 2.59808i) q^{3} +(-4.00000 + 6.92820i) q^{4} +(-20.7426 + 11.9758i) q^{5} -14.6969i q^{6} +(-47.1985 + 13.1645i) q^{7} -22.6274 q^{8} +(13.5000 + 23.3827i) q^{9} +(-58.6690 - 33.8726i) q^{10} +(-48.9853 + 84.8450i) q^{11} +(36.0000 - 20.7846i) q^{12} -104.211i q^{13} +(-98.9949 - 96.9948i) q^{14} +124.456 q^{15} +(-32.0000 - 55.4256i) q^{16} +(93.2498 + 53.8378i) q^{17} +(-38.1838 + 66.1362i) q^{18} +(33.2498 - 19.1968i) q^{19} -191.612i q^{20} +(246.595 + 63.3852i) q^{21} -277.103 q^{22} +(510.749 + 884.644i) q^{23} +(101.823 + 58.7878i) q^{24} +(-25.6619 + 44.4477i) q^{25} +(255.265 - 147.377i) q^{26} -140.296i q^{27} +(97.5879 - 379.659i) q^{28} +621.603 q^{29} +(176.007 + 304.853i) q^{30} +(-1315.61 - 759.568i) q^{31} +(90.5097 - 156.767i) q^{32} +(440.868 - 254.535i) q^{33} +304.553i q^{34} +(821.367 - 838.304i) q^{35} -216.000 q^{36} +(281.118 + 486.910i) q^{37} +(94.0446 + 54.2967i) q^{38} +(-270.749 + 468.952i) q^{39} +(469.352 - 270.981i) q^{40} -1023.20i q^{41} +(193.477 + 693.673i) q^{42} -3382.41 q^{43} +(-391.882 - 678.760i) q^{44} +(-560.051 - 323.346i) q^{45} +(-1444.62 + 2502.15i) q^{46} +(-3416.50 + 1972.52i) q^{47} +332.554i q^{48} +(2054.39 - 1242.69i) q^{49} -145.166 q^{50} +(-279.749 - 484.540i) q^{51} +(721.998 + 416.846i) q^{52} +(-1095.30 + 1897.12i) q^{53} +(343.654 - 198.409i) q^{54} -2346.55i q^{55} +(1067.98 - 297.878i) q^{56} -199.499 q^{57} +(879.079 + 1522.61i) q^{58} +(2541.67 + 1467.44i) q^{59} +(-497.823 + 862.255i) q^{60} +(576.207 - 332.673i) q^{61} -4296.76i q^{62} +(-945.000 - 925.907i) q^{63} +512.000 q^{64} +(1248.01 + 2161.62i) q^{65} +(1246.96 + 719.934i) q^{66} +(2962.69 - 5131.53i) q^{67} +(-745.998 + 430.702i) q^{68} -5307.86i q^{69} +(3215.00 + 826.389i) q^{70} -4494.41 q^{71} +(-305.470 - 529.090i) q^{72} +(7767.32 + 4484.46i) q^{73} +(-795.121 + 1377.19i) q^{74} +(230.957 - 133.343i) q^{75} +307.148i q^{76} +(1195.09 - 4649.42i) q^{77} -1531.59 q^{78} +(5223.41 + 9047.22i) q^{79} +(1327.53 + 766.449i) q^{80} +(-364.500 + 631.333i) q^{81} +(2506.31 - 1447.02i) q^{82} +1269.28i q^{83} +(-1425.53 + 1454.92i) q^{84} -2579.00 q^{85} +(-4783.45 - 8285.17i) q^{86} +(-2797.21 - 1614.97i) q^{87} +(1108.41 - 1919.82i) q^{88} +(-3121.46 + 1802.18i) q^{89} -1829.12i q^{90} +(1371.89 + 4918.62i) q^{91} -8171.99 q^{92} +(3946.83 + 6836.11i) q^{93} +(-9663.32 - 5579.12i) q^{94} +(-459.792 + 796.383i) q^{95} +(-814.587 + 470.302i) q^{96} -1950.53i q^{97} +(5949.30 + 3274.79i) q^{98} -2645.21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{3} - 16 q^{4} - 66 q^{5} - 70 q^{7} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{3} - 16 q^{4} - 66 q^{5} - 70 q^{7} + 54 q^{9} - 48 q^{10} - 162 q^{11} + 144 q^{12} + 396 q^{15} - 128 q^{16} - 204 q^{17} - 444 q^{19} + 630 q^{21} - 192 q^{22} + 312 q^{23} - 476 q^{25} + 1632 q^{26} - 560 q^{28} + 2724 q^{29} + 144 q^{30} - 3786 q^{31} + 1458 q^{33} + 672 q^{35} - 864 q^{36} + 1396 q^{37} + 1632 q^{38} + 648 q^{39} + 384 q^{40} - 1008 q^{42} - 632 q^{43} - 1296 q^{44} - 1782 q^{45} - 4896 q^{46} - 7896 q^{47} - 98 q^{49} + 2112 q^{50} + 612 q^{51} - 1728 q^{52} - 1038 q^{53} + 2688 q^{56} + 2664 q^{57} - 336 q^{58} - 966 q^{59} - 1584 q^{60} + 5088 q^{61} - 3780 q^{63} + 2048 q^{64} - 744 q^{65} + 864 q^{66} + 14600 q^{67} + 1632 q^{68} + 5376 q^{70} - 9696 q^{71} + 22584 q^{73} + 768 q^{74} + 4284 q^{75} - 3654 q^{77} - 9792 q^{78} + 3974 q^{79} + 4224 q^{80} - 1458 q^{81} + 18816 q^{82} + 1224 q^{85} - 18240 q^{86} - 12258 q^{87} + 768 q^{88} - 33156 q^{89} - 18984 q^{91} - 4992 q^{92} + 11358 q^{93} - 16320 q^{94} + 3252 q^{95} + 23520 q^{98} - 8748 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421 + 2.44949i 0.353553 + 0.612372i
\(3\) −4.50000 2.59808i −0.500000 0.288675i
\(4\) −4.00000 + 6.92820i −0.250000 + 0.433013i
\(5\) −20.7426 + 11.9758i −0.829706 + 0.479031i −0.853752 0.520680i \(-0.825678\pi\)
0.0240462 + 0.999711i \(0.492345\pi\)
\(6\) 14.6969i 0.408248i
\(7\) −47.1985 + 13.1645i −0.963234 + 0.268662i
\(8\) −22.6274 −0.353553
\(9\) 13.5000 + 23.3827i 0.166667 + 0.288675i
\(10\) −58.6690 33.8726i −0.586690 0.338726i
\(11\) −48.9853 + 84.8450i −0.404837 + 0.701198i −0.994302 0.106595i \(-0.966005\pi\)
0.589465 + 0.807794i \(0.299338\pi\)
\(12\) 36.0000 20.7846i 0.250000 0.144338i
\(13\) 104.211i 0.616636i −0.951283 0.308318i \(-0.900234\pi\)
0.951283 0.308318i \(-0.0997661\pi\)
\(14\) −98.9949 96.9948i −0.505076 0.494872i
\(15\) 124.456 0.553137
\(16\) −32.0000 55.4256i −0.125000 0.216506i
\(17\) 93.2498 + 53.8378i 0.322664 + 0.186290i 0.652579 0.757721i \(-0.273687\pi\)
−0.329916 + 0.944010i \(0.607020\pi\)
\(18\) −38.1838 + 66.1362i −0.117851 + 0.204124i
\(19\) 33.2498 19.1968i 0.0921047 0.0531767i −0.453240 0.891388i \(-0.649732\pi\)
0.545345 + 0.838212i \(0.316399\pi\)
\(20\) 191.612i 0.479031i
\(21\) 246.595 + 63.3852i 0.559173 + 0.143731i
\(22\) −277.103 −0.572526
\(23\) 510.749 + 884.644i 0.965500 + 1.67229i 0.708266 + 0.705945i \(0.249478\pi\)
0.257233 + 0.966349i \(0.417189\pi\)
\(24\) 101.823 + 58.7878i 0.176777 + 0.102062i
\(25\) −25.6619 + 44.4477i −0.0410590 + 0.0711164i
\(26\) 255.265 147.377i 0.377611 0.218014i
\(27\) 140.296i 0.192450i
\(28\) 97.5879 379.659i 0.124474 0.484258i
\(29\) 621.603 0.739124 0.369562 0.929206i \(-0.379508\pi\)
0.369562 + 0.929206i \(0.379508\pi\)
\(30\) 176.007 + 304.853i 0.195563 + 0.338726i
\(31\) −1315.61 759.568i −1.36900 0.790393i −0.378200 0.925724i \(-0.623457\pi\)
−0.990800 + 0.135331i \(0.956790\pi\)
\(32\) 90.5097 156.767i 0.0883883 0.153093i
\(33\) 440.868 254.535i 0.404837 0.233733i
\(34\) 304.553i 0.263454i
\(35\) 821.367 838.304i 0.670503 0.684330i
\(36\) −216.000 −0.166667
\(37\) 281.118 + 486.910i 0.205345 + 0.355669i 0.950243 0.311511i \(-0.100835\pi\)
−0.744897 + 0.667179i \(0.767502\pi\)
\(38\) 94.0446 + 54.2967i 0.0651278 + 0.0376016i
\(39\) −270.749 + 468.952i −0.178007 + 0.308318i
\(40\) 469.352 270.981i 0.293345 0.169363i
\(41\) 1023.20i 0.608684i −0.952563 0.304342i \(-0.901563\pi\)
0.952563 0.304342i \(-0.0984365\pi\)
\(42\) 193.477 + 693.673i 0.109681 + 0.393239i
\(43\) −3382.41 −1.82932 −0.914658 0.404228i \(-0.867540\pi\)
−0.914658 + 0.404228i \(0.867540\pi\)
\(44\) −391.882 678.760i −0.202419 0.350599i
\(45\) −560.051 323.346i −0.276569 0.159677i
\(46\) −1444.62 + 2502.15i −0.682711 + 1.18249i
\(47\) −3416.50 + 1972.52i −1.54663 + 0.892945i −0.548231 + 0.836327i \(0.684698\pi\)
−0.998396 + 0.0566179i \(0.981968\pi\)
\(48\) 332.554i 0.144338i
\(49\) 2054.39 1242.69i 0.855641 0.517570i
\(50\) −145.166 −0.0580663
\(51\) −279.749 484.540i −0.107555 0.186290i
\(52\) 721.998 + 416.846i 0.267011 + 0.154159i
\(53\) −1095.30 + 1897.12i −0.389925 + 0.675370i −0.992439 0.122738i \(-0.960833\pi\)
0.602514 + 0.798108i \(0.294166\pi\)
\(54\) 343.654 198.409i 0.117851 0.0680414i
\(55\) 2346.55i 0.775718i
\(56\) 1067.98 297.878i 0.340555 0.0949865i
\(57\) −199.499 −0.0614031
\(58\) 879.079 + 1522.61i 0.261320 + 0.452619i
\(59\) 2541.67 + 1467.44i 0.730156 + 0.421556i 0.818479 0.574536i \(-0.194818\pi\)
−0.0883234 + 0.996092i \(0.528151\pi\)
\(60\) −497.823 + 862.255i −0.138284 + 0.239515i
\(61\) 576.207 332.673i 0.154853 0.0894043i −0.420571 0.907259i \(-0.638170\pi\)
0.575424 + 0.817855i \(0.304837\pi\)
\(62\) 4296.76i 1.11778i
\(63\) −945.000 925.907i −0.238095 0.233285i
\(64\) 512.000 0.125000
\(65\) 1248.01 + 2161.62i 0.295388 + 0.511626i
\(66\) 1246.96 + 719.934i 0.286263 + 0.165274i
\(67\) 2962.69 5131.53i 0.659989 1.14314i −0.320629 0.947205i \(-0.603894\pi\)
0.980618 0.195930i \(-0.0627726\pi\)
\(68\) −745.998 + 430.702i −0.161332 + 0.0931450i
\(69\) 5307.86i 1.11486i
\(70\) 3215.00 + 826.389i 0.656123 + 0.168651i
\(71\) −4494.41 −0.891571 −0.445785 0.895140i \(-0.647076\pi\)
−0.445785 + 0.895140i \(0.647076\pi\)
\(72\) −305.470 529.090i −0.0589256 0.102062i
\(73\) 7767.32 + 4484.46i 1.45756 + 0.841521i 0.998891 0.0470879i \(-0.0149941\pi\)
0.458666 + 0.888609i \(0.348327\pi\)
\(74\) −795.121 + 1377.19i −0.145201 + 0.251496i
\(75\) 230.957 133.343i 0.0410590 0.0237055i
\(76\) 307.148i 0.0531767i
\(77\) 1195.09 4649.42i 0.201567 0.784183i
\(78\) −1531.59 −0.251741
\(79\) 5223.41 + 9047.22i 0.836951 + 1.44964i 0.892432 + 0.451182i \(0.148998\pi\)
−0.0554805 + 0.998460i \(0.517669\pi\)
\(80\) 1327.53 + 766.449i 0.207426 + 0.119758i
\(81\) −364.500 + 631.333i −0.0555556 + 0.0962250i
\(82\) 2506.31 1447.02i 0.372741 0.215202i
\(83\) 1269.28i 0.184247i 0.995748 + 0.0921234i \(0.0293654\pi\)
−0.995748 + 0.0921234i \(0.970635\pi\)
\(84\) −1425.53 + 1454.92i −0.202031 + 0.206197i
\(85\) −2579.00 −0.356954
\(86\) −4783.45 8285.17i −0.646761 1.12022i
\(87\) −2797.21 1614.97i −0.369562 0.213367i
\(88\) 1108.41 1919.82i 0.143132 0.247911i
\(89\) −3121.46 + 1802.18i −0.394074 + 0.227519i −0.683924 0.729553i \(-0.739728\pi\)
0.289850 + 0.957072i \(0.406395\pi\)
\(90\) 1829.12i 0.225817i
\(91\) 1371.89 + 4918.62i 0.165667 + 0.593965i
\(92\) −8171.99 −0.965500
\(93\) 3946.83 + 6836.11i 0.456334 + 0.790393i
\(94\) −9663.32 5579.12i −1.09363 0.631408i
\(95\) −459.792 + 796.383i −0.0509465 + 0.0882419i
\(96\) −814.587 + 470.302i −0.0883883 + 0.0510310i
\(97\) 1950.53i 0.207304i −0.994614 0.103652i \(-0.966947\pi\)
0.994614 0.103652i \(-0.0330529\pi\)
\(98\) 5949.30 + 3274.79i 0.619460 + 0.340982i
\(99\) −2645.21 −0.269891
\(100\) −205.295 355.582i −0.0205295 0.0355582i
\(101\) 9808.81 + 5663.12i 0.961554 + 0.555153i 0.896651 0.442738i \(-0.145993\pi\)
0.0649030 + 0.997892i \(0.479326\pi\)
\(102\) 791.251 1370.49i 0.0760525 0.131727i
\(103\) −14141.2 + 8164.43i −1.33294 + 0.769576i −0.985750 0.168217i \(-0.946199\pi\)
−0.347195 + 0.937793i \(0.612866\pi\)
\(104\) 2358.04i 0.218014i
\(105\) −5874.13 + 1638.39i −0.532801 + 0.148607i
\(106\) −6195.95 −0.551438
\(107\) −2198.23 3807.45i −0.192002 0.332557i 0.753912 0.656976i \(-0.228165\pi\)
−0.945914 + 0.324419i \(0.894831\pi\)
\(108\) 972.000 + 561.184i 0.0833333 + 0.0481125i
\(109\) 7348.89 12728.6i 0.618541 1.07134i −0.371211 0.928548i \(-0.621057\pi\)
0.989752 0.142796i \(-0.0456093\pi\)
\(110\) 5747.84 3318.52i 0.475028 0.274258i
\(111\) 2921.46i 0.237112i
\(112\) 2240.00 + 2194.74i 0.178571 + 0.174964i
\(113\) 2124.36 0.166368 0.0831842 0.996534i \(-0.473491\pi\)
0.0831842 + 0.996534i \(0.473491\pi\)
\(114\) −282.134 488.670i −0.0217093 0.0376016i
\(115\) −21188.6 12233.2i −1.60216 0.925008i
\(116\) −2486.41 + 4306.59i −0.184781 + 0.320050i
\(117\) 2436.74 1406.85i 0.178007 0.102773i
\(118\) 8301.07i 0.596170i
\(119\) −5109.99 1313.48i −0.360850 0.0927533i
\(120\) −2816.11 −0.195563
\(121\) 2521.38 + 4367.17i 0.172214 + 0.298283i
\(122\) 1629.76 + 940.942i 0.109497 + 0.0632184i
\(123\) −2658.35 + 4604.39i −0.175712 + 0.304342i
\(124\) 10524.9 6076.54i 0.684500 0.395196i
\(125\) 16199.0i 1.03674i
\(126\) 931.568 3624.20i 0.0586778 0.228282i
\(127\) 8498.07 0.526881 0.263441 0.964676i \(-0.415143\pi\)
0.263441 + 0.964676i \(0.415143\pi\)
\(128\) 724.077 + 1254.14i 0.0441942 + 0.0765466i
\(129\) 15220.8 + 8787.75i 0.914658 + 0.528078i
\(130\) −3529.91 + 6113.99i −0.208871 + 0.361774i
\(131\) 12533.4 7236.14i 0.730340 0.421662i −0.0882063 0.996102i \(-0.528113\pi\)
0.818547 + 0.574440i \(0.194780\pi\)
\(132\) 4072.56i 0.233733i
\(133\) −1316.62 + 1343.77i −0.0744318 + 0.0759666i
\(134\) 16759.5 0.933366
\(135\) 1680.15 + 2910.11i 0.0921895 + 0.159677i
\(136\) −2110.00 1218.21i −0.114079 0.0658634i
\(137\) −6427.59 + 11132.9i −0.342458 + 0.593154i −0.984888 0.173190i \(-0.944593\pi\)
0.642431 + 0.766344i \(0.277926\pi\)
\(138\) 13001.6 7506.45i 0.682711 0.394164i
\(139\) 5009.46i 0.259275i 0.991561 + 0.129638i \(0.0413814\pi\)
−0.991561 + 0.129638i \(0.958619\pi\)
\(140\) 2522.47 + 9043.81i 0.128698 + 0.461419i
\(141\) 20499.0 1.03108
\(142\) −6356.05 11009.0i −0.315218 0.545973i
\(143\) 8841.82 + 5104.83i 0.432384 + 0.249637i
\(144\) 864.000 1496.49i 0.0416667 0.0721688i
\(145\) −12893.7 + 7444.17i −0.613255 + 0.354063i
\(146\) 25368.0i 1.19009i
\(147\) −12473.4 + 254.611i −0.577230 + 0.0117827i
\(148\) −4497.88 −0.205345
\(149\) −12699.5 21996.1i −0.572022 0.990771i −0.996358 0.0852664i \(-0.972826\pi\)
0.424336 0.905505i \(-0.360507\pi\)
\(150\) 653.245 + 377.151i 0.0290331 + 0.0167623i
\(151\) 9154.39 15855.9i 0.401491 0.695402i −0.592415 0.805633i \(-0.701826\pi\)
0.993906 + 0.110230i \(0.0351589\pi\)
\(152\) −752.357 + 434.373i −0.0325639 + 0.0188008i
\(153\) 2907.24i 0.124193i
\(154\) 13078.8 3647.91i 0.551477 0.153816i
\(155\) 36385.6 1.51449
\(156\) −2165.99 3751.61i −0.0890037 0.154159i
\(157\) −30522.6 17622.2i −1.23829 0.714926i −0.269544 0.962988i \(-0.586873\pi\)
−0.968744 + 0.248062i \(0.920206\pi\)
\(158\) −14774.0 + 25589.4i −0.591814 + 1.02505i
\(159\) 9857.70 5691.35i 0.389925 0.225123i
\(160\) 4335.69i 0.169363i
\(161\) −35752.5 35030.1i −1.37929 1.35142i
\(162\) −2061.92 −0.0785674
\(163\) −72.9693 126.386i −0.00274641 0.00475691i 0.864649 0.502377i \(-0.167541\pi\)
−0.867395 + 0.497620i \(0.834208\pi\)
\(164\) 7088.92 + 4092.79i 0.263568 + 0.152171i
\(165\) −6096.50 + 10559.5i −0.223930 + 0.387859i
\(166\) −3109.08 + 1795.03i −0.112828 + 0.0651411i
\(167\) 31314.1i 1.12281i 0.827541 + 0.561405i \(0.189739\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(168\) −5579.82 1434.24i −0.197698 0.0508164i
\(169\) 17701.0 0.619760
\(170\) −3647.25 6317.22i −0.126202 0.218589i
\(171\) 897.744 + 518.313i 0.0307016 + 0.0177256i
\(172\) 13529.6 23434.0i 0.457329 0.792117i
\(173\) −34741.3 + 20057.9i −1.16079 + 0.670183i −0.951494 0.307669i \(-0.900451\pi\)
−0.209298 + 0.977852i \(0.567118\pi\)
\(174\) 9135.66i 0.301746i
\(175\) 626.073 2435.69i 0.0204432 0.0795327i
\(176\) 6270.12 0.202419
\(177\) −7625.02 13206.9i −0.243385 0.421556i
\(178\) −8828.83 5097.33i −0.278653 0.160880i
\(179\) 25077.2 43435.0i 0.782661 1.35561i −0.147726 0.989028i \(-0.547195\pi\)
0.930387 0.366580i \(-0.119471\pi\)
\(180\) 4480.41 2586.77i 0.138284 0.0798385i
\(181\) 63974.3i 1.95276i 0.216069 + 0.976378i \(0.430677\pi\)
−0.216069 + 0.976378i \(0.569323\pi\)
\(182\) −10108.0 + 10316.4i −0.305156 + 0.311448i
\(183\) −3457.24 −0.103235
\(184\) −11556.9 20017.2i −0.341356 0.591245i
\(185\) −11662.2 6733.20i −0.340752 0.196733i
\(186\) −11163.3 + 19335.4i −0.322677 + 0.558892i
\(187\) −9135.73 + 5274.52i −0.261252 + 0.150834i
\(188\) 31560.3i 0.892945i
\(189\) 1846.92 + 6621.76i 0.0517041 + 0.185375i
\(190\) −2600.98 −0.0720492
\(191\) 21384.4 + 37039.0i 0.586180 + 1.01529i 0.994727 + 0.102557i \(0.0327024\pi\)
−0.408547 + 0.912737i \(0.633964\pi\)
\(192\) −2304.00 1330.22i −0.0625000 0.0360844i
\(193\) 4386.29 7597.28i 0.117756 0.203959i −0.801122 0.598501i \(-0.795763\pi\)
0.918878 + 0.394542i \(0.129097\pi\)
\(194\) 4777.80 2758.46i 0.126947 0.0732932i
\(195\) 12969.7i 0.341084i
\(196\) 392.000 + 19204.0i 0.0102041 + 0.499896i
\(197\) −32825.0 −0.845808 −0.422904 0.906174i \(-0.638989\pi\)
−0.422904 + 0.906174i \(0.638989\pi\)
\(198\) −3740.89 6479.40i −0.0954210 0.165274i
\(199\) −22918.7 13232.1i −0.578740 0.334136i 0.181893 0.983318i \(-0.441778\pi\)
−0.760632 + 0.649183i \(0.775111\pi\)
\(200\) 580.663 1005.74i 0.0145166 0.0251434i
\(201\) −26664.2 + 15394.6i −0.659989 + 0.381045i
\(202\) 32035.4i 0.785106i
\(203\) −29338.7 + 8183.07i −0.711949 + 0.198575i
\(204\) 4475.99 0.107555
\(205\) 12253.6 + 21223.8i 0.291578 + 0.505028i
\(206\) −39997.4 23092.5i −0.942534 0.544172i
\(207\) −13790.2 + 23885.4i −0.321833 + 0.557432i
\(208\) −5775.99 + 3334.77i −0.133506 + 0.0770795i
\(209\) 3761.44i 0.0861115i
\(210\) −12320.5 12071.6i −0.279376 0.273732i
\(211\) 67056.3 1.50617 0.753087 0.657921i \(-0.228564\pi\)
0.753087 + 0.657921i \(0.228564\pi\)
\(212\) −8762.40 15176.9i −0.194963 0.337685i
\(213\) 20224.8 + 11676.8i 0.445785 + 0.257374i
\(214\) 6217.54 10769.1i 0.135766 0.235154i
\(215\) 70160.1 40506.9i 1.51779 0.876299i
\(216\) 3174.54i 0.0680414i
\(217\) 72094.1 + 18531.1i 1.53102 + 0.393535i
\(218\) 41571.6 0.874749
\(219\) −23302.0 40360.2i −0.485852 0.841521i
\(220\) 16257.3 + 9386.18i 0.335896 + 0.193929i
\(221\) 5610.52 9717.70i 0.114873 0.198966i
\(222\) 7156.09 4131.57i 0.145201 0.0838319i
\(223\) 56260.1i 1.13133i 0.824634 + 0.565666i \(0.191381\pi\)
−0.824634 + 0.565666i \(0.808619\pi\)
\(224\) −2208.16 + 8590.69i −0.0440083 + 0.171211i
\(225\) −1385.74 −0.0273727
\(226\) 3004.30 + 5203.59i 0.0588201 + 0.101879i
\(227\) 52955.8 + 30574.1i 1.02769 + 0.593337i 0.916322 0.400442i \(-0.131143\pi\)
0.111368 + 0.993779i \(0.464477\pi\)
\(228\) 797.995 1382.17i 0.0153508 0.0265883i
\(229\) 29274.9 16901.9i 0.558244 0.322303i −0.194196 0.980963i \(-0.562210\pi\)
0.752441 + 0.658660i \(0.228877\pi\)
\(230\) 69201.6i 1.30816i
\(231\) −17457.5 + 17817.4i −0.327158 + 0.333904i
\(232\) −14065.3 −0.261320
\(233\) −4343.63 7523.39i −0.0800094 0.138580i 0.823244 0.567687i \(-0.192162\pi\)
−0.903254 + 0.429107i \(0.858828\pi\)
\(234\) 6892.15 + 3979.19i 0.125870 + 0.0726712i
\(235\) 47244.8 81830.4i 0.855496 1.48176i
\(236\) −20333.4 + 11739.5i −0.365078 + 0.210778i
\(237\) 54283.3i 0.966428i
\(238\) −4009.27 14374.4i −0.0707801 0.253768i
\(239\) −15715.0 −0.275118 −0.137559 0.990494i \(-0.543926\pi\)
−0.137559 + 0.990494i \(0.543926\pi\)
\(240\) −3982.59 6898.04i −0.0691421 0.119758i
\(241\) −4744.80 2739.41i −0.0816928 0.0471654i 0.458597 0.888644i \(-0.348352\pi\)
−0.540290 + 0.841479i \(0.681685\pi\)
\(242\) −7131.55 + 12352.2i −0.121774 + 0.210918i
\(243\) 3280.50 1894.00i 0.0555556 0.0320750i
\(244\) 5322.77i 0.0894043i
\(245\) −27731.4 + 50379.5i −0.461998 + 0.839309i
\(246\) −15037.9 −0.248494
\(247\) −2000.52 3465.01i −0.0327906 0.0567950i
\(248\) 29768.9 + 17187.1i 0.484015 + 0.279446i
\(249\) 3297.68 5711.74i 0.0531875 0.0921234i
\(250\) 39679.3 22908.8i 0.634868 0.366541i
\(251\) 24350.9i 0.386516i −0.981148 0.193258i \(-0.938095\pi\)
0.981148 0.193258i \(-0.0619054\pi\)
\(252\) 10194.9 2843.52i 0.160539 0.0447771i
\(253\) −100077. −1.56348
\(254\) 12018.1 + 20815.9i 0.186281 + 0.322647i
\(255\) 11605.5 + 6700.43i 0.178477 + 0.103044i
\(256\) −2048.00 + 3547.24i −0.0312500 + 0.0541266i
\(257\) 10051.7 5803.37i 0.152186 0.0878647i −0.421973 0.906608i \(-0.638662\pi\)
0.574159 + 0.818744i \(0.305329\pi\)
\(258\) 49711.0i 0.746815i
\(259\) −19678.2 19280.7i −0.293350 0.287424i
\(260\) −19968.2 −0.295388
\(261\) 8391.64 + 14534.7i 0.123187 + 0.213367i
\(262\) 35449.7 + 20466.9i 0.516429 + 0.298160i
\(263\) −60333.8 + 104501.i −0.872266 + 1.51081i −0.0126200 + 0.999920i \(0.504017\pi\)
−0.859646 + 0.510889i \(0.829316\pi\)
\(264\) −9975.69 + 5759.47i −0.143132 + 0.0826370i
\(265\) 52468.3i 0.747145i
\(266\) −5153.55 1324.67i −0.0728355 0.0187217i
\(267\) 18728.8 0.262716
\(268\) 23701.5 + 41052.3i 0.329995 + 0.571568i
\(269\) −23596.3 13623.3i −0.326091 0.188269i 0.328013 0.944673i \(-0.393621\pi\)
−0.654104 + 0.756404i \(0.726954\pi\)
\(270\) −4752.19 + 8231.04i −0.0651878 + 0.112909i
\(271\) −84041.9 + 48521.6i −1.14435 + 0.660689i −0.947503 0.319746i \(-0.896402\pi\)
−0.196843 + 0.980435i \(0.563069\pi\)
\(272\) 6891.24i 0.0931450i
\(273\) 6605.46 25698.1i 0.0886294 0.344806i
\(274\) −36359.9 −0.484308
\(275\) −2514.11 4354.57i −0.0332444 0.0575811i
\(276\) 36774.0 + 21231.5i 0.482750 + 0.278716i
\(277\) −14876.4 + 25766.7i −0.193882 + 0.335814i −0.946534 0.322605i \(-0.895441\pi\)
0.752651 + 0.658419i \(0.228775\pi\)
\(278\) −12270.6 + 7084.44i −0.158773 + 0.0916676i
\(279\) 41016.7i 0.526929i
\(280\) −18585.4 + 18968.7i −0.237059 + 0.241947i
\(281\) −122275. −1.54855 −0.774276 0.632849i \(-0.781886\pi\)
−0.774276 + 0.632849i \(0.781886\pi\)
\(282\) 28989.9 + 50212.1i 0.364543 + 0.631408i
\(283\) −52568.4 30350.4i −0.656374 0.378958i 0.134520 0.990911i \(-0.457051\pi\)
−0.790894 + 0.611953i \(0.790384\pi\)
\(284\) 17977.6 31138.2i 0.222893 0.386062i
\(285\) 4138.13 2389.15i 0.0509465 0.0294140i
\(286\) 28877.3i 0.353040i
\(287\) 13469.8 + 48293.4i 0.163531 + 0.586305i
\(288\) 4887.52 0.0589256
\(289\) −35963.5 62290.6i −0.430592 0.745807i
\(290\) −36468.9 21055.3i −0.433637 0.250360i
\(291\) −5067.62 + 8777.37i −0.0598436 + 0.103652i
\(292\) −62138.6 + 35875.7i −0.728778 + 0.420760i
\(293\) 29557.4i 0.344296i −0.985071 0.172148i \(-0.944929\pi\)
0.985071 0.172148i \(-0.0550707\pi\)
\(294\) −18263.7 30193.3i −0.211297 0.349314i
\(295\) −70294.7 −0.807752
\(296\) −6360.97 11017.5i −0.0726005 0.125748i
\(297\) 11903.4 + 6872.44i 0.134946 + 0.0779109i
\(298\) 35919.5 62214.4i 0.404481 0.700581i
\(299\) 92190.0 53225.9i 1.03120 0.595362i
\(300\) 2133.49i 0.0237055i
\(301\) 159644. 44527.6i 1.76206 0.491469i
\(302\) 51785.0 0.567794
\(303\) −29426.4 50968.1i −0.320518 0.555153i
\(304\) −2127.99 1228.59i −0.0230262 0.0132942i
\(305\) −7968.04 + 13801.0i −0.0856548 + 0.148358i
\(306\) −7121.26 + 4111.46i −0.0760525 + 0.0439090i
\(307\) 107567.i 1.14131i −0.821191 0.570654i \(-0.806690\pi\)
0.821191 0.570654i \(-0.193310\pi\)
\(308\) 27431.8 + 26877.5i 0.289169 + 0.283327i
\(309\) 84847.3 0.888630
\(310\) 51457.0 + 89126.2i 0.535453 + 0.927432i
\(311\) 37561.0 + 21685.9i 0.388344 + 0.224211i 0.681442 0.731872i \(-0.261353\pi\)
−0.293098 + 0.956082i \(0.594686\pi\)
\(312\) 6126.36 10611.2i 0.0629351 0.109007i
\(313\) −93311.1 + 53873.2i −0.952455 + 0.549900i −0.893843 0.448381i \(-0.852001\pi\)
−0.0586125 + 0.998281i \(0.518668\pi\)
\(314\) 99686.3i 1.01106i
\(315\) 30690.2 + 7888.66i 0.309300 + 0.0795027i
\(316\) −83574.6 −0.836951
\(317\) 77996.9 + 135095.i 0.776174 + 1.34437i 0.934133 + 0.356926i \(0.116175\pi\)
−0.157959 + 0.987446i \(0.550491\pi\)
\(318\) 27881.8 + 16097.6i 0.275719 + 0.159186i
\(319\) −30449.4 + 52739.9i −0.299225 + 0.518272i
\(320\) −10620.2 + 6131.59i −0.103713 + 0.0598788i
\(321\) 22844.7i 0.221705i
\(322\) 35244.3 137115.i 0.339920 1.32243i
\(323\) 4134.05 0.0396251
\(324\) −2916.00 5050.66i −0.0277778 0.0481125i
\(325\) 4631.96 + 2674.26i 0.0438529 + 0.0253185i
\(326\) 206.388 357.475i 0.00194200 0.00336365i
\(327\) −66140.0 + 38185.9i −0.618541 + 0.357115i
\(328\) 23152.3i 0.215202i
\(329\) 135286. 138076.i 1.24986 1.27564i
\(330\) −34487.0 −0.316685
\(331\) −20109.4 34830.4i −0.183545 0.317909i 0.759540 0.650460i \(-0.225424\pi\)
−0.943085 + 0.332551i \(0.892091\pi\)
\(332\) −8793.80 5077.10i −0.0797812 0.0460617i
\(333\) −7590.18 + 13146.6i −0.0684484 + 0.118556i
\(334\) −76703.5 + 44284.8i −0.687578 + 0.396974i
\(335\) 141922.i 1.26462i
\(336\) −4377.89 15696.0i −0.0387781 0.139031i
\(337\) 90476.4 0.796665 0.398332 0.917241i \(-0.369589\pi\)
0.398332 + 0.917241i \(0.369589\pi\)
\(338\) 25033.0 + 43358.3i 0.219118 + 0.379524i
\(339\) −9559.61 5519.25i −0.0831842 0.0480264i
\(340\) 10316.0 17867.8i 0.0892386 0.154566i
\(341\) 128891. 74415.3i 1.10844 0.639961i
\(342\) 2932.02i 0.0250677i
\(343\) −80605.0 + 85697.8i −0.685131 + 0.728420i
\(344\) 76535.1 0.646761
\(345\) 63565.7 + 110099.i 0.534054 + 0.925008i
\(346\) −98263.3 56732.3i −0.820803 0.473891i
\(347\) −16037.2 + 27777.3i −0.133190 + 0.230691i −0.924904 0.380200i \(-0.875855\pi\)
0.791715 + 0.610891i \(0.209189\pi\)
\(348\) 22377.7 12919.8i 0.184781 0.106683i
\(349\) 116783.i 0.958805i −0.877595 0.479402i \(-0.840853\pi\)
0.877595 0.479402i \(-0.159147\pi\)
\(350\) 6851.60 1911.03i 0.0559314 0.0156002i
\(351\) −14620.5 −0.118672
\(352\) 8867.28 + 15358.6i 0.0715658 + 0.123956i
\(353\) 107957. + 62329.1i 0.866367 + 0.500197i 0.866139 0.499803i \(-0.166594\pi\)
0.000227639 1.00000i \(0.499928\pi\)
\(354\) 21566.8 37354.8i 0.172099 0.298085i
\(355\) 93225.9 53824.0i 0.739741 0.427090i
\(356\) 28834.8i 0.227519i
\(357\) 19582.5 + 19186.8i 0.153649 + 0.150545i
\(358\) 141858. 1.10685
\(359\) −49721.0 86119.4i −0.385790 0.668208i 0.606088 0.795397i \(-0.292738\pi\)
−0.991878 + 0.127189i \(0.959404\pi\)
\(360\) 12672.5 + 7316.48i 0.0977817 + 0.0564543i
\(361\) −64423.5 + 111585.i −0.494344 + 0.856230i
\(362\) −156704. + 90473.3i −1.19581 + 0.690404i
\(363\) 26203.0i 0.198856i
\(364\) −39564.8 10169.8i −0.298611 0.0767553i
\(365\) −214820. −1.61246
\(366\) −4889.28 8468.48i −0.0364991 0.0632184i
\(367\) 77002.3 + 44457.3i 0.571704 + 0.330074i 0.757830 0.652452i \(-0.226260\pi\)
−0.186126 + 0.982526i \(0.559593\pi\)
\(368\) 32688.0 56617.2i 0.241375 0.418074i
\(369\) 23925.1 13813.2i 0.175712 0.101447i
\(370\) 38088.7i 0.278223i
\(371\) 26722.0 103960.i 0.194143 0.755298i
\(372\) −63149.3 −0.456334
\(373\) 45676.4 + 79113.9i 0.328303 + 0.568637i 0.982175 0.187968i \(-0.0601900\pi\)
−0.653872 + 0.756605i \(0.726857\pi\)
\(374\) −25839.8 14918.6i −0.184733 0.106656i
\(375\) −42086.2 + 72895.5i −0.299280 + 0.518368i
\(376\) 77306.5 44632.9i 0.546815 0.315704i
\(377\) 64778.2i 0.455770i
\(378\) −13608.0 + 13888.6i −0.0952381 + 0.0972020i
\(379\) 6328.51 0.0440578 0.0220289 0.999757i \(-0.492987\pi\)
0.0220289 + 0.999757i \(0.492987\pi\)
\(380\) −3678.34 6371.07i −0.0254733 0.0441210i
\(381\) −38241.3 22078.6i −0.263441 0.152097i
\(382\) −60484.4 + 104762.i −0.414492 + 0.717922i
\(383\) −11635.9 + 6717.98i −0.0793235 + 0.0457974i −0.539137 0.842218i \(-0.681250\pi\)
0.459814 + 0.888015i \(0.347916\pi\)
\(384\) 7524.83i 0.0510310i
\(385\) 30891.0 + 110753.i 0.208406 + 0.747198i
\(386\) 24812.6 0.166532
\(387\) −45662.5 79089.8i −0.304886 0.528078i
\(388\) 13513.6 + 7802.11i 0.0897654 + 0.0518261i
\(389\) −44148.1 + 76466.8i −0.291752 + 0.505328i −0.974224 0.225583i \(-0.927571\pi\)
0.682472 + 0.730911i \(0.260905\pi\)
\(390\) 31769.2 18342.0i 0.208871 0.120591i
\(391\) 109990.i 0.719451i
\(392\) −46485.6 + 28118.8i −0.302515 + 0.182989i
\(393\) −75200.2 −0.486894
\(394\) −46421.5 80404.4i −0.299038 0.517950i
\(395\) −216695. 125109.i −1.38885 0.801851i
\(396\) 10580.8 18326.5i 0.0674728 0.116866i
\(397\) 187570. 108294.i 1.19010 0.687103i 0.231769 0.972771i \(-0.425549\pi\)
0.958329 + 0.285668i \(0.0922155\pi\)
\(398\) 74852.1i 0.472539i
\(399\) 9416.04 2626.29i 0.0591456 0.0164967i
\(400\) 3284.72 0.0205295
\(401\) 2583.42 + 4474.61i 0.0160659 + 0.0278270i 0.873947 0.486022i \(-0.161553\pi\)
−0.857881 + 0.513849i \(0.828219\pi\)
\(402\) −75417.8 43542.5i −0.466683 0.269440i
\(403\) −79155.7 + 137102.i −0.487385 + 0.844175i
\(404\) −78470.5 + 45305.0i −0.480777 + 0.277577i
\(405\) 17460.7i 0.106451i
\(406\) −61535.6 60292.3i −0.373314 0.365771i
\(407\) −55082.5 −0.332526
\(408\) 6330.01 + 10963.9i 0.0380263 + 0.0658634i
\(409\) 33697.7 + 19455.3i 0.201443 + 0.116303i 0.597329 0.801997i \(-0.296229\pi\)
−0.395885 + 0.918300i \(0.629562\pi\)
\(410\) −34658.4 + 60030.0i −0.206177 + 0.357109i
\(411\) 57848.3 33398.7i 0.342458 0.197718i
\(412\) 130631.i 0.769576i
\(413\) −139281. 35801.0i −0.816567 0.209891i
\(414\) −78009.3 −0.455141
\(415\) −15200.6 26328.1i −0.0882599 0.152871i
\(416\) −16337.0 9432.15i −0.0944027 0.0545034i
\(417\) 13015.0 22542.6i 0.0748463 0.129638i
\(418\) −9213.60 + 5319.48i −0.0527323 + 0.0304450i
\(419\) 263425.i 1.50048i 0.661167 + 0.750239i \(0.270062\pi\)
−0.661167 + 0.750239i \(0.729938\pi\)
\(420\) 12145.4 47250.7i 0.0688514 0.267861i
\(421\) −16375.1 −0.0923889 −0.0461944 0.998932i \(-0.514709\pi\)
−0.0461944 + 0.998932i \(0.514709\pi\)
\(422\) 94832.0 + 164254.i 0.532513 + 0.922339i
\(423\) −92245.4 53257.9i −0.515542 0.297648i
\(424\) 24783.8 42926.8i 0.137859 0.238780i
\(425\) −4785.93 + 2763.16i −0.0264965 + 0.0152978i
\(426\) 66054.0i 0.363982i
\(427\) −22816.6 + 23287.1i −0.125140 + 0.127720i
\(428\) 35171.7 0.192002
\(429\) −26525.5 45943.5i −0.144128 0.249637i
\(430\) 198443. + 114571.i 1.07324 + 0.619637i
\(431\) 125208. 216867.i 0.674028 1.16745i −0.302724 0.953078i \(-0.597896\pi\)
0.976752 0.214373i \(-0.0687708\pi\)
\(432\) −7776.00 + 4489.48i −0.0416667 + 0.0240563i
\(433\) 91495.1i 0.488002i −0.969775 0.244001i \(-0.921540\pi\)
0.969775 0.244001i \(-0.0784601\pi\)
\(434\) 56564.6 + 202801.i 0.300307 + 1.07669i
\(435\) 77362.1 0.408837
\(436\) 58791.1 + 101829.i 0.309270 + 0.535672i
\(437\) 33964.6 + 19609.5i 0.177854 + 0.102684i
\(438\) 65907.9 114156.i 0.343549 0.595045i
\(439\) 7672.44 4429.69i 0.0398111 0.0229850i −0.479962 0.877289i \(-0.659350\pi\)
0.519773 + 0.854304i \(0.326016\pi\)
\(440\) 53096.3i 0.274258i
\(441\) 56791.6 + 31261.0i 0.292016 + 0.160741i
\(442\) 31737.9 0.162455
\(443\) −150105. 259989.i −0.764868 1.32479i −0.940316 0.340302i \(-0.889471\pi\)
0.175448 0.984489i \(-0.443863\pi\)
\(444\) 20240.5 + 11685.8i 0.102673 + 0.0592781i
\(445\) 43164.9 74763.9i 0.217977 0.377548i
\(446\) −137808. + 79563.7i −0.692797 + 0.399987i
\(447\) 131977.i 0.660514i
\(448\) −24165.6 + 6740.20i −0.120404 + 0.0335828i
\(449\) 116866. 0.579691 0.289846 0.957073i \(-0.406396\pi\)
0.289846 + 0.957073i \(0.406396\pi\)
\(450\) −1959.74 3394.36i −0.00967771 0.0167623i
\(451\) 86813.2 + 50121.6i 0.426808 + 0.246418i
\(452\) −8497.43 + 14718.0i −0.0415921 + 0.0720396i
\(453\) −82389.5 + 47567.6i −0.401491 + 0.231801i
\(454\) 172953.i 0.839105i
\(455\) −87360.9 85595.8i −0.421982 0.413456i
\(456\) 4514.14 0.0217093
\(457\) −36872.9 63865.7i −0.176553 0.305798i 0.764145 0.645045i \(-0.223161\pi\)
−0.940698 + 0.339246i \(0.889828\pi\)
\(458\) 82801.9 + 47805.7i 0.394738 + 0.227902i
\(459\) 7553.23 13082.6i 0.0358515 0.0620966i
\(460\) 169509. 97865.9i 0.801081 0.462504i
\(461\) 88219.1i 0.415108i −0.978224 0.207554i \(-0.933450\pi\)
0.978224 0.207554i \(-0.0665502\pi\)
\(462\) −68332.2 17564.2i −0.320141 0.0822895i
\(463\) 297880. 1.38957 0.694784 0.719219i \(-0.255500\pi\)
0.694784 + 0.719219i \(0.255500\pi\)
\(464\) −19891.3 34452.7i −0.0923905 0.160025i
\(465\) −163735. 94532.6i −0.757245 0.437196i
\(466\) 12285.6 21279.4i 0.0565752 0.0979911i
\(467\) −162353. + 93734.8i −0.744436 + 0.429801i −0.823680 0.567055i \(-0.808083\pi\)
0.0792437 + 0.996855i \(0.474749\pi\)
\(468\) 22509.7i 0.102773i
\(469\) −72280.7 + 281203.i −0.328607 + 1.27842i
\(470\) 267257. 1.20985
\(471\) 91567.7 + 158600.i 0.412763 + 0.714926i
\(472\) −57511.5 33204.3i −0.258149 0.149042i
\(473\) 165688. 286980.i 0.740575 1.28271i
\(474\) 132966. 76768.2i 0.591814 0.341684i
\(475\) 1970.50i 0.00873353i
\(476\) 29540.0 30149.2i 0.130376 0.133064i
\(477\) −59146.2 −0.259950
\(478\) −22224.4 38493.8i −0.0972690 0.168475i
\(479\) −104347. 60244.5i −0.454786 0.262571i 0.255063 0.966924i \(-0.417904\pi\)
−0.709849 + 0.704354i \(0.751237\pi\)
\(480\) 11264.5 19510.6i 0.0488909 0.0846815i
\(481\) 50741.6 29295.7i 0.219318 0.126623i
\(482\) 15496.4i 0.0667019i
\(483\) 69875.2 + 250523.i 0.299522 + 1.07387i
\(484\) −40342.2 −0.172214
\(485\) 23359.1 + 40459.1i 0.0993052 + 0.172002i
\(486\) 9278.66 + 5357.03i 0.0392837 + 0.0226805i
\(487\) 133697. 231570.i 0.563721 0.976393i −0.433447 0.901179i \(-0.642703\pi\)
0.997167 0.0752136i \(-0.0239639\pi\)
\(488\) −13038.1 + 7527.54i −0.0547487 + 0.0316092i
\(489\) 758.319i 0.00317128i
\(490\) −162622. + 3319.51i −0.677311 + 0.0138255i
\(491\) 178364. 0.739851 0.369926 0.929061i \(-0.379383\pi\)
0.369926 + 0.929061i \(0.379383\pi\)
\(492\) −21266.8 36835.1i −0.0878560 0.152171i
\(493\) 57964.3 + 33465.7i 0.238488 + 0.137691i
\(494\) 5658.34 9800.53i 0.0231865 0.0401602i
\(495\) 54868.5 31678.4i 0.223930 0.129286i
\(496\) 97224.7i 0.395196i
\(497\) 212129. 59166.5i 0.858792 0.239532i
\(498\) 18654.5 0.0752184
\(499\) −131873. 228411.i −0.529610 0.917311i −0.999403 0.0345349i \(-0.989005\pi\)
0.469794 0.882776i \(-0.344328\pi\)
\(500\) 112230. + 64796.0i 0.448920 + 0.259184i
\(501\) 81356.3 140913.i 0.324128 0.561405i
\(502\) 59647.2 34437.4i 0.236692 0.136654i
\(503\) 480056.i 1.89739i 0.316197 + 0.948694i \(0.397594\pi\)
−0.316197 + 0.948694i \(0.602406\pi\)
\(504\) 21382.9 + 20950.9i 0.0841794 + 0.0824786i
\(505\) −271281. −1.06374
\(506\) −141530. 245137.i −0.552774 0.957432i
\(507\) −79654.4 45988.5i −0.309880 0.178909i
\(508\) −33992.3 + 58876.3i −0.131720 + 0.228146i
\(509\) −52192.6 + 30133.4i −0.201453 + 0.116309i −0.597333 0.801993i \(-0.703773\pi\)
0.395880 + 0.918302i \(0.370440\pi\)
\(510\) 37903.3i 0.145726i
\(511\) −425641. 109407.i −1.63005 0.418991i
\(512\) −11585.2 −0.0441942
\(513\) −2693.23 4664.82i −0.0102339 0.0177256i
\(514\) 28430.6 + 16414.4i 0.107612 + 0.0621297i
\(515\) 195551. 338704.i 0.737301 1.27704i
\(516\) −121767. + 70302.0i −0.457329 + 0.264039i
\(517\) 386497.i 1.44599i
\(518\) 19398.5 75468.6i 0.0722952 0.281259i
\(519\) 208448. 0.773861
\(520\) −28239.3 48911.9i −0.104435 0.180887i
\(521\) 248823. + 143658.i 0.916674 + 0.529242i 0.882573 0.470176i \(-0.155810\pi\)
0.0341018 + 0.999418i \(0.489143\pi\)
\(522\) −23735.1 + 41110.5i −0.0871066 + 0.150873i
\(523\) −239407. + 138222.i −0.875254 + 0.505328i −0.869091 0.494653i \(-0.835295\pi\)
−0.00616355 + 0.999981i \(0.501962\pi\)
\(524\) 115778.i 0.421662i
\(525\) −9145.44 + 9334.02i −0.0331807 + 0.0338649i
\(526\) −341300. −1.23357
\(527\) −81786.9 141659.i −0.294484 0.510062i
\(528\) −28215.5 16290.2i −0.101209 0.0584332i
\(529\) −381809. + 661313.i −1.36438 + 2.36317i
\(530\) 128520. 74201.3i 0.457531 0.264156i
\(531\) 79241.5i 0.281037i
\(532\) −4043.44 14496.9i −0.0142866 0.0512216i
\(533\) −106629. −0.375336
\(534\) 26486.5 + 45876.0i 0.0928842 + 0.160880i
\(535\) 91194.3 + 52651.0i 0.318610 + 0.183950i
\(536\) −67038.1 + 116113.i −0.233341 + 0.404159i
\(537\) −225695. + 130305.i −0.782661 + 0.451869i
\(538\) 77065.1i 0.266252i
\(539\) 4800.56 + 235178.i 0.0165240 + 0.809505i
\(540\) −26882.5 −0.0921895
\(541\) 29832.0 + 51670.6i 0.101927 + 0.176542i 0.912478 0.409125i \(-0.134166\pi\)
−0.810552 + 0.585667i \(0.800833\pi\)
\(542\) −237707. 137240.i −0.809175 0.467177i
\(543\) 166210. 287884.i 0.563712 0.976378i
\(544\) 16880.0 9745.68i 0.0570394 0.0329317i
\(545\) 352034.i 1.18520i
\(546\) 72288.7 20162.6i 0.242485 0.0676332i
\(547\) 489585. 1.63627 0.818133 0.575030i \(-0.195010\pi\)
0.818133 + 0.575030i \(0.195010\pi\)
\(548\) −51420.7 89063.3i −0.171229 0.296577i
\(549\) 15557.6 + 8982.18i 0.0516176 + 0.0298014i
\(550\) 7110.98 12316.6i 0.0235074 0.0407160i
\(551\) 20668.2 11932.8i 0.0680767 0.0393041i
\(552\) 120103.i 0.394164i
\(553\) −365639. 358251.i −1.19564 1.17149i
\(554\) −84153.6 −0.274191
\(555\) 34986.7 + 60598.8i 0.113584 + 0.196733i
\(556\) −34706.5 20037.8i −0.112269 0.0648188i
\(557\) −254267. + 440404.i −0.819558 + 1.41952i 0.0864495 + 0.996256i \(0.472448\pi\)
−0.906008 + 0.423261i \(0.860885\pi\)
\(558\) 100470. 58006.3i 0.322677 0.186297i
\(559\) 352486.i 1.12802i
\(560\) −72747.2 18699.0i −0.231975 0.0596270i
\(561\) 54814.4 0.174168
\(562\) −172923. 299512.i −0.547496 0.948290i
\(563\) 103765. + 59908.5i 0.327365 + 0.189004i 0.654671 0.755914i \(-0.272807\pi\)
−0.327306 + 0.944919i \(0.606141\pi\)
\(564\) −81995.9 + 142021.i −0.257771 + 0.446473i
\(565\) −44064.8 + 25440.8i −0.138037 + 0.0796956i
\(566\) 171688.i 0.535927i
\(567\) 8892.70 34596.4i 0.0276610 0.107613i
\(568\) 101697. 0.315218
\(569\) 48829.7 + 84575.5i 0.150820 + 0.261228i 0.931529 0.363667i \(-0.118475\pi\)
−0.780709 + 0.624895i \(0.785142\pi\)
\(570\) 11704.4 + 6757.54i 0.0360246 + 0.0207988i
\(571\) −23825.7 + 41267.3i −0.0730757 + 0.126571i −0.900248 0.435378i \(-0.856615\pi\)
0.827172 + 0.561949i \(0.189948\pi\)
\(572\) −70734.6 + 40838.6i −0.216192 + 0.124819i
\(573\) 222234.i 0.676863i
\(574\) −99244.9 + 101291.i −0.301220 + 0.307432i
\(575\) −52427.2 −0.158570
\(576\) 6912.00 + 11971.9i 0.0208333 + 0.0360844i
\(577\) −113845. 65728.4i −0.341949 0.197425i 0.319184 0.947693i \(-0.396591\pi\)
−0.661134 + 0.750268i \(0.729924\pi\)
\(578\) 101720. 176184.i 0.304475 0.527366i
\(579\) −39476.6 + 22791.8i −0.117756 + 0.0679864i
\(580\) 119107.i 0.354063i
\(581\) −16709.3 59907.9i −0.0495002 0.177473i
\(582\) −28666.8 −0.0846316
\(583\) −107307. 185861.i −0.315712 0.546830i
\(584\) −175754. 101472.i −0.515324 0.297523i
\(585\) −33696.3 + 58363.8i −0.0984625 + 0.170542i
\(586\) 72400.6 41800.5i 0.210837 0.121727i
\(587\) 135493.i 0.393224i −0.980481 0.196612i \(-0.937006\pi\)
0.980481 0.196612i \(-0.0629940\pi\)
\(588\) 48129.5 87436.4i 0.139205 0.252894i
\(589\) −58325.0 −0.168122
\(590\) −99411.7 172186.i −0.285584 0.494645i
\(591\) 147712. + 85281.8i 0.422904 + 0.244164i
\(592\) 17991.5 31162.3i 0.0513363 0.0889171i
\(593\) 162993. 94104.0i 0.463510 0.267608i −0.250009 0.968244i \(-0.580433\pi\)
0.713519 + 0.700636i \(0.247100\pi\)
\(594\) 38876.4i 0.110183i
\(595\) 121725. 33951.1i 0.343831 0.0959003i
\(596\) 203191. 0.572022
\(597\) 68756.0 + 119089.i 0.192913 + 0.334136i
\(598\) 260753. + 150546.i 0.729166 + 0.420984i
\(599\) 39202.4 67900.5i 0.109259 0.189243i −0.806211 0.591628i \(-0.798485\pi\)
0.915470 + 0.402385i \(0.131819\pi\)
\(600\) −5225.96 + 3017.21i −0.0145166 + 0.00838114i
\(601\) 254898.i 0.705695i −0.935681 0.352848i \(-0.885213\pi\)
0.935681 0.352848i \(-0.114787\pi\)
\(602\) 334841. + 328076.i 0.923945 + 0.905277i
\(603\) 159985. 0.439993
\(604\) 73235.1 + 126847.i 0.200745 + 0.347701i
\(605\) −104600. 60391.0i −0.285774 0.164992i
\(606\) 83230.5 144160.i 0.226640 0.392553i
\(607\) 489896. 282842.i 1.32962 0.767655i 0.344378 0.938831i \(-0.388090\pi\)
0.985241 + 0.171176i \(0.0547566\pi\)
\(608\) 6949.97i 0.0188008i
\(609\) 153284. + 39400.4i 0.413298 + 0.106235i
\(610\) −45074.0 −0.121134
\(611\) 205559. + 356038.i 0.550622 + 0.953705i
\(612\) −20142.0 11629.0i −0.0537773 0.0310483i
\(613\) 207111. 358726.i 0.551164 0.954645i −0.447026 0.894521i \(-0.647517\pi\)
0.998191 0.0601241i \(-0.0191496\pi\)
\(614\) 263485. 152123.i 0.698905 0.403513i
\(615\) 127343.i 0.336686i
\(616\) −27041.9 + 105204.i −0.0712648 + 0.277251i
\(617\) 22896.0 0.0601435 0.0300717 0.999548i \(-0.490426\pi\)
0.0300717 + 0.999548i \(0.490426\pi\)
\(618\) 119992. + 207832.i 0.314178 + 0.544172i
\(619\) 139564. + 80577.4i 0.364244 + 0.210296i 0.670941 0.741511i \(-0.265890\pi\)
−0.306697 + 0.951807i \(0.599224\pi\)
\(620\) −145543. + 252087.i −0.378623 + 0.655793i
\(621\) 124112. 71656.1i 0.321833 0.185811i
\(622\) 122674.i 0.317082i
\(623\) 123604. 126152.i 0.318460 0.325027i
\(624\) 34655.9 0.0890037
\(625\) 177957. + 308230.i 0.455569 + 0.789069i
\(626\) −263924. 152376.i −0.673488 0.388838i
\(627\) 9772.50 16926.5i 0.0248583 0.0430558i
\(628\) 244181. 140978.i 0.619144 0.357463i
\(629\) 60539.0i 0.153015i
\(630\) 24079.4 + 86331.7i 0.0606686 + 0.217515i
\(631\) 489038. 1.22824 0.614121 0.789212i \(-0.289511\pi\)
0.614121 + 0.789212i \(0.289511\pi\)
\(632\) −118192. 204715.i −0.295907 0.512526i
\(633\) −301754. 174217.i −0.753087 0.434795i
\(634\) −220609. + 382105.i −0.548838 + 0.950615i
\(635\) −176272. + 101771.i −0.437156 + 0.252392i
\(636\) 91061.5i 0.225123i
\(637\) −129502. 214091.i −0.319152 0.527619i
\(638\) −172248. −0.423168
\(639\) −60674.5 105091.i −0.148595 0.257374i
\(640\) −30038.6 17342.8i −0.0733363 0.0423407i
\(641\) −59669.8 + 103351.i −0.145224 + 0.251536i −0.929457 0.368932i \(-0.879724\pi\)
0.784232 + 0.620467i \(0.213057\pi\)
\(642\) −55957.8 + 32307.3i −0.135766 + 0.0783845i
\(643\) 324224.i 0.784194i −0.919924 0.392097i \(-0.871750\pi\)
0.919924 0.392097i \(-0.128250\pi\)
\(644\) 385706. 107580.i 0.930003 0.259394i
\(645\) −420960. −1.01186
\(646\) 5846.43 + 10126.3i 0.0140096 + 0.0242653i
\(647\) −399048. 230391.i −0.953272 0.550372i −0.0591759 0.998248i \(-0.518847\pi\)
−0.894096 + 0.447876i \(0.852181\pi\)
\(648\) 8247.69 14285.4i 0.0196419 0.0340207i
\(649\) −249009. + 143765.i −0.591188 + 0.341323i
\(650\) 15127.9i 0.0358057i
\(651\) −276278. 270696.i −0.651905 0.638734i
\(652\) 1167.51 0.00274641
\(653\) 279562. + 484216.i 0.655620 + 1.13557i 0.981738 + 0.190238i \(0.0609260\pi\)
−0.326118 + 0.945329i \(0.605741\pi\)
\(654\) −187072. 108006.i −0.437375 0.252518i
\(655\) −173317. + 300193.i −0.403978 + 0.699711i
\(656\) −56711.4 + 32742.3i −0.131784 + 0.0760855i
\(657\) 242161.i 0.561014i
\(658\) 529540. + 136114.i 1.22306 + 0.314376i
\(659\) −184372. −0.424546 −0.212273 0.977210i \(-0.568087\pi\)
−0.212273 + 0.977210i \(0.568087\pi\)
\(660\) −48772.0 84475.6i −0.111965 0.193929i
\(661\) 68612.1 + 39613.2i 0.157035 + 0.0906645i 0.576458 0.817126i \(-0.304434\pi\)
−0.419423 + 0.907791i \(0.637768\pi\)
\(662\) 56877.9 98515.3i 0.129786 0.224796i
\(663\) −50494.6 + 29153.1i −0.114873 + 0.0663220i
\(664\) 28720.4i 0.0651411i
\(665\) 11217.5 43641.0i 0.0253661 0.0986851i
\(666\) −42936.5 −0.0968007
\(667\) 317483. + 549897.i 0.713624 + 1.23603i
\(668\) −216950. 125256.i −0.486191 0.280703i
\(669\) 146168. 253170.i 0.326588 0.565666i
\(670\) −347637. + 200708.i −0.774419 + 0.447111i
\(671\) 65184.4i 0.144777i
\(672\) 32256.0 32921.1i 0.0714286 0.0729015i
\(673\) −482896. −1.06616 −0.533082 0.846064i \(-0.678966\pi\)
−0.533082 + 0.846064i \(0.678966\pi\)
\(674\) 127953. + 221621.i 0.281663 + 0.487855i
\(675\) 6235.84 + 3600.27i 0.0136863 + 0.00790182i
\(676\) −70803.9 + 122636.i −0.154940 + 0.268364i
\(677\) −329375. + 190165.i −0.718642 + 0.414908i −0.814253 0.580511i \(-0.802853\pi\)
0.0956105 + 0.995419i \(0.469520\pi\)
\(678\) 31221.6i 0.0679196i
\(679\) 25677.6 + 92061.9i 0.0556949 + 0.199683i
\(680\) 58356.0 0.126202
\(681\) −158868. 275167.i −0.342563 0.593337i
\(682\) 364559. + 210478.i 0.783789 + 0.452521i
\(683\) 171034. 296240.i 0.366642 0.635042i −0.622396 0.782702i \(-0.713841\pi\)
0.989038 + 0.147660i \(0.0471742\pi\)
\(684\) −7181.95 + 4146.50i −0.0153508 + 0.00886278i
\(685\) 307901.i 0.656191i
\(686\) −323909. 76246.1i −0.688295 0.162020i
\(687\) −175649. −0.372163
\(688\) 108237. + 187472.i 0.228665 + 0.396059i
\(689\) 197701. + 114143.i 0.416458 + 0.240442i
\(690\) −179791. + 311407.i −0.377633 + 0.654080i
\(691\) 63274.0 36531.3i 0.132516 0.0765084i −0.432276 0.901741i \(-0.642289\pi\)
0.564793 + 0.825233i \(0.308956\pi\)
\(692\) 320927.i 0.670183i
\(693\) 124850. 34822.7i 0.259969 0.0725097i
\(694\) −90720.3 −0.188359
\(695\) −59992.1 103909.i −0.124201 0.215122i
\(696\) 63293.7 + 36542.6i 0.130660 + 0.0754365i
\(697\) 55086.7 95413.0i 0.113392 0.196400i
\(698\) 286060. 165157.i 0.587145 0.338989i
\(699\) 45140.3i 0.0923869i
\(700\) 14370.7 + 14080.3i 0.0293279 + 0.0287353i
\(701\) −288287. −0.586664 −0.293332 0.956011i \(-0.594764\pi\)
−0.293332 + 0.956011i \(0.594764\pi\)
\(702\) −20676.5 35812.7i −0.0419568 0.0726712i
\(703\) 18694.2 + 10793.1i 0.0378265 + 0.0218392i
\(704\) −25080.5 + 43440.6i −0.0506046 + 0.0876498i
\(705\) −425203. + 245491.i −0.855496 + 0.493921i
\(706\) 352586.i 0.707386i
\(707\) −537513. 138163.i −1.07535 0.276409i
\(708\) 122000. 0.243385
\(709\) 155256. + 268911.i 0.308856 + 0.534954i 0.978112 0.208078i \(-0.0667206\pi\)
−0.669257 + 0.743031i \(0.733387\pi\)
\(710\) 263683. + 152237.i 0.523076 + 0.301998i
\(711\) −141032. + 244275.i −0.278984 + 0.483214i
\(712\) 70630.7 40778.6i 0.139326 0.0804401i
\(713\) 1.55179e6i 3.05250i
\(714\) −19304.1 + 75101.3i −0.0378664 + 0.147316i
\(715\) −244537. −0.478335
\(716\) 200618. + 347480.i 0.391330 + 0.677804i
\(717\) 70717.6 + 40828.8i 0.137559 + 0.0794198i
\(718\) 140632. 243582.i 0.272795 0.472495i
\(719\) 8733.60 5042.35i 0.0168941 0.00975383i −0.491529 0.870861i \(-0.663562\pi\)
0.508423 + 0.861107i \(0.330229\pi\)
\(720\) 41388.3i 0.0798385i
\(721\) 559963. 571510.i 1.07718 1.09939i
\(722\) −364434. −0.699109
\(723\) 14234.4 + 24654.7i 0.0272309 + 0.0471654i
\(724\) −443227. 255897.i −0.845568 0.488189i
\(725\) −15951.5 + 27628.8i −0.0303477 + 0.0525638i
\(726\) 64184.0 37056.6i 0.121774 0.0703060i
\(727\) 638552.i 1.20817i −0.796921 0.604084i \(-0.793539\pi\)
0.796921 0.604084i \(-0.206461\pi\)
\(728\) −31042.3 111296.i −0.0585721 0.209998i
\(729\) −19683.0 −0.0370370
\(730\) −303801. 526199.i −0.570090 0.987425i
\(731\) −315409. 182101.i −0.590254 0.340783i
\(732\) 13829.0 23952.5i 0.0258088 0.0447021i
\(733\) −715410. + 413042.i −1.33152 + 0.768752i −0.985532 0.169488i \(-0.945789\pi\)
−0.345985 + 0.938240i \(0.612455\pi\)
\(734\) 251488.i 0.466795i
\(735\) 255681. 154659.i 0.473287 0.286287i
\(736\) 184911. 0.341356
\(737\) 290257. + 502739.i 0.534376 + 0.925567i
\(738\) 67670.4 + 39069.5i 0.124247 + 0.0717341i
\(739\) −384995. + 666831.i −0.704962 + 1.22103i 0.261743 + 0.965138i \(0.415703\pi\)
−0.966705 + 0.255893i \(0.917630\pi\)
\(740\) 93298.0 53865.6i 0.170376 0.0983667i
\(741\) 20790.1i 0.0378634i
\(742\) 292440. 81566.4i 0.531164 0.148151i
\(743\) −611777. −1.10819 −0.554097 0.832452i \(-0.686936\pi\)
−0.554097 + 0.832452i \(0.686936\pi\)
\(744\) −89306.6 154683.i −0.161338 0.279446i
\(745\) 526841. + 304172.i 0.949220 + 0.548032i
\(746\) −129193. + 223768.i −0.232145 + 0.402087i
\(747\) −29679.1 + 17135.2i −0.0531875 + 0.0307078i
\(748\) 84392.3i 0.150834i
\(749\) 153876. + 150767.i 0.274289 + 0.268747i
\(750\) −238076. −0.423246
\(751\) −185311. 320968.i −0.328565 0.569091i 0.653663 0.756786i \(-0.273232\pi\)
−0.982227 + 0.187695i \(0.939898\pi\)
\(752\) 218656. + 126241.i 0.386657 + 0.223236i
\(753\) −63265.5 + 109579.i −0.111578 + 0.193258i
\(754\) 158673. 91610.2i 0.279101 0.161139i
\(755\) 438523.i 0.769305i
\(756\) −53264.6 13691.2i −0.0931956 0.0239551i
\(757\) 298778. 0.521384 0.260692 0.965422i \(-0.416049\pi\)
0.260692 + 0.965422i \(0.416049\pi\)
\(758\) 8949.87 + 15501.6i 0.0155768 + 0.0269798i
\(759\) 450346. + 260007.i 0.781740 + 0.451338i
\(760\) 10403.9 18020.1i 0.0180123 0.0311982i
\(761\) 695541. 401571.i 1.20103 0.693414i 0.240245 0.970712i \(-0.422772\pi\)
0.960784 + 0.277298i \(0.0894389\pi\)
\(762\) 124896.i 0.215098i
\(763\) −179291. + 697517.i −0.307970 + 1.19813i
\(764\) −342151. −0.586180
\(765\) −34816.4 60303.8i −0.0594924 0.103044i
\(766\) −32911.2 19001.3i −0.0560902 0.0323837i
\(767\) 152924. 264871.i 0.259946 0.450240i
\(768\) 18432.0 10641.7i 0.0312500 0.0180422i
\(769\) 452541.i 0.765253i 0.923903 + 0.382626i \(0.124980\pi\)
−0.923903 + 0.382626i \(0.875020\pi\)
\(770\) −227603. + 232296.i −0.383881 + 0.391797i
\(771\) −60310.4 −0.101457
\(772\) 35090.3 + 60778.2i 0.0588780 + 0.101980i
\(773\) 908057. + 524267.i 1.51969 + 0.877392i 0.999731 + 0.0231996i \(0.00738531\pi\)
0.519957 + 0.854193i \(0.325948\pi\)
\(774\) 129153. 223700.i 0.215587 0.373408i
\(775\) 67522.1 38983.9i 0.112420 0.0649056i
\(776\) 44135.4i 0.0732932i
\(777\) 38459.5 + 137889.i 0.0637032 + 0.228395i
\(778\) −249740. −0.412599
\(779\) −19642.1 34021.1i −0.0323678 0.0560626i
\(780\) 89856.9 + 51878.9i 0.147694 + 0.0852711i
\(781\) 220160. 381328.i 0.360941 0.625168i
\(782\) −269421. + 155550.i −0.440572 + 0.254365i
\(783\) 87208.5i 0.142244i
\(784\) −134617. 74100.1i −0.219012 0.120555i
\(785\) 844159. 1.36989
\(786\) −106349. 184202.i −0.172143 0.298160i
\(787\) 169712. + 97983.5i 0.274009 + 0.158199i 0.630708 0.776020i \(-0.282765\pi\)
−0.356699 + 0.934219i \(0.616098\pi\)
\(788\) 131300. 227418.i 0.211452 0.366246i
\(789\) 543004. 313504.i 0.872266 0.503603i
\(790\) 707722.i 1.13399i
\(791\) −100266. + 27966.0i −0.160252 + 0.0446970i
\(792\) 59854.2 0.0954210
\(793\) −34668.4 60047.4i −0.0551299 0.0954877i
\(794\) 530528. + 306301.i 0.841526 + 0.485855i
\(795\) −136317. + 236107.i −0.215682 + 0.373572i
\(796\) 183349. 105857.i 0.289370 0.167068i
\(797\) 66453.8i 0.104617i 0.998631 + 0.0523086i \(0.0166579\pi\)
−0.998631 + 0.0523086i \(0.983342\pi\)
\(798\) 19749.4 + 19350.3i 0.0310133 + 0.0303867i
\(799\) −424784. −0.665387
\(800\) 4645.30 + 8045.90i 0.00725828 + 0.0125717i
\(801\) −84279.5 48658.8i −0.131358 0.0758397i
\(802\) −7307.01 + 12656.1i −0.0113603 + 0.0196767i
\(803\) −760969. + 439346.i −1.18015 + 0.681358i
\(804\) 246314.i 0.381045i
\(805\) 1.16111e6 + 298454.i 1.79177 + 0.460559i
\(806\) −447772. −0.689266
\(807\) 70788.8 + 122610.i 0.108697 + 0.188269i
\(808\) −221948. 128142.i −0.339961 0.196276i
\(809\) −41152.3 + 71277.9i −0.0628777 + 0.108907i −0.895751 0.444557i \(-0.853361\pi\)
0.832873 + 0.553464i \(0.186694\pi\)
\(810\) 42769.7 24693.1i 0.0651878 0.0376362i
\(811\) 469097.i 0.713215i 0.934254 + 0.356608i \(0.116067\pi\)
−0.934254 + 0.356608i \(0.883933\pi\)
\(812\) 60660.9 235997.i 0.0920019 0.357927i
\(813\) 504252. 0.762898
\(814\) −77898.5 134924.i −0.117566 0.203629i
\(815\) 3027.15 + 1747.73i 0.00455742 + 0.00263123i
\(816\) −17904.0 + 31010.6i −0.0268886 + 0.0465725i
\(817\) −112464. + 64931.3i −0.168489 + 0.0972769i
\(818\) 110056.i 0.164478i
\(819\) −96490.1 + 98479.8i −0.143852 + 0.146818i
\(820\) −196057. −0.291578
\(821\) 2689.76 + 4658.80i 0.00399050 + 0.00691174i 0.868014 0.496540i \(-0.165396\pi\)
−0.864023 + 0.503452i \(0.832063\pi\)
\(822\) 163620. + 94465.8i 0.242154 + 0.139808i
\(823\) 484903. 839877.i 0.715905 1.23998i −0.246704 0.969091i \(-0.579348\pi\)
0.962609 0.270893i \(-0.0873190\pi\)
\(824\) 319979. 184740.i 0.471267 0.272086i
\(825\) 26127.4i 0.0383874i
\(826\) −109279. 391798.i −0.160168 0.574251i
\(827\) 838747. 1.22637 0.613183 0.789941i \(-0.289889\pi\)
0.613183 + 0.789941i \(0.289889\pi\)
\(828\) −110322. 191083.i −0.160917 0.278716i
\(829\) −765309. 441852.i −1.11360 0.642935i −0.173838 0.984774i \(-0.555617\pi\)
−0.939759 + 0.341839i \(0.888950\pi\)
\(830\) 42993.7 74467.2i 0.0624091 0.108096i
\(831\) 133888. 77300.0i 0.193882 0.111938i
\(832\) 53356.3i 0.0770795i
\(833\) 258475. 5276.10i 0.372502 0.00760367i
\(834\) 73623.7 0.105849
\(835\) −375010. 649536.i −0.537861 0.931602i
\(836\) −26060.0 15045.7i −0.0372874 0.0215279i
\(837\) −106564. + 184575.i −0.152111 + 0.263464i
\(838\) −645258. + 372540.i −0.918852 + 0.530499i
\(839\) 1.12626e6i 1.59998i −0.600011 0.799992i \(-0.704837\pi\)
0.600011 0.799992i \(-0.295163\pi\)
\(840\) 132916. 37072.6i 0.188373 0.0525406i
\(841\) −320891. −0.453696
\(842\) −23157.9 40110.6i −0.0326644 0.0565764i
\(843\) 550238. + 317680.i 0.774276 + 0.447028i
\(844\) −268225. + 464580.i −0.376543 + 0.652192i
\(845\) −367165. + 211983.i −0.514218 + 0.296884i
\(846\) 301272.i 0.420938i
\(847\) −176497. 172931.i −0.246020 0.241049i
\(848\) 140198. 0.194963
\(849\) 157705. + 273153.i 0.218791 + 0.378958i
\(850\) −13536.7 7815.40i −0.0187359 0.0108172i
\(851\) −287161. + 497378.i −0.396522 + 0.686796i
\(852\) −161799. + 93414.5i −0.222893 + 0.128687i
\(853\) 805486.i 1.10703i 0.832839 + 0.553516i \(0.186714\pi\)
−0.832839 + 0.553516i \(0.813286\pi\)
\(854\) −89309.2 22956.1i −0.122456 0.0314762i
\(855\) −24828.8 −0.0339643
\(856\) 49740.3 + 86152.7i 0.0678830 + 0.117577i
\(857\) −849118. 490238.i −1.15613 0.667491i −0.205756 0.978603i \(-0.565965\pi\)
−0.950373 + 0.311112i \(0.899299\pi\)
\(858\) 75025.3 129948.i 0.101914 0.176520i
\(859\) −375665. + 216890.i −0.509113 + 0.293936i −0.732469 0.680800i \(-0.761632\pi\)
0.223356 + 0.974737i \(0.428299\pi\)
\(860\) 648111.i 0.876299i
\(861\) 64855.6 252316.i 0.0874865 0.340360i
\(862\) 708284. 0.953220
\(863\) 151578. + 262542.i 0.203524 + 0.352514i 0.949661 0.313278i \(-0.101427\pi\)
−0.746137 + 0.665792i \(0.768094\pi\)
\(864\) −21993.8 12698.2i −0.0294628 0.0170103i
\(865\) 480418. 832108.i 0.642077 1.11211i
\(866\) 224116. 129394.i 0.298839 0.172535i
\(867\) 373744.i 0.497205i
\(868\) −416764. + 425358.i −0.553160 + 0.564566i
\(869\) −1.02348e6 −1.35532
\(870\) 109407. + 189498.i 0.144546 + 0.250360i
\(871\) −534765. 308747.i −0.704898 0.406973i
\(872\) −166286. + 288016.i −0.218687 + 0.378777i
\(873\) 45608.6 26332.1i 0.0598436 0.0345507i
\(874\) 110928.i 0.145217i
\(875\) 213251. + 764568.i 0.278532 + 0.998619i
\(876\) 372831. 0.485852
\(877\) −177500. 307439.i −0.230781 0.399724i 0.727257 0.686365i \(-0.240795\pi\)
−0.958038 + 0.286641i \(0.907461\pi\)
\(878\) 21700.9 + 12529.0i 0.0281507 + 0.0162528i
\(879\) −76792.5 + 133008.i −0.0993896 + 0.172148i
\(880\) −130059. + 75089.5i −0.167948 + 0.0969647i
\(881\) 320002.i 0.412288i −0.978522 0.206144i \(-0.933909\pi\)
0.978522 0.206144i \(-0.0660915\pi\)
\(882\) 3742.01 + 183320.i 0.00481025 + 0.235653i
\(883\) −1.08605e6 −1.39293 −0.696467 0.717589i \(-0.745246\pi\)
−0.696467 + 0.717589i \(0.745246\pi\)
\(884\) 44884.1 + 77741.6i 0.0574365 + 0.0994830i
\(885\) 316326. + 182631.i 0.403876 + 0.233178i
\(886\) 424560. 735360.i 0.540844 0.936769i
\(887\) 1.11218e6 642117.i 1.41360 0.816144i 0.417878 0.908503i \(-0.362774\pi\)
0.995726 + 0.0923591i \(0.0294408\pi\)
\(888\) 66105.1i 0.0838319i
\(889\) −401096. + 111872.i −0.507510 + 0.141553i
\(890\) 244178. 0.308266
\(891\) −35710.3 61852.0i −0.0449819 0.0779109i
\(892\) −389781. 225040.i −0.489882 0.282833i
\(893\) −75731.9 + 131171.i −0.0949677 + 0.164489i
\(894\) −323275. + 186643.i −0.404481 + 0.233527i
\(895\) 1.20128e6i 1.49967i
\(896\) −50685.4 49661.4i −0.0631345 0.0618590i
\(897\) −553140. −0.687465
\(898\) 165274. + 286263.i 0.204952 + 0.354987i
\(899\) −817787. 472150.i −1.01186 0.584198i
\(900\) 5542.97 9600.71i 0.00684317 0.0118527i
\(901\) −204273. + 117937.i −0.251629 + 0.145278i
\(902\) 283531.i 0.348487i
\(903\) −834086. 214394.i −1.02291 0.262929i
\(904\) −48068.7 −0.0588201
\(905\) −766141. 1.32699e6i −0.935430 1.62021i
\(906\) −233033. 134541.i −0.283897 0.163908i
\(907\) −24217.8 + 41946.4i −0.0294388 + 0.0509894i −0.880369 0.474289i \(-0.842705\pi\)
0.850931 + 0.525278i \(0.176039\pi\)
\(908\) −423647. + 244593.i −0.513845 + 0.296669i
\(909\) 305808.i 0.370102i
\(910\) 86119.2 335040.i 0.103996 0.404589i
\(911\) 727675. 0.876801 0.438400 0.898780i \(-0.355545\pi\)
0.438400 + 0.898780i \(0.355545\pi\)
\(912\) 6383.96 + 11057.3i 0.00767539 + 0.0132942i
\(913\) −107692. 62175.8i −0.129194 0.0745899i
\(914\) 104292. 180639.i 0.124842 0.216232i
\(915\) 71712.3 41403.1i 0.0856548 0.0494528i
\(916\) 270430.i 0.322303i
\(917\) −496296. + 506530.i −0.590204 + 0.602375i
\(918\) 42727.5 0.0507017
\(919\) −43858.0 75964.2i −0.0519299 0.0899452i 0.838892 0.544298i \(-0.183204\pi\)
−0.890822 + 0.454353i \(0.849871\pi\)
\(920\) 479443. + 276806.i 0.566449 + 0.327040i
\(921\) −279468. + 484052.i −0.329467 + 0.570654i
\(922\) 216092. 124761.i 0.254201 0.146763i
\(923\) 468369.i 0.549775i
\(924\) −53613.1 192219.i −0.0627952 0.225139i
\(925\) −28856.1 −0.0337251
\(926\) 421266. + 729655.i 0.491286 + 0.850933i
\(927\) −381813. 220440.i −0.444315 0.256525i
\(928\) 56261.1 97447.1i 0.0653299 0.113155i
\(929\) 781079. 450956.i 0.905032 0.522520i 0.0262024 0.999657i \(-0.491659\pi\)
0.878829 + 0.477136i \(0.158325\pi\)
\(930\) 534757.i 0.618288i
\(931\) 44452.6 80756.7i 0.0512859 0.0931707i
\(932\) 69498.1 0.0800094
\(933\) −112683. 195173.i −0.129448 0.224211i
\(934\) −459205. 265122.i −0.526396 0.303915i
\(935\) 126333. 218815.i 0.144508 0.250296i
\(936\) −55137.2 + 31833.5i −0.0629351 + 0.0363356i
\(937\) 1.24186e6i 1.41447i 0.706978 + 0.707236i \(0.250058\pi\)
−0.706978 + 0.707236i \(0.749942\pi\)
\(938\) −791024. + 220630.i −0.899050 + 0.250760i
\(939\) 559867. 0.634970
\(940\) 377958. + 654643.i 0.427748 + 0.740882i
\(941\) 369139. + 213122.i 0.416879 + 0.240685i 0.693741 0.720224i \(-0.255961\pi\)
−0.276862 + 0.960910i \(0.589294\pi\)
\(942\) −258993. + 448588.i −0.291867 + 0.505529i
\(943\) 905165. 522598.i 1.01790 0.587684i
\(944\) 187832.i 0.210778i
\(945\) −117611. 115235.i −0.131699 0.129038i
\(946\) 937274. 1.04733
\(947\) −13665.2 23668.9i −0.0152376 0.0263923i 0.858306 0.513138i \(-0.171517\pi\)
−0.873544 + 0.486746i \(0.838184\pi\)
\(948\) 376086. + 217133.i 0.418476 + 0.241607i
\(949\) 467333. 809444.i 0.518912 0.898782i
\(950\) −4826.73 + 2786.71i −0.00534817 + 0.00308777i
\(951\) 810568.i 0.896248i
\(952\) 115626. + 29720.6i 0.127580 + 0.0327932i
\(953\) 1.30093e6 1.43242 0.716208 0.697887i \(-0.245876\pi\)
0.716208 + 0.697887i \(0.245876\pi\)
\(954\) −83645.4 144878.i −0.0919063 0.159186i
\(955\) −887140. 512190.i −0.972714 0.561597i
\(956\) 62860.1 108877.i 0.0687796 0.119130i
\(957\) 274045. 158220.i 0.299225 0.172757i
\(958\) 340794.i 0.371331i
\(959\) 156814. 610072.i 0.170509 0.663352i
\(960\) 63721.4 0.0691421
\(961\) 692125. + 1.19880e6i 0.749442 + 1.29807i
\(962\) 143519. + 82860.7i 0.155081 + 0.0895362i
\(963\) 59352.3 102801.i 0.0640007 0.110852i
\(964\) 37958.4 21915.3i 0.0408464 0.0235827i
\(965\) 210117.i 0.225635i
\(966\) −514835. + 525452.i −0.551714 + 0.563091i
\(967\) 463079. 0.495225 0.247612 0.968859i \(-0.420354\pi\)
0.247612 + 0.968859i \(0.420354\pi\)
\(968\) −57052.4 98817.7i −0.0608868 0.105459i
\(969\) −18603.2 10740.6i −0.0198125 0.0114388i
\(970\) −66069.4 + 114436.i −0.0702194 + 0.121623i
\(971\) 54723.1 31594.4i 0.0580406 0.0335098i −0.470699 0.882294i \(-0.655998\pi\)
0.528739 + 0.848784i \(0.322665\pi\)
\(972\) 30304.0i 0.0320750i
\(973\) −65946.8 236439.i −0.0696575 0.249743i
\(974\) 756305. 0.797221
\(975\) −13895.9 24068.4i −0.0146176 0.0253185i
\(976\) −36877.2 21291.1i −0.0387132 0.0223511i
\(977\) −719497. + 1.24621e6i −0.753772 + 1.30557i 0.192210 + 0.981354i \(0.438434\pi\)
−0.945982 + 0.324218i \(0.894899\pi\)
\(978\) −1857.49 + 1072.42i −0.00194200 + 0.00112122i
\(979\) 353121.i 0.368432i
\(980\) −238114. 393647.i −0.247932 0.409878i
\(981\) 396840. 0.412361
\(982\) 252245. + 436901.i 0.261577 + 0.453064i
\(983\) 346926. + 200298.i 0.359030 + 0.207286i 0.668655 0.743573i \(-0.266870\pi\)
−0.309625 + 0.950859i \(0.600204\pi\)
\(984\) 60151.5 104185.i 0.0621235 0.107601i
\(985\) 680877. 393104.i 0.701772 0.405168i
\(986\) 189311.i 0.194725i
\(987\) −967521. + 269858.i −0.993176 + 0.277014i
\(988\) 32008.4 0.0327906
\(989\) −1.72756e6 2.99223e6i −1.76620 3.05916i
\(990\) 155192. + 89600.0i 0.158343 + 0.0914192i
\(991\) −99274.5 + 171949.i −0.101086 + 0.175086i −0.912132 0.409896i \(-0.865565\pi\)
0.811046 + 0.584982i \(0.198898\pi\)
\(992\) −238151. + 137496.i −0.242007 + 0.139723i
\(993\) 208983.i 0.211939i
\(994\) 444924. + 435934.i 0.450311 + 0.441213i
\(995\) 633858. 0.640245
\(996\) 26381.4 + 45693.9i 0.0265937 + 0.0460617i
\(997\) 792228. + 457393.i 0.797003 + 0.460150i 0.842422 0.538818i \(-0.181129\pi\)
−0.0454194 + 0.998968i \(0.514462\pi\)
\(998\) 372994. 646045.i 0.374491 0.648637i
\(999\) 68311.6 39439.7i 0.0684484 0.0395187i
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 42.5.g.a.31.2 yes 4
3.2 odd 2 126.5.n.b.73.1 4
4.3 odd 2 336.5.bh.d.241.1 4
7.2 even 3 294.5.g.c.19.2 4
7.3 odd 6 294.5.c.a.97.1 4
7.4 even 3 294.5.c.a.97.2 4
7.5 odd 6 inner 42.5.g.a.19.2 4
7.6 odd 2 294.5.g.c.31.2 4
21.5 even 6 126.5.n.b.19.1 4
21.11 odd 6 882.5.c.a.685.4 4
21.17 even 6 882.5.c.a.685.3 4
28.19 even 6 336.5.bh.d.145.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.5.g.a.19.2 4 7.5 odd 6 inner
42.5.g.a.31.2 yes 4 1.1 even 1 trivial
126.5.n.b.19.1 4 21.5 even 6
126.5.n.b.73.1 4 3.2 odd 2
294.5.c.a.97.1 4 7.3 odd 6
294.5.c.a.97.2 4 7.4 even 3
294.5.g.c.19.2 4 7.2 even 3
294.5.g.c.31.2 4 7.6 odd 2
336.5.bh.d.145.1 4 28.19 even 6
336.5.bh.d.241.1 4 4.3 odd 2
882.5.c.a.685.3 4 21.17 even 6
882.5.c.a.685.4 4 21.11 odd 6