Properties

Label 29.6.d.a.16.11
Level $29$
Weight $6$
Character 29.16
Analytic conductor $4.651$
Analytic rank $0$
Dimension $66$
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] = [29,6,Mod(7,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.7");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 29.d (of order \(7\), degree \(6\), 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: \(4.65113077458\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 16.11
Character \(\chi\) \(=\) 29.16
Dual form 29.6.d.a.20.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(8.40631 + 4.04827i) q^{2} +(-6.82615 + 8.55972i) q^{3} +(34.3260 + 43.0434i) q^{4} +(14.9245 + 7.18727i) q^{5} +(-92.0348 + 44.3216i) q^{6} +(-4.02352 + 5.04533i) q^{7} +(47.8656 + 209.713i) q^{8} +(27.4001 + 120.048i) q^{9} +O(q^{10})\) \(q+(8.40631 + 4.04827i) q^{2} +(-6.82615 + 8.55972i) q^{3} +(34.3260 + 43.0434i) q^{4} +(14.9245 + 7.18727i) q^{5} +(-92.0348 + 44.3216i) q^{6} +(-4.02352 + 5.04533i) q^{7} +(47.8656 + 209.713i) q^{8} +(27.4001 + 120.048i) q^{9} +(96.3641 + 120.837i) q^{10} +(77.6267 - 340.105i) q^{11} -602.754 q^{12} +(156.232 - 684.496i) q^{13} +(-54.2478 + 26.1244i) q^{14} +(-163.398 + 78.6883i) q^{15} +(-54.5753 + 239.110i) q^{16} +833.769 q^{17} +(-255.651 + 1120.08i) q^{18} +(449.395 + 563.523i) q^{19} +(202.934 + 889.111i) q^{20} +(-15.7215 - 68.8804i) q^{21} +(2029.39 - 2544.77i) q^{22} +(-290.165 + 139.736i) q^{23} +(-2121.82 - 1021.82i) q^{24} +(-1777.32 - 2228.69i) q^{25} +(4084.35 - 5121.62i) q^{26} +(-3611.58 - 1739.25i) q^{27} -355.280 q^{28} +(-2562.61 + 3734.19i) q^{29} -1692.13 q^{30} +(-3108.95 - 1497.19i) q^{31} +(2864.97 - 3592.56i) q^{32} +(2381.31 + 2986.07i) q^{33} +(7008.92 + 3375.32i) q^{34} +(-96.3112 + 46.3810i) q^{35} +(-4226.72 + 5300.14i) q^{36} +(2513.15 + 11010.8i) q^{37} +(1496.46 + 6556.42i) q^{38} +(4792.63 + 6009.77i) q^{39} +(-792.892 + 3473.89i) q^{40} -704.091 q^{41} +(146.686 - 642.675i) q^{42} +(-20067.5 + 9664.02i) q^{43} +(17303.9 - 8333.10i) q^{44} +(-453.881 + 1988.58i) q^{45} -3004.90 q^{46} +(4118.50 - 18044.3i) q^{47} +(-1674.18 - 2099.35i) q^{48} +(3730.64 + 16345.0i) q^{49} +(-5918.39 - 25930.1i) q^{50} +(-5691.43 + 7136.83i) q^{51} +(34825.8 - 16771.2i) q^{52} +(-2714.04 - 1307.01i) q^{53} +(-23319.1 - 29241.3i) q^{54} +(3602.96 - 4517.97i) q^{55} +(-1250.66 - 602.286i) q^{56} -7891.24 q^{57} +(-36659.1 + 21016.6i) q^{58} +291.536 q^{59} +(-8995.80 - 4332.15i) q^{60} +(7308.80 - 9164.95i) q^{61} +(-20073.8 - 25171.7i) q^{62} +(-715.925 - 344.771i) q^{63} +(45698.5 - 22007.2i) q^{64} +(7251.33 - 9092.88i) q^{65} +(7929.64 + 34742.0i) q^{66} +(-4560.97 - 19982.9i) q^{67} +(28619.9 + 35888.2i) q^{68} +(784.607 - 3437.59i) q^{69} -997.385 q^{70} +(-9889.13 + 43327.1i) q^{71} +(-23864.0 + 11492.3i) q^{72} +(73100.7 - 35203.5i) q^{73} +(-23448.5 + 102734. i) q^{74} +31209.2 q^{75} +(-8830.05 + 38687.0i) q^{76} +(1403.61 + 1760.07i) q^{77} +(15959.2 + 69921.9i) q^{78} +(-17980.2 - 78776.3i) q^{79} +(-2533.06 + 3176.35i) q^{80} +(12582.1 - 6059.21i) q^{81} +(-5918.81 - 2850.35i) q^{82} +(-30691.3 - 38485.7i) q^{83} +(2425.19 - 3041.09i) q^{84} +(12443.6 + 5992.52i) q^{85} -207817. q^{86} +(-14470.9 - 47425.4i) q^{87} +75040.0 q^{88} +(-72226.1 - 34782.3i) q^{89} +(-11865.8 + 14879.2i) q^{90} +(2824.91 + 3542.32i) q^{91} +(-15974.9 - 7693.10i) q^{92} +(34037.7 - 16391.7i) q^{93} +(107670. - 135013. i) q^{94} +(2656.81 + 11640.2i) q^{95} +(11194.6 + 49046.7i) q^{96} +(98642.4 + 123694. i) q^{97} +(-34808.0 + 152504. i) q^{98} +42955.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9} - 141 q^{10} + 1125 q^{11} - 248 q^{12} - 1789 q^{13} + 1233 q^{14} + 1061 q^{15} + 2629 q^{16} + 676 q^{17} - 10896 q^{18} - 1903 q^{19} + 4081 q^{20} - 439 q^{21} - 2980 q^{22} + 9945 q^{23} + 10741 q^{24} - 22114 q^{25} - 1641 q^{26} - 4427 q^{27} + 7508 q^{28} - 13100 q^{29} - 40018 q^{30} + 8541 q^{31} + 18996 q^{32} + 20725 q^{33} - 8839 q^{34} + 14127 q^{35} + 70172 q^{36} + 3791 q^{37} + 36322 q^{38} + 25843 q^{39} - 72621 q^{40} - 18720 q^{41} - 72614 q^{42} - 10419 q^{43} + 35796 q^{44} + 23163 q^{45} + 15848 q^{46} - 40549 q^{47} - 4194 q^{48} + 19808 q^{49} + 201932 q^{50} + 51998 q^{51} + 8330 q^{52} - 72275 q^{53} - 197108 q^{54} + 42183 q^{55} + 31599 q^{56} - 40162 q^{57} - 258031 q^{58} - 333512 q^{59} + 26920 q^{60} - 175281 q^{61} + 213745 q^{62} + 354423 q^{63} - 19790 q^{64} - 79593 q^{65} + 103783 q^{66} + 135179 q^{67} + 334644 q^{68} + 73673 q^{69} - 511678 q^{70} - 187563 q^{71} - 17551 q^{72} - 56675 q^{73} + 159980 q^{74} + 538208 q^{75} - 215041 q^{76} + 106099 q^{77} + 37481 q^{78} + 273775 q^{79} + 571652 q^{80} - 61356 q^{81} - 37092 q^{82} - 237831 q^{83} + 127523 q^{84} - 148844 q^{85} - 348400 q^{86} - 110493 q^{87} - 985638 q^{88} + 74239 q^{89} - 630714 q^{90} + 100309 q^{91} + 132694 q^{92} - 307921 q^{93} + 206074 q^{94} + 37965 q^{95} + 687094 q^{96} + 136055 q^{97} - 115704 q^{98} + 438608 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.40631 + 4.04827i 1.48604 + 0.715639i 0.988418 0.151755i \(-0.0484924\pi\)
0.497622 + 0.867394i \(0.334207\pi\)
\(3\) −6.82615 + 8.55972i −0.437898 + 0.549106i −0.950988 0.309228i \(-0.899929\pi\)
0.513090 + 0.858335i \(0.328501\pi\)
\(4\) 34.3260 + 43.0434i 1.07269 + 1.34511i
\(5\) 14.9245 + 7.18727i 0.266978 + 0.128570i 0.562584 0.826740i \(-0.309807\pi\)
−0.295606 + 0.955310i \(0.595522\pi\)
\(6\) −92.0348 + 44.3216i −1.04370 + 0.502617i
\(7\) −4.02352 + 5.04533i −0.0310357 + 0.0389175i −0.797107 0.603838i \(-0.793637\pi\)
0.766071 + 0.642755i \(0.222209\pi\)
\(8\) 47.8656 + 209.713i 0.264423 + 1.15851i
\(9\) 27.4001 + 120.048i 0.112758 + 0.494023i
\(10\) 96.3641 + 120.837i 0.304730 + 0.382120i
\(11\) 77.6267 340.105i 0.193432 0.847483i −0.781309 0.624145i \(-0.785448\pi\)
0.974741 0.223338i \(-0.0716954\pi\)
\(12\) −602.754 −1.20833
\(13\) 156.232 684.496i 0.256396 1.12334i −0.668677 0.743553i \(-0.733139\pi\)
0.925073 0.379790i \(-0.124004\pi\)
\(14\) −54.2478 + 26.1244i −0.0739711 + 0.0356226i
\(15\) −163.398 + 78.6883i −0.187507 + 0.0902988i
\(16\) −54.5753 + 239.110i −0.0532962 + 0.233506i
\(17\) 833.769 0.699718 0.349859 0.936802i \(-0.386229\pi\)
0.349859 + 0.936802i \(0.386229\pi\)
\(18\) −255.651 + 1120.08i −0.185980 + 0.814832i
\(19\) 449.395 + 563.523i 0.285591 + 0.358119i 0.903846 0.427858i \(-0.140732\pi\)
−0.618255 + 0.785977i \(0.712160\pi\)
\(20\) 202.934 + 889.111i 0.113443 + 0.497028i
\(21\) −15.7215 68.8804i −0.00777940 0.0340838i
\(22\) 2029.39 2544.77i 0.893940 1.12097i
\(23\) −290.165 + 139.736i −0.114373 + 0.0550793i −0.490196 0.871613i \(-0.663075\pi\)
0.375822 + 0.926692i \(0.377360\pi\)
\(24\) −2121.82 1021.82i −0.751936 0.362113i
\(25\) −1777.32 2228.69i −0.568743 0.713181i
\(26\) 4084.35 5121.62i 1.18492 1.48585i
\(27\) −3611.58 1739.25i −0.953428 0.459147i
\(28\) −355.280 −0.0856397
\(29\) −2562.61 + 3734.19i −0.565832 + 0.824520i
\(30\) −1692.13 −0.343265
\(31\) −3108.95 1497.19i −0.581044 0.279816i 0.120186 0.992751i \(-0.461651\pi\)
−0.701230 + 0.712935i \(0.747365\pi\)
\(32\) 2864.97 3592.56i 0.494589 0.620196i
\(33\) 2381.31 + 2986.07i 0.380655 + 0.477326i
\(34\) 7008.92 + 3375.32i 1.03981 + 0.500746i
\(35\) −96.3112 + 46.3810i −0.0132894 + 0.00639986i
\(36\) −4226.72 + 5300.14i −0.543560 + 0.681602i
\(37\) 2513.15 + 11010.8i 0.301796 + 1.32226i 0.867413 + 0.497589i \(0.165781\pi\)
−0.565617 + 0.824668i \(0.691362\pi\)
\(38\) 1496.46 + 6556.42i 0.168115 + 0.736560i
\(39\) 4792.63 + 6009.77i 0.504560 + 0.632698i
\(40\) −792.892 + 3473.89i −0.0783545 + 0.343294i
\(41\) −704.091 −0.0654138 −0.0327069 0.999465i \(-0.510413\pi\)
−0.0327069 + 0.999465i \(0.510413\pi\)
\(42\) 146.686 642.675i 0.0128312 0.0562171i
\(43\) −20067.5 + 9664.02i −1.65510 + 0.797052i −0.655990 + 0.754770i \(0.727749\pi\)
−0.999106 + 0.0422824i \(0.986537\pi\)
\(44\) 17303.9 8333.10i 1.34745 0.648896i
\(45\) −453.881 + 1988.58i −0.0334126 + 0.146390i
\(46\) −3004.90 −0.209380
\(47\) 4118.50 18044.3i 0.271953 1.19151i −0.635751 0.771894i \(-0.719309\pi\)
0.907704 0.419611i \(-0.137833\pi\)
\(48\) −1674.18 2099.35i −0.104881 0.131517i
\(49\) 3730.64 + 16345.0i 0.221970 + 0.972512i
\(50\) −5918.39 25930.1i −0.334794 1.46683i
\(51\) −5691.43 + 7136.83i −0.306405 + 0.384220i
\(52\) 34825.8 16771.2i 1.78605 0.860115i
\(53\) −2714.04 1307.01i −0.132717 0.0639131i 0.366347 0.930478i \(-0.380608\pi\)
−0.499064 + 0.866565i \(0.666323\pi\)
\(54\) −23319.1 29241.3i −1.08825 1.36462i
\(55\) 3602.96 4517.97i 0.160603 0.201390i
\(56\) −1250.66 602.286i −0.0532929 0.0256645i
\(57\) −7891.24 −0.321705
\(58\) −36659.1 + 21016.6i −1.43091 + 0.820339i
\(59\) 291.536 0.0109034 0.00545171 0.999985i \(-0.498265\pi\)
0.00545171 + 0.999985i \(0.498265\pi\)
\(60\) −8995.80 4332.15i −0.322598 0.155355i
\(61\) 7308.80 9164.95i 0.251490 0.315359i −0.640021 0.768358i \(-0.721074\pi\)
0.891511 + 0.452998i \(0.149646\pi\)
\(62\) −20073.8 25171.7i −0.663208 0.831636i
\(63\) −715.925 344.771i −0.0227256 0.0109441i
\(64\) 45698.5 22007.2i 1.39461 0.671608i
\(65\) 7251.33 9092.88i 0.212880 0.266943i
\(66\) 7929.64 + 34742.0i 0.224075 + 0.981737i
\(67\) −4560.97 19982.9i −0.124128 0.543841i −0.998303 0.0582298i \(-0.981454\pi\)
0.874175 0.485611i \(-0.161403\pi\)
\(68\) 28619.9 + 35888.2i 0.750578 + 0.941195i
\(69\) 784.607 3437.59i 0.0198394 0.0869222i
\(70\) −997.385 −0.0243286
\(71\) −9889.13 + 43327.1i −0.232816 + 1.02003i 0.714476 + 0.699660i \(0.246665\pi\)
−0.947292 + 0.320372i \(0.896192\pi\)
\(72\) −23864.0 + 11492.3i −0.542516 + 0.261262i
\(73\) 73100.7 35203.5i 1.60552 0.773176i 0.605768 0.795641i \(-0.292866\pi\)
0.999748 + 0.0224653i \(0.00715153\pi\)
\(74\) −23448.5 + 102734.i −0.497777 + 2.18090i
\(75\) 31209.2 0.640664
\(76\) −8830.05 + 38687.0i −0.175359 + 0.768300i
\(77\) 1403.61 + 1760.07i 0.0269786 + 0.0338301i
\(78\) 15959.2 + 69921.9i 0.297013 + 1.30130i
\(79\) −17980.2 78776.3i −0.324135 1.42013i −0.830119 0.557586i \(-0.811728\pi\)
0.505984 0.862543i \(-0.331129\pi\)
\(80\) −2533.06 + 3176.35i −0.0442507 + 0.0554886i
\(81\) 12582.1 6059.21i 0.213079 0.102613i
\(82\) −5918.81 2850.35i −0.0972075 0.0468127i
\(83\) −30691.3 38485.7i −0.489013 0.613202i 0.474699 0.880148i \(-0.342557\pi\)
−0.963712 + 0.266946i \(0.913986\pi\)
\(84\) 2425.19 3041.09i 0.0375014 0.0470253i
\(85\) 12443.6 + 5992.52i 0.186809 + 0.0899626i
\(86\) −207817. −3.02994
\(87\) −14470.9 47425.4i −0.204973 0.671758i
\(88\) 75040.0 1.03297
\(89\) −72226.1 34782.3i −0.966539 0.465461i −0.117084 0.993122i \(-0.537355\pi\)
−0.849455 + 0.527661i \(0.823069\pi\)
\(90\) −11865.8 + 14879.2i −0.154415 + 0.193631i
\(91\) 2824.91 + 3542.32i 0.0357603 + 0.0448420i
\(92\) −15974.9 7693.10i −0.196774 0.0947614i
\(93\) 34037.7 16391.7i 0.408087 0.196524i
\(94\) 107670. 135013.i 1.25682 1.57600i
\(95\) 2656.81 + 11640.2i 0.0302031 + 0.132328i
\(96\) 11194.6 + 49046.7i 0.123974 + 0.543165i
\(97\) 98642.4 + 123694.i 1.06447 + 1.33481i 0.939463 + 0.342651i \(0.111325\pi\)
0.125010 + 0.992156i \(0.460104\pi\)
\(98\) −34808.0 + 152504.i −0.366112 + 1.60404i
\(99\) 42955.7 0.440487
\(100\) 34922.1 153004.i 0.349221 1.53004i
\(101\) 27161.2 13080.2i 0.264939 0.127588i −0.296699 0.954971i \(-0.595886\pi\)
0.561638 + 0.827383i \(0.310171\pi\)
\(102\) −76735.7 + 36954.0i −0.730293 + 0.351691i
\(103\) −21572.3 + 94514.6i −0.200357 + 0.877821i 0.770363 + 0.637606i \(0.220075\pi\)
−0.970720 + 0.240215i \(0.922782\pi\)
\(104\) 151026. 1.36920
\(105\) 260.426 1141.00i 0.00230521 0.0100998i
\(106\) −17523.9 21974.3i −0.151484 0.189955i
\(107\) 9842.38 + 43122.3i 0.0831076 + 0.364118i 0.999332 0.0365475i \(-0.0116360\pi\)
−0.916224 + 0.400666i \(0.868779\pi\)
\(108\) −49107.9 215156.i −0.405128 1.77498i
\(109\) 84571.0 106049.i 0.681797 0.854946i −0.313721 0.949515i \(-0.601576\pi\)
0.995518 + 0.0945689i \(0.0301473\pi\)
\(110\) 48577.6 23393.7i 0.382784 0.184339i
\(111\) −111405. 53649.7i −0.858216 0.413295i
\(112\) −986.806 1237.42i −0.00743339 0.00932117i
\(113\) −116060. + 145534.i −0.855036 + 1.07218i 0.141575 + 0.989928i \(0.454783\pi\)
−0.996611 + 0.0822542i \(0.973788\pi\)
\(114\) −66336.2 31945.8i −0.478067 0.230225i
\(115\) −5334.88 −0.0376167
\(116\) −248696. + 17876.2i −1.71603 + 0.123348i
\(117\) 86452.8 0.583868
\(118\) 2450.75 + 1180.22i 0.0162029 + 0.00780291i
\(119\) −3354.69 + 4206.64i −0.0217162 + 0.0272313i
\(120\) −24323.1 30500.2i −0.154193 0.193352i
\(121\) 35456.6 + 17075.0i 0.220158 + 0.106022i
\(122\) 98542.2 47455.4i 0.599408 0.288660i
\(123\) 4806.23 6026.83i 0.0286446 0.0359191i
\(124\) −42273.5 185212.i −0.246896 1.08172i
\(125\) −22026.4 96503.8i −0.126086 0.552420i
\(126\) −4622.56 5796.51i −0.0259392 0.0325267i
\(127\) −74210.7 + 325138.i −0.408279 + 1.78879i 0.183861 + 0.982952i \(0.441141\pi\)
−0.592140 + 0.805835i \(0.701717\pi\)
\(128\) 326206. 1.75981
\(129\) 54262.8 237741.i 0.287096 1.25785i
\(130\) 97767.4 47082.3i 0.507383 0.244343i
\(131\) −232330. + 111884.i −1.18284 + 0.569628i −0.918739 0.394866i \(-0.870791\pi\)
−0.264106 + 0.964494i \(0.585077\pi\)
\(132\) −46789.8 + 204999.i −0.233731 + 1.02404i
\(133\) −4651.31 −0.0228006
\(134\) 42555.2 186447.i 0.204734 0.897000i
\(135\) −41400.7 51914.8i −0.195512 0.245164i
\(136\) 39908.9 + 174852.i 0.185021 + 0.810632i
\(137\) 41314.6 + 181011.i 0.188063 + 0.823956i 0.977637 + 0.210301i \(0.0674444\pi\)
−0.789574 + 0.613655i \(0.789698\pi\)
\(138\) 20511.9 25721.1i 0.0916871 0.114972i
\(139\) 84648.9 40764.8i 0.371607 0.178957i −0.238753 0.971080i \(-0.576739\pi\)
0.610361 + 0.792124i \(0.291024\pi\)
\(140\) −5302.37 2553.49i −0.0228639 0.0110107i
\(141\) 126341. + 158426.i 0.535176 + 0.671089i
\(142\) −258531. + 324187.i −1.07595 + 1.34920i
\(143\) −220672. 106270.i −0.902419 0.434582i
\(144\) −30200.0 −0.121367
\(145\) −65084.3 + 37312.8i −0.257073 + 0.147380i
\(146\) 757021. 2.93918
\(147\) −165375. 79640.3i −0.631213 0.303976i
\(148\) −387677. + 486132.i −1.45484 + 1.82432i
\(149\) −130546. 163699.i −0.481722 0.604060i 0.480276 0.877118i \(-0.340537\pi\)
−0.961998 + 0.273057i \(0.911965\pi\)
\(150\) 262355. + 126343.i 0.952052 + 0.458484i
\(151\) −139756. + 67302.8i −0.498801 + 0.240210i −0.666329 0.745657i \(-0.732136\pi\)
0.167529 + 0.985867i \(0.446421\pi\)
\(152\) −96667.6 + 121217.i −0.339369 + 0.425555i
\(153\) 22845.3 + 100092.i 0.0788985 + 0.345677i
\(154\) 4673.94 + 20477.9i 0.0158811 + 0.0695798i
\(155\) −35638.8 44689.7i −0.119150 0.149409i
\(156\) −94169.2 + 412582.i −0.309811 + 1.35737i
\(157\) 389317. 1.26053 0.630267 0.776378i \(-0.282945\pi\)
0.630267 + 0.776378i \(0.282945\pi\)
\(158\) 167760. 735006.i 0.534622 2.34233i
\(159\) 29714.1 14309.6i 0.0932116 0.0448883i
\(160\) 68578.9 33025.9i 0.211783 0.101989i
\(161\) 462.469 2026.21i 0.00140610 0.00616055i
\(162\) 130298. 0.390078
\(163\) 26837.6 117583.i 0.0791178 0.346638i −0.919839 0.392295i \(-0.871681\pi\)
0.998957 + 0.0456576i \(0.0145383\pi\)
\(164\) −24168.6 30306.5i −0.0701685 0.0879885i
\(165\) 14078.2 + 61680.7i 0.0402567 + 0.176376i
\(166\) −102200. 447769.i −0.287861 1.26120i
\(167\) 266473. 334147.i 0.739371 0.927141i −0.259888 0.965639i \(-0.583686\pi\)
0.999259 + 0.0384973i \(0.0122571\pi\)
\(168\) 13692.6 6594.01i 0.0374294 0.0180250i
\(169\) −109603. 52781.8i −0.295192 0.142157i
\(170\) 80345.4 + 100750.i 0.213225 + 0.267376i
\(171\) −55336.2 + 69389.3i −0.144717 + 0.181469i
\(172\) −1.10481e6 532048.i −2.84752 1.37129i
\(173\) 219794. 0.558342 0.279171 0.960241i \(-0.409940\pi\)
0.279171 + 0.960241i \(0.409940\pi\)
\(174\) 70344.0 457255.i 0.176138 1.14495i
\(175\) 18395.6 0.0454065
\(176\) 77086.0 + 37122.7i 0.187583 + 0.0903353i
\(177\) −1990.07 + 2495.47i −0.00477458 + 0.00598714i
\(178\) −466348. 584781.i −1.10321 1.38339i
\(179\) −540182. 260138.i −1.26011 0.606836i −0.319904 0.947450i \(-0.603651\pi\)
−0.940203 + 0.340614i \(0.889365\pi\)
\(180\) −101175. + 48723.4i −0.232752 + 0.112087i
\(181\) 73593.2 92283.0i 0.166971 0.209375i −0.691305 0.722563i \(-0.742964\pi\)
0.858276 + 0.513188i \(0.171535\pi\)
\(182\) 9406.80 + 41213.9i 0.0210505 + 0.0922284i
\(183\) 28558.4 + 125123.i 0.0630386 + 0.276190i
\(184\) −43193.3 54162.7i −0.0940529 0.117939i
\(185\) −41630.2 + 182394.i −0.0894292 + 0.391815i
\(186\) 352489. 0.747074
\(187\) 64722.7 283569.i 0.135348 0.592999i
\(188\) 918060. 442115.i 1.89442 0.912305i
\(189\) 23306.3 11223.7i 0.0474591 0.0228551i
\(190\) −24788.8 + 108607.i −0.0498163 + 0.218260i
\(191\) −199938. −0.396563 −0.198281 0.980145i \(-0.563536\pi\)
−0.198281 + 0.980145i \(0.563536\pi\)
\(192\) −123569. + 541391.i −0.241912 + 1.05988i
\(193\) 576881. + 723385.i 1.11479 + 1.39790i 0.907721 + 0.419575i \(0.137821\pi\)
0.207068 + 0.978327i \(0.433608\pi\)
\(194\) 328474. + 1.43914e6i 0.626609 + 2.74535i
\(195\) 28333.9 + 124139.i 0.0533604 + 0.233787i
\(196\) −575487. + 721638.i −1.07003 + 1.34177i
\(197\) −293299. + 141245.i −0.538450 + 0.259304i −0.683285 0.730152i \(-0.739449\pi\)
0.144835 + 0.989456i \(0.453735\pi\)
\(198\) 361099. + 173896.i 0.654581 + 0.315230i
\(199\) 74990.1 + 94034.6i 0.134237 + 0.168327i 0.844407 0.535703i \(-0.179953\pi\)
−0.710170 + 0.704030i \(0.751382\pi\)
\(200\) 382313. 479405.i 0.675840 0.847476i
\(201\) 202182. + 97365.7i 0.352982 + 0.169987i
\(202\) 281278. 0.485017
\(203\) −8529.53 27953.8i −0.0145273 0.0476103i
\(204\) −502557. −0.845493
\(205\) −10508.2 5060.49i −0.0174640 0.00841023i
\(206\) −563964. + 707189.i −0.925941 + 1.16109i
\(207\) −24725.5 31004.8i −0.0401069 0.0502924i
\(208\) 155143. + 74713.2i 0.248642 + 0.119740i
\(209\) 226542. 109097.i 0.358743 0.172761i
\(210\) 6808.30 8537.34i 0.0106535 0.0133590i
\(211\) 46361.8 + 203124.i 0.0716893 + 0.314091i 0.998041 0.0625692i \(-0.0199294\pi\)
−0.926351 + 0.376661i \(0.877072\pi\)
\(212\) −36903.8 161686.i −0.0563937 0.247077i
\(213\) −303363. 380405.i −0.458157 0.574510i
\(214\) −91832.4 + 402344.i −0.137076 + 0.600569i
\(215\) −368956. −0.544350
\(216\) 191872. 840645.i 0.279819 1.22597i
\(217\) 20062.7 9661.71i 0.0289228 0.0139285i
\(218\) 1.14024e6 549112.i 1.62501 0.782564i
\(219\) −197665. + 866026.i −0.278496 + 1.22017i
\(220\) 318144. 0.443167
\(221\) 130261. 570711.i 0.179405 0.786024i
\(222\) −719315. 901993.i −0.979573 1.22835i
\(223\) −85036.0 372567.i −0.114509 0.501698i −0.999358 0.0358201i \(-0.988596\pi\)
0.884849 0.465878i \(-0.154261\pi\)
\(224\) 6598.39 + 28909.4i 0.00878654 + 0.0384964i
\(225\) 218850. 274429.i 0.288198 0.361389i
\(226\) −1.56479e6 + 753565.i −2.03791 + 0.981408i
\(227\) 313749. + 151094.i 0.404127 + 0.194617i 0.624895 0.780709i \(-0.285142\pi\)
−0.220768 + 0.975326i \(0.570856\pi\)
\(228\) −270874. 339666.i −0.345089 0.432728i
\(229\) −102801. + 128908.i −0.129541 + 0.162439i −0.842372 0.538897i \(-0.818841\pi\)
0.712831 + 0.701336i \(0.247413\pi\)
\(230\) −44846.7 21597.0i −0.0558999 0.0269200i
\(231\) −24647.0 −0.0303902
\(232\) −905769. 358673.i −1.10484 0.437501i
\(233\) −504827. −0.609190 −0.304595 0.952482i \(-0.598521\pi\)
−0.304595 + 0.952482i \(0.598521\pi\)
\(234\) 726749. + 349984.i 0.867651 + 0.417839i
\(235\) 191156. 239702.i 0.225797 0.283140i
\(236\) 10007.3 + 12548.7i 0.0116959 + 0.0146663i
\(237\) 797038. + 383833.i 0.921740 + 0.443886i
\(238\) −45230.1 + 21781.7i −0.0517590 + 0.0249258i
\(239\) −42185.0 + 52898.4i −0.0477709 + 0.0599029i −0.805143 0.593081i \(-0.797912\pi\)
0.757372 + 0.652984i \(0.226483\pi\)
\(240\) −9897.68 43364.6i −0.0110919 0.0485967i
\(241\) 166661. + 730191.i 0.184838 + 0.809830i 0.979283 + 0.202494i \(0.0649047\pi\)
−0.794445 + 0.607336i \(0.792238\pi\)
\(242\) 228935. + 287076.i 0.251290 + 0.315107i
\(243\) 182731. 800596.i 0.198516 0.869756i
\(244\) 645372. 0.693962
\(245\) −61797.9 + 270754.i −0.0657747 + 0.288178i
\(246\) 64800.9 31206.5i 0.0682721 0.0328781i
\(247\) 455939. 219569.i 0.475515 0.228996i
\(248\) 165169. 723651.i 0.170529 0.747136i
\(249\) 538930. 0.550851
\(250\) 205513. 900410.i 0.207964 0.911151i
\(251\) −1.11027e6 1.39223e6i −1.11235 1.39485i −0.909533 0.415632i \(-0.863560\pi\)
−0.202822 0.979216i \(-0.565011\pi\)
\(252\) −9734.69 42650.4i −0.00965652 0.0423080i
\(253\) 25000.3 + 109534.i 0.0245552 + 0.107584i
\(254\) −1.94008e6 + 2.43279e6i −1.88685 + 2.36603i
\(255\) −136236. + 65607.8i −0.131202 + 0.0631837i
\(256\) 1.27983e6 + 616336.i 1.22054 + 0.587783i
\(257\) −976768. 1.22483e6i −0.922484 1.15676i −0.987301 0.158861i \(-0.949218\pi\)
0.0648173 0.997897i \(-0.479354\pi\)
\(258\) 1.41859e6 1.77885e6i 1.32680 1.66376i
\(259\) −65665.0 31622.6i −0.0608254 0.0292920i
\(260\) 640298. 0.587420
\(261\) −518496. 205318.i −0.471134 0.186563i
\(262\) −2.40598e6 −2.16540
\(263\) 1.63452e6 + 787145.i 1.45714 + 0.701722i 0.983819 0.179167i \(-0.0573401\pi\)
0.473323 + 0.880889i \(0.343054\pi\)
\(264\) −512234. + 642322.i −0.452334 + 0.567209i
\(265\) −31111.9 39013.0i −0.0272152 0.0341268i
\(266\) −39100.4 18829.8i −0.0338826 0.0163170i
\(267\) 790753. 380807.i 0.678833 0.326909i
\(268\) 703572. 882252.i 0.598373 0.750336i
\(269\) 318710. + 1.39636e6i 0.268543 + 1.17657i 0.911708 + 0.410838i \(0.134764\pi\)
−0.643165 + 0.765728i \(0.722379\pi\)
\(270\) −137862. 604013.i −0.115089 0.504239i
\(271\) 1.00099e6 + 1.25520e6i 0.827957 + 1.03822i 0.998600 + 0.0528919i \(0.0168439\pi\)
−0.170644 + 0.985333i \(0.554585\pi\)
\(272\) −45503.2 + 199363.i −0.0372923 + 0.163388i
\(273\) −49604.6 −0.0402824
\(274\) −385478. + 1.68889e6i −0.310187 + 1.35902i
\(275\) −895956. + 431469.i −0.714422 + 0.344047i
\(276\) 174898. 84226.3i 0.138201 0.0665541i
\(277\) 506689. 2.21995e6i 0.396773 1.73837i −0.243200 0.969976i \(-0.578197\pi\)
0.639972 0.768398i \(-0.278946\pi\)
\(278\) 876612. 0.680292
\(279\) 94548.7 414245.i 0.0727185 0.318601i
\(280\) −14336.7 17977.7i −0.0109283 0.0137037i
\(281\) −175886. 770606.i −0.132882 0.582193i −0.996896 0.0787259i \(-0.974915\pi\)
0.864015 0.503467i \(-0.167942\pi\)
\(282\) 420709. + 1.84324e6i 0.315035 + 1.38026i
\(283\) 711677. 892415.i 0.528223 0.662370i −0.444110 0.895972i \(-0.646480\pi\)
0.972332 + 0.233602i \(0.0750514\pi\)
\(284\) −2.20440e6 + 1.06158e6i −1.62179 + 0.781012i
\(285\) −117773. 56716.4i −0.0858881 0.0413615i
\(286\) −1.42483e6 1.78668e6i −1.03003 1.29161i
\(287\) 2832.93 3552.38i 0.00203016 0.00254574i
\(288\) 509778. + 245496.i 0.362159 + 0.174407i
\(289\) −724687. −0.510394
\(290\) −698171. + 50184.4i −0.487491 + 0.0350408i
\(291\) −1.73213e6 −1.19908
\(292\) 4.02453e6 + 1.93811e6i 2.76222 + 1.33021i
\(293\) 752917. 944128.i 0.512363 0.642483i −0.456605 0.889670i \(-0.650935\pi\)
0.968968 + 0.247187i \(0.0795061\pi\)
\(294\) −1.06779e6 1.33896e6i −0.720470 0.903441i
\(295\) 4351.04 + 2095.35i 0.00291097 + 0.00140185i
\(296\) −2.18882e6 + 1.05408e6i −1.45205 + 0.699269i
\(297\) −871881. + 1.09330e6i −0.573543 + 0.719200i
\(298\) −434710. 1.90459e6i −0.283569 1.24240i
\(299\) 50315.7 + 220448.i 0.0325481 + 0.142603i
\(300\) 1.07129e6 + 1.34335e6i 0.687231 + 0.861760i
\(301\) 31984.0 140131.i 0.0203477 0.0891492i
\(302\) −1.44729e6 −0.913141
\(303\) −73444.1 + 321780.i −0.0459569 + 0.201350i
\(304\) −159270. + 76700.4i −0.0988440 + 0.0476007i
\(305\) 174951. 84252.1i 0.107688 0.0518598i
\(306\) −213154. + 933888.i −0.130134 + 0.570153i
\(307\) 2.17451e6 1.31679 0.658394 0.752674i \(-0.271236\pi\)
0.658394 + 0.752674i \(0.271236\pi\)
\(308\) −27579.2 + 120832.i −0.0165655 + 0.0725782i
\(309\) −661763. 829824.i −0.394281 0.494413i
\(310\) −118675. 519951.i −0.0701385 0.307297i
\(311\) 638269. + 2.79644e6i 0.374199 + 1.63947i 0.714847 + 0.699281i \(0.246497\pi\)
−0.340648 + 0.940191i \(0.610646\pi\)
\(312\) −1.03092e6 + 1.29274e6i −0.599571 + 0.751838i
\(313\) −1.24882e6 + 601399.i −0.720508 + 0.346978i −0.757943 0.652321i \(-0.773795\pi\)
0.0374353 + 0.999299i \(0.488081\pi\)
\(314\) 3.27272e6 + 1.57606e6i 1.87320 + 0.902088i
\(315\) −8206.87 10291.1i −0.00466016 0.00584366i
\(316\) 2.77361e6 3.47800e6i 1.56253 1.95935i
\(317\) −946069. 455603.i −0.528780 0.254647i 0.150392 0.988626i \(-0.451946\pi\)
−0.679171 + 0.733980i \(0.737661\pi\)
\(318\) 307715. 0.170640
\(319\) 1.07109e6 + 1.16143e6i 0.589317 + 0.639022i
\(320\) 840200. 0.458678
\(321\) −436300. 210111.i −0.236332 0.113812i
\(322\) 12090.3 15160.7i 0.00649826 0.00814855i
\(323\) 374691. + 469848.i 0.199833 + 0.250583i
\(324\) 692701. + 333587.i 0.366592 + 0.176542i
\(325\) −1.80320e6 + 868377.i −0.946970 + 0.456037i
\(326\) 701612. 879794.i 0.365640 0.458498i
\(327\) 330453. + 1.44781e6i 0.170899 + 0.748758i
\(328\) −33701.8 147657.i −0.0172969 0.0757826i
\(329\) 74468.8 + 93380.9i 0.0379302 + 0.0475629i
\(330\) −131354. + 575500.i −0.0663986 + 0.290911i
\(331\) −725050. −0.363746 −0.181873 0.983322i \(-0.558216\pi\)
−0.181873 + 0.983322i \(0.558216\pi\)
\(332\) 603046. 2.64212e6i 0.300265 1.31555i
\(333\) −1.25296e6 + 603395.i −0.619195 + 0.298189i
\(334\) 3.59277e6 1.73019e6i 1.76223 0.848647i
\(335\) 75552.2 331016.i 0.0367820 0.161152i
\(336\) 17328.0 0.00837338
\(337\) −476908. + 2.08947e6i −0.228749 + 1.00222i 0.721912 + 0.691985i \(0.243264\pi\)
−0.950661 + 0.310231i \(0.899594\pi\)
\(338\) −707679. 887401.i −0.336934 0.422502i
\(339\) −453491. 1.98687e6i −0.214323 0.939012i
\(340\) 169200. + 741313.i 0.0793785 + 0.347780i
\(341\) −750539. + 941146.i −0.349532 + 0.438300i
\(342\) −746080. + 359293.i −0.344921 + 0.166105i
\(343\) −195195. 94000.9i −0.0895846 0.0431416i
\(344\) −2.98722e6 3.74585e6i −1.36104 1.70669i
\(345\) 36416.7 45665.1i 0.0164723 0.0206555i
\(346\) 1.84766e6 + 889785.i 0.829719 + 0.399572i
\(347\) 1.33133e6 0.593558 0.296779 0.954946i \(-0.404088\pi\)
0.296779 + 0.954946i \(0.404088\pi\)
\(348\) 1.54462e6 2.25080e6i 0.683714 0.996296i
\(349\) −3.21152e6 −1.41139 −0.705694 0.708516i \(-0.749365\pi\)
−0.705694 + 0.708516i \(0.749365\pi\)
\(350\) 154639. + 74470.2i 0.0674759 + 0.0324947i
\(351\) −1.75475e6 + 2.20039e6i −0.760234 + 0.953303i
\(352\) −999447. 1.25327e6i −0.429935 0.539122i
\(353\) −2.11990e6 1.02089e6i −0.905478 0.436055i −0.0776134 0.996984i \(-0.524730\pi\)
−0.827864 + 0.560928i \(0.810444\pi\)
\(354\) −26831.5 + 12921.4i −0.0113798 + 0.00548025i
\(355\) −458994. + 575560.i −0.193302 + 0.242393i
\(356\) −982084. 4.30279e6i −0.410699 1.79939i
\(357\) −13108.1 57430.3i −0.00544339 0.0238490i
\(358\) −3.48783e6 4.37360e6i −1.43829 1.80356i
\(359\) 547091. 2.39696e6i 0.224039 0.981579i −0.730364 0.683058i \(-0.760650\pi\)
0.954403 0.298521i \(-0.0964933\pi\)
\(360\) −438757. −0.178430
\(361\) 435381. 1.90753e6i 0.175833 0.770377i
\(362\) 992234. 477834.i 0.397963 0.191649i
\(363\) −388190. + 186942.i −0.154624 + 0.0744631i
\(364\) −55505.9 + 243187.i −0.0219576 + 0.0962027i
\(365\) 1.34401e6 0.528044
\(366\) −266459. + 1.16743e6i −0.103975 + 0.455543i
\(367\) 226413. + 283913.i 0.0877478 + 0.110032i 0.823767 0.566928i \(-0.191868\pi\)
−0.736019 + 0.676960i \(0.763297\pi\)
\(368\) −17576.4 77007.4i −0.00676568 0.0296424i
\(369\) −19292.2 84524.5i −0.00737590 0.0323159i
\(370\) −1.08834e6 + 1.36473e6i −0.413294 + 0.518254i
\(371\) 17514.3 8434.45i 0.00660630 0.00318143i
\(372\) 1.87393e6 + 902437.i 0.702095 + 0.338111i
\(373\) 2.91114e6 + 3.65045e6i 1.08341 + 1.35855i 0.928804 + 0.370571i \(0.120838\pi\)
0.154601 + 0.987977i \(0.450591\pi\)
\(374\) 1.69204e6 2.12175e6i 0.625506 0.784360i
\(375\) 976401. + 470210.i 0.358550 + 0.172669i
\(376\) 3.98126e6 1.45228
\(377\) 2.15568e6 + 2.33749e6i 0.781142 + 0.847027i
\(378\) 241357. 0.0868822
\(379\) 3.44935e6 + 1.66112e6i 1.23350 + 0.594022i 0.933040 0.359773i \(-0.117146\pi\)
0.300459 + 0.953795i \(0.402860\pi\)
\(380\) −409838. + 513920.i −0.145597 + 0.182573i
\(381\) −2.27652e6 2.85467e6i −0.803450 1.00749i
\(382\) −1.68074e6 809402.i −0.589308 0.283796i
\(383\) 2.67789e6 1.28960e6i 0.932816 0.449220i 0.0951863 0.995459i \(-0.469655\pi\)
0.837629 + 0.546239i \(0.183941\pi\)
\(384\) −2.22673e6 + 2.79223e6i −0.770618 + 0.966325i
\(385\) 8298.09 + 36356.3i 0.00285316 + 0.0125005i
\(386\) 1.92098e6 + 8.41637e6i 0.656228 + 2.87512i
\(387\) −1.70999e6 2.14427e6i −0.580386 0.727782i
\(388\) −1.93820e6 + 8.49181e6i −0.653611 + 2.86366i
\(389\) 313465. 0.105030 0.0525152 0.998620i \(-0.483276\pi\)
0.0525152 + 0.998620i \(0.483276\pi\)
\(390\) −264364. + 1.15825e6i −0.0880117 + 0.385604i
\(391\) −241930. + 116507.i −0.0800291 + 0.0385400i
\(392\) −3.24919e6 + 1.56473e6i −1.06797 + 0.514309i
\(393\) 628222. 2.75242e6i 0.205179 0.898946i
\(394\) −3.03736e6 −0.985726
\(395\) 297841. 1.30493e6i 0.0960487 0.420817i
\(396\) 1.47450e6 + 1.84896e6i 0.472504 + 0.592502i
\(397\) 400262. + 1.75366e6i 0.127458 + 0.558431i 0.997819 + 0.0660158i \(0.0210288\pi\)
−0.870360 + 0.492415i \(0.836114\pi\)
\(398\) 249713. + 1.09406e6i 0.0790193 + 0.346206i
\(399\) 31750.6 39813.9i 0.00998434 0.0125200i
\(400\) 629900. 303344.i 0.196844 0.0947950i
\(401\) −1.93068e6 929767.i −0.599584 0.288744i 0.109368 0.994001i \(-0.465117\pi\)
−0.708952 + 0.705257i \(0.750832\pi\)
\(402\) 1.30544e6 + 1.63697e6i 0.402896 + 0.505215i
\(403\) −1.51054e6 + 1.89415e6i −0.463307 + 0.580968i
\(404\) 1.49535e6 + 720122.i 0.455816 + 0.219509i
\(405\) 231331. 0.0700802
\(406\) 41462.7 269518.i 0.0124837 0.0811471i
\(407\) 3.93992e6 1.17897
\(408\) −1.76911e6 851958.i −0.526144 0.253377i
\(409\) 1.44667e6 1.81406e6i 0.427622 0.536221i −0.520612 0.853793i \(-0.674296\pi\)
0.948234 + 0.317573i \(0.102868\pi\)
\(410\) −67849.2 85080.2i −0.0199336 0.0249959i
\(411\) −1.83143e6 881968.i −0.534792 0.257542i
\(412\) −4.80872e6 + 2.31576e6i −1.39568 + 0.672125i
\(413\) −1173.00 + 1470.90i −0.000338395 + 0.000424334i
\(414\) −82334.5 360731.i −0.0236092 0.103439i
\(415\) −181446. 794966.i −0.0517162 0.226584i
\(416\) −2.01149e6 2.52233e6i −0.569882 0.714609i
\(417\) −228891. + 1.00284e6i −0.0644598 + 0.282417i
\(418\) 2.34604e6 0.656741
\(419\) 841838. 3.68833e6i 0.234257 1.02635i −0.711808 0.702374i \(-0.752123\pi\)
0.946066 0.323975i \(-0.105019\pi\)
\(420\) 58052.0 27956.3i 0.0160581 0.00773316i
\(421\) 1.69168e6 814672.i 0.465173 0.224015i −0.186591 0.982438i \(-0.559744\pi\)
0.651763 + 0.758422i \(0.274030\pi\)
\(422\) −432570. + 1.89521e6i −0.118243 + 0.518056i
\(423\) 2.27902e6 0.619296
\(424\) 144188. 631730.i 0.0389507 0.170654i
\(425\) −1.48187e6 1.85821e6i −0.397960 0.499026i
\(426\) −1.01018e6 4.42590e6i −0.269697 1.18162i
\(427\) 16833.1 + 73750.7i 0.00446781 + 0.0195748i
\(428\) −1.51828e6 + 1.90386e6i −0.400629 + 0.502373i
\(429\) 2.41599e6 1.16348e6i 0.633799 0.305221i
\(430\) −3.10156e6 1.49363e6i −0.808927 0.389559i
\(431\) 2.30452e6 + 2.88978e6i 0.597568 + 0.749327i 0.984997 0.172573i \(-0.0552081\pi\)
−0.387429 + 0.921900i \(0.626637\pi\)
\(432\) 612975. 768646.i 0.158028 0.198160i
\(433\) −3.07421e6 1.48046e6i −0.787977 0.379469i −0.00378854 0.999993i \(-0.501206\pi\)
−0.784188 + 0.620523i \(0.786920\pi\)
\(434\) 207767. 0.0529483
\(435\) 124888. 811807.i 0.0316445 0.205698i
\(436\) 7.46767e6 1.88135
\(437\) −209143. 100718.i −0.0523889 0.0252292i
\(438\) −5.16754e6 + 6.47989e6i −1.28706 + 1.61392i
\(439\) −1.64042e6 2.05702e6i −0.406250 0.509421i 0.536052 0.844185i \(-0.319915\pi\)
−0.942302 + 0.334764i \(0.891344\pi\)
\(440\) 1.11994e6 + 539332.i 0.275779 + 0.132808i
\(441\) −1.85996e6 + 895709.i −0.455415 + 0.219316i
\(442\) 3.40541e6 4.27024e6i 0.829112 1.03967i
\(443\) −413195. 1.81033e6i −0.100034 0.438276i −0.999997 0.00231105i \(-0.999264\pi\)
0.899964 0.435965i \(-0.143593\pi\)
\(444\) −1.51481e6 6.63682e6i −0.364671 1.59773i
\(445\) −827950. 1.03822e6i −0.198200 0.248535i
\(446\) 793412. 3.47617e6i 0.188869 0.827491i
\(447\) 2.29234e6 0.542638
\(448\) −72835.0 + 319111.i −0.0171453 + 0.0751185i
\(449\) 3.16345e6 1.52344e6i 0.740534 0.356622i −0.0252836 0.999680i \(-0.508049\pi\)
0.765817 + 0.643058i \(0.222335\pi\)
\(450\) 2.95069e6 1.42098e6i 0.686897 0.330792i
\(451\) −54656.3 + 239465.i −0.0126531 + 0.0554371i
\(452\) −1.02481e7 −2.35938
\(453\) 377900. 1.65569e6i 0.0865230 0.379082i
\(454\) 2.02581e6 + 2.54028e6i 0.461273 + 0.578418i
\(455\) 16700.8 + 73170.8i 0.00378188 + 0.0165695i
\(456\) −377719. 1.65490e6i −0.0850662 0.372699i
\(457\) 4.30328e6 5.39614e6i 0.963848 1.20863i −0.0141254 0.999900i \(-0.504496\pi\)
0.977974 0.208727i \(-0.0669322\pi\)
\(458\) −1.38603e6 + 667476.i −0.308751 + 0.148687i
\(459\) −3.01122e6 1.45013e6i −0.667131 0.321273i
\(460\) −183125. 229631.i −0.0403509 0.0505984i
\(461\) −5.39552e6 + 6.76577e6i −1.18245 + 1.48274i −0.342966 + 0.939348i \(0.611432\pi\)
−0.839479 + 0.543392i \(0.817140\pi\)
\(462\) −207190. 99777.5i −0.0451611 0.0217484i
\(463\) −1.20821e6 −0.261933 −0.130966 0.991387i \(-0.541808\pi\)
−0.130966 + 0.991387i \(0.541808\pi\)
\(464\) −753028. 816541.i −0.162374 0.176069i
\(465\) 625807. 0.134217
\(466\) −4.24374e6 2.04368e6i −0.905282 0.435961i
\(467\) 3.14147e6 3.93928e6i 0.666562 0.835842i −0.327478 0.944859i \(-0.606199\pi\)
0.994040 + 0.109016i \(0.0347701\pi\)
\(468\) 2.96758e6 + 3.72122e6i 0.626307 + 0.785364i
\(469\) 119172. + 57390.0i 0.0250173 + 0.0120477i
\(470\) 2.57729e6 1.24116e6i 0.538170 0.259169i
\(471\) −2.65754e6 + 3.33245e6i −0.551985 + 0.692167i
\(472\) 13954.6 + 61138.9i 0.00288311 + 0.0126317i
\(473\) 1.72900e6 + 7.57525e6i 0.355339 + 1.55684i
\(474\) 5.14629e6 + 6.45325e6i 1.05208 + 1.31927i
\(475\) 457200. 2.00312e6i 0.0929763 0.407356i
\(476\) −296221. −0.0599237
\(477\) 82538.8 361626.i 0.0166097 0.0727719i
\(478\) −568767. + 273904.i −0.113858 + 0.0548313i
\(479\) −6.27630e6 + 3.02251e6i −1.24987 + 0.601906i −0.937477 0.348047i \(-0.886845\pi\)
−0.312394 + 0.949953i \(0.601131\pi\)
\(480\) −185438. + 812456.i −0.0367363 + 0.160952i
\(481\) 7.92950e6 1.56273
\(482\) −1.55500e6 + 6.81291e6i −0.304869 + 1.33572i
\(483\) 14186.9 + 17789.8i 0.00276707 + 0.00346979i
\(484\) 482117. + 2.11229e6i 0.0935489 + 0.409865i
\(485\) 583171. + 2.55504e6i 0.112575 + 0.493223i
\(486\) 4.77712e6 5.99032e6i 0.917435 1.15043i
\(487\) −1.07127e6 + 515896.i −0.204681 + 0.0985690i −0.533416 0.845853i \(-0.679092\pi\)
0.328735 + 0.944422i \(0.393378\pi\)
\(488\) 2.27185e6 + 1.09406e6i 0.431847 + 0.207967i
\(489\) 823281. + 1.03236e6i 0.155695 + 0.195236i
\(490\) −1.61558e6 + 2.02587e6i −0.303975 + 0.381173i
\(491\) −6.15986e6 2.96643e6i −1.15310 0.555304i −0.243137 0.969992i \(-0.578176\pi\)
−0.909964 + 0.414688i \(0.863891\pi\)
\(492\) 424394. 0.0790417
\(493\) −2.13662e6 + 3.11345e6i −0.395923 + 0.576932i
\(494\) 4.72164e6 0.870513
\(495\) 641093. + 308734.i 0.117600 + 0.0566333i
\(496\) 527665. 661671.i 0.0963062 0.120764i
\(497\) −178811. 224221.i −0.0324715 0.0407180i
\(498\) 4.53042e6 + 2.18173e6i 0.818587 + 0.394211i
\(499\) 3.69637e6 1.78008e6i 0.664544 0.320028i −0.0710276 0.997474i \(-0.522628\pi\)
0.735572 + 0.677447i \(0.236914\pi\)
\(500\) 3.39778e6 4.26068e6i 0.607813 0.762173i
\(501\) 1.04122e6 + 4.56187e6i 0.185331 + 0.811986i
\(502\) −3.69713e6 1.61982e7i −0.654795 2.86884i
\(503\) 6.16667e6 + 7.73276e6i 1.08675 + 1.36275i 0.926771 + 0.375626i \(0.122572\pi\)
0.159982 + 0.987120i \(0.448856\pi\)
\(504\) 38034.8 166641.i 0.00666968 0.0292218i
\(505\) 499378. 0.0871367
\(506\) −233261. + 1.02198e6i −0.0405009 + 0.177446i
\(507\) 1.19996e6 577871.i 0.207323 0.0998415i
\(508\) −1.65424e7 + 7.96640e6i −2.84406 + 1.36963i
\(509\) −39323.8 + 172289.i −0.00672762 + 0.0294756i −0.978180 0.207758i \(-0.933383\pi\)
0.971453 + 0.237233i \(0.0762406\pi\)
\(510\) −1.41084e6 −0.240189
\(511\) −116509. + 510460.i −0.0197382 + 0.0864787i
\(512\) 1.75525e6 + 2.20101e6i 0.295912 + 0.371062i
\(513\) −642920. 2.81682e6i −0.107861 0.472569i
\(514\) −3.25259e6 1.42505e7i −0.543027 2.37915i
\(515\) −1.00126e6 + 1.25554e6i −0.166352 + 0.208599i
\(516\) 1.20958e7 5.82502e6i 1.99991 0.963105i
\(517\) −5.81725e6 2.80144e6i −0.957176 0.460952i
\(518\) −423984. 531659.i −0.0694265 0.0870581i
\(519\) −1.50035e6 + 1.88138e6i −0.244497 + 0.306589i
\(520\) 2.25399e6 + 1.08546e6i 0.365547 + 0.176038i
\(521\) −9.92218e6 −1.60145 −0.800724 0.599034i \(-0.795551\pi\)
−0.800724 + 0.599034i \(0.795551\pi\)
\(522\) −3.52746e6 3.82498e6i −0.566612 0.614402i
\(523\) −8.88884e6 −1.42099 −0.710494 0.703703i \(-0.751529\pi\)
−0.710494 + 0.703703i \(0.751529\pi\)
\(524\) −1.27908e7 6.15975e6i −2.03503 0.980019i
\(525\) −125571. + 157461.i −0.0198834 + 0.0249330i
\(526\) 1.05537e7 + 1.32340e7i 1.66319 + 2.08558i
\(527\) −2.59214e6 1.24831e6i −0.406567 0.195793i
\(528\) −843960. + 406430.i −0.131746 + 0.0634455i
\(529\) −3.94832e6 + 4.95104e6i −0.613442 + 0.769232i
\(530\) −103601. 453905.i −0.0160204 0.0701900i
\(531\) 7988.12 + 34998.2i 0.00122944 + 0.00538654i
\(532\) −159661. 200208.i −0.0244579 0.0306692i
\(533\) −110001. + 481948.i −0.0167718 + 0.0734821i
\(534\) 8.18892e6 1.24272
\(535\) −163039. + 714319.i −0.0246267 + 0.107897i
\(536\) 3.97236e6 1.91299e6i 0.597223 0.287608i
\(537\) 5.91407e6 2.84807e6i 0.885015 0.426201i
\(538\) −2.97366e6 + 1.30284e7i −0.442930 + 1.94060i
\(539\) 5.84861e6 0.867124
\(540\) 813471. 3.56405e6i 0.120049 0.525968i
\(541\) 1.46717e6 + 1.83977e6i 0.215520 + 0.270253i 0.877826 0.478980i \(-0.158993\pi\)
−0.662306 + 0.749234i \(0.730422\pi\)
\(542\) 3.33325e6 + 1.46039e7i 0.487382 + 2.13536i
\(543\) 287558. + 1.25987e6i 0.0418530 + 0.183370i
\(544\) 2.38872e6 2.99536e6i 0.346073 0.433962i
\(545\) 2.02438e6 974890.i 0.291945 0.140593i
\(546\) −416991. 200813.i −0.0598612 0.0288276i
\(547\) 196078. + 245874.i 0.0280195 + 0.0351353i 0.795644 0.605765i \(-0.207133\pi\)
−0.767624 + 0.640900i \(0.778561\pi\)
\(548\) −6.37317e6 + 7.99171e6i −0.906576 + 1.13681i
\(549\) 1.30049e6 + 626284.i 0.184152 + 0.0886830i
\(550\) −9.27839e6 −1.30787
\(551\) −3.25593e6 + 234035.i −0.456873 + 0.0328399i
\(552\) 758462. 0.105946
\(553\) 469796. + 226242.i 0.0653276 + 0.0314601i
\(554\) 1.32463e7 1.66104e7i 1.83367 2.29935i
\(555\) −1.27707e6 1.60139e6i −0.175987 0.220681i
\(556\) 4.66031e6 + 2.24429e6i 0.639334 + 0.307887i
\(557\) 1.20047e7 5.78116e6i 1.63951 0.789545i 0.639727 0.768602i \(-0.279047\pi\)
0.999781 0.0209430i \(-0.00666686\pi\)
\(558\) 2.47178e6 3.09951e6i 0.336066 0.421413i
\(559\) 3.47979e6 + 1.52460e7i 0.471003 + 2.06360i
\(560\) −5833.96 25560.3i −0.000786128 0.00344425i
\(561\) 1.98546e6 + 2.48969e6i 0.266351 + 0.333994i
\(562\) 1.64107e6 7.18999e6i 0.219172 0.960257i
\(563\) −8.91016e6 −1.18472 −0.592359 0.805674i \(-0.701803\pi\)
−0.592359 + 0.805674i \(0.701803\pi\)
\(564\) −2.48244e6 + 1.08763e7i −0.328610 + 1.43974i
\(565\) −2.77812e6 + 1.33787e6i −0.366126 + 0.176317i
\(566\) 9.59531e6 4.62086e6i 1.25898 0.606292i
\(567\) −20053.5 + 87860.2i −0.00261959 + 0.0114772i
\(568\) −9.55960e6 −1.24328
\(569\) 2.90870e6 1.27438e7i 0.376633 1.65014i −0.331056 0.943611i \(-0.607405\pi\)
0.707689 0.706524i \(-0.249738\pi\)
\(570\) −760433. 953552.i −0.0980333 0.122930i
\(571\) 453529. + 1.98704e6i 0.0582123 + 0.255045i 0.995658 0.0930868i \(-0.0296734\pi\)
−0.937446 + 0.348131i \(0.886816\pi\)
\(572\) −3.00056e6 1.31463e7i −0.383453 1.68002i
\(573\) 1.36481e6 1.71141e6i 0.173654 0.217755i
\(574\) 38195.4 18394.0i 0.00483873 0.00233021i
\(575\) 827144. + 398331.i 0.104331 + 0.0502429i
\(576\) 3.89406e6 + 4.88300e6i 0.489042 + 0.613240i
\(577\) −2.55680e6 + 3.20612e6i −0.319710 + 0.400904i −0.915553 0.402197i \(-0.868247\pi\)
0.595843 + 0.803101i \(0.296818\pi\)
\(578\) −6.09194e6 2.93373e6i −0.758466 0.365258i
\(579\) −1.01299e7 −1.25576
\(580\) −3.84015e6 1.52065e6i −0.474000 0.187698i
\(581\) 317660. 0.0390411
\(582\) −1.45608e7 7.01213e6i −1.78188 0.858109i
\(583\) −655203. + 821598.i −0.0798370 + 0.100112i
\(584\) 1.08816e7 + 1.36451e7i 1.32027 + 1.65556i
\(585\) 1.29027e6 + 621359.i 0.155880 + 0.0750677i
\(586\) 1.01513e7 4.88862e6i 1.22118 0.588088i
\(587\) 7.46996e6 9.36703e6i 0.894794 1.12204i −0.0971390 0.995271i \(-0.530969\pi\)
0.991933 0.126765i \(-0.0404594\pi\)
\(588\) −2.24866e6 9.85202e6i −0.268213 1.17512i
\(589\) −553444. 2.42479e6i −0.0657332 0.287996i
\(590\) 28093.6 + 35228.3i 0.00332260 + 0.00416641i
\(591\) 793083. 3.47472e6i 0.0934006 0.409215i
\(592\) −2.76996e6 −0.324840
\(593\) 165555. 725343.i 0.0193333 0.0847046i −0.964341 0.264663i \(-0.914739\pi\)
0.983674 + 0.179959i \(0.0575964\pi\)
\(594\) −1.17553e7 + 5.66105e6i −1.36700 + 0.658310i
\(595\) −80301.3 + 38671.1i −0.00929887 + 0.00447810i
\(596\) 2.56506e6 1.12383e7i 0.295789 1.29593i
\(597\) −1.31680e6 −0.151212
\(598\) −469461. + 2.05684e6i −0.0536842 + 0.235206i
\(599\) −4.88518e6 6.12582e6i −0.556305 0.697585i 0.421565 0.906798i \(-0.361481\pi\)
−0.977870 + 0.209214i \(0.932910\pi\)
\(600\) 1.49385e6 + 6.54498e6i 0.169406 + 0.742216i
\(601\) −2.29686e6 1.00632e7i −0.259388 1.13645i −0.921908 0.387408i \(-0.873371\pi\)
0.662521 0.749043i \(-0.269487\pi\)
\(602\) 836154. 1.04850e6i 0.0940362 0.117918i
\(603\) 2.27393e6 1.09507e6i 0.254673 0.122644i
\(604\) −7.69419e6 3.70533e6i −0.858164 0.413270i
\(605\) 406450. + 509673.i 0.0451460 + 0.0566113i
\(606\) −1.92004e6 + 2.40766e6i −0.212388 + 0.266326i
\(607\) 1.05707e7 + 5.09059e6i 1.16448 + 0.560785i 0.913353 0.407169i \(-0.133484\pi\)
0.251128 + 0.967954i \(0.419198\pi\)
\(608\) 3.31199e6 0.363354
\(609\) 297501. + 117807.i 0.0325046 + 0.0128714i
\(610\) 1.81177e6 0.197142
\(611\) −1.17078e7 5.63819e6i −1.26874 0.610994i
\(612\) −3.52411e6 + 4.41909e6i −0.380339 + 0.476930i
\(613\) −5.05243e6 6.33555e6i −0.543062 0.680978i 0.432264 0.901747i \(-0.357715\pi\)
−0.975326 + 0.220769i \(0.929143\pi\)
\(614\) 1.82796e7 + 8.80300e6i 1.95680 + 0.942345i
\(615\) 115047. 55403.8i 0.0122656 0.00590679i
\(616\) −301925. + 378602.i −0.0320588 + 0.0402005i
\(617\) 2.50335e6 + 1.09679e7i 0.264733 + 1.15987i 0.916049 + 0.401066i \(0.131360\pi\)
−0.651316 + 0.758807i \(0.725783\pi\)
\(618\) −2.20363e6 9.65475e6i −0.232096 1.01688i
\(619\) −5.42479e6 6.80247e6i −0.569058 0.713576i 0.411146 0.911570i \(-0.365129\pi\)
−0.980203 + 0.197994i \(0.936557\pi\)
\(620\) 700258. 3.06803e6i 0.0731609 0.320539i
\(621\) 1.29099e6 0.134336
\(622\) −5.95524e6 + 2.60916e7i −0.617196 + 2.70411i
\(623\) 466091. 224458.i 0.0481117 0.0231694i
\(624\) −1.69856e6 + 817982.i −0.174630 + 0.0840973i
\(625\) −1.61738e6 + 7.08620e6i −0.165620 + 0.725627i
\(626\) −1.29326e7 −1.31901
\(627\) −612571. + 2.68385e6i −0.0622282 + 0.272640i
\(628\) 1.33637e7 + 1.67575e7i 1.35216 + 1.69555i
\(629\) 2.09539e6 + 9.18049e6i 0.211173 + 0.925207i
\(630\) −27328.4 119734.i −0.00274324 0.0120189i
\(631\) 7.65846e6 9.60340e6i 0.765716 0.960178i −0.234212 0.972186i \(-0.575251\pi\)
0.999928 + 0.0120079i \(0.00382233\pi\)
\(632\) 1.56598e7 7.54135e6i 1.55953 0.751028i
\(633\) −2.05516e6 989714.i −0.203862 0.0981749i
\(634\) −6.10855e6 7.65988e6i −0.603552 0.756831i
\(635\) −3.44441e6 + 4.31916e6i −0.338985 + 0.425074i
\(636\) 1.63590e6 + 787807.i 0.160366 + 0.0772284i
\(637\) 1.17709e7 1.14938
\(638\) 4.30213e6 + 1.40994e7i 0.418439 + 1.37135i
\(639\) −5.47227e6 −0.530171
\(640\) 4.86846e6 + 2.34453e6i 0.469831 + 0.226259i
\(641\) −278353. + 349044.i −0.0267578 + 0.0335532i −0.795030 0.606570i \(-0.792545\pi\)
0.768273 + 0.640123i \(0.221117\pi\)
\(642\) −2.81709e6 3.53252e6i −0.269751 0.338257i
\(643\) −1.30155e7 6.26793e6i −1.24146 0.597857i −0.306252 0.951950i \(-0.599075\pi\)
−0.935210 + 0.354094i \(0.884789\pi\)
\(644\) 103090. 49645.3i 0.00979490 0.00471697i
\(645\) 2.51855e6 3.15816e6i 0.238370 0.298906i
\(646\) 1.24770e6 + 5.46654e6i 0.117633 + 0.515384i
\(647\) 3.37972e6 + 1.48075e7i 0.317410 + 1.39066i 0.842078 + 0.539356i \(0.181332\pi\)
−0.524668 + 0.851307i \(0.675811\pi\)
\(648\) 1.87294e6 + 2.34860e6i 0.175221 + 0.219721i
\(649\) 22631.0 99152.8i 0.00210907 0.00924046i
\(650\) −1.86737e7 −1.73359
\(651\) −54249.8 + 237684.i −0.00501702 + 0.0219810i
\(652\) 5.98240e6 2.88097e6i 0.551133 0.265412i
\(653\) 577234. 277981.i 0.0529748 0.0255113i −0.407209 0.913335i \(-0.633498\pi\)
0.460184 + 0.887824i \(0.347784\pi\)
\(654\) −3.08322e6 + 1.35085e7i −0.281878 + 1.23499i
\(655\) −4.27156e6 −0.389030
\(656\) 38426.0 168355.i 0.00348631 0.0152745i
\(657\) 6.22906e6 + 7.81099e6i 0.563001 + 0.705980i
\(658\) 247977. + 1.08646e6i 0.0223278 + 0.0978247i
\(659\) −431640. 1.89114e6i −0.0387176 0.169633i 0.951873 0.306494i \(-0.0991558\pi\)
−0.990590 + 0.136861i \(0.956299\pi\)
\(660\) −2.17170e6 + 2.72322e6i −0.194062 + 0.243346i
\(661\) 7.14118e6 3.43901e6i 0.635721 0.306147i −0.0881243 0.996109i \(-0.528087\pi\)
0.723845 + 0.689962i \(0.242373\pi\)
\(662\) −6.09500e6 2.93520e6i −0.540541 0.260311i
\(663\) 3.99595e6 + 5.01076e6i 0.353050 + 0.442710i
\(664\) 6.60189e6 8.27851e6i 0.581096 0.728671i
\(665\) −69418.6 33430.2i −0.00608726 0.00293147i
\(666\) −1.29755e7 −1.13354
\(667\) 221778. 1.44162e6i 0.0193021 0.125469i
\(668\) 2.35298e7 2.04022
\(669\) 3.76954e6 + 1.81532e6i 0.325629 + 0.156815i
\(670\) 1.97516e6 2.47677e6i 0.169987 0.213156i
\(671\) −2.54968e6 3.19720e6i −0.218615 0.274135i
\(672\) −292498. 140860.i −0.0249862 0.0120327i
\(673\) 1.35420e7 6.52149e6i 1.15251 0.555021i 0.242725 0.970095i \(-0.421959\pi\)
0.909787 + 0.415074i \(0.136244\pi\)
\(674\) −1.24678e7 + 1.56341e7i −1.05716 + 1.32563i
\(675\) 2.54270e6 + 1.11403e7i 0.214801 + 0.941103i
\(676\) −1.49031e6 6.52946e6i −0.125432 0.549554i
\(677\) 9.27603e6 + 1.16318e7i 0.777840 + 0.975381i 1.00000 0.000370611i \(0.000117969\pi\)
−0.222160 + 0.975010i \(0.571311\pi\)
\(678\) 4.23121e6 1.85381e7i 0.353501 1.54879i
\(679\) −1.02097e6 −0.0849839
\(680\) −661088. + 2.89642e6i −0.0548261 + 0.240209i
\(681\) −3.43502e6 + 1.65422e6i −0.283832 + 0.136686i
\(682\) −1.01193e7 + 4.87319e6i −0.833083 + 0.401192i
\(683\) 4.15106e6 1.81870e7i 0.340492 1.49179i −0.457545 0.889186i \(-0.651271\pi\)
0.798037 0.602608i \(-0.205872\pi\)
\(684\) −4.88622e6 −0.399331
\(685\) −684375. + 2.99844e6i −0.0557273 + 0.244157i
\(686\) −1.26033e6 1.58040e6i −0.102252 0.128220i
\(687\) −401683. 1.75989e6i −0.0324707 0.142264i
\(688\) −1.21557e6 5.32577e6i −0.0979061 0.428955i
\(689\) −1.31866e6 + 1.65355e6i −0.105824 + 0.132700i
\(690\) 490995. 236451.i 0.0392604 0.0189068i
\(691\) 1.86964e6 + 900374.i 0.148958 + 0.0717344i 0.506878 0.862018i \(-0.330800\pi\)
−0.357920 + 0.933752i \(0.616514\pi\)
\(692\) 7.54464e6 + 9.46068e6i 0.598926 + 0.751030i
\(693\) −172833. + 216726.i −0.0136708 + 0.0171426i
\(694\) 1.11916e7 + 5.38959e6i 0.882051 + 0.424773i
\(695\) 1.55633e6 0.122219
\(696\) 9.25306e6 5.30477e6i 0.724040 0.415091i
\(697\) −587049. −0.0457712
\(698\) −2.69970e7 1.30011e7i −2.09738 1.01005i
\(699\) 3.44603e6 4.32118e6i 0.266763 0.334510i
\(700\) 631446. + 791808.i 0.0487070 + 0.0610766i
\(701\) −1.93650e7 9.32568e6i −1.48841 0.716780i −0.499639 0.866233i \(-0.666534\pi\)
−0.988769 + 0.149454i \(0.952248\pi\)
\(702\) −2.36587e7 + 1.13934e7i −1.81196 + 0.872594i
\(703\) −5.07546e6 + 6.36443e6i −0.387336 + 0.485703i
\(704\) −3.93734e6 1.72506e7i −0.299414 1.31182i
\(705\) 746923. + 3.27248e6i 0.0565983 + 0.247973i
\(706\) −1.36877e7 1.71638e7i −1.03352 1.29599i
\(707\) −43290.0 + 189666.i −0.00325716 + 0.0142705i
\(708\) −175725. −0.0131750
\(709\) 3.06222e6 1.34165e7i 0.228782 1.00236i −0.721853 0.692046i \(-0.756709\pi\)
0.950635 0.310312i \(-0.100433\pi\)
\(710\) −6.18846e6 + 2.98021e6i −0.460720 + 0.221871i
\(711\) 8.96424e6 4.31695e6i 0.665027 0.320260i
\(712\) 3.83714e6 1.68116e7i 0.283667 1.24282i
\(713\) 1.11132e6 0.0818680
\(714\) 122303. 535843.i 0.00897822 0.0393361i
\(715\) −2.52964e6 3.17206e6i −0.185052 0.232047i
\(716\) −7.34504e6 3.21807e7i −0.535441 2.34592i
\(717\) −164834. 722184.i −0.0119743 0.0524627i
\(718\) 1.43026e7 1.79349e7i 1.03539 1.29833i
\(719\) −1.16922e7 + 5.63068e6i −0.843480 + 0.406199i −0.805153 0.593067i \(-0.797917\pi\)
−0.0383266 + 0.999265i \(0.512203\pi\)
\(720\) −450720. 217055.i −0.0324023 0.0156041i
\(721\) −390061. 489121.i −0.0279444 0.0350411i
\(722\) 1.13821e7 1.42727e7i 0.812607 1.01898i
\(723\) −7.38789e6 3.55782e6i −0.525623 0.253127i
\(724\) 6.49833e6 0.460739
\(725\) 1.28769e7 925591.i 0.909845 0.0653994i
\(726\) −4.02004e6 −0.283067
\(727\) 1.72085e7 + 8.28716e6i 1.20755 + 0.581527i 0.925820 0.377966i \(-0.123376\pi\)
0.281734 + 0.959493i \(0.409091\pi\)
\(728\) −607655. + 761975.i −0.0424941 + 0.0532859i
\(729\) 7.72135e6 + 9.68226e6i 0.538114 + 0.674774i
\(730\) 1.12982e7 + 5.44091e6i 0.784695 + 0.377889i
\(731\) −1.67317e7 + 8.05756e6i −1.15810 + 0.557712i
\(732\) −4.40541e6 + 5.52421e6i −0.303884 + 0.381059i
\(733\) −2.40065e6 1.05179e7i −0.165032 0.723053i −0.987935 0.154870i \(-0.950504\pi\)
0.822903 0.568182i \(-0.192353\pi\)
\(734\) 753943. + 3.30324e6i 0.0516533 + 0.226308i
\(735\) −1.89574e6 2.37718e6i −0.129438 0.162310i
\(736\) −329303. + 1.44277e6i −0.0224079 + 0.0981755i
\(737\) −7.15033e6 −0.484906
\(738\) 180002. 788639.i 0.0121657 0.0533012i
\(739\) −825295. + 397441.i −0.0555902 + 0.0267708i −0.461472 0.887155i \(-0.652679\pi\)
0.405882 + 0.913925i \(0.366964\pi\)
\(740\) −9.27985e6 + 4.46894e6i −0.622962 + 0.300003i
\(741\) −1.23286e6 + 5.40152e6i −0.0824838 + 0.361385i
\(742\) 181376. 0.0120940
\(743\) 769522. 3.37150e6i 0.0511386 0.224053i −0.942901 0.333073i \(-0.891914\pi\)
0.994039 + 0.109021i \(0.0347714\pi\)
\(744\) 5.06678e6 + 6.35355e6i 0.335583 + 0.420808i
\(745\) −771781. 3.38139e6i −0.0509452 0.223206i
\(746\) 9.69394e6 + 4.24719e7i 0.637754 + 2.79418i
\(747\) 3.77917e6 4.73893e6i 0.247796 0.310727i
\(748\) 1.44274e7 6.94788e6i 0.942833 0.454044i
\(749\) −257167. 123845.i −0.0167499 0.00806631i
\(750\) 6.30440e6 + 7.90547e6i 0.409252 + 0.513185i
\(751\) −8.04156e6 + 1.00838e7i −0.520284 + 0.652415i −0.970669 0.240419i \(-0.922715\pi\)
0.450385 + 0.892834i \(0.351287\pi\)
\(752\) 4.08981e6 + 1.96955e6i 0.263730 + 0.127005i
\(753\) 1.94960e7 1.25302
\(754\) 8.65849e6 + 2.83765e7i 0.554643 + 1.81773i
\(755\) −2.56951e6 −0.164052
\(756\) 1.28312e6 + 617918.i 0.0816513 + 0.0393212i
\(757\) 1.75473e6 2.20036e6i 0.111294 0.139558i −0.723065 0.690780i \(-0.757267\pi\)
0.834358 + 0.551223i \(0.185839\pi\)
\(758\) 2.22716e7 + 2.79277e7i 1.40792 + 1.76548i
\(759\) −1.10823e6 533697.i −0.0698275 0.0336272i
\(760\) −2.31394e6 + 1.11433e6i −0.145317 + 0.0699812i
\(761\) −2.82466e6 + 3.54201e6i −0.176809 + 0.221711i −0.862337 0.506335i \(-0.831000\pi\)
0.685528 + 0.728046i \(0.259571\pi\)
\(762\) −7.58069e6 3.32132e7i −0.472957 2.07216i
\(763\) 194778. + 853378.i 0.0121123 + 0.0530677i
\(764\) −6.86306e6 8.60601e6i −0.425387 0.533419i
\(765\) −378432. + 1.65802e6i −0.0233794 + 0.102432i
\(766\) 2.77318e7 1.70768
\(767\) 45547.2 199555.i 0.00279559 0.0122483i
\(768\) −1.40120e7 + 6.74782e6i −0.857230 + 0.412820i
\(769\) −2.42356e7 + 1.16712e7i −1.47787 + 0.711707i −0.987178 0.159623i \(-0.948972\pi\)
−0.490697 + 0.871330i \(0.663258\pi\)
\(770\) −77423.7 + 339215.i −0.00470595 + 0.0206181i
\(771\) 1.71518e7 1.03914
\(772\) −1.13350e7 + 4.96618e7i −0.684507 + 2.99902i
\(773\) −6.70232e6 8.40444e6i −0.403438 0.505895i 0.538064 0.842904i \(-0.319156\pi\)
−0.941501 + 0.337009i \(0.890585\pi\)
\(774\) −5.69419e6 2.49479e7i −0.341649 1.49686i
\(775\) 2.18883e6 + 9.58987e6i 0.130905 + 0.573533i
\(776\) −2.12186e7 + 2.66073e7i −1.26492 + 1.58616i
\(777\) 718920. 346214.i 0.0427197 0.0205727i
\(778\) 2.63508e6 + 1.26899e6i 0.156079 + 0.0751638i
\(779\) −316415. 396772.i −0.0186816 0.0234260i
\(780\) −4.37077e6 + 5.48077e6i −0.257230 + 0.322556i
\(781\) 1.39681e7 + 6.72668e6i 0.819425 + 0.394614i
\(782\) −2.50539e6 −0.146507
\(783\) 1.57497e7 9.02932e6i 0.918056 0.526321i
\(784\) −4.11186e6 −0.238918
\(785\) 5.81037e6 + 2.79813e6i 0.336535 + 0.162066i
\(786\) 1.64236e7 2.05945e7i 0.948225 1.18904i
\(787\) −1.84716e7 2.31627e7i −1.06309 1.33307i −0.940191 0.340647i \(-0.889354\pi\)
−0.122894 0.992420i \(-0.539217\pi\)
\(788\) −1.61475e7 7.77621e6i −0.926379 0.446120i
\(789\) −1.78952e7 + 8.61790e6i −1.02340 + 0.492843i
\(790\) 7.78643e6 9.76387e6i 0.443885 0.556614i
\(791\) −267300. 1.17112e6i −0.0151900 0.0665518i
\(792\) 2.05610e6 + 9.00837e6i 0.116475 + 0.510309i
\(793\) −5.13150e6 6.43470e6i −0.289775 0.363367i
\(794\) −3.73457e6 + 1.63622e7i −0.210227 + 0.921065i
\(795\) 546315. 0.0306567
\(796\) −1.47346e6 + 6.45565e6i −0.0824244 + 0.361125i
\(797\) 1.16562e7 5.61333e6i 0.649997 0.313022i −0.0796737 0.996821i \(-0.525388\pi\)
0.729670 + 0.683799i \(0.239674\pi\)
\(798\) 428083. 206154.i 0.0237969 0.0114600i
\(799\) 3.43388e6 1.50448e7i 0.190291 0.833718i
\(800\) −1.30987e7 −0.723606
\(801\) 2.19653e6 9.62361e6i 0.120964 0.529976i
\(802\) −1.24660e7 1.56318e7i −0.684369 0.858171i
\(803\) −6.29829e6 2.75946e7i −0.344694 1.51020i
\(804\) 2.74914e6 + 1.20448e7i 0.149988 + 0.657141i
\(805\) 21465.0 26916.3i 0.00116746 0.00146395i
\(806\) −2.03661e7 + 9.80779e6i −1.10426 + 0.531782i
\(807\) −1.41280e7 6.80368e6i −0.763654 0.367756i
\(808\) 4.04317e6 + 5.06997e6i 0.217868 + 0.273198i
\(809\) −1.06980e7 + 1.34149e7i −0.574689 + 0.720638i −0.981197 0.193010i \(-0.938175\pi\)
0.406507 + 0.913647i \(0.366747\pi\)
\(810\) 1.94464e6 + 936488.i 0.104142 + 0.0501522i
\(811\) 2.76780e7 1.47769 0.738845 0.673876i \(-0.235372\pi\)
0.738845 + 0.673876i \(0.235372\pi\)
\(812\) 910443. 1.32668e6i 0.0484577 0.0706117i
\(813\) −1.75771e7 −0.932656
\(814\) 3.31202e7 + 1.59499e7i 1.75199 + 0.843715i
\(815\) 1.24564e6 1.56198e6i 0.0656898 0.0823724i
\(816\) −1.39588e6 1.75037e6i −0.0733874 0.0920249i
\(817\) −1.44642e7 6.96557e6i −0.758120 0.365091i
\(818\) 1.95049e7 9.39307e6i 1.01920 0.490823i
\(819\) −347845. + 436183.i −0.0181207 + 0.0227227i
\(820\) −142884. 626016.i −0.00742077 0.0325125i
\(821\) 1.90517e6 + 8.34712e6i 0.0986454 + 0.432194i 1.00000 0.000888872i \(-0.000282937\pi\)
−0.901354 + 0.433083i \(0.857426\pi\)
\(822\) −1.18251e7 1.48282e7i −0.610415 0.765436i
\(823\) −2.37392e6 + 1.04008e7i −0.122170 + 0.535263i 0.876389 + 0.481604i \(0.159946\pi\)
−0.998559 + 0.0536592i \(0.982912\pi\)
\(824\) −2.08535e7 −1.06994
\(825\) 2.42267e6 1.06144e7i 0.123925 0.542951i
\(826\) −15815.2 + 7616.20i −0.000806538 + 0.000388408i
\(827\) −1.63283e6 + 786331.i −0.0830191 + 0.0399799i −0.474933 0.880022i \(-0.657528\pi\)
0.391913 + 0.920002i \(0.371813\pi\)
\(828\) 485825. 2.12854e6i 0.0246266 0.107896i
\(829\) −1.19392e7 −0.603378 −0.301689 0.953406i \(-0.597550\pi\)
−0.301689 + 0.953406i \(0.597550\pi\)
\(830\) 1.69295e6 7.41728e6i 0.0852997 0.373723i
\(831\) 1.55434e7 + 1.94908e7i 0.780807 + 0.979101i
\(832\) −7.92431e6 3.47187e7i −0.396874 1.73882i
\(833\) 3.11049e6 + 1.36280e7i 0.155316 + 0.680485i
\(834\) −5.98388e6 + 7.50355e6i −0.297898 + 0.373553i
\(835\) 6.37858e6 3.07176e6i 0.316598 0.152465i
\(836\) 1.24722e7 + 6.00628e6i 0.617201 + 0.297228i
\(837\) 8.62424e6 + 1.08144e7i 0.425507 + 0.533569i
\(838\) 2.20081e7 2.75973e7i 1.08261 1.35755i
\(839\) 3.34162e7 + 1.60924e7i 1.63890 + 0.789251i 0.999797 + 0.0201274i \(0.00640718\pi\)
0.639100 + 0.769124i \(0.279307\pi\)
\(840\) 251748. 0.0123103
\(841\) −7.37721e6 1.91385e7i −0.359668 0.933080i
\(842\) 1.75188e7 0.851579
\(843\) 7.79680e6 + 3.75474e6i 0.377874 + 0.181975i
\(844\) −7.15175e6 + 8.96801e6i −0.345586 + 0.433351i
\(845\) −1.25641e6 1.57549e6i −0.0605326 0.0759054i
\(846\) 1.91582e7 + 9.22610e6i 0.920298 + 0.443192i
\(847\) −228810. + 110189.i −0.0109589 + 0.00527752i
\(848\) 460640. 577624.i 0.0219974 0.0275839i
\(849\) 2.78081e6 + 1.21835e7i 0.132404 + 0.580101i
\(850\) −4.93456e6 2.16197e7i −0.234262 1.02637i
\(851\) −2.26784e6 2.84378e6i −0.107346 0.134608i
\(852\) 5.96071e6 2.61156e7i 0.281319 1.23254i
\(853\) −1.42682e7 −0.671424 −0.335712 0.941965i \(-0.608977\pi\)
−0.335712 + 0.941965i \(0.608977\pi\)
\(854\) −157058. + 688116.i −0.00736912 + 0.0322862i
\(855\) −1.32458e6 + 637886.i −0.0619676 + 0.0298420i
\(856\) −8.57219e6 + 4.12815e6i −0.399860 + 0.192562i
\(857\) 1.38233e6 6.05637e6i 0.0642923 0.281683i −0.932555 0.361028i \(-0.882426\pi\)
0.996847 + 0.0793452i \(0.0252830\pi\)
\(858\) 2.50196e7 1.16028
\(859\) −1.62076e6 + 7.10100e6i −0.0749436 + 0.328349i −0.998477 0.0551684i \(-0.982430\pi\)
0.923533 + 0.383518i \(0.125288\pi\)
\(860\) −1.26648e7 1.58811e7i −0.583917 0.732209i
\(861\) 11069.4 + 48498.1i 0.000508880 + 0.00222955i
\(862\) 7.67393e6 + 3.36217e7i 0.351763 + 1.54117i
\(863\) −2.23148e7 + 2.79819e7i −1.01992 + 1.27894i −0.0601384 + 0.998190i \(0.519154\pi\)
−0.959781 + 0.280749i \(0.909417\pi\)
\(864\) −1.65954e7 + 7.99192e6i −0.756316 + 0.364223i
\(865\) 3.28032e6 + 1.57972e6i 0.149065 + 0.0717859i
\(866\) −1.98494e7 2.48904e7i −0.899402 1.12781i
\(867\) 4.94682e6 6.20312e6i 0.223501 0.280261i
\(868\) 1.10455e6 + 531921.i 0.0497605 + 0.0239634i
\(869\) −2.81879e7 −1.26623
\(870\) 4.33626e6 6.31872e6i 0.194230 0.283029i
\(871\) −1.43908e7 −0.642745
\(872\) 2.62878e7 + 1.26595e7i 1.17075 + 0.563802i
\(873\) −1.21463e7 + 1.52310e7i −0.539398 + 0.676383i
\(874\) −1.35039e6 1.69333e6i −0.0597971 0.0749831i
\(875\) 575518. + 277155.i 0.0254120 + 0.0122378i
\(876\) −4.40617e7 + 2.12190e7i −1.94000 + 0.934254i
\(877\) 2.94377e6 3.69138e6i 0.129243 0.162065i −0.713000 0.701164i \(-0.752664\pi\)
0.842242 + 0.539099i \(0.181235\pi\)
\(878\) −5.46250e6 2.39328e7i −0.239142 1.04775i
\(879\) 2.94195e6 + 1.28895e7i 0.128429 + 0.562684i
\(880\) 883660. + 1.10807e6i 0.0384661 + 0.0482350i
\(881\) 2.97373e6 1.30288e7i 0.129081 0.565541i −0.868479 0.495726i \(-0.834902\pi\)
0.997560 0.0698149i \(-0.0222409\pi\)
\(882\) −1.92615e7 −0.833716
\(883\) −9.29521e6 + 4.07250e7i −0.401197 + 1.75776i 0.221368 + 0.975190i \(0.428948\pi\)
−0.622565 + 0.782568i \(0.713909\pi\)
\(884\) 2.90367e7 1.39833e7i 1.24973 0.601838i
\(885\) −47636.4 + 22940.5i −0.00204447 + 0.000984565i
\(886\) 3.85524e6 1.68909e7i 0.164993 0.722883i
\(887\) 1.93468e6 0.0825659 0.0412830 0.999147i \(-0.486855\pi\)
0.0412830 + 0.999147i \(0.486855\pi\)
\(888\) 5.91858e6 2.59310e7i 0.251875 1.10354i
\(889\) −1.34184e6 1.68262e6i −0.0569439 0.0714054i
\(890\) −2.75703e6 1.20793e7i −0.116672 0.511173i
\(891\) −1.08406e6 4.74958e6i −0.0457467 0.200429i
\(892\) 1.31176e7 1.64490e7i 0.552005 0.692192i
\(893\) 1.20192e7 5.78816e6i 0.504369 0.242891i
\(894\) 1.92701e7 + 9.28001e6i 0.806383 + 0.388333i
\(895\) −6.19227e6 7.76486e6i −0.258400 0.324023i
\(896\) −1.31249e6 + 1.64582e6i −0.0546170 + 0.0684875i
\(897\) −2.23043e6 1.07412e6i −0.0925567 0.0445730i
\(898\) 3.27602e7 1.35568
\(899\) 1.35578e7 7.77269e6i 0.559488 0.320754i
\(900\) 1.93246e7 0.795252
\(901\) −2.26288e6 1.08975e6i −0.0928645 0.0447212i
\(902\) −1.42888e6 + 1.79175e6i −0.0584760 + 0.0733266i
\(903\) 981154. + 1.23033e6i 0.0400422 + 0.0502113i
\(904\) −3.60756e7 1.73731e7i −1.46823 0.707060i
\(905\) 1.76160e6 848344.i 0.0714969 0.0344311i
\(906\) 9.87942e6 1.23884e7i 0.399863 0.501412i
\(907\) 1.01799e6 + 4.46012e6i 0.0410891 + 0.180023i 0.991308 0.131559i \(-0.0419983\pi\)
−0.950219 + 0.311582i \(0.899141\pi\)
\(908\) 4.26616e6 + 1.86913e7i 0.171721 + 0.752357i
\(909\) 2.31446e6 + 2.90224e6i 0.0929052 + 0.116499i
\(910\) −155823. + 682706.i −0.00623776 + 0.0273294i
\(911\) 3.71598e6 0.148346 0.0741732 0.997245i \(-0.476368\pi\)
0.0741732 + 0.997245i \(0.476368\pi\)
\(912\) 430667. 1.88688e6i 0.0171457 0.0751201i
\(913\) −1.54716e7 + 7.45074e6i −0.614269 + 0.295817i
\(914\) 5.80197e7 2.79408e7i 2.29726 1.10630i
\(915\) −473069. + 2.07265e6i −0.0186798 + 0.0818415i
\(916\) −9.07736e6 −0.357455
\(917\) 370291. 1.62235e6i 0.0145419 0.0637121i
\(918\) −1.94428e7 2.43805e7i −0.761468 0.954850i
\(919\) 3.03461e6 + 1.32955e7i 0.118526 + 0.519297i 0.998980 + 0.0451643i \(0.0143811\pi\)
−0.880453 + 0.474133i \(0.842762\pi\)
\(920\) −255357. 1.11879e6i −0.00994670 0.0435793i
\(921\) −1.48435e7 + 1.86132e7i −0.576618 + 0.723057i
\(922\) −7.27461e7 + 3.50327e7i −2.81827 + 1.35721i
\(923\) 2.81122e7 + 1.35381e7i 1.08615 + 0.523063i
\(924\) −846031. 1.06089e6i −0.0325991 0.0408780i
\(925\) 2.00731e7 2.51708e7i 0.771364 0.967260i
\(926\) −1.01566e7 4.89116e6i −0.389243 0.187450i
\(927\) −1.19373e7 −0.456255
\(928\) 6.07349e6 + 1.99047e7i 0.231509 + 0.758726i
\(929\) −1.50420e7 −0.571830 −0.285915 0.958255i \(-0.592297\pi\)
−0.285915 + 0.958255i \(0.592297\pi\)
\(930\) 5.26073e6 + 2.53343e6i 0.199452 + 0.0960511i
\(931\) −7.53426e6 + 9.44767e6i −0.284883 + 0.357232i
\(932\) −1.73287e7 2.17295e7i −0.653470 0.819426i
\(933\) −2.82936e7 1.36255e7i −1.06411 0.512446i
\(934\) 4.23554e7 2.03973e7i 1.58870 0.765078i
\(935\) 3.00404e6 3.76694e6i 0.112377 0.140916i
\(936\) 4.13812e6 + 1.81303e7i 0.154388 + 0.676417i
\(937\) −1.67537e6 7.34029e6i −0.0623394 0.273127i 0.934146 0.356890i \(-0.116163\pi\)
−0.996486 + 0.0837636i \(0.973306\pi\)
\(938\) 769464. + 964877.i 0.0285549 + 0.0358067i
\(939\) 3.37681e6 1.47948e7i 0.124981 0.547576i
\(940\) 1.68792e7 0.623063
\(941\) −1.38724e6 + 6.07790e6i −0.0510714 + 0.223758i −0.994023 0.109172i \(-0.965180\pi\)
0.942952 + 0.332930i \(0.108037\pi\)
\(942\) −3.58307e7 + 1.72552e7i −1.31561 + 0.633566i
\(943\) 204302. 98386.8i 0.00748159 0.00360295i
\(944\) −15910.7 + 69709.3i −0.000581111 + 0.00254601i
\(945\) 428504. 0.0156090
\(946\) −1.61321e7 + 7.06794e7i −0.586089 + 2.56782i
\(947\) 1.73875e7 + 2.18033e7i 0.630033 + 0.790036i 0.989717 0.143038i \(-0.0456871\pi\)
−0.359685 + 0.933074i \(0.617116\pi\)
\(948\) 1.08376e7 + 4.74827e7i 0.391663 + 1.71599i
\(949\) −1.26760e7 5.55370e7i −0.456894 2.00178i
\(950\) 1.19525e7 1.49880e7i 0.429686 0.538810i
\(951\) 1.03578e7 4.98807e6i 0.371380 0.178847i
\(952\) −1.04276e6 502167.i −0.0372900 0.0179579i
\(953\) 1.32326e7 + 1.65931e7i 0.471968 + 0.591829i 0.959652 0.281191i \(-0.0907295\pi\)
−0.487684 + 0.873020i \(0.662158\pi\)
\(954\) 2.15781e6 2.70580e6i 0.0767611 0.0962554i
\(955\) −2.98398e6 1.43701e6i −0.105873 0.0509860i
\(956\) −3.72497e6 −0.131819
\(957\) −1.72529e7 + 1.24014e6i −0.608952 + 0.0437713i
\(958\) −6.49965e7 −2.28811
\(959\) −1.07949e6 519856.i −0.0379030 0.0182531i
\(960\) −5.73533e6 + 7.19188e6i −0.200854 + 0.251863i
\(961\) −1.04260e7 1.30738e7i −0.364174 0.456660i
\(962\) 6.66579e7 + 3.21007e7i 2.32228 + 1.11835i
\(963\) −4.90704e6 + 2.36311e6i −0.170512 + 0.0821141i
\(964\) −2.57091e7 + 3.22382e7i −0.891034 + 1.11732i
\(965\) 3.41050e6 + 1.49424e7i 0.117896 + 0.516537i
\(966\) 47241.6 + 206979.i 0.00162885 + 0.00713647i
\(967\) 2.19830e7 + 2.75659e7i 0.755999 + 0.947993i 0.999761 0.0218418i \(-0.00695302\pi\)
−0.243762 + 0.969835i \(0.578382\pi\)
\(968\) −1.88370e6 + 8.25303e6i −0.0646135 + 0.283090i
\(969\) −6.57947e6 −0.225103
\(970\) −5.44116e6 + 2.38393e7i −0.185679 + 0.813511i
\(971\) 2.85378e7 1.37431e7i 0.971344 0.467774i 0.120224 0.992747i \(-0.461639\pi\)
0.851119 + 0.524972i \(0.175924\pi\)
\(972\) 4.07328e7 1.96159e7i 1.38286 0.665950i
\(973\) −134915. + 591100.i −0.00456854 + 0.0200161i
\(974\) −1.10939e7 −0.374703
\(975\) 4.87587e6 2.13626e7i 0.164263 0.719685i
\(976\) 1.79255e6 + 2.24779e6i 0.0602348 + 0.0755320i
\(977\) 3.33511e6 + 1.46121e7i 0.111783 + 0.489751i 0.999565 + 0.0294883i \(0.00938776\pi\)
−0.887783 + 0.460263i \(0.847755\pi\)
\(978\) 2.74148e6 + 1.20112e7i 0.0916512 + 0.401550i
\(979\) −1.74363e7 + 2.18644e7i −0.581430 + 0.729090i
\(980\) −1.37755e7 + 6.63391e6i −0.458185 + 0.220650i
\(981\) 1.50481e7 + 7.24680e6i 0.499241 + 0.240422i
\(982\) −3.97728e7 4.98735e7i −1.31616 1.65041i
\(983\) 3.76074e7 4.71582e7i 1.24134 1.55659i 0.546366 0.837547i \(-0.316011\pi\)
0.694970 0.719039i \(-0.255418\pi\)
\(984\) 1.49396e6 + 719452.i 0.0491870 + 0.0236872i
\(985\) −5.39251e6 −0.177093
\(986\) −3.05652e7 + 1.75230e7i −1.00123 + 0.574006i
\(987\) −1.30765e6 −0.0427266
\(988\) 2.51015e7 + 1.20883e7i 0.818103 + 0.393977i
\(989\) 4.47248e6 5.60831e6i 0.145398 0.182323i
\(990\) 4.13939e6 + 5.19063e6i 0.134230 + 0.168319i
\(991\) 2.05406e7 + 9.89185e6i 0.664400 + 0.319958i 0.735514 0.677510i \(-0.236941\pi\)
−0.0711135 + 0.997468i \(0.522655\pi\)
\(992\) −1.42858e7 + 6.87967e6i −0.460919 + 0.221967i
\(993\) 4.94930e6 6.20623e6i 0.159284 0.199735i
\(994\) −595430. 2.60875e6i −0.0191146 0.0837464i
\(995\) 443339. + 1.94239e6i 0.0141964 + 0.0621984i
\(996\) 1.84993e7 + 2.31974e7i 0.590890 + 0.740953i
\(997\) −4.91320e6 + 2.15261e7i −0.156541 + 0.685849i 0.834356 + 0.551226i \(0.185840\pi\)
−0.990897 + 0.134623i \(0.957018\pi\)
\(998\) 3.82791e7 1.21656
\(999\) 1.00741e7 4.41375e7i 0.319369 1.39925i
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 29.6.d.a.16.11 66
29.7 even 7 841.6.a.i.1.3 33
29.20 even 7 inner 29.6.d.a.20.11 yes 66
29.22 even 14 841.6.a.h.1.31 33
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.6.d.a.16.11 66 1.1 even 1 trivial
29.6.d.a.20.11 yes 66 29.20 even 7 inner
841.6.a.h.1.31 33 29.22 even 14
841.6.a.i.1.3 33 29.7 even 7