Properties

Label 147.6.e.p.79.4
Level $147$
Weight $6$
Character 147.79
Analytic conductor $23.576$
Analytic rank $0$
Dimension $12$
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] = [147,6,Mod(67,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("147.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not 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: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + 973971 x^{4} - 1176024 x^{3} + 5644794 x^{2} + 4339328 x + 5466244 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8}\cdot 7^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.4
Root \(2.13607 + 3.69977i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.6.e.p.67.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.54581 - 2.67743i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(11.2209 + 19.4352i) q^{4} +(-6.89630 + 11.9448i) q^{5} -27.8246 q^{6} +168.314 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(1.54581 - 2.67743i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(11.2209 + 19.4352i) q^{4} +(-6.89630 + 11.9448i) q^{5} -27.8246 q^{6} +168.314 q^{8} +(-40.5000 + 70.1481i) q^{9} +(21.3208 + 36.9287i) q^{10} +(1.83329 + 3.17536i) q^{11} +(100.988 - 174.917i) q^{12} -780.229 q^{13} +124.133 q^{15} +(-98.8879 + 171.279i) q^{16} +(-25.0416 - 43.3733i) q^{17} +(125.211 + 216.872i) q^{18} +(-531.692 + 920.918i) q^{19} -309.532 q^{20} +11.3357 q^{22} +(-2051.23 + 3552.83i) q^{23} +(-757.412 - 1311.88i) q^{24} +(1467.38 + 2541.58i) q^{25} +(-1206.09 + 2089.01i) q^{26} +729.000 q^{27} -1487.11 q^{29} +(191.887 - 332.358i) q^{30} +(-2759.98 - 4780.43i) q^{31} +(2998.75 + 5193.98i) q^{32} +(16.4997 - 28.5782i) q^{33} -154.838 q^{34} -1817.79 q^{36} +(-3071.63 + 5320.23i) q^{37} +(1643.79 + 2847.13i) q^{38} +(3511.03 + 6081.28i) q^{39} +(-1160.74 + 2010.47i) q^{40} +10757.9 q^{41} +17696.7 q^{43} +(-41.1425 + 71.2609i) q^{44} +(-558.601 - 967.525i) q^{45} +(6341.63 + 10984.0i) q^{46} +(-14734.2 + 25520.4i) q^{47} +1779.98 q^{48} +9073.19 q^{50} +(-225.374 + 390.360i) q^{51} +(-8754.89 - 15163.9i) q^{52} +(9627.95 + 16676.1i) q^{53} +(1126.90 - 1951.84i) q^{54} -50.5718 q^{55} +9570.46 q^{57} +(-2298.79 + 3981.62i) q^{58} +(-3309.59 - 5732.38i) q^{59} +(1392.89 + 2412.56i) q^{60} +(-18375.1 + 31826.7i) q^{61} -17065.7 q^{62} +12213.2 q^{64} +(5380.70 - 9319.64i) q^{65} +(-51.0107 - 88.3532i) q^{66} +(-23454.6 - 40624.5i) q^{67} +(561.979 - 973.377i) q^{68} +36922.1 q^{69} -41693.7 q^{71} +(-6816.71 + 11806.9i) q^{72} +(-14725.6 - 25505.4i) q^{73} +(9496.35 + 16448.2i) q^{74} +(13206.4 - 22874.2i) q^{75} -23864.3 q^{76} +21709.6 q^{78} +(-11062.2 + 19160.3i) q^{79} +(-1363.92 - 2362.38i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(16629.7 - 28803.6i) q^{82} -3896.35 q^{83} +690.778 q^{85} +(27355.8 - 47381.6i) q^{86} +(6691.98 + 11590.9i) q^{87} +(308.569 + 534.457i) q^{88} +(-10265.4 + 17780.2i) q^{89} -3453.97 q^{90} -92066.6 q^{92} +(-24839.9 + 43023.9i) q^{93} +(45552.7 + 78899.6i) q^{94} +(-7333.42 - 12701.9i) q^{95} +(26988.7 - 46745.8i) q^{96} +17742.9 q^{97} -296.994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 54 q^{3} - 150 q^{4} - 100 q^{5} + 36 q^{6} - 228 q^{8} - 486 q^{9} - 864 q^{10} - 604 q^{11} - 1350 q^{12} + 2704 q^{13} + 1800 q^{15} - 4578 q^{16} - 3028 q^{17} - 162 q^{18} - 1728 q^{19} + 904 q^{20} - 8232 q^{22} + 4484 q^{23} + 1026 q^{24} - 4806 q^{25} - 14172 q^{26} + 8748 q^{27} - 10640 q^{29} - 7776 q^{30} - 3976 q^{31} + 37326 q^{32} - 5436 q^{33} - 32672 q^{34} + 24300 q^{36} - 22680 q^{37} - 52744 q^{38} - 12168 q^{39} - 100600 q^{40} + 57512 q^{41} - 13536 q^{43} + 64940 q^{44} - 8100 q^{45} - 540 q^{46} - 51552 q^{47} + 82404 q^{48} - 81244 q^{50} - 27252 q^{51} - 119296 q^{52} - 80884 q^{53} - 1458 q^{54} + 23312 q^{55} + 31104 q^{57} + 70464 q^{58} - 8872 q^{59} - 4068 q^{60} - 50896 q^{61} + 23648 q^{62} + 399180 q^{64} - 3492 q^{65} + 37044 q^{66} - 6480 q^{67} - 37348 q^{68} - 80712 q^{69} - 221704 q^{71} + 9234 q^{72} - 64232 q^{73} + 27464 q^{74} - 43254 q^{75} - 389728 q^{76} + 255096 q^{78} - 111696 q^{79} + 308940 q^{80} - 39366 q^{81} + 189640 q^{82} + 202256 q^{83} - 46584 q^{85} - 3824 q^{86} + 47880 q^{87} + 97788 q^{88} + 35012 q^{89} + 139968 q^{90} - 898520 q^{92} - 35784 q^{93} + 121016 q^{94} + 119080 q^{95} + 335934 q^{96} + 141904 q^{97} + 97848 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.54581 2.67743i 0.273264 0.473307i −0.696432 0.717623i \(-0.745230\pi\)
0.969696 + 0.244316i \(0.0785635\pi\)
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) 11.2209 + 19.4352i 0.350654 + 0.607350i
\(5\) −6.89630 + 11.9448i −0.123365 + 0.213674i −0.921093 0.389344i \(-0.872702\pi\)
0.797728 + 0.603018i \(0.206035\pi\)
\(6\) −27.8246 −0.315538
\(7\) 0 0
\(8\) 168.314 0.929811
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 21.3208 + 36.9287i 0.0674223 + 0.116779i
\(11\) 1.83329 + 3.17536i 0.00456826 + 0.00791245i 0.868300 0.496039i \(-0.165213\pi\)
−0.863732 + 0.503951i \(0.831879\pi\)
\(12\) 100.988 174.917i 0.202450 0.350654i
\(13\) −780.229 −1.28045 −0.640226 0.768186i \(-0.721159\pi\)
−0.640226 + 0.768186i \(0.721159\pi\)
\(14\) 0 0
\(15\) 124.133 0.142449
\(16\) −98.8879 + 171.279i −0.0965702 + 0.167264i
\(17\) −25.0416 43.3733i −0.0210155 0.0363999i 0.855326 0.518090i \(-0.173357\pi\)
−0.876342 + 0.481690i \(0.840023\pi\)
\(18\) 125.211 + 216.872i 0.0910879 + 0.157769i
\(19\) −531.692 + 920.918i −0.337891 + 0.585244i −0.984036 0.177971i \(-0.943047\pi\)
0.646145 + 0.763215i \(0.276380\pi\)
\(20\) −309.532 −0.173033
\(21\) 0 0
\(22\) 11.3357 0.00499336
\(23\) −2051.23 + 3552.83i −0.808526 + 1.40041i 0.105358 + 0.994434i \(0.466401\pi\)
−0.913885 + 0.405974i \(0.866932\pi\)
\(24\) −757.412 1311.88i −0.268413 0.464906i
\(25\) 1467.38 + 2541.58i 0.469562 + 0.813306i
\(26\) −1206.09 + 2089.01i −0.349901 + 0.606047i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −1487.11 −0.328358 −0.164179 0.986431i \(-0.552497\pi\)
−0.164179 + 0.986431i \(0.552497\pi\)
\(30\) 191.887 332.358i 0.0389263 0.0674223i
\(31\) −2759.98 4780.43i −0.515825 0.893435i −0.999831 0.0183707i \(-0.994152\pi\)
0.484006 0.875065i \(-0.339181\pi\)
\(32\) 2998.75 + 5193.98i 0.517684 + 0.896655i
\(33\) 16.4997 28.5782i 0.00263748 0.00456826i
\(34\) −154.838 −0.0229711
\(35\) 0 0
\(36\) −1817.79 −0.233769
\(37\) −3071.63 + 5320.23i −0.368863 + 0.638890i −0.989388 0.145297i \(-0.953586\pi\)
0.620525 + 0.784187i \(0.286920\pi\)
\(38\) 1643.79 + 2847.13i 0.184667 + 0.319852i
\(39\) 3511.03 + 6081.28i 0.369635 + 0.640226i
\(40\) −1160.74 + 2010.47i −0.114706 + 0.198677i
\(41\) 10757.9 0.999468 0.499734 0.866179i \(-0.333431\pi\)
0.499734 + 0.866179i \(0.333431\pi\)
\(42\) 0 0
\(43\) 17696.7 1.45956 0.729779 0.683683i \(-0.239623\pi\)
0.729779 + 0.683683i \(0.239623\pi\)
\(44\) −41.1425 + 71.2609i −0.00320375 + 0.00554906i
\(45\) −558.601 967.525i −0.0411216 0.0712247i
\(46\) 6341.63 + 10984.0i 0.441882 + 0.765362i
\(47\) −14734.2 + 25520.4i −0.972933 + 1.68517i −0.286337 + 0.958129i \(0.592438\pi\)
−0.686595 + 0.727040i \(0.740896\pi\)
\(48\) 1779.98 0.111510
\(49\) 0 0
\(50\) 9073.19 0.513257
\(51\) −225.374 + 390.360i −0.0121333 + 0.0210155i
\(52\) −8754.89 15163.9i −0.448996 0.777683i
\(53\) 9627.95 + 16676.1i 0.470808 + 0.815464i 0.999443 0.0333860i \(-0.0106291\pi\)
−0.528634 + 0.848850i \(0.677296\pi\)
\(54\) 1126.90 1951.84i 0.0525896 0.0910879i
\(55\) −50.5718 −0.00225425
\(56\) 0 0
\(57\) 9570.46 0.390163
\(58\) −2298.79 + 3981.62i −0.0897283 + 0.155414i
\(59\) −3309.59 5732.38i −0.123778 0.214390i 0.797476 0.603350i \(-0.206168\pi\)
−0.921255 + 0.388960i \(0.872834\pi\)
\(60\) 1392.89 + 2412.56i 0.0499505 + 0.0865167i
\(61\) −18375.1 + 31826.7i −0.632275 + 1.09513i 0.354810 + 0.934938i \(0.384545\pi\)
−0.987086 + 0.160194i \(0.948788\pi\)
\(62\) −17065.7 −0.563825
\(63\) 0 0
\(64\) 12213.2 0.372717
\(65\) 5380.70 9319.64i 0.157963 0.273600i
\(66\) −51.0107 88.3532i −0.00144146 0.00249668i
\(67\) −23454.6 40624.5i −0.638323 1.10561i −0.985801 0.167920i \(-0.946295\pi\)
0.347477 0.937688i \(-0.387038\pi\)
\(68\) 561.979 973.377i 0.0147383 0.0255275i
\(69\) 36922.1 0.933606
\(70\) 0 0
\(71\) −41693.7 −0.981577 −0.490789 0.871279i \(-0.663291\pi\)
−0.490789 + 0.871279i \(0.663291\pi\)
\(72\) −6816.71 + 11806.9i −0.154969 + 0.268413i
\(73\) −14725.6 25505.4i −0.323418 0.560177i 0.657773 0.753217i \(-0.271499\pi\)
−0.981191 + 0.193039i \(0.938165\pi\)
\(74\) 9496.35 + 16448.2i 0.201594 + 0.349171i
\(75\) 13206.4 22874.2i 0.271102 0.469562i
\(76\) −23864.3 −0.473931
\(77\) 0 0
\(78\) 21709.6 0.404031
\(79\) −11062.2 + 19160.3i −0.199422 + 0.345409i −0.948341 0.317252i \(-0.897240\pi\)
0.748919 + 0.662661i \(0.230573\pi\)
\(80\) −1363.92 2362.38i −0.0238267 0.0412691i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 16629.7 28803.6i 0.273118 0.473055i
\(83\) −3896.35 −0.0620816 −0.0310408 0.999518i \(-0.509882\pi\)
−0.0310408 + 0.999518i \(0.509882\pi\)
\(84\) 0 0
\(85\) 690.778 0.0103703
\(86\) 27355.8 47381.6i 0.398844 0.690819i
\(87\) 6691.98 + 11590.9i 0.0947887 + 0.164179i
\(88\) 308.569 + 534.457i 0.00424762 + 0.00735709i
\(89\) −10265.4 + 17780.2i −0.137373 + 0.237937i −0.926501 0.376291i \(-0.877199\pi\)
0.789129 + 0.614228i \(0.210533\pi\)
\(90\) −3453.97 −0.0449482
\(91\) 0 0
\(92\) −92066.6 −1.13405
\(93\) −24839.9 + 43023.9i −0.297812 + 0.515825i
\(94\) 45552.7 + 78899.6i 0.531734 + 0.920991i
\(95\) −7333.42 12701.9i −0.0833677 0.144397i
\(96\) 26988.7 46745.8i 0.298885 0.517684i
\(97\) 17742.9 0.191468 0.0957338 0.995407i \(-0.469480\pi\)
0.0957338 + 0.995407i \(0.469480\pi\)
\(98\) 0 0
\(99\) −296.994 −0.00304550
\(100\) −32930.8 + 57037.8i −0.329308 + 0.570378i
\(101\) 71042.6 + 123049.i 0.692971 + 1.20026i 0.970860 + 0.239648i \(0.0770321\pi\)
−0.277888 + 0.960613i \(0.589635\pi\)
\(102\) 696.773 + 1206.85i 0.00663118 + 0.0114855i
\(103\) 105269. 182331.i 0.977702 1.69343i 0.306990 0.951713i \(-0.400678\pi\)
0.670713 0.741717i \(-0.265988\pi\)
\(104\) −131323. −1.19058
\(105\) 0 0
\(106\) 59532.0 0.514619
\(107\) 101335. 175518.i 0.855660 1.48205i −0.0203712 0.999792i \(-0.506485\pi\)
0.876031 0.482254i \(-0.160182\pi\)
\(108\) 8180.05 + 14168.3i 0.0674834 + 0.116885i
\(109\) −69768.9 120843.i −0.562466 0.974219i −0.997281 0.0736991i \(-0.976520\pi\)
0.434815 0.900520i \(-0.356814\pi\)
\(110\) −78.1746 + 135.402i −0.000616005 + 0.00106695i
\(111\) 55289.4 0.425926
\(112\) 0 0
\(113\) −206316. −1.51998 −0.759989 0.649936i \(-0.774796\pi\)
−0.759989 + 0.649936i \(0.774796\pi\)
\(114\) 14794.1 25624.2i 0.106617 0.184667i
\(115\) −28291.8 49002.8i −0.199487 0.345522i
\(116\) −16686.7 28902.2i −0.115140 0.199428i
\(117\) 31599.3 54731.5i 0.213409 0.369635i
\(118\) −20464.0 −0.135296
\(119\) 0 0
\(120\) 20893.4 0.132451
\(121\) 80518.8 139463.i 0.499958 0.865953i
\(122\) 56809.1 + 98396.2i 0.345556 + 0.598520i
\(123\) −48410.7 83849.8i −0.288522 0.499734i
\(124\) 61939.2 107282.i 0.361752 0.626573i
\(125\) −83580.0 −0.478440
\(126\) 0 0
\(127\) 89874.2 0.494454 0.247227 0.968958i \(-0.420481\pi\)
0.247227 + 0.968958i \(0.420481\pi\)
\(128\) −77080.6 + 133507.i −0.415834 + 0.720246i
\(129\) −79635.2 137932.i −0.421338 0.729779i
\(130\) −16635.1 28812.8i −0.0863310 0.149530i
\(131\) −160058. + 277228.i −0.814889 + 1.41143i 0.0945188 + 0.995523i \(0.469869\pi\)
−0.909408 + 0.415906i \(0.863465\pi\)
\(132\) 740.565 0.00369938
\(133\) 0 0
\(134\) −145026. −0.697722
\(135\) −5027.41 + 8707.72i −0.0237416 + 0.0411216i
\(136\) −4214.85 7300.33i −0.0195404 0.0338450i
\(137\) −129486. 224276.i −0.589414 1.02089i −0.994309 0.106532i \(-0.966025\pi\)
0.404895 0.914363i \(-0.367308\pi\)
\(138\) 57074.6 98856.2i 0.255121 0.441882i
\(139\) 282366. 1.23958 0.619791 0.784767i \(-0.287217\pi\)
0.619791 + 0.784767i \(0.287217\pi\)
\(140\) 0 0
\(141\) 265216. 1.12345
\(142\) −64450.7 + 111632.i −0.268229 + 0.464587i
\(143\) −1430.39 2477.51i −0.00584944 0.0101315i
\(144\) −8009.92 13873.6i −0.0321901 0.0557548i
\(145\) 10255.5 17763.1i 0.0405078 0.0701616i
\(146\) −91051.9 −0.353514
\(147\) 0 0
\(148\) −137866. −0.517373
\(149\) 159834. 276841.i 0.589800 1.02156i −0.404458 0.914556i \(-0.632540\pi\)
0.994258 0.107007i \(-0.0341268\pi\)
\(150\) −40829.4 70718.5i −0.148165 0.256629i
\(151\) 42023.2 + 72786.3i 0.149985 + 0.259781i 0.931221 0.364454i \(-0.118744\pi\)
−0.781237 + 0.624235i \(0.785411\pi\)
\(152\) −89491.1 + 155003.i −0.314175 + 0.544166i
\(153\) 4056.74 0.0140103
\(154\) 0 0
\(155\) 76134.8 0.254539
\(156\) −78794.0 + 136475.i −0.259228 + 0.448996i
\(157\) −63097.6 109288.i −0.204298 0.353854i 0.745611 0.666382i \(-0.232158\pi\)
−0.949909 + 0.312527i \(0.898824\pi\)
\(158\) 34200.1 + 59236.4i 0.108990 + 0.188775i
\(159\) 86651.5 150085.i 0.271821 0.470808i
\(160\) −82721.1 −0.255456
\(161\) 0 0
\(162\) −20284.2 −0.0607253
\(163\) 117895. 204200.i 0.347557 0.601986i −0.638258 0.769823i \(-0.720345\pi\)
0.985815 + 0.167836i \(0.0536780\pi\)
\(164\) 120714. + 209083.i 0.350467 + 0.607027i
\(165\) 227.573 + 394.168i 0.000650746 + 0.00112712i
\(166\) −6023.04 + 10432.2i −0.0169647 + 0.0293837i
\(167\) 149843. 0.415761 0.207881 0.978154i \(-0.433343\pi\)
0.207881 + 0.978154i \(0.433343\pi\)
\(168\) 0 0
\(169\) 237464. 0.639559
\(170\) 1067.81 1849.51i 0.00283382 0.00490833i
\(171\) −43067.1 74594.3i −0.112630 0.195081i
\(172\) 198573. + 343939.i 0.511800 + 0.886463i
\(173\) −352230. + 610080.i −0.894769 + 1.54979i −0.0606783 + 0.998157i \(0.519326\pi\)
−0.834090 + 0.551628i \(0.814007\pi\)
\(174\) 41378.2 0.103609
\(175\) 0 0
\(176\) −725.162 −0.00176463
\(177\) −29786.3 + 51591.4i −0.0714634 + 0.123778i
\(178\) 31736.8 + 54969.7i 0.0750780 + 0.130039i
\(179\) 278786. + 482872.i 0.650337 + 1.12642i 0.983041 + 0.183386i \(0.0587058\pi\)
−0.332704 + 0.943031i \(0.607961\pi\)
\(180\) 12536.0 21713.0i 0.0288389 0.0499505i
\(181\) 443092. 1.00530 0.502652 0.864489i \(-0.332358\pi\)
0.502652 + 0.864489i \(0.332358\pi\)
\(182\) 0 0
\(183\) 330752. 0.730088
\(184\) −345250. + 597990.i −0.751777 + 1.30212i
\(185\) −42365.9 73379.8i −0.0910095 0.157633i
\(186\) 76795.6 + 133014.i 0.162762 + 0.281913i
\(187\) 91.8172 159.032i 0.000192008 0.000332568i
\(188\) −661327. −1.36465
\(189\) 0 0
\(190\) −45344.4 −0.0911254
\(191\) −78740.7 + 136383.i −0.156177 + 0.270506i −0.933487 0.358612i \(-0.883250\pi\)
0.777310 + 0.629117i \(0.216584\pi\)
\(192\) −54959.3 95192.3i −0.107594 0.186358i
\(193\) 389020. + 673803.i 0.751759 + 1.30209i 0.946969 + 0.321324i \(0.104128\pi\)
−0.195210 + 0.980761i \(0.562539\pi\)
\(194\) 27427.2 47505.3i 0.0523211 0.0906228i
\(195\) −96852.5 −0.182400
\(196\) 0 0
\(197\) −340283. −0.624704 −0.312352 0.949966i \(-0.601117\pi\)
−0.312352 + 0.949966i \(0.601117\pi\)
\(198\) −459.097 + 795.179i −0.000832226 + 0.00144146i
\(199\) −148254. 256784.i −0.265384 0.459659i 0.702280 0.711901i \(-0.252165\pi\)
−0.967664 + 0.252242i \(0.918832\pi\)
\(200\) 246981. + 427783.i 0.436604 + 0.756221i
\(201\) −211091. + 365621.i −0.368536 + 0.638323i
\(202\) 439274. 0.757456
\(203\) 0 0
\(204\) −10115.6 −0.0170184
\(205\) −74190.0 + 128501.i −0.123299 + 0.213561i
\(206\) −325452. 563699.i −0.534341 0.925506i
\(207\) −166149. 287779.i −0.269509 0.466803i
\(208\) 77155.2 133637.i 0.123654 0.214174i
\(209\) −3898.99 −0.00617429
\(210\) 0 0
\(211\) 506728. 0.783554 0.391777 0.920060i \(-0.371860\pi\)
0.391777 + 0.920060i \(0.371860\pi\)
\(212\) −216069. + 374242.i −0.330181 + 0.571891i
\(213\) 187622. + 324970.i 0.283357 + 0.490789i
\(214\) −313291. 542636.i −0.467642 0.809979i
\(215\) −122042. + 211383.i −0.180058 + 0.311870i
\(216\) 122701. 0.178942
\(217\) 0 0
\(218\) −431399. −0.614806
\(219\) −132530. + 229549.i −0.186726 + 0.323418i
\(220\) −567.463 982.874i −0.000790461 0.00136912i
\(221\) 19538.2 + 33841.1i 0.0269093 + 0.0466083i
\(222\) 85467.1 148033.i 0.116390 0.201594i
\(223\) −462362. −0.622615 −0.311308 0.950309i \(-0.600767\pi\)
−0.311308 + 0.950309i \(0.600767\pi\)
\(224\) 0 0
\(225\) −237716. −0.313041
\(226\) −318926. + 552396.i −0.415355 + 0.719415i
\(227\) 49113.3 + 85066.7i 0.0632607 + 0.109571i 0.895921 0.444213i \(-0.146517\pi\)
−0.832660 + 0.553784i \(0.813183\pi\)
\(228\) 107389. + 186004.i 0.136812 + 0.236965i
\(229\) −250702. + 434228.i −0.315914 + 0.547178i −0.979631 0.200805i \(-0.935644\pi\)
0.663718 + 0.747983i \(0.268978\pi\)
\(230\) −174935. −0.218051
\(231\) 0 0
\(232\) −250301. −0.305311
\(233\) 306958. 531667.i 0.370415 0.641578i −0.619214 0.785222i \(-0.712549\pi\)
0.989629 + 0.143644i \(0.0458820\pi\)
\(234\) −97693.1 169209.i −0.116634 0.202016i
\(235\) −203223. 351993.i −0.240051 0.415781i
\(236\) 74273.4 128645.i 0.0868067 0.150354i
\(237\) 199119. 0.230273
\(238\) 0 0
\(239\) 1.10020e6 1.24588 0.622940 0.782269i \(-0.285938\pi\)
0.622940 + 0.782269i \(0.285938\pi\)
\(240\) −12275.3 + 21261.4i −0.0137564 + 0.0238267i
\(241\) −44941.8 77841.4i −0.0498434 0.0863313i 0.840027 0.542544i \(-0.182539\pi\)
−0.889871 + 0.456213i \(0.849206\pi\)
\(242\) −248934. 431166.i −0.273241 0.473267i
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) −824744. −0.886839
\(245\) 0 0
\(246\) −299335. −0.315370
\(247\) 414841. 718527.i 0.432653 0.749377i
\(248\) −464544. 804613.i −0.479620 0.830726i
\(249\) 17533.6 + 30369.1i 0.0179214 + 0.0310408i
\(250\) −129199. + 223779.i −0.130740 + 0.226449i
\(251\) 1.01050e6 1.01240 0.506202 0.862415i \(-0.331049\pi\)
0.506202 + 0.862415i \(0.331049\pi\)
\(252\) 0 0
\(253\) −15042.0 −0.0147742
\(254\) 138929. 240632.i 0.135116 0.234028i
\(255\) −3108.50 5384.08i −0.00299365 0.00518515i
\(256\) 433715. + 751217.i 0.413623 + 0.716416i
\(257\) 606163. 1.04991e6i 0.572475 0.991556i −0.423835 0.905739i \(-0.639317\pi\)
0.996311 0.0858173i \(-0.0273501\pi\)
\(258\) −492405. −0.460546
\(259\) 0 0
\(260\) 241505. 0.221561
\(261\) 60227.8 104318.i 0.0547263 0.0947887i
\(262\) 494839. + 857086.i 0.445359 + 0.771385i
\(263\) −192451. 333334.i −0.171566 0.297160i 0.767402 0.641167i \(-0.221549\pi\)
−0.938967 + 0.344006i \(0.888216\pi\)
\(264\) 2777.12 4810.11i 0.00245236 0.00424762i
\(265\) −265589. −0.232325
\(266\) 0 0
\(267\) 184777. 0.158625
\(268\) 526364. 911689.i 0.447661 0.775372i
\(269\) 787275. + 1.36360e6i 0.663355 + 1.14896i 0.979729 + 0.200329i \(0.0642012\pi\)
−0.316374 + 0.948634i \(0.602465\pi\)
\(270\) 15542.9 + 26921.0i 0.0129754 + 0.0224741i
\(271\) −166135. + 287754.i −0.137416 + 0.238012i −0.926518 0.376251i \(-0.877213\pi\)
0.789102 + 0.614263i \(0.210546\pi\)
\(272\) 9905.24 0.00811788
\(273\) 0 0
\(274\) −800643. −0.644262
\(275\) −5380.29 + 9318.93i −0.00429016 + 0.00743078i
\(276\) 414300. + 717588.i 0.327372 + 0.567026i
\(277\) −1.11772e6 1.93594e6i −0.875251 1.51598i −0.856495 0.516155i \(-0.827363\pi\)
−0.0187556 0.999824i \(-0.505970\pi\)
\(278\) 436485. 756014.i 0.338733 0.586702i
\(279\) 447118. 0.343883
\(280\) 0 0
\(281\) 69723.6 0.0526761 0.0263381 0.999653i \(-0.491615\pi\)
0.0263381 + 0.999653i \(0.491615\pi\)
\(282\) 409975. 710097.i 0.306997 0.531734i
\(283\) 238226. + 412620.i 0.176817 + 0.306256i 0.940788 0.338994i \(-0.110087\pi\)
−0.763972 + 0.645250i \(0.776753\pi\)
\(284\) −467842. 810326.i −0.344194 0.596161i
\(285\) −66000.8 + 114317.i −0.0481323 + 0.0833677i
\(286\) −8844.46 −0.00639376
\(287\) 0 0
\(288\) −485797. −0.345123
\(289\) 708674. 1.22746e6i 0.499117 0.864495i
\(290\) −31706.3 54916.9i −0.0221386 0.0383452i
\(291\) −79843.0 138292.i −0.0552719 0.0957338i
\(292\) 330469. 572389.i 0.226816 0.392857i
\(293\) 2.27589e6 1.54875 0.774377 0.632724i \(-0.218063\pi\)
0.774377 + 0.632724i \(0.218063\pi\)
\(294\) 0 0
\(295\) 91295.8 0.0610796
\(296\) −516999. + 895468.i −0.342973 + 0.594047i
\(297\) 1336.47 + 2314.84i 0.000879161 + 0.00152275i
\(298\) −494148. 855890.i −0.322342 0.558313i
\(299\) 1.60043e6 2.77202e6i 1.03528 1.79316i
\(300\) 592754. 0.380252
\(301\) 0 0
\(302\) 259840. 0.163941
\(303\) 639383. 1.10744e6i 0.400087 0.692971i
\(304\) −105156. 182135.i −0.0652603 0.113034i
\(305\) −253441. 438973.i −0.156001 0.270202i
\(306\) 6270.96 10861.6i 0.00382851 0.00663118i
\(307\) −1.61790e6 −0.979731 −0.489866 0.871798i \(-0.662954\pi\)
−0.489866 + 0.871798i \(0.662954\pi\)
\(308\) 0 0
\(309\) −1.89484e6 −1.12895
\(310\) 117690. 203845.i 0.0695562 0.120475i
\(311\) 513337. + 889125.i 0.300955 + 0.521269i 0.976352 0.216185i \(-0.0693613\pi\)
−0.675398 + 0.737454i \(0.736028\pi\)
\(312\) 590955. + 1.02356e6i 0.343691 + 0.595290i
\(313\) −158607. + 274715.i −0.0915085 + 0.158497i −0.908146 0.418653i \(-0.862502\pi\)
0.816638 + 0.577151i \(0.195836\pi\)
\(314\) −390149. −0.223309
\(315\) 0 0
\(316\) −496512. −0.279712
\(317\) −785629. + 1.36075e6i −0.439106 + 0.760554i −0.997621 0.0689406i \(-0.978038\pi\)
0.558515 + 0.829495i \(0.311371\pi\)
\(318\) −267894. 464006.i −0.148558 0.257310i
\(319\) −2726.31 4722.10i −0.00150002 0.00259812i
\(320\) −84225.8 + 145883.i −0.0459801 + 0.0796399i
\(321\) −1.82404e6 −0.988031
\(322\) 0 0
\(323\) 53257.7 0.0284038
\(324\) 73620.5 127514.i 0.0389615 0.0674834i
\(325\) −1.14489e6 1.98301e6i −0.601252 1.04140i
\(326\) −364487. 631310.i −0.189949 0.329002i
\(327\) −627921. + 1.08759e6i −0.324740 + 0.562466i
\(328\) 1.81071e6 0.929317
\(329\) 0 0
\(330\) 1407.14 0.000711301
\(331\) −769161. + 1.33223e6i −0.385875 + 0.668356i −0.991890 0.127098i \(-0.959434\pi\)
0.606015 + 0.795453i \(0.292767\pi\)
\(332\) −43720.7 75726.5i −0.0217692 0.0377053i
\(333\) −248802. 430938.i −0.122954 0.212963i
\(334\) 231629. 401193.i 0.113612 0.196783i
\(335\) 647000. 0.314987
\(336\) 0 0
\(337\) −2.86811e6 −1.37569 −0.687846 0.725857i \(-0.741444\pi\)
−0.687846 + 0.725857i \(0.741444\pi\)
\(338\) 367075. 635792.i 0.174768 0.302708i
\(339\) 928423. + 1.60808e6i 0.438780 + 0.759989i
\(340\) 7751.16 + 13425.4i 0.00363638 + 0.00629840i
\(341\) 10119.7 17527.9i 0.00471284 0.00816288i
\(342\) −266295. −0.123111
\(343\) 0 0
\(344\) 2.97860e6 1.35711
\(345\) −254626. + 441025.i −0.115174 + 0.199487i
\(346\) 1.08896e6 + 1.88614e6i 0.489016 + 0.847000i
\(347\) 55982.9 + 96965.2i 0.0249593 + 0.0432307i 0.878235 0.478229i \(-0.158721\pi\)
−0.853276 + 0.521460i \(0.825388\pi\)
\(348\) −150180. + 260120.i −0.0664761 + 0.115140i
\(349\) −3.75314e6 −1.64942 −0.824711 0.565555i \(-0.808662\pi\)
−0.824711 + 0.565555i \(0.808662\pi\)
\(350\) 0 0
\(351\) −568787. −0.246423
\(352\) −10995.2 + 19044.2i −0.00472983 + 0.00819230i
\(353\) −1.61461e6 2.79659e6i −0.689655 1.19452i −0.971950 0.235189i \(-0.924429\pi\)
0.282295 0.959328i \(-0.408904\pi\)
\(354\) 92088.2 + 159501.i 0.0390567 + 0.0676482i
\(355\) 287532. 498021.i 0.121092 0.209738i
\(356\) −460749. −0.192681
\(357\) 0 0
\(358\) 1.72381e6 0.710855
\(359\) −918294. + 1.59053e6i −0.376050 + 0.651338i −0.990484 0.137631i \(-0.956051\pi\)
0.614433 + 0.788969i \(0.289385\pi\)
\(360\) −94020.2 162848.i −0.0382353 0.0662256i
\(361\) 672656. + 1.16508e6i 0.271660 + 0.470528i
\(362\) 684938. 1.18635e6i 0.274713 0.475817i
\(363\) −1.44934e6 −0.577302
\(364\) 0 0
\(365\) 406208. 0.159594
\(366\) 511281. 885566.i 0.199507 0.345556i
\(367\) 169513. + 293605.i 0.0656957 + 0.113788i 0.897002 0.442026i \(-0.145740\pi\)
−0.831307 + 0.555814i \(0.812407\pi\)
\(368\) −405683. 702663.i −0.156159 0.270475i
\(369\) −435696. + 754648.i −0.166578 + 0.288522i
\(370\) −261959. −0.0994784
\(371\) 0 0
\(372\) −1.11490e6 −0.417715
\(373\) 353311. 611952.i 0.131488 0.227743i −0.792763 0.609531i \(-0.791358\pi\)
0.924250 + 0.381787i \(0.124691\pi\)
\(374\) −283.864 491.668i −0.000104938 0.000181758i
\(375\) 376110. + 651441.i 0.138114 + 0.239220i
\(376\) −2.47997e6 + 4.29544e6i −0.904644 + 1.56689i
\(377\) 1.16028e6 0.420447
\(378\) 0 0
\(379\) 648296. 0.231833 0.115917 0.993259i \(-0.463019\pi\)
0.115917 + 0.993259i \(0.463019\pi\)
\(380\) 164576. 285053.i 0.0584664 0.101267i
\(381\) −404434. 700500.i −0.142737 0.247227i
\(382\) 243437. + 421645.i 0.0853547 + 0.147839i
\(383\) 1.53511e6 2.65889e6i 0.534741 0.926198i −0.464435 0.885607i \(-0.653743\pi\)
0.999176 0.0405910i \(-0.0129241\pi\)
\(384\) 1.38745e6 0.480164
\(385\) 0 0
\(386\) 2.40541e6 0.821714
\(387\) −716717. + 1.24139e6i −0.243260 + 0.421338i
\(388\) 199092. + 344837.i 0.0671388 + 0.116288i
\(389\) 2.29999e6 + 3.98370e6i 0.770641 + 1.33479i 0.937212 + 0.348759i \(0.113397\pi\)
−0.166572 + 0.986029i \(0.553270\pi\)
\(390\) −149716. + 259315.i −0.0498432 + 0.0863310i
\(391\) 205464. 0.0679663
\(392\) 0 0
\(393\) 2.88104e6 0.940953
\(394\) −526013. + 911082.i −0.170709 + 0.295677i
\(395\) −152576. 264270.i −0.0492033 0.0852227i
\(396\) −3332.54 5772.14i −0.00106792 0.00184969i
\(397\) −1.32080e6 + 2.28768e6i −0.420590 + 0.728484i −0.995997 0.0893835i \(-0.971510\pi\)
0.575407 + 0.817867i \(0.304844\pi\)
\(398\) −916694. −0.290079
\(399\) 0 0
\(400\) −580425. −0.181383
\(401\) −2.44839e6 + 4.24073e6i −0.760359 + 1.31698i 0.182306 + 0.983242i \(0.441644\pi\)
−0.942665 + 0.333739i \(0.891689\pi\)
\(402\) 652615. + 1.13036e6i 0.201415 + 0.348861i
\(403\) 2.15342e6 + 3.72983e6i 0.660490 + 1.14400i
\(404\) −1.59433e6 + 2.76146e6i −0.485986 + 0.841753i
\(405\) 90493.3 0.0274144
\(406\) 0 0
\(407\) −22524.8 −0.00674025
\(408\) −37933.6 + 65702.9i −0.0112817 + 0.0195404i
\(409\) −48168.1 83429.6i −0.0142381 0.0246611i 0.858819 0.512280i \(-0.171199\pi\)
−0.873057 + 0.487619i \(0.837866\pi\)
\(410\) 229368. + 397276.i 0.0673864 + 0.116717i
\(411\) −1.16537e6 + 2.01848e6i −0.340298 + 0.589414i
\(412\) 4.72485e6 1.37134
\(413\) 0 0
\(414\) −1.02734e6 −0.294588
\(415\) 26870.4 46541.0i 0.00765869 0.0132652i
\(416\) −2.33971e6 4.05249e6i −0.662870 1.14812i
\(417\) −1.27065e6 2.20082e6i −0.357836 0.619791i
\(418\) −6027.11 + 10439.3i −0.00168721 + 0.00292233i
\(419\) 1.09657e6 0.305142 0.152571 0.988292i \(-0.451245\pi\)
0.152571 + 0.988292i \(0.451245\pi\)
\(420\) 0 0
\(421\) −1.93660e6 −0.532517 −0.266259 0.963902i \(-0.585788\pi\)
−0.266259 + 0.963902i \(0.585788\pi\)
\(422\) 783307. 1.35673e6i 0.214117 0.370861i
\(423\) −1.19347e6 2.06716e6i −0.324311 0.561723i
\(424\) 1.62052e6 + 2.80682e6i 0.437763 + 0.758227i
\(425\) 73491.1 127290.i 0.0197362 0.0341840i
\(426\) 1.16011e6 0.309725
\(427\) 0 0
\(428\) 4.54830e6 1.20016
\(429\) −12873.5 + 22297.6i −0.00337717 + 0.00584944i
\(430\) 377308. + 653517.i 0.0984067 + 0.170445i
\(431\) 1.53665e6 + 2.66155e6i 0.398457 + 0.690148i 0.993536 0.113519i \(-0.0362124\pi\)
−0.595079 + 0.803667i \(0.702879\pi\)
\(432\) −72089.3 + 124862.i −0.0185849 + 0.0321901i
\(433\) 3.80919e6 0.976366 0.488183 0.872741i \(-0.337660\pi\)
0.488183 + 0.872741i \(0.337660\pi\)
\(434\) 0 0
\(435\) −184600. −0.0467744
\(436\) 1.56574e6 2.71195e6i 0.394461 0.683227i
\(437\) −2.18124e6 3.77802e6i −0.546387 0.946370i
\(438\) 409733. + 709679.i 0.102051 + 0.176757i
\(439\) −266509. + 461608.i −0.0660011 + 0.114317i −0.897138 0.441751i \(-0.854357\pi\)
0.831137 + 0.556068i \(0.187691\pi\)
\(440\) −8511.94 −0.00209603
\(441\) 0 0
\(442\) 120809. 0.0294134
\(443\) 2.33373e6 4.04213e6i 0.564990 0.978592i −0.432061 0.901845i \(-0.642213\pi\)
0.997051 0.0767469i \(-0.0244533\pi\)
\(444\) 620398. + 1.07456e6i 0.149353 + 0.258687i
\(445\) −141587. 245235.i −0.0338940 0.0587061i
\(446\) −714725. + 1.23794e6i −0.170138 + 0.294688i
\(447\) −2.87702e6 −0.681042
\(448\) 0 0
\(449\) −6.10134e6 −1.42827 −0.714133 0.700010i \(-0.753179\pi\)
−0.714133 + 0.700010i \(0.753179\pi\)
\(450\) −367464. + 636467.i −0.0855429 + 0.148165i
\(451\) 19722.5 + 34160.3i 0.00456583 + 0.00790825i
\(452\) −2.31506e6 4.00980e6i −0.532986 0.923159i
\(453\) 378208. 655076.i 0.0865936 0.149985i
\(454\) 303680. 0.0691475
\(455\) 0 0
\(456\) 1.61084e6 0.362778
\(457\) −2.97249e6 + 5.14851e6i −0.665779 + 1.15316i 0.313295 + 0.949656i \(0.398567\pi\)
−0.979073 + 0.203507i \(0.934766\pi\)
\(458\) 775076. + 1.34247e6i 0.172655 + 0.299048i
\(459\) −18255.3 31619.1i −0.00404443 0.00700516i
\(460\) 634920. 1.09971e6i 0.139902 0.242318i
\(461\) 2.09415e6 0.458940 0.229470 0.973316i \(-0.426301\pi\)
0.229470 + 0.973316i \(0.426301\pi\)
\(462\) 0 0
\(463\) 2.41123e6 0.522741 0.261371 0.965239i \(-0.415826\pi\)
0.261371 + 0.965239i \(0.415826\pi\)
\(464\) 147057. 254710.i 0.0317096 0.0549226i
\(465\) −342607. 593412.i −0.0734790 0.127269i
\(466\) −948999. 1.64371e6i −0.202442 0.350640i
\(467\) −2.25916e6 + 3.91298e6i −0.479353 + 0.830264i −0.999720 0.0236794i \(-0.992462\pi\)
0.520367 + 0.853943i \(0.325795\pi\)
\(468\) 1.41829e6 0.299330
\(469\) 0 0
\(470\) −1.25658e6 −0.262389
\(471\) −567879. + 983595.i −0.117951 + 0.204298i
\(472\) −557050. 964839.i −0.115090 0.199342i
\(473\) 32443.3 + 56193.4i 0.00666764 + 0.0115487i
\(474\) 307801. 533127.i 0.0629252 0.108990i
\(475\) −3.12078e6 −0.634643
\(476\) 0 0
\(477\) −1.55973e6 −0.313872
\(478\) 1.70070e6 2.94570e6i 0.340454 0.589683i
\(479\) 4.17964e6 + 7.23935e6i 0.832339 + 1.44165i 0.896179 + 0.443694i \(0.146332\pi\)
−0.0638394 + 0.997960i \(0.520335\pi\)
\(480\) 372245. + 644747.i 0.0737438 + 0.127728i
\(481\) 2.39658e6 4.15099e6i 0.472312 0.818068i
\(482\) −277886. −0.0544815
\(483\) 0 0
\(484\) 3.61398e6 0.701249
\(485\) −122360. + 211934.i −0.0236204 + 0.0409117i
\(486\) 91278.7 + 158099.i 0.0175299 + 0.0303626i
\(487\) −299152. 518147.i −0.0571570 0.0989989i 0.836031 0.548682i \(-0.184870\pi\)
−0.893188 + 0.449683i \(0.851537\pi\)
\(488\) −3.09279e6 + 5.35687e6i −0.587897 + 1.01827i
\(489\) −2.12211e6 −0.401324
\(490\) 0 0
\(491\) 2.76760e6 0.518084 0.259042 0.965866i \(-0.416593\pi\)
0.259042 + 0.965866i \(0.416593\pi\)
\(492\) 1.08643e6 1.88174e6i 0.202342 0.350467i
\(493\) 37239.5 + 64500.8i 0.00690060 + 0.0119522i
\(494\) −1.28253e6 2.22142e6i −0.236457 0.409555i
\(495\) 2048.16 3547.52i 0.000375708 0.000650746i
\(496\) 1.09172e6 0.199253
\(497\) 0 0
\(498\) 108415. 0.0195891
\(499\) −1.51960e6 + 2.63203e6i −0.273199 + 0.473195i −0.969679 0.244381i \(-0.921415\pi\)
0.696480 + 0.717576i \(0.254748\pi\)
\(500\) −937844. 1.62439e6i −0.167767 0.290580i
\(501\) −674292. 1.16791e6i −0.120020 0.207881i
\(502\) 1.56205e6 2.70555e6i 0.276653 0.479178i
\(503\) −9.37896e6 −1.65286 −0.826428 0.563043i \(-0.809631\pi\)
−0.826428 + 0.563043i \(0.809631\pi\)
\(504\) 0 0
\(505\) −1.95973e6 −0.341953
\(506\) −23252.1 + 40273.9i −0.00403726 + 0.00699274i
\(507\) −1.06859e6 1.85085e6i −0.184625 0.319780i
\(508\) 1.00847e6 + 1.74672e6i 0.173382 + 0.300307i
\(509\) 2.95069e6 5.11075e6i 0.504812 0.874360i −0.495172 0.868795i \(-0.664895\pi\)
0.999985 0.00556552i \(-0.00177157\pi\)
\(510\) −19220.6 −0.00327222
\(511\) 0 0
\(512\) −2.25139e6 −0.379555
\(513\) −387604. + 671349.i −0.0650271 + 0.112630i
\(514\) −1.87403e6 3.24592e6i −0.312874 0.541913i
\(515\) 1.45193e6 + 2.51482e6i 0.241228 + 0.417820i
\(516\) 1.78716e6 3.09545e6i 0.295488 0.511800i
\(517\) −108049. −0.0177784
\(518\) 0 0
\(519\) 6.34014e6 1.03319
\(520\) 905645. 1.56862e6i 0.146876 0.254396i
\(521\) 4.68713e6 + 8.11834e6i 0.756506 + 1.31031i 0.944622 + 0.328160i \(0.106429\pi\)
−0.188116 + 0.982147i \(0.560238\pi\)
\(522\) −186202. 322511.i −0.0299094 0.0518046i
\(523\) 3.23415e6 5.60171e6i 0.517018 0.895501i −0.482787 0.875738i \(-0.660375\pi\)
0.999805 0.0197635i \(-0.00629132\pi\)
\(524\) −7.18398e6 −1.14298
\(525\) 0 0
\(526\) −1.18997e6 −0.187531
\(527\) −138229. + 239419.i −0.0216806 + 0.0375520i
\(528\) 3263.23 + 5652.08i 0.000509405 + 0.000882315i
\(529\) −5.19689e6 9.00128e6i −0.807429 1.39851i
\(530\) −410551. + 711095.i −0.0634859 + 0.109961i
\(531\) 536154. 0.0825188
\(532\) 0 0
\(533\) −8.39364e6 −1.27977
\(534\) 285631. 494728.i 0.0433463 0.0750780i
\(535\) 1.39768e6 + 2.42085e6i 0.211117 + 0.365665i
\(536\) −3.94773e6 6.83767e6i −0.593520 1.02801i
\(537\) 2.50908e6 4.34585e6i 0.375473 0.650337i
\(538\) 4.86792e6 0.725083
\(539\) 0 0
\(540\) −225649. −0.0333003
\(541\) 1.23044e6 2.13119e6i 0.180746 0.313061i −0.761389 0.648296i \(-0.775482\pi\)
0.942135 + 0.335234i \(0.108815\pi\)
\(542\) 513627. + 889628.i 0.0751017 + 0.130080i
\(543\) −1.99392e6 3.45356e6i −0.290207 0.502652i
\(544\) 150187. 260131.i 0.0217588 0.0376873i
\(545\) 1.92459e6 0.277554
\(546\) 0 0
\(547\) 503726. 0.0719824 0.0359912 0.999352i \(-0.488541\pi\)
0.0359912 + 0.999352i \(0.488541\pi\)
\(548\) 2.90590e6 5.03316e6i 0.413361 0.715961i
\(549\) −1.48839e6 2.57796e6i −0.210758 0.365044i
\(550\) 16633.8 + 28810.6i 0.00234469 + 0.00406112i
\(551\) 790683. 1.36950e6i 0.110949 0.192169i
\(552\) 6.21450e6 0.868077
\(553\) 0 0
\(554\) −6.91113e6 −0.956697
\(555\) −381293. + 660418.i −0.0525444 + 0.0910095i
\(556\) 3.16841e6 + 5.48784e6i 0.434664 + 0.752860i
\(557\) −316324. 547890.i −0.0432011 0.0748264i 0.843616 0.536946i \(-0.180422\pi\)
−0.886817 + 0.462120i \(0.847089\pi\)
\(558\) 691160. 1.19712e6i 0.0939709 0.162762i
\(559\) −1.38075e7 −1.86890
\(560\) 0 0
\(561\) −1652.71 −0.000221712
\(562\) 107780. 186680.i 0.0143945 0.0249320i
\(563\) 5.03898e6 + 8.72777e6i 0.669995 + 1.16047i 0.977905 + 0.209050i \(0.0670371\pi\)
−0.307910 + 0.951415i \(0.599630\pi\)
\(564\) 2.97597e6 + 5.15453e6i 0.393941 + 0.682325i
\(565\) 1.42282e6 2.46439e6i 0.187512 0.324780i
\(566\) 1.47301e6 0.193270
\(567\) 0 0
\(568\) −7.01763e6 −0.912682
\(569\) −1.00842e6 + 1.74664e6i −0.130576 + 0.226164i −0.923899 0.382637i \(-0.875016\pi\)
0.793323 + 0.608801i \(0.208349\pi\)
\(570\) 204050. + 353425.i 0.0263056 + 0.0455627i
\(571\) −2.04864e6 3.54834e6i −0.262951 0.455444i 0.704074 0.710127i \(-0.251362\pi\)
−0.967025 + 0.254682i \(0.918029\pi\)
\(572\) 32100.6 55599.8i 0.00410226 0.00710532i
\(573\) 1.41733e6 0.180337
\(574\) 0 0
\(575\) −1.20397e7 −1.51861
\(576\) −494634. + 856731.i −0.0621194 + 0.107594i
\(577\) −4.07161e6 7.05224e6i −0.509128 0.881835i −0.999944 0.0105723i \(-0.996635\pi\)
0.490816 0.871263i \(-0.336699\pi\)
\(578\) −2.19096e6 3.79485e6i −0.272781 0.472470i
\(579\) 3.50118e6 6.06423e6i 0.434029 0.751759i
\(580\) 460307. 0.0568169
\(581\) 0 0
\(582\) −493689. −0.0604152
\(583\) −35301.7 + 61144.4i −0.00430155 + 0.00745050i
\(584\) −2.47852e6 4.29292e6i −0.300718 0.520859i
\(585\) 435836. + 754891.i 0.0526543 + 0.0911999i
\(586\) 3.51810e6 6.09354e6i 0.423219 0.733036i
\(587\) 8.81465e6 1.05587 0.527934 0.849285i \(-0.322967\pi\)
0.527934 + 0.849285i \(0.322967\pi\)
\(588\) 0 0
\(589\) 5.86985e6 0.697170
\(590\) 141126. 244438.i 0.0166908 0.0289094i
\(591\) 1.53127e6 + 2.65224e6i 0.180336 + 0.312352i
\(592\) −607495. 1.05221e6i −0.0712424 0.123395i
\(593\) −5.78695e6 + 1.00233e7i −0.675792 + 1.17051i 0.300445 + 0.953799i \(0.402865\pi\)
−0.976237 + 0.216706i \(0.930469\pi\)
\(594\) 8263.74 0.000960972
\(595\) 0 0
\(596\) 7.17396e6 0.827263
\(597\) −1.33429e6 + 2.31106e6i −0.153220 + 0.265384i
\(598\) −4.94792e6 8.57005e6i −0.565809 0.980009i
\(599\) 6.17753e6 + 1.06998e7i 0.703474 + 1.21845i 0.967240 + 0.253865i \(0.0817020\pi\)
−0.263766 + 0.964587i \(0.584965\pi\)
\(600\) 2.22283e6 3.85005e6i 0.252074 0.436604i
\(601\) 8.33752e6 0.941566 0.470783 0.882249i \(-0.343971\pi\)
0.470783 + 0.882249i \(0.343971\pi\)
\(602\) 0 0
\(603\) 3.79964e6 0.425549
\(604\) −943078. + 1.63346e6i −0.105185 + 0.182186i
\(605\) 1.11056e6 + 1.92355e6i 0.123355 + 0.213656i
\(606\) −1.97673e6 3.42380e6i −0.218659 0.378728i
\(607\) −4.33595e6 + 7.51008e6i −0.477653 + 0.827319i −0.999672 0.0256151i \(-0.991846\pi\)
0.522019 + 0.852934i \(0.325179\pi\)
\(608\) −6.37764e6 −0.699682
\(609\) 0 0
\(610\) −1.56709e6 −0.170518
\(611\) 1.14961e7 1.99118e7i 1.24579 2.15778i
\(612\) 45520.3 + 78843.5i 0.00491278 + 0.00850918i
\(613\) −2.62016e6 4.53825e6i −0.281628 0.487794i 0.690158 0.723659i \(-0.257541\pi\)
−0.971786 + 0.235865i \(0.924208\pi\)
\(614\) −2.50098e6 + 4.33182e6i −0.267725 + 0.463713i
\(615\) 1.33542e6 0.142374
\(616\) 0 0
\(617\) −6.95644e6 −0.735655 −0.367828 0.929894i \(-0.619898\pi\)
−0.367828 + 0.929894i \(0.619898\pi\)
\(618\) −2.92907e6 + 5.07329e6i −0.308502 + 0.534341i
\(619\) 9.13814e6 + 1.58277e7i 0.958586 + 1.66032i 0.725939 + 0.687759i \(0.241406\pi\)
0.232647 + 0.972561i \(0.425261\pi\)
\(620\) 854303. + 1.47970e6i 0.0892550 + 0.154594i
\(621\) −1.49534e6 + 2.59001e6i −0.155601 + 0.269509i
\(622\) 3.17409e6 0.328960
\(623\) 0 0
\(624\) −1.38879e6 −0.142783
\(625\) −4.00918e6 + 6.94410e6i −0.410540 + 0.711075i
\(626\) 490354. + 849317.i 0.0500119 + 0.0866232i
\(627\) 17545.5 + 30389.6i 0.00178236 + 0.00308714i
\(628\) 1.41603e6 2.45263e6i 0.143276 0.248161i
\(629\) 307674. 0.0310074
\(630\) 0 0
\(631\) 1.90708e7 1.90676 0.953379 0.301777i \(-0.0975798\pi\)
0.953379 + 0.301777i \(0.0975798\pi\)
\(632\) −1.86192e6 + 3.22494e6i −0.185425 + 0.321165i
\(633\) −2.28028e6 3.94956e6i −0.226193 0.391777i
\(634\) 2.42887e6 + 4.20693e6i 0.239984 + 0.415664i
\(635\) −619800. + 1.07353e6i −0.0609983 + 0.105652i
\(636\) 3.88924e6 0.381261
\(637\) 0 0
\(638\) −16857.4 −0.00163961
\(639\) 1.68859e6 2.92473e6i 0.163596 0.283357i
\(640\) −1.06314e6 1.84142e6i −0.102599 0.177706i
\(641\) −1.60312e6 2.77668e6i −0.154106 0.266920i 0.778627 0.627487i \(-0.215917\pi\)
−0.932733 + 0.360567i \(0.882583\pi\)
\(642\) −2.81962e6 + 4.88372e6i −0.269993 + 0.467642i
\(643\) −4.35153e6 −0.415063 −0.207532 0.978228i \(-0.566543\pi\)
−0.207532 + 0.978228i \(0.566543\pi\)
\(644\) 0 0
\(645\) 2.19675e6 0.207913
\(646\) 82326.4 142593.i 0.00776172 0.0134437i
\(647\) −2.79988e6 4.84953e6i −0.262953 0.455448i 0.704072 0.710129i \(-0.251363\pi\)
−0.967025 + 0.254680i \(0.918030\pi\)
\(648\) −552154. 956358.i −0.0516562 0.0894711i
\(649\) 12134.9 21018.3i 0.00113090 0.00195878i
\(650\) −7.07917e6 −0.657202
\(651\) 0 0
\(652\) 5.29156e6 0.487489
\(653\) 3.37247e6 5.84130e6i 0.309504 0.536076i −0.668750 0.743487i \(-0.733170\pi\)
0.978254 + 0.207411i \(0.0665038\pi\)
\(654\) 1.94130e6 + 3.36242e6i 0.177479 + 0.307403i
\(655\) −2.20761e6 3.82370e6i −0.201057 0.348241i
\(656\) −1.06383e6 + 1.84261e6i −0.0965188 + 0.167176i
\(657\) 2.38554e6 0.215612
\(658\) 0 0
\(659\) 2.09622e6 0.188029 0.0940143 0.995571i \(-0.470030\pi\)
0.0940143 + 0.995571i \(0.470030\pi\)
\(660\) −5107.16 + 8845.87i −0.000456373 + 0.000790461i
\(661\) −9.70925e6 1.68169e7i −0.864335 1.49707i −0.867706 0.497077i \(-0.834406\pi\)
0.00337135 0.999994i \(-0.498927\pi\)
\(662\) 2.37796e6 + 4.11874e6i 0.210891 + 0.365275i
\(663\) 175843. 304570.i 0.0155361 0.0269093i
\(664\) −655810. −0.0577242
\(665\) 0 0
\(666\) −1.53841e6 −0.134396
\(667\) 3.05039e6 5.28344e6i 0.265486 0.459835i
\(668\) 1.68137e6 + 2.91222e6i 0.145788 + 0.252513i
\(669\) 2.08063e6 + 3.60375e6i 0.179734 + 0.311308i
\(670\) 1.00014e6 1.73229e6i 0.0860744 0.149085i
\(671\) −134748. −0.0115536
\(672\) 0 0
\(673\) 1.27627e7 1.08619 0.543094 0.839672i \(-0.317253\pi\)
0.543094 + 0.839672i \(0.317253\pi\)
\(674\) −4.43356e6 + 7.67916e6i −0.375927 + 0.651124i
\(675\) 1.06972e6 + 1.85281e6i 0.0903673 + 0.156521i
\(676\) 2.66456e6 + 4.61516e6i 0.224264 + 0.388437i
\(677\) −1.93251e6 + 3.34720e6i −0.162050 + 0.280679i −0.935604 0.353052i \(-0.885144\pi\)
0.773554 + 0.633731i \(0.218477\pi\)
\(678\) 5.74067e6 0.479610
\(679\) 0 0
\(680\) 116267. 0.00964241
\(681\) 442020. 765600.i 0.0365236 0.0632607i
\(682\) −31286.4 54189.7i −0.00257570 0.00446124i
\(683\) 1.03209e7 + 1.78764e7i 0.846578 + 1.46632i 0.884244 + 0.467025i \(0.154674\pi\)
−0.0376665 + 0.999290i \(0.511992\pi\)
\(684\) 966505. 1.67403e6i 0.0789885 0.136812i
\(685\) 3.57189e6 0.290852
\(686\) 0 0
\(687\) 4.51263e6 0.364786
\(688\) −1.74999e6 + 3.03107e6i −0.140950 + 0.244132i
\(689\) −7.51200e6 1.30112e7i −0.602848 1.04416i
\(690\) 787208. + 1.36348e6i 0.0629458 + 0.109025i
\(691\) −8.11643e6 + 1.40581e7i −0.646651 + 1.12003i 0.337267 + 0.941409i \(0.390498\pi\)
−0.983918 + 0.178623i \(0.942836\pi\)
\(692\) −1.58094e7 −1.25502
\(693\) 0 0
\(694\) 346156. 0.0272818
\(695\) −1.94728e6 + 3.37279e6i −0.152921 + 0.264867i
\(696\) 1.12635e6 + 1.95090e6i 0.0881356 + 0.152655i
\(697\) −269396. 466607.i −0.0210043 0.0363805i
\(698\) −5.80166e6 + 1.00488e7i −0.450727 + 0.780682i
\(699\) −5.52524e6 −0.427719
\(700\) 0 0
\(701\) −8.27590e6 −0.636092 −0.318046 0.948075i \(-0.603027\pi\)
−0.318046 + 0.948075i \(0.603027\pi\)
\(702\) −879238. + 1.52288e6i −0.0673385 + 0.116634i
\(703\) −3.26633e6 5.65745e6i −0.249271 0.431750i
\(704\) 22390.3 + 38781.2i 0.00170267 + 0.00294910i
\(705\) −1.82901e6 + 3.16794e6i −0.138594 + 0.240051i
\(706\) −9.98356e6 −0.753830
\(707\) 0 0
\(708\) −1.33692e6 −0.100236
\(709\) −1.19487e7 + 2.06957e7i −0.892696 + 1.54619i −0.0560652 + 0.998427i \(0.517855\pi\)
−0.836631 + 0.547767i \(0.815478\pi\)
\(710\) −888943. 1.53969e6i −0.0661802 0.114627i
\(711\) −896037. 1.55198e6i −0.0664740 0.115136i
\(712\) −1.72781e6 + 2.99265e6i −0.127731 + 0.221236i
\(713\) 2.26454e7 1.66823
\(714\) 0 0
\(715\) 39457.6 0.00288646
\(716\) −6.25648e6 + 1.08365e7i −0.456087 + 0.789965i
\(717\) −4.95089e6 8.57520e6i −0.359655 0.622940i
\(718\) 2.83902e6 + 4.91733e6i 0.205522 + 0.355974i
\(719\) −392175. + 679266.i −0.0282916 + 0.0490025i −0.879825 0.475299i \(-0.842340\pi\)
0.851533 + 0.524301i \(0.175673\pi\)
\(720\) 220955. 0.0158845
\(721\) 0 0
\(722\) 4.15920e6 0.296939
\(723\) −404476. + 700573.i −0.0287771 + 0.0498434i
\(724\) 4.97191e6 + 8.61159e6i 0.352514 + 0.610572i
\(725\) −2.18215e6 3.77960e6i −0.154184 0.267055i
\(726\) −2.24041e6 + 3.88050e6i −0.157756 + 0.273241i
\(727\) 1.61766e7 1.13514 0.567571 0.823324i \(-0.307883\pi\)
0.567571 + 0.823324i \(0.307883\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 627921. 1.08759e6i 0.0436112 0.0755368i
\(731\) −443154. 767565.i −0.0306733 0.0531278i
\(732\) 3.71135e6 + 6.42824e6i 0.256008 + 0.443419i
\(733\) −6.84890e6 + 1.18627e7i −0.470827 + 0.815496i −0.999443 0.0333649i \(-0.989378\pi\)
0.528616 + 0.848861i \(0.322711\pi\)
\(734\) 1.04814e6 0.0718090
\(735\) 0 0
\(736\) −2.46044e7 −1.67424
\(737\) 85998.3 148953.i 0.00583205 0.0101014i
\(738\) 1.34701e6 + 2.33309e6i 0.0910395 + 0.157685i
\(739\) 1.26856e7 + 2.19721e7i 0.854477 + 1.48000i 0.877130 + 0.480253i \(0.159455\pi\)
−0.0226532 + 0.999743i \(0.507211\pi\)
\(740\) 950768. 1.64678e6i 0.0638257 0.110549i
\(741\) −7.46715e6 −0.499585
\(742\) 0 0
\(743\) 2.45336e7 1.63038 0.815192 0.579191i \(-0.196632\pi\)
0.815192 + 0.579191i \(0.196632\pi\)
\(744\) −4.18089e6 + 7.24152e6i −0.276909 + 0.479620i
\(745\) 2.20453e6 + 3.81837e6i 0.145521 + 0.252050i
\(746\) −1.09230e6 1.89193e6i −0.0718616 0.124468i
\(747\) 157802. 273322.i 0.0103469 0.0179214i
\(748\) 4121.10 0.000269314
\(749\) 0 0
\(750\) 2.32558e6 0.150966
\(751\) 9.24536e6 1.60134e7i 0.598169 1.03606i −0.394922 0.918715i \(-0.629228\pi\)
0.993091 0.117345i \(-0.0374384\pi\)
\(752\) −2.91407e6 5.04732e6i −0.187913 0.325474i
\(753\) −4.54727e6 7.87610e6i −0.292256 0.506202i
\(754\) 1.79358e6 3.10657e6i 0.114893 0.199000i
\(755\) −1.15922e6 −0.0740113
\(756\) 0 0
\(757\) −2.94413e7 −1.86732 −0.933658 0.358166i \(-0.883402\pi\)
−0.933658 + 0.358166i \(0.883402\pi\)
\(758\) 1.00214e6 1.73577e6i 0.0633516 0.109728i
\(759\) 67689.1 + 117241.i 0.00426495 + 0.00738711i
\(760\) −1.23432e6 2.13790e6i −0.0775162 0.134262i
\(761\) 9.31179e6 1.61285e7i 0.582870 1.00956i −0.412267 0.911063i \(-0.635263\pi\)
0.995137 0.0984975i \(-0.0314036\pi\)
\(762\) −2.50072e6 −0.156019
\(763\) 0 0
\(764\) −3.53417e6 −0.219056
\(765\) −27976.5 + 48456.7i −0.00172838 + 0.00299365i
\(766\) −4.74599e6 8.22030e6i −0.292250 0.506193i
\(767\) 2.58224e6 + 4.47257e6i 0.158492 + 0.274517i
\(768\) 3.90344e6 6.76095e6i 0.238805 0.413623i
\(769\) −1.13326e7 −0.691056 −0.345528 0.938408i \(-0.612300\pi\)
−0.345528 + 0.938408i \(0.612300\pi\)
\(770\) 0 0
\(771\) −1.09109e7 −0.661038
\(772\) −8.73033e6 + 1.51214e7i −0.527215 + 0.913163i
\(773\) 4.11010e6 + 7.11890e6i 0.247402 + 0.428513i 0.962804 0.270200i \(-0.0870898\pi\)
−0.715402 + 0.698713i \(0.753756\pi\)
\(774\) 2.21582e6 + 3.83791e6i 0.132948 + 0.230273i
\(775\) 8.09990e6 1.40294e7i 0.484424 0.839047i
\(776\) 2.98637e6 0.178029
\(777\) 0 0
\(778\) 1.42214e7 0.842352
\(779\) −5.71991e6 + 9.90717e6i −0.337711 + 0.584933i
\(780\) −1.08677e6 1.88235e6i −0.0639592 0.110781i
\(781\) −76436.8 132392.i −0.00448410 0.00776668i
\(782\) 317609. 550114.i 0.0185727 0.0321689i
\(783\) −1.08410e6 −0.0631925
\(784\) 0 0
\(785\) 1.74056e6 0.100813
\(786\) 4.45355e6 7.71377e6i 0.257128 0.445359i
\(787\) 2.71541e6 + 4.70322e6i 0.156278 + 0.270681i 0.933524 0.358516i \(-0.116717\pi\)
−0.777246 + 0.629197i \(0.783384\pi\)
\(788\) −3.81829e6 6.61347e6i −0.219055 0.379414i
\(789\) −1.73206e6 + 3.00001e6i −0.0990534 + 0.171566i
\(790\) −943418. −0.0537819
\(791\) 0 0
\(792\) −49988.1 −0.00283174
\(793\) 1.43368e7 2.48321e7i 0.809598 1.40227i
\(794\) 4.08340e6 + 7.07266e6i 0.229864 + 0.398136i
\(795\) 1.19515e6 + 2.07006e6i 0.0670664 + 0.116162i
\(796\) 3.32710e6 5.76271e6i 0.186116 0.322362i
\(797\) 1.78388e7 0.994765 0.497382 0.867531i \(-0.334295\pi\)
0.497382 + 0.867531i \(0.334295\pi\)
\(798\) 0 0
\(799\) 1.47587e6 0.0817866
\(800\) −8.80061e6 + 1.52431e7i −0.486170 + 0.842071i
\(801\) −831498. 1.44020e6i −0.0457910 0.0793123i
\(802\) 7.56949e6 + 1.31107e7i 0.415557 + 0.719766i
\(803\) 53992.6 93517.9i 0.00295492 0.00511807i
\(804\) −9.47455e6 −0.516914
\(805\) 0 0
\(806\) 1.33151e7 0.721951
\(807\) 7.08547e6 1.22724e7i 0.382988 0.663355i
\(808\) 1.19574e7 + 2.07109e7i 0.644333 + 1.11602i
\(809\) −5.92153e6 1.02564e7i −0.318099 0.550964i 0.661992 0.749511i \(-0.269711\pi\)
−0.980091 + 0.198546i \(0.936378\pi\)
\(810\) 139886. 242289.i 0.00749136 0.0129754i
\(811\) 618053. 0.0329969 0.0164985 0.999864i \(-0.494748\pi\)
0.0164985 + 0.999864i \(0.494748\pi\)
\(812\) 0 0
\(813\) 2.99043e6 0.158674
\(814\) −34819.2 + 60308.6i −0.00184186 + 0.00319020i
\(815\) 1.62608e6 + 2.81645e6i 0.0857526 + 0.148528i
\(816\) −44573.6 77203.7i −0.00234343 0.00405894i
\(817\) −9.40920e6 + 1.62972e7i −0.493171 + 0.854198i
\(818\) −297836. −0.0155630
\(819\) 0 0
\(820\) −3.32992e6 −0.172941
\(821\) −2.15628e6 + 3.73479e6i −0.111647 + 0.193378i −0.916434 0.400185i \(-0.868946\pi\)
0.804787 + 0.593563i \(0.202279\pi\)
\(822\) 3.60289e6 + 6.24039e6i 0.185982 + 0.322131i
\(823\) −1.43310e7 2.48220e7i −0.737524 1.27743i −0.953607 0.301054i \(-0.902662\pi\)
0.216083 0.976375i \(-0.430672\pi\)
\(824\) 1.77182e7 3.06888e7i 0.909079 1.57457i
\(825\) 96845.2 0.00495385
\(826\) 0 0
\(827\) 1.86894e7 0.950235 0.475117 0.879922i \(-0.342406\pi\)
0.475117 + 0.879922i \(0.342406\pi\)
\(828\) 3.72870e6 6.45830e6i 0.189009 0.327372i
\(829\) −6.62429e6 1.14736e7i −0.334775 0.579847i 0.648667 0.761073i \(-0.275327\pi\)
−0.983442 + 0.181225i \(0.941994\pi\)
\(830\) −83073.4 143887.i −0.00418569 0.00724982i
\(831\) −1.00595e7 + 1.74235e7i −0.505326 + 0.875251i
\(832\) −9.52907e6 −0.477246
\(833\) 0 0
\(834\) −7.85673e6 −0.391135
\(835\) −1.03336e6 + 1.78983e6i −0.0512903 + 0.0888375i
\(836\) −43750.3 75777.8i −0.00216504 0.00374995i
\(837\) −2.01203e6 3.48494e6i −0.0992706 0.171942i
\(838\) 1.69510e6 2.93599e6i 0.0833843 0.144426i
\(839\) −2.52930e7 −1.24049 −0.620247 0.784406i \(-0.712968\pi\)
−0.620247 + 0.784406i \(0.712968\pi\)
\(840\) 0 0
\(841\) −1.82997e7 −0.892181
\(842\) −2.99361e6 + 5.18509e6i −0.145518 + 0.252044i
\(843\) −313756. 543441.i −0.0152063 0.0263381i
\(844\) 5.68596e6 + 9.84837e6i 0.274756 + 0.475892i
\(845\) −1.63762e6 + 2.83645e6i −0.0788991 + 0.136657i
\(846\) −7.37954e6 −0.354490
\(847\) 0 0
\(848\) −3.80835e6 −0.181864
\(849\) 2.14404e6 3.71358e6i 0.102085 0.176817i
\(850\) −227207. 393534.i −0.0107864 0.0186825i
\(851\) −1.26012e7 2.18260e7i −0.596471 1.03312i
\(852\) −4.21058e6 + 7.29293e6i −0.198720 + 0.344194i
\(853\) 4.05806e7 1.90962 0.954808 0.297223i \(-0.0960605\pi\)
0.954808 + 0.297223i \(0.0960605\pi\)
\(854\) 0 0
\(855\) 1.18801e6 0.0555784
\(856\) 1.70561e7 2.95421e7i 0.795602 1.37802i
\(857\) −9.72346e6 1.68415e7i −0.452240 0.783302i 0.546285 0.837599i \(-0.316042\pi\)
−0.998525 + 0.0542970i \(0.982708\pi\)
\(858\) 39800.1 + 68935.7i 0.00184572 + 0.00319688i
\(859\) 1.01621e7 1.76012e7i 0.469894 0.813880i −0.529513 0.848302i \(-0.677625\pi\)
0.999407 + 0.0344214i \(0.0109588\pi\)
\(860\) −5.47769e6 −0.252552
\(861\) 0 0
\(862\) 9.50149e6 0.435536
\(863\) 1.30601e7 2.26208e7i 0.596926 1.03391i −0.396346 0.918101i \(-0.629722\pi\)
0.993272 0.115804i \(-0.0369446\pi\)
\(864\) 2.18609e6 + 3.78641e6i 0.0996283 + 0.172561i
\(865\) −4.85817e6 8.41459e6i −0.220766 0.382378i
\(866\) 5.88829e6 1.01988e7i 0.266805 0.462121i
\(867\) −1.27561e7 −0.576330
\(868\) 0 0
\(869\) −81120.9 −0.00364404
\(870\) −285357. + 494252.i −0.0127817 + 0.0221386i
\(871\) 1.82999e7 + 3.16964e7i 0.817343 + 1.41568i
\(872\) −1.17431e7 2.03396e7i −0.522987 0.905840i
\(873\) −718587. + 1.24463e6i −0.0319113 + 0.0552719i
\(874\) −1.34872e7 −0.597231
\(875\) 0 0
\(876\) −5.94844e6 −0.261904
\(877\) 8.14779e6 1.41124e7i 0.357718 0.619585i −0.629861 0.776708i \(-0.716888\pi\)
0.987579 + 0.157122i \(0.0502216\pi\)
\(878\) 823947. + 1.42712e6i 0.0360714 + 0.0624775i
\(879\) −1.02415e7 1.77388e7i −0.447087 0.774377i
\(880\) 5000.94 8661.88i 0.000217693 0.000377056i
\(881\) 2.93722e7 1.27496 0.637479 0.770467i \(-0.279977\pi\)
0.637479 + 0.770467i \(0.279977\pi\)
\(882\) 0 0
\(883\) 1.21821e7 0.525800 0.262900 0.964823i \(-0.415321\pi\)
0.262900 + 0.964823i \(0.415321\pi\)
\(884\) −438473. + 759457.i −0.0188717 + 0.0326868i
\(885\) −410831. 711580.i −0.0176321 0.0305398i
\(886\) −7.21501e6 1.24968e7i −0.308783 0.534827i
\(887\) 1.19010e7 2.06132e7i 0.507897 0.879704i −0.492061 0.870561i \(-0.663756\pi\)
0.999958 0.00914296i \(-0.00291033\pi\)
\(888\) 9.30597e6 0.396031
\(889\) 0 0
\(890\) −875466. −0.0370480
\(891\) 12028.2 20833.5i 0.000507584 0.000879161i
\(892\) −5.18813e6 8.98610e6i −0.218323 0.378146i
\(893\) −1.56681e7 2.71380e7i −0.657490 1.13881i
\(894\) −4.44734e6 + 7.70301e6i −0.186104 + 0.322342i
\(895\) −7.69038e6 −0.320915
\(896\) 0 0
\(897\) −2.88077e7 −1.19544
\(898\) −9.43153e6 + 1.63359e7i −0.390293 + 0.676008i
\(899\) 4.10439e6 + 7.10902e6i 0.169375 + 0.293366i
\(900\) −2.66739e6 4.62006e6i −0.109769 0.190126i
\(901\) 482198. 835192.i 0.0197885 0.0342747i
\(902\) 121949. 0.00499070
\(903\) 0 0
\(904\) −3.47259e7 −1.41329
\(905\) −3.05570e6 + 5.29263e6i −0.124019 + 0.214808i
\(906\) −1.16928e6 2.02525e6i −0.0473258 0.0819706i
\(907\) −1.05435e7 1.82619e7i −0.425566 0.737102i 0.570907 0.821015i \(-0.306592\pi\)
−0.996473 + 0.0839124i \(0.973258\pi\)
\(908\) −1.10219e6 + 1.90905e6i −0.0443653 + 0.0768429i
\(909\) −1.15089e7 −0.461981
\(910\) 0 0
\(911\) 1.71528e7 0.684761 0.342381 0.939561i \(-0.388767\pi\)
0.342381 + 0.939561i \(0.388767\pi\)
\(912\) −946402. + 1.63922e6i −0.0376781 + 0.0652603i
\(913\) −7143.16 12372.3i −0.000283605 0.000491218i
\(914\) 9.18983e6 + 1.59173e7i 0.363866 + 0.630235i
\(915\) −2.28097e6 + 3.95076e6i −0.0900672 + 0.156001i
\(916\) −1.12524e7 −0.443105
\(917\) 0 0
\(918\) −112877. −0.00442079
\(919\) −3.67771e6 + 6.36997e6i −0.143644 + 0.248799i −0.928866 0.370415i \(-0.879215\pi\)
0.785222 + 0.619214i \(0.212549\pi\)
\(920\) −4.76190e6 8.24785e6i −0.185486 0.321271i
\(921\) 7.28057e6 + 1.26103e7i 0.282824 + 0.489866i
\(922\) 3.23717e6 5.60694e6i 0.125412 0.217219i
\(923\) 3.25306e7 1.25686
\(924\) 0 0
\(925\) −1.80290e7 −0.692817
\(926\) 3.72732e6 6.45590e6i 0.142846 0.247417i
\(927\) 8.52677e6 + 1.47688e7i 0.325901 + 0.564477i
\(928\) −4.45946e6 7.72401e6i −0.169986 0.294424i
\(929\) 1.67099e7 2.89424e7i 0.635236 1.10026i −0.351229 0.936290i \(-0.614236\pi\)
0.986465 0.163972i \(-0.0524306\pi\)
\(930\) −2.11842e6 −0.0803166
\(931\) 0 0
\(932\) 1.37774e7 0.519550
\(933\) 4.62003e6 8.00213e6i 0.173756 0.300955i
\(934\) 6.98449e6 + 1.20975e7i 0.261979 + 0.453762i
\(935\) 1266.40 + 2193.47i 4.73742e−5 + 8.20544e-5i
\(936\) 5.31859e6 9.21207e6i 0.198430 0.343691i
\(937\) −2.87696e7 −1.07049 −0.535247 0.844696i \(-0.679781\pi\)
−0.535247 + 0.844696i \(0.679781\pi\)
\(938\) 0 0
\(939\) 2.85493e6 0.105665
\(940\) 4.56071e6 7.89938e6i 0.168350 0.291591i
\(941\) −1.08189e7 1.87390e7i −0.398300 0.689876i 0.595216 0.803566i \(-0.297066\pi\)
−0.993516 + 0.113689i \(0.963733\pi\)
\(942\) 1.75567e6 + 3.04091e6i 0.0644637 + 0.111654i
\(943\) −2.20670e7 + 3.82211e7i −0.808096 + 1.39966i
\(944\) 1.30911e6 0.0478132
\(945\) 0 0
\(946\) 200605. 0.00728809
\(947\) 3.15627e6 5.46682e6i 0.114367 0.198089i −0.803160 0.595764i \(-0.796849\pi\)
0.917526 + 0.397675i \(0.130183\pi\)
\(948\) 2.23430e6 + 3.86992e6i 0.0807460 + 0.139856i
\(949\) 1.14893e7 + 1.99001e7i 0.414122 + 0.717280i
\(950\) −4.82415e6 + 8.35566e6i −0.173425 + 0.300381i
\(951\) 1.41413e7 0.507036
\(952\) 0 0
\(953\) −5.59599e6 −0.199593 −0.0997963 0.995008i \(-0.531819\pi\)
−0.0997963 + 0.995008i \(0.531819\pi\)
\(954\) −2.41105e6 + 4.17606e6i −0.0857699 + 0.148558i
\(955\) −1.08604e6 1.88108e6i −0.0385334 0.0667418i
\(956\) 1.23452e7 + 2.13826e7i 0.436873 + 0.756686i
\(957\) −24536.8 + 42498.9i −0.000866039 + 0.00150002i
\(958\) 2.58438e7 0.909792
\(959\) 0 0
\(960\) 1.51606e6 0.0530933
\(961\) −920457. + 1.59428e6i −0.0321510 + 0.0556872i
\(962\) −7.40932e6 1.28333e7i −0.258131 0.447097i
\(963\) 8.20816e6 + 1.42169e7i 0.285220 + 0.494016i
\(964\) 1.00858e6 1.74691e6i 0.0349555 0.0605448i
\(965\) −1.07312e7 −0.370963
\(966\) 0 0
\(967\) 1.33277e7 0.458340 0.229170 0.973386i \(-0.426399\pi\)
0.229170 + 0.973386i \(0.426399\pi\)
\(968\) 1.35524e7 2.34735e7i 0.464867 0.805173i
\(969\) −239659. 415102.i −0.00819946 0.0142019i
\(970\) 378293. + 655222.i 0.0129092 + 0.0223593i
\(971\) 1.81628e7 3.14590e7i 0.618210 1.07077i −0.371603 0.928392i \(-0.621192\pi\)
0.989812 0.142379i \(-0.0454751\pi\)
\(972\) −1.32517e6 −0.0449889
\(973\) 0 0
\(974\) −1.84973e6 −0.0624758
\(975\) −1.03040e7 + 1.78471e7i −0.347133 + 0.601252i
\(976\) −3.63416e6 6.29454e6i −0.122118 0.211514i
\(977\) 4.51869e6 + 7.82661e6i 0.151453 + 0.262323i 0.931762 0.363071i \(-0.118272\pi\)
−0.780309 + 0.625394i \(0.784938\pi\)
\(978\) −3.28038e6 + 5.68179e6i −0.109667 + 0.189949i
\(979\) −75278.0 −0.00251022
\(980\) 0 0
\(981\) 1.13026e7 0.374977
\(982\) 4.27819e6 7.41005e6i 0.141573 0.245212i
\(983\) −9.92693e6 1.71939e7i −0.327666 0.567534i 0.654382 0.756164i \(-0.272929\pi\)
−0.982048 + 0.188630i \(0.939595\pi\)
\(984\) −8.14819e6 1.41131e7i −0.268271 0.464658i
\(985\) 2.34669e6 4.06459e6i 0.0770665 0.133483i
\(986\) 230261. 0.00754273
\(987\) 0 0
\(988\) 1.86196e7 0.606846
\(989\) −3.63000e7 + 6.28734e7i −1.18009 + 2.04398i
\(990\) −6332.14 10967.6i −0.000205335 0.000355650i
\(991\) 2.27779e7 + 3.94524e7i 0.736764 + 1.27611i 0.953945 + 0.299982i \(0.0969806\pi\)
−0.217181 + 0.976131i \(0.569686\pi\)
\(992\) 1.65530e7 2.86706e7i 0.534069 0.925034i
\(993\) 1.38449e7 0.445570
\(994\) 0 0
\(995\) 4.08963e6 0.130956
\(996\) −393486. + 681538.i −0.0125684 + 0.0217692i
\(997\) 2.25832e7 + 3.91153e7i 0.719529 + 1.24626i 0.961187 + 0.275899i \(0.0889756\pi\)
−0.241658 + 0.970362i \(0.577691\pi\)
\(998\) 4.69805e6 + 8.13726e6i 0.149311 + 0.258614i
\(999\) −2.23922e6 + 3.87845e6i −0.0709877 + 0.122954i
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 147.6.e.p.79.4 12
7.2 even 3 147.6.a.o.1.3 yes 6
7.3 odd 6 147.6.e.q.67.4 12
7.4 even 3 inner 147.6.e.p.67.4 12
7.5 odd 6 147.6.a.n.1.3 6
7.6 odd 2 147.6.e.q.79.4 12
21.2 odd 6 441.6.a.ba.1.4 6
21.5 even 6 441.6.a.bb.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.6.a.n.1.3 6 7.5 odd 6
147.6.a.o.1.3 yes 6 7.2 even 3
147.6.e.p.67.4 12 7.4 even 3 inner
147.6.e.p.79.4 12 1.1 even 1 trivial
147.6.e.q.67.4 12 7.3 odd 6
147.6.e.q.79.4 12 7.6 odd 2
441.6.a.ba.1.4 6 21.2 odd 6
441.6.a.bb.1.4 6 21.5 even 6