Properties

Label 147.6.e.n.79.1
Level $147$
Weight $6$
Character 147.79
Analytic conductor $23.576$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(-3.22311 + 5.58259i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.6.e.n.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.72311 + 4.71657i) q^{2} +(4.50000 + 7.79423i) q^{3} +(1.16933 + 2.02534i) q^{4} +(-18.0000 + 31.1769i) q^{5} -49.0160 q^{6} -187.016 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-2.72311 + 4.71657i) q^{2} +(4.50000 + 7.79423i) q^{3} +(1.16933 + 2.02534i) q^{4} +(-18.0000 + 31.1769i) q^{5} -49.0160 q^{6} -187.016 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-98.0320 - 169.796i) q^{10} +(-92.2151 - 159.721i) q^{11} +(-10.5240 + 18.2281i) q^{12} +147.872 q^{13} -324.000 q^{15} +(471.847 - 817.262i) q^{16} +(-984.192 - 1704.67i) q^{17} +(-220.572 - 382.042i) q^{18} +(-946.256 + 1638.96i) q^{19} -84.1920 q^{20} +1004.45 q^{22} +(-68.4942 + 118.635i) q^{23} +(-841.572 - 1457.65i) q^{24} +(914.500 + 1583.96i) q^{25} +(-402.672 + 697.448i) q^{26} -729.000 q^{27} -1259.58 q^{29} +(882.288 - 1528.17i) q^{30} +(-4484.51 - 7767.40i) q^{31} +(-422.474 - 731.747i) q^{32} +(829.936 - 1437.49i) q^{33} +10720.3 q^{34} -189.432 q^{36} +(-6448.61 + 11169.3i) q^{37} +(-5153.52 - 8926.16i) q^{38} +(665.424 + 1152.55i) q^{39} +(3366.29 - 5830.58i) q^{40} +8975.62 q^{41} +13538.9 q^{43} +(215.660 - 373.535i) q^{44} +(-1458.00 - 2525.33i) q^{45} +(-373.035 - 646.115i) q^{46} +(10023.1 - 17360.5i) q^{47} +8493.24 q^{48} -9961.14 q^{50} +(8857.73 - 15342.0i) q^{51} +(172.912 + 299.492i) q^{52} +(-4667.16 - 8083.76i) q^{53} +(1985.15 - 3438.38i) q^{54} +6639.49 q^{55} -17032.6 q^{57} +(3429.98 - 5940.90i) q^{58} +(-4433.23 - 7678.58i) q^{59} +(-378.864 - 656.212i) q^{60} +(20574.2 - 35635.5i) q^{61} +48847.3 q^{62} +34800.0 q^{64} +(-2661.70 + 4610.19i) q^{65} +(4520.02 + 7828.90i) q^{66} +(27675.8 + 47935.8i) q^{67} +(2301.70 - 3986.65i) q^{68} -1232.90 q^{69} -63866.8 q^{71} +(7574.15 - 13118.8i) q^{72} +(-20649.7 - 35766.3i) q^{73} +(-35120.5 - 60830.6i) q^{74} +(-8230.50 + 14255.6i) q^{75} -4425.95 q^{76} -7248.09 q^{78} +(-8481.76 + 14690.8i) q^{79} +(16986.5 + 29421.4i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-24441.6 + 42334.1i) q^{82} -101693. q^{83} +70861.8 q^{85} +(-36868.0 + 63857.3i) q^{86} +(-5668.12 - 9817.47i) q^{87} +(17245.7 + 29870.4i) q^{88} +(-43551.3 + 75433.0i) q^{89} +15881.2 q^{90} -320.370 q^{92} +(40360.6 - 69906.6i) q^{93} +(54587.9 + 94549.0i) q^{94} +(-34065.2 - 59002.7i) q^{95} +(3802.27 - 6585.72i) q^{96} -118107. q^{97} +14938.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} + 18 q^{3} - 37 q^{4} - 72 q^{5} + 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} + 18 q^{3} - 37 q^{4} - 72 q^{5} + 54 q^{6} - 498 q^{8} - 162 q^{9} + 108 q^{10} - 480 q^{11} + 333 q^{12} + 2592 q^{13} - 1296 q^{15} + 1679 q^{16} - 936 q^{17} + 243 q^{18} + 216 q^{19} + 2664 q^{20} - 2984 q^{22} + 504 q^{23} - 2241 q^{24} + 3658 q^{25} + 8892 q^{26} - 2916 q^{27} + 12744 q^{29} - 972 q^{30} - 9936 q^{31} - 9039 q^{32} + 4320 q^{33} + 38880 q^{34} + 5994 q^{36} - 11124 q^{37} - 28116 q^{38} + 11664 q^{39} + 8964 q^{40} + 41904 q^{41} - 12528 q^{43} - 11196 q^{44} - 5832 q^{45} - 6160 q^{46} - 7920 q^{47} + 30222 q^{48} + 10974 q^{50} + 8424 q^{51} - 44820 q^{52} - 2220 q^{53} - 2187 q^{54} + 34560 q^{55} + 3888 q^{57} + 71318 q^{58} - 29736 q^{59} + 11988 q^{60} + 17280 q^{61} + 81360 q^{62} - 21758 q^{64} - 46656 q^{65} - 13428 q^{66} + 20680 q^{67} + 45216 q^{68} + 9072 q^{69} - 184560 q^{71} + 20169 q^{72} - 56592 q^{73} - 85218 q^{74} - 32922 q^{75} - 174744 q^{76} + 160056 q^{78} + 56096 q^{79} + 60444 q^{80} - 13122 q^{81} + 52272 q^{82} - 142704 q^{83} + 67392 q^{85} - 240996 q^{86} + 57348 q^{87} + 52812 q^{88} - 123192 q^{89} - 17496 q^{90} - 51072 q^{92} + 89424 q^{93} + 345384 q^{94} + 7776 q^{95} + 81351 q^{96} + 71712 q^{97} + 77760 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72311 + 4.71657i −0.481383 + 0.833779i −0.999772 0.0213658i \(-0.993199\pi\)
0.518389 + 0.855145i \(0.326532\pi\)
\(3\) 4.50000 + 7.79423i 0.288675 + 0.500000i
\(4\) 1.16933 + 2.02534i 0.0365417 + 0.0632920i
\(5\) −18.0000 + 31.1769i −0.321994 + 0.557710i −0.980899 0.194516i \(-0.937686\pi\)
0.658906 + 0.752226i \(0.271020\pi\)
\(6\) −49.0160 −0.555853
\(7\) 0 0
\(8\) −187.016 −1.03313
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) −98.0320 169.796i −0.310004 0.536943i
\(11\) −92.2151 159.721i −0.229784 0.397998i 0.727960 0.685620i \(-0.240469\pi\)
−0.957744 + 0.287622i \(0.907135\pi\)
\(12\) −10.5240 + 18.2281i −0.0210973 + 0.0365417i
\(13\) 147.872 0.242676 0.121338 0.992611i \(-0.461281\pi\)
0.121338 + 0.992611i \(0.461281\pi\)
\(14\) 0 0
\(15\) −324.000 −0.371806
\(16\) 471.847 817.262i 0.460788 0.798108i
\(17\) −984.192 1704.67i −0.825957 1.43060i −0.901186 0.433433i \(-0.857302\pi\)
0.0752284 0.997166i \(-0.476031\pi\)
\(18\) −220.572 382.042i −0.160461 0.277926i
\(19\) −946.256 + 1638.96i −0.601346 + 1.04156i 0.391271 + 0.920275i \(0.372035\pi\)
−0.992617 + 0.121287i \(0.961298\pi\)
\(20\) −84.1920 −0.0470647
\(21\) 0 0
\(22\) 1004.45 0.442457
\(23\) −68.4942 + 118.635i −0.0269982 + 0.0467622i −0.879209 0.476437i \(-0.841928\pi\)
0.852211 + 0.523199i \(0.175261\pi\)
\(24\) −841.572 1457.65i −0.298238 0.516564i
\(25\) 914.500 + 1583.96i 0.292640 + 0.506867i
\(26\) −402.672 + 697.448i −0.116820 + 0.202339i
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) −1259.58 −0.278120 −0.139060 0.990284i \(-0.544408\pi\)
−0.139060 + 0.990284i \(0.544408\pi\)
\(30\) 882.288 1528.17i 0.178981 0.310004i
\(31\) −4484.51 7767.40i −0.838129 1.45168i −0.891457 0.453105i \(-0.850316\pi\)
0.0533279 0.998577i \(-0.483017\pi\)
\(32\) −422.474 731.747i −0.0729332 0.126324i
\(33\) 829.936 1437.49i 0.132666 0.229784i
\(34\) 10720.3 1.59041
\(35\) 0 0
\(36\) −189.432 −0.0243611
\(37\) −6448.61 + 11169.3i −0.774393 + 1.34129i 0.160742 + 0.986996i \(0.448611\pi\)
−0.935135 + 0.354292i \(0.884722\pi\)
\(38\) −5153.52 8926.16i −0.578955 1.00278i
\(39\) 665.424 + 1152.55i 0.0700547 + 0.121338i
\(40\) 3366.29 5830.58i 0.332661 0.576185i
\(41\) 8975.62 0.833882 0.416941 0.908934i \(-0.363102\pi\)
0.416941 + 0.908934i \(0.363102\pi\)
\(42\) 0 0
\(43\) 13538.9 1.11664 0.558320 0.829626i \(-0.311446\pi\)
0.558320 + 0.829626i \(0.311446\pi\)
\(44\) 215.660 373.535i 0.0167934 0.0290870i
\(45\) −1458.00 2525.33i −0.107331 0.185903i
\(46\) −373.035 646.115i −0.0259929 0.0450210i
\(47\) 10023.1 17360.5i 0.661845 1.14635i −0.318286 0.947995i \(-0.603107\pi\)
0.980130 0.198354i \(-0.0635596\pi\)
\(48\) 8493.24 0.532072
\(49\) 0 0
\(50\) −9961.14 −0.563487
\(51\) 8857.73 15342.0i 0.476867 0.825957i
\(52\) 172.912 + 299.492i 0.00886780 + 0.0153595i
\(53\) −4667.16 8083.76i −0.228225 0.395297i 0.729057 0.684453i \(-0.239959\pi\)
−0.957282 + 0.289155i \(0.906626\pi\)
\(54\) 1985.15 3438.38i 0.0926421 0.160461i
\(55\) 6639.49 0.295956
\(56\) 0 0
\(57\) −17032.6 −0.694375
\(58\) 3429.98 5940.90i 0.133882 0.231890i
\(59\) −4433.23 7678.58i −0.165802 0.287178i 0.771138 0.636668i \(-0.219688\pi\)
−0.936940 + 0.349491i \(0.886355\pi\)
\(60\) −378.864 656.212i −0.0135864 0.0235324i
\(61\) 20574.2 35635.5i 0.707942 1.22619i −0.257678 0.966231i \(-0.582957\pi\)
0.965619 0.259960i \(-0.0837094\pi\)
\(62\) 48847.3 1.61384
\(63\) 0 0
\(64\) 34800.0 1.06201
\(65\) −2661.70 + 4610.19i −0.0781403 + 0.135343i
\(66\) 4520.02 + 7828.90i 0.127726 + 0.221228i
\(67\) 27675.8 + 47935.8i 0.753204 + 1.30459i 0.946262 + 0.323400i \(0.104826\pi\)
−0.193058 + 0.981187i \(0.561841\pi\)
\(68\) 2301.70 3986.65i 0.0603637 0.104553i
\(69\) −1232.90 −0.0311748
\(70\) 0 0
\(71\) −63866.8 −1.50359 −0.751794 0.659398i \(-0.770811\pi\)
−0.751794 + 0.659398i \(0.770811\pi\)
\(72\) 7574.15 13118.8i 0.172188 0.298238i
\(73\) −20649.7 35766.3i −0.453530 0.785537i 0.545073 0.838389i \(-0.316502\pi\)
−0.998602 + 0.0528522i \(0.983169\pi\)
\(74\) −35120.5 60830.6i −0.745559 1.29135i
\(75\) −8230.50 + 14255.6i −0.168956 + 0.292640i
\(76\) −4425.95 −0.0878968
\(77\) 0 0
\(78\) −7248.09 −0.134892
\(79\) −8481.76 + 14690.8i −0.152904 + 0.264837i −0.932294 0.361702i \(-0.882196\pi\)
0.779390 + 0.626539i \(0.215529\pi\)
\(80\) 16986.5 + 29421.4i 0.296742 + 0.513972i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) −24441.6 + 42334.1i −0.401416 + 0.695273i
\(83\) −101693. −1.62030 −0.810150 0.586223i \(-0.800614\pi\)
−0.810150 + 0.586223i \(0.800614\pi\)
\(84\) 0 0
\(85\) 70861.8 1.06381
\(86\) −36868.0 + 63857.3i −0.537531 + 0.931031i
\(87\) −5668.12 9817.47i −0.0802862 0.139060i
\(88\) 17245.7 + 29870.4i 0.237396 + 0.411183i
\(89\) −43551.3 + 75433.0i −0.582808 + 1.00945i 0.412336 + 0.911032i \(0.364713\pi\)
−0.995145 + 0.0984220i \(0.968621\pi\)
\(90\) 15881.2 0.206670
\(91\) 0 0
\(92\) −320.370 −0.00394623
\(93\) 40360.6 69906.6i 0.483894 0.838129i
\(94\) 54587.9 + 94549.0i 0.637201 + 1.10366i
\(95\) −34065.2 59002.7i −0.387260 0.670753i
\(96\) 3802.27 6585.72i 0.0421080 0.0729332i
\(97\) −118107. −1.27452 −0.637258 0.770650i \(-0.719932\pi\)
−0.637258 + 0.770650i \(0.719932\pi\)
\(98\) 0 0
\(99\) 14938.8 0.153190
\(100\) −2138.71 + 3704.35i −0.0213871 + 0.0370435i
\(101\) −11116.4 19254.1i −0.108432 0.187811i 0.806703 0.590957i \(-0.201250\pi\)
−0.915135 + 0.403147i \(0.867916\pi\)
\(102\) 48241.2 + 83556.1i 0.459111 + 0.795203i
\(103\) −67965.3 + 117719.i −0.631239 + 1.09334i 0.356059 + 0.934463i \(0.384120\pi\)
−0.987299 + 0.158875i \(0.949213\pi\)
\(104\) −27654.4 −0.250716
\(105\) 0 0
\(106\) 50836.8 0.439454
\(107\) −58813.1 + 101867.i −0.496609 + 0.860152i −0.999992 0.00391112i \(-0.998755\pi\)
0.503383 + 0.864063i \(0.332088\pi\)
\(108\) −852.444 1476.48i −0.00703244 0.0121806i
\(109\) 17332.1 + 30020.1i 0.139729 + 0.242017i 0.927394 0.374086i \(-0.122044\pi\)
−0.787665 + 0.616103i \(0.788710\pi\)
\(110\) −18080.1 + 31315.6i −0.142468 + 0.246762i
\(111\) −116075. −0.894192
\(112\) 0 0
\(113\) −26584.5 −0.195854 −0.0979269 0.995194i \(-0.531221\pi\)
−0.0979269 + 0.995194i \(0.531221\pi\)
\(114\) 46381.7 80335.4i 0.334260 0.578955i
\(115\) −2465.79 4270.88i −0.0173865 0.0301143i
\(116\) −1472.87 2551.09i −0.0101629 0.0176027i
\(117\) −5988.82 + 10372.9i −0.0404461 + 0.0700547i
\(118\) 48288.7 0.319257
\(119\) 0 0
\(120\) 60593.2 0.384123
\(121\) 63518.2 110017.i 0.394398 0.683118i
\(122\) 112051. + 194079.i 0.681582 + 1.18053i
\(123\) 40390.3 + 69958.0i 0.240721 + 0.416941i
\(124\) 10487.8 18165.4i 0.0612533 0.106094i
\(125\) −178344. −1.02090
\(126\) 0 0
\(127\) −137111. −0.754334 −0.377167 0.926145i \(-0.623102\pi\)
−0.377167 + 0.926145i \(0.623102\pi\)
\(128\) −81245.0 + 140720.i −0.438300 + 0.759158i
\(129\) 60925.2 + 105526.i 0.322346 + 0.558320i
\(130\) −14496.2 25108.1i −0.0752308 0.130304i
\(131\) 27044.6 46842.6i 0.137690 0.238486i −0.788932 0.614481i \(-0.789366\pi\)
0.926622 + 0.375995i \(0.122699\pi\)
\(132\) 3881.89 0.0193913
\(133\) 0 0
\(134\) −301457. −1.45032
\(135\) 13122.0 22728.0i 0.0619677 0.107331i
\(136\) 184060. + 318801.i 0.853319 + 1.47799i
\(137\) −211424. 366198.i −0.962395 1.66692i −0.716456 0.697632i \(-0.754237\pi\)
−0.245939 0.969285i \(-0.579096\pi\)
\(138\) 3357.31 5815.04i 0.0150070 0.0259929i
\(139\) −9913.38 −0.0435196 −0.0217598 0.999763i \(-0.506927\pi\)
−0.0217598 + 0.999763i \(0.506927\pi\)
\(140\) 0 0
\(141\) 180415. 0.764233
\(142\) 173916. 301232.i 0.723801 1.25366i
\(143\) −13636.0 23618.3i −0.0557632 0.0965848i
\(144\) 38219.6 + 66198.3i 0.153596 + 0.266036i
\(145\) 22672.5 39269.9i 0.0895528 0.155110i
\(146\) 224925. 0.873285
\(147\) 0 0
\(148\) −30162.3 −0.113190
\(149\) −252731. + 437743.i −0.932595 + 1.61530i −0.153727 + 0.988113i \(0.549128\pi\)
−0.778868 + 0.627188i \(0.784206\pi\)
\(150\) −44825.1 77639.4i −0.162665 0.281744i
\(151\) 96551.4 + 167232.i 0.344601 + 0.596866i 0.985281 0.170942i \(-0.0546810\pi\)
−0.640680 + 0.767808i \(0.721348\pi\)
\(152\) 176965. 306512.i 0.621267 1.07607i
\(153\) 159439. 0.550638
\(154\) 0 0
\(155\) 322885. 1.07949
\(156\) −1556.20 + 2695.43i −0.00511983 + 0.00886780i
\(157\) −132462. 229430.i −0.428885 0.742850i 0.567890 0.823105i \(-0.307760\pi\)
−0.996774 + 0.0802545i \(0.974427\pi\)
\(158\) −46193.5 80009.6i −0.147210 0.254976i
\(159\) 42004.5 72753.9i 0.131766 0.228225i
\(160\) 30418.1 0.0939362
\(161\) 0 0
\(162\) 35732.7 0.106974
\(163\) 269546. 466868.i 0.794629 1.37634i −0.128446 0.991717i \(-0.540999\pi\)
0.923075 0.384621i \(-0.125668\pi\)
\(164\) 10495.5 + 18178.7i 0.0304714 + 0.0527781i
\(165\) 29877.7 + 51749.7i 0.0854353 + 0.147978i
\(166\) 276921. 479641.i 0.779984 1.35097i
\(167\) 218748. 0.606949 0.303475 0.952840i \(-0.401853\pi\)
0.303475 + 0.952840i \(0.401853\pi\)
\(168\) 0 0
\(169\) −349427. −0.941108
\(170\) −192965. + 334225.i −0.512101 + 0.886984i
\(171\) −76646.7 132756.i −0.200449 0.347187i
\(172\) 15831.5 + 27421.0i 0.0408039 + 0.0706744i
\(173\) −295101. + 511129.i −0.749644 + 1.29842i 0.198350 + 0.980131i \(0.436442\pi\)
−0.947994 + 0.318289i \(0.896892\pi\)
\(174\) 61739.7 0.154593
\(175\) 0 0
\(176\) −174046. −0.423527
\(177\) 39899.1 69107.2i 0.0957260 0.165802i
\(178\) −237190. 410825.i −0.561108 0.971867i
\(179\) 108676. + 188232.i 0.253513 + 0.439098i 0.964491 0.264117i \(-0.0850805\pi\)
−0.710977 + 0.703215i \(0.751747\pi\)
\(180\) 3409.78 5905.90i 0.00784412 0.0135864i
\(181\) 188109. 0.426790 0.213395 0.976966i \(-0.431548\pi\)
0.213395 + 0.976966i \(0.431548\pi\)
\(182\) 0 0
\(183\) 370335. 0.817461
\(184\) 12809.5 22186.7i 0.0278925 0.0483113i
\(185\) −232150. 402095.i −0.498700 0.863773i
\(186\) 219813. + 380727.i 0.465876 + 0.806922i
\(187\) −181515. + 314393.i −0.379584 + 0.657459i
\(188\) 46881.2 0.0967396
\(189\) 0 0
\(190\) 371053. 0.745680
\(191\) −86761.3 + 150275.i −0.172085 + 0.298060i −0.939149 0.343511i \(-0.888384\pi\)
0.767064 + 0.641571i \(0.221717\pi\)
\(192\) 156600. + 271239.i 0.306576 + 0.531005i
\(193\) −58890.7 102002.i −0.113803 0.197113i 0.803498 0.595308i \(-0.202970\pi\)
−0.917301 + 0.398195i \(0.869637\pi\)
\(194\) 321618. 557059.i 0.613530 1.06267i
\(195\) −47910.5 −0.0902287
\(196\) 0 0
\(197\) 224734. 0.412575 0.206288 0.978491i \(-0.433862\pi\)
0.206288 + 0.978491i \(0.433862\pi\)
\(198\) −40680.1 + 70460.1i −0.0737428 + 0.127726i
\(199\) −370137. 641096.i −0.662567 1.14760i −0.979939 0.199298i \(-0.936134\pi\)
0.317372 0.948301i \(-0.397199\pi\)
\(200\) −171026. 296226.i −0.302334 0.523658i
\(201\) −249082. + 431422.i −0.434862 + 0.753204i
\(202\) 121084. 0.208790
\(203\) 0 0
\(204\) 41430.5 0.0697020
\(205\) −161561. + 279832.i −0.268505 + 0.465064i
\(206\) −370154. 641126.i −0.607735 1.05263i
\(207\) −5548.03 9609.47i −0.00899939 0.0155874i
\(208\) 69772.9 120850.i 0.111822 0.193682i
\(209\) 349036. 0.552720
\(210\) 0 0
\(211\) −705896. −1.09153 −0.545763 0.837939i \(-0.683760\pi\)
−0.545763 + 0.837939i \(0.683760\pi\)
\(212\) 10914.9 18905.2i 0.0166794 0.0288896i
\(213\) −287400. 497792.i −0.434049 0.751794i
\(214\) −320309. 554792.i −0.478118 0.828124i
\(215\) −243701. + 422102.i −0.359551 + 0.622761i
\(216\) 136335. 0.198825
\(217\) 0 0
\(218\) −188789. −0.269052
\(219\) 185847. 321896.i 0.261846 0.453530i
\(220\) 7763.77 + 13447.2i 0.0108147 + 0.0187317i
\(221\) −145534. 252073.i −0.200440 0.347173i
\(222\) 316085. 547475.i 0.430449 0.745559i
\(223\) 42214.3 0.0568456 0.0284228 0.999596i \(-0.490952\pi\)
0.0284228 + 0.999596i \(0.490952\pi\)
\(224\) 0 0
\(225\) −148149. −0.195093
\(226\) 72392.5 125387.i 0.0942806 0.163299i
\(227\) −371201. 642940.i −0.478129 0.828144i 0.521557 0.853217i \(-0.325351\pi\)
−0.999686 + 0.0250731i \(0.992018\pi\)
\(228\) −19916.8 34496.9i −0.0253736 0.0439484i
\(229\) −470618. + 815134.i −0.593034 + 1.02717i 0.400787 + 0.916171i \(0.368737\pi\)
−0.993821 + 0.110994i \(0.964596\pi\)
\(230\) 26858.5 0.0334782
\(231\) 0 0
\(232\) 235562. 0.287333
\(233\) 256166. 443692.i 0.309123 0.535416i −0.669048 0.743219i \(-0.733298\pi\)
0.978171 + 0.207803i \(0.0666313\pi\)
\(234\) −32616.4 56493.3i −0.0389401 0.0674462i
\(235\) 360831. + 624977.i 0.426220 + 0.738234i
\(236\) 10367.8 17957.6i 0.0121174 0.0209879i
\(237\) −152672. −0.176558
\(238\) 0 0
\(239\) −115323. −0.130593 −0.0652966 0.997866i \(-0.520799\pi\)
−0.0652966 + 0.997866i \(0.520799\pi\)
\(240\) −152878. + 264793.i −0.171324 + 0.296742i
\(241\) 454932. + 787965.i 0.504549 + 0.873905i 0.999986 + 0.00526118i \(0.00167469\pi\)
−0.495437 + 0.868644i \(0.664992\pi\)
\(242\) 345934. + 599176.i 0.379713 + 0.657682i
\(243\) 29524.5 51137.9i 0.0320750 0.0555556i
\(244\) 96232.2 0.103477
\(245\) 0 0
\(246\) −439949. −0.463516
\(247\) −139925. + 242357.i −0.145933 + 0.252763i
\(248\) 838675. + 1.45263e6i 0.865894 + 1.49977i
\(249\) −457618. 792618.i −0.467740 0.810150i
\(250\) 485651. 841171.i 0.491444 0.851206i
\(251\) −321264. −0.321868 −0.160934 0.986965i \(-0.551451\pi\)
−0.160934 + 0.986965i \(0.551451\pi\)
\(252\) 0 0
\(253\) 25264.8 0.0248150
\(254\) 373369. 646694.i 0.363123 0.628948i
\(255\) 318878. + 552313.i 0.307096 + 0.531906i
\(256\) 114321. + 198010.i 0.109025 + 0.188837i
\(257\) 278246. 481936.i 0.262782 0.455152i −0.704198 0.710004i \(-0.748693\pi\)
0.966980 + 0.254851i \(0.0820265\pi\)
\(258\) −663624. −0.620688
\(259\) 0 0
\(260\) −12449.6 −0.0114215
\(261\) 51013.1 88357.2i 0.0463533 0.0802862i
\(262\) 147291. + 255115.i 0.132563 + 0.229606i
\(263\) 116690. + 202112.i 0.104026 + 0.180179i 0.913340 0.407198i \(-0.133494\pi\)
−0.809314 + 0.587377i \(0.800161\pi\)
\(264\) −155211. + 268834.i −0.137061 + 0.237396i
\(265\) 336036. 0.293948
\(266\) 0 0
\(267\) −783923. −0.672969
\(268\) −64724.4 + 112106.i −0.0550466 + 0.0953436i
\(269\) 739286. + 1.28048e6i 0.622919 + 1.07893i 0.988939 + 0.148321i \(0.0473868\pi\)
−0.366020 + 0.930607i \(0.619280\pi\)
\(270\) 71465.3 + 123782.i 0.0596604 + 0.103335i
\(271\) −88880.8 + 153946.i −0.0735165 + 0.127334i −0.900440 0.434980i \(-0.856755\pi\)
0.826924 + 0.562314i \(0.190089\pi\)
\(272\) −1.85755e6 −1.52236
\(273\) 0 0
\(274\) 2.30293e6 1.85312
\(275\) 168661. 292130.i 0.134488 0.232940i
\(276\) −1441.67 2497.04i −0.00113918 0.00197312i
\(277\) 611259. + 1.05873e6i 0.478659 + 0.829062i 0.999701 0.0244697i \(-0.00778972\pi\)
−0.521042 + 0.853531i \(0.674456\pi\)
\(278\) 26995.2 46757.1i 0.0209496 0.0362857i
\(279\) 726491. 0.558753
\(280\) 0 0
\(281\) 177799. 0.134327 0.0671636 0.997742i \(-0.478605\pi\)
0.0671636 + 0.997742i \(0.478605\pi\)
\(282\) −491291. + 850941.i −0.367888 + 0.637201i
\(283\) 545259. + 944416.i 0.404703 + 0.700966i 0.994287 0.106741i \(-0.0340415\pi\)
−0.589584 + 0.807707i \(0.700708\pi\)
\(284\) −74681.5 129352.i −0.0549436 0.0951651i
\(285\) 306587. 531024.i 0.223584 0.387260i
\(286\) 148530. 0.107374
\(287\) 0 0
\(288\) 68440.8 0.0486221
\(289\) −1.22734e6 + 2.12581e6i −0.864410 + 1.49720i
\(290\) 123479. + 213872.i 0.0862183 + 0.149334i
\(291\) −531481. 920551.i −0.367921 0.637258i
\(292\) 48292.7 83645.4i 0.0331455 0.0574096i
\(293\) 545742. 0.371380 0.185690 0.982608i \(-0.440548\pi\)
0.185690 + 0.982608i \(0.440548\pi\)
\(294\) 0 0
\(295\) 319193. 0.213549
\(296\) 1.20599e6 2.08884e6i 0.800047 1.38572i
\(297\) 67224.8 + 116437.i 0.0442220 + 0.0765948i
\(298\) −1.37643e6 2.38405e6i −0.897870 1.55516i
\(299\) −10128.4 + 17542.9i −0.00655182 + 0.0113481i
\(300\) −38496.8 −0.0246957
\(301\) 0 0
\(302\) −1.05168e6 −0.663539
\(303\) 100047. 173287.i 0.0626035 0.108432i
\(304\) 892975. + 1.54668e6i 0.554186 + 0.959878i
\(305\) 740670. + 1.28288e6i 0.455906 + 0.789652i
\(306\) −434170. + 752005.i −0.265068 + 0.459111i
\(307\) −3.29000e6 −1.99228 −0.996138 0.0878052i \(-0.972015\pi\)
−0.996138 + 0.0878052i \(0.972015\pi\)
\(308\) 0 0
\(309\) −1.22338e6 −0.728892
\(310\) −879251. + 1.52291e6i −0.519647 + 0.900056i
\(311\) 349856. + 605968.i 0.205111 + 0.355262i 0.950168 0.311738i \(-0.100911\pi\)
−0.745057 + 0.667000i \(0.767578\pi\)
\(312\) −124445. 215545.i −0.0723754 0.125358i
\(313\) −311609. + 539723.i −0.179783 + 0.311394i −0.941806 0.336156i \(-0.890873\pi\)
0.762023 + 0.647550i \(0.224206\pi\)
\(314\) 1.44283e6 0.825831
\(315\) 0 0
\(316\) −39672.0 −0.0223494
\(317\) 319622. 553601.i 0.178644 0.309420i −0.762772 0.646667i \(-0.776162\pi\)
0.941416 + 0.337247i \(0.109496\pi\)
\(318\) 228766. + 396234.i 0.126860 + 0.219727i
\(319\) 116153. + 201182.i 0.0639075 + 0.110691i
\(320\) −626399. + 1.08496e6i −0.341961 + 0.592294i
\(321\) −1.05864e6 −0.573435
\(322\) 0 0
\(323\) 3.72519e6 1.98675
\(324\) 7671.99 13288.3i 0.00406018 0.00703244i
\(325\) 135229. + 234223.i 0.0710168 + 0.123005i
\(326\) 1.46801e6 + 2.54267e6i 0.765041 + 1.32509i
\(327\) −155989. + 270181.i −0.0806724 + 0.139729i
\(328\) −1.67858e6 −0.861506
\(329\) 0 0
\(330\) −325441. −0.164508
\(331\) −704817. + 1.22078e6i −0.353595 + 0.612445i −0.986876 0.161477i \(-0.948374\pi\)
0.633281 + 0.773922i \(0.281708\pi\)
\(332\) −118913. 205963.i −0.0592084 0.102552i
\(333\) −522337. 904714.i −0.258131 0.447096i
\(334\) −595674. + 1.03174e6i −0.292175 + 0.506062i
\(335\) −1.99265e6 −0.970108
\(336\) 0 0
\(337\) −1.55677e6 −0.746704 −0.373352 0.927690i \(-0.621792\pi\)
−0.373352 + 0.927690i \(0.621792\pi\)
\(338\) 951528. 1.64810e6i 0.453033 0.784676i
\(339\) −119630. 207205.i −0.0565381 0.0979269i
\(340\) 82861.1 + 143520.i 0.0388735 + 0.0673308i
\(341\) −827080. + 1.43254e6i −0.385178 + 0.667148i
\(342\) 834870. 0.385970
\(343\) 0 0
\(344\) −2.53200e6 −1.15363
\(345\) 22192.1 38437.9i 0.0100381 0.0173865i
\(346\) −1.60718e6 2.78372e6i −0.721731 1.25007i
\(347\) −124148. 215031.i −0.0553500 0.0958690i 0.837023 0.547168i \(-0.184294\pi\)
−0.892373 + 0.451299i \(0.850961\pi\)
\(348\) 13255.8 22959.8i 0.00586758 0.0101629i
\(349\) 1.86169e6 0.818171 0.409086 0.912496i \(-0.365848\pi\)
0.409086 + 0.912496i \(0.365848\pi\)
\(350\) 0 0
\(351\) −107799. −0.0467031
\(352\) −77917.0 + 134956.i −0.0335178 + 0.0580546i
\(353\) −885642. 1.53398e6i −0.378287 0.655212i 0.612526 0.790450i \(-0.290153\pi\)
−0.990813 + 0.135238i \(0.956820\pi\)
\(354\) 217299. + 376373.i 0.0921616 + 0.159629i
\(355\) 1.14960e6 1.99117e6i 0.484146 0.838566i
\(356\) −203704. −0.0851871
\(357\) 0 0
\(358\) −1.18375e6 −0.488147
\(359\) 2.23780e6 3.87599e6i 0.916401 1.58725i 0.111563 0.993757i \(-0.464414\pi\)
0.804837 0.593495i \(-0.202253\pi\)
\(360\) 272669. + 472277.i 0.110887 + 0.192062i
\(361\) −552751. 957393.i −0.223235 0.386654i
\(362\) −512243. + 887230.i −0.205449 + 0.355848i
\(363\) 1.14333e6 0.455412
\(364\) 0 0
\(365\) 1.48678e6 0.584135
\(366\) −1.00846e6 + 1.74671e6i −0.393511 + 0.681582i
\(367\) −1.58548e6 2.74614e6i −0.614465 1.06428i −0.990478 0.137670i \(-0.956039\pi\)
0.376014 0.926614i \(-0.377295\pi\)
\(368\) 64637.5 + 111955.i 0.0248809 + 0.0430949i
\(369\) −363512. + 629622.i −0.138980 + 0.240721i
\(370\) 2.52868e6 0.960261
\(371\) 0 0
\(372\) 188780. 0.0707292
\(373\) 1.15590e6 2.00207e6i 0.430177 0.745088i −0.566712 0.823916i \(-0.691785\pi\)
0.996888 + 0.0788285i \(0.0251179\pi\)
\(374\) −988570. 1.71225e6i −0.365450 0.632978i
\(375\) −802548. 1.39005e6i −0.294709 0.510450i
\(376\) −1.87447e6 + 3.24669e6i −0.683770 + 1.18432i
\(377\) −186257. −0.0674931
\(378\) 0 0
\(379\) −591840. −0.211644 −0.105822 0.994385i \(-0.533747\pi\)
−0.105822 + 0.994385i \(0.533747\pi\)
\(380\) 79667.2 137988.i 0.0283022 0.0490209i
\(381\) −617000. 1.06868e6i −0.217757 0.377167i
\(382\) −472521. 818431.i −0.165677 0.286961i
\(383\) 1.79883e6 3.11567e6i 0.626605 1.08531i −0.361623 0.932324i \(-0.617777\pi\)
0.988228 0.152987i \(-0.0488893\pi\)
\(384\) −1.46241e6 −0.506105
\(385\) 0 0
\(386\) 641464. 0.219131
\(387\) −548327. + 949730.i −0.186107 + 0.322346i
\(388\) −138106. 239207.i −0.0465730 0.0806667i
\(389\) 1.12373e6 + 1.94636e6i 0.376520 + 0.652152i 0.990553 0.137128i \(-0.0437873\pi\)
−0.614033 + 0.789280i \(0.710454\pi\)
\(390\) 130466. 225973.i 0.0434345 0.0752308i
\(391\) 269646. 0.0891973
\(392\) 0 0
\(393\) 486803. 0.158991
\(394\) −611976. + 1.05997e6i −0.198607 + 0.343997i
\(395\) −305343. 528870.i −0.0984681 0.170552i
\(396\) 17468.5 + 30256.3i 0.00559780 + 0.00969567i
\(397\) 2.29335e6 3.97220e6i 0.730288 1.26490i −0.226471 0.974018i \(-0.572719\pi\)
0.956760 0.290879i \(-0.0939477\pi\)
\(398\) 4.03169e6 1.27579
\(399\) 0 0
\(400\) 1.72602e6 0.539380
\(401\) −3.00216e6 + 5.19990e6i −0.932338 + 1.61486i −0.153023 + 0.988223i \(0.548901\pi\)
−0.779314 + 0.626633i \(0.784432\pi\)
\(402\) −1.35655e6 2.34962e6i −0.418670 0.725158i
\(403\) −663134. 1.14858e6i −0.203394 0.352289i
\(404\) 25997.5 45028.9i 0.00792461 0.0137258i
\(405\) 236196. 0.0715542
\(406\) 0 0
\(407\) 2.37864e6 0.711774
\(408\) −1.65654e6 + 2.86921e6i −0.492664 + 0.853319i
\(409\) 1.77670e6 + 3.07733e6i 0.525177 + 0.909633i 0.999570 + 0.0293196i \(0.00933407\pi\)
−0.474393 + 0.880313i \(0.657333\pi\)
\(410\) −879898. 1.52403e6i −0.258507 0.447747i
\(411\) 1.90282e6 3.29578e6i 0.555639 0.962395i
\(412\) −317896. −0.0922661
\(413\) 0 0
\(414\) 60431.6 0.0173286
\(415\) 1.83047e6 3.17047e6i 0.521726 0.903657i
\(416\) −62472.1 108205.i −0.0176992 0.0306559i
\(417\) −44610.2 77267.1i −0.0125630 0.0217598i
\(418\) −950465. + 1.64625e6i −0.266070 + 0.460846i
\(419\) 2.01375e6 0.560365 0.280182 0.959947i \(-0.409605\pi\)
0.280182 + 0.959947i \(0.409605\pi\)
\(420\) 0 0
\(421\) −5.89987e6 −1.62232 −0.811161 0.584823i \(-0.801164\pi\)
−0.811161 + 0.584823i \(0.801164\pi\)
\(422\) 1.92223e6 3.32940e6i 0.525442 0.910092i
\(423\) 811869. + 1.40620e6i 0.220615 + 0.382116i
\(424\) 872834. + 1.51179e6i 0.235786 + 0.408392i
\(425\) 1.80009e6 3.11784e6i 0.483416 0.837301i
\(426\) 3.13049e6 0.835774
\(427\) 0 0
\(428\) −275088. −0.0725877
\(429\) 122724. 212565.i 0.0321949 0.0557632i
\(430\) −1.32725e6 2.29886e6i −0.346163 0.599573i
\(431\) 1.90524e6 + 3.29997e6i 0.494033 + 0.855690i 0.999976 0.00687645i \(-0.00218886\pi\)
−0.505943 + 0.862567i \(0.668856\pi\)
\(432\) −343976. + 595784.i −0.0886786 + 0.153596i
\(433\) 6.59449e6 1.69029 0.845146 0.534536i \(-0.179513\pi\)
0.845146 + 0.534536i \(0.179513\pi\)
\(434\) 0 0
\(435\) 408105. 0.103407
\(436\) −40534.0 + 70207.0i −0.0102118 + 0.0176874i
\(437\) −129626. 224519.i −0.0324705 0.0562406i
\(438\) 1.01216e6 + 1.75312e6i 0.252096 + 0.436643i
\(439\) 2.27514e6 3.94065e6i 0.563438 0.975904i −0.433755 0.901031i \(-0.642812\pi\)
0.997193 0.0748729i \(-0.0238551\pi\)
\(440\) −1.24169e6 −0.305761
\(441\) 0 0
\(442\) 1.58523e6 0.385954
\(443\) −2.55769e6 + 4.43004e6i −0.619210 + 1.07250i 0.370420 + 0.928864i \(0.379214\pi\)
−0.989630 + 0.143639i \(0.954120\pi\)
\(444\) −135730. 235092.i −0.0326753 0.0565952i
\(445\) −1.56785e6 2.71559e6i −0.375321 0.650076i
\(446\) −114954. + 199106.i −0.0273645 + 0.0473967i
\(447\) −4.54916e6 −1.07687
\(448\) 0 0
\(449\) 5.95600e6 1.39424 0.697122 0.716953i \(-0.254464\pi\)
0.697122 + 0.716953i \(0.254464\pi\)
\(450\) 403426. 698755.i 0.0939145 0.162665i
\(451\) −827687. 1.43360e6i −0.191613 0.331883i
\(452\) −31086.1 53842.7i −0.00715682 0.0123960i
\(453\) −868962. + 1.50509e6i −0.198955 + 0.344601i
\(454\) 4.04329e6 0.920652
\(455\) 0 0
\(456\) 3.18537e6 0.717378
\(457\) 1.29917e6 2.25022e6i 0.290988 0.504006i −0.683056 0.730366i \(-0.739349\pi\)
0.974044 + 0.226361i \(0.0726828\pi\)
\(458\) −2.56309e6 4.43940e6i −0.570953 0.988919i
\(459\) 717476. + 1.24270e6i 0.158956 + 0.275319i
\(460\) 5766.66 9988.15i 0.00127066 0.00220085i
\(461\) 4.51513e6 0.989505 0.494752 0.869034i \(-0.335259\pi\)
0.494752 + 0.869034i \(0.335259\pi\)
\(462\) 0 0
\(463\) −5.55129e6 −1.20349 −0.601744 0.798689i \(-0.705527\pi\)
−0.601744 + 0.798689i \(0.705527\pi\)
\(464\) −594330. + 1.02941e6i −0.128154 + 0.221969i
\(465\) 1.45298e6 + 2.51664e6i 0.311622 + 0.539745i
\(466\) 1.39513e6 + 2.41644e6i 0.297613 + 0.515480i
\(467\) 3.97675e6 6.88794e6i 0.843794 1.46149i −0.0428708 0.999081i \(-0.513650\pi\)
0.886665 0.462413i \(-0.153016\pi\)
\(468\) −28011.7 −0.00591187
\(469\) 0 0
\(470\) −3.93033e6 −0.820699
\(471\) 1.19215e6 2.06487e6i 0.247617 0.428885i
\(472\) 829085. + 1.43602e6i 0.171295 + 0.296691i
\(473\) −1.24849e6 2.16246e6i −0.256586 0.444421i
\(474\) 415742. 720086.i 0.0849920 0.147210i
\(475\) −3.46140e6 −0.703912
\(476\) 0 0
\(477\) 756080. 0.152150
\(478\) 314037. 543928.i 0.0628653 0.108886i
\(479\) 3.28185e6 + 5.68433e6i 0.653552 + 1.13199i 0.982255 + 0.187552i \(0.0600553\pi\)
−0.328703 + 0.944433i \(0.606611\pi\)
\(480\) 136882. + 237086.i 0.0271170 + 0.0469681i
\(481\) −953568. + 1.65163e6i −0.187927 + 0.325499i
\(482\) −4.95532e6 −0.971525
\(483\) 0 0
\(484\) 297096. 0.0576479
\(485\) 2.12592e6 3.68221e6i 0.410387 0.710810i
\(486\) 160797. + 278509.i 0.0308807 + 0.0534870i
\(487\) −2.33185e6 4.03888e6i −0.445531 0.771683i 0.552558 0.833475i \(-0.313652\pi\)
−0.998089 + 0.0617918i \(0.980319\pi\)
\(488\) −3.84770e6 + 6.66441e6i −0.731394 + 1.26681i
\(489\) 4.85183e6 0.917558
\(490\) 0 0
\(491\) −917227. −0.171701 −0.0858506 0.996308i \(-0.527361\pi\)
−0.0858506 + 0.996308i \(0.527361\pi\)
\(492\) −94459.4 + 163608.i −0.0175927 + 0.0304714i
\(493\) 1.23967e6 + 2.14717e6i 0.229715 + 0.397878i
\(494\) −762061. 1.31993e6i −0.140499 0.243351i
\(495\) −268899. + 465747.i −0.0493261 + 0.0854353i
\(496\) −8.46401e6 −1.54480
\(497\) 0 0
\(498\) 4.98458e6 0.900648
\(499\) −156718. + 271443.i −0.0281752 + 0.0488009i −0.879769 0.475401i \(-0.842303\pi\)
0.851594 + 0.524202i \(0.175636\pi\)
\(500\) −208544. 361208.i −0.0373054 0.0646148i
\(501\) 984365. + 1.70497e6i 0.175211 + 0.303475i
\(502\) 874837. 1.51526e6i 0.154942 0.268367i
\(503\) −3.74110e6 −0.659294 −0.329647 0.944104i \(-0.606930\pi\)
−0.329647 + 0.944104i \(0.606930\pi\)
\(504\) 0 0
\(505\) 800378. 0.139658
\(506\) −68798.9 + 119163.i −0.0119455 + 0.0206902i
\(507\) −1.57242e6 2.72351e6i −0.271675 0.470554i
\(508\) −160329. 277697.i −0.0275646 0.0477433i
\(509\) −5.15085e6 + 8.92153e6i −0.881220 + 1.52632i −0.0312337 + 0.999512i \(0.509944\pi\)
−0.849986 + 0.526805i \(0.823390\pi\)
\(510\) −3.47336e6 −0.591323
\(511\) 0 0
\(512\) −6.44492e6 −1.08653
\(513\) 689821. 1.19480e6i 0.115729 0.200449i
\(514\) 1.51539e6 + 2.62473e6i 0.252998 + 0.438205i
\(515\) −2.44675e6 4.23790e6i −0.406510 0.704096i
\(516\) −142484. + 246789.i −0.0235581 + 0.0408039i
\(517\) −3.69711e6 −0.608326
\(518\) 0 0
\(519\) −5.31181e6 −0.865614
\(520\) 497780. 862180.i 0.0807289 0.139827i
\(521\) 3.28663e6 + 5.69260e6i 0.530464 + 0.918791i 0.999368 + 0.0355415i \(0.0113156\pi\)
−0.468904 + 0.883249i \(0.655351\pi\)
\(522\) 277829. + 481213.i 0.0446273 + 0.0772967i
\(523\) −4.18266e6 + 7.24458e6i −0.668650 + 1.15814i 0.309632 + 0.950856i \(0.399794\pi\)
−0.978282 + 0.207279i \(0.933539\pi\)
\(524\) 126497. 0.0201257
\(525\) 0 0
\(526\) −1.27103e6 −0.200306
\(527\) −8.82724e6 + 1.52892e7i −1.38452 + 2.39805i
\(528\) −783205. 1.35655e6i −0.122262 0.211764i
\(529\) 3.20879e6 + 5.55778e6i 0.498542 + 0.863500i
\(530\) −915063. + 1.58494e6i −0.141502 + 0.245088i
\(531\) 718184. 0.110535
\(532\) 0 0
\(533\) 1.32724e6 0.202364
\(534\) 2.13471e6 3.69742e6i 0.323956 0.561108i
\(535\) −2.11727e6 3.66722e6i −0.319810 0.553927i
\(536\) −5.17581e6 8.96477e6i −0.778155 1.34780i
\(537\) −978083. + 1.69409e6i −0.146366 + 0.253513i
\(538\) −8.05263e6 −1.19945
\(539\) 0 0
\(540\) 61376.0 0.00905761
\(541\) 4.03311e6 6.98556e6i 0.592444 1.02614i −0.401458 0.915877i \(-0.631496\pi\)
0.993902 0.110266i \(-0.0351702\pi\)
\(542\) −484064. 838424.i −0.0707791 0.122593i
\(543\) 846492. + 1.46617e6i 0.123204 + 0.213395i
\(544\) −831592. + 1.44036e6i −0.120479 + 0.208676i
\(545\) −1.24791e6 −0.179967
\(546\) 0 0
\(547\) 3.90775e6 0.558416 0.279208 0.960231i \(-0.409928\pi\)
0.279208 + 0.960231i \(0.409928\pi\)
\(548\) 494451. 856414.i 0.0703350 0.121824i
\(549\) 1.66651e6 + 2.88647e6i 0.235981 + 0.408730i
\(550\) 918568. + 1.59101e6i 0.129481 + 0.224267i
\(551\) 1.19189e6 2.06441e6i 0.167246 0.289679i
\(552\) 230571. 0.0322075
\(553\) 0 0
\(554\) −6.65811e6 −0.921672
\(555\) 2.08935e6 3.61886e6i 0.287924 0.498700i
\(556\) −11592.0 20078.0i −0.00159028 0.00275444i
\(557\) 5.79311e6 + 1.00340e7i 0.791177 + 1.37036i 0.925239 + 0.379385i \(0.123864\pi\)
−0.134062 + 0.990973i \(0.542802\pi\)
\(558\) −1.97832e6 + 3.42654e6i −0.268974 + 0.465876i
\(559\) 2.00203e6 0.270982
\(560\) 0 0
\(561\) −3.26727e6 −0.438306
\(562\) −484167. + 838602.i −0.0646628 + 0.111999i
\(563\) −955879. 1.65563e6i −0.127096 0.220137i 0.795454 0.606014i \(-0.207232\pi\)
−0.922550 + 0.385877i \(0.873899\pi\)
\(564\) 210966. + 365403.i 0.0279263 + 0.0483698i
\(565\) 478520. 828822.i 0.0630637 0.109230i
\(566\) −5.93920e6 −0.779268
\(567\) 0 0
\(568\) 1.19441e7 1.55340
\(569\) −4.08409e6 + 7.07385e6i −0.528828 + 0.915957i 0.470607 + 0.882343i \(0.344035\pi\)
−0.999435 + 0.0336138i \(0.989298\pi\)
\(570\) 1.66974e6 + 2.89208e6i 0.215259 + 0.372840i
\(571\) 3.73297e6 + 6.46569e6i 0.479141 + 0.829897i 0.999714 0.0239203i \(-0.00761479\pi\)
−0.520573 + 0.853817i \(0.674281\pi\)
\(572\) 31890.1 55235.3i 0.00407536 0.00705873i
\(573\) −1.56170e6 −0.198706
\(574\) 0 0
\(575\) −250552. −0.0316030
\(576\) −1.40940e6 + 2.44115e6i −0.177002 + 0.306576i
\(577\) 3.44219e6 + 5.96205e6i 0.430423 + 0.745514i 0.996910 0.0785568i \(-0.0250312\pi\)
−0.566487 + 0.824071i \(0.691698\pi\)
\(578\) −6.68436e6 1.15777e7i −0.832224 1.44145i
\(579\) 530017. 918016.i 0.0657042 0.113803i
\(580\) 106047. 0.0130896
\(581\) 0 0
\(582\) 5.78912e6 0.708444
\(583\) −860766. + 1.49089e6i −0.104885 + 0.181666i
\(584\) 3.86182e6 + 6.68886e6i 0.468554 + 0.811559i
\(585\) −215597. 373426.i −0.0260468 0.0451143i
\(586\) −1.48612e6 + 2.57403e6i −0.178776 + 0.309649i
\(587\) −8.91086e6 −1.06739 −0.533696 0.845676i \(-0.679197\pi\)
−0.533696 + 0.845676i \(0.679197\pi\)
\(588\) 0 0
\(589\) 1.69740e7 2.01602
\(590\) −869197. + 1.50549e6i −0.102799 + 0.178053i
\(591\) 1.01130e6 + 1.75163e6i 0.119100 + 0.206288i
\(592\) 6.08551e6 + 1.05404e7i 0.713662 + 1.23610i
\(593\) −6.17151e6 + 1.06894e7i −0.720700 + 1.24829i 0.240019 + 0.970768i \(0.422846\pi\)
−0.960720 + 0.277521i \(0.910487\pi\)
\(594\) −732243. −0.0851508
\(595\) 0 0
\(596\) −1.18211e6 −0.136314
\(597\) 3.33123e6 5.76986e6i 0.382533 0.662567i
\(598\) −55161.4 95542.3i −0.00630786 0.0109255i
\(599\) −4.52866e6 7.84387e6i −0.515707 0.893230i −0.999834 0.0182325i \(-0.994196\pi\)
0.484127 0.874998i \(-0.339137\pi\)
\(600\) 1.53924e6 2.66603e6i 0.174553 0.302334i
\(601\) 7.41700e6 0.837611 0.418805 0.908076i \(-0.362449\pi\)
0.418805 + 0.908076i \(0.362449\pi\)
\(602\) 0 0
\(603\) −4.48347e6 −0.502136
\(604\) −225801. + 391100.i −0.0251846 + 0.0436209i
\(605\) 2.28666e6 + 3.96061e6i 0.253988 + 0.439919i
\(606\) 544880. + 943760.i 0.0602725 + 0.104395i
\(607\) 2.88907e6 5.00401e6i 0.318263 0.551247i −0.661863 0.749625i \(-0.730234\pi\)
0.980126 + 0.198378i \(0.0635673\pi\)
\(608\) 1.59908e6 0.175432
\(609\) 0 0
\(610\) −8.06770e6 −0.877860
\(611\) 1.48213e6 2.56713e6i 0.160614 0.278192i
\(612\) 186437. + 322919.i 0.0201212 + 0.0348510i
\(613\) −3.14632e6 5.44959e6i −0.338183 0.585750i 0.645908 0.763415i \(-0.276479\pi\)
−0.984091 + 0.177665i \(0.943146\pi\)
\(614\) 8.95902e6 1.55175e7i 0.959047 1.66112i
\(615\) −2.90810e6 −0.310043
\(616\) 0 0
\(617\) −9.79133e6 −1.03545 −0.517725 0.855547i \(-0.673221\pi\)
−0.517725 + 0.855547i \(0.673221\pi\)
\(618\) 3.33139e6 5.77013e6i 0.350876 0.607735i
\(619\) 6.63386e6 + 1.14902e7i 0.695889 + 1.20531i 0.969880 + 0.243583i \(0.0783227\pi\)
−0.273991 + 0.961732i \(0.588344\pi\)
\(620\) 377560. + 653953.i 0.0394463 + 0.0683231i
\(621\) 49932.3 86485.3i 0.00519580 0.00899939i
\(622\) −3.81079e6 −0.394947
\(623\) 0 0
\(624\) 1.25591e6 0.129121
\(625\) 352380. 610339.i 0.0360837 0.0624987i
\(626\) −1.69709e6 2.93945e6i −0.173089 0.299799i
\(627\) 1.57066e6 + 2.72047e6i 0.159556 + 0.276360i
\(628\) 309783. 536560.i 0.0313443 0.0542900i
\(629\) 2.53867e7 2.55846
\(630\) 0 0
\(631\) 4.41233e6 0.441158 0.220579 0.975369i \(-0.429205\pi\)
0.220579 + 0.975369i \(0.429205\pi\)
\(632\) 1.58622e6 2.74742e6i 0.157969 0.273610i
\(633\) −3.17653e6 5.50191e6i −0.315097 0.545763i
\(634\) 1.74073e6 + 3.01504e6i 0.171992 + 0.297899i
\(635\) 2.46800e6 4.27470e6i 0.242891 0.420699i
\(636\) 196469. 0.0192598
\(637\) 0 0
\(638\) −1.26518e6 −0.123056
\(639\) 2.58660e6 4.48013e6i 0.250598 0.434049i
\(640\) −2.92482e6 5.06594e6i −0.282260 0.488888i
\(641\) −4.06518e6 7.04109e6i −0.390782 0.676854i 0.601771 0.798669i \(-0.294462\pi\)
−0.992553 + 0.121815i \(0.961129\pi\)
\(642\) 2.88278e6 4.99313e6i 0.276041 0.478118i
\(643\) −3.12961e6 −0.298513 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(644\) 0 0
\(645\) −4.38661e6 −0.415174
\(646\) −1.01441e7 + 1.75701e7i −0.956384 + 1.65651i
\(647\) −6.73300e6 1.16619e7i −0.632336 1.09524i −0.987073 0.160271i \(-0.948763\pi\)
0.354737 0.934966i \(-0.384570\pi\)
\(648\) 613506. + 1.06262e6i 0.0573960 + 0.0994127i
\(649\) −817622. + 1.41616e6i −0.0761975 + 0.131978i
\(650\) −1.47297e6 −0.136745
\(651\) 0 0
\(652\) 1.26076e6 0.116148
\(653\) −7.23861e6 + 1.25376e7i −0.664312 + 1.15062i 0.315159 + 0.949039i \(0.397942\pi\)
−0.979471 + 0.201584i \(0.935391\pi\)
\(654\) −849551. 1.47147e6i −0.0776685 0.134526i
\(655\) 973605. + 1.68633e6i 0.0886706 + 0.153582i
\(656\) 4.23511e6 7.33543e6i 0.384243 0.665528i
\(657\) 3.34525e6 0.302353
\(658\) 0 0
\(659\) 432708. 0.0388134 0.0194067 0.999812i \(-0.493822\pi\)
0.0194067 + 0.999812i \(0.493822\pi\)
\(660\) −69874.0 + 121025.i −0.00624389 + 0.0108147i
\(661\) 14982.6 + 25950.6i 0.00133378 + 0.00231017i 0.866692 0.498844i \(-0.166242\pi\)
−0.865358 + 0.501155i \(0.832909\pi\)
\(662\) −3.83859e6 6.64863e6i −0.340429 0.589640i
\(663\) 1.30981e6 2.26866e6i 0.115724 0.200440i
\(664\) 1.90182e7 1.67398
\(665\) 0 0
\(666\) 5.68953e6 0.497039
\(667\) 86274.1 149431.i 0.00750872 0.0130055i
\(668\) 255789. + 443039.i 0.0221789 + 0.0384150i
\(669\) 189964. + 329028.i 0.0164099 + 0.0284228i
\(670\) 5.42622e6 9.39849e6i 0.466993 0.808856i
\(671\) −7.58899e6 −0.650696
\(672\) 0 0
\(673\) −6.71329e6 −0.571344 −0.285672 0.958327i \(-0.592217\pi\)
−0.285672 + 0.958327i \(0.592217\pi\)
\(674\) 4.23925e6 7.34259e6i 0.359450 0.622586i
\(675\) −666670. 1.15471e6i −0.0563186 0.0975467i
\(676\) −408596. 707710.i −0.0343897 0.0595646i
\(677\) 2.22965e6 3.86186e6i 0.186967 0.323836i −0.757271 0.653101i \(-0.773468\pi\)
0.944237 + 0.329265i \(0.106801\pi\)
\(678\) 1.30306e6 0.108866
\(679\) 0 0
\(680\) −1.32523e7 −1.09905
\(681\) 3.34081e6 5.78646e6i 0.276048 0.478129i
\(682\) −4.50446e6 7.80195e6i −0.370836 0.642306i
\(683\) 8.99196e6 + 1.55745e7i 0.737569 + 1.27751i 0.953587 + 0.301117i \(0.0973596\pi\)
−0.216018 + 0.976389i \(0.569307\pi\)
\(684\) 179251. 310472.i 0.0146495 0.0253736i
\(685\) 1.52225e7 1.23954
\(686\) 0 0
\(687\) −8.47112e6 −0.684777
\(688\) 6.38830e6 1.10649e7i 0.514534 0.891199i
\(689\) −690143. 1.19536e6i −0.0553848 0.0959294i
\(690\) 120863. + 209341.i 0.00966432 + 0.0167391i
\(691\) −1.25468e6 + 2.17316e6i −0.0999624 + 0.173140i −0.911669 0.410926i \(-0.865206\pi\)
0.811706 + 0.584066i \(0.198539\pi\)
\(692\) −1.38028e6 −0.109573
\(693\) 0 0
\(694\) 1.35228e6 0.106578
\(695\) 178441. 309069.i 0.0140130 0.0242713i
\(696\) 1.06003e6 + 1.83602e6i 0.0829458 + 0.143666i
\(697\) −8.83373e6 1.53005e7i −0.688751 1.19295i
\(698\) −5.06959e6 + 8.78079e6i −0.393853 + 0.682174i
\(699\) 4.61098e6 0.356944
\(700\) 0 0
\(701\) 9.68649e6 0.744512 0.372256 0.928130i \(-0.378584\pi\)
0.372256 + 0.928130i \(0.378584\pi\)
\(702\) 293548. 508440.i 0.0224821 0.0389401i
\(703\) −1.22041e7 2.11381e7i −0.931357 1.61316i
\(704\) −3.20908e6 5.55829e6i −0.244033 0.422678i
\(705\) −3.24748e6 + 5.62479e6i −0.246078 + 0.426220i
\(706\) 9.64681e6 0.728403
\(707\) 0 0
\(708\) 186621. 0.0139919
\(709\) 4.76360e6 8.25079e6i 0.355893 0.616425i −0.631377 0.775476i \(-0.717510\pi\)
0.987270 + 0.159051i \(0.0508434\pi\)
\(710\) 6.26099e6 + 1.08443e7i 0.466119 + 0.807342i
\(711\) −687023. 1.18996e6i −0.0509679 0.0882790i
\(712\) 8.14478e6 1.41072e7i 0.602115 1.04289i
\(713\) 1.22865e6 0.0905118
\(714\) 0 0
\(715\) 981794. 0.0718217
\(716\) −254157. + 440212.i −0.0185276 + 0.0320907i
\(717\) −518953. 898853.i −0.0376990 0.0652966i
\(718\) 1.21876e7 + 2.11095e7i 0.882279 + 1.52815i
\(719\) −378588. + 655734.i −0.0273114 + 0.0473048i −0.879358 0.476161i \(-0.842028\pi\)
0.852047 + 0.523466i \(0.175361\pi\)
\(720\) −2.75181e6 −0.197828
\(721\) 0 0
\(722\) 6.02081e6 0.429845
\(723\) −4.09439e6 + 7.09169e6i −0.291302 + 0.504549i
\(724\) 219962. + 380986.i 0.0155956 + 0.0270124i
\(725\) −1.15189e6 1.99513e6i −0.0813889 0.140970i
\(726\) −3.11341e6 + 5.39258e6i −0.219227 + 0.379713i
\(727\) −2.66570e7 −1.87058 −0.935288 0.353888i \(-0.884859\pi\)
−0.935288 + 0.353888i \(0.884859\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −4.04866e6 + 7.01248e6i −0.281192 + 0.487040i
\(731\) −1.33249e7 2.30794e7i −0.922297 1.59747i
\(732\) 433045. + 750056.i 0.0298714 + 0.0517387i
\(733\) −1.35429e7 + 2.34569e7i −0.931001 + 1.61254i −0.149387 + 0.988779i \(0.547730\pi\)
−0.781614 + 0.623762i \(0.785603\pi\)
\(734\) 1.72698e7 1.18317
\(735\) 0 0
\(736\) 115748. 0.00787625
\(737\) 5.10425e6 8.84081e6i 0.346149 0.599547i
\(738\) −1.97977e6 3.42906e6i −0.133805 0.231758i
\(739\) −1.09753e7 1.90098e7i −0.739276 1.28046i −0.952822 0.303531i \(-0.901834\pi\)
0.213545 0.976933i \(-0.431499\pi\)
\(740\) 542921. 940366.i 0.0364466 0.0631274i
\(741\) −2.51865e6 −0.168508
\(742\) 0 0
\(743\) 5.77370e6 0.383691 0.191846 0.981425i \(-0.438553\pi\)
0.191846 + 0.981425i \(0.438553\pi\)
\(744\) −7.54808e6 + 1.30737e7i −0.499924 + 0.865894i
\(745\) −9.09832e6 1.57587e7i −0.600579 1.04023i
\(746\) 6.29527e6 + 1.09037e7i 0.414159 + 0.717345i
\(747\) 4.11856e6 7.13356e6i 0.270050 0.467740i
\(748\) −849005. −0.0554825
\(749\) 0 0
\(750\) 8.74171e6 0.567470
\(751\) 4.18875e6 7.25512e6i 0.271009 0.469402i −0.698111 0.715989i \(-0.745976\pi\)
0.969121 + 0.246587i \(0.0793093\pi\)
\(752\) −9.45871e6 1.63830e7i −0.609940 1.05645i
\(753\) −1.44569e6 2.50400e6i −0.0929153 0.160934i
\(754\) 507198. 878493.i 0.0324900 0.0562743i
\(755\) −6.95170e6 −0.443837
\(756\) 0 0
\(757\) 1.18828e7 0.753665 0.376833 0.926281i \(-0.377013\pi\)
0.376833 + 0.926281i \(0.377013\pi\)
\(758\) 1.61165e6 2.79145e6i 0.101882 0.176465i
\(759\) 113692. + 196920.i 0.00716348 + 0.0124075i
\(760\) 6.37074e6 + 1.10344e7i 0.400088 + 0.692973i
\(761\) −8.84701e6 + 1.53235e7i −0.553777 + 0.959170i 0.444221 + 0.895917i \(0.353481\pi\)
−0.997998 + 0.0632523i \(0.979853\pi\)
\(762\) 6.72064e6 0.419298
\(763\) 0 0
\(764\) −405811. −0.0251531
\(765\) −2.86990e6 + 4.97082e6i −0.177302 + 0.307096i
\(766\) 9.79684e6 + 1.69686e7i 0.603273 + 1.04490i
\(767\) −655551. 1.13545e6i −0.0402363 0.0696913i
\(768\) −1.02889e6 + 1.78209e6i −0.0629457 + 0.109025i
\(769\) −4.12006e6 −0.251239 −0.125620 0.992078i \(-0.540092\pi\)
−0.125620 + 0.992078i \(0.540092\pi\)
\(770\) 0 0
\(771\) 5.00843e6 0.303435
\(772\) 137726. 238548.i 0.00831710 0.0144056i
\(773\) −6.34320e6 1.09868e7i −0.381821 0.661334i 0.609502 0.792785i \(-0.291370\pi\)
−0.991323 + 0.131451i \(0.958036\pi\)
\(774\) −2.98631e6 5.17244e6i −0.179177 0.310344i
\(775\) 8.20217e6 1.42066e7i 0.490540 0.849641i
\(776\) 2.20879e7 1.31674
\(777\) 0 0
\(778\) −1.22402e7 −0.725001
\(779\) −8.49323e6 + 1.47107e7i −0.501452 + 0.868540i
\(780\) −56023.4 97035.3i −0.00329710 0.00571075i
\(781\) 5.88948e6 + 1.02009e7i 0.345501 + 0.598425i
\(782\) −734276. + 1.27180e6i −0.0429380 + 0.0743709i
\(783\) 918235. 0.0535241
\(784\) 0 0
\(785\) 9.53723e6 0.552393
\(786\) −1.32562e6 + 2.29604e6i −0.0765353 + 0.132563i
\(787\) −4.57405e6 7.92248e6i −0.263247 0.455957i 0.703856 0.710343i \(-0.251460\pi\)
−0.967103 + 0.254385i \(0.918127\pi\)
\(788\) 262789. + 455164.i 0.0150762 + 0.0261127i
\(789\) −1.05021e6 + 1.81901e6i −0.0600596 + 0.104026i
\(790\) 3.32594e6 0.189603
\(791\) 0 0
\(792\) −2.79380e6 −0.158264
\(793\) 3.04234e6 5.26949e6i 0.171801 0.297568i
\(794\) 1.24901e7 + 2.16335e7i 0.703096 + 1.21780i
\(795\) 1.51216e6 + 2.61914e6i 0.0848555 + 0.146974i
\(796\) 865626. 1.49931e6i 0.0484226 0.0838703i
\(797\) −1.10180e7 −0.614408 −0.307204 0.951644i \(-0.599393\pi\)
−0.307204 + 0.951644i \(0.599393\pi\)
\(798\) 0 0
\(799\) −3.94585e7 −2.18662
\(800\) 772705. 1.33837e6i 0.0426863 0.0739349i
\(801\) −3.52765e6 6.11007e6i −0.194269 0.336485i
\(802\) −1.63504e7 2.83198e7i −0.897622 1.55473i
\(803\) −3.80842e6 + 6.59638e6i −0.208428 + 0.361008i
\(804\) −1.16504e6 −0.0635624
\(805\) 0 0
\(806\) 7.22315e6 0.391642
\(807\) −6.65357e6 + 1.15243e7i −0.359643 + 0.622919i
\(808\) 2.07894e6 + 3.60083e6i 0.112025 + 0.194032i
\(809\) 1.55136e7 + 2.68704e7i 0.833378 + 1.44345i 0.895344 + 0.445375i \(0.146930\pi\)
−0.0619660 + 0.998078i \(0.519737\pi\)
\(810\) −643188. + 1.11403e6i −0.0344449 + 0.0596604i
\(811\) −2.94456e7 −1.57206 −0.786028 0.618191i \(-0.787866\pi\)
−0.786028 + 0.618191i \(0.787866\pi\)
\(812\) 0 0
\(813\) −1.59985e6 −0.0848895
\(814\) −6.47729e6 + 1.12190e7i −0.342635 + 0.593462i
\(815\) 9.70367e6 + 1.68072e7i 0.511731 + 0.886344i
\(816\) −8.35898e6 1.44782e7i −0.439469 0.761182i
\(817\) −1.28113e7 + 2.21898e7i −0.671487 + 1.16305i
\(818\) −1.93526e7 −1.01124
\(819\) 0 0
\(820\) −755675. −0.0392464
\(821\) 2.61656e6 4.53201e6i 0.135479 0.234657i −0.790301 0.612718i \(-0.790076\pi\)
0.925780 + 0.378062i \(0.123409\pi\)
\(822\) 1.03632e7 + 1.79495e7i 0.534950 + 0.926561i
\(823\) −7.08154e6 1.22656e7i −0.364442 0.631232i 0.624245 0.781229i \(-0.285407\pi\)
−0.988686 + 0.149997i \(0.952074\pi\)
\(824\) 1.27106e7 2.20154e7i 0.652151 1.12956i
\(825\) 3.03591e6 0.155294
\(826\) 0 0
\(827\) 2.98006e7 1.51517 0.757585 0.652737i \(-0.226379\pi\)
0.757585 + 0.652737i \(0.226379\pi\)
\(828\) 12975.0 22473.3i 0.000657705 0.00113918i
\(829\) 9.96521e6 + 1.72602e7i 0.503617 + 0.872289i 0.999991 + 0.00418109i \(0.00133089\pi\)
−0.496375 + 0.868108i \(0.665336\pi\)
\(830\) 9.96916e6 + 1.72671e7i 0.502300 + 0.870009i
\(831\) −5.50134e6 + 9.52859e6i −0.276354 + 0.478659i
\(832\) 5.14594e6 0.257725
\(833\) 0 0
\(834\) 485914. 0.0241905
\(835\) −3.93746e6 + 6.81988e6i −0.195434 + 0.338501i
\(836\) 408140. + 706919.i 0.0201973 + 0.0349827i
\(837\) 3.26921e6 + 5.66244e6i 0.161298 + 0.279376i
\(838\) −5.48367e6 + 9.49799e6i −0.269750 + 0.467220i
\(839\) −1.88103e7 −0.922552 −0.461276 0.887257i \(-0.652608\pi\)
−0.461276 + 0.887257i \(0.652608\pi\)
\(840\) 0 0
\(841\) −1.89246e7 −0.922650
\(842\) 1.60660e7 2.78271e7i 0.780957 1.35266i
\(843\) 800096. + 1.38581e6i 0.0387769 + 0.0671636i
\(844\) −825427. 1.42968e6i −0.0398862 0.0690849i
\(845\) 6.28968e6 1.08941e7i 0.303031 0.524865i
\(846\) −8.84324e6 −0.424801
\(847\) 0 0
\(848\) −8.80874e6 −0.420653
\(849\) −4.90733e6 + 8.49974e6i −0.233655 + 0.404703i
\(850\) 9.80367e6 + 1.69805e7i 0.465416 + 0.806125i
\(851\) −883384. 1.53007e6i −0.0418144 0.0724247i
\(852\) 672134. 1.16417e6i 0.0317217 0.0549436i
\(853\) 2.05980e7 0.969285 0.484643 0.874712i \(-0.338950\pi\)
0.484643 + 0.874712i \(0.338950\pi\)
\(854\) 0 0
\(855\) 5.51856e6 0.258173
\(856\) 1.09990e7 1.90508e7i 0.513060 0.888647i
\(857\) 1.23786e7 + 2.14404e7i 0.575731 + 0.997195i 0.995962 + 0.0897778i \(0.0286157\pi\)
−0.420231 + 0.907417i \(0.638051\pi\)
\(858\) 668384. + 1.15767e6i 0.0309961 + 0.0536869i
\(859\) 1.95533e7 3.38672e7i 0.904141 1.56602i 0.0820751 0.996626i \(-0.473845\pi\)
0.822066 0.569392i \(-0.192821\pi\)
\(860\) −1.13987e6 −0.0525544
\(861\) 0 0
\(862\) −2.07527e7 −0.951275
\(863\) 1.96681e7 3.40662e7i 0.898952 1.55703i 0.0701154 0.997539i \(-0.477663\pi\)
0.828836 0.559491i \(-0.189003\pi\)
\(864\) 307984. + 533444.i 0.0140360 + 0.0243111i
\(865\) −1.06236e7 1.84007e7i −0.482761 0.836167i
\(866\) −1.79575e7 + 3.11034e7i −0.813677 + 1.40933i
\(867\) −2.20921e7 −0.998135
\(868\) 0 0
\(869\) 3.12859e6 0.140540
\(870\) −1.11131e6 + 1.92485e6i −0.0497781 + 0.0862183i
\(871\) 4.09247e6 + 7.08837e6i 0.182785 + 0.316593i
\(872\) −3.24138e6 5.61424e6i −0.144357 0.250034i
\(873\) 4.78333e6 8.28496e6i 0.212419 0.367921i
\(874\) 1.41195e6 0.0625229
\(875\) 0 0
\(876\) 869268. 0.0382731
\(877\) −4.04626e6 + 7.00833e6i −0.177646 + 0.307692i −0.941074 0.338201i \(-0.890182\pi\)
0.763428 + 0.645893i \(0.223515\pi\)
\(878\) 1.23909e7 + 2.14617e7i 0.542459 + 0.939566i
\(879\) 2.45584e6 + 4.25364e6i 0.107208 + 0.185690i
\(880\) 3.13282e6 5.42620e6i 0.136373 0.236205i
\(881\) −4.05755e6 −0.176126 −0.0880631 0.996115i \(-0.528068\pi\)
−0.0880631 + 0.996115i \(0.528068\pi\)
\(882\) 0 0
\(883\) 1.79813e7 0.776102 0.388051 0.921638i \(-0.373148\pi\)
0.388051 + 0.921638i \(0.373148\pi\)
\(884\) 340356. 589515.i 0.0146488 0.0253725i
\(885\) 1.43637e6 + 2.48786e6i 0.0616463 + 0.106775i
\(886\) −1.39297e7 2.41270e7i −0.596154 1.03257i
\(887\) 7.65695e6 1.32622e7i 0.326773 0.565988i −0.655096 0.755545i \(-0.727372\pi\)
0.981870 + 0.189557i \(0.0607053\pi\)
\(888\) 2.17079e7 0.923814
\(889\) 0 0
\(890\) 1.70777e7 0.722693
\(891\) −605023. + 1.04793e6i −0.0255316 + 0.0442220i
\(892\) 49362.5 + 85498.4i 0.00207723 + 0.00359787i
\(893\) 1.89688e7 + 3.28549e7i 0.795996 + 1.37871i
\(894\) 1.23879e7 2.14564e7i 0.518385 0.897870i
\(895\) −7.82466e6 −0.326519
\(896\) 0 0
\(897\) −182311. −0.00756539
\(898\) −1.62188e7 + 2.80919e7i −0.671165 + 1.16249i
\(899\) 5.64861e6 + 9.78368e6i 0.233100 + 0.403741i
\(900\) −173236. 300053.i −0.00712903 0.0123478i
\(901\) −9.18677e6 + 1.59120e7i −0.377008 + 0.652997i
\(902\) 9.01554e6 0.368957
\(903\) 0 0
\(904\) 4.97172e6 0.202342
\(905\) −3.38597e6 + 5.86467e6i −0.137424 + 0.238025i
\(906\) −4.73256e6 8.19704e6i −0.191547 0.331769i
\(907\) 1.08879e7 + 1.88583e7i 0.439465 + 0.761176i 0.997648 0.0685419i \(-0.0218347\pi\)
−0.558183 + 0.829718i \(0.688501\pi\)
\(908\) 868116. 1.50362e6i 0.0349432 0.0605235i
\(909\) 1.80085e6 0.0722883
\(910\) 0 0
\(911\) −5.35112e6 −0.213623 −0.106812 0.994279i \(-0.534064\pi\)
−0.106812 + 0.994279i \(0.534064\pi\)
\(912\) −8.03678e6 + 1.39201e7i −0.319959 + 0.554186i
\(913\) 9.37762e6 + 1.62425e7i 0.372319 + 0.644876i
\(914\) 7.07556e6 + 1.22552e7i 0.280153 + 0.485239i
\(915\) −6.66603e6 + 1.15459e7i −0.263217 + 0.455906i
\(916\) −2.20124e6 −0.0866818
\(917\) 0 0
\(918\) −7.81507e6 −0.306074
\(919\) 1.33929e7 2.31972e7i 0.523102 0.906040i −0.476536 0.879155i \(-0.658108\pi\)
0.999639 0.0268850i \(-0.00855878\pi\)
\(920\) 461143. + 798722.i 0.0179625 + 0.0311119i
\(921\) −1.48050e7 2.56430e7i −0.575120 0.996138i
\(922\) −1.22952e7 + 2.12959e7i −0.476330 + 0.825028i
\(923\) −9.44411e6 −0.364886
\(924\) 0 0
\(925\) −2.35890e7 −0.906474
\(926\) 1.51168e7 2.61830e7i 0.579338 1.00344i
\(927\) −5.50519e6 9.53526e6i −0.210413 0.364446i
\(928\) 532141. + 921695.i 0.0202841 + 0.0351332i
\(929\) −369987. + 640836.i −0.0140652 + 0.0243617i −0.872972 0.487770i \(-0.837811\pi\)
0.858907 + 0.512131i \(0.171144\pi\)
\(930\) −1.58265e7 −0.600037
\(931\) 0 0
\(932\) 1.19817e6 0.0451834
\(933\) −3.14870e6 + 5.45371e6i −0.118421 + 0.205111i
\(934\) 2.16583e7 + 3.75132e7i 0.812375 + 1.40708i
\(935\) −6.53453e6 1.13181e7i −0.244447 0.423395i
\(936\) 1.12000e6 1.93990e6i 0.0417859 0.0723754i
\(937\) −122654. −0.00456385 −0.00228193 0.999997i \(-0.500726\pi\)
−0.00228193 + 0.999997i \(0.500726\pi\)
\(938\) 0 0
\(939\) −5.60897e6 −0.207596
\(940\) −843862. + 1.46161e6i −0.0311496 + 0.0539526i
\(941\) −6.12332e6 1.06059e7i −0.225431 0.390457i 0.731018 0.682358i \(-0.239046\pi\)
−0.956449 + 0.291901i \(0.905712\pi\)
\(942\) 6.49273e6 + 1.12457e7i 0.238397 + 0.412915i
\(943\) −614778. + 1.06483e6i −0.0225133 + 0.0389942i
\(944\) −8.36722e6 −0.305599
\(945\) 0 0
\(946\) 1.35992e7 0.494065
\(947\) 1.85587e6 3.21446e6i 0.0672470 0.116475i −0.830442 0.557106i \(-0.811912\pi\)
0.897689 + 0.440631i \(0.145245\pi\)
\(948\) −178524. 309213.i −0.00645172 0.0111747i
\(949\) −3.05351e6 5.28883e6i −0.110061 0.190631i
\(950\) 9.42579e6 1.63259e7i 0.338851 0.586907i
\(951\) 5.75319e6 0.206280
\(952\) 0 0
\(953\) −2.32857e7 −0.830533 −0.415266 0.909700i \(-0.636312\pi\)
−0.415266 + 0.909700i \(0.636312\pi\)
\(954\) −2.05889e6 + 3.56610e6i −0.0732424 + 0.126860i
\(955\) −3.12341e6 5.40990e6i −0.110820 0.191947i
\(956\) −134851. 233568.i −0.00477209 0.00826551i
\(957\) −1.04537e6 + 1.81064e6i −0.0368970 + 0.0639075i
\(958\) −3.57474e7 −1.25843
\(959\) 0 0
\(960\) −1.12752e7 −0.394862
\(961\) −2.59071e7 + 4.48724e7i −0.904921 + 1.56737i
\(962\) −5.19334e6 8.99514e6i −0.180930 0.313379i
\(963\) −4.76386e6 8.25125e6i −0.165536 0.286717i
\(964\) −1.06393e6 + 1.84279e6i −0.0368741 + 0.0638679i
\(965\) 4.24013e6 0.146575
\(966\) 0 0
\(967\) 2.25257e7 0.774661 0.387330 0.921941i \(-0.373397\pi\)
0.387330 + 0.921941i \(0.373397\pi\)
\(968\) −1.18789e7 + 2.05749e7i −0.407464 + 0.705748i
\(969\) 1.67634e7 + 2.90350e7i 0.573524 + 0.993373i
\(970\) 1.15782e7 + 2.00541e7i 0.395106 + 0.684343i
\(971\) −9.97281e6 + 1.72734e7i −0.339445 + 0.587936i −0.984328 0.176345i \(-0.943573\pi\)
0.644883 + 0.764281i \(0.276906\pi\)
\(972\) 138096. 0.00468830
\(973\) 0 0
\(974\) 2.53995e7 0.857884
\(975\) −1.21706e6 + 2.10801e6i −0.0410016 + 0.0710168i
\(976\) −1.94157e7 3.36290e7i −0.652422 1.13003i
\(977\) 479671. + 830815.i 0.0160771 + 0.0278463i 0.873952 0.486012i \(-0.161549\pi\)
−0.857875 + 0.513859i \(0.828216\pi\)
\(978\) −1.32121e7 + 2.28840e7i −0.441697 + 0.765041i
\(979\) 1.60643e7 0.535681
\(980\) 0 0
\(981\) −2.80780e6 −0.0931524
\(982\) 2.49771e6 4.32616e6i 0.0826539 0.143161i
\(983\) −2.61049e7 4.52149e7i −0.861663 1.49244i −0.870323 0.492482i \(-0.836090\pi\)
0.00865985 0.999963i \(-0.497243\pi\)
\(984\) −7.55363e6 1.30833e7i −0.248695 0.430753i
\(985\) −4.04521e6 + 7.00651e6i −0.132847 + 0.230097i
\(986\) −1.35030e7 −0.442323
\(987\) 0 0
\(988\) −654475. −0.0213305
\(989\) −927339. + 1.60620e6i −0.0301472 + 0.0522166i
\(990\) −1.46449e6 2.53656e6i −0.0474894 0.0822541i
\(991\) 8.81523e6 + 1.52684e7i 0.285134 + 0.493867i 0.972642 0.232310i \(-0.0746285\pi\)
−0.687507 + 0.726177i \(0.741295\pi\)
\(992\) −3.78918e6 + 6.56306e6i −0.122255 + 0.211752i
\(993\) −1.26867e7 −0.408296
\(994\) 0 0
\(995\) 2.66498e7 0.853369
\(996\) 1.07022e6 1.85367e6i 0.0341840 0.0592084i
\(997\) −2.02437e7 3.50632e7i −0.644990 1.11716i −0.984304 0.176482i \(-0.943528\pi\)
0.339314 0.940673i \(-0.389805\pi\)
\(998\) −853521. 1.47834e6i −0.0271261 0.0469838i
\(999\) 4.70103e6 8.14243e6i 0.149032 0.258131i
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.n.79.1 4
7.2 even 3 147.6.a.h.1.2 2
7.3 odd 6 147.6.e.m.67.1 4
7.4 even 3 inner 147.6.e.n.67.1 4
7.5 odd 6 147.6.a.j.1.2 yes 2
7.6 odd 2 147.6.e.m.79.1 4
21.2 odd 6 441.6.a.q.1.1 2
21.5 even 6 441.6.a.r.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.6.a.h.1.2 2 7.2 even 3
147.6.a.j.1.2 yes 2 7.5 odd 6
147.6.e.m.67.1 4 7.3 odd 6
147.6.e.m.79.1 4 7.6 odd 2
147.6.e.n.67.1 4 7.4 even 3 inner
147.6.e.n.79.1 4 1.1 even 1 trivial
441.6.a.q.1.1 2 21.2 odd 6
441.6.a.r.1.1 2 21.5 even 6