Properties

Label 147.6.e.g.79.1
Level $147$
Weight $6$
Character 147.79
Analytic conductor $23.576$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.6.e.g.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(14.0000 + 24.2487i) q^{4} +(5.50000 - 9.52628i) q^{5} -18.0000 q^{6} +120.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(14.0000 + 24.2487i) q^{4} +(5.50000 - 9.52628i) q^{5} -18.0000 q^{6} +120.000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-11.0000 - 19.0526i) q^{10} +(-134.500 - 232.961i) q^{11} +(126.000 - 218.238i) q^{12} +308.000 q^{13} -99.0000 q^{15} +(-328.000 + 568.113i) q^{16} +(948.000 + 1641.98i) q^{17} +(81.0000 + 140.296i) q^{18} +(-82.0000 + 142.028i) q^{19} +308.000 q^{20} -538.000 q^{22} +(1632.00 - 2826.71i) q^{23} +(-540.000 - 935.307i) q^{24} +(1502.00 + 2601.54i) q^{25} +(308.000 - 533.472i) q^{26} +729.000 q^{27} +2417.00 q^{29} +(-99.0000 + 171.473i) q^{30} +(1420.50 + 2460.38i) q^{31} +(2576.00 + 4461.76i) q^{32} +(-1210.50 + 2096.65i) q^{33} +3792.00 q^{34} -2268.00 q^{36} +(5664.00 - 9810.34i) q^{37} +(164.000 + 284.056i) q^{38} +(-1386.00 - 2400.62i) q^{39} +(660.000 - 1143.15i) q^{40} +16856.0 q^{41} -7894.00 q^{43} +(3766.00 - 6522.90i) q^{44} +(445.500 + 771.629i) q^{45} +(-3264.00 - 5653.41i) q^{46} +(10551.0 - 18274.9i) q^{47} +5904.00 q^{48} +6008.00 q^{50} +(8532.00 - 14777.9i) q^{51} +(4312.00 + 7468.60i) q^{52} +(14845.5 + 25713.2i) q^{53} +(729.000 - 1262.67i) q^{54} -2959.00 q^{55} +1476.00 q^{57} +(2417.00 - 4186.37i) q^{58} +(-4081.50 - 7069.37i) q^{59} +(-1386.00 - 2400.62i) q^{60} +(7583.00 - 13134.1i) q^{61} +5682.00 q^{62} -10688.0 q^{64} +(1694.00 - 2934.09i) q^{65} +(2421.00 + 4193.30i) q^{66} +(16039.0 + 27780.4i) q^{67} +(-26544.0 + 45975.6i) q^{68} -29376.0 q^{69} -38274.0 q^{71} +(-4860.00 + 8417.77i) q^{72} +(17433.0 + 30194.8i) q^{73} +(-11328.0 - 19620.7i) q^{74} +(13518.0 - 23413.9i) q^{75} -4592.00 q^{76} -5544.00 q^{78} +(-6764.50 + 11716.5i) q^{79} +(3608.00 + 6249.24i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(16856.0 - 29195.4i) q^{82} +68103.0 q^{83} +20856.0 q^{85} +(-7894.00 + 13672.8i) q^{86} +(-10876.5 - 18838.7i) q^{87} +(-16140.0 - 27955.3i) q^{88} +(-57461.0 + 99525.4i) q^{89} +1782.00 q^{90} +91392.0 q^{92} +(12784.5 - 22143.4i) q^{93} +(-21102.0 - 36549.7i) q^{94} +(902.000 + 1562.31i) q^{95} +(23184.0 - 40155.9i) q^{96} -154959. q^{97} +21789.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 9 q^{3} + 28 q^{4} + 11 q^{5} - 36 q^{6} + 240 q^{8} - 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 9 q^{3} + 28 q^{4} + 11 q^{5} - 36 q^{6} + 240 q^{8} - 81 q^{9} - 22 q^{10} - 269 q^{11} + 252 q^{12} + 616 q^{13} - 198 q^{15} - 656 q^{16} + 1896 q^{17} + 162 q^{18} - 164 q^{19} + 616 q^{20} - 1076 q^{22} + 3264 q^{23} - 1080 q^{24} + 3004 q^{25} + 616 q^{26} + 1458 q^{27} + 4834 q^{29} - 198 q^{30} + 2841 q^{31} + 5152 q^{32} - 2421 q^{33} + 7584 q^{34} - 4536 q^{36} + 11328 q^{37} + 328 q^{38} - 2772 q^{39} + 1320 q^{40} + 33712 q^{41} - 15788 q^{43} + 7532 q^{44} + 891 q^{45} - 6528 q^{46} + 21102 q^{47} + 11808 q^{48} + 12016 q^{50} + 17064 q^{51} + 8624 q^{52} + 29691 q^{53} + 1458 q^{54} - 5918 q^{55} + 2952 q^{57} + 4834 q^{58} - 8163 q^{59} - 2772 q^{60} + 15166 q^{61} + 11364 q^{62} - 21376 q^{64} + 3388 q^{65} + 4842 q^{66} + 32078 q^{67} - 53088 q^{68} - 58752 q^{69} - 76548 q^{71} - 9720 q^{72} + 34866 q^{73} - 22656 q^{74} + 27036 q^{75} - 9184 q^{76} - 11088 q^{78} - 13529 q^{79} + 7216 q^{80} - 6561 q^{81} + 33712 q^{82} + 136206 q^{83} + 41712 q^{85} - 15788 q^{86} - 21753 q^{87} - 32280 q^{88} - 114922 q^{89} + 3564 q^{90} + 182784 q^{92} + 25569 q^{93} - 42204 q^{94} + 1804 q^{95} + 46368 q^{96} - 309918 q^{97} + 43578 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.176777 0.306186i −0.763998 0.645219i \(-0.776766\pi\)
0.940775 + 0.339032i \(0.110100\pi\)
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) 14.0000 + 24.2487i 0.437500 + 0.757772i
\(5\) 5.50000 9.52628i 0.0983870 0.170411i −0.812630 0.582780i \(-0.801965\pi\)
0.911017 + 0.412368i \(0.135298\pi\)
\(6\) −18.0000 −0.204124
\(7\) 0 0
\(8\) 120.000 0.662913
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) −11.0000 19.0526i −0.0347851 0.0602495i
\(11\) −134.500 232.961i −0.335151 0.580499i 0.648363 0.761332i \(-0.275454\pi\)
−0.983514 + 0.180833i \(0.942121\pi\)
\(12\) 126.000 218.238i 0.252591 0.437500i
\(13\) 308.000 0.505466 0.252733 0.967536i \(-0.418671\pi\)
0.252733 + 0.967536i \(0.418671\pi\)
\(14\) 0 0
\(15\) −99.0000 −0.113608
\(16\) −328.000 + 568.113i −0.320312 + 0.554798i
\(17\) 948.000 + 1641.98i 0.795584 + 1.37799i 0.922468 + 0.386074i \(0.126169\pi\)
−0.126884 + 0.991918i \(0.540498\pi\)
\(18\) 81.0000 + 140.296i 0.0589256 + 0.102062i
\(19\) −82.0000 + 142.028i −0.0521111 + 0.0902590i −0.890904 0.454191i \(-0.849928\pi\)
0.838793 + 0.544450i \(0.183262\pi\)
\(20\) 308.000 0.172177
\(21\) 0 0
\(22\) −538.000 −0.236988
\(23\) 1632.00 2826.71i 0.643281 1.11419i −0.341415 0.939913i \(-0.610906\pi\)
0.984696 0.174282i \(-0.0557605\pi\)
\(24\) −540.000 935.307i −0.191366 0.331456i
\(25\) 1502.00 + 2601.54i 0.480640 + 0.832493i
\(26\) 308.000 533.472i 0.0893547 0.154767i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 2417.00 0.533681 0.266840 0.963741i \(-0.414020\pi\)
0.266840 + 0.963741i \(0.414020\pi\)
\(30\) −99.0000 + 171.473i −0.0200832 + 0.0347851i
\(31\) 1420.50 + 2460.38i 0.265483 + 0.459830i 0.967690 0.252143i \(-0.0811352\pi\)
−0.702207 + 0.711973i \(0.747802\pi\)
\(32\) 2576.00 + 4461.76i 0.444704 + 0.770250i
\(33\) −1210.50 + 2096.65i −0.193500 + 0.335151i
\(34\) 3792.00 0.562563
\(35\) 0 0
\(36\) −2268.00 −0.291667
\(37\) 5664.00 9810.34i 0.680172 1.17809i −0.294756 0.955573i \(-0.595238\pi\)
0.974928 0.222520i \(-0.0714284\pi\)
\(38\) 164.000 + 284.056i 0.0184240 + 0.0319114i
\(39\) −1386.00 2400.62i −0.145916 0.252733i
\(40\) 660.000 1143.15i 0.0652220 0.112968i
\(41\) 16856.0 1.56601 0.783006 0.622015i \(-0.213686\pi\)
0.783006 + 0.622015i \(0.213686\pi\)
\(42\) 0 0
\(43\) −7894.00 −0.651067 −0.325534 0.945530i \(-0.605544\pi\)
−0.325534 + 0.945530i \(0.605544\pi\)
\(44\) 3766.00 6522.90i 0.293257 0.507936i
\(45\) 445.500 + 771.629i 0.0327957 + 0.0568038i
\(46\) −3264.00 5653.41i −0.227434 0.393927i
\(47\) 10551.0 18274.9i 0.696705 1.20673i −0.272897 0.962043i \(-0.587982\pi\)
0.969603 0.244685i \(-0.0786847\pi\)
\(48\) 5904.00 0.369865
\(49\) 0 0
\(50\) 6008.00 0.339864
\(51\) 8532.00 14777.9i 0.459331 0.795584i
\(52\) 4312.00 + 7468.60i 0.221142 + 0.383028i
\(53\) 14845.5 + 25713.2i 0.725947 + 1.25738i 0.958583 + 0.284814i \(0.0919318\pi\)
−0.232635 + 0.972564i \(0.574735\pi\)
\(54\) 729.000 1262.67i 0.0340207 0.0589256i
\(55\) −2959.00 −0.131898
\(56\) 0 0
\(57\) 1476.00 0.0601727
\(58\) 2417.00 4186.37i 0.0943423 0.163406i
\(59\) −4081.50 7069.37i −0.152648 0.264393i 0.779552 0.626337i \(-0.215447\pi\)
−0.932200 + 0.361944i \(0.882113\pi\)
\(60\) −1386.00 2400.62i −0.0497033 0.0860886i
\(61\) 7583.00 13134.1i 0.260925 0.451936i −0.705563 0.708648i \(-0.749306\pi\)
0.966488 + 0.256711i \(0.0826390\pi\)
\(62\) 5682.00 0.187725
\(63\) 0 0
\(64\) −10688.0 −0.326172
\(65\) 1694.00 2934.09i 0.0497313 0.0861372i
\(66\) 2421.00 + 4193.30i 0.0684124 + 0.118494i
\(67\) 16039.0 + 27780.4i 0.436506 + 0.756051i 0.997417 0.0718253i \(-0.0228824\pi\)
−0.560911 + 0.827876i \(0.689549\pi\)
\(68\) −26544.0 + 45975.6i −0.696136 + 1.20574i
\(69\) −29376.0 −0.742797
\(70\) 0 0
\(71\) −38274.0 −0.901069 −0.450534 0.892759i \(-0.648767\pi\)
−0.450534 + 0.892759i \(0.648767\pi\)
\(72\) −4860.00 + 8417.77i −0.110485 + 0.191366i
\(73\) 17433.0 + 30194.8i 0.382882 + 0.663171i 0.991473 0.130313i \(-0.0415982\pi\)
−0.608591 + 0.793484i \(0.708265\pi\)
\(74\) −11328.0 19620.7i −0.240477 0.416519i
\(75\) 13518.0 23413.9i 0.277498 0.480640i
\(76\) −4592.00 −0.0911943
\(77\) 0 0
\(78\) −5544.00 −0.103178
\(79\) −6764.50 + 11716.5i −0.121946 + 0.211217i −0.920535 0.390660i \(-0.872247\pi\)
0.798589 + 0.601877i \(0.205580\pi\)
\(80\) 3608.00 + 6249.24i 0.0630292 + 0.109170i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 16856.0 29195.4i 0.276834 0.479491i
\(83\) 68103.0 1.08510 0.542552 0.840023i \(-0.317458\pi\)
0.542552 + 0.840023i \(0.317458\pi\)
\(84\) 0 0
\(85\) 20856.0 0.313100
\(86\) −7894.00 + 13672.8i −0.115094 + 0.199348i
\(87\) −10876.5 18838.7i −0.154060 0.266840i
\(88\) −16140.0 27955.3i −0.222176 0.384820i
\(89\) −57461.0 + 99525.4i −0.768950 + 1.33186i 0.169183 + 0.985585i \(0.445887\pi\)
−0.938133 + 0.346276i \(0.887446\pi\)
\(90\) 1782.00 0.0231900
\(91\) 0 0
\(92\) 91392.0 1.12574
\(93\) 12784.5 22143.4i 0.153277 0.265483i
\(94\) −21102.0 36549.7i −0.246322 0.426643i
\(95\) 902.000 + 1562.31i 0.0102541 + 0.0177606i
\(96\) 23184.0 40155.9i 0.256750 0.444704i
\(97\) −154959. −1.67220 −0.836099 0.548579i \(-0.815169\pi\)
−0.836099 + 0.548579i \(0.815169\pi\)
\(98\) 0 0
\(99\) 21789.0 0.223434
\(100\) −42056.0 + 72843.1i −0.420560 + 0.728431i
\(101\) −53785.0 93158.4i −0.524636 0.908695i −0.999589 0.0286843i \(-0.990868\pi\)
0.474953 0.880011i \(-0.342465\pi\)
\(102\) −17064.0 29555.7i −0.162398 0.281281i
\(103\) 4468.00 7738.80i 0.0414973 0.0718755i −0.844531 0.535507i \(-0.820121\pi\)
0.886028 + 0.463632i \(0.153454\pi\)
\(104\) 36960.0 0.335080
\(105\) 0 0
\(106\) 59382.0 0.513322
\(107\) −96833.5 + 167721.i −0.817648 + 1.41621i 0.0897634 + 0.995963i \(0.471389\pi\)
−0.907411 + 0.420244i \(0.861944\pi\)
\(108\) 10206.0 + 17677.3i 0.0841969 + 0.145833i
\(109\) −102555. 177630.i −0.826781 1.43203i −0.900550 0.434752i \(-0.856836\pi\)
0.0737692 0.997275i \(-0.476497\pi\)
\(110\) −2959.00 + 5125.14i −0.0233165 + 0.0403854i
\(111\) −101952. −0.785395
\(112\) 0 0
\(113\) 46664.0 0.343784 0.171892 0.985116i \(-0.445012\pi\)
0.171892 + 0.985116i \(0.445012\pi\)
\(114\) 1476.00 2556.51i 0.0106371 0.0184240i
\(115\) −17952.0 31093.8i −0.126581 0.219245i
\(116\) 33838.0 + 58609.1i 0.233485 + 0.404409i
\(117\) −12474.0 + 21605.6i −0.0842444 + 0.145916i
\(118\) −16326.0 −0.107938
\(119\) 0 0
\(120\) −11880.0 −0.0753119
\(121\) 44345.0 76807.8i 0.275348 0.476916i
\(122\) −15166.0 26268.3i −0.0922511 0.159784i
\(123\) −75852.0 131380.i −0.452069 0.783006i
\(124\) −39774.0 + 68890.6i −0.232298 + 0.402352i
\(125\) 67419.0 0.385929
\(126\) 0 0
\(127\) −304365. −1.67450 −0.837250 0.546820i \(-0.815838\pi\)
−0.837250 + 0.546820i \(0.815838\pi\)
\(128\) −93120.0 + 161289.i −0.502363 + 0.870119i
\(129\) 35523.0 + 61527.6i 0.187947 + 0.325534i
\(130\) −3388.00 5868.19i −0.0175827 0.0304541i
\(131\) −6651.50 + 11520.7i −0.0338642 + 0.0586546i −0.882461 0.470386i \(-0.844115\pi\)
0.848597 + 0.529041i \(0.177448\pi\)
\(132\) −67788.0 −0.338624
\(133\) 0 0
\(134\) 64156.0 0.308656
\(135\) 4009.50 6944.66i 0.0189346 0.0327957i
\(136\) 113760. + 197038.i 0.527403 + 0.913488i
\(137\) 199131. + 344905.i 0.906437 + 1.56999i 0.818977 + 0.573826i \(0.194542\pi\)
0.0874596 + 0.996168i \(0.472125\pi\)
\(138\) −29376.0 + 50880.7i −0.131309 + 0.227434i
\(139\) −230286. −1.01095 −0.505476 0.862841i \(-0.668683\pi\)
−0.505476 + 0.862841i \(0.668683\pi\)
\(140\) 0 0
\(141\) −189918. −0.804486
\(142\) −38274.0 + 66292.5i −0.159288 + 0.275895i
\(143\) −41426.0 71751.9i −0.169408 0.293423i
\(144\) −26568.0 46017.1i −0.106771 0.184933i
\(145\) 13293.5 23025.0i 0.0525073 0.0909452i
\(146\) 69732.0 0.270738
\(147\) 0 0
\(148\) 317184. 1.19030
\(149\) 48567.0 84120.5i 0.179216 0.310410i −0.762397 0.647110i \(-0.775977\pi\)
0.941612 + 0.336700i \(0.109311\pi\)
\(150\) −27036.0 46827.7i −0.0981102 0.169932i
\(151\) 14523.5 + 25155.4i 0.0518357 + 0.0897821i 0.890779 0.454437i \(-0.150159\pi\)
−0.838943 + 0.544219i \(0.816826\pi\)
\(152\) −9840.00 + 17043.4i −0.0345451 + 0.0598338i
\(153\) −153576. −0.530389
\(154\) 0 0
\(155\) 31251.0 0.104480
\(156\) 38808.0 67217.4i 0.127676 0.221142i
\(157\) −288250. 499264.i −0.933298 1.61652i −0.777642 0.628708i \(-0.783584\pi\)
−0.155656 0.987811i \(-0.549749\pi\)
\(158\) 13529.0 + 23432.9i 0.0431145 + 0.0746764i
\(159\) 133610. 231418.i 0.419126 0.725947i
\(160\) 56672.0 0.175012
\(161\) 0 0
\(162\) −13122.0 −0.0392837
\(163\) 132616. 229698.i 0.390955 0.677154i −0.601621 0.798782i \(-0.705478\pi\)
0.992576 + 0.121628i \(0.0388114\pi\)
\(164\) 235984. + 408736.i 0.685130 + 1.18668i
\(165\) 13315.5 + 23063.1i 0.0380757 + 0.0659490i
\(166\) 68103.0 117958.i 0.191821 0.332244i
\(167\) 363790. 1.00939 0.504696 0.863297i \(-0.331605\pi\)
0.504696 + 0.863297i \(0.331605\pi\)
\(168\) 0 0
\(169\) −276429. −0.744504
\(170\) 20856.0 36123.7i 0.0553489 0.0958670i
\(171\) −6642.00 11504.3i −0.0173704 0.0300863i
\(172\) −110516. 191419.i −0.284842 0.493361i
\(173\) −82423.0 + 142761.i −0.209379 + 0.362655i −0.951519 0.307590i \(-0.900478\pi\)
0.742140 + 0.670245i \(0.233811\pi\)
\(174\) −43506.0 −0.108937
\(175\) 0 0
\(176\) 176464. 0.429412
\(177\) −36733.5 + 63624.3i −0.0881311 + 0.152648i
\(178\) 114922. + 199051.i 0.271865 + 0.470884i
\(179\) −15314.0 26524.6i −0.0357237 0.0618752i 0.847611 0.530618i \(-0.178040\pi\)
−0.883334 + 0.468743i \(0.844707\pi\)
\(180\) −12474.0 + 21605.6i −0.0286962 + 0.0497033i
\(181\) 651392. 1.47790 0.738952 0.673759i \(-0.235321\pi\)
0.738952 + 0.673759i \(0.235321\pi\)
\(182\) 0 0
\(183\) −136494. −0.301291
\(184\) 195840. 339205.i 0.426439 0.738614i
\(185\) −62304.0 107914.i −0.133840 0.231818i
\(186\) −25569.0 44286.8i −0.0541915 0.0938625i
\(187\) 255012. 441694.i 0.533282 0.923671i
\(188\) 590856. 1.21923
\(189\) 0 0
\(190\) 3608.00 0.00725074
\(191\) 378680. 655893.i 0.751085 1.30092i −0.196213 0.980561i \(-0.562864\pi\)
0.947297 0.320356i \(-0.103802\pi\)
\(192\) 48096.0 + 83304.7i 0.0941577 + 0.163086i
\(193\) 80169.5 + 138858.i 0.154923 + 0.268335i 0.933031 0.359796i \(-0.117154\pi\)
−0.778108 + 0.628131i \(0.783820\pi\)
\(194\) −154959. + 268397.i −0.295605 + 0.512004i
\(195\) −30492.0 −0.0574248
\(196\) 0 0
\(197\) −61738.0 −0.113341 −0.0566705 0.998393i \(-0.518048\pi\)
−0.0566705 + 0.998393i \(0.518048\pi\)
\(198\) 21789.0 37739.7i 0.0394979 0.0684124i
\(199\) 185454. + 321216.i 0.331974 + 0.574995i 0.982899 0.184147i \(-0.0589522\pi\)
−0.650925 + 0.759142i \(0.725619\pi\)
\(200\) 180240. + 312185.i 0.318622 + 0.551870i
\(201\) 144351. 250023.i 0.252017 0.436506i
\(202\) −215140. −0.370973
\(203\) 0 0
\(204\) 477792. 0.803829
\(205\) 92708.0 160575.i 0.154075 0.266866i
\(206\) −8936.00 15477.6i −0.0146715 0.0254118i
\(207\) 132192. + 228963.i 0.214427 + 0.371398i
\(208\) −101024. + 174979.i −0.161907 + 0.280432i
\(209\) 44116.0 0.0698603
\(210\) 0 0
\(211\) 217450. 0.336243 0.168122 0.985766i \(-0.446230\pi\)
0.168122 + 0.985766i \(0.446230\pi\)
\(212\) −415674. + 719968.i −0.635204 + 1.10021i
\(213\) 172233. + 298316.i 0.260116 + 0.450534i
\(214\) 193667. + 335441.i 0.289082 + 0.500705i
\(215\) −43417.0 + 75200.4i −0.0640566 + 0.110949i
\(216\) 87480.0 0.127578
\(217\) 0 0
\(218\) −410220. −0.584623
\(219\) 156897. 271754.i 0.221057 0.382882i
\(220\) −41426.0 71751.9i −0.0577054 0.0999486i
\(221\) 291984. + 505731.i 0.402141 + 0.696529i
\(222\) −101952. + 176586.i −0.138840 + 0.240477i
\(223\) −589771. −0.794184 −0.397092 0.917779i \(-0.629981\pi\)
−0.397092 + 0.917779i \(0.629981\pi\)
\(224\) 0 0
\(225\) −243324. −0.320427
\(226\) 46664.0 80824.4i 0.0607730 0.105262i
\(227\) −193522. 335191.i −0.249268 0.431745i 0.714055 0.700090i \(-0.246857\pi\)
−0.963323 + 0.268345i \(0.913523\pi\)
\(228\) 20664.0 + 35791.1i 0.0263255 + 0.0455972i
\(229\) −116366. + 201552.i −0.146635 + 0.253979i −0.929982 0.367606i \(-0.880178\pi\)
0.783347 + 0.621585i \(0.213511\pi\)
\(230\) −71808.0 −0.0895062
\(231\) 0 0
\(232\) 290040. 0.353784
\(233\) −21048.0 + 36456.2i −0.0253993 + 0.0439928i −0.878446 0.477842i \(-0.841419\pi\)
0.853046 + 0.521835i \(0.174752\pi\)
\(234\) 24948.0 + 43211.2i 0.0297849 + 0.0515890i
\(235\) −116061. 201024.i −0.137093 0.237453i
\(236\) 114282. 197942.i 0.133567 0.231344i
\(237\) 121761. 0.140811
\(238\) 0 0
\(239\) −313416. −0.354917 −0.177458 0.984128i \(-0.556788\pi\)
−0.177458 + 0.984128i \(0.556788\pi\)
\(240\) 32472.0 56243.2i 0.0363899 0.0630292i
\(241\) 428904. + 742883.i 0.475682 + 0.823906i 0.999612 0.0278556i \(-0.00886787\pi\)
−0.523930 + 0.851762i \(0.675535\pi\)
\(242\) −88690.0 153616.i −0.0973501 0.168615i
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) 424648. 0.456620
\(245\) 0 0
\(246\) −303408. −0.319661
\(247\) −25256.0 + 43744.7i −0.0263404 + 0.0456229i
\(248\) 170460. + 295245.i 0.175992 + 0.304827i
\(249\) −306464. 530810.i −0.313242 0.542552i
\(250\) 67419.0 116773.i 0.0682232 0.118166i
\(251\) −454517. −0.455371 −0.227686 0.973735i \(-0.573116\pi\)
−0.227686 + 0.973735i \(0.573116\pi\)
\(252\) 0 0
\(253\) −878016. −0.862385
\(254\) −304365. + 527176.i −0.296013 + 0.512709i
\(255\) −93852.0 162556.i −0.0903843 0.156550i
\(256\) 15232.0 + 26382.6i 0.0145264 + 0.0251604i
\(257\) 439091. 760528.i 0.414688 0.718261i −0.580707 0.814112i \(-0.697224\pi\)
0.995396 + 0.0958512i \(0.0305573\pi\)
\(258\) 142092. 0.132899
\(259\) 0 0
\(260\) 94864.0 0.0870298
\(261\) −97888.5 + 169548.i −0.0889468 + 0.154060i
\(262\) 13303.0 + 23041.5i 0.0119728 + 0.0207375i
\(263\) −980467. 1.69822e6i −0.874065 1.51392i −0.857756 0.514058i \(-0.828142\pi\)
−0.0163091 0.999867i \(-0.505192\pi\)
\(264\) −145260. + 251598.i −0.128273 + 0.222176i
\(265\) 326601. 0.285695
\(266\) 0 0
\(267\) 1.03430e6 0.887907
\(268\) −449092. + 777850.i −0.381943 + 0.661544i
\(269\) −526898. 912613.i −0.443962 0.768964i 0.554018 0.832505i \(-0.313094\pi\)
−0.997979 + 0.0635408i \(0.979761\pi\)
\(270\) −8019.00 13889.3i −0.00669439 0.0115950i
\(271\) −52529.5 + 90983.8i −0.0434490 + 0.0752559i −0.886932 0.461900i \(-0.847168\pi\)
0.843483 + 0.537156i \(0.180501\pi\)
\(272\) −1.24378e6 −1.01934
\(273\) 0 0
\(274\) 796524. 0.640948
\(275\) 404038. 699814.i 0.322174 0.558022i
\(276\) −411264. 712330.i −0.324974 0.562871i
\(277\) 213796. + 370306.i 0.167417 + 0.289975i 0.937511 0.347955i \(-0.113124\pi\)
−0.770094 + 0.637931i \(0.779791\pi\)
\(278\) −230286. + 398867.i −0.178713 + 0.309540i
\(279\) −230121. −0.176989
\(280\) 0 0
\(281\) 638878. 0.482672 0.241336 0.970442i \(-0.422414\pi\)
0.241336 + 0.970442i \(0.422414\pi\)
\(282\) −189918. + 328948.i −0.142214 + 0.246322i
\(283\) −1.22571e6 2.12299e6i −0.909750 1.57573i −0.814411 0.580288i \(-0.802940\pi\)
−0.0953386 0.995445i \(-0.530393\pi\)
\(284\) −535836. 928095.i −0.394218 0.682805i
\(285\) 8118.00 14060.8i 0.00592021 0.0102541i
\(286\) −165704. −0.119789
\(287\) 0 0
\(288\) −417312. −0.296469
\(289\) −1.08748e6 + 1.88357e6i −0.765908 + 1.32659i
\(290\) −26587.0 46050.0i −0.0185641 0.0321540i
\(291\) 697316. + 1.20779e6i 0.482722 + 0.836099i
\(292\) −488124. + 845456.i −0.335022 + 0.580275i
\(293\) −1.71617e6 −1.16786 −0.583930 0.811804i \(-0.698486\pi\)
−0.583930 + 0.811804i \(0.698486\pi\)
\(294\) 0 0
\(295\) −89793.0 −0.0600741
\(296\) 679680. 1.17724e6i 0.450895 0.780973i
\(297\) −98050.5 169828.i −0.0644998 0.111717i
\(298\) −97134.0 168241.i −0.0633623 0.109747i
\(299\) 502656. 870626.i 0.325157 0.563188i
\(300\) 757008. 0.485621
\(301\) 0 0
\(302\) 58094.0 0.0366534
\(303\) −484065. + 838425.i −0.302898 + 0.524636i
\(304\) −53792.0 93170.5i −0.0333836 0.0578222i
\(305\) −83413.0 144476.i −0.0513433 0.0889293i
\(306\) −153576. + 266001.i −0.0937605 + 0.162398i
\(307\) −1.80897e6 −1.09543 −0.547715 0.836665i \(-0.684502\pi\)
−0.547715 + 0.836665i \(0.684502\pi\)
\(308\) 0 0
\(309\) −80424.0 −0.0479170
\(310\) 31251.0 54128.3i 0.0184697 0.0319904i
\(311\) 760728. + 1.31762e6i 0.445993 + 0.772483i 0.998121 0.0612765i \(-0.0195171\pi\)
−0.552127 + 0.833760i \(0.686184\pi\)
\(312\) −166320. 288075.i −0.0967293 0.167540i
\(313\) −674200. + 1.16775e6i −0.388980 + 0.673734i −0.992313 0.123756i \(-0.960506\pi\)
0.603332 + 0.797490i \(0.293839\pi\)
\(314\) −1.15300e6 −0.659941
\(315\) 0 0
\(316\) −378812. −0.213406
\(317\) 24847.5 43037.1i 0.0138878 0.0240544i −0.858998 0.511979i \(-0.828913\pi\)
0.872886 + 0.487925i \(0.162246\pi\)
\(318\) −267219. 462837.i −0.148183 0.256661i
\(319\) −325086. 563066.i −0.178864 0.309801i
\(320\) −58784.0 + 101817.i −0.0320911 + 0.0555834i
\(321\) 1.74300e6 0.944138
\(322\) 0 0
\(323\) −310944. −0.165835
\(324\) 91854.0 159096.i 0.0486111 0.0841969i
\(325\) 462616. + 801274.i 0.242947 + 0.420797i
\(326\) −265232. 459395.i −0.138224 0.239410i
\(327\) −922995. + 1.59867e6i −0.477342 + 0.826781i
\(328\) 2.02272e6 1.03813
\(329\) 0 0
\(330\) 53262.0 0.0269236
\(331\) −793918. + 1.37511e6i −0.398296 + 0.689868i −0.993516 0.113694i \(-0.963732\pi\)
0.595220 + 0.803563i \(0.297065\pi\)
\(332\) 953442. + 1.65141e6i 0.474733 + 0.822261i
\(333\) 458784. + 794637.i 0.226724 + 0.392698i
\(334\) 363790. 630103.i 0.178437 0.309062i
\(335\) 352858. 0.171786
\(336\) 0 0
\(337\) 214825. 0.103041 0.0515205 0.998672i \(-0.483593\pi\)
0.0515205 + 0.998672i \(0.483593\pi\)
\(338\) −276429. + 478789.i −0.131611 + 0.227957i
\(339\) −209988. 363710.i −0.0992419 0.171892i
\(340\) 291984. + 505731.i 0.136981 + 0.237259i
\(341\) 382114. 661842.i 0.177954 0.308225i
\(342\) −26568.0 −0.0122827
\(343\) 0 0
\(344\) −947280. −0.431601
\(345\) −161568. + 279844.i −0.0730815 + 0.126581i
\(346\) 164846. + 285522.i 0.0740267 + 0.128218i
\(347\) −1.29430e6 2.24179e6i −0.577046 0.999473i −0.995816 0.0913809i \(-0.970872\pi\)
0.418770 0.908092i \(-0.362461\pi\)
\(348\) 304542. 527482.i 0.134803 0.233485i
\(349\) 24878.0 0.0109333 0.00546666 0.999985i \(-0.498260\pi\)
0.00546666 + 0.999985i \(0.498260\pi\)
\(350\) 0 0
\(351\) 224532. 0.0972771
\(352\) 692944. 1.20021e6i 0.298086 0.516300i
\(353\) −868004. 1.50343e6i −0.370753 0.642163i 0.618928 0.785447i \(-0.287567\pi\)
−0.989682 + 0.143284i \(0.954234\pi\)
\(354\) 73467.0 + 127249.i 0.0311590 + 0.0539691i
\(355\) −210507. + 364609.i −0.0886535 + 0.153552i
\(356\) −3.21782e6 −1.34566
\(357\) 0 0
\(358\) −61256.0 −0.0252604
\(359\) −431213. + 746883.i −0.176586 + 0.305856i −0.940709 0.339215i \(-0.889839\pi\)
0.764123 + 0.645070i \(0.223172\pi\)
\(360\) 53460.0 + 92595.4i 0.0217407 + 0.0376559i
\(361\) 1.22460e6 + 2.12107e6i 0.494569 + 0.856618i
\(362\) 651392. 1.12824e6i 0.261259 0.452514i
\(363\) −798210. −0.317944
\(364\) 0 0
\(365\) 383526. 0.150682
\(366\) −136494. + 236415.i −0.0532612 + 0.0922511i
\(367\) 1.55771e6 + 2.69803e6i 0.603700 + 1.04564i 0.992255 + 0.124214i \(0.0396409\pi\)
−0.388555 + 0.921425i \(0.627026\pi\)
\(368\) 1.07059e6 + 1.85432e6i 0.412102 + 0.713781i
\(369\) −682668. + 1.18242e6i −0.261002 + 0.452069i
\(370\) −249216. −0.0946393
\(371\) 0 0
\(372\) 715932. 0.268234
\(373\) 898472. 1.55620e6i 0.334374 0.579153i −0.648990 0.760797i \(-0.724808\pi\)
0.983364 + 0.181644i \(0.0581418\pi\)
\(374\) −510024. 883387.i −0.188544 0.326567i
\(375\) −303386. 525479.i −0.111408 0.192964i
\(376\) 1.26612e6 2.19298e6i 0.461855 0.799956i
\(377\) 744436. 0.269758
\(378\) 0 0
\(379\) 3.45466e6 1.23540 0.617699 0.786415i \(-0.288065\pi\)
0.617699 + 0.786415i \(0.288065\pi\)
\(380\) −25256.0 + 43744.7i −0.00897234 + 0.0155405i
\(381\) 1.36964e6 + 2.37229e6i 0.483387 + 0.837250i
\(382\) −757360. 1.31179e6i −0.265549 0.459944i
\(383\) 1.07752e6 1.86632e6i 0.375343 0.650113i −0.615036 0.788499i \(-0.710858\pi\)
0.990378 + 0.138387i \(0.0441917\pi\)
\(384\) 1.67616e6 0.580079
\(385\) 0 0
\(386\) 320678. 0.109547
\(387\) 319707. 553749.i 0.108511 0.187947i
\(388\) −2.16943e6 3.75756e6i −0.731586 1.26714i
\(389\) 231387. + 400774.i 0.0775291 + 0.134284i 0.902183 0.431353i \(-0.141964\pi\)
−0.824654 + 0.565637i \(0.808630\pi\)
\(390\) −30492.0 + 52813.7i −0.0101514 + 0.0175827i
\(391\) 6.18854e6 2.04714
\(392\) 0 0
\(393\) 119727. 0.0391031
\(394\) −61738.0 + 106933.i −0.0200360 + 0.0347034i
\(395\) 74409.5 + 128881.i 0.0239958 + 0.0415620i
\(396\) 305046. + 528355.i 0.0977524 + 0.169312i
\(397\) −2.03311e6 + 3.52144e6i −0.647416 + 1.12136i 0.336321 + 0.941747i \(0.390817\pi\)
−0.983738 + 0.179611i \(0.942516\pi\)
\(398\) 741816. 0.234741
\(399\) 0 0
\(400\) −1.97062e6 −0.615820
\(401\) 2.53432e6 4.38956e6i 0.787045 1.36320i −0.140724 0.990049i \(-0.544943\pi\)
0.927769 0.373154i \(-0.121724\pi\)
\(402\) −288702. 500047.i −0.0891014 0.154328i
\(403\) 437514. + 757796.i 0.134193 + 0.232429i
\(404\) 1.50598e6 2.60843e6i 0.459056 0.795109i
\(405\) −72171.0 −0.0218638
\(406\) 0 0
\(407\) −3.04723e6 −0.911842
\(408\) 1.02384e6 1.77334e6i 0.304496 0.527403i
\(409\) 1.43867e6 + 2.49185e6i 0.425258 + 0.736568i 0.996444 0.0842522i \(-0.0268501\pi\)
−0.571187 + 0.820820i \(0.693517\pi\)
\(410\) −185416. 321150.i −0.0544738 0.0943514i
\(411\) 1.79218e6 3.10415e6i 0.523331 0.906437i
\(412\) 250208. 0.0726203
\(413\) 0 0
\(414\) 528768. 0.151623
\(415\) 374567. 648768.i 0.106760 0.184914i
\(416\) 793408. + 1.37422e6i 0.224783 + 0.389335i
\(417\) 1.03629e6 + 1.79490e6i 0.291837 + 0.505476i
\(418\) 44116.0 76411.2i 0.0123497 0.0213903i
\(419\) 3.41342e6 0.949850 0.474925 0.880026i \(-0.342475\pi\)
0.474925 + 0.880026i \(0.342475\pi\)
\(420\) 0 0
\(421\) −1.30737e6 −0.359496 −0.179748 0.983713i \(-0.557528\pi\)
−0.179748 + 0.983713i \(0.557528\pi\)
\(422\) 217450. 376634.i 0.0594399 0.102953i
\(423\) 854631. + 1.48026e6i 0.232235 + 0.402243i
\(424\) 1.78146e6 + 3.08558e6i 0.481240 + 0.833532i
\(425\) −2.84779e6 + 4.93252e6i −0.764779 + 1.32464i
\(426\) 688932. 0.183930
\(427\) 0 0
\(428\) −5.42268e6 −1.43088
\(429\) −372834. + 645767.i −0.0978075 + 0.169408i
\(430\) 86834.0 + 150401.i 0.0226474 + 0.0392265i
\(431\) −967734. 1.67616e6i −0.250936 0.434634i 0.712848 0.701319i \(-0.247405\pi\)
−0.963784 + 0.266685i \(0.914072\pi\)
\(432\) −239112. + 414154.i −0.0616442 + 0.106771i
\(433\) −516670. −0.132432 −0.0662161 0.997805i \(-0.521093\pi\)
−0.0662161 + 0.997805i \(0.521093\pi\)
\(434\) 0 0
\(435\) −239283. −0.0606302
\(436\) 2.87154e6 4.97365e6i 0.723434 1.25302i
\(437\) 267648. + 463580.i 0.0670441 + 0.116124i
\(438\) −313794. 543507.i −0.0781555 0.135369i
\(439\) 1.45765e6 2.52472e6i 0.360987 0.625249i −0.627136 0.778910i \(-0.715773\pi\)
0.988124 + 0.153661i \(0.0491064\pi\)
\(440\) −355080. −0.0874369
\(441\) 0 0
\(442\) 1.16794e6 0.284357
\(443\) 891896. 1.54481e6i 0.215926 0.373995i −0.737633 0.675202i \(-0.764056\pi\)
0.953559 + 0.301208i \(0.0973897\pi\)
\(444\) −1.42733e6 2.47220e6i −0.343610 0.595151i
\(445\) 632071. + 1.09478e6i 0.151309 + 0.262076i
\(446\) −589771. + 1.02151e6i −0.140393 + 0.243168i
\(447\) −874206. −0.206940
\(448\) 0 0
\(449\) 4.00158e6 0.936733 0.468366 0.883534i \(-0.344843\pi\)
0.468366 + 0.883534i \(0.344843\pi\)
\(450\) −243324. + 421450.i −0.0566440 + 0.0981102i
\(451\) −2.26713e6 3.92679e6i −0.524850 0.909067i
\(452\) 653296. + 1.13154e6i 0.150406 + 0.260510i
\(453\) 130712. 226399.i 0.0299274 0.0518357i
\(454\) −774090. −0.176259
\(455\) 0 0
\(456\) 177120. 0.0398892
\(457\) 583832. 1.01123e6i 0.130767 0.226495i −0.793206 0.608954i \(-0.791589\pi\)
0.923972 + 0.382459i \(0.124923\pi\)
\(458\) 232732. + 403104.i 0.0518433 + 0.0897952i
\(459\) 691092. + 1.19701e6i 0.153110 + 0.265195i
\(460\) 502656. 870626.i 0.110758 0.191839i
\(461\) −3.61358e6 −0.791928 −0.395964 0.918266i \(-0.629589\pi\)
−0.395964 + 0.918266i \(0.629589\pi\)
\(462\) 0 0
\(463\) −1.80111e6 −0.390471 −0.195235 0.980756i \(-0.562547\pi\)
−0.195235 + 0.980756i \(0.562547\pi\)
\(464\) −792776. + 1.37313e6i −0.170945 + 0.296085i
\(465\) −140630. 243577.i −0.0301609 0.0522402i
\(466\) 42096.0 + 72912.4i 0.00897999 + 0.0155538i
\(467\) −1.18487e6 + 2.05226e6i −0.251409 + 0.435452i −0.963914 0.266214i \(-0.914227\pi\)
0.712505 + 0.701667i \(0.247560\pi\)
\(468\) −698544. −0.147428
\(469\) 0 0
\(470\) −464244. −0.0969397
\(471\) −2.59425e6 + 4.49337e6i −0.538840 + 0.933298i
\(472\) −489780. 848324.i −0.101192 0.175270i
\(473\) 1.06174e6 + 1.83899e6i 0.218206 + 0.377944i
\(474\) 121761. 210896.i 0.0248921 0.0431145i
\(475\) −492656. −0.100187
\(476\) 0 0
\(477\) −2.40497e6 −0.483965
\(478\) −313416. + 542852.i −0.0627410 + 0.108671i
\(479\) 259073. + 448728.i 0.0515921 + 0.0893602i 0.890668 0.454654i \(-0.150237\pi\)
−0.839076 + 0.544014i \(0.816904\pi\)
\(480\) −255024. 441715.i −0.0505217 0.0875062i
\(481\) 1.74451e6 3.02158e6i 0.343804 0.595486i
\(482\) 1.71561e6 0.336358
\(483\) 0 0
\(484\) 2.48332e6 0.481858
\(485\) −852274. + 1.47618e6i −0.164522 + 0.284961i
\(486\) 59049.0 + 102276.i 0.0113402 + 0.0196419i
\(487\) −1.41306e6 2.44750e6i −0.269985 0.467627i 0.698873 0.715246i \(-0.253685\pi\)
−0.968858 + 0.247619i \(0.920352\pi\)
\(488\) 909960. 1.57610e6i 0.172971 0.299594i
\(489\) −2.38709e6 −0.451436
\(490\) 0 0
\(491\) 9.34747e6 1.74981 0.874904 0.484296i \(-0.160924\pi\)
0.874904 + 0.484296i \(0.160924\pi\)
\(492\) 2.12386e6 3.67863e6i 0.395560 0.685130i
\(493\) 2.29132e6 + 3.96868e6i 0.424588 + 0.735408i
\(494\) 50512.0 + 87489.4i 0.00931273 + 0.0161301i
\(495\) 119840. 207568.i 0.0219830 0.0380757i
\(496\) −1.86370e6 −0.340150
\(497\) 0 0
\(498\) −1.22585e6 −0.221496
\(499\) −4.08593e6 + 7.07703e6i −0.734580 + 1.27233i 0.220327 + 0.975426i \(0.429288\pi\)
−0.954907 + 0.296904i \(0.904046\pi\)
\(500\) 943866. + 1.63482e6i 0.168844 + 0.292446i
\(501\) −1.63706e6 2.83546e6i −0.291386 0.504696i
\(502\) −454517. + 787247.i −0.0804991 + 0.139428i
\(503\) 7.37713e6 1.30007 0.650036 0.759903i \(-0.274754\pi\)
0.650036 + 0.759903i \(0.274754\pi\)
\(504\) 0 0
\(505\) −1.18327e6 −0.206469
\(506\) −878016. + 1.52077e6i −0.152450 + 0.264050i
\(507\) 1.24393e6 + 2.15455e6i 0.214920 + 0.372252i
\(508\) −4.26111e6 7.38046e6i −0.732594 1.26889i
\(509\) −163158. + 282597.i −0.0279134 + 0.0483474i −0.879645 0.475631i \(-0.842220\pi\)
0.851731 + 0.523979i \(0.175553\pi\)
\(510\) −375408. −0.0639114
\(511\) 0 0
\(512\) −5.89875e6 −0.994455
\(513\) −59778.0 + 103539.i −0.0100288 + 0.0173704i
\(514\) −878182. 1.52106e6i −0.146614 0.253944i
\(515\) −49148.0 85126.8i −0.00816559 0.0141432i
\(516\) −994644. + 1.72277e6i −0.164454 + 0.284842i
\(517\) −5.67644e6 −0.934006
\(518\) 0 0
\(519\) 1.48361e6 0.241770
\(520\) 203280. 352091.i 0.0329675 0.0571014i
\(521\) −1.08351e6 1.87670e6i −0.174880 0.302901i 0.765240 0.643745i \(-0.222620\pi\)
−0.940120 + 0.340844i \(0.889287\pi\)
\(522\) 195777. + 339096.i 0.0314474 + 0.0544686i
\(523\) −361702. + 626486.i −0.0578225 + 0.100151i −0.893488 0.449088i \(-0.851749\pi\)
0.835665 + 0.549239i \(0.185082\pi\)
\(524\) −372484. −0.0592624
\(525\) 0 0
\(526\) −3.92187e6 −0.618057
\(527\) −2.69327e6 + 4.66488e6i −0.422428 + 0.731667i
\(528\) −794088. 1.37540e6i −0.123961 0.214706i
\(529\) −2.10868e6 3.65233e6i −0.327620 0.567455i
\(530\) 326601. 565690.i 0.0505042 0.0874759i
\(531\) 661203. 0.101765
\(532\) 0 0
\(533\) 5.19165e6 0.791566
\(534\) 1.03430e6 1.79146e6i 0.156961 0.271865i
\(535\) 1.06517e6 + 1.84493e6i 0.160892 + 0.278673i
\(536\) 1.92468e6 + 3.33364e6i 0.289365 + 0.501196i
\(537\) −137826. + 238722.i −0.0206251 + 0.0357237i
\(538\) −2.10759e6 −0.313928
\(539\) 0 0
\(540\) 224532. 0.0331355
\(541\) −2.99982e6 + 5.19584e6i −0.440659 + 0.763243i −0.997738 0.0672159i \(-0.978588\pi\)
0.557080 + 0.830459i \(0.311922\pi\)
\(542\) 105059. + 181968.i 0.0153616 + 0.0266070i
\(543\) −2.93126e6 5.07710e6i −0.426634 0.738952i
\(544\) −4.88410e6 + 8.45950e6i −0.707599 + 1.22560i
\(545\) −2.25621e6 −0.325378
\(546\) 0 0
\(547\) 7.01570e6 1.00254 0.501271 0.865290i \(-0.332866\pi\)
0.501271 + 0.865290i \(0.332866\pi\)
\(548\) −5.57567e6 + 9.65734e6i −0.793132 + 1.37375i
\(549\) 614223. + 1.06387e6i 0.0869752 + 0.150645i
\(550\) −808076. 1.39963e6i −0.113906 0.197290i
\(551\) −198194. + 343282.i −0.0278107 + 0.0481695i
\(552\) −3.52512e6 −0.492409
\(553\) 0 0
\(554\) 855184. 0.118382
\(555\) −560736. + 971223.i −0.0772727 + 0.133840i
\(556\) −3.22400e6 5.58414e6i −0.442291 0.766071i
\(557\) 4.45936e6 + 7.72384e6i 0.609025 + 1.05486i 0.991402 + 0.130855i \(0.0417722\pi\)
−0.382377 + 0.924006i \(0.624894\pi\)
\(558\) −230121. + 398581.i −0.0312875 + 0.0541915i
\(559\) −2.43135e6 −0.329093
\(560\) 0 0
\(561\) −4.59022e6 −0.615781
\(562\) 638878. 1.10657e6i 0.0853252 0.147788i
\(563\) −6.67412e6 1.15599e7i −0.887407 1.53703i −0.842930 0.538023i \(-0.819171\pi\)
−0.0444767 0.999010i \(-0.514162\pi\)
\(564\) −2.65885e6 4.60527e6i −0.351963 0.609617i
\(565\) 256652. 444534.i 0.0338239 0.0585847i
\(566\) −4.90284e6 −0.643290
\(567\) 0 0
\(568\) −4.59288e6 −0.597330
\(569\) −551074. + 954488.i −0.0713558 + 0.123592i −0.899496 0.436930i \(-0.856066\pi\)
0.828140 + 0.560521i \(0.189399\pi\)
\(570\) −16236.0 28121.6i −0.00209311 0.00362537i
\(571\) −946741. 1.63980e6i −0.121518 0.210475i 0.798848 0.601532i \(-0.205443\pi\)
−0.920367 + 0.391057i \(0.872110\pi\)
\(572\) 1.15993e6 2.00905e6i 0.148232 0.256745i
\(573\) −6.81624e6 −0.867278
\(574\) 0 0
\(575\) 9.80506e6 1.23675
\(576\) 432864. 749742.i 0.0543620 0.0941577i
\(577\) 1.41476e6 + 2.45043e6i 0.176906 + 0.306410i 0.940819 0.338909i \(-0.110058\pi\)
−0.763913 + 0.645319i \(0.776725\pi\)
\(578\) 2.17496e6 + 3.76714e6i 0.270789 + 0.469021i
\(579\) 721526. 1.24972e6i 0.0894448 0.154923i
\(580\) 744436. 0.0918877
\(581\) 0 0
\(582\) 2.78926e6 0.341336
\(583\) 3.99344e6 6.91684e6i 0.486604 0.842823i
\(584\) 2.09196e6 + 3.62338e6i 0.253817 + 0.439624i
\(585\) 137214. + 237662.i 0.0165771 + 0.0287124i
\(586\) −1.71617e6 + 2.97249e6i −0.206451 + 0.357583i
\(587\) 1.06799e7 1.27930 0.639649 0.768667i \(-0.279080\pi\)
0.639649 + 0.768667i \(0.279080\pi\)
\(588\) 0 0
\(589\) −465924. −0.0553384
\(590\) −89793.0 + 155526.i −0.0106197 + 0.0183939i
\(591\) 277821. + 481200.i 0.0327187 + 0.0566705i
\(592\) 3.71558e6 + 6.43558e6i 0.435735 + 0.754716i
\(593\) −7.34984e6 + 1.27303e7i −0.858304 + 1.48663i 0.0152406 + 0.999884i \(0.495149\pi\)
−0.873545 + 0.486743i \(0.838185\pi\)
\(594\) −392202. −0.0456083
\(595\) 0 0
\(596\) 2.71975e6 0.313627
\(597\) 1.66909e6 2.89094e6i 0.191665 0.331974i
\(598\) −1.00531e6 1.74125e6i −0.114960 0.199117i
\(599\) −4.24581e6 7.35396e6i −0.483497 0.837441i 0.516323 0.856394i \(-0.327300\pi\)
−0.999820 + 0.0189523i \(0.993967\pi\)
\(600\) 1.62216e6 2.80966e6i 0.183957 0.318622i
\(601\) −8.62947e6 −0.974536 −0.487268 0.873253i \(-0.662006\pi\)
−0.487268 + 0.873253i \(0.662006\pi\)
\(602\) 0 0
\(603\) −2.59832e6 −0.291004
\(604\) −406658. + 704352.i −0.0453562 + 0.0785593i
\(605\) −487795. 844886.i −0.0541812 0.0938447i
\(606\) 968130. + 1.67685e6i 0.107091 + 0.185487i
\(607\) 5.29037e6 9.16319e6i 0.582793 1.00943i −0.412354 0.911024i \(-0.635293\pi\)
0.995147 0.0984029i \(-0.0313734\pi\)
\(608\) −844928. −0.0926959
\(609\) 0 0
\(610\) −333652. −0.0363052
\(611\) 3.24971e6 5.62866e6i 0.352161 0.609961i
\(612\) −2.15006e6 3.72402e6i −0.232045 0.401914i
\(613\) −1.92392e6 3.33233e6i −0.206793 0.358176i 0.743910 0.668280i \(-0.232969\pi\)
−0.950703 + 0.310104i \(0.899636\pi\)
\(614\) −1.80897e6 + 3.13322e6i −0.193647 + 0.335406i
\(615\) −1.66874e6 −0.177911
\(616\) 0 0
\(617\) −1.51001e7 −1.59686 −0.798428 0.602090i \(-0.794335\pi\)
−0.798428 + 0.602090i \(0.794335\pi\)
\(618\) −80424.0 + 139298.i −0.00847061 + 0.0146715i
\(619\) 4.96551e6 + 8.60051e6i 0.520879 + 0.902190i 0.999705 + 0.0242796i \(0.00772920\pi\)
−0.478826 + 0.877910i \(0.658937\pi\)
\(620\) 437514. + 757796.i 0.0457102 + 0.0791723i
\(621\) 1.18973e6 2.06067e6i 0.123799 0.214427i
\(622\) 3.04291e6 0.315365
\(623\) 0 0
\(624\) 1.81843e6 0.186954
\(625\) −4.32295e6 + 7.48756e6i −0.442670 + 0.766726i
\(626\) 1.34840e6 + 2.33550e6i 0.137525 + 0.238201i
\(627\) −198522. 343850.i −0.0201669 0.0349301i
\(628\) 8.07100e6 1.39794e7i 0.816635 1.41445i
\(629\) 2.14779e7 2.16454
\(630\) 0 0
\(631\) −9.25224e6 −0.925068 −0.462534 0.886602i \(-0.653060\pi\)
−0.462534 + 0.886602i \(0.653060\pi\)
\(632\) −811740. + 1.40597e6i −0.0808396 + 0.140018i
\(633\) −978525. 1.69486e6i −0.0970650 0.168122i
\(634\) −49695.0 86074.3i −0.00491009 0.00850453i
\(635\) −1.67401e6 + 2.89947e6i −0.164749 + 0.285354i
\(636\) 7.48213e6 0.733470
\(637\) 0 0
\(638\) −1.30035e6 −0.126476
\(639\) 1.55010e6 2.68485e6i 0.150178 0.260116i
\(640\) 1.02432e6 + 1.77417e6i 0.0988521 + 0.171217i
\(641\) −2.50214e6 4.33384e6i −0.240529 0.416608i 0.720336 0.693625i \(-0.243987\pi\)
−0.960865 + 0.277017i \(0.910654\pi\)
\(642\) 1.74300e6 3.01897e6i 0.166902 0.289082i
\(643\) −1.26137e7 −1.20314 −0.601569 0.798821i \(-0.705457\pi\)
−0.601569 + 0.798821i \(0.705457\pi\)
\(644\) 0 0
\(645\) 781506. 0.0739662
\(646\) −310944. + 538571.i −0.0293157 + 0.0507764i
\(647\) −6.26916e6 1.08585e7i −0.588774 1.01979i −0.994393 0.105744i \(-0.966278\pi\)
0.405620 0.914042i \(-0.367056\pi\)
\(648\) −393660. 681839.i −0.0368285 0.0637888i
\(649\) −1.09792e6 + 1.90166e6i −0.102320 + 0.177223i
\(650\) 1.85046e6 0.171790
\(651\) 0 0
\(652\) 7.42650e6 0.684171
\(653\) 4.33033e6 7.50035e6i 0.397409 0.688333i −0.595996 0.802987i \(-0.703243\pi\)
0.993405 + 0.114654i \(0.0365760\pi\)
\(654\) 1.84599e6 + 3.19735e6i 0.168766 + 0.292311i
\(655\) 73166.5 + 126728.i 0.00666360 + 0.0115417i
\(656\) −5.52877e6 + 9.57611e6i −0.501613 + 0.868819i
\(657\) −2.82415e6 −0.255255
\(658\) 0 0
\(659\) 7.94177e6 0.712367 0.356183 0.934416i \(-0.384078\pi\)
0.356183 + 0.934416i \(0.384078\pi\)
\(660\) −372834. + 645767.i −0.0333162 + 0.0577054i
\(661\) −1.05708e6 1.83092e6i −0.0941032 0.162992i 0.815131 0.579277i \(-0.196665\pi\)
−0.909234 + 0.416285i \(0.863332\pi\)
\(662\) 1.58784e6 + 2.75021e6i 0.140819 + 0.243905i
\(663\) 2.62786e6 4.55158e6i 0.232176 0.402141i
\(664\) 8.17236e6 0.719329
\(665\) 0 0
\(666\) 1.83514e6 0.160318
\(667\) 3.94454e6 6.83215e6i 0.343307 0.594625i
\(668\) 5.09306e6 + 8.82144e6i 0.441609 + 0.764889i
\(669\) 2.65397e6 + 4.59681e6i 0.229261 + 0.397092i
\(670\) 352858. 611168.i 0.0303678 0.0525985i
\(671\) −4.07965e6 −0.349798
\(672\) 0 0
\(673\) −442307. −0.0376432 −0.0188216 0.999823i \(-0.505991\pi\)
−0.0188216 + 0.999823i \(0.505991\pi\)
\(674\) 214825. 372088.i 0.0182152 0.0315497i
\(675\) 1.09496e6 + 1.89652e6i 0.0924992 + 0.160213i
\(676\) −3.87001e6 6.70305e6i −0.325720 0.564164i
\(677\) 5.37804e6 9.31503e6i 0.450975 0.781111i −0.547472 0.836824i \(-0.684410\pi\)
0.998447 + 0.0557130i \(0.0177432\pi\)
\(678\) −839952. −0.0701746
\(679\) 0 0
\(680\) 2.50272e6 0.207558
\(681\) −1.74170e6 + 3.01672e6i −0.143915 + 0.249268i
\(682\) −764229. 1.32368e6i −0.0629162 0.108974i
\(683\) 5.74430e6 + 9.94941e6i 0.471178 + 0.816104i 0.999456 0.0329669i \(-0.0104956\pi\)
−0.528278 + 0.849071i \(0.677162\pi\)
\(684\) 185976. 322120.i 0.0151991 0.0263255i
\(685\) 4.38088e6 0.356726
\(686\) 0 0
\(687\) 2.09459e6 0.169319
\(688\) 2.58923e6 4.48468e6i 0.208545 0.361211i
\(689\) 4.57241e6 + 7.91965e6i 0.366942 + 0.635562i
\(690\) 323136. + 559688.i 0.0258382 + 0.0447531i
\(691\) 5.06942e6 8.78049e6i 0.403890 0.699558i −0.590302 0.807183i \(-0.700991\pi\)
0.994192 + 0.107625i \(0.0343246\pi\)
\(692\) −4.61569e6 −0.366413
\(693\) 0 0
\(694\) −5.17719e6 −0.408033
\(695\) −1.26657e6 + 2.19377e6i −0.0994645 + 0.172278i
\(696\) −1.30518e6 2.26064e6i −0.102129 0.176892i
\(697\) 1.59795e7 + 2.76773e7i 1.24589 + 2.15795i
\(698\) 24878.0 43090.0i 0.00193276 0.00334763i
\(699\) 378864. 0.0293285
\(700\) 0 0
\(701\) −1.96839e7 −1.51292 −0.756459 0.654041i \(-0.773073\pi\)
−0.756459 + 0.654041i \(0.773073\pi\)
\(702\) 224532. 388901.i 0.0171963 0.0297849i
\(703\) 928896. + 1.60890e6i 0.0708890 + 0.122783i
\(704\) 1.43754e6 + 2.48989e6i 0.109317 + 0.189342i
\(705\) −1.04455e6 + 1.80921e6i −0.0791509 + 0.137093i
\(706\) −3.47202e6 −0.262162
\(707\) 0 0
\(708\) −2.05708e6 −0.154229
\(709\) 1.00859e7 1.74692e7i 0.753524 1.30514i −0.192581 0.981281i \(-0.561686\pi\)
0.946105 0.323861i \(-0.104981\pi\)
\(710\) 421014. + 729218.i 0.0313437 + 0.0542889i
\(711\) −547924. 949033.i −0.0406487 0.0704056i
\(712\) −6.89532e6 + 1.19430e7i −0.509747 + 0.882907i
\(713\) 9.27302e6 0.683121
\(714\) 0 0
\(715\) −911372. −0.0666700
\(716\) 428792. 742690.i 0.0312582 0.0541408i
\(717\) 1.41037e6 + 2.44284e6i 0.102456 + 0.177458i
\(718\) 862426. + 1.49377e6i 0.0624325 + 0.108136i
\(719\) 2.07867e6 3.60037e6i 0.149956 0.259731i −0.781255 0.624212i \(-0.785420\pi\)
0.931211 + 0.364481i \(0.118753\pi\)
\(720\) −584496. −0.0420194
\(721\) 0 0
\(722\) 4.89841e6 0.349713
\(723\) 3.86013e6 6.68594e6i 0.274635 0.475682i
\(724\) 9.11949e6 + 1.57954e7i 0.646583 + 1.11991i
\(725\) 3.63033e6 + 6.28792e6i 0.256508 + 0.444286i
\(726\) −798210. + 1.38254e6i −0.0562051 + 0.0973501i
\(727\) 1.54433e7 1.08369 0.541845 0.840479i \(-0.317726\pi\)
0.541845 + 0.840479i \(0.317726\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 383526. 664287.i 0.0266371 0.0461369i
\(731\) −7.48351e6 1.29618e7i −0.517979 0.897166i
\(732\) −1.91092e6 3.30980e6i −0.131815 0.228310i
\(733\) −3.10207e6 + 5.37294e6i −0.213251 + 0.369362i −0.952730 0.303818i \(-0.901739\pi\)
0.739479 + 0.673180i \(0.235072\pi\)
\(734\) 6.23084e6 0.426880
\(735\) 0 0
\(736\) 1.68161e7 1.14428
\(737\) 4.31449e6 7.47292e6i 0.292591 0.506782i
\(738\) 1.36534e6 + 2.36483e6i 0.0922781 + 0.159830i
\(739\) −1.09492e7 1.89646e7i −0.737517 1.27742i −0.953610 0.301045i \(-0.902665\pi\)
0.216093 0.976373i \(-0.430669\pi\)
\(740\) 1.74451e6 3.02158e6i 0.117110 0.202841i
\(741\) 454608. 0.0304153
\(742\) 0 0
\(743\) −2.75483e6 −0.183073 −0.0915363 0.995802i \(-0.529178\pi\)
−0.0915363 + 0.995802i \(0.529178\pi\)
\(744\) 1.53414e6 2.65721e6i 0.101609 0.175992i
\(745\) −534237. 925326.i −0.0352650 0.0610807i
\(746\) −1.79694e6 3.11240e6i −0.118219 0.204761i
\(747\) −2.75817e6 + 4.77729e6i −0.180851 + 0.313242i
\(748\) 1.42807e7 0.933243
\(749\) 0 0
\(750\) −1.21354e6 −0.0787774
\(751\) −6.45604e6 + 1.11822e7i −0.417702 + 0.723481i −0.995708 0.0925517i \(-0.970498\pi\)
0.578006 + 0.816032i \(0.303831\pi\)
\(752\) 6.92146e6 + 1.19883e7i 0.446327 + 0.773061i
\(753\) 2.04533e6 + 3.54261e6i 0.131454 + 0.227686i
\(754\) 744436. 1.28940e6i 0.0476869 0.0825961i
\(755\) 319517. 0.0203998
\(756\) 0 0
\(757\) −2.64315e7 −1.67642 −0.838209 0.545349i \(-0.816397\pi\)
−0.838209 + 0.545349i \(0.816397\pi\)
\(758\) 3.45466e6 5.98364e6i 0.218390 0.378262i
\(759\) 3.95107e6 + 6.84346e6i 0.248949 + 0.431192i
\(760\) 108240. + 187477.i 0.00679757 + 0.0117737i
\(761\) 6.11069e6 1.05840e7i 0.382498 0.662506i −0.608921 0.793231i \(-0.708397\pi\)
0.991419 + 0.130725i \(0.0417306\pi\)
\(762\) 5.47857e6 0.341806
\(763\) 0 0
\(764\) 2.12061e7 1.31440
\(765\) −844668. + 1.46301e6i −0.0521834 + 0.0903843i
\(766\) −2.15504e6 3.73264e6i −0.132704 0.229850i
\(767\) −1.25710e6 2.17736e6i −0.0771582 0.133642i
\(768\) 137088. 237443.i 0.00838680 0.0145264i
\(769\) −6.10654e6 −0.372374 −0.186187 0.982514i \(-0.559613\pi\)
−0.186187 + 0.982514i \(0.559613\pi\)
\(770\) 0 0
\(771\) −7.90364e6 −0.478841
\(772\) −2.24475e6 + 3.88801e6i −0.135558 + 0.234793i
\(773\) −1.51110e6 2.61730e6i −0.0909588 0.157545i 0.816956 0.576700i \(-0.195660\pi\)
−0.907915 + 0.419155i \(0.862326\pi\)
\(774\) −639414. 1.10750e6i −0.0383645 0.0664493i
\(775\) −4.26718e6 + 7.39098e6i −0.255204 + 0.442026i
\(776\) −1.85951e7 −1.10852
\(777\) 0 0
\(778\) 925548. 0.0548214
\(779\) −1.38219e6 + 2.39403e6i −0.0816065 + 0.141347i
\(780\) −426888. 739392.i −0.0251233 0.0435149i
\(781\) 5.14785e6 + 8.91634e6i 0.301994 + 0.523069i
\(782\) 6.18854e6 1.07189e7i 0.361886 0.626805i
\(783\) 1.76199e6 0.102707
\(784\) 0 0
\(785\) −6.34150e6 −0.367297
\(786\) 119727. 207373.i 0.00691251 0.0119728i
\(787\) −1.04143e7 1.80380e7i −0.599365 1.03813i −0.992915 0.118828i \(-0.962086\pi\)
0.393550 0.919303i \(-0.371247\pi\)
\(788\) −864332. 1.49707e6i −0.0495867 0.0858867i
\(789\) −8.82420e6 + 1.52840e7i −0.504642 + 0.874065i
\(790\) 297638. 0.0169676
\(791\) 0 0
\(792\) 2.61468e6 0.148117
\(793\) 2.33556e6 4.04532e6i 0.131889 0.228439i
\(794\) 4.06621e6 + 7.04289e6i 0.228896 + 0.396460i
\(795\) −1.46970e6 2.54560e6i −0.0824731 0.142848i
\(796\) −5.19271e6 + 8.99404e6i −0.290477 + 0.503121i
\(797\) −2.32328e7 −1.29556 −0.647778 0.761829i \(-0.724302\pi\)
−0.647778 + 0.761829i \(0.724302\pi\)
\(798\) 0 0
\(799\) 4.00094e7 2.21715
\(800\) −7.73830e6 + 1.34031e7i −0.427485 + 0.740426i
\(801\) −4.65434e6 8.06156e6i −0.256317 0.443954i
\(802\) −5.06863e6 8.77913e6i −0.278263 0.481965i
\(803\) 4.68948e6 8.12241e6i 0.256647 0.444525i
\(804\) 8.08366e6 0.441030
\(805\) 0 0
\(806\) 1.75006e6 0.0948887
\(807\) −4.74208e6 + 8.21352e6i −0.256321 + 0.443962i
\(808\) −6.45420e6 1.11790e7i −0.347788 0.602386i
\(809\) −5.43338e6 9.41090e6i −0.291876 0.505545i 0.682377 0.731000i \(-0.260946\pi\)
−0.974253 + 0.225456i \(0.927613\pi\)
\(810\) −72171.0 + 125004.i −0.00386501 + 0.00669439i
\(811\) 2.22632e7 1.18860 0.594299 0.804244i \(-0.297430\pi\)
0.594299 + 0.804244i \(0.297430\pi\)
\(812\) 0 0
\(813\) 945531. 0.0501706
\(814\) −3.04723e6 + 5.27796e6i −0.161192 + 0.279193i
\(815\) −1.45878e6 2.52667e6i −0.0769298 0.133246i
\(816\) 5.59699e6 + 9.69427e6i 0.294259 + 0.509671i
\(817\) 647308. 1.12117e6i 0.0339278 0.0587647i
\(818\) 5.75467e6 0.300703
\(819\) 0 0
\(820\) 5.19165e6 0.269631
\(821\) 6.19405e6 1.07284e7i 0.320713 0.555491i −0.659922 0.751334i \(-0.729411\pi\)
0.980635 + 0.195843i \(0.0627442\pi\)
\(822\) −3.58436e6 6.20829e6i −0.185026 0.320474i
\(823\) −847404. 1.46775e6i −0.0436105 0.0755356i 0.843396 0.537292i \(-0.180553\pi\)
−0.887007 + 0.461757i \(0.847219\pi\)
\(824\) 536160. 928656.i 0.0275091 0.0476472i
\(825\) −7.27268e6 −0.372014
\(826\) 0 0
\(827\) −378495. −0.0192440 −0.00962202 0.999954i \(-0.503063\pi\)
−0.00962202 + 0.999954i \(0.503063\pi\)
\(828\) −3.70138e6 + 6.41097e6i −0.187624 + 0.324974i
\(829\) −5.21437e6 9.03156e6i −0.263521 0.456432i 0.703654 0.710543i \(-0.251551\pi\)
−0.967175 + 0.254111i \(0.918217\pi\)
\(830\) −749133. 1.29754e6i −0.0377454 0.0653769i
\(831\) 1.92416e6 3.33275e6i 0.0966584 0.167417i
\(832\) −3.29190e6 −0.164869
\(833\) 0 0
\(834\) 4.14515e6 0.206360
\(835\) 2.00084e6 3.46557e6i 0.0993110 0.172012i
\(836\) 617624. + 1.06976e6i 0.0305639 + 0.0529382i
\(837\) 1.03554e6 + 1.79362e6i 0.0510923 + 0.0884944i
\(838\) 3.41342e6 5.91222e6i 0.167911 0.290831i
\(839\) −3.04082e7 −1.49137 −0.745686 0.666297i \(-0.767878\pi\)
−0.745686 + 0.666297i \(0.767878\pi\)
\(840\) 0 0
\(841\) −1.46693e7 −0.715185
\(842\) −1.30737e6 + 2.26444e6i −0.0635506 + 0.110073i
\(843\) −2.87495e6 4.97956e6i −0.139335 0.241336i
\(844\) 3.04430e6 + 5.27288e6i 0.147106 + 0.254796i
\(845\) −1.52036e6 + 2.63334e6i −0.0732495 + 0.126872i
\(846\) 3.41852e6 0.164215
\(847\) 0 0
\(848\) −1.94773e7 −0.930120
\(849\) −1.10314e7 + 1.91069e7i −0.525244 + 0.909750i
\(850\) 5.69558e6 + 9.86504e6i 0.270390 + 0.468330i
\(851\) −1.84873e7 3.20209e7i −0.875083 1.51569i
\(852\) −4.82252e6 + 8.35286e6i −0.227602 + 0.394218i
\(853\) −2.80315e7 −1.31909 −0.659544 0.751666i \(-0.729250\pi\)
−0.659544 + 0.751666i \(0.729250\pi\)
\(854\) 0 0
\(855\) −146124. −0.00683607
\(856\) −1.16200e7 + 2.01265e7i −0.542029 + 0.938822i
\(857\) 9.40148e6 + 1.62838e7i 0.437264 + 0.757364i 0.997477 0.0709844i \(-0.0226141\pi\)
−0.560213 + 0.828349i \(0.689281\pi\)
\(858\) 745668. + 1.29153e6i 0.0345802 + 0.0598946i
\(859\) 3.93162e6 6.80976e6i 0.181798 0.314883i −0.760695 0.649109i \(-0.775142\pi\)
0.942493 + 0.334227i \(0.108475\pi\)
\(860\) −2.43135e6 −0.112099
\(861\) 0 0
\(862\) −3.87094e6 −0.177438
\(863\) 5.64288e6 9.77376e6i 0.257913 0.446719i −0.707769 0.706444i \(-0.750298\pi\)
0.965683 + 0.259724i \(0.0836317\pi\)
\(864\) 1.87790e6 + 3.25263e6i 0.0855833 + 0.148235i
\(865\) 906653. + 1.57037e6i 0.0412003 + 0.0713611i
\(866\) −516670. + 894899.i −0.0234109 + 0.0405489i
\(867\) 1.95746e7 0.884394
\(868\) 0 0
\(869\) 3.63930e6 0.163481
\(870\) −239283. + 414450.i −0.0107180 + 0.0185641i
\(871\) 4.94001e6 + 8.55635e6i 0.220639 + 0.382158i
\(872\) −1.23066e7 2.13157e7i −0.548084 0.949309i
\(873\) 6.27584e6 1.08701e7i 0.278700 0.482722i
\(874\) 1.07059e6 0.0474073
\(875\) 0 0
\(876\) 8.78623e6 0.386850
\(877\) −6.70750e6 + 1.16177e7i −0.294484 + 0.510062i −0.974865 0.222797i \(-0.928481\pi\)
0.680381 + 0.732859i \(0.261814\pi\)
\(878\) −2.91530e6 5.04945e6i −0.127628 0.221059i
\(879\) 7.72276e6 + 1.33762e7i 0.337132 + 0.583930i
\(880\) 970552. 1.68105e6i 0.0422486 0.0731767i
\(881\) −3.18547e7 −1.38272 −0.691359 0.722511i \(-0.742988\pi\)
−0.691359 + 0.722511i \(0.742988\pi\)
\(882\) 0 0
\(883\) −3.05922e7 −1.32041 −0.660205 0.751086i \(-0.729530\pi\)
−0.660205 + 0.751086i \(0.729530\pi\)
\(884\) −8.17555e6 + 1.41605e7i −0.351873 + 0.609463i
\(885\) 404068. + 699867.i 0.0173419 + 0.0300371i
\(886\) −1.78379e6 3.08962e6i −0.0763413 0.132227i
\(887\) −2.31886e6 + 4.01638e6i −0.0989613 + 0.171406i −0.911255 0.411843i \(-0.864885\pi\)
0.812294 + 0.583249i \(0.198219\pi\)
\(888\) −1.22342e7 −0.520648
\(889\) 0 0
\(890\) 2.52828e6 0.106992
\(891\) −882454. + 1.52846e6i −0.0372390 + 0.0644998i
\(892\) −8.25679e6 1.43012e7i −0.347456 0.601811i
\(893\) 1.73036e6 + 2.99708e6i 0.0726121 + 0.125768i
\(894\) −874206. + 1.51417e6i −0.0365822 + 0.0633623i
\(895\) −336908. −0.0140590
\(896\) 0 0
\(897\) −9.04781e6 −0.375459
\(898\) 4.00158e6 6.93094e6i 0.165592 0.286815i
\(899\) 3.43335e6 + 5.94673e6i 0.141683 + 0.245403i
\(900\) −3.40654e6 5.90029e6i −0.140187 0.242810i
\(901\) −2.81471e7 + 4.87522e7i −1.15510 + 2.00070i
\(902\) −9.06853e6 −0.371125
\(903\) 0 0
\(904\) 5.59968e6 0.227899
\(905\) 3.58266e6 6.20534e6i 0.145406 0.251851i
\(906\) −261423. 452798.i −0.0105809 0.0183267i
\(907\) −302188. 523405.i −0.0121972 0.0211261i 0.859862 0.510526i \(-0.170549\pi\)
−0.872060 + 0.489400i \(0.837216\pi\)
\(908\) 5.41863e6 9.38534e6i 0.218110 0.377777i
\(909\) 8.71317e6 0.349757
\(910\) 0 0
\(911\) −2.44059e7 −0.974315 −0.487157 0.873314i \(-0.661966\pi\)
−0.487157 + 0.873314i \(0.661966\pi\)
\(912\) −484128. + 838534.i −0.0192741 + 0.0333836i
\(913\) −9.15985e6 1.58653e7i −0.363673 0.629901i
\(914\) −1.16766e6 2.02246e6i −0.0462331 0.0800780i
\(915\) −750717. + 1.30028e6i −0.0296431 + 0.0513433i
\(916\) −6.51650e6 −0.256611
\(917\) 0 0
\(918\) 2.76437e6 0.108265
\(919\) −1.83547e7 + 3.17914e7i −0.716902 + 1.24171i 0.245320 + 0.969442i \(0.421107\pi\)
−0.962221 + 0.272268i \(0.912226\pi\)
\(920\) −2.15424e6 3.73125e6i −0.0839121 0.145340i
\(921\) 8.14036e6 + 1.40995e7i 0.316224 + 0.547715i
\(922\) −3.61358e6 + 6.25891e6i −0.139994 + 0.242477i
\(923\) −1.17884e7 −0.455460
\(924\) 0 0
\(925\) 3.40293e7 1.30767
\(926\) −1.80111e6 + 3.11962e6i −0.0690261 + 0.119557i
\(927\) 361908. + 626843.i 0.0138324 + 0.0239585i
\(928\) 6.22619e6 + 1.07841e7i 0.237330 + 0.411068i
\(929\) −1.14544e7 + 1.98396e7i −0.435446 + 0.754214i −0.997332 0.0730004i \(-0.976743\pi\)
0.561886 + 0.827215i \(0.310076\pi\)
\(930\) −562518. −0.0213270
\(931\) 0 0
\(932\) −1.17869e6 −0.0444487
\(933\) 6.84655e6 1.18586e7i 0.257494 0.445993i
\(934\) 2.36975e6 + 4.10452e6i 0.0888863 + 0.153956i
\(935\) −2.80513e6 4.85863e6i −0.104936 0.181754i
\(936\) −1.49688e6 + 2.59267e6i −0.0558467 + 0.0967293i
\(937\) 5.99611e6 0.223111 0.111555 0.993758i \(-0.464417\pi\)
0.111555 + 0.993758i \(0.464417\pi\)
\(938\) 0 0
\(939\) 1.21356e7 0.449156
\(940\) 3.24971e6 5.62866e6i 0.119957 0.207771i
\(941\) −5.82579e6 1.00906e7i −0.214477 0.371485i 0.738634 0.674107i \(-0.235471\pi\)
−0.953111 + 0.302622i \(0.902138\pi\)
\(942\) 5.18850e6 + 8.98675e6i 0.190509 + 0.329971i
\(943\) 2.75090e7 4.76470e7i 1.00738 1.74484i
\(944\) 5.35493e6 0.195580
\(945\) 0 0
\(946\) 4.24697e6 0.154295
\(947\) 554632. 960651.i 0.0200969 0.0348089i −0.855802 0.517303i \(-0.826936\pi\)
0.875899 + 0.482495i \(0.160269\pi\)
\(948\) 1.70465e6 + 2.95255e6i 0.0616049 + 0.106703i
\(949\) 5.36936e6 + 9.30001e6i 0.193534 + 0.335211i
\(950\) −492656. + 853305.i −0.0177107 + 0.0306758i
\(951\) −447255. −0.0160363
\(952\) 0 0
\(953\) 1.05743e7 0.377155 0.188578 0.982058i \(-0.439612\pi\)
0.188578 + 0.982058i \(0.439612\pi\)
\(954\) −2.40497e6 + 4.16553e6i −0.0855537 + 0.148183i
\(955\) −4.16548e6 7.21482e6i −0.147794 0.255987i
\(956\) −4.38782e6 7.59993e6i −0.155276 0.268946i
\(957\) −2.92578e6 + 5.06760e6i −0.103267 + 0.178864i
\(958\) 1.03629e6 0.0364811
\(959\) 0 0
\(960\) 1.05811e6 0.0370556
\(961\) 1.02789e7 1.78036e7i 0.359037 0.621871i
\(962\) −3.48902e6 6.04317e6i −0.121553 0.210536i
\(963\) −7.84351e6 1.35854e7i −0.272549 0.472069i
\(964\) −1.20093e7 + 2.08007e7i −0.416222 + 0.720918i
\(965\) 1.76373e6 0.0609696
\(966\) 0 0
\(967\) 6.32666e6 0.217575 0.108787 0.994065i \(-0.465303\pi\)
0.108787 + 0.994065i \(0.465303\pi\)
\(968\) 5.32140e6 9.21694e6i 0.182531 0.316154i
\(969\) 1.39925e6 + 2.42357e6i 0.0478724 + 0.0829174i
\(970\) 1.70455e6 + 2.95237e6i 0.0581675 + 0.100749i
\(971\) 1.96197e7 3.39824e7i 0.667798 1.15666i −0.310721 0.950501i \(-0.600570\pi\)
0.978519 0.206158i \(-0.0660962\pi\)
\(972\) −1.65337e6 −0.0561313
\(973\) 0 0
\(974\) −5.65225e6 −0.190908
\(975\) 4.16354e6 7.21147e6i 0.140266 0.242947i
\(976\) 4.97445e6 + 8.61600e6i 0.167155 + 0.289522i
\(977\) 775371. + 1.34298e6i 0.0259880 + 0.0450126i 0.878727 0.477325i \(-0.158393\pi\)
−0.852739 + 0.522337i \(0.825060\pi\)
\(978\) −2.38709e6 + 4.13456e6i −0.0798034 + 0.138224i
\(979\) 3.09140e7 1.03086
\(980\) 0 0
\(981\) 1.66139e7 0.551187
\(982\) 9.34747e6 1.61903e7i 0.309325 0.535767i
\(983\) −2.43742e7 4.22174e7i −0.804538 1.39350i −0.916602 0.399801i \(-0.869079\pi\)
0.112064 0.993701i \(-0.464254\pi\)
\(984\) −9.10224e6 1.57655e7i −0.299682 0.519064i
\(985\) −339559. + 588133.i −0.0111513 + 0.0193146i
\(986\) 9.16526e6 0.300229
\(987\) 0 0
\(988\) −1.41434e6 −0.0460957
\(989\) −1.28830e7 + 2.23140e7i −0.418819 + 0.725416i
\(990\) −239679. 415136.i −0.00777216 0.0134618i
\(991\) 962758. + 1.66754e6i 0.0311410 + 0.0539378i 0.881176 0.472789i \(-0.156753\pi\)
−0.850035 + 0.526726i \(0.823419\pi\)
\(992\) −7.31842e6 + 1.26759e7i −0.236123 + 0.408977i
\(993\) 1.42905e7 0.459912
\(994\) 0 0
\(995\) 4.07999e6 0.130648
\(996\) 8.58098e6 1.48627e7i 0.274087 0.474733i
\(997\) 2.71282e7 + 4.69874e7i 0.864337 + 1.49708i 0.867704 + 0.497081i \(0.165595\pi\)
−0.00336739 + 0.999994i \(0.501072\pi\)
\(998\) 8.17185e6 + 1.41541e7i 0.259713 + 0.449837i
\(999\) 4.12906e6 7.15173e6i 0.130899 0.226724i
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.g.79.1 2
7.2 even 3 147.6.a.d.1.1 1
7.3 odd 6 21.6.e.a.4.1 2
7.4 even 3 inner 147.6.e.g.67.1 2
7.5 odd 6 147.6.a.c.1.1 1
7.6 odd 2 21.6.e.a.16.1 yes 2
21.2 odd 6 441.6.a.h.1.1 1
21.5 even 6 441.6.a.g.1.1 1
21.17 even 6 63.6.e.a.46.1 2
21.20 even 2 63.6.e.a.37.1 2
28.3 even 6 336.6.q.b.193.1 2
28.27 even 2 336.6.q.b.289.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.e.a.4.1 2 7.3 odd 6
21.6.e.a.16.1 yes 2 7.6 odd 2
63.6.e.a.37.1 2 21.20 even 2
63.6.e.a.46.1 2 21.17 even 6
147.6.a.c.1.1 1 7.5 odd 6
147.6.a.d.1.1 1 7.2 even 3
147.6.e.g.67.1 2 7.4 even 3 inner
147.6.e.g.79.1 2 1.1 even 1 trivial
336.6.q.b.193.1 2 28.3 even 6
336.6.q.b.289.1 2 28.27 even 2
441.6.a.g.1.1 1 21.5 even 6
441.6.a.h.1.1 1 21.2 odd 6