Properties

Label 162.7.d.d.107.1
Level $162$
Weight $7$
Character 162.107
Analytic conductor $37.269$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,7,Mod(53,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.53");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), 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: \(37.2687615464\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.1
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.7.d.d.53.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(150.644 - 86.9741i) q^{5} +(242.000 - 419.156i) q^{7} -181.019i q^{8} +O(q^{10})\) \(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(150.644 - 86.9741i) q^{5} +(242.000 - 419.156i) q^{7} -181.019i q^{8} -984.000 q^{10} +(-1161.06 - 670.337i) q^{11} +(-1684.00 - 2916.77i) q^{13} +(-2371.11 + 1368.96i) q^{14} +(-512.000 + 886.810i) q^{16} +12.7279i q^{17} +5744.00 q^{19} +(4820.60 + 2783.17i) q^{20} +(3792.00 + 6567.94i) q^{22} +(-2924.69 + 1688.57i) q^{23} +(7316.50 - 12672.5i) q^{25} +19052.3i q^{26} +15488.0 q^{28} +(-25422.0 - 14677.4i) q^{29} +(19898.0 + 34464.3i) q^{31} +(5016.55 - 2896.31i) q^{32} +(36.0000 - 62.3538i) q^{34} -84191.0i q^{35} +52526.0 q^{37} +(-28139.7 - 16246.5i) q^{38} +(-15744.0 - 27269.4i) q^{40} +(-32079.7 + 18521.2i) q^{41} +(-1900.00 + 3290.90i) q^{43} -42901.6i q^{44} +19104.0 q^{46} +(-66503.6 - 38395.9i) q^{47} +(-58303.5 - 100985. i) q^{49} +(-71686.8 + 41388.4i) q^{50} +(53888.0 - 93336.8i) q^{52} +238738. i q^{53} -233208. q^{55} +(-75875.4 - 43806.7i) q^{56} +(83028.0 + 143809. i) q^{58} +(-216368. + 124920. i) q^{59} +(-6625.00 + 11474.8i) q^{61} -225120. i q^{62} -32768.0 q^{64} +(-507368. - 292929. i) q^{65} +(-84484.0 - 146331. i) q^{67} +(-352.727 + 203.647i) q^{68} +(-238128. + 412450. i) q^{70} -531467. i q^{71} +236144. q^{73} +(-257324. - 148566. i) q^{74} +(91904.0 + 159182. i) q^{76} +(-561952. + 324443. i) q^{77} +(17558.0 - 30411.3i) q^{79} +178123. i q^{80} +209544. q^{82} +(9508.92 + 5489.98i) q^{83} +(1107.00 + 1917.38i) q^{85} +(18616.1 - 10748.0i) q^{86} +(-121344. + 210174. i) q^{88} -129328. i q^{89} -1.63011e6 q^{91} +(-93590.1 - 54034.3i) q^{92} +(217200. + 376201. i) q^{94} +(865297. - 499579. i) q^{95} +(160712. - 278361. i) q^{97} +659629. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 64 q^{4} + 968 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 64 q^{4} + 968 q^{7} - 3936 q^{10} - 6736 q^{13} - 2048 q^{16} + 22976 q^{19} + 15168 q^{22} + 29266 q^{25} + 61952 q^{28} + 79592 q^{31} + 144 q^{34} + 210104 q^{37} - 62976 q^{40} - 7600 q^{43} + 76416 q^{46} - 233214 q^{49} + 215552 q^{52} - 932832 q^{55} + 332112 q^{58} - 26500 q^{61} - 131072 q^{64} - 337936 q^{67} - 952512 q^{70} + 944576 q^{73} + 367616 q^{76} + 70232 q^{79} + 838176 q^{82} + 4428 q^{85} - 485376 q^{88} - 6520448 q^{91} + 868800 q^{94} + 642848 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.89898 2.82843i −0.612372 0.353553i
\(3\) 0 0
\(4\) 16.0000 + 27.7128i 0.250000 + 0.433013i
\(5\) 150.644 86.9741i 1.20515 0.695793i 0.243453 0.969913i \(-0.421720\pi\)
0.961696 + 0.274120i \(0.0883864\pi\)
\(6\) 0 0
\(7\) 242.000 419.156i 0.705539 1.22203i −0.260957 0.965350i \(-0.584038\pi\)
0.966497 0.256680i \(-0.0826285\pi\)
\(8\) 181.019i 0.353553i
\(9\) 0 0
\(10\) −984.000 −0.984000
\(11\) −1161.06 670.337i −0.872320 0.503634i −0.00420160 0.999991i \(-0.501337\pi\)
−0.868119 + 0.496357i \(0.834671\pi\)
\(12\) 0 0
\(13\) −1684.00 2916.77i −0.766500 1.32762i −0.939450 0.342686i \(-0.888663\pi\)
0.172950 0.984931i \(-0.444670\pi\)
\(14\) −2371.11 + 1368.96i −0.864106 + 0.498892i
\(15\) 0 0
\(16\) −512.000 + 886.810i −0.125000 + 0.216506i
\(17\) 12.7279i 0.00259066i 0.999999 + 0.00129533i \(0.000412317\pi\)
−0.999999 + 0.00129533i \(0.999588\pi\)
\(18\) 0 0
\(19\) 5744.00 0.837440 0.418720 0.908115i \(-0.362479\pi\)
0.418720 + 0.908115i \(0.362479\pi\)
\(20\) 4820.60 + 2783.17i 0.602574 + 0.347897i
\(21\) 0 0
\(22\) 3792.00 + 6567.94i 0.356123 + 0.616824i
\(23\) −2924.69 + 1688.57i −0.240379 + 0.138783i −0.615351 0.788253i \(-0.710986\pi\)
0.374972 + 0.927036i \(0.377652\pi\)
\(24\) 0 0
\(25\) 7316.50 12672.5i 0.468256 0.811043i
\(26\) 19052.3i 1.08399i
\(27\) 0 0
\(28\) 15488.0 0.705539
\(29\) −25422.0 14677.4i −1.04236 0.601805i −0.121857 0.992548i \(-0.538885\pi\)
−0.920500 + 0.390743i \(0.872218\pi\)
\(30\) 0 0
\(31\) 19898.0 + 34464.3i 0.667920 + 1.15687i 0.978485 + 0.206319i \(0.0661484\pi\)
−0.310565 + 0.950552i \(0.600518\pi\)
\(32\) 5016.55 2896.31i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 36.0000 62.3538i 0.000915937 0.00158645i
\(35\) 84191.0i 1.96364i
\(36\) 0 0
\(37\) 52526.0 1.03698 0.518489 0.855085i \(-0.326495\pi\)
0.518489 + 0.855085i \(0.326495\pi\)
\(38\) −28139.7 16246.5i −0.512825 0.296080i
\(39\) 0 0
\(40\) −15744.0 27269.4i −0.246000 0.426084i
\(41\) −32079.7 + 18521.2i −0.465457 + 0.268732i −0.714336 0.699803i \(-0.753271\pi\)
0.248879 + 0.968535i \(0.419938\pi\)
\(42\) 0 0
\(43\) −1900.00 + 3290.90i −0.0238973 + 0.0413913i −0.877727 0.479162i \(-0.840941\pi\)
0.853829 + 0.520553i \(0.174274\pi\)
\(44\) 42901.6i 0.503634i
\(45\) 0 0
\(46\) 19104.0 0.196269
\(47\) −66503.6 38395.9i −0.640548 0.369821i 0.144277 0.989537i \(-0.453914\pi\)
−0.784826 + 0.619717i \(0.787248\pi\)
\(48\) 0 0
\(49\) −58303.5 100985.i −0.495572 0.858355i
\(50\) −71686.8 + 41388.4i −0.573494 + 0.331107i
\(51\) 0 0
\(52\) 53888.0 93336.8i 0.383250 0.663808i
\(53\) 238738.i 1.60359i 0.597599 + 0.801795i \(0.296121\pi\)
−0.597599 + 0.801795i \(0.703879\pi\)
\(54\) 0 0
\(55\) −233208. −1.40170
\(56\) −75875.4 43806.7i −0.432053 0.249446i
\(57\) 0 0
\(58\) 83028.0 + 143809.i 0.425540 + 0.737057i
\(59\) −216368. + 124920.i −1.05351 + 0.608243i −0.923629 0.383287i \(-0.874792\pi\)
−0.129878 + 0.991530i \(0.541459\pi\)
\(60\) 0 0
\(61\) −6625.00 + 11474.8i −0.0291875 + 0.0505542i −0.880250 0.474510i \(-0.842625\pi\)
0.851063 + 0.525064i \(0.175959\pi\)
\(62\) 225120.i 0.944581i
\(63\) 0 0
\(64\) −32768.0 −0.125000
\(65\) −507368. 292929.i −1.84749 1.06665i
\(66\) 0 0
\(67\) −84484.0 146331.i −0.280899 0.486531i 0.690707 0.723134i \(-0.257299\pi\)
−0.971606 + 0.236603i \(0.923966\pi\)
\(68\) −352.727 + 203.647i −0.00112179 + 0.000647665i
\(69\) 0 0
\(70\) −238128. + 412450.i −0.694251 + 1.20248i
\(71\) 531467.i 1.48491i −0.669894 0.742457i \(-0.733660\pi\)
0.669894 0.742457i \(-0.266340\pi\)
\(72\) 0 0
\(73\) 236144. 0.607027 0.303514 0.952827i \(-0.401840\pi\)
0.303514 + 0.952827i \(0.401840\pi\)
\(74\) −257324. 148566.i −0.635016 0.366627i
\(75\) 0 0
\(76\) 91904.0 + 159182.i 0.209360 + 0.362622i
\(77\) −561952. + 324443.i −1.23091 + 0.710668i
\(78\) 0 0
\(79\) 17558.0 30411.3i 0.0356118 0.0616814i −0.847670 0.530524i \(-0.821995\pi\)
0.883282 + 0.468842i \(0.155329\pi\)
\(80\) 178123.i 0.347897i
\(81\) 0 0
\(82\) 209544. 0.380044
\(83\) 9508.92 + 5489.98i 0.0166302 + 0.00960144i 0.508292 0.861185i \(-0.330277\pi\)
−0.491662 + 0.870786i \(0.663610\pi\)
\(84\) 0 0
\(85\) 1107.00 + 1917.38i 0.00180256 + 0.00312213i
\(86\) 18616.1 10748.0i 0.0292681 0.0168979i
\(87\) 0 0
\(88\) −121344. + 210174.i −0.178062 + 0.308412i
\(89\) 129328.i 0.183453i −0.995784 0.0917263i \(-0.970762\pi\)
0.995784 0.0917263i \(-0.0292385\pi\)
\(90\) 0 0
\(91\) −1.63011e6 −2.16318
\(92\) −93590.1 54034.3i −0.120189 0.0693914i
\(93\) 0 0
\(94\) 217200. + 376201.i 0.261503 + 0.452936i
\(95\) 865297. 499579.i 1.00924 0.582685i
\(96\) 0 0
\(97\) 160712. 278361.i 0.176089 0.304996i −0.764448 0.644685i \(-0.776989\pi\)
0.940538 + 0.339689i \(0.110322\pi\)
\(98\) 659629.i 0.700844i
\(99\) 0 0
\(100\) 468256. 0.468256
\(101\) −579181. 334390.i −0.562147 0.324556i 0.191860 0.981422i \(-0.438548\pi\)
−0.754007 + 0.656867i \(0.771881\pi\)
\(102\) 0 0
\(103\) −996706. 1.72635e6i −0.912127 1.57985i −0.811054 0.584972i \(-0.801106\pi\)
−0.101073 0.994879i \(-0.532228\pi\)
\(104\) −527992. + 304837.i −0.469383 + 0.270999i
\(105\) 0 0
\(106\) 675252. 1.16957e6i 0.566955 0.981994i
\(107\) 260668.i 0.212783i −0.994324 0.106391i \(-0.966070\pi\)
0.994324 0.106391i \(-0.0339296\pi\)
\(108\) 0 0
\(109\) 194456. 0.150156 0.0750779 0.997178i \(-0.476079\pi\)
0.0750779 + 0.997178i \(0.476079\pi\)
\(110\) 1.14248e6 + 659612.i 0.858363 + 0.495576i
\(111\) 0 0
\(112\) 247808. + 429216.i 0.176385 + 0.305508i
\(113\) −711784. + 410949.i −0.493302 + 0.284808i −0.725943 0.687755i \(-0.758596\pi\)
0.232641 + 0.972563i \(0.425263\pi\)
\(114\) 0 0
\(115\) −293724. + 508745.i −0.193128 + 0.334508i
\(116\) 939355.i 0.601805i
\(117\) 0 0
\(118\) 1.41331e6 0.860185
\(119\) 5334.99 + 3080.16i 0.00316587 + 0.00182781i
\(120\) 0 0
\(121\) 12923.5 + 22384.2i 0.00729498 + 0.0126353i
\(122\) 64911.5 37476.7i 0.0357472 0.0206387i
\(123\) 0 0
\(124\) −636736. + 1.10286e6i −0.333960 + 0.578436i
\(125\) 172557.i 0.0883490i
\(126\) 0 0
\(127\) 3.05721e6 1.49250 0.746250 0.665666i \(-0.231852\pi\)
0.746250 + 0.665666i \(0.231852\pi\)
\(128\) 160530. + 92681.9i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 1.65706e6 + 2.87011e6i 0.754236 + 1.30637i
\(131\) 2.66206e6 1.53694e6i 1.18414 0.683664i 0.227172 0.973855i \(-0.427052\pi\)
0.956969 + 0.290191i \(0.0937187\pi\)
\(132\) 0 0
\(133\) 1.39005e6 2.40763e6i 0.590847 1.02338i
\(134\) 955827.i 0.397251i
\(135\) 0 0
\(136\) 2304.00 0.000915937
\(137\) 3.88336e6 + 2.24206e6i 1.51024 + 0.871938i 0.999929 + 0.0119482i \(0.00380331\pi\)
0.510312 + 0.859990i \(0.329530\pi\)
\(138\) 0 0
\(139\) 546164. + 945984.i 0.203366 + 0.352241i 0.949611 0.313431i \(-0.101478\pi\)
−0.746245 + 0.665672i \(0.768145\pi\)
\(140\) 2.33317e6 1.34706e6i 0.850280 0.490909i
\(141\) 0 0
\(142\) −1.50322e6 + 2.60365e6i −0.524996 + 0.909321i
\(143\) 4.51539e6i 1.54414i
\(144\) 0 0
\(145\) −5.10622e6 −1.67493
\(146\) −1.15686e6 667916.i −0.371727 0.214617i
\(147\) 0 0
\(148\) 840416. + 1.45564e6i 0.259244 + 0.449024i
\(149\) −1.92333e6 + 1.11044e6i −0.581428 + 0.335687i −0.761701 0.647929i \(-0.775635\pi\)
0.180273 + 0.983617i \(0.442302\pi\)
\(150\) 0 0
\(151\) 2.03935e6 3.53226e6i 0.592327 1.02594i −0.401591 0.915819i \(-0.631543\pi\)
0.993918 0.110122i \(-0.0351241\pi\)
\(152\) 1.03978e6i 0.296080i
\(153\) 0 0
\(154\) 3.67066e6 1.00504
\(155\) 5.99501e6 + 3.46122e6i 1.60989 + 0.929468i
\(156\) 0 0
\(157\) −3.07784e6 5.33097e6i −0.795329 1.37755i −0.922630 0.385686i \(-0.873965\pi\)
0.127301 0.991864i \(-0.459369\pi\)
\(158\) −172033. + 99323.0i −0.0436154 + 0.0251813i
\(159\) 0 0
\(160\) 503808. 872621.i 0.123000 0.213042i
\(161\) 1.63454e6i 0.391667i
\(162\) 0 0
\(163\) 800696. 0.184886 0.0924432 0.995718i \(-0.470532\pi\)
0.0924432 + 0.995718i \(0.470532\pi\)
\(164\) −1.02655e6 592680.i −0.232728 0.134366i
\(165\) 0 0
\(166\) −31056.0 53790.6i −0.00678924 0.0117593i
\(167\) 4.16097e6 2.40234e6i 0.893398 0.515804i 0.0183455 0.999832i \(-0.494160\pi\)
0.875052 + 0.484028i \(0.160827\pi\)
\(168\) 0 0
\(169\) −3.25831e6 + 5.64355e6i −0.675044 + 1.16921i
\(170\) 12524.3i 0.00254921i
\(171\) 0 0
\(172\) −121600. −0.0238973
\(173\) 3.09164e6 + 1.78496e6i 0.597106 + 0.344739i 0.767902 0.640567i \(-0.221301\pi\)
−0.170796 + 0.985306i \(0.554634\pi\)
\(174\) 0 0
\(175\) −3.54119e6 6.13351e6i −0.660746 1.14445i
\(176\) 1.18892e6 686425.i 0.218080 0.125909i
\(177\) 0 0
\(178\) −365796. + 633577.i −0.0648603 + 0.112341i
\(179\) 7.43698e6i 1.29669i −0.761345 0.648347i \(-0.775461\pi\)
0.761345 0.648347i \(-0.224539\pi\)
\(180\) 0 0
\(181\) −1.03812e7 −1.75070 −0.875350 0.483491i \(-0.839369\pi\)
−0.875350 + 0.483491i \(0.839369\pi\)
\(182\) 7.98589e6 + 4.61065e6i 1.32467 + 0.764801i
\(183\) 0 0
\(184\) 305664. + 529426.i 0.0490671 + 0.0849868i
\(185\) 7.91271e6 4.56840e6i 1.24971 0.721521i
\(186\) 0 0
\(187\) 8532.00 14777.9i 0.00130475 0.00225989i
\(188\) 2.45734e6i 0.369821i
\(189\) 0 0
\(190\) −5.65210e6 −0.824041
\(191\) −1.12532e7 6.49703e6i −1.61501 0.932426i −0.988185 0.153266i \(-0.951021\pi\)
−0.626825 0.779160i \(-0.715646\pi\)
\(192\) 0 0
\(193\) 1.96598e6 + 3.40517e6i 0.273468 + 0.473660i 0.969747 0.244110i \(-0.0784959\pi\)
−0.696279 + 0.717771i \(0.745163\pi\)
\(194\) −1.57465e6 + 909124.i −0.215665 + 0.124514i
\(195\) 0 0
\(196\) 1.86571e6 3.23151e6i 0.247786 0.429178i
\(197\) 5.37967e6i 0.703651i 0.936066 + 0.351825i \(0.114439\pi\)
−0.936066 + 0.351825i \(0.885561\pi\)
\(198\) 0 0
\(199\) −565900. −0.0718093 −0.0359046 0.999355i \(-0.511431\pi\)
−0.0359046 + 0.999355i \(0.511431\pi\)
\(200\) −2.29398e6 1.32443e6i −0.286747 0.165553i
\(201\) 0 0
\(202\) 1.89160e6 + 3.27634e6i 0.229496 + 0.397498i
\(203\) −1.23043e7 + 7.10387e6i −1.47085 + 0.849194i
\(204\) 0 0
\(205\) −3.22174e6 + 5.58022e6i −0.373963 + 0.647723i
\(206\) 1.12764e7i 1.28994i
\(207\) 0 0
\(208\) 3.44883e6 0.383250
\(209\) −6.66912e6 3.85042e6i −0.730516 0.421763i
\(210\) 0 0
\(211\) 6.75825e6 + 1.17056e7i 0.719427 + 1.24608i 0.961227 + 0.275759i \(0.0889291\pi\)
−0.241799 + 0.970326i \(0.577738\pi\)
\(212\) −6.61609e6 + 3.81980e6i −0.694375 + 0.400897i
\(213\) 0 0
\(214\) −737280. + 1.27701e6i −0.0752300 + 0.130302i
\(215\) 661003.i 0.0665102i
\(216\) 0 0
\(217\) 1.92613e7 1.88497
\(218\) −952636. 550005.i −0.0919512 0.0530881i
\(219\) 0 0
\(220\) −3.73133e6 6.46285e6i −0.350425 0.606954i
\(221\) 37124.5 21433.8i 0.00343941 0.00198574i
\(222\) 0 0
\(223\) 2.67742e6 4.63742e6i 0.241436 0.418179i −0.719688 0.694298i \(-0.755715\pi\)
0.961123 + 0.276119i \(0.0890484\pi\)
\(224\) 2.80363e6i 0.249446i
\(225\) 0 0
\(226\) 4.64935e6 0.402779
\(227\) 1.17834e7 + 6.80317e6i 1.00738 + 0.581612i 0.910424 0.413676i \(-0.135755\pi\)
0.0969580 + 0.995288i \(0.469089\pi\)
\(228\) 0 0
\(229\) −2.17320e6 3.76410e6i −0.180965 0.313440i 0.761245 0.648465i \(-0.224589\pi\)
−0.942209 + 0.335025i \(0.891255\pi\)
\(230\) 2.87790e6 1.66155e6i 0.236533 0.136562i
\(231\) 0 0
\(232\) −2.65690e6 + 4.60188e6i −0.212770 + 0.368529i
\(233\) 2.02333e7i 1.59956i −0.600297 0.799778i \(-0.704951\pi\)
0.600297 0.799778i \(-0.295049\pi\)
\(234\) 0 0
\(235\) −1.33578e7 −1.02927
\(236\) −6.92379e6 3.99745e6i −0.526754 0.304121i
\(237\) 0 0
\(238\) −17424.0 30179.3i −0.00129246 0.00223861i
\(239\) −1.76623e7 + 1.01973e7i −1.29376 + 0.746953i −0.979319 0.202324i \(-0.935151\pi\)
−0.314442 + 0.949277i \(0.601817\pi\)
\(240\) 0 0
\(241\) 1.56046e6 2.70280e6i 0.111481 0.193092i −0.804886 0.593429i \(-0.797774\pi\)
0.916368 + 0.400337i \(0.131107\pi\)
\(242\) 146213.i 0.0103167i
\(243\) 0 0
\(244\) −424000. −0.0291875
\(245\) −1.75661e7 1.01418e7i −1.19448 0.689631i
\(246\) 0 0
\(247\) −9.67290e6 1.67539e7i −0.641897 1.11180i
\(248\) 6.23871e6 3.60192e6i 0.409016 0.236145i
\(249\) 0 0
\(250\) 488064. 845352.i 0.0312361 0.0541025i
\(251\) 5.09519e6i 0.322210i 0.986937 + 0.161105i \(0.0515058\pi\)
−0.986937 + 0.161105i \(0.948494\pi\)
\(252\) 0 0
\(253\) 4.52765e6 0.279583
\(254\) −1.49772e7 8.64710e6i −0.913966 0.527678i
\(255\) 0 0
\(256\) −524288. 908093.i −0.0312500 0.0541266i
\(257\) 1.25031e7 7.21869e6i 0.736580 0.425264i −0.0842448 0.996445i \(-0.526848\pi\)
0.820824 + 0.571181i \(0.193514\pi\)
\(258\) 0 0
\(259\) 1.27113e7 2.20166e7i 0.731628 1.26722i
\(260\) 1.87474e7i 1.06665i
\(261\) 0 0
\(262\) −1.73885e7 −0.966847
\(263\) −2.70691e7 1.56283e7i −1.48801 0.859104i −0.488105 0.872785i \(-0.662312\pi\)
−0.999906 + 0.0136808i \(0.995645\pi\)
\(264\) 0 0
\(265\) 2.07640e7 + 3.59643e7i 1.11577 + 1.93256i
\(266\) −1.36196e7 + 7.86330e6i −0.723637 + 0.417792i
\(267\) 0 0
\(268\) 2.70349e6 4.68258e6i 0.140449 0.243266i
\(269\) 251338.i 0.0129122i 0.999979 + 0.00645612i \(0.00205506\pi\)
−0.999979 + 0.00645612i \(0.997945\pi\)
\(270\) 0 0
\(271\) 2.96399e7 1.48925 0.744627 0.667481i \(-0.232627\pi\)
0.744627 + 0.667481i \(0.232627\pi\)
\(272\) −11287.2 6516.70i −0.000560895 0.000323833i
\(273\) 0 0
\(274\) −1.26830e7 2.19676e7i −0.616553 1.06790i
\(275\) −1.69898e7 + 9.80904e6i −0.816938 + 0.471660i
\(276\) 0 0
\(277\) −6.61064e6 + 1.14500e7i −0.311031 + 0.538722i −0.978586 0.205839i \(-0.934008\pi\)
0.667555 + 0.744561i \(0.267341\pi\)
\(278\) 6.17914e6i 0.287603i
\(279\) 0 0
\(280\) −1.52402e7 −0.694251
\(281\) 5.30320e6 + 3.06180e6i 0.239011 + 0.137993i 0.614722 0.788744i \(-0.289268\pi\)
−0.375711 + 0.926737i \(0.622601\pi\)
\(282\) 0 0
\(283\) 3.37162e6 + 5.83982e6i 0.148758 + 0.257656i 0.930769 0.365609i \(-0.119139\pi\)
−0.782011 + 0.623265i \(0.785806\pi\)
\(284\) 1.47284e7 8.50347e6i 0.642987 0.371229i
\(285\) 0 0
\(286\) 1.27715e7 2.21208e7i 0.545937 0.945590i
\(287\) 1.79286e7i 0.758403i
\(288\) 0 0
\(289\) 2.41374e7 0.999993
\(290\) 2.50153e7 + 1.44426e7i 1.02568 + 0.592176i
\(291\) 0 0
\(292\) 3.77830e6 + 6.54421e6i 0.151757 + 0.262851i
\(293\) −8.68096e6 + 5.01195e6i −0.345116 + 0.199253i −0.662532 0.749034i \(-0.730518\pi\)
0.317416 + 0.948286i \(0.397185\pi\)
\(294\) 0 0
\(295\) −2.17297e7 + 3.76369e7i −0.846422 + 1.46605i
\(296\) 9.50822e6i 0.366627i
\(297\) 0 0
\(298\) 1.25632e7 0.474734
\(299\) 9.85036e6 + 5.68711e6i 0.368501 + 0.212754i
\(300\) 0 0
\(301\) 919600. + 1.59279e6i 0.0337209 + 0.0584064i
\(302\) −1.99815e7 + 1.15363e7i −0.725450 + 0.418839i
\(303\) 0 0
\(304\) −2.94093e6 + 5.09384e6i −0.104680 + 0.181311i
\(305\) 2.30481e6i 0.0812337i
\(306\) 0 0
\(307\) −5.23060e6 −0.180774 −0.0903871 0.995907i \(-0.528810\pi\)
−0.0903871 + 0.995907i \(0.528810\pi\)
\(308\) −1.79825e7 1.03822e7i −0.615456 0.355334i
\(309\) 0 0
\(310\) −1.95796e7 3.39129e7i −0.657233 1.13836i
\(311\) 2.70392e7 1.56111e7i 0.898901 0.518981i 0.0220578 0.999757i \(-0.492978\pi\)
0.876844 + 0.480776i \(0.159645\pi\)
\(312\) 0 0
\(313\) −1.12389e7 + 1.94664e7i −0.366515 + 0.634822i −0.989018 0.147795i \(-0.952782\pi\)
0.622503 + 0.782617i \(0.286116\pi\)
\(314\) 3.48218e7i 1.12477i
\(315\) 0 0
\(316\) 1.12371e6 0.0356118
\(317\) 2.39206e7 + 1.38106e7i 0.750921 + 0.433544i 0.826026 0.563631i \(-0.190596\pi\)
−0.0751058 + 0.997176i \(0.523929\pi\)
\(318\) 0 0
\(319\) 1.96776e7 + 3.40827e7i 0.606179 + 1.04993i
\(320\) −4.93629e6 + 2.84997e6i −0.150644 + 0.0869741i
\(321\) 0 0
\(322\) 4.62317e6 8.00756e6i 0.138475 0.239846i
\(323\) 73109.2i 0.00216952i
\(324\) 0 0
\(325\) −4.92839e7 −1.43567
\(326\) −3.92259e6 2.26471e6i −0.113219 0.0653672i
\(327\) 0 0
\(328\) 3.35270e6 + 5.80705e6i 0.0950110 + 0.164564i
\(329\) −3.21878e7 + 1.85836e7i −0.903864 + 0.521846i
\(330\) 0 0
\(331\) 2.88069e6 4.98950e6i 0.0794352 0.137586i −0.823571 0.567213i \(-0.808022\pi\)
0.903006 + 0.429627i \(0.141355\pi\)
\(332\) 351359.i 0.00960144i
\(333\) 0 0
\(334\) −2.71793e7 −0.729456
\(335\) −2.54540e7 1.46958e7i −0.677050 0.390895i
\(336\) 0 0
\(337\) 2.00526e7 + 3.47321e7i 0.523939 + 0.907489i 0.999612 + 0.0278665i \(0.00887132\pi\)
−0.475673 + 0.879622i \(0.657795\pi\)
\(338\) 3.19248e7 1.84318e7i 0.826756 0.477328i
\(339\) 0 0
\(340\) −35424.0 + 61356.2i −0.000901282 + 0.00156107i
\(341\) 5.33535e7i 1.34555i
\(342\) 0 0
\(343\) 504328. 0.0124977
\(344\) 595716. + 343937.i 0.0146340 + 0.00844896i
\(345\) 0 0
\(346\) −1.00973e7 1.74890e7i −0.243767 0.422217i
\(347\) 5.87275e7 3.39064e7i 1.40557 0.811508i 0.410616 0.911808i \(-0.365314\pi\)
0.994957 + 0.100301i \(0.0319804\pi\)
\(348\) 0 0
\(349\) 2.10319e7 3.64284e7i 0.494769 0.856965i −0.505213 0.862995i \(-0.668586\pi\)
0.999982 + 0.00602956i \(0.00191928\pi\)
\(350\) 4.00639e7i 0.934436i
\(351\) 0 0
\(352\) −7.76602e6 −0.178062
\(353\) 1.52399e7 + 8.79878e6i 0.346465 + 0.200032i 0.663127 0.748507i \(-0.269229\pi\)
−0.316662 + 0.948538i \(0.602562\pi\)
\(354\) 0 0
\(355\) −4.62239e7 8.00621e7i −1.03319 1.78954i
\(356\) 3.58405e6 2.06925e6i 0.0794373 0.0458632i
\(357\) 0 0
\(358\) −2.10349e7 + 3.64336e7i −0.458450 + 0.794059i
\(359\) 1.39920e7i 0.302410i −0.988502 0.151205i \(-0.951685\pi\)
0.988502 0.151205i \(-0.0483154\pi\)
\(360\) 0 0
\(361\) −1.40523e7 −0.298694
\(362\) 5.08572e7 + 2.93624e7i 1.07208 + 0.618966i
\(363\) 0 0
\(364\) −2.60818e7 4.51750e7i −0.540796 0.936686i
\(365\) 3.55736e7 2.05384e7i 0.731559 0.422365i
\(366\) 0 0
\(367\) 1.32927e7 2.30237e7i 0.268916 0.465776i −0.699666 0.714470i \(-0.746668\pi\)
0.968582 + 0.248694i \(0.0800013\pi\)
\(368\) 3.45819e6i 0.0693914i
\(369\) 0 0
\(370\) −5.16856e7 −1.02039
\(371\) 1.00068e8 + 5.77745e7i 1.95963 + 1.13140i
\(372\) 0 0
\(373\) −8.94146e6 1.54871e7i −0.172299 0.298430i 0.766924 0.641737i \(-0.221786\pi\)
−0.939223 + 0.343307i \(0.888453\pi\)
\(374\) −83596.2 + 48264.3i −0.00159798 + 0.000922595i
\(375\) 0 0
\(376\) −6.95040e6 + 1.20384e7i −0.130751 + 0.226468i
\(377\) 9.88671e7i 1.84513i
\(378\) 0 0
\(379\) 7.20978e7 1.32435 0.662177 0.749347i \(-0.269633\pi\)
0.662177 + 0.749347i \(0.269633\pi\)
\(380\) 2.76895e7 + 1.59865e7i 0.504620 + 0.291342i
\(381\) 0 0
\(382\) 3.67527e7 + 6.36576e7i 0.659325 + 1.14198i
\(383\) 7.52272e6 4.34324e6i 0.133899 0.0773068i −0.431554 0.902087i \(-0.642035\pi\)
0.565453 + 0.824780i \(0.308701\pi\)
\(384\) 0 0
\(385\) −5.64363e7 + 9.77506e7i −0.988955 + 1.71292i
\(386\) 2.22425e7i 0.386742i
\(387\) 0 0
\(388\) 1.02856e7 0.176089
\(389\) 4.28173e7 + 2.47206e7i 0.727395 + 0.419962i 0.817468 0.575974i \(-0.195377\pi\)
−0.0900736 + 0.995935i \(0.528710\pi\)
\(390\) 0 0
\(391\) −21492.0 37225.2i −0.000359539 0.000622741i
\(392\) −1.82802e7 + 1.05541e7i −0.303474 + 0.175211i
\(393\) 0 0
\(394\) 1.52160e7 2.63549e7i 0.248778 0.430896i
\(395\) 6.10837e6i 0.0991137i
\(396\) 0 0
\(397\) 1.56911e7 0.250774 0.125387 0.992108i \(-0.459983\pi\)
0.125387 + 0.992108i \(0.459983\pi\)
\(398\) 2.77233e6 + 1.60061e6i 0.0439740 + 0.0253884i
\(399\) 0 0
\(400\) 7.49210e6 + 1.29767e7i 0.117064 + 0.202761i
\(401\) −4.10941e7 + 2.37257e7i −0.637304 + 0.367947i −0.783575 0.621297i \(-0.786606\pi\)
0.146272 + 0.989244i \(0.453273\pi\)
\(402\) 0 0
\(403\) 6.70165e7 1.16076e8i 1.02392 1.77348i
\(404\) 2.14010e7i 0.324556i
\(405\) 0 0
\(406\) 8.03711e7 1.20094
\(407\) −6.09857e7 3.52101e7i −0.904576 0.522257i
\(408\) 0 0
\(409\) 5.77558e7 + 1.00036e8i 0.844162 + 1.46213i 0.886347 + 0.463022i \(0.153235\pi\)
−0.0421850 + 0.999110i \(0.513432\pi\)
\(410\) 3.15665e7 1.82249e7i 0.458009 0.264432i
\(411\) 0 0
\(412\) 3.18946e7 5.52431e7i 0.456064 0.789925i
\(413\) 1.20923e8i 1.71656i
\(414\) 0 0
\(415\) 1.90994e6 0.0267225
\(416\) −1.68958e7 9.75477e6i −0.234692 0.135499i
\(417\) 0 0
\(418\) 2.17812e7 + 3.77262e7i 0.298232 + 0.516553i
\(419\) 1.27040e8 7.33466e7i 1.72702 0.997098i 0.825447 0.564480i \(-0.190923\pi\)
0.901577 0.432618i \(-0.142410\pi\)
\(420\) 0 0
\(421\) −6.96194e7 + 1.20584e8i −0.933005 + 1.61601i −0.154852 + 0.987938i \(0.549490\pi\)
−0.778153 + 0.628075i \(0.783843\pi\)
\(422\) 7.64609e7i 1.01742i
\(423\) 0 0
\(424\) 4.32161e7 0.566955
\(425\) 161295. + 93123.8i 0.00210114 + 0.00121309i
\(426\) 0 0
\(427\) 3.20650e6 + 5.55382e6i 0.0411858 + 0.0713359i
\(428\) 7.22384e6 4.17069e6i 0.0921376 0.0531957i
\(429\) 0 0
\(430\) 1.86960e6 3.23824e6i 0.0235149 0.0407290i
\(431\) 1.00392e8i 1.25391i −0.779056 0.626954i \(-0.784301\pi\)
0.779056 0.626954i \(-0.215699\pi\)
\(432\) 0 0
\(433\) −4.00631e7 −0.493493 −0.246747 0.969080i \(-0.579362\pi\)
−0.246747 + 0.969080i \(0.579362\pi\)
\(434\) −9.43605e7 5.44791e7i −1.15431 0.666439i
\(435\) 0 0
\(436\) 3.11130e6 + 5.38892e6i 0.0375389 + 0.0650193i
\(437\) −1.67994e7 + 9.69915e6i −0.201303 + 0.116222i
\(438\) 0 0
\(439\) 6.92959e7 1.20024e8i 0.819057 1.41865i −0.0873208 0.996180i \(-0.527831\pi\)
0.906378 0.422468i \(-0.138836\pi\)
\(440\) 4.22152e7i 0.495576i
\(441\) 0 0
\(442\) −242496. −0.00280826
\(443\) 9.65121e7 + 5.57213e7i 1.11012 + 0.640929i 0.938861 0.344296i \(-0.111883\pi\)
0.171261 + 0.985226i \(0.445216\pi\)
\(444\) 0 0
\(445\) −1.12482e7 1.94825e7i −0.127645 0.221088i
\(446\) −2.62332e7 + 1.51458e7i −0.295697 + 0.170721i
\(447\) 0 0
\(448\) −7.92986e6 + 1.37349e7i −0.0881924 + 0.152754i
\(449\) 6.11166e7i 0.675181i −0.941293 0.337591i \(-0.890388\pi\)
0.941293 0.337591i \(-0.109612\pi\)
\(450\) 0 0
\(451\) 4.96619e7 0.541370
\(452\) −2.27771e7 1.31504e7i −0.246651 0.142404i
\(453\) 0 0
\(454\) −3.84845e7 6.66572e7i −0.411262 0.712327i
\(455\) −2.45566e8 + 1.41778e8i −2.60696 + 1.50513i
\(456\) 0 0
\(457\) −1.78332e7 + 3.08881e7i −0.186845 + 0.323625i −0.944197 0.329382i \(-0.893160\pi\)
0.757352 + 0.653007i \(0.226493\pi\)
\(458\) 2.45870e7i 0.255923i
\(459\) 0 0
\(460\) −1.87983e7 −0.193128
\(461\) −1.31621e8 7.59914e7i −1.34345 0.775642i −0.356139 0.934433i \(-0.615907\pi\)
−0.987312 + 0.158791i \(0.949241\pi\)
\(462\) 0 0
\(463\) −5.74891e7 9.95740e7i −0.579218 1.00324i −0.995569 0.0940314i \(-0.970025\pi\)
0.416351 0.909204i \(-0.363309\pi\)
\(464\) 2.60322e7 1.50297e7i 0.260589 0.150451i
\(465\) 0 0
\(466\) −5.72284e7 + 9.91226e7i −0.565528 + 0.979523i
\(467\) 8.81705e7i 0.865711i 0.901463 + 0.432855i \(0.142494\pi\)
−0.901463 + 0.432855i \(0.857506\pi\)
\(468\) 0 0
\(469\) −8.17805e7 −0.792741
\(470\) 6.54396e7 + 3.77816e7i 0.630300 + 0.363904i
\(471\) 0 0
\(472\) 2.26130e7 + 3.91669e7i 0.215046 + 0.372471i
\(473\) 4.41202e6 2.54728e6i 0.0416921 0.0240710i
\(474\) 0 0
\(475\) 4.20260e7 7.27911e7i 0.392136 0.679200i
\(476\) 197130.i 0.00182781i
\(477\) 0 0
\(478\) 1.15370e8 1.05635
\(479\) 7.74563e7 + 4.47194e7i 0.704774 + 0.406902i 0.809123 0.587639i \(-0.199943\pi\)
−0.104349 + 0.994541i \(0.533276\pi\)
\(480\) 0 0
\(481\) −8.84538e7 1.53206e8i −0.794843 1.37671i
\(482\) −1.52894e7 + 8.82732e6i −0.136536 + 0.0788293i
\(483\) 0 0
\(484\) −413552. + 716293.i −0.00364749 + 0.00631764i
\(485\) 5.59111e7i 0.490087i
\(486\) 0 0
\(487\) −7.51688e7 −0.650805 −0.325403 0.945576i \(-0.605500\pi\)
−0.325403 + 0.945576i \(0.605500\pi\)
\(488\) 2.07717e6 + 1.19925e6i 0.0178736 + 0.0103193i
\(489\) 0 0
\(490\) 5.73706e7 + 9.93689e7i 0.487642 + 0.844621i
\(491\) 3.90424e7 2.25411e7i 0.329831 0.190428i −0.325935 0.945392i \(-0.605679\pi\)
0.655766 + 0.754964i \(0.272346\pi\)
\(492\) 0 0
\(493\) 186813. 323570.i 0.00155907 0.00270039i
\(494\) 1.09436e8i 0.907780i
\(495\) 0 0
\(496\) −4.07511e7 −0.333960
\(497\) −2.22768e8 1.28615e8i −1.81461 1.04767i
\(498\) 0 0
\(499\) −4.57729e7 7.92810e7i −0.368389 0.638069i 0.620925 0.783870i \(-0.286757\pi\)
−0.989314 + 0.145801i \(0.953424\pi\)
\(500\) −4.78203e6 + 2.76091e6i −0.0382562 + 0.0220873i
\(501\) 0 0
\(502\) 1.44114e7 2.49612e7i 0.113919 0.197313i
\(503\) 1.61043e8i 1.26543i −0.774386 0.632713i \(-0.781941\pi\)
0.774386 0.632713i \(-0.218059\pi\)
\(504\) 0 0
\(505\) −1.16333e8 −0.903295
\(506\) −2.21809e7 1.28061e7i −0.171209 0.0988476i
\(507\) 0 0
\(508\) 4.89154e7 + 8.47239e7i 0.373125 + 0.646272i
\(509\) 2.07841e7 1.19997e7i 0.157608 0.0909951i −0.419122 0.907930i \(-0.637662\pi\)
0.576730 + 0.816935i \(0.304329\pi\)
\(510\) 0 0
\(511\) 5.71468e7 9.89812e7i 0.428282 0.741806i
\(512\) 5.93164e6i 0.0441942i
\(513\) 0 0
\(514\) −8.16702e7 −0.601415
\(515\) −3.00295e8 1.73375e8i −2.19850 1.26930i
\(516\) 0 0
\(517\) 5.14764e7 + 8.91597e7i 0.372509 + 0.645204i
\(518\) −1.24545e8 + 7.19059e7i −0.896058 + 0.517339i
\(519\) 0 0
\(520\) −5.30258e7 + 9.18434e7i −0.377118 + 0.653187i
\(521\) 9.00897e7i 0.637033i −0.947917 0.318517i \(-0.896815\pi\)
0.947917 0.318517i \(-0.103185\pi\)
\(522\) 0 0
\(523\) −3.77691e7 −0.264016 −0.132008 0.991249i \(-0.542143\pi\)
−0.132008 + 0.991249i \(0.542143\pi\)
\(524\) 8.51858e7 + 4.91820e7i 0.592070 + 0.341832i
\(525\) 0 0
\(526\) 8.84073e7 + 1.53126e8i 0.607478 + 1.05218i
\(527\) −438660. + 253260.i −0.00299706 + 0.00173035i
\(528\) 0 0
\(529\) −6.83154e7 + 1.18326e8i −0.461479 + 0.799304i
\(530\) 2.34918e8i 1.57793i
\(531\) 0 0
\(532\) 8.89631e7 0.590847
\(533\) 1.08045e8 + 6.23796e7i 0.713545 + 0.411965i
\(534\) 0 0
\(535\) −2.26714e7 3.92679e7i −0.148053 0.256435i
\(536\) −2.64887e7 + 1.52932e7i −0.172015 + 0.0993128i
\(537\) 0 0
\(538\) 710892. 1.23130e6i 0.00456517 0.00790710i
\(539\) 1.56332e8i 0.998347i
\(540\) 0 0
\(541\) 2.54800e7 0.160919 0.0804595 0.996758i \(-0.474361\pi\)
0.0804595 + 0.996758i \(0.474361\pi\)
\(542\) −1.45205e8 8.38343e7i −0.911978 0.526531i
\(543\) 0 0
\(544\) 36864.0 + 63850.3i 0.000228984 + 0.000396612i
\(545\) 2.92936e7 1.69126e7i 0.180960 0.104477i
\(546\) 0 0
\(547\) −1.02608e8 + 1.77722e8i −0.626930 + 1.08587i 0.361234 + 0.932475i \(0.382355\pi\)
−0.988164 + 0.153399i \(0.950978\pi\)
\(548\) 1.43492e8i 0.871938i
\(549\) 0 0
\(550\) 1.10977e8 0.667027
\(551\) −1.46024e8 8.43071e7i −0.872911 0.503975i
\(552\) 0 0
\(553\) −8.49807e6 1.47191e7i −0.0502510 0.0870373i
\(554\) 6.47707e7 3.73954e7i 0.380934 0.219932i
\(555\) 0 0
\(556\) −1.74772e7 + 3.02715e7i −0.101683 + 0.176120i
\(557\) 2.41143e8i 1.39543i −0.716375 0.697715i \(-0.754200\pi\)
0.716375 0.697715i \(-0.245800\pi\)
\(558\) 0 0
\(559\) 1.27984e7 0.0732690
\(560\) 7.46614e7 + 4.31058e7i 0.425140 + 0.245455i
\(561\) 0 0
\(562\) −1.73202e7 2.99994e7i −0.0975760 0.169007i
\(563\) −1.46252e8 + 8.44386e7i −0.819552 + 0.473168i −0.850262 0.526360i \(-0.823556\pi\)
0.0307102 + 0.999528i \(0.490223\pi\)
\(564\) 0 0
\(565\) −7.14838e7 + 1.23814e8i −0.396335 + 0.686472i
\(566\) 3.81456e7i 0.210375i
\(567\) 0 0
\(568\) −9.62058e7 −0.524996
\(569\) 2.11306e8 + 1.21998e8i 1.14703 + 0.662238i 0.948162 0.317788i \(-0.102940\pi\)
0.198869 + 0.980026i \(0.436273\pi\)
\(570\) 0 0
\(571\) −1.20751e8 2.09147e8i −0.648608 1.12342i −0.983456 0.181149i \(-0.942018\pi\)
0.334848 0.942272i \(-0.391315\pi\)
\(572\) −1.25134e8 + 7.22463e7i −0.668633 + 0.386036i
\(573\) 0 0
\(574\) 5.07096e7 8.78317e7i 0.268136 0.464425i
\(575\) 4.94177e7i 0.259944i
\(576\) 0 0
\(577\) −4.93979e7 −0.257147 −0.128573 0.991700i \(-0.541040\pi\)
−0.128573 + 0.991700i \(0.541040\pi\)
\(578\) −1.18249e8 6.82709e7i −0.612368 0.353551i
\(579\) 0 0
\(580\) −8.16996e7 1.41508e8i −0.418732 0.725264i
\(581\) 4.60232e6 2.65715e6i 0.0234665 0.0135484i
\(582\) 0 0
\(583\) 1.60035e8 2.77188e8i 0.807623 1.39884i
\(584\) 4.27466e7i 0.214617i
\(585\) 0 0
\(586\) 5.67038e7 0.281786
\(587\) 1.49001e8 + 8.60260e7i 0.736675 + 0.425320i 0.820859 0.571131i \(-0.193495\pi\)
−0.0841840 + 0.996450i \(0.526828\pi\)
\(588\) 0 0
\(589\) 1.14294e8 + 1.97963e8i 0.559343 + 0.968810i
\(590\) 2.12906e8 1.22922e8i 1.03665 0.598511i
\(591\) 0 0
\(592\) −2.68933e7 + 4.65806e7i −0.129622 + 0.224512i
\(593\) 2.70643e8i 1.29788i 0.760841 + 0.648938i \(0.224787\pi\)
−0.760841 + 0.648938i \(0.775213\pi\)
\(594\) 0 0
\(595\) 1.07158e6 0.00508712
\(596\) −6.15467e7 3.55340e7i −0.290714 0.167844i
\(597\) 0 0
\(598\) −3.21711e7 5.57220e7i −0.150440 0.260569i
\(599\) −1.50082e8 + 8.66497e7i −0.698308 + 0.403169i −0.806717 0.590938i \(-0.798758\pi\)
0.108409 + 0.994106i \(0.465425\pi\)
\(600\) 0 0
\(601\) 2.15545e8 3.73335e8i 0.992921 1.71979i 0.393598 0.919282i \(-0.371230\pi\)
0.599323 0.800507i \(-0.295437\pi\)
\(602\) 1.04041e7i 0.0476886i
\(603\) 0 0
\(604\) 1.30519e8 0.592327
\(605\) 3.89369e6 + 2.24802e6i 0.0175831 + 0.0101516i
\(606\) 0 0
\(607\) −8.34953e6 1.44618e7i −0.0373332 0.0646631i 0.846755 0.531983i \(-0.178553\pi\)
−0.884088 + 0.467320i \(0.845220\pi\)
\(608\) 2.88151e7 1.66364e7i 0.128206 0.0740199i
\(609\) 0 0
\(610\) 6.51900e6 1.12912e7i 0.0287205 0.0497453i
\(611\) 2.58635e8i 1.13387i
\(612\) 0 0
\(613\) −1.92321e8 −0.834920 −0.417460 0.908695i \(-0.637080\pi\)
−0.417460 + 0.908695i \(0.637080\pi\)
\(614\) 2.56246e7 + 1.47944e7i 0.110701 + 0.0639133i
\(615\) 0 0
\(616\) 5.87305e7 + 1.01724e8i 0.251259 + 0.435193i
\(617\) −1.61967e8 + 9.35117e7i −0.689558 + 0.398117i −0.803447 0.595377i \(-0.797003\pi\)
0.113888 + 0.993494i \(0.463669\pi\)
\(618\) 0 0
\(619\) −1.27437e8 + 2.20727e8i −0.537307 + 0.930643i 0.461741 + 0.887015i \(0.347225\pi\)
−0.999048 + 0.0436278i \(0.986108\pi\)
\(620\) 2.21518e8i 0.929468i
\(621\) 0 0
\(622\) −1.76619e8 −0.733950
\(623\) −5.42088e7 3.12975e7i −0.224185 0.129433i
\(624\) 0 0
\(625\) 1.29328e8 + 2.24003e8i 0.529729 + 0.917517i
\(626\) 1.10118e8 6.35769e7i 0.448887 0.259165i
\(627\) 0 0
\(628\) 9.84908e7 1.70591e8i 0.397665 0.688775i
\(629\) 668547.i 0.00268646i
\(630\) 0 0
\(631\) 9.23602e7 0.367618 0.183809 0.982962i \(-0.441157\pi\)
0.183809 + 0.982962i \(0.441157\pi\)
\(632\) −5.50504e6 3.17834e6i −0.0218077 0.0125907i
\(633\) 0 0
\(634\) −7.81243e7 1.35315e8i −0.306562 0.530981i
\(635\) 4.60549e8 2.65898e8i 1.79869 1.03847i
\(636\) 0 0
\(637\) −1.96366e8 + 3.40116e8i −0.759711 + 1.31586i
\(638\) 2.22627e8i 0.857267i
\(639\) 0 0
\(640\) 3.22437e7 0.123000
\(641\) 3.67771e8 + 2.12333e8i 1.39638 + 0.806200i 0.994011 0.109278i \(-0.0348537\pi\)
0.402368 + 0.915478i \(0.368187\pi\)
\(642\) 0 0
\(643\) −1.87973e8 3.25579e8i −0.707071 1.22468i −0.965939 0.258770i \(-0.916683\pi\)
0.258868 0.965913i \(-0.416650\pi\)
\(644\) −4.52976e7 + 2.61526e7i −0.169597 + 0.0979168i
\(645\) 0 0
\(646\) 206784. 358160.i 0.000767042 0.00132856i
\(647\) 2.63747e7i 0.0973813i 0.998814 + 0.0486906i \(0.0155048\pi\)
−0.998814 + 0.0486906i \(0.984495\pi\)
\(648\) 0 0
\(649\) 3.34955e8 1.22533
\(650\) 2.41441e8 + 1.39396e8i 0.879166 + 0.507587i
\(651\) 0 0
\(652\) 1.28111e7 + 2.21895e7i 0.0462216 + 0.0800581i
\(653\) 2.24090e8 1.29378e8i 0.804790 0.464645i −0.0403536 0.999185i \(-0.512848\pi\)
0.845143 + 0.534540i \(0.179515\pi\)
\(654\) 0 0
\(655\) 2.67348e8 4.63060e8i 0.951377 1.64783i
\(656\) 3.79315e7i 0.134366i
\(657\) 0 0
\(658\) 2.10250e8 0.738002
\(659\) 1.20676e8 + 6.96725e7i 0.421663 + 0.243447i 0.695789 0.718247i \(-0.255055\pi\)
−0.274126 + 0.961694i \(0.588388\pi\)
\(660\) 0 0
\(661\) 2.36272e8 + 4.09236e8i 0.818104 + 1.41700i 0.907077 + 0.420964i \(0.138308\pi\)
−0.0889731 + 0.996034i \(0.528359\pi\)
\(662\) −2.82249e7 + 1.62957e7i −0.0972878 + 0.0561691i
\(663\) 0 0
\(664\) 993792. 1.72130e6i 0.00339462 0.00587966i
\(665\) 4.83593e8i 1.64443i
\(666\) 0 0
\(667\) 9.91354e7 0.334081
\(668\) 1.33151e8 + 7.68747e7i 0.446699 + 0.257902i
\(669\) 0 0
\(670\) 8.31323e7 + 1.43989e8i 0.276405 + 0.478747i
\(671\) 1.53840e7 8.88197e6i 0.0509216 0.0293996i
\(672\) 0 0
\(673\) −2.74417e8 + 4.75304e8i −0.900254 + 1.55929i −0.0730906 + 0.997325i \(0.523286\pi\)
−0.827164 + 0.561961i \(0.810047\pi\)
\(674\) 2.26869e8i 0.740961i
\(675\) 0 0
\(676\) −2.08532e8 −0.675044
\(677\) 8.72609e7 + 5.03801e7i 0.281225 + 0.162365i 0.633978 0.773351i \(-0.281421\pi\)
−0.352753 + 0.935717i \(0.614754\pi\)
\(678\) 0 0
\(679\) −7.77846e7 1.34727e8i −0.248476 0.430373i
\(680\) 347083. 200388.i 0.00110384 0.000637303i
\(681\) 0 0
\(682\) −1.50906e8 + 2.61378e8i −0.475724 + 0.823977i
\(683\) 313056.i 0.000982562i −1.00000 0.000491281i \(-0.999844\pi\)
1.00000 0.000491281i \(-0.000156380\pi\)
\(684\) 0 0
\(685\) 7.80005e8 2.42675
\(686\) −2.47069e6 1.42645e6i −0.00765326 0.00441861i
\(687\) 0 0
\(688\) −1.94560e6 3.36988e6i −0.00597432 0.0103478i
\(689\) 6.96344e8 4.02034e8i 2.12895 1.22915i
\(690\) 0 0
\(691\) 1.86406e8 3.22865e8i 0.564971 0.978558i −0.432082 0.901834i \(-0.642221\pi\)
0.997052 0.0767236i \(-0.0244459\pi\)
\(692\) 1.14238e8i 0.344739i
\(693\) 0 0
\(694\) −3.83607e8 −1.14765
\(695\) 1.64552e8 + 9.50043e7i 0.490173 + 0.283002i
\(696\) 0 0
\(697\) −235737. 408308.i −0.000696193 0.00120584i
\(698\) −2.06070e8 + 1.18975e8i −0.605966 + 0.349855i
\(699\) 0 0
\(700\) 1.13318e8 1.96272e8i 0.330373 0.572223i
\(701\) 6.21170e8i 1.80325i 0.432517 + 0.901626i \(0.357626\pi\)
−0.432517 + 0.901626i \(0.642374\pi\)
\(702\) 0 0
\(703\) 3.01709e8 0.868406
\(704\) 3.80456e7 + 2.19656e7i 0.109040 + 0.0629543i
\(705\) 0 0
\(706\) −4.97734e7 8.62101e7i −0.141444 0.244988i
\(707\) −2.80323e8 + 1.61845e8i −0.793234 + 0.457974i
\(708\) 0 0
\(709\) 1.23255e8 2.13484e8i 0.345833 0.599000i −0.639672 0.768648i \(-0.720930\pi\)
0.985505 + 0.169648i \(0.0542631\pi\)
\(710\) 5.22964e8i 1.46116i
\(711\) 0 0
\(712\) −2.34109e7 −0.0648603
\(713\) −1.16391e8 6.71984e7i −0.321108 0.185392i
\(714\) 0 0
\(715\) 3.92722e8 + 6.80215e8i 1.07440 + 1.86092i
\(716\) 2.06100e8 1.18992e8i 0.561485 0.324173i
\(717\) 0 0
\(718\) −3.95754e7 + 6.85466e7i −0.106918 + 0.185188i
\(719\) 9.60389e7i 0.258381i −0.991620 0.129191i \(-0.958762\pi\)
0.991620 0.129191i \(-0.0412379\pi\)
\(720\) 0 0
\(721\) −9.64811e8 −2.57417
\(722\) 6.88421e7 + 3.97460e7i 0.182912 + 0.105604i
\(723\) 0 0
\(724\) −1.66099e8 2.87692e8i −0.437675 0.758075i
\(725\) −3.72001e8 + 2.14775e8i −0.976179 + 0.563597i
\(726\) 0 0
\(727\) −1.95685e8 + 3.38937e8i −0.509278 + 0.882096i 0.490664 + 0.871349i \(0.336754\pi\)
−0.999942 + 0.0107471i \(0.996579\pi\)
\(728\) 2.95082e8i 0.764801i
\(729\) 0 0
\(730\) −2.32366e8 −0.597315
\(731\) −41886.3 24183.1i −0.000107231 6.19097e-5i
\(732\) 0 0
\(733\) −1.74539e7 3.02311e7i −0.0443181 0.0767611i 0.843015 0.537889i \(-0.180778\pi\)
−0.887334 + 0.461128i \(0.847445\pi\)
\(734\) −1.30242e8 + 7.51951e7i −0.329353 + 0.190152i
\(735\) 0 0
\(736\) −9.78125e6 + 1.69416e7i −0.0245336 + 0.0424934i
\(737\) 2.26531e8i 0.565881i
\(738\) 0 0
\(739\) −3.02999e8 −0.750773 −0.375386 0.926868i \(-0.622490\pi\)
−0.375386 + 0.926868i \(0.622490\pi\)
\(740\) 2.53207e8 + 1.46189e8i 0.624856 + 0.360761i
\(741\) 0 0
\(742\) −3.26822e8 5.66072e8i −0.800018 1.38567i
\(743\) 2.12720e8 1.22814e8i 0.518612 0.299421i −0.217754 0.976004i \(-0.569873\pi\)
0.736367 + 0.676583i \(0.236540\pi\)
\(744\) 0 0
\(745\) −1.93159e8 + 3.34560e8i −0.467138 + 0.809107i
\(746\) 1.01161e8i 0.243667i
\(747\) 0 0
\(748\) 546048. 0.00130475
\(749\) −1.09261e8 6.30816e7i −0.260027 0.150127i
\(750\) 0 0
\(751\) 4.11635e7 + 7.12973e7i 0.0971835 + 0.168327i 0.910518 0.413470i \(-0.135683\pi\)
−0.813334 + 0.581797i \(0.802350\pi\)
\(752\) 6.80997e7 3.93174e7i 0.160137 0.0924552i
\(753\) 0 0
\(754\) 2.79638e8 4.84348e8i 0.652353 1.12991i
\(755\) 7.09484e8i 1.64855i
\(756\) 0 0
\(757\) −6.03579e8 −1.39138 −0.695691 0.718341i \(-0.744902\pi\)
−0.695691 + 0.718341i \(0.744902\pi\)
\(758\) −3.53205e8 2.03923e8i −0.810998 0.468230i
\(759\) 0 0
\(760\) −9.04335e7 1.56635e8i −0.206010 0.356820i
\(761\) −2.01769e8 + 1.16491e8i −0.457825 + 0.264325i −0.711129 0.703061i \(-0.751816\pi\)
0.253304 + 0.967387i \(0.418483\pi\)
\(762\) 0 0
\(763\) 4.70584e7 8.15075e7i 0.105941 0.183495i
\(764\) 4.15810e8i 0.932426i
\(765\) 0 0
\(766\) −4.91382e7 −0.109328
\(767\) 7.28729e8 + 4.20732e8i 1.61503 + 0.932436i
\(768\) 0 0
\(769\) −4.07898e8 7.06500e8i −0.896958 1.55358i −0.831362 0.555731i \(-0.812438\pi\)
−0.0655965 0.997846i \(-0.520895\pi\)
\(770\) 5.52961e8 3.19252e8i 1.21122 0.699297i
\(771\) 0 0
\(772\) −6.29113e7 + 1.08966e8i −0.136734 + 0.236830i
\(773\) 3.66587e8i 0.793667i −0.917891 0.396833i \(-0.870109\pi\)
0.917891 0.396833i \(-0.129891\pi\)
\(774\) 0 0
\(775\) 5.82335e8 1.25103
\(776\) −5.03888e7 2.90920e7i −0.107832 0.0622570i
\(777\) 0 0
\(778\) −1.39841e8 2.42211e8i −0.296958 0.514346i
\(779\) −1.84266e8 + 1.06386e8i −0.389792 + 0.225047i
\(780\) 0 0
\(781\) −3.56262e8 + 6.17064e8i −0.747854 + 1.29532i
\(782\) 243154.i 0.000508466i
\(783\) 0 0
\(784\) 1.19406e8 0.247786
\(785\) −9.27314e8 5.35385e8i −1.91698 1.10677i
\(786\) 0 0
\(787\) 2.01231e8 + 3.48542e8i 0.412830 + 0.715042i 0.995198 0.0978832i \(-0.0312072\pi\)
−0.582368 + 0.812925i \(0.697874\pi\)
\(788\) −1.49086e8 + 8.60748e7i −0.304690 + 0.175913i
\(789\) 0 0
\(790\) −1.72771e7 + 2.99248e7i −0.0350420 + 0.0606945i
\(791\) 3.97798e8i 0.803773i
\(792\) 0 0
\(793\) 4.46260e7 0.0894887
\(794\) −7.68704e7 4.43811e7i −0.153567 0.0886619i
\(795\) 0 0
\(796\) −9.05440e6 1.56827e7i −0.0179523 0.0310943i
\(797\) −4.49415e8 + 2.59470e8i −0.887713 + 0.512521i −0.873194 0.487373i \(-0.837955\pi\)
−0.0145190 + 0.999895i \(0.504622\pi\)
\(798\) 0 0
\(799\) 488700. 846453.i 0.000958081 0.00165944i
\(800\) 8.47634e7i 0.165553i
\(801\) 0 0
\(802\) 2.68426e8 0.520356
\(803\) −2.74177e8 1.58296e8i −0.529522 0.305720i
\(804\) 0 0
\(805\) 1.42162e8 + 2.46233e8i 0.272519 + 0.472017i
\(806\) −6.56625e8 + 3.79102e8i −1.25404 + 0.724021i
\(807\) 0 0
\(808\) −6.05311e7 + 1.04843e8i −0.114748 + 0.198749i
\(809\) 3.04036e6i 0.00574221i −0.999996 0.00287110i \(-0.999086\pi\)
0.999996 0.00287110i \(-0.000913902\pi\)
\(810\) 0 0
\(811\) 2.25521e8 0.422790 0.211395 0.977401i \(-0.432199\pi\)
0.211395 + 0.977401i \(0.432199\pi\)
\(812\) −3.93736e8 2.27324e8i −0.735423 0.424597i
\(813\) 0 0
\(814\) 1.99179e8 + 3.44987e8i 0.369292 + 0.639632i
\(815\) 1.20620e8 6.96398e7i 0.222816 0.128643i
\(816\) 0 0
\(817\) −1.09136e7 + 1.89029e7i −0.0200125 + 0.0346627i
\(818\) 6.53432e8i 1.19383i
\(819\) 0 0
\(820\) −2.06191e8 −0.373963
\(821\) −2.39920e8 1.38518e8i −0.433547 0.250309i 0.267309 0.963611i \(-0.413865\pi\)
−0.700857 + 0.713302i \(0.747199\pi\)
\(822\) 0 0
\(823\) 3.53668e8 + 6.12571e8i 0.634448 + 1.09890i 0.986632 + 0.162966i \(0.0521059\pi\)
−0.352184 + 0.935931i \(0.614561\pi\)
\(824\) −3.12502e8 + 1.80423e8i −0.558562 + 0.322486i
\(825\) 0 0
\(826\) 3.42022e8 5.92399e8i 0.606895 1.05117i
\(827\) 2.66346e8i 0.470900i −0.971886 0.235450i \(-0.924344\pi\)
0.971886 0.235450i \(-0.0756564\pi\)
\(828\) 0 0
\(829\) 5.03826e8 0.884336 0.442168 0.896932i \(-0.354209\pi\)
0.442168 + 0.896932i \(0.354209\pi\)
\(830\) −9.35678e6 5.40214e6i −0.0163641 0.00944781i
\(831\) 0 0
\(832\) 5.51813e7 + 9.55768e7i 0.0958125 + 0.165952i
\(833\) 1.28532e6 742082.i 0.00222371 0.00128386i
\(834\) 0 0
\(835\) 4.17882e8 7.23793e8i 0.717785 1.24324i
\(836\) 2.46427e8i 0.421763i
\(837\) 0 0
\(838\) −8.29822e8 −1.41011
\(839\) −6.61093e8 3.81682e8i −1.11938 0.646273i −0.178136 0.984006i \(-0.557007\pi\)
−0.941242 + 0.337733i \(0.890340\pi\)
\(840\) 0 0
\(841\) 1.33441e8 + 2.31127e8i 0.224338 + 0.388565i
\(842\) 6.82128e8 3.93827e8i 1.14269 0.659734i
\(843\) 0 0
\(844\) −2.16264e8 + 3.74580e8i −0.359714 + 0.623042i
\(845\) 1.13355e9i 1.87876i
\(846\) 0 0
\(847\) 1.25099e7 0.0205876
\(848\) −2.11715e8 1.22234e8i −0.347187 0.200449i
\(849\) 0 0
\(850\) −526788. 912424.i −0.000857786 0.00148573i
\(851\) −1.53622e8 + 8.86939e7i −0.249267 + 0.143915i
\(852\) 0 0
\(853\) 9.39926e6 1.62800e7i 0.0151442 0.0262305i −0.858354 0.513058i \(-0.828513\pi\)
0.873498 + 0.486827i \(0.161846\pi\)
\(854\) 3.62774e7i 0.0582455i
\(855\) 0 0
\(856\) −4.71859e7 −0.0752300
\(857\) 5.94463e8 + 3.43214e8i 0.944458 + 0.545283i 0.891355 0.453306i \(-0.149755\pi\)
0.0531031 + 0.998589i \(0.483089\pi\)
\(858\) 0 0
\(859\) −2.75966e8 4.77987e8i −0.435387 0.754113i 0.561940 0.827178i \(-0.310055\pi\)
−0.997327 + 0.0730651i \(0.976722\pi\)
\(860\) −1.83183e7 + 1.05761e7i −0.0287998 + 0.0166276i
\(861\) 0 0
\(862\) −2.83950e8 + 4.91816e8i −0.443323 + 0.767858i
\(863\) 3.65665e8i 0.568920i 0.958688 + 0.284460i \(0.0918142\pi\)
−0.958688 + 0.284460i \(0.908186\pi\)
\(864\) 0 0
\(865\) 6.20982e8 0.959468
\(866\) 1.96268e8 + 1.13316e8i 0.302202 + 0.174476i
\(867\) 0 0
\(868\) 3.08180e8 + 5.33784e8i 0.471244 + 0.816218i
\(869\) −4.07717e7 + 2.35396e7i −0.0621298 + 0.0358706i
\(870\) 0 0
\(871\) −2.84542e8 + 4.92841e8i −0.430618 + 0.745852i
\(872\) 3.52003e7i 0.0530881i
\(873\) 0 0
\(874\) 1.09733e8 0.164363
\(875\) 7.23282e7 + 4.17587e7i 0.107965 + 0.0623337i
\(876\) 0 0
\(877\) 2.92694e8 + 5.06960e8i 0.433925 + 0.751580i 0.997207 0.0746848i \(-0.0237951\pi\)
−0.563283 + 0.826264i \(0.690462\pi\)
\(878\) −6.78959e8 + 3.91997e8i −1.00314 + 0.579161i
\(879\) 0 0
\(880\) 1.19402e8 2.06811e8i 0.175213 0.303477i
\(881\) 4.29761e8i 0.628491i −0.949342 0.314246i \(-0.898248\pi\)
0.949342 0.314246i \(-0.101752\pi\)
\(882\) 0 0
\(883\) 2.20085e8 0.319675 0.159837 0.987143i \(-0.448903\pi\)
0.159837 + 0.987143i \(0.448903\pi\)
\(884\) 1.18798e6 + 685882.i 0.00171970 + 0.000992871i
\(885\) 0 0
\(886\) −3.15207e8 5.45955e8i −0.453205 0.784975i
\(887\) 1.01495e9 5.85981e8i 1.45437 0.839678i 0.455641 0.890164i \(-0.349410\pi\)
0.998725 + 0.0504855i \(0.0160769\pi\)
\(888\) 0 0
\(889\) 7.39845e8 1.28145e9i 1.05302 1.82388i
\(890\) 1.27259e8i 0.180517i
\(891\) 0 0
\(892\) 1.71355e8 0.241436
\(893\) −3.81997e8 2.20546e8i −0.536421 0.309703i
\(894\) 0 0
\(895\) −6.46825e8 1.12033e9i −0.902230 1.56271i
\(896\) 7.76964e7 4.48580e7i 0.108013 0.0623615i
\(897\) 0 0
\(898\) −1.72864e8 + 2.99409e8i −0.238713 + 0.413462i
\(899\) 1.16820e9i 1.60783i
\(900\) 0 0
\(901\) −3.03863e6 −0.00415436
\(902\) −2.43293e8 1.40465e8i −0.331520 0.191403i
\(903\) 0 0
\(904\) 7.43896e7 + 1.28847e8i 0.100695 + 0.174409i
\(905\) −1.56386e9 + 9.02895e8i −2.10985 + 1.21812i
\(906\) 0 0
\(907\) −3.65807e8 + 6.33597e8i −0.490264 + 0.849163i −0.999937 0.0112055i \(-0.996433\pi\)
0.509673 + 0.860368i \(0.329766\pi\)
\(908\) 4.35403e8i 0.581612i
\(909\) 0 0
\(910\) 1.60403e9 2.12857
\(911\) −7.95527e8 4.59298e8i −1.05220 0.607490i −0.128938 0.991653i \(-0.541157\pi\)
−0.923265 + 0.384163i \(0.874490\pi\)
\(912\) 0 0
\(913\) −7.36027e6 1.27484e7i −0.00967123 0.0167511i
\(914\) 1.74729e8 1.00880e8i 0.228838 0.132119i
\(915\) 0 0
\(916\) 6.95425e7 1.20451e8i 0.0904824 0.156720i
\(917\) 1.48776e9i 1.92941i
\(918\) 0 0
\(919\) −2.15987e8 −0.278279 −0.139139 0.990273i \(-0.544434\pi\)
−0.139139 + 0.990273i \(0.544434\pi\)
\(920\) 9.20927e7 + 5.31697e7i 0.118266 + 0.0682812i
\(921\) 0 0
\(922\) 4.29872e8 + 7.44560e8i 0.548462 + 0.949964i
\(923\) −1.55017e9 + 8.94991e8i −1.97140 + 1.13819i
\(924\) 0 0
\(925\) 3.84306e8 6.65638e8i 0.485571 0.841033i
\(926\) 6.50414e8i 0.819138i
\(927\) 0 0
\(928\) −1.70041e8 −0.212770
\(929\) −2.68575e8 1.55062e8i −0.334980 0.193401i 0.323070 0.946375i \(-0.395285\pi\)
−0.658050 + 0.752974i \(0.728618\pi\)
\(930\) 0 0
\(931\) −3.34895e8 5.80056e8i −0.415011 0.718821i
\(932\) 5.60722e8 3.23733e8i 0.692628 0.399889i
\(933\) 0 0
\(934\) 2.49384e8 4.31946e8i 0.306075 0.530137i
\(935\) 2.96825e6i 0.00363133i
\(936\) 0 0
\(937\) −7.42448e8 −0.902501 −0.451250 0.892397i \(-0.649022\pi\)
−0.451250 + 0.892397i \(0.649022\pi\)
\(938\) 4.00641e8 + 2.31310e8i 0.485453 + 0.280276i
\(939\) 0 0
\(940\) −2.13725e8 3.70182e8i −0.257319 0.445689i
\(941\) 1.57414e8 9.08828e7i 0.188918 0.109072i −0.402558 0.915395i \(-0.631879\pi\)
0.591476 + 0.806323i \(0.298545\pi\)
\(942\) 0 0
\(943\) 6.25489e7 1.08338e8i 0.0745907 0.129195i
\(944\) 2.55837e8i 0.304121i
\(945\) 0 0
\(946\) −2.88192e7 −0.0340415
\(947\) −7.44080e8 4.29595e8i −0.876132 0.505835i −0.00675089 0.999977i \(-0.502149\pi\)
−0.869381 + 0.494142i \(0.835482\pi\)
\(948\) 0 0
\(949\) −3.97666e8 6.88779e8i −0.465286 0.805900i
\(950\) −4.11769e8 + 2.37735e8i −0.480267 + 0.277282i
\(951\) 0 0
\(952\) 557568. 965736.i 0.000646230 0.00111930i
\(953\) 6.86819e8i 0.793530i 0.917920 + 0.396765i \(0.129867\pi\)
−0.917920 + 0.396765i \(0.870133\pi\)
\(954\) 0 0
\(955\) −2.26029e9 −2.59510
\(956\) −5.65194e8 3.26315e8i −0.646880 0.373476i
\(957\) 0 0
\(958\) −2.52971e8 4.38159e8i −0.287723 0.498351i
\(959\) 1.87955e9 1.08516e9i 2.13107 1.23037i
\(960\) 0 0
\(961\) −3.48109e8 + 6.02942e8i −0.392234 + 0.679369i
\(962\) 1.00074e9i 1.12408i
\(963\) 0 0
\(964\) 9.98697e7 0.111481
\(965\) 5.92324e8 + 3.41978e8i 0.659139 + 0.380554i
\(966\) 0 0
\(967\) 5.47055e8 + 9.47527e8i 0.604995 + 1.04788i 0.992052 + 0.125826i \(0.0401581\pi\)
−0.387058 + 0.922055i \(0.626509\pi\)
\(968\) 4.05197e6 2.33940e6i 0.00446724 0.00257916i
\(969\) 0 0
\(970\) −1.58141e8 + 2.73908e8i −0.173272 + 0.300116i
\(971\) 4.43115e8i 0.484014i 0.970274 + 0.242007i \(0.0778058\pi\)
−0.970274 + 0.242007i \(0.922194\pi\)
\(972\) 0 0
\(973\) 5.28687e8 0.573931
\(974\) 3.68251e8 + 2.12610e8i 0.398535 + 0.230094i
\(975\) 0 0
\(976\) −6.78400e6 1.17502e7i −0.00729687 0.0126385i
\(977\) 1.03061e9 5.95022e8i 1.10512 0.638042i 0.167560 0.985862i \(-0.446411\pi\)
0.937561 + 0.347820i \(0.113078\pi\)
\(978\) 0 0
\(979\) −8.66937e7 + 1.50158e8i −0.0923930 + 0.160029i
\(980\) 6.49075e8i 0.689631i
\(981\) 0 0
\(982\) −2.55024e8 −0.269306
\(983\) 1.02353e9 + 5.90933e8i 1.07755 + 0.622125i 0.930235 0.366965i \(-0.119603\pi\)
0.147317 + 0.989089i \(0.452936\pi\)
\(984\) 0 0
\(985\) 4.67892e8 + 8.10413e8i 0.489595 + 0.848004i
\(986\) −1.83039e6 + 1.05677e6i −0.00190947 + 0.00110243i
\(987\) 0 0
\(988\) 3.09533e8 5.36126e8i 0.320949 0.555900i
\(989\) 1.28331e7i 0.0132661i
\(990\) 0 0
\(991\) 5.09602e8 0.523613 0.261806 0.965120i \(-0.415682\pi\)
0.261806 + 0.965120i \(0.415682\pi\)
\(992\) 1.99639e8 + 1.15262e8i 0.204508 + 0.118073i
\(993\) 0 0
\(994\) 7.27557e8 + 1.26016e9i 0.740811 + 1.28312i
\(995\) −8.52492e7 + 4.92187e7i −0.0865409 + 0.0499644i
\(996\) 0 0
\(997\) 4.95390e8 8.58041e8i 0.499875 0.865810i −0.500125 0.865953i \(-0.666712\pi\)
1.00000 0.000143848i \(4.57883e-5\pi\)
\(998\) 5.17861e8i 0.520981i
\(999\) 0 0
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 162.7.d.d.107.1 4
3.2 odd 2 inner 162.7.d.d.107.2 4
9.2 odd 6 18.7.b.a.17.1 2
9.4 even 3 inner 162.7.d.d.53.2 4
9.5 odd 6 inner 162.7.d.d.53.1 4
9.7 even 3 18.7.b.a.17.2 yes 2
36.7 odd 6 144.7.e.d.17.2 2
36.11 even 6 144.7.e.d.17.1 2
45.2 even 12 450.7.b.a.449.3 4
45.7 odd 12 450.7.b.a.449.1 4
45.29 odd 6 450.7.d.a.251.2 2
45.34 even 6 450.7.d.a.251.1 2
45.38 even 12 450.7.b.a.449.2 4
45.43 odd 12 450.7.b.a.449.4 4
72.11 even 6 576.7.e.k.449.2 2
72.29 odd 6 576.7.e.b.449.2 2
72.43 odd 6 576.7.e.k.449.1 2
72.61 even 6 576.7.e.b.449.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.7.b.a.17.1 2 9.2 odd 6
18.7.b.a.17.2 yes 2 9.7 even 3
144.7.e.d.17.1 2 36.11 even 6
144.7.e.d.17.2 2 36.7 odd 6
162.7.d.d.53.1 4 9.5 odd 6 inner
162.7.d.d.53.2 4 9.4 even 3 inner
162.7.d.d.107.1 4 1.1 even 1 trivial
162.7.d.d.107.2 4 3.2 odd 2 inner
450.7.b.a.449.1 4 45.7 odd 12
450.7.b.a.449.2 4 45.38 even 12
450.7.b.a.449.3 4 45.2 even 12
450.7.b.a.449.4 4 45.43 odd 12
450.7.d.a.251.1 2 45.34 even 6
450.7.d.a.251.2 2 45.29 odd 6
576.7.e.b.449.1 2 72.61 even 6
576.7.e.b.449.2 2 72.29 odd 6
576.7.e.k.449.1 2 72.43 odd 6
576.7.e.k.449.2 2 72.11 even 6