Properties

Label 76.7.j.a.13.9
Level $76$
Weight $7$
Character 76.13
Analytic conductor $17.484$
Analytic rank $0$
Dimension $60$
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] = [76,7,Mod(13,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.13");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(17.4841103551\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 13.9
Character \(\chi\) \(=\) 76.13
Dual form 76.7.j.a.41.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(10.8061 - 29.6895i) q^{3} +(-26.2824 - 149.055i) q^{5} +(184.362 - 319.324i) q^{7} +(-206.249 - 173.063i) q^{9} +O(q^{10})\) \(q+(10.8061 - 29.6895i) q^{3} +(-26.2824 - 149.055i) q^{5} +(184.362 - 319.324i) q^{7} +(-206.249 - 173.063i) q^{9} +(-225.114 - 389.909i) q^{11} +(37.2019 + 102.211i) q^{13} +(-4709.38 - 830.391i) q^{15} +(2568.33 - 2155.09i) q^{17} +(-3464.43 + 5919.76i) q^{19} +(-7488.34 - 8924.26i) q^{21} +(-1553.39 + 8809.72i) q^{23} +(-6843.92 + 2490.98i) q^{25} +(12580.0 - 7263.06i) q^{27} +(-14794.5 + 17631.4i) q^{29} +(-44102.3 - 25462.5i) q^{31} +(-14008.8 + 2470.13i) q^{33} +(-52442.3 - 19087.4i) q^{35} -45616.7i q^{37} +3436.61 q^{39} +(10605.5 - 29138.3i) q^{41} +(-3702.47 - 20997.8i) q^{43} +(-20375.2 + 35290.9i) q^{45} +(2924.09 + 2453.60i) q^{47} +(-9154.08 - 15855.3i) q^{49} +(-36229.8 - 99540.6i) q^{51} +(185484. + 32705.9i) q^{53} +(-52201.3 + 43802.1i) q^{55} +(138318. + 166827. i) q^{57} +(46671.8 + 55621.3i) q^{59} +(-55776.1 + 316322. i) q^{61} +(-93287.6 + 33953.9i) q^{63} +(14257.4 - 8231.49i) q^{65} +(40189.5 - 47895.9i) q^{67} +(244770. + 141318. i) q^{69} +(494343. - 87166.0i) q^{71} +(307710. + 111997. i) q^{73} +230111. i q^{75} -166010. q^{77} +(187028. - 513856. i) q^{79} +(-113779. - 645272. i) q^{81} +(487024. - 843551. i) q^{83} +(-388728. - 326182. i) q^{85} +(363597. + 629769. i) q^{87} +(-6095.00 - 16745.9i) q^{89} +(39497.2 + 6964.41i) q^{91} +(-1.23254e6 + 1.03423e6i) q^{93} +(973424. + 360805. i) q^{95} +(118115. + 140764. i) q^{97} +(-21049.4 + 119377. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 10.8061 29.6895i 0.400226 1.09961i −0.561947 0.827173i \(-0.689948\pi\)
0.962173 0.272438i \(-0.0878301\pi\)
\(4\) 0 0
\(5\) −26.2824 149.055i −0.210259 1.19244i −0.888946 0.458012i \(-0.848562\pi\)
0.678687 0.734428i \(-0.262549\pi\)
\(6\) 0 0
\(7\) 184.362 319.324i 0.537498 0.930974i −0.461540 0.887119i \(-0.652703\pi\)
0.999038 0.0438545i \(-0.0139638\pi\)
\(8\) 0 0
\(9\) −206.249 173.063i −0.282920 0.237398i
\(10\) 0 0
\(11\) −225.114 389.909i −0.169131 0.292944i 0.768983 0.639269i \(-0.220763\pi\)
−0.938115 + 0.346325i \(0.887430\pi\)
\(12\) 0 0
\(13\) 37.2019 + 102.211i 0.0169330 + 0.0465231i 0.947871 0.318654i \(-0.103231\pi\)
−0.930938 + 0.365177i \(0.881008\pi\)
\(14\) 0 0
\(15\) −4709.38 830.391i −1.39537 0.246042i
\(16\) 0 0
\(17\) 2568.33 2155.09i 0.522762 0.438650i −0.342831 0.939397i \(-0.611386\pi\)
0.865593 + 0.500747i \(0.166941\pi\)
\(18\) 0 0
\(19\) −3464.43 + 5919.76i −0.505093 + 0.863065i
\(20\) 0 0
\(21\) −7488.34 8924.26i −0.808589 0.963639i
\(22\) 0 0
\(23\) −1553.39 + 8809.72i −0.127673 + 0.724067i 0.852012 + 0.523522i \(0.175382\pi\)
−0.979685 + 0.200545i \(0.935729\pi\)
\(24\) 0 0
\(25\) −6843.92 + 2490.98i −0.438011 + 0.159423i
\(26\) 0 0
\(27\) 12580.0 7263.06i 0.639130 0.369002i
\(28\) 0 0
\(29\) −14794.5 + 17631.4i −0.606607 + 0.722926i −0.978706 0.205267i \(-0.934194\pi\)
0.372099 + 0.928193i \(0.378638\pi\)
\(30\) 0 0
\(31\) −44102.3 25462.5i −1.48039 0.854704i −0.480638 0.876919i \(-0.659595\pi\)
−0.999753 + 0.0222148i \(0.992928\pi\)
\(32\) 0 0
\(33\) −14008.8 + 2470.13i −0.389815 + 0.0687350i
\(34\) 0 0
\(35\) −52442.3 19087.4i −1.22314 0.445188i
\(36\) 0 0
\(37\) 45616.7i 0.900573i −0.892884 0.450287i \(-0.851322\pi\)
0.892884 0.450287i \(-0.148678\pi\)
\(38\) 0 0
\(39\) 3436.61 0.0579344
\(40\) 0 0
\(41\) 10605.5 29138.3i 0.153878 0.422778i −0.838668 0.544643i \(-0.816665\pi\)
0.992547 + 0.121865i \(0.0388875\pi\)
\(42\) 0 0
\(43\) −3702.47 20997.8i −0.0465679 0.264100i 0.952631 0.304130i \(-0.0983657\pi\)
−0.999198 + 0.0400303i \(0.987255\pi\)
\(44\) 0 0
\(45\) −20375.2 + 35290.9i −0.223596 + 0.387280i
\(46\) 0 0
\(47\) 2924.09 + 2453.60i 0.0281642 + 0.0236326i 0.656761 0.754099i \(-0.271926\pi\)
−0.628597 + 0.777731i \(0.716370\pi\)
\(48\) 0 0
\(49\) −9154.08 15855.3i −0.0778084 0.134768i
\(50\) 0 0
\(51\) −36229.8 99540.6i −0.273121 0.750394i
\(52\) 0 0
\(53\) 185484. + 32705.9i 1.24589 + 0.219684i 0.757438 0.652907i \(-0.226451\pi\)
0.488452 + 0.872591i \(0.337562\pi\)
\(54\) 0 0
\(55\) −52201.3 + 43802.1i −0.313757 + 0.263273i
\(56\) 0 0
\(57\) 138318. + 166827.i 0.746885 + 0.900827i
\(58\) 0 0
\(59\) 46671.8 + 55621.3i 0.227247 + 0.270822i 0.867605 0.497254i \(-0.165658\pi\)
−0.640358 + 0.768077i \(0.721214\pi\)
\(60\) 0 0
\(61\) −55776.1 + 316322.i −0.245730 + 1.39361i 0.573060 + 0.819514i \(0.305756\pi\)
−0.818790 + 0.574093i \(0.805355\pi\)
\(62\) 0 0
\(63\) −93287.6 + 33953.9i −0.373080 + 0.135790i
\(64\) 0 0
\(65\) 14257.4 8231.49i 0.0519157 0.0299736i
\(66\) 0 0
\(67\) 40189.5 47895.9i 0.133625 0.159248i −0.695083 0.718930i \(-0.744632\pi\)
0.828708 + 0.559682i \(0.189077\pi\)
\(68\) 0 0
\(69\) 244770. + 141318.i 0.745095 + 0.430181i
\(70\) 0 0
\(71\) 494343. 87166.0i 1.38119 0.243541i 0.566798 0.823857i \(-0.308182\pi\)
0.814392 + 0.580316i \(0.197071\pi\)
\(72\) 0 0
\(73\) 307710. + 111997.i 0.790994 + 0.287898i 0.705749 0.708462i \(-0.250611\pi\)
0.0852448 + 0.996360i \(0.472833\pi\)
\(74\) 0 0
\(75\) 230111.i 0.545447i
\(76\) 0 0
\(77\) −166010. −0.363631
\(78\) 0 0
\(79\) 187028. 513856.i 0.379338 1.04222i −0.592293 0.805722i \(-0.701777\pi\)
0.971631 0.236500i \(-0.0760004\pi\)
\(80\) 0 0
\(81\) −113779. 645272.i −0.214095 1.21419i
\(82\) 0 0
\(83\) 487024. 843551.i 0.851758 1.47529i −0.0278621 0.999612i \(-0.508870\pi\)
0.879620 0.475677i \(-0.157797\pi\)
\(84\) 0 0
\(85\) −388728. 326182.i −0.632979 0.531132i
\(86\) 0 0
\(87\) 363597. + 629769.i 0.552158 + 0.956365i
\(88\) 0 0
\(89\) −6095.00 16745.9i −0.00864577 0.0237541i 0.935295 0.353870i \(-0.115134\pi\)
−0.943940 + 0.330116i \(0.892912\pi\)
\(90\) 0 0
\(91\) 39497.2 + 6964.41i 0.0524133 + 0.00924188i
\(92\) 0 0
\(93\) −1.23254e6 + 1.03423e6i −1.53233 + 1.28578i
\(94\) 0 0
\(95\) 973424. + 360805.i 1.13535 + 0.420825i
\(96\) 0 0
\(97\) 118115. + 140764.i 0.129416 + 0.154232i 0.826861 0.562406i \(-0.190124\pi\)
−0.697445 + 0.716638i \(0.745680\pi\)
\(98\) 0 0
\(99\) −21049.4 + 119377.i −0.0216937 + 0.123031i
\(100\) 0 0
\(101\) −1.17347e6 + 427107.i −1.13896 + 0.414546i −0.841536 0.540201i \(-0.818348\pi\)
−0.297419 + 0.954747i \(0.596126\pi\)
\(102\) 0 0
\(103\) 503201. 290523.i 0.460500 0.265870i −0.251754 0.967791i \(-0.581007\pi\)
0.712255 + 0.701921i \(0.247674\pi\)
\(104\) 0 0
\(105\) −1.13339e6 + 1.35073e6i −0.979068 + 1.16681i
\(106\) 0 0
\(107\) 164984. + 95253.7i 0.134676 + 0.0777554i 0.565824 0.824526i \(-0.308558\pi\)
−0.431148 + 0.902281i \(0.641891\pi\)
\(108\) 0 0
\(109\) −1.50267e6 + 264961.i −1.16034 + 0.204599i −0.720484 0.693472i \(-0.756080\pi\)
−0.439852 + 0.898070i \(0.644969\pi\)
\(110\) 0 0
\(111\) −1.35434e6 492939.i −0.990280 0.360433i
\(112\) 0 0
\(113\) 892967.i 0.618871i −0.950920 0.309435i \(-0.899860\pi\)
0.950920 0.309435i \(-0.100140\pi\)
\(114\) 0 0
\(115\) 1.35396e6 0.890251
\(116\) 0 0
\(117\) 10016.2 27519.2i 0.00625381 0.0171822i
\(118\) 0 0
\(119\) −214669. 1.21745e6i −0.127388 0.722451i
\(120\) 0 0
\(121\) 784428. 1.35867e6i 0.442789 0.766933i
\(122\) 0 0
\(123\) −750497. 629742.i −0.403305 0.338413i
\(124\) 0 0
\(125\) −631288. 1.09342e6i −0.323219 0.559832i
\(126\) 0 0
\(127\) −1.35804e6 3.73119e6i −0.662983 1.82153i −0.562853 0.826557i \(-0.690296\pi\)
−0.100131 0.994974i \(-0.531926\pi\)
\(128\) 0 0
\(129\) −663423. 116979.i −0.309045 0.0544929i
\(130\) 0 0
\(131\) −1.02333e6 + 858677.i −0.455200 + 0.381958i −0.841361 0.540473i \(-0.818245\pi\)
0.386161 + 0.922431i \(0.373801\pi\)
\(132\) 0 0
\(133\) 1.25161e6 + 2.19765e6i 0.532005 + 0.934124i
\(134\) 0 0
\(135\) −1.41323e6 1.68422e6i −0.574395 0.684538i
\(136\) 0 0
\(137\) −664096. + 3.76627e6i −0.258267 + 1.46471i 0.529278 + 0.848448i \(0.322463\pi\)
−0.787545 + 0.616257i \(0.788648\pi\)
\(138\) 0 0
\(139\) −489194. + 178052.i −0.182153 + 0.0662983i −0.431487 0.902119i \(-0.642011\pi\)
0.249333 + 0.968418i \(0.419789\pi\)
\(140\) 0 0
\(141\) 104444. 60301.0i 0.0372587 0.0215113i
\(142\) 0 0
\(143\) 31478.4 37514.5i 0.0107648 0.0128290i
\(144\) 0 0
\(145\) 3.01689e6 + 1.74180e6i 0.989590 + 0.571340i
\(146\) 0 0
\(147\) −569657. + 100446.i −0.179334 + 0.0316213i
\(148\) 0 0
\(149\) 1.55770e6 + 566955.i 0.470895 + 0.171392i 0.566558 0.824022i \(-0.308275\pi\)
−0.0956628 + 0.995414i \(0.530497\pi\)
\(150\) 0 0
\(151\) 6.59787e6i 1.91634i −0.286195 0.958171i \(-0.592391\pi\)
0.286195 0.958171i \(-0.407609\pi\)
\(152\) 0 0
\(153\) −902681. −0.252035
\(154\) 0 0
\(155\) −2.63620e6 + 7.24289e6i −0.707917 + 1.94499i
\(156\) 0 0
\(157\) 269740. + 1.52977e6i 0.0697021 + 0.395300i 0.999621 + 0.0275353i \(0.00876585\pi\)
−0.929919 + 0.367765i \(0.880123\pi\)
\(158\) 0 0
\(159\) 2.97538e6 5.15351e6i 0.740204 1.28207i
\(160\) 0 0
\(161\) 2.52677e6 + 2.12021e6i 0.605464 + 0.508045i
\(162\) 0 0
\(163\) 802239. + 1.38952e6i 0.185243 + 0.320850i 0.943658 0.330922i \(-0.107360\pi\)
−0.758416 + 0.651771i \(0.774026\pi\)
\(164\) 0 0
\(165\) 736370. + 2.02316e6i 0.163925 + 0.450379i
\(166\) 0 0
\(167\) 6.29458e6 + 1.10990e6i 1.35150 + 0.238307i 0.802070 0.597230i \(-0.203732\pi\)
0.549435 + 0.835537i \(0.314843\pi\)
\(168\) 0 0
\(169\) 3.68849e6 3.09501e6i 0.764167 0.641212i
\(170\) 0 0
\(171\) 1.73903e6 621378.i 0.347791 0.124270i
\(172\) 0 0
\(173\) 1.30069e6 + 1.55010e6i 0.251209 + 0.299379i 0.876881 0.480707i \(-0.159620\pi\)
−0.625673 + 0.780086i \(0.715175\pi\)
\(174\) 0 0
\(175\) −466327. + 2.64467e6i −0.0870115 + 0.493466i
\(176\) 0 0
\(177\) 2.15571e6 784613.i 0.388750 0.141493i
\(178\) 0 0
\(179\) −3.13240e6 + 1.80849e6i −0.546158 + 0.315324i −0.747571 0.664182i \(-0.768780\pi\)
0.201413 + 0.979506i \(0.435447\pi\)
\(180\) 0 0
\(181\) −4.70737e6 + 5.61002e6i −0.793858 + 0.946083i −0.999470 0.0325509i \(-0.989637\pi\)
0.205613 + 0.978633i \(0.434081\pi\)
\(182\) 0 0
\(183\) 8.78873e6 + 5.07417e6i 1.43408 + 0.827965i
\(184\) 0 0
\(185\) −6.79940e6 + 1.19892e6i −1.07388 + 0.189354i
\(186\) 0 0
\(187\) −1.41845e6 516275.i −0.216915 0.0789507i
\(188\) 0 0
\(189\) 5.35613e6i 0.793351i
\(190\) 0 0
\(191\) 1.15455e7 1.65696 0.828478 0.560022i \(-0.189207\pi\)
0.828478 + 0.560022i \(0.189207\pi\)
\(192\) 0 0
\(193\) −486893. + 1.33773e6i −0.0677270 + 0.186078i −0.968939 0.247300i \(-0.920457\pi\)
0.901212 + 0.433379i \(0.142679\pi\)
\(194\) 0 0
\(195\) −90322.5 512244.i −0.0121813 0.0690833i
\(196\) 0 0
\(197\) 5.10625e6 8.84428e6i 0.667887 1.15681i −0.310607 0.950539i \(-0.600532\pi\)
0.978494 0.206276i \(-0.0661345\pi\)
\(198\) 0 0
\(199\) −1.11842e7 9.38462e6i −1.41920 1.19085i −0.951766 0.306824i \(-0.900734\pi\)
−0.467435 0.884027i \(-0.654822\pi\)
\(200\) 0 0
\(201\) −987716. 1.71077e6i −0.121631 0.210671i
\(202\) 0 0
\(203\) 2.90259e6 + 7.97481e6i 0.346975 + 0.953306i
\(204\) 0 0
\(205\) −4.62194e6 814972.i −0.536491 0.0945979i
\(206\) 0 0
\(207\) 1.84502e6 1.54816e6i 0.208013 0.174544i
\(208\) 0 0
\(209\) 3.08806e6 + 18191.1i 0.338257 + 0.00199260i
\(210\) 0 0
\(211\) −400307. 477067.i −0.0426134 0.0507846i 0.744317 0.667827i \(-0.232775\pi\)
−0.786930 + 0.617042i \(0.788331\pi\)
\(212\) 0 0
\(213\) 2.75400e6 1.56187e7i 0.284987 1.61624i
\(214\) 0 0
\(215\) −3.03251e6 + 1.10374e6i −0.305132 + 0.111059i
\(216\) 0 0
\(217\) −1.62616e7 + 9.38863e6i −1.59141 + 0.918804i
\(218\) 0 0
\(219\) 6.65029e6 7.92551e6i 0.633152 0.754562i
\(220\) 0 0
\(221\) 315821. + 182339.i 0.0292593 + 0.0168929i
\(222\) 0 0
\(223\) −1.46561e7 + 2.58426e6i −1.32161 + 0.233035i −0.789557 0.613678i \(-0.789689\pi\)
−0.532051 + 0.846713i \(0.678578\pi\)
\(224\) 0 0
\(225\) 1.84265e6 + 670669.i 0.161769 + 0.0588790i
\(226\) 0 0
\(227\) 3.31518e6i 0.283420i 0.989908 + 0.141710i \(0.0452600\pi\)
−0.989908 + 0.141710i \(0.954740\pi\)
\(228\) 0 0
\(229\) 7.74965e6 0.645321 0.322660 0.946515i \(-0.395423\pi\)
0.322660 + 0.946515i \(0.395423\pi\)
\(230\) 0 0
\(231\) −1.79392e6 + 4.92874e6i −0.145535 + 0.399853i
\(232\) 0 0
\(233\) 2.99338e6 + 1.69763e7i 0.236643 + 1.34207i 0.839126 + 0.543938i \(0.183067\pi\)
−0.602483 + 0.798132i \(0.705822\pi\)
\(234\) 0 0
\(235\) 288870. 500337.i 0.0222586 0.0385531i
\(236\) 0 0
\(237\) −1.32351e7 1.11056e7i −0.994219 0.834249i
\(238\) 0 0
\(239\) −2.61961e6 4.53729e6i −0.191886 0.332356i 0.753989 0.656887i \(-0.228127\pi\)
−0.945875 + 0.324531i \(0.894794\pi\)
\(240\) 0 0
\(241\) 4.33966e6 + 1.19231e7i 0.310030 + 0.851801i 0.992649 + 0.121027i \(0.0386187\pi\)
−0.682619 + 0.730775i \(0.739159\pi\)
\(242\) 0 0
\(243\) −9.95865e6 1.75598e6i −0.694036 0.122377i
\(244\) 0 0
\(245\) −2.12273e6 + 1.78118e6i −0.144343 + 0.121118i
\(246\) 0 0
\(247\) −733950. 133878.i −0.0487053 0.00888419i
\(248\) 0 0
\(249\) −1.97818e7 2.35750e7i −1.28135 1.52705i
\(250\) 0 0
\(251\) −4.59717e6 + 2.60718e7i −0.290716 + 1.64873i 0.393406 + 0.919365i \(0.371297\pi\)
−0.684122 + 0.729368i \(0.739814\pi\)
\(252\) 0 0
\(253\) 3.78468e6 1.37751e6i 0.233705 0.0850615i
\(254\) 0 0
\(255\) −1.38848e7 + 8.01640e6i −0.837374 + 0.483458i
\(256\) 0 0
\(257\) 28759.1 34273.7i 0.00169424 0.00201912i −0.765197 0.643797i \(-0.777358\pi\)
0.766891 + 0.641777i \(0.221803\pi\)
\(258\) 0 0
\(259\) −1.45665e7 8.40998e6i −0.838410 0.484056i
\(260\) 0 0
\(261\) 6.10270e6 1.07607e6i 0.343242 0.0605229i
\(262\) 0 0
\(263\) 9.70928e6 + 3.53389e6i 0.533728 + 0.194261i 0.594802 0.803872i \(-0.297230\pi\)
−0.0610742 + 0.998133i \(0.519453\pi\)
\(264\) 0 0
\(265\) 2.85069e7i 1.53184i
\(266\) 0 0
\(267\) −563040. −0.0295805
\(268\) 0 0
\(269\) −72655.6 + 199620.i −0.00373261 + 0.0102553i −0.941545 0.336887i \(-0.890626\pi\)
0.937812 + 0.347143i \(0.112848\pi\)
\(270\) 0 0
\(271\) −967244. 5.48551e6i −0.0485991 0.275619i 0.950818 0.309749i \(-0.100245\pi\)
−0.999417 + 0.0341301i \(0.989134\pi\)
\(272\) 0 0
\(273\) 633580. 1.09739e6i 0.0311396 0.0539354i
\(274\) 0 0
\(275\) 2.51192e6 + 2.10775e6i 0.120783 + 0.101349i
\(276\) 0 0
\(277\) −7.42323e6 1.28574e7i −0.349264 0.604943i 0.636855 0.770984i \(-0.280235\pi\)
−0.986119 + 0.166041i \(0.946902\pi\)
\(278\) 0 0
\(279\) 4.68943e6 + 1.28841e7i 0.215927 + 0.593255i
\(280\) 0 0
\(281\) 3.62505e7 + 6.39194e6i 1.63379 + 0.288081i 0.913878 0.405989i \(-0.133073\pi\)
0.719908 + 0.694069i \(0.244184\pi\)
\(282\) 0 0
\(283\) 1.82719e7 1.53319e7i 0.806166 0.676454i −0.143523 0.989647i \(-0.545843\pi\)
0.949689 + 0.313193i \(0.101399\pi\)
\(284\) 0 0
\(285\) 2.12310e7 2.50016e7i 0.917142 1.08002i
\(286\) 0 0
\(287\) −7.34930e6 8.75856e6i −0.310886 0.370499i
\(288\) 0 0
\(289\) −2.23951e6 + 1.27009e7i −0.0927813 + 0.526189i
\(290\) 0 0
\(291\) 5.45556e6 1.98566e6i 0.221391 0.0805798i
\(292\) 0 0
\(293\) −2.37069e7 + 1.36872e7i −0.942479 + 0.544140i −0.890736 0.454520i \(-0.849811\pi\)
−0.0517423 + 0.998660i \(0.516477\pi\)
\(294\) 0 0
\(295\) 7.06398e6 8.41852e6i 0.275159 0.327921i
\(296\) 0 0
\(297\) −5.66386e6 3.27003e6i −0.216194 0.124820i
\(298\) 0 0
\(299\) −958243. + 168964.i −0.0358478 + 0.00632093i
\(300\) 0 0
\(301\) −7.38769e6 2.68890e6i −0.270900 0.0985995i
\(302\) 0 0
\(303\) 3.94550e7i 1.41832i
\(304\) 0 0
\(305\) 4.86153e7 1.71346
\(306\) 0 0
\(307\) 9.22093e6 2.53343e7i 0.318683 0.875576i −0.672141 0.740423i \(-0.734625\pi\)
0.990825 0.135153i \(-0.0431525\pi\)
\(308\) 0 0
\(309\) −3.18785e6 1.80792e7i −0.108050 0.612779i
\(310\) 0 0
\(311\) −2.69261e7 + 4.66374e7i −0.895144 + 1.55043i −0.0615172 + 0.998106i \(0.519594\pi\)
−0.833627 + 0.552328i \(0.813739\pi\)
\(312\) 0 0
\(313\) 3.63013e7 + 3.04604e7i 1.18383 + 0.993350i 0.999946 + 0.0104022i \(0.00331118\pi\)
0.183883 + 0.982948i \(0.441133\pi\)
\(314\) 0 0
\(315\) 7.51283e6 + 1.30126e7i 0.240365 + 0.416325i
\(316\) 0 0
\(317\) 4.85632e6 + 1.33426e7i 0.152451 + 0.418855i 0.992283 0.123990i \(-0.0395692\pi\)
−0.839833 + 0.542845i \(0.817347\pi\)
\(318\) 0 0
\(319\) 1.02051e7 + 1.79943e6i 0.314373 + 0.0554324i
\(320\) 0 0
\(321\) 4.61087e6 3.86898e6i 0.139402 0.116972i
\(322\) 0 0
\(323\) 3.85979e6 + 2.26701e7i 0.114540 + 0.672737i
\(324\) 0 0
\(325\) −509214. 606857.i −0.0148337 0.0176781i
\(326\) 0 0
\(327\) −8.37142e6 + 4.74767e7i −0.239418 + 1.35780i
\(328\) 0 0
\(329\) 1.32259e6 481382.i 0.0371395 0.0135177i
\(330\) 0 0
\(331\) −9.27360e6 + 5.35411e6i −0.255720 + 0.147640i −0.622380 0.782715i \(-0.713834\pi\)
0.366661 + 0.930355i \(0.380501\pi\)
\(332\) 0 0
\(333\) −7.89458e6 + 9.40839e6i −0.213794 + 0.254790i
\(334\) 0 0
\(335\) −8.19541e6 4.73162e6i −0.217990 0.125856i
\(336\) 0 0
\(337\) 4.37363e7 7.71189e6i 1.14275 0.201498i 0.429943 0.902856i \(-0.358534\pi\)
0.712809 + 0.701358i \(0.247422\pi\)
\(338\) 0 0
\(339\) −2.65117e7 9.64948e6i −0.680517 0.247688i
\(340\) 0 0
\(341\) 2.29278e7i 0.578229i
\(342\) 0 0
\(343\) 3.66293e7 0.907709
\(344\) 0 0
\(345\) 1.46310e7 4.01984e7i 0.356301 0.978930i
\(346\) 0 0
\(347\) 7.13257e6 + 4.04508e7i 0.170710 + 0.968142i 0.942980 + 0.332849i \(0.108010\pi\)
−0.772271 + 0.635294i \(0.780879\pi\)
\(348\) 0 0
\(349\) 3.25666e7 5.64069e7i 0.766118 1.32695i −0.173536 0.984828i \(-0.555519\pi\)
0.939654 0.342127i \(-0.111147\pi\)
\(350\) 0 0
\(351\) 1.21037e6 + 1.01562e6i 0.0279895 + 0.0234860i
\(352\) 0 0
\(353\) 3.34770e7 + 5.79839e7i 0.761067 + 1.31821i 0.942301 + 0.334766i \(0.108657\pi\)
−0.181234 + 0.983440i \(0.558009\pi\)
\(354\) 0 0
\(355\) −2.59851e7 7.13934e7i −0.580816 1.59578i
\(356\) 0 0
\(357\) −3.84651e7 6.78243e6i −0.845400 0.149067i
\(358\) 0 0
\(359\) 2.21296e7 1.85690e7i 0.478290 0.401333i −0.371518 0.928426i \(-0.621163\pi\)
0.849808 + 0.527093i \(0.176718\pi\)
\(360\) 0 0
\(361\) −2.30413e7 4.10172e7i −0.489762 0.871856i
\(362\) 0 0
\(363\) −3.18616e7 3.79712e7i −0.666113 0.793843i
\(364\) 0 0
\(365\) 8.60639e6 4.88093e7i 0.176988 1.00375i
\(366\) 0 0
\(367\) −5.50834e7 + 2.00487e7i −1.11435 + 0.405591i −0.832588 0.553893i \(-0.813142\pi\)
−0.281764 + 0.959484i \(0.590920\pi\)
\(368\) 0 0
\(369\) −7.23012e6 + 4.17431e6i −0.143902 + 0.0830818i
\(370\) 0 0
\(371\) 4.46400e7 5.31999e7i 0.874183 1.04181i
\(372\) 0 0
\(373\) −1.57281e7 9.08065e6i −0.303076 0.174981i 0.340748 0.940155i \(-0.389320\pi\)
−0.643824 + 0.765174i \(0.722653\pi\)
\(374\) 0 0
\(375\) −3.92849e7 + 6.92699e6i −0.744959 + 0.131356i
\(376\) 0 0
\(377\) −2.35252e6 856246.i −0.0439045 0.0159799i
\(378\) 0 0
\(379\) 2.26118e7i 0.415353i 0.978198 + 0.207676i \(0.0665901\pi\)
−0.978198 + 0.207676i \(0.933410\pi\)
\(380\) 0 0
\(381\) −1.25452e8 −2.26832
\(382\) 0 0
\(383\) 2.74512e7 7.54217e7i 0.488614 1.34246i −0.413322 0.910585i \(-0.635632\pi\)
0.901936 0.431871i \(-0.142146\pi\)
\(384\) 0 0
\(385\) 4.36313e6 + 2.47446e7i 0.0764568 + 0.433608i
\(386\) 0 0
\(387\) −2.87031e6 + 4.97152e6i −0.0495218 + 0.0857742i
\(388\) 0 0
\(389\) 4.45855e7 + 3.74117e7i 0.757434 + 0.635563i 0.937458 0.348099i \(-0.113173\pi\)
−0.180023 + 0.983662i \(0.557617\pi\)
\(390\) 0 0
\(391\) 1.49961e7 + 2.59740e7i 0.250869 + 0.434519i
\(392\) 0 0
\(393\) 1.44355e7 + 3.96612e7i 0.237823 + 0.653413i
\(394\) 0 0
\(395\) −8.15084e7 1.43721e7i −1.32255 0.233201i
\(396\) 0 0
\(397\) −9.05042e7 + 7.59421e7i −1.44643 + 1.21370i −0.511295 + 0.859405i \(0.670834\pi\)
−0.935134 + 0.354293i \(0.884721\pi\)
\(398\) 0 0
\(399\) 7.87724e7 1.34117e7i 1.24010 0.211138i
\(400\) 0 0
\(401\) −1.23650e7 1.47361e7i −0.191762 0.228533i 0.661594 0.749863i \(-0.269880\pi\)
−0.853355 + 0.521330i \(0.825436\pi\)
\(402\) 0 0
\(403\) 961866. 5.45501e6i 0.0146960 0.0833452i
\(404\) 0 0
\(405\) −9.31906e7 + 3.39186e7i −1.40284 + 0.510591i
\(406\) 0 0
\(407\) −1.77864e7 + 1.02690e7i −0.263818 + 0.152315i
\(408\) 0 0
\(409\) −8.57247e6 + 1.02163e7i −0.125296 + 0.149322i −0.825045 0.565067i \(-0.808850\pi\)
0.699750 + 0.714388i \(0.253295\pi\)
\(410\) 0 0
\(411\) 1.04643e8 + 6.04154e7i 1.50724 + 0.870206i
\(412\) 0 0
\(413\) 2.63657e7 4.64898e6i 0.374274 0.0659945i
\(414\) 0 0
\(415\) −1.38536e8 5.04228e7i −1.93828 0.705477i
\(416\) 0 0
\(417\) 1.64480e7i 0.226832i
\(418\) 0 0
\(419\) −6.46049e7 −0.878260 −0.439130 0.898424i \(-0.644713\pi\)
−0.439130 + 0.898424i \(0.644713\pi\)
\(420\) 0 0
\(421\) 2.84890e7 7.82730e7i 0.381796 1.04898i −0.588804 0.808276i \(-0.700401\pi\)
0.970600 0.240700i \(-0.0773769\pi\)
\(422\) 0 0
\(423\) −178461. 1.01211e6i −0.00235789 0.0133723i
\(424\) 0 0
\(425\) −1.22092e7 + 2.11469e7i −0.159045 + 0.275474i
\(426\) 0 0
\(427\) 9.07263e7 + 7.61284e7i 1.16533 + 0.977829i
\(428\) 0 0
\(429\) −773629. 1.33996e6i −0.00979853 0.0169715i
\(430\) 0 0
\(431\) −2.67393e7 7.34656e7i −0.333978 0.917598i −0.987066 0.160315i \(-0.948749\pi\)
0.653088 0.757282i \(-0.273473\pi\)
\(432\) 0 0
\(433\) −7.38034e7 1.30135e7i −0.909102 0.160299i −0.300507 0.953780i \(-0.597156\pi\)
−0.608596 + 0.793480i \(0.708267\pi\)
\(434\) 0 0
\(435\) 8.43140e7 7.07479e7i 1.02431 0.859499i
\(436\) 0 0
\(437\) −4.67699e7 3.97164e7i −0.560431 0.475911i
\(438\) 0 0
\(439\) 3.56726e7 + 4.25130e7i 0.421640 + 0.502491i 0.934491 0.355987i \(-0.115855\pi\)
−0.512851 + 0.858478i \(0.671411\pi\)
\(440\) 0 0
\(441\) −855958. + 4.85438e6i −0.00998014 + 0.0566002i
\(442\) 0 0
\(443\) 9.25030e7 3.36684e7i 1.06401 0.387267i 0.250075 0.968226i \(-0.419545\pi\)
0.813933 + 0.580959i \(0.197322\pi\)
\(444\) 0 0
\(445\) −2.33586e6 + 1.34861e6i −0.0265074 + 0.0153041i
\(446\) 0 0
\(447\) 3.36652e7 4.01207e7i 0.376929 0.449206i
\(448\) 0 0
\(449\) 1.27534e8 + 7.36319e7i 1.40892 + 0.813443i 0.995285 0.0969978i \(-0.0309240\pi\)
0.413640 + 0.910441i \(0.364257\pi\)
\(450\) 0 0
\(451\) −1.37487e7 + 2.42426e6i −0.149876 + 0.0264272i
\(452\) 0 0
\(453\) −1.95888e8 7.12973e7i −2.10723 0.766970i
\(454\) 0 0
\(455\) 6.07029e6i 0.0644429i
\(456\) 0 0
\(457\) −7.56567e7 −0.792682 −0.396341 0.918103i \(-0.629720\pi\)
−0.396341 + 0.918103i \(0.629720\pi\)
\(458\) 0 0
\(459\) 1.66571e7 4.57649e7i 0.172250 0.473254i
\(460\) 0 0
\(461\) 2.21117e7 + 1.25401e8i 0.225693 + 1.27997i 0.861356 + 0.508003i \(0.169616\pi\)
−0.635662 + 0.771967i \(0.719273\pi\)
\(462\) 0 0
\(463\) 6.46610e6 1.11996e7i 0.0651478 0.112839i −0.831612 0.555357i \(-0.812581\pi\)
0.896760 + 0.442518i \(0.145915\pi\)
\(464\) 0 0
\(465\) 1.86551e8 + 1.56535e8i 1.85540 + 1.55687i
\(466\) 0 0
\(467\) −5.44457e6 9.43027e6i −0.0534580 0.0925920i 0.838058 0.545581i \(-0.183691\pi\)
−0.891516 + 0.452989i \(0.850358\pi\)
\(468\) 0 0
\(469\) −7.88492e6 2.16637e7i −0.0764327 0.209997i
\(470\) 0 0
\(471\) 4.83330e7 + 8.52240e6i 0.462573 + 0.0815642i
\(472\) 0 0
\(473\) −7.35373e6 + 6.17051e6i −0.0694903 + 0.0583093i
\(474\) 0 0
\(475\) 8.96427e6 4.91442e7i 0.0836438 0.458555i
\(476\) 0 0
\(477\) −3.25957e7 3.88461e7i −0.300335 0.357925i
\(478\) 0 0
\(479\) −1.79938e7 + 1.02048e8i −0.163726 + 0.928535i 0.786643 + 0.617408i \(0.211817\pi\)
−0.950369 + 0.311126i \(0.899294\pi\)
\(480\) 0 0
\(481\) 4.66255e6 1.69703e6i 0.0418975 0.0152494i
\(482\) 0 0
\(483\) 9.02526e7 5.21074e7i 0.800974 0.462442i
\(484\) 0 0
\(485\) 1.78772e7 2.13052e7i 0.156702 0.186750i
\(486\) 0 0
\(487\) 2.82914e7 + 1.63341e7i 0.244945 + 0.141419i 0.617447 0.786612i \(-0.288167\pi\)
−0.372503 + 0.928031i \(0.621500\pi\)
\(488\) 0 0
\(489\) 4.99232e7 8.80281e6i 0.426949 0.0752826i
\(490\) 0 0
\(491\) −1.23032e8 4.47798e7i −1.03937 0.378301i −0.234732 0.972060i \(-0.575421\pi\)
−0.804643 + 0.593759i \(0.797643\pi\)
\(492\) 0 0
\(493\) 7.71668e7i 0.644006i
\(494\) 0 0
\(495\) 1.83470e7 0.151269
\(496\) 0 0
\(497\) 6.33038e7 1.73926e8i 0.515657 1.41675i
\(498\) 0 0
\(499\) 3.22712e7 + 1.83019e8i 0.259725 + 1.47297i 0.783646 + 0.621207i \(0.213357\pi\)
−0.523921 + 0.851767i \(0.675531\pi\)
\(500\) 0 0
\(501\) 1.00972e8 1.74889e8i 0.802952 1.39075i
\(502\) 0 0
\(503\) 1.35672e8 + 1.13842e8i 1.06607 + 0.894537i 0.994690 0.102912i \(-0.0328161\pi\)
0.0713774 + 0.997449i \(0.477261\pi\)
\(504\) 0 0
\(505\) 9.45039e7 + 1.63686e8i 0.733797 + 1.27097i
\(506\) 0 0
\(507\) −5.20311e7 1.42954e8i −0.399245 1.09692i
\(508\) 0 0
\(509\) −1.69354e7 2.98617e6i −0.128423 0.0226444i 0.109067 0.994034i \(-0.465214\pi\)
−0.237490 + 0.971390i \(0.576325\pi\)
\(510\) 0 0
\(511\) 9.24934e7 7.76112e7i 0.693184 0.581650i
\(512\) 0 0
\(513\) −586918. + 9.96329e7i −0.00434735 + 0.737991i
\(514\) 0 0
\(515\) −5.65293e7 6.73690e7i −0.413858 0.493217i
\(516\) 0 0
\(517\) 298428. 1.69247e6i 0.00215957 0.0122475i
\(518\) 0 0
\(519\) 6.00770e7 2.18662e7i 0.429741 0.156413i
\(520\) 0 0
\(521\) −1.68696e8 + 9.73969e7i −1.19287 + 0.688703i −0.958956 0.283555i \(-0.908486\pi\)
−0.233912 + 0.972258i \(0.575153\pi\)
\(522\) 0 0
\(523\) 6.28541e7 7.49066e7i 0.439368 0.523618i −0.500233 0.865891i \(-0.666752\pi\)
0.939601 + 0.342273i \(0.111197\pi\)
\(524\) 0 0
\(525\) 7.34798e7 + 4.24236e7i 0.507797 + 0.293177i
\(526\) 0 0
\(527\) −1.68143e8 + 2.96482e7i −1.14881 + 0.202566i
\(528\) 0 0
\(529\) 6.39100e7 + 2.32613e7i 0.431720 + 0.157133i
\(530\) 0 0
\(531\) 1.95490e7i 0.130569i
\(532\) 0 0
\(533\) 3.37280e6 0.0222746
\(534\) 0 0
\(535\) 9.86185e6 2.70952e7i 0.0644017 0.176942i
\(536\) 0 0
\(537\) 1.98442e7 + 1.12542e8i 0.128148 + 0.726762i
\(538\) 0 0
\(539\) −4.12142e6 + 7.13851e6i −0.0263197 + 0.0455870i
\(540\) 0 0
\(541\) 1.26152e8 + 1.05854e8i 0.796715 + 0.668523i 0.947398 0.320059i \(-0.103703\pi\)
−0.150683 + 0.988582i \(0.548147\pi\)
\(542\) 0 0
\(543\) 1.15691e8 + 2.00382e8i 0.722601 + 1.25158i
\(544\) 0 0
\(545\) 7.89875e7 + 2.17017e8i 0.487943 + 1.34061i
\(546\) 0 0
\(547\) −5.15937e7 9.09736e6i −0.315235 0.0555845i 0.0137921 0.999905i \(-0.495610\pi\)
−0.329027 + 0.944320i \(0.606721\pi\)
\(548\) 0 0
\(549\) 6.62475e7 5.55882e7i 0.400362 0.335943i
\(550\) 0 0
\(551\) −5.31193e7 1.48663e8i −0.317539 0.888685i
\(552\) 0 0
\(553\) −1.29606e8 1.54458e8i −0.766389 0.913347i
\(554\) 0 0
\(555\) −3.78797e7 + 2.14826e8i −0.221578 + 1.25663i
\(556\) 0 0
\(557\) −1.78323e8 + 6.49042e7i −1.03191 + 0.375584i −0.801807 0.597583i \(-0.796128\pi\)
−0.230101 + 0.973167i \(0.573906\pi\)
\(558\) 0 0
\(559\) 2.00847e6 1.15959e6i 0.0114982 0.00663849i
\(560\) 0 0
\(561\) −3.06559e7 + 3.65343e7i −0.173630 + 0.206924i
\(562\) 0 0
\(563\) −2.18365e8 1.26073e8i −1.22365 0.706477i −0.257959 0.966156i \(-0.583050\pi\)
−0.965695 + 0.259679i \(0.916383\pi\)
\(564\) 0 0
\(565\) −1.33101e8 + 2.34693e7i −0.737966 + 0.130123i
\(566\) 0 0
\(567\) −2.27027e8 8.26312e7i −1.24546 0.453310i
\(568\) 0 0
\(569\) 2.03896e8i 1.10680i 0.832914 + 0.553402i \(0.186671\pi\)
−0.832914 + 0.553402i \(0.813329\pi\)
\(570\) 0 0
\(571\) −2.71370e7 −0.145765 −0.0728825 0.997341i \(-0.523220\pi\)
−0.0728825 + 0.997341i \(0.523220\pi\)
\(572\) 0 0
\(573\) 1.24761e8 3.42779e8i 0.663156 1.82201i
\(574\) 0 0
\(575\) −1.13136e7 6.41626e7i −0.0595109 0.337503i
\(576\) 0 0
\(577\) −4.73598e7 + 8.20296e7i −0.246537 + 0.427015i −0.962563 0.271059i \(-0.912626\pi\)
0.716026 + 0.698074i \(0.245959\pi\)
\(578\) 0 0
\(579\) 3.44551e7 + 2.89112e7i 0.177508 + 0.148947i
\(580\) 0 0
\(581\) −1.79577e8 3.11037e8i −0.915637 1.58593i
\(582\) 0 0
\(583\) −2.90028e7 7.96845e7i −0.146364 0.402131i
\(584\) 0 0
\(585\) −4.36513e6 769690.i −0.0218037 0.00384457i
\(586\) 0 0
\(587\) 1.00753e8 8.45419e7i 0.498132 0.417982i −0.358798 0.933415i \(-0.616813\pi\)
0.856930 + 0.515433i \(0.172369\pi\)
\(588\) 0 0
\(589\) 3.03521e8 1.72862e8i 1.48540 0.845969i
\(590\) 0 0
\(591\) −2.07404e8 2.47174e8i −1.00474 1.19740i
\(592\) 0 0
\(593\) 4.14002e7 2.34792e8i 0.198536 1.12595i −0.708758 0.705452i \(-0.750744\pi\)
0.907293 0.420499i \(-0.138145\pi\)
\(594\) 0 0
\(595\) −1.75824e8 + 6.39948e7i −0.834695 + 0.303804i
\(596\) 0 0
\(597\) −3.99482e8 + 2.30641e8i −1.87747 + 1.08396i
\(598\) 0 0
\(599\) 1.94899e8 2.32271e8i 0.906835 1.08072i −0.0895677 0.995981i \(-0.528549\pi\)
0.996403 0.0847433i \(-0.0270070\pi\)
\(600\) 0 0
\(601\) 3.36020e8 + 1.94001e8i 1.54790 + 0.893679i 0.998302 + 0.0582485i \(0.0185516\pi\)
0.549596 + 0.835431i \(0.314782\pi\)
\(602\) 0 0
\(603\) −1.65781e7 + 2.92316e6i −0.0756104 + 0.0133322i
\(604\) 0 0
\(605\) −2.23133e8 8.12138e7i −1.00762 0.366745i
\(606\) 0 0
\(607\) 6.17165e7i 0.275953i −0.990435 0.137977i \(-0.955940\pi\)
0.990435 0.137977i \(-0.0440599\pi\)
\(608\) 0 0
\(609\) 2.68134e8 1.18713
\(610\) 0 0
\(611\) −142004. + 390154.i −0.000622556 + 0.00171046i
\(612\) 0 0
\(613\) −4.11788e7 2.33536e8i −0.178769 1.01385i −0.933703 0.358048i \(-0.883442\pi\)
0.754934 0.655800i \(-0.227669\pi\)
\(614\) 0 0
\(615\) −7.41412e7 + 1.28416e8i −0.318738 + 0.552071i
\(616\) 0 0
\(617\) −3.43987e8 2.88639e8i −1.46449 1.22885i −0.921072 0.389391i \(-0.872685\pi\)
−0.543418 0.839462i \(-0.682870\pi\)
\(618\) 0 0
\(619\) 1.28267e8 + 2.22166e8i 0.540809 + 0.936709i 0.998858 + 0.0477820i \(0.0152153\pi\)
−0.458048 + 0.888927i \(0.651451\pi\)
\(620\) 0 0
\(621\) 4.44439e7 + 1.22109e8i 0.185583 + 0.509884i
\(622\) 0 0
\(623\) −6.47105e6 1.14102e6i −0.0267615 0.00471877i
\(624\) 0 0
\(625\) −2.33564e8 + 1.95983e8i −0.956676 + 0.802747i
\(626\) 0 0
\(627\) 3.39099e7 9.14863e7i 0.137570 0.371154i
\(628\) 0 0
\(629\) −9.83080e7 1.17159e8i −0.395036 0.470786i
\(630\) 0 0
\(631\) −4.48960e7 + 2.54618e8i −0.178698 + 1.01345i 0.755090 + 0.655621i \(0.227593\pi\)
−0.933788 + 0.357826i \(0.883518\pi\)
\(632\) 0 0
\(633\) −1.84896e7 + 6.72968e6i −0.0728983 + 0.0265328i
\(634\) 0 0
\(635\) −5.20460e8 + 3.00488e8i −2.03267 + 1.17356i
\(636\) 0 0
\(637\) 1.28005e6 1.52550e6i 0.00495230 0.00590193i
\(638\) 0 0
\(639\) −1.17043e8 6.75747e7i −0.448582 0.258989i
\(640\) 0 0
\(641\) 3.90880e8 6.89226e7i 1.48412 0.261690i 0.627897 0.778297i \(-0.283916\pi\)
0.856223 + 0.516606i \(0.172805\pi\)
\(642\) 0 0
\(643\) 2.19268e8 + 7.98069e7i 0.824787 + 0.300198i 0.719717 0.694267i \(-0.244271\pi\)
0.105069 + 0.994465i \(0.466494\pi\)
\(644\) 0 0
\(645\) 1.01961e8i 0.379975i
\(646\) 0 0
\(647\) 1.87538e8 0.692430 0.346215 0.938155i \(-0.387467\pi\)
0.346215 + 0.938155i \(0.387467\pi\)
\(648\) 0 0
\(649\) 1.11807e7 3.07188e7i 0.0409012 0.112375i
\(650\) 0 0
\(651\) 1.03019e8 + 5.84253e8i 0.373402 + 2.11767i
\(652\) 0 0
\(653\) 1.63875e8 2.83839e8i 0.588535 1.01937i −0.405889 0.913922i \(-0.633038\pi\)
0.994425 0.105451i \(-0.0336286\pi\)
\(654\) 0 0
\(655\) 1.54886e8 + 1.29965e8i 0.551172 + 0.462489i
\(656\) 0 0
\(657\) −4.40822e7 7.63526e7i −0.155442 0.269233i
\(658\) 0 0
\(659\) 1.52189e8 + 4.18137e8i 0.531775 + 1.46104i 0.856957 + 0.515389i \(0.172352\pi\)
−0.325181 + 0.945652i \(0.605425\pi\)
\(660\) 0 0
\(661\) −3.44042e8 6.06639e7i −1.19126 0.210052i −0.457344 0.889290i \(-0.651199\pi\)
−0.733918 + 0.679238i \(0.762310\pi\)
\(662\) 0 0
\(663\) 8.82636e6 7.40619e6i 0.0302859 0.0254129i
\(664\) 0 0
\(665\) 2.94676e8 2.44319e8i 1.00203 0.830792i
\(666\) 0 0
\(667\) −1.32346e8 1.57724e8i −0.446000 0.531522i
\(668\) 0 0
\(669\) −8.16494e7 + 4.63057e8i −0.272693 + 1.54652i
\(670\) 0 0
\(671\) 1.35893e8 4.94609e7i 0.449809 0.163717i
\(672\) 0 0
\(673\) −4.27015e8 + 2.46537e8i −1.40087 + 0.808793i −0.994482 0.104908i \(-0.966545\pi\)
−0.406388 + 0.913701i \(0.633212\pi\)
\(674\) 0 0
\(675\) −6.80043e7 + 8.10444e7i −0.221119 + 0.263519i
\(676\) 0 0
\(677\) −3.15559e8 1.82188e8i −1.01698 0.587157i −0.103756 0.994603i \(-0.533086\pi\)
−0.913229 + 0.407446i \(0.866419\pi\)
\(678\) 0 0
\(679\) 6.67251e7 1.17654e7i 0.213147 0.0375836i
\(680\) 0 0
\(681\) 9.84262e7 + 3.58242e7i 0.311652 + 0.113432i
\(682\) 0 0
\(683\) 3.58919e8i 1.12651i −0.826283 0.563255i \(-0.809549\pi\)
0.826283 0.563255i \(-0.190451\pi\)
\(684\) 0 0
\(685\) 5.78836e8 1.80088
\(686\) 0 0
\(687\) 8.37435e7 2.30083e8i 0.258274 0.709602i
\(688\) 0 0
\(689\) 3.55745e6 + 2.01753e7i 0.0108763 + 0.0616826i
\(690\) 0 0
\(691\) 4.33802e7 7.51368e7i 0.131479 0.227729i −0.792768 0.609524i \(-0.791361\pi\)
0.924247 + 0.381795i \(0.124694\pi\)
\(692\) 0 0
\(693\) 3.42393e7 + 2.87302e7i 0.102879 + 0.0863253i
\(694\) 0 0
\(695\) 3.93968e7 + 6.82372e7i 0.117356 + 0.203267i
\(696\) 0 0
\(697\) −3.55571e7 9.76923e7i −0.105009 0.288511i
\(698\) 0 0
\(699\) 5.36364e8 + 9.45755e7i 1.57047 + 0.276915i
\(700\) 0 0
\(701\) 4.22172e8 3.54244e8i 1.22556 1.02837i 0.227048 0.973884i \(-0.427093\pi\)
0.998515 0.0544851i \(-0.0173517\pi\)
\(702\) 0 0
\(703\) 2.70040e8 + 1.58036e8i 0.777253 + 0.454873i
\(704\) 0 0
\(705\) −1.17332e7 1.39831e7i −0.0334849 0.0399058i
\(706\) 0 0
\(707\) −7.99569e7 + 4.53458e8i −0.226255 + 1.28316i
\(708\) 0 0
\(709\) −1.96618e8 + 7.15633e7i −0.551678 + 0.200794i −0.602792 0.797898i \(-0.705945\pi\)
0.0511139 + 0.998693i \(0.483723\pi\)
\(710\) 0 0
\(711\) −1.27504e8 + 7.36145e7i −0.354744 + 0.204812i
\(712\) 0 0
\(713\) 2.92826e8 3.48976e8i 0.807869 0.962780i
\(714\) 0 0
\(715\) −6.41906e6 3.70604e6i −0.0175612 0.0101389i
\(716\) 0 0
\(717\) −1.63018e8 + 2.87444e7i −0.442260 + 0.0779823i
\(718\) 0 0
\(719\) 1.14127e8 + 4.15387e7i 0.307044 + 0.111755i 0.490947 0.871190i \(-0.336651\pi\)
−0.183903 + 0.982944i \(0.558873\pi\)
\(720\) 0 0
\(721\) 2.14246e8i 0.571618i
\(722\) 0 0
\(723\) 4.00886e8 1.06073
\(724\) 0 0
\(725\) 5.73330e7 1.57521e8i 0.150449 0.413356i
\(726\) 0 0
\(727\) −2.09178e6 1.18631e7i −0.00544392 0.0308740i 0.981965 0.189064i \(-0.0605453\pi\)
−0.987409 + 0.158190i \(0.949434\pi\)
\(728\) 0 0
\(729\) 7.90817e7 1.36974e8i 0.204124 0.353553i
\(730\) 0 0
\(731\) −5.47612e7 4.59501e7i −0.140191 0.117634i
\(732\) 0 0
\(733\) 1.32635e8 + 2.29731e8i 0.336780 + 0.583320i 0.983825 0.179132i \(-0.0573288\pi\)
−0.647045 + 0.762452i \(0.723995\pi\)
\(734\) 0 0
\(735\) 2.99439e7 + 8.22703e7i 0.0754131 + 0.207196i
\(736\) 0 0
\(737\) −2.77222e7 4.88818e6i −0.0692510 0.0122108i
\(738\) 0 0
\(739\) 5.76193e8 4.83483e8i 1.42769 1.19798i 0.480631 0.876923i \(-0.340408\pi\)
0.947061 0.321053i \(-0.104037\pi\)
\(740\) 0 0
\(741\) −1.19059e7 + 2.03439e7i −0.0292623 + 0.0500012i
\(742\) 0 0
\(743\) −4.52971e8 5.39830e8i −1.10434 1.31611i −0.944334 0.328990i \(-0.893292\pi\)
−0.160010 0.987115i \(-0.551153\pi\)
\(744\) 0 0
\(745\) 4.35675e7 2.47083e8i 0.105364 0.597550i
\(746\) 0 0
\(747\) −2.46436e8 + 8.96953e7i −0.591210 + 0.215183i
\(748\) 0 0
\(749\) 6.08336e7 3.51223e7i 0.144776 0.0835867i
\(750\) 0 0
\(751\) −3.09013e8 + 3.68268e8i −0.729554 + 0.869449i −0.995522 0.0945331i \(-0.969864\pi\)
0.265968 + 0.963982i \(0.414309\pi\)
\(752\) 0 0
\(753\) 7.24382e8 + 4.18222e8i 1.69661 + 0.979540i
\(754\) 0 0
\(755\) −9.83446e8 + 1.73408e8i −2.28512 + 0.402929i
\(756\) 0 0
\(757\) −2.42937e8 8.84218e7i −0.560023 0.203832i 0.0464713 0.998920i \(-0.485202\pi\)
−0.606494 + 0.795088i \(0.707425\pi\)
\(758\) 0 0
\(759\) 1.27251e8i 0.291028i
\(760\) 0 0
\(761\) 3.41143e8 0.774074 0.387037 0.922064i \(-0.373499\pi\)
0.387037 + 0.922064i \(0.373499\pi\)
\(762\) 0 0
\(763\) −1.92426e8 + 5.28687e8i −0.433203 + 1.19021i
\(764\) 0 0
\(765\) 2.37246e7 + 1.34549e8i 0.0529926 + 0.300536i
\(766\) 0 0
\(767\) −3.94885e6 + 6.83960e6i −0.00875153 + 0.0151581i
\(768\) 0 0
\(769\) 9.91980e7 + 8.32370e7i 0.218134 + 0.183036i 0.745306 0.666722i \(-0.232303\pi\)
−0.527172 + 0.849759i \(0.676748\pi\)
\(770\) 0 0
\(771\) −706796. 1.22421e6i −0.00154217 0.00267111i
\(772\) 0 0
\(773\) 1.97391e8 + 5.42328e8i 0.427355 + 1.17415i 0.947412 + 0.320017i \(0.103689\pi\)
−0.520056 + 0.854132i \(0.674089\pi\)
\(774\) 0 0
\(775\) 3.65260e8 + 6.44051e7i 0.784687 + 0.138362i
\(776\) 0 0
\(777\) −4.07096e8 + 3.41594e8i −0.867827 + 0.728193i
\(778\) 0 0
\(779\) 1.35750e8 + 1.63729e8i 0.287162 + 0.346349i
\(780\) 0 0
\(781\) −1.45270e8 1.73126e8i −0.304946 0.363421i
\(782\) 0 0
\(783\) −5.80569e7 + 3.29257e8i −0.120940 + 0.685882i
\(784\) 0 0
\(785\) 2.20930e8 8.04121e7i 0.456716 0.166231i
\(786\) 0 0
\(787\) −6.01161e8 + 3.47080e8i −1.23329 + 0.712042i −0.967715 0.252047i \(-0.918896\pi\)
−0.265578 + 0.964089i \(0.585563\pi\)
\(788\) 0 0
\(789\) 2.09839e8 2.50076e8i 0.427223 0.509145i
\(790\) 0 0
\(791\) −2.85146e8 1.64629e8i −0.576153 0.332642i
\(792\) 0 0
\(793\) −3.44067e7 + 6.06683e6i −0.0689959 + 0.0121658i
\(794\) 0 0
\(795\) −8.46357e8 3.08049e8i −1.68443 0.613081i
\(796\) 0 0
\(797\) 2.25917e8i 0.446246i 0.974790 + 0.223123i \(0.0716252\pi\)
−0.974790 + 0.223123i \(0.928375\pi\)
\(798\) 0 0
\(799\) 1.27978e7 0.0250896
\(800\) 0 0
\(801\) −1.64101e6 + 4.50864e6i −0.00319311 + 0.00877299i
\(802\) 0 0
\(803\) −2.56011e7 1.45191e8i −0.0494438 0.280410i
\(804\) 0 0
\(805\) 2.49619e8 4.32352e8i 0.478508 0.828800i
\(806\) 0 0
\(807\) 5.14149e6 + 4.31422e6i 0.00978291 + 0.00820884i
\(808\) 0 0
\(809\) 7.70982e7 + 1.33538e8i 0.145612 + 0.252208i 0.929601 0.368567i \(-0.120151\pi\)
−0.783989 + 0.620775i \(0.786818\pi\)
\(810\) 0 0
\(811\) −1.85758e8 5.10365e8i −0.348245 0.956795i −0.982923 0.184018i \(-0.941090\pi\)
0.634678 0.772777i \(-0.281133\pi\)
\(812\) 0 0
\(813\) −1.73314e8 3.05600e7i −0.322524 0.0568698i
\(814\) 0 0
\(815\) 1.86030e8 1.56098e8i 0.343645 0.288352i
\(816\) 0 0
\(817\) 1.37129e8 + 5.08276e7i 0.251456 + 0.0932037i
\(818\) 0 0
\(819\) −6.94095e6 8.27191e6i −0.0126348 0.0150575i
\(820\) 0 0
\(821\) −1.15650e7 + 6.55882e7i −0.0208985 + 0.118521i −0.993472 0.114073i \(-0.963610\pi\)
0.972574 + 0.232594i \(0.0747214\pi\)
\(822\) 0 0
\(823\) −1.54820e7 + 5.63498e6i −0.0277733 + 0.0101086i −0.355869 0.934536i \(-0.615815\pi\)
0.328096 + 0.944644i \(0.393593\pi\)
\(824\) 0 0
\(825\) 8.97221e7 5.18011e7i 0.159786 0.0922522i
\(826\) 0 0
\(827\) −4.31288e8 + 5.13989e8i −0.762520 + 0.908735i −0.998005 0.0631426i \(-0.979888\pi\)
0.235485 + 0.971878i \(0.424332\pi\)
\(828\) 0 0
\(829\) 6.40853e8 + 3.69997e8i 1.12485 + 0.649433i 0.942635 0.333826i \(-0.108340\pi\)
0.182215 + 0.983259i \(0.441673\pi\)
\(830\) 0 0
\(831\) −4.61946e8 + 8.14536e7i −0.804986 + 0.141941i
\(832\) 0 0
\(833\) −5.76803e7 2.09939e7i −0.0997913 0.0363211i
\(834\) 0 0
\(835\) 9.67410e8i 1.66169i
\(836\) 0 0
\(837\) −7.39743e8 −1.26155
\(838\) 0 0
\(839\) 3.98732e7 1.09551e8i 0.0675141 0.185494i −0.901347 0.433097i \(-0.857421\pi\)
0.968861 + 0.247603i \(0.0796430\pi\)
\(840\) 0 0
\(841\) 1.13007e7 + 6.40892e7i 0.0189984 + 0.107745i
\(842\) 0 0
\(843\) 5.81500e8 1.00719e9i 0.970660 1.68123i
\(844\) 0 0
\(845\) −5.58269e8 4.68443e8i −0.925280 0.776402i
\(846\) 0 0
\(847\) −2.89237e8 5.00974e8i −0.475997 0.824450i
\(848\) 0 0
\(849\) −2.57750e8 7.08162e8i −0.421188 1.15720i
\(850\) 0 0
\(851\) 4.01871e8 + 7.08607e7i 0.652075 + 0.114978i
\(852\) 0 0
\(853\) −4.85755e8 + 4.07597e8i −0.782654 + 0.656725i −0.943916 0.330187i \(-0.892888\pi\)
0.161261 + 0.986912i \(0.448444\pi\)
\(854\) 0 0
\(855\) −1.38325e8 2.42879e8i −0.221311 0.388591i
\(856\) 0 0
\(857\) −3.43320e8 4.09153e8i −0.545452 0.650045i 0.420949 0.907084i \(-0.361697\pi\)
−0.966401 + 0.257040i \(0.917253\pi\)
\(858\) 0 0
\(859\) 4.02335e7 2.28175e8i 0.0634758 0.359989i −0.936481 0.350718i \(-0.885938\pi\)
0.999957 0.00927140i \(-0.00295122\pi\)
\(860\) 0 0
\(861\) −3.39455e8 + 1.23551e8i −0.531829 + 0.193570i
\(862\) 0 0
\(863\) −6.16932e8 + 3.56186e8i −0.959854 + 0.554172i −0.896128 0.443796i \(-0.853632\pi\)
−0.0637256 + 0.997967i \(0.520298\pi\)
\(864\) 0 0
\(865\) 1.96865e8 2.34614e8i 0.304172 0.362498i
\(866\) 0 0
\(867\) 3.52884e8 + 2.03737e8i 0.541470 + 0.312618i
\(868\) 0 0
\(869\) −2.42460e8 + 4.27522e7i −0.369471 + 0.0651477i
\(870\) 0 0
\(871\) 6.39063e6 + 2.32600e6i 0.00967140 + 0.00352010i
\(872\) 0 0
\(873\) 4.94736e7i 0.0743586i
\(874\) 0 0
\(875\) −4.65541e8 −0.694919
\(876\) 0 0
\(877\) −2.45336e8 + 6.74054e8i −0.363715 + 0.999300i 0.613989 + 0.789315i \(0.289564\pi\)
−0.977705 + 0.209985i \(0.932658\pi\)
\(878\) 0 0
\(879\) 1.50187e8 + 8.51751e8i 0.221139 + 1.25414i
\(880\) 0 0
\(881\) 1.36418e8 2.36282e8i 0.199500 0.345544i −0.748866 0.662721i \(-0.769402\pi\)
0.948366 + 0.317177i \(0.102735\pi\)
\(882\) 0 0
\(883\) 8.84280e8 + 7.41999e8i 1.28442 + 1.07776i 0.992618 + 0.121280i \(0.0386999\pi\)
0.291804 + 0.956478i \(0.405745\pi\)
\(884\) 0 0
\(885\) −1.73608e8 3.00697e8i −0.250460 0.433810i
\(886\) 0 0
\(887\) 3.37195e7 + 9.26435e7i 0.0483181 + 0.132753i 0.961504 0.274789i \(-0.0886081\pi\)
−0.913186 + 0.407542i \(0.866386\pi\)
\(888\) 0 0
\(889\) −1.44183e9 2.54234e8i −2.05215 0.361850i
\(890\) 0 0
\(891\) −2.25984e8 + 1.89623e8i −0.319481 + 0.268076i
\(892\) 0 0
\(893\) −2.46551e7 + 8.80959e6i −0.0346220 + 0.0123709i
\(894\) 0 0
\(895\) 3.51892e8 + 4.19368e8i 0.490840 + 0.584960i
\(896\) 0 0
\(897\) −5.33841e6 + 3.02756e7i −0.00739664 + 0.0419484i
\(898\) 0 0
\(899\) 1.10141e9 4.00882e8i 1.51590 0.551743i
\(900\) 0 0
\(901\) 5.46869e8 3.15735e8i 0.747668 0.431667i
\(902\) 0 0
\(903\) −1.59664e8 + 1.90280e8i −0.216842 + 0.258423i
\(904\) 0 0
\(905\) 9.59923e8 + 5.54212e8i 1.29506 + 0.747705i
\(906\) 0 0
\(907\) 7.76127e8 1.36852e8i 1.04019 0.183413i 0.372636 0.927978i \(-0.378454\pi\)
0.667550 + 0.744565i \(0.267343\pi\)
\(908\) 0 0
\(909\) 3.15942e8 + 1.14994e8i 0.420646 + 0.153102i
\(910\) 0 0
\(911\) 6.31995e8i 0.835909i 0.908468 + 0.417954i \(0.137253\pi\)
−0.908468 + 0.417954i \(0.862747\pi\)
\(912\) 0 0
\(913\) −4.38544e8 −0.576236
\(914\) 0 0
\(915\) 5.25342e8 1.44337e9i 0.685770 1.88414i
\(916\) 0 0
\(917\) 8.55330e7 + 4.85082e8i 0.110924 + 0.629081i
\(918\) 0 0
\(919\) 1.15541e8 2.00123e8i 0.148864 0.257840i −0.781944 0.623349i \(-0.785772\pi\)
0.930808 + 0.365509i \(0.119105\pi\)
\(920\) 0 0
\(921\) −6.52520e8 5.47530e8i −0.835248 0.700856i
\(922\) 0 0
\(923\) 2.72999e7 + 4.72847e7i 0.0347180 + 0.0601334i
\(924\) 0 0
\(925\) 1.13631e8 + 3.12197e8i 0.143572 + 0.394461i
\(926\) 0 0
\(927\) −1.54063e8 2.71655e7i −0.193402 0.0341020i
\(928\) 0 0
\(929\) −6.41783e8 + 5.38520e8i −0.800462 + 0.671668i −0.948311 0.317342i \(-0.897210\pi\)
0.147849 + 0.989010i \(0.452765\pi\)
\(930\) 0 0
\(931\) 1.25574e8 + 739728.i 0.155614 + 0.000916691i
\(932\) 0 0
\(933\) 1.09368e9 + 1.30339e9i 1.34662 + 1.60483i
\(934\) 0 0
\(935\) −3.96729e7 + 2.24996e8i −0.0485355 + 0.275259i
\(936\) 0 0
\(937\) −1.28866e9 + 4.69032e8i −1.56646 + 0.570143i −0.972204 0.234136i \(-0.924774\pi\)
−0.594252 + 0.804279i \(0.702552\pi\)
\(938\) 0 0
\(939\) 1.29663e9 7.48609e8i 1.56610 0.904187i
\(940\) 0 0
\(941\) 1.90860e8 2.27458e8i 0.229058 0.272981i −0.639258 0.768993i \(-0.720758\pi\)
0.868316 + 0.496012i \(0.165203\pi\)
\(942\) 0 0
\(943\) 2.40226e8 + 1.38694e8i 0.286473 + 0.165395i
\(944\) 0 0
\(945\) −7.98357e8 + 1.40772e8i −0.946023 + 0.166809i
\(946\) 0 0
\(947\) 2.26227e7 + 8.23401e6i 0.0266376 + 0.00969530i 0.355305 0.934751i \(-0.384377\pi\)
−0.328667 + 0.944446i \(0.606599\pi\)
\(948\) 0 0
\(949\) 3.56180e7i 0.0416745i
\(950\) 0 0
\(951\) 4.48614e8 0.521592
\(952\) 0 0
\(953\) −4.49991e7 + 1.23634e8i −0.0519906 + 0.142843i −0.962970 0.269609i \(-0.913105\pi\)
0.910979 + 0.412452i \(0.135328\pi\)
\(954\) 0 0
\(955\) −3.03442e8 1.72091e9i −0.348390 1.97582i
\(956\) 0 0
\(957\) 1.63702e8 2.83539e8i 0.186774 0.323503i
\(958\) 0 0
\(959\) 1.08023e9 + 9.06419e8i 1.22478 + 1.02772i
\(960\) 0 0
\(961\) 8.52925e8 + 1.47731e9i 0.961039 + 1.66457i
\(962\) 0 0
\(963\) −1.75429e7 4.81986e7i −0.0196436 0.0539704i
\(964\) 0 0
\(965\) 2.12192e8 + 3.74151e7i 0.236127 + 0.0416356i
\(966\) 0 0
\(967\) 5.84539e8 4.90487e8i 0.646449 0.542435i −0.259542 0.965732i \(-0.583572\pi\)
0.905991 + 0.423297i \(0.139127\pi\)
\(968\) 0 0
\(969\) 7.14772e8 + 1.30380e8i 0.785591 + 0.143297i
\(970\) 0 0
\(971\) 7.57997e7 + 9.03345e7i 0.0827960 + 0.0986725i 0.805852 0.592117i \(-0.201708\pi\)
−0.723056 + 0.690789i \(0.757263\pi\)
\(972\) 0 0
\(973\) −3.33324e7 + 1.89037e8i −0.0361850 + 0.205215i
\(974\) 0 0
\(975\) −2.35199e7 + 8.56055e6i −0.0253759 + 0.00923608i
\(976\) 0 0
\(977\) 4.90689e8 2.83299e8i 0.526165 0.303782i −0.213288 0.976989i \(-0.568417\pi\)
0.739453 + 0.673208i \(0.235084\pi\)
\(978\) 0 0
\(979\) −5.15729e6 + 6.14622e6i −0.00549634 + 0.00655028i
\(980\) 0 0
\(981\) 3.55779e8 + 2.05409e8i 0.376854 + 0.217577i
\(982\) 0 0
\(983\) 8.45217e8 1.49035e8i 0.889832 0.156901i 0.289999 0.957027i \(-0.406345\pi\)
0.599833 + 0.800126i \(0.295234\pi\)
\(984\) 0 0
\(985\) −1.45249e9 5.28662e8i −1.51986 0.553184i
\(986\) 0 0
\(987\) 4.44688e7i 0.0462492i
\(988\) 0 0
\(989\) 1.90736e8 0.197171
\(990\) 0 0
\(991\) −3.40887e8 + 9.36578e8i −0.350259 + 0.962328i 0.632028 + 0.774945i \(0.282223\pi\)
−0.982287 + 0.187383i \(0.940000\pi\)
\(992\) 0 0
\(993\) 5.87496e7 + 3.33186e8i 0.0600008 + 0.340282i
\(994\) 0 0
\(995\) −1.10488e9 + 1.91370e9i −1.12162 + 1.94270i
\(996\) 0 0
\(997\) 1.50315e8 + 1.26129e8i 0.151676 + 0.127271i 0.715468 0.698646i \(-0.246214\pi\)
−0.563792 + 0.825917i \(0.690658\pi\)
\(998\) 0 0
\(999\) −3.31317e8 5.73858e8i −0.332313 0.575583i
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 76.7.j.a.13.9 60
19.3 odd 18 inner 76.7.j.a.41.9 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.7.j.a.13.9 60 1.1 even 1 trivial
76.7.j.a.41.9 yes 60 19.3 odd 18 inner