Properties

Label 76.6.i.a.9.1
Level $76$
Weight $6$
Character 76.9
Analytic conductor $12.189$
Analytic rank $0$
Dimension $48$
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] = [76,6,Mod(5,76)]
 
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, 16]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\), 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: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.1
Character \(\chi\) \(=\) 76.9
Dual form 76.6.i.a.17.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-16.5327 + 13.8726i) q^{3} +(17.0893 + 6.21998i) q^{5} +(-92.6180 + 160.419i) q^{7} +(38.6850 - 219.393i) q^{9} +O(q^{10})\) \(q+(-16.5327 + 13.8726i) q^{3} +(17.0893 + 6.21998i) q^{5} +(-92.6180 + 160.419i) q^{7} +(38.6850 - 219.393i) q^{9} +(107.339 + 185.917i) q^{11} +(-318.074 - 266.896i) q^{13} +(-368.819 + 134.239i) q^{15} +(-270.266 - 1532.75i) q^{17} +(-287.327 - 1547.11i) q^{19} +(-694.201 - 3937.01i) q^{21} +(1754.94 - 638.746i) q^{23} +(-2140.53 - 1796.12i) q^{25} +(-218.216 - 377.960i) q^{27} +(-754.646 + 4279.81i) q^{29} +(-2536.15 + 4392.74i) q^{31} +(-4353.75 - 1584.63i) q^{33} +(-2580.58 + 2165.36i) q^{35} +33.9163 q^{37} +8961.15 q^{39} +(9726.48 - 8161.49i) q^{41} +(-4690.09 - 1707.05i) q^{43} +(2025.72 - 3508.65i) q^{45} +(-2242.48 + 12717.7i) q^{47} +(-8752.70 - 15160.1i) q^{49} +(25731.4 + 21591.2i) q^{51} +(-24560.0 + 8939.11i) q^{53} +(677.947 + 3844.83i) q^{55} +(26212.6 + 21591.9i) q^{57} +(-3322.45 - 18842.6i) q^{59} +(29662.1 - 10796.1i) q^{61} +(31612.0 + 26525.6i) q^{63} +(-3775.56 - 6539.47i) q^{65} +(-5288.86 + 29994.6i) q^{67} +(-20152.8 + 34905.7i) q^{69} +(-34086.9 - 12406.6i) q^{71} +(-62821.4 + 52713.4i) q^{73} +60305.6 q^{75} -39766.1 q^{77} +(8486.16 - 7120.74i) q^{79} +(59721.3 + 21736.8i) q^{81} +(7468.07 - 12935.1i) q^{83} +(4915.05 - 27874.6i) q^{85} +(-46895.7 - 81225.7i) q^{87} +(-73562.7 - 61726.4i) q^{89} +(72274.6 - 26305.8i) q^{91} +(-19009.2 - 107807. i) q^{93} +(4712.78 - 28226.1i) q^{95} +(-11066.5 - 62761.3i) q^{97} +(44941.3 - 16357.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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
\(3\) −16.5327 + 13.8726i −1.06057 + 0.889926i −0.994165 0.107867i \(-0.965598\pi\)
−0.0664069 + 0.997793i \(0.521154\pi\)
\(4\) 0 0
\(5\) 17.0893 + 6.21998i 0.305702 + 0.111266i 0.490316 0.871545i \(-0.336881\pi\)
−0.184614 + 0.982811i \(0.559104\pi\)
\(6\) 0 0
\(7\) −92.6180 + 160.419i −0.714415 + 1.23740i 0.248770 + 0.968563i \(0.419974\pi\)
−0.963185 + 0.268840i \(0.913360\pi\)
\(8\) 0 0
\(9\) 38.6850 219.393i 0.159197 0.902854i
\(10\) 0 0
\(11\) 107.339 + 185.917i 0.267471 + 0.463273i 0.968208 0.250147i \(-0.0804788\pi\)
−0.700737 + 0.713419i \(0.747146\pi\)
\(12\) 0 0
\(13\) −318.074 266.896i −0.521999 0.438009i 0.343329 0.939215i \(-0.388445\pi\)
−0.865328 + 0.501206i \(0.832890\pi\)
\(14\) 0 0
\(15\) −368.819 + 134.239i −0.423238 + 0.154046i
\(16\) 0 0
\(17\) −270.266 1532.75i −0.226813 1.28632i −0.859188 0.511659i \(-0.829031\pi\)
0.632375 0.774662i \(-0.282080\pi\)
\(18\) 0 0
\(19\) −287.327 1547.11i −0.182596 0.983188i
\(20\) 0 0
\(21\) −694.201 3937.01i −0.343508 1.94813i
\(22\) 0 0
\(23\) 1754.94 638.746i 0.691740 0.251773i 0.0278598 0.999612i \(-0.491131\pi\)
0.663880 + 0.747839i \(0.268909\pi\)
\(24\) 0 0
\(25\) −2140.53 1796.12i −0.684971 0.574759i
\(26\) 0 0
\(27\) −218.216 377.960i −0.0576071 0.0997785i
\(28\) 0 0
\(29\) −754.646 + 4279.81i −0.166628 + 0.944995i 0.780742 + 0.624854i \(0.214842\pi\)
−0.947370 + 0.320141i \(0.896270\pi\)
\(30\) 0 0
\(31\) −2536.15 + 4392.74i −0.473992 + 0.820977i −0.999557 0.0297760i \(-0.990521\pi\)
0.525565 + 0.850753i \(0.323854\pi\)
\(32\) 0 0
\(33\) −4353.75 1584.63i −0.695950 0.253305i
\(34\) 0 0
\(35\) −2580.58 + 2165.36i −0.356079 + 0.298786i
\(36\) 0 0
\(37\) 33.9163 0.00407290 0.00203645 0.999998i \(-0.499352\pi\)
0.00203645 + 0.999998i \(0.499352\pi\)
\(38\) 0 0
\(39\) 8961.15 0.943414
\(40\) 0 0
\(41\) 9726.48 8161.49i 0.903642 0.758245i −0.0672571 0.997736i \(-0.521425\pi\)
0.970899 + 0.239490i \(0.0769803\pi\)
\(42\) 0 0
\(43\) −4690.09 1707.05i −0.386821 0.140791i 0.141287 0.989969i \(-0.454876\pi\)
−0.528108 + 0.849177i \(0.677098\pi\)
\(44\) 0 0
\(45\) 2025.72 3508.65i 0.149124 0.258291i
\(46\) 0 0
\(47\) −2242.48 + 12717.7i −0.148076 + 0.839779i 0.816770 + 0.576963i \(0.195762\pi\)
−0.964846 + 0.262816i \(0.915349\pi\)
\(48\) 0 0
\(49\) −8752.70 15160.1i −0.520777 0.902013i
\(50\) 0 0
\(51\) 25731.4 + 21591.2i 1.38528 + 1.16239i
\(52\) 0 0
\(53\) −24560.0 + 8939.11i −1.20099 + 0.437124i −0.863569 0.504230i \(-0.831776\pi\)
−0.337419 + 0.941354i \(0.609554\pi\)
\(54\) 0 0
\(55\) 677.947 + 3844.83i 0.0302196 + 0.171384i
\(56\) 0 0
\(57\) 26212.6 + 21591.9i 1.06862 + 0.880245i
\(58\) 0 0
\(59\) −3322.45 18842.6i −0.124259 0.704710i −0.981745 0.190202i \(-0.939086\pi\)
0.857486 0.514508i \(-0.172025\pi\)
\(60\) 0 0
\(61\) 29662.1 10796.1i 1.02065 0.371487i 0.223138 0.974787i \(-0.428370\pi\)
0.797514 + 0.603300i \(0.206148\pi\)
\(62\) 0 0
\(63\) 31612.0 + 26525.6i 1.00346 + 0.842003i
\(64\) 0 0
\(65\) −3775.56 6539.47i −0.110840 0.191981i
\(66\) 0 0
\(67\) −5288.86 + 29994.6i −0.143938 + 0.816313i 0.824276 + 0.566189i \(0.191583\pi\)
−0.968214 + 0.250124i \(0.919529\pi\)
\(68\) 0 0
\(69\) −20152.8 + 34905.7i −0.509581 + 0.882620i
\(70\) 0 0
\(71\) −34086.9 12406.6i −0.802494 0.292084i −0.0919742 0.995761i \(-0.529318\pi\)
−0.710519 + 0.703678i \(0.751540\pi\)
\(72\) 0 0
\(73\) −62821.4 + 52713.4i −1.37975 + 1.15775i −0.410445 + 0.911886i \(0.634626\pi\)
−0.969305 + 0.245862i \(0.920929\pi\)
\(74\) 0 0
\(75\) 60305.6 1.23795
\(76\) 0 0
\(77\) −39766.1 −0.764340
\(78\) 0 0
\(79\) 8486.16 7120.74i 0.152983 0.128368i −0.563084 0.826400i \(-0.690385\pi\)
0.716067 + 0.698032i \(0.245941\pi\)
\(80\) 0 0
\(81\) 59721.3 + 21736.8i 1.01138 + 0.368114i
\(82\) 0 0
\(83\) 7468.07 12935.1i 0.118991 0.206098i −0.800377 0.599497i \(-0.795367\pi\)
0.919368 + 0.393399i \(0.128701\pi\)
\(84\) 0 0
\(85\) 4915.05 27874.6i 0.0737872 0.418468i
\(86\) 0 0
\(87\) −46895.7 81225.7i −0.664255 1.15052i
\(88\) 0 0
\(89\) −73562.7 61726.4i −0.984425 0.826030i 0.000326264 1.00000i \(-0.499896\pi\)
−0.984751 + 0.173969i \(0.944341\pi\)
\(90\) 0 0
\(91\) 72274.6 26305.8i 0.914918 0.333003i
\(92\) 0 0
\(93\) −19009.2 107807.i −0.227907 1.29252i
\(94\) 0 0
\(95\) 4712.78 28226.1i 0.0535758 0.320879i
\(96\) 0 0
\(97\) −11066.5 62761.3i −0.119421 0.677271i −0.984466 0.175576i \(-0.943821\pi\)
0.865045 0.501695i \(-0.167290\pi\)
\(98\) 0 0
\(99\) 44941.3 16357.3i 0.460848 0.167735i
\(100\) 0 0
\(101\) −36817.5 30893.5i −0.359129 0.301345i 0.445314 0.895374i \(-0.353092\pi\)
−0.804444 + 0.594029i \(0.797536\pi\)
\(102\) 0 0
\(103\) −33680.8 58336.8i −0.312816 0.541813i 0.666155 0.745813i \(-0.267939\pi\)
−0.978971 + 0.204000i \(0.934606\pi\)
\(104\) 0 0
\(105\) 12624.7 71598.5i 0.111751 0.633769i
\(106\) 0 0
\(107\) −104101. + 180308.i −0.879011 + 1.52249i −0.0265842 + 0.999647i \(0.508463\pi\)
−0.852427 + 0.522846i \(0.824870\pi\)
\(108\) 0 0
\(109\) −3826.82 1392.85i −0.0308512 0.0112289i 0.326548 0.945180i \(-0.394114\pi\)
−0.357400 + 0.933952i \(0.616337\pi\)
\(110\) 0 0
\(111\) −560.728 + 470.506i −0.00431961 + 0.00362458i
\(112\) 0 0
\(113\) −172879. −1.27364 −0.636819 0.771013i \(-0.719750\pi\)
−0.636819 + 0.771013i \(0.719750\pi\)
\(114\) 0 0
\(115\) 33963.6 0.239480
\(116\) 0 0
\(117\) −70859.9 + 59458.5i −0.478559 + 0.401559i
\(118\) 0 0
\(119\) 270914. + 98604.7i 1.75374 + 0.638308i
\(120\) 0 0
\(121\) 57482.2 99562.0i 0.356919 0.618202i
\(122\) 0 0
\(123\) −47584.1 + 269863.i −0.283595 + 1.60835i
\(124\) 0 0
\(125\) −53823.9 93225.8i −0.308106 0.533656i
\(126\) 0 0
\(127\) −247017. 207272.i −1.35900 1.14033i −0.976291 0.216462i \(-0.930548\pi\)
−0.382704 0.923871i \(-0.625007\pi\)
\(128\) 0 0
\(129\) 101221. 36841.5i 0.535546 0.194923i
\(130\) 0 0
\(131\) 60080.8 + 340735.i 0.305885 + 1.73476i 0.619311 + 0.785146i \(0.287412\pi\)
−0.313426 + 0.949612i \(0.601477\pi\)
\(132\) 0 0
\(133\) 274797. + 97197.4i 1.34705 + 0.476459i
\(134\) 0 0
\(135\) −1378.24 7816.36i −0.00650862 0.0369122i
\(136\) 0 0
\(137\) −94710.1 + 34471.7i −0.431117 + 0.156914i −0.548458 0.836178i \(-0.684785\pi\)
0.117341 + 0.993092i \(0.462563\pi\)
\(138\) 0 0
\(139\) 226390. + 189964.i 0.993851 + 0.833940i 0.986121 0.166030i \(-0.0530950\pi\)
0.00773009 + 0.999970i \(0.497539\pi\)
\(140\) 0 0
\(141\) −139353. 241367.i −0.590296 1.02242i
\(142\) 0 0
\(143\) 15478.6 87783.6i 0.0632983 0.358983i
\(144\) 0 0
\(145\) −39516.7 + 68444.9i −0.156085 + 0.270347i
\(146\) 0 0
\(147\) 355016. + 129215.i 1.35505 + 0.493197i
\(148\) 0 0
\(149\) 122658. 102922.i 0.452615 0.379789i −0.387790 0.921748i \(-0.626761\pi\)
0.840405 + 0.541958i \(0.182317\pi\)
\(150\) 0 0
\(151\) −315290. −1.12530 −0.562649 0.826696i \(-0.690218\pi\)
−0.562649 + 0.826696i \(0.690218\pi\)
\(152\) 0 0
\(153\) −346731. −1.19747
\(154\) 0 0
\(155\) −70663.7 + 59293.9i −0.236247 + 0.198235i
\(156\) 0 0
\(157\) 497814. + 181190.i 1.61183 + 0.586657i 0.981800 0.189917i \(-0.0608219\pi\)
0.630026 + 0.776574i \(0.283044\pi\)
\(158\) 0 0
\(159\) 282035. 488498.i 0.884727 1.53239i
\(160\) 0 0
\(161\) −60072.0 + 340685.i −0.182645 + 1.03583i
\(162\) 0 0
\(163\) 170727. + 295707.i 0.503306 + 0.871752i 0.999993 + 0.00382173i \(0.00121650\pi\)
−0.496687 + 0.867930i \(0.665450\pi\)
\(164\) 0 0
\(165\) −64545.9 54160.4i −0.184569 0.154872i
\(166\) 0 0
\(167\) −95436.5 + 34736.0i −0.264803 + 0.0963805i −0.471010 0.882128i \(-0.656110\pi\)
0.206207 + 0.978508i \(0.433888\pi\)
\(168\) 0 0
\(169\) −34536.6 195867.i −0.0930172 0.527527i
\(170\) 0 0
\(171\) −350540. + 3187.75i −0.916744 + 0.00833670i
\(172\) 0 0
\(173\) 43202.3 + 245012.i 0.109747 + 0.622405i 0.989218 + 0.146452i \(0.0467855\pi\)
−0.879471 + 0.475953i \(0.842103\pi\)
\(174\) 0 0
\(175\) 486384. 177029.i 1.20056 0.436969i
\(176\) 0 0
\(177\) 316324. + 265427.i 0.758925 + 0.636814i
\(178\) 0 0
\(179\) −331263. 573765.i −0.772753 1.33845i −0.936049 0.351871i \(-0.885546\pi\)
0.163295 0.986577i \(-0.447788\pi\)
\(180\) 0 0
\(181\) −122306. + 693629.i −0.277492 + 1.57373i 0.453443 + 0.891285i \(0.350196\pi\)
−0.730935 + 0.682447i \(0.760916\pi\)
\(182\) 0 0
\(183\) −340625. + 589979.i −0.751880 + 1.30229i
\(184\) 0 0
\(185\) 579.605 + 210.959i 0.00124509 + 0.000453177i
\(186\) 0 0
\(187\) 255954. 214771.i 0.535252 0.449130i
\(188\) 0 0
\(189\) 80842.8 0.164622
\(190\) 0 0
\(191\) −730125. −1.44815 −0.724075 0.689721i \(-0.757733\pi\)
−0.724075 + 0.689721i \(0.757733\pi\)
\(192\) 0 0
\(193\) 268839. 225583.i 0.519516 0.435925i −0.344947 0.938622i \(-0.612103\pi\)
0.864463 + 0.502697i \(0.167659\pi\)
\(194\) 0 0
\(195\) 153139. + 55738.2i 0.288403 + 0.104970i
\(196\) 0 0
\(197\) −302321. + 523636.i −0.555013 + 0.961311i 0.442889 + 0.896576i \(0.353953\pi\)
−0.997903 + 0.0647347i \(0.979380\pi\)
\(198\) 0 0
\(199\) 2245.00 12732.0i 0.00401868 0.0227911i −0.982732 0.185032i \(-0.940761\pi\)
0.986751 + 0.162241i \(0.0518722\pi\)
\(200\) 0 0
\(201\) −328664. 569262.i −0.573801 0.993853i
\(202\) 0 0
\(203\) −616670. 517448.i −1.05030 0.881305i
\(204\) 0 0
\(205\) 216983. 78975.3i 0.360612 0.131252i
\(206\) 0 0
\(207\) −72246.8 409732.i −0.117191 0.664621i
\(208\) 0 0
\(209\) 256792. 219484.i 0.406645 0.347566i
\(210\) 0 0
\(211\) −105477. 598191.i −0.163100 0.924983i −0.951002 0.309184i \(-0.899944\pi\)
0.787903 0.615800i \(-0.211167\pi\)
\(212\) 0 0
\(213\) 735660. 267758.i 1.11104 0.404384i
\(214\) 0 0
\(215\) −69532.4 58344.6i −0.102587 0.0860804i
\(216\) 0 0
\(217\) −469786. 813694.i −0.677253 1.17304i
\(218\) 0 0
\(219\) 307336. 1.74299e6i 0.433015 2.45575i
\(220\) 0 0
\(221\) −323121. + 559661.i −0.445025 + 0.770805i
\(222\) 0 0
\(223\) −439331. 159903.i −0.591602 0.215325i 0.0288320 0.999584i \(-0.490821\pi\)
−0.620434 + 0.784259i \(0.713043\pi\)
\(224\) 0 0
\(225\) −476864. + 400136.i −0.627969 + 0.526928i
\(226\) 0 0
\(227\) −301861. −0.388814 −0.194407 0.980921i \(-0.562278\pi\)
−0.194407 + 0.980921i \(0.562278\pi\)
\(228\) 0 0
\(229\) 1.09881e6 1.38463 0.692313 0.721598i \(-0.256592\pi\)
0.692313 + 0.721598i \(0.256592\pi\)
\(230\) 0 0
\(231\) 657441. 551659.i 0.810638 0.680206i
\(232\) 0 0
\(233\) −166874. 60737.2i −0.201372 0.0732935i 0.239365 0.970930i \(-0.423061\pi\)
−0.440737 + 0.897636i \(0.645283\pi\)
\(234\) 0 0
\(235\) −117426. + 203388.i −0.138706 + 0.240246i
\(236\) 0 0
\(237\) −41516.2 + 235450.i −0.0480116 + 0.272287i
\(238\) 0 0
\(239\) 116816. + 202331.i 0.132284 + 0.229123i 0.924557 0.381045i \(-0.124436\pi\)
−0.792273 + 0.610167i \(0.791102\pi\)
\(240\) 0 0
\(241\) 791942. + 664518.i 0.878315 + 0.736994i 0.965832 0.259169i \(-0.0834486\pi\)
−0.0875166 + 0.996163i \(0.527893\pi\)
\(242\) 0 0
\(243\) −1.18924e6 + 432848.i −1.29197 + 0.470240i
\(244\) 0 0
\(245\) −55281.5 313517.i −0.0588389 0.333692i
\(246\) 0 0
\(247\) −321525. + 568781.i −0.335330 + 0.593202i
\(248\) 0 0
\(249\) 55975.5 + 317453.i 0.0572136 + 0.324475i
\(250\) 0 0
\(251\) −1.16252e6 + 423122.i −1.16470 + 0.423917i −0.850775 0.525530i \(-0.823867\pi\)
−0.313928 + 0.949447i \(0.601645\pi\)
\(252\) 0 0
\(253\) 307127. + 257710.i 0.301659 + 0.253122i
\(254\) 0 0
\(255\) 305434. + 529027.i 0.294149 + 0.509480i
\(256\) 0 0
\(257\) −166782. + 945869.i −0.157513 + 0.893301i 0.798939 + 0.601412i \(0.205395\pi\)
−0.956452 + 0.291889i \(0.905716\pi\)
\(258\) 0 0
\(259\) −3141.26 + 5440.82i −0.00290974 + 0.00503982i
\(260\) 0 0
\(261\) 909769. + 331129.i 0.826666 + 0.300882i
\(262\) 0 0
\(263\) −1.04243e6 + 874704.i −0.929304 + 0.779779i −0.975692 0.219145i \(-0.929673\pi\)
0.0463880 + 0.998923i \(0.485229\pi\)
\(264\) 0 0
\(265\) −475314. −0.415782
\(266\) 0 0
\(267\) 2.07249e6 1.77916
\(268\) 0 0
\(269\) 1.73934e6 1.45948e6i 1.46556 1.22975i 0.545413 0.838167i \(-0.316373\pi\)
0.920144 0.391581i \(-0.128072\pi\)
\(270\) 0 0
\(271\) 881034. + 320670.i 0.728734 + 0.265238i 0.679629 0.733556i \(-0.262141\pi\)
0.0491053 + 0.998794i \(0.484363\pi\)
\(272\) 0 0
\(273\) −829964. + 1.43754e6i −0.673989 + 1.16738i
\(274\) 0 0
\(275\) 104166. 590755.i 0.0830605 0.471059i
\(276\) 0 0
\(277\) −417874. 723778.i −0.327224 0.566769i 0.654736 0.755858i \(-0.272780\pi\)
−0.981960 + 0.189089i \(0.939447\pi\)
\(278\) 0 0
\(279\) 865627. + 726348.i 0.665764 + 0.558642i
\(280\) 0 0
\(281\) −1.47381e6 + 536423.i −1.11346 + 0.405268i −0.832263 0.554381i \(-0.812955\pi\)
−0.281201 + 0.959649i \(0.590733\pi\)
\(282\) 0 0
\(283\) −359924. 2.04123e6i −0.267143 1.51504i −0.762862 0.646561i \(-0.776206\pi\)
0.495719 0.868483i \(-0.334905\pi\)
\(284\) 0 0
\(285\) 313654. + 532032.i 0.228738 + 0.387994i
\(286\) 0 0
\(287\) 408411. + 2.31622e6i 0.292680 + 1.65987i
\(288\) 0 0
\(289\) −942056. + 342880.i −0.663486 + 0.241489i
\(290\) 0 0
\(291\) 1.05362e6 + 884092.i 0.729376 + 0.612019i
\(292\) 0 0
\(293\) 126571. + 219228.i 0.0861324 + 0.149186i 0.905873 0.423549i \(-0.139216\pi\)
−0.819741 + 0.572735i \(0.805883\pi\)
\(294\) 0 0
\(295\) 60422.2 342671.i 0.0404242 0.229257i
\(296\) 0 0
\(297\) 46846.1 81139.8i 0.0308164 0.0533756i
\(298\) 0 0
\(299\) −728680. 265218.i −0.471366 0.171563i
\(300\) 0 0
\(301\) 708231. 594277.i 0.450567 0.378070i
\(302\) 0 0
\(303\) 1.03726e6 0.649057
\(304\) 0 0
\(305\) 574056. 0.353349
\(306\) 0 0
\(307\) −1.45169e6 + 1.21811e6i −0.879078 + 0.737634i −0.965989 0.258582i \(-0.916745\pi\)
0.0869114 + 0.996216i \(0.472300\pi\)
\(308\) 0 0
\(309\) 1.36612e6 + 497225.i 0.813938 + 0.296249i
\(310\) 0 0
\(311\) 486478. 842605.i 0.285209 0.493996i −0.687451 0.726231i \(-0.741270\pi\)
0.972660 + 0.232235i \(0.0746038\pi\)
\(312\) 0 0
\(313\) 578383. 3.28017e6i 0.333699 1.89250i −0.106022 0.994364i \(-0.533811\pi\)
0.439720 0.898135i \(-0.355078\pi\)
\(314\) 0 0
\(315\) 375237. + 649929.i 0.213073 + 0.369054i
\(316\) 0 0
\(317\) 559388. + 469382.i 0.312655 + 0.262349i 0.785588 0.618750i \(-0.212360\pi\)
−0.472933 + 0.881098i \(0.656805\pi\)
\(318\) 0 0
\(319\) −876692. + 319090.i −0.482359 + 0.175564i
\(320\) 0 0
\(321\) −780268. 4.42512e6i −0.422650 2.39697i
\(322\) 0 0
\(323\) −2.29368e6 + 858530.i −1.22328 + 0.457878i
\(324\) 0 0
\(325\) 201471. + 1.14260e6i 0.105805 + 0.600047i
\(326\) 0 0
\(327\) 82590.0 30060.3i 0.0427128 0.0155462i
\(328\) 0 0
\(329\) −1.83247e6 1.53763e6i −0.933358 0.783180i
\(330\) 0 0
\(331\) 973238. + 1.68570e6i 0.488258 + 0.845687i 0.999909 0.0135063i \(-0.00429933\pi\)
−0.511651 + 0.859193i \(0.670966\pi\)
\(332\) 0 0
\(333\) 1312.05 7441.01i 0.000648396 0.00367724i
\(334\) 0 0
\(335\) −276949. + 479690.i −0.134830 + 0.233533i
\(336\) 0 0
\(337\) 2.05743e6 + 748842.i 0.986846 + 0.359183i 0.784498 0.620131i \(-0.212921\pi\)
0.202348 + 0.979314i \(0.435143\pi\)
\(338\) 0 0
\(339\) 2.85815e6 2.39828e6i 1.35079 1.13344i
\(340\) 0 0
\(341\) −1.08891e6 −0.507115
\(342\) 0 0
\(343\) 129370. 0.0593744
\(344\) 0 0
\(345\) −561510. + 471163.i −0.253986 + 0.213120i
\(346\) 0 0
\(347\) −2.28044e6 830011.i −1.01670 0.370050i −0.220700 0.975342i \(-0.570834\pi\)
−0.796004 + 0.605292i \(0.793056\pi\)
\(348\) 0 0
\(349\) −1.65873e6 + 2.87300e6i −0.728973 + 1.26262i 0.228345 + 0.973580i \(0.426669\pi\)
−0.957318 + 0.289037i \(0.906665\pi\)
\(350\) 0 0
\(351\) −31467.4 + 178460.i −0.0136330 + 0.0773168i
\(352\) 0 0
\(353\) 1.26131e6 + 2.18466e6i 0.538749 + 0.933141i 0.998972 + 0.0453374i \(0.0144363\pi\)
−0.460222 + 0.887804i \(0.652230\pi\)
\(354\) 0 0
\(355\) −505351. 424040.i −0.212825 0.178581i
\(356\) 0 0
\(357\) −5.84684e6 + 2.12808e6i −2.42801 + 0.883724i
\(358\) 0 0
\(359\) −573983. 3.25522e6i −0.235051 1.33304i −0.842505 0.538688i \(-0.818920\pi\)
0.607454 0.794355i \(-0.292191\pi\)
\(360\) 0 0
\(361\) −2.31099e6 + 889051.i −0.933317 + 0.359053i
\(362\) 0 0
\(363\) 430847. + 2.44345e6i 0.171615 + 0.973279i
\(364\) 0 0
\(365\) −1.40145e6 + 510085.i −0.550611 + 0.200406i
\(366\) 0 0
\(367\) 20776.9 + 17433.9i 0.00805222 + 0.00675661i 0.646805 0.762656i \(-0.276105\pi\)
−0.638753 + 0.769412i \(0.720549\pi\)
\(368\) 0 0
\(369\) −1.41431e6 2.44965e6i −0.540727 0.936567i
\(370\) 0 0
\(371\) 840695. 4.76782e6i 0.317106 1.79839i
\(372\) 0 0
\(373\) 2.45951e6 4.26000e6i 0.915329 1.58540i 0.108910 0.994052i \(-0.465264\pi\)
0.806419 0.591345i \(-0.201403\pi\)
\(374\) 0 0
\(375\) 2.18314e6 + 794597.i 0.801683 + 0.291789i
\(376\) 0 0
\(377\) 1.38230e6 1.15989e6i 0.500897 0.420302i
\(378\) 0 0
\(379\) −1.21025e6 −0.432791 −0.216396 0.976306i \(-0.569430\pi\)
−0.216396 + 0.976306i \(0.569430\pi\)
\(380\) 0 0
\(381\) 6.95926e6 2.45612
\(382\) 0 0
\(383\) 4.18047e6 3.50783e6i 1.45622 1.22192i 0.528349 0.849027i \(-0.322811\pi\)
0.927875 0.372891i \(-0.121633\pi\)
\(384\) 0 0
\(385\) −679574. 247345.i −0.233660 0.0850454i
\(386\) 0 0
\(387\) −555953. + 962938.i −0.188695 + 0.326829i
\(388\) 0 0
\(389\) 149883. 850029.i 0.0502202 0.284813i −0.949347 0.314229i \(-0.898254\pi\)
0.999567 + 0.0294167i \(0.00936497\pi\)
\(390\) 0 0
\(391\) −1.45334e6 2.51726e6i −0.480756 0.832694i
\(392\) 0 0
\(393\) −5.72017e6 4.79979e6i −1.86822 1.56762i
\(394\) 0 0
\(395\) 189313. 68904.3i 0.0610503 0.0222205i
\(396\) 0 0
\(397\) 335321. + 1.90170e6i 0.106779 + 0.605572i 0.990495 + 0.137549i \(0.0439225\pi\)
−0.883716 + 0.468023i \(0.844966\pi\)
\(398\) 0 0
\(399\) −5.89152e6 + 2.20521e6i −1.85266 + 0.693455i
\(400\) 0 0
\(401\) 427729. + 2.42577e6i 0.132834 + 0.753337i 0.976344 + 0.216224i \(0.0693740\pi\)
−0.843510 + 0.537113i \(0.819515\pi\)
\(402\) 0 0
\(403\) 1.97909e6 720329.i 0.607019 0.220937i
\(404\) 0 0
\(405\) 885390. + 742930.i 0.268224 + 0.225066i
\(406\) 0 0
\(407\) 3640.54 + 6305.61i 0.00108938 + 0.00188687i
\(408\) 0 0
\(409\) 162994. 924382.i 0.0481795 0.273239i −0.951196 0.308589i \(-0.900143\pi\)
0.999375 + 0.0353494i \(0.0112544\pi\)
\(410\) 0 0
\(411\) 1.08760e6 1.88378e6i 0.317589 0.550080i
\(412\) 0 0
\(413\) 3.33043e6 + 1.21218e6i 0.960783 + 0.349696i
\(414\) 0 0
\(415\) 208080. 174600.i 0.0593075 0.0497649i
\(416\) 0 0
\(417\) −6.37813e6 −1.79620
\(418\) 0 0
\(419\) 715148. 0.199003 0.0995017 0.995037i \(-0.468275\pi\)
0.0995017 + 0.995037i \(0.468275\pi\)
\(420\) 0 0
\(421\) 418023. 350763.i 0.114946 0.0964515i −0.583503 0.812111i \(-0.698318\pi\)
0.698449 + 0.715660i \(0.253874\pi\)
\(422\) 0 0
\(423\) 2.70344e6 + 983970.i 0.734624 + 0.267381i
\(424\) 0 0
\(425\) −2.17450e6 + 3.76634e6i −0.583964 + 1.01146i
\(426\) 0 0
\(427\) −1.01534e6 + 5.75829e6i −0.269490 + 1.52835i
\(428\) 0 0
\(429\) 961881. + 1.66603e6i 0.252335 + 0.437058i
\(430\) 0 0
\(431\) 5.61843e6 + 4.71442e6i 1.45687 + 1.22246i 0.927366 + 0.374154i \(0.122067\pi\)
0.529506 + 0.848306i \(0.322377\pi\)
\(432\) 0 0
\(433\) −677794. + 246697.i −0.173731 + 0.0632330i −0.427421 0.904053i \(-0.640578\pi\)
0.253690 + 0.967286i \(0.418356\pi\)
\(434\) 0 0
\(435\) −296190. 1.67978e6i −0.0750494 0.425626i
\(436\) 0 0
\(437\) −1.49245e6 2.53155e6i −0.373849 0.634137i
\(438\) 0 0
\(439\) 561812. + 3.18620e6i 0.139133 + 0.789062i 0.971892 + 0.235427i \(0.0756488\pi\)
−0.832759 + 0.553635i \(0.813240\pi\)
\(440\) 0 0
\(441\) −3.66463e6 + 1.33382e6i −0.897292 + 0.326587i
\(442\) 0 0
\(443\) 5.79583e6 + 4.86328e6i 1.40316 + 1.17739i 0.959678 + 0.281103i \(0.0907002\pi\)
0.443478 + 0.896285i \(0.353744\pi\)
\(444\) 0 0
\(445\) −873195. 1.51242e6i −0.209031 0.362053i
\(446\) 0 0
\(447\) −600068. + 3.40315e6i −0.142047 + 0.805588i
\(448\) 0 0
\(449\) −425393. + 736803.i −0.0995806 + 0.172479i −0.911511 0.411275i \(-0.865083\pi\)
0.811931 + 0.583754i \(0.198417\pi\)
\(450\) 0 0
\(451\) 2.56139e6 + 932269.i 0.592972 + 0.215824i
\(452\) 0 0
\(453\) 5.21259e6 4.37388e6i 1.19346 1.00143i
\(454\) 0 0
\(455\) 1.39874e6 0.316744
\(456\) 0 0
\(457\) 3.57687e6 0.801147 0.400574 0.916265i \(-0.368811\pi\)
0.400574 + 0.916265i \(0.368811\pi\)
\(458\) 0 0
\(459\) −520343. + 436620.i −0.115281 + 0.0967324i
\(460\) 0 0
\(461\) 3.94449e6 + 1.43568e6i 0.864448 + 0.314633i 0.735917 0.677072i \(-0.236752\pi\)
0.128531 + 0.991705i \(0.458974\pi\)
\(462\) 0 0
\(463\) −3.12019e6 + 5.40434e6i −0.676440 + 1.17163i 0.299606 + 0.954063i \(0.403145\pi\)
−0.976046 + 0.217565i \(0.930189\pi\)
\(464\) 0 0
\(465\) 345702. 1.96057e6i 0.0741429 0.420485i
\(466\) 0 0
\(467\) 2.52384e6 + 4.37142e6i 0.535512 + 0.927534i 0.999138 + 0.0415034i \(0.0132147\pi\)
−0.463626 + 0.886031i \(0.653452\pi\)
\(468\) 0 0
\(469\) −4.32187e6 3.62648e6i −0.907276 0.761295i
\(470\) 0 0
\(471\) −1.07438e7 + 3.91041e6i −2.23154 + 0.812214i
\(472\) 0 0
\(473\) −186060. 1.05520e6i −0.0382385 0.216861i
\(474\) 0 0
\(475\) −2.16376e6 + 3.82771e6i −0.440023 + 0.778404i
\(476\) 0 0
\(477\) 1.01108e6 + 5.73411e6i 0.203465 + 1.15391i
\(478\) 0 0
\(479\) 7.88321e6 2.86925e6i 1.56987 0.571387i 0.596901 0.802315i \(-0.296399\pi\)
0.972971 + 0.230928i \(0.0741763\pi\)
\(480\) 0 0
\(481\) −10787.9 9052.12i −0.00212605 0.00178397i
\(482\) 0 0
\(483\) −3.73303e6 6.46580e6i −0.728105 1.26111i
\(484\) 0 0
\(485\) 201256. 1.14138e6i 0.0388503 0.220331i
\(486\) 0 0
\(487\) −1.80494e6 + 3.12624e6i −0.344858 + 0.597311i −0.985328 0.170672i \(-0.945406\pi\)
0.640470 + 0.767983i \(0.278739\pi\)
\(488\) 0 0
\(489\) −6.92479e6 2.52042e6i −1.30959 0.476651i
\(490\) 0 0
\(491\) −1.13684e6 + 953919.i −0.212811 + 0.178570i −0.742962 0.669334i \(-0.766580\pi\)
0.530151 + 0.847903i \(0.322135\pi\)
\(492\) 0 0
\(493\) 6.76384e6 1.25336
\(494\) 0 0
\(495\) 869756. 0.159545
\(496\) 0 0
\(497\) 5.14732e6 4.31911e6i 0.934739 0.784339i
\(498\) 0 0
\(499\) 3.14449e6 + 1.14450e6i 0.565326 + 0.205762i 0.608843 0.793291i \(-0.291634\pi\)
−0.0435166 + 0.999053i \(0.513856\pi\)
\(500\) 0 0
\(501\) 1.09594e6 1.89823e6i 0.195071 0.337874i
\(502\) 0 0
\(503\) 1.17470e6 6.66206e6i 0.207017 1.17405i −0.687216 0.726453i \(-0.741167\pi\)
0.894233 0.447601i \(-0.147722\pi\)
\(504\) 0 0
\(505\) −437026. 756952.i −0.0762569 0.132081i
\(506\) 0 0
\(507\) 3.28816e6 + 2.75909e6i 0.568111 + 0.476702i
\(508\) 0 0
\(509\) 695885. 253281.i 0.119054 0.0433320i −0.281806 0.959471i \(-0.590934\pi\)
0.400860 + 0.916139i \(0.368711\pi\)
\(510\) 0 0
\(511\) −2.63784e6 1.49600e7i −0.446886 2.53442i
\(512\) 0 0
\(513\) −522046. + 446201.i −0.0875822 + 0.0748578i
\(514\) 0 0
\(515\) −212726. 1.20643e6i −0.0353429 0.200439i
\(516\) 0 0
\(517\) −2.60514e6 + 948195.i −0.428653 + 0.156017i
\(518\) 0 0
\(519\) −4.11320e6 3.45139e6i −0.670289 0.562439i
\(520\) 0 0
\(521\) −4.40631e6 7.63196e6i −0.711183 1.23180i −0.964414 0.264399i \(-0.914827\pi\)
0.253231 0.967406i \(-0.418507\pi\)
\(522\) 0 0
\(523\) 1.50040e6 8.50919e6i 0.239857 1.36030i −0.592282 0.805731i \(-0.701773\pi\)
0.832139 0.554567i \(-0.187116\pi\)
\(524\) 0 0
\(525\) −5.58539e6 + 9.67417e6i −0.884413 + 1.53185i
\(526\) 0 0
\(527\) 7.41841e6 + 2.70008e6i 1.16355 + 0.423497i
\(528\) 0 0
\(529\) −2.25871e6 + 1.89528e6i −0.350930 + 0.294465i
\(530\) 0 0
\(531\) −4.26247e6 −0.656031
\(532\) 0 0
\(533\) −5.27201e6 −0.803819
\(534\) 0 0
\(535\) −2.90052e6 + 2.43382e6i −0.438118 + 0.367625i
\(536\) 0 0
\(537\) 1.34363e7 + 4.89040e6i 2.01068 + 0.731828i
\(538\) 0 0
\(539\) 1.87901e6 3.25455e6i 0.278585 0.482524i
\(540\) 0 0
\(541\) −783205. + 4.44178e6i −0.115049 + 0.652475i 0.871677 + 0.490081i \(0.163033\pi\)
−0.986726 + 0.162394i \(0.948078\pi\)
\(542\) 0 0
\(543\) −7.60038e6 1.31642e7i −1.10621 1.91600i
\(544\) 0 0
\(545\) −56734.0 47605.5i −0.00818187 0.00686540i
\(546\) 0 0
\(547\) −6.26270e6 + 2.27944e6i −0.894939 + 0.325731i −0.748223 0.663448i \(-0.769093\pi\)
−0.146716 + 0.989179i \(0.546870\pi\)
\(548\) 0 0
\(549\) −1.22112e6 6.92532e6i −0.172913 0.980639i
\(550\) 0 0
\(551\) 6.83816e6 62185.0i 0.959534 0.00872582i
\(552\) 0 0
\(553\) 356331. + 2.02085e6i 0.0495496 + 0.281010i
\(554\) 0 0
\(555\) −12509.0 + 4552.89i −0.00172381 + 0.000627415i
\(556\) 0 0
\(557\) 6.16086e6 + 5.16958e6i 0.841402 + 0.706020i 0.957879 0.287174i \(-0.0927157\pi\)
−0.116477 + 0.993193i \(0.537160\pi\)
\(558\) 0 0
\(559\) 1.03619e6 + 1.79474e6i 0.140252 + 0.242924i
\(560\) 0 0
\(561\) −1.25218e6 + 7.10148e6i −0.167981 + 0.952669i
\(562\) 0 0
\(563\) −3.97212e6 + 6.87992e6i −0.528143 + 0.914771i 0.471318 + 0.881963i \(0.343778\pi\)
−0.999462 + 0.0328080i \(0.989555\pi\)
\(564\) 0 0
\(565\) −2.95437e6 1.07530e6i −0.389354 0.141713i
\(566\) 0 0
\(567\) −9.01826e6 + 7.56722e6i −1.17805 + 0.988504i
\(568\) 0 0
\(569\) −1.10265e7 −1.42777 −0.713883 0.700265i \(-0.753065\pi\)
−0.713883 + 0.700265i \(0.753065\pi\)
\(570\) 0 0
\(571\) −1.93966e6 −0.248963 −0.124482 0.992222i \(-0.539727\pi\)
−0.124482 + 0.992222i \(0.539727\pi\)
\(572\) 0 0
\(573\) 1.20709e7 1.01287e7i 1.53587 1.28875i
\(574\) 0 0
\(575\) −4.90378e6 1.78483e6i −0.618530 0.225127i
\(576\) 0 0
\(577\) 4.83163e6 8.36863e6i 0.604163 1.04644i −0.388020 0.921651i \(-0.626841\pi\)
0.992183 0.124790i \(-0.0398258\pi\)
\(578\) 0 0
\(579\) −1.31522e6 + 7.45897e6i −0.163043 + 0.924661i
\(580\) 0 0
\(581\) 1.38336e6 + 2.39604e6i 0.170017 + 0.294479i
\(582\) 0 0
\(583\) −4.29818e6 3.60660e6i −0.523737 0.439467i
\(584\) 0 0
\(585\) −1.58077e6 + 575355.i −0.190977 + 0.0695098i
\(586\) 0 0
\(587\) −968493. 5.49260e6i −0.116012 0.657934i −0.986244 0.165294i \(-0.947143\pi\)
0.870233 0.492641i \(-0.163968\pi\)
\(588\) 0 0
\(589\) 7.52475e6 + 2.66155e6i 0.893724 + 0.316115i
\(590\) 0 0
\(591\) −2.26599e6 1.28511e7i −0.266864 1.51346i
\(592\) 0 0
\(593\) −7.93353e6 + 2.88757e6i −0.926467 + 0.337206i −0.760808 0.648977i \(-0.775197\pi\)
−0.165659 + 0.986183i \(0.552975\pi\)
\(594\) 0 0
\(595\) 4.01640e6 + 3.37016e6i 0.465099 + 0.390264i
\(596\) 0 0
\(597\) 139510. + 241639.i 0.0160203 + 0.0277479i
\(598\) 0 0
\(599\) 2.33109e6 1.32202e7i 0.265455 1.50547i −0.502281 0.864704i \(-0.667506\pi\)
0.767736 0.640766i \(-0.221383\pi\)
\(600\) 0 0
\(601\) −6.15660e6 + 1.06636e7i −0.695273 + 1.20425i 0.274816 + 0.961497i \(0.411383\pi\)
−0.970089 + 0.242751i \(0.921950\pi\)
\(602\) 0 0
\(603\) 6.37603e6 + 2.32068e6i 0.714096 + 0.259910i
\(604\) 0 0
\(605\) 1.60160e6 1.34390e6i 0.177896 0.149272i
\(606\) 0 0
\(607\) −1.00810e7 −1.11053 −0.555266 0.831673i \(-0.687384\pi\)
−0.555266 + 0.831673i \(0.687384\pi\)
\(608\) 0 0
\(609\) 1.73735e7 1.89821
\(610\) 0 0
\(611\) 4.10758e6 3.44667e6i 0.445127 0.373506i
\(612\) 0 0
\(613\) 2.53346e6 + 922102.i 0.272309 + 0.0991124i 0.474565 0.880220i \(-0.342605\pi\)
−0.202256 + 0.979333i \(0.564827\pi\)
\(614\) 0 0
\(615\) −2.49172e6 + 4.31578e6i −0.265651 + 0.460121i
\(616\) 0 0
\(617\) 1.33623e6 7.57813e6i 0.141308 0.801400i −0.828949 0.559324i \(-0.811061\pi\)
0.970257 0.242076i \(-0.0778282\pi\)
\(618\) 0 0
\(619\) −8.28561e6 1.43511e7i −0.869156 1.50542i −0.862860 0.505443i \(-0.831329\pi\)
−0.00629600 0.999980i \(-0.502004\pi\)
\(620\) 0 0
\(621\) −624376. 523914.i −0.0649706 0.0545168i
\(622\) 0 0
\(623\) 1.67153e7 6.08388e6i 1.72542 0.628002i
\(624\) 0 0
\(625\) 1.17636e6 + 6.67149e6i 0.120460 + 0.683160i
\(626\) 0 0
\(627\) −1.20065e6 + 7.19102e6i −0.121969 + 0.730503i
\(628\) 0 0
\(629\) −9166.41 51985.3i −0.000923788 0.00523906i
\(630\) 0 0
\(631\) 8.16546e6 2.97198e6i 0.816408 0.297148i 0.100140 0.994973i \(-0.468071\pi\)
0.716268 + 0.697825i \(0.245849\pi\)
\(632\) 0 0
\(633\) 1.00423e7 + 8.42647e6i 0.996146 + 0.835865i
\(634\) 0 0
\(635\) −2.93211e6 5.07857e6i −0.288567 0.499813i
\(636\) 0 0
\(637\) −1.26217e6 + 7.15810e6i −0.123245 + 0.698955i
\(638\) 0 0
\(639\) −4.04058e6 + 6.99849e6i −0.391464 + 0.678035i
\(640\) 0 0
\(641\) −4.46130e6 1.62378e6i −0.428861 0.156092i 0.118566 0.992946i \(-0.462170\pi\)
−0.547427 + 0.836854i \(0.684392\pi\)
\(642\) 0 0
\(643\) −1.01365e7 + 8.50555e6i −0.966856 + 0.811288i −0.982055 0.188596i \(-0.939606\pi\)
0.0151991 + 0.999884i \(0.495162\pi\)
\(644\) 0 0
\(645\) 1.95895e6 0.185406
\(646\) 0 0
\(647\) −1.09494e7 −1.02833 −0.514163 0.857693i \(-0.671897\pi\)
−0.514163 + 0.857693i \(0.671897\pi\)
\(648\) 0 0
\(649\) 3.14652e6 2.64024e6i 0.293237 0.246055i
\(650\) 0 0
\(651\) 1.90549e7 + 6.93540e6i 1.76219 + 0.641385i
\(652\) 0 0
\(653\) −4.84673e6 + 8.39478e6i −0.444801 + 0.770418i −0.998038 0.0626059i \(-0.980059\pi\)
0.553238 + 0.833024i \(0.313392\pi\)
\(654\) 0 0
\(655\) −1.09263e6 + 6.19662e6i −0.0995108 + 0.564354i
\(656\) 0 0
\(657\) 9.13473e6 + 1.58218e7i 0.825624 + 1.43002i
\(658\) 0 0
\(659\) −4.53873e6 3.80845e6i −0.407119 0.341613i 0.416119 0.909310i \(-0.363390\pi\)
−0.823238 + 0.567697i \(0.807835\pi\)
\(660\) 0 0
\(661\) −8.42106e6 + 3.06502e6i −0.749658 + 0.272853i −0.688462 0.725272i \(-0.741714\pi\)
−0.0611963 + 0.998126i \(0.519492\pi\)
\(662\) 0 0
\(663\) −2.42189e6 1.37352e7i −0.213979 1.21353i
\(664\) 0 0
\(665\) 4.09152e6 + 3.37027e6i 0.358782 + 0.295536i
\(666\) 0 0
\(667\) 1.40935e6 + 7.99284e6i 0.122661 + 0.695643i
\(668\) 0 0
\(669\) 9.48159e6 3.45102e6i 0.819060 0.298114i
\(670\) 0 0
\(671\) 5.19109e6 + 4.35584e6i 0.445094 + 0.373478i
\(672\) 0 0
\(673\) −3.16540e6 5.48263e6i −0.269396 0.466607i 0.699310 0.714818i \(-0.253491\pi\)
−0.968706 + 0.248211i \(0.920157\pi\)
\(674\) 0 0
\(675\) −211765. + 1.20098e6i −0.0178894 + 0.101456i
\(676\) 0 0
\(677\) −1.00287e7 + 1.73702e7i −0.840955 + 1.45658i 0.0481324 + 0.998841i \(0.484673\pi\)
−0.889088 + 0.457737i \(0.848660\pi\)
\(678\) 0 0
\(679\) 1.10931e7 + 4.03755e6i 0.923374 + 0.336081i
\(680\) 0 0
\(681\) 4.99057e6 4.18759e6i 0.412366 0.346016i
\(682\) 0 0
\(683\) 4.18639e6 0.343391 0.171695 0.985150i \(-0.445076\pi\)
0.171695 + 0.985150i \(0.445076\pi\)
\(684\) 0 0
\(685\) −1.83294e6 −0.149252
\(686\) 0 0
\(687\) −1.81662e7 + 1.52433e7i −1.46849 + 1.23221i
\(688\) 0 0
\(689\) 1.01977e7 + 3.71167e6i 0.818380 + 0.297866i
\(690\) 0 0
\(691\) 5.52964e6 9.57762e6i 0.440557 0.763067i −0.557174 0.830396i \(-0.688114\pi\)
0.997731 + 0.0673289i \(0.0214477\pi\)
\(692\) 0 0
\(693\) −1.53835e6 + 8.72443e6i −0.121681 + 0.690087i
\(694\) 0 0
\(695\) 2.68727e6 + 4.65449e6i 0.211033 + 0.365519i
\(696\) 0 0
\(697\) −1.51383e7 1.27025e7i −1.18031 0.990394i
\(698\) 0 0
\(699\) 3.60146e6 1.31082e6i 0.278795 0.101473i
\(700\) 0 0
\(701\) 3.34964e6 + 1.89967e7i 0.257456 + 1.46010i 0.789689 + 0.613507i \(0.210242\pi\)
−0.532234 + 0.846597i \(0.678647\pi\)
\(702\) 0 0
\(703\) −9745.06 52472.2i −0.000743697 0.00400443i
\(704\) 0 0
\(705\) −880147. 4.99156e6i −0.0666934 0.378237i
\(706\) 0 0
\(707\) 8.36588e6 3.04493e6i 0.629453 0.229102i
\(708\) 0 0
\(709\) −1.27087e7 1.06639e7i −0.949478 0.796707i 0.0297315 0.999558i \(-0.490535\pi\)
−0.979210 + 0.202851i \(0.934979\pi\)
\(710\) 0 0
\(711\) −1.23396e6 2.13727e6i −0.0915431 0.158557i
\(712\) 0 0
\(713\) −1.64495e6 + 9.32895e6i −0.121179 + 0.687241i
\(714\) 0 0
\(715\) 810531. 1.40388e6i 0.0592931 0.102699i
\(716\) 0 0
\(717\) −4.73814e6 1.72454e6i −0.344199 0.125278i
\(718\) 0 0
\(719\) 8.94784e6 7.50813e6i 0.645500 0.541639i −0.260202 0.965554i \(-0.583789\pi\)
0.905702 + 0.423916i \(0.139345\pi\)
\(720\) 0 0
\(721\) 1.24778e7 0.893922
\(722\) 0 0
\(723\) −2.23115e7 −1.58739
\(724\) 0 0
\(725\) 9.30241e6 7.80565e6i 0.657280 0.551523i
\(726\) 0 0
\(727\) −1.81999e6 662421.i −0.127712 0.0464834i 0.277373 0.960762i \(-0.410536\pi\)
−0.405086 + 0.914279i \(0.632758\pi\)
\(728\) 0 0
\(729\) 5.93481e6 1.02794e7i 0.413607 0.716388i
\(730\) 0 0
\(731\) −1.34892e6 + 7.65011e6i −0.0933669 + 0.529510i
\(732\) 0 0
\(733\) −4.19699e6 7.26941e6i −0.288522 0.499734i 0.684935 0.728604i \(-0.259830\pi\)
−0.973457 + 0.228870i \(0.926497\pi\)
\(734\) 0 0
\(735\) 5.26324e6 + 4.41638e6i 0.359364 + 0.301542i
\(736\) 0 0
\(737\) −6.14421e6 + 2.23631e6i −0.416675 + 0.151657i
\(738\) 0 0
\(739\) 2.00935e6 + 1.13956e7i 0.135346 + 0.767584i 0.974618 + 0.223873i \(0.0718702\pi\)
−0.839272 + 0.543711i \(0.817019\pi\)
\(740\) 0 0
\(741\) −2.57478e6 1.38639e7i −0.172264 0.927553i
\(742\) 0 0
\(743\) 2.55970e6 + 1.45168e7i 0.170105 + 0.964712i 0.943644 + 0.330963i \(0.107374\pi\)
−0.773539 + 0.633749i \(0.781515\pi\)
\(744\) 0 0
\(745\) 2.73630e6 995933.i 0.180623 0.0657415i
\(746\) 0 0
\(747\) −2.54897e6 2.13884e6i −0.167133 0.140241i
\(748\) 0 0
\(749\) −1.92832e7 3.33995e7i −1.25596 2.17538i
\(750\) 0 0
\(751\) −1.70521e6 + 9.67074e6i −0.110326 + 0.625691i 0.878632 + 0.477499i \(0.158457\pi\)
−0.988959 + 0.148192i \(0.952655\pi\)
\(752\) 0 0
\(753\) 1.33497e7 2.31224e7i 0.857997 1.48609i
\(754\) 0 0
\(755\) −5.38807e6 1.96110e6i −0.344006 0.125208i
\(756\) 0 0
\(757\) 1.32786e7 1.11421e7i 0.842195 0.706685i −0.115861 0.993265i \(-0.536963\pi\)
0.958056 + 0.286580i \(0.0925184\pi\)
\(758\) 0 0
\(759\) −8.65274e6 −0.545192
\(760\) 0 0
\(761\) −9.96741e6 −0.623908 −0.311954 0.950097i \(-0.600984\pi\)
−0.311954 + 0.950097i \(0.600984\pi\)
\(762\) 0 0
\(763\) 577872. 484892.i 0.0359352 0.0301532i
\(764\) 0 0
\(765\) −5.92537e6 2.15666e6i −0.366068 0.133238i
\(766\) 0 0
\(767\) −3.97222e6 + 6.88008e6i −0.243806 + 0.422285i
\(768\) 0 0
\(769\) 3.52845e6 2.00108e7i 0.215163 1.22025i −0.665459 0.746434i \(-0.731764\pi\)
0.880623 0.473818i \(-0.157125\pi\)
\(770\) 0 0
\(771\) −1.03643e7 1.79514e7i −0.627918 1.08759i
\(772\) 0 0
\(773\) −4.32321e6 3.62761e6i −0.260230 0.218359i 0.503332 0.864093i \(-0.332107\pi\)
−0.763563 + 0.645734i \(0.776552\pi\)
\(774\) 0 0
\(775\) 1.33186e7 4.84758e6i 0.796535 0.289915i
\(776\) 0 0
\(777\) −23544.7 133529.i −0.00139908 0.00793455i
\(778\) 0 0
\(779\) −1.54214e7 1.27029e7i −0.910499 0.749997i
\(780\) 0 0
\(781\) −1.35226e6 7.66904e6i −0.0793290 0.449897i
\(782\) 0 0
\(783\) 1.78228e6 648695.i 0.103889 0.0378126i
\(784\) 0 0
\(785\) 7.38028e6 + 6.19279e6i 0.427463 + 0.358684i
\(786\) 0 0
\(787\) 1.04324e7 + 1.80695e7i 0.600410 + 1.03994i 0.992759 + 0.120125i \(0.0383294\pi\)
−0.392348 + 0.919817i \(0.628337\pi\)
\(788\) 0 0
\(789\) 5.09980e6 2.89224e7i 0.291649 1.65402i
\(790\) 0 0
\(791\) 1.60117e7 2.77331e7i 0.909906 1.57600i
\(792\) 0 0
\(793\) −1.23162e7 4.48273e6i −0.695495 0.253139i
\(794\) 0 0
\(795\) 7.85821e6 6.59382e6i 0.440967 0.370015i
\(796\) 0 0
\(797\) −3.50950e6 −0.195704 −0.0978520 0.995201i \(-0.531197\pi\)
−0.0978520 + 0.995201i \(0.531197\pi\)
\(798\) 0 0
\(799\) 2.00992e7 1.11381
\(800\) 0 0
\(801\) −1.63881e7 + 1.37513e7i −0.902502 + 0.757289i
\(802\) 0 0
\(803\) −1.65435e7 6.02134e6i −0.905395 0.329537i
\(804\) 0 0
\(805\) −3.14564e6 + 5.44842e6i −0.171088 + 0.296333i
\(806\) 0 0
\(807\) −8.50921e6 + 4.82581e7i −0.459944 + 2.60847i
\(808\) 0 0
\(809\) 5.36926e6 + 9.29983e6i 0.288432 + 0.499579i 0.973436 0.228961i \(-0.0735328\pi\)
−0.685004 + 0.728540i \(0.740199\pi\)
\(810\) 0 0
\(811\) −5.20532e6 4.36778e6i −0.277904 0.233189i 0.493173 0.869932i \(-0.335837\pi\)
−0.771077 + 0.636742i \(0.780282\pi\)
\(812\) 0 0
\(813\) −1.90144e7 + 6.92066e6i −1.00892 + 0.367216i
\(814\) 0 0
\(815\) 1.07830e6 + 6.11533e6i 0.0568650 + 0.322497i
\(816\) 0 0
\(817\) −1.29341e6 + 7.74656e6i −0.0677923 + 0.406026i
\(818\) 0 0
\(819\) −2.97538e6 1.68742e7i −0.155000 0.879050i
\(820\) 0 0
\(821\) −3.22864e7 + 1.17513e7i −1.67171 + 0.608454i −0.992138 0.125151i \(-0.960059\pi\)
−0.679576 + 0.733605i \(0.737836\pi\)
\(822\) 0 0
\(823\) 1.52514e7 + 1.27975e7i 0.784894 + 0.658604i 0.944476 0.328581i \(-0.106570\pi\)
−0.159582 + 0.987185i \(0.551015\pi\)
\(824\) 0 0
\(825\) 6.47315e6 + 1.12118e7i 0.331116 + 0.573510i
\(826\) 0 0
\(827\) 102834. 583203.i 0.00522847 0.0296521i −0.982082 0.188455i \(-0.939652\pi\)
0.987310 + 0.158802i \(0.0507633\pi\)
\(828\) 0 0
\(829\) 1.40762e6 2.43806e6i 0.0711374 0.123214i −0.828263 0.560340i \(-0.810670\pi\)
0.899400 + 0.437126i \(0.144004\pi\)
\(830\) 0 0
\(831\) 1.69492e7 + 6.16902e6i 0.851428 + 0.309894i
\(832\) 0 0
\(833\) −2.08712e7 + 1.75130e7i −1.04216 + 0.874475i
\(834\) 0 0
\(835\) −1.84700e6 −0.0916748
\(836\) 0 0
\(837\) 2.21371e6 0.109221
\(838\) 0 0
\(839\) −1.48642e7 + 1.24725e7i −0.729013 + 0.611715i −0.929862 0.367908i \(-0.880074\pi\)
0.200849 + 0.979622i \(0.435630\pi\)
\(840\) 0 0
\(841\) 1.52688e6 + 555738.i 0.0744413 + 0.0270944i
\(842\) 0 0
\(843\) 1.69245e7 2.93141e7i 0.820250 1.42072i
\(844\) 0 0
\(845\) 628083. 3.56204e6i 0.0302605 0.171616i
\(846\) 0 0
\(847\) 1.06478e7 + 1.84425e7i 0.509976 + 0.883305i
\(848\) 0 0
\(849\) 3.42676e7 + 2.87539e7i 1.63160 + 1.36908i
\(850\) 0 0
\(851\) 59521.1 21663.9i 0.00281739 0.00102545i
\(852\) 0 0
\(853\) 3.78417e6 + 2.14611e7i 0.178073 + 1.00990i 0.934537 + 0.355866i \(0.115814\pi\)
−0.756464 + 0.654035i \(0.773075\pi\)
\(854\) 0 0
\(855\) −6.01031e6 2.12588e6i −0.281178 0.0994542i
\(856\) 0 0
\(857\) −100216. 568351.i −0.00466104 0.0264341i 0.982389 0.186850i \(-0.0598277\pi\)
−0.987050 + 0.160415i \(0.948717\pi\)
\(858\) 0 0
\(859\) 5.53782e6 2.01560e6i 0.256069 0.0932013i −0.210796 0.977530i \(-0.567606\pi\)
0.466865 + 0.884329i \(0.345383\pi\)
\(860\) 0 0
\(861\) −3.88840e7 3.26275e7i −1.78757 1.49995i
\(862\) 0 0
\(863\) 6.07495e6 + 1.05221e7i 0.277661 + 0.480924i 0.970803 0.239878i \(-0.0771073\pi\)
−0.693142 + 0.720801i \(0.743774\pi\)
\(864\) 0 0
\(865\) −785678. + 4.45580e6i −0.0357030 + 0.202482i
\(866\) 0 0
\(867\) 1.08181e7 1.87375e7i 0.488768 0.846571i
\(868\) 0 0
\(869\) 2.23476e6 + 813386.i 0.100388 + 0.0365382i
\(870\) 0 0
\(871\) 9.68769e6 8.12894e6i 0.432688 0.363069i
\(872\) 0 0
\(873\) −1.41975e7 −0.630488
\(874\) 0 0
\(875\) 1.99403e7 0.880463
\(876\) 0 0
\(877\) 9.25529e6 7.76611e6i 0.406342 0.340961i −0.416597 0.909091i \(-0.636777\pi\)
0.822939 + 0.568130i \(0.192333\pi\)
\(878\) 0 0
\(879\) −5.13382e6 1.86856e6i −0.224114 0.0815708i
\(880\) 0 0
\(881\) −1.47705e7 + 2.55833e7i −0.641146 + 1.11050i 0.344032 + 0.938958i \(0.388207\pi\)
−0.985177 + 0.171539i \(0.945126\pi\)
\(882\) 0 0
\(883\) 5.44168e6 3.08613e7i 0.234872 1.33203i −0.608011 0.793929i \(-0.708032\pi\)
0.842883 0.538097i \(-0.180857\pi\)
\(884\) 0 0
\(885\) 3.75479e6 + 6.50349e6i 0.161149 + 0.279118i
\(886\) 0 0
\(887\) −5.64474e6 4.73650e6i −0.240899 0.202138i 0.514343 0.857585i \(-0.328036\pi\)
−0.755241 + 0.655447i \(0.772480\pi\)
\(888\) 0 0
\(889\) 5.61287e7 2.04292e7i 2.38194 0.866954i
\(890\) 0 0
\(891\) 2.36920e6 + 1.34364e7i 0.0999786 + 0.567007i
\(892\) 0 0
\(893\) 2.03200e7 184787.i 0.852699 0.00775428i
\(894\) 0 0
\(895\) −2.09224e6 1.18657e7i −0.0873079 0.495148i
\(896\) 0 0
\(897\) 1.57263e7 5.72390e6i 0.652597 0.237526i
\(898\) 0 0
\(899\) −1.68862e7 1.41692e7i −0.696840 0.584718i
\(900\) 0 0
\(901\) 2.03392e7 + 3.52285e7i 0.834682 + 1.44571i
\(902\) 0 0
\(903\) −3.46482e6 + 1.96500e7i −0.141404 + 0.801942i
\(904\) 0 0
\(905\) −6.40447e6 + 1.10929e7i −0.259933 + 0.450218i
\(906\) 0 0
\(907\) −1.61833e7 5.89023e6i −0.653203 0.237747i −0.00590416 0.999983i \(-0.501879\pi\)
−0.647299 + 0.762236i \(0.724102\pi\)
\(908\) 0 0
\(909\) −8.20212e6 + 6.88240e6i −0.329243 + 0.276268i
\(910\) 0 0
\(911\) 4.31231e7 1.72153 0.860764 0.509004i \(-0.169986\pi\)
0.860764 + 0.509004i \(0.169986\pi\)
\(912\) 0 0
\(913\) 3.20646e6 0.127306
\(914\) 0 0
\(915\) −9.49068e6 + 7.96363e6i −0.374753 + 0.314455i
\(916\) 0 0
\(917\) −6.02250e7 2.19201e7i −2.36512 0.860834i
\(918\) 0 0
\(919\) −1.77789e7 + 3.07940e7i −0.694411 + 1.20275i 0.275968 + 0.961167i \(0.411002\pi\)
−0.970379 + 0.241588i \(0.922332\pi\)
\(920\) 0 0
\(921\) 7.10197e6 4.02773e7i 0.275886 1.56463i
\(922\) 0 0
\(923\) 7.53088e6 + 1.30439e7i 0.290966 + 0.503967i
\(924\) 0 0
\(925\) −72599.0 60917.8i −0.00278982 0.00234094i
\(926\) 0 0
\(927\) −1.41016e7 + 5.13258e6i −0.538977 + 0.196172i
\(928\) 0 0
\(929\) −2.75211e6 1.56080e7i −0.104623 0.593346i −0.991370 0.131091i \(-0.958152\pi\)
0.886747 0.462254i \(-0.152959\pi\)
\(930\) 0 0
\(931\) −2.09395e7 + 1.78973e7i −0.791756 + 0.676726i
\(932\) 0 0
\(933\) 3.64631e6 + 2.06792e7i 0.137135 + 0.777732i
\(934\) 0 0
\(935\) 5.70994e6 2.07825e6i 0.213601 0.0777443i
\(936\) 0 0
\(937\) 816887. + 685449.i 0.0303957 + 0.0255051i 0.657859 0.753141i \(-0.271462\pi\)
−0.627463 + 0.778646i \(0.715907\pi\)
\(938\) 0 0
\(939\) 3.59422e7 + 6.22537e7i 1.33027 + 2.30410i
\(940\) 0 0
\(941\) −4.83721e6 + 2.74332e7i −0.178083 + 1.00996i 0.756443 + 0.654060i \(0.226936\pi\)
−0.934525 + 0.355896i \(0.884176\pi\)
\(942\) 0 0
\(943\) 1.18563e7 2.05357e7i 0.434179 0.752021i
\(944\) 0 0
\(945\) 1.38154e6 + 502841.i 0.0503251 + 0.0183169i
\(946\) 0 0
\(947\) −1.07632e7 + 9.03137e6i −0.390001 + 0.327249i −0.816613 0.577185i \(-0.804151\pi\)
0.426613 + 0.904434i \(0.359707\pi\)
\(948\) 0 0
\(949\) 3.40508e7 1.22733
\(950\) 0 0
\(951\) −1.57597e7 −0.565064
\(952\) 0 0
\(953\) −6.01258e6 + 5.04516e6i −0.214451 + 0.179946i −0.743685 0.668530i \(-0.766924\pi\)
0.529234 + 0.848476i \(0.322479\pi\)
\(954\) 0 0
\(955\) −1.24773e7 4.54136e6i −0.442703 0.161131i
\(956\) 0 0
\(957\) 1.00675e7 1.74374e7i 0.355337 0.615462i
\(958\) 0 0
\(959\) 3.24195e6 1.83860e7i 0.113831 0.645567i
\(960\) 0 0
\(961\) 1.45047e6 + 2.51228e6i 0.0506640 + 0.0877526i
\(962\) 0 0
\(963\) 3.55312e7 + 2.98142e7i 1.23465 + 1.03600i
\(964\) 0 0
\(965\) 5.99738e6 2.18287e6i 0.207321 0.0754586i
\(966\) 0 0
\(967\) −955958. 5.42151e6i −0.0328755 0.186446i 0.963948 0.266092i \(-0.0857324\pi\)
−0.996823 + 0.0796453i \(0.974621\pi\)
\(968\) 0 0
\(969\) 2.60106e7 4.60130e7i 0.889901 1.57424i
\(970\) 0 0
\(971\) 2.29383e6 + 1.30090e7i 0.0780752 + 0.442787i 0.998637 + 0.0521900i \(0.0166201\pi\)
−0.920562 + 0.390597i \(0.872269\pi\)
\(972\) 0 0
\(973\) −5.14417e7 + 1.87233e7i −1.74194 + 0.634015i
\(974\) 0 0
\(975\) −1.91816e7 1.60953e7i −0.646211 0.542235i
\(976\) 0 0
\(977\) 2.17762e7 + 3.77175e7i 0.729871 + 1.26417i 0.956938 + 0.290294i \(0.0937531\pi\)
−0.227067 + 0.973879i \(0.572914\pi\)
\(978\) 0 0
\(979\) 3.57982e6 2.03022e7i 0.119373 0.676996i
\(980\) 0 0
\(981\) −453622. + 785697.i −0.0150495 + 0.0260665i
\(982\) 0 0
\(983\) −3.18118e7 1.15786e7i −1.05004 0.382183i −0.241361 0.970435i \(-0.577594\pi\)
−0.808677 + 0.588253i \(0.799816\pi\)
\(984\) 0 0
\(985\) −8.42346e6 + 7.06812e6i −0.276630 + 0.232120i
\(986\) 0 0
\(987\) 5.16266e7 1.68687
\(988\) 0 0
\(989\) −9.32121e6 −0.303027
\(990\) 0 0
\(991\) 1.36635e6 1.14651e6i 0.0441956 0.0370845i −0.620422 0.784268i \(-0.713039\pi\)
0.664618 + 0.747183i \(0.268594\pi\)
\(992\) 0 0
\(993\) −3.94752e7 1.43678e7i −1.27043 0.462399i
\(994\) 0 0
\(995\) 117558. 203617.i 0.00376440 0.00652014i
\(996\) 0 0
\(997\) 6.61966e6 3.75420e7i 0.210910 1.19613i −0.676953 0.736026i \(-0.736700\pi\)
0.887864 0.460107i \(-0.152189\pi\)
\(998\) 0 0
\(999\) −7401.06 12819.0i −0.000234628 0.000406388i
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 76.6.i.a.9.1 48
19.17 even 9 inner 76.6.i.a.17.1 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.6.i.a.9.1 48 1.1 even 1 trivial
76.6.i.a.17.1 yes 48 19.17 even 9 inner