Properties

Label 63.6.e.f.37.3
Level $63$
Weight $6$
Character 63.37
Analytic conductor $10.104$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,6,Mod(37,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), 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: \(10.1041806482\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 187x^{10} + 25399x^{8} + 1518438x^{6} + 66232188x^{4} + 1297462320x^{2} + 18380851776 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.3
Root \(-2.44476 + 4.23445i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.6.e.f.46.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.44476 + 4.23445i) q^{2} +(4.04630 + 7.00840i) q^{4} +(21.3752 - 37.0229i) q^{5} +(43.2256 - 122.223i) q^{7} -196.034 q^{8} +O(q^{10})\) \(q+(-2.44476 + 4.23445i) q^{2} +(4.04630 + 7.00840i) q^{4} +(21.3752 - 37.0229i) q^{5} +(43.2256 - 122.223i) q^{7} -196.034 q^{8} +(104.514 + 181.024i) q^{10} +(-355.439 - 615.638i) q^{11} +885.624 q^{13} +(411.872 + 481.843i) q^{14} +(349.773 - 605.825i) q^{16} +(350.659 + 607.359i) q^{17} +(627.946 - 1087.63i) q^{19} +345.962 q^{20} +3475.85 q^{22} +(523.092 - 906.022i) q^{23} +(648.701 + 1123.58i) q^{25} +(-2165.14 + 3750.13i) q^{26} +(1031.49 - 191.611i) q^{28} +6150.88 q^{29} +(-1147.12 - 1986.87i) q^{31} +(-1426.31 - 2470.45i) q^{32} -3429.10 q^{34} +(-3601.11 - 4212.89i) q^{35} +(-202.054 + 349.968i) q^{37} +(3070.35 + 5318.01i) q^{38} +(-4190.26 + 7257.74i) q^{40} -17891.4 q^{41} -14604.8 q^{43} +(2876.43 - 4982.11i) q^{44} +(2557.67 + 4430.01i) q^{46} +(10568.6 - 18305.4i) q^{47} +(-13070.1 - 10566.3i) q^{49} -6343.67 q^{50} +(3583.50 + 6206.80i) q^{52} +(-53.6064 - 92.8490i) q^{53} -30390.3 q^{55} +(-8473.66 + 23959.9i) q^{56} +(-15037.4 + 26045.6i) q^{58} +(22249.4 + 38537.1i) q^{59} +(11606.2 - 20102.5i) q^{61} +11217.7 q^{62} +36333.5 q^{64} +(18930.4 - 32788.4i) q^{65} +(3335.66 + 5777.53i) q^{67} +(-2837.74 + 4915.11i) q^{68} +(26643.1 - 4949.23i) q^{70} +25110.5 q^{71} +(-4737.49 - 8205.57i) q^{73} +(-987.948 - 1711.18i) q^{74} +10163.4 q^{76} +(-90609.5 + 16831.6i) q^{77} +(13238.1 - 22929.0i) q^{79} +(-14953.0 - 25899.3i) q^{80} +(43740.2 - 75760.2i) q^{82} -7494.03 q^{83} +29981.6 q^{85} +(35705.3 - 61843.3i) q^{86} +(69678.0 + 120686. i) q^{88} +(-16085.6 + 27861.2i) q^{89} +(38281.6 - 108244. i) q^{91} +8466.35 q^{92} +(51675.5 + 89504.7i) q^{94} +(-26845.0 - 46496.8i) q^{95} -155070. q^{97} +(76695.9 - 29512.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44476 + 4.23445i −0.432177 + 0.748552i −0.997060 0.0766186i \(-0.975588\pi\)
0.564884 + 0.825170i \(0.308921\pi\)
\(3\) 0 0
\(4\) 4.04630 + 7.00840i 0.126447 + 0.219012i
\(5\) 21.3752 37.0229i 0.382371 0.662286i −0.609029 0.793148i \(-0.708441\pi\)
0.991401 + 0.130861i \(0.0417742\pi\)
\(6\) 0 0
\(7\) 43.2256 122.223i 0.333423 0.942777i
\(8\) −196.034 −1.08294
\(9\) 0 0
\(10\) 104.514 + 181.024i 0.330504 + 0.572449i
\(11\) −355.439 615.638i −0.885693 1.53407i −0.844917 0.534898i \(-0.820350\pi\)
−0.0407765 0.999168i \(-0.512983\pi\)
\(12\) 0 0
\(13\) 885.624 1.45342 0.726709 0.686945i \(-0.241049\pi\)
0.726709 + 0.686945i \(0.241049\pi\)
\(14\) 411.872 + 481.843i 0.561620 + 0.657031i
\(15\) 0 0
\(16\) 349.773 605.825i 0.341576 0.591626i
\(17\) 350.659 + 607.359i 0.294281 + 0.509710i 0.974817 0.223005i \(-0.0715865\pi\)
−0.680536 + 0.732714i \(0.738253\pi\)
\(18\) 0 0
\(19\) 627.946 1087.63i 0.399060 0.691192i −0.594550 0.804059i \(-0.702670\pi\)
0.993610 + 0.112866i \(0.0360031\pi\)
\(20\) 345.962 0.193399
\(21\) 0 0
\(22\) 3475.85 1.53110
\(23\) 523.092 906.022i 0.206186 0.357124i −0.744324 0.667818i \(-0.767228\pi\)
0.950510 + 0.310694i \(0.100562\pi\)
\(24\) 0 0
\(25\) 648.701 + 1123.58i 0.207584 + 0.359547i
\(26\) −2165.14 + 3750.13i −0.628134 + 1.08796i
\(27\) 0 0
\(28\) 1031.49 191.611i 0.248640 0.0461875i
\(29\) 6150.88 1.35813 0.679067 0.734077i \(-0.262385\pi\)
0.679067 + 0.734077i \(0.262385\pi\)
\(30\) 0 0
\(31\) −1147.12 1986.87i −0.214390 0.371334i 0.738694 0.674041i \(-0.235443\pi\)
−0.953084 + 0.302707i \(0.902110\pi\)
\(32\) −1426.31 2470.45i −0.246229 0.426482i
\(33\) 0 0
\(34\) −3429.10 −0.508725
\(35\) −3601.11 4212.89i −0.496897 0.581312i
\(36\) 0 0
\(37\) −202.054 + 349.968i −0.0242641 + 0.0420266i −0.877902 0.478839i \(-0.841058\pi\)
0.853638 + 0.520866i \(0.174391\pi\)
\(38\) 3070.35 + 5318.01i 0.344929 + 0.597434i
\(39\) 0 0
\(40\) −4190.26 + 7257.74i −0.414086 + 0.717218i
\(41\) −17891.4 −1.66221 −0.831103 0.556119i \(-0.812290\pi\)
−0.831103 + 0.556119i \(0.812290\pi\)
\(42\) 0 0
\(43\) −14604.8 −1.20455 −0.602275 0.798289i \(-0.705739\pi\)
−0.602275 + 0.798289i \(0.705739\pi\)
\(44\) 2876.43 4982.11i 0.223986 0.387956i
\(45\) 0 0
\(46\) 2557.67 + 4430.01i 0.178217 + 0.308681i
\(47\) 10568.6 18305.4i 0.697870 1.20875i −0.271334 0.962485i \(-0.587465\pi\)
0.969204 0.246260i \(-0.0792018\pi\)
\(48\) 0 0
\(49\) −13070.1 10566.3i −0.777658 0.628687i
\(50\) −6343.67 −0.358852
\(51\) 0 0
\(52\) 3583.50 + 6206.80i 0.183780 + 0.318317i
\(53\) −53.6064 92.8490i −0.00262136 0.00454033i 0.864712 0.502268i \(-0.167501\pi\)
−0.867333 + 0.497728i \(0.834168\pi\)
\(54\) 0 0
\(55\) −30390.3 −1.35465
\(56\) −8473.66 + 23959.9i −0.361078 + 1.02097i
\(57\) 0 0
\(58\) −15037.4 + 26045.6i −0.586953 + 1.01663i
\(59\) 22249.4 + 38537.1i 0.832124 + 1.44128i 0.896351 + 0.443346i \(0.146209\pi\)
−0.0642267 + 0.997935i \(0.520458\pi\)
\(60\) 0 0
\(61\) 11606.2 20102.5i 0.399360 0.691712i −0.594287 0.804253i \(-0.702566\pi\)
0.993647 + 0.112541i \(0.0358990\pi\)
\(62\) 11217.7 0.370617
\(63\) 0 0
\(64\) 36333.5 1.10881
\(65\) 18930.4 32788.4i 0.555746 0.962580i
\(66\) 0 0
\(67\) 3335.66 + 5777.53i 0.0907809 + 0.157237i 0.907840 0.419317i \(-0.137730\pi\)
−0.817059 + 0.576554i \(0.804397\pi\)
\(68\) −2837.74 + 4915.11i −0.0744218 + 0.128902i
\(69\) 0 0
\(70\) 26643.1 4949.23i 0.649890 0.120724i
\(71\) 25110.5 0.591166 0.295583 0.955317i \(-0.404486\pi\)
0.295583 + 0.955317i \(0.404486\pi\)
\(72\) 0 0
\(73\) −4737.49 8205.57i −0.104050 0.180219i 0.809300 0.587396i \(-0.199847\pi\)
−0.913350 + 0.407176i \(0.866513\pi\)
\(74\) −987.948 1711.18i −0.0209727 0.0363258i
\(75\) 0 0
\(76\) 10163.4 0.201840
\(77\) −90609.5 + 16831.6i −1.74159 + 0.323519i
\(78\) 0 0
\(79\) 13238.1 22929.0i 0.238647 0.413349i −0.721679 0.692228i \(-0.756629\pi\)
0.960326 + 0.278879i \(0.0899627\pi\)
\(80\) −14953.0 25899.3i −0.261217 0.452442i
\(81\) 0 0
\(82\) 43740.2 75760.2i 0.718366 1.24425i
\(83\) −7494.03 −0.119404 −0.0597022 0.998216i \(-0.519015\pi\)
−0.0597022 + 0.998216i \(0.519015\pi\)
\(84\) 0 0
\(85\) 29981.6 0.450098
\(86\) 35705.3 61843.3i 0.520578 0.901668i
\(87\) 0 0
\(88\) 69678.0 + 120686.i 0.959155 + 1.66131i
\(89\) −16085.6 + 27861.2i −0.215260 + 0.372841i −0.953353 0.301858i \(-0.902393\pi\)
0.738093 + 0.674699i \(0.235727\pi\)
\(90\) 0 0
\(91\) 38281.6 108244.i 0.484603 1.37025i
\(92\) 8466.35 0.104286
\(93\) 0 0
\(94\) 51675.5 + 89504.7i 0.603206 + 1.04478i
\(95\) −26845.0 46496.8i −0.305178 0.528584i
\(96\) 0 0
\(97\) −155070. −1.67340 −0.836699 0.547664i \(-0.815517\pi\)
−0.836699 + 0.547664i \(0.815517\pi\)
\(98\) 76695.9 29512.5i 0.806691 0.310414i
\(99\) 0 0
\(100\) −5249.68 + 9092.71i −0.0524968 + 0.0909271i
\(101\) 55960.9 + 96927.1i 0.545860 + 0.945457i 0.998552 + 0.0537904i \(0.0171303\pi\)
−0.452692 + 0.891667i \(0.649536\pi\)
\(102\) 0 0
\(103\) 30342.1 52554.1i 0.281808 0.488105i −0.690022 0.723788i \(-0.742399\pi\)
0.971830 + 0.235683i \(0.0757326\pi\)
\(104\) −173612. −1.57397
\(105\) 0 0
\(106\) 524.219 0.00453156
\(107\) −56266.4 + 97456.3i −0.475105 + 0.822906i −0.999593 0.0285115i \(-0.990923\pi\)
0.524488 + 0.851418i \(0.324257\pi\)
\(108\) 0 0
\(109\) 3811.67 + 6602.01i 0.0307291 + 0.0532243i 0.880981 0.473152i \(-0.156884\pi\)
−0.850252 + 0.526376i \(0.823550\pi\)
\(110\) 74297.0 128686.i 0.585450 1.01403i
\(111\) 0 0
\(112\) −58926.9 68937.6i −0.443883 0.519291i
\(113\) 41498.7 0.305730 0.152865 0.988247i \(-0.451150\pi\)
0.152865 + 0.988247i \(0.451150\pi\)
\(114\) 0 0
\(115\) −22362.4 38732.8i −0.157679 0.273108i
\(116\) 24888.3 + 43107.8i 0.171732 + 0.297448i
\(117\) 0 0
\(118\) −217578. −1.43850
\(119\) 89390.8 16605.3i 0.578663 0.107493i
\(120\) 0 0
\(121\) −172148. + 298170.i −1.06891 + 1.85140i
\(122\) 56748.6 + 98291.5i 0.345188 + 0.597883i
\(123\) 0 0
\(124\) 9283.17 16078.9i 0.0542178 0.0939080i
\(125\) 189060. 1.08224
\(126\) 0 0
\(127\) 94796.7 0.521535 0.260768 0.965402i \(-0.416024\pi\)
0.260768 + 0.965402i \(0.416024\pi\)
\(128\) −43184.6 + 74797.9i −0.232972 + 0.403519i
\(129\) 0 0
\(130\) 92560.5 + 160319.i 0.480360 + 0.832009i
\(131\) −105547. + 182814.i −0.537365 + 0.930744i 0.461679 + 0.887047i \(0.347247\pi\)
−0.999045 + 0.0436972i \(0.986086\pi\)
\(132\) 0 0
\(133\) −105791. 123763.i −0.518585 0.606684i
\(134\) −32619.5 −0.156934
\(135\) 0 0
\(136\) −68740.8 119063.i −0.318689 0.551986i
\(137\) −48096.6 83305.7i −0.218934 0.379204i 0.735549 0.677472i \(-0.236924\pi\)
−0.954482 + 0.298268i \(0.903591\pi\)
\(138\) 0 0
\(139\) −401994. −1.76475 −0.882375 0.470548i \(-0.844056\pi\)
−0.882375 + 0.470548i \(0.844056\pi\)
\(140\) 14954.4 42284.6i 0.0644835 0.182332i
\(141\) 0 0
\(142\) −61389.1 + 106329.i −0.255488 + 0.442518i
\(143\) −314785. 545224.i −1.28728 2.22964i
\(144\) 0 0
\(145\) 131476. 227724.i 0.519311 0.899474i
\(146\) 46328.1 0.179871
\(147\) 0 0
\(148\) −3270.29 −0.0122725
\(149\) 37650.0 65211.8i 0.138931 0.240636i −0.788161 0.615469i \(-0.788967\pi\)
0.927092 + 0.374833i \(0.122300\pi\)
\(150\) 0 0
\(151\) 245297. + 424867.i 0.875488 + 1.51639i 0.856242 + 0.516574i \(0.172793\pi\)
0.0192454 + 0.999815i \(0.493874\pi\)
\(152\) −123098. + 213213.i −0.432159 + 0.748522i
\(153\) 0 0
\(154\) 150246. 424830.i 0.510505 1.44349i
\(155\) −98079.6 −0.327906
\(156\) 0 0
\(157\) 230508. + 399251.i 0.746339 + 1.29270i 0.949567 + 0.313566i \(0.101524\pi\)
−0.203228 + 0.979132i \(0.565143\pi\)
\(158\) 64727.7 + 112112.i 0.206276 + 0.357280i
\(159\) 0 0
\(160\) −121951. −0.376604
\(161\) −88126.1 103097.i −0.267941 0.313461i
\(162\) 0 0
\(163\) 239222. 414344.i 0.705232 1.22150i −0.261376 0.965237i \(-0.584176\pi\)
0.966608 0.256260i \(-0.0824904\pi\)
\(164\) −72393.9 125390.i −0.210181 0.364043i
\(165\) 0 0
\(166\) 18321.1 31733.1i 0.0516038 0.0893803i
\(167\) 498852. 1.38414 0.692070 0.721830i \(-0.256699\pi\)
0.692070 + 0.721830i \(0.256699\pi\)
\(168\) 0 0
\(169\) 413036. 1.11243
\(170\) −73297.8 + 126956.i −0.194522 + 0.336922i
\(171\) 0 0
\(172\) −59095.5 102356.i −0.152312 0.263811i
\(173\) 130322. 225724.i 0.331056 0.573405i −0.651663 0.758508i \(-0.725928\pi\)
0.982719 + 0.185103i \(0.0592618\pi\)
\(174\) 0 0
\(175\) 165369. 30718.9i 0.408186 0.0758248i
\(176\) −497292. −1.21012
\(177\) 0 0
\(178\) −78651.1 136228.i −0.186061 0.322267i
\(179\) 266709. + 461954.i 0.622164 + 1.07762i 0.989082 + 0.147367i \(0.0470798\pi\)
−0.366918 + 0.930253i \(0.619587\pi\)
\(180\) 0 0
\(181\) 185798. 0.421546 0.210773 0.977535i \(-0.432402\pi\)
0.210773 + 0.977535i \(0.432402\pi\)
\(182\) 364764. + 426732.i 0.816269 + 0.954941i
\(183\) 0 0
\(184\) −102544. + 177611.i −0.223287 + 0.386745i
\(185\) 8637.90 + 14961.3i 0.0185558 + 0.0321395i
\(186\) 0 0
\(187\) 249275. 431758.i 0.521285 0.902893i
\(188\) 171055. 0.352974
\(189\) 0 0
\(190\) 262518. 0.527564
\(191\) −354418. + 613871.i −0.702964 + 1.21757i 0.264458 + 0.964397i \(0.414807\pi\)
−0.967421 + 0.253171i \(0.918526\pi\)
\(192\) 0 0
\(193\) 361752. + 626573.i 0.699065 + 1.21082i 0.968791 + 0.247879i \(0.0797337\pi\)
−0.269726 + 0.962937i \(0.586933\pi\)
\(194\) 379109. 656637.i 0.723203 1.25262i
\(195\) 0 0
\(196\) 21167.6 134355.i 0.0393578 0.249812i
\(197\) 147313. 0.270443 0.135222 0.990815i \(-0.456825\pi\)
0.135222 + 0.990815i \(0.456825\pi\)
\(198\) 0 0
\(199\) −710.490 1230.60i −0.00127182 0.00220285i 0.865389 0.501101i \(-0.167071\pi\)
−0.866661 + 0.498898i \(0.833738\pi\)
\(200\) −127167. 220260.i −0.224802 0.389368i
\(201\) 0 0
\(202\) −547244. −0.943632
\(203\) 265875. 751782.i 0.452833 1.28042i
\(204\) 0 0
\(205\) −382432. + 662392.i −0.635579 + 1.10086i
\(206\) 148358. + 256964.i 0.243581 + 0.421895i
\(207\) 0 0
\(208\) 309768. 536533.i 0.496452 0.859881i
\(209\) −892786. −1.41378
\(210\) 0 0
\(211\) −30296.2 −0.0468470 −0.0234235 0.999726i \(-0.507457\pi\)
−0.0234235 + 0.999726i \(0.507457\pi\)
\(212\) 433.815 751.389i 0.000662926 0.00114822i
\(213\) 0 0
\(214\) −275116. 476514.i −0.410659 0.711281i
\(215\) −312181. + 540713.i −0.460585 + 0.797757i
\(216\) 0 0
\(217\) −292427. + 54321.2i −0.421568 + 0.0783106i
\(218\) −37274.5 −0.0531215
\(219\) 0 0
\(220\) −122968. 212987.i −0.171292 0.296686i
\(221\) 310552. + 537891.i 0.427714 + 0.740822i
\(222\) 0 0
\(223\) −147864. −0.199114 −0.0995570 0.995032i \(-0.531743\pi\)
−0.0995570 + 0.995032i \(0.531743\pi\)
\(224\) −363599. + 67542.4i −0.484176 + 0.0899407i
\(225\) 0 0
\(226\) −101454. + 175724.i −0.132129 + 0.228855i
\(227\) −406723. 704464.i −0.523882 0.907391i −0.999614 0.0277999i \(-0.991150\pi\)
0.475731 0.879591i \(-0.342183\pi\)
\(228\) 0 0
\(229\) −641094. + 1.11041e6i −0.807854 + 1.39924i 0.106493 + 0.994313i \(0.466038\pi\)
−0.914347 + 0.404931i \(0.867295\pi\)
\(230\) 218683. 0.272581
\(231\) 0 0
\(232\) −1.20578e6 −1.47078
\(233\) 617850. 1.07015e6i 0.745578 1.29138i −0.204346 0.978899i \(-0.565507\pi\)
0.949924 0.312481i \(-0.101160\pi\)
\(234\) 0 0
\(235\) −451813. 782564.i −0.533691 0.924379i
\(236\) −180055. + 311865.i −0.210439 + 0.364491i
\(237\) 0 0
\(238\) −148225. + 419117.i −0.169621 + 0.479615i
\(239\) 874240. 0.990001 0.495001 0.868893i \(-0.335168\pi\)
0.495001 + 0.868893i \(0.335168\pi\)
\(240\) 0 0
\(241\) 489805. + 848367.i 0.543226 + 0.940895i 0.998716 + 0.0506545i \(0.0161307\pi\)
−0.455490 + 0.890241i \(0.650536\pi\)
\(242\) −841722. 1.45791e6i −0.923912 1.60026i
\(243\) 0 0
\(244\) 187848. 0.201991
\(245\) −670573. + 258036.i −0.713725 + 0.274641i
\(246\) 0 0
\(247\) 556124. 963235.i 0.580002 1.00459i
\(248\) 224874. + 389493.i 0.232172 + 0.402133i
\(249\) 0 0
\(250\) −462205. + 800563.i −0.467719 + 0.810113i
\(251\) −213005. −0.213406 −0.106703 0.994291i \(-0.534029\pi\)
−0.106703 + 0.994291i \(0.534029\pi\)
\(252\) 0 0
\(253\) −743709. −0.730469
\(254\) −231755. + 401412.i −0.225395 + 0.390396i
\(255\) 0 0
\(256\) 370184. + 641177.i 0.353035 + 0.611474i
\(257\) −789506. + 1.36746e6i −0.745629 + 1.29147i 0.204272 + 0.978914i \(0.434517\pi\)
−0.949900 + 0.312553i \(0.898816\pi\)
\(258\) 0 0
\(259\) 34040.4 + 39823.3i 0.0315315 + 0.0368883i
\(260\) 306392. 0.281089
\(261\) 0 0
\(262\) −516076. 893871.i −0.464473 0.804492i
\(263\) −144544. 250357.i −0.128857 0.223188i 0.794377 0.607425i \(-0.207798\pi\)
−0.923234 + 0.384238i \(0.874464\pi\)
\(264\) 0 0
\(265\) −4583.39 −0.00400933
\(266\) 782703. 145395.i 0.678255 0.125993i
\(267\) 0 0
\(268\) −26994.2 + 46755.2i −0.0229579 + 0.0397643i
\(269\) 1.02244e6 + 1.77092e6i 0.861506 + 1.49217i 0.870475 + 0.492213i \(0.163812\pi\)
−0.00896851 + 0.999960i \(0.502855\pi\)
\(270\) 0 0
\(271\) 302981. 524779.i 0.250607 0.434063i −0.713086 0.701076i \(-0.752703\pi\)
0.963693 + 0.267013i \(0.0860366\pi\)
\(272\) 490604. 0.402077
\(273\) 0 0
\(274\) 470338. 0.378472
\(275\) 461147. 798731.i 0.367712 0.636896i
\(276\) 0 0
\(277\) −611375. 1.05893e6i −0.478750 0.829219i 0.520953 0.853585i \(-0.325576\pi\)
−0.999703 + 0.0243664i \(0.992243\pi\)
\(278\) 982780. 1.70222e6i 0.762683 1.32101i
\(279\) 0 0
\(280\) 705939. + 825867.i 0.538111 + 0.629528i
\(281\) 639205. 0.482919 0.241460 0.970411i \(-0.422374\pi\)
0.241460 + 0.970411i \(0.422374\pi\)
\(282\) 0 0
\(283\) −236827. 410197.i −0.175779 0.304457i 0.764652 0.644444i \(-0.222911\pi\)
−0.940430 + 0.339986i \(0.889578\pi\)
\(284\) 101605. + 175984.i 0.0747511 + 0.129473i
\(285\) 0 0
\(286\) 3.07830e6 2.22533
\(287\) −773365. + 2.18675e6i −0.554217 + 1.56709i
\(288\) 0 0
\(289\) 464006. 803681.i 0.326797 0.566030i
\(290\) 642856. + 1.11346e6i 0.448868 + 0.777463i
\(291\) 0 0
\(292\) 38338.6 66404.3i 0.0263135 0.0455763i
\(293\) −829294. −0.564338 −0.282169 0.959365i \(-0.591054\pi\)
−0.282169 + 0.959365i \(0.591054\pi\)
\(294\) 0 0
\(295\) 1.90234e6 1.27272
\(296\) 39609.4 68605.5i 0.0262766 0.0455124i
\(297\) 0 0
\(298\) 184091. + 318854.i 0.120086 + 0.207994i
\(299\) 463263. 802394.i 0.299674 0.519051i
\(300\) 0 0
\(301\) −631301. + 1.78505e6i −0.401625 + 1.13562i
\(302\) −2.39877e6 −1.51346
\(303\) 0 0
\(304\) −439278. 760851.i −0.272618 0.472189i
\(305\) −496169. 859390.i −0.305408 0.528981i
\(306\) 0 0
\(307\) 1.63715e6 0.991385 0.495693 0.868498i \(-0.334914\pi\)
0.495693 + 0.868498i \(0.334914\pi\)
\(308\) −484596. 566921.i −0.291074 0.340522i
\(309\) 0 0
\(310\) 239781. 415313.i 0.141713 0.245455i
\(311\) −303729. 526074.i −0.178068 0.308422i 0.763151 0.646220i \(-0.223651\pi\)
−0.941219 + 0.337798i \(0.890318\pi\)
\(312\) 0 0
\(313\) −789012. + 1.36661e6i −0.455222 + 0.788467i −0.998701 0.0509555i \(-0.983773\pi\)
0.543479 + 0.839423i \(0.317107\pi\)
\(314\) −2.25414e6 −1.29020
\(315\) 0 0
\(316\) 214261. 0.120705
\(317\) 1.09343e6 1.89387e6i 0.611142 1.05853i −0.379906 0.925025i \(-0.624044\pi\)
0.991048 0.133505i \(-0.0426231\pi\)
\(318\) 0 0
\(319\) −2.18626e6 3.78672e6i −1.20289 2.08347i
\(320\) 776635. 1.34517e6i 0.423977 0.734349i
\(321\) 0 0
\(322\) 652008. 121117.i 0.350439 0.0650977i
\(323\) 880779. 0.469743
\(324\) 0 0
\(325\) 574505. + 995072.i 0.301707 + 0.522572i
\(326\) 1.16968e6 + 2.02595e6i 0.609569 + 1.05580i
\(327\) 0 0
\(328\) 3.50731e6 1.80007
\(329\) −1.78051e6 2.08300e6i −0.906892 1.06096i
\(330\) 0 0
\(331\) 1.38434e6 2.39775e6i 0.694503 1.20291i −0.275845 0.961202i \(-0.588958\pi\)
0.970348 0.241712i \(-0.0777090\pi\)
\(332\) −30323.1 52521.1i −0.0150983 0.0261510i
\(333\) 0 0
\(334\) −1.21957e6 + 2.11236e6i −0.598193 + 1.03610i
\(335\) 285202. 0.138848
\(336\) 0 0
\(337\) −2.45187e6 −1.17604 −0.588021 0.808846i \(-0.700093\pi\)
−0.588021 + 0.808846i \(0.700093\pi\)
\(338\) −1.00977e6 + 1.74898e6i −0.480765 + 0.832709i
\(339\) 0 0
\(340\) 121315. + 210123.i 0.0569135 + 0.0985771i
\(341\) −815461. + 1.41242e6i −0.379767 + 0.657776i
\(342\) 0 0
\(343\) −1.85642e6 + 1.14074e6i −0.852001 + 0.523540i
\(344\) 2.86303e6 1.30446
\(345\) 0 0
\(346\) 637210. + 1.10368e6i 0.286149 + 0.495625i
\(347\) 740499. + 1.28258e6i 0.330142 + 0.571823i 0.982539 0.186054i \(-0.0595701\pi\)
−0.652398 + 0.757877i \(0.726237\pi\)
\(348\) 0 0
\(349\) −1.28643e6 −0.565357 −0.282678 0.959215i \(-0.591223\pi\)
−0.282678 + 0.959215i \(0.591223\pi\)
\(350\) −274209. + 775345.i −0.119650 + 0.338318i
\(351\) 0 0
\(352\) −1.01393e6 + 1.75619e6i −0.436167 + 0.755464i
\(353\) −1.12562e6 1.94963e6i −0.480790 0.832752i 0.518967 0.854794i \(-0.326317\pi\)
−0.999757 + 0.0220418i \(0.992983\pi\)
\(354\) 0 0
\(355\) 536742. 929664.i 0.226045 0.391521i
\(356\) −260349. −0.108876
\(357\) 0 0
\(358\) −2.60816e6 −1.07554
\(359\) 362932. 628617.i 0.148624 0.257424i −0.782095 0.623159i \(-0.785849\pi\)
0.930719 + 0.365735i \(0.119182\pi\)
\(360\) 0 0
\(361\) 449417. + 778413.i 0.181502 + 0.314371i
\(362\) −454232. + 786753.i −0.182182 + 0.315549i
\(363\) 0 0
\(364\) 913515. 169695.i 0.361378 0.0671298i
\(365\) −405059. −0.159142
\(366\) 0 0
\(367\) −1.71382e6 2.96843e6i −0.664202 1.15043i −0.979501 0.201440i \(-0.935438\pi\)
0.315298 0.948993i \(-0.397895\pi\)
\(368\) −365927. 633805.i −0.140856 0.243970i
\(369\) 0 0
\(370\) −84470.4 −0.0320775
\(371\) −13665.5 + 2538.50i −0.00515454 + 0.000957509i
\(372\) 0 0
\(373\) 546522. 946604.i 0.203393 0.352287i −0.746227 0.665692i \(-0.768136\pi\)
0.949619 + 0.313405i \(0.101470\pi\)
\(374\) 1.21884e6 + 2.11109e6i 0.450575 + 0.780418i
\(375\) 0 0
\(376\) −2.07181e6 + 3.58847e6i −0.755753 + 1.30900i
\(377\) 5.44737e6 1.97394
\(378\) 0 0
\(379\) −2.92579e6 −1.04627 −0.523137 0.852249i \(-0.675238\pi\)
−0.523137 + 0.852249i \(0.675238\pi\)
\(380\) 217245. 376280.i 0.0771777 0.133676i
\(381\) 0 0
\(382\) −1.73294e6 3.00153e6i −0.607609 1.05241i
\(383\) 51966.3 90008.2i 0.0181019 0.0313534i −0.856833 0.515595i \(-0.827571\pi\)
0.874934 + 0.484241i \(0.160904\pi\)
\(384\) 0 0
\(385\) −1.31364e6 + 3.71441e6i −0.451673 + 1.27714i
\(386\) −3.53759e6 −1.20848
\(387\) 0 0
\(388\) −627460. 1.08679e6i −0.211596 0.366495i
\(389\) −86465.6 149763.i −0.0289714 0.0501799i 0.851176 0.524880i \(-0.175890\pi\)
−0.880148 + 0.474700i \(0.842557\pi\)
\(390\) 0 0
\(391\) 733707. 0.242706
\(392\) 2.56218e6 + 2.07136e6i 0.842159 + 0.680832i
\(393\) 0 0
\(394\) −360146. + 623791.i −0.116879 + 0.202441i
\(395\) −565932. 980224.i −0.182504 0.316106i
\(396\) 0 0
\(397\) −1.29983e6 + 2.25137e6i −0.413913 + 0.716918i −0.995314 0.0966990i \(-0.969172\pi\)
0.581401 + 0.813617i \(0.302505\pi\)
\(398\) 6947.91 0.00219860
\(399\) 0 0
\(400\) 907594. 0.283623
\(401\) −1.72506e6 + 2.98789e6i −0.535726 + 0.927904i 0.463402 + 0.886148i \(0.346629\pi\)
−0.999128 + 0.0417559i \(0.986705\pi\)
\(402\) 0 0
\(403\) −1.01592e6 1.75962e6i −0.311598 0.539704i
\(404\) −452869. + 784392.i −0.138045 + 0.239100i
\(405\) 0 0
\(406\) 2.53338e6 + 2.96376e6i 0.762755 + 0.892335i
\(407\) 287272. 0.0859621
\(408\) 0 0
\(409\) 721374. + 1.24946e6i 0.213232 + 0.369329i 0.952724 0.303837i \(-0.0982677\pi\)
−0.739492 + 0.673165i \(0.764934\pi\)
\(410\) −1.86991e6 3.23878e6i −0.549365 0.951528i
\(411\) 0 0
\(412\) 491093. 0.142535
\(413\) 5.67187e6 1.05361e6i 1.63626 0.303952i
\(414\) 0 0
\(415\) −160186. + 277451.i −0.0456568 + 0.0790799i
\(416\) −1.26318e6 2.18789e6i −0.357874 0.619857i
\(417\) 0 0
\(418\) 2.18265e6 3.78046e6i 0.611002 1.05829i
\(419\) −5.10039e6 −1.41928 −0.709641 0.704564i \(-0.751143\pi\)
−0.709641 + 0.704564i \(0.751143\pi\)
\(420\) 0 0
\(421\) 5.08241e6 1.39754 0.698771 0.715346i \(-0.253731\pi\)
0.698771 + 0.715346i \(0.253731\pi\)
\(422\) 74066.9 128288.i 0.0202462 0.0350674i
\(423\) 0 0
\(424\) 10508.6 + 18201.5i 0.00283878 + 0.00491692i
\(425\) −454945. + 787988.i −0.122176 + 0.211616i
\(426\) 0 0
\(427\) −1.95531e6 2.28749e6i −0.518974 0.607140i
\(428\) −910683. −0.240302
\(429\) 0 0
\(430\) −1.52641e6 2.64383e6i −0.398109 0.689544i
\(431\) −1.23720e6 2.14290e6i −0.320810 0.555659i 0.659845 0.751401i \(-0.270622\pi\)
−0.980655 + 0.195742i \(0.937288\pi\)
\(432\) 0 0
\(433\) −331952. −0.0850855 −0.0425428 0.999095i \(-0.513546\pi\)
−0.0425428 + 0.999095i \(0.513546\pi\)
\(434\) 484892. 1.37107e6i 0.123572 0.349409i
\(435\) 0 0
\(436\) −30846.3 + 53427.4i −0.00777119 + 0.0134601i
\(437\) −656947. 1.13787e6i −0.164561 0.285028i
\(438\) 0 0
\(439\) 2.05610e6 3.56127e6i 0.509193 0.881948i −0.490750 0.871300i \(-0.663277\pi\)
0.999943 0.0106480i \(-0.00338942\pi\)
\(440\) 5.95752e6 1.46701
\(441\) 0 0
\(442\) −3.03690e6 −0.739391
\(443\) −2.92674e6 + 5.06927e6i −0.708558 + 1.22726i 0.256835 + 0.966455i \(0.417320\pi\)
−0.965392 + 0.260802i \(0.916013\pi\)
\(444\) 0 0
\(445\) 687668. + 1.19108e6i 0.164619 + 0.285128i
\(446\) 361493. 626124.i 0.0860524 0.149047i
\(447\) 0 0
\(448\) 1.57053e6 4.44080e6i 0.369702 1.04536i
\(449\) −3.86497e6 −0.904754 −0.452377 0.891827i \(-0.649424\pi\)
−0.452377 + 0.891827i \(0.649424\pi\)
\(450\) 0 0
\(451\) 6.35930e6 + 1.10146e7i 1.47220 + 2.54993i
\(452\) 167916. + 290839.i 0.0386586 + 0.0669586i
\(453\) 0 0
\(454\) 3.97736e6 0.905638
\(455\) −3.18923e6 3.73103e6i −0.722200 0.844891i
\(456\) 0 0
\(457\) 2.69523e6 4.66828e6i 0.603678 1.04560i −0.388581 0.921415i \(-0.627035\pi\)
0.992259 0.124186i \(-0.0396321\pi\)
\(458\) −3.13464e6 5.42936e6i −0.698271 1.20944i
\(459\) 0 0
\(460\) 180970. 313449.i 0.0398760 0.0690673i
\(461\) 1.17429e6 0.257350 0.128675 0.991687i \(-0.458928\pi\)
0.128675 + 0.991687i \(0.458928\pi\)
\(462\) 0 0
\(463\) 4.03702e6 0.875203 0.437601 0.899169i \(-0.355828\pi\)
0.437601 + 0.899169i \(0.355828\pi\)
\(464\) 2.15141e6 3.72636e6i 0.463905 0.803507i
\(465\) 0 0
\(466\) 3.02099e6 + 5.23251e6i 0.644443 + 1.11621i
\(467\) −718550. + 1.24456e6i −0.152463 + 0.264074i −0.932132 0.362118i \(-0.882054\pi\)
0.779669 + 0.626191i \(0.215387\pi\)
\(468\) 0 0
\(469\) 850335. 157959.i 0.178508 0.0331597i
\(470\) 4.41830e6 0.922594
\(471\) 0 0
\(472\) −4.36163e6 7.55456e6i −0.901143 1.56082i
\(473\) 5.19112e6 + 8.99129e6i 1.06686 + 1.84786i
\(474\) 0 0
\(475\) 1.62940e6 0.331355
\(476\) 478078. + 559296.i 0.0967123 + 0.113142i
\(477\) 0 0
\(478\) −2.13731e6 + 3.70192e6i −0.427855 + 0.741067i
\(479\) 1.18608e6 + 2.05436e6i 0.236198 + 0.409107i 0.959620 0.281299i \(-0.0907652\pi\)
−0.723422 + 0.690406i \(0.757432\pi\)
\(480\) 0 0
\(481\) −178944. + 309940.i −0.0352659 + 0.0610823i
\(482\) −4.78982e6 −0.939079
\(483\) 0 0
\(484\) −2.78625e6 −0.540639
\(485\) −3.31466e6 + 5.74116e6i −0.639859 + 1.10827i
\(486\) 0 0
\(487\) −334534. 579430.i −0.0639172 0.110708i 0.832296 0.554332i \(-0.187026\pi\)
−0.896213 + 0.443624i \(0.853693\pi\)
\(488\) −2.27520e6 + 3.94076e6i −0.432484 + 0.749084i
\(489\) 0 0
\(490\) 546751. 3.47034e6i 0.102873 0.652954i
\(491\) 9.58134e6 1.79359 0.896794 0.442448i \(-0.145890\pi\)
0.896794 + 0.442448i \(0.145890\pi\)
\(492\) 0 0
\(493\) 2.15686e6 + 3.73579e6i 0.399673 + 0.692254i
\(494\) 2.71918e6 + 4.70976e6i 0.501326 + 0.868322i
\(495\) 0 0
\(496\) −1.60493e6 −0.292921
\(497\) 1.08541e6 3.06909e6i 0.197108 0.557338i
\(498\) 0 0
\(499\) 1.08902e6 1.88625e6i 0.195788 0.339115i −0.751370 0.659881i \(-0.770607\pi\)
0.947159 + 0.320766i \(0.103940\pi\)
\(500\) 764991. + 1.32500e6i 0.136846 + 0.237024i
\(501\) 0 0
\(502\) 520746. 901959.i 0.0922289 0.159745i
\(503\) 5.11108e6 0.900726 0.450363 0.892846i \(-0.351295\pi\)
0.450363 + 0.892846i \(0.351295\pi\)
\(504\) 0 0
\(505\) 4.78470e6 0.834885
\(506\) 1.81819e6 3.14920e6i 0.315692 0.546794i
\(507\) 0 0
\(508\) 383576. + 664373.i 0.0659465 + 0.114223i
\(509\) 3.54335e6 6.13725e6i 0.606204 1.04998i −0.385656 0.922643i \(-0.626025\pi\)
0.991860 0.127334i \(-0.0406420\pi\)
\(510\) 0 0
\(511\) −1.20769e6 + 224341.i −0.204599 + 0.0380064i
\(512\) −6.38385e6 −1.07624
\(513\) 0 0
\(514\) −3.86031e6 6.68624e6i −0.644487 1.11628i
\(515\) −1.29714e6 2.24671e6i −0.215510 0.373275i
\(516\) 0 0
\(517\) −1.50260e7 −2.47239
\(518\) −251850. + 46783.8i −0.0412400 + 0.00766075i
\(519\) 0 0
\(520\) −3.71099e6 + 6.42762e6i −0.601841 + 1.04242i
\(521\) −1.72694e6 2.99114e6i −0.278729 0.482772i 0.692340 0.721571i \(-0.256580\pi\)
−0.971069 + 0.238799i \(0.923246\pi\)
\(522\) 0 0
\(523\) 278599. 482548.i 0.0445375 0.0771413i −0.842897 0.538074i \(-0.819152\pi\)
0.887435 + 0.460933i \(0.152485\pi\)
\(524\) −1.70831e6 −0.271793
\(525\) 0 0
\(526\) 1.41350e6 0.222757
\(527\) 804494. 1.39342e6i 0.126182 0.218553i
\(528\) 0 0
\(529\) 2.67092e6 + 4.62617e6i 0.414975 + 0.718758i
\(530\) 11205.3 19408.1i 0.00173274 0.00300119i
\(531\) 0 0
\(532\) 439320. 1.24221e6i 0.0672979 0.190290i
\(533\) −1.58450e7 −2.41588
\(534\) 0 0
\(535\) 2.40541e6 + 4.16629e6i 0.363333 + 0.629311i
\(536\) −653901. 1.13259e6i −0.0983106 0.170279i
\(537\) 0 0
\(538\) −9.99851e6 −1.48929
\(539\) −1.85942e6 + 1.18021e7i −0.275681 + 1.74980i
\(540\) 0 0
\(541\) −2.39364e6 + 4.14591e6i −0.351614 + 0.609013i −0.986532 0.163566i \(-0.947700\pi\)
0.634919 + 0.772579i \(0.281034\pi\)
\(542\) 1.48143e6 + 2.56592e6i 0.216613 + 0.375184i
\(543\) 0 0
\(544\) 1.00030e6 1.73257e6i 0.144921 0.251011i
\(545\) 325901. 0.0469997
\(546\) 0 0
\(547\) 2.30360e6 0.329184 0.164592 0.986362i \(-0.447369\pi\)
0.164592 + 0.986362i \(0.447369\pi\)
\(548\) 389226. 674159.i 0.0553669 0.0958984i
\(549\) 0 0
\(550\) 2.25479e6 + 3.90541e6i 0.317833 + 0.550503i
\(551\) 3.86242e6 6.68991e6i 0.541977 0.938732i
\(552\) 0 0
\(553\) −2.23024e6 2.60912e6i −0.310126 0.362811i
\(554\) 5.97866e6 0.827617
\(555\) 0 0
\(556\) −1.62659e6 2.81734e6i −0.223147 0.386502i
\(557\) −6.94253e6 1.20248e7i −0.948156 1.64225i −0.749305 0.662225i \(-0.769612\pi\)
−0.198851 0.980030i \(-0.563721\pi\)
\(558\) 0 0
\(559\) −1.29344e7 −1.75072
\(560\) −3.81185e6 + 708090.i −0.513648 + 0.0954154i
\(561\) 0 0
\(562\) −1.56270e6 + 2.70668e6i −0.208706 + 0.361490i
\(563\) 1.97962e6 + 3.42880e6i 0.263215 + 0.455902i 0.967094 0.254417i \(-0.0818837\pi\)
−0.703879 + 0.710320i \(0.748550\pi\)
\(564\) 0 0
\(565\) 887042. 1.53640e6i 0.116902 0.202481i
\(566\) 2.31595e6 0.303870
\(567\) 0 0
\(568\) −4.92250e6 −0.640199
\(569\) 4.75540e6 8.23659e6i 0.615752 1.06651i −0.374500 0.927227i \(-0.622185\pi\)
0.990252 0.139287i \(-0.0444812\pi\)
\(570\) 0 0
\(571\) 4.53978e6 + 7.86313e6i 0.582699 + 1.00926i 0.995158 + 0.0982881i \(0.0313367\pi\)
−0.412459 + 0.910976i \(0.635330\pi\)
\(572\) 2.54743e6 4.41228e6i 0.325546 0.563862i
\(573\) 0 0
\(574\) −7.36897e6 8.62085e6i −0.933528 1.09212i
\(575\) 1.35732e6 0.171204
\(576\) 0 0
\(577\) 1.79193e6 + 3.10371e6i 0.224069 + 0.388099i 0.956040 0.293237i \(-0.0947326\pi\)
−0.731971 + 0.681336i \(0.761399\pi\)
\(578\) 2.26876e6 + 3.92962e6i 0.282468 + 0.489250i
\(579\) 0 0
\(580\) 2.12797e6 0.262661
\(581\) −323934. + 915945.i −0.0398121 + 0.112572i
\(582\) 0 0
\(583\) −38107.6 + 66004.3i −0.00464344 + 0.00804268i
\(584\) 928706. + 1.60857e6i 0.112680 + 0.195167i
\(585\) 0 0
\(586\) 2.02742e6 3.51160e6i 0.243894 0.422436i
\(587\) −6.14848e6 −0.736499 −0.368250 0.929727i \(-0.620043\pi\)
−0.368250 + 0.929727i \(0.620043\pi\)
\(588\) 0 0
\(589\) −2.88131e6 −0.342218
\(590\) −4.65077e6 + 8.05536e6i −0.550040 + 0.952698i
\(591\) 0 0
\(592\) 141346. + 244819.i 0.0165760 + 0.0287105i
\(593\) −6.64979e6 + 1.15178e7i −0.776554 + 1.34503i 0.157363 + 0.987541i \(0.449701\pi\)
−0.933917 + 0.357490i \(0.883633\pi\)
\(594\) 0 0
\(595\) 1.29597e6 3.66445e6i 0.150073 0.424343i
\(596\) 609373. 0.0702697
\(597\) 0 0
\(598\) 2.26513e6 + 3.92332e6i 0.259024 + 0.448643i
\(599\) −2.30732e6 3.99639e6i −0.262748 0.455094i 0.704223 0.709979i \(-0.251296\pi\)
−0.966971 + 0.254885i \(0.917962\pi\)
\(600\) 0 0
\(601\) 8.17563e6 0.923284 0.461642 0.887066i \(-0.347260\pi\)
0.461642 + 0.887066i \(0.347260\pi\)
\(602\) −6.01532e6 7.03723e6i −0.676500 0.791426i
\(603\) 0 0
\(604\) −1.98509e6 + 3.43828e6i −0.221405 + 0.383485i
\(605\) 7.35941e6 + 1.27469e7i 0.817437 + 1.41584i
\(606\) 0 0
\(607\) 2.18494e6 3.78443e6i 0.240696 0.416897i −0.720217 0.693749i \(-0.755958\pi\)
0.960913 + 0.276852i \(0.0892911\pi\)
\(608\) −3.58259e6 −0.393041
\(609\) 0 0
\(610\) 4.85205e6 0.527960
\(611\) 9.35983e6 1.62117e7i 1.01430 1.75681i
\(612\) 0 0
\(613\) −2.72460e6 4.71914e6i −0.292854 0.507238i 0.681629 0.731698i \(-0.261272\pi\)
−0.974483 + 0.224460i \(0.927938\pi\)
\(614\) −4.00244e6 + 6.93243e6i −0.428453 + 0.742103i
\(615\) 0 0
\(616\) 1.77625e7 3.29957e6i 1.88605 0.350352i
\(617\) 1.32758e7 1.40394 0.701969 0.712208i \(-0.252305\pi\)
0.701969 + 0.712208i \(0.252305\pi\)
\(618\) 0 0
\(619\) 2.23142e6 + 3.86494e6i 0.234075 + 0.405430i 0.959004 0.283394i \(-0.0914605\pi\)
−0.724928 + 0.688824i \(0.758127\pi\)
\(620\) −396859. 687381.i −0.0414627 0.0718155i
\(621\) 0 0
\(622\) 2.97018e6 0.307827
\(623\) 2.70997e6 + 3.17036e6i 0.279734 + 0.327256i
\(624\) 0 0
\(625\) 2.01399e6 3.48834e6i 0.206233 0.357206i
\(626\) −3.85789e6 6.68206e6i −0.393472 0.681514i
\(627\) 0 0
\(628\) −1.86541e6 + 3.23098e6i −0.188744 + 0.326915i
\(629\) −283408. −0.0285618
\(630\) 0 0
\(631\) 8.00421e6 0.800286 0.400143 0.916453i \(-0.368960\pi\)
0.400143 + 0.916453i \(0.368960\pi\)
\(632\) −2.59510e6 + 4.49485e6i −0.258441 + 0.447634i
\(633\) 0 0
\(634\) 5.34634e6 + 9.26014e6i 0.528243 + 0.914943i
\(635\) 2.02630e6 3.50965e6i 0.199420 0.345406i
\(636\) 0 0
\(637\) −1.15752e7 9.35780e6i −1.13026 0.913746i
\(638\) 2.13796e7 2.07944
\(639\) 0 0
\(640\) 1.84616e6 + 3.19764e6i 0.178164 + 0.308588i
\(641\) 1.94455e6 + 3.36806e6i 0.186928 + 0.323768i 0.944224 0.329303i \(-0.106814\pi\)
−0.757297 + 0.653071i \(0.773480\pi\)
\(642\) 0 0
\(643\) −1.77478e7 −1.69285 −0.846423 0.532511i \(-0.821249\pi\)
−0.846423 + 0.532511i \(0.821249\pi\)
\(644\) 365962. 1.03479e6i 0.0347714 0.0983186i
\(645\) 0 0
\(646\) −2.15329e6 + 3.72961e6i −0.203012 + 0.351627i
\(647\) 4.36138e6 + 7.55413e6i 0.409603 + 0.709453i 0.994845 0.101405i \(-0.0323339\pi\)
−0.585242 + 0.810858i \(0.699001\pi\)
\(648\) 0 0
\(649\) 1.58166e7 2.73952e7i 1.47401 2.55307i
\(650\) −5.61811e6 −0.521563
\(651\) 0 0
\(652\) 3.87185e6 0.356697
\(653\) −714958. + 1.23834e6i −0.0656141 + 0.113647i −0.896966 0.442099i \(-0.854234\pi\)
0.831352 + 0.555746i \(0.187567\pi\)
\(654\) 0 0
\(655\) 4.51220e6 + 7.81536e6i 0.410946 + 0.711780i
\(656\) −6.25793e6 + 1.08391e7i −0.567769 + 0.983404i
\(657\) 0 0
\(658\) 1.31733e7 2.44707e6i 1.18612 0.220334i
\(659\) −9.20182e6 −0.825392 −0.412696 0.910869i \(-0.635413\pi\)
−0.412696 + 0.910869i \(0.635413\pi\)
\(660\) 0 0
\(661\) −717566. 1.24286e6i −0.0638790 0.110642i 0.832317 0.554300i \(-0.187014\pi\)
−0.896196 + 0.443658i \(0.853681\pi\)
\(662\) 6.76878e6 + 1.17239e7i 0.600296 + 1.03974i
\(663\) 0 0
\(664\) 1.46908e6 0.129308
\(665\) −6.84339e6 + 1.27123e6i −0.600091 + 0.111473i
\(666\) 0 0
\(667\) 3.21748e6 5.57283e6i 0.280028 0.485022i
\(668\) 2.01850e6 + 3.49615e6i 0.175020 + 0.303144i
\(669\) 0 0
\(670\) −697249. + 1.20767e6i −0.0600069 + 0.103935i
\(671\) −1.65012e7 −1.41484
\(672\) 0 0
\(673\) 2.10985e7 1.79562 0.897808 0.440388i \(-0.145159\pi\)
0.897808 + 0.440388i \(0.145159\pi\)
\(674\) 5.99423e6 1.03823e7i 0.508258 0.880328i
\(675\) 0 0
\(676\) 1.67127e6 + 2.89472e6i 0.140663 + 0.243635i
\(677\) 1.16835e7 2.02364e7i 0.979720 1.69692i 0.316333 0.948648i \(-0.397548\pi\)
0.663387 0.748276i \(-0.269118\pi\)
\(678\) 0 0
\(679\) −6.70300e6 + 1.89532e7i −0.557949 + 1.57764i
\(680\) −5.87740e6 −0.487431
\(681\) 0 0
\(682\) −3.98721e6 6.90606e6i −0.328253 0.568551i
\(683\) −6.67445e6 1.15605e7i −0.547474 0.948253i −0.998447 0.0557153i \(-0.982256\pi\)
0.450972 0.892538i \(-0.351077\pi\)
\(684\) 0 0
\(685\) −4.11229e6 −0.334856
\(686\) −291894. 1.06497e7i −0.0236818 0.864029i
\(687\) 0 0
\(688\) −5.10838e6 + 8.84797e6i −0.411445 + 0.712644i
\(689\) −47475.1 82229.2i −0.00380993 0.00659900i
\(690\) 0 0
\(691\) −6.57343e6 + 1.13855e7i −0.523717 + 0.907105i 0.475901 + 0.879499i \(0.342122\pi\)
−0.999619 + 0.0276066i \(0.991211\pi\)
\(692\) 2.10928e6 0.167444
\(693\) 0 0
\(694\) −7.24137e6 −0.570718
\(695\) −8.59271e6 + 1.48830e7i −0.674789 + 1.16877i
\(696\) 0 0
\(697\) −6.27377e6 1.08665e7i −0.489155 0.847242i
\(698\) 3.14501e6 5.44732e6i 0.244334 0.423199i
\(699\) 0 0
\(700\) 884421. + 1.03467e6i 0.0682204 + 0.0798100i
\(701\) −7.87304e6 −0.605128 −0.302564 0.953129i \(-0.597843\pi\)
−0.302564 + 0.953129i \(0.597843\pi\)
\(702\) 0 0
\(703\) 253758. + 439522.i 0.0193657 + 0.0335423i
\(704\) −1.29143e7 2.23683e7i −0.982065 1.70099i
\(705\) 0 0
\(706\) 1.10075e7 0.831144
\(707\) 1.42657e7 2.65000e6i 1.07336 0.199387i
\(708\) 0 0
\(709\) 7.47288e6 1.29434e7i 0.558306 0.967014i −0.439332 0.898325i \(-0.644785\pi\)
0.997638 0.0686895i \(-0.0218818\pi\)
\(710\) 2.62441e6 + 4.54561e6i 0.195383 + 0.338413i
\(711\) 0 0
\(712\) 3.15333e6 5.46172e6i 0.233114 0.403766i
\(713\) −2.40019e6 −0.176816
\(714\) 0 0
\(715\) −2.69144e7 −1.96888
\(716\) −2.15837e6 + 3.73840e6i −0.157341 + 0.272523i
\(717\) 0 0
\(718\) 1.77456e6 + 3.07363e6i 0.128464 + 0.222506i
\(719\) −177912. + 308153.i −0.0128347 + 0.0222303i −0.872371 0.488844i \(-0.837419\pi\)
0.859537 + 0.511074i \(0.170752\pi\)
\(720\) 0 0
\(721\) −5.11178e6 5.98020e6i −0.366214 0.428428i
\(722\) −4.39487e6 −0.313764
\(723\) 0 0
\(724\) 751795. + 1.30215e6i 0.0533032 + 0.0923238i
\(725\) 3.99009e6 + 6.91103e6i 0.281927 + 0.488312i
\(726\) 0 0
\(727\) −1.16451e7 −0.817160 −0.408580 0.912722i \(-0.633976\pi\)
−0.408580 + 0.912722i \(0.633976\pi\)
\(728\) −7.50447e6 + 2.12194e7i −0.524797 + 1.48390i
\(729\) 0 0
\(730\) 990272. 1.71520e6i 0.0687776 0.119126i
\(731\) −5.12130e6 8.87036e6i −0.354476 0.613971i
\(732\) 0 0
\(733\) −7.84459e6 + 1.35872e7i −0.539275 + 0.934052i 0.459668 + 0.888091i \(0.347968\pi\)
−0.998943 + 0.0459613i \(0.985365\pi\)
\(734\) 1.67595e7 1.14821
\(735\) 0 0
\(736\) −2.98437e6 −0.203076
\(737\) 2.37125e6 4.10712e6i 0.160808 0.278528i
\(738\) 0 0
\(739\) −7.48534e6 1.29650e7i −0.504197 0.873295i −0.999988 0.00485312i \(-0.998455\pi\)
0.495791 0.868442i \(-0.334878\pi\)
\(740\) −69903.1 + 121076.i −0.00469264 + 0.00812789i
\(741\) 0 0
\(742\) 22659.6 64071.8i 0.00151093 0.00427225i
\(743\) −1.51503e7 −1.00682 −0.503408 0.864049i \(-0.667921\pi\)
−0.503408 + 0.864049i \(0.667921\pi\)
\(744\) 0 0
\(745\) −1.60955e6 2.78783e6i −0.106247 0.184025i
\(746\) 2.67223e6 + 4.62844e6i 0.175803 + 0.304500i
\(747\) 0 0
\(748\) 4.03457e6 0.263660
\(749\) 9.47929e6 + 1.10897e7i 0.617406 + 0.722294i
\(750\) 0 0
\(751\) −1.06857e7 + 1.85082e7i −0.691359 + 1.19747i 0.280034 + 0.959990i \(0.409654\pi\)
−0.971393 + 0.237478i \(0.923679\pi\)
\(752\) −7.39325e6 1.28055e7i −0.476750 0.825756i
\(753\) 0 0
\(754\) −1.33175e7 + 2.30666e7i −0.853089 + 1.47759i
\(755\) 2.09731e7 1.33905
\(756\) 0 0
\(757\) −1.74578e7 −1.10726 −0.553632 0.832762i \(-0.686758\pi\)
−0.553632 + 0.832762i \(0.686758\pi\)
\(758\) 7.15286e6 1.23891e7i 0.452175 0.783190i
\(759\) 0 0
\(760\) 5.26251e6 + 9.11494e6i 0.330491 + 0.572426i
\(761\) −6.12587e6 + 1.06103e7i −0.383448 + 0.664151i −0.991553 0.129706i \(-0.958597\pi\)
0.608105 + 0.793857i \(0.291930\pi\)
\(762\) 0 0
\(763\) 971682. 180500.i 0.0604245 0.0112245i
\(764\) −5.73633e6 −0.355550
\(765\) 0 0
\(766\) 254090. + 440097.i 0.0156465 + 0.0271004i
\(767\) 1.97046e7 + 3.41293e7i 1.20942 + 2.09479i
\(768\) 0 0
\(769\) 7.26941e6 0.443285 0.221643 0.975128i \(-0.428858\pi\)
0.221643 + 0.975128i \(0.428858\pi\)
\(770\) −1.25169e7 1.46434e7i −0.760801 0.890050i
\(771\) 0 0
\(772\) −2.92751e6 + 5.07060e6i −0.176789 + 0.306208i
\(773\) −1.01072e6 1.75062e6i −0.0608389 0.105376i 0.834002 0.551762i \(-0.186044\pi\)
−0.894841 + 0.446386i \(0.852711\pi\)
\(774\) 0 0
\(775\) 1.48827e6 2.57777e6i 0.0890080 0.154166i
\(776\) 3.03990e7 1.81219
\(777\) 0 0
\(778\) 845550. 0.0500830
\(779\) −1.12348e7 + 1.94593e7i −0.663320 + 1.14890i
\(780\) 0 0
\(781\) −8.92525e6 1.54590e7i −0.523592 0.906887i
\(782\) −1.79374e6 + 3.10684e6i −0.104892 + 0.181678i
\(783\) 0 0
\(784\) −1.09729e7 + 4.22237e6i −0.637577 + 0.245339i
\(785\) 1.97086e7 1.14151
\(786\) 0 0
\(787\) 6.05566e6 + 1.04887e7i 0.348517 + 0.603650i 0.985986 0.166826i \(-0.0533519\pi\)
−0.637469 + 0.770476i \(0.720019\pi\)
\(788\) 596074. + 1.03243e6i 0.0341967 + 0.0592305i
\(789\) 0 0
\(790\) 5.53428e6 0.315495
\(791\) 1.79380e6 5.07211e6i 0.101937 0.288235i
\(792\) 0 0
\(793\) 1.02787e7 1.78032e7i 0.580437 1.00535i
\(794\) −6.35553e6 1.10081e7i −0.357767 0.619671i
\(795\) 0 0
\(796\) 5749.71 9958.79i 0.000321635 0.000557088i
\(797\) −2.45062e7 −1.36657 −0.683283 0.730154i \(-0.739448\pi\)
−0.683283 + 0.730154i \(0.739448\pi\)
\(798\) 0 0
\(799\) 1.48239e7 0.821479
\(800\) 1.85050e6 3.20516e6i 0.102227 0.177062i
\(801\) 0 0
\(802\) −8.43470e6 1.46093e7i −0.463056 0.802037i
\(803\) −3.36777e6 + 5.83316e6i −0.184312 + 0.319238i
\(804\) 0 0
\(805\) −5.70068e6 + 1.05896e6i −0.310054 + 0.0575957i
\(806\) 9.93468e6 0.538662
\(807\) 0 0
\(808\) −1.09702e7 1.90010e7i −0.591135 1.02388i
\(809\) −2.99377e6 5.18536e6i −0.160823 0.278553i 0.774341 0.632768i \(-0.218081\pi\)
−0.935164 + 0.354215i \(0.884748\pi\)
\(810\) 0 0
\(811\) 1.57094e7 0.838699 0.419350 0.907825i \(-0.362258\pi\)
0.419350 + 0.907825i \(0.362258\pi\)
\(812\) 6.34459e6 1.17857e6i 0.337687 0.0627288i
\(813\) 0 0
\(814\) −702311. + 1.21644e6i −0.0371508 + 0.0643471i
\(815\) −1.02268e7 1.77134e7i −0.539321 0.934131i
\(816\) 0 0
\(817\) −9.17104e6 + 1.58847e7i −0.480688 + 0.832576i
\(818\) −7.05435e6 −0.368615
\(819\) 0 0
\(820\) −6.18974e6 −0.321468
\(821\) −55578.8 + 96265.3i −0.00287774 + 0.00498439i −0.867461 0.497506i \(-0.834249\pi\)
0.864583 + 0.502490i \(0.167583\pi\)
\(822\) 0 0
\(823\) −1.71946e6 2.97820e6i −0.0884898 0.153269i 0.818383 0.574673i \(-0.194871\pi\)
−0.906873 + 0.421404i \(0.861537\pi\)
\(824\) −5.94807e6 + 1.03024e7i −0.305182 + 0.528590i
\(825\) 0 0
\(826\) −9.40491e6 + 2.65931e7i −0.479628 + 1.35618i
\(827\) −1.87782e7 −0.954751 −0.477375 0.878700i \(-0.658412\pi\)
−0.477375 + 0.878700i \(0.658412\pi\)
\(828\) 0 0
\(829\) −3.76889e6 6.52791e6i −0.190470 0.329904i 0.754936 0.655799i \(-0.227668\pi\)
−0.945406 + 0.325894i \(0.894335\pi\)
\(830\) −783234. 1.35660e6i −0.0394636 0.0683529i
\(831\) 0 0
\(832\) 3.21778e7 1.61156
\(833\) 1.83442e6 1.16434e7i 0.0915978 0.581391i
\(834\) 0 0
\(835\) 1.06631e7 1.84690e7i 0.529256 0.916698i
\(836\) −3.61248e6 6.25700e6i −0.178768 0.309635i
\(837\) 0 0
\(838\) 1.24692e7 2.15973e7i 0.613380 1.06241i
\(839\) 1.65147e7 0.809962 0.404981 0.914325i \(-0.367278\pi\)
0.404981 + 0.914325i \(0.367278\pi\)
\(840\) 0 0
\(841\) 1.73222e7 0.844527
\(842\) −1.24253e7 + 2.15212e7i −0.603984 + 1.04613i
\(843\) 0 0
\(844\) −122587. 212328.i −0.00592365 0.0102601i
\(845\) 8.82873e6 1.52918e7i 0.425360 0.736745i
\(846\) 0 0
\(847\) 2.90021e7 + 3.39291e7i 1.38906 + 1.62504i
\(848\) −75000.3 −0.00358157
\(849\) 0 0
\(850\) −2.22446e6 3.85288e6i −0.105603 0.182911i
\(851\) 211386. + 366131.i 0.0100058 + 0.0173306i
\(852\) 0 0
\(853\) 2.36772e7 1.11418 0.557092 0.830451i \(-0.311917\pi\)
0.557092 + 0.830451i \(0.311917\pi\)
\(854\) 1.44665e7 2.68730e6i 0.678764 0.126088i
\(855\) 0 0
\(856\) 1.10301e7 1.91047e7i 0.514511 0.891160i
\(857\) 148276. + 256821.i 0.00689633 + 0.0119448i 0.869453 0.494016i \(-0.164471\pi\)
−0.862557 + 0.505961i \(0.831138\pi\)
\(858\) 0 0
\(859\) −6.06474e6 + 1.05044e7i −0.280433 + 0.485725i −0.971491 0.237074i \(-0.923811\pi\)
0.691058 + 0.722799i \(0.257145\pi\)
\(860\) −5.05271e6 −0.232958
\(861\) 0 0
\(862\) 1.20987e7 0.554586
\(863\) −6.50899e6 + 1.12739e7i −0.297500 + 0.515285i −0.975563 0.219718i \(-0.929486\pi\)
0.678063 + 0.735003i \(0.262819\pi\)
\(864\) 0 0
\(865\) −5.57130e6 9.64978e6i −0.253172 0.438508i
\(866\) 811543. 1.40563e6i 0.0367720 0.0636909i
\(867\) 0 0
\(868\) −1.56395e6 1.82964e6i −0.0704569 0.0824264i
\(869\) −1.88213e7 −0.845473
\(870\) 0 0
\(871\) 2.95414e6 + 5.11672e6i 0.131943 + 0.228532i
\(872\) −747216. 1.29422e6i −0.0332778 0.0576389i
\(873\) 0 0
\(874\) 6.42431e6 0.284478
\(875\) 8.17220e6 2.31075e7i 0.360844 1.02031i
\(876\) 0 0
\(877\) 1.04463e6 1.80935e6i 0.0458630 0.0794371i −0.842183 0.539192i \(-0.818730\pi\)
0.888046 + 0.459755i \(0.152063\pi\)
\(878\) 1.00533e7 + 1.74129e7i 0.440123 + 0.762315i
\(879\) 0 0
\(880\) −1.06297e7 + 1.84112e7i −0.462717 + 0.801449i
\(881\) 2.84897e6 0.123665 0.0618327 0.998087i \(-0.480305\pi\)
0.0618327 + 0.998087i \(0.480305\pi\)
\(882\) 0 0
\(883\) −1.75998e7 −0.759636 −0.379818 0.925061i \(-0.624013\pi\)
−0.379818 + 0.925061i \(0.624013\pi\)
\(884\) −2.51317e6 + 4.35294e6i −0.108166 + 0.187349i
\(885\) 0 0
\(886\) −1.43104e7 2.47863e7i −0.612444 1.06078i
\(887\) 1.18659e7 2.05523e7i 0.506397 0.877106i −0.493575 0.869703i \(-0.664310\pi\)
0.999973 0.00740294i \(-0.00235645\pi\)
\(888\) 0 0
\(889\) 4.09764e6 1.15864e7i 0.173892 0.491692i
\(890\) −6.72473e6 −0.284577
\(891\) 0 0
\(892\) −598304. 1.03629e6i −0.0251773 0.0436084i
\(893\) −1.32731e7 2.29896e7i −0.556984 0.964724i
\(894\) 0 0
\(895\) 2.28038e7 0.951591
\(896\) 7.27537e6 + 8.51134e6i 0.302751 + 0.354183i
\(897\) 0 0
\(898\) 9.44893e6 1.63660e7i 0.391013 0.677255i
\(899\) −7.05579e6 1.22210e7i −0.291170 0.504321i
\(900\) 0 0
\(901\) 37595.1 65116.6i 0.00154283 0.00267227i
\(902\) −6.21878e7 −2.54501
\(903\) 0 0
\(904\) −8.13513e6 −0.331088
\(905\) 3.97148e6 6.87880e6i 0.161187 0.279184i
\(906\) 0 0
\(907\) 1.23813e7 + 2.14450e7i 0.499744 + 0.865583i 1.00000 0.000295096i \(-9.39319e-5\pi\)
−0.500256 + 0.865878i \(0.666761\pi\)
\(908\) 3.29144e6 5.70095e6i 0.132486 0.229473i
\(909\) 0 0
\(910\) 2.35958e7 4.38316e6i 0.944562 0.175462i
\(911\) 1.67991e7 0.670639 0.335320 0.942104i \(-0.391156\pi\)
0.335320 + 0.942104i \(0.391156\pi\)
\(912\) 0 0
\(913\) 2.66367e6 + 4.61361e6i 0.105756 + 0.183174i
\(914\) 1.31784e7 + 2.28256e7i 0.521791 + 0.903768i
\(915\) 0 0
\(916\) −1.03762e7 −0.408602
\(917\) 1.77817e7 + 2.08026e7i 0.698314 + 0.816947i
\(918\) 0 0
\(919\) −7.08247e6 + 1.22672e7i −0.276628 + 0.479133i −0.970545 0.240922i \(-0.922550\pi\)
0.693917 + 0.720055i \(0.255884\pi\)
\(920\) 4.38378e6 + 7.59293e6i 0.170757 + 0.295760i
\(921\) 0 0
\(922\) −2.87087e6 + 4.97249e6i −0.111221 + 0.192640i
\(923\) 2.22384e7 0.859212
\(924\) 0 0
\(925\) −524292. −0.0201474
\(926\) −9.86955e6 + 1.70946e7i −0.378242 + 0.655134i
\(927\) 0 0
\(928\) −8.77308e6 1.51954e7i −0.334412 0.579219i
\(929\) −1.47777e7 + 2.55957e7i −0.561781 + 0.973033i 0.435560 + 0.900160i \(0.356550\pi\)
−0.997341 + 0.0728736i \(0.976783\pi\)
\(930\) 0 0
\(931\) −1.96996e7 + 7.58040e6i −0.744876 + 0.286628i
\(932\) 1.00000e7 0.377104
\(933\) 0 0
\(934\) −3.51336e6 6.08532e6i −0.131782 0.228253i
\(935\) −1.06566e7 1.84578e7i −0.398649 0.690481i
\(936\) 0 0
\(937\) 3.20477e7 1.19247 0.596235 0.802810i \(-0.296663\pi\)
0.596235 + 0.802810i \(0.296663\pi\)
\(938\) −1.41000e6 + 3.98687e6i −0.0523253 + 0.147953i
\(939\) 0 0
\(940\) 3.65634e6 6.33298e6i 0.134967 0.233770i
\(941\) 1.84473e7 + 3.19517e7i 0.679141 + 1.17631i 0.975240 + 0.221149i \(0.0709806\pi\)
−0.296100 + 0.955157i \(0.595686\pi\)
\(942\) 0 0
\(943\) −9.35885e6 + 1.62100e7i −0.342723 + 0.593613i
\(944\) 3.11290e7 1.13693
\(945\) 0 0
\(946\) −5.07642e7 −1.84429
\(947\) 7.28703e6 1.26215e7i 0.264044 0.457337i −0.703269 0.710924i \(-0.748277\pi\)
0.967313 + 0.253587i \(0.0816104\pi\)
\(948\) 0 0
\(949\) −4.19563e6 7.26704e6i −0.151228 0.261934i
\(950\) −3.98349e6 + 6.89960e6i −0.143204 + 0.248036i
\(951\) 0 0
\(952\) −1.75236e7 + 3.25519e6i −0.626658 + 0.116408i
\(953\) 2.34882e7 0.837757 0.418878 0.908042i \(-0.362423\pi\)
0.418878 + 0.908042i \(0.362423\pi\)
\(954\) 0 0
\(955\) 1.51515e7 + 2.62432e7i 0.537586 + 0.931126i
\(956\) 3.53744e6 + 6.12702e6i 0.125183 + 0.216823i
\(957\) 0 0
\(958\) −1.15988e7 −0.408317
\(959\) −1.22609e7 + 2.27759e6i −0.430503 + 0.0799703i
\(960\) 0 0
\(961\) 1.16828e7 2.02352e7i 0.408074 0.706805i
\(962\) −874950. 1.51546e6i −0.0304822 0.0527967i
\(963\) 0 0
\(964\) −3.96380e6 + 6.86550e6i −0.137378 + 0.237947i
\(965\) 3.09301e7 1.06921
\(966\) 0 0
\(967\) −2.25237e7 −0.774593 −0.387296 0.921955i \(-0.626591\pi\)
−0.387296 + 0.921955i \(0.626591\pi\)
\(968\) 3.37468e7 5.84512e7i 1.15756 2.00496i
\(969\) 0 0
\(970\) −1.62071e7 2.80715e7i −0.553064 0.957935i
\(971\) −2.65863e7 + 4.60488e7i −0.904920 + 1.56737i −0.0838945 + 0.996475i \(0.526736\pi\)
−0.821025 + 0.570892i \(0.806597\pi\)
\(972\) 0 0
\(973\) −1.73764e7 + 4.91331e7i −0.588408 + 1.66377i
\(974\) 3.27142e6 0.110494
\(975\) 0 0
\(976\) −8.11906e6 1.40626e7i −0.272823 0.472544i
\(977\) −1.41109e7 2.44408e7i −0.472953 0.819178i 0.526568 0.850133i \(-0.323478\pi\)
−0.999521 + 0.0309550i \(0.990145\pi\)
\(978\) 0 0
\(979\) 2.28699e7 0.762618
\(980\) −4.52176e6 3.65555e6i −0.150398 0.121587i
\(981\) 0 0
\(982\) −2.34241e7 + 4.05717e7i −0.775147 + 1.34259i
\(983\) −8.58072e6 1.48622e7i −0.283230 0.490570i 0.688948 0.724811i \(-0.258073\pi\)
−0.972179 + 0.234241i \(0.924739\pi\)
\(984\) 0 0
\(985\) 3.14885e6 5.45397e6i 0.103410 0.179111i
\(986\) −2.10920e7 −0.690917
\(987\) 0 0
\(988\) 9.00097e6 0.293357
\(989\) −7.63966e6 + 1.32323e7i −0.248361 + 0.430174i
\(990\) 0 0
\(991\) −1.52871e7 2.64780e7i −0.494471 0.856448i 0.505509 0.862821i \(-0.331305\pi\)
−0.999980 + 0.00637296i \(0.997971\pi\)
\(992\) −3.27230e6 + 5.66779e6i −0.105578 + 0.182867i
\(993\) 0 0
\(994\) 1.03423e7 + 1.20993e7i 0.332011 + 0.388414i
\(995\) −60747.5 −0.00194523
\(996\) 0 0
\(997\) −2.37741e7 4.11779e7i −0.757470 1.31198i −0.944137 0.329553i \(-0.893102\pi\)
0.186667 0.982423i \(-0.440232\pi\)
\(998\) 5.32481e6 + 9.22284e6i 0.169230 + 0.293115i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 63.6.e.f.37.3 12
3.2 odd 2 inner 63.6.e.f.37.4 yes 12
7.2 even 3 441.6.a.bc.1.4 6
7.4 even 3 inner 63.6.e.f.46.3 yes 12
7.5 odd 6 441.6.a.bd.1.4 6
21.2 odd 6 441.6.a.bc.1.3 6
21.5 even 6 441.6.a.bd.1.3 6
21.11 odd 6 inner 63.6.e.f.46.4 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.6.e.f.37.3 12 1.1 even 1 trivial
63.6.e.f.37.4 yes 12 3.2 odd 2 inner
63.6.e.f.46.3 yes 12 7.4 even 3 inner
63.6.e.f.46.4 yes 12 21.11 odd 6 inner
441.6.a.bc.1.3 6 21.2 odd 6
441.6.a.bc.1.4 6 7.2 even 3
441.6.a.bd.1.3 6 21.5 even 6
441.6.a.bd.1.4 6 7.5 odd 6