Properties

Label 688.2.bg.c.17.1
Level $688$
Weight $2$
Character 688.17
Analytic conductor $5.494$
Analytic rank $0$
Dimension $36$
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] = [688,2,Mod(17,688)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(688, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 0, 38]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("688.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 688 = 2^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 688.bg (of order \(21\), degree \(12\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.49370765906\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(3\) over \(\Q(\zeta_{21})\)
Twist minimal: no (minimal twist has level 43)
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 17.1
Character \(\chi\) \(=\) 688.17
Dual form 688.2.bg.c.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28860 + 0.397480i) q^{3} +(-1.48781 + 3.79089i) q^{5} +(-1.38920 + 2.40617i) q^{7} +(-0.976224 + 0.665578i) q^{9} +O(q^{10})\) \(q+(-1.28860 + 0.397480i) q^{3} +(-1.48781 + 3.79089i) q^{5} +(-1.38920 + 2.40617i) q^{7} +(-0.976224 + 0.665578i) q^{9} +(0.678323 + 0.326663i) q^{11} +(1.70167 - 0.256486i) q^{13} +(0.410392 - 5.47630i) q^{15} +(-1.18750 - 3.02571i) q^{17} +(0.0395049 + 0.0269340i) q^{19} +(0.833720 - 3.65277i) q^{21} +(-0.152371 - 2.03326i) q^{23} +(-8.49199 - 7.87942i) q^{25} +(3.51575 - 4.40861i) q^{27} +(0.714324 + 0.220340i) q^{29} +(-2.52247 + 2.34051i) q^{31} +(-1.00393 - 0.151318i) q^{33} +(-7.05465 - 8.84626i) q^{35} +(3.91502 + 6.78101i) q^{37} +(-2.09082 + 1.00689i) q^{39} +(-1.86928 - 8.18985i) q^{41} +(4.39142 + 4.86985i) q^{43} +(-1.07069 - 4.69101i) q^{45} +(-7.05780 + 3.39886i) q^{47} +(-0.359777 - 0.623151i) q^{49} +(2.73287 + 3.42691i) q^{51} +(-1.76849 - 0.266557i) q^{53} +(-2.24756 + 2.08543i) q^{55} +(-0.0616116 - 0.0190047i) q^{57} +(-3.60798 + 4.52427i) q^{59} +(2.15836 + 2.00266i) q^{61} +(-0.245321 - 3.27359i) q^{63} +(-1.55946 + 6.83245i) q^{65} +(-4.62708 - 3.15469i) q^{67} +(1.00452 + 2.55948i) q^{69} +(0.543672 - 7.25480i) q^{71} +(-10.0746 + 1.51850i) q^{73} +(14.0747 + 6.77800i) q^{75} +(-1.72834 + 1.17836i) q^{77} +(6.70519 - 11.6137i) q^{79} +(-1.48307 + 3.77880i) q^{81} +(-5.42706 + 1.67402i) q^{83} +13.2369 q^{85} -1.00806 q^{87} +(-11.7786 + 3.63323i) q^{89} +(-1.74682 + 4.45083i) q^{91} +(2.32015 - 4.01861i) q^{93} +(-0.160880 + 0.109686i) q^{95} +(9.41101 + 4.53210i) q^{97} +(-0.879615 + 0.132581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 16 q^{3} - 17 q^{5} - 6 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 16 q^{3} - 17 q^{5} - 6 q^{7} - q^{9} + 4 q^{11} + 3 q^{15} - 10 q^{17} - 10 q^{19} - 21 q^{21} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 9 q^{29} - 40 q^{31} - 11 q^{33} - 11 q^{35} - 19 q^{37} + q^{39} - 28 q^{41} + 8 q^{43} - 46 q^{45} + 30 q^{47} + 6 q^{49} - 57 q^{51} - 24 q^{53} - 14 q^{55} + 52 q^{57} + q^{59} - 14 q^{61} - 47 q^{63} + 38 q^{65} - 66 q^{67} - 7 q^{69} + 33 q^{71} + 29 q^{73} + 55 q^{75} - 27 q^{77} + 17 q^{79} + 38 q^{81} + 23 q^{83} - 56 q^{85} + 86 q^{87} - 19 q^{89} + 13 q^{91} - 30 q^{93} - q^{95} - 31 q^{97} + 31 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).

\(n\) \(431\) \(433\) \(517\)
\(\chi(n)\) \(1\) \(e\left(\frac{19}{21}\right)\) \(1\)

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
\(3\) −1.28860 + 0.397480i −0.743972 + 0.229485i −0.643491 0.765454i \(-0.722514\pi\)
−0.100481 + 0.994939i \(0.532038\pi\)
\(4\) 0 0
\(5\) −1.48781 + 3.79089i −0.665371 + 1.69534i 0.0520012 + 0.998647i \(0.483440\pi\)
−0.717372 + 0.696690i \(0.754655\pi\)
\(6\) 0 0
\(7\) −1.38920 + 2.40617i −0.525070 + 0.909448i 0.474504 + 0.880253i \(0.342627\pi\)
−0.999574 + 0.0291942i \(0.990706\pi\)
\(8\) 0 0
\(9\) −0.976224 + 0.665578i −0.325408 + 0.221859i
\(10\) 0 0
\(11\) 0.678323 + 0.326663i 0.204522 + 0.0984926i 0.533341 0.845900i \(-0.320936\pi\)
−0.328819 + 0.944393i \(0.606651\pi\)
\(12\) 0 0
\(13\) 1.70167 0.256486i 0.471959 0.0711364i 0.0912435 0.995829i \(-0.470916\pi\)
0.380715 + 0.924692i \(0.375678\pi\)
\(14\) 0 0
\(15\) 0.410392 5.47630i 0.105963 1.41398i
\(16\) 0 0
\(17\) −1.18750 3.02571i −0.288012 0.733842i −0.999514 0.0311584i \(-0.990080\pi\)
0.711503 0.702683i \(-0.248015\pi\)
\(18\) 0 0
\(19\) 0.0395049 + 0.0269340i 0.00906304 + 0.00617908i 0.567843 0.823137i \(-0.307778\pi\)
−0.558780 + 0.829316i \(0.688730\pi\)
\(20\) 0 0
\(21\) 0.833720 3.65277i 0.181933 0.797099i
\(22\) 0 0
\(23\) −0.152371 2.03326i −0.0317717 0.423963i −0.990298 0.138960i \(-0.955624\pi\)
0.958526 0.285004i \(-0.0919948\pi\)
\(24\) 0 0
\(25\) −8.49199 7.87942i −1.69840 1.57588i
\(26\) 0 0
\(27\) 3.51575 4.40861i 0.676606 0.848437i
\(28\) 0 0
\(29\) 0.714324 + 0.220340i 0.132647 + 0.0409161i 0.360368 0.932810i \(-0.382651\pi\)
−0.227721 + 0.973726i \(0.573127\pi\)
\(30\) 0 0
\(31\) −2.52247 + 2.34051i −0.453050 + 0.420369i −0.873408 0.486990i \(-0.838095\pi\)
0.420358 + 0.907358i \(0.361904\pi\)
\(32\) 0 0
\(33\) −1.00393 0.151318i −0.174761 0.0263410i
\(34\) 0 0
\(35\) −7.05465 8.84626i −1.19245 1.49529i
\(36\) 0 0
\(37\) 3.91502 + 6.78101i 0.643625 + 1.11479i 0.984617 + 0.174725i \(0.0559037\pi\)
−0.340992 + 0.940066i \(0.610763\pi\)
\(38\) 0 0
\(39\) −2.09082 + 1.00689i −0.334799 + 0.161231i
\(40\) 0 0
\(41\) −1.86928 8.18985i −0.291932 1.27904i −0.881832 0.471563i \(-0.843690\pi\)
0.589900 0.807476i \(-0.299167\pi\)
\(42\) 0 0
\(43\) 4.39142 + 4.86985i 0.669685 + 0.742645i
\(44\) 0 0
\(45\) −1.07069 4.69101i −0.159610 0.699295i
\(46\) 0 0
\(47\) −7.05780 + 3.39886i −1.02949 + 0.495775i −0.870843 0.491561i \(-0.836426\pi\)
−0.158644 + 0.987336i \(0.550712\pi\)
\(48\) 0 0
\(49\) −0.359777 0.623151i −0.0513966 0.0890216i
\(50\) 0 0
\(51\) 2.73287 + 3.42691i 0.382678 + 0.479863i
\(52\) 0 0
\(53\) −1.76849 0.266557i −0.242920 0.0366144i 0.0264535 0.999650i \(-0.491579\pi\)
−0.269374 + 0.963036i \(0.586817\pi\)
\(54\) 0 0
\(55\) −2.24756 + 2.08543i −0.303061 + 0.281200i
\(56\) 0 0
\(57\) −0.0616116 0.0190047i −0.00816065 0.00251723i
\(58\) 0 0
\(59\) −3.60798 + 4.52427i −0.469719 + 0.589009i −0.959102 0.283060i \(-0.908651\pi\)
0.489383 + 0.872069i \(0.337222\pi\)
\(60\) 0 0
\(61\) 2.15836 + 2.00266i 0.276349 + 0.256415i 0.806155 0.591704i \(-0.201545\pi\)
−0.529806 + 0.848119i \(0.677735\pi\)
\(62\) 0 0
\(63\) −0.245321 3.27359i −0.0309076 0.412433i
\(64\) 0 0
\(65\) −1.55946 + 6.83245i −0.193428 + 0.847462i
\(66\) 0 0
\(67\) −4.62708 3.15469i −0.565288 0.385407i 0.246691 0.969094i \(-0.420657\pi\)
−0.811978 + 0.583688i \(0.801609\pi\)
\(68\) 0 0
\(69\) 1.00452 + 2.55948i 0.120930 + 0.308126i
\(70\) 0 0
\(71\) 0.543672 7.25480i 0.0645220 0.860987i −0.867234 0.497901i \(-0.834104\pi\)
0.931756 0.363086i \(-0.118277\pi\)
\(72\) 0 0
\(73\) −10.0746 + 1.51850i −1.17914 + 0.177727i −0.709224 0.704983i \(-0.750955\pi\)
−0.469918 + 0.882710i \(0.655716\pi\)
\(74\) 0 0
\(75\) 14.0747 + 6.77800i 1.62520 + 0.782656i
\(76\) 0 0
\(77\) −1.72834 + 1.17836i −0.196962 + 0.134287i
\(78\) 0 0
\(79\) 6.70519 11.6137i 0.754393 1.30665i −0.191283 0.981535i \(-0.561265\pi\)
0.945676 0.325112i \(-0.105402\pi\)
\(80\) 0 0
\(81\) −1.48307 + 3.77880i −0.164785 + 0.419866i
\(82\) 0 0
\(83\) −5.42706 + 1.67402i −0.595697 + 0.183748i −0.577919 0.816094i \(-0.696135\pi\)
−0.0177773 + 0.999842i \(0.505659\pi\)
\(84\) 0 0
\(85\) 13.2369 1.43574
\(86\) 0 0
\(87\) −1.00806 −0.108075
\(88\) 0 0
\(89\) −11.7786 + 3.63323i −1.24853 + 0.385121i −0.847428 0.530911i \(-0.821850\pi\)
−0.401105 + 0.916032i \(0.631374\pi\)
\(90\) 0 0
\(91\) −1.74682 + 4.45083i −0.183117 + 0.466573i
\(92\) 0 0
\(93\) 2.32015 4.01861i 0.240588 0.416710i
\(94\) 0 0
\(95\) −0.160880 + 0.109686i −0.0165059 + 0.0112535i
\(96\) 0 0
\(97\) 9.41101 + 4.53210i 0.955543 + 0.460165i 0.845626 0.533775i \(-0.179227\pi\)
0.109917 + 0.993941i \(0.464941\pi\)
\(98\) 0 0
\(99\) −0.879615 + 0.132581i −0.0884046 + 0.0133249i
\(100\) 0 0
\(101\) 0.171298 2.28582i 0.0170448 0.227447i −0.982175 0.187966i \(-0.939810\pi\)
0.999220 0.0394811i \(-0.0125705\pi\)
\(102\) 0 0
\(103\) 1.94001 + 4.94307i 0.191155 + 0.487056i 0.994032 0.109090i \(-0.0347935\pi\)
−0.802877 + 0.596145i \(0.796698\pi\)
\(104\) 0 0
\(105\) 12.6068 + 8.59518i 1.23030 + 0.838804i
\(106\) 0 0
\(107\) −0.800089 + 3.50542i −0.0773475 + 0.338882i −0.998765 0.0496936i \(-0.984176\pi\)
0.921417 + 0.388575i \(0.127033\pi\)
\(108\) 0 0
\(109\) 0.415847 + 5.54910i 0.0398310 + 0.531507i 0.981056 + 0.193726i \(0.0620573\pi\)
−0.941225 + 0.337781i \(0.890324\pi\)
\(110\) 0 0
\(111\) −7.74019 7.18185i −0.734667 0.681671i
\(112\) 0 0
\(113\) 0.0874119 0.109611i 0.00822302 0.0103113i −0.777703 0.628632i \(-0.783615\pi\)
0.785926 + 0.618321i \(0.212187\pi\)
\(114\) 0 0
\(115\) 7.93455 + 2.44748i 0.739901 + 0.228229i
\(116\) 0 0
\(117\) −1.49050 + 1.38298i −0.137797 + 0.127857i
\(118\) 0 0
\(119\) 8.93005 + 1.34599i 0.818617 + 0.123387i
\(120\) 0 0
\(121\) −6.50497 8.15698i −0.591361 0.741544i
\(122\) 0 0
\(123\) 5.66405 + 9.81041i 0.510710 + 0.884575i
\(124\) 0 0
\(125\) 24.1590 11.6344i 2.16084 1.04061i
\(126\) 0 0
\(127\) 0.384858 + 1.68617i 0.0341507 + 0.149624i 0.989129 0.147053i \(-0.0469788\pi\)
−0.954978 + 0.296677i \(0.904122\pi\)
\(128\) 0 0
\(129\) −7.59444 4.52977i −0.668653 0.398824i
\(130\) 0 0
\(131\) −4.87229 21.3469i −0.425694 1.86509i −0.497180 0.867647i \(-0.665631\pi\)
0.0714858 0.997442i \(-0.477226\pi\)
\(132\) 0 0
\(133\) −0.119688 + 0.0576388i −0.0103783 + 0.00499791i
\(134\) 0 0
\(135\) 11.4818 + 19.8870i 0.988193 + 1.71160i
\(136\) 0 0
\(137\) 13.3197 + 16.7024i 1.13798 + 1.42698i 0.888665 + 0.458557i \(0.151634\pi\)
0.249314 + 0.968423i \(0.419795\pi\)
\(138\) 0 0
\(139\) 12.0494 + 1.81616i 1.02202 + 0.154044i 0.638606 0.769534i \(-0.279511\pi\)
0.383411 + 0.923578i \(0.374749\pi\)
\(140\) 0 0
\(141\) 7.74369 7.18509i 0.652136 0.605094i
\(142\) 0 0
\(143\) 1.23807 + 0.381893i 0.103532 + 0.0319355i
\(144\) 0 0
\(145\) −1.89807 + 2.38010i −0.157626 + 0.197656i
\(146\) 0 0
\(147\) 0.711297 + 0.659987i 0.0586668 + 0.0544348i
\(148\) 0 0
\(149\) −0.617820 8.24424i −0.0506138 0.675395i −0.963590 0.267383i \(-0.913841\pi\)
0.912977 0.408012i \(-0.133778\pi\)
\(150\) 0 0
\(151\) −1.01707 + 4.45608i −0.0827681 + 0.362631i −0.999303 0.0373233i \(-0.988117\pi\)
0.916535 + 0.399954i \(0.130974\pi\)
\(152\) 0 0
\(153\) 3.17311 + 2.16339i 0.256531 + 0.174900i
\(154\) 0 0
\(155\) −5.11966 13.0447i −0.411221 1.04777i
\(156\) 0 0
\(157\) −0.748623 + 9.98968i −0.0597466 + 0.797263i 0.884188 + 0.467131i \(0.154712\pi\)
−0.943935 + 0.330132i \(0.892907\pi\)
\(158\) 0 0
\(159\) 2.38482 0.359453i 0.189128 0.0285065i
\(160\) 0 0
\(161\) 5.10404 + 2.45798i 0.402255 + 0.193716i
\(162\) 0 0
\(163\) −17.6610 + 12.0410i −1.38331 + 0.943128i −0.383506 + 0.923538i \(0.625284\pi\)
−0.999808 + 0.0195896i \(0.993764\pi\)
\(164\) 0 0
\(165\) 2.06728 3.58064i 0.160938 0.278753i
\(166\) 0 0
\(167\) −8.02372 + 20.4441i −0.620894 + 1.58201i 0.180302 + 0.983611i \(0.442292\pi\)
−0.801197 + 0.598401i \(0.795803\pi\)
\(168\) 0 0
\(169\) −9.59254 + 2.95891i −0.737888 + 0.227608i
\(170\) 0 0
\(171\) −0.0564923 −0.00432007
\(172\) 0 0
\(173\) −15.5770 −1.18430 −0.592151 0.805827i \(-0.701721\pi\)
−0.592151 + 0.805827i \(0.701721\pi\)
\(174\) 0 0
\(175\) 30.7563 9.48708i 2.32496 0.717155i
\(176\) 0 0
\(177\) 2.85093 7.26405i 0.214289 0.546000i
\(178\) 0 0
\(179\) −3.49011 + 6.04505i −0.260863 + 0.451828i −0.966472 0.256774i \(-0.917340\pi\)
0.705608 + 0.708602i \(0.250674\pi\)
\(180\) 0 0
\(181\) −4.54803 + 3.10080i −0.338053 + 0.230480i −0.720433 0.693525i \(-0.756057\pi\)
0.382380 + 0.924005i \(0.375104\pi\)
\(182\) 0 0
\(183\) −3.57727 1.72272i −0.264439 0.127347i
\(184\) 0 0
\(185\) −31.5309 + 4.75252i −2.31820 + 0.349412i
\(186\) 0 0
\(187\) 0.182877 2.44032i 0.0133733 0.178454i
\(188\) 0 0
\(189\) 5.72378 + 14.5840i 0.416344 + 1.06083i
\(190\) 0 0
\(191\) 15.7034 + 10.7064i 1.13626 + 0.774689i 0.977146 0.212571i \(-0.0681837\pi\)
0.159115 + 0.987260i \(0.449136\pi\)
\(192\) 0 0
\(193\) 0.685255 3.00230i 0.0493257 0.216110i −0.944258 0.329205i \(-0.893219\pi\)
0.993584 + 0.113095i \(0.0360764\pi\)
\(194\) 0 0
\(195\) −0.706241 9.42413i −0.0505750 0.674876i
\(196\) 0 0
\(197\) −8.60862 7.98763i −0.613339 0.569095i 0.311123 0.950370i \(-0.399295\pi\)
−0.924462 + 0.381274i \(0.875485\pi\)
\(198\) 0 0
\(199\) −0.166901 + 0.209287i −0.0118313 + 0.0148360i −0.787712 0.616044i \(-0.788734\pi\)
0.775881 + 0.630880i \(0.217306\pi\)
\(200\) 0 0
\(201\) 7.21637 + 2.22595i 0.509003 + 0.157007i
\(202\) 0 0
\(203\) −1.52252 + 1.41269i −0.106860 + 0.0991514i
\(204\) 0 0
\(205\) 33.8280 + 5.09874i 2.36265 + 0.356112i
\(206\) 0 0
\(207\) 1.50204 + 1.88350i 0.104399 + 0.130912i
\(208\) 0 0
\(209\) 0.0179987 + 0.0311747i 0.00124500 + 0.00215640i
\(210\) 0 0
\(211\) 14.7666 7.11124i 1.01658 0.489558i 0.150045 0.988679i \(-0.452058\pi\)
0.866532 + 0.499122i \(0.166344\pi\)
\(212\) 0 0
\(213\) 2.18306 + 9.56462i 0.149581 + 0.655357i
\(214\) 0 0
\(215\) −24.9947 + 9.40196i −1.70462 + 0.641208i
\(216\) 0 0
\(217\) −2.12745 9.32096i −0.144421 0.632748i
\(218\) 0 0
\(219\) 12.3785 5.96118i 0.836463 0.402819i
\(220\) 0 0
\(221\) −2.79679 4.84418i −0.188132 0.325855i
\(222\) 0 0
\(223\) −3.03608 3.80712i −0.203311 0.254944i 0.669714 0.742619i \(-0.266417\pi\)
−0.873025 + 0.487675i \(0.837845\pi\)
\(224\) 0 0
\(225\) 13.5345 + 2.03999i 0.902297 + 0.135999i
\(226\) 0 0
\(227\) −14.1316 + 13.1122i −0.937947 + 0.870288i −0.991740 0.128265i \(-0.959059\pi\)
0.0537930 + 0.998552i \(0.482869\pi\)
\(228\) 0 0
\(229\) −6.90123 2.12875i −0.456046 0.140672i 0.0582171 0.998304i \(-0.481458\pi\)
−0.514263 + 0.857632i \(0.671935\pi\)
\(230\) 0 0
\(231\) 1.75875 2.20541i 0.115718 0.145105i
\(232\) 0 0
\(233\) −6.45459 5.98898i −0.422854 0.392351i 0.439841 0.898076i \(-0.355035\pi\)
−0.862695 + 0.505724i \(0.831225\pi\)
\(234\) 0 0
\(235\) −2.38400 31.8122i −0.155515 2.07520i
\(236\) 0 0
\(237\) −4.02407 + 17.6306i −0.261391 + 1.14523i
\(238\) 0 0
\(239\) −4.97430 3.39142i −0.321761 0.219373i 0.391658 0.920111i \(-0.371902\pi\)
−0.713418 + 0.700738i \(0.752854\pi\)
\(240\) 0 0
\(241\) −6.42983 16.3830i −0.414182 1.05532i −0.973969 0.226682i \(-0.927212\pi\)
0.559787 0.828637i \(-0.310883\pi\)
\(242\) 0 0
\(243\) −0.855086 + 11.4103i −0.0548538 + 0.731973i
\(244\) 0 0
\(245\) 2.89758 0.436740i 0.185119 0.0279023i
\(246\) 0 0
\(247\) 0.0741325 + 0.0357003i 0.00471694 + 0.00227156i
\(248\) 0 0
\(249\) 6.32790 4.31429i 0.401014 0.273407i
\(250\) 0 0
\(251\) −8.69184 + 15.0547i −0.548624 + 0.950245i 0.449745 + 0.893157i \(0.351515\pi\)
−0.998369 + 0.0570882i \(0.981818\pi\)
\(252\) 0 0
\(253\) 0.560833 1.42898i 0.0352592 0.0898391i
\(254\) 0 0
\(255\) −17.0570 + 5.26140i −1.06815 + 0.329481i
\(256\) 0 0
\(257\) −24.3517 −1.51902 −0.759508 0.650498i \(-0.774560\pi\)
−0.759508 + 0.650498i \(0.774560\pi\)
\(258\) 0 0
\(259\) −21.7550 −1.35179
\(260\) 0 0
\(261\) −0.843994 + 0.260338i −0.0522419 + 0.0161145i
\(262\) 0 0
\(263\) 7.49599 19.0995i 0.462223 1.17772i −0.489838 0.871814i \(-0.662944\pi\)
0.952060 0.305910i \(-0.0989608\pi\)
\(264\) 0 0
\(265\) 3.64167 6.30755i 0.223706 0.387470i
\(266\) 0 0
\(267\) 13.7338 9.36353i 0.840493 0.573039i
\(268\) 0 0
\(269\) 15.3360 + 7.38545i 0.935055 + 0.450299i 0.838422 0.545021i \(-0.183478\pi\)
0.0966331 + 0.995320i \(0.469193\pi\)
\(270\) 0 0
\(271\) 3.41724 0.515067i 0.207583 0.0312881i −0.0444275 0.999013i \(-0.514146\pi\)
0.252010 + 0.967725i \(0.418908\pi\)
\(272\) 0 0
\(273\) 0.481835 6.42965i 0.0291620 0.389140i
\(274\) 0 0
\(275\) −3.18640 8.11881i −0.192147 0.489582i
\(276\) 0 0
\(277\) 19.9087 + 13.5735i 1.19619 + 0.815552i 0.986747 0.162268i \(-0.0518809\pi\)
0.209448 + 0.977820i \(0.432833\pi\)
\(278\) 0 0
\(279\) 0.904705 3.96377i 0.0541632 0.237305i
\(280\) 0 0
\(281\) 0.429939 + 5.73714i 0.0256480 + 0.342249i 0.995235 + 0.0975031i \(0.0310856\pi\)
−0.969587 + 0.244746i \(0.921295\pi\)
\(282\) 0 0
\(283\) −11.6970 10.8533i −0.695317 0.645160i 0.251154 0.967947i \(-0.419190\pi\)
−0.946472 + 0.322787i \(0.895380\pi\)
\(284\) 0 0
\(285\) 0.163711 0.205287i 0.00969741 0.0121602i
\(286\) 0 0
\(287\) 22.3030 + 6.87956i 1.31650 + 0.406088i
\(288\) 0 0
\(289\) 4.71715 4.37687i 0.277479 0.257463i
\(290\) 0 0
\(291\) −13.9284 2.09937i −0.816498 0.123067i
\(292\) 0 0
\(293\) −3.77347 4.73178i −0.220449 0.276434i 0.659293 0.751886i \(-0.270856\pi\)
−0.879741 + 0.475453i \(0.842284\pi\)
\(294\) 0 0
\(295\) −11.7830 20.4087i −0.686032 1.18824i
\(296\) 0 0
\(297\) 3.82494 1.84199i 0.221946 0.106883i
\(298\) 0 0
\(299\) −0.780788 3.42085i −0.0451541 0.197833i
\(300\) 0 0
\(301\) −17.8183 + 3.80130i −1.02703 + 0.219103i
\(302\) 0 0
\(303\) 0.687831 + 3.01359i 0.0395149 + 0.173126i
\(304\) 0 0
\(305\) −10.8031 + 5.20250i −0.618584 + 0.297894i
\(306\) 0 0
\(307\) 11.7476 + 20.3475i 0.670472 + 1.16129i 0.977770 + 0.209679i \(0.0672418\pi\)
−0.307298 + 0.951613i \(0.599425\pi\)
\(308\) 0 0
\(309\) −4.46467 5.59852i −0.253986 0.318488i
\(310\) 0 0
\(311\) −1.16489 0.175579i −0.0660550 0.00995619i 0.115932 0.993257i \(-0.463015\pi\)
−0.181987 + 0.983301i \(0.558253\pi\)
\(312\) 0 0
\(313\) 21.8138 20.2403i 1.23299 1.14405i 0.248496 0.968633i \(-0.420064\pi\)
0.984495 0.175415i \(-0.0561268\pi\)
\(314\) 0 0
\(315\) 12.7748 + 3.94050i 0.719778 + 0.222022i
\(316\) 0 0
\(317\) −16.7284 + 20.9767i −0.939560 + 1.17817i 0.0442619 + 0.999020i \(0.485906\pi\)
−0.983822 + 0.179151i \(0.942665\pi\)
\(318\) 0 0
\(319\) 0.412565 + 0.382805i 0.0230992 + 0.0214330i
\(320\) 0 0
\(321\) −0.362340 4.83509i −0.0202239 0.269869i
\(322\) 0 0
\(323\) 0.0345821 0.151514i 0.00192420 0.00843048i
\(324\) 0 0
\(325\) −16.4715 11.2301i −0.913677 0.622934i
\(326\) 0 0
\(327\) −2.74151 6.98526i −0.151606 0.386286i
\(328\) 0 0
\(329\) 1.62649 21.7040i 0.0896713 1.19658i
\(330\) 0 0
\(331\) −2.75598 + 0.415397i −0.151482 + 0.0228323i −0.224346 0.974510i \(-0.572024\pi\)
0.0728632 + 0.997342i \(0.476786\pi\)
\(332\) 0 0
\(333\) −8.33523 4.01403i −0.456768 0.219968i
\(334\) 0 0
\(335\) 18.8433 12.8472i 1.02952 0.701915i
\(336\) 0 0
\(337\) −4.52447 + 7.83661i −0.246463 + 0.426887i −0.962542 0.271132i \(-0.912602\pi\)
0.716079 + 0.698020i \(0.245935\pi\)
\(338\) 0 0
\(339\) −0.0690706 + 0.175989i −0.00375140 + 0.00955841i
\(340\) 0 0
\(341\) −2.47561 + 0.763625i −0.134062 + 0.0413526i
\(342\) 0 0
\(343\) −17.4496 −0.942192
\(344\) 0 0
\(345\) −11.1973 −0.602840
\(346\) 0 0
\(347\) −10.0705 + 3.10634i −0.540613 + 0.166757i −0.553023 0.833166i \(-0.686526\pi\)
0.0124100 + 0.999923i \(0.496050\pi\)
\(348\) 0 0
\(349\) −4.48874 + 11.4371i −0.240277 + 0.612215i −0.999242 0.0389157i \(-0.987610\pi\)
0.758966 + 0.651130i \(0.225705\pi\)
\(350\) 0 0
\(351\) 4.85190 8.40374i 0.258975 0.448559i
\(352\) 0 0
\(353\) 3.53890 2.41278i 0.188356 0.128419i −0.465470 0.885063i \(-0.654115\pi\)
0.653827 + 0.756644i \(0.273162\pi\)
\(354\) 0 0
\(355\) 26.6933 + 12.8548i 1.41673 + 0.682262i
\(356\) 0 0
\(357\) −12.0422 + 1.81508i −0.637343 + 0.0960640i
\(358\) 0 0
\(359\) 2.55838 34.1392i 0.135026 1.80180i −0.360036 0.932938i \(-0.617236\pi\)
0.495062 0.868858i \(-0.335145\pi\)
\(360\) 0 0
\(361\) −6.94064 17.6845i −0.365297 0.930762i
\(362\) 0 0
\(363\) 11.6245 + 7.92547i 0.610129 + 0.415979i
\(364\) 0 0
\(365\) 9.23266 40.4509i 0.483259 2.11730i
\(366\) 0 0
\(367\) 2.31138 + 30.8433i 0.120653 + 1.61000i 0.648873 + 0.760897i \(0.275241\pi\)
−0.528219 + 0.849108i \(0.677140\pi\)
\(368\) 0 0
\(369\) 7.27582 + 6.75098i 0.378764 + 0.351442i
\(370\) 0 0
\(371\) 3.09817 3.88498i 0.160849 0.201698i
\(372\) 0 0
\(373\) 7.58815 + 2.34063i 0.392900 + 0.121193i 0.484909 0.874565i \(-0.338853\pi\)
−0.0920093 + 0.995758i \(0.529329\pi\)
\(374\) 0 0
\(375\) −26.5068 + 24.5947i −1.36880 + 1.27006i
\(376\) 0 0
\(377\) 1.27206 + 0.191732i 0.0655144 + 0.00987471i
\(378\) 0 0
\(379\) −13.9219 17.4576i −0.715122 0.896735i 0.282929 0.959141i \(-0.408694\pi\)
−0.998051 + 0.0624060i \(0.980123\pi\)
\(380\) 0 0
\(381\) −1.16615 2.01983i −0.0597435 0.103479i
\(382\) 0 0
\(383\) −22.6340 + 10.8999i −1.15654 + 0.556961i −0.910992 0.412423i \(-0.864682\pi\)
−0.245549 + 0.969384i \(0.578968\pi\)
\(384\) 0 0
\(385\) −1.89559 8.30511i −0.0966081 0.423268i
\(386\) 0 0
\(387\) −7.52828 1.83123i −0.382684 0.0930867i
\(388\) 0 0
\(389\) 3.91826 + 17.1670i 0.198664 + 0.870403i 0.971733 + 0.236081i \(0.0758632\pi\)
−0.773070 + 0.634321i \(0.781280\pi\)
\(390\) 0 0
\(391\) −5.97109 + 2.87553i −0.301971 + 0.145422i
\(392\) 0 0
\(393\) 14.7634 + 25.5709i 0.744714 + 1.28988i
\(394\) 0 0
\(395\) 34.0503 + 42.6977i 1.71326 + 2.14836i
\(396\) 0 0
\(397\) −1.43147 0.215759i −0.0718434 0.0108287i 0.113022 0.993592i \(-0.463947\pi\)
−0.184866 + 0.982764i \(0.559185\pi\)
\(398\) 0 0
\(399\) 0.131320 0.121847i 0.00657420 0.00609996i
\(400\) 0 0
\(401\) 7.37812 + 2.27585i 0.368446 + 0.113650i 0.473448 0.880822i \(-0.343009\pi\)
−0.105003 + 0.994472i \(0.533485\pi\)
\(402\) 0 0
\(403\) −3.69211 + 4.62976i −0.183917 + 0.230625i
\(404\) 0 0
\(405\) −12.1185 11.2443i −0.602172 0.558734i
\(406\) 0 0
\(407\) 0.440541 + 5.87861i 0.0218368 + 0.291392i
\(408\) 0 0
\(409\) −7.12781 + 31.2290i −0.352448 + 1.54417i 0.419063 + 0.907957i \(0.362359\pi\)
−0.771511 + 0.636216i \(0.780499\pi\)
\(410\) 0 0
\(411\) −23.8026 16.2283i −1.17409 0.800484i
\(412\) 0 0
\(413\) −5.87394 14.9666i −0.289038 0.736456i
\(414\) 0 0
\(415\) 1.72841 23.0640i 0.0848442 1.13217i
\(416\) 0 0
\(417\) −16.2487 + 2.44910i −0.795703 + 0.119933i
\(418\) 0 0
\(419\) −19.9028 9.58467i −0.972314 0.468242i −0.120859 0.992670i \(-0.538565\pi\)
−0.851455 + 0.524428i \(0.824279\pi\)
\(420\) 0 0
\(421\) −12.5748 + 8.57335i −0.612858 + 0.417840i −0.829575 0.558395i \(-0.811417\pi\)
0.216717 + 0.976234i \(0.430465\pi\)
\(422\) 0 0
\(423\) 4.62779 8.01557i 0.225011 0.389730i
\(424\) 0 0
\(425\) −13.7565 + 35.0511i −0.667290 + 1.70023i
\(426\) 0 0
\(427\) −7.81715 + 2.41127i −0.378298 + 0.116690i
\(428\) 0 0
\(429\) −1.74716 −0.0843539
\(430\) 0 0
\(431\) −16.5109 −0.795301 −0.397651 0.917537i \(-0.630174\pi\)
−0.397651 + 0.917537i \(0.630174\pi\)
\(432\) 0 0
\(433\) 24.1153 7.43859i 1.15891 0.357476i 0.345075 0.938575i \(-0.387853\pi\)
0.813833 + 0.581099i \(0.197377\pi\)
\(434\) 0 0
\(435\) 1.49980 3.82143i 0.0719100 0.183224i
\(436\) 0 0
\(437\) 0.0487442 0.0844275i 0.00233175 0.00403872i
\(438\) 0 0
\(439\) −15.6707 + 10.6841i −0.747922 + 0.509924i −0.876279 0.481804i \(-0.839982\pi\)
0.128358 + 0.991728i \(0.459029\pi\)
\(440\) 0 0
\(441\) 0.765978 + 0.368876i 0.0364752 + 0.0175655i
\(442\) 0 0
\(443\) 37.0756 5.58825i 1.76152 0.265506i 0.813007 0.582254i \(-0.197829\pi\)
0.948510 + 0.316748i \(0.102591\pi\)
\(444\) 0 0
\(445\) 3.75126 50.0571i 0.177827 2.37293i
\(446\) 0 0
\(447\) 4.07304 + 10.3779i 0.192648 + 0.490859i
\(448\) 0 0
\(449\) −14.9462 10.1902i −0.705357 0.480904i 0.156745 0.987639i \(-0.449900\pi\)
−0.862102 + 0.506735i \(0.830852\pi\)
\(450\) 0 0
\(451\) 1.40735 6.16599i 0.0662693 0.290345i
\(452\) 0 0
\(453\) −0.460606 6.14636i −0.0216412 0.288781i
\(454\) 0 0
\(455\) −14.2736 13.2440i −0.669159 0.620889i
\(456\) 0 0
\(457\) 4.42658 5.55075i 0.207067 0.259653i −0.667444 0.744660i \(-0.732612\pi\)
0.874510 + 0.485007i \(0.161183\pi\)
\(458\) 0 0
\(459\) −17.5141 5.40239i −0.817489 0.252162i
\(460\) 0 0
\(461\) 1.48177 1.37488i 0.0690130 0.0640347i −0.644912 0.764257i \(-0.723106\pi\)
0.713925 + 0.700222i \(0.246916\pi\)
\(462\) 0 0
\(463\) 23.5610 + 3.55125i 1.09497 + 0.165041i 0.671600 0.740914i \(-0.265608\pi\)
0.423374 + 0.905955i \(0.360846\pi\)
\(464\) 0 0
\(465\) 11.7822 + 14.7744i 0.546385 + 0.685145i
\(466\) 0 0
\(467\) 8.68583 + 15.0443i 0.401932 + 0.696167i 0.993959 0.109751i \(-0.0350054\pi\)
−0.592027 + 0.805918i \(0.701672\pi\)
\(468\) 0 0
\(469\) 14.0187 6.75104i 0.647323 0.311734i
\(470\) 0 0
\(471\) −3.00602 13.1702i −0.138510 0.606852i
\(472\) 0 0
\(473\) 1.38800 + 4.73784i 0.0638203 + 0.217846i
\(474\) 0 0
\(475\) −0.123251 0.539998i −0.00565515 0.0247768i
\(476\) 0 0
\(477\) 1.90385 0.916848i 0.0871715 0.0419796i
\(478\) 0 0
\(479\) 3.86370 + 6.69213i 0.176537 + 0.305771i 0.940692 0.339261i \(-0.110177\pi\)
−0.764155 + 0.645033i \(0.776844\pi\)
\(480\) 0 0
\(481\) 8.40131 + 10.5349i 0.383067 + 0.480350i
\(482\) 0 0
\(483\) −7.55405 1.13859i −0.343721 0.0518076i
\(484\) 0 0
\(485\) −31.1825 + 28.9332i −1.41593 + 1.31379i
\(486\) 0 0
\(487\) −16.7051 5.15285i −0.756982 0.233498i −0.107843 0.994168i \(-0.534394\pi\)
−0.649139 + 0.760670i \(0.724871\pi\)
\(488\) 0 0
\(489\) 17.9718 22.5359i 0.812713 1.01911i
\(490\) 0 0
\(491\) −15.9175 14.7693i −0.718346 0.666528i 0.233760 0.972294i \(-0.424897\pi\)
−0.952107 + 0.305766i \(0.901087\pi\)
\(492\) 0 0
\(493\) −0.181578 2.42299i −0.00817786 0.109126i
\(494\) 0 0
\(495\) 0.806105 3.53178i 0.0362317 0.158742i
\(496\) 0 0
\(497\) 16.7010 + 11.3866i 0.749144 + 0.510758i
\(498\) 0 0
\(499\) 13.1125 + 33.4100i 0.586995 + 1.49564i 0.847837 + 0.530257i \(0.177905\pi\)
−0.260842 + 0.965382i \(0.584000\pi\)
\(500\) 0 0
\(501\) 2.21323 29.5335i 0.0988797 1.31946i
\(502\) 0 0
\(503\) −0.0899578 + 0.0135590i −0.00401102 + 0.000604564i −0.151047 0.988527i \(-0.548265\pi\)
0.147036 + 0.989131i \(0.453027\pi\)
\(504\) 0 0
\(505\) 8.41042 + 4.05025i 0.374259 + 0.180234i
\(506\) 0 0
\(507\) 11.1848 7.62568i 0.496735 0.338668i
\(508\) 0 0
\(509\) −11.3425 + 19.6459i −0.502749 + 0.870787i 0.497246 + 0.867610i \(0.334345\pi\)
−0.999995 + 0.00317746i \(0.998989\pi\)
\(510\) 0 0
\(511\) 10.3419 26.3507i 0.457498 1.16569i
\(512\) 0 0
\(513\) 0.257630 0.0794685i 0.0113747 0.00350862i
\(514\) 0 0
\(515\) −21.6250 −0.952913
\(516\) 0 0
\(517\) −5.89775 −0.259383
\(518\) 0 0
\(519\) 20.0725 6.19156i 0.881087 0.271779i
\(520\) 0 0
\(521\) 1.72346 4.39129i 0.0755060 0.192386i −0.888137 0.459578i \(-0.848001\pi\)
0.963643 + 0.267192i \(0.0860958\pi\)
\(522\) 0 0
\(523\) 0.853098 1.47761i 0.0373034 0.0646113i −0.846771 0.531958i \(-0.821457\pi\)
0.884074 + 0.467346i \(0.154790\pi\)
\(524\) 0 0
\(525\) −35.8616 + 24.4500i −1.56513 + 1.06709i
\(526\) 0 0
\(527\) 10.0771 + 4.85290i 0.438968 + 0.211396i
\(528\) 0 0
\(529\) 18.6322 2.80835i 0.810095 0.122102i
\(530\) 0 0
\(531\) 0.510945 6.81809i 0.0221731 0.295880i
\(532\) 0 0
\(533\) −5.28148 13.4570i −0.228766 0.582887i
\(534\) 0 0
\(535\) −12.0983 8.24846i −0.523054 0.356612i
\(536\) 0 0
\(537\) 2.09456 9.17688i 0.0903870 0.396011i
\(538\) 0 0
\(539\) −0.0404841 0.540223i −0.00174378 0.0232691i
\(540\) 0 0
\(541\) −8.33253 7.73145i −0.358243 0.332401i 0.480433 0.877031i \(-0.340480\pi\)
−0.838676 + 0.544630i \(0.816670\pi\)
\(542\) 0 0
\(543\) 4.62808 5.80343i 0.198610 0.249049i
\(544\) 0 0
\(545\) −21.6547 6.67960i −0.927586 0.286123i
\(546\) 0 0
\(547\) 17.1076 15.8735i 0.731467 0.678703i −0.223737 0.974650i \(-0.571826\pi\)
0.955204 + 0.295947i \(0.0956352\pi\)
\(548\) 0 0
\(549\) −3.43997 0.518492i −0.146814 0.0221287i
\(550\) 0 0
\(551\) 0.0222847 + 0.0279441i 0.000949358 + 0.00119046i
\(552\) 0 0
\(553\) 18.6298 + 32.2677i 0.792218 + 1.37216i
\(554\) 0 0
\(555\) 38.7416 18.6570i 1.64449 0.791944i
\(556\) 0 0
\(557\) −1.28534 5.63146i −0.0544618 0.238613i 0.940369 0.340155i \(-0.110479\pi\)
−0.994831 + 0.101542i \(0.967622\pi\)
\(558\) 0 0
\(559\) 8.72180 + 7.16055i 0.368893 + 0.302859i
\(560\) 0 0
\(561\) 0.734322 + 3.21728i 0.0310031 + 0.135834i
\(562\) 0 0
\(563\) 3.42474 1.64927i 0.144336 0.0695084i −0.360322 0.932828i \(-0.617333\pi\)
0.504657 + 0.863320i \(0.331619\pi\)
\(564\) 0 0
\(565\) 0.285471 + 0.494450i 0.0120098 + 0.0208017i
\(566\) 0 0
\(567\) −7.03215 8.81804i −0.295323 0.370323i
\(568\) 0 0
\(569\) 35.8718 + 5.40680i 1.50382 + 0.226665i 0.848707 0.528863i \(-0.177381\pi\)
0.655116 + 0.755528i \(0.272620\pi\)
\(570\) 0 0
\(571\) 19.4633 18.0593i 0.814514 0.755758i −0.158289 0.987393i \(-0.550598\pi\)
0.972803 + 0.231635i \(0.0744073\pi\)
\(572\) 0 0
\(573\) −24.4910 7.55446i −1.02312 0.315592i
\(574\) 0 0
\(575\) −14.7269 + 18.4670i −0.614156 + 0.770127i
\(576\) 0 0
\(577\) 9.54816 + 8.85940i 0.397495 + 0.368821i 0.853444 0.521184i \(-0.174510\pi\)
−0.455949 + 0.890006i \(0.650700\pi\)
\(578\) 0 0
\(579\) 0.310335 + 4.14113i 0.0128971 + 0.172099i
\(580\) 0 0
\(581\) 3.51130 15.3840i 0.145673 0.638236i
\(582\) 0 0
\(583\) −1.11253 0.758511i −0.0460763 0.0314143i
\(584\) 0 0
\(585\) −3.02515 7.70795i −0.125074 0.318685i
\(586\) 0 0
\(587\) 0.430770 5.74822i 0.0177798 0.237255i −0.981233 0.192827i \(-0.938234\pi\)
0.999013 0.0444278i \(-0.0141465\pi\)
\(588\) 0 0
\(589\) −0.162689 + 0.0245215i −0.00670350 + 0.00101039i
\(590\) 0 0
\(591\) 14.2680 + 6.87109i 0.586905 + 0.282639i
\(592\) 0 0
\(593\) 6.69370 4.56369i 0.274877 0.187408i −0.418033 0.908432i \(-0.637280\pi\)
0.692911 + 0.721024i \(0.256328\pi\)
\(594\) 0 0
\(595\) −18.3888 + 31.8503i −0.753866 + 1.30573i
\(596\) 0 0
\(597\) 0.131881 0.336026i 0.00539752 0.0137526i
\(598\) 0 0
\(599\) 8.12129 2.50509i 0.331827 0.102355i −0.124365 0.992237i \(-0.539689\pi\)
0.456192 + 0.889882i \(0.349213\pi\)
\(600\) 0 0
\(601\) 35.6791 1.45538 0.727691 0.685905i \(-0.240594\pi\)
0.727691 + 0.685905i \(0.240594\pi\)
\(602\) 0 0
\(603\) 6.61676 0.269455
\(604\) 0 0
\(605\) 40.6004 12.5236i 1.65064 0.509155i
\(606\) 0 0
\(607\) −12.0041 + 30.5861i −0.487233 + 1.24145i 0.450088 + 0.892984i \(0.351393\pi\)
−0.937321 + 0.348466i \(0.886703\pi\)
\(608\) 0 0
\(609\) 1.40040 2.42556i 0.0567469 0.0982886i
\(610\) 0 0
\(611\) −11.1383 + 7.59397i −0.450608 + 0.307219i
\(612\) 0 0
\(613\) 2.01111 + 0.968499i 0.0812280 + 0.0391173i 0.474057 0.880494i \(-0.342789\pi\)
−0.392829 + 0.919612i \(0.628503\pi\)
\(614\) 0 0
\(615\) −45.6172 + 6.87569i −1.83946 + 0.277255i
\(616\) 0 0
\(617\) −0.983300 + 13.1212i −0.0395862 + 0.528241i 0.941797 + 0.336182i \(0.109136\pi\)
−0.981383 + 0.192059i \(0.938483\pi\)
\(618\) 0 0
\(619\) 5.06713 + 12.9108i 0.203665 + 0.518930i 0.995815 0.0913968i \(-0.0291332\pi\)
−0.792149 + 0.610327i \(0.791038\pi\)
\(620\) 0 0
\(621\) −9.49953 6.47667i −0.381203 0.259900i
\(622\) 0 0
\(623\) 7.62076 33.3887i 0.305319 1.33769i
\(624\) 0 0
\(625\) 3.83193 + 51.1336i 0.153277 + 2.04534i
\(626\) 0 0
\(627\) −0.0355844 0.0330175i −0.00142110 0.00131859i
\(628\) 0 0
\(629\) 15.8683 19.8982i 0.632709 0.793392i
\(630\) 0 0
\(631\) 5.11794 + 1.57867i 0.203742 + 0.0628461i 0.394946 0.918704i \(-0.370763\pi\)
−0.191204 + 0.981550i \(0.561239\pi\)
\(632\) 0 0
\(633\) −16.2017 + 15.0330i −0.643959 + 0.597506i
\(634\) 0 0
\(635\) −6.96470 1.04976i −0.276386 0.0416584i
\(636\) 0 0
\(637\) −0.772051 0.968121i −0.0305898 0.0383584i
\(638\) 0 0
\(639\) 4.29789 + 7.44417i 0.170022 + 0.294487i
\(640\) 0 0
\(641\) −4.56273 + 2.19729i −0.180217 + 0.0867879i −0.521817 0.853058i \(-0.674746\pi\)
0.341600 + 0.939845i \(0.389031\pi\)
\(642\) 0 0
\(643\) 4.59652 + 20.1387i 0.181269 + 0.794191i 0.981027 + 0.193869i \(0.0621037\pi\)
−0.799758 + 0.600322i \(0.795039\pi\)
\(644\) 0 0
\(645\) 28.4710 22.0502i 1.12104 0.868226i
\(646\) 0 0
\(647\) 6.78518 + 29.7278i 0.266753 + 1.16872i 0.913766 + 0.406242i \(0.133161\pi\)
−0.647013 + 0.762479i \(0.723982\pi\)
\(648\) 0 0
\(649\) −3.92529 + 1.89032i −0.154081 + 0.0742015i
\(650\) 0 0
\(651\) 6.44631 + 11.1653i 0.252651 + 0.437604i
\(652\) 0 0
\(653\) 25.9574 + 32.5496i 1.01579 + 1.27376i 0.961374 + 0.275244i \(0.0887587\pi\)
0.0544173 + 0.998518i \(0.482670\pi\)
\(654\) 0 0
\(655\) 88.1729 + 13.2899i 3.44520 + 0.519280i
\(656\) 0 0
\(657\) 8.82438 8.18783i 0.344272 0.319438i
\(658\) 0 0
\(659\) 20.9158 + 6.45166i 0.814762 + 0.251321i 0.674008 0.738724i \(-0.264571\pi\)
0.140754 + 0.990045i \(0.455047\pi\)
\(660\) 0 0
\(661\) −3.40742 + 4.27277i −0.132533 + 0.166191i −0.843670 0.536863i \(-0.819609\pi\)
0.711136 + 0.703054i \(0.248181\pi\)
\(662\) 0 0
\(663\) 5.52940 + 5.13053i 0.214744 + 0.199253i
\(664\) 0 0
\(665\) −0.0404284 0.539480i −0.00156775 0.0209201i
\(666\) 0 0
\(667\) 0.339165 1.48598i 0.0131325 0.0575373i
\(668\) 0 0
\(669\) 5.42554 + 3.69907i 0.209763 + 0.143014i
\(670\) 0 0
\(671\) 0.809867 + 2.06351i 0.0312646 + 0.0796608i
\(672\) 0 0
\(673\) 0.265593 3.54410i 0.0102379 0.136615i −0.989743 0.142862i \(-0.954369\pi\)
0.999980 + 0.00624712i \(0.00198853\pi\)
\(674\) 0 0
\(675\) −64.5930 + 9.73582i −2.48618 + 0.374732i
\(676\) 0 0
\(677\) −8.78571 4.23097i −0.337662 0.162610i 0.257367 0.966314i \(-0.417145\pi\)
−0.595029 + 0.803704i \(0.702859\pi\)
\(678\) 0 0
\(679\) −23.9788 + 16.3485i −0.920223 + 0.627398i
\(680\) 0 0
\(681\) 12.9981 22.5134i 0.498088 0.862714i
\(682\) 0 0
\(683\) 7.66440 19.5286i 0.293270 0.747240i −0.705969 0.708242i \(-0.749488\pi\)
0.999239 0.0389974i \(-0.0124164\pi\)
\(684\) 0 0
\(685\) −83.1341 + 25.6435i −3.17639 + 0.979787i
\(686\) 0 0
\(687\) 9.73904 0.371568
\(688\) 0 0
\(689\) −3.07775 −0.117253
\(690\) 0 0
\(691\) −8.48595 + 2.61757i −0.322821 + 0.0995770i −0.451930 0.892053i \(-0.649264\pi\)
0.129109 + 0.991630i \(0.458788\pi\)
\(692\) 0 0
\(693\) 0.902953 2.30069i 0.0343003 0.0873958i
\(694\) 0 0
\(695\) −24.8121 + 42.9758i −0.941177 + 1.63017i
\(696\) 0 0
\(697\) −22.5603 + 15.3814i −0.854532 + 0.582610i
\(698\) 0 0
\(699\) 10.6979 + 5.15182i 0.404630 + 0.194860i
\(700\) 0 0
\(701\) 24.8182 3.74074i 0.937370 0.141286i 0.337448 0.941344i \(-0.390436\pi\)
0.599922 + 0.800058i \(0.295198\pi\)
\(702\) 0 0
\(703\) −0.0279772 + 0.373330i −0.00105518 + 0.0140804i
\(704\) 0 0
\(705\) 15.7167 + 40.0456i 0.591926 + 1.50820i
\(706\) 0 0
\(707\) 5.26210 + 3.58764i 0.197902 + 0.134927i
\(708\) 0 0
\(709\) −11.1254 + 48.7436i −0.417824 + 1.83060i 0.126806 + 0.991928i \(0.459528\pi\)
−0.544629 + 0.838677i \(0.683330\pi\)
\(710\) 0 0
\(711\) 1.18408 + 15.8004i 0.0444064 + 0.592563i
\(712\) 0 0
\(713\) 5.14322 + 4.77221i 0.192615 + 0.178721i
\(714\) 0 0
\(715\) −3.28973 + 4.12519i −0.123029 + 0.154273i
\(716\) 0 0
\(717\) 7.75789 + 2.39299i 0.289724 + 0.0893679i
\(718\) 0 0
\(719\) 8.04392 7.46367i 0.299988 0.278348i −0.515788 0.856716i \(-0.672501\pi\)
0.815776 + 0.578368i \(0.196310\pi\)
\(720\) 0 0
\(721\) −14.5890 2.19893i −0.543321 0.0818925i
\(722\) 0 0
\(723\) 14.7974 + 18.5553i 0.550319 + 0.690079i
\(724\) 0 0
\(725\) −4.32989 7.49958i −0.160808 0.278527i
\(726\) 0 0
\(727\) 21.2553 10.2360i 0.788316 0.379633i 0.00399815 0.999992i \(-0.498727\pi\)
0.784318 + 0.620359i \(0.213013\pi\)
\(728\) 0 0
\(729\) −6.14342 26.9161i −0.227534 0.996892i
\(730\) 0 0
\(731\) 9.51991 19.0701i 0.352107 0.705333i
\(732\) 0 0
\(733\) 7.85287 + 34.4057i 0.290052 + 1.27080i 0.884451 + 0.466633i \(0.154533\pi\)
−0.594399 + 0.804170i \(0.702610\pi\)
\(734\) 0 0
\(735\) −3.56022 + 1.71451i −0.131321 + 0.0632406i
\(736\) 0 0
\(737\) −2.10813 3.65139i −0.0776541 0.134501i
\(738\) 0 0
\(739\) 13.7042 + 17.1846i 0.504119 + 0.632145i 0.967153 0.254196i \(-0.0818107\pi\)
−0.463034 + 0.886340i \(0.653239\pi\)
\(740\) 0 0
\(741\) −0.109717 0.0165372i −0.00403056 0.000607509i
\(742\) 0 0
\(743\) 1.34948 1.25213i 0.0495075 0.0459362i −0.655031 0.755602i \(-0.727344\pi\)
0.704539 + 0.709666i \(0.251154\pi\)
\(744\) 0 0
\(745\) 32.1722 + 9.92381i 1.17870 + 0.363580i
\(746\) 0 0
\(747\) 4.18383 5.24635i 0.153078 0.191954i
\(748\) 0 0
\(749\) −7.32316 6.79490i −0.267582 0.248280i
\(750\) 0 0
\(751\) 2.39276 + 31.9291i 0.0873129 + 1.16511i 0.853005 + 0.521903i \(0.174778\pi\)
−0.765692 + 0.643207i \(0.777603\pi\)
\(752\) 0 0
\(753\) 5.21634 22.8543i 0.190094 0.832857i
\(754\) 0 0
\(755\) −15.3793 10.4854i −0.559710 0.381604i
\(756\) 0 0
\(757\) 6.22743 + 15.8672i 0.226340 + 0.576704i 0.998257 0.0590188i \(-0.0187972\pi\)
−0.771917 + 0.635723i \(0.780702\pi\)
\(758\) 0 0
\(759\) −0.154698 + 2.06430i −0.00561517 + 0.0749292i
\(760\) 0 0
\(761\) −2.81970 + 0.425001i −0.102214 + 0.0154063i −0.199950 0.979806i \(-0.564078\pi\)
0.0977361 + 0.995212i \(0.468840\pi\)
\(762\) 0 0
\(763\) −13.9298 6.70823i −0.504292 0.242854i
\(764\) 0 0
\(765\) −12.9222 + 8.81019i −0.467202 + 0.318533i
\(766\) 0 0
\(767\) −4.97919 + 8.62421i −0.179788 + 0.311402i
\(768\) 0 0
\(769\) 17.5058 44.6040i 0.631275 1.60846i −0.153126 0.988207i \(-0.548934\pi\)
0.784400 0.620255i \(-0.212971\pi\)
\(770\) 0 0
\(771\) 31.3795 9.67930i 1.13011 0.348591i
\(772\) 0 0
\(773\) 12.7995 0.460366 0.230183 0.973147i \(-0.426067\pi\)
0.230183 + 0.973147i \(0.426067\pi\)
\(774\) 0 0
\(775\) 39.8627 1.43191
\(776\) 0 0
\(777\) 28.0335 8.64718i 1.00570 0.310216i
\(778\) 0 0
\(779\) 0.146739 0.373886i 0.00525749 0.0133959i
\(780\) 0 0
\(781\) 2.73866 4.74350i 0.0979970 0.169736i
\(782\) 0 0
\(783\) 3.48278 2.37452i 0.124464 0.0848583i
\(784\) 0 0
\(785\) −36.7559 17.7007i −1.31188 0.631766i
\(786\) 0 0
\(787\) 13.0915 1.97322i 0.466660 0.0703377i 0.0884966 0.996076i \(-0.471794\pi\)
0.378164 + 0.925739i \(0.376556\pi\)
\(788\) 0 0
\(789\) −2.06766 + 27.5910i −0.0736107 + 0.982267i
\(790\) 0 0
\(791\) 0.142310 + 0.362600i 0.00505997 + 0.0128926i
\(792\) 0 0
\(793\) 4.18647 + 2.85429i 0.148666 + 0.101359i
\(794\) 0 0
\(795\) −2.18552 + 9.57538i −0.0775123 + 0.339604i
\(796\) 0 0
\(797\) 0.866491 + 11.5625i 0.0306927 + 0.409566i 0.991297 + 0.131645i \(0.0420260\pi\)
−0.960604 + 0.277920i \(0.910355\pi\)
\(798\) 0 0
\(799\) 18.6651 + 17.3187i 0.660324 + 0.612691i
\(800\) 0 0
\(801\) 9.08039 11.3864i 0.320840 0.402320i
\(802\) 0 0
\(803\) −7.32986 2.26096i −0.258665 0.0797876i
\(804\) 0 0
\(805\) −16.9118 + 15.6918i −0.596062 + 0.553065i
\(806\) 0 0
\(807\) −22.6976 3.42111i −0.798992 0.120429i
\(808\) 0 0
\(809\) −15.0173 18.8311i −0.527980 0.662066i 0.444302 0.895877i \(-0.353452\pi\)
−0.972282 + 0.233811i \(0.924880\pi\)
\(810\) 0 0
\(811\) −9.67307 16.7542i −0.339667 0.588321i 0.644703 0.764433i \(-0.276981\pi\)
−0.984370 + 0.176112i \(0.943648\pi\)
\(812\) 0 0
\(813\) −4.19872 + 2.02200i −0.147256 + 0.0709146i
\(814\) 0 0
\(815\) −19.3700 84.8657i −0.678503 2.97271i
\(816\) 0 0
\(817\) 0.0423181 + 0.310661i 0.00148052 + 0.0108687i
\(818\) 0 0
\(819\) −1.25709 5.50765i −0.0439261 0.192453i
\(820\) 0 0
\(821\) 4.68010 2.25382i 0.163336 0.0786587i −0.350429 0.936589i \(-0.613964\pi\)
0.513766 + 0.857930i \(0.328250\pi\)
\(822\) 0 0
\(823\) −27.1185 46.9706i −0.945290 1.63729i −0.755169 0.655530i \(-0.772445\pi\)
−0.190122 0.981761i \(-0.560888\pi\)
\(824\) 0 0
\(825\) 7.33304 + 9.19534i 0.255304 + 0.320141i
\(826\) 0 0
\(827\) 3.32662 + 0.501407i 0.115678 + 0.0174356i 0.206626 0.978420i \(-0.433752\pi\)
−0.0909482 + 0.995856i \(0.528990\pi\)
\(828\) 0 0
\(829\) −29.6523 + 27.5133i −1.02987 + 0.955578i −0.999034 0.0439467i \(-0.986007\pi\)
−0.0308341 + 0.999525i \(0.509816\pi\)
\(830\) 0 0
\(831\) −31.0494 9.57747i −1.07709 0.332239i
\(832\) 0 0
\(833\) −1.45824 + 1.82857i −0.0505249 + 0.0633562i
\(834\) 0 0
\(835\) −65.5635 60.8341i −2.26892 2.10525i
\(836\) 0 0
\(837\) 1.45003 + 19.3493i 0.0501202 + 0.668808i
\(838\) 0 0
\(839\) −0.0182394 + 0.0799120i −0.000629694 + 0.00275887i −0.975242 0.221141i \(-0.929022\pi\)
0.974612 + 0.223900i \(0.0718790\pi\)
\(840\) 0 0
\(841\) −23.4992 16.0215i −0.810318 0.552465i
\(842\) 0 0
\(843\) −2.83442 7.22197i −0.0976225 0.248738i
\(844\) 0 0
\(845\) 3.05503 40.7666i 0.105096 1.40241i
\(846\) 0 0
\(847\) 28.6638 4.32038i 0.984901 0.148450i
\(848\) 0 0
\(849\) 19.3867 + 9.33616i 0.665351 + 0.320416i
\(850\) 0 0
\(851\) 13.1910 8.99347i 0.452181 0.308292i
\(852\) 0 0
\(853\) 12.0750 20.9145i 0.413441 0.716101i −0.581823 0.813316i \(-0.697660\pi\)
0.995263 + 0.0972152i \(0.0309935\pi\)
\(854\) 0 0
\(855\) 0.0840500 0.214156i 0.00287445 0.00732398i
\(856\) 0 0
\(857\) 40.2162 12.4051i 1.37376 0.423749i 0.481966 0.876190i \(-0.339923\pi\)
0.891794 + 0.452441i \(0.149447\pi\)
\(858\) 0 0
\(859\) 2.35350 0.0803004 0.0401502 0.999194i \(-0.487216\pi\)
0.0401502 + 0.999194i \(0.487216\pi\)
\(860\) 0 0
\(861\) −31.4741 −1.07263
\(862\) 0 0
\(863\) 29.2992 9.03761i 0.997356 0.307644i 0.247243 0.968953i \(-0.420475\pi\)
0.750113 + 0.661310i \(0.229999\pi\)
\(864\) 0 0
\(865\) 23.1758 59.0509i 0.787999 2.00779i
\(866\) 0 0
\(867\) −4.33878 + 7.51499i −0.147353 + 0.255222i
\(868\) 0 0
\(869\) 8.34206 5.68752i 0.282985 0.192936i
\(870\) 0 0
\(871\) −8.68290 4.18147i −0.294209 0.141684i
\(872\) 0 0
\(873\) −12.2037 + 1.83942i −0.413033 + 0.0622548i
\(874\) 0 0
\(875\) −5.56750 + 74.2932i −0.188216 + 2.51157i
\(876\) 0 0
\(877\) −16.8677 42.9782i −0.569582 1.45127i −0.867868 0.496794i \(-0.834510\pi\)
0.298287 0.954476i \(-0.403585\pi\)
\(878\) 0 0
\(879\) 6.74327 + 4.59748i 0.227445 + 0.155069i
\(880\) 0 0
\(881\) −2.29329 + 10.0475i −0.0772627 + 0.338510i −0.998755 0.0498868i \(-0.984114\pi\)
0.921492 + 0.388397i \(0.126971\pi\)
\(882\) 0 0
\(883\) −0.882701 11.7788i −0.0297053 0.396389i −0.992162 0.124955i \(-0.960121\pi\)
0.962457 0.271434i \(-0.0874978\pi\)
\(884\) 0 0
\(885\) 23.2956 + 21.6151i 0.783072 + 0.726585i
\(886\) 0 0
\(887\) 13.8680 17.3899i 0.465640 0.583895i −0.492457 0.870337i \(-0.663901\pi\)
0.958098 + 0.286442i \(0.0924726\pi\)
\(888\) 0 0
\(889\) −4.59187 1.41641i −0.154006 0.0475047i
\(890\) 0 0
\(891\) −2.24039 + 2.07878i −0.0750560 + 0.0696418i
\(892\) 0 0
\(893\) −0.370362 0.0558232i −0.0123937 0.00186805i
\(894\) 0 0
\(895\) −17.7235 22.2245i −0.592430 0.742884i
\(896\) 0 0
\(897\) 2.36584 + 4.09776i 0.0789931 + 0.136820i
\(898\) 0 0
\(899\) −2.31757 + 1.11608i −0.0772954 + 0.0372235i
\(900\) 0 0
\(901\) 1.29356 + 5.66746i 0.0430947 + 0.188810i
\(902\) 0 0
\(903\) 21.4496 11.9807i 0.713799 0.398694i
\(904\) 0 0
\(905\) −4.98815 21.8545i −0.165812 0.726468i
\(906\) 0 0
\(907\) 31.5843 15.2102i 1.04874 0.505046i 0.171541 0.985177i \(-0.445125\pi\)
0.877197 + 0.480131i \(0.159411\pi\)
\(908\) 0 0
\(909\) 1.35416 + 2.34548i 0.0449148 + 0.0777947i
\(910\) 0 0
\(911\) −34.7823 43.6156i −1.15239 1.44505i −0.874890 0.484322i \(-0.839066\pi\)
−0.277498 0.960726i \(-0.589505\pi\)
\(912\) 0 0
\(913\) −4.22814 0.637289i −0.139931 0.0210912i
\(914\) 0 0
\(915\) 11.8530 10.9979i 0.391847 0.363581i
\(916\) 0 0
\(917\) 58.1330 + 17.9316i 1.91972 + 0.592155i
\(918\) 0 0
\(919\) −27.4108 + 34.3720i −0.904198 + 1.13383i 0.0862951 + 0.996270i \(0.472497\pi\)
−0.990494 + 0.137559i \(0.956074\pi\)
\(920\) 0 0
\(921\) −23.2257 21.5503i −0.765312 0.710105i
\(922\) 0 0
\(923\) −0.935602 12.4847i −0.0307957 0.410940i
\(924\) 0 0
\(925\) 20.1841 88.4323i 0.663649 2.90764i
\(926\) 0 0
\(927\) −5.18389 3.53432i −0.170261 0.116082i
\(928\) 0 0
\(929\) −2.10522 5.36400i −0.0690699 0.175987i 0.892171 0.451699i \(-0.149182\pi\)
−0.961240 + 0.275711i \(0.911087\pi\)
\(930\) 0 0
\(931\) 0.00257101 0.0343077i 8.42614e−5 0.00112439i
\(932\) 0 0
\(933\) 1.57087 0.236770i 0.0514278 0.00775150i
\(934\) 0 0
\(935\) 8.97889 + 4.32401i 0.293641 + 0.141410i
\(936\) 0 0
\(937\) −18.1263 + 12.3583i −0.592161 + 0.403729i −0.821990 0.569503i \(-0.807136\pi\)
0.229828 + 0.973231i \(0.426184\pi\)
\(938\) 0 0
\(939\) −20.0641 + 34.7521i −0.654769 + 1.13409i
\(940\) 0 0
\(941\) −6.91668 + 17.6234i −0.225477 + 0.574507i −0.998183 0.0602578i \(-0.980808\pi\)
0.772706 + 0.634765i \(0.218903\pi\)
\(942\) 0 0
\(943\) −16.3672 + 5.04862i −0.532991 + 0.164406i
\(944\) 0 0
\(945\) −63.8021 −2.07548
\(946\) 0 0
\(947\) −40.2434 −1.30774 −0.653868 0.756609i \(-0.726855\pi\)
−0.653868 + 0.756609i \(0.726855\pi\)
\(948\) 0 0
\(949\) −16.7542 + 5.16798i −0.543864 + 0.167760i
\(950\) 0 0
\(951\) 13.2183 33.6797i 0.428634 1.09214i
\(952\) 0 0
\(953\) −18.3255 + 31.7407i −0.593621 + 1.02818i 0.400119 + 0.916463i \(0.368969\pi\)
−0.993740 + 0.111718i \(0.964365\pi\)
\(954\) 0 0
\(955\) −63.9506 + 43.6008i −2.06939 + 1.41089i
\(956\) 0 0
\(957\) −0.683788 0.329295i −0.0221037 0.0106446i
\(958\) 0 0
\(959\) −58.6926 + 8.84648i −1.89528 + 0.285668i
\(960\) 0 0
\(961\) −1.43176 + 19.1056i −0.0461859 + 0.616308i
\(962\) 0 0
\(963\) −1.55207 3.95460i −0.0500146 0.127435i
\(964\) 0 0
\(965\) 10.3619 + 7.06459i 0.333560 + 0.227417i
\(966\) 0 0
\(967\) −1.90500 + 8.34635i −0.0612607 + 0.268400i −0.996278 0.0862025i \(-0.972527\pi\)
0.935017 + 0.354603i \(0.115384\pi\)
\(968\) 0 0
\(969\) 0.0156614 + 0.208987i 0.000503116 + 0.00671362i
\(970\) 0 0
\(971\) −36.2742 33.6575i −1.16409 1.08012i −0.995531 0.0944301i \(-0.969897\pi\)
−0.168562 0.985691i \(-0.553912\pi\)
\(972\) 0 0
\(973\) −21.1091 + 26.4699i −0.676725 + 0.848587i
\(974\) 0 0
\(975\) 25.6889 + 7.92398i 0.822704 + 0.253770i
\(976\) 0 0
\(977\) −13.4546 + 12.4840i −0.430450 + 0.399399i −0.865421 0.501045i \(-0.832949\pi\)
0.434971 + 0.900444i \(0.356759\pi\)
\(978\) 0 0
\(979\) −9.17655 1.38314i −0.293284 0.0442054i
\(980\) 0 0
\(981\) −4.09932 5.14038i −0.130881 0.164120i
\(982\) 0 0
\(983\) −2.35817 4.08447i −0.0752140 0.130274i 0.825965 0.563721i \(-0.190631\pi\)
−0.901179 + 0.433446i \(0.857297\pi\)
\(984\) 0 0
\(985\) 43.0882 20.7502i 1.37291 0.661157i
\(986\) 0 0
\(987\) 6.53101 + 28.6142i 0.207884 + 0.910800i
\(988\) 0 0
\(989\) 9.23252 9.67091i 0.293577 0.307517i
\(990\) 0 0
\(991\) 10.0778 + 44.1536i 0.320131 + 1.40259i 0.837319 + 0.546714i \(0.184122\pi\)
−0.517188 + 0.855872i \(0.673021\pi\)
\(992\) 0 0
\(993\) 3.38623 1.63072i 0.107459 0.0517495i
\(994\) 0 0
\(995\) −0.545067 0.944083i −0.0172798 0.0299295i
\(996\) 0 0
\(997\) −18.2570 22.8935i −0.578204 0.725045i 0.403601 0.914935i \(-0.367758\pi\)
−0.981805 + 0.189890i \(0.939187\pi\)
\(998\) 0 0
\(999\) 43.6590 + 6.58054i 1.38131 + 0.208199i
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 688.2.bg.c.17.1 36
4.3 odd 2 43.2.g.a.17.1 36
12.11 even 2 387.2.y.c.361.3 36
43.38 even 21 inner 688.2.bg.c.81.1 36
172.95 odd 42 1849.2.a.n.1.18 18
172.163 even 42 1849.2.a.o.1.1 18
172.167 odd 42 43.2.g.a.38.1 yes 36
516.167 even 42 387.2.y.c.253.3 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.2.g.a.17.1 36 4.3 odd 2
43.2.g.a.38.1 yes 36 172.167 odd 42
387.2.y.c.253.3 36 516.167 even 42
387.2.y.c.361.3 36 12.11 even 2
688.2.bg.c.17.1 36 1.1 even 1 trivial
688.2.bg.c.81.1 36 43.38 even 21 inner
1849.2.a.n.1.18 18 172.95 odd 42
1849.2.a.o.1.1 18 172.163 even 42