Properties

Label 585.2.j.d.451.2
Level $585$
Weight $2$
Character 585.451
Analytic conductor $4.671$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [585,2,Mod(406,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.j (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: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{13})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 4x^{2} + 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.2
Root \(-0.651388 + 1.12824i\) of defining polynomial
Character \(\chi\) \(=\) 585.451
Dual form 585.2.j.d.406.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.651388 - 1.12824i) q^{2} +(0.151388 + 0.262211i) q^{4} +1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +3.00000 q^{8} +(0.651388 - 1.12824i) q^{10} +(-2.80278 + 4.85455i) q^{11} +3.60555 q^{13} +1.30278 q^{14} +(1.65139 - 2.86029i) q^{16} +(0.197224 + 0.341603i) q^{17} +(-0.802776 - 1.39045i) q^{19} +(0.151388 + 0.262211i) q^{20} +(3.65139 + 6.32439i) q^{22} +(-1.50000 + 2.59808i) q^{23} +1.00000 q^{25} +(2.34861 - 4.06792i) q^{26} +(-0.151388 + 0.262211i) q^{28} +(4.10555 - 7.11102i) q^{29} -4.00000 q^{31} +(0.848612 + 1.46984i) q^{32} +0.513878 q^{34} +(0.500000 + 0.866025i) q^{35} +(1.80278 - 3.12250i) q^{37} -2.09167 q^{38} +3.00000 q^{40} +(1.50000 - 2.59808i) q^{41} +(-2.10555 - 3.64692i) q^{43} -1.69722 q^{44} +(1.95416 + 3.38471i) q^{46} +5.21110 q^{47} +(3.00000 - 5.19615i) q^{49} +(0.651388 - 1.12824i) q^{50} +(0.545837 + 0.945417i) q^{52} -11.2111 q^{53} +(-2.80278 + 4.85455i) q^{55} +(1.50000 + 2.59808i) q^{56} +(-5.34861 - 9.26407i) q^{58} +(5.40833 + 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-2.60555 + 4.51295i) q^{62} +8.81665 q^{64} +3.60555 q^{65} +(3.50000 - 6.06218i) q^{67} +(-0.0597147 + 0.103429i) q^{68} +1.30278 q^{70} +(-8.40833 - 14.5636i) q^{71} -15.2111 q^{73} +(-2.34861 - 4.06792i) q^{74} +(0.243061 - 0.420994i) q^{76} -5.60555 q^{77} -9.21110 q^{79} +(1.65139 - 2.86029i) q^{80} +(-1.95416 - 3.38471i) q^{82} -5.21110 q^{83} +(0.197224 + 0.341603i) q^{85} -5.48612 q^{86} +(-8.40833 + 14.5636i) q^{88} +(4.10555 - 7.11102i) q^{89} +(1.80278 + 3.12250i) q^{91} -0.908327 q^{92} +(3.39445 - 5.87936i) q^{94} +(-0.802776 - 1.39045i) q^{95} +(7.80278 + 13.5148i) q^{97} +(-3.90833 - 6.76942i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 3 q^{4} + 4 q^{5} + 2 q^{7} + 12 q^{8} - q^{10} - 4 q^{11} - 2 q^{14} + 3 q^{16} + 8 q^{17} + 4 q^{19} - 3 q^{20} + 11 q^{22} - 6 q^{23} + 4 q^{25} + 13 q^{26} + 3 q^{28} + 2 q^{29} - 16 q^{31}+ \cdots + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.651388 1.12824i 0.460601 0.797784i −0.538390 0.842696i \(-0.680967\pi\)
0.998991 + 0.0449118i \(0.0143007\pi\)
\(3\) 0 0
\(4\) 0.151388 + 0.262211i 0.0756939 + 0.131106i
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i \(-0.106148\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) 0.651388 1.12824i 0.205987 0.356780i
\(11\) −2.80278 + 4.85455i −0.845069 + 1.46370i 0.0404929 + 0.999180i \(0.487107\pi\)
−0.885562 + 0.464522i \(0.846226\pi\)
\(12\) 0 0
\(13\) 3.60555 1.00000
\(14\) 1.30278 0.348181
\(15\) 0 0
\(16\) 1.65139 2.86029i 0.412847 0.715072i
\(17\) 0.197224 + 0.341603i 0.0478339 + 0.0828508i 0.888951 0.458002i \(-0.151435\pi\)
−0.841117 + 0.540853i \(0.818102\pi\)
\(18\) 0 0
\(19\) −0.802776 1.39045i −0.184169 0.318991i 0.759127 0.650943i \(-0.225626\pi\)
−0.943296 + 0.331952i \(0.892293\pi\)
\(20\) 0.151388 + 0.262211i 0.0338513 + 0.0586323i
\(21\) 0 0
\(22\) 3.65139 + 6.32439i 0.778478 + 1.34836i
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 2.34861 4.06792i 0.460601 0.797784i
\(27\) 0 0
\(28\) −0.151388 + 0.262211i −0.0286096 + 0.0495533i
\(29\) 4.10555 7.11102i 0.762382 1.32048i −0.179238 0.983806i \(-0.557363\pi\)
0.941620 0.336678i \(-0.109303\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0.848612 + 1.46984i 0.150015 + 0.259833i
\(33\) 0 0
\(34\) 0.513878 0.0881294
\(35\) 0.500000 + 0.866025i 0.0845154 + 0.146385i
\(36\) 0 0
\(37\) 1.80278 3.12250i 0.296374 0.513336i −0.678929 0.734204i \(-0.737556\pi\)
0.975304 + 0.220868i \(0.0708890\pi\)
\(38\) −2.09167 −0.339314
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 0 0
\(43\) −2.10555 3.64692i −0.321094 0.556150i 0.659620 0.751599i \(-0.270717\pi\)
−0.980714 + 0.195449i \(0.937384\pi\)
\(44\) −1.69722 −0.255866
\(45\) 0 0
\(46\) 1.95416 + 3.38471i 0.288126 + 0.499048i
\(47\) 5.21110 0.760117 0.380059 0.924962i \(-0.375904\pi\)
0.380059 + 0.924962i \(0.375904\pi\)
\(48\) 0 0
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 0.651388 1.12824i 0.0921201 0.159557i
\(51\) 0 0
\(52\) 0.545837 + 0.945417i 0.0756939 + 0.131106i
\(53\) −11.2111 −1.53996 −0.769982 0.638066i \(-0.779735\pi\)
−0.769982 + 0.638066i \(0.779735\pi\)
\(54\) 0 0
\(55\) −2.80278 + 4.85455i −0.377926 + 0.654587i
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) 0 0
\(58\) −5.34861 9.26407i −0.702307 1.21643i
\(59\) 5.40833 + 9.36750i 0.704104 + 1.21954i 0.967014 + 0.254724i \(0.0819845\pi\)
−0.262910 + 0.964820i \(0.584682\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −2.60555 + 4.51295i −0.330905 + 0.573145i
\(63\) 0 0
\(64\) 8.81665 1.10208
\(65\) 3.60555 0.447214
\(66\) 0 0
\(67\) 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) −0.0597147 + 0.103429i −0.00724147 + 0.0125426i
\(69\) 0 0
\(70\) 1.30278 0.155711
\(71\) −8.40833 14.5636i −0.997885 1.72839i −0.555240 0.831690i \(-0.687374\pi\)
−0.442645 0.896697i \(-0.645960\pi\)
\(72\) 0 0
\(73\) −15.2111 −1.78032 −0.890162 0.455643i \(-0.849409\pi\)
−0.890162 + 0.455643i \(0.849409\pi\)
\(74\) −2.34861 4.06792i −0.273021 0.472886i
\(75\) 0 0
\(76\) 0.243061 0.420994i 0.0278810 0.0482913i
\(77\) −5.60555 −0.638812
\(78\) 0 0
\(79\) −9.21110 −1.03633 −0.518165 0.855281i \(-0.673385\pi\)
−0.518165 + 0.855281i \(0.673385\pi\)
\(80\) 1.65139 2.86029i 0.184631 0.319790i
\(81\) 0 0
\(82\) −1.95416 3.38471i −0.215801 0.373779i
\(83\) −5.21110 −0.571993 −0.285996 0.958231i \(-0.592325\pi\)
−0.285996 + 0.958231i \(0.592325\pi\)
\(84\) 0 0
\(85\) 0.197224 + 0.341603i 0.0213920 + 0.0370520i
\(86\) −5.48612 −0.591584
\(87\) 0 0
\(88\) −8.40833 + 14.5636i −0.896331 + 1.55249i
\(89\) 4.10555 7.11102i 0.435188 0.753767i −0.562123 0.827053i \(-0.690015\pi\)
0.997311 + 0.0732864i \(0.0233487\pi\)
\(90\) 0 0
\(91\) 1.80278 + 3.12250i 0.188982 + 0.327327i
\(92\) −0.908327 −0.0946996
\(93\) 0 0
\(94\) 3.39445 5.87936i 0.350111 0.606409i
\(95\) −0.802776 1.39045i −0.0823630 0.142657i
\(96\) 0 0
\(97\) 7.80278 + 13.5148i 0.792252 + 1.37222i 0.924570 + 0.381013i \(0.124425\pi\)
−0.132318 + 0.991207i \(0.542242\pi\)
\(98\) −3.90833 6.76942i −0.394801 0.683815i
\(99\) 0 0
\(100\) 0.151388 + 0.262211i 0.0151388 + 0.0262211i
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 10.8167 1.06066
\(105\) 0 0
\(106\) −7.30278 + 12.6488i −0.709308 + 1.22856i
\(107\) −4.10555 + 7.11102i −0.396899 + 0.687449i −0.993342 0.115207i \(-0.963247\pi\)
0.596443 + 0.802656i \(0.296580\pi\)
\(108\) 0 0
\(109\) −4.78890 −0.458693 −0.229347 0.973345i \(-0.573659\pi\)
−0.229347 + 0.973345i \(0.573659\pi\)
\(110\) 3.65139 + 6.32439i 0.348146 + 0.603007i
\(111\) 0 0
\(112\) 3.30278 0.312083
\(113\) 2.80278 + 4.85455i 0.263663 + 0.456678i 0.967212 0.253969i \(-0.0817360\pi\)
−0.703550 + 0.710646i \(0.748403\pi\)
\(114\) 0 0
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) 2.48612 0.230831
\(117\) 0 0
\(118\) 14.0917 1.29724
\(119\) −0.197224 + 0.341603i −0.0180795 + 0.0313147i
\(120\) 0 0
\(121\) −10.2111 17.6861i −0.928282 1.60783i
\(122\) 1.30278 0.117948
\(123\) 0 0
\(124\) −0.605551 1.04885i −0.0543801 0.0941891i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.10555 + 8.84307i −0.453044 + 0.784696i −0.998573 0.0533960i \(-0.982995\pi\)
0.545529 + 0.838092i \(0.316329\pi\)
\(128\) 4.04584 7.00759i 0.357605 0.619390i
\(129\) 0 0
\(130\) 2.34861 4.06792i 0.205987 0.356780i
\(131\) 6.78890 0.593149 0.296574 0.955010i \(-0.404156\pi\)
0.296574 + 0.955010i \(0.404156\pi\)
\(132\) 0 0
\(133\) 0.802776 1.39045i 0.0696095 0.120567i
\(134\) −4.55971 7.89766i −0.393899 0.682254i
\(135\) 0 0
\(136\) 0.591673 + 1.02481i 0.0507355 + 0.0878765i
\(137\) 2.80278 + 4.85455i 0.239457 + 0.414752i 0.960559 0.278077i \(-0.0896972\pi\)
−0.721101 + 0.692830i \(0.756364\pi\)
\(138\) 0 0
\(139\) −6.80278 11.7828i −0.577004 0.999400i −0.995821 0.0913293i \(-0.970888\pi\)
0.418817 0.908071i \(-0.362445\pi\)
\(140\) −0.151388 + 0.262211i −0.0127946 + 0.0221609i
\(141\) 0 0
\(142\) −21.9083 −1.83851
\(143\) −10.1056 + 17.5033i −0.845069 + 1.46370i
\(144\) 0 0
\(145\) 4.10555 7.11102i 0.340947 0.590538i
\(146\) −9.90833 + 17.1617i −0.820019 + 1.42031i
\(147\) 0 0
\(148\) 1.09167 0.0897350
\(149\) 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i \(-0.127452\pi\)
−0.798019 + 0.602632i \(0.794119\pi\)
\(150\) 0 0
\(151\) 13.2111 1.07510 0.537552 0.843231i \(-0.319349\pi\)
0.537552 + 0.843231i \(0.319349\pi\)
\(152\) −2.40833 4.17134i −0.195341 0.338341i
\(153\) 0 0
\(154\) −3.65139 + 6.32439i −0.294237 + 0.509634i
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −3.21110 −0.256274 −0.128137 0.991756i \(-0.540900\pi\)
−0.128137 + 0.991756i \(0.540900\pi\)
\(158\) −6.00000 + 10.3923i −0.477334 + 0.826767i
\(159\) 0 0
\(160\) 0.848612 + 1.46984i 0.0670887 + 0.116201i
\(161\) −3.00000 −0.236433
\(162\) 0 0
\(163\) 9.10555 + 15.7713i 0.713202 + 1.23530i 0.963649 + 0.267172i \(0.0860890\pi\)
−0.250447 + 0.968130i \(0.580578\pi\)
\(164\) 0.908327 0.0709284
\(165\) 0 0
\(166\) −3.39445 + 5.87936i −0.263460 + 0.456327i
\(167\) 4.50000 7.79423i 0.348220 0.603136i −0.637713 0.770274i \(-0.720119\pi\)
0.985933 + 0.167139i \(0.0534527\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0.513878 0.0394127
\(171\) 0 0
\(172\) 0.637510 1.10420i 0.0486097 0.0841944i
\(173\) −8.40833 14.5636i −0.639273 1.10725i −0.985593 0.169137i \(-0.945902\pi\)
0.346319 0.938117i \(-0.387431\pi\)
\(174\) 0 0
\(175\) 0.500000 + 0.866025i 0.0377964 + 0.0654654i
\(176\) 9.25694 + 16.0335i 0.697768 + 1.20857i
\(177\) 0 0
\(178\) −5.34861 9.26407i −0.400895 0.694371i
\(179\) 0.591673 1.02481i 0.0442237 0.0765977i −0.843066 0.537810i \(-0.819252\pi\)
0.887290 + 0.461212i \(0.152585\pi\)
\(180\) 0 0
\(181\) −25.6333 −1.90531 −0.952654 0.304055i \(-0.901659\pi\)
−0.952654 + 0.304055i \(0.901659\pi\)
\(182\) 4.69722 0.348181
\(183\) 0 0
\(184\) −4.50000 + 7.79423i −0.331744 + 0.574598i
\(185\) 1.80278 3.12250i 0.132543 0.229571i
\(186\) 0 0
\(187\) −2.21110 −0.161692
\(188\) 0.788897 + 1.36641i 0.0575363 + 0.0996557i
\(189\) 0 0
\(190\) −2.09167 −0.151746
\(191\) −2.40833 4.17134i −0.174260 0.301828i 0.765645 0.643264i \(-0.222420\pi\)
−0.939905 + 0.341436i \(0.889087\pi\)
\(192\) 0 0
\(193\) −4.19722 + 7.26981i −0.302123 + 0.523292i −0.976617 0.214988i \(-0.931029\pi\)
0.674494 + 0.738281i \(0.264362\pi\)
\(194\) 20.3305 1.45965
\(195\) 0 0
\(196\) 1.81665 0.129761
\(197\) 11.4083 19.7598i 0.812810 1.40783i −0.0980804 0.995178i \(-0.531270\pi\)
0.910890 0.412649i \(-0.135396\pi\)
\(198\) 0 0
\(199\) 4.40833 + 7.63545i 0.312498 + 0.541262i 0.978902 0.204328i \(-0.0655009\pi\)
−0.666404 + 0.745590i \(0.732168\pi\)
\(200\) 3.00000 0.212132
\(201\) 0 0
\(202\) 5.86249 + 10.1541i 0.412483 + 0.714442i
\(203\) 8.21110 0.576306
\(204\) 0 0
\(205\) 1.50000 2.59808i 0.104765 0.181458i
\(206\) −2.60555 + 4.51295i −0.181537 + 0.314432i
\(207\) 0 0
\(208\) 5.95416 10.3129i 0.412847 0.715072i
\(209\) 9.00000 0.622543
\(210\) 0 0
\(211\) 8.19722 14.1980i 0.564320 0.977431i −0.432792 0.901494i \(-0.642472\pi\)
0.997113 0.0759376i \(-0.0241950\pi\)
\(212\) −1.69722 2.93968i −0.116566 0.201898i
\(213\) 0 0
\(214\) 5.34861 + 9.26407i 0.365624 + 0.633279i
\(215\) −2.10555 3.64692i −0.143597 0.248718i
\(216\) 0 0
\(217\) −2.00000 3.46410i −0.135769 0.235159i
\(218\) −3.11943 + 5.40301i −0.211274 + 0.365938i
\(219\) 0 0
\(220\) −1.69722 −0.114427
\(221\) 0.711103 + 1.23167i 0.0478339 + 0.0828508i
\(222\) 0 0
\(223\) −5.10555 + 8.84307i −0.341893 + 0.592176i −0.984784 0.173781i \(-0.944401\pi\)
0.642891 + 0.765957i \(0.277735\pi\)
\(224\) −0.848612 + 1.46984i −0.0567003 + 0.0982078i
\(225\) 0 0
\(226\) 7.30278 0.485773
\(227\) 0.711103 + 1.23167i 0.0471975 + 0.0817485i 0.888659 0.458569i \(-0.151638\pi\)
−0.841462 + 0.540317i \(0.818304\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 1.95416 + 3.38471i 0.128854 + 0.223181i
\(231\) 0 0
\(232\) 12.3167 21.3331i 0.808628 1.40058i
\(233\) −0.788897 −0.0516824 −0.0258412 0.999666i \(-0.508226\pi\)
−0.0258412 + 0.999666i \(0.508226\pi\)
\(234\) 0 0
\(235\) 5.21110 0.339935
\(236\) −1.63751 + 2.83625i −0.106593 + 0.184624i
\(237\) 0 0
\(238\) 0.256939 + 0.445032i 0.0166549 + 0.0288471i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −8.10555 14.0392i −0.522124 0.904346i −0.999669 0.0257384i \(-0.991806\pi\)
0.477544 0.878608i \(-0.341527\pi\)
\(242\) −26.6056 −1.71027
\(243\) 0 0
\(244\) −0.151388 + 0.262211i −0.00969161 + 0.0167864i
\(245\) 3.00000 5.19615i 0.191663 0.331970i
\(246\) 0 0
\(247\) −2.89445 5.01333i −0.184169 0.318991i
\(248\) −12.0000 −0.762001
\(249\) 0 0
\(250\) 0.651388 1.12824i 0.0411974 0.0713560i
\(251\) −14.4083 24.9560i −0.909446 1.57521i −0.814836 0.579691i \(-0.803173\pi\)
−0.0946094 0.995514i \(-0.530160\pi\)
\(252\) 0 0
\(253\) −8.40833 14.5636i −0.528627 0.915609i
\(254\) 6.65139 + 11.5205i 0.417345 + 0.722863i
\(255\) 0 0
\(256\) 3.54584 + 6.14157i 0.221615 + 0.383848i
\(257\) −11.8028 + 20.4430i −0.736237 + 1.27520i 0.217942 + 0.975962i \(0.430066\pi\)
−0.954179 + 0.299238i \(0.903268\pi\)
\(258\) 0 0
\(259\) 3.60555 0.224038
\(260\) 0.545837 + 0.945417i 0.0338513 + 0.0586323i
\(261\) 0 0
\(262\) 4.42221 7.65948i 0.273205 0.473204i
\(263\) 13.1056 22.6995i 0.808123 1.39971i −0.106040 0.994362i \(-0.533817\pi\)
0.914162 0.405348i \(-0.132850\pi\)
\(264\) 0 0
\(265\) −11.2111 −0.688693
\(266\) −1.04584 1.81144i −0.0641244 0.111067i
\(267\) 0 0
\(268\) 2.11943 0.129465
\(269\) −4.50000 7.79423i −0.274370 0.475223i 0.695606 0.718423i \(-0.255136\pi\)
−0.969976 + 0.243201i \(0.921803\pi\)
\(270\) 0 0
\(271\) −0.408327 + 0.707243i −0.0248041 + 0.0429620i −0.878161 0.478365i \(-0.841230\pi\)
0.853357 + 0.521327i \(0.174563\pi\)
\(272\) 1.30278 0.0789924
\(273\) 0 0
\(274\) 7.30278 0.441177
\(275\) −2.80278 + 4.85455i −0.169014 + 0.292740i
\(276\) 0 0
\(277\) −10.1972 17.6621i −0.612692 1.06121i −0.990785 0.135446i \(-0.956753\pi\)
0.378093 0.925768i \(-0.376580\pi\)
\(278\) −17.7250 −1.06307
\(279\) 0 0
\(280\) 1.50000 + 2.59808i 0.0896421 + 0.155265i
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −2.50000 + 4.33013i −0.148610 + 0.257399i −0.930714 0.365748i \(-0.880813\pi\)
0.782104 + 0.623148i \(0.214146\pi\)
\(284\) 2.54584 4.40952i 0.151068 0.261657i
\(285\) 0 0
\(286\) 13.1653 + 22.8029i 0.778478 + 1.34836i
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) 8.42221 14.5877i 0.495424 0.858099i
\(290\) −5.34861 9.26407i −0.314081 0.544005i
\(291\) 0 0
\(292\) −2.30278 3.98852i −0.134760 0.233411i
\(293\) 8.80278 + 15.2469i 0.514264 + 0.890731i 0.999863 + 0.0165493i \(0.00526805\pi\)
−0.485599 + 0.874181i \(0.661399\pi\)
\(294\) 0 0
\(295\) 5.40833 + 9.36750i 0.314885 + 0.545397i
\(296\) 5.40833 9.36750i 0.314353 0.544475i
\(297\) 0 0
\(298\) 3.90833 0.226403
\(299\) −5.40833 + 9.36750i −0.312772 + 0.541736i
\(300\) 0 0
\(301\) 2.10555 3.64692i 0.121362 0.210205i
\(302\) 8.60555 14.9053i 0.495194 0.857701i
\(303\) 0 0
\(304\) −5.30278 −0.304135
\(305\) 0.500000 + 0.866025i 0.0286299 + 0.0495885i
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) −0.848612 1.46984i −0.0483542 0.0837519i
\(309\) 0 0
\(310\) −2.60555 + 4.51295i −0.147985 + 0.256318i
\(311\) −5.21110 −0.295495 −0.147747 0.989025i \(-0.547202\pi\)
−0.147747 + 0.989025i \(0.547202\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) −2.09167 + 3.62288i −0.118040 + 0.204451i
\(315\) 0 0
\(316\) −1.39445 2.41526i −0.0784439 0.135869i
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) 23.0139 + 39.8612i 1.28853 + 2.23180i
\(320\) 8.81665 0.492866
\(321\) 0 0
\(322\) −1.95416 + 3.38471i −0.108901 + 0.188623i
\(323\) 0.316654 0.548461i 0.0176191 0.0305172i
\(324\) 0 0
\(325\) 3.60555 0.200000
\(326\) 23.7250 1.31401
\(327\) 0 0
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) 2.60555 + 4.51295i 0.143649 + 0.248807i
\(330\) 0 0
\(331\) 13.0139 + 22.5407i 0.715307 + 1.23895i 0.962841 + 0.270069i \(0.0870467\pi\)
−0.247533 + 0.968879i \(0.579620\pi\)
\(332\) −0.788897 1.36641i −0.0432964 0.0749915i
\(333\) 0 0
\(334\) −5.86249 10.1541i −0.320781 0.555609i
\(335\) 3.50000 6.06218i 0.191225 0.331212i
\(336\) 0 0
\(337\) 17.6333 0.960547 0.480274 0.877119i \(-0.340537\pi\)
0.480274 + 0.877119i \(0.340537\pi\)
\(338\) 8.46804 14.6671i 0.460601 0.797784i
\(339\) 0 0
\(340\) −0.0597147 + 0.103429i −0.00323849 + 0.00560922i
\(341\) 11.2111 19.4182i 0.607115 1.05155i
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) −6.31665 10.9408i −0.340571 0.589887i
\(345\) 0 0
\(346\) −21.9083 −1.17780
\(347\) 10.1056 + 17.5033i 0.542494 + 0.939628i 0.998760 + 0.0497842i \(0.0158534\pi\)
−0.456266 + 0.889844i \(0.650813\pi\)
\(348\) 0 0
\(349\) 9.10555 15.7713i 0.487409 0.844217i −0.512486 0.858695i \(-0.671275\pi\)
0.999895 + 0.0144783i \(0.00460876\pi\)
\(350\) 1.30278 0.0696363
\(351\) 0 0
\(352\) −9.51388 −0.507091
\(353\) −2.40833 + 4.17134i −0.128182 + 0.222018i −0.922972 0.384866i \(-0.874248\pi\)
0.794790 + 0.606884i \(0.207581\pi\)
\(354\) 0 0
\(355\) −8.40833 14.5636i −0.446268 0.772958i
\(356\) 2.48612 0.131764
\(357\) 0 0
\(358\) −0.770817 1.33509i −0.0407390 0.0705619i
\(359\) 10.4222 0.550063 0.275031 0.961435i \(-0.411312\pi\)
0.275031 + 0.961435i \(0.411312\pi\)
\(360\) 0 0
\(361\) 8.21110 14.2220i 0.432163 0.748529i
\(362\) −16.6972 + 28.9204i −0.877587 + 1.52002i
\(363\) 0 0
\(364\) −0.545837 + 0.945417i −0.0286096 + 0.0495533i
\(365\) −15.2111 −0.796185
\(366\) 0 0
\(367\) 8.71110 15.0881i 0.454716 0.787591i −0.543956 0.839114i \(-0.683074\pi\)
0.998672 + 0.0515228i \(0.0164075\pi\)
\(368\) 4.95416 + 8.58086i 0.258254 + 0.447308i
\(369\) 0 0
\(370\) −2.34861 4.06792i −0.122099 0.211481i
\(371\) −5.60555 9.70910i −0.291026 0.504071i
\(372\) 0 0
\(373\) 13.8028 + 23.9071i 0.714681 + 1.23786i 0.963083 + 0.269206i \(0.0867613\pi\)
−0.248402 + 0.968657i \(0.579905\pi\)
\(374\) −1.44029 + 2.49465i −0.0744754 + 0.128995i
\(375\) 0 0
\(376\) 15.6333 0.806226
\(377\) 14.8028 25.6392i 0.762382 1.32048i
\(378\) 0 0
\(379\) −1.19722 + 2.07365i −0.0614973 + 0.106516i −0.895135 0.445795i \(-0.852921\pi\)
0.833638 + 0.552312i \(0.186254\pi\)
\(380\) 0.243061 0.420994i 0.0124688 0.0215965i
\(381\) 0 0
\(382\) −6.27502 −0.321058
\(383\) 9.31665 + 16.1369i 0.476059 + 0.824558i 0.999624 0.0274277i \(-0.00873162\pi\)
−0.523565 + 0.851986i \(0.675398\pi\)
\(384\) 0 0
\(385\) −5.60555 −0.285685
\(386\) 5.46804 + 9.47093i 0.278316 + 0.482057i
\(387\) 0 0
\(388\) −2.36249 + 4.09195i −0.119937 + 0.207737i
\(389\) 0.788897 0.0399987 0.0199993 0.999800i \(-0.493634\pi\)
0.0199993 + 0.999800i \(0.493634\pi\)
\(390\) 0 0
\(391\) −1.18335 −0.0598444
\(392\) 9.00000 15.5885i 0.454569 0.787336i
\(393\) 0 0
\(394\) −14.8625 25.7426i −0.748761 1.29689i
\(395\) −9.21110 −0.463461
\(396\) 0 0
\(397\) 7.01388 + 12.1484i 0.352016 + 0.609710i 0.986603 0.163142i \(-0.0521628\pi\)
−0.634586 + 0.772852i \(0.718829\pi\)
\(398\) 11.4861 0.575747
\(399\) 0 0
\(400\) 1.65139 2.86029i 0.0825694 0.143014i
\(401\) −1.10555 + 1.91487i −0.0552086 + 0.0956241i −0.892309 0.451425i \(-0.850916\pi\)
0.837100 + 0.547049i \(0.184249\pi\)
\(402\) 0 0
\(403\) −14.4222 −0.718421
\(404\) −2.72498 −0.135573
\(405\) 0 0
\(406\) 5.34861 9.26407i 0.265447 0.459768i
\(407\) 10.1056 + 17.5033i 0.500914 + 0.867608i
\(408\) 0 0
\(409\) 3.10555 + 5.37897i 0.153560 + 0.265973i 0.932534 0.361083i \(-0.117593\pi\)
−0.778974 + 0.627056i \(0.784260\pi\)
\(410\) −1.95416 3.38471i −0.0965093 0.167159i
\(411\) 0 0
\(412\) −0.605551 1.04885i −0.0298334 0.0516729i
\(413\) −5.40833 + 9.36750i −0.266126 + 0.460944i
\(414\) 0 0
\(415\) −5.21110 −0.255803
\(416\) 3.05971 + 5.29958i 0.150015 + 0.259833i
\(417\) 0 0
\(418\) 5.86249 10.1541i 0.286744 0.496655i
\(419\) −16.6194 + 28.7857i −0.811912 + 1.40627i 0.0996117 + 0.995026i \(0.468240\pi\)
−0.911524 + 0.411247i \(0.865093\pi\)
\(420\) 0 0
\(421\) 3.57779 0.174371 0.0871855 0.996192i \(-0.472213\pi\)
0.0871855 + 0.996192i \(0.472213\pi\)
\(422\) −10.6791 18.4968i −0.519853 0.900411i
\(423\) 0 0
\(424\) −33.6333 −1.63338
\(425\) 0.197224 + 0.341603i 0.00956679 + 0.0165702i
\(426\) 0 0
\(427\) −0.500000 + 0.866025i −0.0241967 + 0.0419099i
\(428\) −2.48612 −0.120171
\(429\) 0 0
\(430\) −5.48612 −0.264564
\(431\) −10.6194 + 18.3934i −0.511520 + 0.885978i 0.488391 + 0.872625i \(0.337584\pi\)
−0.999911 + 0.0133535i \(0.995749\pi\)
\(432\) 0 0
\(433\) 1.80278 + 3.12250i 0.0866359 + 0.150058i 0.906087 0.423091i \(-0.139055\pi\)
−0.819451 + 0.573149i \(0.805722\pi\)
\(434\) −5.21110 −0.250141
\(435\) 0 0
\(436\) −0.724981 1.25570i −0.0347203 0.0601373i
\(437\) 4.81665 0.230412
\(438\) 0 0
\(439\) −11.6194 + 20.1254i −0.554565 + 0.960535i 0.443372 + 0.896338i \(0.353782\pi\)
−0.997937 + 0.0641973i \(0.979551\pi\)
\(440\) −8.40833 + 14.5636i −0.400851 + 0.694295i
\(441\) 0 0
\(442\) 1.85281 0.0881294
\(443\) 22.4222 1.06531 0.532656 0.846332i \(-0.321194\pi\)
0.532656 + 0.846332i \(0.321194\pi\)
\(444\) 0 0
\(445\) 4.10555 7.11102i 0.194622 0.337095i
\(446\) 6.65139 + 11.5205i 0.314952 + 0.545513i
\(447\) 0 0
\(448\) 4.40833 + 7.63545i 0.208274 + 0.360741i
\(449\) −6.31665 10.9408i −0.298101 0.516327i 0.677600 0.735430i \(-0.263020\pi\)
−0.975702 + 0.219104i \(0.929687\pi\)
\(450\) 0 0
\(451\) 8.40833 + 14.5636i 0.395933 + 0.685775i
\(452\) −0.848612 + 1.46984i −0.0399154 + 0.0691354i
\(453\) 0 0
\(454\) 1.85281 0.0869569
\(455\) 1.80278 + 3.12250i 0.0845154 + 0.146385i
\(456\) 0 0
\(457\) 2.59167 4.48891i 0.121233 0.209982i −0.799021 0.601303i \(-0.794648\pi\)
0.920254 + 0.391321i \(0.127982\pi\)
\(458\) 9.11943 15.7953i 0.426123 0.738067i
\(459\) 0 0
\(460\) −0.908327 −0.0423510
\(461\) 10.8944 + 18.8697i 0.507405 + 0.878851i 0.999963 + 0.00857184i \(0.00272854\pi\)
−0.492558 + 0.870280i \(0.663938\pi\)
\(462\) 0 0
\(463\) −5.57779 −0.259222 −0.129611 0.991565i \(-0.541373\pi\)
−0.129611 + 0.991565i \(0.541373\pi\)
\(464\) −13.5597 23.4861i −0.629494 1.09032i
\(465\) 0 0
\(466\) −0.513878 + 0.890063i −0.0238049 + 0.0412314i
\(467\) −17.2111 −0.796435 −0.398217 0.917291i \(-0.630371\pi\)
−0.398217 + 0.917291i \(0.630371\pi\)
\(468\) 0 0
\(469\) 7.00000 0.323230
\(470\) 3.39445 5.87936i 0.156574 0.271195i
\(471\) 0 0
\(472\) 16.2250 + 28.1025i 0.746815 + 1.29352i
\(473\) 23.6056 1.08538
\(474\) 0 0
\(475\) −0.802776 1.39045i −0.0368339 0.0637981i
\(476\) −0.119429 −0.00547404
\(477\) 0 0
\(478\) 0 0
\(479\) −3.59167 + 6.22096i −0.164108 + 0.284243i −0.936338 0.351100i \(-0.885808\pi\)
0.772230 + 0.635343i \(0.219141\pi\)
\(480\) 0 0
\(481\) 6.50000 11.2583i 0.296374 0.513336i
\(482\) −21.1194 −0.961964
\(483\) 0 0
\(484\) 3.09167 5.35493i 0.140531 0.243406i
\(485\) 7.80278 + 13.5148i 0.354306 + 0.613676i
\(486\) 0 0
\(487\) 0.500000 + 0.866025i 0.0226572 + 0.0392434i 0.877132 0.480250i \(-0.159454\pi\)
−0.854475 + 0.519493i \(0.826121\pi\)
\(488\) 1.50000 + 2.59808i 0.0679018 + 0.117609i
\(489\) 0 0
\(490\) −3.90833 6.76942i −0.176560 0.305811i
\(491\) 2.40833 4.17134i 0.108686 0.188250i −0.806552 0.591163i \(-0.798669\pi\)
0.915238 + 0.402913i \(0.132002\pi\)
\(492\) 0 0
\(493\) 3.23886 0.145871
\(494\) −7.54163 −0.339314
\(495\) 0 0
\(496\) −6.60555 + 11.4412i −0.296598 + 0.513723i
\(497\) 8.40833 14.5636i 0.377165 0.653269i
\(498\) 0 0
\(499\) −26.4222 −1.18282 −0.591410 0.806371i \(-0.701429\pi\)
−0.591410 + 0.806371i \(0.701429\pi\)
\(500\) 0.151388 + 0.262211i 0.00677027 + 0.0117265i
\(501\) 0 0
\(502\) −37.5416 −1.67557
\(503\) 1.50000 + 2.59808i 0.0668817 + 0.115842i 0.897527 0.440959i \(-0.145362\pi\)
−0.830645 + 0.556802i \(0.812028\pi\)
\(504\) 0 0
\(505\) −4.50000 + 7.79423i −0.200247 + 0.346839i
\(506\) −21.9083 −0.973944
\(507\) 0 0
\(508\) −3.09167 −0.137171
\(509\) 1.50000 2.59808i 0.0664863 0.115158i −0.830866 0.556473i \(-0.812154\pi\)
0.897352 + 0.441315i \(0.145488\pi\)
\(510\) 0 0
\(511\) −7.60555 13.1732i −0.336450 0.582748i
\(512\) 25.4222 1.12351
\(513\) 0 0
\(514\) 15.3764 + 26.6327i 0.678223 + 1.17472i
\(515\) −4.00000 −0.176261
\(516\) 0 0
\(517\) −14.6056 + 25.2976i −0.642351 + 1.11259i
\(518\) 2.34861 4.06792i 0.103192 0.178734i
\(519\) 0 0
\(520\) 10.8167 0.474342
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) −13.7111 + 23.7483i −0.599545 + 1.03844i 0.393344 + 0.919392i \(0.371318\pi\)
−0.992888 + 0.119050i \(0.962015\pi\)
\(524\) 1.02776 + 1.78013i 0.0448977 + 0.0777652i
\(525\) 0 0
\(526\) −17.0736 29.5723i −0.744444 1.28941i
\(527\) −0.788897 1.36641i −0.0343649 0.0595218i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) −7.30278 + 12.6488i −0.317212 + 0.549428i
\(531\) 0 0
\(532\) 0.486122 0.0210761
\(533\) 5.40833 9.36750i 0.234261 0.405751i
\(534\) 0 0
\(535\) −4.10555 + 7.11102i −0.177498 + 0.307436i
\(536\) 10.5000 18.1865i 0.453531 0.785539i
\(537\) 0 0
\(538\) −11.7250 −0.505500
\(539\) 16.8167 + 29.1273i 0.724345 + 1.25460i
\(540\) 0 0
\(541\) 17.6333 0.758115 0.379058 0.925373i \(-0.376248\pi\)
0.379058 + 0.925373i \(0.376248\pi\)
\(542\) 0.531958 + 0.921379i 0.0228496 + 0.0395766i
\(543\) 0 0
\(544\) −0.334734 + 0.579776i −0.0143516 + 0.0248577i
\(545\) −4.78890 −0.205134
\(546\) 0 0
\(547\) −24.8444 −1.06227 −0.531135 0.847287i \(-0.678234\pi\)
−0.531135 + 0.847287i \(0.678234\pi\)
\(548\) −0.848612 + 1.46984i −0.0362509 + 0.0627884i
\(549\) 0 0
\(550\) 3.65139 + 6.32439i 0.155696 + 0.269673i
\(551\) −13.1833 −0.561629
\(552\) 0 0
\(553\) −4.60555 7.97705i −0.195848 0.339219i
\(554\) −26.5694 −1.12883
\(555\) 0 0
\(556\) 2.05971 3.56753i 0.0873514 0.151297i
\(557\) 2.80278 4.85455i 0.118757 0.205694i −0.800518 0.599309i \(-0.795442\pi\)
0.919276 + 0.393615i \(0.128776\pi\)
\(558\) 0 0
\(559\) −7.59167 13.1492i −0.321094 0.556150i
\(560\) 3.30278 0.139568
\(561\) 0 0
\(562\) 3.90833 6.76942i 0.164863 0.285551i
\(563\) −9.71110 16.8201i −0.409274 0.708884i 0.585534 0.810648i \(-0.300885\pi\)
−0.994809 + 0.101764i \(0.967551\pi\)
\(564\) 0 0
\(565\) 2.80278 + 4.85455i 0.117914 + 0.204232i
\(566\) 3.25694 + 5.64118i 0.136899 + 0.237117i
\(567\) 0 0
\(568\) −25.2250 43.6909i −1.05842 1.83323i
\(569\) 0.711103 1.23167i 0.0298110 0.0516341i −0.850735 0.525595i \(-0.823843\pi\)
0.880546 + 0.473961i \(0.157176\pi\)
\(570\) 0 0
\(571\) −36.8444 −1.54189 −0.770945 0.636901i \(-0.780216\pi\)
−0.770945 + 0.636901i \(0.780216\pi\)
\(572\) −6.11943 −0.255866
\(573\) 0 0
\(574\) 1.95416 3.38471i 0.0815652 0.141275i
\(575\) −1.50000 + 2.59808i −0.0625543 + 0.108347i
\(576\) 0 0
\(577\) 29.6333 1.23365 0.616825 0.787100i \(-0.288418\pi\)
0.616825 + 0.787100i \(0.288418\pi\)
\(578\) −10.9722 19.0045i −0.456385 0.790482i
\(579\) 0 0
\(580\) 2.48612 0.103231
\(581\) −2.60555 4.51295i −0.108096 0.187229i
\(582\) 0 0
\(583\) 31.4222 54.4249i 1.30137 2.25405i
\(584\) −45.6333 −1.88832
\(585\) 0 0
\(586\) 22.9361 0.947481
\(587\) −2.28890 + 3.96449i −0.0944729 + 0.163632i −0.909389 0.415948i \(-0.863450\pi\)
0.814916 + 0.579580i \(0.196783\pi\)
\(588\) 0 0
\(589\) 3.21110 + 5.56179i 0.132311 + 0.229170i
\(590\) 14.0917 0.580145
\(591\) 0 0
\(592\) −5.95416 10.3129i −0.244715 0.423858i
\(593\) −35.2111 −1.44595 −0.722973 0.690876i \(-0.757225\pi\)
−0.722973 + 0.690876i \(0.757225\pi\)
\(594\) 0 0
\(595\) −0.197224 + 0.341603i −0.00808541 + 0.0140043i
\(596\) −0.454163 + 0.786634i −0.0186033 + 0.0322218i
\(597\) 0 0
\(598\) 7.04584 + 12.2037i 0.288126 + 0.499048i
\(599\) 6.78890 0.277387 0.138693 0.990335i \(-0.455710\pi\)
0.138693 + 0.990335i \(0.455710\pi\)
\(600\) 0 0
\(601\) −14.1056 + 24.4315i −0.575377 + 0.996583i 0.420623 + 0.907235i \(0.361811\pi\)
−0.996001 + 0.0893475i \(0.971522\pi\)
\(602\) −2.74306 4.75112i −0.111799 0.193641i
\(603\) 0 0
\(604\) 2.00000 + 3.46410i 0.0813788 + 0.140952i
\(605\) −10.2111 17.6861i −0.415140 0.719044i
\(606\) 0 0
\(607\) 9.89445 + 17.1377i 0.401603 + 0.695597i 0.993920 0.110108i \(-0.0351197\pi\)
−0.592316 + 0.805706i \(0.701786\pi\)
\(608\) 1.36249 2.35990i 0.0552563 0.0957067i
\(609\) 0 0
\(610\) 1.30278 0.0527478
\(611\) 18.7889 0.760117
\(612\) 0 0
\(613\) −0.802776 + 1.39045i −0.0324238 + 0.0561597i −0.881782 0.471657i \(-0.843656\pi\)
0.849358 + 0.527817i \(0.176989\pi\)
\(614\) −10.4222 + 18.0518i −0.420606 + 0.728511i
\(615\) 0 0
\(616\) −16.8167 −0.677562
\(617\) 13.2250 + 22.9063i 0.532418 + 0.922174i 0.999284 + 0.0378463i \(0.0120497\pi\)
−0.466866 + 0.884328i \(0.654617\pi\)
\(618\) 0 0
\(619\) −14.4222 −0.579677 −0.289839 0.957076i \(-0.593602\pi\)
−0.289839 + 0.957076i \(0.593602\pi\)
\(620\) −0.605551 1.04885i −0.0243195 0.0421227i
\(621\) 0 0
\(622\) −3.39445 + 5.87936i −0.136105 + 0.235741i
\(623\) 8.21110 0.328971
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 9.11943 15.7953i 0.364486 0.631308i
\(627\) 0 0
\(628\) −0.486122 0.841988i −0.0193984 0.0335990i
\(629\) 1.42221 0.0567070
\(630\) 0 0
\(631\) −0.0138782 0.0240377i −0.000552482 0.000956927i 0.865749 0.500478i \(-0.166843\pi\)
−0.866302 + 0.499521i \(0.833509\pi\)
\(632\) −27.6333 −1.09919
\(633\) 0 0
\(634\) −3.90833 + 6.76942i −0.155219 + 0.268848i
\(635\) −5.10555 + 8.84307i −0.202608 + 0.350927i
\(636\) 0 0
\(637\) 10.8167 18.7350i 0.428571 0.742307i
\(638\) 59.9638 2.37399
\(639\) 0 0
\(640\) 4.04584 7.00759i 0.159926 0.276999i
\(641\) −9.71110 16.8201i −0.383565 0.664355i 0.608004 0.793934i \(-0.291971\pi\)
−0.991569 + 0.129579i \(0.958637\pi\)
\(642\) 0 0
\(643\) 20.3167 + 35.1895i 0.801211 + 1.38774i 0.918820 + 0.394678i \(0.129144\pi\)
−0.117609 + 0.993060i \(0.537523\pi\)
\(644\) −0.454163 0.786634i −0.0178965 0.0309977i
\(645\) 0 0
\(646\) −0.412529 0.714521i −0.0162307 0.0281125i
\(647\) 5.28890 9.16064i 0.207928 0.360142i −0.743134 0.669143i \(-0.766661\pi\)
0.951062 + 0.309001i \(0.0999947\pi\)
\(648\) 0 0
\(649\) −60.6333 −2.38007
\(650\) 2.34861 4.06792i 0.0921201 0.159557i
\(651\) 0 0
\(652\) −2.75694 + 4.77516i −0.107970 + 0.187010i
\(653\) −14.4083 + 24.9560i −0.563841 + 0.976602i 0.433315 + 0.901243i \(0.357344\pi\)
−0.997156 + 0.0753594i \(0.975990\pi\)
\(654\) 0 0
\(655\) 6.78890 0.265264
\(656\) −4.95416 8.58086i −0.193428 0.335026i
\(657\) 0 0
\(658\) 6.78890 0.264659
\(659\) −6.59167 11.4171i −0.256775 0.444748i 0.708601 0.705609i \(-0.249327\pi\)
−0.965376 + 0.260862i \(0.915993\pi\)
\(660\) 0 0
\(661\) −19.3167 + 33.4574i −0.751331 + 1.30134i 0.195847 + 0.980634i \(0.437254\pi\)
−0.947178 + 0.320709i \(0.896079\pi\)
\(662\) 33.9083 1.31788
\(663\) 0 0
\(664\) −15.6333 −0.606690
\(665\) 0.802776 1.39045i 0.0311303 0.0539193i
\(666\) 0 0
\(667\) 12.3167 + 21.3331i 0.476903 + 0.826020i
\(668\) 2.72498 0.105433
\(669\) 0 0
\(670\) −4.55971 7.89766i −0.176157 0.305113i
\(671\) −5.60555 −0.216400
\(672\) 0 0
\(673\) 5.19722 9.00186i 0.200338 0.346996i −0.748299 0.663361i \(-0.769129\pi\)
0.948637 + 0.316365i \(0.102463\pi\)
\(674\) 11.4861 19.8945i 0.442429 0.766309i
\(675\) 0 0
\(676\) 1.96804 + 3.40875i 0.0756939 + 0.131106i
\(677\) −33.6333 −1.29263 −0.646317 0.763069i \(-0.723691\pi\)
−0.646317 + 0.763069i \(0.723691\pi\)
\(678\) 0 0
\(679\) −7.80278 + 13.5148i −0.299443 + 0.518651i
\(680\) 0.591673 + 1.02481i 0.0226896 + 0.0392996i
\(681\) 0 0
\(682\) −14.6056 25.2976i −0.559275 0.968694i
\(683\) 10.8944 + 18.8697i 0.416864 + 0.722030i 0.995622 0.0934691i \(-0.0297956\pi\)
−0.578758 + 0.815500i \(0.696462\pi\)
\(684\) 0 0
\(685\) 2.80278 + 4.85455i 0.107089 + 0.185483i
\(686\) 8.46804 14.6671i 0.323311 0.559992i
\(687\) 0 0
\(688\) −13.9083 −0.530250
\(689\) −40.4222 −1.53996
\(690\) 0 0
\(691\) −3.01388 + 5.22019i −0.114653 + 0.198585i −0.917641 0.397410i \(-0.869909\pi\)
0.802988 + 0.595995i \(0.203242\pi\)
\(692\) 2.54584 4.40952i 0.0967782 0.167625i
\(693\) 0 0
\(694\) 26.3305 0.999493
\(695\) −6.80278 11.7828i −0.258044 0.446945i
\(696\) 0 0
\(697\) 1.18335 0.0448224
\(698\) −11.8625 20.5464i −0.449002 0.777694i
\(699\) 0 0
\(700\) −0.151388 + 0.262211i −0.00572192 + 0.00991066i
\(701\) 7.57779 0.286209 0.143105 0.989708i \(-0.454291\pi\)
0.143105 + 0.989708i \(0.454291\pi\)
\(702\) 0 0
\(703\) −5.78890 −0.218332
\(704\) −24.7111 + 42.8009i −0.931335 + 1.61312i
\(705\) 0 0
\(706\) 3.13751 + 5.43433i 0.118082 + 0.204524i
\(707\) −9.00000 −0.338480
\(708\) 0 0
\(709\) −21.9222 37.9704i −0.823306 1.42601i −0.903207 0.429205i \(-0.858794\pi\)
0.0799016 0.996803i \(-0.474539\pi\)
\(710\) −21.9083 −0.822205
\(711\) 0 0
\(712\) 12.3167 21.3331i 0.461586 0.799491i
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 0 0
\(715\) −10.1056 + 17.5033i −0.377926 + 0.654587i
\(716\) 0.358288 0.0133899
\(717\) 0 0
\(718\) 6.78890 11.7587i 0.253359 0.438831i
\(719\) −9.19722 15.9301i −0.342999 0.594091i 0.641989 0.766713i \(-0.278109\pi\)
−0.984988 + 0.172622i \(0.944776\pi\)
\(720\) 0 0
\(721\) −2.00000 3.46410i −0.0744839 0.129010i
\(722\) −10.6972 18.5281i −0.398109 0.689546i
\(723\) 0 0
\(724\) −3.88057 6.72135i −0.144220 0.249797i
\(725\) 4.10555 7.11102i 0.152476 0.264097i
\(726\) 0 0
\(727\) 42.4222 1.57335 0.786676 0.617366i \(-0.211800\pi\)
0.786676 + 0.617366i \(0.211800\pi\)
\(728\) 5.40833 + 9.36750i 0.200446 + 0.347183i
\(729\) 0 0
\(730\) −9.90833 + 17.1617i −0.366724 + 0.635184i
\(731\) 0.830532 1.43852i 0.0307183 0.0532057i
\(732\) 0 0
\(733\) 10.8444 0.400547 0.200274 0.979740i \(-0.435817\pi\)
0.200274 + 0.979740i \(0.435817\pi\)
\(734\) −11.3486 19.6564i −0.418885 0.725530i
\(735\) 0 0
\(736\) −5.09167 −0.187682
\(737\) 19.6194 + 33.9818i 0.722691 + 1.25174i
\(738\) 0 0
\(739\) 14.1972 24.5903i 0.522253 0.904569i −0.477411 0.878680i \(-0.658425\pi\)
0.999665 0.0258895i \(-0.00824179\pi\)
\(740\) 1.09167 0.0401307
\(741\) 0 0
\(742\) −14.6056 −0.536187
\(743\) −3.31665 + 5.74461i −0.121676 + 0.210749i −0.920429 0.390910i \(-0.872160\pi\)
0.798753 + 0.601660i \(0.205494\pi\)
\(744\) 0 0
\(745\) 1.50000 + 2.59808i 0.0549557 + 0.0951861i
\(746\) 35.9638 1.31673
\(747\) 0 0
\(748\) −0.334734 0.579776i −0.0122391 0.0211987i
\(749\) −8.21110 −0.300027
\(750\) 0 0
\(751\) 9.22498 15.9781i 0.336624 0.583050i −0.647171 0.762345i \(-0.724048\pi\)
0.983795 + 0.179294i \(0.0573814\pi\)
\(752\) 8.60555 14.9053i 0.313812 0.543539i
\(753\) 0 0
\(754\) −19.2847 33.4021i −0.702307 1.21643i
\(755\) 13.2111 0.480801
\(756\) 0 0
\(757\) 10.4083 18.0278i 0.378297 0.655230i −0.612518 0.790457i \(-0.709843\pi\)
0.990815 + 0.135227i \(0.0431764\pi\)
\(758\) 1.55971 + 2.70151i 0.0566514 + 0.0981231i
\(759\) 0 0
\(760\) −2.40833 4.17134i −0.0873592 0.151311i
\(761\) −12.3167 21.3331i −0.446478 0.773323i 0.551676 0.834059i \(-0.313989\pi\)
−0.998154 + 0.0607356i \(0.980655\pi\)
\(762\) 0 0
\(763\) −2.39445 4.14731i −0.0866849 0.150143i
\(764\) 0.729183 1.26298i 0.0263809 0.0456931i
\(765\) 0 0
\(766\) 24.2750 0.877092
\(767\) 19.5000 + 33.7750i 0.704104 + 1.21954i
\(768\) 0 0
\(769\) −5.50000 + 9.52628i −0.198335 + 0.343526i −0.947989 0.318304i \(-0.896887\pi\)
0.749654 + 0.661830i \(0.230220\pi\)
\(770\) −3.65139 + 6.32439i −0.131587 + 0.227915i
\(771\) 0 0
\(772\) −2.54163 −0.0914754
\(773\) 14.8028 + 25.6392i 0.532419 + 0.922176i 0.999284 + 0.0378477i \(0.0120502\pi\)
−0.466865 + 0.884329i \(0.654616\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 23.4083 + 40.5444i 0.840310 + 1.45546i
\(777\) 0 0
\(778\) 0.513878 0.890063i 0.0184234 0.0319103i
\(779\) −4.81665 −0.172575
\(780\) 0 0
\(781\) 94.2666 3.37312
\(782\) −0.770817 + 1.33509i −0.0275644 + 0.0477429i
\(783\) 0 0
\(784\) −9.90833 17.1617i −0.353869 0.612919i
\(785\) −3.21110 −0.114609
\(786\) 0 0
\(787\) 14.3167 + 24.7972i 0.510334 + 0.883924i 0.999928 + 0.0119736i \(0.00381140\pi\)
−0.489595 + 0.871950i \(0.662855\pi\)
\(788\) 6.90833 0.246099
\(789\) 0 0
\(790\) −6.00000 + 10.3923i −0.213470 + 0.369742i
\(791\) −2.80278 + 4.85455i −0.0996552 + 0.172608i
\(792\) 0 0
\(793\) 1.80278 + 3.12250i 0.0640184 + 0.110883i
\(794\) 18.2750 0.648556
\(795\) 0 0
\(796\) −1.33473 + 2.31183i −0.0473084 + 0.0819405i
\(797\) 25.2250 + 43.6909i 0.893515 + 1.54761i 0.835632 + 0.549289i \(0.185102\pi\)
0.0578825 + 0.998323i \(0.481565\pi\)
\(798\) 0 0
\(799\) 1.02776 + 1.78013i 0.0363594 + 0.0629763i
\(800\) 0.848612 + 1.46984i 0.0300030 + 0.0519667i
\(801\) 0 0
\(802\) 1.44029 + 2.49465i 0.0508582 + 0.0880891i
\(803\) 42.6333 73.8431i 1.50450 2.60586i
\(804\) 0 0
\(805\) −3.00000 −0.105736
\(806\) −9.39445 + 16.2717i −0.330905 + 0.573145i
\(807\) 0 0
\(808\) −13.5000 + 23.3827i −0.474928 + 0.822600i
\(809\) 8.52776 14.7705i 0.299820 0.519303i −0.676275 0.736650i \(-0.736407\pi\)
0.976095 + 0.217346i \(0.0697401\pi\)
\(810\) 0 0
\(811\) −17.5778 −0.617240 −0.308620 0.951185i \(-0.599867\pi\)
−0.308620 + 0.951185i \(0.599867\pi\)
\(812\) 1.24306 + 2.15304i 0.0436229 + 0.0755571i
\(813\) 0 0
\(814\) 26.3305 0.922885
\(815\) 9.10555 + 15.7713i 0.318954 + 0.552444i
\(816\) 0 0
\(817\) −3.38057 + 5.85532i −0.118271 + 0.204852i
\(818\) 8.09167 0.282919
\(819\) 0 0
\(820\) 0.908327 0.0317202
\(821\) −3.71110 + 6.42782i −0.129518 + 0.224332i −0.923490 0.383622i \(-0.874676\pi\)
0.793972 + 0.607955i \(0.208010\pi\)
\(822\) 0 0
\(823\) −13.3167 23.0651i −0.464189 0.804000i 0.534975 0.844868i \(-0.320321\pi\)
−0.999165 + 0.0408682i \(0.986988\pi\)
\(824\) −12.0000 −0.418040
\(825\) 0 0
\(826\) 7.04584 + 12.2037i 0.245156 + 0.424623i
\(827\) 13.5778 0.472146 0.236073 0.971735i \(-0.424140\pi\)
0.236073 + 0.971735i \(0.424140\pi\)
\(828\) 0 0
\(829\) −0.288897 + 0.500385i −0.0100338 + 0.0173791i −0.870999 0.491285i \(-0.836527\pi\)
0.860965 + 0.508664i \(0.169861\pi\)
\(830\) −3.39445 + 5.87936i −0.117823 + 0.204075i
\(831\) 0 0
\(832\) 31.7889 1.10208
\(833\) 2.36669 0.0820010
\(834\) 0 0
\(835\) 4.50000 7.79423i 0.155729 0.269730i
\(836\) 1.36249 + 2.35990i 0.0471227 + 0.0816189i
\(837\) 0 0
\(838\) 21.6514 + 37.5013i 0.747935 + 1.29546i
\(839\) 8.01388 + 13.8804i 0.276670 + 0.479206i 0.970555 0.240879i \(-0.0774358\pi\)
−0.693885 + 0.720086i \(0.744103\pi\)
\(840\) 0 0
\(841\) −19.2111 33.2746i −0.662452 1.14740i
\(842\) 2.33053 4.03660i 0.0803154 0.139110i
\(843\) 0 0
\(844\) 4.96384 0.170862
\(845\) 13.0000 0.447214
\(846\) 0 0
\(847\) 10.2111 17.6861i 0.350858 0.607703i
\(848\) −18.5139 + 32.0670i −0.635769 + 1.10118i
\(849\) 0 0
\(850\) 0.513878 0.0176259
\(851\) 5.40833 + 9.36750i 0.185395 + 0.321114i
\(852\) 0 0
\(853\) 32.7889 1.12267 0.561335 0.827589i \(-0.310288\pi\)
0.561335 + 0.827589i \(0.310288\pi\)
\(854\) 0.651388 + 1.12824i 0.0222900 + 0.0386075i
\(855\) 0 0
\(856\) −12.3167 + 21.3331i −0.420975 + 0.729149i
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 0 0
\(859\) 25.2111 0.860192 0.430096 0.902783i \(-0.358480\pi\)
0.430096 + 0.902783i \(0.358480\pi\)
\(860\) 0.637510 1.10420i 0.0217389 0.0376529i
\(861\) 0 0
\(862\) 13.8347 + 23.9625i 0.471213 + 0.816165i
\(863\) −36.0000 −1.22545 −0.612727 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 0 0
\(865\) −8.40833 14.5636i −0.285892 0.495179i
\(866\) 4.69722 0.159618
\(867\) 0 0
\(868\) 0.605551 1.04885i 0.0205537 0.0356001i
\(869\) 25.8167 44.7158i 0.875770 1.51688i
\(870\) 0 0
\(871\) 12.6194 21.8575i 0.427593 0.740613i
\(872\) −14.3667 −0.486518
\(873\) 0 0
\(874\) 3.13751 5.43433i 0.106128 0.183819i
\(875\) 0.500000 + 0.866025i 0.0169031 + 0.0292770i
\(876\) 0 0
\(877\) 19.0139 + 32.9330i 0.642053 + 1.11207i 0.984974 + 0.172704i \(0.0552504\pi\)
−0.342921 + 0.939364i \(0.611416\pi\)
\(878\) 15.1375 + 26.2189i 0.510866 + 0.884846i
\(879\) 0 0
\(880\) 9.25694 + 16.0335i 0.312051 + 0.540489i
\(881\) 17.9222 31.0422i 0.603814 1.04584i −0.388423 0.921481i \(-0.626980\pi\)
0.992238 0.124356i \(-0.0396865\pi\)
\(882\) 0 0
\(883\) −31.6333 −1.06455 −0.532273 0.846573i \(-0.678662\pi\)
−0.532273 + 0.846573i \(0.678662\pi\)
\(884\) −0.215305 + 0.372918i −0.00724147 + 0.0125426i
\(885\) 0 0
\(886\) 14.6056 25.2976i 0.490683 0.849888i
\(887\) 17.5278 30.3590i 0.588524 1.01935i −0.405901 0.913917i \(-0.633042\pi\)
0.994426 0.105437i \(-0.0336243\pi\)
\(888\) 0 0
\(889\) −10.2111 −0.342469
\(890\) −5.34861 9.26407i −0.179286 0.310532i
\(891\) 0 0
\(892\) −3.09167 −0.103517
\(893\) −4.18335 7.24577i −0.139990 0.242470i
\(894\) 0 0
\(895\) 0.591673 1.02481i 0.0197775 0.0342555i
\(896\) 8.09167 0.270324
\(897\) 0 0
\(898\) −16.4584 −0.549223
\(899\) −16.4222 + 28.4441i −0.547711 + 0.948664i
\(900\) 0 0
\(901\) −2.21110 3.82974i −0.0736625 0.127587i
\(902\) 21.9083 0.729467
\(903\) 0 0
\(904\) 8.40833 + 14.5636i 0.279657 + 0.484380i
\(905\) −25.6333 −0.852080
\(906\) 0 0
\(907\) −24.1333 + 41.8001i −0.801333 + 1.38795i 0.117405 + 0.993084i \(0.462542\pi\)
−0.918739 + 0.394866i \(0.870791\pi\)
\(908\) −0.215305 + 0.372918i −0.00714513 + 0.0123757i
\(909\) 0 0
\(910\) 4.69722 0.155711
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 0 0
\(913\) 14.6056 25.2976i 0.483373 0.837227i
\(914\) −3.37637 5.84804i −0.111680 0.193436i
\(915\) 0 0
\(916\) 2.11943 + 3.67096i 0.0700279 + 0.121292i
\(917\) 3.39445 + 5.87936i 0.112095 + 0.194153i
\(918\) 0 0
\(919\) 8.59167 + 14.8812i 0.283413 + 0.490886i 0.972223 0.234056i \(-0.0751999\pi\)
−0.688810 + 0.724942i \(0.741867\pi\)
\(920\) −4.50000 + 7.79423i −0.148361 + 0.256968i
\(921\) 0 0
\(922\) 28.3860 0.934845
\(923\) −30.3167 52.5100i −0.997885 1.72839i
\(924\) 0 0
\(925\) 1.80278 3.12250i 0.0592749 0.102667i
\(926\) −3.63331 + 6.29307i −0.119398 + 0.206803i
\(927\) 0 0
\(928\) 13.9361 0.457474
\(929\) 6.71110 + 11.6240i 0.220184 + 0.381370i 0.954864 0.297044i \(-0.0960008\pi\)
−0.734680 + 0.678414i \(0.762668\pi\)
\(930\) 0 0
\(931\) −9.63331 −0.315719
\(932\) −0.119429 0.206858i −0.00391204 0.00677586i
\(933\) 0 0
\(934\) −11.2111 + 19.4182i −0.366838 + 0.635383i
\(935\) −2.21110 −0.0723108
\(936\) 0 0
\(937\) −46.4777 −1.51836 −0.759180 0.650880i \(-0.774400\pi\)
−0.759180 + 0.650880i \(0.774400\pi\)
\(938\) 4.55971 7.89766i 0.148880 0.257868i
\(939\) 0 0
\(940\) 0.788897 + 1.36641i 0.0257310 + 0.0445674i
\(941\) −33.6333 −1.09641 −0.548207 0.836343i \(-0.684689\pi\)
−0.548207 + 0.836343i \(0.684689\pi\)
\(942\) 0 0
\(943\) 4.50000 + 7.79423i 0.146540 + 0.253815i
\(944\) 35.7250 1.16275
\(945\) 0 0
\(946\) 15.3764 26.6327i 0.499929 0.865902i
\(947\) 12.3167 21.3331i 0.400237 0.693232i −0.593517 0.804822i \(-0.702261\pi\)
0.993754 + 0.111590i \(0.0355943\pi\)
\(948\) 0 0
\(949\) −54.8444 −1.78032
\(950\) −2.09167 −0.0678628
\(951\) 0 0
\(952\) −0.591673 + 1.02481i −0.0191762 + 0.0332142i
\(953\) 25.2250 + 43.6909i 0.817117 + 1.41529i 0.907798 + 0.419409i \(0.137763\pi\)
−0.0906803 + 0.995880i \(0.528904\pi\)
\(954\) 0 0
\(955\) −2.40833 4.17134i −0.0779316 0.134982i
\(956\) 0 0
\(957\) 0 0
\(958\) 4.67914 + 8.10452i 0.151176 + 0.261845i
\(959\) −2.80278 + 4.85455i −0.0905063 + 0.156762i
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −8.46804 14.6671i −0.273021 0.472886i
\(963\) 0 0
\(964\) 2.45416 4.25074i 0.0790433 0.136907i
\(965\) −4.19722 + 7.26981i −0.135113 + 0.234023i
\(966\) 0 0
\(967\) 56.4777 1.81620 0.908100 0.418752i \(-0.137532\pi\)
0.908100 + 0.418752i \(0.137532\pi\)
\(968\) −30.6333 53.0584i −0.984592 1.70536i
\(969\) 0 0
\(970\) 20.3305 0.652774
\(971\) −3.98612 6.90417i −0.127921 0.221565i 0.794950 0.606675i \(-0.207497\pi\)
−0.922871 + 0.385110i \(0.874164\pi\)
\(972\) 0 0
\(973\) 6.80278 11.7828i 0.218087 0.377738i
\(974\) 1.30278 0.0417436
\(975\) 0 0
\(976\) 3.30278 0.105719
\(977\) 3.59167 6.22096i 0.114908 0.199026i −0.802835 0.596201i \(-0.796676\pi\)
0.917743 + 0.397175i \(0.130009\pi\)
\(978\) 0 0
\(979\) 23.0139 + 39.8612i 0.735527 + 1.27397i
\(980\) 1.81665 0.0580309
\(981\) 0 0
\(982\) −3.13751 5.43433i −0.100122 0.173416i
\(983\) 10.4222 0.332417 0.166208 0.986091i \(-0.446848\pi\)
0.166208 + 0.986091i \(0.446848\pi\)
\(984\) 0 0
\(985\) 11.4083 19.7598i 0.363500 0.629600i
\(986\) 2.10975 3.65420i 0.0671882 0.116373i
\(987\) 0 0
\(988\) 0.876369 1.51791i 0.0278810 0.0482913i
\(989\) 12.6333 0.401716
\(990\) 0 0
\(991\) −1.98612 + 3.44006i −0.0630912 + 0.109277i −0.895846 0.444365i \(-0.853429\pi\)
0.832754 + 0.553642i \(0.186763\pi\)
\(992\) −3.39445 5.87936i −0.107774 0.186670i
\(993\) 0 0
\(994\) −10.9542 18.9732i −0.347445 0.601792i
\(995\) 4.40833 + 7.63545i 0.139753 + 0.242060i
\(996\) 0 0
\(997\) −23.2250 40.2268i −0.735543 1.27400i −0.954485 0.298259i \(-0.903594\pi\)
0.218942 0.975738i \(-0.429739\pi\)
\(998\) −17.2111 + 29.8105i −0.544808 + 0.943635i
\(999\) 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 585.2.j.d.451.2 4
3.2 odd 2 65.2.e.b.61.1 yes 4
12.11 even 2 1040.2.q.o.321.1 4
13.3 even 3 inner 585.2.j.d.406.2 4
13.4 even 6 7605.2.a.bb.1.2 2
13.9 even 3 7605.2.a.bg.1.1 2
15.2 even 4 325.2.o.b.74.2 8
15.8 even 4 325.2.o.b.74.3 8
15.14 odd 2 325.2.e.a.126.2 4
39.2 even 12 845.2.m.d.361.2 8
39.5 even 4 845.2.m.d.316.3 8
39.8 even 4 845.2.m.d.316.2 8
39.11 even 12 845.2.m.d.361.3 8
39.17 odd 6 845.2.a.f.1.1 2
39.20 even 12 845.2.c.d.506.3 4
39.23 odd 6 845.2.e.d.146.2 4
39.29 odd 6 65.2.e.b.16.1 4
39.32 even 12 845.2.c.d.506.2 4
39.35 odd 6 845.2.a.c.1.2 2
39.38 odd 2 845.2.e.d.191.2 4
156.107 even 6 1040.2.q.o.81.1 4
195.29 odd 6 325.2.e.a.276.2 4
195.68 even 12 325.2.o.b.224.2 8
195.74 odd 6 4225.2.a.x.1.1 2
195.107 even 12 325.2.o.b.224.3 8
195.134 odd 6 4225.2.a.t.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.e.b.16.1 4 39.29 odd 6
65.2.e.b.61.1 yes 4 3.2 odd 2
325.2.e.a.126.2 4 15.14 odd 2
325.2.e.a.276.2 4 195.29 odd 6
325.2.o.b.74.2 8 15.2 even 4
325.2.o.b.74.3 8 15.8 even 4
325.2.o.b.224.2 8 195.68 even 12
325.2.o.b.224.3 8 195.107 even 12
585.2.j.d.406.2 4 13.3 even 3 inner
585.2.j.d.451.2 4 1.1 even 1 trivial
845.2.a.c.1.2 2 39.35 odd 6
845.2.a.f.1.1 2 39.17 odd 6
845.2.c.d.506.2 4 39.32 even 12
845.2.c.d.506.3 4 39.20 even 12
845.2.e.d.146.2 4 39.23 odd 6
845.2.e.d.191.2 4 39.38 odd 2
845.2.m.d.316.2 8 39.8 even 4
845.2.m.d.316.3 8 39.5 even 4
845.2.m.d.361.2 8 39.2 even 12
845.2.m.d.361.3 8 39.11 even 12
1040.2.q.o.81.1 4 156.107 even 6
1040.2.q.o.321.1 4 12.11 even 2
4225.2.a.t.1.2 2 195.134 odd 6
4225.2.a.x.1.1 2 195.74 odd 6
7605.2.a.bb.1.2 2 13.4 even 6
7605.2.a.bg.1.1 2 13.9 even 3