Properties

Label 585.2.j.d.406.1
Level $585$
Weight $2$
Character 585.406
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 406.1
Root \(1.15139 + 1.99426i\) of defining polynomial
Character \(\chi\) \(=\) 585.406
Dual form 585.2.j.d.451.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +1.00000 q^{5} +(0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(-1.15139 - 1.99426i) q^{10} +(0.802776 + 1.39045i) q^{11} -3.60555 q^{13} -2.30278 q^{14} +(-0.151388 - 0.262211i) q^{16} +(3.80278 - 6.58660i) q^{17} +(2.80278 - 4.85455i) q^{19} +(-1.65139 + 2.86029i) q^{20} +(1.84861 - 3.20189i) q^{22} +(-1.50000 - 2.59808i) q^{23} +1.00000 q^{25} +(4.15139 + 7.19041i) q^{26} +(1.65139 + 2.86029i) q^{28} +(-3.10555 - 5.37897i) q^{29} -4.00000 q^{31} +(2.65139 - 4.59234i) q^{32} -17.5139 q^{34} +(0.500000 - 0.866025i) q^{35} +(-1.80278 - 3.12250i) q^{37} -12.9083 q^{38} +3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(5.10555 - 8.84307i) q^{43} -5.30278 q^{44} +(-3.45416 + 5.98279i) q^{46} -9.21110 q^{47} +(3.00000 + 5.19615i) q^{49} +(-1.15139 - 1.99426i) q^{50} +(5.95416 - 10.3129i) q^{52} +3.21110 q^{53} +(0.802776 + 1.39045i) q^{55} +(1.50000 - 2.59808i) q^{56} +(-7.15139 + 12.3866i) q^{58} +(-5.40833 + 9.36750i) q^{59} +(0.500000 - 0.866025i) q^{61} +(4.60555 + 7.97705i) q^{62} -12.8167 q^{64} -3.60555 q^{65} +(3.50000 + 6.06218i) q^{67} +(12.5597 + 21.7541i) q^{68} -2.30278 q^{70} +(2.40833 - 4.17134i) q^{71} -0.788897 q^{73} +(-4.15139 + 7.19041i) q^{74} +(9.25694 + 16.0335i) q^{76} +1.60555 q^{77} +5.21110 q^{79} +(-0.151388 - 0.262211i) q^{80} +(3.45416 - 5.98279i) q^{82} +9.21110 q^{83} +(3.80278 - 6.58660i) q^{85} -23.5139 q^{86} +(2.40833 + 4.17134i) q^{88} +(-3.10555 - 5.37897i) q^{89} +(-1.80278 + 3.12250i) q^{91} +9.90833 q^{92} +(10.6056 + 18.3694i) q^{94} +(2.80278 - 4.85455i) q^{95} +(4.19722 - 7.26981i) q^{97} +(6.90833 - 11.9656i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 3 q^{4} + 4 q^{5} + 2 q^{7} + 12 q^{8} - q^{10} - 4 q^{11} - 2 q^{14} + 3 q^{16} + 8 q^{17} + 4 q^{19} - 3 q^{20} + 11 q^{22} - 6 q^{23} + 4 q^{25} + 13 q^{26} + 3 q^{28} + 2 q^{29} - 16 q^{31}+ \cdots + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15139 1.99426i −0.814154 1.41016i −0.909934 0.414754i \(-0.863868\pi\)
0.0957796 0.995403i \(-0.469466\pi\)
\(3\) 0 0
\(4\) −1.65139 + 2.86029i −0.825694 + 1.43014i
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i −0.755929 0.654654i \(-0.772814\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −1.15139 1.99426i −0.364101 0.630641i
\(11\) 0.802776 + 1.39045i 0.242046 + 0.419236i 0.961297 0.275514i \(-0.0888482\pi\)
−0.719251 + 0.694750i \(0.755515\pi\)
\(12\) 0 0
\(13\) −3.60555 −1.00000
\(14\) −2.30278 −0.615443
\(15\) 0 0
\(16\) −0.151388 0.262211i −0.0378470 0.0655528i
\(17\) 3.80278 6.58660i 0.922309 1.59749i 0.126475 0.991970i \(-0.459634\pi\)
0.795834 0.605516i \(-0.207033\pi\)
\(18\) 0 0
\(19\) 2.80278 4.85455i 0.643001 1.11371i −0.341759 0.939788i \(-0.611023\pi\)
0.984759 0.173922i \(-0.0556442\pi\)
\(20\) −1.65139 + 2.86029i −0.369262 + 0.639580i
\(21\) 0 0
\(22\) 1.84861 3.20189i 0.394125 0.682645i
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 4.15139 + 7.19041i 0.814154 + 1.41016i
\(27\) 0 0
\(28\) 1.65139 + 2.86029i 0.312083 + 0.540544i
\(29\) −3.10555 5.37897i −0.576686 0.998850i −0.995856 0.0909423i \(-0.971012\pi\)
0.419170 0.907908i \(-0.362321\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 2.65139 4.59234i 0.468704 0.811818i
\(33\) 0 0
\(34\) −17.5139 −3.00361
\(35\) 0.500000 0.866025i 0.0845154 0.146385i
\(36\) 0 0
\(37\) −1.80278 3.12250i −0.296374 0.513336i 0.678929 0.734204i \(-0.262444\pi\)
−0.975304 + 0.220868i \(0.929111\pi\)
\(38\) −12.9083 −2.09401
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 5.10555 8.84307i 0.778589 1.34856i −0.154166 0.988045i \(-0.549269\pi\)
0.932755 0.360511i \(-0.117398\pi\)
\(44\) −5.30278 −0.799424
\(45\) 0 0
\(46\) −3.45416 + 5.98279i −0.509289 + 0.882114i
\(47\) −9.21110 −1.34358 −0.671789 0.740743i \(-0.734474\pi\)
−0.671789 + 0.740743i \(0.734474\pi\)
\(48\) 0 0
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) −1.15139 1.99426i −0.162831 0.282031i
\(51\) 0 0
\(52\) 5.95416 10.3129i 0.825694 1.43014i
\(53\) 3.21110 0.441079 0.220539 0.975378i \(-0.429218\pi\)
0.220539 + 0.975378i \(0.429218\pi\)
\(54\) 0 0
\(55\) 0.802776 + 1.39045i 0.108246 + 0.187488i
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) 0 0
\(58\) −7.15139 + 12.3866i −0.939023 + 1.62644i
\(59\) −5.40833 + 9.36750i −0.704104 + 1.21954i 0.262910 + 0.964820i \(0.415318\pi\)
−0.967014 + 0.254724i \(0.918015\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 4.60555 + 7.97705i 0.584906 + 1.01309i
\(63\) 0 0
\(64\) −12.8167 −1.60208
\(65\) −3.60555 −0.447214
\(66\) 0 0
\(67\) 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i \(-0.0260283\pi\)
−0.569066 + 0.822292i \(0.692695\pi\)
\(68\) 12.5597 + 21.7541i 1.52309 + 2.63807i
\(69\) 0 0
\(70\) −2.30278 −0.275234
\(71\) 2.40833 4.17134i 0.285816 0.495048i −0.686991 0.726666i \(-0.741069\pi\)
0.972807 + 0.231619i \(0.0744021\pi\)
\(72\) 0 0
\(73\) −0.788897 −0.0923335 −0.0461667 0.998934i \(-0.514701\pi\)
−0.0461667 + 0.998934i \(0.514701\pi\)
\(74\) −4.15139 + 7.19041i −0.482589 + 0.835869i
\(75\) 0 0
\(76\) 9.25694 + 16.0335i 1.06184 + 1.83917i
\(77\) 1.60555 0.182970
\(78\) 0 0
\(79\) 5.21110 0.586295 0.293147 0.956067i \(-0.405297\pi\)
0.293147 + 0.956067i \(0.405297\pi\)
\(80\) −0.151388 0.262211i −0.0169257 0.0293161i
\(81\) 0 0
\(82\) 3.45416 5.98279i 0.381449 0.660688i
\(83\) 9.21110 1.01105 0.505525 0.862812i \(-0.331299\pi\)
0.505525 + 0.862812i \(0.331299\pi\)
\(84\) 0 0
\(85\) 3.80278 6.58660i 0.412469 0.714417i
\(86\) −23.5139 −2.53557
\(87\) 0 0
\(88\) 2.40833 + 4.17134i 0.256729 + 0.444667i
\(89\) −3.10555 5.37897i −0.329188 0.570170i 0.653163 0.757217i \(-0.273442\pi\)
−0.982351 + 0.187047i \(0.940108\pi\)
\(90\) 0 0
\(91\) −1.80278 + 3.12250i −0.188982 + 0.327327i
\(92\) 9.90833 1.03301
\(93\) 0 0
\(94\) 10.6056 + 18.3694i 1.09388 + 1.89465i
\(95\) 2.80278 4.85455i 0.287559 0.498066i
\(96\) 0 0
\(97\) 4.19722 7.26981i 0.426164 0.738137i −0.570365 0.821392i \(-0.693198\pi\)
0.996528 + 0.0832546i \(0.0265315\pi\)
\(98\) 6.90833 11.9656i 0.697846 1.20871i
\(99\) 0 0
\(100\) −1.65139 + 2.86029i −0.165139 + 0.286029i
\(101\) −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i \(-0.314447\pi\)
−0.998240 + 0.0592978i \(0.981114\pi\)
\(102\) 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
\(106\) −3.69722 6.40378i −0.359106 0.621990i
\(107\) 3.10555 + 5.37897i 0.300225 + 0.520005i 0.976187 0.216932i \(-0.0696049\pi\)
−0.675962 + 0.736937i \(0.736272\pi\)
\(108\) 0 0
\(109\) −19.2111 −1.84009 −0.920045 0.391813i \(-0.871848\pi\)
−0.920045 + 0.391813i \(0.871848\pi\)
\(110\) 1.84861 3.20189i 0.176258 0.305288i
\(111\) 0 0
\(112\) −0.302776 −0.0286096
\(113\) −0.802776 + 1.39045i −0.0755188 + 0.130802i −0.901312 0.433171i \(-0.857395\pi\)
0.825793 + 0.563973i \(0.190728\pi\)
\(114\) 0 0
\(115\) −1.50000 2.59808i −0.139876 0.242272i
\(116\) 20.5139 1.90467
\(117\) 0 0
\(118\) 24.9083 2.29300
\(119\) −3.80278 6.58660i −0.348600 0.603793i
\(120\) 0 0
\(121\) 4.21110 7.29384i 0.382828 0.663077i
\(122\) −2.30278 −0.208484
\(123\) 0 0
\(124\) 6.60555 11.4412i 0.593196 1.02745i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.10555 + 3.64692i 0.186837 + 0.323612i 0.944194 0.329389i \(-0.106843\pi\)
−0.757357 + 0.653001i \(0.773510\pi\)
\(128\) 9.45416 + 16.3751i 0.835638 + 1.44737i
\(129\) 0 0
\(130\) 4.15139 + 7.19041i 0.364101 + 0.630641i
\(131\) 21.2111 1.85322 0.926611 0.376021i \(-0.122708\pi\)
0.926611 + 0.376021i \(0.122708\pi\)
\(132\) 0 0
\(133\) −2.80278 4.85455i −0.243031 0.420943i
\(134\) 8.05971 13.9598i 0.696253 1.20595i
\(135\) 0 0
\(136\) 11.4083 19.7598i 0.978256 1.69439i
\(137\) −0.802776 + 1.39045i −0.0685858 + 0.118794i −0.898279 0.439426i \(-0.855182\pi\)
0.829693 + 0.558220i \(0.188515\pi\)
\(138\) 0 0
\(139\) −3.19722 + 5.53776i −0.271185 + 0.469706i −0.969166 0.246410i \(-0.920749\pi\)
0.697981 + 0.716117i \(0.254082\pi\)
\(140\) 1.65139 + 2.86029i 0.139568 + 0.241738i
\(141\) 0 0
\(142\) −11.0917 −0.930793
\(143\) −2.89445 5.01333i −0.242046 0.419236i
\(144\) 0 0
\(145\) −3.10555 5.37897i −0.257902 0.446699i
\(146\) 0.908327 + 1.57327i 0.0751737 + 0.130205i
\(147\) 0 0
\(148\) 11.9083 0.978858
\(149\) 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i \(-0.794119\pi\)
0.920904 + 0.389789i \(0.127452\pi\)
\(150\) 0 0
\(151\) −1.21110 −0.0985581 −0.0492791 0.998785i \(-0.515692\pi\)
−0.0492791 + 0.998785i \(0.515692\pi\)
\(152\) 8.40833 14.5636i 0.682005 1.18127i
\(153\) 0 0
\(154\) −1.84861 3.20189i −0.148965 0.258016i
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) 11.2111 0.894743 0.447372 0.894348i \(-0.352360\pi\)
0.447372 + 0.894348i \(0.352360\pi\)
\(158\) −6.00000 10.3923i −0.477334 0.826767i
\(159\) 0 0
\(160\) 2.65139 4.59234i 0.209611 0.363056i
\(161\) −3.00000 −0.236433
\(162\) 0 0
\(163\) 1.89445 3.28128i 0.148385 0.257010i −0.782246 0.622970i \(-0.785926\pi\)
0.930631 + 0.365960i \(0.119259\pi\)
\(164\) −9.90833 −0.773710
\(165\) 0 0
\(166\) −10.6056 18.3694i −0.823150 1.42574i
\(167\) 4.50000 + 7.79423i 0.348220 + 0.603136i 0.985933 0.167139i \(-0.0534527\pi\)
−0.637713 + 0.770274i \(0.720119\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) −17.5139 −1.34325
\(171\) 0 0
\(172\) 16.8625 + 29.2067i 1.28575 + 2.22699i
\(173\) 2.40833 4.17134i 0.183102 0.317141i −0.759834 0.650118i \(-0.774720\pi\)
0.942935 + 0.332976i \(0.108053\pi\)
\(174\) 0 0
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) 0.243061 0.420994i 0.0183214 0.0317336i
\(177\) 0 0
\(178\) −7.15139 + 12.3866i −0.536019 + 0.928412i
\(179\) 11.4083 + 19.7598i 0.852698 + 1.47692i 0.878764 + 0.477257i \(0.158369\pi\)
−0.0260655 + 0.999660i \(0.508298\pi\)
\(180\) 0 0
\(181\) 17.6333 1.31067 0.655337 0.755337i \(-0.272527\pi\)
0.655337 + 0.755337i \(0.272527\pi\)
\(182\) 8.30278 0.615443
\(183\) 0 0
\(184\) −4.50000 7.79423i −0.331744 0.574598i
\(185\) −1.80278 3.12250i −0.132543 0.229571i
\(186\) 0 0
\(187\) 12.2111 0.892964
\(188\) 15.2111 26.3464i 1.10938 1.92151i
\(189\) 0 0
\(190\) −12.9083 −0.936468
\(191\) 8.40833 14.5636i 0.608405 1.05379i −0.383098 0.923708i \(-0.625143\pi\)
0.991503 0.130081i \(-0.0415238\pi\)
\(192\) 0 0
\(193\) −7.80278 13.5148i −0.561656 0.972817i −0.997352 0.0727230i \(-0.976831\pi\)
0.435696 0.900094i \(-0.356502\pi\)
\(194\) −19.3305 −1.38785
\(195\) 0 0
\(196\) −19.8167 −1.41548
\(197\) 0.591673 + 1.02481i 0.0421550 + 0.0730145i 0.886333 0.463048i \(-0.153244\pi\)
−0.844178 + 0.536063i \(0.819911\pi\)
\(198\) 0 0
\(199\) −6.40833 + 11.0995i −0.454274 + 0.786826i −0.998646 0.0520179i \(-0.983435\pi\)
0.544372 + 0.838844i \(0.316768\pi\)
\(200\) 3.00000 0.212132
\(201\) 0 0
\(202\) −10.3625 + 17.9484i −0.729102 + 1.26284i
\(203\) −6.21110 −0.435934
\(204\) 0 0
\(205\) 1.50000 + 2.59808i 0.104765 + 0.181458i
\(206\) 4.60555 + 7.97705i 0.320884 + 0.555787i
\(207\) 0 0
\(208\) 0.545837 + 0.945417i 0.0378470 + 0.0655528i
\(209\) 9.00000 0.622543
\(210\) 0 0
\(211\) 11.8028 + 20.4430i 0.812537 + 1.40735i 0.911083 + 0.412222i \(0.135247\pi\)
−0.0985467 + 0.995132i \(0.531419\pi\)
\(212\) −5.30278 + 9.18468i −0.364196 + 0.630806i
\(213\) 0 0
\(214\) 7.15139 12.3866i 0.488859 0.846728i
\(215\) 5.10555 8.84307i 0.348196 0.603093i
\(216\) 0 0
\(217\) −2.00000 + 3.46410i −0.135769 + 0.235159i
\(218\) 22.1194 + 38.3120i 1.49812 + 2.59481i
\(219\) 0 0
\(220\) −5.30278 −0.357513
\(221\) −13.7111 + 23.7483i −0.922309 + 1.59749i
\(222\) 0 0
\(223\) 2.10555 + 3.64692i 0.140998 + 0.244216i 0.927873 0.372897i \(-0.121636\pi\)
−0.786875 + 0.617113i \(0.788302\pi\)
\(224\) −2.65139 4.59234i −0.177153 0.306839i
\(225\) 0 0
\(226\) 3.69722 0.245936
\(227\) −13.7111 + 23.7483i −0.910038 + 1.57623i −0.0960296 + 0.995378i \(0.530614\pi\)
−0.814008 + 0.580853i \(0.802719\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) −3.45416 + 5.98279i −0.227761 + 0.394493i
\(231\) 0 0
\(232\) −9.31665 16.1369i −0.611668 1.05944i
\(233\) −15.2111 −0.996512 −0.498256 0.867030i \(-0.666026\pi\)
−0.498256 + 0.867030i \(0.666026\pi\)
\(234\) 0 0
\(235\) −9.21110 −0.600866
\(236\) −17.8625 30.9387i −1.16275 2.01394i
\(237\) 0 0
\(238\) −8.75694 + 15.1675i −0.567628 + 0.983161i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −0.894449 + 1.54923i −0.0576165 + 0.0997947i −0.893395 0.449272i \(-0.851683\pi\)
0.835778 + 0.549067i \(0.185017\pi\)
\(242\) −19.3944 −1.24672
\(243\) 0 0
\(244\) 1.65139 + 2.86029i 0.105719 + 0.183111i
\(245\) 3.00000 + 5.19615i 0.191663 + 0.331970i
\(246\) 0 0
\(247\) −10.1056 + 17.5033i −0.643001 + 1.11371i
\(248\) −12.0000 −0.762001
\(249\) 0 0
\(250\) −1.15139 1.99426i −0.0728202 0.126128i
\(251\) −3.59167 + 6.22096i −0.226704 + 0.392664i −0.956829 0.290650i \(-0.906128\pi\)
0.730125 + 0.683314i \(0.239462\pi\)
\(252\) 0 0
\(253\) 2.40833 4.17134i 0.151410 0.262250i
\(254\) 4.84861 8.39804i 0.304229 0.526940i
\(255\) 0 0
\(256\) 8.95416 15.5091i 0.559635 0.969317i
\(257\) −8.19722 14.1980i −0.511329 0.885647i −0.999914 0.0131312i \(-0.995820\pi\)
0.488585 0.872516i \(-0.337513\pi\)
\(258\) 0 0
\(259\) −3.60555 −0.224038
\(260\) 5.95416 10.3129i 0.369262 0.639580i
\(261\) 0 0
\(262\) −24.4222 42.3005i −1.50881 2.61333i
\(263\) 5.89445 + 10.2095i 0.363467 + 0.629544i 0.988529 0.151032i \(-0.0482595\pi\)
−0.625062 + 0.780575i \(0.714926\pi\)
\(264\) 0 0
\(265\) 3.21110 0.197256
\(266\) −6.45416 + 11.1789i −0.395730 + 0.685425i
\(267\) 0 0
\(268\) −23.1194 −1.41224
\(269\) −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i \(-0.921803\pi\)
0.695606 + 0.718423i \(0.255136\pi\)
\(270\) 0 0
\(271\) 10.4083 + 18.0278i 0.632261 + 1.09511i 0.987088 + 0.160176i \(0.0512062\pi\)
−0.354828 + 0.934932i \(0.615460\pi\)
\(272\) −2.30278 −0.139626
\(273\) 0 0
\(274\) 3.69722 0.223357
\(275\) 0.802776 + 1.39045i 0.0484092 + 0.0838472i
\(276\) 0 0
\(277\) −13.8028 + 23.9071i −0.829328 + 1.43644i 0.0692374 + 0.997600i \(0.477943\pi\)
−0.898566 + 0.438839i \(0.855390\pi\)
\(278\) 14.7250 0.883146
\(279\) 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 0.782104 0.623148i \(-0.214146\pi\)
−0.930714 + 0.365748i \(0.880813\pi\)
\(284\) 7.95416 + 13.7770i 0.471993 + 0.817515i
\(285\) 0 0
\(286\) −6.66527 + 11.5446i −0.394125 + 0.682645i
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) −20.4222 35.3723i −1.20131 2.08072i
\(290\) −7.15139 + 12.3866i −0.419944 + 0.727364i
\(291\) 0 0
\(292\) 1.30278 2.25647i 0.0762392 0.132050i
\(293\) 5.19722 9.00186i 0.303625 0.525894i −0.673329 0.739343i \(-0.735136\pi\)
0.976954 + 0.213449i \(0.0684696\pi\)
\(294\) 0 0
\(295\) −5.40833 + 9.36750i −0.314885 + 0.545397i
\(296\) −5.40833 9.36750i −0.314353 0.544475i
\(297\) 0 0
\(298\) −6.90833 −0.400189
\(299\) 5.40833 + 9.36750i 0.312772 + 0.541736i
\(300\) 0 0
\(301\) −5.10555 8.84307i −0.294279 0.509706i
\(302\) 1.39445 + 2.41526i 0.0802415 + 0.138982i
\(303\) 0 0
\(304\) −1.69722 −0.0973425
\(305\) 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 \(0.650927\pi\)
\(308\) −2.65139 + 4.59234i −0.151077 + 0.261673i
\(309\) 0 0
\(310\) 4.60555 + 7.97705i 0.261578 + 0.453066i
\(311\) 9.21110 0.522314 0.261157 0.965296i \(-0.415896\pi\)
0.261157 + 0.965296i \(0.415896\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) −12.9083 22.3579i −0.728459 1.26173i
\(315\) 0 0
\(316\) −8.60555 + 14.9053i −0.484100 + 0.838486i
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) 4.98612 8.63622i 0.279169 0.483535i
\(320\) −12.8167 −0.716473
\(321\) 0 0
\(322\) 3.45416 + 5.98279i 0.192493 + 0.333408i
\(323\) −21.3167 36.9215i −1.18609 2.05437i
\(324\) 0 0
\(325\) −3.60555 −0.200000
\(326\) −8.72498 −0.483232
\(327\) 0 0
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) −4.60555 + 7.97705i −0.253912 + 0.439789i
\(330\) 0 0
\(331\) −5.01388 + 8.68429i −0.275588 + 0.477332i −0.970283 0.241972i \(-0.922206\pi\)
0.694696 + 0.719304i \(0.255539\pi\)
\(332\) −15.2111 + 26.3464i −0.834818 + 1.44595i
\(333\) 0 0
\(334\) 10.3625 17.9484i 0.567010 0.982091i
\(335\) 3.50000 + 6.06218i 0.191225 + 0.331212i
\(336\) 0 0
\(337\) −25.6333 −1.39634 −0.698168 0.715934i \(-0.746001\pi\)
−0.698168 + 0.715934i \(0.746001\pi\)
\(338\) −14.9680 25.9254i −0.814154 1.41016i
\(339\) 0 0
\(340\) 12.5597 + 21.7541i 0.681146 + 1.17978i
\(341\) −3.21110 5.56179i −0.173891 0.301188i
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 15.3167 26.5292i 0.825819 1.43036i
\(345\) 0 0
\(346\) −11.0917 −0.596292
\(347\) 2.89445 5.01333i 0.155382 0.269130i −0.777816 0.628492i \(-0.783672\pi\)
0.933198 + 0.359362i \(0.117006\pi\)
\(348\) 0 0
\(349\) 1.89445 + 3.28128i 0.101408 + 0.175643i 0.912265 0.409601i \(-0.134332\pi\)
−0.810857 + 0.585244i \(0.800999\pi\)
\(350\) −2.30278 −0.123089
\(351\) 0 0
\(352\) 8.51388 0.453791
\(353\) 8.40833 + 14.5636i 0.447530 + 0.775145i 0.998225 0.0595620i \(-0.0189704\pi\)
−0.550695 + 0.834707i \(0.685637\pi\)
\(354\) 0 0
\(355\) 2.40833 4.17134i 0.127821 0.221392i
\(356\) 20.5139 1.08723
\(357\) 0 0
\(358\) 26.2708 45.5024i 1.38846 2.40488i
\(359\) −18.4222 −0.972287 −0.486143 0.873879i \(-0.661597\pi\)
−0.486143 + 0.873879i \(0.661597\pi\)
\(360\) 0 0
\(361\) −6.21110 10.7579i −0.326900 0.566208i
\(362\) −20.3028 35.1654i −1.06709 1.84825i
\(363\) 0 0
\(364\) −5.95416 10.3129i −0.312083 0.540544i
\(365\) −0.788897 −0.0412928
\(366\) 0 0
\(367\) −5.71110 9.89192i −0.298117 0.516354i 0.677588 0.735442i \(-0.263025\pi\)
−0.975705 + 0.219088i \(0.929692\pi\)
\(368\) −0.454163 + 0.786634i −0.0236749 + 0.0410061i
\(369\) 0 0
\(370\) −4.15139 + 7.19041i −0.215820 + 0.373812i
\(371\) 1.60555 2.78090i 0.0833561 0.144377i
\(372\) 0 0
\(373\) 10.1972 17.6621i 0.527992 0.914509i −0.471475 0.881879i \(-0.656278\pi\)
0.999467 0.0326301i \(-0.0103883\pi\)
\(374\) −14.0597 24.3521i −0.727011 1.25922i
\(375\) 0 0
\(376\) −27.6333 −1.42508
\(377\) 11.1972 + 19.3942i 0.576686 + 0.998850i
\(378\) 0 0
\(379\) −4.80278 8.31865i −0.246702 0.427300i 0.715907 0.698196i \(-0.246014\pi\)
−0.962609 + 0.270895i \(0.912680\pi\)
\(380\) 9.25694 + 16.0335i 0.474871 + 0.822501i
\(381\) 0 0
\(382\) −38.7250 −1.98134
\(383\) −12.3167 + 21.3331i −0.629352 + 1.09007i 0.358330 + 0.933595i \(0.383346\pi\)
−0.987682 + 0.156474i \(0.949987\pi\)
\(384\) 0 0
\(385\) 1.60555 0.0818265
\(386\) −17.9680 + 31.1216i −0.914549 + 1.58405i
\(387\) 0 0
\(388\) 13.8625 + 24.0105i 0.703761 + 1.21895i
\(389\) 15.2111 0.771234 0.385617 0.922659i \(-0.373989\pi\)
0.385617 + 0.922659i \(0.373989\pi\)
\(390\) 0 0
\(391\) −22.8167 −1.15389
\(392\) 9.00000 + 15.5885i 0.454569 + 0.787336i
\(393\) 0 0
\(394\) 1.36249 2.35990i 0.0686413 0.118890i
\(395\) 5.21110 0.262199
\(396\) 0 0
\(397\) −11.0139 + 19.0766i −0.552771 + 0.957427i 0.445303 + 0.895380i \(0.353096\pi\)
−0.998073 + 0.0620468i \(0.980237\pi\)
\(398\) 29.5139 1.47940
\(399\) 0 0
\(400\) −0.151388 0.262211i −0.00756939 0.0131106i
\(401\) 6.10555 + 10.5751i 0.304897 + 0.528097i 0.977238 0.212144i \(-0.0680447\pi\)
−0.672342 + 0.740241i \(0.734711\pi\)
\(402\) 0 0
\(403\) 14.4222 0.718421
\(404\) 29.7250 1.47887
\(405\) 0 0
\(406\) 7.15139 + 12.3866i 0.354917 + 0.614735i
\(407\) 2.89445 5.01333i 0.143472 0.248502i
\(408\) 0 0
\(409\) −4.10555 + 7.11102i −0.203006 + 0.351617i −0.949496 0.313780i \(-0.898405\pi\)
0.746489 + 0.665397i \(0.231738\pi\)
\(410\) 3.45416 5.98279i 0.170589 0.295469i
\(411\) 0 0
\(412\) 6.60555 11.4412i 0.325432 0.563665i
\(413\) 5.40833 + 9.36750i 0.266126 + 0.460944i
\(414\) 0 0
\(415\) 9.21110 0.452155
\(416\) −9.55971 + 16.5579i −0.468704 + 0.811818i
\(417\) 0 0
\(418\) −10.3625 17.9484i −0.506846 0.877883i
\(419\) 8.61943 + 14.9293i 0.421087 + 0.729344i 0.996046 0.0888384i \(-0.0283155\pi\)
−0.574959 + 0.818182i \(0.694982\pi\)
\(420\) 0 0
\(421\) 32.4222 1.58016 0.790081 0.613003i \(-0.210039\pi\)
0.790081 + 0.613003i \(0.210039\pi\)
\(422\) 27.1791 47.0757i 1.32306 2.29161i
\(423\) 0 0
\(424\) 9.63331 0.467835
\(425\) 3.80278 6.58660i 0.184462 0.319497i
\(426\) 0 0
\(427\) −0.500000 0.866025i −0.0241967 0.0419099i
\(428\) −20.5139 −0.991576
\(429\) 0 0
\(430\) −23.5139 −1.13394
\(431\) 14.6194 + 25.3216i 0.704193 + 1.21970i 0.966982 + 0.254845i \(0.0820244\pi\)
−0.262789 + 0.964853i \(0.584642\pi\)
\(432\) 0 0
\(433\) −1.80278 + 3.12250i −0.0866359 + 0.150058i −0.906087 0.423091i \(-0.860945\pi\)
0.819451 + 0.573149i \(0.194278\pi\)
\(434\) 9.21110 0.442147
\(435\) 0 0
\(436\) 31.7250 54.9493i 1.51935 2.63159i
\(437\) −16.8167 −0.804450
\(438\) 0 0
\(439\) 13.6194 + 23.5895i 0.650020 + 1.12587i 0.983118 + 0.182975i \(0.0585728\pi\)
−0.333098 + 0.942892i \(0.608094\pi\)
\(440\) 2.40833 + 4.17134i 0.114812 + 0.198861i
\(441\) 0 0
\(442\) 63.1472 3.00361
\(443\) −6.42221 −0.305128 −0.152564 0.988294i \(-0.548753\pi\)
−0.152564 + 0.988294i \(0.548753\pi\)
\(444\) 0 0
\(445\) −3.10555 5.37897i −0.147217 0.254988i
\(446\) 4.84861 8.39804i 0.229588 0.397659i
\(447\) 0 0
\(448\) −6.40833 + 11.0995i −0.302765 + 0.524404i
\(449\) 15.3167 26.5292i 0.722838 1.25199i −0.237020 0.971505i \(-0.576171\pi\)
0.959858 0.280487i \(-0.0904959\pi\)
\(450\) 0 0
\(451\) −2.40833 + 4.17134i −0.113404 + 0.196421i
\(452\) −2.65139 4.59234i −0.124711 0.216005i
\(453\) 0 0
\(454\) 63.1472 2.96364
\(455\) −1.80278 + 3.12250i −0.0845154 + 0.146385i
\(456\) 0 0
\(457\) 13.4083 + 23.2239i 0.627215 + 1.08637i 0.988108 + 0.153761i \(0.0491386\pi\)
−0.360893 + 0.932607i \(0.617528\pi\)
\(458\) −16.1194 27.9197i −0.753211 1.30460i
\(459\) 0 0
\(460\) 9.90833 0.461978
\(461\) 18.1056 31.3597i 0.843260 1.46057i −0.0438645 0.999037i \(-0.513967\pi\)
0.887124 0.461531i \(-0.152700\pi\)
\(462\) 0 0
\(463\) −34.4222 −1.59974 −0.799868 0.600176i \(-0.795097\pi\)
−0.799868 + 0.600176i \(0.795097\pi\)
\(464\) −0.940285 + 1.62862i −0.0436516 + 0.0756069i
\(465\) 0 0
\(466\) 17.5139 + 30.3349i 0.811315 + 1.40524i
\(467\) −2.78890 −0.129055 −0.0645274 0.997916i \(-0.520554\pi\)
−0.0645274 + 0.997916i \(0.520554\pi\)
\(468\) 0 0
\(469\) 7.00000 0.323230
\(470\) 10.6056 + 18.3694i 0.489198 + 0.847315i
\(471\) 0 0
\(472\) −16.2250 + 28.1025i −0.746815 + 1.29352i
\(473\) 16.3944 0.753818
\(474\) 0 0
\(475\) 2.80278 4.85455i 0.128600 0.222742i
\(476\) 25.1194 1.15135
\(477\) 0 0
\(478\) 0 0
\(479\) −14.4083 24.9560i −0.658333 1.14027i −0.981047 0.193770i \(-0.937928\pi\)
0.322714 0.946497i \(-0.395405\pi\)
\(480\) 0 0
\(481\) 6.50000 + 11.2583i 0.296374 + 0.513336i
\(482\) 4.11943 0.187635
\(483\) 0 0
\(484\) 13.9083 + 24.0899i 0.632197 + 1.09500i
\(485\) 4.19722 7.26981i 0.190586 0.330105i
\(486\) 0 0
\(487\) 0.500000 0.866025i 0.0226572 0.0392434i −0.854475 0.519493i \(-0.826121\pi\)
0.877132 + 0.480250i \(0.159454\pi\)
\(488\) 1.50000 2.59808i 0.0679018 0.117609i
\(489\) 0 0
\(490\) 6.90833 11.9656i 0.312086 0.540549i
\(491\) −8.40833 14.5636i −0.379462 0.657248i 0.611522 0.791228i \(-0.290558\pi\)
−0.990984 + 0.133979i \(0.957224\pi\)
\(492\) 0 0
\(493\) −47.2389 −2.12753
\(494\) 46.5416 2.09401
\(495\) 0 0
\(496\) 0.605551 + 1.04885i 0.0271901 + 0.0470946i
\(497\) −2.40833 4.17134i −0.108028 0.187110i
\(498\) 0 0
\(499\) 2.42221 0.108433 0.0542164 0.998529i \(-0.482734\pi\)
0.0542164 + 0.998529i \(0.482734\pi\)
\(500\) −1.65139 + 2.86029i −0.0738523 + 0.127916i
\(501\) 0 0
\(502\) 16.5416 0.738289
\(503\) 1.50000 2.59808i 0.0668817 0.115842i −0.830645 0.556802i \(-0.812028\pi\)
0.897527 + 0.440959i \(0.145362\pi\)
\(504\) 0 0
\(505\) −4.50000 7.79423i −0.200247 0.346839i
\(506\) −11.0917 −0.493085
\(507\) 0 0
\(508\) −13.9083 −0.617082
\(509\) 1.50000 + 2.59808i 0.0664863 + 0.115158i 0.897352 0.441315i \(-0.145488\pi\)
−0.830866 + 0.556473i \(0.812154\pi\)
\(510\) 0 0
\(511\) −0.394449 + 0.683205i −0.0174494 + 0.0302232i
\(512\) −3.42221 −0.151242
\(513\) 0 0
\(514\) −18.8764 + 32.6948i −0.832601 + 1.44211i
\(515\) −4.00000 −0.176261
\(516\) 0 0
\(517\) −7.39445 12.8076i −0.325207 0.563276i
\(518\) 4.15139 + 7.19041i 0.182402 + 0.315929i
\(519\) 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
\(523\) 0.711103 + 1.23167i 0.0310943 + 0.0538570i 0.881154 0.472830i \(-0.156767\pi\)
−0.850059 + 0.526687i \(0.823434\pi\)
\(524\) −35.0278 + 60.6699i −1.53019 + 2.65037i
\(525\) 0 0
\(526\) 13.5736 23.5102i 0.591837 1.02509i
\(527\) −15.2111 + 26.3464i −0.662606 + 1.14767i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) −3.69722 6.40378i −0.160597 0.278162i
\(531\) 0 0
\(532\) 18.5139 0.802678
\(533\) −5.40833 9.36750i −0.234261 0.405751i
\(534\) 0 0
\(535\) 3.10555 + 5.37897i 0.134265 + 0.232553i
\(536\) 10.5000 + 18.1865i 0.453531 + 0.785539i
\(537\) 0 0
\(538\) 20.7250 0.893517
\(539\) −4.81665 + 8.34269i −0.207468 + 0.359345i
\(540\) 0 0
\(541\) −25.6333 −1.10206 −0.551031 0.834485i \(-0.685765\pi\)
−0.551031 + 0.834485i \(0.685765\pi\)
\(542\) 23.9680 41.5139i 1.02952 1.78317i
\(543\) 0 0
\(544\) −20.1653 34.9273i −0.864579 1.49749i
\(545\) −19.2111 −0.822913
\(546\) 0 0
\(547\) 32.8444 1.40433 0.702163 0.712016i \(-0.252218\pi\)
0.702163 + 0.712016i \(0.252218\pi\)
\(548\) −2.65139 4.59234i −0.113262 0.196175i
\(549\) 0 0
\(550\) 1.84861 3.20189i 0.0788251 0.136529i
\(551\) −34.8167 −1.48324
\(552\) 0 0
\(553\) 2.60555 4.51295i 0.110799 0.191910i
\(554\) 63.5694 2.70080
\(555\) 0 0
\(556\) −10.5597 18.2900i −0.447832 0.775667i
\(557\) −0.802776 1.39045i −0.0340147 0.0589152i 0.848517 0.529168i \(-0.177496\pi\)
−0.882532 + 0.470253i \(0.844163\pi\)
\(558\) 0 0
\(559\) −18.4083 + 31.8842i −0.778589 + 1.34856i
\(560\) −0.302776 −0.0127946
\(561\) 0 0
\(562\) −6.90833 11.9656i −0.291410 0.504737i
\(563\) 4.71110 8.15987i 0.198549 0.343897i −0.749509 0.661994i \(-0.769710\pi\)
0.948058 + 0.318097i \(0.103044\pi\)
\(564\) 0 0
\(565\) −0.802776 + 1.39045i −0.0337730 + 0.0584966i
\(566\) −5.75694 + 9.97131i −0.241982 + 0.419125i
\(567\) 0 0
\(568\) 7.22498 12.5140i 0.303153 0.525077i
\(569\) −13.7111 23.7483i −0.574799 0.995582i −0.996063 0.0886436i \(-0.971747\pi\)
0.421264 0.906938i \(-0.361587\pi\)
\(570\) 0 0
\(571\) 20.8444 0.872311 0.436156 0.899871i \(-0.356340\pi\)
0.436156 + 0.899871i \(0.356340\pi\)
\(572\) 19.1194 0.799424
\(573\) 0 0
\(574\) −3.45416 5.98279i −0.144174 0.249717i
\(575\) −1.50000 2.59808i −0.0625543 0.108347i
\(576\) 0 0
\(577\) −13.6333 −0.567562 −0.283781 0.958889i \(-0.591589\pi\)
−0.283781 + 0.958889i \(0.591589\pi\)
\(578\) −47.0278 + 81.4545i −1.95610 + 3.38806i
\(579\) 0 0
\(580\) 20.5139 0.851792
\(581\) 4.60555 7.97705i 0.191070 0.330944i
\(582\) 0 0
\(583\) 2.57779 + 4.46487i 0.106761 + 0.184916i
\(584\) −2.36669 −0.0979344
\(585\) 0 0
\(586\) −23.9361 −0.988790
\(587\) −16.7111 28.9445i −0.689741 1.19467i −0.971922 0.235305i \(-0.924391\pi\)
0.282181 0.959361i \(-0.408942\pi\)
\(588\) 0 0
\(589\) −11.2111 + 19.4182i −0.461945 + 0.800113i
\(590\) 24.9083 1.02546
\(591\) 0 0
\(592\) −0.545837 + 0.945417i −0.0224337 + 0.0388564i
\(593\) −20.7889 −0.853698 −0.426849 0.904323i \(-0.640376\pi\)
−0.426849 + 0.904323i \(0.640376\pi\)
\(594\) 0 0
\(595\) −3.80278 6.58660i −0.155899 0.270024i
\(596\) 4.95416 + 8.58086i 0.202930 + 0.351486i
\(597\) 0 0
\(598\) 12.4542 21.5712i 0.509289 0.882114i
\(599\) 21.2111 0.866662 0.433331 0.901235i \(-0.357338\pi\)
0.433331 + 0.901235i \(0.357338\pi\)
\(600\) 0 0
\(601\) −6.89445 11.9415i −0.281230 0.487105i 0.690458 0.723373i \(-0.257409\pi\)
−0.971688 + 0.236267i \(0.924076\pi\)
\(602\) −11.7569 + 20.3636i −0.479177 + 0.829959i
\(603\) 0 0
\(604\) 2.00000 3.46410i 0.0813788 0.140952i
\(605\) 4.21110 7.29384i 0.171206 0.296537i
\(606\) 0 0
\(607\) 17.1056 29.6277i 0.694293 1.20255i −0.276126 0.961122i \(-0.589051\pi\)
0.970418 0.241429i \(-0.0776161\pi\)
\(608\) −14.8625 25.7426i −0.602754 1.04400i
\(609\) 0 0
\(610\) −2.30278 −0.0932367
\(611\) 33.2111 1.34358
\(612\) 0 0
\(613\) 2.80278 + 4.85455i 0.113203 + 0.196073i 0.917060 0.398749i \(-0.130556\pi\)
−0.803857 + 0.594823i \(0.797222\pi\)
\(614\) 18.4222 + 31.9082i 0.743460 + 1.28771i
\(615\) 0 0
\(616\) 4.81665 0.194069
\(617\) −19.2250 + 33.2986i −0.773969 + 1.34055i 0.161404 + 0.986888i \(0.448398\pi\)
−0.935372 + 0.353664i \(0.884935\pi\)
\(618\) 0 0
\(619\) 14.4222 0.579677 0.289839 0.957076i \(-0.406398\pi\)
0.289839 + 0.957076i \(0.406398\pi\)
\(620\) 6.60555 11.4412i 0.265285 0.459488i
\(621\) 0 0
\(622\) −10.6056 18.3694i −0.425244 0.736544i
\(623\) −6.21110 −0.248843
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −16.1194 27.9197i −0.644262 1.11589i
\(627\) 0 0
\(628\) −18.5139 + 32.0670i −0.738784 + 1.27961i
\(629\) −27.4222 −1.09339
\(630\) 0 0
\(631\) 18.0139 31.2010i 0.717121 1.24209i −0.245015 0.969519i \(-0.578793\pi\)
0.962136 0.272571i \(-0.0878739\pi\)
\(632\) 15.6333 0.621860
\(633\) 0 0
\(634\) 6.90833 + 11.9656i 0.274365 + 0.475214i
\(635\) 2.10555 + 3.64692i 0.0835563 + 0.144724i
\(636\) 0 0
\(637\) −10.8167 18.7350i −0.428571 0.742307i
\(638\) −22.9638 −0.909147
\(639\) 0 0
\(640\) 9.45416 + 16.3751i 0.373709 + 0.647282i
\(641\) 4.71110 8.15987i 0.186077 0.322295i −0.757862 0.652415i \(-0.773756\pi\)
0.943939 + 0.330120i \(0.107089\pi\)
\(642\) 0 0
\(643\) −1.31665 + 2.28051i −0.0519238 + 0.0899346i −0.890819 0.454358i \(-0.849869\pi\)
0.838895 + 0.544293i \(0.183202\pi\)
\(644\) 4.95416 8.58086i 0.195221 0.338133i
\(645\) 0 0
\(646\) −49.0875 + 85.0220i −1.93132 + 3.34515i
\(647\) 19.7111 + 34.1406i 0.774923 + 1.34221i 0.934838 + 0.355076i \(0.115545\pi\)
−0.159914 + 0.987131i \(0.551122\pi\)
\(648\) 0 0
\(649\) −17.3667 −0.681702
\(650\) 4.15139 + 7.19041i 0.162831 + 0.282031i
\(651\) 0 0
\(652\) 6.25694 + 10.8373i 0.245041 + 0.424423i
\(653\) −3.59167 6.22096i −0.140553 0.243445i 0.787152 0.616759i \(-0.211555\pi\)
−0.927705 + 0.373314i \(0.878221\pi\)
\(654\) 0 0
\(655\) 21.2111 0.828786
\(656\) 0.454163 0.786634i 0.0177321 0.0307129i
\(657\) 0 0
\(658\) 21.2111 0.826895
\(659\) −17.4083 + 30.1521i −0.678132 + 1.17456i 0.297411 + 0.954750i \(0.403877\pi\)
−0.975543 + 0.219810i \(0.929456\pi\)
\(660\) 0 0
\(661\) 2.31665 + 4.01256i 0.0901074 + 0.156071i 0.907556 0.419931i \(-0.137946\pi\)
−0.817449 + 0.576001i \(0.804612\pi\)
\(662\) 23.0917 0.897483
\(663\) 0 0
\(664\) 27.6333 1.07238
\(665\) −2.80278 4.85455i −0.108687 0.188251i
\(666\) 0 0
\(667\) −9.31665 + 16.1369i −0.360742 + 0.624824i
\(668\) −29.7250 −1.15009
\(669\) 0 0
\(670\) 8.05971 13.9598i 0.311374 0.539315i
\(671\) 1.60555 0.0619816
\(672\) 0 0
\(673\) 8.80278 + 15.2469i 0.339322 + 0.587723i 0.984305 0.176474i \(-0.0564690\pi\)
−0.644983 + 0.764197i \(0.723136\pi\)
\(674\) 29.5139 + 51.1195i 1.13683 + 1.96905i
\(675\) 0 0
\(676\) −21.4680 + 37.1837i −0.825694 + 1.43014i
\(677\) 9.63331 0.370238 0.185119 0.982716i \(-0.440733\pi\)
0.185119 + 0.982716i \(0.440733\pi\)
\(678\) 0 0
\(679\) −4.19722 7.26981i −0.161075 0.278990i
\(680\) 11.4083 19.7598i 0.437489 0.757754i
\(681\) 0 0
\(682\) −7.39445 + 12.8076i −0.283148 + 0.490427i
\(683\) 18.1056 31.3597i 0.692790 1.19995i −0.278130 0.960543i \(-0.589715\pi\)
0.970920 0.239404i \(-0.0769519\pi\)
\(684\) 0 0
\(685\) −0.802776 + 1.39045i −0.0306725 + 0.0531263i
\(686\) −14.9680 25.9254i −0.571482 0.989837i
\(687\) 0 0
\(688\) −3.09167 −0.117869
\(689\) −11.5778 −0.441079
\(690\) 0 0
\(691\) 15.0139 + 26.0048i 0.571155 + 0.989269i 0.996448 + 0.0842134i \(0.0268378\pi\)
−0.425293 + 0.905056i \(0.639829\pi\)
\(692\) 7.95416 + 13.7770i 0.302372 + 0.523724i
\(693\) 0 0
\(694\) −13.3305 −0.506020
\(695\) −3.19722 + 5.53776i −0.121278 + 0.210059i
\(696\) 0 0
\(697\) 22.8167 0.864242
\(698\) 4.36249 7.55605i 0.165123 0.286001i
\(699\) 0 0
\(700\) 1.65139 + 2.86029i 0.0624166 + 0.108109i
\(701\) 36.4222 1.37565 0.687824 0.725878i \(-0.258566\pi\)
0.687824 + 0.725878i \(0.258566\pi\)
\(702\) 0 0
\(703\) −20.2111 −0.762276
\(704\) −10.2889 17.8209i −0.387777 0.671650i
\(705\) 0 0
\(706\) 19.3625 33.5368i 0.728717 1.26217i
\(707\) −9.00000 −0.338480
\(708\) 0 0
\(709\) 6.92221 11.9896i 0.259969 0.450279i −0.706264 0.707948i \(-0.749621\pi\)
0.966233 + 0.257669i \(0.0829544\pi\)
\(710\) −11.0917 −0.416263
\(711\) 0 0
\(712\) −9.31665 16.1369i −0.349156 0.604757i
\(713\) 6.00000 + 10.3923i 0.224702 + 0.389195i
\(714\) 0 0
\(715\) −2.89445 5.01333i −0.108246 0.187488i
\(716\) −75.3583 −2.81627
\(717\) 0 0
\(718\) 21.2111 + 36.7387i 0.791591 + 1.37108i
\(719\) −12.8028 + 22.1751i −0.477463 + 0.826990i −0.999666 0.0258309i \(-0.991777\pi\)
0.522203 + 0.852821i \(0.325110\pi\)
\(720\) 0 0
\(721\) −2.00000 + 3.46410i −0.0744839 + 0.129010i
\(722\) −14.3028 + 24.7731i −0.532294 + 0.921961i
\(723\) 0 0
\(724\) −29.1194 + 50.4363i −1.08222 + 1.87445i
\(725\) −3.10555 5.37897i −0.115337 0.199770i
\(726\) 0 0
\(727\) 13.5778 0.503573 0.251786 0.967783i \(-0.418982\pi\)
0.251786 + 0.967783i \(0.418982\pi\)
\(728\) −5.40833 + 9.36750i −0.200446 + 0.347183i
\(729\) 0 0
\(730\) 0.908327 + 1.57327i 0.0336187 + 0.0582293i
\(731\) −38.8305 67.2565i −1.43620 2.48757i
\(732\) 0 0
\(733\) −46.8444 −1.73024 −0.865119 0.501567i \(-0.832757\pi\)
−0.865119 + 0.501567i \(0.832757\pi\)
\(734\) −13.1514 + 22.7789i −0.485427 + 0.840784i
\(735\) 0 0
\(736\) −15.9083 −0.586389
\(737\) −5.61943 + 9.73314i −0.206994 + 0.358525i
\(738\) 0 0
\(739\) 17.8028 + 30.8353i 0.654886 + 1.13430i 0.981922 + 0.189284i \(0.0606166\pi\)
−0.327037 + 0.945012i \(0.606050\pi\)
\(740\) 11.9083 0.437759
\(741\) 0 0
\(742\) −7.39445 −0.271459
\(743\) 18.3167 + 31.7254i 0.671973 + 1.16389i 0.977344 + 0.211658i \(0.0678862\pi\)
−0.305371 + 0.952233i \(0.598780\pi\)
\(744\) 0 0
\(745\) 1.50000 2.59808i 0.0549557 0.0951861i
\(746\) −46.9638 −1.71947
\(747\) 0 0
\(748\) −20.1653 + 34.9273i −0.737315 + 1.27707i
\(749\) 6.21110 0.226949
\(750\) 0 0
\(751\) −23.2250 40.2268i −0.847492 1.46790i −0.883440 0.468545i \(-0.844778\pi\)
0.0359481 0.999354i \(-0.488555\pi\)
\(752\) 1.39445 + 2.41526i 0.0508503 + 0.0880753i
\(753\) 0 0
\(754\) 25.7847 44.6604i 0.939023 1.62644i
\(755\) −1.21110 −0.0440765
\(756\) 0 0
\(757\) −0.408327 0.707243i −0.0148409 0.0257052i 0.858510 0.512798i \(-0.171391\pi\)
−0.873350 + 0.487092i \(0.838058\pi\)
\(758\) −11.0597 + 19.1560i −0.401707 + 0.695777i
\(759\) 0 0
\(760\) 8.40833 14.5636i 0.305002 0.528279i
\(761\) 9.31665 16.1369i 0.337728 0.584963i −0.646277 0.763103i \(-0.723675\pi\)
0.984005 + 0.178140i \(0.0570081\pi\)
\(762\) 0 0
\(763\) −9.60555 + 16.6373i −0.347744 + 0.602311i
\(764\) 27.7708 + 48.1005i 1.00471 + 1.74021i
\(765\) 0 0
\(766\) 56.7250 2.04956
\(767\) 19.5000 33.7750i 0.704104 1.21954i
\(768\) 0 0
\(769\) −5.50000 9.52628i −0.198335 0.343526i 0.749654 0.661830i \(-0.230220\pi\)
−0.947989 + 0.318304i \(0.896887\pi\)
\(770\) −1.84861 3.20189i −0.0666194 0.115388i
\(771\) 0 0
\(772\) 51.5416 1.85502
\(773\) 11.1972 19.3942i 0.402736 0.697560i −0.591319 0.806438i \(-0.701393\pi\)
0.994055 + 0.108878i \(0.0347259\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 12.5917 21.8094i 0.452015 0.782912i
\(777\) 0 0
\(778\) −17.5139 30.3349i −0.627903 1.08756i
\(779\) 16.8167 0.602519
\(780\) 0 0
\(781\) 7.73338 0.276722
\(782\) 26.2708 + 45.5024i 0.939443 + 1.62716i
\(783\) 0 0
\(784\) 0.908327 1.57327i 0.0324402 0.0561882i
\(785\) 11.2111 0.400141
\(786\) 0 0
\(787\) −7.31665 + 12.6728i −0.260811 + 0.451737i −0.966458 0.256826i \(-0.917323\pi\)
0.705647 + 0.708564i \(0.250656\pi\)
\(788\) −3.90833 −0.139228
\(789\) 0 0
\(790\) −6.00000 10.3923i −0.213470 0.369742i
\(791\) 0.802776 + 1.39045i 0.0285434 + 0.0494386i
\(792\) 0 0
\(793\) −1.80278 + 3.12250i −0.0640184 + 0.110883i
\(794\) 50.7250 1.80016
\(795\) 0 0
\(796\) −21.1653 36.6593i −0.750183 1.29936i
\(797\) −7.22498 + 12.5140i −0.255922 + 0.443270i −0.965146 0.261714i \(-0.915712\pi\)
0.709224 + 0.704984i \(0.249046\pi\)
\(798\) 0 0
\(799\) −35.0278 + 60.6699i −1.23919 + 2.14635i
\(800\) 2.65139 4.59234i 0.0937407 0.162364i
\(801\) 0 0
\(802\) 14.0597 24.3521i 0.496466 0.859904i
\(803\) −0.633308 1.09692i −0.0223489 0.0387095i
\(804\) 0 0
\(805\) −3.00000 −0.105736
\(806\) −16.6056 28.7617i −0.584906 1.01309i
\(807\) 0 0
\(808\) −13.5000 23.3827i −0.474928 0.822600i
\(809\) −27.5278 47.6795i −0.967824 1.67632i −0.701827 0.712347i \(-0.747632\pi\)
−0.265997 0.963974i \(-0.585701\pi\)
\(810\) 0 0
\(811\) −46.4222 −1.63010 −0.815052 0.579388i \(-0.803292\pi\)
−0.815052 + 0.579388i \(0.803292\pi\)
\(812\) 10.2569 17.7655i 0.359948 0.623448i
\(813\) 0 0
\(814\) −13.3305 −0.467235
\(815\) 1.89445 3.28128i 0.0663596 0.114938i
\(816\) 0 0
\(817\) −28.6194 49.5703i −1.00127 1.73425i
\(818\) 18.9083 0.661114
\(819\) 0 0
\(820\) −9.90833 −0.346014
\(821\) 10.7111 + 18.5522i 0.373820 + 0.647475i 0.990150 0.140013i \(-0.0447144\pi\)
−0.616330 + 0.787488i \(0.711381\pi\)
\(822\) 0 0
\(823\) 8.31665 14.4049i 0.289900 0.502122i −0.683885 0.729589i \(-0.739711\pi\)
0.973786 + 0.227467i \(0.0730445\pi\)
\(824\) −12.0000 −0.418040
\(825\) 0 0
\(826\) 12.4542 21.5712i 0.433336 0.750560i
\(827\) 42.4222 1.47516 0.737582 0.675257i \(-0.235967\pi\)
0.737582 + 0.675257i \(0.235967\pi\)
\(828\) 0 0
\(829\) −14.7111 25.4804i −0.510938 0.884970i −0.999920 0.0126762i \(-0.995965\pi\)
0.488982 0.872294i \(-0.337368\pi\)
\(830\) −10.6056 18.3694i −0.368124 0.637610i
\(831\) 0 0
\(832\) 46.2111 1.60208
\(833\) 45.6333 1.58110
\(834\) 0 0
\(835\) 4.50000 + 7.79423i 0.155729 + 0.269730i
\(836\) −14.8625 + 25.7426i −0.514030 + 0.890326i
\(837\) 0 0
\(838\) 19.8486 34.3788i 0.685659 1.18760i
\(839\) −10.0139 + 17.3445i −0.345717 + 0.598800i −0.985484 0.169769i \(-0.945698\pi\)
0.639766 + 0.768569i \(0.279031\pi\)
\(840\) 0 0
\(841\) −4.78890 + 8.29461i −0.165134 + 0.286021i
\(842\) −37.3305 64.6584i −1.28650 2.22827i
\(843\) 0 0
\(844\) −77.9638 −2.68363
\(845\) 13.0000 0.447214
\(846\) 0 0
\(847\) −4.21110 7.29384i −0.144695 0.250619i
\(848\) −0.486122 0.841988i −0.0166935 0.0289140i
\(849\) 0 0
\(850\) −17.5139 −0.600721
\(851\) −5.40833 + 9.36750i −0.185395 + 0.321114i
\(852\) 0 0
\(853\) 47.2111 1.61648 0.808239 0.588855i \(-0.200421\pi\)
0.808239 + 0.588855i \(0.200421\pi\)
\(854\) −1.15139 + 1.99426i −0.0393997 + 0.0682422i
\(855\) 0 0
\(856\) 9.31665 + 16.1369i 0.318437 + 0.551548i
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 0 0
\(859\) 10.7889 0.368112 0.184056 0.982916i \(-0.441077\pi\)
0.184056 + 0.982916i \(0.441077\pi\)
\(860\) 16.8625 + 29.2067i 0.575006 + 0.995940i
\(861\) 0 0
\(862\) 33.6653 58.3100i 1.14664 1.98604i
\(863\) −36.0000 −1.22545 −0.612727 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 0 0
\(865\) 2.40833 4.17134i 0.0818856 0.141830i
\(866\) 8.30278 0.282140
\(867\) 0 0
\(868\) −6.60555 11.4412i −0.224207 0.388338i
\(869\) 4.18335 + 7.24577i 0.141910 + 0.245796i
\(870\) 0 0
\(871\) −12.6194 21.8575i −0.427593 0.740613i
\(872\) −57.6333 −1.95171
\(873\) 0 0
\(874\) 19.3625 + 33.5368i 0.654946 + 1.13440i
\(875\) 0.500000 0.866025i 0.0169031 0.0292770i
\(876\) 0 0
\(877\) 0.986122 1.70801i 0.0332990 0.0576755i −0.848896 0.528560i \(-0.822732\pi\)
0.882195 + 0.470885i \(0.156065\pi\)
\(878\) 31.3625 54.3214i 1.05843 1.83326i
\(879\) 0 0
\(880\) 0.243061 0.420994i 0.00819358 0.0141917i
\(881\) −10.9222 18.9178i −0.367978 0.637357i 0.621271 0.783596i \(-0.286617\pi\)
−0.989249 + 0.146238i \(0.953283\pi\)
\(882\) 0 0
\(883\) 11.6333 0.391492 0.195746 0.980655i \(-0.437287\pi\)
0.195746 + 0.980655i \(0.437287\pi\)
\(884\) −45.2847 78.4354i −1.52309 2.63807i
\(885\) 0 0
\(886\) 7.39445 + 12.8076i 0.248421 + 0.430278i
\(887\) −18.5278 32.0910i −0.622101 1.07751i −0.989094 0.147287i \(-0.952946\pi\)
0.366993 0.930224i \(-0.380387\pi\)
\(888\) 0 0
\(889\) 4.21110 0.141236
\(890\) −7.15139 + 12.3866i −0.239715 + 0.415199i
\(891\) 0 0
\(892\) −13.9083 −0.465685
\(893\) −25.8167 + 44.7158i −0.863921 + 1.49636i
\(894\) 0 0
\(895\) 11.4083 + 19.7598i 0.381338 + 0.660497i
\(896\) 18.9083 0.631683
\(897\) 0 0
\(898\) −70.5416 −2.35400
\(899\) 12.4222 + 21.5159i 0.414304 + 0.717595i
\(900\) 0 0
\(901\) 12.2111 21.1503i 0.406811 0.704617i
\(902\) 11.0917 0.369312
\(903\) 0 0
\(904\) −2.40833 + 4.17134i −0.0800998 + 0.138737i
\(905\) 17.6333 0.586151
\(906\) 0 0
\(907\) 19.1333 + 33.1399i 0.635311 + 1.10039i 0.986449 + 0.164067i \(0.0524614\pi\)
−0.351138 + 0.936324i \(0.614205\pi\)
\(908\) −45.2847 78.4354i −1.50283 2.60297i
\(909\) 0 0
\(910\) 8.30278 0.275234
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 0 0
\(913\) 7.39445 + 12.8076i 0.244721 + 0.423868i
\(914\) 30.8764 53.4794i 1.02130 1.76894i
\(915\) 0 0
\(916\) −23.1194 + 40.0440i −0.763887 + 1.32309i
\(917\) 10.6056 18.3694i 0.350226 0.606610i
\(918\) 0 0
\(919\) 19.4083 33.6162i 0.640222 1.10890i −0.345161 0.938543i \(-0.612176\pi\)
0.985383 0.170353i \(-0.0544908\pi\)
\(920\) −4.50000 7.79423i −0.148361 0.256968i
\(921\) 0 0
\(922\) −83.3860 −2.74617
\(923\) −8.68335 + 15.0400i −0.285816 + 0.495048i
\(924\) 0 0
\(925\) −1.80278 3.12250i −0.0592749 0.102667i
\(926\) 39.6333 + 68.6469i 1.30243 + 2.25588i
\(927\) 0 0
\(928\) −32.9361 −1.08118
\(929\) −7.71110 + 13.3560i −0.252993 + 0.438197i −0.964348 0.264636i \(-0.914748\pi\)
0.711355 + 0.702832i \(0.248082\pi\)
\(930\) 0 0
\(931\) 33.6333 1.10229
\(932\) 25.1194 43.5081i 0.822814 1.42516i
\(933\) 0 0
\(934\) 3.21110 + 5.56179i 0.105070 + 0.181987i
\(935\) 12.2111 0.399346
\(936\) 0 0
\(937\) 54.4777 1.77971 0.889855 0.456244i \(-0.150806\pi\)
0.889855 + 0.456244i \(0.150806\pi\)
\(938\) −8.05971 13.9598i −0.263159 0.455805i
\(939\) 0 0
\(940\) 15.2111 26.3464i 0.496131 0.859325i
\(941\) 9.63331 0.314037 0.157018 0.987596i \(-0.449812\pi\)
0.157018 + 0.987596i \(0.449812\pi\)
\(942\) 0 0
\(943\) 4.50000 7.79423i 0.146540 0.253815i
\(944\) 3.27502 0.106593
\(945\) 0 0
\(946\) −18.8764 32.6948i −0.613724 1.06300i
\(947\) −9.31665 16.1369i −0.302751 0.524379i 0.674007 0.738725i \(-0.264572\pi\)
−0.976758 + 0.214345i \(0.931238\pi\)
\(948\) 0 0
\(949\) 2.84441 0.0923335
\(950\) −12.9083 −0.418801
\(951\) 0 0
\(952\) −11.4083 19.7598i −0.369746 0.640419i
\(953\) −7.22498 + 12.5140i −0.234040 + 0.405369i −0.958993 0.283429i \(-0.908528\pi\)
0.724953 + 0.688798i \(0.241861\pi\)
\(954\) 0 0
\(955\) 8.40833 14.5636i 0.272087 0.471269i
\(956\) 0 0
\(957\) 0 0
\(958\) −33.1791 + 57.4680i −1.07197 + 1.85671i
\(959\) 0.802776 + 1.39045i 0.0259230 + 0.0448999i
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 14.9680 25.9254i 0.482589 0.835869i
\(963\) 0 0
\(964\) −2.95416 5.11676i −0.0951472 0.164800i
\(965\) −7.80278 13.5148i −0.251180 0.435057i
\(966\) 0 0
\(967\) −44.4777 −1.43031 −0.715153 0.698967i \(-0.753643\pi\)
−0.715153 + 0.698967i \(0.753643\pi\)
\(968\) 12.6333 21.8815i 0.406050 0.703299i
\(969\) 0 0
\(970\) −19.3305 −0.620666
\(971\) −22.0139 + 38.1292i −0.706459 + 1.22362i 0.259703 + 0.965688i \(0.416375\pi\)
−0.966162 + 0.257934i \(0.916958\pi\)
\(972\) 0 0
\(973\) 3.19722 + 5.53776i 0.102498 + 0.177532i
\(974\) −2.30278 −0.0737857
\(975\) 0 0
\(976\) −0.302776 −0.00969161
\(977\) 14.4083 + 24.9560i 0.460963 + 0.798412i 0.999009 0.0445038i \(-0.0141707\pi\)
−0.538046 + 0.842915i \(0.680837\pi\)
\(978\) 0 0
\(979\) 4.98612 8.63622i 0.159357 0.276015i
\(980\) −19.8167 −0.633020
\(981\) 0 0
\(982\) −19.3625 + 33.5368i −0.617882 + 1.07020i
\(983\) −18.4222 −0.587577 −0.293789 0.955870i \(-0.594916\pi\)
−0.293789 + 0.955870i \(0.594916\pi\)
\(984\) 0 0
\(985\) 0.591673 + 1.02481i 0.0188523 + 0.0326531i
\(986\) 54.3902 + 94.2067i 1.73214 + 3.00015i
\(987\) 0 0
\(988\) −33.3764 57.8096i −1.06184 1.83917i
\(989\) −30.6333 −0.974083
\(990\) 0 0
\(991\) −20.0139 34.6651i −0.635762 1.10117i −0.986353 0.164643i \(-0.947353\pi\)
0.350591 0.936529i \(-0.385981\pi\)
\(992\) −10.6056 + 18.3694i −0.336727 + 0.583228i
\(993\) 0 0
\(994\) −5.54584 + 9.60567i −0.175903 + 0.304673i
\(995\) −6.40833 + 11.0995i −0.203158 + 0.351879i
\(996\) 0 0
\(997\) 9.22498 15.9781i 0.292158 0.506033i −0.682162 0.731201i \(-0.738960\pi\)
0.974320 + 0.225169i \(0.0722933\pi\)
\(998\) −2.78890 4.83051i −0.0882810 0.152907i
\(999\) 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.406.1 4
3.2 odd 2 65.2.e.b.16.2 4
12.11 even 2 1040.2.q.o.81.2 4
13.3 even 3 7605.2.a.bg.1.2 2
13.9 even 3 inner 585.2.j.d.451.1 4
13.10 even 6 7605.2.a.bb.1.1 2
15.2 even 4 325.2.o.b.224.1 8
15.8 even 4 325.2.o.b.224.4 8
15.14 odd 2 325.2.e.a.276.1 4
39.2 even 12 845.2.c.d.506.4 4
39.5 even 4 845.2.m.d.361.4 8
39.8 even 4 845.2.m.d.361.1 8
39.11 even 12 845.2.c.d.506.1 4
39.17 odd 6 845.2.e.d.191.1 4
39.20 even 12 845.2.m.d.316.4 8
39.23 odd 6 845.2.a.f.1.2 2
39.29 odd 6 845.2.a.c.1.1 2
39.32 even 12 845.2.m.d.316.1 8
39.35 odd 6 65.2.e.b.61.2 yes 4
39.38 odd 2 845.2.e.d.146.1 4
156.35 even 6 1040.2.q.o.321.2 4
195.29 odd 6 4225.2.a.x.1.2 2
195.74 odd 6 325.2.e.a.126.1 4
195.113 even 12 325.2.o.b.74.1 8
195.152 even 12 325.2.o.b.74.4 8
195.179 odd 6 4225.2.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.e.b.16.2 4 3.2 odd 2
65.2.e.b.61.2 yes 4 39.35 odd 6
325.2.e.a.126.1 4 195.74 odd 6
325.2.e.a.276.1 4 15.14 odd 2
325.2.o.b.74.1 8 195.113 even 12
325.2.o.b.74.4 8 195.152 even 12
325.2.o.b.224.1 8 15.2 even 4
325.2.o.b.224.4 8 15.8 even 4
585.2.j.d.406.1 4 1.1 even 1 trivial
585.2.j.d.451.1 4 13.9 even 3 inner
845.2.a.c.1.1 2 39.29 odd 6
845.2.a.f.1.2 2 39.23 odd 6
845.2.c.d.506.1 4 39.11 even 12
845.2.c.d.506.4 4 39.2 even 12
845.2.e.d.146.1 4 39.38 odd 2
845.2.e.d.191.1 4 39.17 odd 6
845.2.m.d.316.1 8 39.32 even 12
845.2.m.d.316.4 8 39.20 even 12
845.2.m.d.361.1 8 39.8 even 4
845.2.m.d.361.4 8 39.5 even 4
1040.2.q.o.81.2 4 12.11 even 2
1040.2.q.o.321.2 4 156.35 even 6
4225.2.a.t.1.1 2 195.179 odd 6
4225.2.a.x.1.2 2 195.29 odd 6
7605.2.a.bb.1.1 2 13.10 even 6
7605.2.a.bg.1.2 2 13.3 even 3