Properties

Label 325.2.e.a.126.2
Level $325$
Weight $2$
Character 325.126
Analytic conductor $2.595$
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] = [325,2,Mod(126,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.126");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.59513806569\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 126.2
Root \(-0.651388 + 1.12824i\) of defining polynomial
Character \(\chi\) \(=\) 325.126
Dual form 325.2.e.a.276.2

$q$-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} +(0.500000 - 0.866025i) q^{3} +(0.151388 + 0.262211i) q^{4} +(-0.651388 - 1.12824i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(2.80278 - 4.85455i) q^{11} +0.302776 q^{12} -3.60555 q^{13} -1.30278 q^{14} +(1.65139 - 2.86029i) q^{16} +(0.197224 + 0.341603i) q^{17} +2.60555 q^{18} +(-0.802776 - 1.39045i) q^{19} -1.00000 q^{21} +(-3.65139 - 6.32439i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +(-2.34861 + 4.06792i) q^{26} +5.00000 q^{27} +(0.151388 - 0.262211i) q^{28} +(-4.10555 + 7.11102i) q^{29} -4.00000 q^{31} +(0.848612 + 1.46984i) q^{32} +(-2.80278 - 4.85455i) q^{33} +0.513878 q^{34} +(-0.302776 + 0.524423i) q^{36} +(-1.80278 + 3.12250i) q^{37} -2.09167 q^{38} +(-1.80278 + 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-0.651388 + 1.12824i) q^{42} +(2.10555 + 3.64692i) q^{43} +1.69722 q^{44} +(1.95416 + 3.38471i) q^{46} +5.21110 q^{47} +(-1.65139 - 2.86029i) q^{48} +(3.00000 - 5.19615i) q^{49} +0.394449 q^{51} +(-0.545837 - 0.945417i) q^{52} -11.2111 q^{53} +(3.25694 - 5.64118i) q^{54} +(-1.50000 - 2.59808i) q^{56} -1.60555 q^{57} +(5.34861 + 9.26407i) q^{58} +(-5.40833 - 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-2.60555 + 4.51295i) q^{62} +(1.00000 - 1.73205i) q^{63} +8.81665 q^{64} -7.30278 q^{66} +(-3.50000 + 6.06218i) q^{67} +(-0.0597147 + 0.103429i) q^{68} +(1.50000 + 2.59808i) q^{69} +(8.40833 + 14.5636i) q^{71} +(3.00000 + 5.19615i) q^{72} +15.2111 q^{73} +(2.34861 + 4.06792i) q^{74} +(0.243061 - 0.420994i) q^{76} -5.60555 q^{77} +(2.34861 + 4.06792i) q^{78} -9.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.95416 + 3.38471i) q^{82} -5.21110 q^{83} +(-0.151388 - 0.262211i) q^{84} +5.48612 q^{86} +(4.10555 + 7.11102i) q^{87} +(8.40833 - 14.5636i) q^{88} +(-4.10555 + 7.11102i) q^{89} +(1.80278 + 3.12250i) q^{91} -0.908327 q^{92} +(-2.00000 + 3.46410i) q^{93} +(3.39445 - 5.87936i) q^{94} +1.69722 q^{96} +(-7.80278 - 13.5148i) q^{97} +(-3.90833 - 6.76942i) q^{98} +11.2111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + 2 q^{3} - 3 q^{4} + q^{6} - 2 q^{7} + 12 q^{8} + 4 q^{9} + 4 q^{11} - 6 q^{12} + 2 q^{14} + 3 q^{16} + 8 q^{17} - 4 q^{18} + 4 q^{19} - 4 q^{21} - 11 q^{22} - 6 q^{23} + 6 q^{24} - 13 q^{26}+ \cdots + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(0.0143007\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0.151388 + 0.262211i 0.0756939 + 0.131106i
\(5\) 0 0
\(6\) −0.651388 1.12824i −0.265928 0.460601i
\(7\) −0.500000 0.866025i −0.188982 0.327327i 0.755929 0.654654i \(-0.227186\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 2.80278 4.85455i 0.845069 1.46370i −0.0404929 0.999180i \(-0.512893\pi\)
0.885562 0.464522i \(-0.153774\pi\)
\(12\) 0.302776 0.0874038
\(13\) −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 \(0.818102\pi\)
\(18\) 2.60555 0.614134
\(19\) −0.802776 1.39045i −0.184169 0.318991i 0.759127 0.650943i \(-0.225626\pi\)
−0.943296 + 0.331952i \(0.892293\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) −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 \(0.267924\pi\)
\(24\) 1.50000 2.59808i 0.306186 0.530330i
\(25\) 0 0
\(26\) −2.34861 + 4.06792i −0.460601 + 0.797784i
\(27\) 5.00000 0.962250
\(28\) 0.151388 0.262211i 0.0286096 0.0495533i
\(29\) −4.10555 + 7.11102i −0.762382 + 1.32048i 0.179238 + 0.983806i \(0.442637\pi\)
−0.941620 + 0.336678i \(0.890697\pi\)
\(30\) 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
\(33\) −2.80278 4.85455i −0.487901 0.845069i
\(34\) 0.513878 0.0881294
\(35\) 0 0
\(36\) −0.302776 + 0.524423i −0.0504626 + 0.0874038i
\(37\) −1.80278 + 3.12250i −0.296374 + 0.513336i −0.975304 0.220868i \(-0.929111\pi\)
0.678929 + 0.734204i \(0.262444\pi\)
\(38\) −2.09167 −0.339314
\(39\) −1.80278 + 3.12250i −0.288675 + 0.500000i
\(40\) 0 0
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) −0.651388 + 1.12824i −0.100511 + 0.174091i
\(43\) 2.10555 + 3.64692i 0.321094 + 0.556150i 0.980714 0.195449i \(-0.0626163\pi\)
−0.659620 + 0.751599i \(0.729283\pi\)
\(44\) 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 \(0.375904\pi\)
\(48\) −1.65139 2.86029i −0.238357 0.412847i
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 0 0
\(51\) 0.394449 0.0552339
\(52\) −0.545837 0.945417i −0.0756939 0.131106i
\(53\) −11.2111 −1.53996 −0.769982 0.638066i \(-0.779735\pi\)
−0.769982 + 0.638066i \(0.779735\pi\)
\(54\) 3.25694 5.64118i 0.443213 0.767668i
\(55\) 0 0
\(56\) −1.50000 2.59808i −0.200446 0.347183i
\(57\) −1.60555 −0.212660
\(58\) 5.34861 + 9.26407i 0.702307 + 1.21643i
\(59\) −5.40833 9.36750i −0.704104 1.21954i −0.967014 0.254724i \(-0.918015\pi\)
0.262910 0.964820i \(-0.415318\pi\)
\(60\) 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
\(63\) 1.00000 1.73205i 0.125988 0.218218i
\(64\) 8.81665 1.10208
\(65\) 0 0
\(66\) −7.30278 −0.898910
\(67\) −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) −0.0597147 + 0.103429i −0.00724147 + 0.0125426i
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) 0 0
\(71\) 8.40833 + 14.5636i 0.997885 + 1.72839i 0.555240 + 0.831690i \(0.312626\pi\)
0.442645 + 0.896697i \(0.354040\pi\)
\(72\) 3.00000 + 5.19615i 0.353553 + 0.612372i
\(73\) 15.2111 1.78032 0.890162 0.455643i \(-0.150591\pi\)
0.890162 + 0.455643i \(0.150591\pi\)
\(74\) 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
\(78\) 2.34861 + 4.06792i 0.265928 + 0.460601i
\(79\) −9.21110 −1.03633 −0.518165 0.855281i \(-0.673385\pi\)
−0.518165 + 0.855281i \(0.673385\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.95416 + 3.38471i 0.215801 + 0.373779i
\(83\) −5.21110 −0.571993 −0.285996 0.958231i \(-0.592325\pi\)
−0.285996 + 0.958231i \(0.592325\pi\)
\(84\) −0.151388 0.262211i −0.0165178 0.0286096i
\(85\) 0 0
\(86\) 5.48612 0.591584
\(87\) 4.10555 + 7.11102i 0.440161 + 0.762382i
\(88\) 8.40833 14.5636i 0.896331 1.55249i
\(89\) −4.10555 + 7.11102i −0.435188 + 0.753767i −0.997311 0.0732864i \(-0.976651\pi\)
0.562123 + 0.827053i \(0.309985\pi\)
\(90\) 0 0
\(91\) 1.80278 + 3.12250i 0.188982 + 0.327327i
\(92\) −0.908327 −0.0946996
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) 3.39445 5.87936i 0.350111 0.606409i
\(95\) 0 0
\(96\) 1.69722 0.173222
\(97\) −7.80278 13.5148i −0.792252 1.37222i −0.924570 0.381013i \(-0.875575\pi\)
0.132318 0.991207i \(-0.457758\pi\)
\(98\) −3.90833 6.76942i −0.394801 0.683815i
\(99\) 11.2111 1.12676
\(100\) 0 0
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) 0.256939 0.445032i 0.0254408 0.0440647i
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) −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 \(0.296580\pi\)
\(108\) 0.756939 + 1.31106i 0.0728365 + 0.126157i
\(109\) −4.78890 −0.458693 −0.229347 0.973345i \(-0.573659\pi\)
−0.229347 + 0.973345i \(0.573659\pi\)
\(110\) 0 0
\(111\) 1.80278 + 3.12250i 0.171112 + 0.296374i
\(112\) −3.30278 −0.312083
\(113\) 2.80278 + 4.85455i 0.263663 + 0.456678i 0.967212 0.253969i \(-0.0817360\pi\)
−0.703550 + 0.710646i \(0.748403\pi\)
\(114\) −1.04584 + 1.81144i −0.0979516 + 0.169657i
\(115\) 0 0
\(116\) −2.48612 −0.230831
\(117\) −3.60555 6.24500i −0.333333 0.577350i
\(118\) −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
\(123\) 1.50000 + 2.59808i 0.135250 + 0.234261i
\(124\) −0.605551 1.04885i −0.0543801 0.0941891i
\(125\) 0 0
\(126\) −1.30278 2.25647i −0.116060 0.201023i
\(127\) 5.10555 8.84307i 0.453044 0.784696i −0.545529 0.838092i \(-0.683671\pi\)
0.998573 + 0.0533960i \(0.0170046\pi\)
\(128\) 4.04584 7.00759i 0.357605 0.619390i
\(129\) 4.21110 0.370767
\(130\) 0 0
\(131\) −6.78890 −0.593149 −0.296574 0.955010i \(-0.595844\pi\)
−0.296574 + 0.955010i \(0.595844\pi\)
\(132\) 0.848612 1.46984i 0.0738622 0.127933i
\(133\) −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 \(0.756364\pi\)
\(138\) 3.90833 0.332699
\(139\) −6.80278 11.7828i −0.577004 0.999400i −0.995821 0.0913293i \(-0.970888\pi\)
0.418817 0.908071i \(-0.362445\pi\)
\(140\) 0 0
\(141\) 2.60555 4.51295i 0.219427 0.380059i
\(142\) 21.9083 1.83851
\(143\) −10.1056 + 17.5033i −0.845069 + 1.46370i
\(144\) 6.60555 0.550463
\(145\) 0 0
\(146\) 9.90833 17.1617i 0.820019 1.42031i
\(147\) −3.00000 5.19615i −0.247436 0.428571i
\(148\) −1.09167 −0.0897350
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 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
\(153\) −0.394449 + 0.683205i −0.0318893 + 0.0552339i
\(154\) −3.65139 + 6.32439i −0.294237 + 0.509634i
\(155\) 0 0
\(156\) −1.09167 −0.0874038
\(157\) 3.21110 0.256274 0.128137 0.991756i \(-0.459100\pi\)
0.128137 + 0.991756i \(0.459100\pi\)
\(158\) −6.00000 + 10.3923i −0.477334 + 0.826767i
\(159\) −5.60555 + 9.70910i −0.444549 + 0.769982i
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0.651388 + 1.12824i 0.0511779 + 0.0886427i
\(163\) −9.10555 15.7713i −0.713202 1.23530i −0.963649 0.267172i \(-0.913911\pi\)
0.250447 0.968130i \(-0.419422\pi\)
\(164\) −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 \(0.0534527\pi\)
\(168\) −3.00000 −0.231455
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 1.60555 2.78090i 0.122780 0.212660i
\(172\) −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 \(-0.387431\pi\)
\(174\) 10.6972 0.810954
\(175\) 0 0
\(176\) −9.25694 16.0335i −0.697768 1.20857i
\(177\) −10.8167 −0.813029
\(178\) 5.34861 + 9.26407i 0.400895 + 0.694371i
\(179\) −0.591673 + 1.02481i −0.0442237 + 0.0765977i −0.887290 0.461212i \(-0.847415\pi\)
0.843066 + 0.537810i \(0.180748\pi\)
\(180\) 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
\(183\) 1.00000 0.0739221
\(184\) −4.50000 + 7.79423i −0.331744 + 0.574598i
\(185\) 0 0
\(186\) 2.60555 + 4.51295i 0.191048 + 0.330905i
\(187\) 2.21110 0.161692
\(188\) 0.788897 + 1.36641i 0.0575363 + 0.0996557i
\(189\) −2.50000 4.33013i −0.181848 0.314970i
\(190\) 0 0
\(191\) 2.40833 + 4.17134i 0.174260 + 0.301828i 0.939905 0.341436i \(-0.110913\pi\)
−0.765645 + 0.643264i \(0.777580\pi\)
\(192\) 4.40833 7.63545i 0.318144 0.551041i
\(193\) 4.19722 7.26981i 0.302123 0.523292i −0.674494 0.738281i \(-0.735638\pi\)
0.976617 + 0.214988i \(0.0689714\pi\)
\(194\) −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 \(-0.135396\pi\)
\(198\) 7.30278 12.6488i 0.518986 0.898910i
\(199\) 4.40833 + 7.63545i 0.312498 + 0.541262i 0.978902 0.204328i \(-0.0655009\pi\)
−0.666404 + 0.745590i \(0.732168\pi\)
\(200\) 0 0
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) −5.86249 10.1541i −0.412483 0.714442i
\(203\) 8.21110 0.576306
\(204\) 0.0597147 + 0.103429i 0.00418087 + 0.00724147i
\(205\) 0 0
\(206\) 2.60555 4.51295i 0.181537 0.314432i
\(207\) −6.00000 −0.417029
\(208\) −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
\(213\) 16.8167 1.15226
\(214\) 5.34861 + 9.26407i 0.365624 + 0.633279i
\(215\) 0 0
\(216\) 15.0000 1.02062
\(217\) 2.00000 + 3.46410i 0.135769 + 0.235159i
\(218\) −3.11943 + 5.40301i −0.211274 + 0.365938i
\(219\) 7.60555 13.1732i 0.513936 0.890162i
\(220\) 0 0
\(221\) −0.711103 1.23167i −0.0478339 0.0828508i
\(222\) 4.69722 0.315257
\(223\) 5.10555 8.84307i 0.341893 0.592176i −0.642891 0.765957i \(-0.722265\pi\)
0.984784 + 0.173781i \(0.0555986\pi\)
\(224\) 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 \(0.818304\pi\)
\(228\) −0.243061 0.420994i −0.0160971 0.0278810i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) −2.80278 + 4.85455i −0.184409 + 0.319406i
\(232\) −12.3167 + 21.3331i −0.808628 + 1.40058i
\(233\) −0.788897 −0.0516824 −0.0258412 0.999666i \(-0.508226\pi\)
−0.0258412 + 0.999666i \(0.508226\pi\)
\(234\) −9.39445 −0.614134
\(235\) 0 0
\(236\) 1.63751 2.83625i 0.106593 0.184624i
\(237\) −4.60555 + 7.97705i −0.299163 + 0.518165i
\(238\) −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
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) −0.151388 + 0.262211i −0.00969161 + 0.0167864i
\(245\) 0 0
\(246\) 3.90833 0.249186
\(247\) 2.89445 + 5.01333i 0.184169 + 0.318991i
\(248\) −12.0000 −0.762001
\(249\) −2.60555 + 4.51295i −0.165120 + 0.285996i
\(250\) 0 0
\(251\) 14.4083 + 24.9560i 0.909446 + 1.57521i 0.814836 + 0.579691i \(0.196827\pi\)
0.0946094 + 0.995514i \(0.469840\pi\)
\(252\) 0.605551 0.0381461
\(253\) 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 \(0.903268\pi\)
\(258\) 2.74306 4.75112i 0.170776 0.295792i
\(259\) 3.60555 0.224038
\(260\) 0 0
\(261\) −16.4222 −1.01651
\(262\) −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 \(-0.132850\pi\)
\(264\) −8.40833 14.5636i −0.517497 0.896331i
\(265\) 0 0
\(266\) 1.04584 + 1.81144i 0.0641244 + 0.111067i
\(267\) 4.10555 + 7.11102i 0.251256 + 0.435188i
\(268\) −2.11943 −0.129465
\(269\) 4.50000 + 7.79423i 0.274370 + 0.475223i 0.969976 0.243201i \(-0.0781974\pi\)
−0.695606 + 0.718423i \(0.744864\pi\)
\(270\) 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
\(273\) 3.60555 0.218218
\(274\) 7.30278 0.441177
\(275\) 0 0
\(276\) −0.454163 + 0.786634i −0.0273374 + 0.0473498i
\(277\) 10.1972 + 17.6621i 0.612692 + 1.06121i 0.990785 + 0.135446i \(0.0432466\pi\)
−0.378093 + 0.925768i \(0.623420\pi\)
\(278\) −17.7250 −1.06307
\(279\) −4.00000 6.92820i −0.239474 0.414781i
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −3.39445 5.87936i −0.202136 0.350111i
\(283\) 2.50000 4.33013i 0.148610 0.257399i −0.782104 0.623148i \(-0.785854\pi\)
0.930714 + 0.365748i \(0.119187\pi\)
\(284\) −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
\(288\) −1.69722 + 2.93968i −0.100010 + 0.173222i
\(289\) 8.42221 14.5877i 0.495424 0.858099i
\(290\) 0 0
\(291\) −15.6056 −0.914814
\(292\) 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 \(0.661399\pi\)
\(294\) −7.81665 −0.455877
\(295\) 0 0
\(296\) −5.40833 + 9.36750i −0.314353 + 0.544475i
\(297\) 14.0139 24.2727i 0.813168 1.40845i
\(298\) −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
\(303\) −4.50000 7.79423i −0.258518 0.447767i
\(304\) −5.30278 −0.304135
\(305\) 0 0
\(306\) 0.513878 + 0.890063i 0.0293765 + 0.0508815i
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) −0.848612 1.46984i −0.0483542 0.0837519i
\(309\) 2.00000 3.46410i 0.113776 0.197066i
\(310\) 0 0
\(311\) 5.21110 0.295495 0.147747 0.989025i \(-0.452798\pi\)
0.147747 + 0.989025i \(0.452798\pi\)
\(312\) −5.40833 + 9.36750i −0.306186 + 0.530330i
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 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 \(0.553891\pi\)
\(318\) 7.30278 + 12.6488i 0.409519 + 0.709308i
\(319\) 23.0139 + 39.8612i 1.28853 + 2.23180i
\(320\) 0 0
\(321\) 4.10555 + 7.11102i 0.229150 + 0.396899i
\(322\) 1.95416 3.38471i 0.108901 0.188623i
\(323\) 0.316654 0.548461i 0.0176191 0.0305172i
\(324\) −0.302776 −0.0168209
\(325\) 0 0
\(326\) −23.7250 −1.31401
\(327\) −2.39445 + 4.14731i −0.132413 + 0.229347i
\(328\) −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
\(333\) −7.21110 −0.395166
\(334\) −5.86249 10.1541i −0.320781 0.555609i
\(335\) 0 0
\(336\) −1.65139 + 2.86029i −0.0900906 + 0.156041i
\(337\) −17.6333 −0.960547 −0.480274 0.877119i \(-0.659463\pi\)
−0.480274 + 0.877119i \(0.659463\pi\)
\(338\) 8.46804 14.6671i 0.460601 0.797784i
\(339\) 5.60555 0.304452
\(340\) 0 0
\(341\) −11.2111 + 19.4182i −0.607115 + 1.05155i
\(342\) −2.09167 3.62288i −0.113105 0.195903i
\(343\) −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 \(0.650813\pi\)
\(348\) −1.24306 + 2.15304i −0.0666351 + 0.115415i
\(349\) 9.10555 15.7713i 0.487409 0.844217i −0.512486 0.858695i \(-0.671275\pi\)
0.999895 + 0.0144783i \(0.00460876\pi\)
\(350\) 0 0
\(351\) −18.0278 −0.962250
\(352\) 9.51388 0.507091
\(353\) −2.40833 + 4.17134i −0.128182 + 0.222018i −0.922972 0.384866i \(-0.874248\pi\)
0.794790 + 0.606884i \(0.207581\pi\)
\(354\) −7.04584 + 12.2037i −0.374482 + 0.648622i
\(355\) 0 0
\(356\) −2.48612 −0.131764
\(357\) −0.197224 0.341603i −0.0104382 0.0180795i
\(358\) 0.770817 + 1.33509i 0.0407390 + 0.0705619i
\(359\) −10.4222 −0.550063 −0.275031 0.961435i \(-0.588688\pi\)
−0.275031 + 0.961435i \(0.588688\pi\)
\(360\) 0 0
\(361\) 8.21110 14.2220i 0.432163 0.748529i
\(362\) −16.6972 + 28.9204i −0.877587 + 1.52002i
\(363\) −20.4222 −1.07189
\(364\) −0.545837 + 0.945417i −0.0286096 + 0.0495533i
\(365\) 0 0
\(366\) 0.651388 1.12824i 0.0340486 0.0589739i
\(367\) −8.71110 + 15.0881i −0.454716 + 0.787591i −0.998672 0.0515228i \(-0.983593\pi\)
0.543956 + 0.839114i \(0.316926\pi\)
\(368\) 4.95416 + 8.58086i 0.258254 + 0.447308i
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 5.60555 + 9.70910i 0.291026 + 0.504071i
\(372\) −1.21110 −0.0627927
\(373\) −13.8028 23.9071i −0.714681 1.23786i −0.963083 0.269206i \(-0.913239\pi\)
0.248402 0.968657i \(-0.420095\pi\)
\(374\) 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
\(378\) −6.51388 −0.335038
\(379\) −1.19722 + 2.07365i −0.0614973 + 0.106516i −0.895135 0.445795i \(-0.852921\pi\)
0.833638 + 0.552312i \(0.186254\pi\)
\(380\) 0 0
\(381\) −5.10555 8.84307i −0.261565 0.453044i
\(382\) 6.27502 0.321058
\(383\) 9.31665 + 16.1369i 0.476059 + 0.824558i 0.999624 0.0274277i \(-0.00873162\pi\)
−0.523565 + 0.851986i \(0.675398\pi\)
\(384\) −4.04584 7.00759i −0.206463 0.357605i
\(385\) 0 0
\(386\) −5.46804 9.47093i −0.278316 0.482057i
\(387\) −4.21110 + 7.29384i −0.214062 + 0.370767i
\(388\) 2.36249 4.09195i 0.119937 0.207737i
\(389\) −0.788897 −0.0399987 −0.0199993 0.999800i \(-0.506366\pi\)
−0.0199993 + 0.999800i \(0.506366\pi\)
\(390\) 0 0
\(391\) −1.18335 −0.0598444
\(392\) 9.00000 15.5885i 0.454569 0.787336i
\(393\) −3.39445 + 5.87936i −0.171227 + 0.296574i
\(394\) −14.8625 25.7426i −0.748761 1.29689i
\(395\) 0 0
\(396\) 1.69722 + 2.93968i 0.0852887 + 0.147724i
\(397\) −7.01388 12.1484i −0.352016 0.609710i 0.634586 0.772852i \(-0.281171\pi\)
−0.986603 + 0.163142i \(0.947837\pi\)
\(398\) 11.4861 0.575747
\(399\) 0.802776 + 1.39045i 0.0401890 + 0.0696095i
\(400\) 0 0
\(401\) 1.10555 1.91487i 0.0552086 0.0956241i −0.837100 0.547049i \(-0.815751\pi\)
0.892309 + 0.451425i \(0.149084\pi\)
\(402\) 9.11943 0.454836
\(403\) 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
\(408\) 1.18335 0.0585844
\(409\) 3.10555 + 5.37897i 0.153560 + 0.265973i 0.932534 0.361083i \(-0.117593\pi\)
−0.778974 + 0.627056i \(0.784260\pi\)
\(410\) 0 0
\(411\) 5.60555 0.276501
\(412\) 0.605551 + 1.04885i 0.0298334 + 0.0516729i
\(413\) −5.40833 + 9.36750i −0.266126 + 0.460944i
\(414\) −3.90833 + 6.76942i −0.192084 + 0.332699i
\(415\) 0 0
\(416\) −3.05971 5.29958i −0.150015 0.259833i
\(417\) −13.6056 −0.666267
\(418\) −5.86249 + 10.1541i −0.286744 + 0.496655i
\(419\) 16.6194 28.7857i 0.811912 1.40627i −0.0996117 0.995026i \(-0.531760\pi\)
0.911524 0.411247i \(-0.134907\pi\)
\(420\) 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
\(423\) 5.21110 + 9.02589i 0.253372 + 0.438854i
\(424\) −33.6333 −1.63338
\(425\) 0 0
\(426\) 10.9542 18.9732i 0.530731 0.919253i
\(427\) 0.500000 0.866025i 0.0241967 0.0419099i
\(428\) −2.48612 −0.120171
\(429\) 10.1056 + 17.5033i 0.487901 + 0.845069i
\(430\) 0 0
\(431\) 10.6194 18.3934i 0.511520 0.885978i −0.488391 0.872625i \(-0.662416\pi\)
0.999911 0.0133535i \(-0.00425069\pi\)
\(432\) 8.25694 14.3014i 0.397262 0.688078i
\(433\) −1.80278 3.12250i −0.0866359 0.150058i 0.819451 0.573149i \(-0.194278\pi\)
−0.906087 + 0.423091i \(0.860945\pi\)
\(434\) 5.21110 0.250141
\(435\) 0 0
\(436\) −0.724981 1.25570i −0.0347203 0.0601373i
\(437\) 4.81665 0.230412
\(438\) −9.90833 17.1617i −0.473438 0.820019i
\(439\) −11.6194 + 20.1254i −0.554565 + 0.960535i 0.443372 + 0.896338i \(0.353782\pi\)
−0.997937 + 0.0641973i \(0.979551\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) −1.85281 −0.0881294
\(443\) 22.4222 1.06531 0.532656 0.846332i \(-0.321194\pi\)
0.532656 + 0.846332i \(0.321194\pi\)
\(444\) −0.545837 + 0.945417i −0.0259043 + 0.0448675i
\(445\) 0 0
\(446\) −6.65139 11.5205i −0.314952 0.545513i
\(447\) −3.00000 −0.141895
\(448\) −4.40833 7.63545i −0.208274 0.360741i
\(449\) 6.31665 + 10.9408i 0.298101 + 0.516327i 0.975702 0.219104i \(-0.0703133\pi\)
−0.677600 + 0.735430i \(0.736980\pi\)
\(450\) 0 0
\(451\) 8.40833 + 14.5636i 0.395933 + 0.685775i
\(452\) −0.848612 + 1.46984i −0.0399154 + 0.0691354i
\(453\) 6.60555 11.4412i 0.310356 0.537552i
\(454\) 1.85281 0.0869569
\(455\) 0 0
\(456\) −4.81665 −0.225560
\(457\) −2.59167 + 4.48891i −0.121233 + 0.209982i −0.920254 0.391321i \(-0.872018\pi\)
0.799021 + 0.601303i \(0.205352\pi\)
\(458\) 9.11943 15.7953i 0.426123 0.738067i
\(459\) 0.986122 + 1.70801i 0.0460282 + 0.0797232i
\(460\) 0 0
\(461\) −10.8944 18.8697i −0.507405 0.878851i −0.999963 0.00857184i \(-0.997271\pi\)
0.492558 0.870280i \(-0.336062\pi\)
\(462\) 3.65139 + 6.32439i 0.169878 + 0.294237i
\(463\) 5.57779 0.259222 0.129611 0.991565i \(-0.458627\pi\)
0.129611 + 0.991565i \(0.458627\pi\)
\(464\) 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 \(0.630371\pi\)
\(468\) 1.09167 1.89083i 0.0504626 0.0874038i
\(469\) 7.00000 0.323230
\(470\) 0 0
\(471\) 1.60555 2.78090i 0.0739799 0.128137i
\(472\) −16.2250 28.1025i −0.746815 1.29352i
\(473\) 23.6056 1.08538
\(474\) 6.00000 + 10.3923i 0.275589 + 0.477334i
\(475\) 0 0
\(476\) 0.119429 0.00547404
\(477\) −11.2111 19.4182i −0.513321 0.889098i
\(478\) 0 0
\(479\) 3.59167 6.22096i 0.164108 0.284243i −0.772230 0.635343i \(-0.780859\pi\)
0.936338 + 0.351100i \(0.114192\pi\)
\(480\) 0 0
\(481\) 6.50000 11.2583i 0.296374 0.513336i
\(482\) −21.1194 −0.961964
\(483\) 1.50000 2.59808i 0.0682524 0.118217i
\(484\) 3.09167 5.35493i 0.140531 0.243406i
\(485\) 0 0
\(486\) 20.8444 0.945522
\(487\) −0.500000 0.866025i −0.0226572 0.0392434i 0.854475 0.519493i \(-0.173879\pi\)
−0.877132 + 0.480250i \(0.840546\pi\)
\(488\) 1.50000 + 2.59808i 0.0679018 + 0.117609i
\(489\) −18.2111 −0.823535
\(490\) 0 0
\(491\) −2.40833 + 4.17134i −0.108686 + 0.188250i −0.915238 0.402913i \(-0.867998\pi\)
0.806552 + 0.591163i \(0.201331\pi\)
\(492\) −0.454163 + 0.786634i −0.0204753 + 0.0354642i
\(493\) −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
\(498\) 3.39445 + 5.87936i 0.152109 + 0.263460i
\(499\) −26.4222 −1.18282 −0.591410 0.806371i \(-0.701429\pi\)
−0.591410 + 0.806371i \(0.701429\pi\)
\(500\) 0 0
\(501\) −4.50000 7.79423i −0.201045 0.348220i
\(502\) 37.5416 1.67557
\(503\) 1.50000 + 2.59808i 0.0668817 + 0.115842i 0.897527 0.440959i \(-0.145362\pi\)
−0.830645 + 0.556802i \(0.812028\pi\)
\(504\) 3.00000 5.19615i 0.133631 0.231455i
\(505\) 0 0
\(506\) 21.9083 0.973944
\(507\) 6.50000 11.2583i 0.288675 0.500000i
\(508\) 3.09167 0.137171
\(509\) −1.50000 + 2.59808i −0.0664863 + 0.115158i −0.897352 0.441315i \(-0.854512\pi\)
0.830866 + 0.556473i \(0.187846\pi\)
\(510\) 0 0
\(511\) −7.60555 13.1732i −0.336450 0.582748i
\(512\) 25.4222 1.12351
\(513\) −4.01388 6.95224i −0.177217 0.306949i
\(514\) 15.3764 + 26.6327i 0.678223 + 1.17472i
\(515\) 0 0
\(516\) 0.637510 + 1.10420i 0.0280648 + 0.0486097i
\(517\) 14.6056 25.2976i 0.642351 1.11259i
\(518\) 2.34861 4.06792i 0.103192 0.178734i
\(519\) −16.8167 −0.738169
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) −10.6972 + 18.5281i −0.468205 + 0.810954i
\(523\) 13.7111 23.7483i 0.599545 1.03844i −0.393344 0.919392i \(-0.628682\pi\)
0.992888 0.119050i \(-0.0379850\pi\)
\(524\) −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
\(528\) −18.5139 −0.805713
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 10.8167 18.7350i 0.469403 0.813029i
\(532\) −0.486122 −0.0210761
\(533\) 5.40833 9.36750i 0.234261 0.405751i
\(534\) 10.6972 0.462914
\(535\) 0 0
\(536\) −10.5000 + 18.1865i −0.453531 + 0.785539i
\(537\) 0.591673 + 1.02481i 0.0255326 + 0.0442237i
\(538\) 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
\(543\) −12.8167 + 22.1991i −0.550015 + 0.952654i
\(544\) −0.334734 + 0.579776i −0.0143516 + 0.0248577i
\(545\) 0 0
\(546\) 2.34861 4.06792i 0.100511 0.174091i
\(547\) 24.8444 1.06227 0.531135 0.847287i \(-0.321766\pi\)
0.531135 + 0.847287i \(0.321766\pi\)
\(548\) −0.848612 + 1.46984i −0.0362509 + 0.0627884i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 13.1833 0.561629
\(552\) 4.50000 + 7.79423i 0.191533 + 0.331744i
\(553\) 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 \(0.128776\pi\)
\(558\) −10.4222 −0.441207
\(559\) −7.59167 13.1492i −0.321094 0.556150i
\(560\) 0 0
\(561\) 1.10555 1.91487i 0.0466764 0.0808459i
\(562\) −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 \(0.967551\pi\)
\(564\) 1.57779 0.0664372
\(565\) 0 0
\(566\) −3.25694 5.64118i −0.136899 0.237117i
\(567\) 1.00000 0.0419961
\(568\) 25.2250 + 43.6909i 1.05842 + 1.83323i
\(569\) −0.711103 + 1.23167i −0.0298110 + 0.0516341i −0.880546 0.473961i \(-0.842824\pi\)
0.850735 + 0.525595i \(0.176157\pi\)
\(570\) 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
\(573\) 4.81665 0.201219
\(574\) 1.95416 3.38471i 0.0815652 0.141275i
\(575\) 0 0
\(576\) 8.81665 + 15.2709i 0.367361 + 0.636287i
\(577\) −29.6333 −1.23365 −0.616825 0.787100i \(-0.711582\pi\)
−0.616825 + 0.787100i \(0.711582\pi\)
\(578\) −10.9722 19.0045i −0.456385 0.790482i
\(579\) −4.19722 7.26981i −0.174431 0.302123i
\(580\) 0 0
\(581\) 2.60555 + 4.51295i 0.108096 + 0.187229i
\(582\) −10.1653 + 17.6068i −0.421364 + 0.729824i
\(583\) −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 \(0.196783\pi\)
\(588\) 0.908327 1.57327i 0.0374588 0.0648805i
\(589\) 3.21110 + 5.56179i 0.132311 + 0.229170i
\(590\) 0 0
\(591\) −11.4083 19.7598i −0.469276 0.812810i
\(592\) 5.95416 + 10.3129i 0.244715 + 0.423858i
\(593\) −35.2111 −1.44595 −0.722973 0.690876i \(-0.757225\pi\)
−0.722973 + 0.690876i \(0.757225\pi\)
\(594\) −18.2569 31.6219i −0.749091 1.29746i
\(595\) 0 0
\(596\) 0.454163 0.786634i 0.0186033 0.0322218i
\(597\) 8.81665 0.360842
\(598\) −7.04584 12.2037i −0.288126 0.499048i
\(599\) −6.78890 −0.277387 −0.138693 0.990335i \(-0.544290\pi\)
−0.138693 + 0.990335i \(0.544290\pi\)
\(600\) 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
\(603\) −14.0000 −0.570124
\(604\) 2.00000 + 3.46410i 0.0813788 + 0.140952i
\(605\) 0 0
\(606\) −11.7250 −0.476295
\(607\) −9.89445 17.1377i −0.401603 0.695597i 0.592316 0.805706i \(-0.298214\pi\)
−0.993920 + 0.110108i \(0.964880\pi\)
\(608\) 1.36249 2.35990i 0.0552563 0.0957067i
\(609\) 4.10555 7.11102i 0.166365 0.288153i
\(610\) 0 0
\(611\) −18.7889 −0.760117
\(612\) −0.238859 −0.00965530
\(613\) 0.802776 1.39045i 0.0324238 0.0561597i −0.849358 0.527817i \(-0.823011\pi\)
0.881782 + 0.471657i \(0.156344\pi\)
\(614\) 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 \(0.654617\pi\)
\(618\) −2.60555 4.51295i −0.104811 0.181537i
\(619\) −14.4222 −0.579677 −0.289839 0.957076i \(-0.593602\pi\)
−0.289839 + 0.957076i \(0.593602\pi\)
\(620\) 0 0
\(621\) −7.50000 + 12.9904i −0.300965 + 0.521286i
\(622\) 3.39445 5.87936i 0.136105 0.235741i
\(623\) 8.21110 0.328971
\(624\) 5.95416 + 10.3129i 0.238357 + 0.412847i
\(625\) 0 0
\(626\) −9.11943 + 15.7953i −0.364486 + 0.631308i
\(627\) −4.50000 + 7.79423i −0.179713 + 0.311272i
\(628\) 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
\(633\) −8.19722 14.1980i −0.325810 0.564320i
\(634\) −3.90833 + 6.76942i −0.155219 + 0.268848i
\(635\) 0 0
\(636\) −3.39445 −0.134599
\(637\) −10.8167 + 18.7350i −0.428571 + 0.742307i
\(638\) 59.9638 2.37399
\(639\) −16.8167 + 29.1273i −0.665257 + 1.15226i
\(640\) 0 0
\(641\) 9.71110 + 16.8201i 0.383565 + 0.664355i 0.991569 0.129579i \(-0.0413627\pi\)
−0.608004 + 0.793934i \(0.708029\pi\)
\(642\) 10.6972 0.422186
\(643\) −20.3167 35.1895i −0.801211 1.38774i −0.918820 0.394678i \(-0.870856\pi\)
0.117609 0.993060i \(-0.462477\pi\)
\(644\) 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 \(0.0999947\pi\)
\(648\) −1.50000 + 2.59808i −0.0589256 + 0.102062i
\(649\) −60.6333 −2.38007
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) 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 \(0.975990\pi\)
\(654\) 3.11943 + 5.40301i 0.121979 + 0.211274i
\(655\) 0 0
\(656\) 4.95416 + 8.58086i 0.193428 + 0.335026i
\(657\) 15.2111 + 26.3464i 0.593442 + 1.02787i
\(658\) −6.78890 −0.264659
\(659\) 6.59167 + 11.4171i 0.256775 + 0.444748i 0.965376 0.260862i \(-0.0840067\pi\)
−0.708601 + 0.705609i \(0.750673\pi\)
\(660\) 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
\(663\) −1.42221 −0.0552339
\(664\) −15.6333 −0.606690
\(665\) 0 0
\(666\) −4.69722 + 8.13583i −0.182014 + 0.315257i
\(667\) −12.3167 21.3331i −0.476903 0.826020i
\(668\) 2.72498 0.105433
\(669\) −5.10555 8.84307i −0.197392 0.341893i
\(670\) 0 0
\(671\) 5.60555 0.216400
\(672\) −0.848612 1.46984i −0.0327359 0.0567003i
\(673\) −5.19722 + 9.00186i −0.200338 + 0.346996i −0.948637 0.316365i \(-0.897537\pi\)
0.748299 + 0.663361i \(0.230871\pi\)
\(674\) −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 \(0.723691\pi\)
\(678\) 3.65139 6.32439i 0.140231 0.242887i
\(679\) −7.80278 + 13.5148i −0.299443 + 0.518651i
\(680\) 0 0
\(681\) 1.42221 0.0544990
\(682\) 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 \(0.696462\pi\)
\(684\) 0.972244 0.0371747
\(685\) 0 0
\(686\) −8.46804 + 14.6671i −0.323311 + 0.559992i
\(687\) 7.00000 12.1244i 0.267067 0.462573i
\(688\) 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
\(693\) −5.60555 9.70910i −0.212937 0.368818i
\(694\) 26.3305 0.999493
\(695\) 0 0
\(696\) 12.3167 + 21.3331i 0.466862 + 0.808628i
\(697\) −1.18335 −0.0448224
\(698\) −11.8625 20.5464i −0.449002 0.777694i
\(699\) −0.394449 + 0.683205i −0.0149194 + 0.0258412i
\(700\) 0 0
\(701\) −7.57779 −0.286209 −0.143105 0.989708i \(-0.545709\pi\)
−0.143105 + 0.989708i \(0.545709\pi\)
\(702\) −11.7431 + 20.3396i −0.443213 + 0.767668i
\(703\) 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
\(708\) −1.63751 2.83625i −0.0615414 0.106593i
\(709\) −21.9222 37.9704i −0.823306 1.42601i −0.903207 0.429205i \(-0.858794\pi\)
0.0799016 0.996803i \(-0.474539\pi\)
\(710\) 0 0
\(711\) −9.21110 15.9541i −0.345443 0.598325i
\(712\) −12.3167 + 21.3331i −0.461586 + 0.799491i
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) −0.513878 −0.0192314
\(715\) 0 0
\(716\) −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 0.984988 0.172622i \(-0.0552241\pi\)
−0.641989 + 0.766713i \(0.721891\pi\)
\(720\) 0 0
\(721\) −2.00000 3.46410i −0.0744839 0.129010i
\(722\) −10.6972 18.5281i −0.398109 0.689546i
\(723\) −16.2111 −0.602897
\(724\) −3.88057 6.72135i −0.144220 0.249797i
\(725\) 0 0
\(726\) −13.3028 + 23.0411i −0.493712 + 0.855135i
\(727\) −42.4222 −1.57335 −0.786676 0.617366i \(-0.788200\pi\)
−0.786676 + 0.617366i \(0.788200\pi\)
\(728\) 5.40833 + 9.36750i 0.200446 + 0.347183i
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −0.830532 + 1.43852i −0.0307183 + 0.0532057i
\(732\) 0.151388 + 0.262211i 0.00559545 + 0.00969161i
\(733\) −10.8444 −0.400547 −0.200274 0.979740i \(-0.564183\pi\)
−0.200274 + 0.979740i \(0.564183\pi\)
\(734\) 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
\(738\) −3.90833 + 6.76942i −0.143868 + 0.249186i
\(739\) 14.1972 24.5903i 0.522253 0.904569i −0.477411 0.878680i \(-0.658425\pi\)
0.999665 0.0258895i \(-0.00824179\pi\)
\(740\) 0 0
\(741\) 5.78890 0.212660
\(742\) 14.6056 0.536187
\(743\) −3.31665 + 5.74461i −0.121676 + 0.210749i −0.920429 0.390910i \(-0.872160\pi\)
0.798753 + 0.601660i \(0.205494\pi\)
\(744\) −6.00000 + 10.3923i −0.219971 + 0.381000i
\(745\) 0 0
\(746\) −35.9638 −1.31673
\(747\) −5.21110 9.02589i −0.190664 0.330240i
\(748\) 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
\(753\) 28.8167 1.05014
\(754\) −19.2847 33.4021i −0.702307 1.21643i
\(755\) 0 0
\(756\) 0.756939 1.31106i 0.0275296 0.0476827i
\(757\) −10.4083 + 18.0278i −0.378297 + 0.655230i −0.990815 0.135227i \(-0.956824\pi\)
0.612518 + 0.790457i \(0.290157\pi\)
\(758\) 1.55971 + 2.70151i 0.0566514 + 0.0981231i
\(759\) 16.8167 0.610406
\(760\) 0 0
\(761\) 12.3167 + 21.3331i 0.446478 + 0.773323i 0.998154 0.0607356i \(-0.0193447\pi\)
−0.551676 + 0.834059i \(0.686011\pi\)
\(762\) −13.3028 −0.481909
\(763\) 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
\(768\) 7.09167 0.255899
\(769\) −5.50000 + 9.52628i −0.198335 + 0.343526i −0.947989 0.318304i \(-0.896887\pi\)
0.749654 + 0.661830i \(0.230220\pi\)
\(770\) 0 0
\(771\) 11.8028 + 20.4430i 0.425067 + 0.736237i
\(772\) 2.54163 0.0914754
\(773\) 14.8028 + 25.6392i 0.532419 + 0.922176i 0.999284 + 0.0378477i \(0.0120502\pi\)
−0.466865 + 0.884329i \(0.654616\pi\)
\(774\) 5.48612 + 9.50224i 0.197195 + 0.341551i
\(775\) 0 0
\(776\) −23.4083 40.5444i −0.840310 1.45546i
\(777\) 1.80278 3.12250i 0.0646742 0.112019i
\(778\) −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
\(783\) −20.5278 + 35.5551i −0.733602 + 1.27064i
\(784\) −9.90833 17.1617i −0.353869 0.612919i
\(785\) 0 0
\(786\) 4.42221 + 7.65948i 0.157735 + 0.273205i
\(787\) −14.3167 24.7972i −0.510334 0.883924i −0.999928 0.0119736i \(-0.996189\pi\)
0.489595 0.871950i \(-0.337145\pi\)
\(788\) 6.90833 0.246099
\(789\) −13.1056 22.6995i −0.466570 0.808123i
\(790\) 0 0
\(791\) 2.80278 4.85455i 0.0996552 0.172608i
\(792\) 33.6333 1.19511
\(793\) −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 \(0.481565\pi\)
\(798\) 2.09167 0.0740444
\(799\) 1.02776 + 1.78013i 0.0363594 + 0.0629763i
\(800\) 0 0
\(801\) −16.4222 −0.580250
\(802\) −1.44029 2.49465i −0.0508582 0.0880891i
\(803\) 42.6333 73.8431i 1.50450 2.60586i
\(804\) −1.05971 + 1.83548i −0.0373733 + 0.0647324i
\(805\) 0 0
\(806\) 9.39445 16.2717i 0.330905 0.573145i
\(807\) 9.00000 0.316815
\(808\) 13.5000 23.3827i 0.474928 0.822600i
\(809\) −8.52776 + 14.7705i −0.299820 + 0.519303i −0.976095 0.217346i \(-0.930260\pi\)
0.676275 + 0.736650i \(0.263593\pi\)
\(810\) 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
\(813\) 0.408327 + 0.707243i 0.0143207 + 0.0248041i
\(814\) 26.3305 0.922885
\(815\) 0 0
\(816\) 0.651388 1.12824i 0.0228031 0.0394962i
\(817\) 3.38057 5.85532i 0.118271 0.204852i
\(818\) 8.09167 0.282919
\(819\) −3.60555 + 6.24500i −0.125988 + 0.218218i
\(820\) 0 0
\(821\) 3.71110 6.42782i 0.129518 0.224332i −0.793972 0.607955i \(-0.791990\pi\)
0.923490 + 0.383622i \(0.125324\pi\)
\(822\) 3.65139 6.32439i 0.127357 0.220588i
\(823\) 13.3167 + 23.0651i 0.464189 + 0.804000i 0.999165 0.0408682i \(-0.0130124\pi\)
−0.534975 + 0.844868i \(0.679679\pi\)
\(824\) 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 \(0.424140\pi\)
\(828\) −0.908327 1.57327i −0.0315665 0.0546749i
\(829\) −0.288897 + 0.500385i −0.0100338 + 0.0173791i −0.870999 0.491285i \(-0.836527\pi\)
0.860965 + 0.508664i \(0.169861\pi\)
\(830\) 0 0
\(831\) 20.3944 0.707476
\(832\) −31.7889 −1.10208
\(833\) 2.36669 0.0820010
\(834\) −8.86249 + 15.3503i −0.306883 + 0.531537i
\(835\) 0 0
\(836\) −1.36249 2.35990i −0.0471227 0.0816189i
\(837\) −20.0000 −0.691301
\(838\) −21.6514 37.5013i −0.747935 1.29546i
\(839\) −8.01388 13.8804i −0.276670 0.479206i 0.693885 0.720086i \(-0.255897\pi\)
−0.970555 + 0.240879i \(0.922564\pi\)
\(840\) 0 0
\(841\) −19.2111 33.2746i −0.662452 1.14740i
\(842\) 2.33053 4.03660i 0.0803154 0.139110i
\(843\) −3.00000 + 5.19615i −0.103325 + 0.178965i
\(844\) 4.96384 0.170862
\(845\) 0 0
\(846\) 13.5778 0.466814
\(847\) −10.2111 + 17.6861i −0.350858 + 0.607703i
\(848\) −18.5139 + 32.0670i −0.635769 + 1.10118i
\(849\) −2.50000 4.33013i −0.0857998 0.148610i
\(850\) 0 0
\(851\) −5.40833 9.36750i −0.185395 0.321114i
\(852\) 2.54584 + 4.40952i 0.0872189 + 0.151068i
\(853\) −32.7889 −1.12267 −0.561335 0.827589i \(-0.689712\pi\)
−0.561335 + 0.827589i \(0.689712\pi\)
\(854\) −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 \(0.532677\pi\)
\(858\) 26.3305 0.898910
\(859\) 25.2111 0.860192 0.430096 0.902783i \(-0.358480\pi\)
0.430096 + 0.902783i \(0.358480\pi\)
\(860\) 0 0
\(861\) 1.50000 2.59808i 0.0511199 0.0885422i
\(862\) −13.8347 23.9625i −0.471213 0.816165i
\(863\) −36.0000 −1.22545 −0.612727 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 4.24306 + 7.34920i 0.144352 + 0.250025i
\(865\) 0 0
\(866\) −4.69722 −0.159618
\(867\) −8.42221 14.5877i −0.286033 0.495424i
\(868\) −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
\(873\) 15.6056 27.0296i 0.528168 0.914814i
\(874\) 3.13751 5.43433i 0.106128 0.183819i
\(875\) 0 0
\(876\) 4.60555 0.155607
\(877\) −19.0139 32.9330i −0.642053 1.11207i −0.984974 0.172704i \(-0.944750\pi\)
0.342921 0.939364i \(-0.388584\pi\)
\(878\) 15.1375 + 26.2189i 0.510866 + 0.884846i
\(879\) 17.6056 0.593821
\(880\) 0 0
\(881\) −17.9222 + 31.0422i −0.603814 + 1.04584i 0.388423 + 0.921481i \(0.373020\pi\)
−0.992238 + 0.124356i \(0.960313\pi\)
\(882\) 7.81665 13.5388i 0.263200 0.455877i
\(883\) 31.6333 1.06455 0.532273 0.846573i \(-0.321338\pi\)
0.532273 + 0.846573i \(0.321338\pi\)
\(884\) 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 \(-0.0336243\pi\)
\(888\) 5.40833 + 9.36750i 0.181492 + 0.314353i
\(889\) −10.2111 −0.342469
\(890\) 0 0
\(891\) 2.80278 + 4.85455i 0.0938965 + 0.162634i
\(892\) 3.09167 0.103517
\(893\) −4.18335 7.24577i −0.139990 0.242470i
\(894\) −1.95416 + 3.38471i −0.0653570 + 0.113202i
\(895\) 0 0
\(896\) −8.09167 −0.270324
\(897\) −5.40833 9.36750i −0.180579 0.312772i
\(898\) 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
\(903\) −2.10555 3.64692i −0.0700684 0.121362i
\(904\) 8.40833 + 14.5636i 0.279657 + 0.484380i
\(905\) 0 0
\(906\) −8.60555 14.9053i −0.285900 0.495194i
\(907\) 24.1333 41.8001i 0.801333 1.38795i −0.117405 0.993084i \(-0.537458\pi\)
0.918739 0.394866i \(-0.129209\pi\)
\(908\) −0.215305 + 0.372918i −0.00714513 + 0.0123757i
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) −36.0000 −1.19273 −0.596367 0.802712i \(-0.703390\pi\)
−0.596367 + 0.802712i \(0.703390\pi\)
\(912\) −2.65139 + 4.59234i −0.0877962 + 0.152068i
\(913\) −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
\(918\) 2.56939 0.0848025
\(919\) 8.59167 + 14.8812i 0.283413 + 0.490886i 0.972223 0.234056i \(-0.0751999\pi\)
−0.688810 + 0.724942i \(0.741867\pi\)
\(920\) 0 0
\(921\) 8.00000 13.8564i 0.263609 0.456584i
\(922\) −28.3860 −0.934845
\(923\) −30.3167 52.5100i −0.997885 1.72839i
\(924\) −1.69722 −0.0558346
\(925\) 0 0
\(926\) 3.63331 6.29307i 0.119398 0.206803i
\(927\) 4.00000 + 6.92820i 0.131377 + 0.227552i
\(928\) −13.9361 −0.457474
\(929\) −6.71110 11.6240i −0.220184 0.381370i 0.734680 0.678414i \(-0.237332\pi\)
−0.954864 + 0.297044i \(0.903999\pi\)
\(930\) 0 0
\(931\) −9.63331 −0.315719
\(932\) −0.119429 0.206858i −0.00391204 0.00677586i
\(933\) 2.60555 4.51295i 0.0853019 0.147747i
\(934\) −11.2111 + 19.4182i −0.366838 + 0.635383i
\(935\) 0 0
\(936\) −10.8167 18.7350i −0.353553 0.612372i
\(937\) 46.4777 1.51836 0.759180 0.650880i \(-0.225600\pi\)
0.759180 + 0.650880i \(0.225600\pi\)
\(938\) 4.55971 7.89766i 0.148880 0.257868i
\(939\) −7.00000 + 12.1244i −0.228436 + 0.395663i
\(940\) 0 0
\(941\) 33.6333 1.09641 0.548207 0.836343i \(-0.315311\pi\)
0.548207 + 0.836343i \(0.315311\pi\)
\(942\) −2.09167 3.62288i −0.0681504 0.118040i
\(943\) −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 \(0.0355943\pi\)
\(948\) −2.78890 −0.0905792
\(949\) −54.8444 −1.78032
\(950\) 0 0
\(951\) −3.00000 + 5.19615i −0.0972817 + 0.168497i
\(952\) 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 \(0.528904\pi\)
\(954\) −29.2111 −0.945744
\(955\) 0 0
\(956\) 0 0
\(957\) 46.0278 1.48787
\(958\) −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
\(963\) −16.4222 −0.529198
\(964\) 2.45416 4.25074i 0.0790433 0.136907i
\(965\) 0 0
\(966\) −1.95416 3.38471i −0.0628742 0.108901i
\(967\) −56.4777 −1.81620 −0.908100 0.418752i \(-0.862468\pi\)
−0.908100 + 0.418752i \(0.862468\pi\)
\(968\) −30.6333 53.0584i −0.984592 1.70536i
\(969\) −0.316654 0.548461i −0.0101724 0.0176191i
\(970\) 0 0
\(971\) 3.98612 + 6.90417i 0.127921 + 0.221565i 0.922871 0.385110i \(-0.125836\pi\)
−0.794950 + 0.606675i \(0.792503\pi\)
\(972\) −2.42221 + 4.19538i −0.0776923 + 0.134567i
\(973\) −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 \(0.130009\pi\)
\(978\) −11.8625 + 20.5464i −0.379321 + 0.657003i
\(979\) 23.0139 + 39.8612i 0.735527 + 1.27397i
\(980\) 0 0
\(981\) −4.78890 8.29461i −0.152898 0.264827i
\(982\) 3.13751 + 5.43433i 0.100122 + 0.173416i
\(983\) 10.4222 0.332417 0.166208 0.986091i \(-0.446848\pi\)
0.166208 + 0.986091i \(0.446848\pi\)
\(984\) 4.50000 + 7.79423i 0.143455 + 0.248471i
\(985\) 0 0
\(986\) −2.10975 + 3.65420i −0.0671882 + 0.116373i
\(987\) −5.21110 −0.165871
\(988\) −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
\(993\) 26.0278 0.825966
\(994\) −10.9542 18.9732i −0.347445 0.601792i
\(995\) 0 0
\(996\) −1.57779 −0.0499943
\(997\) 23.2250 + 40.2268i 0.735543 + 1.27400i 0.954485 + 0.298259i \(0.0964060\pi\)
−0.218942 + 0.975738i \(0.570261\pi\)
\(998\) −17.2111 + 29.8105i −0.544808 + 0.943635i
\(999\) −9.01388 + 15.6125i −0.285186 + 0.493957i
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 325.2.e.a.126.2 4
5.2 odd 4 325.2.o.b.74.3 8
5.3 odd 4 325.2.o.b.74.2 8
5.4 even 2 65.2.e.b.61.1 yes 4
13.3 even 3 inner 325.2.e.a.276.2 4
13.4 even 6 4225.2.a.t.1.2 2
13.9 even 3 4225.2.a.x.1.1 2
15.14 odd 2 585.2.j.d.451.2 4
20.19 odd 2 1040.2.q.o.321.1 4
65.3 odd 12 325.2.o.b.224.3 8
65.4 even 6 845.2.a.f.1.1 2
65.9 even 6 845.2.a.c.1.2 2
65.19 odd 12 845.2.c.d.506.2 4
65.24 odd 12 845.2.m.d.361.3 8
65.29 even 6 65.2.e.b.16.1 4
65.34 odd 4 845.2.m.d.316.2 8
65.42 odd 12 325.2.o.b.224.2 8
65.44 odd 4 845.2.m.d.316.3 8
65.49 even 6 845.2.e.d.146.2 4
65.54 odd 12 845.2.m.d.361.2 8
65.59 odd 12 845.2.c.d.506.3 4
65.64 even 2 845.2.e.d.191.2 4
195.29 odd 6 585.2.j.d.406.2 4
195.74 odd 6 7605.2.a.bg.1.1 2
195.134 odd 6 7605.2.a.bb.1.2 2
260.159 odd 6 1040.2.q.o.81.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.e.b.16.1 4 65.29 even 6
65.2.e.b.61.1 yes 4 5.4 even 2
325.2.e.a.126.2 4 1.1 even 1 trivial
325.2.e.a.276.2 4 13.3 even 3 inner
325.2.o.b.74.2 8 5.3 odd 4
325.2.o.b.74.3 8 5.2 odd 4
325.2.o.b.224.2 8 65.42 odd 12
325.2.o.b.224.3 8 65.3 odd 12
585.2.j.d.406.2 4 195.29 odd 6
585.2.j.d.451.2 4 15.14 odd 2
845.2.a.c.1.2 2 65.9 even 6
845.2.a.f.1.1 2 65.4 even 6
845.2.c.d.506.2 4 65.19 odd 12
845.2.c.d.506.3 4 65.59 odd 12
845.2.e.d.146.2 4 65.49 even 6
845.2.e.d.191.2 4 65.64 even 2
845.2.m.d.316.2 8 65.34 odd 4
845.2.m.d.316.3 8 65.44 odd 4
845.2.m.d.361.2 8 65.54 odd 12
845.2.m.d.361.3 8 65.24 odd 12
1040.2.q.o.81.1 4 260.159 odd 6
1040.2.q.o.321.1 4 20.19 odd 2
4225.2.a.t.1.2 2 13.4 even 6
4225.2.a.x.1.1 2 13.9 even 3
7605.2.a.bb.1.2 2 195.134 odd 6
7605.2.a.bg.1.1 2 195.74 odd 6