Properties

Label 546.2.g.d.209.1
Level $546$
Weight $2$
Character 546.209
Analytic conductor $4.360$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(209,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.g (of order \(2\), degree \(1\), 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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.1
Root \(-0.814390 - 1.52865i\) of defining polynomial
Character \(\chi\) \(=\) 546.209
Dual form 546.2.g.d.209.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.52865 - 0.814390i) q^{3} -1.00000 q^{4} -1.76081 q^{5} +(-0.814390 + 1.52865i) q^{6} +(2.58450 + 0.566014i) q^{7} +1.00000i q^{8} +(1.67354 + 2.48983i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.52865 - 0.814390i) q^{3} -1.00000 q^{4} -1.76081 q^{5} +(-0.814390 + 1.52865i) q^{6} +(2.58450 + 0.566014i) q^{7} +1.00000i q^{8} +(1.67354 + 2.48983i) q^{9} +1.76081i q^{10} +3.38959i q^{11} +(1.52865 + 0.814390i) q^{12} +1.00000i q^{13} +(0.566014 - 2.58450i) q^{14} +(2.69166 + 1.43399i) q^{15} +1.00000 q^{16} +5.58785 q^{17} +(2.48983 - 1.67354i) q^{18} -3.39471i q^{19} +1.76081 q^{20} +(-3.48983 - 2.97003i) q^{21} +3.38959 q^{22} -3.58404i q^{23} +(0.814390 - 1.52865i) q^{24} -1.89955 q^{25} +1.00000 q^{26} +(-0.530556 - 5.16900i) q^{27} +(-2.58450 - 0.566014i) q^{28} -3.65877i q^{29} +(1.43399 - 2.69166i) q^{30} +9.08755i q^{31} -1.00000i q^{32} +(2.76045 - 5.18149i) q^{33} -5.58785i q^{34} +(-4.55081 - 0.996643i) q^{35} +(-1.67354 - 2.48983i) q^{36} +9.49548 q^{37} -3.39471 q^{38} +(0.814390 - 1.52865i) q^{39} -1.76081i q^{40} +4.47910 q^{41} +(-2.97003 + 3.48983i) q^{42} +7.79778 q^{43} -3.38959i q^{44} +(-2.94678 - 4.38412i) q^{45} -3.58404 q^{46} +6.44515 q^{47} +(-1.52865 - 0.814390i) q^{48} +(6.35926 + 2.92573i) q^{49} +1.89955i q^{50} +(-8.54187 - 4.55069i) q^{51} -1.00000i q^{52} +4.99350i q^{53} +(-5.16900 + 0.530556i) q^{54} -5.96842i q^{55} +(-0.566014 + 2.58450i) q^{56} +(-2.76462 + 5.18933i) q^{57} -3.65877 q^{58} +0.204075 q^{59} +(-2.69166 - 1.43399i) q^{60} +3.18551i q^{61} +9.08755 q^{62} +(2.91597 + 7.38222i) q^{63} -1.00000 q^{64} -1.76081i q^{65} +(-5.18149 - 2.76045i) q^{66} -14.9381 q^{67} -5.58785 q^{68} +(-2.91881 + 5.47874i) q^{69} +(-0.996643 + 4.55081i) q^{70} -5.92908i q^{71} +(-2.48983 + 1.67354i) q^{72} +8.84923i q^{73} -9.49548i q^{74} +(2.90375 + 1.54698i) q^{75} +3.39471i q^{76} +(-1.91856 + 8.76039i) q^{77} +(-1.52865 - 0.814390i) q^{78} +1.31682 q^{79} -1.76081 q^{80} +(-3.39855 + 8.33366i) q^{81} -4.47910i q^{82} -0.878906 q^{83} +(3.48983 + 2.97003i) q^{84} -9.83914 q^{85} -7.79778i q^{86} +(-2.97967 + 5.59298i) q^{87} -3.38959 q^{88} +13.3915 q^{89} +(-4.38412 + 2.94678i) q^{90} +(-0.566014 + 2.58450i) q^{91} +3.58404i q^{92} +(7.40081 - 13.8917i) q^{93} -6.44515i q^{94} +5.97744i q^{95} +(-0.814390 + 1.52865i) q^{96} -5.82999i q^{97} +(2.92573 - 6.35926i) q^{98} +(-8.43951 + 5.67260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{3} - 12 q^{4} - 4 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} - 2 q^{12} + 10 q^{14} + 4 q^{15} + 12 q^{16} + 12 q^{17} + 8 q^{18} + 4 q^{20} - 20 q^{21} - 2 q^{24} + 20 q^{25} + 12 q^{26} + 8 q^{27} + 8 q^{28} + 14 q^{30} + 46 q^{33} - 22 q^{35} - 4 q^{36} + 16 q^{37} - 8 q^{38} - 2 q^{39} + 28 q^{41} + 4 q^{42} - 8 q^{43} + 24 q^{46} - 68 q^{47} + 2 q^{48} + 26 q^{49} - 50 q^{51} + 16 q^{54} - 10 q^{56} - 28 q^{57} - 24 q^{58} + 8 q^{59} - 4 q^{60} + 16 q^{62} - 2 q^{63} - 12 q^{64} - 12 q^{66} + 8 q^{67} - 12 q^{68} - 24 q^{69} - 28 q^{70} - 8 q^{72} + 92 q^{75} - 8 q^{77} + 2 q^{78} + 36 q^{79} - 4 q^{80} + 16 q^{81} - 32 q^{83} + 20 q^{84} + 8 q^{87} - 48 q^{89} + 2 q^{90} - 10 q^{91} + 8 q^{93} + 2 q^{96} + 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.52865 0.814390i −0.882566 0.470188i
\(4\) −1.00000 −0.500000
\(5\) −1.76081 −0.787458 −0.393729 0.919227i \(-0.628815\pi\)
−0.393729 + 0.919227i \(0.628815\pi\)
\(6\) −0.814390 + 1.52865i −0.332473 + 0.624068i
\(7\) 2.58450 + 0.566014i 0.976848 + 0.213933i
\(8\) 1.00000i 0.353553i
\(9\) 1.67354 + 2.48983i 0.557846 + 0.829945i
\(10\) 1.76081i 0.556817i
\(11\) 3.38959i 1.02200i 0.859581 + 0.511000i \(0.170725\pi\)
−0.859581 + 0.511000i \(0.829275\pi\)
\(12\) 1.52865 + 0.814390i 0.441283 + 0.235094i
\(13\) 1.00000i 0.277350i
\(14\) 0.566014 2.58450i 0.151274 0.690736i
\(15\) 2.69166 + 1.43399i 0.694984 + 0.370253i
\(16\) 1.00000 0.250000
\(17\) 5.58785 1.35525 0.677627 0.735406i \(-0.263008\pi\)
0.677627 + 0.735406i \(0.263008\pi\)
\(18\) 2.48983 1.67354i 0.586859 0.394457i
\(19\) 3.39471i 0.778801i −0.921069 0.389400i \(-0.872682\pi\)
0.921069 0.389400i \(-0.127318\pi\)
\(20\) 1.76081 0.393729
\(21\) −3.48983 2.97003i −0.761544 0.648113i
\(22\) 3.38959 0.722663
\(23\) 3.58404i 0.747324i −0.927565 0.373662i \(-0.878102\pi\)
0.927565 0.373662i \(-0.121898\pi\)
\(24\) 0.814390 1.52865i 0.166237 0.312034i
\(25\) −1.89955 −0.379910
\(26\) 1.00000 0.196116
\(27\) −0.530556 5.16900i −0.102105 0.994774i
\(28\) −2.58450 0.566014i −0.488424 0.106967i
\(29\) 3.65877i 0.679417i −0.940531 0.339708i \(-0.889672\pi\)
0.940531 0.339708i \(-0.110328\pi\)
\(30\) 1.43399 2.69166i 0.261809 0.491428i
\(31\) 9.08755i 1.63217i 0.577930 + 0.816086i \(0.303861\pi\)
−0.577930 + 0.816086i \(0.696139\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.76045 5.18149i 0.480532 0.901982i
\(34\) 5.58785i 0.958309i
\(35\) −4.55081 0.996643i −0.769227 0.168463i
\(36\) −1.67354 2.48983i −0.278923 0.414972i
\(37\) 9.49548 1.56105 0.780523 0.625127i \(-0.214953\pi\)
0.780523 + 0.625127i \(0.214953\pi\)
\(38\) −3.39471 −0.550695
\(39\) 0.814390 1.52865i 0.130407 0.244780i
\(40\) 1.76081i 0.278408i
\(41\) 4.47910 0.699518 0.349759 0.936840i \(-0.386263\pi\)
0.349759 + 0.936840i \(0.386263\pi\)
\(42\) −2.97003 + 3.48983i −0.458285 + 0.538493i
\(43\) 7.79778 1.18915 0.594575 0.804040i \(-0.297320\pi\)
0.594575 + 0.804040i \(0.297320\pi\)
\(44\) 3.38959i 0.511000i
\(45\) −2.94678 4.38412i −0.439280 0.653546i
\(46\) −3.58404 −0.528438
\(47\) 6.44515 0.940122 0.470061 0.882634i \(-0.344232\pi\)
0.470061 + 0.882634i \(0.344232\pi\)
\(48\) −1.52865 0.814390i −0.220642 0.117547i
\(49\) 6.35926 + 2.92573i 0.908465 + 0.417961i
\(50\) 1.89955i 0.268637i
\(51\) −8.54187 4.55069i −1.19610 0.637225i
\(52\) 1.00000i 0.138675i
\(53\) 4.99350i 0.685910i 0.939352 + 0.342955i \(0.111428\pi\)
−0.939352 + 0.342955i \(0.888572\pi\)
\(54\) −5.16900 + 0.530556i −0.703411 + 0.0721995i
\(55\) 5.96842i 0.804782i
\(56\) −0.566014 + 2.58450i −0.0756369 + 0.345368i
\(57\) −2.76462 + 5.18933i −0.366183 + 0.687343i
\(58\) −3.65877 −0.480420
\(59\) 0.204075 0.0265682 0.0132841 0.999912i \(-0.495771\pi\)
0.0132841 + 0.999912i \(0.495771\pi\)
\(60\) −2.69166 1.43399i −0.347492 0.185127i
\(61\) 3.18551i 0.407863i 0.978985 + 0.203932i \(0.0653720\pi\)
−0.978985 + 0.203932i \(0.934628\pi\)
\(62\) 9.08755 1.15412
\(63\) 2.91597 + 7.38222i 0.367378 + 0.930072i
\(64\) −1.00000 −0.125000
\(65\) 1.76081i 0.218401i
\(66\) −5.18149 2.76045i −0.637798 0.339788i
\(67\) −14.9381 −1.82498 −0.912489 0.409101i \(-0.865842\pi\)
−0.912489 + 0.409101i \(0.865842\pi\)
\(68\) −5.58785 −0.677627
\(69\) −2.91881 + 5.47874i −0.351383 + 0.659563i
\(70\) −0.996643 + 4.55081i −0.119122 + 0.543925i
\(71\) 5.92908i 0.703653i −0.936065 0.351826i \(-0.885561\pi\)
0.936065 0.351826i \(-0.114439\pi\)
\(72\) −2.48983 + 1.67354i −0.293430 + 0.197228i
\(73\) 8.84923i 1.03572i 0.855464 + 0.517862i \(0.173272\pi\)
−0.855464 + 0.517862i \(0.826728\pi\)
\(74\) 9.49548i 1.10383i
\(75\) 2.90375 + 1.54698i 0.335296 + 0.178629i
\(76\) 3.39471i 0.389400i
\(77\) −1.91856 + 8.76039i −0.218640 + 0.998339i
\(78\) −1.52865 0.814390i −0.173085 0.0922115i
\(79\) 1.31682 0.148154 0.0740770 0.997253i \(-0.476399\pi\)
0.0740770 + 0.997253i \(0.476399\pi\)
\(80\) −1.76081 −0.196864
\(81\) −3.39855 + 8.33366i −0.377616 + 0.925962i
\(82\) 4.47910i 0.494634i
\(83\) −0.878906 −0.0964724 −0.0482362 0.998836i \(-0.515360\pi\)
−0.0482362 + 0.998836i \(0.515360\pi\)
\(84\) 3.48983 + 2.97003i 0.380772 + 0.324057i
\(85\) −9.83914 −1.06721
\(86\) 7.79778i 0.840856i
\(87\) −2.97967 + 5.59298i −0.319454 + 0.599630i
\(88\) −3.38959 −0.361331
\(89\) 13.3915 1.41949 0.709747 0.704457i \(-0.248809\pi\)
0.709747 + 0.704457i \(0.248809\pi\)
\(90\) −4.38412 + 2.94678i −0.462127 + 0.310618i
\(91\) −0.566014 + 2.58450i −0.0593344 + 0.270929i
\(92\) 3.58404i 0.373662i
\(93\) 7.40081 13.8917i 0.767429 1.44050i
\(94\) 6.44515i 0.664767i
\(95\) 5.97744i 0.613273i
\(96\) −0.814390 + 1.52865i −0.0831183 + 0.156017i
\(97\) 5.82999i 0.591946i −0.955196 0.295973i \(-0.904356\pi\)
0.955196 0.295973i \(-0.0956438\pi\)
\(98\) 2.92573 6.35926i 0.295543 0.642382i
\(99\) −8.43951 + 5.67260i −0.848203 + 0.570118i
\(100\) 1.89955 0.189955
\(101\) 12.1410 1.20808 0.604039 0.796955i \(-0.293557\pi\)
0.604039 + 0.796955i \(0.293557\pi\)
\(102\) −4.55069 + 8.54187i −0.450586 + 0.845771i
\(103\) 7.20411i 0.709842i 0.934896 + 0.354921i \(0.115492\pi\)
−0.934896 + 0.354921i \(0.884508\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 6.14493 + 5.22965i 0.599684 + 0.510362i
\(106\) 4.99350 0.485012
\(107\) 13.3798i 1.29347i −0.762714 0.646736i \(-0.776133\pi\)
0.762714 0.646736i \(-0.223867\pi\)
\(108\) 0.530556 + 5.16900i 0.0510527 + 0.497387i
\(109\) −3.07251 −0.294293 −0.147146 0.989115i \(-0.547009\pi\)
−0.147146 + 0.989115i \(0.547009\pi\)
\(110\) −5.96842 −0.569067
\(111\) −14.5153 7.73302i −1.37773 0.733986i
\(112\) 2.58450 + 0.566014i 0.244212 + 0.0534833i
\(113\) 19.8770i 1.86987i 0.354820 + 0.934934i \(0.384542\pi\)
−0.354820 + 0.934934i \(0.615458\pi\)
\(114\) 5.18933 + 2.76462i 0.486025 + 0.258931i
\(115\) 6.31081i 0.588486i
\(116\) 3.65877i 0.339708i
\(117\) −2.48983 + 1.67354i −0.230185 + 0.154719i
\(118\) 0.204075i 0.0187866i
\(119\) 14.4418 + 3.16281i 1.32388 + 0.289934i
\(120\) −1.43399 + 2.69166i −0.130904 + 0.245714i
\(121\) −0.489316 −0.0444833
\(122\) 3.18551 0.288403
\(123\) −6.84698 3.64774i −0.617371 0.328905i
\(124\) 9.08755i 0.816086i
\(125\) 12.1488 1.08662
\(126\) 7.38222 2.91597i 0.657660 0.259775i
\(127\) 1.58088 0.140280 0.0701402 0.997537i \(-0.477655\pi\)
0.0701402 + 0.997537i \(0.477655\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −11.9201 6.35043i −1.04950 0.559124i
\(130\) −1.76081 −0.154433
\(131\) −18.2002 −1.59015 −0.795077 0.606508i \(-0.792570\pi\)
−0.795077 + 0.606508i \(0.792570\pi\)
\(132\) −2.76045 + 5.18149i −0.240266 + 0.450991i
\(133\) 1.92146 8.77363i 0.166611 0.760770i
\(134\) 14.9381i 1.29045i
\(135\) 0.934207 + 9.10161i 0.0804038 + 0.783342i
\(136\) 5.58785i 0.479155i
\(137\) 11.0958i 0.947981i 0.880530 + 0.473991i \(0.157187\pi\)
−0.880530 + 0.473991i \(0.842813\pi\)
\(138\) 5.47874 + 2.91881i 0.466382 + 0.248465i
\(139\) 13.5283i 1.14746i −0.819045 0.573729i \(-0.805496\pi\)
0.819045 0.573729i \(-0.194504\pi\)
\(140\) 4.55081 + 0.996643i 0.384613 + 0.0842317i
\(141\) −9.85238 5.24887i −0.829720 0.442034i
\(142\) −5.92908 −0.497558
\(143\) −3.38959 −0.283452
\(144\) 1.67354 + 2.48983i 0.139461 + 0.207486i
\(145\) 6.44240i 0.535012i
\(146\) 8.84923 0.732367
\(147\) −7.33839 9.65132i −0.605260 0.796028i
\(148\) −9.49548 −0.780523
\(149\) 6.12739i 0.501976i 0.967990 + 0.250988i \(0.0807554\pi\)
−0.967990 + 0.250988i \(0.919245\pi\)
\(150\) 1.54698 2.90375i 0.126310 0.237090i
\(151\) −17.1388 −1.39474 −0.697368 0.716713i \(-0.745646\pi\)
−0.697368 + 0.716713i \(0.745646\pi\)
\(152\) 3.39471 0.275348
\(153\) 9.35148 + 13.9128i 0.756023 + 1.12479i
\(154\) 8.76039 + 1.91856i 0.705932 + 0.154602i
\(155\) 16.0014i 1.28527i
\(156\) −0.814390 + 1.52865i −0.0652034 + 0.122390i
\(157\) 4.50214i 0.359310i −0.983730 0.179655i \(-0.942502\pi\)
0.983730 0.179655i \(-0.0574981\pi\)
\(158\) 1.31682i 0.104761i
\(159\) 4.06666 7.63331i 0.322507 0.605361i
\(160\) 1.76081i 0.139204i
\(161\) 2.02862 9.26295i 0.159878 0.730022i
\(162\) 8.33366 + 3.39855i 0.654754 + 0.267015i
\(163\) 1.40702 0.110206 0.0551032 0.998481i \(-0.482451\pi\)
0.0551032 + 0.998481i \(0.482451\pi\)
\(164\) −4.47910 −0.349759
\(165\) −4.86062 + 9.12362i −0.378399 + 0.710273i
\(166\) 0.878906i 0.0682163i
\(167\) −2.93743 −0.227305 −0.113653 0.993521i \(-0.536255\pi\)
−0.113653 + 0.993521i \(0.536255\pi\)
\(168\) 2.97003 3.48983i 0.229143 0.269247i
\(169\) −1.00000 −0.0769231
\(170\) 9.83914i 0.754628i
\(171\) 8.45227 5.68118i 0.646362 0.434451i
\(172\) −7.79778 −0.594575
\(173\) −7.62715 −0.579881 −0.289941 0.957045i \(-0.593636\pi\)
−0.289941 + 0.957045i \(0.593636\pi\)
\(174\) 5.59298 + 2.97967i 0.424003 + 0.225888i
\(175\) −4.90939 1.07517i −0.371115 0.0812755i
\(176\) 3.38959i 0.255500i
\(177\) −0.311958 0.166196i −0.0234482 0.0124921i
\(178\) 13.3915i 1.00373i
\(179\) 5.02398i 0.375510i −0.982216 0.187755i \(-0.939879\pi\)
0.982216 0.187755i \(-0.0601211\pi\)
\(180\) 2.94678 + 4.38412i 0.219640 + 0.326773i
\(181\) 5.50980i 0.409540i 0.978810 + 0.204770i \(0.0656447\pi\)
−0.978810 + 0.204770i \(0.934355\pi\)
\(182\) 2.58450 + 0.566014i 0.191576 + 0.0419558i
\(183\) 2.59425 4.86953i 0.191773 0.359966i
\(184\) 3.58404 0.264219
\(185\) −16.7197 −1.22926
\(186\) −13.8917 7.40081i −1.01859 0.542654i
\(187\) 18.9405i 1.38507i
\(188\) −6.44515 −0.470061
\(189\) 1.55451 13.6596i 0.113074 0.993587i
\(190\) 5.97744 0.433649
\(191\) 4.76107i 0.344499i −0.985053 0.172249i \(-0.944896\pi\)
0.985053 0.172249i \(-0.0551035\pi\)
\(192\) 1.52865 + 0.814390i 0.110321 + 0.0587735i
\(193\) 22.5891 1.62600 0.812998 0.582267i \(-0.197834\pi\)
0.812998 + 0.582267i \(0.197834\pi\)
\(194\) −5.82999 −0.418569
\(195\) −1.43399 + 2.69166i −0.102690 + 0.192754i
\(196\) −6.35926 2.92573i −0.454233 0.208980i
\(197\) 18.3675i 1.30863i 0.756221 + 0.654316i \(0.227043\pi\)
−0.756221 + 0.654316i \(0.772957\pi\)
\(198\) 5.67260 + 8.43951i 0.403134 + 0.599770i
\(199\) 16.2052i 1.14876i −0.818589 0.574379i \(-0.805243\pi\)
0.818589 0.574379i \(-0.194757\pi\)
\(200\) 1.89955i 0.134319i
\(201\) 22.8351 + 12.1654i 1.61066 + 0.858084i
\(202\) 12.1410i 0.854240i
\(203\) 2.07092 9.45609i 0.145350 0.663687i
\(204\) 8.54187 + 4.55069i 0.598050 + 0.318612i
\(205\) −7.88685 −0.550841
\(206\) 7.20411 0.501934
\(207\) 8.92367 5.99803i 0.620238 0.416892i
\(208\) 1.00000i 0.0693375i
\(209\) 11.5067 0.795934
\(210\) 5.22965 6.14493i 0.360880 0.424041i
\(211\) −16.9761 −1.16868 −0.584342 0.811508i \(-0.698647\pi\)
−0.584342 + 0.811508i \(0.698647\pi\)
\(212\) 4.99350i 0.342955i
\(213\) −4.82859 + 9.06349i −0.330849 + 0.621020i
\(214\) −13.3798 −0.914623
\(215\) −13.7304 −0.936405
\(216\) 5.16900 0.530556i 0.351706 0.0360997i
\(217\) −5.14369 + 23.4868i −0.349176 + 1.59438i
\(218\) 3.07251i 0.208096i
\(219\) 7.20672 13.5274i 0.486985 0.914095i
\(220\) 5.96842i 0.402391i
\(221\) 5.58785i 0.375880i
\(222\) −7.73302 + 14.5153i −0.519006 + 0.974200i
\(223\) 9.25112i 0.619501i 0.950818 + 0.309751i \(0.100246\pi\)
−0.950818 + 0.309751i \(0.899754\pi\)
\(224\) 0.566014 2.58450i 0.0378184 0.172684i
\(225\) −3.17897 4.72957i −0.211931 0.315304i
\(226\) 19.8770 1.32220
\(227\) 15.1216 1.00366 0.501828 0.864967i \(-0.332661\pi\)
0.501828 + 0.864967i \(0.332661\pi\)
\(228\) 2.76462 5.18933i 0.183092 0.343672i
\(229\) 20.2697i 1.33946i −0.742605 0.669730i \(-0.766410\pi\)
0.742605 0.669730i \(-0.233590\pi\)
\(230\) 6.31081 0.416123
\(231\) 10.0672 11.8291i 0.662371 0.778298i
\(232\) 3.65877 0.240210
\(233\) 5.58290i 0.365748i −0.983136 0.182874i \(-0.941460\pi\)
0.983136 0.182874i \(-0.0585400\pi\)
\(234\) 1.67354 + 2.48983i 0.109403 + 0.162766i
\(235\) −11.3487 −0.740306
\(236\) −0.204075 −0.0132841
\(237\) −2.01296 1.07241i −0.130756 0.0696603i
\(238\) 3.16281 14.4418i 0.205014 0.936123i
\(239\) 24.2290i 1.56725i −0.621237 0.783623i \(-0.713369\pi\)
0.621237 0.783623i \(-0.286631\pi\)
\(240\) 2.69166 + 1.43399i 0.173746 + 0.0925634i
\(241\) 28.6978i 1.84859i −0.381678 0.924295i \(-0.624654\pi\)
0.381678 0.924295i \(-0.375346\pi\)
\(242\) 0.489316i 0.0314544i
\(243\) 11.9820 9.97150i 0.768648 0.639672i
\(244\) 3.18551i 0.203932i
\(245\) −11.1974 5.15164i −0.715378 0.329126i
\(246\) −3.64774 + 6.84698i −0.232571 + 0.436547i
\(247\) 3.39471 0.216000
\(248\) −9.08755 −0.577060
\(249\) 1.34354 + 0.715772i 0.0851433 + 0.0453602i
\(250\) 12.1488i 0.768357i
\(251\) −22.5258 −1.42181 −0.710907 0.703286i \(-0.751716\pi\)
−0.710907 + 0.703286i \(0.751716\pi\)
\(252\) −2.91597 7.38222i −0.183689 0.465036i
\(253\) 12.1484 0.763765
\(254\) 1.58088i 0.0991932i
\(255\) 15.0406 + 8.01290i 0.941879 + 0.501787i
\(256\) 1.00000 0.0625000
\(257\) −27.5068 −1.71582 −0.857912 0.513796i \(-0.828239\pi\)
−0.857912 + 0.513796i \(0.828239\pi\)
\(258\) −6.35043 + 11.9201i −0.395361 + 0.742111i
\(259\) 24.5410 + 5.37458i 1.52491 + 0.333960i
\(260\) 1.76081i 0.109201i
\(261\) 9.10973 6.12309i 0.563878 0.379010i
\(262\) 18.2002i 1.12441i
\(263\) 7.57623i 0.467171i 0.972336 + 0.233585i \(0.0750458\pi\)
−0.972336 + 0.233585i \(0.924954\pi\)
\(264\) 5.18149 + 2.76045i 0.318899 + 0.169894i
\(265\) 8.79261i 0.540125i
\(266\) −8.77363 1.92146i −0.537946 0.117812i
\(267\) −20.4709 10.9059i −1.25280 0.667429i
\(268\) 14.9381 0.912489
\(269\) −17.8846 −1.09044 −0.545222 0.838292i \(-0.683555\pi\)
−0.545222 + 0.838292i \(0.683555\pi\)
\(270\) 9.10161 0.934207i 0.553907 0.0568540i
\(271\) 21.5689i 1.31022i 0.755533 + 0.655110i \(0.227378\pi\)
−0.755533 + 0.655110i \(0.772622\pi\)
\(272\) 5.58785 0.338813
\(273\) 2.97003 3.48983i 0.179754 0.211214i
\(274\) 11.0958 0.670324
\(275\) 6.43870i 0.388268i
\(276\) 2.91881 5.47874i 0.175692 0.329782i
\(277\) −3.31754 −0.199332 −0.0996659 0.995021i \(-0.531777\pi\)
−0.0996659 + 0.995021i \(0.531777\pi\)
\(278\) −13.5283 −0.811375
\(279\) −22.6265 + 15.2084i −1.35461 + 0.910501i
\(280\) 0.996643 4.55081i 0.0595608 0.271963i
\(281\) 31.8619i 1.90072i −0.311147 0.950362i \(-0.600713\pi\)
0.311147 0.950362i \(-0.399287\pi\)
\(282\) −5.24887 + 9.85238i −0.312566 + 0.586701i
\(283\) 24.2711i 1.44277i 0.692536 + 0.721384i \(0.256494\pi\)
−0.692536 + 0.721384i \(0.743506\pi\)
\(284\) 5.92908i 0.351826i
\(285\) 4.86797 9.13742i 0.288354 0.541254i
\(286\) 3.38959i 0.200431i
\(287\) 11.5762 + 2.53524i 0.683323 + 0.149650i
\(288\) 2.48983 1.67354i 0.146715 0.0986141i
\(289\) 14.2241 0.836713
\(290\) 6.44240 0.378311
\(291\) −4.74789 + 8.91201i −0.278326 + 0.522431i
\(292\) 8.84923i 0.517862i
\(293\) −17.4689 −1.02055 −0.510273 0.860012i \(-0.670456\pi\)
−0.510273 + 0.860012i \(0.670456\pi\)
\(294\) −9.65132 + 7.33839i −0.562877 + 0.427984i
\(295\) −0.359336 −0.0209214
\(296\) 9.49548i 0.551913i
\(297\) 17.5208 1.79837i 1.01666 0.104352i
\(298\) 6.12739 0.354950
\(299\) 3.58404 0.207270
\(300\) −2.90375 1.54698i −0.167648 0.0893147i
\(301\) 20.1533 + 4.41365i 1.16162 + 0.254399i
\(302\) 17.1388i 0.986228i
\(303\) −18.5594 9.88754i −1.06621 0.568024i
\(304\) 3.39471i 0.194700i
\(305\) 5.60908i 0.321175i
\(306\) 13.9128 9.35148i 0.795343 0.534589i
\(307\) 10.6490i 0.607773i 0.952708 + 0.303886i \(0.0982843\pi\)
−0.952708 + 0.303886i \(0.901716\pi\)
\(308\) 1.91856 8.76039i 0.109320 0.499169i
\(309\) 5.86696 11.0126i 0.333760 0.626483i
\(310\) −16.0014 −0.908821
\(311\) −12.6195 −0.715584 −0.357792 0.933801i \(-0.616470\pi\)
−0.357792 + 0.933801i \(0.616470\pi\)
\(312\) 1.52865 + 0.814390i 0.0865427 + 0.0461058i
\(313\) 22.9015i 1.29447i −0.762292 0.647234i \(-0.775926\pi\)
0.762292 0.647234i \(-0.224074\pi\)
\(314\) −4.50214 −0.254070
\(315\) −5.13447 12.9987i −0.289295 0.732392i
\(316\) −1.31682 −0.0740770
\(317\) 19.9238i 1.11903i 0.828820 + 0.559515i \(0.189012\pi\)
−0.828820 + 0.559515i \(0.810988\pi\)
\(318\) −7.63331 4.06666i −0.428055 0.228047i
\(319\) 12.4017 0.694364
\(320\) 1.76081 0.0984322
\(321\) −10.8964 + 20.4530i −0.608176 + 1.14157i
\(322\) −9.26295 2.02862i −0.516204 0.113051i
\(323\) 18.9692i 1.05547i
\(324\) 3.39855 8.33366i 0.188808 0.462981i
\(325\) 1.89955i 0.105368i
\(326\) 1.40702i 0.0779277i
\(327\) 4.69678 + 2.50222i 0.259733 + 0.138373i
\(328\) 4.47910i 0.247317i
\(329\) 16.6575 + 3.64805i 0.918357 + 0.201123i
\(330\) 9.12362 + 4.86062i 0.502239 + 0.267568i
\(331\) 18.8267 1.03481 0.517404 0.855741i \(-0.326899\pi\)
0.517404 + 0.855741i \(0.326899\pi\)
\(332\) 0.878906 0.0482362
\(333\) 15.8910 + 23.6422i 0.870823 + 1.29558i
\(334\) 2.93743i 0.160729i
\(335\) 26.3031 1.43709
\(336\) −3.48983 2.97003i −0.190386 0.162028i
\(337\) −30.0841 −1.63879 −0.819393 0.573231i \(-0.805690\pi\)
−0.819393 + 0.573231i \(0.805690\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 16.1876 30.3849i 0.879191 1.65028i
\(340\) 9.83914 0.533603
\(341\) −30.8031 −1.66808
\(342\) −5.68118 8.45227i −0.307203 0.457047i
\(343\) 14.7795 + 11.1610i 0.798017 + 0.602635i
\(344\) 7.79778i 0.420428i
\(345\) 5.13946 9.64702i 0.276699 0.519378i
\(346\) 7.62715i 0.410038i
\(347\) 16.2862i 0.874287i −0.899392 0.437144i \(-0.855990\pi\)
0.899392 0.437144i \(-0.144010\pi\)
\(348\) 2.97967 5.59298i 0.159727 0.299815i
\(349\) 24.0366i 1.28665i 0.765594 + 0.643324i \(0.222445\pi\)
−0.765594 + 0.643324i \(0.777555\pi\)
\(350\) −1.07517 + 4.90939i −0.0574704 + 0.262418i
\(351\) 5.16900 0.530556i 0.275901 0.0283190i
\(352\) 3.38959 0.180666
\(353\) 18.6483 0.992550 0.496275 0.868165i \(-0.334701\pi\)
0.496275 + 0.868165i \(0.334701\pi\)
\(354\) −0.166196 + 0.311958i −0.00883324 + 0.0165804i
\(355\) 10.4400i 0.554097i
\(356\) −13.3915 −0.709747
\(357\) −19.5007 16.5961i −1.03209 0.878358i
\(358\) −5.02398 −0.265526
\(359\) 6.78798i 0.358256i 0.983826 + 0.179128i \(0.0573276\pi\)
−0.983826 + 0.179128i \(0.942672\pi\)
\(360\) 4.38412 2.94678i 0.231064 0.155309i
\(361\) 7.47592 0.393469
\(362\) 5.50980 0.289589
\(363\) 0.747993 + 0.398494i 0.0392595 + 0.0209155i
\(364\) 0.566014 2.58450i 0.0296672 0.135464i
\(365\) 15.5818i 0.815589i
\(366\) −4.86953 2.59425i −0.254535 0.135604i
\(367\) 21.2093i 1.10711i −0.832811 0.553557i \(-0.813270\pi\)
0.832811 0.553557i \(-0.186730\pi\)
\(368\) 3.58404i 0.186831i
\(369\) 7.49595 + 11.1522i 0.390223 + 0.580562i
\(370\) 16.7197i 0.869217i
\(371\) −2.82639 + 12.9057i −0.146739 + 0.670030i
\(372\) −7.40081 + 13.8917i −0.383714 + 0.720250i
\(373\) −3.41020 −0.176573 −0.0882867 0.996095i \(-0.528139\pi\)
−0.0882867 + 0.996095i \(0.528139\pi\)
\(374\) 18.9405 0.979392
\(375\) −18.5712 9.89386i −0.959015 0.510917i
\(376\) 6.44515i 0.332383i
\(377\) 3.65877 0.188436
\(378\) −13.6596 1.55451i −0.702572 0.0799552i
\(379\) −13.7818 −0.707921 −0.353960 0.935260i \(-0.615165\pi\)
−0.353960 + 0.935260i \(0.615165\pi\)
\(380\) 5.97744i 0.306636i
\(381\) −2.41661 1.28745i −0.123807 0.0659582i
\(382\) −4.76107 −0.243598
\(383\) 20.6937 1.05740 0.528699 0.848809i \(-0.322680\pi\)
0.528699 + 0.848809i \(0.322680\pi\)
\(384\) 0.814390 1.52865i 0.0415592 0.0780086i
\(385\) 3.37821 15.4254i 0.172170 0.786149i
\(386\) 22.5891i 1.14975i
\(387\) 13.0499 + 19.4152i 0.663362 + 0.986928i
\(388\) 5.82999i 0.295973i
\(389\) 13.7432i 0.696807i 0.937345 + 0.348404i \(0.113276\pi\)
−0.937345 + 0.348404i \(0.886724\pi\)
\(390\) 2.69166 + 1.43399i 0.136297 + 0.0726127i
\(391\) 20.0271i 1.01281i
\(392\) −2.92573 + 6.35926i −0.147771 + 0.321191i
\(393\) 27.8216 + 14.8220i 1.40342 + 0.747672i
\(394\) 18.3675 0.925342
\(395\) −2.31867 −0.116665
\(396\) 8.43951 5.67260i 0.424102 0.285059i
\(397\) 9.96913i 0.500336i −0.968202 0.250168i \(-0.919514\pi\)
0.968202 0.250168i \(-0.0804859\pi\)
\(398\) −16.2052 −0.812295
\(399\) −10.0824 + 11.8470i −0.504751 + 0.593091i
\(400\) −1.89955 −0.0949776
\(401\) 3.80987i 0.190256i −0.995465 0.0951280i \(-0.969674\pi\)
0.995465 0.0951280i \(-0.0303261\pi\)
\(402\) 12.1654 22.8351i 0.606757 1.13891i
\(403\) −9.08755 −0.452683
\(404\) −12.1410 −0.604039
\(405\) 5.98419 14.6740i 0.297357 0.729156i
\(406\) −9.45609 2.07092i −0.469298 0.102778i
\(407\) 32.1858i 1.59539i
\(408\) 4.55069 8.54187i 0.225293 0.422886i
\(409\) 6.06247i 0.299770i 0.988703 + 0.149885i \(0.0478903\pi\)
−0.988703 + 0.149885i \(0.952110\pi\)
\(410\) 7.88685i 0.389504i
\(411\) 9.03634 16.9616i 0.445730 0.836656i
\(412\) 7.20411i 0.354921i
\(413\) 0.527430 + 0.115509i 0.0259531 + 0.00568383i
\(414\) −5.99803 8.92367i −0.294787 0.438574i
\(415\) 1.54759 0.0759680
\(416\) 1.00000 0.0490290
\(417\) −11.0173 + 20.6801i −0.539521 + 1.01271i
\(418\) 11.5067i 0.562810i
\(419\) 2.46363 0.120356 0.0601782 0.998188i \(-0.480833\pi\)
0.0601782 + 0.998188i \(0.480833\pi\)
\(420\) −6.14493 5.22965i −0.299842 0.255181i
\(421\) 2.44268 0.119049 0.0595244 0.998227i \(-0.481042\pi\)
0.0595244 + 0.998227i \(0.481042\pi\)
\(422\) 16.9761i 0.826384i
\(423\) 10.7862 + 16.0474i 0.524443 + 0.780249i
\(424\) −4.99350 −0.242506
\(425\) −10.6144 −0.514875
\(426\) 9.06349 + 4.82859i 0.439127 + 0.233946i
\(427\) −1.80305 + 8.23296i −0.0872556 + 0.398421i
\(428\) 13.3798i 0.646736i
\(429\) 5.18149 + 2.76045i 0.250165 + 0.133276i
\(430\) 13.7304i 0.662138i
\(431\) 28.7881i 1.38667i 0.720614 + 0.693337i \(0.243860\pi\)
−0.720614 + 0.693337i \(0.756140\pi\)
\(432\) −0.530556 5.16900i −0.0255264 0.248693i
\(433\) 32.1412i 1.54461i −0.635255 0.772303i \(-0.719105\pi\)
0.635255 0.772303i \(-0.280895\pi\)
\(434\) 23.4868 + 5.14369i 1.12740 + 0.246905i
\(435\) 5.24663 9.84817i 0.251556 0.472184i
\(436\) 3.07251 0.147146
\(437\) −12.1668 −0.582017
\(438\) −13.5274 7.20672i −0.646363 0.344351i
\(439\) 9.12045i 0.435295i 0.976027 + 0.217648i \(0.0698384\pi\)
−0.976027 + 0.217648i \(0.930162\pi\)
\(440\) 5.96842 0.284533
\(441\) 3.35788 + 20.7298i 0.159899 + 0.987133i
\(442\) 5.58785 0.265787
\(443\) 3.69881i 0.175736i 0.996132 + 0.0878680i \(0.0280054\pi\)
−0.996132 + 0.0878680i \(0.971995\pi\)
\(444\) 14.5153 + 7.73302i 0.688863 + 0.366993i
\(445\) −23.5798 −1.11779
\(446\) 9.25112 0.438053
\(447\) 4.99009 9.36663i 0.236023 0.443027i
\(448\) −2.58450 0.566014i −0.122106 0.0267417i
\(449\) 16.5731i 0.782133i −0.920363 0.391066i \(-0.872106\pi\)
0.920363 0.391066i \(-0.127894\pi\)
\(450\) −4.72957 + 3.17897i −0.222954 + 0.149858i
\(451\) 15.1823i 0.714908i
\(452\) 19.8770i 0.934934i
\(453\) 26.1992 + 13.9577i 1.23095 + 0.655789i
\(454\) 15.1216i 0.709693i
\(455\) 0.996643 4.55081i 0.0467234 0.213345i
\(456\) −5.18933 2.76462i −0.243013 0.129465i
\(457\) −27.3619 −1.27994 −0.639968 0.768402i \(-0.721052\pi\)
−0.639968 + 0.768402i \(0.721052\pi\)
\(458\) −20.2697 −0.947141
\(459\) −2.96467 28.8836i −0.138379 1.34817i
\(460\) 6.31081i 0.294243i
\(461\) 21.5496 1.00367 0.501833 0.864964i \(-0.332659\pi\)
0.501833 + 0.864964i \(0.332659\pi\)
\(462\) −11.8291 10.0672i −0.550340 0.468367i
\(463\) 23.3617 1.08571 0.542856 0.839826i \(-0.317343\pi\)
0.542856 + 0.839826i \(0.317343\pi\)
\(464\) 3.65877i 0.169854i
\(465\) −13.0314 + 24.4606i −0.604318 + 1.13433i
\(466\) −5.58290 −0.258623
\(467\) −1.04693 −0.0484461 −0.0242230 0.999707i \(-0.507711\pi\)
−0.0242230 + 0.999707i \(0.507711\pi\)
\(468\) 2.48983 1.67354i 0.115093 0.0773593i
\(469\) −38.6075 8.45517i −1.78273 0.390424i
\(470\) 11.3487i 0.523476i
\(471\) −3.66650 + 6.88219i −0.168943 + 0.317115i
\(472\) 0.204075i 0.00939329i
\(473\) 26.4313i 1.21531i
\(474\) −1.07241 + 2.01296i −0.0492573 + 0.0924583i
\(475\) 6.44843i 0.295874i
\(476\) −14.4418 3.16281i −0.661939 0.144967i
\(477\) −12.4330 + 8.35681i −0.569268 + 0.382632i
\(478\) −24.2290 −1.10821
\(479\) −1.19995 −0.0548271 −0.0274135 0.999624i \(-0.508727\pi\)
−0.0274135 + 0.999624i \(0.508727\pi\)
\(480\) 1.43399 2.69166i 0.0654522 0.122857i
\(481\) 9.49548i 0.432956i
\(482\) −28.6978 −1.30715
\(483\) −10.6447 + 12.5077i −0.484351 + 0.569120i
\(484\) 0.489316 0.0222416
\(485\) 10.2655i 0.466132i
\(486\) −9.97150 11.9820i −0.452317 0.543516i
\(487\) 13.6246 0.617389 0.308695 0.951161i \(-0.400108\pi\)
0.308695 + 0.951161i \(0.400108\pi\)
\(488\) −3.18551 −0.144201
\(489\) −2.15084 1.14586i −0.0972644 0.0518178i
\(490\) −5.15164 + 11.1974i −0.232728 + 0.505849i
\(491\) 6.31588i 0.285032i 0.989793 + 0.142516i \(0.0455192\pi\)
−0.989793 + 0.142516i \(0.954481\pi\)
\(492\) 6.84698 + 3.64774i 0.308686 + 0.164453i
\(493\) 20.4447i 0.920782i
\(494\) 3.39471i 0.152735i
\(495\) 14.8604 9.98837i 0.667924 0.448944i
\(496\) 9.08755i 0.408043i
\(497\) 3.35595 15.3237i 0.150535 0.687362i
\(498\) 0.715772 1.34354i 0.0320745 0.0602054i
\(499\) 7.28573 0.326154 0.163077 0.986613i \(-0.447858\pi\)
0.163077 + 0.986613i \(0.447858\pi\)
\(500\) −12.1488 −0.543311
\(501\) 4.49030 + 2.39221i 0.200612 + 0.106876i
\(502\) 22.5258i 1.00537i
\(503\) −15.4358 −0.688250 −0.344125 0.938924i \(-0.611824\pi\)
−0.344125 + 0.938924i \(0.611824\pi\)
\(504\) −7.38222 + 2.91597i −0.328830 + 0.129888i
\(505\) −21.3780 −0.951311
\(506\) 12.1484i 0.540064i
\(507\) 1.52865 + 0.814390i 0.0678897 + 0.0361683i
\(508\) −1.58088 −0.0701402
\(509\) −8.02621 −0.355756 −0.177878 0.984053i \(-0.556923\pi\)
−0.177878 + 0.984053i \(0.556923\pi\)
\(510\) 8.01290 15.0406i 0.354817 0.666009i
\(511\) −5.00879 + 22.8708i −0.221576 + 1.01174i
\(512\) 1.00000i 0.0441942i
\(513\) −17.5473 + 1.80108i −0.774730 + 0.0795198i
\(514\) 27.5068i 1.21327i
\(515\) 12.6851i 0.558971i
\(516\) 11.9201 + 6.35043i 0.524752 + 0.279562i
\(517\) 21.8464i 0.960804i
\(518\) 5.37458 24.5410i 0.236145 1.07827i
\(519\) 11.6592 + 6.21147i 0.511783 + 0.272653i
\(520\) 1.76081 0.0772166
\(521\) −20.7278 −0.908102 −0.454051 0.890976i \(-0.650022\pi\)
−0.454051 + 0.890976i \(0.650022\pi\)
\(522\) −6.12309 9.10973i −0.268000 0.398722i
\(523\) 1.29750i 0.0567359i 0.999598 + 0.0283679i \(0.00903100\pi\)
−0.999598 + 0.0283679i \(0.990969\pi\)
\(524\) 18.2002 0.795077
\(525\) 6.62912 + 5.64172i 0.289318 + 0.246225i
\(526\) 7.57623 0.330339
\(527\) 50.7799i 2.21201i
\(528\) 2.76045 5.18149i 0.120133 0.225496i
\(529\) 10.1546 0.441506
\(530\) −8.79261 −0.381926
\(531\) 0.341526 + 0.508112i 0.0148210 + 0.0220502i
\(532\) −1.92146 + 8.77363i −0.0833057 + 0.380385i
\(533\) 4.47910i 0.194012i
\(534\) −10.9059 + 20.4709i −0.471944 + 0.885861i
\(535\) 23.5592i 1.01855i
\(536\) 14.9381i 0.645227i
\(537\) −4.09148 + 7.67991i −0.176560 + 0.331412i
\(538\) 17.8846i 0.771060i
\(539\) −9.91701 + 21.5553i −0.427156 + 0.928451i
\(540\) −0.934207 9.10161i −0.0402019 0.391671i
\(541\) 8.41510 0.361793 0.180897 0.983502i \(-0.442100\pi\)
0.180897 + 0.983502i \(0.442100\pi\)
\(542\) 21.5689 0.926466
\(543\) 4.48713 8.42255i 0.192561 0.361446i
\(544\) 5.58785i 0.239577i
\(545\) 5.41010 0.231743
\(546\) −3.48983 2.97003i −0.149351 0.127105i
\(547\) −26.0661 −1.11451 −0.557254 0.830342i \(-0.688145\pi\)
−0.557254 + 0.830342i \(0.688145\pi\)
\(548\) 11.0958i 0.473991i
\(549\) −7.93140 + 5.33108i −0.338504 + 0.227525i
\(550\) −6.43870 −0.274547
\(551\) −12.4205 −0.529130
\(552\) −5.47874 2.91881i −0.233191 0.124233i
\(553\) 3.40332 + 0.745340i 0.144724 + 0.0316951i
\(554\) 3.31754i 0.140949i
\(555\) 25.5586 + 13.6164i 1.08490 + 0.577983i
\(556\) 13.5283i 0.573729i
\(557\) 14.7515i 0.625043i 0.949911 + 0.312522i \(0.101174\pi\)
−0.949911 + 0.312522i \(0.898826\pi\)
\(558\) 15.2084 + 22.6265i 0.643821 + 0.957856i
\(559\) 7.79778i 0.329811i
\(560\) −4.55081 0.996643i −0.192307 0.0421159i
\(561\) 15.4250 28.9534i 0.651243 1.22241i
\(562\) −31.8619 −1.34401
\(563\) −43.4063 −1.82936 −0.914679 0.404182i \(-0.867556\pi\)
−0.914679 + 0.404182i \(0.867556\pi\)
\(564\) 9.85238 + 5.24887i 0.414860 + 0.221017i
\(565\) 34.9996i 1.47244i
\(566\) 24.2711 1.02019
\(567\) −13.5005 + 19.6147i −0.566968 + 0.823740i
\(568\) 5.92908 0.248779
\(569\) 19.1247i 0.801748i −0.916133 0.400874i \(-0.868706\pi\)
0.916133 0.400874i \(-0.131294\pi\)
\(570\) −9.13742 4.86797i −0.382724 0.203897i
\(571\) 20.0263 0.838073 0.419036 0.907969i \(-0.362368\pi\)
0.419036 + 0.907969i \(0.362368\pi\)
\(572\) 3.38959 0.141726
\(573\) −3.87737 + 7.27801i −0.161979 + 0.304043i
\(574\) 2.53524 11.5762i 0.105819 0.483183i
\(575\) 6.80807i 0.283916i
\(576\) −1.67354 2.48983i −0.0697307 0.103743i
\(577\) 27.0600i 1.12652i −0.826279 0.563261i \(-0.809546\pi\)
0.826279 0.563261i \(-0.190454\pi\)
\(578\) 14.2241i 0.591645i
\(579\) −34.5307 18.3963i −1.43505 0.764524i
\(580\) 6.44240i 0.267506i
\(581\) −2.27153 0.497473i −0.0942389 0.0206387i
\(582\) 8.91201 + 4.74789i 0.369415 + 0.196806i
\(583\) −16.9259 −0.701000
\(584\) −8.84923 −0.366184
\(585\) 4.38412 2.94678i 0.181261 0.121834i
\(586\) 17.4689i 0.721635i
\(587\) 11.1995 0.462252 0.231126 0.972924i \(-0.425759\pi\)
0.231126 + 0.972924i \(0.425759\pi\)
\(588\) 7.33839 + 9.65132i 0.302630 + 0.398014i
\(589\) 30.8496 1.27114
\(590\) 0.359336i 0.0147936i
\(591\) 14.9583 28.0775i 0.615303 1.15495i
\(592\) 9.49548 0.390262
\(593\) −5.03154 −0.206621 −0.103310 0.994649i \(-0.532943\pi\)
−0.103310 + 0.994649i \(0.532943\pi\)
\(594\) −1.79837 17.5208i −0.0737878 0.718886i
\(595\) −25.4292 5.56910i −1.04250 0.228311i
\(596\) 6.12739i 0.250988i
\(597\) −13.1974 + 24.7721i −0.540133 + 1.01386i
\(598\) 3.58404i 0.146562i
\(599\) 36.7468i 1.50143i −0.660625 0.750716i \(-0.729709\pi\)
0.660625 0.750716i \(-0.270291\pi\)
\(600\) −1.54698 + 2.90375i −0.0631550 + 0.118545i
\(601\) 4.32636i 0.176476i −0.996099 0.0882380i \(-0.971876\pi\)
0.996099 0.0882380i \(-0.0281236\pi\)
\(602\) 4.41365 20.1533i 0.179887 0.821388i
\(603\) −24.9995 37.1934i −1.01806 1.51463i
\(604\) 17.1388 0.697368
\(605\) 0.861593 0.0350287
\(606\) −9.88754 + 18.5594i −0.401654 + 0.753924i
\(607\) 11.0662i 0.449163i 0.974455 + 0.224582i \(0.0721015\pi\)
−0.974455 + 0.224582i \(0.927898\pi\)
\(608\) −3.39471 −0.137674
\(609\) −10.8667 + 12.7685i −0.440339 + 0.517406i
\(610\) −5.60908 −0.227105
\(611\) 6.44515i 0.260743i
\(612\) −9.35148 13.9128i −0.378011 0.562393i
\(613\) 7.04915 0.284712 0.142356 0.989815i \(-0.454532\pi\)
0.142356 + 0.989815i \(0.454532\pi\)
\(614\) 10.6490 0.429760
\(615\) 12.0562 + 6.42297i 0.486154 + 0.258999i
\(616\) −8.76039 1.91856i −0.352966 0.0773008i
\(617\) 31.6993i 1.27617i 0.769967 + 0.638083i \(0.220273\pi\)
−0.769967 + 0.638083i \(0.779727\pi\)
\(618\) −11.0126 5.86696i −0.442990 0.236004i
\(619\) 29.9020i 1.20186i 0.799301 + 0.600931i \(0.205203\pi\)
−0.799301 + 0.600931i \(0.794797\pi\)
\(620\) 16.0014i 0.642633i
\(621\) −18.5259 + 1.90153i −0.743419 + 0.0763059i
\(622\) 12.6195i 0.505995i
\(623\) 34.6102 + 7.57977i 1.38663 + 0.303677i
\(624\) 0.814390 1.52865i 0.0326017 0.0611949i
\(625\) −11.8939 −0.475758
\(626\) −22.9015 −0.915327
\(627\) −17.5897 9.37093i −0.702465 0.374239i
\(628\) 4.50214i 0.179655i
\(629\) 53.0593 2.11561
\(630\) −12.9987 + 5.13447i −0.517880 + 0.204562i
\(631\) −39.2320 −1.56180 −0.780900 0.624655i \(-0.785239\pi\)
−0.780900 + 0.624655i \(0.785239\pi\)
\(632\) 1.31682i 0.0523804i
\(633\) 25.9505 + 13.8252i 1.03144 + 0.549501i
\(634\) 19.9238 0.791273
\(635\) −2.78363 −0.110465
\(636\) −4.06666 + 7.63331i −0.161254 + 0.302681i
\(637\) −2.92573 + 6.35926i −0.115921 + 0.251963i
\(638\) 12.4017i 0.490989i
\(639\) 14.7624 9.92254i 0.583993 0.392530i
\(640\) 1.76081i 0.0696021i
\(641\) 4.48351i 0.177088i 0.996072 + 0.0885439i \(0.0282214\pi\)
−0.996072 + 0.0885439i \(0.971779\pi\)
\(642\) 20.4530 + 10.8964i 0.807215 + 0.430045i
\(643\) 27.5681i 1.08718i −0.839351 0.543590i \(-0.817065\pi\)
0.839351 0.543590i \(-0.182935\pi\)
\(644\) −2.02862 + 9.26295i −0.0799388 + 0.365011i
\(645\) 20.9890 + 11.1819i 0.826439 + 0.440287i
\(646\) −18.9692 −0.746332
\(647\) −20.4352 −0.803389 −0.401695 0.915774i \(-0.631579\pi\)
−0.401695 + 0.915774i \(0.631579\pi\)
\(648\) −8.33366 3.39855i −0.327377 0.133507i
\(649\) 0.691729i 0.0271527i
\(650\) −1.89955 −0.0745065
\(651\) 26.9903 31.7140i 1.05783 1.24297i
\(652\) −1.40702 −0.0551032
\(653\) 7.32638i 0.286703i −0.989672 0.143352i \(-0.954212\pi\)
0.989672 0.143352i \(-0.0457880\pi\)
\(654\) 2.50222 4.69678i 0.0978445 0.183659i
\(655\) 32.0470 1.25218
\(656\) 4.47910 0.174880
\(657\) −22.0331 + 14.8095i −0.859593 + 0.577774i
\(658\) 3.64805 16.6575i 0.142216 0.649376i
\(659\) 46.0263i 1.79293i −0.443116 0.896464i \(-0.646127\pi\)
0.443116 0.896464i \(-0.353873\pi\)
\(660\) 4.86062 9.12362i 0.189199 0.355136i
\(661\) 38.8111i 1.50958i −0.655969 0.754788i \(-0.727740\pi\)
0.655969 0.754788i \(-0.272260\pi\)
\(662\) 18.8267i 0.731719i
\(663\) 4.55069 8.54187i 0.176734 0.331739i
\(664\) 0.878906i 0.0341082i
\(665\) −3.38332 + 15.4487i −0.131199 + 0.599074i
\(666\) 23.6422 15.8910i 0.916115 0.615765i
\(667\) −13.1132 −0.507745
\(668\) 2.93743 0.113653
\(669\) 7.53402 14.1417i 0.291282 0.546751i
\(670\) 26.3031i 1.01618i
\(671\) −10.7976 −0.416836
\(672\) −2.97003 + 3.48983i −0.114571 + 0.134623i
\(673\) −4.35748 −0.167969 −0.0839843 0.996467i \(-0.526765\pi\)
−0.0839843 + 0.996467i \(0.526765\pi\)
\(674\) 30.0841i 1.15880i
\(675\) 1.00782 + 9.81877i 0.0387909 + 0.377925i
\(676\) 1.00000 0.0384615
\(677\) 19.1334 0.735355 0.367677 0.929953i \(-0.380153\pi\)
0.367677 + 0.929953i \(0.380153\pi\)
\(678\) −30.3849 16.1876i −1.16693 0.621682i
\(679\) 3.29986 15.0676i 0.126637 0.578241i
\(680\) 9.83914i 0.377314i
\(681\) −23.1156 12.3149i −0.885794 0.471908i
\(682\) 30.8031i 1.17951i
\(683\) 28.9373i 1.10726i 0.832764 + 0.553628i \(0.186757\pi\)
−0.832764 + 0.553628i \(0.813243\pi\)
\(684\) −8.45227 + 5.68118i −0.323181 + 0.217225i
\(685\) 19.5377i 0.746495i
\(686\) 11.1610 14.7795i 0.426127 0.564283i
\(687\) −16.5074 + 30.9853i −0.629798 + 1.18216i
\(688\) 7.79778 0.297287
\(689\) −4.99350 −0.190237
\(690\) −9.64702 5.13946i −0.367256 0.195656i
\(691\) 42.5806i 1.61984i −0.586539 0.809921i \(-0.699510\pi\)
0.586539 0.809921i \(-0.300490\pi\)
\(692\) 7.62715 0.289941
\(693\) −25.0227 + 9.88395i −0.950533 + 0.375460i
\(694\) −16.2862 −0.618214
\(695\) 23.8208i 0.903575i
\(696\) −5.59298 2.97967i −0.212001 0.112944i
\(697\) 25.0286 0.948025
\(698\) 24.0366 0.909798
\(699\) −4.54666 + 8.53429i −0.171970 + 0.322797i
\(700\) 4.90939 + 1.07517i 0.185557 + 0.0406377i
\(701\) 20.7064i 0.782069i −0.920376 0.391034i \(-0.872117\pi\)
0.920376 0.391034i \(-0.127883\pi\)
\(702\) −0.530556 5.16900i −0.0200245 0.195091i
\(703\) 32.2344i 1.21574i
\(704\) 3.38959i 0.127750i
\(705\) 17.3482 + 9.24226i 0.653369 + 0.348083i
\(706\) 18.6483i 0.701839i
\(707\) 31.3785 + 6.87200i 1.18011 + 0.258448i
\(708\) 0.311958 + 0.166196i 0.0117241 + 0.00624604i
\(709\) −12.1165 −0.455046 −0.227523 0.973773i \(-0.573063\pi\)
−0.227523 + 0.973773i \(0.573063\pi\)
\(710\) 10.4400 0.391806
\(711\) 2.20375 + 3.27867i 0.0826471 + 0.122960i
\(712\) 13.3915i 0.501867i
\(713\) 32.5702 1.21976
\(714\) −16.5961 + 19.5007i −0.621093 + 0.729795i
\(715\) 5.96842 0.223206
\(716\) 5.02398i 0.187755i
\(717\) −19.7319 + 37.0377i −0.736901 + 1.38320i
\(718\) 6.78798 0.253325
\(719\) −43.1786 −1.61029 −0.805144 0.593079i \(-0.797912\pi\)
−0.805144 + 0.593079i \(0.797912\pi\)
\(720\) −2.94678 4.38412i −0.109820 0.163387i
\(721\) −4.07763 + 18.6190i −0.151859 + 0.693408i
\(722\) 7.47592i 0.278225i
\(723\) −23.3712 + 43.8689i −0.869186 + 1.63150i
\(724\) 5.50980i 0.204770i
\(725\) 6.95002i 0.258117i
\(726\) 0.398494 0.747993i 0.0147895 0.0277606i
\(727\) 38.9882i 1.44599i −0.690852 0.722996i \(-0.742764\pi\)
0.690852 0.722996i \(-0.257236\pi\)
\(728\) −2.58450 0.566014i −0.0957879 0.0209779i
\(729\) −26.4370 + 5.48488i −0.979149 + 0.203144i
\(730\) −15.5818 −0.576708
\(731\) 43.5728 1.61160
\(732\) −2.59425 + 4.86953i −0.0958863 + 0.179983i
\(733\) 44.4475i 1.64171i 0.571139 + 0.820853i \(0.306502\pi\)
−0.571139 + 0.820853i \(0.693498\pi\)
\(734\) −21.2093 −0.782848
\(735\) 12.9215 + 16.9941i 0.476617 + 0.626838i
\(736\) −3.58404 −0.132110
\(737\) 50.6340i 1.86513i
\(738\) 11.1522 7.49595i 0.410519 0.275930i
\(739\) 43.9802 1.61784 0.808920 0.587919i \(-0.200053\pi\)
0.808920 + 0.587919i \(0.200053\pi\)
\(740\) 16.7197 0.614629
\(741\) −5.18933 2.76462i −0.190635 0.101561i
\(742\) 12.9057 + 2.82639i 0.473783 + 0.103760i
\(743\) 7.77737i 0.285324i −0.989771 0.142662i \(-0.954434\pi\)
0.989771 0.142662i \(-0.0455662\pi\)
\(744\) 13.8917 + 7.40081i 0.509294 + 0.271327i
\(745\) 10.7892i 0.395285i
\(746\) 3.41020i 0.124856i
\(747\) −1.47088 2.18833i −0.0538167 0.0800668i
\(748\) 18.9405i 0.692534i
\(749\) 7.57315 34.5800i 0.276717 1.26353i
\(750\) −9.89386 + 18.5712i −0.361273 + 0.678126i
\(751\) 10.8242 0.394979 0.197490 0.980305i \(-0.436721\pi\)
0.197490 + 0.980305i \(0.436721\pi\)
\(752\) 6.44515 0.235031
\(753\) 34.4340 + 18.3448i 1.25485 + 0.668521i
\(754\) 3.65877i 0.133245i
\(755\) 30.1782 1.09830
\(756\) −1.55451 + 13.6596i −0.0565368 + 0.496793i
\(757\) 49.3460 1.79351 0.896756 0.442525i \(-0.145917\pi\)
0.896756 + 0.442525i \(0.145917\pi\)
\(758\) 13.7818i 0.500576i
\(759\) −18.5707 9.89356i −0.674073 0.359114i
\(760\) −5.97744 −0.216825
\(761\) −1.65026 −0.0598219 −0.0299109 0.999553i \(-0.509522\pi\)
−0.0299109 + 0.999553i \(0.509522\pi\)
\(762\) −1.28745 + 2.41661i −0.0466395 + 0.0875446i
\(763\) −7.94088 1.73908i −0.287479 0.0629590i
\(764\) 4.76107i 0.172249i
\(765\) −16.4662 24.4978i −0.595336 0.885721i
\(766\) 20.6937i 0.747693i
\(767\) 0.204075i 0.00736871i
\(768\) −1.52865 0.814390i −0.0551604 0.0293868i
\(769\) 5.66416i 0.204255i −0.994771 0.102127i \(-0.967435\pi\)
0.994771 0.102127i \(-0.0325649\pi\)
\(770\) −15.4254 3.37821i −0.555892 0.121742i
\(771\) 42.0482 + 22.4012i 1.51433 + 0.806761i
\(772\) −22.5891 −0.812998
\(773\) 16.2379 0.584037 0.292019 0.956413i \(-0.405673\pi\)
0.292019 + 0.956413i \(0.405673\pi\)
\(774\) 19.4152 13.0499i 0.697864 0.469068i
\(775\) 17.2623i 0.620079i
\(776\) 5.82999 0.209284
\(777\) −33.1376 28.2018i −1.18881 1.01173i
\(778\) 13.7432 0.492717
\(779\) 15.2053i 0.544786i
\(780\) 1.43399 2.69166i 0.0513449 0.0963769i
\(781\) 20.0972 0.719133
\(782\) −20.0271 −0.716168
\(783\) −18.9122 + 1.94118i −0.675866 + 0.0693722i
\(784\) 6.35926 + 2.92573i 0.227116 + 0.104490i
\(785\) 7.92741i 0.282941i
\(786\) 14.8220 27.8216i 0.528684 0.992365i
\(787\) 21.0932i 0.751893i 0.926641 + 0.375946i \(0.122682\pi\)
−0.926641 + 0.375946i \(0.877318\pi\)
\(788\) 18.3675i 0.654316i
\(789\) 6.17001 11.5814i 0.219658 0.412309i
\(790\) 2.31867i 0.0824946i
\(791\) −11.2507 + 51.3720i −0.400027 + 1.82658i
\(792\) −5.67260 8.43951i −0.201567 0.299885i
\(793\) −3.18551 −0.113121
\(794\) −9.96913 −0.353791
\(795\) −7.16061 + 13.4408i −0.253961 + 0.476696i
\(796\) 16.2052i 0.574379i
\(797\) 55.1246 1.95261 0.976307 0.216392i \(-0.0694288\pi\)
0.976307 + 0.216392i \(0.0694288\pi\)
\(798\) 11.8470 + 10.0824i 0.419379 + 0.356913i
\(799\) 36.0146 1.27410
\(800\) 1.89955i 0.0671593i
\(801\) 22.4111 + 33.3426i 0.791859 + 1.17810i
\(802\) −3.80987 −0.134531
\(803\) −29.9952 −1.05851
\(804\) −22.8351 12.1654i −0.805332 0.429042i
\(805\) −3.57201 + 16.3103i −0.125897 + 0.574862i
\(806\) 9.08755i 0.320095i
\(807\) 27.3393 + 14.5650i 0.962389 + 0.512714i
\(808\) 12.1410i 0.427120i
\(809\) 26.5257i 0.932594i −0.884628 0.466297i \(-0.845588\pi\)
0.884628 0.466297i \(-0.154412\pi\)
\(810\) −14.6740 5.98419i −0.515591 0.210263i
\(811\) 50.5615i 1.77545i −0.460370 0.887727i \(-0.652283\pi\)
0.460370 0.887727i \(-0.347717\pi\)
\(812\) −2.07092 + 9.45609i −0.0726750 + 0.331844i
\(813\) 17.5655 32.9714i 0.616050 1.15636i
\(814\) 32.1858 1.12811
\(815\) −2.47750 −0.0867829
\(816\) −8.54187 4.55069i −0.299025 0.159306i
\(817\) 26.4712i 0.926111i
\(818\) 6.06247 0.211969
\(819\) −7.38222 + 2.91597i −0.257955 + 0.101892i
\(820\) 7.88685 0.275421
\(821\) 27.9672i 0.976062i −0.872826 0.488031i \(-0.837715\pi\)
0.872826 0.488031i \(-0.162285\pi\)
\(822\) −16.9616 9.03634i −0.591605 0.315179i
\(823\) 14.9297 0.520416 0.260208 0.965553i \(-0.416209\pi\)
0.260208 + 0.965553i \(0.416209\pi\)
\(824\) −7.20411 −0.250967
\(825\) −5.24361 + 9.84251i −0.182559 + 0.342672i
\(826\) 0.115509 0.527430i 0.00401908 0.0183516i
\(827\) 8.32248i 0.289401i −0.989476 0.144700i \(-0.953778\pi\)
0.989476 0.144700i \(-0.0462219\pi\)
\(828\) −8.92367 + 5.99803i −0.310119 + 0.208446i
\(829\) 34.0881i 1.18393i 0.805964 + 0.591965i \(0.201648\pi\)
−0.805964 + 0.591965i \(0.798352\pi\)
\(830\) 1.54759i 0.0537175i
\(831\) 5.07136 + 2.70177i 0.175924 + 0.0937235i
\(832\) 1.00000i 0.0346688i
\(833\) 35.5346 + 16.3485i 1.23120 + 0.566443i
\(834\) 20.6801 + 11.0173i 0.716092 + 0.381499i
\(835\) 5.17225 0.178993
\(836\) −11.5067 −0.397967
\(837\) 46.9735 4.82145i 1.62364 0.166654i
\(838\) 2.46363i 0.0851048i
\(839\) −19.0851 −0.658889 −0.329445 0.944175i \(-0.606862\pi\)
−0.329445 + 0.944175i \(0.606862\pi\)
\(840\) −5.22965 + 6.14493i −0.180440 + 0.212020i
\(841\) 15.6134 0.538393
\(842\) 2.44268i 0.0841802i
\(843\) −25.9480 + 48.7057i −0.893698 + 1.67751i
\(844\) 16.9761 0.584342
\(845\) 1.76081 0.0605737
\(846\) 16.0474 10.7862i 0.551720 0.370837i
\(847\) −1.26464 0.276960i −0.0434534 0.00951646i
\(848\) 4.99350i 0.171478i
\(849\) 19.7661 37.1020i 0.678372 1.27334i
\(850\) 10.6144i 0.364071i
\(851\) 34.0322i 1.16661i
\(852\) 4.82859 9.06349i 0.165425 0.310510i
\(853\) 29.6954i 1.01675i 0.861135 + 0.508376i \(0.169754\pi\)
−0.861135 + 0.508376i \(0.830246\pi\)
\(854\) 8.23296 + 1.80305i 0.281726 + 0.0616990i
\(855\) −14.8828 + 10.0035i −0.508982 + 0.342112i
\(856\) 13.3798 0.457312
\(857\) −9.71299 −0.331790 −0.165895 0.986143i \(-0.553051\pi\)
−0.165895 + 0.986143i \(0.553051\pi\)
\(858\) 2.76045 5.18149i 0.0942401 0.176893i
\(859\) 48.7424i 1.66307i 0.555473 + 0.831535i \(0.312537\pi\)
−0.555473 + 0.831535i \(0.687463\pi\)
\(860\) 13.7304 0.468203
\(861\) −15.6313 13.3031i −0.532714 0.453367i
\(862\) 28.7881 0.980526
\(863\) 9.46910i 0.322332i 0.986927 + 0.161166i \(0.0515254\pi\)
−0.986927 + 0.161166i \(0.948475\pi\)
\(864\) −5.16900 + 0.530556i −0.175853 + 0.0180499i
\(865\) 13.4299 0.456632
\(866\) −32.1412 −1.09220
\(867\) −21.7437 11.5840i −0.738454 0.393413i
\(868\) 5.14369 23.4868i 0.174588 0.797192i
\(869\) 4.46349i 0.151413i
\(870\) −9.84817 5.24663i −0.333884 0.177877i
\(871\) 14.9381i 0.506158i
\(872\) 3.07251i 0.104048i
\(873\) 14.5157 9.75671i 0.491282 0.330215i
\(874\) 12.1668i 0.411548i
\(875\) 31.3985 + 6.87639i 1.06146 + 0.232464i
\(876\) −7.20672 + 13.5274i −0.243493 + 0.457047i
\(877\) −30.6530 −1.03508 −0.517538 0.855660i \(-0.673152\pi\)
−0.517538 + 0.855660i \(0.673152\pi\)
\(878\) 9.12045 0.307800
\(879\) 26.7039 + 14.2265i 0.900700 + 0.479849i
\(880\) 5.96842i 0.201195i
\(881\) −9.61977 −0.324098 −0.162049 0.986783i \(-0.551810\pi\)
−0.162049 + 0.986783i \(0.551810\pi\)
\(882\) 20.7298 3.35788i 0.698009 0.113066i
\(883\) −16.5344 −0.556427 −0.278214 0.960519i \(-0.589742\pi\)
−0.278214 + 0.960519i \(0.589742\pi\)
\(884\) 5.58785i 0.187940i
\(885\) 0.549299 + 0.292640i 0.0184645 + 0.00983699i
\(886\) 3.69881 0.124264
\(887\) 6.47491 0.217406 0.108703 0.994074i \(-0.465330\pi\)
0.108703 + 0.994074i \(0.465330\pi\)
\(888\) 7.73302 14.5153i 0.259503 0.487100i
\(889\) 4.08578 + 0.894801i 0.137033 + 0.0300106i
\(890\) 23.5798i 0.790398i
\(891\) −28.2477 11.5197i −0.946333 0.385924i
\(892\) 9.25112i 0.309751i
\(893\) 21.8794i 0.732168i
\(894\) −9.36663 4.99009i −0.313267 0.166894i
\(895\) 8.84627i 0.295698i
\(896\) −0.566014 + 2.58450i −0.0189092 + 0.0863420i
\(897\) −5.47874 2.91881i −0.182930 0.0974562i
\(898\) −16.5731 −0.553051
\(899\) 33.2493 1.10893
\(900\) 3.17897 + 4.72957i 0.105966 + 0.157652i
\(901\) 27.9030i 0.929583i
\(902\) 15.1823 0.505516
\(903\) −27.2129 23.1596i −0.905590 0.770703i
\(904\) −19.8770 −0.661099
\(905\) 9.70171i 0.322496i
\(906\) 13.9577 26.1992i 0.463713 0.870411i
\(907\) −41.8043 −1.38809 −0.694045 0.719931i \(-0.744173\pi\)
−0.694045 + 0.719931i \(0.744173\pi\)
\(908\) −15.1216 −0.501828
\(909\) 20.3185 + 30.2292i 0.673921 + 1.00264i
\(910\) −4.55081 0.996643i −0.150858 0.0330384i
\(911\) 24.1762i 0.800995i 0.916298 + 0.400497i \(0.131163\pi\)
−0.916298 + 0.400497i \(0.868837\pi\)
\(912\) −2.76462 + 5.18933i −0.0915458 + 0.171836i
\(913\) 2.97913i 0.0985948i
\(914\) 27.3619i 0.905051i
\(915\) −4.56798 + 8.57432i −0.151013 + 0.283458i
\(916\) 20.2697i 0.669730i
\(917\) −47.0382 10.3015i −1.55334 0.340187i
\(918\) −28.8836 + 2.96467i −0.953301 + 0.0978486i
\(919\) 0.658058 0.0217073 0.0108537 0.999941i \(-0.496545\pi\)
0.0108537 + 0.999941i \(0.496545\pi\)
\(920\) −6.31081 −0.208061
\(921\) 8.67247 16.2786i 0.285768 0.536400i
\(922\) 21.5496i 0.709699i
\(923\) 5.92908 0.195158
\(924\) −10.0672 + 11.8291i −0.331186 + 0.389149i
\(925\) −18.0371 −0.593058
\(926\) 23.3617i 0.767715i
\(927\) −17.9370 + 12.0563i −0.589130 + 0.395982i
\(928\) −3.65877 −0.120105
\(929\) 3.26561 0.107141 0.0535707 0.998564i \(-0.482940\pi\)
0.0535707 + 0.998564i \(0.482940\pi\)
\(930\) 24.4606 + 13.0314i 0.802095 + 0.427317i
\(931\) 9.93200 21.5879i 0.325508 0.707513i
\(932\) 5.58290i 0.182874i
\(933\) 19.2907 + 10.2772i 0.631551 + 0.336459i
\(934\) 1.04693i 0.0342565i
\(935\) 33.3507i 1.09068i
\(936\) −1.67354 2.48983i −0.0547013 0.0813828i
\(937\) 16.9455i 0.553586i 0.960930 + 0.276793i \(0.0892716\pi\)
−0.960930 + 0.276793i \(0.910728\pi\)
\(938\) −8.45517 + 38.6075i −0.276071 + 1.26058i
\(939\) −18.6507 + 35.0083i −0.608644 + 1.14245i
\(940\) 11.3487 0.370153
\(941\) −29.5843 −0.964421 −0.482210 0.876055i \(-0.660166\pi\)
−0.482210 + 0.876055i \(0.660166\pi\)
\(942\) 6.88219 + 3.66650i 0.224234 + 0.119461i
\(943\) 16.0533i 0.522767i
\(944\) 0.204075 0.00664206
\(945\) −2.73719 + 24.0519i −0.0890407 + 0.782407i
\(946\) 26.4313 0.859354
\(947\) 19.8609i 0.645391i −0.946503 0.322696i \(-0.895411\pi\)
0.946503 0.322696i \(-0.104589\pi\)
\(948\) 2.01296 + 1.07241i 0.0653779 + 0.0348302i
\(949\) −8.84923 −0.287258
\(950\) 6.44843 0.209215
\(951\) 16.2257 30.4564i 0.526155 0.987617i
\(952\) −3.16281 + 14.4418i −0.102507 + 0.468061i
\(953\) 3.71754i 0.120423i −0.998186 0.0602114i \(-0.980823\pi\)
0.998186 0.0602114i \(-0.0191775\pi\)
\(954\) 8.35681 + 12.4330i 0.270562 + 0.402533i
\(955\) 8.38334i 0.271278i
\(956\) 24.2290i 0.783623i
\(957\) −18.9579 10.0999i −0.612822 0.326482i
\(958\) 1.19995i 0.0387686i
\(959\) −6.28040 + 28.6772i −0.202805 + 0.926034i
\(960\) −2.69166 1.43399i −0.0868729 0.0462817i
\(961\) −51.5836 −1.66399
\(962\) 9.49548 0.306146
\(963\) 33.3134 22.3916i 1.07351 0.721558i
\(964\) 28.6978i 0.924295i
\(965\) −39.7750 −1.28040
\(966\) 12.5077 + 10.6447i 0.402429 + 0.342488i
\(967\) 19.3495 0.622239 0.311120 0.950371i \(-0.399296\pi\)
0.311120 + 0.950371i \(0.399296\pi\)
\(968\) 0.489316i 0.0157272i
\(969\) −15.4483 + 28.9972i −0.496271 + 0.931524i
\(970\) 10.2655 0.329605
\(971\) 16.4867 0.529083 0.264542 0.964374i \(-0.414779\pi\)
0.264542 + 0.964374i \(0.414779\pi\)
\(972\) −11.9820 + 9.97150i −0.384324 + 0.319836i
\(973\) 7.65723 34.9639i 0.245480 1.12089i
\(974\) 13.6246i 0.436560i
\(975\) −1.54698 + 2.90375i −0.0495429 + 0.0929944i
\(976\) 3.18551i 0.101966i
\(977\) 43.6047i 1.39504i −0.716566 0.697519i \(-0.754287\pi\)
0.716566 0.697519i \(-0.245713\pi\)
\(978\) −1.14586 + 2.15084i −0.0366407 + 0.0687763i
\(979\) 45.3916i 1.45072i
\(980\) 11.1974 + 5.15164i 0.357689 + 0.164563i
\(981\) −5.14195 7.65003i −0.164170 0.244247i
\(982\) 6.31588 0.201548
\(983\) 27.8266 0.887532 0.443766 0.896143i \(-0.353642\pi\)
0.443766 + 0.896143i \(0.353642\pi\)
\(984\) 3.64774 6.84698i 0.116286 0.218274i
\(985\) 32.3417i 1.03049i
\(986\) −20.4447 −0.651091
\(987\) −22.4925 19.1423i −0.715945 0.609305i
\(988\) −3.39471 −0.108000
\(989\) 27.9476i 0.888680i
\(990\) −9.98837 14.8604i −0.317451 0.472294i
\(991\) 13.6266 0.432863 0.216431 0.976298i \(-0.430558\pi\)
0.216431 + 0.976298i \(0.430558\pi\)
\(992\) 9.08755 0.288530
\(993\) −28.7794 15.3323i −0.913286 0.486554i
\(994\) −15.3237 3.35595i −0.486038 0.106444i
\(995\) 28.5343i 0.904599i
\(996\) −1.34354 0.715772i −0.0425716 0.0226801i
\(997\) 53.7319i 1.70171i −0.525403 0.850854i \(-0.676085\pi\)
0.525403 0.850854i \(-0.323915\pi\)
\(998\) 7.28573i 0.230626i
\(999\) −5.03788 49.0821i −0.159391 1.55289i
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 546.2.g.d.209.1 yes 12
3.2 odd 2 546.2.g.c.209.12 yes 12
7.6 odd 2 546.2.g.c.209.6 12
21.20 even 2 inner 546.2.g.d.209.7 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.g.c.209.6 12 7.6 odd 2
546.2.g.c.209.12 yes 12 3.2 odd 2
546.2.g.d.209.1 yes 12 1.1 even 1 trivial
546.2.g.d.209.7 yes 12 21.20 even 2 inner