Properties

Label 572.2.e.b.131.8
Level $572$
Weight $2$
Character 572.131
Analytic conductor $4.567$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [572,2,Mod(131,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, 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("572.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.e (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: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(64\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 131.8
Character \(\chi\) \(=\) 572.131
Dual form 572.2.e.b.131.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33395 + 0.469670i) q^{2} -3.04863i q^{3} +(1.55882 - 1.25303i) q^{4} -2.77923 q^{5} +(1.43185 + 4.06671i) q^{6} -0.398342 q^{7} +(-1.49087 + 2.40360i) q^{8} -6.29417 q^{9} +O(q^{10})\) \(q+(-1.33395 + 0.469670i) q^{2} -3.04863i q^{3} +(1.55882 - 1.25303i) q^{4} -2.77923 q^{5} +(1.43185 + 4.06671i) q^{6} -0.398342 q^{7} +(-1.49087 + 2.40360i) q^{8} -6.29417 q^{9} +(3.70734 - 1.30532i) q^{10} +(1.84401 + 2.75674i) q^{11} +(-3.82002 - 4.75227i) q^{12} +1.00000i q^{13} +(0.531366 - 0.187089i) q^{14} +8.47286i q^{15} +(0.859843 - 3.90649i) q^{16} +4.37142i q^{17} +(8.39608 - 2.95618i) q^{18} -5.64036 q^{19} +(-4.33232 + 3.48245i) q^{20} +1.21440i q^{21} +(-3.75457 - 2.81127i) q^{22} -0.542331i q^{23} +(7.32770 + 4.54512i) q^{24} +2.72413 q^{25} +(-0.469670 - 1.33395i) q^{26} +10.0427i q^{27} +(-0.620944 + 0.499134i) q^{28} -2.16310i q^{29} +(-3.97945 - 11.3023i) q^{30} -3.59359i q^{31} +(0.687778 + 5.61489i) q^{32} +(8.40430 - 5.62172i) q^{33} +(-2.05312 - 5.83124i) q^{34} +1.10708 q^{35} +(-9.81149 + 7.88677i) q^{36} +10.6214 q^{37} +(7.52394 - 2.64911i) q^{38} +3.04863 q^{39} +(4.14348 - 6.68017i) q^{40} +10.6003i q^{41} +(-0.570367 - 1.61994i) q^{42} +1.79968 q^{43} +(6.32876 + 1.98667i) q^{44} +17.4930 q^{45} +(0.254716 + 0.723440i) q^{46} +3.13709i q^{47} +(-11.9095 - 2.62135i) q^{48} -6.84132 q^{49} +(-3.63384 + 1.27944i) q^{50} +13.3269 q^{51} +(1.25303 + 1.55882i) q^{52} -2.00293 q^{53} +(-4.71677 - 13.3965i) q^{54} +(-5.12494 - 7.66162i) q^{55} +(0.593877 - 0.957455i) q^{56} +17.1954i q^{57} +(1.01594 + 2.88546i) q^{58} +3.35411i q^{59} +(10.6167 + 13.2077i) q^{60} -5.99977i q^{61} +(1.68780 + 4.79366i) q^{62} +2.50723 q^{63} +(-3.55460 - 7.16692i) q^{64} -2.77923i q^{65} +(-8.57052 + 11.4463i) q^{66} +1.31372i q^{67} +(5.47751 + 6.81426i) q^{68} -1.65337 q^{69} +(-1.47679 + 0.519964i) q^{70} +2.74132i q^{71} +(9.38381 - 15.1287i) q^{72} +11.0605i q^{73} +(-14.1684 + 4.98855i) q^{74} -8.30488i q^{75} +(-8.79231 + 7.06753i) q^{76} +(-0.734547 - 1.09813i) q^{77} +(-4.06671 + 1.43185i) q^{78} -15.8741 q^{79} +(-2.38970 + 10.8570i) q^{80} +11.7341 q^{81} +(-4.97866 - 14.1403i) q^{82} -12.6524 q^{83} +(1.52168 + 1.89303i) q^{84} -12.1492i q^{85} +(-2.40067 + 0.845253i) q^{86} -6.59450 q^{87} +(-9.37529 + 0.322321i) q^{88} -10.5207 q^{89} +(-23.3347 + 8.21592i) q^{90} -0.398342i q^{91} +(-0.679555 - 0.845396i) q^{92} -10.9556 q^{93} +(-1.47340 - 4.18471i) q^{94} +15.6759 q^{95} +(17.1177 - 2.09678i) q^{96} +12.5793 q^{97} +(9.12595 - 3.21316i) q^{98} +(-11.6065 - 17.3514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33395 + 0.469670i −0.943242 + 0.332107i
\(3\) 3.04863i 1.76013i −0.474853 0.880065i \(-0.657499\pi\)
0.474853 0.880065i \(-0.342501\pi\)
\(4\) 1.55882 1.25303i 0.779410 0.626514i
\(5\) −2.77923 −1.24291 −0.621455 0.783450i \(-0.713458\pi\)
−0.621455 + 0.783450i \(0.713458\pi\)
\(6\) 1.43185 + 4.06671i 0.584551 + 1.66023i
\(7\) −0.398342 −0.150559 −0.0752795 0.997162i \(-0.523985\pi\)
−0.0752795 + 0.997162i \(0.523985\pi\)
\(8\) −1.49087 + 2.40360i −0.527103 + 0.849801i
\(9\) −6.29417 −2.09806
\(10\) 3.70734 1.30532i 1.17237 0.412779i
\(11\) 1.84401 + 2.75674i 0.555990 + 0.831189i
\(12\) −3.82002 4.75227i −1.10275 1.37186i
\(13\) 1.00000i 0.277350i
\(14\) 0.531366 0.187089i 0.142014 0.0500017i
\(15\) 8.47286i 2.18768i
\(16\) 0.859843 3.90649i 0.214961 0.976623i
\(17\) 4.37142i 1.06023i 0.847927 + 0.530113i \(0.177850\pi\)
−0.847927 + 0.530113i \(0.822150\pi\)
\(18\) 8.39608 2.95618i 1.97898 0.696779i
\(19\) −5.64036 −1.29399 −0.646994 0.762495i \(-0.723974\pi\)
−0.646994 + 0.762495i \(0.723974\pi\)
\(20\) −4.33232 + 3.48245i −0.968737 + 0.778701i
\(21\) 1.21440i 0.265004i
\(22\) −3.75457 2.81127i −0.800477 0.599364i
\(23\) 0.542331i 0.113084i −0.998400 0.0565419i \(-0.981993\pi\)
0.998400 0.0565419i \(-0.0180074\pi\)
\(24\) 7.32770 + 4.54512i 1.49576 + 0.927770i
\(25\) 2.72413 0.544826
\(26\) −0.469670 1.33395i −0.0921098 0.261608i
\(27\) 10.0427i 1.93272i
\(28\) −0.620944 + 0.499134i −0.117347 + 0.0943274i
\(29\) 2.16310i 0.401678i −0.979624 0.200839i \(-0.935633\pi\)
0.979624 0.200839i \(-0.0643667\pi\)
\(30\) −3.97945 11.3023i −0.726544 2.06351i
\(31\) 3.59359i 0.645429i −0.946496 0.322714i \(-0.895405\pi\)
0.946496 0.322714i \(-0.104595\pi\)
\(32\) 0.687778 + 5.61489i 0.121583 + 0.992581i
\(33\) 8.40430 5.62172i 1.46300 0.978615i
\(34\) −2.05312 5.83124i −0.352108 1.00005i
\(35\) 1.10708 0.187131
\(36\) −9.81149 + 7.88677i −1.63525 + 1.31446i
\(37\) 10.6214 1.74615 0.873074 0.487588i \(-0.162123\pi\)
0.873074 + 0.487588i \(0.162123\pi\)
\(38\) 7.52394 2.64911i 1.22054 0.429742i
\(39\) 3.04863 0.488172
\(40\) 4.14348 6.68017i 0.655142 1.05623i
\(41\) 10.6003i 1.65550i 0.561100 + 0.827748i \(0.310378\pi\)
−0.561100 + 0.827748i \(0.689622\pi\)
\(42\) −0.570367 1.61994i −0.0880095 0.249962i
\(43\) 1.79968 0.274448 0.137224 0.990540i \(-0.456182\pi\)
0.137224 + 0.990540i \(0.456182\pi\)
\(44\) 6.32876 + 1.98667i 0.954096 + 0.299501i
\(45\) 17.4930 2.60770
\(46\) 0.254716 + 0.723440i 0.0375559 + 0.106665i
\(47\) 3.13709i 0.457592i 0.973474 + 0.228796i \(0.0734789\pi\)
−0.973474 + 0.228796i \(0.926521\pi\)
\(48\) −11.9095 2.62135i −1.71898 0.378359i
\(49\) −6.84132 −0.977332
\(50\) −3.63384 + 1.27944i −0.513903 + 0.180940i
\(51\) 13.3269 1.86613
\(52\) 1.25303 + 1.55882i 0.173764 + 0.216170i
\(53\) −2.00293 −0.275124 −0.137562 0.990493i \(-0.543927\pi\)
−0.137562 + 0.990493i \(0.543927\pi\)
\(54\) −4.71677 13.3965i −0.641871 1.82303i
\(55\) −5.12494 7.66162i −0.691046 1.03309i
\(56\) 0.593877 0.957455i 0.0793601 0.127945i
\(57\) 17.1954i 2.27759i
\(58\) 1.01594 + 2.88546i 0.133400 + 0.378879i
\(59\) 3.35411i 0.436668i 0.975874 + 0.218334i \(0.0700622\pi\)
−0.975874 + 0.218334i \(0.929938\pi\)
\(60\) 10.6167 + 13.2077i 1.37061 + 1.70510i
\(61\) 5.99977i 0.768192i −0.923293 0.384096i \(-0.874513\pi\)
0.923293 0.384096i \(-0.125487\pi\)
\(62\) 1.68780 + 4.79366i 0.214351 + 0.608795i
\(63\) 2.50723 0.315882
\(64\) −3.55460 7.16692i −0.444325 0.895866i
\(65\) 2.77923i 0.344721i
\(66\) −8.57052 + 11.4463i −1.05496 + 1.40894i
\(67\) 1.31372i 0.160496i 0.996775 + 0.0802481i \(0.0255713\pi\)
−0.996775 + 0.0802481i \(0.974429\pi\)
\(68\) 5.47751 + 6.81426i 0.664246 + 0.826350i
\(69\) −1.65337 −0.199042
\(70\) −1.47679 + 0.519964i −0.176510 + 0.0621476i
\(71\) 2.74132i 0.325334i 0.986681 + 0.162667i \(0.0520097\pi\)
−0.986681 + 0.162667i \(0.947990\pi\)
\(72\) 9.38381 15.1287i 1.10589 1.78293i
\(73\) 11.0605i 1.29454i 0.762263 + 0.647268i \(0.224089\pi\)
−0.762263 + 0.647268i \(0.775911\pi\)
\(74\) −14.1684 + 4.98855i −1.64704 + 0.579907i
\(75\) 8.30488i 0.958965i
\(76\) −8.79231 + 7.06753i −1.00855 + 0.810701i
\(77\) −0.734547 1.09813i −0.0837094 0.125143i
\(78\) −4.06671 + 1.43185i −0.460464 + 0.162125i
\(79\) −15.8741 −1.78598 −0.892990 0.450076i \(-0.851397\pi\)
−0.892990 + 0.450076i \(0.851397\pi\)
\(80\) −2.38970 + 10.8570i −0.267177 + 1.21385i
\(81\) 11.7341 1.30379
\(82\) −4.97866 14.1403i −0.549801 1.56153i
\(83\) −12.6524 −1.38878 −0.694391 0.719598i \(-0.744326\pi\)
−0.694391 + 0.719598i \(0.744326\pi\)
\(84\) 1.52168 + 1.89303i 0.166028 + 0.206547i
\(85\) 12.1492i 1.31776i
\(86\) −2.40067 + 0.845253i −0.258871 + 0.0911460i
\(87\) −6.59450 −0.707005
\(88\) −9.37529 + 0.322321i −0.999410 + 0.0343595i
\(89\) −10.5207 −1.11519 −0.557595 0.830113i \(-0.688276\pi\)
−0.557595 + 0.830113i \(0.688276\pi\)
\(90\) −23.3347 + 8.21592i −2.45969 + 0.866034i
\(91\) 0.398342i 0.0417576i
\(92\) −0.679555 0.845396i −0.0708486 0.0881387i
\(93\) −10.9556 −1.13604
\(94\) −1.47340 4.18471i −0.151969 0.431620i
\(95\) 15.6759 1.60831
\(96\) 17.1177 2.09678i 1.74707 0.214002i
\(97\) 12.5793 1.27724 0.638619 0.769523i \(-0.279506\pi\)
0.638619 + 0.769523i \(0.279506\pi\)
\(98\) 9.12595 3.21316i 0.921860 0.324579i
\(99\) −11.6065 17.3514i −1.16650 1.74388i
\(100\) 4.24643 3.41341i 0.424643 0.341341i
\(101\) 9.24664i 0.920075i 0.887899 + 0.460038i \(0.152164\pi\)
−0.887899 + 0.460038i \(0.847836\pi\)
\(102\) −17.7773 + 6.25923i −1.76022 + 0.619756i
\(103\) 16.2399i 1.60017i 0.599887 + 0.800084i \(0.295212\pi\)
−0.599887 + 0.800084i \(0.704788\pi\)
\(104\) −2.40360 1.49087i −0.235693 0.146192i
\(105\) 3.37510i 0.329376i
\(106\) 2.67180 0.940717i 0.259508 0.0913705i
\(107\) 3.19262 0.308642 0.154321 0.988021i \(-0.450681\pi\)
0.154321 + 0.988021i \(0.450681\pi\)
\(108\) 12.5838 + 15.6548i 1.21088 + 1.50638i
\(109\) 1.52765i 0.146323i 0.997320 + 0.0731614i \(0.0233088\pi\)
−0.997320 + 0.0731614i \(0.976691\pi\)
\(110\) 10.4348 + 7.81316i 0.994921 + 0.744955i
\(111\) 32.3808i 3.07345i
\(112\) −0.342511 + 1.55612i −0.0323643 + 0.147039i
\(113\) 4.50879 0.424151 0.212076 0.977253i \(-0.431978\pi\)
0.212076 + 0.977253i \(0.431978\pi\)
\(114\) −8.07616 22.9377i −0.756402 2.14832i
\(115\) 1.50726i 0.140553i
\(116\) −2.71042 3.37188i −0.251657 0.313072i
\(117\) 6.29417i 0.581896i
\(118\) −1.57532 4.47420i −0.145020 0.411883i
\(119\) 1.74132i 0.159627i
\(120\) −20.3654 12.6320i −1.85910 1.15313i
\(121\) −4.19924 + 10.1669i −0.381749 + 0.924266i
\(122\) 2.81791 + 8.00337i 0.255122 + 0.724591i
\(123\) 32.3166 2.91389
\(124\) −4.50287 5.60177i −0.404370 0.503054i
\(125\) 6.32517 0.565740
\(126\) −3.34451 + 1.17757i −0.297953 + 0.104906i
\(127\) 3.98567 0.353671 0.176835 0.984240i \(-0.443414\pi\)
0.176835 + 0.984240i \(0.443414\pi\)
\(128\) 8.10773 + 7.89080i 0.716629 + 0.697455i
\(129\) 5.48655i 0.483064i
\(130\) 1.30532 + 3.70734i 0.114484 + 0.325156i
\(131\) −10.5958 −0.925755 −0.462878 0.886422i \(-0.653183\pi\)
−0.462878 + 0.886422i \(0.653183\pi\)
\(132\) 6.05662 19.2941i 0.527161 1.67933i
\(133\) 2.24679 0.194822
\(134\) −0.617013 1.75243i −0.0533018 0.151387i
\(135\) 27.9111i 2.40220i
\(136\) −10.5072 6.51723i −0.900981 0.558848i
\(137\) −20.2489 −1.72998 −0.864992 0.501786i \(-0.832677\pi\)
−0.864992 + 0.501786i \(0.832677\pi\)
\(138\) 2.20550 0.776537i 0.187745 0.0661032i
\(139\) 2.34340 0.198765 0.0993823 0.995049i \(-0.468313\pi\)
0.0993823 + 0.995049i \(0.468313\pi\)
\(140\) 1.72575 1.38721i 0.145852 0.117240i
\(141\) 9.56385 0.805422
\(142\) −1.28751 3.65677i −0.108046 0.306869i
\(143\) −2.75674 + 1.84401i −0.230530 + 0.154204i
\(144\) −5.41200 + 24.5881i −0.451000 + 2.04901i
\(145\) 6.01176i 0.499249i
\(146\) −5.19479 14.7541i −0.429924 1.22106i
\(147\) 20.8567i 1.72023i
\(148\) 16.5569 13.3089i 1.36097 1.09399i
\(149\) 20.6774i 1.69396i −0.531625 0.846980i \(-0.678418\pi\)
0.531625 0.846980i \(-0.321582\pi\)
\(150\) 3.90055 + 11.0783i 0.318479 + 0.904536i
\(151\) −22.6843 −1.84602 −0.923009 0.384778i \(-0.874278\pi\)
−0.923009 + 0.384778i \(0.874278\pi\)
\(152\) 8.40906 13.5572i 0.682065 1.09963i
\(153\) 27.5145i 2.22441i
\(154\) 1.49560 + 1.11984i 0.120519 + 0.0902397i
\(155\) 9.98743i 0.802210i
\(156\) 4.75227 3.82002i 0.380486 0.305847i
\(157\) 20.0985 1.60403 0.802016 0.597303i \(-0.203761\pi\)
0.802016 + 0.597303i \(0.203761\pi\)
\(158\) 21.1752 7.45560i 1.68461 0.593136i
\(159\) 6.10621i 0.484254i
\(160\) −1.91149 15.6051i −0.151117 1.23369i
\(161\) 0.216033i 0.0170258i
\(162\) −15.6526 + 5.51115i −1.22979 + 0.432997i
\(163\) 7.36228i 0.576658i 0.957531 + 0.288329i \(0.0930998\pi\)
−0.957531 + 0.288329i \(0.906900\pi\)
\(164\) 13.2825 + 16.5240i 1.03719 + 1.29031i
\(165\) −23.3575 + 15.6241i −1.81838 + 1.21633i
\(166\) 16.8776 5.94245i 1.30996 0.461224i
\(167\) −20.9937 −1.62454 −0.812271 0.583280i \(-0.801769\pi\)
−0.812271 + 0.583280i \(0.801769\pi\)
\(168\) −2.91893 1.81051i −0.225200 0.139684i
\(169\) −1.00000 −0.0769231
\(170\) 5.70611 + 16.2064i 0.437639 + 1.24297i
\(171\) 35.5014 2.71486
\(172\) 2.80537 2.25504i 0.213908 0.171945i
\(173\) 18.2803i 1.38982i −0.719095 0.694912i \(-0.755443\pi\)
0.719095 0.694912i \(-0.244557\pi\)
\(174\) 8.79670 3.09724i 0.666876 0.234801i
\(175\) −1.08514 −0.0820285
\(176\) 12.3547 4.83325i 0.931274 0.364320i
\(177\) 10.2255 0.768592
\(178\) 14.0340 4.94124i 1.05189 0.370362i
\(179\) 14.0224i 1.04808i 0.851692 + 0.524042i \(0.175577\pi\)
−0.851692 + 0.524042i \(0.824423\pi\)
\(180\) 27.2684 21.9192i 2.03247 1.63376i
\(181\) −8.16756 −0.607090 −0.303545 0.952817i \(-0.598170\pi\)
−0.303545 + 0.952817i \(0.598170\pi\)
\(182\) 0.187089 + 0.531366i 0.0138680 + 0.0393875i
\(183\) −18.2911 −1.35212
\(184\) 1.30355 + 0.808546i 0.0960988 + 0.0596068i
\(185\) −29.5193 −2.17030
\(186\) 14.6141 5.14549i 1.07156 0.377286i
\(187\) −12.0509 + 8.06095i −0.881247 + 0.589475i
\(188\) 3.93087 + 4.89017i 0.286688 + 0.356652i
\(189\) 4.00044i 0.290989i
\(190\) −20.9108 + 7.36249i −1.51703 + 0.534131i
\(191\) 13.3593i 0.966648i −0.875441 0.483324i \(-0.839429\pi\)
0.875441 0.483324i \(-0.160571\pi\)
\(192\) −21.8493 + 10.8367i −1.57684 + 0.782070i
\(193\) 18.5956i 1.33854i −0.743018 0.669271i \(-0.766607\pi\)
0.743018 0.669271i \(-0.233393\pi\)
\(194\) −16.7802 + 5.90814i −1.20474 + 0.424180i
\(195\) −8.47286 −0.606754
\(196\) −10.6644 + 8.57237i −0.761743 + 0.612312i
\(197\) 2.33017i 0.166018i 0.996549 + 0.0830090i \(0.0264530\pi\)
−0.996549 + 0.0830090i \(0.973547\pi\)
\(198\) 23.6319 + 17.6946i 1.67945 + 1.25750i
\(199\) 10.2603i 0.727331i −0.931530 0.363665i \(-0.881525\pi\)
0.931530 0.363665i \(-0.118475\pi\)
\(200\) −4.06133 + 6.54772i −0.287179 + 0.462994i
\(201\) 4.00504 0.282494
\(202\) −4.34287 12.3345i −0.305563 0.867853i
\(203\) 0.861653i 0.0604762i
\(204\) 20.7742 16.6989i 1.45448 1.16916i
\(205\) 29.4608i 2.05763i
\(206\) −7.62741 21.6632i −0.531427 1.50935i
\(207\) 3.41352i 0.237256i
\(208\) 3.90649 + 0.859843i 0.270866 + 0.0596194i
\(209\) −10.4009 15.5490i −0.719445 1.07555i
\(210\) 1.58518 + 4.50219i 0.109388 + 0.310681i
\(211\) 26.2772 1.80899 0.904497 0.426479i \(-0.140246\pi\)
0.904497 + 0.426479i \(0.140246\pi\)
\(212\) −3.12221 + 2.50973i −0.214434 + 0.172369i
\(213\) 8.35727 0.572631
\(214\) −4.25878 + 1.49948i −0.291124 + 0.102502i
\(215\) −5.00172 −0.341114
\(216\) −24.1387 14.9724i −1.64243 1.01874i
\(217\) 1.43148i 0.0971752i
\(218\) −0.717493 2.03781i −0.0485948 0.138018i
\(219\) 33.7195 2.27855
\(220\) −17.5891 5.52141i −1.18586 0.372253i
\(221\) −4.37142 −0.294054
\(222\) 15.2083 + 43.1942i 1.02071 + 2.89900i
\(223\) 23.7985i 1.59366i 0.604202 + 0.796831i \(0.293492\pi\)
−0.604202 + 0.796831i \(0.706508\pi\)
\(224\) −0.273971 2.23665i −0.0183054 0.149442i
\(225\) −17.1461 −1.14308
\(226\) −6.01448 + 2.11764i −0.400077 + 0.140864i
\(227\) −13.8822 −0.921397 −0.460699 0.887557i \(-0.652401\pi\)
−0.460699 + 0.887557i \(0.652401\pi\)
\(228\) 21.5463 + 26.8045i 1.42694 + 1.77517i
\(229\) −25.6686 −1.69623 −0.848113 0.529815i \(-0.822261\pi\)
−0.848113 + 0.529815i \(0.822261\pi\)
\(230\) −0.707916 2.01061i −0.0466786 0.132575i
\(231\) −3.34778 + 2.23937i −0.220268 + 0.147339i
\(232\) 5.19923 + 3.22491i 0.341346 + 0.211725i
\(233\) 8.23801i 0.539690i 0.962904 + 0.269845i \(0.0869725\pi\)
−0.962904 + 0.269845i \(0.913027\pi\)
\(234\) 2.95618 + 8.39608i 0.193252 + 0.548869i
\(235\) 8.71871i 0.568746i
\(236\) 4.20279 + 5.22845i 0.273578 + 0.340343i
\(237\) 48.3945i 3.14356i
\(238\) 0.817845 + 2.32283i 0.0530130 + 0.150566i
\(239\) 4.50382 0.291328 0.145664 0.989334i \(-0.453468\pi\)
0.145664 + 0.989334i \(0.453468\pi\)
\(240\) 33.0992 + 7.28533i 2.13654 + 0.470266i
\(241\) 26.5414i 1.70968i 0.518892 + 0.854840i \(0.326345\pi\)
−0.518892 + 0.854840i \(0.673655\pi\)
\(242\) 0.826463 15.5344i 0.0531271 0.998588i
\(243\) 5.64477i 0.362112i
\(244\) −7.51788 9.35257i −0.481283 0.598737i
\(245\) 19.0136 1.21474
\(246\) −43.1085 + 15.1781i −2.74850 + 0.967722i
\(247\) 5.64036i 0.358888i
\(248\) 8.63757 + 5.35759i 0.548486 + 0.340207i
\(249\) 38.5726i 2.44444i
\(250\) −8.43743 + 2.97074i −0.533630 + 0.187886i
\(251\) 24.5386i 1.54886i 0.632660 + 0.774430i \(0.281963\pi\)
−0.632660 + 0.774430i \(0.718037\pi\)
\(252\) 3.90833 3.14163i 0.246201 0.197904i
\(253\) 1.49507 1.00006i 0.0939940 0.0628735i
\(254\) −5.31666 + 1.87195i −0.333597 + 0.117456i
\(255\) −37.0384 −2.31944
\(256\) −14.5213 6.71794i −0.907584 0.419871i
\(257\) −7.69395 −0.479935 −0.239968 0.970781i \(-0.577137\pi\)
−0.239968 + 0.970781i \(0.577137\pi\)
\(258\) 2.57687 + 7.31876i 0.160429 + 0.455646i
\(259\) −4.23095 −0.262898
\(260\) −3.48245 4.33232i −0.215973 0.268679i
\(261\) 13.6149i 0.842743i
\(262\) 14.1342 4.97651i 0.873211 0.307450i
\(263\) 20.1790 1.24429 0.622147 0.782901i \(-0.286261\pi\)
0.622147 + 0.782901i \(0.286261\pi\)
\(264\) 0.982638 + 28.5818i 0.0604772 + 1.75909i
\(265\) 5.56661 0.341954
\(266\) −2.99710 + 1.05525i −0.183764 + 0.0647016i
\(267\) 32.0737i 1.96288i
\(268\) 1.64612 + 2.04785i 0.100553 + 0.125092i
\(269\) 9.03850 0.551087 0.275544 0.961289i \(-0.411142\pi\)
0.275544 + 0.961289i \(0.411142\pi\)
\(270\) 13.1090 + 37.2318i 0.797788 + 2.26586i
\(271\) −9.82055 −0.596556 −0.298278 0.954479i \(-0.596412\pi\)
−0.298278 + 0.954479i \(0.596412\pi\)
\(272\) 17.0769 + 3.75873i 1.03544 + 0.227907i
\(273\) −1.21440 −0.0734988
\(274\) 27.0110 9.51032i 1.63179 0.574539i
\(275\) 5.02333 + 7.50972i 0.302918 + 0.452853i
\(276\) −2.57730 + 2.07172i −0.155135 + 0.124703i
\(277\) 10.0070i 0.601265i −0.953740 0.300632i \(-0.902802\pi\)
0.953740 0.300632i \(-0.0971978\pi\)
\(278\) −3.12597 + 1.10062i −0.187483 + 0.0660110i
\(279\) 22.6187i 1.35415i
\(280\) −1.65052 + 2.66099i −0.0986375 + 0.159025i
\(281\) 10.9285i 0.651937i −0.945381 0.325968i \(-0.894310\pi\)
0.945381 0.325968i \(-0.105690\pi\)
\(282\) −12.7577 + 4.49185i −0.759708 + 0.267486i
\(283\) 9.99728 0.594277 0.297138 0.954834i \(-0.403968\pi\)
0.297138 + 0.954834i \(0.403968\pi\)
\(284\) 3.43495 + 4.27322i 0.203827 + 0.253569i
\(285\) 47.7900i 2.83084i
\(286\) 2.81127 3.75457i 0.166234 0.222012i
\(287\) 4.22256i 0.249250i
\(288\) −4.32899 35.3411i −0.255088 2.08249i
\(289\) −2.10931 −0.124077
\(290\) −2.82354 8.01935i −0.165804 0.470913i
\(291\) 38.3498i 2.24811i
\(292\) 13.8591 + 17.2414i 0.811045 + 1.00897i
\(293\) 8.30235i 0.485029i −0.970148 0.242514i \(-0.922028\pi\)
0.970148 0.242514i \(-0.0779721\pi\)
\(294\) −9.79576 27.8217i −0.571300 1.62259i
\(295\) 9.32185i 0.542739i
\(296\) −15.8351 + 25.5296i −0.920399 + 1.48388i
\(297\) −27.6852 + 18.5189i −1.60646 + 1.07458i
\(298\) 9.71156 + 27.5825i 0.562575 + 1.59781i
\(299\) 0.542331 0.0313638
\(300\) −10.4062 12.9458i −0.600805 0.747427i
\(301\) −0.716886 −0.0413206
\(302\) 30.2596 10.6541i 1.74124 0.613075i
\(303\) 28.1896 1.61945
\(304\) −4.84982 + 22.0340i −0.278157 + 1.26374i
\(305\) 16.6748i 0.954794i
\(306\) 12.9227 + 36.7028i 0.738743 + 2.09816i
\(307\) −14.5500 −0.830412 −0.415206 0.909727i \(-0.636290\pi\)
−0.415206 + 0.909727i \(0.636290\pi\)
\(308\) −2.52101 0.791373i −0.143648 0.0450926i
\(309\) 49.5096 2.81651
\(310\) −4.69080 13.3227i −0.266419 0.756678i
\(311\) 6.87576i 0.389889i −0.980814 0.194944i \(-0.937547\pi\)
0.980814 0.194944i \(-0.0624526\pi\)
\(312\) −4.54512 + 7.32770i −0.257317 + 0.414849i
\(313\) −11.2456 −0.635637 −0.317819 0.948152i \(-0.602950\pi\)
−0.317819 + 0.948152i \(0.602950\pi\)
\(314\) −26.8102 + 9.43964i −1.51299 + 0.532710i
\(315\) −6.96818 −0.392613
\(316\) −24.7449 + 19.8907i −1.39201 + 1.11894i
\(317\) 12.1388 0.681784 0.340892 0.940102i \(-0.389271\pi\)
0.340892 + 0.940102i \(0.389271\pi\)
\(318\) −2.86790 8.14535i −0.160824 0.456769i
\(319\) 5.96311 3.98878i 0.333870 0.223329i
\(320\) 9.87906 + 19.9185i 0.552256 + 1.11348i
\(321\) 9.73313i 0.543250i
\(322\) −0.101464 0.288176i −0.00565438 0.0160594i
\(323\) 24.6564i 1.37192i
\(324\) 18.2913 14.7031i 1.01619 0.816841i
\(325\) 2.72413i 0.151108i
\(326\) −3.45784 9.82088i −0.191512 0.543928i
\(327\) 4.65726 0.257547
\(328\) −25.4790 15.8038i −1.40684 0.872616i
\(329\) 1.24964i 0.0688947i
\(330\) 23.8195 31.8119i 1.31122 1.75119i
\(331\) 32.4843i 1.78550i −0.450556 0.892748i \(-0.648774\pi\)
0.450556 0.892748i \(-0.351226\pi\)
\(332\) −19.7228 + 15.8538i −1.08243 + 0.870091i
\(333\) −66.8529 −3.66352
\(334\) 28.0045 9.86011i 1.53234 0.539521i
\(335\) 3.65113i 0.199482i
\(336\) 4.74404 + 1.04419i 0.258809 + 0.0569654i
\(337\) 17.7181i 0.965164i 0.875851 + 0.482582i \(0.160301\pi\)
−0.875851 + 0.482582i \(0.839699\pi\)
\(338\) 1.33395 0.469670i 0.0725571 0.0255467i
\(339\) 13.7457i 0.746562i
\(340\) −15.2233 18.9384i −0.825598 1.02708i
\(341\) 9.90661 6.62663i 0.536473 0.358852i
\(342\) −47.3569 + 16.6739i −2.56077 + 0.901624i
\(343\) 5.51358 0.297705
\(344\) −2.68309 + 4.32570i −0.144662 + 0.233226i
\(345\) 4.59509 0.247392
\(346\) 8.58570 + 24.3849i 0.461570 + 1.31094i
\(347\) −3.14912 −0.169054 −0.0845269 0.996421i \(-0.526938\pi\)
−0.0845269 + 0.996421i \(0.526938\pi\)
\(348\) −10.2796 + 8.26309i −0.551047 + 0.442948i
\(349\) 18.5071i 0.990663i 0.868704 + 0.495332i \(0.164953\pi\)
−0.868704 + 0.495332i \(0.835047\pi\)
\(350\) 1.44751 0.509655i 0.0773727 0.0272422i
\(351\) −10.0427 −0.536041
\(352\) −14.2105 + 12.2499i −0.757423 + 0.652924i
\(353\) −17.3977 −0.925987 −0.462994 0.886362i \(-0.653225\pi\)
−0.462994 + 0.886362i \(0.653225\pi\)
\(354\) −13.6402 + 4.80259i −0.724968 + 0.255255i
\(355\) 7.61876i 0.404362i
\(356\) −16.3998 + 13.1827i −0.869190 + 0.698682i
\(357\) −5.30865 −0.280963
\(358\) −6.58591 18.7051i −0.348076 0.988597i
\(359\) 30.6959 1.62007 0.810033 0.586384i \(-0.199449\pi\)
0.810033 + 0.586384i \(0.199449\pi\)
\(360\) −26.0798 + 42.0461i −1.37452 + 2.21603i
\(361\) 12.8137 0.674405
\(362\) 10.8951 3.83606i 0.572633 0.201619i
\(363\) 30.9952 + 12.8020i 1.62683 + 0.671929i
\(364\) −0.499134 0.620944i −0.0261617 0.0325463i
\(365\) 30.7398i 1.60899i
\(366\) 24.3994 8.59079i 1.27537 0.449048i
\(367\) 1.67921i 0.0876542i −0.999039 0.0438271i \(-0.986045\pi\)
0.999039 0.0438271i \(-0.0139551\pi\)
\(368\) −2.11861 0.466319i −0.110440 0.0243086i
\(369\) 66.7204i 3.47332i
\(370\) 39.3772 13.8643i 2.04712 0.720773i
\(371\) 0.797852 0.0414224
\(372\) −17.0777 + 13.7276i −0.885440 + 0.711744i
\(373\) 9.13778i 0.473136i 0.971615 + 0.236568i \(0.0760226\pi\)
−0.971615 + 0.236568i \(0.923977\pi\)
\(374\) 12.2892 16.4128i 0.635461 0.848686i
\(375\) 19.2831i 0.995776i
\(376\) −7.54032 4.67701i −0.388863 0.241198i
\(377\) 2.16310 0.111405
\(378\) 1.87889 + 5.33637i 0.0966395 + 0.274473i
\(379\) 5.76958i 0.296363i −0.988960 0.148182i \(-0.952658\pi\)
0.988960 0.148182i \(-0.0473420\pi\)
\(380\) 24.4359 19.6423i 1.25353 1.00763i
\(381\) 12.1508i 0.622507i
\(382\) 6.27448 + 17.8206i 0.321030 + 0.911783i
\(383\) 13.1633i 0.672615i −0.941752 0.336308i \(-0.890822\pi\)
0.941752 0.336308i \(-0.109178\pi\)
\(384\) 24.0562 24.7175i 1.22761 1.26136i
\(385\) 2.04148 + 3.05195i 0.104043 + 0.155542i
\(386\) 8.73380 + 24.8055i 0.444539 + 1.26257i
\(387\) −11.3275 −0.575808
\(388\) 19.6089 15.7623i 0.995493 0.800208i
\(389\) −25.5589 −1.29589 −0.647943 0.761688i \(-0.724371\pi\)
−0.647943 + 0.761688i \(0.724371\pi\)
\(390\) 11.3023 3.97945i 0.572316 0.201507i
\(391\) 2.37076 0.119894
\(392\) 10.1995 16.4438i 0.515154 0.830538i
\(393\) 32.3026i 1.62945i
\(394\) −1.09441 3.10832i −0.0551357 0.156595i
\(395\) 44.1179 2.21981
\(396\) −39.8343 12.5044i −2.00175 0.628371i
\(397\) −5.52154 −0.277118 −0.138559 0.990354i \(-0.544247\pi\)
−0.138559 + 0.990354i \(0.544247\pi\)
\(398\) 4.81894 + 13.6866i 0.241551 + 0.686049i
\(399\) 6.84965i 0.342911i
\(400\) 2.34232 10.6418i 0.117116 0.532090i
\(401\) −18.2270 −0.910214 −0.455107 0.890437i \(-0.650399\pi\)
−0.455107 + 0.890437i \(0.650399\pi\)
\(402\) −5.34251 + 1.88105i −0.266460 + 0.0938182i
\(403\) 3.59359 0.179010
\(404\) 11.5863 + 14.4139i 0.576440 + 0.717116i
\(405\) −32.6118 −1.62049
\(406\) −0.404693 1.14940i −0.0200846 0.0570437i
\(407\) 19.5860 + 29.2804i 0.970841 + 1.45138i
\(408\) −19.8686 + 32.0325i −0.983645 + 1.58584i
\(409\) 24.0118i 1.18730i −0.804722 0.593652i \(-0.797685\pi\)
0.804722 0.593652i \(-0.202315\pi\)
\(410\) 13.8369 + 39.2991i 0.683354 + 1.94084i
\(411\) 61.7316i 3.04500i
\(412\) 20.3491 + 25.3152i 1.00253 + 1.24719i
\(413\) 1.33608i 0.0657443i
\(414\) −1.60323 4.55345i −0.0787944 0.223790i
\(415\) 35.1640 1.72613
\(416\) −5.61489 + 0.687778i −0.275293 + 0.0337211i
\(417\) 7.14417i 0.349851i
\(418\) 21.1771 + 15.8566i 1.03581 + 0.775570i
\(419\) 19.6547i 0.960195i −0.877215 0.480098i \(-0.840601\pi\)
0.877215 0.480098i \(-0.159399\pi\)
\(420\) −4.22909 5.26117i −0.206358 0.256719i
\(421\) 15.0542 0.733699 0.366849 0.930280i \(-0.380436\pi\)
0.366849 + 0.930280i \(0.380436\pi\)
\(422\) −35.0523 + 12.3416i −1.70632 + 0.600779i
\(423\) 19.7454i 0.960055i
\(424\) 2.98612 4.81425i 0.145019 0.233801i
\(425\) 11.9083i 0.577638i
\(426\) −11.1481 + 3.92516i −0.540129 + 0.190175i
\(427\) 2.38996i 0.115658i
\(428\) 4.97672 4.00044i 0.240559 0.193369i
\(429\) 5.62172 + 8.40430i 0.271419 + 0.405763i
\(430\) 6.67202 2.34916i 0.321753 0.113286i
\(431\) −24.4855 −1.17942 −0.589711 0.807614i \(-0.700759\pi\)
−0.589711 + 0.807614i \(0.700759\pi\)
\(432\) 39.2318 + 8.63517i 1.88754 + 0.415460i
\(433\) 18.6992 0.898627 0.449313 0.893374i \(-0.351669\pi\)
0.449313 + 0.893374i \(0.351669\pi\)
\(434\) −0.672323 1.90952i −0.0322725 0.0916597i
\(435\) 18.3276 0.878743
\(436\) 1.91419 + 2.38134i 0.0916732 + 0.114045i
\(437\) 3.05894i 0.146329i
\(438\) −44.9799 + 15.8370i −2.14923 + 0.756722i
\(439\) 12.8816 0.614806 0.307403 0.951579i \(-0.400540\pi\)
0.307403 + 0.951579i \(0.400540\pi\)
\(440\) 26.0561 0.895804i 1.24218 0.0427058i
\(441\) 43.0605 2.05050
\(442\) 5.83124 2.05312i 0.277364 0.0976572i
\(443\) 21.8314i 1.03724i −0.855005 0.518620i \(-0.826446\pi\)
0.855005 0.518620i \(-0.173554\pi\)
\(444\) −40.5740 50.4758i −1.92556 2.39548i
\(445\) 29.2394 1.38608
\(446\) −11.1774 31.7458i −0.529266 1.50321i
\(447\) −63.0379 −2.98159
\(448\) 1.41595 + 2.85489i 0.0668972 + 0.134881i
\(449\) 23.8044 1.12340 0.561699 0.827341i \(-0.310148\pi\)
0.561699 + 0.827341i \(0.310148\pi\)
\(450\) 22.8720 8.05303i 1.07820 0.379623i
\(451\) −29.2224 + 19.5472i −1.37603 + 0.920440i
\(452\) 7.02840 5.64964i 0.330588 0.265737i
\(453\) 69.1560i 3.24923i
\(454\) 18.5182 6.52007i 0.869100 0.306002i
\(455\) 1.10708i 0.0519009i
\(456\) −41.3309 25.6361i −1.93550 1.20052i
\(457\) 31.0035i 1.45028i −0.688599 0.725142i \(-0.741774\pi\)
0.688599 0.725142i \(-0.258226\pi\)
\(458\) 34.2405 12.0558i 1.59995 0.563328i
\(459\) −43.9010 −2.04912
\(460\) 1.88864 + 2.34955i 0.0880584 + 0.109548i
\(461\) 6.53832i 0.304520i 0.988340 + 0.152260i \(0.0486551\pi\)
−0.988340 + 0.152260i \(0.951345\pi\)
\(462\) 3.41400 4.55954i 0.158834 0.212129i
\(463\) 4.13457i 0.192150i 0.995374 + 0.0960750i \(0.0306289\pi\)
−0.995374 + 0.0960750i \(0.969371\pi\)
\(464\) −8.45013 1.85993i −0.392287 0.0863449i
\(465\) 30.4480 1.41199
\(466\) −3.86915 10.9891i −0.179235 0.509058i
\(467\) 18.9956i 0.879014i 0.898239 + 0.439507i \(0.144847\pi\)
−0.898239 + 0.439507i \(0.855153\pi\)
\(468\) −7.88677 9.81149i −0.364566 0.453536i
\(469\) 0.523309i 0.0241642i
\(470\) 4.09492 + 11.6303i 0.188884 + 0.536465i
\(471\) 61.2729i 2.82330i
\(472\) −8.06194 5.00055i −0.371081 0.230169i
\(473\) 3.31862 + 4.96124i 0.152590 + 0.228118i
\(474\) −22.7294 64.5556i −1.04400 2.96513i
\(475\) −15.3651 −0.704998
\(476\) −2.18192 2.71441i −0.100008 0.124415i
\(477\) 12.6068 0.577226
\(478\) −6.00784 + 2.11531i −0.274792 + 0.0967519i
\(479\) −13.2771 −0.606644 −0.303322 0.952888i \(-0.598096\pi\)
−0.303322 + 0.952888i \(0.598096\pi\)
\(480\) −47.5742 + 5.82745i −2.17145 + 0.265985i
\(481\) 10.6214i 0.484294i
\(482\) −12.4657 35.4047i −0.567796 1.61264i
\(483\) 0.658606 0.0299676
\(484\) 6.19357 + 21.1102i 0.281526 + 0.959554i
\(485\) −34.9609 −1.58749
\(486\) 2.65118 + 7.52981i 0.120260 + 0.341559i
\(487\) 21.6937i 0.983036i 0.870867 + 0.491518i \(0.163558\pi\)
−0.870867 + 0.491518i \(0.836442\pi\)
\(488\) 14.4211 + 8.94490i 0.652811 + 0.404916i
\(489\) 22.4449 1.01499
\(490\) −25.3631 + 8.93013i −1.14579 + 0.403422i
\(491\) 17.5909 0.793867 0.396933 0.917847i \(-0.370074\pi\)
0.396933 + 0.917847i \(0.370074\pi\)
\(492\) 50.3757 40.4936i 2.27111 1.82559i
\(493\) 9.45582 0.425869
\(494\) 2.64911 + 7.52394i 0.119189 + 0.338518i
\(495\) 32.2572 + 48.2236i 1.44985 + 2.16749i
\(496\) −14.0383 3.08993i −0.630340 0.138742i
\(497\) 1.09198i 0.0489821i
\(498\) −18.1164 51.4537i −0.811814 2.30569i
\(499\) 24.1164i 1.07960i 0.841794 + 0.539799i \(0.181500\pi\)
−0.841794 + 0.539799i \(0.818500\pi\)
\(500\) 9.85980 7.92561i 0.440944 0.354444i
\(501\) 64.0021i 2.85940i
\(502\) −11.5250 32.7331i −0.514387 1.46095i
\(503\) 10.6931 0.476781 0.238390 0.971169i \(-0.423380\pi\)
0.238390 + 0.971169i \(0.423380\pi\)
\(504\) −3.73796 + 6.02639i −0.166502 + 0.268437i
\(505\) 25.6986i 1.14357i
\(506\) −1.52464 + 2.03622i −0.0677783 + 0.0905209i
\(507\) 3.04863i 0.135395i
\(508\) 6.21294 4.99415i 0.275655 0.221580i
\(509\) 4.63668 0.205517 0.102759 0.994706i \(-0.467233\pi\)
0.102759 + 0.994706i \(0.467233\pi\)
\(510\) 49.4073 17.3958i 2.18779 0.770301i
\(511\) 4.40587i 0.194904i
\(512\) 22.5259 + 2.14112i 0.995513 + 0.0946252i
\(513\) 56.6446i 2.50092i
\(514\) 10.2633 3.61361i 0.452695 0.159390i
\(515\) 45.1346i 1.98887i
\(516\) −6.87480 8.55255i −0.302646 0.376505i
\(517\) −8.64816 + 5.78484i −0.380346 + 0.254417i
\(518\) 5.64385 1.98715i 0.247977 0.0873103i
\(519\) −55.7299 −2.44627
\(520\) 6.68017 + 4.14348i 0.292945 + 0.181704i
\(521\) 21.2044 0.928982 0.464491 0.885578i \(-0.346237\pi\)
0.464491 + 0.885578i \(0.346237\pi\)
\(522\) −6.39452 18.1616i −0.279880 0.794910i
\(523\) −41.4207 −1.81120 −0.905599 0.424134i \(-0.860579\pi\)
−0.905599 + 0.424134i \(0.860579\pi\)
\(524\) −16.5169 + 13.2768i −0.721543 + 0.579999i
\(525\) 3.30818i 0.144381i
\(526\) −26.9177 + 9.47749i −1.17367 + 0.413238i
\(527\) 15.7091 0.684300
\(528\) −14.7348 37.6651i −0.641250 1.63916i
\(529\) 22.7059 0.987212
\(530\) −7.42556 + 2.61447i −0.322546 + 0.113565i
\(531\) 21.1113i 0.916154i
\(532\) 3.50235 2.81529i 0.151846 0.122058i
\(533\) −10.6003 −0.459152
\(534\) −15.0640 42.7846i −0.651885 1.85147i
\(535\) −8.87303 −0.383614
\(536\) −3.15765 1.95858i −0.136390 0.0845980i
\(537\) 42.7492 1.84477
\(538\) −12.0569 + 4.24511i −0.519808 + 0.183020i
\(539\) −12.6155 18.8598i −0.543387 0.812347i
\(540\) −34.9733 43.5084i −1.50501 1.87230i
\(541\) 27.5097i 1.18274i −0.806402 0.591368i \(-0.798588\pi\)
0.806402 0.591368i \(-0.201412\pi\)
\(542\) 13.1001 4.61242i 0.562696 0.198120i
\(543\) 24.8999i 1.06856i
\(544\) −24.5450 + 3.00657i −1.05236 + 0.128905i
\(545\) 4.24570i 0.181866i
\(546\) 1.61994 0.570367i 0.0693271 0.0244094i
\(547\) 0.394737 0.0168777 0.00843887 0.999964i \(-0.497314\pi\)
0.00843887 + 0.999964i \(0.497314\pi\)
\(548\) −31.5645 + 25.3725i −1.34837 + 1.08386i
\(549\) 37.7636i 1.61171i
\(550\) −10.2279 7.65825i −0.436121 0.326549i
\(551\) 12.2007i 0.519766i
\(552\) 2.46496 3.97404i 0.104916 0.169146i
\(553\) 6.32334 0.268896
\(554\) 4.70001 + 13.3488i 0.199684 + 0.567138i
\(555\) 89.9937i 3.82002i
\(556\) 3.65294 2.93634i 0.154919 0.124529i
\(557\) 21.0202i 0.890654i −0.895368 0.445327i \(-0.853087\pi\)
0.895368 0.445327i \(-0.146913\pi\)
\(558\) −10.6233 30.1721i −0.449721 1.27729i
\(559\) 1.79968i 0.0761182i
\(560\) 0.951919 4.32482i 0.0402259 0.182757i
\(561\) 24.5749 + 36.7387i 1.03755 + 1.55111i
\(562\) 5.13276 + 14.5780i 0.216513 + 0.614934i
\(563\) 24.4448 1.03023 0.515113 0.857122i \(-0.327750\pi\)
0.515113 + 0.857122i \(0.327750\pi\)
\(564\) 14.9083 11.9838i 0.627754 0.504608i
\(565\) −12.5310 −0.527182
\(566\) −13.3358 + 4.69542i −0.560547 + 0.197363i
\(567\) −4.67418 −0.196297
\(568\) −6.58903 4.08695i −0.276470 0.171485i
\(569\) 0.868758i 0.0364202i −0.999834 0.0182101i \(-0.994203\pi\)
0.999834 0.0182101i \(-0.00579678\pi\)
\(570\) 22.4455 + 63.7493i 0.940140 + 2.67016i
\(571\) −3.23890 −0.135544 −0.0677719 0.997701i \(-0.521589\pi\)
−0.0677719 + 0.997701i \(0.521589\pi\)
\(572\) −1.98667 + 6.32876i −0.0830667 + 0.264619i
\(573\) −40.7278 −1.70143
\(574\) 1.98321 + 5.63267i 0.0827776 + 0.235103i
\(575\) 1.47738i 0.0616110i
\(576\) 22.3733 + 45.1099i 0.932220 + 1.87958i
\(577\) 14.9094 0.620687 0.310344 0.950624i \(-0.399556\pi\)
0.310344 + 0.950624i \(0.399556\pi\)
\(578\) 2.81371 0.990681i 0.117035 0.0412069i
\(579\) −56.6912 −2.35601
\(580\) 7.53290 + 9.37125i 0.312787 + 0.389120i
\(581\) 5.03998 0.209094
\(582\) 18.0118 + 51.1566i 0.746611 + 2.12051i
\(583\) −3.69343 5.52157i −0.152966 0.228680i
\(584\) −26.5851 16.4898i −1.10010 0.682354i
\(585\) 17.4930i 0.723245i
\(586\) 3.89936 + 11.0749i 0.161081 + 0.457499i
\(587\) 39.7810i 1.64194i −0.570974 0.820968i \(-0.693434\pi\)
0.570974 0.820968i \(-0.306566\pi\)
\(588\) 26.1340 + 32.5118i 1.07775 + 1.34077i
\(589\) 20.2692i 0.835177i
\(590\) 4.37819 + 12.4348i 0.180247 + 0.511934i
\(591\) 7.10385 0.292213
\(592\) 9.13273 41.4924i 0.375353 1.70533i
\(593\) 19.6509i 0.806966i 0.914987 + 0.403483i \(0.132200\pi\)
−0.914987 + 0.403483i \(0.867800\pi\)
\(594\) 28.2328 37.7061i 1.15840 1.54710i
\(595\) 4.83953i 0.198401i
\(596\) −25.9094 32.2324i −1.06129 1.32029i
\(597\) −31.2798 −1.28020
\(598\) −0.723440 + 0.254716i −0.0295836 + 0.0104161i
\(599\) 17.3473i 0.708793i 0.935095 + 0.354397i \(0.115314\pi\)
−0.935095 + 0.354397i \(0.884686\pi\)
\(600\) 19.9616 + 12.3815i 0.814930 + 0.505473i
\(601\) 16.1383i 0.658293i −0.944279 0.329147i \(-0.893239\pi\)
0.944279 0.329147i \(-0.106761\pi\)
\(602\) 0.956287 0.336700i 0.0389754 0.0137229i
\(603\) 8.26876i 0.336730i
\(604\) −35.3607 + 28.4240i −1.43881 + 1.15656i
\(605\) 11.6707 28.2562i 0.474480 1.14878i
\(606\) −37.6034 + 13.2398i −1.52753 + 0.537831i
\(607\) 17.2287 0.699291 0.349645 0.936882i \(-0.386302\pi\)
0.349645 + 0.936882i \(0.386302\pi\)
\(608\) −3.87932 31.6700i −0.157327 1.28439i
\(609\) 2.62687 0.106446
\(610\) −7.83163 22.2432i −0.317094 0.900602i
\(611\) −3.13709 −0.126913
\(612\) −34.4764 42.8901i −1.39363 1.73373i
\(613\) 4.08340i 0.164927i −0.996594 0.0824634i \(-0.973721\pi\)
0.996594 0.0824634i \(-0.0262788\pi\)
\(614\) 19.4089 6.83369i 0.783279 0.275785i
\(615\) −89.8153 −3.62170
\(616\) 3.73457 0.128394i 0.150470 0.00517314i
\(617\) −15.6375 −0.629540 −0.314770 0.949168i \(-0.601927\pi\)
−0.314770 + 0.949168i \(0.601927\pi\)
\(618\) −66.0432 + 23.2532i −2.65665 + 0.935380i
\(619\) 3.23623i 0.130075i 0.997883 + 0.0650375i \(0.0207167\pi\)
−0.997883 + 0.0650375i \(0.979283\pi\)
\(620\) 12.5145 + 15.5686i 0.502596 + 0.625251i
\(621\) 5.44648 0.218560
\(622\) 3.22934 + 9.17189i 0.129485 + 0.367759i
\(623\) 4.19083 0.167902
\(624\) 2.62135 11.9095i 0.104938 0.476760i
\(625\) −31.1998 −1.24799
\(626\) 15.0010 5.28170i 0.599560 0.211099i
\(627\) −47.4033 + 31.7085i −1.89310 + 1.26632i
\(628\) 31.3299 25.1839i 1.25020 1.00495i
\(629\) 46.4306i 1.85131i
\(630\) 9.29517 3.27274i 0.370329 0.130389i
\(631\) 16.8096i 0.669178i 0.942364 + 0.334589i \(0.108598\pi\)
−0.942364 + 0.334589i \(0.891402\pi\)
\(632\) 23.6663 38.1551i 0.941395 1.51773i
\(633\) 80.1095i 3.18407i
\(634\) −16.1925 + 5.70124i −0.643087 + 0.226425i
\(635\) −11.0771 −0.439581
\(636\) 7.65125 + 9.51849i 0.303392 + 0.377432i
\(637\) 6.84132i 0.271063i
\(638\) −6.08105 + 8.12151i −0.240751 + 0.321534i
\(639\) 17.2543i 0.682570i
\(640\) −22.5333 21.9304i −0.890706 0.866873i
\(641\) −19.6035 −0.774292 −0.387146 0.922018i \(-0.626539\pi\)
−0.387146 + 0.922018i \(0.626539\pi\)
\(642\) 4.57136 + 12.9835i 0.180417 + 0.512416i
\(643\) 30.6343i 1.20810i −0.796947 0.604049i \(-0.793553\pi\)
0.796947 0.604049i \(-0.206447\pi\)
\(644\) 0.270695 + 0.336757i 0.0106669 + 0.0132701i
\(645\) 15.2484i 0.600405i
\(646\) 11.5804 + 32.8903i 0.455623 + 1.29405i
\(647\) 5.31737i 0.209047i −0.994522 0.104524i \(-0.966668\pi\)
0.994522 0.104524i \(-0.0333318\pi\)
\(648\) −17.4940 + 28.2041i −0.687230 + 1.10796i
\(649\) −9.24641 + 6.18501i −0.362953 + 0.242783i
\(650\) −1.27944 3.63384i −0.0501838 0.142531i
\(651\) 4.36406 0.171041
\(652\) 9.22514 + 11.4765i 0.361285 + 0.449454i
\(653\) −20.2079 −0.790796 −0.395398 0.918510i \(-0.629393\pi\)
−0.395398 + 0.918510i \(0.629393\pi\)
\(654\) −6.21253 + 2.18737i −0.242929 + 0.0855331i
\(655\) 29.4481 1.15063
\(656\) 41.4101 + 9.11463i 1.61679 + 0.355866i
\(657\) 69.6168i 2.71601i
\(658\) 0.586916 + 1.66695i 0.0228804 + 0.0649843i
\(659\) −26.7656 −1.04264 −0.521320 0.853361i \(-0.674560\pi\)
−0.521320 + 0.853361i \(0.674560\pi\)
\(660\) −16.8328 + 53.6227i −0.655214 + 2.08726i
\(661\) −26.7508 −1.04048 −0.520242 0.854019i \(-0.674158\pi\)
−0.520242 + 0.854019i \(0.674158\pi\)
\(662\) 15.2569 + 43.3322i 0.592975 + 1.68415i
\(663\) 13.3269i 0.517572i
\(664\) 18.8631 30.4113i 0.732031 1.18019i
\(665\) −6.24436 −0.242146
\(666\) 89.1781 31.3988i 3.45558 1.21668i
\(667\) −1.17312 −0.0454232
\(668\) −32.7254 + 26.3057i −1.26618 + 1.01780i
\(669\) 72.5528 2.80505
\(670\) 1.71482 + 4.87040i 0.0662494 + 0.188160i
\(671\) 16.5398 11.0637i 0.638513 0.427108i
\(672\) −6.81871 + 0.835236i −0.263038 + 0.0322199i
\(673\) 1.05814i 0.0407881i −0.999792 0.0203941i \(-0.993508\pi\)
0.999792 0.0203941i \(-0.00649208\pi\)
\(674\) −8.32164 23.6349i −0.320538 0.910383i
\(675\) 27.3577i 1.05300i
\(676\) −1.55882 + 1.25303i −0.0599546 + 0.0481934i
\(677\) 6.91957i 0.265941i 0.991120 + 0.132970i \(0.0424515\pi\)
−0.991120 + 0.132970i \(0.957548\pi\)
\(678\) 6.45592 + 18.3360i 0.247938 + 0.704188i
\(679\) −5.01088 −0.192300
\(680\) 29.2018 + 18.1129i 1.11984 + 0.694598i
\(681\) 42.3219i 1.62178i
\(682\) −10.1025 + 13.4924i −0.386847 + 0.516651i
\(683\) 24.2529i 0.928010i 0.885833 + 0.464005i \(0.153588\pi\)
−0.885833 + 0.464005i \(0.846412\pi\)
\(684\) 55.3403 44.4843i 2.11599 1.70090i
\(685\) 56.2765 2.15022
\(686\) −7.35481 + 2.58956i −0.280808 + 0.0988699i
\(687\) 78.2541i 2.98558i
\(688\) 1.54744 7.03042i 0.0589955 0.268032i
\(689\) 2.00293i 0.0763057i
\(690\) −6.12960 + 2.15818i −0.233350 + 0.0821604i
\(691\) 3.44537i 0.131068i −0.997850 0.0655341i \(-0.979125\pi\)
0.997850 0.0655341i \(-0.0208751\pi\)
\(692\) −22.9057 28.4957i −0.870744 1.08324i
\(693\) 4.62337 + 6.91179i 0.175627 + 0.262557i
\(694\) 4.20076 1.47905i 0.159459 0.0561439i
\(695\) −6.51285 −0.247047
\(696\) 9.83156 15.8506i 0.372664 0.600814i
\(697\) −46.3386 −1.75520
\(698\) −8.69223 24.6875i −0.329006 0.934435i
\(699\) 25.1147 0.949925
\(700\) −1.69153 + 1.35970i −0.0639339 + 0.0513920i
\(701\) 0.151692i 0.00572934i −0.999996 0.00286467i \(-0.999088\pi\)
0.999996 0.00286467i \(-0.000911854\pi\)
\(702\) 13.3965 4.71677i 0.505616 0.178023i
\(703\) −59.9085 −2.25949
\(704\) 13.2026 23.0150i 0.497593 0.867411i
\(705\) −26.5802 −1.00107
\(706\) 23.2076 8.17118i 0.873430 0.307527i
\(707\) 3.68332i 0.138526i
\(708\) 15.9396 12.8128i 0.599048 0.481534i
\(709\) 47.3746 1.77919 0.889595 0.456750i \(-0.150987\pi\)
0.889595 + 0.456750i \(0.150987\pi\)
\(710\) 3.57830 + 10.1630i 0.134291 + 0.381411i
\(711\) 99.9146 3.74709
\(712\) 15.6850 25.2875i 0.587819 0.947690i
\(713\) −1.94892 −0.0729875
\(714\) 7.08145 2.49331i 0.265016 0.0933099i
\(715\) 7.66162 5.12494i 0.286528 0.191662i
\(716\) 17.5705 + 21.8584i 0.656640 + 0.816888i
\(717\) 13.7305i 0.512774i
\(718\) −40.9466 + 14.4169i −1.52811 + 0.538035i
\(719\) 7.18100i 0.267806i −0.990994 0.133903i \(-0.957249\pi\)
0.990994 0.133903i \(-0.0427511\pi\)
\(720\) 15.0412 68.3361i 0.560552 2.54674i
\(721\) 6.46905i 0.240920i
\(722\) −17.0928 + 6.01820i −0.636127 + 0.223974i
\(723\) 80.9149 3.00926
\(724\) −12.7318 + 10.2342i −0.473172 + 0.380350i
\(725\) 5.89257i 0.218844i
\(726\) −47.3586 2.51958i −1.75764 0.0935105i
\(727\) 4.27355i 0.158497i −0.996855 0.0792486i \(-0.974748\pi\)
0.996855 0.0792486i \(-0.0252521\pi\)
\(728\) 0.957455 + 0.593877i 0.0354857 + 0.0220105i
\(729\) 17.9934 0.666423
\(730\) 14.4375 + 41.0051i 0.534357 + 1.51767i
\(731\) 7.86714i 0.290977i
\(732\) −28.5126 + 22.9193i −1.05386 + 0.847121i
\(733\) 18.8094i 0.694741i 0.937728 + 0.347371i \(0.112925\pi\)
−0.937728 + 0.347371i \(0.887075\pi\)
\(734\) 0.788675 + 2.23998i 0.0291105 + 0.0826791i
\(735\) 57.9656i 2.13809i
\(736\) 3.04513 0.373003i 0.112245 0.0137491i
\(737\) −3.62158 + 2.42251i −0.133403 + 0.0892343i
\(738\) 31.3366 + 89.0014i 1.15351 + 3.27619i
\(739\) 15.2080 0.559435 0.279718 0.960082i \(-0.409759\pi\)
0.279718 + 0.960082i \(0.409759\pi\)
\(740\) −46.0153 + 36.9885i −1.69156 + 1.35973i
\(741\) −17.1954 −0.631689
\(742\) −1.06429 + 0.374727i −0.0390714 + 0.0137567i
\(743\) −7.71852 −0.283165 −0.141583 0.989926i \(-0.545219\pi\)
−0.141583 + 0.989926i \(0.545219\pi\)
\(744\) 16.3333 26.3328i 0.598809 0.965407i
\(745\) 57.4673i 2.10544i
\(746\) −4.29174 12.1893i −0.157132 0.446282i
\(747\) 79.6364 2.91374
\(748\) −8.68456 + 27.6657i −0.317539 + 1.01156i
\(749\) −1.27175 −0.0464689
\(750\) 9.05670 + 25.7226i 0.330704 + 0.939258i
\(751\) 13.8636i 0.505891i −0.967481 0.252945i \(-0.918601\pi\)
0.967481 0.252945i \(-0.0813993\pi\)
\(752\) 12.2550 + 2.69741i 0.446895 + 0.0983643i
\(753\) 74.8091 2.72619
\(754\) −2.88546 + 1.01594i −0.105082 + 0.0369985i
\(755\) 63.0448 2.29444
\(756\) −5.01266 6.23597i −0.182309 0.226800i
\(757\) 13.5309 0.491790 0.245895 0.969296i \(-0.420918\pi\)
0.245895 + 0.969296i \(0.420918\pi\)
\(758\) 2.70980 + 7.69630i 0.0984243 + 0.279542i
\(759\) −3.04883 4.55791i −0.110666 0.165442i
\(760\) −23.3707 + 37.6786i −0.847745 + 1.36674i
\(761\) 17.1462i 0.621549i −0.950484 0.310775i \(-0.899412\pi\)
0.950484 0.310775i \(-0.100588\pi\)
\(762\) 5.70688 + 16.2086i 0.206739 + 0.587174i
\(763\) 0.608529i 0.0220302i
\(764\) −16.7396 20.8248i −0.605619 0.753416i
\(765\) 76.4691i 2.76475i
\(766\) 6.18242 + 17.5592i 0.223380 + 0.634439i
\(767\) −3.35411 −0.121110
\(768\) −20.4805 + 44.2703i −0.739027 + 1.59747i
\(769\) 20.8264i 0.751018i 0.926819 + 0.375509i \(0.122532\pi\)
−0.926819 + 0.375509i \(0.877468\pi\)
\(770\) −4.15663 3.11231i −0.149794 0.112160i
\(771\) 23.4560i 0.844748i
\(772\) −23.3008 28.9872i −0.838615 1.04327i
\(773\) −2.70966 −0.0974595 −0.0487298 0.998812i \(-0.515517\pi\)
−0.0487298 + 0.998812i \(0.515517\pi\)
\(774\) 15.1102 5.32017i 0.543126 0.191230i
\(775\) 9.78942i 0.351646i
\(776\) −18.7542 + 30.2357i −0.673236 + 1.08540i
\(777\) 12.8986i 0.462735i
\(778\) 34.0942 12.0042i 1.22233 0.430373i
\(779\) 59.7898i 2.14219i
\(780\) −13.2077 + 10.6167i −0.472911 + 0.380140i
\(781\) −7.55710 + 5.05502i −0.270414 + 0.180883i
\(782\) −3.16246 + 1.11347i −0.113089 + 0.0398177i
\(783\) 21.7234 0.776332
\(784\) −5.88246 + 26.7256i −0.210088 + 0.954485i
\(785\) −55.8583 −1.99367
\(786\) −15.1715 43.0899i −0.541151 1.53697i
\(787\) 11.8080 0.420908 0.210454 0.977604i \(-0.432506\pi\)
0.210454 + 0.977604i \(0.432506\pi\)
\(788\) 2.91977 + 3.63232i 0.104013 + 0.129396i
\(789\) 61.5185i 2.19012i
\(790\) −58.8509 + 20.7209i −2.09382 + 0.737215i
\(791\) −1.79604 −0.0638599
\(792\) 59.0097 2.02874i 2.09682 0.0720882i
\(793\) 5.99977 0.213058
\(794\) 7.36544 2.59330i 0.261390 0.0920329i
\(795\) 16.9706i 0.601884i
\(796\) −12.8564 15.9939i −0.455683 0.566889i
\(797\) −8.02123 −0.284127 −0.142063 0.989858i \(-0.545374\pi\)
−0.142063 + 0.989858i \(0.545374\pi\)
\(798\) 3.21707 + 9.13706i 0.113883 + 0.323448i
\(799\) −13.7136 −0.485151
\(800\) 1.87360 + 15.2957i 0.0662416 + 0.540784i
\(801\) 66.2189 2.33973
\(802\) 24.3139 8.56068i 0.858552 0.302288i
\(803\) −30.4910 + 20.3957i −1.07600 + 0.719750i
\(804\) 6.24315 5.01843i 0.220179 0.176986i
\(805\) 0.600406i 0.0211615i
\(806\) −4.79366 + 1.68780i −0.168849 + 0.0594503i
\(807\) 27.5551i 0.969985i
\(808\) −22.2252 13.7856i −0.781881 0.484974i
\(809\) 21.2989i 0.748829i 0.927262 + 0.374414i \(0.122156\pi\)
−0.927262 + 0.374414i \(0.877844\pi\)
\(810\) 43.5023 15.3168i 1.52852 0.538176i
\(811\) 42.2055 1.48203 0.741017 0.671486i \(-0.234344\pi\)
0.741017 + 0.671486i \(0.234344\pi\)
\(812\) 1.07968 + 1.34316i 0.0378892 + 0.0471358i
\(813\) 29.9393i 1.05002i
\(814\) −39.8788 29.8596i −1.39775 1.04658i
\(815\) 20.4615i 0.716735i
\(816\) 11.4590 52.0613i 0.401145 1.82251i
\(817\) −10.1508 −0.355132
\(818\) 11.2776 + 32.0304i 0.394312 + 1.11992i
\(819\) 2.50723i 0.0876098i
\(820\) −36.9152 45.9241i −1.28914 1.60374i
\(821\) 6.73040i 0.234893i 0.993079 + 0.117446i \(0.0374708\pi\)
−0.993079 + 0.117446i \(0.962529\pi\)
\(822\) −28.9935 82.3466i −1.01126 2.87217i
\(823\) 3.03370i 0.105748i −0.998601 0.0528740i \(-0.983162\pi\)
0.998601 0.0528740i \(-0.0168382\pi\)
\(824\) −39.0343 24.2117i −1.35983 0.843454i
\(825\) 22.8944 15.3143i 0.797081 0.533175i
\(826\) 0.627517 + 1.78226i 0.0218341 + 0.0620128i
\(827\) −31.7649 −1.10457 −0.552286 0.833654i \(-0.686244\pi\)
−0.552286 + 0.833654i \(0.686244\pi\)
\(828\) 4.27724 + 5.32107i 0.148644 + 0.184920i
\(829\) −39.2573 −1.36346 −0.681732 0.731602i \(-0.738773\pi\)
−0.681732 + 0.731602i \(0.738773\pi\)
\(830\) −46.9068 + 16.5155i −1.62816 + 0.573260i
\(831\) −30.5078 −1.05830
\(832\) 7.16692 3.55460i 0.248468 0.123234i
\(833\) 29.9063i 1.03619i
\(834\) 3.35540 + 9.52993i 0.116188 + 0.329995i
\(835\) 58.3464 2.01916
\(836\) −35.6965 11.2055i −1.23459 0.387551i
\(837\) 36.0895 1.24744
\(838\) 9.23122 + 26.2183i 0.318887 + 0.905696i
\(839\) 15.8911i 0.548621i −0.961641 0.274311i \(-0.911550\pi\)
0.961641 0.274311i \(-0.0884497\pi\)
\(840\) 8.11239 + 5.03184i 0.279904 + 0.173615i
\(841\) 24.3210 0.838655
\(842\) −20.0815 + 7.07052i −0.692056 + 0.243666i
\(843\) −33.3169 −1.14749
\(844\) 40.9614 32.9260i 1.40995 1.13336i
\(845\) 2.77923 0.0956085
\(846\) 9.27382 + 26.3393i 0.318841 + 0.905564i
\(847\) 1.67273 4.04991i 0.0574758 0.139157i
\(848\) −1.72221 + 7.82444i −0.0591408 + 0.268692i
\(849\) 30.4781i 1.04600i
\(850\) −5.59298 15.8850i −0.191838 0.544853i
\(851\) 5.76031i 0.197461i
\(852\) 13.0275 10.4719i 0.446314 0.358761i
\(853\) 38.2952i 1.31120i 0.755107 + 0.655602i \(0.227585\pi\)
−0.755107 + 0.655602i \(0.772415\pi\)
\(854\) −1.12249 3.18808i −0.0384109 0.109094i
\(855\) −98.6667 −3.37433
\(856\) −4.75978 + 7.67378i −0.162686 + 0.262284i
\(857\) 34.9983i 1.19552i −0.801675 0.597760i \(-0.796058\pi\)
0.801675 0.597760i \(-0.203942\pi\)
\(858\) −11.4463 8.57052i −0.390771 0.292593i
\(859\) 19.2913i 0.658212i −0.944293 0.329106i \(-0.893253\pi\)
0.944293 0.329106i \(-0.106747\pi\)
\(860\) −7.79678 + 6.26729i −0.265868 + 0.213713i
\(861\) −12.8730 −0.438712
\(862\) 32.6623 11.5001i 1.11248 0.391694i
\(863\) 21.2878i 0.724644i 0.932053 + 0.362322i \(0.118016\pi\)
−0.932053 + 0.362322i \(0.881984\pi\)
\(864\) −56.3888 + 6.90716i −1.91839 + 0.234986i
\(865\) 50.8052i 1.72743i
\(866\) −24.9437 + 8.78246i −0.847623 + 0.298440i
\(867\) 6.43053i 0.218392i
\(868\) 1.79368 + 2.23142i 0.0608816 + 0.0757393i
\(869\) −29.2721 43.7609i −0.992988 1.48449i
\(870\) −24.4481 + 8.60794i −0.828868 + 0.291837i
\(871\) −1.31372 −0.0445136
\(872\) −3.67187 2.27754i −0.124345 0.0771271i
\(873\) −79.1766 −2.67972
\(874\) −1.43669 4.08046i −0.0485969 0.138024i
\(875\) −2.51958 −0.0851774
\(876\) 52.5626 42.2514i 1.77593 1.42754i
\(877\) 25.5294i 0.862065i −0.902336 0.431033i \(-0.858149\pi\)
0.902336 0.431033i \(-0.141851\pi\)
\(878\) −17.1834 + 6.05011i −0.579911 + 0.204181i
\(879\) −25.3108 −0.853713
\(880\) −34.3367 + 13.4327i −1.15749 + 0.452817i
\(881\) −16.6394 −0.560595 −0.280297 0.959913i \(-0.590433\pi\)
−0.280297 + 0.959913i \(0.590433\pi\)
\(882\) −57.4403 + 20.2242i −1.93412 + 0.680984i
\(883\) 23.3708i 0.786489i 0.919434 + 0.393245i \(0.128647\pi\)
−0.919434 + 0.393245i \(0.871353\pi\)
\(884\) −6.81426 + 5.47751i −0.229188 + 0.184229i
\(885\) −28.4189 −0.955291
\(886\) 10.2535 + 29.1218i 0.344474 + 0.978367i
\(887\) 24.0995 0.809181 0.404590 0.914498i \(-0.367414\pi\)
0.404590 + 0.914498i \(0.367414\pi\)
\(888\) 77.8305 + 48.2756i 2.61182 + 1.62002i
\(889\) −1.58766 −0.0532484
\(890\) −39.0038 + 13.7329i −1.30741 + 0.460327i
\(891\) 21.6378 + 32.3479i 0.724894 + 1.08369i
\(892\) 29.8201 + 37.0975i 0.998452 + 1.24212i
\(893\) 17.6943i 0.592119i
\(894\) 84.0891 29.6070i 2.81236 0.990206i
\(895\) 38.9715i 1.30268i
\(896\) −3.22965 3.14324i −0.107895 0.105008i
\(897\) 1.65337i 0.0552044i
\(898\) −31.7538 + 11.1802i −1.05964 + 0.373088i
\(899\) −7.77330 −0.259254
\(900\) −26.7278 + 21.4846i −0.890926 + 0.716153i
\(901\) 8.75566i 0.291693i
\(902\) 29.8004 39.7997i 0.992244 1.32519i
\(903\) 2.18552i 0.0727297i
\(904\) −6.72203 + 10.8373i −0.223571 + 0.360445i
\(905\) 22.6996 0.754559
\(906\) −32.4805 92.2503i −1.07909 3.06481i
\(907\) 7.57714i 0.251595i 0.992056 + 0.125797i \(0.0401489\pi\)
−0.992056 + 0.125797i \(0.959851\pi\)
\(908\) −21.6399 + 17.3948i −0.718146 + 0.577268i
\(909\) 58.2000i 1.93037i
\(910\) −0.519964 1.47679i −0.0172366 0.0489551i
\(911\) 20.2403i 0.670592i 0.942113 + 0.335296i \(0.108836\pi\)
−0.942113 + 0.335296i \(0.891164\pi\)
\(912\) 67.1737 + 14.7853i 2.22434 + 0.489592i
\(913\) −23.3312 34.8794i −0.772149 1.15434i
\(914\) 14.5614 + 41.3570i 0.481649 + 1.36797i
\(915\) 50.8353 1.68056
\(916\) −40.0127 + 32.1634i −1.32206 + 1.06271i
\(917\) 4.22073 0.139381
\(918\) 58.5615 20.6190i 1.93282 0.680527i
\(919\) −19.8045 −0.653292 −0.326646 0.945147i \(-0.605918\pi\)
−0.326646 + 0.945147i \(0.605918\pi\)
\(920\) −3.62286 2.24714i −0.119442 0.0740859i
\(921\) 44.3576i 1.46163i
\(922\) −3.07085 8.72176i −0.101133 0.287236i
\(923\) −2.74132 −0.0902315
\(924\) −2.41261 + 7.68564i −0.0793689 + 0.252839i
\(925\) 28.9341 0.951347
\(926\) −1.94188 5.51529i −0.0638143 0.181244i
\(927\) 102.217i 3.35725i
\(928\) 12.1456 1.48773i 0.398698 0.0488372i
\(929\) 29.5708 0.970186 0.485093 0.874463i \(-0.338786\pi\)
0.485093 + 0.874463i \(0.338786\pi\)
\(930\) −40.6160 + 14.3005i −1.33185 + 0.468933i
\(931\) 38.5875 1.26466
\(932\) 10.3225 + 12.8416i 0.338123 + 0.420640i
\(933\) −20.9617 −0.686255
\(934\) −8.92168 25.3392i −0.291926 0.829123i
\(935\) 33.4922 22.4032i 1.09531 0.732665i
\(936\) 15.1287 + 9.38381i 0.494496 + 0.306719i
\(937\) 30.9032i 1.00956i 0.863247 + 0.504782i \(0.168427\pi\)
−0.863247 + 0.504782i \(0.831573\pi\)
\(938\) 0.245782 + 0.698065i 0.00802508 + 0.0227926i
\(939\) 34.2836i 1.11880i
\(940\) −10.9248 13.5909i −0.356327 0.443287i
\(941\) 7.58140i 0.247147i −0.992335 0.123573i \(-0.960565\pi\)
0.992335 0.123573i \(-0.0394354\pi\)
\(942\) 28.7780 + 81.7346i 0.937638 + 2.66306i
\(943\) 5.74889 0.187210
\(944\) 13.1028 + 2.88401i 0.426460 + 0.0938664i
\(945\) 11.1182i 0.361673i
\(946\) −6.75701 5.05937i −0.219689 0.164494i
\(947\) 49.0637i 1.59436i −0.603744 0.797178i \(-0.706325\pi\)
0.603744 0.797178i \(-0.293675\pi\)
\(948\) 60.6396 + 75.4383i 1.96948 + 2.45012i
\(949\) −11.0605 −0.359040
\(950\) 20.4962 7.21652i 0.664984 0.234135i
\(951\) 37.0068i 1.20003i
\(952\) 4.18544 + 2.59609i 0.135651 + 0.0841396i
\(953\) 21.8247i 0.706973i 0.935440 + 0.353486i \(0.115004\pi\)
−0.935440 + 0.353486i \(0.884996\pi\)
\(954\) −16.8168 + 5.92104i −0.544464 + 0.191701i
\(955\) 37.1287i 1.20146i
\(956\) 7.02064 5.64341i 0.227064 0.182521i
\(957\) −12.1603 18.1793i −0.393088 0.587654i
\(958\) 17.7109 6.23583i 0.572212 0.201471i
\(959\) 8.06600 0.260465
\(960\) 60.7244 30.1176i 1.95987 0.972043i
\(961\) 18.0861 0.583422
\(962\) −4.98855 14.1684i −0.160837 0.456806i
\(963\) −20.0949 −0.647549
\(964\) 33.2571 + 41.3732i 1.07114 + 1.33254i
\(965\) 51.6815i 1.66369i
\(966\) −0.878544 + 0.309327i −0.0282667 + 0.00995244i
\(967\) 21.1479 0.680071 0.340036 0.940413i \(-0.389561\pi\)
0.340036 + 0.940413i \(0.389561\pi\)
\(968\) −18.1767 25.2509i −0.584221 0.811594i
\(969\) −75.1683 −2.41475
\(970\) 46.6359 16.4201i 1.49739 0.527217i
\(971\) 17.7242i 0.568798i 0.958706 + 0.284399i \(0.0917941\pi\)
−0.958706 + 0.284399i \(0.908206\pi\)
\(972\) −7.07305 8.79918i −0.226868 0.282234i
\(973\) −0.933474 −0.0299258
\(974\) −10.1889 28.9382i −0.326473 0.927241i
\(975\) 8.30488 0.265969
\(976\) −23.4381 5.15886i −0.750234 0.165131i
\(977\) 47.7847 1.52877 0.764384 0.644761i \(-0.223043\pi\)
0.764384 + 0.644761i \(0.223043\pi\)
\(978\) −29.9403 + 10.5417i −0.957385 + 0.337086i
\(979\) −19.4002 29.0028i −0.620035 0.926933i
\(980\) 29.6388 23.8246i 0.946778 0.761049i
\(981\) 9.61532i 0.306993i
\(982\) −23.4653 + 8.26192i −0.748808 + 0.263648i
\(983\) 16.4652i 0.525158i 0.964911 + 0.262579i \(0.0845730\pi\)
−0.964911 + 0.262579i \(0.915427\pi\)
\(984\) −48.1799 + 77.6762i −1.53592 + 2.47623i
\(985\) 6.47609i 0.206345i
\(986\) −12.6135 + 4.44111i −0.401697 + 0.141434i
\(987\) −3.80968 −0.121264
\(988\) −7.06753 8.79231i −0.224848 0.279721i
\(989\) 0.976019i 0.0310356i
\(990\) −65.6785 49.1774i −2.08740 1.56296i
\(991\) 20.8552i 0.662486i 0.943545 + 0.331243i \(0.107468\pi\)
−0.943545 + 0.331243i \(0.892532\pi\)
\(992\) 20.1776 2.47159i 0.640640 0.0784732i
\(993\) −99.0326 −3.14271
\(994\) 0.512871 + 1.45664i 0.0162673 + 0.0462019i
\(995\) 28.5157i 0.904007i
\(996\) 48.3325 + 60.1277i 1.53147 + 1.90522i
\(997\) 40.7675i 1.29112i 0.763709 + 0.645561i \(0.223376\pi\)
−0.763709 + 0.645561i \(0.776624\pi\)
\(998\) −11.3267 32.1700i −0.358542 1.01832i
\(999\) 106.668i 3.37482i
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 572.2.e.b.131.8 yes 64
4.3 odd 2 inner 572.2.e.b.131.58 yes 64
11.10 odd 2 inner 572.2.e.b.131.57 yes 64
44.43 even 2 inner 572.2.e.b.131.7 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.e.b.131.7 64 44.43 even 2 inner
572.2.e.b.131.8 yes 64 1.1 even 1 trivial
572.2.e.b.131.57 yes 64 11.10 odd 2 inner
572.2.e.b.131.58 yes 64 4.3 odd 2 inner