Properties

Label 210.2.x.a.23.10
Level $210$
Weight $2$
Character 210.23
Analytic conductor $1.677$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(23,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.x (of order \(12\), degree \(4\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 23.10
Character \(\chi\) \(=\) 210.23
Dual form 210.2.x.a.137.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(-1.59292 + 0.680155i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.22506 + 0.221605i) q^{5} +(-1.36260 + 1.06926i) q^{6} +(-0.736347 + 2.54122i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.07478 - 2.16686i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(-1.59292 + 0.680155i) q^{3} +(0.866025 - 0.500000i) q^{4} +(2.22506 + 0.221605i) q^{5} +(-1.36260 + 1.06926i) q^{6} +(-0.736347 + 2.54122i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.07478 - 2.16686i) q^{9} +(2.20660 - 0.361834i) q^{10} +(1.83587 - 1.05994i) q^{11} +(-1.03943 + 1.38549i) q^{12} +(3.28206 + 3.28206i) q^{13} +(-0.0535403 + 2.64521i) q^{14} +(-3.69506 + 1.16039i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.375258 + 1.40048i) q^{17} +(1.44326 - 2.63002i) q^{18} +(-4.72549 - 2.72826i) q^{19} +(2.03776 - 0.920615i) q^{20} +(-0.555484 - 4.54878i) q^{21} +(1.49898 - 1.49898i) q^{22} +(-1.47375 - 5.50010i) q^{23} +(-0.645421 + 1.60731i) q^{24} +(4.90178 + 0.986167i) q^{25} +(4.01969 + 2.32077i) q^{26} +(-1.83115 + 4.86281i) q^{27} +(0.632915 + 2.56893i) q^{28} -7.20525 q^{29} +(-3.26883 + 2.07720i) q^{30} +(-0.528063 - 0.914632i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-2.20346 + 2.93707i) q^{33} +1.44989i q^{34} +(-2.20156 + 5.49119i) q^{35} +(0.713378 - 2.91395i) q^{36} +(-1.66812 - 6.22550i) q^{37} +(-5.27060 - 1.41225i) q^{38} +(-7.46037 - 2.99575i) q^{39} +(1.73005 - 1.41666i) q^{40} -1.86758i q^{41} +(-1.71387 - 4.25002i) q^{42} +(1.79293 + 1.79293i) q^{43} +(1.05994 - 1.83587i) q^{44} +(5.09669 - 4.36162i) q^{45} +(-2.84706 - 4.93126i) q^{46} +(-10.7419 + 2.87830i) q^{47} +(-0.207427 + 1.71959i) q^{48} +(-5.91559 - 3.74244i) q^{49} +(4.99000 - 0.316111i) q^{50} +(-0.354790 - 2.48609i) q^{51} +(4.48338 + 1.20132i) q^{52} +(-6.47741 - 1.73562i) q^{53} +(-0.510166 + 5.17105i) q^{54} +(4.31980 - 1.95159i) q^{55} +(1.27624 + 2.31759i) q^{56} +(9.38296 + 1.13183i) q^{57} +(-6.95973 + 1.86485i) q^{58} +(2.63659 + 4.56671i) q^{59} +(-2.61983 + 2.85246i) q^{60} +(4.11857 - 7.13357i) q^{61} +(-0.746794 - 0.746794i) q^{62} +(3.97872 + 6.86803i) q^{63} -1.00000i q^{64} +(6.57547 + 8.03011i) q^{65} +(-1.36821 + 3.40729i) q^{66} +(9.10412 + 2.43944i) q^{67} +(0.375258 + 1.40048i) q^{68} +(6.08848 + 7.75883i) q^{69} +(-0.705321 + 5.87388i) q^{70} -1.75938i q^{71} +(-0.0651145 - 2.99929i) q^{72} +(0.323412 - 1.20699i) q^{73} +(-3.22256 - 5.58163i) q^{74} +(-8.47889 + 1.76309i) q^{75} -5.45653 q^{76} +(1.34170 + 5.44582i) q^{77} +(-7.98152 - 0.962782i) q^{78} +(13.8415 + 7.99137i) q^{79} +(1.30445 - 1.81616i) q^{80} +(-0.390595 - 8.99152i) q^{81} +(-0.483365 - 1.80394i) q^{82} +(9.47707 - 9.47707i) q^{83} +(-2.75545 - 3.66162i) q^{84} +(-1.14532 + 3.03300i) q^{85} +(2.19589 + 1.26779i) q^{86} +(11.4774 - 4.90069i) q^{87} +(0.548664 - 2.04764i) q^{88} +(-0.199936 + 0.346299i) q^{89} +(3.79416 - 5.53212i) q^{90} +(-10.7572 + 5.92370i) q^{91} +(-4.02635 - 4.02635i) q^{92} +(1.46325 + 1.09777i) q^{93} +(-9.63096 + 5.56044i) q^{94} +(-9.90990 - 7.11774i) q^{95} +(0.244702 + 1.71468i) q^{96} +(-8.63390 + 8.63390i) q^{97} +(-6.68263 - 2.08385i) q^{98} +(1.51227 - 6.17721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) −1.59292 + 0.680155i −0.919672 + 0.392688i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 2.22506 + 0.221605i 0.995077 + 0.0991046i
\(6\) −1.36260 + 1.06926i −0.556281 + 0.436522i
\(7\) −0.736347 + 2.54122i −0.278313 + 0.960490i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 2.07478 2.16686i 0.691593 0.722288i
\(10\) 2.20660 0.361834i 0.697788 0.114422i
\(11\) 1.83587 1.05994i 0.553535 0.319583i −0.197012 0.980401i \(-0.563124\pi\)
0.750546 + 0.660818i \(0.229790\pi\)
\(12\) −1.03943 + 1.38549i −0.300058 + 0.399957i
\(13\) 3.28206 + 3.28206i 0.910280 + 0.910280i 0.996294 0.0860135i \(-0.0274128\pi\)
−0.0860135 + 0.996294i \(0.527413\pi\)
\(14\) −0.0535403 + 2.64521i −0.0143092 + 0.706962i
\(15\) −3.69506 + 1.16039i −0.954061 + 0.299611i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −0.375258 + 1.40048i −0.0910134 + 0.339667i −0.996385 0.0849537i \(-0.972926\pi\)
0.905371 + 0.424620i \(0.139592\pi\)
\(18\) 1.44326 2.63002i 0.340179 0.619902i
\(19\) −4.72549 2.72826i −1.08410 0.625906i −0.152102 0.988365i \(-0.548604\pi\)
−0.932000 + 0.362458i \(0.881937\pi\)
\(20\) 2.03776 0.920615i 0.455657 0.205856i
\(21\) −0.555484 4.54878i −0.121216 0.992626i
\(22\) 1.49898 1.49898i 0.319583 0.319583i
\(23\) −1.47375 5.50010i −0.307298 1.14685i −0.930949 0.365148i \(-0.881018\pi\)
0.623652 0.781702i \(-0.285648\pi\)
\(24\) −0.645421 + 1.60731i −0.131746 + 0.328090i
\(25\) 4.90178 + 0.986167i 0.980357 + 0.197233i
\(26\) 4.01969 + 2.32077i 0.788326 + 0.455140i
\(27\) −1.83115 + 4.86281i −0.352405 + 0.935848i
\(28\) 0.632915 + 2.56893i 0.119610 + 0.485483i
\(29\) −7.20525 −1.33798 −0.668990 0.743271i \(-0.733273\pi\)
−0.668990 + 0.743271i \(0.733273\pi\)
\(30\) −3.26883 + 2.07720i −0.596803 + 0.379243i
\(31\) −0.528063 0.914632i −0.0948429 0.164273i 0.814700 0.579882i \(-0.196902\pi\)
−0.909543 + 0.415610i \(0.863568\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) −2.20346 + 2.93707i −0.383574 + 0.511278i
\(34\) 1.44989i 0.248653i
\(35\) −2.20156 + 5.49119i −0.372132 + 0.928180i
\(36\) 0.713378 2.91395i 0.118896 0.485658i
\(37\) −1.66812 6.22550i −0.274237 1.02347i −0.956351 0.292221i \(-0.905606\pi\)
0.682114 0.731246i \(-0.261061\pi\)
\(38\) −5.27060 1.41225i −0.855004 0.229098i
\(39\) −7.46037 2.99575i −1.19462 0.479703i
\(40\) 1.73005 1.41666i 0.273545 0.223993i
\(41\) 1.86758i 0.291667i −0.989309 0.145833i \(-0.953414\pi\)
0.989309 0.145833i \(-0.0465863\pi\)
\(42\) −1.71387 4.25002i −0.264456 0.655792i
\(43\) 1.79293 + 1.79293i 0.273420 + 0.273420i 0.830475 0.557056i \(-0.188069\pi\)
−0.557056 + 0.830475i \(0.688069\pi\)
\(44\) 1.05994 1.83587i 0.159792 0.276767i
\(45\) 5.09669 4.36162i 0.759770 0.650192i
\(46\) −2.84706 4.93126i −0.419776 0.727074i
\(47\) −10.7419 + 2.87830i −1.56687 + 0.419843i −0.934832 0.355091i \(-0.884450\pi\)
−0.632042 + 0.774934i \(0.717783\pi\)
\(48\) −0.207427 + 1.71959i −0.0299396 + 0.248201i
\(49\) −5.91559 3.74244i −0.845084 0.534634i
\(50\) 4.99000 0.316111i 0.705692 0.0447048i
\(51\) −0.354790 2.48609i −0.0496805 0.348122i
\(52\) 4.48338 + 1.20132i 0.621733 + 0.166593i
\(53\) −6.47741 1.73562i −0.889741 0.238405i −0.215136 0.976584i \(-0.569019\pi\)
−0.674605 + 0.738179i \(0.735686\pi\)
\(54\) −0.510166 + 5.17105i −0.0694248 + 0.703690i
\(55\) 4.31980 1.95159i 0.582482 0.263152i
\(56\) 1.27624 + 2.31759i 0.170544 + 0.309701i
\(57\) 9.38296 + 1.13183i 1.24280 + 0.149915i
\(58\) −6.95973 + 1.86485i −0.913858 + 0.244867i
\(59\) 2.63659 + 4.56671i 0.343255 + 0.594535i 0.985035 0.172354i \(-0.0551372\pi\)
−0.641780 + 0.766889i \(0.721804\pi\)
\(60\) −2.61983 + 2.85246i −0.338218 + 0.368251i
\(61\) 4.11857 7.13357i 0.527328 0.913360i −0.472164 0.881511i \(-0.656527\pi\)
0.999493 0.0318490i \(-0.0101396\pi\)
\(62\) −0.746794 0.746794i −0.0948429 0.0948429i
\(63\) 3.97872 + 6.86803i 0.501272 + 0.865290i
\(64\) 1.00000i 0.125000i
\(65\) 6.57547 + 8.03011i 0.815586 + 0.996012i
\(66\) −1.36821 + 3.40729i −0.168415 + 0.419408i
\(67\) 9.10412 + 2.43944i 1.11225 + 0.298025i 0.767742 0.640760i \(-0.221380\pi\)
0.344504 + 0.938785i \(0.388047\pi\)
\(68\) 0.375258 + 1.40048i 0.0455067 + 0.169833i
\(69\) 6.08848 + 7.75883i 0.732967 + 0.934054i
\(70\) −0.705321 + 5.87388i −0.0843020 + 0.702064i
\(71\) 1.75938i 0.208800i −0.994535 0.104400i \(-0.966708\pi\)
0.994535 0.104400i \(-0.0332922\pi\)
\(72\) −0.0651145 2.99929i −0.00767382 0.353470i
\(73\) 0.323412 1.20699i 0.0378525 0.141268i −0.944414 0.328760i \(-0.893369\pi\)
0.982266 + 0.187492i \(0.0600360\pi\)
\(74\) −3.22256 5.58163i −0.374615 0.648852i
\(75\) −8.47889 + 1.76309i −0.979057 + 0.203584i
\(76\) −5.45653 −0.625906
\(77\) 1.34170 + 5.44582i 0.152901 + 0.620609i
\(78\) −7.98152 0.962782i −0.903729 0.109014i
\(79\) 13.8415 + 7.99137i 1.55728 + 0.899099i 0.997515 + 0.0704506i \(0.0224437\pi\)
0.559770 + 0.828648i \(0.310890\pi\)
\(80\) 1.30445 1.81616i 0.145841 0.203052i
\(81\) −0.390595 8.99152i −0.0433995 0.999058i
\(82\) −0.483365 1.80394i −0.0533787 0.199212i
\(83\) 9.47707 9.47707i 1.04024 1.04024i 0.0410882 0.999156i \(-0.486918\pi\)
0.999156 0.0410882i \(-0.0130825\pi\)
\(84\) −2.75545 3.66162i −0.300645 0.399516i
\(85\) −1.14532 + 3.03300i −0.124228 + 0.328975i
\(86\) 2.19589 + 1.26779i 0.236788 + 0.136710i
\(87\) 11.4774 4.90069i 1.23050 0.525409i
\(88\) 0.548664 2.04764i 0.0584878 0.218280i
\(89\) −0.199936 + 0.346299i −0.0211931 + 0.0367076i −0.876427 0.481534i \(-0.840080\pi\)
0.855234 + 0.518242i \(0.173413\pi\)
\(90\) 3.79416 5.53212i 0.399939 0.583137i
\(91\) −10.7572 + 5.92370i −1.12766 + 0.620973i
\(92\) −4.02635 4.02635i −0.419776 0.419776i
\(93\) 1.46325 + 1.09777i 0.151732 + 0.113833i
\(94\) −9.63096 + 5.56044i −0.993358 + 0.573516i
\(95\) −9.90990 7.11774i −1.01673 0.730264i
\(96\) 0.244702 + 1.71468i 0.0249748 + 0.175004i
\(97\) −8.63390 + 8.63390i −0.876640 + 0.876640i −0.993185 0.116546i \(-0.962818\pi\)
0.116546 + 0.993185i \(0.462818\pi\)
\(98\) −6.68263 2.08385i −0.675048 0.210500i
\(99\) 1.51227 6.17721i 0.151989 0.620833i
\(100\) 4.73815 1.59685i 0.473815 0.159685i
\(101\) 3.82984 2.21116i 0.381084 0.220019i −0.297206 0.954813i \(-0.596055\pi\)
0.678290 + 0.734795i \(0.262721\pi\)
\(102\) −0.986147 2.30955i −0.0976431 0.228679i
\(103\) −10.3424 + 2.77123i −1.01906 + 0.273057i −0.729412 0.684075i \(-0.760206\pi\)
−0.289652 + 0.957132i \(0.593539\pi\)
\(104\) 4.64154 0.455140
\(105\) −0.227953 10.2444i −0.0222459 0.999753i
\(106\) −6.70591 −0.651335
\(107\) 10.3122 2.76314i 0.996917 0.267123i 0.276763 0.960938i \(-0.410738\pi\)
0.720153 + 0.693815i \(0.244072\pi\)
\(108\) 0.845583 + 5.12689i 0.0813663 + 0.493335i
\(109\) 7.42120 4.28463i 0.710822 0.410393i −0.100543 0.994933i \(-0.532058\pi\)
0.811365 + 0.584539i \(0.198725\pi\)
\(110\) 3.66750 3.00314i 0.349682 0.286338i
\(111\) 6.89149 + 8.78214i 0.654111 + 0.833564i
\(112\) 1.83259 + 1.90830i 0.173163 + 0.180318i
\(113\) −7.12484 + 7.12484i −0.670249 + 0.670249i −0.957773 0.287524i \(-0.907168\pi\)
0.287524 + 0.957773i \(0.407168\pi\)
\(114\) 9.35618 1.33522i 0.876287 0.125055i
\(115\) −2.06033 12.5646i −0.192127 1.17166i
\(116\) −6.23993 + 3.60262i −0.579363 + 0.334495i
\(117\) 13.9213 0.302232i 1.28703 0.0279413i
\(118\) 3.72870 + 3.72870i 0.343255 + 0.343255i
\(119\) −3.28261 1.98485i −0.300916 0.181951i
\(120\) −1.79229 + 3.43332i −0.163613 + 0.313418i
\(121\) −3.25306 + 5.63447i −0.295733 + 0.512224i
\(122\) 2.13193 7.95646i 0.193016 0.720344i
\(123\) 1.27024 + 2.97490i 0.114534 + 0.268238i
\(124\) −0.914632 0.528063i −0.0821364 0.0474215i
\(125\) 10.6882 + 3.28054i 0.955984 + 0.293420i
\(126\) 5.62072 + 5.60424i 0.500734 + 0.499265i
\(127\) −11.2870 + 11.2870i −1.00156 + 1.00156i −0.00155629 + 0.999999i \(0.500495\pi\)
−0.999999 + 0.00155629i \(0.999505\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) −4.07547 1.63652i −0.358825 0.144088i
\(130\) 8.42976 + 6.05463i 0.739339 + 0.531026i
\(131\) −5.01434 2.89503i −0.438105 0.252940i 0.264689 0.964334i \(-0.414731\pi\)
−0.702793 + 0.711394i \(0.748064\pi\)
\(132\) −0.439721 + 3.64531i −0.0382728 + 0.317283i
\(133\) 10.4127 9.99956i 0.902897 0.867072i
\(134\) 9.42528 0.814220
\(135\) −5.15203 + 10.4142i −0.443416 + 0.896316i
\(136\) 0.724943 + 1.25564i 0.0621633 + 0.107670i
\(137\) −2.90062 + 10.8253i −0.247816 + 0.924864i 0.724130 + 0.689663i \(0.242241\pi\)
−0.971947 + 0.235201i \(0.924425\pi\)
\(138\) 7.88916 + 5.91864i 0.671570 + 0.503828i
\(139\) 20.1333i 1.70768i −0.520535 0.853841i \(-0.674267\pi\)
0.520535 0.853841i \(-0.325733\pi\)
\(140\) 0.838986 + 5.85629i 0.0709072 + 0.494947i
\(141\) 15.1534 11.8911i 1.27614 1.00141i
\(142\) −0.455361 1.69943i −0.0382131 0.142613i
\(143\) 9.50422 + 2.54665i 0.794782 + 0.212961i
\(144\) −0.839170 2.88024i −0.0699308 0.240020i
\(145\) −16.0321 1.59672i −1.33139 0.132600i
\(146\) 1.24957i 0.103415i
\(147\) 11.9685 + 1.93788i 0.987144 + 0.159833i
\(148\) −4.55738 4.55738i −0.374615 0.374615i
\(149\) −5.90510 + 10.2279i −0.483765 + 0.837905i −0.999826 0.0186464i \(-0.994064\pi\)
0.516061 + 0.856552i \(0.327398\pi\)
\(150\) −7.73365 + 3.89751i −0.631450 + 0.318230i
\(151\) 4.33354 + 7.50591i 0.352658 + 0.610822i 0.986714 0.162465i \(-0.0519445\pi\)
−0.634056 + 0.773287i \(0.718611\pi\)
\(152\) −5.27060 + 1.41225i −0.427502 + 0.114549i
\(153\) 2.25608 + 3.71882i 0.182393 + 0.300649i
\(154\) 2.70547 + 4.91300i 0.218013 + 0.395901i
\(155\) −0.972285 2.15213i −0.0780958 0.172863i
\(156\) −7.95874 + 1.13579i −0.637209 + 0.0909362i
\(157\) −16.8625 4.51828i −1.34577 0.360598i −0.487198 0.873291i \(-0.661981\pi\)
−0.858572 + 0.512693i \(0.828648\pi\)
\(158\) 15.4381 + 4.13664i 1.22819 + 0.329093i
\(159\) 11.4985 1.64095i 0.911888 0.130136i
\(160\) 0.789941 2.09189i 0.0624504 0.165378i
\(161\) 15.0621 + 0.304865i 1.18706 + 0.0240267i
\(162\) −2.70446 8.58405i −0.212483 0.674427i
\(163\) −5.03620 + 1.34945i −0.394466 + 0.105697i −0.450599 0.892726i \(-0.648790\pi\)
0.0561330 + 0.998423i \(0.482123\pi\)
\(164\) −0.933789 1.61737i −0.0729167 0.126295i
\(165\) −5.55371 + 6.04686i −0.432355 + 0.470747i
\(166\) 6.70130 11.6070i 0.520122 0.900877i
\(167\) −5.99458 5.99458i −0.463874 0.463874i 0.436049 0.899923i \(-0.356377\pi\)
−0.899923 + 0.436049i \(0.856377\pi\)
\(168\) −3.60926 2.82369i −0.278461 0.217852i
\(169\) 8.54387i 0.657221i
\(170\) −0.321301 + 3.22608i −0.0246427 + 0.247429i
\(171\) −15.7161 + 4.57895i −1.20184 + 0.350161i
\(172\) 2.44919 + 0.656259i 0.186749 + 0.0500393i
\(173\) −1.29750 4.84235i −0.0986474 0.368157i 0.898900 0.438154i \(-0.144368\pi\)
−0.997547 + 0.0699972i \(0.977701\pi\)
\(174\) 9.81790 7.70426i 0.744293 0.584059i
\(175\) −6.11548 + 11.7303i −0.462287 + 0.886731i
\(176\) 2.11988i 0.159792i
\(177\) −7.30595 5.48110i −0.549148 0.411985i
\(178\) −0.103494 + 0.386246i −0.00775723 + 0.0289504i
\(179\) 4.04588 + 7.00767i 0.302403 + 0.523778i 0.976680 0.214701i \(-0.0688777\pi\)
−0.674277 + 0.738479i \(0.735544\pi\)
\(180\) 2.23305 6.32562i 0.166442 0.471484i
\(181\) 10.6946 0.794924 0.397462 0.917619i \(-0.369891\pi\)
0.397462 + 0.917619i \(0.369891\pi\)
\(182\) −8.85747 + 8.50602i −0.656559 + 0.630508i
\(183\) −1.70861 + 14.1645i −0.126304 + 1.04707i
\(184\) −4.93126 2.84706i −0.363537 0.209888i
\(185\) −2.33206 14.2218i −0.171457 1.04561i
\(186\) 1.69752 + 0.681646i 0.124468 + 0.0499807i
\(187\) 0.795501 + 2.96885i 0.0581728 + 0.217104i
\(188\) −7.86365 + 7.86365i −0.573516 + 0.573516i
\(189\) −11.0091 8.23406i −0.800794 0.598940i
\(190\) −11.4144 4.31034i −0.828090 0.312705i
\(191\) −0.647671 0.373933i −0.0468638 0.0270569i 0.476385 0.879237i \(-0.341947\pi\)
−0.523249 + 0.852180i \(0.675280\pi\)
\(192\) 0.680155 + 1.59292i 0.0490860 + 0.114959i
\(193\) 2.39615 8.94254i 0.172478 0.643698i −0.824489 0.565878i \(-0.808537\pi\)
0.996967 0.0778200i \(-0.0247960\pi\)
\(194\) −6.10509 + 10.5743i −0.438320 + 0.759192i
\(195\) −15.9359 8.31897i −1.14119 0.595734i
\(196\) −6.99427 0.283250i −0.499590 0.0202322i
\(197\) 2.71376 + 2.71376i 0.193348 + 0.193348i 0.797141 0.603793i \(-0.206345\pi\)
−0.603793 + 0.797141i \(0.706345\pi\)
\(198\) −0.138035 6.35813i −0.00980971 0.451853i
\(199\) −4.85488 + 2.80297i −0.344153 + 0.198697i −0.662107 0.749409i \(-0.730338\pi\)
0.317954 + 0.948106i \(0.397004\pi\)
\(200\) 4.16341 2.76876i 0.294397 0.195781i
\(201\) −16.1613 + 2.30638i −1.13993 + 0.162680i
\(202\) 3.12705 3.12705i 0.220019 0.220019i
\(203\) 5.30556 18.3101i 0.372377 1.28512i
\(204\) −1.55030 1.97562i −0.108543 0.138321i
\(205\) 0.413864 4.15547i 0.0289055 0.290231i
\(206\) −9.27271 + 5.35360i −0.646060 + 0.373003i
\(207\) −14.9757 8.21808i −1.04088 0.571196i
\(208\) 4.48338 1.20132i 0.310867 0.0832964i
\(209\) −11.5672 −0.800117
\(210\) −2.87164 9.83635i −0.198162 0.678772i
\(211\) 14.8448 1.02196 0.510978 0.859594i \(-0.329283\pi\)
0.510978 + 0.859594i \(0.329283\pi\)
\(212\) −6.47741 + 1.73562i −0.444870 + 0.119203i
\(213\) 1.19665 + 2.80255i 0.0819932 + 0.192028i
\(214\) 9.24565 5.33798i 0.632020 0.364897i
\(215\) 3.59206 + 4.38670i 0.244976 + 0.299171i
\(216\) 2.14371 + 4.73334i 0.145861 + 0.322063i
\(217\) 2.71312 0.668438i 0.184178 0.0453765i
\(218\) 6.05939 6.05939i 0.410393 0.410393i
\(219\) 0.305772 + 2.14261i 0.0206622 + 0.144784i
\(220\) 2.76526 3.85003i 0.186434 0.259569i
\(221\) −5.82809 + 3.36485i −0.392040 + 0.226344i
\(222\) 8.92965 + 6.69925i 0.599319 + 0.449624i
\(223\) 5.02812 + 5.02812i 0.336708 + 0.336708i 0.855127 0.518419i \(-0.173479\pi\)
−0.518419 + 0.855127i \(0.673479\pi\)
\(224\) 2.26405 + 1.36897i 0.151273 + 0.0914683i
\(225\) 12.3070 8.57542i 0.820467 0.571694i
\(226\) −5.03803 + 8.72612i −0.335124 + 0.580453i
\(227\) 3.01201 11.2410i 0.199914 0.746089i −0.791026 0.611783i \(-0.790453\pi\)
0.990940 0.134307i \(-0.0428807\pi\)
\(228\) 8.69180 3.71128i 0.575628 0.245786i
\(229\) −3.58186 2.06799i −0.236696 0.136657i 0.376961 0.926229i \(-0.376969\pi\)
−0.613657 + 0.789572i \(0.710302\pi\)
\(230\) −5.24209 11.6033i −0.345653 0.765096i
\(231\) −5.84122 7.76218i −0.384324 0.510714i
\(232\) −5.09488 + 5.09488i −0.334495 + 0.334495i
\(233\) −5.87626 21.9305i −0.384967 1.43671i −0.838220 0.545333i \(-0.816403\pi\)
0.453253 0.891382i \(-0.350263\pi\)
\(234\) 13.3688 3.89504i 0.873943 0.254627i
\(235\) −24.5393 + 4.02392i −1.60077 + 0.262491i
\(236\) 4.56671 + 2.63659i 0.297267 + 0.171627i
\(237\) −27.4837 3.31526i −1.78526 0.215349i
\(238\) −3.68448 1.06762i −0.238829 0.0692034i
\(239\) −10.6159 −0.686682 −0.343341 0.939211i \(-0.611559\pi\)
−0.343341 + 0.939211i \(0.611559\pi\)
\(240\) −0.842606 + 3.78021i −0.0543900 + 0.244012i
\(241\) 10.0635 + 17.4304i 0.648245 + 1.12279i 0.983542 + 0.180680i \(0.0578300\pi\)
−0.335297 + 0.942112i \(0.608837\pi\)
\(242\) −1.68391 + 6.28443i −0.108246 + 0.403979i
\(243\) 6.73782 + 14.0571i 0.432231 + 0.901763i
\(244\) 8.23713i 0.527328i
\(245\) −12.3332 9.63806i −0.787939 0.615753i
\(246\) 1.99692 + 2.54477i 0.127319 + 0.162249i
\(247\) −6.55502 24.4637i −0.417086 1.55659i
\(248\) −1.02014 0.273346i −0.0647789 0.0173575i
\(249\) −8.65032 + 21.5421i −0.548192 + 1.36517i
\(250\) 11.1731 + 0.402441i 0.706649 + 0.0254526i
\(251\) 17.8395i 1.12602i 0.826450 + 0.563010i \(0.190357\pi\)
−0.826450 + 0.563010i \(0.809643\pi\)
\(252\) 6.87969 + 3.95853i 0.433379 + 0.249364i
\(253\) −8.53537 8.53537i −0.536614 0.536614i
\(254\) −7.98108 + 13.8236i −0.500778 + 0.867372i
\(255\) −0.238500 5.61032i −0.0149355 0.351332i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.963390 0.258140i 0.0600946 0.0161023i −0.228646 0.973510i \(-0.573430\pi\)
0.288741 + 0.957407i \(0.406763\pi\)
\(258\) −4.36016 0.525951i −0.271452 0.0327443i
\(259\) 17.0487 + 0.345073i 1.05935 + 0.0214418i
\(260\) 9.70957 + 3.66654i 0.602162 + 0.227389i
\(261\) −14.9493 + 15.6128i −0.925337 + 0.966407i
\(262\) −5.59277 1.49858i −0.345522 0.0925824i
\(263\) 16.6722 + 4.46730i 1.02805 + 0.275466i 0.733153 0.680063i \(-0.238048\pi\)
0.294898 + 0.955529i \(0.404714\pi\)
\(264\) 0.518738 + 3.63491i 0.0319261 + 0.223713i
\(265\) −14.0280 5.29728i −0.861733 0.325409i
\(266\) 7.46983 12.3538i 0.458005 0.757462i
\(267\) 0.0829443 0.687613i 0.00507611 0.0420812i
\(268\) 9.10412 2.43944i 0.556123 0.149013i
\(269\) 13.8205 + 23.9379i 0.842653 + 1.45952i 0.887644 + 0.460531i \(0.152341\pi\)
−0.0449907 + 0.998987i \(0.514326\pi\)
\(270\) −2.28108 + 11.3928i −0.138822 + 0.693346i
\(271\) −2.56520 + 4.44305i −0.155825 + 0.269896i −0.933359 0.358944i \(-0.883137\pi\)
0.777534 + 0.628840i \(0.216470\pi\)
\(272\) 1.02522 + 1.02522i 0.0621633 + 0.0621633i
\(273\) 13.1063 16.7525i 0.793227 1.01391i
\(274\) 11.2071i 0.677047i
\(275\) 10.0443 3.38512i 0.605694 0.204130i
\(276\) 9.15220 + 3.67511i 0.550898 + 0.221215i
\(277\) 26.6082 + 7.12965i 1.59873 + 0.428379i 0.944659 0.328053i \(-0.106392\pi\)
0.654073 + 0.756432i \(0.273059\pi\)
\(278\) −5.21087 19.4472i −0.312527 1.16637i
\(279\) −3.07750 0.753417i −0.184245 0.0451059i
\(280\) 2.32612 + 5.43959i 0.139012 + 0.325078i
\(281\) 19.8830i 1.18612i 0.805157 + 0.593062i \(0.202081\pi\)
−0.805157 + 0.593062i \(0.797919\pi\)
\(282\) 11.5594 15.4079i 0.688351 0.917526i
\(283\) 1.36944 5.11082i 0.0814048 0.303807i −0.913204 0.407502i \(-0.866400\pi\)
0.994609 + 0.103695i \(0.0330666\pi\)
\(284\) −0.879690 1.52367i −0.0522000 0.0904131i
\(285\) 20.6268 + 4.59770i 1.22183 + 0.272344i
\(286\) 9.83949 0.581821
\(287\) 4.74593 + 1.37518i 0.280143 + 0.0811746i
\(288\) −1.55604 2.56491i −0.0916904 0.151139i
\(289\) 12.9019 + 7.44892i 0.758935 + 0.438172i
\(290\) −15.8991 + 2.60711i −0.933626 + 0.153094i
\(291\) 7.88070 19.6255i 0.461975 1.15047i
\(292\) −0.323412 1.20699i −0.0189263 0.0706338i
\(293\) −21.3392 + 21.3392i −1.24665 + 1.24665i −0.289456 + 0.957191i \(0.593474\pi\)
−0.957191 + 0.289456i \(0.906526\pi\)
\(294\) 12.0622 1.22583i 0.703483 0.0714917i
\(295\) 4.85457 + 10.7455i 0.282644 + 0.625626i
\(296\) −5.58163 3.22256i −0.324426 0.187307i
\(297\) 1.79253 + 10.8684i 0.104013 + 0.630647i
\(298\) −3.05671 + 11.4078i −0.177070 + 0.660835i
\(299\) 13.2147 22.8886i 0.764228 1.32368i
\(300\) −6.46139 + 5.76632i −0.373048 + 0.332919i
\(301\) −5.87645 + 3.23601i −0.338713 + 0.186521i
\(302\) 6.12855 + 6.12855i 0.352658 + 0.352658i
\(303\) −4.59670 + 6.12709i −0.264073 + 0.351992i
\(304\) −4.72549 + 2.72826i −0.271025 + 0.156477i
\(305\) 10.7449 14.9599i 0.615251 0.856603i
\(306\) 3.14170 + 3.00819i 0.179599 + 0.171967i
\(307\) 17.8595 17.8595i 1.01929 1.01929i 0.0194830 0.999810i \(-0.493798\pi\)
0.999810 0.0194830i \(-0.00620203\pi\)
\(308\) 3.88486 + 4.04537i 0.221360 + 0.230506i
\(309\) 14.5897 11.4488i 0.829978 0.651297i
\(310\) −1.49617 1.82715i −0.0849766 0.103775i
\(311\) −13.1923 + 7.61659i −0.748068 + 0.431897i −0.824996 0.565139i \(-0.808822\pi\)
0.0769272 + 0.997037i \(0.475489\pi\)
\(312\) −7.39359 + 3.15697i −0.418580 + 0.178728i
\(313\) 22.0349 5.90424i 1.24549 0.333727i 0.424895 0.905243i \(-0.360311\pi\)
0.820591 + 0.571515i \(0.193644\pi\)
\(314\) −17.4573 −0.985172
\(315\) 7.33090 + 16.1635i 0.413050 + 0.910709i
\(316\) 15.9827 0.899099
\(317\) 4.77643 1.27984i 0.268271 0.0718830i −0.122176 0.992508i \(-0.538987\pi\)
0.390447 + 0.920625i \(0.372321\pi\)
\(318\) 10.6820 4.56106i 0.599015 0.255771i
\(319\) −13.2279 + 7.63712i −0.740619 + 0.427596i
\(320\) 0.221605 2.22506i 0.0123881 0.124385i
\(321\) −14.5471 + 11.4153i −0.811940 + 0.637142i
\(322\) 14.6278 3.60389i 0.815177 0.200837i
\(323\) 5.59416 5.59416i 0.311267 0.311267i
\(324\) −4.83403 7.59159i −0.268557 0.421755i
\(325\) 12.8513 + 19.3246i 0.712862 + 1.07194i
\(326\) −4.51534 + 2.60693i −0.250081 + 0.144385i
\(327\) −8.90715 + 11.8726i −0.492567 + 0.656558i
\(328\) −1.32058 1.32058i −0.0729167 0.0729167i
\(329\) 0.595415 29.4171i 0.0328263 1.62181i
\(330\) −3.79943 + 7.27822i −0.209152 + 0.400653i
\(331\) 0.118156 0.204653i 0.00649446 0.0112487i −0.862760 0.505614i \(-0.831266\pi\)
0.869254 + 0.494365i \(0.164599\pi\)
\(332\) 3.46885 12.9459i 0.190378 0.710500i
\(333\) −16.9508 9.30195i −0.928898 0.509744i
\(334\) −7.34183 4.23880i −0.401727 0.231937i
\(335\) 19.7166 + 7.44542i 1.07723 + 0.406787i
\(336\) −4.21710 1.79333i −0.230062 0.0978341i
\(337\) −0.442376 + 0.442376i −0.0240977 + 0.0240977i −0.719053 0.694955i \(-0.755424\pi\)
0.694955 + 0.719053i \(0.255424\pi\)
\(338\) 2.21132 + 8.25275i 0.120280 + 0.448890i
\(339\) 6.50329 16.1953i 0.353210 0.879608i
\(340\) 0.524618 + 3.19932i 0.0284514 + 0.173507i
\(341\) −1.93891 1.11943i −0.104998 0.0606204i
\(342\) −13.9955 + 8.49056i −0.756789 + 0.459117i
\(343\) 13.8663 12.2771i 0.748708 0.662900i
\(344\) 2.53559 0.136710
\(345\) 11.8278 + 18.6131i 0.636790 + 1.00210i
\(346\) −2.50658 4.34153i −0.134755 0.233402i
\(347\) 1.05651 3.94296i 0.0567166 0.211669i −0.931752 0.363095i \(-0.881720\pi\)
0.988469 + 0.151426i \(0.0483866\pi\)
\(348\) 7.48935 9.98280i 0.401471 0.535134i
\(349\) 11.9140i 0.637743i 0.947798 + 0.318871i \(0.103304\pi\)
−0.947798 + 0.318871i \(0.896696\pi\)
\(350\) −2.87106 + 12.9134i −0.153465 + 0.690253i
\(351\) −21.9700 + 9.95010i −1.17267 + 0.531097i
\(352\) −0.548664 2.04764i −0.0292439 0.109140i
\(353\) −6.82920 1.82988i −0.363482 0.0973946i 0.0724557 0.997372i \(-0.476916\pi\)
−0.435937 + 0.899977i \(0.643583\pi\)
\(354\) −8.47562 3.40342i −0.450474 0.180890i
\(355\) 0.389887 3.91473i 0.0206930 0.207772i
\(356\) 0.399872i 0.0211931i
\(357\) 6.57894 + 0.929023i 0.348194 + 0.0491691i
\(358\) 5.72174 + 5.72174i 0.302403 + 0.302403i
\(359\) 4.55001 7.88085i 0.240140 0.415935i −0.720614 0.693337i \(-0.756140\pi\)
0.960754 + 0.277401i \(0.0894732\pi\)
\(360\) 0.519773 6.68804i 0.0273945 0.352490i
\(361\) 5.38683 + 9.33027i 0.283518 + 0.491067i
\(362\) 10.3302 2.76797i 0.542943 0.145481i
\(363\) 1.34955 11.1878i 0.0708329 0.587209i
\(364\) −6.35414 + 10.5087i −0.333047 + 0.550804i
\(365\) 0.987086 2.61396i 0.0516665 0.136821i
\(366\) 2.01564 + 14.1240i 0.105359 + 0.738275i
\(367\) −10.6737 2.86001i −0.557163 0.149291i −0.0307603 0.999527i \(-0.509793\pi\)
−0.526403 + 0.850235i \(0.676460\pi\)
\(368\) −5.50010 1.47375i −0.286713 0.0768244i
\(369\) −4.04679 3.87481i −0.210667 0.201715i
\(370\) −5.93347 13.1336i −0.308466 0.682784i
\(371\) 9.18020 15.1825i 0.476612 0.788236i
\(372\) 1.81610 + 0.219070i 0.0941603 + 0.0113582i
\(373\) −33.1354 + 8.87861i −1.71569 + 0.459717i −0.976807 0.214120i \(-0.931312\pi\)
−0.738880 + 0.673837i \(0.764645\pi\)
\(374\) 1.53679 + 2.66180i 0.0794655 + 0.137638i
\(375\) −19.2567 + 2.04402i −0.994414 + 0.105553i
\(376\) −5.56044 + 9.63096i −0.286758 + 0.496679i
\(377\) −23.6481 23.6481i −1.21794 1.21794i
\(378\) −12.7651 5.10413i −0.656566 0.262528i
\(379\) 17.2109i 0.884063i −0.897000 0.442031i \(-0.854258\pi\)
0.897000 0.442031i \(-0.145742\pi\)
\(380\) −12.1411 1.20919i −0.622825 0.0620302i
\(381\) 10.3023 25.6561i 0.527804 1.31440i
\(382\) −0.722383 0.193562i −0.0369604 0.00990350i
\(383\) 4.92466 + 18.3791i 0.251639 + 0.939128i 0.969930 + 0.243385i \(0.0782579\pi\)
−0.718291 + 0.695743i \(0.755075\pi\)
\(384\) 1.06926 + 1.36260i 0.0545653 + 0.0695351i
\(385\) 1.77855 + 12.4146i 0.0906431 + 0.632707i
\(386\) 9.25799i 0.471220i
\(387\) 7.60498 0.165104i 0.386583 0.00839270i
\(388\) −3.16023 + 11.7941i −0.160436 + 0.598756i
\(389\) 18.4175 + 31.9000i 0.933804 + 1.61740i 0.776752 + 0.629806i \(0.216866\pi\)
0.157052 + 0.987590i \(0.449801\pi\)
\(390\) −17.5460 3.91099i −0.888476 0.198041i
\(391\) 8.25583 0.417515
\(392\) −6.82925 + 1.53665i −0.344929 + 0.0776126i
\(393\) 9.95650 + 1.20102i 0.502239 + 0.0605833i
\(394\) 3.32367 + 1.91892i 0.167444 + 0.0966739i
\(395\) 29.0271 + 20.8486i 1.46051 + 1.04901i
\(396\) −1.77894 6.10576i −0.0893949 0.306826i
\(397\) −5.18227 19.3405i −0.260091 0.970672i −0.965187 0.261561i \(-0.915763\pi\)
0.705096 0.709112i \(-0.250904\pi\)
\(398\) −3.96399 + 3.96399i −0.198697 + 0.198697i
\(399\) −9.78535 + 23.0107i −0.489880 + 1.15198i
\(400\) 3.30494 3.75198i 0.165247 0.187599i
\(401\) −9.00824 5.20091i −0.449850 0.259721i 0.257917 0.966167i \(-0.416964\pi\)
−0.707767 + 0.706446i \(0.750297\pi\)
\(402\) −15.0137 + 6.41065i −0.748815 + 0.319734i
\(403\) 1.26874 4.73502i 0.0632006 0.235868i
\(404\) 2.21116 3.82984i 0.110009 0.190542i
\(405\) 1.12346 20.0932i 0.0558254 0.998441i
\(406\) 0.385771 19.0594i 0.0191455 0.945901i
\(407\) −9.66109 9.66109i −0.478883 0.478883i
\(408\) −2.00880 1.50705i −0.0994506 0.0746103i
\(409\) 13.4035 7.73849i 0.662758 0.382644i −0.130569 0.991439i \(-0.541680\pi\)
0.793327 + 0.608796i \(0.208347\pi\)
\(410\) −0.675754 4.12099i −0.0333731 0.203521i
\(411\) −2.74240 19.2166i −0.135273 0.947886i
\(412\) −7.57114 + 7.57114i −0.373003 + 0.373003i
\(413\) −13.5465 + 3.33747i −0.666577 + 0.164226i
\(414\) −16.5924 4.06206i −0.815471 0.199640i
\(415\) 23.1872 18.9869i 1.13822 0.932030i
\(416\) 4.01969 2.32077i 0.197082 0.113785i
\(417\) 13.6937 + 32.0706i 0.670586 + 1.57051i
\(418\) −11.1730 + 2.99380i −0.546490 + 0.146432i
\(419\) 14.9110 0.728451 0.364225 0.931311i \(-0.381334\pi\)
0.364225 + 0.931311i \(0.381334\pi\)
\(420\) −5.31962 8.75795i −0.259571 0.427344i
\(421\) −16.5292 −0.805586 −0.402793 0.915291i \(-0.631960\pi\)
−0.402793 + 0.915291i \(0.631960\pi\)
\(422\) 14.3389 3.84211i 0.698009 0.187031i
\(423\) −16.0503 + 29.2482i −0.780391 + 1.42209i
\(424\) −5.80749 + 3.35295i −0.282036 + 0.162834i
\(425\) −3.22054 + 6.49479i −0.156219 + 0.315044i
\(426\) 1.88123 + 2.39734i 0.0911459 + 0.116151i
\(427\) 15.0953 + 15.7190i 0.730511 + 0.760694i
\(428\) 7.54904 7.54904i 0.364897 0.364897i
\(429\) −16.8716 + 2.40774i −0.814566 + 0.116247i
\(430\) 4.60503 + 3.30754i 0.222074 + 0.159504i
\(431\) 6.60065 3.81089i 0.317942 0.183564i −0.332533 0.943092i \(-0.607903\pi\)
0.650475 + 0.759528i \(0.274570\pi\)
\(432\) 3.29574 + 4.01722i 0.158566 + 0.193279i
\(433\) −7.94117 7.94117i −0.381628 0.381628i 0.490060 0.871689i \(-0.336975\pi\)
−0.871689 + 0.490060i \(0.836975\pi\)
\(434\) 2.44767 1.34787i 0.117492 0.0646997i
\(435\) 26.6238 8.36088i 1.27652 0.400874i
\(436\) 4.28463 7.42120i 0.205197 0.355411i
\(437\) −8.04154 + 30.0114i −0.384679 + 1.43564i
\(438\) 0.849901 + 1.99046i 0.0406098 + 0.0951079i
\(439\) 11.5080 + 6.64413i 0.549245 + 0.317107i 0.748818 0.662776i \(-0.230622\pi\)
−0.199572 + 0.979883i \(0.563955\pi\)
\(440\) 1.67458 4.43454i 0.0798324 0.211409i
\(441\) −20.3829 + 5.05355i −0.970613 + 0.240645i
\(442\) −4.75862 + 4.75862i −0.226344 + 0.226344i
\(443\) 6.35418 + 23.7141i 0.301896 + 1.12669i 0.935584 + 0.353104i \(0.114874\pi\)
−0.633688 + 0.773589i \(0.718460\pi\)
\(444\) 10.3593 + 4.15981i 0.491629 + 0.197416i
\(445\) −0.521610 + 0.726229i −0.0247267 + 0.0344266i
\(446\) 6.15816 + 3.55542i 0.291597 + 0.168354i
\(447\) 2.44976 20.3087i 0.115870 0.960566i
\(448\) 2.54122 + 0.736347i 0.120061 + 0.0347891i
\(449\) −5.93549 −0.280113 −0.140056 0.990144i \(-0.544728\pi\)
−0.140056 + 0.990144i \(0.544728\pi\)
\(450\) 9.66817 11.4685i 0.455762 0.540630i
\(451\) −1.97952 3.42863i −0.0932119 0.161448i
\(452\) −2.60787 + 9.73272i −0.122664 + 0.457789i
\(453\) −12.0082 9.00882i −0.564192 0.423271i
\(454\) 11.6375i 0.546175i
\(455\) −25.2481 + 10.7968i −1.18365 + 0.506160i
\(456\) 7.43508 5.83443i 0.348180 0.273222i
\(457\) −2.69512 10.0583i −0.126072 0.470508i 0.873803 0.486280i \(-0.161646\pi\)
−0.999876 + 0.0157712i \(0.994980\pi\)
\(458\) −3.99505 1.07047i −0.186676 0.0500198i
\(459\) −6.12312 4.38930i −0.285803 0.204875i
\(460\) −8.06662 9.85113i −0.376108 0.459312i
\(461\) 32.7232i 1.52407i −0.647535 0.762035i \(-0.724200\pi\)
0.647535 0.762035i \(-0.275800\pi\)
\(462\) −7.65119 5.98587i −0.355966 0.278488i
\(463\) 6.59995 + 6.59995i 0.306726 + 0.306726i 0.843638 0.536912i \(-0.180409\pi\)
−0.536912 + 0.843638i \(0.680409\pi\)
\(464\) −3.60262 + 6.23993i −0.167248 + 0.289681i
\(465\) 3.01255 + 2.76687i 0.139704 + 0.128310i
\(466\) −11.3521 19.6623i −0.525874 0.910841i
\(467\) 0.776556 0.208078i 0.0359347 0.00962868i −0.240807 0.970573i \(-0.577412\pi\)
0.276742 + 0.960944i \(0.410745\pi\)
\(468\) 11.9051 7.22241i 0.550314 0.333856i
\(469\) −12.9029 + 21.3393i −0.595803 + 0.985357i
\(470\) −22.6617 + 10.2380i −1.04531 + 0.472246i
\(471\) 29.9336 4.27183i 1.37927 0.196836i
\(472\) 5.09350 + 1.36480i 0.234447 + 0.0628200i
\(473\) 5.19198 + 1.39119i 0.238728 + 0.0639669i
\(474\) −27.4052 + 3.91100i −1.25876 + 0.179638i
\(475\) −20.4728 18.0335i −0.939357 0.827432i
\(476\) −3.83525 0.0776272i −0.175788 0.00355804i
\(477\) −17.2000 + 10.4346i −0.787535 + 0.477770i
\(478\) −10.2541 + 2.74758i −0.469013 + 0.125672i
\(479\) −8.48718 14.7002i −0.387789 0.671670i 0.604363 0.796709i \(-0.293428\pi\)
−0.992152 + 0.125039i \(0.960094\pi\)
\(480\) 0.164496 + 3.86949i 0.00750818 + 0.176617i
\(481\) 14.9576 25.9074i 0.682009 1.18127i
\(482\) 14.2319 + 14.2319i 0.648245 + 0.648245i
\(483\) −24.2001 + 9.75897i −1.10114 + 0.444049i
\(484\) 6.50612i 0.295733i
\(485\) −21.1243 + 17.2976i −0.959203 + 0.785445i
\(486\) 10.1465 + 11.8342i 0.460253 + 0.536812i
\(487\) 15.4471 + 4.13903i 0.699974 + 0.187557i 0.591219 0.806511i \(-0.298647\pi\)
0.108755 + 0.994069i \(0.465314\pi\)
\(488\) −2.13193 7.95646i −0.0965078 0.360172i
\(489\) 7.10443 5.57496i 0.321273 0.252108i
\(490\) −14.4075 6.11759i −0.650863 0.276365i
\(491\) 6.87591i 0.310305i −0.987891 0.155153i \(-0.950413\pi\)
0.987891 0.155153i \(-0.0495869\pi\)
\(492\) 2.58751 + 1.94122i 0.116654 + 0.0875168i
\(493\) 2.70383 10.0908i 0.121774 0.454468i
\(494\) −12.6633 21.9335i −0.569750 0.986837i
\(495\) 4.73380 13.4095i 0.212768 0.602714i
\(496\) −1.05613 −0.0474215
\(497\) 4.47097 + 1.29551i 0.200550 + 0.0581117i
\(498\) −2.78007 + 23.0469i −0.124578 + 1.03276i
\(499\) −26.8381 15.4950i −1.20144 0.693651i −0.240564 0.970633i \(-0.577332\pi\)
−0.960875 + 0.276982i \(0.910666\pi\)
\(500\) 10.8965 2.50308i 0.487308 0.111941i
\(501\) 13.6261 + 5.47163i 0.608770 + 0.244454i
\(502\) 4.61720 + 17.2316i 0.206076 + 0.769085i
\(503\) −19.3755 + 19.3755i −0.863913 + 0.863913i −0.991790 0.127877i \(-0.959184\pi\)
0.127877 + 0.991790i \(0.459184\pi\)
\(504\) 7.66981 + 2.04305i 0.341640 + 0.0910046i
\(505\) 9.01164 4.07126i 0.401013 0.181168i
\(506\) −10.4537 6.03542i −0.464722 0.268307i
\(507\) −5.81116 13.6097i −0.258083 0.604428i
\(508\) −4.13131 + 15.4183i −0.183297 + 0.684075i
\(509\) 10.4397 18.0821i 0.462733 0.801477i −0.536363 0.843987i \(-0.680202\pi\)
0.999096 + 0.0425105i \(0.0135356\pi\)
\(510\) −1.68243 5.35742i −0.0744993 0.237231i
\(511\) 2.82909 + 1.71063i 0.125151 + 0.0756736i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 21.9201 17.9833i 0.967795 0.793982i
\(514\) 0.863752 0.498688i 0.0380985 0.0219962i
\(515\) −23.6265 + 3.87423i −1.04111 + 0.170719i
\(516\) −4.34772 + 0.620464i −0.191398 + 0.0273144i
\(517\) −16.6700 + 16.6700i −0.733144 + 0.733144i
\(518\) 16.5571 4.07921i 0.727476 0.179230i
\(519\) 5.36037 + 6.83096i 0.235294 + 0.299846i
\(520\) 10.3277 + 1.02859i 0.452900 + 0.0451065i
\(521\) −18.9520 + 10.9419i −0.830300 + 0.479374i −0.853956 0.520346i \(-0.825803\pi\)
0.0236551 + 0.999720i \(0.492470\pi\)
\(522\) −10.3990 + 18.9500i −0.455152 + 0.829417i
\(523\) 12.6632 3.39310i 0.553724 0.148370i 0.0289028 0.999582i \(-0.490799\pi\)
0.524822 + 0.851212i \(0.324132\pi\)
\(524\) −5.79006 −0.252940
\(525\) 1.76300 22.8450i 0.0769437 0.997035i
\(526\) 17.2603 0.752586
\(527\) 1.47909 0.396320i 0.0644300 0.0172640i
\(528\) 1.44185 + 3.37679i 0.0627483 + 0.146956i
\(529\) −8.16059 + 4.71152i −0.354808 + 0.204849i
\(530\) −14.9210 1.48606i −0.648129 0.0645503i
\(531\) 15.3658 + 3.76177i 0.666818 + 0.163247i
\(532\) 4.01789 13.8662i 0.174198 0.601177i
\(533\) 6.12951 6.12951i 0.265499 0.265499i
\(534\) −0.0978493 0.685651i −0.00423435 0.0296710i
\(535\) 23.5576 3.86293i 1.01848 0.167009i
\(536\) 8.16253 4.71264i 0.352568 0.203555i
\(537\) −11.2111 8.41082i −0.483793 0.362954i
\(538\) 19.5452 + 19.5452i 0.842653 + 0.842653i
\(539\) −14.8270 0.600456i −0.638643 0.0258635i
\(540\) 0.745331 + 11.5950i 0.0320740 + 0.498970i
\(541\) −11.6807 + 20.2316i −0.502194 + 0.869826i 0.497803 + 0.867290i \(0.334140\pi\)
−0.999997 + 0.00253553i \(0.999193\pi\)
\(542\) −1.32784 + 4.95558i −0.0570358 + 0.212860i
\(543\) −17.0356 + 7.27399i −0.731069 + 0.312157i
\(544\) 1.25564 + 0.724943i 0.0538350 + 0.0310817i
\(545\) 17.4621 7.88899i 0.747995 0.337927i
\(546\) 8.32381 19.5738i 0.356226 0.837683i
\(547\) −2.60152 + 2.60152i −0.111233 + 0.111233i −0.760533 0.649300i \(-0.775062\pi\)
0.649300 + 0.760533i \(0.275062\pi\)
\(548\) 2.90062 + 10.8253i 0.123908 + 0.462432i
\(549\) −6.91236 23.7249i −0.295012 1.01256i
\(550\) 8.82591 5.86943i 0.376338 0.250273i
\(551\) 34.0483 + 19.6578i 1.45051 + 0.837451i
\(552\) 9.79153 + 1.18112i 0.416755 + 0.0502717i
\(553\) −30.4999 + 29.2897i −1.29699 + 1.24553i
\(554\) 27.5468 1.17035
\(555\) 13.3878 + 21.0680i 0.568281 + 0.894286i
\(556\) −10.0666 17.4359i −0.426920 0.739448i
\(557\) 9.87848 36.8670i 0.418565 1.56211i −0.359022 0.933329i \(-0.616890\pi\)
0.777587 0.628776i \(-0.216444\pi\)
\(558\) −3.16763 + 0.0687692i −0.134097 + 0.00291123i
\(559\) 11.7690i 0.497777i
\(560\) 3.65473 + 4.65220i 0.154440 + 0.196591i
\(561\) −3.28645 4.18807i −0.138754 0.176820i
\(562\) 5.14611 + 19.2055i 0.217076 + 0.810137i
\(563\) −3.84263 1.02963i −0.161948 0.0433937i 0.176934 0.984223i \(-0.443382\pi\)
−0.338882 + 0.940829i \(0.610049\pi\)
\(564\) 7.17765 17.8747i 0.302234 0.752659i
\(565\) −17.4321 + 14.2743i −0.733374 + 0.600525i
\(566\) 5.29112i 0.222402i
\(567\) 23.1370 + 5.62829i 0.971664 + 0.236366i
\(568\) −1.24407 1.24407i −0.0522000 0.0522000i
\(569\) 2.50482 4.33847i 0.105007 0.181878i −0.808734 0.588175i \(-0.799847\pi\)
0.913741 + 0.406297i \(0.133180\pi\)
\(570\) 21.1140 0.897576i 0.884367 0.0375953i
\(571\) −16.4609 28.5111i −0.688867 1.19315i −0.972205 0.234132i \(-0.924775\pi\)
0.283338 0.959020i \(-0.408558\pi\)
\(572\) 9.50422 2.54665i 0.397391 0.106481i
\(573\) 1.28602 + 0.155128i 0.0537243 + 0.00648057i
\(574\) 4.94014 + 0.0999906i 0.206197 + 0.00417353i
\(575\) −1.79997 28.4137i −0.0750641 1.18493i
\(576\) −2.16686 2.07478i −0.0902860 0.0864491i
\(577\) −22.0443 5.90675i −0.917716 0.245901i −0.231107 0.972928i \(-0.574235\pi\)
−0.686609 + 0.727027i \(0.740901\pi\)
\(578\) 14.3902 + 3.85584i 0.598553 + 0.160382i
\(579\) 2.26545 + 15.8745i 0.0941489 + 0.659721i
\(580\) −14.6826 + 6.63326i −0.609660 + 0.275431i
\(581\) 17.1049 + 31.0617i 0.709631 + 1.28866i
\(582\) 2.53273 20.9964i 0.104985 0.870330i
\(583\) −13.7313 + 3.67929i −0.568693 + 0.152381i
\(584\) −0.624785 1.08216i −0.0258538 0.0447800i
\(585\) 31.0428 + 2.41255i 1.28346 + 0.0997466i
\(586\) −15.0891 + 26.1350i −0.623324 + 1.07963i
\(587\) 29.3071 + 29.3071i 1.20963 + 1.20963i 0.971145 + 0.238489i \(0.0766522\pi\)
0.238489 + 0.971145i \(0.423348\pi\)
\(588\) 11.3340 4.30599i 0.467404 0.177576i
\(589\) 5.76278i 0.237451i
\(590\) 7.47029 + 9.12288i 0.307547 + 0.375583i
\(591\) −6.16859 2.47702i −0.253742 0.101891i
\(592\) −6.22550 1.66812i −0.255867 0.0685593i
\(593\) 5.64362 + 21.0623i 0.231756 + 0.864925i 0.979584 + 0.201033i \(0.0644298\pi\)
−0.747829 + 0.663892i \(0.768904\pi\)
\(594\) 4.54439 + 10.0341i 0.186459 + 0.411704i
\(595\) −6.86415 5.14386i −0.281403 0.210878i
\(596\) 11.8102i 0.483765i
\(597\) 5.82698 7.76697i 0.238482 0.317881i
\(598\) 6.84045 25.5289i 0.279727 1.04396i
\(599\) −6.91835 11.9829i −0.282676 0.489610i 0.689367 0.724413i \(-0.257889\pi\)
−0.972043 + 0.234803i \(0.924556\pi\)
\(600\) −4.74879 + 7.24217i −0.193868 + 0.295660i
\(601\) 7.92094 0.323102 0.161551 0.986864i \(-0.448350\pi\)
0.161551 + 0.986864i \(0.448350\pi\)
\(602\) −4.83868 + 4.64669i −0.197210 + 0.189385i
\(603\) 24.1750 14.6661i 0.984481 0.597249i
\(604\) 7.50591 + 4.33354i 0.305411 + 0.176329i
\(605\) −8.48688 + 11.8161i −0.345041 + 0.480394i
\(606\) −2.85426 + 7.10802i −0.115946 + 0.288744i
\(607\) 8.55795 + 31.9387i 0.347356 + 1.29635i 0.889835 + 0.456282i \(0.150819\pi\)
−0.542479 + 0.840070i \(0.682514\pi\)
\(608\) −3.85835 + 3.85835i −0.156477 + 0.156477i
\(609\) 4.00240 + 32.7751i 0.162185 + 1.32811i
\(610\) 6.50685 17.2312i 0.263455 0.697669i
\(611\) −44.7025 25.8090i −1.80847 1.04412i
\(612\) 3.81323 + 2.09256i 0.154141 + 0.0845866i
\(613\) 2.45744 9.17128i 0.0992549 0.370424i −0.898375 0.439229i \(-0.855252\pi\)
0.997630 + 0.0688043i \(0.0219184\pi\)
\(614\) 12.6285 21.8733i 0.509647 0.882734i
\(615\) 2.16712 + 6.90082i 0.0873865 + 0.278268i
\(616\) 4.79950 + 2.90205i 0.193378 + 0.116927i
\(617\) 13.7827 + 13.7827i 0.554873 + 0.554873i 0.927843 0.372971i \(-0.121661\pi\)
−0.372971 + 0.927843i \(0.621661\pi\)
\(618\) 11.1294 14.8347i 0.447690 0.596741i
\(619\) −6.45537 + 3.72701i −0.259463 + 0.149801i −0.624090 0.781353i \(-0.714530\pi\)
0.364626 + 0.931154i \(0.381197\pi\)
\(620\) −1.91809 1.37766i −0.0770323 0.0553281i
\(621\) 29.4446 + 2.90495i 1.18157 + 0.116571i
\(622\) −10.7715 + 10.7715i −0.431897 + 0.431897i
\(623\) −0.732799 0.763077i −0.0293590 0.0305720i
\(624\) −6.32458 + 4.96300i −0.253186 + 0.198679i
\(625\) 23.0549 + 9.66795i 0.922198 + 0.386718i
\(626\) 19.7560 11.4061i 0.789607 0.455880i
\(627\) 18.4255 7.86747i 0.735845 0.314196i
\(628\) −16.8625 + 4.51828i −0.672885 + 0.180299i
\(629\) 9.34468 0.372597
\(630\) 11.2645 + 13.7153i 0.448789 + 0.546432i
\(631\) −49.0067 −1.95093 −0.975463 0.220162i \(-0.929342\pi\)
−0.975463 + 0.220162i \(0.929342\pi\)
\(632\) 15.4381 4.13664i 0.614096 0.164547i
\(633\) −23.6465 + 10.0967i −0.939864 + 0.401310i
\(634\) 4.28243 2.47246i 0.170077 0.0981940i
\(635\) −27.6154 + 22.6129i −1.09588 + 0.897366i
\(636\) 9.13750 7.17034i 0.362325 0.284322i
\(637\) −7.13242 31.6982i −0.282597 1.25593i
\(638\) −10.8005 + 10.8005i −0.427596 + 0.427596i
\(639\) −3.81234 3.65032i −0.150814 0.144405i
\(640\) −0.361834 2.20660i −0.0143028 0.0872235i
\(641\) 20.1256 11.6195i 0.794915 0.458944i −0.0467751 0.998905i \(-0.514894\pi\)
0.841690 + 0.539961i \(0.181561\pi\)
\(642\) −11.0969 + 14.7914i −0.437960 + 0.583772i
\(643\) 15.5301 + 15.5301i 0.612445 + 0.612445i 0.943583 0.331137i \(-0.107432\pi\)
−0.331137 + 0.943583i \(0.607432\pi\)
\(644\) 13.1966 7.26705i 0.520020 0.286362i
\(645\) −8.70550 4.54450i −0.342779 0.178940i
\(646\) 3.95567 6.85142i 0.155634 0.269565i
\(647\) 11.1785 41.7186i 0.439471 1.64013i −0.290663 0.956825i \(-0.593876\pi\)
0.730135 0.683303i \(-0.239457\pi\)
\(648\) −6.63416 6.08177i −0.260614 0.238915i
\(649\) 9.68086 + 5.58925i 0.380007 + 0.219397i
\(650\) 17.4150 + 15.3400i 0.683072 + 0.601684i
\(651\) −3.86713 + 2.91011i −0.151565 + 0.114056i
\(652\) −3.68676 + 3.68676i −0.144385 + 0.144385i
\(653\) −6.47076 24.1492i −0.253220 0.945031i −0.969072 0.246778i \(-0.920628\pi\)
0.715852 0.698252i \(-0.246039\pi\)
\(654\) −5.53078 + 13.7734i −0.216271 + 0.538584i
\(655\) −10.5156 7.55281i −0.410880 0.295113i
\(656\) −1.61737 0.933789i −0.0631477 0.0364583i
\(657\) −1.94438 3.20503i −0.0758573 0.125040i
\(658\) −7.03857 28.5688i −0.274392 1.11373i
\(659\) −20.0343 −0.780425 −0.390213 0.920725i \(-0.627599\pi\)
−0.390213 + 0.920725i \(0.627599\pi\)
\(660\) −1.78622 + 8.01359i −0.0695286 + 0.311928i
\(661\) −6.62569 11.4760i −0.257709 0.446366i 0.707918 0.706294i \(-0.249634\pi\)
−0.965628 + 0.259928i \(0.916301\pi\)
\(662\) 0.0611622 0.228261i 0.00237714 0.00887160i
\(663\) 6.99505 9.32394i 0.271665 0.362112i
\(664\) 13.4026i 0.520122i
\(665\) 25.3849 19.9421i 0.984382 0.773322i
\(666\) −18.7807 4.59781i −0.727739 0.178161i
\(667\) 10.6187 + 39.6296i 0.411158 + 1.53446i
\(668\) −8.18874 2.19417i −0.316832 0.0848949i
\(669\) −11.4293 4.58948i −0.441882 0.177440i
\(670\) 20.9718 + 2.08869i 0.810212 + 0.0806930i
\(671\) 17.4617i 0.674102i
\(672\) −4.53756 0.640756i −0.175040 0.0247177i
\(673\) −18.6445 18.6445i −0.718692 0.718692i 0.249645 0.968337i \(-0.419686\pi\)
−0.968337 + 0.249645i \(0.919686\pi\)
\(674\) −0.312807 + 0.541798i −0.0120489 + 0.0208693i
\(675\) −13.7714 + 22.0306i −0.530063 + 0.847959i
\(676\) 4.27194 + 7.39921i 0.164305 + 0.284585i
\(677\) −47.8038 + 12.8090i −1.83725 + 0.492290i −0.998625 0.0524196i \(-0.983307\pi\)
−0.838625 + 0.544709i \(0.816640\pi\)
\(678\) 2.09005 17.3266i 0.0802679 0.665425i
\(679\) −15.5831 28.2982i −0.598024 1.08598i
\(680\) 1.33479 + 2.95452i 0.0511867 + 0.113301i
\(681\) 2.84772 + 19.9546i 0.109125 + 0.764661i
\(682\) −2.16257 0.579459i −0.0828091 0.0221886i
\(683\) −9.58678 2.56877i −0.366828 0.0982913i 0.0706962 0.997498i \(-0.477478\pi\)
−0.437524 + 0.899207i \(0.644145\pi\)
\(684\) −11.3211 + 11.8235i −0.432872 + 0.452085i
\(685\) −8.85297 + 23.4440i −0.338255 + 0.895751i
\(686\) 10.2162 15.4476i 0.390058 0.589792i
\(687\) 7.11217 + 0.857916i 0.271346 + 0.0327315i
\(688\) 2.44919 0.656259i 0.0933746 0.0250196i
\(689\) −15.5629 26.9557i −0.592898 1.02693i
\(690\) 16.2422 + 14.9176i 0.618332 + 0.567904i
\(691\) −3.42873 + 5.93874i −0.130435 + 0.225920i −0.923844 0.382768i \(-0.874971\pi\)
0.793409 + 0.608689i \(0.208304\pi\)
\(692\) −3.54485 3.54485i −0.134755 0.134755i
\(693\) 14.5841 + 8.39159i 0.554004 + 0.318770i
\(694\) 4.08205i 0.154953i
\(695\) 4.46162 44.7977i 0.169239 1.69927i
\(696\) 4.65042 11.5810i 0.176274 0.438978i
\(697\) 2.61551 + 0.700824i 0.0990695 + 0.0265456i
\(698\) 3.08358 + 11.5081i 0.116715 + 0.435587i
\(699\) 24.2765 + 30.9367i 0.918223 + 1.17013i
\(700\) 0.569013 + 13.2165i 0.0215067 + 0.499537i
\(701\) 28.8845i 1.09095i 0.838127 + 0.545476i \(0.183651\pi\)
−0.838127 + 0.545476i \(0.816349\pi\)
\(702\) −18.6461 + 15.2973i −0.703752 + 0.577360i
\(703\) −9.10213 + 33.9696i −0.343293 + 1.28119i
\(704\) −1.05994 1.83587i −0.0399479 0.0691918i
\(705\) 36.3522 23.1003i 1.36910 0.870008i
\(706\) −7.07011 −0.266087
\(707\) 2.79895 + 11.3607i 0.105265 + 0.427261i
\(708\) −9.06769 1.09380i −0.340785 0.0411076i
\(709\) 21.3823 + 12.3450i 0.803027 + 0.463628i 0.844529 0.535510i \(-0.179881\pi\)
−0.0415013 + 0.999138i \(0.513214\pi\)
\(710\) −0.636604 3.88225i −0.0238913 0.145698i
\(711\) 46.0341 13.4122i 1.72641 0.502998i
\(712\) 0.103494 + 0.386246i 0.00387862 + 0.0144752i
\(713\) −4.25234 + 4.25234i −0.159251 + 0.159251i
\(714\) 6.59522 0.805388i 0.246820 0.0301409i
\(715\) 20.5831 + 7.77262i 0.769764 + 0.290679i
\(716\) 7.00767 + 4.04588i 0.261889 + 0.151202i
\(717\) 16.9102 7.22043i 0.631522 0.269652i
\(718\) 2.35526 8.78994i 0.0878975 0.328038i
\(719\) −11.2630 + 19.5080i −0.420038 + 0.727527i −0.995943 0.0899900i \(-0.971316\pi\)
0.575905 + 0.817517i \(0.304650\pi\)
\(720\) −1.22893 6.59467i −0.0457995 0.245769i
\(721\) 0.573266 28.3228i 0.0213496 1.05480i
\(722\) 7.61813 + 7.61813i 0.283518 + 0.283518i
\(723\) −27.8857 20.9205i −1.03708 0.778043i
\(724\) 9.26180 5.34730i 0.344212 0.198731i
\(725\) −35.3186 7.10558i −1.31170 0.263894i
\(726\) −1.59206 11.1559i −0.0590869 0.414035i
\(727\) 6.61815 6.61815i 0.245454 0.245454i −0.573648 0.819102i \(-0.694472\pi\)
0.819102 + 0.573648i \(0.194472\pi\)
\(728\) −3.41778 + 11.7952i −0.126671 + 0.437158i
\(729\) −20.2938 17.8090i −0.751622 0.659594i
\(730\) 0.276910 2.78037i 0.0102489 0.102906i
\(731\) −3.18378 + 1.83816i −0.117756 + 0.0679867i
\(732\) 5.60253 + 13.1211i 0.207075 + 0.484969i
\(733\) −1.86630 + 0.500074i −0.0689334 + 0.0184707i −0.293121 0.956075i \(-0.594694\pi\)
0.224188 + 0.974546i \(0.428027\pi\)
\(734\) −11.0502 −0.407872
\(735\) 26.2012 + 6.96416i 0.966444 + 0.256877i
\(736\) −5.69412 −0.209888
\(737\) 19.2996 5.17132i 0.710911 0.190488i
\(738\) −4.91177 2.69539i −0.180805 0.0992188i
\(739\) −9.70996 + 5.60605i −0.357187 + 0.206222i −0.667846 0.744299i \(-0.732784\pi\)
0.310659 + 0.950521i \(0.399450\pi\)
\(740\) −9.13052 11.1504i −0.335644 0.409897i
\(741\) 27.0807 + 34.5102i 0.994835 + 1.26776i
\(742\) 4.93787 17.0412i 0.181275 0.625601i
\(743\) −11.6014 + 11.6014i −0.425613 + 0.425613i −0.887131 0.461518i \(-0.847305\pi\)
0.461518 + 0.887131i \(0.347305\pi\)
\(744\) 1.81092 0.258436i 0.0663914 0.00947473i
\(745\) −15.4058 + 21.4492i −0.564424 + 0.785837i
\(746\) −29.7084 + 17.1522i −1.08770 + 0.627985i
\(747\) −0.872704 40.1983i −0.0319306 1.47078i
\(748\) 2.17335 + 2.17335i 0.0794655 + 0.0794655i
\(749\) −0.571594 + 28.2401i −0.0208856 + 1.03187i
\(750\) −18.0715 + 6.95838i −0.659880 + 0.254084i
\(751\) −6.85013 + 11.8648i −0.249965 + 0.432952i −0.963516 0.267652i \(-0.913752\pi\)
0.713551 + 0.700603i \(0.247086\pi\)
\(752\) −2.87830 + 10.7419i −0.104961 + 0.391718i
\(753\) −12.1336 28.4169i −0.442174 1.03557i
\(754\) −28.9629 16.7217i −1.05476 0.608969i
\(755\) 7.97904 + 17.6614i 0.290387 + 0.642765i
\(756\) −13.6512 1.62635i −0.496489 0.0591499i
\(757\) 28.3749 28.3749i 1.03130 1.03130i 0.0318111 0.999494i \(-0.489873\pi\)
0.999494 0.0318111i \(-0.0101275\pi\)
\(758\) −4.45450 16.6244i −0.161795 0.603826i
\(759\) 19.4015 + 7.79077i 0.704231 + 0.282787i
\(760\) −12.0404 + 1.97436i −0.436750 + 0.0716175i
\(761\) 4.58035 + 2.64447i 0.166038 + 0.0958618i 0.580716 0.814106i \(-0.302773\pi\)
−0.414679 + 0.909968i \(0.636106\pi\)
\(762\) 3.31099 27.4483i 0.119945 0.994347i
\(763\) 5.42361 + 22.0139i 0.196348 + 0.796956i
\(764\) −0.747866 −0.0270569
\(765\) 4.19580 + 8.77456i 0.151699 + 0.317245i
\(766\) 9.51372 + 16.4782i 0.343745 + 0.595383i
\(767\) −6.33477 + 23.6417i −0.228735 + 0.853652i
\(768\) 1.38549 + 1.03943i 0.0499946 + 0.0375072i
\(769\) 0.931143i 0.0335779i −0.999859 0.0167889i \(-0.994656\pi\)
0.999859 0.0167889i \(-0.00534434\pi\)
\(770\) 4.93108 + 11.5313i 0.177704 + 0.415558i
\(771\) −1.35903 + 1.06645i −0.0489442 + 0.0384073i
\(772\) −2.39615 8.94254i −0.0862392 0.321849i
\(773\) 11.1376 + 2.98432i 0.400593 + 0.107339i 0.453490 0.891261i \(-0.350179\pi\)
−0.0528969 + 0.998600i \(0.516845\pi\)
\(774\) 7.30311 2.12779i 0.262505 0.0764819i
\(775\) −1.68647 5.00409i −0.0605798 0.179752i
\(776\) 12.2102i 0.438320i
\(777\) −27.3919 + 11.0461i −0.982678 + 0.396276i
\(778\) 26.0463 + 26.0463i 0.933804 + 0.933804i
\(779\) −5.09524 + 8.82522i −0.182556 + 0.316196i
\(780\) −17.9604 + 0.763514i −0.643085 + 0.0273382i
\(781\) −1.86483 3.22999i −0.0667290 0.115578i
\(782\) 7.97452 2.13677i 0.285168 0.0764106i
\(783\) 13.1939 35.0377i 0.471510 1.25215i
\(784\) −6.19884 + 3.25183i −0.221387 + 0.116137i
\(785\) −36.5187 13.7902i −1.30341 0.492195i
\(786\) 9.92809 1.41684i 0.354123 0.0505370i
\(787\) −19.0519 5.10495i −0.679129 0.181972i −0.0972652 0.995258i \(-0.531010\pi\)
−0.581863 + 0.813287i \(0.697676\pi\)
\(788\) 3.70707 + 0.993307i 0.132059 + 0.0353851i
\(789\) −29.5959 + 4.22363i −1.05364 + 0.150365i
\(790\) 33.4341 + 12.6254i 1.18953 + 0.449192i
\(791\) −12.8594 23.3521i −0.457229 0.830307i
\(792\) −3.29861 5.43729i −0.117211 0.193206i
\(793\) 36.9302 9.89542i 1.31143 0.351397i
\(794\) −10.0114 17.3402i −0.355291 0.615382i
\(795\) 25.9484 1.10309i 0.920296 0.0391227i
\(796\) −2.80297 + 4.85488i −0.0993485 + 0.172077i
\(797\) 13.9935 + 13.9935i 0.495674 + 0.495674i 0.910088 0.414414i \(-0.136014\pi\)
−0.414414 + 0.910088i \(0.636014\pi\)
\(798\) −3.49630 + 24.7593i −0.123768 + 0.876470i
\(799\) 16.1240i 0.570426i
\(800\) 2.22124 4.47952i 0.0785327 0.158375i
\(801\) 0.335560 + 1.15173i 0.0118564 + 0.0406943i
\(802\) −10.0474 2.69219i −0.354786 0.0950645i
\(803\) −0.685594 2.55867i −0.0241941 0.0902936i
\(804\) −12.8429 + 10.0780i −0.452935 + 0.355425i
\(805\) 33.4466 + 4.01618i 1.17884 + 0.141552i
\(806\) 4.90205i 0.172667i
\(807\) −38.2965 28.7310i −1.34810 1.01138i
\(808\) 1.14458 4.27164i 0.0402662 0.150276i
\(809\) 12.8197 + 22.2044i 0.450717 + 0.780666i 0.998431 0.0560005i \(-0.0178349\pi\)
−0.547713 + 0.836666i \(0.684502\pi\)
\(810\) −4.11533 19.6993i −0.144598 0.692164i
\(811\) −11.0170 −0.386858 −0.193429 0.981114i \(-0.561961\pi\)
−0.193429 + 0.981114i \(0.561961\pi\)
\(812\) −4.56031 18.5098i −0.160035 0.649567i
\(813\) 1.06418 8.82215i 0.0373226 0.309406i
\(814\) −11.8324 6.83143i −0.414725 0.239441i
\(815\) −11.5049 + 1.88655i −0.402999 + 0.0660831i
\(816\) −2.33041 0.935787i −0.0815806 0.0327591i
\(817\) −3.58089 13.3641i −0.125280 0.467550i
\(818\) 10.9439 10.9439i 0.382644 0.382644i
\(819\) −9.48289 + 35.5997i −0.331359 + 1.24395i
\(820\) −1.71932 3.80568i −0.0600413 0.132900i
\(821\) −13.0985 7.56242i −0.457141 0.263930i 0.253700 0.967283i \(-0.418352\pi\)
−0.710841 + 0.703352i \(0.751686\pi\)
\(822\) −7.62258 17.8520i −0.265868 0.622661i
\(823\) 10.6131 39.6086i 0.369949 1.38067i −0.490637 0.871364i \(-0.663236\pi\)
0.860586 0.509305i \(-0.170097\pi\)
\(824\) −5.35360 + 9.27271i −0.186502 + 0.323030i
\(825\) −13.6973 + 12.2239i −0.476880 + 0.425581i
\(826\) −12.2211 + 6.72983i −0.425225 + 0.234161i
\(827\) −25.1800 25.1800i −0.875596 0.875596i 0.117480 0.993075i \(-0.462518\pi\)
−0.993075 + 0.117480i \(0.962518\pi\)
\(828\) −17.0783 + 0.370770i −0.593514 + 0.0128852i
\(829\) 25.3933 14.6608i 0.881944 0.509191i 0.0106454 0.999943i \(-0.496611\pi\)
0.871299 + 0.490752i \(0.163278\pi\)
\(830\) 17.4830 24.3412i 0.606842 0.844896i
\(831\) −47.2340 + 6.74076i −1.63853 + 0.233835i
\(832\) 3.28206 3.28206i 0.113785 0.113785i
\(833\) 7.46108 6.88029i 0.258511 0.238388i
\(834\) 21.5276 + 27.4337i 0.745441 + 0.949950i
\(835\) −12.0099 14.6667i −0.415618 0.507563i
\(836\) −10.0175 + 5.78358i −0.346461 + 0.200029i
\(837\) 5.41464 0.893043i 0.187157 0.0308681i
\(838\) 14.4029 3.85925i 0.497541 0.133316i
\(839\) 20.2876 0.700407 0.350203 0.936674i \(-0.386112\pi\)
0.350203 + 0.936674i \(0.386112\pi\)
\(840\) −7.40508 7.08271i −0.255500 0.244377i
\(841\) 22.9156 0.790192
\(842\) −15.9660 + 4.27808i −0.550225 + 0.147432i
\(843\) −13.5236 31.6721i −0.465776 1.09084i
\(844\) 12.8559 7.42239i 0.442520 0.255489i
\(845\) −1.89336 + 19.0106i −0.0651336 + 0.653986i
\(846\) −7.93340 + 32.4057i −0.272756 + 1.11413i
\(847\) −11.9230 12.4157i −0.409680 0.426607i
\(848\) −4.74179 + 4.74179i −0.162834 + 0.162834i
\(849\) 1.29475 + 9.07256i 0.0444356 + 0.311369i
\(850\) −1.42983 + 7.10702i −0.0490427 + 0.243769i
\(851\) −31.7825 + 18.3496i −1.08949 + 0.629018i
\(852\) 2.43761 + 1.82875i 0.0835110 + 0.0626520i
\(853\) −7.01032 7.01032i −0.240029 0.240029i 0.576833 0.816862i \(-0.304288\pi\)
−0.816862 + 0.576833i \(0.804288\pi\)
\(854\) 18.6493 + 11.2764i 0.638165 + 0.385871i
\(855\) −35.9840 + 6.70568i −1.23063 + 0.229329i
\(856\) 5.33798 9.24565i 0.182448 0.316010i
\(857\) −5.41712 + 20.2170i −0.185045 + 0.690599i 0.809575 + 0.587016i \(0.199697\pi\)
−0.994621 + 0.103583i \(0.966969\pi\)
\(858\) −15.6735 + 6.69238i −0.535084 + 0.228474i
\(859\) 11.7809 + 6.80172i 0.401960 + 0.232072i 0.687329 0.726346i \(-0.258783\pi\)
−0.285369 + 0.958418i \(0.592116\pi\)
\(860\) 5.30417 + 2.00297i 0.180871 + 0.0683006i
\(861\) −8.49521 + 1.03741i −0.289516 + 0.0353548i
\(862\) 5.38941 5.38941i 0.183564 0.183564i
\(863\) 12.1635 + 45.3947i 0.414050 + 1.54525i 0.786731 + 0.617296i \(0.211772\pi\)
−0.372681 + 0.927959i \(0.621562\pi\)
\(864\) 4.22318 + 3.02734i 0.143675 + 0.102992i
\(865\) −1.81394 11.0620i −0.0616757 0.376121i
\(866\) −9.72591 5.61526i −0.330500 0.190814i
\(867\) −25.6181 3.09022i −0.870036 0.104949i
\(868\) 2.01541 1.93544i 0.0684075 0.0656932i
\(869\) 33.8814 1.14935
\(870\) 23.5527 14.9668i 0.798512 0.507420i
\(871\) 21.8739 + 37.8867i 0.741169 + 1.28374i
\(872\) 2.21789 8.27727i 0.0751072 0.280304i
\(873\) 0.795060 + 36.6219i 0.0269087 + 1.23946i
\(874\) 31.0701i 1.05096i
\(875\) −16.2068 + 24.7455i −0.547890 + 0.836550i
\(876\) 1.33611 + 1.70267i 0.0451430 + 0.0575278i
\(877\) 5.73970 + 21.4208i 0.193816 + 0.723330i 0.992570 + 0.121673i \(0.0388260\pi\)
−0.798754 + 0.601657i \(0.794507\pi\)
\(878\) 12.8355 + 3.43925i 0.433176 + 0.116069i
\(879\) 19.4776 48.5055i 0.656963 1.63605i
\(880\) 0.469774 4.71685i 0.0158361 0.159005i
\(881\) 44.7263i 1.50687i −0.657525 0.753433i \(-0.728396\pi\)
0.657525 0.753433i \(-0.271604\pi\)
\(882\) −18.3804 + 10.1568i −0.618900 + 0.341998i
\(883\) −3.98957 3.98957i −0.134260 0.134260i 0.636783 0.771043i \(-0.280265\pi\)
−0.771043 + 0.636783i \(0.780265\pi\)
\(884\) −3.36485 + 5.82809i −0.113172 + 0.196020i
\(885\) −15.0415 13.8148i −0.505615 0.464380i
\(886\) 12.2753 + 21.2615i 0.412398 + 0.714295i
\(887\) −29.7508 + 7.97169i −0.998933 + 0.267663i −0.720998 0.692937i \(-0.756317\pi\)
−0.277935 + 0.960600i \(0.589650\pi\)
\(888\) 11.0829 + 1.33689i 0.371919 + 0.0448632i
\(889\) −20.3715 36.9937i −0.683239 1.24073i
\(890\) −0.315875 + 0.836486i −0.0105882 + 0.0280391i
\(891\) −10.2475 16.0932i −0.343305 0.539143i
\(892\) 6.86854 + 1.84042i 0.229976 + 0.0616218i
\(893\) 58.6137 + 15.7055i 1.96143 + 0.525564i
\(894\) −2.88998 20.2507i −0.0966554 0.677285i
\(895\) 7.44939 + 16.4891i 0.249006 + 0.551169i
\(896\) 2.64521 + 0.0535403i 0.0883702 + 0.00178865i
\(897\) −5.48220 + 45.4478i −0.183045 + 1.51746i
\(898\) −5.73324 + 1.53622i −0.191321 + 0.0512642i
\(899\) 3.80482 + 6.59015i 0.126898 + 0.219794i
\(900\) 6.37046 13.5800i 0.212349 0.452668i
\(901\) 4.86140 8.42019i 0.161957 0.280517i
\(902\) −2.79946 2.79946i −0.0932119 0.0932119i
\(903\) 7.15972 9.15161i 0.238261 0.304546i
\(904\) 10.0761i 0.335124i
\(905\) 23.7961 + 2.36997i 0.791010 + 0.0787806i
\(906\) −13.9306 5.59391i −0.462815 0.185845i
\(907\) −23.0840 6.18534i −0.766491 0.205381i −0.145670 0.989333i \(-0.546534\pi\)
−0.620821 + 0.783952i \(0.713201\pi\)
\(908\) −3.01201 11.2410i −0.0999570 0.373045i
\(909\) 3.15479 12.8864i 0.104638 0.427415i
\(910\) −21.5934 + 16.9636i −0.715813 + 0.562336i
\(911\) 27.2518i 0.902892i 0.892298 + 0.451446i \(0.149092\pi\)
−0.892298 + 0.451446i \(0.850908\pi\)
\(912\) 5.67168 7.55997i 0.187808 0.250335i
\(913\) 7.35353 27.4438i 0.243366 0.908256i
\(914\) −5.20657 9.01804i −0.172218 0.298290i
\(915\) −6.94066 + 31.1381i −0.229451 + 1.02939i
\(916\) −4.13598 −0.136657
\(917\) 11.0492 10.6108i 0.364876 0.350399i
\(918\) −7.05051 2.65495i −0.232702 0.0876266i
\(919\) −8.37600 4.83589i −0.276299 0.159521i 0.355448 0.934696i \(-0.384328\pi\)
−0.631747 + 0.775175i \(0.717662\pi\)
\(920\) −10.3414 7.42767i −0.340946 0.244883i
\(921\) −16.3015 + 40.5959i −0.537151 + 1.33768i
\(922\) −8.46938 31.6082i −0.278924 1.04096i
\(923\) 5.77440 5.77440i 0.190067 0.190067i
\(924\) −8.93974 3.80164i −0.294096 0.125065i
\(925\) −2.03737 32.1611i −0.0669883 1.05745i
\(926\) 8.08325 + 4.66687i 0.265632 + 0.153363i
\(927\) −15.4532 + 28.1602i −0.507551 + 0.924902i
\(928\) −1.86485 + 6.95973i −0.0612169 + 0.228464i
\(929\) 15.3159 26.5279i 0.502499 0.870353i −0.497497 0.867466i \(-0.665748\pi\)
0.999996 0.00288755i \(-0.000919138\pi\)
\(930\) 3.62602 + 1.89288i 0.118902 + 0.0620700i
\(931\) 17.7437 + 33.8241i 0.581526 + 1.10854i
\(932\) −16.0542 16.0542i −0.525874 0.525874i
\(933\) 15.8338 21.1054i 0.518376 0.690961i
\(934\) 0.696241 0.401975i 0.0227817 0.0131530i
\(935\) 1.11213 + 6.78215i 0.0363704 + 0.221800i
\(936\) 9.63016 10.0576i 0.314772 0.328742i
\(937\) −0.818219 + 0.818219i −0.0267300 + 0.0267300i −0.720345 0.693615i \(-0.756017\pi\)
0.693615 + 0.720345i \(0.256017\pi\)
\(938\) −6.94027 + 23.9517i −0.226608 + 0.782051i
\(939\) −31.0840 + 24.3921i −1.01439 + 0.796007i
\(940\) −19.2397 + 15.7545i −0.627530 + 0.513854i
\(941\) 39.7684 22.9603i 1.29641 0.748484i 0.316630 0.948549i \(-0.397449\pi\)
0.979783 + 0.200065i \(0.0641154\pi\)
\(942\) 27.8080 11.8737i 0.906035 0.386865i
\(943\) −10.2719 + 2.75234i −0.334498 + 0.0896285i
\(944\) 5.27318 0.171627
\(945\) −22.6712 20.7609i −0.737494 0.675353i
\(946\) 5.37514 0.174761
\(947\) 30.6129 8.20271i 0.994787 0.266552i 0.275527 0.961293i \(-0.411148\pi\)
0.719260 + 0.694741i \(0.244481\pi\)
\(948\) −25.4592 + 10.8707i −0.826876 + 0.353065i
\(949\) 5.02288 2.89996i 0.163050 0.0941367i
\(950\) −24.4426 12.1202i −0.793023 0.393233i
\(951\) −6.73797 + 5.28739i −0.218494 + 0.171456i
\(952\) −3.72466 + 0.917654i −0.120717 + 0.0297413i
\(953\) 12.7159 12.7159i 0.411908 0.411908i −0.470495 0.882403i \(-0.655924\pi\)
0.882403 + 0.470495i \(0.155924\pi\)
\(954\) −13.9133 + 14.5308i −0.450459 + 0.470452i
\(955\) −1.35824 0.975551i −0.0439517 0.0315681i
\(956\) −9.19360 + 5.30793i −0.297342 + 0.171671i
\(957\) 15.8765 21.1623i 0.513214 0.684080i
\(958\) −12.0027 12.0027i −0.387789 0.387789i
\(959\) −25.3735 15.3422i −0.819352 0.495427i
\(960\) 1.16039 + 3.69506i 0.0374514 + 0.119258i
\(961\) 14.9423 25.8808i 0.482010 0.834865i
\(962\) 7.74264 28.8959i 0.249633 0.931642i
\(963\) 15.4081 28.0780i 0.496520 0.904801i
\(964\) 17.4304 + 10.0635i 0.561396 + 0.324122i
\(965\) 7.31327 19.3667i 0.235423 0.623436i
\(966\) −20.8497 + 15.6899i −0.670829 + 0.504814i
\(967\) −3.87679 + 3.87679i −0.124669 + 0.124669i −0.766688 0.642019i \(-0.778097\pi\)
0.642019 + 0.766688i \(0.278097\pi\)
\(968\) 1.68391 + 6.28443i 0.0541229 + 0.201989i
\(969\) −5.10614 + 12.7159i −0.164033 + 0.408495i
\(970\) −15.9275 + 22.1756i −0.511401 + 0.712015i
\(971\) 9.52298 + 5.49809i 0.305607 + 0.176442i 0.644959 0.764217i \(-0.276874\pi\)
−0.339352 + 0.940659i \(0.610208\pi\)
\(972\) 12.8637 + 8.80489i 0.412602 + 0.282417i
\(973\) 51.1630 + 14.8251i 1.64021 + 0.475270i
\(974\) 15.9920 0.512416
\(975\) −33.6148 22.0417i −1.07654 0.705898i
\(976\) −4.11857 7.13357i −0.131832 0.228340i
\(977\) 12.2836 45.8432i 0.392988 1.46665i −0.432191 0.901782i \(-0.642259\pi\)
0.825180 0.564870i \(-0.191074\pi\)
\(978\) 5.41945 7.22376i 0.173295 0.230990i
\(979\) 0.847678i 0.0270919i
\(980\) −15.4999 2.18021i −0.495126 0.0696443i
\(981\) 6.11313 24.9704i 0.195177 0.797243i
\(982\) −1.77962 6.64162i −0.0567898 0.211942i
\(983\) 29.4055 + 7.87919i 0.937891 + 0.251307i 0.695216 0.718801i \(-0.255309\pi\)
0.242675 + 0.970108i \(0.421975\pi\)
\(984\) 3.00177 + 1.20537i 0.0956929 + 0.0384259i
\(985\) 5.43691 + 6.63967i 0.173234 + 0.211557i
\(986\) 10.4468i 0.332693i
\(987\) 19.0597 + 47.2639i 0.606678 + 1.50443i
\(988\) −17.9087 17.9087i −0.569750 0.569750i
\(989\) 7.21898 12.5036i 0.229550 0.397593i
\(990\) 1.10186 14.1778i 0.0350193 0.450600i
\(991\) 7.93677 + 13.7469i 0.252120 + 0.436684i 0.964109 0.265506i \(-0.0855389\pi\)
−0.711989 + 0.702190i \(0.752206\pi\)
\(992\) −1.02014 + 0.273346i −0.0323895 + 0.00867873i
\(993\) −0.0490178 + 0.406360i −0.00155553 + 0.0128954i
\(994\) 4.65393 + 0.0941977i 0.147614 + 0.00298777i
\(995\) −11.4236 + 5.16090i −0.362151 + 0.163612i
\(996\) 3.27964 + 22.9811i 0.103919 + 0.728186i
\(997\) 27.0051 + 7.23598i 0.855259 + 0.229166i 0.659703 0.751527i \(-0.270682\pi\)
0.195556 + 0.980693i \(0.437349\pi\)
\(998\) −29.9340 8.02080i −0.947545 0.253894i
\(999\) 33.3280 + 3.28808i 1.05445 + 0.104030i
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 210.2.x.a.23.10 yes 64
3.2 odd 2 inner 210.2.x.a.23.7 64
5.2 odd 4 inner 210.2.x.a.107.14 yes 64
7.4 even 3 inner 210.2.x.a.53.7 yes 64
15.2 even 4 inner 210.2.x.a.107.7 yes 64
21.11 odd 6 inner 210.2.x.a.53.14 yes 64
35.32 odd 12 inner 210.2.x.a.137.7 yes 64
105.32 even 12 inner 210.2.x.a.137.10 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.x.a.23.7 64 3.2 odd 2 inner
210.2.x.a.23.10 yes 64 1.1 even 1 trivial
210.2.x.a.53.7 yes 64 7.4 even 3 inner
210.2.x.a.53.14 yes 64 21.11 odd 6 inner
210.2.x.a.107.7 yes 64 15.2 even 4 inner
210.2.x.a.107.14 yes 64 5.2 odd 4 inner
210.2.x.a.137.7 yes 64 35.32 odd 12 inner
210.2.x.a.137.10 yes 64 105.32 even 12 inner