Properties

Label 273.2.l.c.16.1
Level $273$
Weight $2$
Character 273.16
Analytic conductor $2.180$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(16,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.l (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} - 2645 x^{11} + 23428 x^{10} - 8506 x^{9} + 54235 x^{8} - 18801 x^{7} + 74141 x^{6} + \cdots + 1369 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.1
Root \(-1.35774 - 2.35168i\) of defining polynomial
Character \(\chi\) \(=\) 273.16
Dual form 273.2.l.c.256.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.71549 q^{2} +(-0.500000 + 0.866025i) q^{3} +5.37387 q^{4} +(1.94413 - 3.36734i) q^{5} +(1.35774 - 2.35168i) q^{6} +(1.94064 - 1.79830i) q^{7} -9.16172 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q-2.71549 q^{2} +(-0.500000 + 0.866025i) q^{3} +5.37387 q^{4} +(1.94413 - 3.36734i) q^{5} +(1.35774 - 2.35168i) q^{6} +(1.94064 - 1.79830i) q^{7} -9.16172 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-5.27927 + 9.14396i) q^{10} +(0.815825 - 1.41305i) q^{11} +(-2.68694 + 4.65391i) q^{12} +(-3.59984 + 0.202826i) q^{13} +(-5.26980 + 4.88327i) q^{14} +(1.94413 + 3.36734i) q^{15} +14.1308 q^{16} -4.19163 q^{17} +(1.35774 + 2.35168i) q^{18} +(-0.847266 - 1.46751i) q^{19} +(10.4475 - 18.0956i) q^{20} +(0.587055 + 2.57980i) q^{21} +(-2.21536 + 3.83712i) q^{22} +0.791415 q^{23} +(4.58086 - 7.93428i) q^{24} +(-5.05930 - 8.76296i) q^{25} +(9.77533 - 0.550770i) q^{26} +1.00000 q^{27} +(10.4288 - 9.66386i) q^{28} +(-0.242434 - 0.419908i) q^{29} +(-5.27927 - 9.14396i) q^{30} +(-0.915382 - 1.58549i) q^{31} -20.0485 q^{32} +(0.815825 + 1.41305i) q^{33} +11.3823 q^{34} +(-2.28262 - 10.0309i) q^{35} +(-2.68694 - 4.65391i) q^{36} +0.689242 q^{37} +(2.30074 + 3.98500i) q^{38} +(1.62427 - 3.21897i) q^{39} +(-17.8116 + 30.8506i) q^{40} +(2.96941 + 5.14316i) q^{41} +(-1.59414 - 7.00542i) q^{42} +(2.79224 - 4.83630i) q^{43} +(4.38414 - 7.59355i) q^{44} -3.88826 q^{45} -2.14908 q^{46} +(-0.292223 + 0.506146i) q^{47} +(-7.06539 + 12.2376i) q^{48} +(0.532204 - 6.97974i) q^{49} +(13.7385 + 23.7957i) q^{50} +(2.09582 - 3.63006i) q^{51} +(-19.3451 + 1.08996i) q^{52} +(3.04896 + 5.28096i) q^{53} -2.71549 q^{54} +(-3.17214 - 5.49431i) q^{55} +(-17.7796 + 16.4756i) q^{56} +1.69453 q^{57} +(0.658326 + 1.14025i) q^{58} +8.27708 q^{59} +(10.4475 + 18.0956i) q^{60} +(4.54246 + 7.86777i) q^{61} +(2.48571 + 4.30537i) q^{62} +(-2.52770 - 0.781496i) q^{63} +26.1800 q^{64} +(-6.31559 + 12.5162i) q^{65} +(-2.21536 - 3.83712i) q^{66} +(-0.500271 + 0.866495i) q^{67} -22.5253 q^{68} +(-0.395707 + 0.685385i) q^{69} +(6.19844 + 27.2389i) q^{70} +(7.93720 - 13.7476i) q^{71} +(4.58086 + 7.93428i) q^{72} +(-2.92626 - 5.06843i) q^{73} -1.87163 q^{74} +10.1186 q^{75} +(-4.55310 - 7.88620i) q^{76} +(-0.957867 - 4.20933i) q^{77} +(-4.41068 + 8.74107i) q^{78} +(0.643065 - 1.11382i) q^{79} +(27.4721 - 47.5831i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.06339 - 13.9662i) q^{82} -6.18202 q^{83} +(3.15476 + 13.8635i) q^{84} +(-8.14908 + 14.1146i) q^{85} +(-7.58229 + 13.1329i) q^{86} +0.484868 q^{87} +(-7.47435 + 12.9460i) q^{88} -4.40869 q^{89} +10.5585 q^{90} +(-6.62127 + 6.86722i) q^{91} +4.25296 q^{92} +1.83076 q^{93} +(0.793529 - 1.37443i) q^{94} -6.58879 q^{95} +(10.0243 - 17.3625i) q^{96} +(5.08782 - 8.81236i) q^{97} +(-1.44519 + 18.9534i) q^{98} -1.63165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71549 −1.92014 −0.960070 0.279760i \(-0.909745\pi\)
−0.960070 + 0.279760i \(0.909745\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 5.37387 2.68694
\(5\) 1.94413 3.36734i 0.869442 1.50592i 0.00687463 0.999976i \(-0.497812\pi\)
0.862568 0.505942i \(-0.168855\pi\)
\(6\) 1.35774 2.35168i 0.554297 0.960070i
\(7\) 1.94064 1.79830i 0.733495 0.679695i
\(8\) −9.16172 −3.23916
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −5.27927 + 9.14396i −1.66945 + 2.89157i
\(11\) 0.815825 1.41305i 0.245980 0.426051i −0.716426 0.697663i \(-0.754223\pi\)
0.962407 + 0.271612i \(0.0875568\pi\)
\(12\) −2.68694 + 4.65391i −0.775652 + 1.34347i
\(13\) −3.59984 + 0.202826i −0.998417 + 0.0562537i
\(14\) −5.26980 + 4.88327i −1.40841 + 1.30511i
\(15\) 1.94413 + 3.36734i 0.501973 + 0.869442i
\(16\) 14.1308 3.53269
\(17\) −4.19163 −1.01662 −0.508310 0.861174i \(-0.669730\pi\)
−0.508310 + 0.861174i \(0.669730\pi\)
\(18\) 1.35774 + 2.35168i 0.320023 + 0.554297i
\(19\) −0.847266 1.46751i −0.194376 0.336669i 0.752320 0.658798i \(-0.228935\pi\)
−0.946696 + 0.322129i \(0.895602\pi\)
\(20\) 10.4475 18.0956i 2.33614 4.04631i
\(21\) 0.587055 + 2.57980i 0.128106 + 0.562958i
\(22\) −2.21536 + 3.83712i −0.472317 + 0.818077i
\(23\) 0.791415 0.165021 0.0825107 0.996590i \(-0.473706\pi\)
0.0825107 + 0.996590i \(0.473706\pi\)
\(24\) 4.58086 7.93428i 0.935064 1.61958i
\(25\) −5.05930 8.76296i −1.01186 1.75259i
\(26\) 9.77533 0.550770i 1.91710 0.108015i
\(27\) 1.00000 0.192450
\(28\) 10.4288 9.66386i 1.97085 1.82630i
\(29\) −0.242434 0.419908i −0.0450188 0.0779749i 0.842638 0.538481i \(-0.181001\pi\)
−0.887657 + 0.460506i \(0.847668\pi\)
\(30\) −5.27927 9.14396i −0.963858 1.66945i
\(31\) −0.915382 1.58549i −0.164407 0.284762i 0.772037 0.635577i \(-0.219238\pi\)
−0.936445 + 0.350815i \(0.885905\pi\)
\(32\) −20.0485 −3.54411
\(33\) 0.815825 + 1.41305i 0.142017 + 0.245980i
\(34\) 11.3823 1.95205
\(35\) −2.28262 10.0309i −0.385834 1.69554i
\(36\) −2.68694 4.65391i −0.447823 0.775652i
\(37\) 0.689242 0.113311 0.0566553 0.998394i \(-0.481956\pi\)
0.0566553 + 0.998394i \(0.481956\pi\)
\(38\) 2.30074 + 3.98500i 0.373229 + 0.646452i
\(39\) 1.62427 3.21897i 0.260091 0.515447i
\(40\) −17.8116 + 30.8506i −2.81626 + 4.87790i
\(41\) 2.96941 + 5.14316i 0.463743 + 0.803227i 0.999144 0.0413712i \(-0.0131726\pi\)
−0.535400 + 0.844598i \(0.679839\pi\)
\(42\) −1.59414 7.00542i −0.245981 1.08096i
\(43\) 2.79224 4.83630i 0.425813 0.737529i −0.570683 0.821170i \(-0.693322\pi\)
0.996496 + 0.0836411i \(0.0266549\pi\)
\(44\) 4.38414 7.59355i 0.660934 1.14477i
\(45\) −3.88826 −0.579628
\(46\) −2.14908 −0.316864
\(47\) −0.292223 + 0.506146i −0.0426252 + 0.0738289i −0.886551 0.462631i \(-0.846905\pi\)
0.843926 + 0.536460i \(0.180239\pi\)
\(48\) −7.06539 + 12.2376i −1.01980 + 1.76635i
\(49\) 0.532204 6.97974i 0.0760292 0.997106i
\(50\) 13.7385 + 23.7957i 1.94291 + 3.36522i
\(51\) 2.09582 3.63006i 0.293473 0.508310i
\(52\) −19.3451 + 1.08996i −2.68268 + 0.151150i
\(53\) 3.04896 + 5.28096i 0.418807 + 0.725396i 0.995820 0.0913397i \(-0.0291149\pi\)
−0.577012 + 0.816735i \(0.695782\pi\)
\(54\) −2.71549 −0.369531
\(55\) −3.17214 5.49431i −0.427731 0.740853i
\(56\) −17.7796 + 16.4756i −2.37590 + 2.20164i
\(57\) 1.69453 0.224446
\(58\) 0.658326 + 1.14025i 0.0864425 + 0.149723i
\(59\) 8.27708 1.07758 0.538792 0.842439i \(-0.318881\pi\)
0.538792 + 0.842439i \(0.318881\pi\)
\(60\) 10.4475 + 18.0956i 1.34877 + 2.33614i
\(61\) 4.54246 + 7.86777i 0.581602 + 1.00736i 0.995290 + 0.0969455i \(0.0309072\pi\)
−0.413688 + 0.910419i \(0.635759\pi\)
\(62\) 2.48571 + 4.30537i 0.315685 + 0.546783i
\(63\) −2.52770 0.781496i −0.318460 0.0984592i
\(64\) 26.1800 3.27250
\(65\) −6.31559 + 12.5162i −0.783352 + 1.55244i
\(66\) −2.21536 3.83712i −0.272692 0.472317i
\(67\) −0.500271 + 0.866495i −0.0611178 + 0.105859i −0.894965 0.446136i \(-0.852800\pi\)
0.833847 + 0.551995i \(0.186133\pi\)
\(68\) −22.5253 −2.73159
\(69\) −0.395707 + 0.685385i −0.0476376 + 0.0825107i
\(70\) 6.19844 + 27.2389i 0.740855 + 3.25567i
\(71\) 7.93720 13.7476i 0.941972 1.63154i 0.180270 0.983617i \(-0.442303\pi\)
0.761703 0.647927i \(-0.224364\pi\)
\(72\) 4.58086 + 7.93428i 0.539859 + 0.935064i
\(73\) −2.92626 5.06843i −0.342492 0.593214i 0.642402 0.766367i \(-0.277938\pi\)
−0.984895 + 0.173153i \(0.944604\pi\)
\(74\) −1.87163 −0.217572
\(75\) 10.1186 1.16839
\(76\) −4.55310 7.88620i −0.522276 0.904609i
\(77\) −0.957867 4.20933i −0.109159 0.479698i
\(78\) −4.41068 + 8.74107i −0.499411 + 0.989731i
\(79\) 0.643065 1.11382i 0.0723505 0.125315i −0.827581 0.561347i \(-0.810283\pi\)
0.899931 + 0.436032i \(0.143617\pi\)
\(80\) 27.4721 47.5831i 3.07147 5.31995i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −8.06339 13.9662i −0.890452 1.54231i
\(83\) −6.18202 −0.678565 −0.339283 0.940684i \(-0.610184\pi\)
−0.339283 + 0.940684i \(0.610184\pi\)
\(84\) 3.15476 + 13.8635i 0.344212 + 1.51263i
\(85\) −8.14908 + 14.1146i −0.883892 + 1.53095i
\(86\) −7.58229 + 13.1329i −0.817620 + 1.41616i
\(87\) 0.484868 0.0519833
\(88\) −7.47435 + 12.9460i −0.796769 + 1.38004i
\(89\) −4.40869 −0.467320 −0.233660 0.972318i \(-0.575070\pi\)
−0.233660 + 0.972318i \(0.575070\pi\)
\(90\) 10.5585 1.11297
\(91\) −6.62127 + 6.86722i −0.694098 + 0.719881i
\(92\) 4.25296 0.443402
\(93\) 1.83076 0.189841
\(94\) 0.793529 1.37443i 0.0818463 0.141762i
\(95\) −6.58879 −0.675995
\(96\) 10.0243 17.3625i 1.02310 1.77206i
\(97\) 5.08782 8.81236i 0.516590 0.894759i −0.483225 0.875496i \(-0.660535\pi\)
0.999814 0.0192631i \(-0.00613202\pi\)
\(98\) −1.44519 + 18.9534i −0.145987 + 1.91458i
\(99\) −1.63165 −0.163987
\(100\) −27.1880 47.0911i −2.71880 4.70911i
\(101\) −7.08643 + 12.2741i −0.705126 + 1.22131i 0.261520 + 0.965198i \(0.415776\pi\)
−0.966646 + 0.256116i \(0.917557\pi\)
\(102\) −5.69116 + 9.85738i −0.563509 + 0.976026i
\(103\) −0.891175 + 1.54356i −0.0878101 + 0.152092i −0.906585 0.422023i \(-0.861320\pi\)
0.818775 + 0.574114i \(0.194654\pi\)
\(104\) 32.9807 1.85823i 3.23403 0.182214i
\(105\) 9.82836 + 3.03866i 0.959150 + 0.296543i
\(106\) −8.27942 14.3404i −0.804169 1.39286i
\(107\) 19.2154 1.85763 0.928814 0.370547i \(-0.120830\pi\)
0.928814 + 0.370547i \(0.120830\pi\)
\(108\) 5.37387 0.517101
\(109\) −5.34907 9.26486i −0.512348 0.887413i −0.999898 0.0143174i \(-0.995442\pi\)
0.487550 0.873095i \(-0.337891\pi\)
\(110\) 8.61391 + 14.9197i 0.821304 + 1.42254i
\(111\) −0.344621 + 0.596901i −0.0327100 + 0.0566553i
\(112\) 27.4228 25.4114i 2.59121 2.40116i
\(113\) −3.82284 + 6.62135i −0.359622 + 0.622884i −0.987898 0.155107i \(-0.950428\pi\)
0.628275 + 0.777991i \(0.283761\pi\)
\(114\) −4.60148 −0.430968
\(115\) 1.53861 2.66496i 0.143477 0.248509i
\(116\) −1.30281 2.25653i −0.120963 0.209514i
\(117\) 1.97557 + 3.01614i 0.182642 + 0.278842i
\(118\) −22.4763 −2.06911
\(119\) −8.13447 + 7.53783i −0.745685 + 0.690991i
\(120\) −17.8116 30.8506i −1.62597 2.81626i
\(121\) 4.16886 + 7.22068i 0.378987 + 0.656425i
\(122\) −12.3350 21.3648i −1.11676 1.93428i
\(123\) −5.93881 −0.535485
\(124\) −4.91915 8.52021i −0.441752 0.765138i
\(125\) −19.9025 −1.78013
\(126\) 6.86394 + 2.12214i 0.611488 + 0.189055i
\(127\) 1.88510 + 3.26510i 0.167276 + 0.289730i 0.937461 0.348090i \(-0.113170\pi\)
−0.770185 + 0.637820i \(0.779836\pi\)
\(128\) −30.9944 −2.73954
\(129\) 2.79224 + 4.83630i 0.245843 + 0.425813i
\(130\) 17.1499 33.9876i 1.50415 2.98091i
\(131\) 9.00807 15.6024i 0.787039 1.36319i −0.140735 0.990047i \(-0.544947\pi\)
0.927774 0.373143i \(-0.121720\pi\)
\(132\) 4.38414 + 7.59355i 0.381590 + 0.660934i
\(133\) −4.28327 1.32427i −0.371406 0.114829i
\(134\) 1.35848 2.35296i 0.117355 0.203264i
\(135\) 1.94413 3.36734i 0.167324 0.289814i
\(136\) 38.4025 3.29299
\(137\) 21.7972 1.86226 0.931128 0.364692i \(-0.118826\pi\)
0.931128 + 0.364692i \(0.118826\pi\)
\(138\) 1.07454 1.86116i 0.0914708 0.158432i
\(139\) 0.355981 0.616576i 0.0301939 0.0522973i −0.850534 0.525921i \(-0.823721\pi\)
0.880727 + 0.473623i \(0.157054\pi\)
\(140\) −12.2665 53.9050i −1.03671 4.55581i
\(141\) −0.292223 0.506146i −0.0246096 0.0426252i
\(142\) −21.5534 + 37.3315i −1.80872 + 3.13279i
\(143\) −2.65024 + 5.25223i −0.221624 + 0.439213i
\(144\) −7.06539 12.2376i −0.588782 1.01980i
\(145\) −1.88529 −0.156565
\(146\) 7.94622 + 13.7632i 0.657633 + 1.13905i
\(147\) 5.77853 + 3.95077i 0.476605 + 0.325854i
\(148\) 3.70390 0.304459
\(149\) 2.79640 + 4.84351i 0.229090 + 0.396796i 0.957539 0.288305i \(-0.0930916\pi\)
−0.728448 + 0.685101i \(0.759758\pi\)
\(150\) −27.4769 −2.24348
\(151\) 4.99718 + 8.65536i 0.406664 + 0.704364i 0.994514 0.104607i \(-0.0333585\pi\)
−0.587849 + 0.808971i \(0.700025\pi\)
\(152\) 7.76241 + 13.4449i 0.629614 + 1.09052i
\(153\) 2.09582 + 3.63006i 0.169437 + 0.293473i
\(154\) 2.60108 + 11.4304i 0.209601 + 0.921086i
\(155\) −7.11849 −0.571771
\(156\) 8.72862 17.2983i 0.698849 1.38497i
\(157\) 9.42039 + 16.3166i 0.751829 + 1.30221i 0.946935 + 0.321424i \(0.104162\pi\)
−0.195106 + 0.980782i \(0.562505\pi\)
\(158\) −1.74624 + 3.02457i −0.138923 + 0.240622i
\(159\) −6.09793 −0.483597
\(160\) −38.9770 + 67.5101i −3.08140 + 5.33714i
\(161\) 1.53586 1.42320i 0.121042 0.112164i
\(162\) 1.35774 2.35168i 0.106674 0.184766i
\(163\) 12.2236 + 21.1718i 0.957423 + 1.65830i 0.728724 + 0.684808i \(0.240114\pi\)
0.228699 + 0.973497i \(0.426553\pi\)
\(164\) 15.9572 + 27.6387i 1.24605 + 2.15822i
\(165\) 6.34428 0.493902
\(166\) 16.7872 1.30294
\(167\) −4.28482 7.42152i −0.331569 0.574295i 0.651251 0.758863i \(-0.274245\pi\)
−0.982820 + 0.184568i \(0.940911\pi\)
\(168\) −5.37843 23.6354i −0.414955 1.82351i
\(169\) 12.9177 1.46028i 0.993671 0.112329i
\(170\) 22.1287 38.3281i 1.69720 2.93963i
\(171\) −0.847266 + 1.46751i −0.0647920 + 0.112223i
\(172\) 15.0051 25.9897i 1.14413 1.98169i
\(173\) −3.84040 6.65176i −0.291980 0.505724i 0.682298 0.731074i \(-0.260981\pi\)
−0.974278 + 0.225350i \(0.927647\pi\)
\(174\) −1.31665 −0.0998152
\(175\) −25.5768 7.90764i −1.93342 0.597761i
\(176\) 11.5282 19.9675i 0.868974 1.50511i
\(177\) −4.13854 + 7.16816i −0.311072 + 0.538792i
\(178\) 11.9717 0.897319
\(179\) −4.87194 + 8.43845i −0.364146 + 0.630719i −0.988639 0.150311i \(-0.951972\pi\)
0.624493 + 0.781031i \(0.285306\pi\)
\(180\) −20.8950 −1.55742
\(181\) −6.23699 −0.463592 −0.231796 0.972764i \(-0.574460\pi\)
−0.231796 + 0.972764i \(0.574460\pi\)
\(182\) 17.9800 18.6479i 1.33277 1.38227i
\(183\) −9.08491 −0.671576
\(184\) −7.25072 −0.534530
\(185\) 1.33998 2.32091i 0.0985171 0.170637i
\(186\) −4.97142 −0.364522
\(187\) −3.41964 + 5.92298i −0.250069 + 0.433131i
\(188\) −1.57037 + 2.71996i −0.114531 + 0.198374i
\(189\) 1.94064 1.79830i 0.141161 0.130807i
\(190\) 17.8918 1.29801
\(191\) −1.52382 2.63934i −0.110260 0.190976i 0.805615 0.592439i \(-0.201835\pi\)
−0.915875 + 0.401464i \(0.868502\pi\)
\(192\) −13.0900 + 22.6725i −0.944689 + 1.63625i
\(193\) −4.49172 + 7.77988i −0.323321 + 0.560008i −0.981171 0.193141i \(-0.938133\pi\)
0.657850 + 0.753149i \(0.271466\pi\)
\(194\) −13.8159 + 23.9299i −0.991924 + 1.71806i
\(195\) −7.68155 11.7276i −0.550087 0.839828i
\(196\) 2.86000 37.5082i 0.204286 2.67916i
\(197\) −8.42977 14.6008i −0.600596 1.04026i −0.992731 0.120355i \(-0.961597\pi\)
0.392135 0.919908i \(-0.371737\pi\)
\(198\) 4.43072 0.314878
\(199\) −2.04525 −0.144984 −0.0724919 0.997369i \(-0.523095\pi\)
−0.0724919 + 0.997369i \(0.523095\pi\)
\(200\) 46.3519 + 80.2838i 3.27757 + 5.67692i
\(201\) −0.500271 0.866495i −0.0352864 0.0611178i
\(202\) 19.2431 33.3300i 1.35394 2.34509i
\(203\) −1.22560 0.378922i −0.0860203 0.0265951i
\(204\) 11.2626 19.5075i 0.788543 1.36580i
\(205\) 23.0917 1.61279
\(206\) 2.41998 4.19152i 0.168608 0.292037i
\(207\) −0.395707 0.685385i −0.0275036 0.0476376i
\(208\) −50.8686 + 2.86608i −3.52710 + 0.198727i
\(209\) −2.76488 −0.191251
\(210\) −26.6888 8.25145i −1.84170 0.569404i
\(211\) 12.3382 + 21.3705i 0.849400 + 1.47120i 0.881745 + 0.471727i \(0.156369\pi\)
−0.0323446 + 0.999477i \(0.510297\pi\)
\(212\) 16.3847 + 28.3792i 1.12531 + 1.94909i
\(213\) 7.93720 + 13.7476i 0.543848 + 0.941972i
\(214\) −52.1793 −3.56690
\(215\) −10.8570 18.8048i −0.740439 1.28248i
\(216\) −9.16172 −0.623376
\(217\) −4.62762 1.43073i −0.314143 0.0971245i
\(218\) 14.5253 + 25.1586i 0.983780 + 1.70396i
\(219\) 5.85251 0.395476
\(220\) −17.0467 29.5257i −1.14929 1.99062i
\(221\) 15.0892 0.850170i 1.01501 0.0571886i
\(222\) 0.935814 1.62088i 0.0628077 0.108786i
\(223\) −8.99595 15.5814i −0.602413 1.04341i −0.992455 0.122613i \(-0.960873\pi\)
0.390041 0.920797i \(-0.372461\pi\)
\(224\) −38.9071 + 36.0534i −2.59959 + 2.40892i
\(225\) −5.05930 + 8.76296i −0.337287 + 0.584197i
\(226\) 10.3809 17.9802i 0.690525 1.19603i
\(227\) −8.34572 −0.553925 −0.276963 0.960881i \(-0.589328\pi\)
−0.276963 + 0.960881i \(0.589328\pi\)
\(228\) 9.10620 0.603073
\(229\) −11.1172 + 19.2556i −0.734647 + 1.27245i 0.220232 + 0.975448i \(0.429319\pi\)
−0.954878 + 0.296998i \(0.904015\pi\)
\(230\) −4.17809 + 7.23666i −0.275495 + 0.477172i
\(231\) 4.12432 + 1.27513i 0.271360 + 0.0838972i
\(232\) 2.22111 + 3.84708i 0.145823 + 0.252573i
\(233\) 2.50918 4.34602i 0.164382 0.284717i −0.772054 0.635557i \(-0.780771\pi\)
0.936435 + 0.350840i \(0.114104\pi\)
\(234\) −5.36464 8.19030i −0.350698 0.535416i
\(235\) 1.13624 + 1.96803i 0.0741202 + 0.128380i
\(236\) 44.4800 2.89540
\(237\) 0.643065 + 1.11382i 0.0417716 + 0.0723505i
\(238\) 22.0890 20.4689i 1.43182 1.32680i
\(239\) 9.28305 0.600470 0.300235 0.953865i \(-0.402935\pi\)
0.300235 + 0.953865i \(0.402935\pi\)
\(240\) 27.4721 + 47.5831i 1.77332 + 3.07147i
\(241\) −14.7894 −0.952668 −0.476334 0.879264i \(-0.658035\pi\)
−0.476334 + 0.879264i \(0.658035\pi\)
\(242\) −11.3205 19.6077i −0.727709 1.26043i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 24.4106 + 42.2804i 1.56273 + 2.70672i
\(245\) −22.4684 15.3616i −1.43546 0.981419i
\(246\) 16.1268 1.02821
\(247\) 3.34767 + 5.11095i 0.213007 + 0.325202i
\(248\) 8.38647 + 14.5258i 0.532541 + 0.922388i
\(249\) 3.09101 5.35379i 0.195885 0.339283i
\(250\) 54.0449 3.41810
\(251\) 4.80626 8.32468i 0.303368 0.525449i −0.673529 0.739161i \(-0.735222\pi\)
0.976897 + 0.213712i \(0.0685555\pi\)
\(252\) −13.5835 4.19966i −0.855683 0.264554i
\(253\) 0.645656 1.11831i 0.0405920 0.0703075i
\(254\) −5.11898 8.86633i −0.321193 0.556323i
\(255\) −8.14908 14.1146i −0.510315 0.883892i
\(256\) 31.8049 1.98780
\(257\) 5.05576 0.315370 0.157685 0.987489i \(-0.449597\pi\)
0.157685 + 0.987489i \(0.449597\pi\)
\(258\) −7.58229 13.1329i −0.472053 0.817620i
\(259\) 1.33757 1.23947i 0.0831128 0.0770167i
\(260\) −33.9392 + 67.2605i −2.10482 + 4.17132i
\(261\) −0.242434 + 0.419908i −0.0150063 + 0.0259916i
\(262\) −24.4613 + 42.3682i −1.51122 + 2.61752i
\(263\) −11.6769 + 20.2250i −0.720027 + 1.24712i 0.240961 + 0.970535i \(0.422537\pi\)
−0.960988 + 0.276589i \(0.910796\pi\)
\(264\) −7.47435 12.9460i −0.460015 0.796769i
\(265\) 23.7104 1.45652
\(266\) 11.6312 + 3.59604i 0.713152 + 0.220487i
\(267\) 2.20434 3.81803i 0.134904 0.233660i
\(268\) −2.68839 + 4.65644i −0.164220 + 0.284437i
\(269\) −31.3914 −1.91397 −0.956984 0.290141i \(-0.906298\pi\)
−0.956984 + 0.290141i \(0.906298\pi\)
\(270\) −5.27927 + 9.14396i −0.321286 + 0.556484i
\(271\) −11.3303 −0.688267 −0.344134 0.938921i \(-0.611827\pi\)
−0.344134 + 0.938921i \(0.611827\pi\)
\(272\) −59.2310 −3.59141
\(273\) −2.63655 9.16780i −0.159571 0.554861i
\(274\) −59.1899 −3.57579
\(275\) −16.5100 −0.995591
\(276\) −2.12648 + 3.68318i −0.127999 + 0.221701i
\(277\) 17.9226 1.07686 0.538432 0.842669i \(-0.319017\pi\)
0.538432 + 0.842669i \(0.319017\pi\)
\(278\) −0.966661 + 1.67431i −0.0579765 + 0.100418i
\(279\) −0.915382 + 1.58549i −0.0548025 + 0.0949207i
\(280\) 20.9127 + 91.9006i 1.24978 + 5.49211i
\(281\) −11.6172 −0.693021 −0.346511 0.938046i \(-0.612634\pi\)
−0.346511 + 0.938046i \(0.612634\pi\)
\(282\) 0.793529 + 1.37443i 0.0472540 + 0.0818463i
\(283\) 4.04596 7.00781i 0.240507 0.416571i −0.720352 0.693609i \(-0.756019\pi\)
0.960859 + 0.277038i \(0.0893528\pi\)
\(284\) 42.6535 73.8781i 2.53102 4.38386i
\(285\) 3.29439 5.70606i 0.195143 0.337998i
\(286\) 7.19669 14.2624i 0.425549 0.843351i
\(287\) 15.0115 + 4.64116i 0.886103 + 0.273959i
\(288\) 10.0243 + 17.3625i 0.590685 + 1.02310i
\(289\) 0.569768 0.0335158
\(290\) 5.11949 0.300627
\(291\) 5.08782 + 8.81236i 0.298253 + 0.516590i
\(292\) −15.7253 27.2371i −0.920256 1.59393i
\(293\) −8.90887 + 15.4306i −0.520461 + 0.901466i 0.479255 + 0.877675i \(0.340907\pi\)
−0.999717 + 0.0237903i \(0.992427\pi\)
\(294\) −15.6915 10.7283i −0.915148 0.625686i
\(295\) 16.0917 27.8717i 0.936897 1.62275i
\(296\) −6.31464 −0.367031
\(297\) 0.815825 1.41305i 0.0473389 0.0819935i
\(298\) −7.59360 13.1525i −0.439885 0.761904i
\(299\) −2.84897 + 0.160519i −0.164760 + 0.00928306i
\(300\) 54.3761 3.13940
\(301\) −3.27840 14.4068i −0.188964 0.830396i
\(302\) −13.5698 23.5035i −0.780853 1.35248i
\(303\) −7.08643 12.2741i −0.407105 0.705126i
\(304\) −11.9725 20.7370i −0.686671 1.18935i
\(305\) 35.3245 2.02268
\(306\) −5.69116 9.85738i −0.325342 0.563509i
\(307\) 16.1633 0.922487 0.461244 0.887274i \(-0.347403\pi\)
0.461244 + 0.887274i \(0.347403\pi\)
\(308\) −5.14746 22.6204i −0.293304 1.28892i
\(309\) −0.891175 1.54356i −0.0506972 0.0878101i
\(310\) 19.3302 1.09788
\(311\) 9.06145 + 15.6949i 0.513827 + 0.889975i 0.999871 + 0.0160409i \(0.00510619\pi\)
−0.486044 + 0.873934i \(0.661560\pi\)
\(312\) −14.8811 + 29.4913i −0.842476 + 1.66961i
\(313\) 12.8068 22.1820i 0.723882 1.25380i −0.235550 0.971862i \(-0.575689\pi\)
0.959432 0.281939i \(-0.0909774\pi\)
\(314\) −25.5810 44.3075i −1.44362 2.50042i
\(315\) −7.54574 + 6.99228i −0.425154 + 0.393970i
\(316\) 3.45575 5.98554i 0.194401 0.336713i
\(317\) 13.7304 23.7817i 0.771174 1.33571i −0.165746 0.986168i \(-0.553003\pi\)
0.936920 0.349544i \(-0.113663\pi\)
\(318\) 16.5588 0.928574
\(319\) −0.791134 −0.0442950
\(320\) 50.8973 88.1568i 2.84525 4.92811i
\(321\) −9.60772 + 16.6411i −0.536251 + 0.928814i
\(322\) −4.17060 + 3.86470i −0.232418 + 0.215371i
\(323\) 3.55143 + 6.15125i 0.197607 + 0.342265i
\(324\) −2.68694 + 4.65391i −0.149274 + 0.258551i
\(325\) 19.9900 + 30.5191i 1.10885 + 1.69290i
\(326\) −33.1929 57.4918i −1.83839 3.18418i
\(327\) 10.6981 0.591609
\(328\) −27.2049 47.1202i −1.50214 2.60178i
\(329\) 0.343102 + 1.50776i 0.0189158 + 0.0831252i
\(330\) −17.2278 −0.948361
\(331\) −3.47563 6.01996i −0.191038 0.330887i 0.754557 0.656235i \(-0.227852\pi\)
−0.945594 + 0.325348i \(0.894519\pi\)
\(332\) −33.2214 −1.82326
\(333\) −0.344621 0.596901i −0.0188851 0.0327100i
\(334\) 11.6354 + 20.1531i 0.636659 + 1.10273i
\(335\) 1.94519 + 3.36916i 0.106277 + 0.184077i
\(336\) 8.29554 + 36.4546i 0.452559 + 1.98876i
\(337\) 29.0505 1.58248 0.791242 0.611503i \(-0.209435\pi\)
0.791242 + 0.611503i \(0.209435\pi\)
\(338\) −35.0779 + 3.96537i −1.90799 + 0.215688i
\(339\) −3.82284 6.62135i −0.207628 0.359622i
\(340\) −43.7922 + 75.8502i −2.37496 + 4.11356i
\(341\) −2.98716 −0.161764
\(342\) 2.30074 3.98500i 0.124410 0.215484i
\(343\) −11.5189 14.5023i −0.621961 0.783048i
\(344\) −25.5817 + 44.3088i −1.37927 + 2.38897i
\(345\) 1.53861 + 2.66496i 0.0828362 + 0.143477i
\(346\) 10.4285 + 18.0628i 0.560642 + 0.971061i
\(347\) 5.10846 0.274236 0.137118 0.990555i \(-0.456216\pi\)
0.137118 + 0.990555i \(0.456216\pi\)
\(348\) 2.60562 0.139676
\(349\) 12.2420 + 21.2038i 0.655300 + 1.13501i 0.981819 + 0.189822i \(0.0607911\pi\)
−0.326519 + 0.945191i \(0.605876\pi\)
\(350\) 69.4534 + 21.4731i 3.71244 + 1.14779i
\(351\) −3.59984 + 0.202826i −0.192145 + 0.0108260i
\(352\) −16.3561 + 28.3296i −0.871782 + 1.50997i
\(353\) −2.07090 + 3.58690i −0.110223 + 0.190912i −0.915860 0.401498i \(-0.868490\pi\)
0.805637 + 0.592409i \(0.201823\pi\)
\(354\) 11.2381 19.4650i 0.597301 1.03456i
\(355\) −30.8619 53.4544i −1.63798 2.83707i
\(356\) −23.6917 −1.25566
\(357\) −2.46072 10.8136i −0.130235 0.572315i
\(358\) 13.2297 22.9145i 0.699211 1.21107i
\(359\) 6.45007 11.1718i 0.340421 0.589627i −0.644090 0.764950i \(-0.722764\pi\)
0.984511 + 0.175323i \(0.0560969\pi\)
\(360\) 35.6232 1.87751
\(361\) 8.06428 13.9677i 0.424436 0.735144i
\(362\) 16.9365 0.890162
\(363\) −8.33772 −0.437617
\(364\) −35.5819 + 36.9036i −1.86500 + 1.93427i
\(365\) −22.7561 −1.19111
\(366\) 24.6700 1.28952
\(367\) −3.68288 + 6.37894i −0.192245 + 0.332978i −0.945994 0.324185i \(-0.894910\pi\)
0.753749 + 0.657162i \(0.228243\pi\)
\(368\) 11.1833 0.582970
\(369\) 2.96941 5.14316i 0.154581 0.267742i
\(370\) −3.63869 + 6.30240i −0.189167 + 0.327646i
\(371\) 15.4137 + 4.76550i 0.800241 + 0.247413i
\(372\) 9.83829 0.510092
\(373\) 11.8284 + 20.4874i 0.612451 + 1.06080i 0.990826 + 0.135144i \(0.0431496\pi\)
−0.378375 + 0.925652i \(0.623517\pi\)
\(374\) 9.28598 16.0838i 0.480167 0.831673i
\(375\) 9.95123 17.2360i 0.513879 0.890065i
\(376\) 2.67727 4.63716i 0.138070 0.239143i
\(377\) 0.957892 + 1.46243i 0.0493339 + 0.0753190i
\(378\) −5.26980 + 4.88327i −0.271049 + 0.251168i
\(379\) −5.12668 8.87966i −0.263340 0.456118i 0.703788 0.710410i \(-0.251491\pi\)
−0.967127 + 0.254293i \(0.918157\pi\)
\(380\) −35.4073 −1.81636
\(381\) −3.77021 −0.193154
\(382\) 4.13792 + 7.16708i 0.211714 + 0.366700i
\(383\) 9.66599 + 16.7420i 0.493909 + 0.855475i 0.999975 0.00701929i \(-0.00223433\pi\)
−0.506067 + 0.862494i \(0.668901\pi\)
\(384\) 15.4972 26.8419i 0.790837 1.36977i
\(385\) −16.0364 4.95803i −0.817293 0.252685i
\(386\) 12.1972 21.1262i 0.620821 1.07529i
\(387\) −5.58448 −0.283875
\(388\) 27.3413 47.3565i 1.38804 2.40416i
\(389\) −5.95876 10.3209i −0.302121 0.523289i 0.674495 0.738279i \(-0.264361\pi\)
−0.976616 + 0.214990i \(0.931028\pi\)
\(390\) 20.8592 + 31.8460i 1.05624 + 1.61259i
\(391\) −3.31732 −0.167764
\(392\) −4.87590 + 63.9464i −0.246270 + 3.22978i
\(393\) 9.00807 + 15.6024i 0.454397 + 0.787039i
\(394\) 22.8909 + 39.6483i 1.15323 + 1.99745i
\(395\) −2.50041 4.33083i −0.125809 0.217908i
\(396\) −8.76828 −0.440623
\(397\) −0.483606 0.837630i −0.0242715 0.0420395i 0.853635 0.520872i \(-0.174393\pi\)
−0.877906 + 0.478833i \(0.841060\pi\)
\(398\) 5.55385 0.278389
\(399\) 3.28848 3.04728i 0.164630 0.152555i
\(400\) −71.4918 123.827i −3.57459 6.19137i
\(401\) −23.4745 −1.17226 −0.586131 0.810217i \(-0.699349\pi\)
−0.586131 + 0.810217i \(0.699349\pi\)
\(402\) 1.35848 + 2.35296i 0.0677548 + 0.117355i
\(403\) 3.61681 + 5.52184i 0.180166 + 0.275063i
\(404\) −38.0816 + 65.9592i −1.89463 + 3.28159i
\(405\) 1.94413 + 3.36734i 0.0966047 + 0.167324i
\(406\) 3.32810 + 1.02896i 0.165171 + 0.0510663i
\(407\) 0.562300 0.973933i 0.0278722 0.0482761i
\(408\) −19.2013 + 33.2576i −0.950604 + 1.64649i
\(409\) −19.0317 −0.941059 −0.470529 0.882384i \(-0.655937\pi\)
−0.470529 + 0.882384i \(0.655937\pi\)
\(410\) −62.7052 −3.09679
\(411\) −10.8986 + 18.8769i −0.537587 + 0.931128i
\(412\) −4.78907 + 8.29490i −0.235940 + 0.408661i
\(413\) 16.0629 14.8847i 0.790402 0.732428i
\(414\) 1.07454 + 1.86116i 0.0528107 + 0.0914708i
\(415\) −12.0187 + 20.8169i −0.589973 + 1.02186i
\(416\) 72.1715 4.06635i 3.53850 0.199369i
\(417\) 0.355981 + 0.616576i 0.0174324 + 0.0301939i
\(418\) 7.50800 0.367228
\(419\) 16.1312 + 27.9400i 0.788060 + 1.36496i 0.927154 + 0.374681i \(0.122248\pi\)
−0.139093 + 0.990279i \(0.544419\pi\)
\(420\) 52.8164 + 16.3294i 2.57718 + 0.796792i
\(421\) −34.4202 −1.67754 −0.838769 0.544488i \(-0.816724\pi\)
−0.838769 + 0.544488i \(0.816724\pi\)
\(422\) −33.5044 58.0313i −1.63097 2.82492i
\(423\) 0.584447 0.0284168
\(424\) −27.9337 48.3827i −1.35658 2.34967i
\(425\) 21.2067 + 36.7311i 1.02868 + 1.78172i
\(426\) −21.5534 37.3315i −1.04426 1.80872i
\(427\) 22.9639 + 7.09982i 1.11130 + 0.343584i
\(428\) 103.261 4.99133
\(429\) −3.22344 4.92129i −0.155629 0.237602i
\(430\) 29.4820 + 51.0643i 1.42175 + 2.46254i
\(431\) −0.996911 + 1.72670i −0.0480195 + 0.0831722i −0.889036 0.457837i \(-0.848624\pi\)
0.841017 + 0.541009i \(0.181958\pi\)
\(432\) 14.1308 0.679867
\(433\) 3.70848 6.42328i 0.178218 0.308683i −0.763052 0.646337i \(-0.776300\pi\)
0.941270 + 0.337654i \(0.109633\pi\)
\(434\) 12.5662 + 3.88514i 0.603199 + 0.186493i
\(435\) 0.942647 1.63271i 0.0451965 0.0782826i
\(436\) −28.7452 49.7882i −1.37665 2.38442i
\(437\) −0.670539 1.16141i −0.0320762 0.0555576i
\(438\) −15.8924 −0.759370
\(439\) 20.7746 0.991520 0.495760 0.868460i \(-0.334890\pi\)
0.495760 + 0.868460i \(0.334890\pi\)
\(440\) 29.0623 + 50.3373i 1.38549 + 2.39974i
\(441\) −6.31073 + 3.02897i −0.300511 + 0.144237i
\(442\) −40.9746 + 2.30863i −1.94896 + 0.109810i
\(443\) −2.67178 + 4.62766i −0.126940 + 0.219867i −0.922490 0.386022i \(-0.873849\pi\)
0.795550 + 0.605889i \(0.207182\pi\)
\(444\) −1.85195 + 3.20767i −0.0878896 + 0.152229i
\(445\) −8.57107 + 14.8455i −0.406308 + 0.703745i
\(446\) 24.4284 + 42.3112i 1.15672 + 2.00349i
\(447\) −5.59281 −0.264531
\(448\) 50.8060 47.0796i 2.40036 2.22430i
\(449\) −15.0969 + 26.1486i −0.712468 + 1.23403i 0.251460 + 0.967868i \(0.419089\pi\)
−0.963928 + 0.266163i \(0.914244\pi\)
\(450\) 13.7385 23.7957i 0.647637 1.12174i
\(451\) 9.69006 0.456287
\(452\) −20.5435 + 35.5823i −0.966283 + 1.67365i
\(453\) −9.99435 −0.469576
\(454\) 22.6627 1.06361
\(455\) 10.2516 + 35.6468i 0.480603 + 1.67115i
\(456\) −15.5248 −0.727016
\(457\) −31.0204 −1.45108 −0.725538 0.688182i \(-0.758409\pi\)
−0.725538 + 0.688182i \(0.758409\pi\)
\(458\) 30.1887 52.2883i 1.41062 2.44327i
\(459\) −4.19163 −0.195649
\(460\) 8.26832 14.3212i 0.385513 0.667727i
\(461\) −2.19226 + 3.79710i −0.102104 + 0.176848i −0.912551 0.408963i \(-0.865891\pi\)
0.810448 + 0.585811i \(0.199224\pi\)
\(462\) −11.1995 3.46259i −0.521050 0.161094i
\(463\) 4.93368 0.229288 0.114644 0.993407i \(-0.463427\pi\)
0.114644 + 0.993407i \(0.463427\pi\)
\(464\) −3.42578 5.93362i −0.159038 0.275462i
\(465\) 3.55925 6.16479i 0.165056 0.285885i
\(466\) −6.81364 + 11.8016i −0.315636 + 0.546697i
\(467\) 3.98764 6.90680i 0.184526 0.319609i −0.758891 0.651218i \(-0.774258\pi\)
0.943417 + 0.331610i \(0.107592\pi\)
\(468\) 10.6165 + 16.2084i 0.490747 + 0.749232i
\(469\) 0.587373 + 2.58120i 0.0271224 + 0.119189i
\(470\) −3.08545 5.34416i −0.142321 0.246508i
\(471\) −18.8408 −0.868138
\(472\) −75.8322 −3.49046
\(473\) −4.55596 7.89115i −0.209483 0.362835i
\(474\) −1.74624 3.02457i −0.0802073 0.138923i
\(475\) −8.57314 + 14.8491i −0.393363 + 0.681324i
\(476\) −43.7136 + 40.5073i −2.00361 + 1.85665i
\(477\) 3.04896 5.28096i 0.139602 0.241799i
\(478\) −25.2080 −1.15299
\(479\) 16.1727 28.0119i 0.738949 1.27990i −0.214020 0.976829i \(-0.568656\pi\)
0.952969 0.303068i \(-0.0980108\pi\)
\(480\) −38.9770 67.5101i −1.77905 3.08140i
\(481\) −2.48116 + 0.139796i −0.113131 + 0.00637414i
\(482\) 40.1604 1.82926
\(483\) 0.464604 + 2.04169i 0.0211402 + 0.0929002i
\(484\) 22.4029 + 38.8030i 1.01832 + 1.76377i
\(485\) −19.7828 34.2648i −0.898290 1.55588i
\(486\) 1.35774 + 2.35168i 0.0615885 + 0.106674i
\(487\) 33.1101 1.50036 0.750182 0.661232i \(-0.229966\pi\)
0.750182 + 0.661232i \(0.229966\pi\)
\(488\) −41.6167 72.0822i −1.88390 3.26301i
\(489\) −24.4471 −1.10554
\(490\) 61.0128 + 41.7144i 2.75628 + 1.88446i
\(491\) 5.01799 + 8.69141i 0.226459 + 0.392238i 0.956756 0.290891i \(-0.0939518\pi\)
−0.730297 + 0.683129i \(0.760618\pi\)
\(492\) −31.9144 −1.43881
\(493\) 1.01619 + 1.76010i 0.0457670 + 0.0792708i
\(494\) −9.09056 13.8787i −0.409004 0.624433i
\(495\) −3.17214 + 5.49431i −0.142577 + 0.246951i
\(496\) −12.9351 22.4042i −0.580801 1.00598i
\(497\) −9.31914 40.9528i −0.418021 1.83698i
\(498\) −8.39361 + 14.5382i −0.376126 + 0.651470i
\(499\) −10.4771 + 18.1469i −0.469021 + 0.812369i −0.999373 0.0354090i \(-0.988727\pi\)
0.530352 + 0.847778i \(0.322060\pi\)
\(500\) −106.953 −4.78310
\(501\) 8.56964 0.382863
\(502\) −13.0513 + 22.6056i −0.582509 + 1.00894i
\(503\) 18.5489 32.1277i 0.827056 1.43250i −0.0732818 0.997311i \(-0.523347\pi\)
0.900338 0.435192i \(-0.143319\pi\)
\(504\) 23.1581 + 7.15984i 1.03154 + 0.318925i
\(505\) 27.5539 + 47.7248i 1.22613 + 2.12372i
\(506\) −1.75327 + 3.03675i −0.0779424 + 0.135000i
\(507\) −5.19422 + 11.9172i −0.230684 + 0.529262i
\(508\) 10.1303 + 17.5462i 0.449460 + 0.778488i
\(509\) 7.42063 0.328913 0.164457 0.986384i \(-0.447413\pi\)
0.164457 + 0.986384i \(0.447413\pi\)
\(510\) 22.1287 + 38.3281i 0.979877 + 1.69720i
\(511\) −14.7934 4.57371i −0.654421 0.202329i
\(512\) −24.3770 −1.07732
\(513\) −0.847266 1.46751i −0.0374077 0.0647920i
\(514\) −13.7289 −0.605554
\(515\) 3.46513 + 6.00177i 0.152692 + 0.264470i
\(516\) 15.0051 + 25.9897i 0.660565 + 1.14413i
\(517\) 0.476806 + 0.825852i 0.0209699 + 0.0363209i
\(518\) −3.63216 + 3.36576i −0.159588 + 0.147883i
\(519\) 7.68079 0.337149
\(520\) 57.8616 114.670i 2.53740 5.02860i
\(521\) −4.32959 7.49907i −0.189683 0.328540i 0.755462 0.655193i \(-0.227413\pi\)
−0.945144 + 0.326653i \(0.894079\pi\)
\(522\) 0.658326 1.14025i 0.0288142 0.0499076i
\(523\) −22.0580 −0.964530 −0.482265 0.876025i \(-0.660186\pi\)
−0.482265 + 0.876025i \(0.660186\pi\)
\(524\) 48.4082 83.8455i 2.11472 3.66281i
\(525\) 19.6366 18.1963i 0.857012 0.794152i
\(526\) 31.7084 54.9206i 1.38255 2.39465i
\(527\) 3.83694 + 6.64578i 0.167140 + 0.289495i
\(528\) 11.5282 + 19.9675i 0.501702 + 0.868974i
\(529\) −22.3737 −0.972768
\(530\) −64.3852 −2.79671
\(531\) −4.13854 7.16816i −0.179597 0.311072i
\(532\) −23.0177 7.11645i −0.997945 0.308537i
\(533\) −11.7326 17.9123i −0.508194 0.775868i
\(534\) −5.98587 + 10.3678i −0.259034 + 0.448660i
\(535\) 37.3574 64.7049i 1.61510 2.79744i
\(536\) 4.58334 7.93858i 0.197970 0.342894i
\(537\) −4.87194 8.43845i −0.210240 0.364146i
\(538\) 85.2430 3.67509
\(539\) −9.42853 6.44627i −0.406116 0.277661i
\(540\) 10.4475 18.0956i 0.449590 0.778712i
\(541\) 1.78963 3.09972i 0.0769421 0.133268i −0.824987 0.565152i \(-0.808818\pi\)
0.901929 + 0.431884i \(0.142151\pi\)
\(542\) 30.7673 1.32157
\(543\) 3.11850 5.40139i 0.133828 0.231796i
\(544\) 84.0360 3.60302
\(545\) −41.5972 −1.78183
\(546\) 7.15953 + 24.8951i 0.306400 + 1.06541i
\(547\) −11.6996 −0.500238 −0.250119 0.968215i \(-0.580470\pi\)
−0.250119 + 0.968215i \(0.580470\pi\)
\(548\) 117.135 5.00377
\(549\) 4.54246 7.86777i 0.193867 0.335788i
\(550\) 44.8327 1.91167
\(551\) −0.410812 + 0.711547i −0.0175012 + 0.0303129i
\(552\) 3.62536 6.27931i 0.154306 0.267265i
\(553\) −0.755029 3.31796i −0.0321071 0.141094i
\(554\) −48.6686 −2.06773
\(555\) 1.33998 + 2.32091i 0.0568788 + 0.0985171i
\(556\) 1.91300 3.31340i 0.0811291 0.140520i
\(557\) −8.08689 + 14.0069i −0.342653 + 0.593492i −0.984924 0.172985i \(-0.944659\pi\)
0.642272 + 0.766477i \(0.277992\pi\)
\(558\) 2.48571 4.30537i 0.105228 0.182261i
\(559\) −9.07070 + 17.9763i −0.383650 + 0.760315i
\(560\) −32.2553 141.745i −1.36303 5.98982i
\(561\) −3.41964 5.92298i −0.144377 0.250069i
\(562\) 31.5462 1.33070
\(563\) −24.7715 −1.04400 −0.521998 0.852947i \(-0.674813\pi\)
−0.521998 + 0.852947i \(0.674813\pi\)
\(564\) −1.57037 2.71996i −0.0661246 0.114531i
\(565\) 14.8642 + 25.7456i 0.625342 + 1.08312i
\(566\) −10.9868 + 19.0296i −0.461808 + 0.799875i
\(567\) 0.587055 + 2.57980i 0.0246540 + 0.108341i
\(568\) −72.7184 + 125.952i −3.05119 + 5.28482i
\(569\) 33.4519 1.40238 0.701189 0.712975i \(-0.252653\pi\)
0.701189 + 0.712975i \(0.252653\pi\)
\(570\) −8.94588 + 15.4947i −0.374702 + 0.649003i
\(571\) −6.32788 10.9602i −0.264814 0.458671i 0.702701 0.711485i \(-0.251977\pi\)
−0.967515 + 0.252815i \(0.918644\pi\)
\(572\) −14.2420 + 28.2248i −0.595490 + 1.18014i
\(573\) 3.04764 0.127317
\(574\) −40.7636 12.6030i −1.70144 0.526039i
\(575\) −4.00400 6.93514i −0.166979 0.289215i
\(576\) −13.0900 22.6725i −0.545416 0.944689i
\(577\) 10.9471 + 18.9609i 0.455733 + 0.789352i 0.998730 0.0503824i \(-0.0160440\pi\)
−0.542997 + 0.839734i \(0.682711\pi\)
\(578\) −1.54720 −0.0643550
\(579\) −4.49172 7.77988i −0.186669 0.323321i
\(580\) −10.1313 −0.420681
\(581\) −11.9971 + 11.1172i −0.497724 + 0.461217i
\(582\) −13.8159 23.9299i −0.572688 0.991924i
\(583\) 9.94968 0.412074
\(584\) 26.8095 + 46.4355i 1.10939 + 1.92151i
\(585\) 13.9971 0.788639i 0.578710 0.0326062i
\(586\) 24.1919 41.9016i 0.999359 1.73094i
\(587\) 20.0260 + 34.6860i 0.826561 + 1.43164i 0.900721 + 0.434399i \(0.143039\pi\)
−0.0741601 + 0.997246i \(0.523628\pi\)
\(588\) 31.0531 + 21.2310i 1.28061 + 0.875550i
\(589\) −1.55114 + 2.68666i −0.0639137 + 0.110702i
\(590\) −43.6969 + 75.6852i −1.79897 + 3.11591i
\(591\) 16.8595 0.693509
\(592\) 9.73952 0.400292
\(593\) 5.18181 8.97516i 0.212791 0.368566i −0.739796 0.672832i \(-0.765078\pi\)
0.952587 + 0.304266i \(0.0984112\pi\)
\(594\) −2.21536 + 3.83712i −0.0908974 + 0.157439i
\(595\) 9.56792 + 42.0460i 0.392246 + 1.72372i
\(596\) 15.0275 + 26.0284i 0.615551 + 1.06617i
\(597\) 1.02262 1.77124i 0.0418532 0.0724919i
\(598\) 7.73634 0.435888i 0.316362 0.0178248i
\(599\) 6.86263 + 11.8864i 0.280400 + 0.485666i 0.971483 0.237108i \(-0.0761997\pi\)
−0.691084 + 0.722775i \(0.742866\pi\)
\(600\) −92.7037 −3.78461
\(601\) −0.234944 0.406935i −0.00958356 0.0165992i 0.861194 0.508277i \(-0.169717\pi\)
−0.870777 + 0.491677i \(0.836384\pi\)
\(602\) 8.90244 + 39.1216i 0.362836 + 1.59448i
\(603\) 1.00054 0.0407452
\(604\) 26.8542 + 46.5128i 1.09268 + 1.89258i
\(605\) 32.4193 1.31803
\(606\) 19.2431 + 33.3300i 0.781698 + 1.35394i
\(607\) −11.5258 19.9633i −0.467819 0.810287i 0.531504 0.847056i \(-0.321627\pi\)
−0.999324 + 0.0367685i \(0.988294\pi\)
\(608\) 16.9864 + 29.4214i 0.688891 + 1.19319i
\(609\) 0.940956 0.871940i 0.0381295 0.0353328i
\(610\) −95.9234 −3.88382
\(611\) 0.949298 1.88131i 0.0384045 0.0761098i
\(612\) 11.2626 + 19.5075i 0.455266 + 0.788543i
\(613\) −17.4005 + 30.1386i −0.702801 + 1.21729i 0.264678 + 0.964337i \(0.414734\pi\)
−0.967479 + 0.252951i \(0.918599\pi\)
\(614\) −43.8912 −1.77130
\(615\) −11.5458 + 19.9980i −0.465573 + 0.806396i
\(616\) 8.77571 + 38.5647i 0.353583 + 1.55381i
\(617\) 15.9481 27.6229i 0.642045 1.11205i −0.342931 0.939361i \(-0.611420\pi\)
0.984976 0.172694i \(-0.0552470\pi\)
\(618\) 2.41998 + 4.19152i 0.0973457 + 0.168608i
\(619\) −11.1376 19.2910i −0.447660 0.775369i 0.550574 0.834787i \(-0.314409\pi\)
−0.998233 + 0.0594173i \(0.981076\pi\)
\(620\) −38.2539 −1.53631
\(621\) 0.791415 0.0317584
\(622\) −24.6062 42.6193i −0.986621 1.70888i
\(623\) −8.55569 + 7.92816i −0.342777 + 0.317635i
\(624\) 22.9522 45.4865i 0.918823 1.82092i
\(625\) −13.3965 + 23.2034i −0.535860 + 0.928137i
\(626\) −34.7767 + 60.2349i −1.38996 + 2.40747i
\(627\) 1.38244 2.39446i 0.0552094 0.0956254i
\(628\) 50.6240 + 87.6834i 2.02012 + 3.49895i
\(629\) −2.88905 −0.115194
\(630\) 20.4904 18.9875i 0.816356 0.756478i
\(631\) 23.9160 41.4237i 0.952081 1.64905i 0.211171 0.977449i \(-0.432272\pi\)
0.740910 0.671604i \(-0.234394\pi\)
\(632\) −5.89158 + 10.2045i −0.234355 + 0.405914i
\(633\) −24.6765 −0.980803
\(634\) −37.2846 + 64.5789i −1.48076 + 2.56475i
\(635\) 14.6596 0.581747
\(636\) −32.7695 −1.29940
\(637\) −0.500181 + 25.2339i −0.0198179 + 0.999804i
\(638\) 2.14832 0.0850526
\(639\) −15.8744 −0.627982
\(640\) −60.2571 + 104.368i −2.38187 + 4.12552i
\(641\) −14.6228 −0.577565 −0.288783 0.957395i \(-0.593250\pi\)
−0.288783 + 0.957395i \(0.593250\pi\)
\(642\) 26.0897 45.1886i 1.02968 1.78345i
\(643\) −17.9675 + 31.1207i −0.708570 + 1.22728i 0.256818 + 0.966460i \(0.417326\pi\)
−0.965388 + 0.260819i \(0.916007\pi\)
\(644\) 8.25349 7.64812i 0.325233 0.301378i
\(645\) 21.7139 0.854985
\(646\) −9.64385 16.7036i −0.379432 0.657196i
\(647\) 15.2232 26.3674i 0.598487 1.03661i −0.394558 0.918871i \(-0.629102\pi\)
0.993045 0.117738i \(-0.0375643\pi\)
\(648\) 4.58086 7.93428i 0.179953 0.311688i
\(649\) 6.75264 11.6959i 0.265064 0.459105i
\(650\) −54.2827 82.8743i −2.12914 3.25060i
\(651\) 3.55286 3.29227i 0.139248 0.129034i
\(652\) 65.6879 + 113.775i 2.57253 + 4.45576i
\(653\) 30.3431 1.18742 0.593709 0.804680i \(-0.297663\pi\)
0.593709 + 0.804680i \(0.297663\pi\)
\(654\) −29.0507 −1.13597
\(655\) −35.0257 60.6664i −1.36857 2.37043i
\(656\) 41.9600 + 72.6769i 1.63826 + 2.83756i
\(657\) −2.92626 + 5.06843i −0.114164 + 0.197738i
\(658\) −0.931690 4.09429i −0.0363210 0.159612i
\(659\) −18.9462 + 32.8157i −0.738038 + 1.27832i 0.215339 + 0.976539i \(0.430914\pi\)
−0.953377 + 0.301781i \(0.902419\pi\)
\(660\) 34.0934 1.32708
\(661\) −5.47928 + 9.49040i −0.213119 + 0.369134i −0.952689 0.303946i \(-0.901696\pi\)
0.739570 + 0.673080i \(0.235029\pi\)
\(662\) 9.43802 + 16.3471i 0.366819 + 0.635349i
\(663\) −6.80834 + 13.4927i −0.264414 + 0.524014i
\(664\) 56.6379 2.19798
\(665\) −12.7865 + 11.8486i −0.495839 + 0.459471i
\(666\) 0.935814 + 1.62088i 0.0362620 + 0.0628077i
\(667\) −0.191866 0.332321i −0.00742907 0.0128675i
\(668\) −23.0261 39.8823i −0.890906 1.54309i
\(669\) 17.9919 0.695607
\(670\) −5.28213 9.14892i −0.204066 0.353453i
\(671\) 14.8234 0.572251
\(672\) −11.7696 51.7212i −0.454022 1.99519i
\(673\) −11.7007 20.2661i −0.451027 0.781202i 0.547423 0.836856i \(-0.315609\pi\)
−0.998450 + 0.0556538i \(0.982276\pi\)
\(674\) −78.8864 −3.03859
\(675\) −5.05930 8.76296i −0.194732 0.337287i
\(676\) 69.4182 7.84736i 2.66993 0.301822i
\(677\) −4.05218 + 7.01858i −0.155738 + 0.269746i −0.933327 0.359026i \(-0.883109\pi\)
0.777590 + 0.628772i \(0.216442\pi\)
\(678\) 10.3809 + 17.9802i 0.398675 + 0.690525i
\(679\) −5.97365 26.2511i −0.229248 1.00742i
\(680\) 74.6596 129.314i 2.86306 4.95897i
\(681\) 4.17286 7.22761i 0.159904 0.276963i
\(682\) 8.11161 0.310609
\(683\) 0.681766 0.0260870 0.0130435 0.999915i \(-0.495848\pi\)
0.0130435 + 0.999915i \(0.495848\pi\)
\(684\) −4.55310 + 7.88620i −0.174092 + 0.301536i
\(685\) 42.3765 73.3983i 1.61912 2.80441i
\(686\) 31.2794 + 39.3807i 1.19425 + 1.50356i
\(687\) −11.1172 19.2556i −0.424148 0.734647i
\(688\) 39.4565 68.3407i 1.50427 2.60547i
\(689\) −12.0469 18.3922i −0.458950 0.700688i
\(690\) −4.17809 7.23666i −0.159057 0.275495i
\(691\) 41.9339 1.59524 0.797620 0.603161i \(-0.206092\pi\)
0.797620 + 0.603161i \(0.206092\pi\)
\(692\) −20.6378 35.7457i −0.784532 1.35885i
\(693\) −3.16645 + 2.93420i −0.120284 + 0.111461i
\(694\) −13.8720 −0.526572
\(695\) −1.38415 2.39741i −0.0525037 0.0909390i
\(696\) −4.44222 −0.168382
\(697\) −12.4467 21.5582i −0.471451 0.816577i
\(698\) −33.2430 57.5786i −1.25827 2.17938i
\(699\) 2.50918 + 4.34602i 0.0949057 + 0.164382i
\(700\) −137.446 42.4947i −5.19498 1.60615i
\(701\) 5.85701 0.221216 0.110608 0.993864i \(-0.464720\pi\)
0.110608 + 0.993864i \(0.464720\pi\)
\(702\) 9.77533 0.550770i 0.368946 0.0207875i
\(703\) −0.583971 1.01147i −0.0220249 0.0381482i
\(704\) 21.3583 36.9936i 0.804970 1.39425i
\(705\) −2.27248 −0.0855867
\(706\) 5.62350 9.74019i 0.211643 0.366577i
\(707\) 8.32024 + 36.5631i 0.312915 + 1.37510i
\(708\) −22.2400 + 38.5208i −0.835830 + 1.44770i
\(709\) 7.31760 + 12.6745i 0.274818 + 0.475999i 0.970089 0.242748i \(-0.0780489\pi\)
−0.695271 + 0.718748i \(0.744716\pi\)
\(710\) 83.8052 + 145.155i 3.14515 + 5.44756i
\(711\) −1.28613 −0.0482337
\(712\) 40.3911 1.51372
\(713\) −0.724447 1.25478i −0.0271307 0.0469918i
\(714\) 6.68205 + 29.3641i 0.250069 + 1.09892i
\(715\) 12.5336 + 19.1353i 0.468730 + 0.715618i
\(716\) −26.1812 + 45.3472i −0.978438 + 1.69470i
\(717\) −4.64152 + 8.03935i −0.173341 + 0.300235i
\(718\) −17.5151 + 30.3370i −0.653657 + 1.13217i
\(719\) −4.80565 8.32363i −0.179220 0.310419i 0.762393 0.647114i \(-0.224024\pi\)
−0.941614 + 0.336695i \(0.890691\pi\)
\(720\) −54.9442 −2.04765
\(721\) 1.04634 + 4.59811i 0.0389676 + 0.171243i
\(722\) −21.8985 + 37.9292i −0.814976 + 1.41158i
\(723\) 7.39469 12.8080i 0.275012 0.476334i
\(724\) −33.5168 −1.24564
\(725\) −2.45309 + 4.24888i −0.0911055 + 0.157799i
\(726\) 22.6410 0.840286
\(727\) −42.7269 −1.58465 −0.792327 0.610097i \(-0.791131\pi\)
−0.792327 + 0.610097i \(0.791131\pi\)
\(728\) 60.6622 62.9155i 2.24829 2.33181i
\(729\) 1.00000 0.0370370
\(730\) 61.7940 2.28710
\(731\) −11.7040 + 20.2720i −0.432890 + 0.749787i
\(732\) −48.8212 −1.80448
\(733\) 4.17505 7.23139i 0.154209 0.267098i −0.778562 0.627568i \(-0.784050\pi\)
0.932771 + 0.360470i \(0.117384\pi\)
\(734\) 10.0008 17.3219i 0.369137 0.639364i
\(735\) 24.5378 11.7774i 0.905090 0.434417i
\(736\) −15.8667 −0.584854
\(737\) 0.816267 + 1.41382i 0.0300676 + 0.0520786i
\(738\) −8.06339 + 13.9662i −0.296817 + 0.514103i
\(739\) −14.5181 + 25.1461i −0.534056 + 0.925013i 0.465152 + 0.885231i \(0.346000\pi\)
−0.999208 + 0.0397818i \(0.987334\pi\)
\(740\) 7.20087 12.4723i 0.264709 0.458490i
\(741\) −6.10005 + 0.343694i −0.224091 + 0.0126259i
\(742\) −41.8558 12.9407i −1.53657 0.475067i
\(743\) −12.5402 21.7202i −0.460055 0.796838i 0.538909 0.842364i \(-0.318837\pi\)
−0.998963 + 0.0455263i \(0.985504\pi\)
\(744\) −16.7729 −0.614926
\(745\) 21.7463 0.796723
\(746\) −32.1199 55.6332i −1.17599 2.03688i
\(747\) 3.09101 + 5.35379i 0.113094 + 0.195885i
\(748\) −18.3767 + 31.8294i −0.671918 + 1.16380i
\(749\) 37.2904 34.5552i 1.36256 1.26262i
\(750\) −27.0224 + 46.8042i −0.986720 + 1.70905i
\(751\) 0.357389 0.0130413 0.00652065 0.999979i \(-0.497924\pi\)
0.00652065 + 0.999979i \(0.497924\pi\)
\(752\) −4.12934 + 7.15223i −0.150582 + 0.260815i
\(753\) 4.80626 + 8.32468i 0.175150 + 0.303368i
\(754\) −2.60114 3.97121i −0.0947281 0.144623i
\(755\) 38.8607 1.41429
\(756\) 10.4288 9.66386i 0.379291 0.351471i
\(757\) −25.0343 43.3607i −0.909888 1.57597i −0.814219 0.580558i \(-0.802834\pi\)
−0.0956688 0.995413i \(-0.530499\pi\)
\(758\) 13.9214 + 24.1126i 0.505649 + 0.875810i
\(759\) 0.645656 + 1.11831i 0.0234358 + 0.0405920i
\(760\) 60.3646 2.18965
\(761\) 4.41889 + 7.65375i 0.160185 + 0.277448i 0.934935 0.354819i \(-0.115458\pi\)
−0.774750 + 0.632268i \(0.782124\pi\)
\(762\) 10.2380 0.370882
\(763\) −27.0417 8.36055i −0.978975 0.302672i
\(764\) −8.18882 14.1835i −0.296261 0.513139i
\(765\) 16.2982 0.589261
\(766\) −26.2479 45.4626i −0.948374 1.64263i
\(767\) −29.7962 + 1.67880i −1.07588 + 0.0606180i
\(768\) −15.9024 + 27.5438i −0.573829 + 0.993902i
\(769\) −13.9753 24.2059i −0.503962 0.872887i −0.999990 0.00458075i \(-0.998542\pi\)
0.496028 0.868307i \(-0.334791\pi\)
\(770\) 43.5468 + 13.4635i 1.56932 + 0.485190i
\(771\) −2.52788 + 4.37842i −0.0910394 + 0.157685i
\(772\) −24.1379 + 41.8081i −0.868743 + 1.50471i
\(773\) −30.7833 −1.10720 −0.553600 0.832783i \(-0.686746\pi\)
−0.553600 + 0.832783i \(0.686746\pi\)
\(774\) 15.1646 0.545080
\(775\) −9.26238 + 16.0429i −0.332714 + 0.576278i
\(776\) −46.6131 + 80.7363i −1.67331 + 2.89827i
\(777\) 0.404623 + 1.77811i 0.0145158 + 0.0637892i
\(778\) 16.1809 + 28.0262i 0.580115 + 1.00479i
\(779\) 5.03175 8.71525i 0.180281 0.312256i
\(780\) −41.2797 63.0224i −1.47805 2.25656i
\(781\) −12.9507 22.4313i −0.463413 0.802656i
\(782\) 9.00814 0.322130
\(783\) −0.242434 0.419908i −0.00866388 0.0150063i
\(784\) 7.52046 98.6292i 0.268588 3.52247i
\(785\) 73.2579 2.61469
\(786\) −24.4613 42.3682i −0.872506 1.51122i
\(787\) 44.3310 1.58023 0.790114 0.612959i \(-0.210021\pi\)
0.790114 + 0.612959i \(0.210021\pi\)
\(788\) −45.3005 78.4628i −1.61376 2.79512i
\(789\) −11.6769 20.2250i −0.415708 0.720027i
\(790\) 6.78983 + 11.7603i 0.241571 + 0.418414i
\(791\) 4.48843 + 19.7243i 0.159590 + 0.701316i
\(792\) 14.9487 0.531179
\(793\) −17.9479 27.4014i −0.637349 0.973052i
\(794\) 1.31323 + 2.27458i 0.0466047 + 0.0807217i
\(795\) −11.8552 + 20.5338i −0.420460 + 0.728258i
\(796\) −10.9909 −0.389562
\(797\) 2.40661 4.16837i 0.0852464 0.147651i −0.820250 0.572005i \(-0.806166\pi\)
0.905496 + 0.424354i \(0.139499\pi\)
\(798\) −8.92984 + 8.27486i −0.316113 + 0.292927i
\(799\) 1.22489 2.12158i 0.0433336 0.0750560i
\(800\) 101.431 + 175.684i 3.58614 + 6.21138i
\(801\) 2.20434 + 3.81803i 0.0778866 + 0.134904i
\(802\) 63.7448 2.25091
\(803\) −9.54925 −0.336986
\(804\) −2.68839 4.65644i −0.0948124 0.164220i
\(805\) −1.80650 7.93864i −0.0636708 0.279800i
\(806\) −9.82139 14.9945i −0.345944 0.528159i
\(807\) 15.6957 27.1858i 0.552515 0.956984i
\(808\) 64.9238 112.451i 2.28401 3.95603i
\(809\) −3.98543 + 6.90297i −0.140120 + 0.242696i −0.927542 0.373719i \(-0.878082\pi\)
0.787421 + 0.616415i \(0.211416\pi\)
\(810\) −5.27927 9.14396i −0.185495 0.321286i
\(811\) −41.5780 −1.46000 −0.730000 0.683447i \(-0.760480\pi\)
−0.730000 + 0.683447i \(0.760480\pi\)
\(812\) −6.58622 2.03628i −0.231131 0.0714594i
\(813\) 5.66515 9.81233i 0.198686 0.344134i
\(814\) −1.52692 + 2.64470i −0.0535185 + 0.0926968i
\(815\) 95.0568 3.32970
\(816\) 29.6155 51.2956i 1.03675 1.79570i
\(817\) −9.46308 −0.331071
\(818\) 51.6804 1.80696
\(819\) 9.25783 + 2.30058i 0.323495 + 0.0803887i
\(820\) 124.092 4.33347
\(821\) −10.5631 −0.368656 −0.184328 0.982865i \(-0.559011\pi\)
−0.184328 + 0.982865i \(0.559011\pi\)
\(822\) 29.5950 51.2600i 1.03224 1.78790i
\(823\) 39.0405 1.36087 0.680433 0.732810i \(-0.261792\pi\)
0.680433 + 0.732810i \(0.261792\pi\)
\(824\) 8.16470 14.1417i 0.284431 0.492648i
\(825\) 8.25500 14.2981i 0.287402 0.497795i
\(826\) −43.6185 + 40.4192i −1.51768 + 1.40636i
\(827\) 35.0709 1.21954 0.609768 0.792580i \(-0.291263\pi\)
0.609768 + 0.792580i \(0.291263\pi\)
\(828\) −2.12648 3.68318i −0.0739004 0.127999i
\(829\) −4.55649 + 7.89208i −0.158254 + 0.274103i −0.934239 0.356648i \(-0.883920\pi\)
0.775985 + 0.630751i \(0.217253\pi\)
\(830\) 32.6366 56.5282i 1.13283 1.96212i
\(831\) −8.96129 + 15.5214i −0.310864 + 0.538432i
\(832\) −94.2438 + 5.30997i −3.26732 + 0.184090i
\(833\) −2.23080 + 29.2565i −0.0772928 + 1.01368i
\(834\) −0.966661 1.67431i −0.0334727 0.0579765i
\(835\) −33.3210 −1.15312
\(836\) −14.8581 −0.513879
\(837\) −0.915382 1.58549i −0.0316402 0.0548025i
\(838\) −43.8041 75.8709i −1.51319 2.62092i
\(839\) −7.08223 + 12.2668i −0.244506 + 0.423496i −0.961993 0.273076i \(-0.911959\pi\)
0.717487 + 0.696572i \(0.245292\pi\)
\(840\) −90.0447 27.8393i −3.10684 0.960549i
\(841\) 14.3825 24.9111i 0.495947 0.859005i
\(842\) 93.4676 3.22111
\(843\) 5.80858 10.0607i 0.200058 0.346511i
\(844\) 66.3042 + 114.842i 2.28228 + 3.95303i
\(845\) 20.1965 46.3373i 0.694781 1.59405i
\(846\) −1.58706 −0.0545642
\(847\) 21.0753 + 6.51589i 0.724154 + 0.223889i
\(848\) 43.0842 + 74.6241i 1.47952 + 2.56260i
\(849\) 4.04596 + 7.00781i 0.138857 + 0.240507i
\(850\) −57.5866 99.7429i −1.97520 3.42115i
\(851\) 0.545476 0.0186987
\(852\) 42.6535 + 73.8781i 1.46129 + 2.53102i
\(853\) 0.914536 0.0313131 0.0156566 0.999877i \(-0.495016\pi\)
0.0156566 + 0.999877i \(0.495016\pi\)
\(854\) −62.3583 19.2795i −2.13386 0.659730i
\(855\) 3.29439 + 5.70606i 0.112666 + 0.195143i
\(856\) −176.046 −6.01714
\(857\) −9.58886 16.6084i −0.327549 0.567332i 0.654476 0.756083i \(-0.272889\pi\)
−0.982025 + 0.188751i \(0.939556\pi\)
\(858\) 8.75322 + 13.3637i 0.298830 + 0.456229i
\(859\) −2.83001 + 4.90173i −0.0965588 + 0.167245i −0.910258 0.414041i \(-0.864117\pi\)
0.813699 + 0.581286i \(0.197450\pi\)
\(860\) −58.3440 101.055i −1.98951 3.44594i
\(861\) −11.5251 + 10.6798i −0.392775 + 0.363966i
\(862\) 2.70710 4.68883i 0.0922042 0.159702i
\(863\) −14.6246 + 25.3305i −0.497826 + 0.862259i −0.999997 0.00250891i \(-0.999201\pi\)
0.502171 + 0.864768i \(0.332535\pi\)
\(864\) −20.0485 −0.682065
\(865\) −29.8649 −1.01544
\(866\) −10.0703 + 17.4423i −0.342204 + 0.592714i
\(867\) −0.284884 + 0.493434i −0.00967518 + 0.0167579i
\(868\) −24.8682 7.68858i −0.844083 0.260967i
\(869\) −1.04926 1.81737i −0.0355936 0.0616499i
\(870\) −2.55975 + 4.43361i −0.0867835 + 0.150313i
\(871\) 1.62515 3.22071i 0.0550661 0.109130i
\(872\) 49.0067 + 84.8820i 1.65957 + 2.87447i
\(873\) −10.1756 −0.344393
\(874\) 1.82084 + 3.15379i 0.0615908 + 0.106678i
\(875\) −38.6236 + 35.7907i −1.30572 + 1.20995i
\(876\) 31.4507 1.06262
\(877\) 4.54681 + 7.87530i 0.153535 + 0.265930i 0.932525 0.361107i \(-0.117601\pi\)
−0.778990 + 0.627037i \(0.784268\pi\)
\(878\) −56.4133 −1.90386
\(879\) −8.90887 15.4306i −0.300489 0.520461i
\(880\) −44.8248 77.6389i −1.51104 2.61721i
\(881\) −4.38792 7.60010i −0.147833 0.256054i 0.782593 0.622533i \(-0.213896\pi\)
−0.930426 + 0.366479i \(0.880563\pi\)
\(882\) 17.1367 8.22512i 0.577023 0.276954i
\(883\) −53.6724 −1.80622 −0.903111 0.429408i \(-0.858722\pi\)
−0.903111 + 0.429408i \(0.858722\pi\)
\(884\) 81.0875 4.56871i 2.72727 0.153662i
\(885\) 16.0917 + 27.8717i 0.540917 + 0.936897i
\(886\) 7.25519 12.5664i 0.243743 0.422175i
\(887\) −29.8272 −1.00150 −0.500749 0.865593i \(-0.666942\pi\)
−0.500749 + 0.865593i \(0.666942\pi\)
\(888\) 3.15732 5.46864i 0.105953 0.183515i
\(889\) 9.52995 + 2.94640i 0.319624 + 0.0988191i
\(890\) 23.2746 40.3128i 0.780167 1.35129i
\(891\) 0.815825 + 1.41305i 0.0273312 + 0.0473389i
\(892\) −48.3431 83.7327i −1.61865 2.80358i
\(893\) 0.990363 0.0331412
\(894\) 15.1872 0.507936
\(895\) 18.9434 + 32.8109i 0.633208 + 1.09675i
\(896\) −60.1490 + 55.7373i −2.00944 + 1.86205i
\(897\) 1.28547 2.54754i 0.0429206 0.0850598i
\(898\) 40.9955 71.0063i 1.36804 2.36951i
\(899\) −0.443839 + 0.768752i −0.0148029 + 0.0256393i
\(900\) −27.1880 + 47.0911i −0.906268 + 1.56970i
\(901\) −12.7801 22.1358i −0.425768 0.737452i
\(902\) −26.3132 −0.876135
\(903\) 14.1159 + 4.36425i 0.469747 + 0.145233i
\(904\) 35.0238 60.6629i 1.16487 2.01762i
\(905\) −12.1255 + 21.0020i −0.403067 + 0.698132i
\(906\) 27.1395 0.901651
\(907\) −8.20448 + 14.2106i −0.272425 + 0.471855i −0.969482 0.245161i \(-0.921159\pi\)
0.697057 + 0.717016i \(0.254492\pi\)
\(908\) −44.8489 −1.48836
\(909\) 14.1729 0.470084
\(910\) −27.8381 96.7985i −0.922825 3.20884i
\(911\) −30.3790 −1.00650 −0.503251 0.864140i \(-0.667863\pi\)
−0.503251 + 0.864140i \(0.667863\pi\)
\(912\) 23.9451 0.792900
\(913\) −5.04345 + 8.73551i −0.166914 + 0.289103i
\(914\) 84.2357 2.78627
\(915\) −17.6623 + 30.5920i −0.583897 + 1.01134i
\(916\) −59.7426 + 103.477i −1.97395 + 3.41898i
\(917\) −10.5765 46.4780i −0.349265 1.53484i
\(918\) 11.3823 0.375673
\(919\) −0.579644 1.00397i −0.0191207 0.0331180i 0.856307 0.516468i \(-0.172753\pi\)
−0.875427 + 0.483350i \(0.839420\pi\)
\(920\) −14.0964 + 24.4156i −0.464743 + 0.804958i
\(921\) −8.08164 + 13.9978i −0.266299 + 0.461244i
\(922\) 5.95304 10.3110i 0.196053 0.339574i
\(923\) −25.7843 + 51.0992i −0.848700 + 1.68195i
\(924\) 22.1636 + 6.85237i 0.729128 + 0.225426i
\(925\) −3.48708 6.03980i −0.114654 0.198587i
\(926\) −13.3973 −0.440264
\(927\) 1.78235 0.0585401
\(928\) 4.86044 + 8.41853i 0.159552 + 0.276352i
\(929\) −11.5792 20.0557i −0.379901 0.658008i 0.611147 0.791517i \(-0.290709\pi\)
−0.991048 + 0.133510i \(0.957375\pi\)
\(930\) −9.66509 + 16.7404i −0.316931 + 0.548940i
\(931\) −10.6937 + 5.13268i −0.350473 + 0.168217i
\(932\) 13.4840 23.3550i 0.441683 0.765017i
\(933\) −18.1229 −0.593317
\(934\) −10.8284 + 18.7553i −0.354316 + 0.613693i
\(935\) 13.2964 + 23.0301i 0.434840 + 0.753165i
\(936\) −18.0996 27.6330i −0.591605 0.903214i
\(937\) 40.2025 1.31336 0.656679 0.754170i \(-0.271961\pi\)
0.656679 + 0.754170i \(0.271961\pi\)
\(938\) −1.59500 7.00921i −0.0520787 0.228859i
\(939\) 12.8068 + 22.1820i 0.417934 + 0.723882i
\(940\) 6.10602 + 10.5759i 0.199156 + 0.344949i
\(941\) −0.479740 0.830934i −0.0156391 0.0270877i 0.858100 0.513483i \(-0.171645\pi\)
−0.873739 + 0.486395i \(0.838312\pi\)
\(942\) 51.1619 1.66695
\(943\) 2.35003 + 4.07038i 0.0765276 + 0.132550i
\(944\) 116.962 3.80677
\(945\) −2.28262 10.0309i −0.0742538 0.326307i
\(946\) 12.3716 + 21.4283i 0.402237 + 0.696695i
\(947\) −34.0561 −1.10668 −0.553338 0.832957i \(-0.686646\pi\)
−0.553338 + 0.832957i \(0.686646\pi\)
\(948\) 3.45575 + 5.98554i 0.112238 + 0.194401i
\(949\) 11.5621 + 17.6520i 0.375321 + 0.573009i
\(950\) 23.2803 40.3226i 0.755311 1.30824i
\(951\) 13.7304 + 23.7817i 0.445237 + 0.771174i
\(952\) 74.5257 69.0594i 2.41539 2.23823i
\(953\) −19.1908 + 33.2394i −0.621651 + 1.07673i 0.367528 + 0.930013i \(0.380204\pi\)
−0.989178 + 0.146718i \(0.953129\pi\)
\(954\) −8.27942 + 14.3404i −0.268056 + 0.464287i
\(955\) −11.8500 −0.383458
\(956\) 49.8859 1.61343
\(957\) 0.395567 0.685142i 0.0127869 0.0221475i
\(958\) −43.9167 + 76.0660i −1.41888 + 2.45758i
\(959\) 42.3005 39.1979i 1.36596 1.26577i
\(960\) 50.8973 + 88.1568i 1.64270 + 2.84525i
\(961\) 13.8242 23.9441i 0.445940 0.772391i
\(962\) 6.73756 0.379614i 0.217228 0.0122392i
\(963\) −9.60772 16.6411i −0.309605 0.536251i
\(964\) −79.4763 −2.55976
\(965\) 17.4650 + 30.2502i 0.562217 + 0.973789i
\(966\) −1.26163 5.54419i −0.0405922 0.178381i
\(967\) −10.7031 −0.344188 −0.172094 0.985080i \(-0.555053\pi\)
−0.172094 + 0.985080i \(0.555053\pi\)
\(968\) −38.1939 66.1538i −1.22760 2.12626i
\(969\) −7.10285 −0.228176
\(970\) 53.7199 + 93.0456i 1.72484 + 2.98751i
\(971\) 9.99173 + 17.3062i 0.320650 + 0.555382i 0.980622 0.195908i \(-0.0627654\pi\)
−0.659972 + 0.751290i \(0.729432\pi\)
\(972\) −2.68694 4.65391i −0.0861836 0.149274i
\(973\) −0.417960 1.83672i −0.0133992 0.0588825i
\(974\) −89.9102 −2.88091
\(975\) −36.4253 + 2.05231i −1.16654 + 0.0657265i
\(976\) 64.1885 + 111.178i 2.05462 + 3.55871i
\(977\) 1.51427 2.62279i 0.0484457 0.0839105i −0.840786 0.541368i \(-0.817907\pi\)
0.889231 + 0.457458i \(0.151240\pi\)
\(978\) 66.3858 2.12278
\(979\) −3.59671 + 6.22969i −0.114952 + 0.199102i
\(980\) −120.743 82.5516i −3.85698 2.63701i
\(981\) −5.34907 + 9.26486i −0.170783 + 0.295804i
\(982\) −13.6263 23.6014i −0.434832 0.753152i
\(983\) −17.7590 30.7595i −0.566425 0.981076i −0.996916 0.0784815i \(-0.974993\pi\)
0.430491 0.902595i \(-0.358340\pi\)
\(984\) 54.4097 1.73452
\(985\) −65.5543 −2.08873
\(986\) −2.75946 4.77953i −0.0878791 0.152211i
\(987\) −1.47731 0.456742i −0.0470232 0.0145383i
\(988\) 17.9900 + 27.4656i 0.572337 + 0.873797i
\(989\) 2.20982 3.82752i 0.0702682 0.121708i
\(990\) 8.61391 14.9197i 0.273768 0.474180i
\(991\) 17.6510 30.5724i 0.560701 0.971163i −0.436734 0.899591i \(-0.643865\pi\)
0.997435 0.0715726i \(-0.0228017\pi\)
\(992\) 18.3521 + 31.7867i 0.582678 + 1.00923i
\(993\) 6.95125 0.220591
\(994\) 25.3060 + 111.207i 0.802658 + 3.52726i
\(995\) −3.97623 + 6.88704i −0.126055 + 0.218334i
\(996\) 16.6107 28.7706i 0.526331 0.911631i
\(997\) −15.4531 −0.489406 −0.244703 0.969598i \(-0.578690\pi\)
−0.244703 + 0.969598i \(0.578690\pi\)
\(998\) 28.4506 49.2778i 0.900587 1.55986i
\(999\) 0.689242 0.0218066
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 273.2.l.c.16.1 yes 20
3.2 odd 2 819.2.s.f.289.10 20
7.4 even 3 273.2.j.c.172.10 yes 20
13.9 even 3 273.2.j.c.100.10 20
21.11 odd 6 819.2.n.f.172.1 20
39.35 odd 6 819.2.n.f.100.1 20
91.74 even 3 inner 273.2.l.c.256.1 yes 20
273.74 odd 6 819.2.s.f.802.10 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.j.c.100.10 20 13.9 even 3
273.2.j.c.172.10 yes 20 7.4 even 3
273.2.l.c.16.1 yes 20 1.1 even 1 trivial
273.2.l.c.256.1 yes 20 91.74 even 3 inner
819.2.n.f.100.1 20 39.35 odd 6
819.2.n.f.172.1 20 21.11 odd 6
819.2.s.f.289.10 20 3.2 odd 2
819.2.s.f.802.10 20 273.74 odd 6