Properties

Label 471.2.e.b.169.1
Level $471$
Weight $2$
Character 471.169
Analytic conductor $3.761$
Analytic rank $0$
Dimension $22$
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] = [471,2,Mod(169,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 169.1
Character \(\chi\) \(=\) 471.169
Dual form 471.2.e.b.301.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.48879 q^{2} +(0.500000 + 0.866025i) q^{3} +4.19406 q^{4} +(-1.91720 - 3.32070i) q^{5} +(-1.24439 - 2.15535i) q^{6} +3.28748 q^{7} -5.46054 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q-2.48879 q^{2} +(0.500000 + 0.866025i) q^{3} +4.19406 q^{4} +(-1.91720 - 3.32070i) q^{5} +(-1.24439 - 2.15535i) q^{6} +3.28748 q^{7} -5.46054 q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.77151 + 8.26450i) q^{10} +(2.86691 + 4.96564i) q^{11} +(2.09703 + 3.63216i) q^{12} +(0.294686 - 0.510411i) q^{13} -8.18183 q^{14} +(1.91720 - 3.32070i) q^{15} +5.20199 q^{16} +(-1.45406 - 2.51851i) q^{17} +(1.24439 - 2.15535i) q^{18} +(-3.24844 - 5.62646i) q^{19} +(-8.04086 - 13.9272i) q^{20} +(1.64374 + 2.84704i) q^{21} +(-7.13513 - 12.3584i) q^{22} +4.26360 q^{23} +(-2.73027 - 4.72896i) q^{24} +(-4.85135 + 8.40278i) q^{25} +(-0.733410 + 1.27030i) q^{26} -1.00000 q^{27} +13.7879 q^{28} +5.15961 q^{29} +(-4.77151 + 8.26450i) q^{30} +(2.41760 - 4.18740i) q^{31} -2.02557 q^{32} +(-2.86691 + 4.96564i) q^{33} +(3.61885 + 6.26804i) q^{34} +(-6.30277 - 10.9167i) q^{35} +(-2.09703 + 3.63216i) q^{36} +(-1.51929 + 2.63149i) q^{37} +(8.08466 + 14.0030i) q^{38} +0.589372 q^{39} +(10.4690 + 18.1328i) q^{40} +5.55271 q^{41} +(-4.09091 - 7.08567i) q^{42} +(1.19864 - 2.07610i) q^{43} +(12.0240 + 20.8262i) q^{44} +3.83441 q^{45} -10.6112 q^{46} +(3.10809 - 5.38337i) q^{47} +(2.60100 + 4.50506i) q^{48} +3.80751 q^{49} +(12.0740 - 20.9127i) q^{50} +(1.45406 - 2.51851i) q^{51} +(1.23593 - 2.14069i) q^{52} +(4.32275 - 7.48722i) q^{53} +2.48879 q^{54} +(10.9929 - 19.0403i) q^{55} -17.9514 q^{56} +(3.24844 - 5.62646i) q^{57} -12.8412 q^{58} -7.89086 q^{59} +(8.04086 - 13.9272i) q^{60} +(7.10113 + 12.2995i) q^{61} +(-6.01688 + 10.4215i) q^{62} +(-1.64374 + 2.84704i) q^{63} -5.36276 q^{64} -2.25989 q^{65} +(7.13513 - 12.3584i) q^{66} +11.4780 q^{67} +(-6.09843 - 10.5628i) q^{68} +(2.13180 + 3.69239i) q^{69} +(15.6862 + 27.1694i) q^{70} +(1.26829 - 2.19675i) q^{71} +(2.73027 - 4.72896i) q^{72} +(-7.03106 - 12.1781i) q^{73} +(3.78120 - 6.54922i) q^{74} -9.70269 q^{75} +(-13.6241 - 23.5977i) q^{76} +(9.42491 + 16.3244i) q^{77} -1.46682 q^{78} +2.02742 q^{79} +(-9.97328 - 17.2742i) q^{80} +(-0.500000 - 0.866025i) q^{81} -13.8195 q^{82} +(5.53712 - 9.59057i) q^{83} +(6.89393 + 11.9406i) q^{84} +(-5.57548 + 9.65701i) q^{85} +(-2.98316 + 5.16698i) q^{86} +(2.57981 + 4.46836i) q^{87} +(-15.6549 - 27.1150i) q^{88} +(4.67557 + 8.09833i) q^{89} -9.54302 q^{90} +(0.968773 - 1.67796i) q^{91} +17.8818 q^{92} +4.83519 q^{93} +(-7.73537 + 13.3981i) q^{94} +(-12.4558 + 21.5741i) q^{95} +(-1.01279 - 1.75420i) q^{96} +(7.98334 - 13.8275i) q^{97} -9.47607 q^{98} -5.73382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48879 −1.75984 −0.879919 0.475124i \(-0.842403\pi\)
−0.879919 + 0.475124i \(0.842403\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 4.19406 2.09703
\(5\) −1.91720 3.32070i −0.857400 1.48506i −0.874401 0.485205i \(-0.838745\pi\)
0.0170005 0.999855i \(-0.494588\pi\)
\(6\) −1.24439 2.15535i −0.508021 0.879919i
\(7\) 3.28748 1.24255 0.621275 0.783593i \(-0.286615\pi\)
0.621275 + 0.783593i \(0.286615\pi\)
\(8\) −5.46054 −1.93059
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 4.77151 + 8.26450i 1.50888 + 2.61346i
\(11\) 2.86691 + 4.96564i 0.864406 + 1.49720i 0.867635 + 0.497201i \(0.165639\pi\)
−0.00322889 + 0.999995i \(0.501028\pi\)
\(12\) 2.09703 + 3.63216i 0.605360 + 1.04851i
\(13\) 0.294686 0.510411i 0.0817311 0.141562i −0.822262 0.569108i \(-0.807288\pi\)
0.903994 + 0.427546i \(0.140622\pi\)
\(14\) −8.18183 −2.18669
\(15\) 1.91720 3.32070i 0.495020 0.857400i
\(16\) 5.20199 1.30050
\(17\) −1.45406 2.51851i −0.352662 0.610829i 0.634053 0.773290i \(-0.281390\pi\)
−0.986715 + 0.162461i \(0.948057\pi\)
\(18\) 1.24439 2.15535i 0.293306 0.508021i
\(19\) −3.24844 5.62646i −0.745242 1.29080i −0.950081 0.312002i \(-0.899000\pi\)
0.204839 0.978796i \(-0.434333\pi\)
\(20\) −8.04086 13.9272i −1.79799 3.11421i
\(21\) 1.64374 + 2.84704i 0.358693 + 0.621275i
\(22\) −7.13513 12.3584i −1.52121 2.63482i
\(23\) 4.26360 0.889023 0.444511 0.895773i \(-0.353377\pi\)
0.444511 + 0.895773i \(0.353377\pi\)
\(24\) −2.73027 4.72896i −0.557314 0.965295i
\(25\) −4.85135 + 8.40278i −0.970269 + 1.68056i
\(26\) −0.733410 + 1.27030i −0.143834 + 0.249127i
\(27\) −1.00000 −0.192450
\(28\) 13.7879 2.60566
\(29\) 5.15961 0.958116 0.479058 0.877783i \(-0.340978\pi\)
0.479058 + 0.877783i \(0.340978\pi\)
\(30\) −4.77151 + 8.26450i −0.871155 + 1.50888i
\(31\) 2.41760 4.18740i 0.434213 0.752079i −0.563018 0.826445i \(-0.690360\pi\)
0.997231 + 0.0743653i \(0.0236931\pi\)
\(32\) −2.02557 −0.358074
\(33\) −2.86691 + 4.96564i −0.499065 + 0.864406i
\(34\) 3.61885 + 6.26804i 0.620628 + 1.07496i
\(35\) −6.30277 10.9167i −1.06536 1.84526i
\(36\) −2.09703 + 3.63216i −0.349505 + 0.605360i
\(37\) −1.51929 + 2.63149i −0.249770 + 0.432615i −0.963462 0.267845i \(-0.913688\pi\)
0.713692 + 0.700460i \(0.247022\pi\)
\(38\) 8.08466 + 14.0030i 1.31151 + 2.27159i
\(39\) 0.589372 0.0943750
\(40\) 10.4690 + 18.1328i 1.65529 + 2.86704i
\(41\) 5.55271 0.867187 0.433594 0.901108i \(-0.357245\pi\)
0.433594 + 0.901108i \(0.357245\pi\)
\(42\) −4.09091 7.08567i −0.631242 1.09334i
\(43\) 1.19864 2.07610i 0.182791 0.316603i −0.760039 0.649877i \(-0.774820\pi\)
0.942830 + 0.333274i \(0.108154\pi\)
\(44\) 12.0240 + 20.8262i 1.81268 + 3.13966i
\(45\) 3.83441 0.571600
\(46\) −10.6112 −1.56454
\(47\) 3.10809 5.38337i 0.453362 0.785245i −0.545231 0.838286i \(-0.683558\pi\)
0.998592 + 0.0530407i \(0.0168913\pi\)
\(48\) 2.60100 + 4.50506i 0.375421 + 0.650249i
\(49\) 3.80751 0.543930
\(50\) 12.0740 20.9127i 1.70752 2.95751i
\(51\) 1.45406 2.51851i 0.203610 0.352662i
\(52\) 1.23593 2.14069i 0.171392 0.296860i
\(53\) 4.32275 7.48722i 0.593775 1.02845i −0.399943 0.916540i \(-0.630970\pi\)
0.993718 0.111909i \(-0.0356964\pi\)
\(54\) 2.48879 0.338681
\(55\) 10.9929 19.0403i 1.48228 2.56739i
\(56\) −17.9514 −2.39885
\(57\) 3.24844 5.62646i 0.430266 0.745242i
\(58\) −12.8412 −1.68613
\(59\) −7.89086 −1.02730 −0.513651 0.857999i \(-0.671708\pi\)
−0.513651 + 0.857999i \(0.671708\pi\)
\(60\) 8.04086 13.9272i 1.03807 1.79799i
\(61\) 7.10113 + 12.2995i 0.909207 + 1.57479i 0.815169 + 0.579224i \(0.196644\pi\)
0.0940379 + 0.995569i \(0.470023\pi\)
\(62\) −6.01688 + 10.4215i −0.764145 + 1.32354i
\(63\) −1.64374 + 2.84704i −0.207092 + 0.358693i
\(64\) −5.36276 −0.670345
\(65\) −2.25989 −0.280305
\(66\) 7.13513 12.3584i 0.878274 1.52121i
\(67\) 11.4780 1.40226 0.701131 0.713033i \(-0.252679\pi\)
0.701131 + 0.713033i \(0.252679\pi\)
\(68\) −6.09843 10.5628i −0.739543 1.28093i
\(69\) 2.13180 + 3.69239i 0.256639 + 0.444511i
\(70\) 15.6862 + 27.1694i 1.87486 + 3.24736i
\(71\) 1.26829 2.19675i 0.150518 0.260706i −0.780900 0.624656i \(-0.785239\pi\)
0.931418 + 0.363951i \(0.118572\pi\)
\(72\) 2.73027 4.72896i 0.321765 0.557314i
\(73\) −7.03106 12.1781i −0.822923 1.42534i −0.903496 0.428596i \(-0.859009\pi\)
0.0805735 0.996749i \(-0.474325\pi\)
\(74\) 3.78120 6.54922i 0.439555 0.761332i
\(75\) −9.70269 −1.12037
\(76\) −13.6241 23.5977i −1.56279 2.70684i
\(77\) 9.42491 + 16.3244i 1.07407 + 1.86034i
\(78\) −1.46682 −0.166085
\(79\) 2.02742 0.228103 0.114052 0.993475i \(-0.463617\pi\)
0.114052 + 0.993475i \(0.463617\pi\)
\(80\) −9.97328 17.2742i −1.11505 1.93132i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −13.8195 −1.52611
\(83\) 5.53712 9.59057i 0.607778 1.05270i −0.383828 0.923405i \(-0.625394\pi\)
0.991606 0.129297i \(-0.0412722\pi\)
\(84\) 6.89393 + 11.9406i 0.752190 + 1.30283i
\(85\) −5.57548 + 9.65701i −0.604745 + 1.04745i
\(86\) −2.98316 + 5.16698i −0.321682 + 0.557170i
\(87\) 2.57981 + 4.46836i 0.276584 + 0.479058i
\(88\) −15.6549 27.1150i −1.66882 2.89047i
\(89\) 4.67557 + 8.09833i 0.495610 + 0.858421i 0.999987 0.00506201i \(-0.00161130\pi\)
−0.504377 + 0.863483i \(0.668278\pi\)
\(90\) −9.54302 −1.00592
\(91\) 0.968773 1.67796i 0.101555 0.175898i
\(92\) 17.8818 1.86431
\(93\) 4.83519 0.501386
\(94\) −7.73537 + 13.3981i −0.797843 + 1.38190i
\(95\) −12.4558 + 21.5741i −1.27794 + 2.21346i
\(96\) −1.01279 1.75420i −0.103367 0.179037i
\(97\) 7.98334 13.8275i 0.810585 1.40397i −0.101870 0.994798i \(-0.532482\pi\)
0.912455 0.409177i \(-0.134184\pi\)
\(98\) −9.47607 −0.957228
\(99\) −5.73382 −0.576271
\(100\) −20.3468 + 35.2417i −2.03468 + 3.52417i
\(101\) −8.87995 −0.883588 −0.441794 0.897117i \(-0.645658\pi\)
−0.441794 + 0.897117i \(0.645658\pi\)
\(102\) −3.61885 + 6.26804i −0.358320 + 0.620628i
\(103\) −1.20897 −0.119124 −0.0595619 0.998225i \(-0.518970\pi\)
−0.0595619 + 0.998225i \(0.518970\pi\)
\(104\) −1.60914 + 2.78712i −0.157789 + 0.273299i
\(105\) 6.30277 10.9167i 0.615087 1.06536i
\(106\) −10.7584 + 18.6341i −1.04495 + 1.80990i
\(107\) −4.68099 + 8.10771i −0.452528 + 0.783801i −0.998542 0.0539744i \(-0.982811\pi\)
0.546014 + 0.837776i \(0.316144\pi\)
\(108\) −4.19406 −0.403573
\(109\) 1.20401 + 2.08540i 0.115323 + 0.199745i 0.917909 0.396791i \(-0.129876\pi\)
−0.802586 + 0.596537i \(0.796543\pi\)
\(110\) −27.3590 + 47.3872i −2.60858 + 4.51819i
\(111\) −3.03859 −0.288410
\(112\) 17.1014 1.61593
\(113\) −8.43059 14.6022i −0.793083 1.37366i −0.924049 0.382273i \(-0.875141\pi\)
0.130966 0.991387i \(-0.458192\pi\)
\(114\) −8.08466 + 14.0030i −0.757198 + 1.31151i
\(115\) −8.17420 14.1581i −0.762248 1.32025i
\(116\) 21.6397 2.00920
\(117\) 0.294686 + 0.510411i 0.0272437 + 0.0471875i
\(118\) 19.6387 1.80789
\(119\) −4.78020 8.27956i −0.438201 0.758986i
\(120\) −10.4690 + 18.1328i −0.955681 + 1.65529i
\(121\) −10.9384 + 18.9458i −0.994397 + 1.72235i
\(122\) −17.6732 30.6109i −1.60006 2.77138i
\(123\) 2.77635 + 4.80879i 0.250335 + 0.433594i
\(124\) 10.1395 17.5622i 0.910557 1.57713i
\(125\) 18.0321 1.61284
\(126\) 4.09091 7.08567i 0.364448 0.631242i
\(127\) 4.52807 7.84284i 0.401801 0.695940i −0.592142 0.805833i \(-0.701718\pi\)
0.993943 + 0.109894i \(0.0350510\pi\)
\(128\) 17.3979 1.53777
\(129\) 2.39728 0.211069
\(130\) 5.62439 0.493291
\(131\) −3.39639 + 5.88272i −0.296744 + 0.513975i −0.975389 0.220491i \(-0.929234\pi\)
0.678645 + 0.734466i \(0.262567\pi\)
\(132\) −12.0240 + 20.8262i −1.04655 + 1.81268i
\(133\) −10.6792 18.4968i −0.926001 1.60388i
\(134\) −28.5663 −2.46775
\(135\) 1.91720 + 3.32070i 0.165007 + 0.285800i
\(136\) 7.93997 + 13.7524i 0.680847 + 1.17926i
\(137\) 4.23509 + 7.33539i 0.361828 + 0.626705i 0.988262 0.152770i \(-0.0488194\pi\)
−0.626434 + 0.779475i \(0.715486\pi\)
\(138\) −5.30560 9.18957i −0.451643 0.782268i
\(139\) −2.86496 + 4.96226i −0.243003 + 0.420893i −0.961568 0.274566i \(-0.911466\pi\)
0.718565 + 0.695459i \(0.244799\pi\)
\(140\) −26.4342 45.7853i −2.23409 3.86956i
\(141\) 6.21618 0.523497
\(142\) −3.15651 + 5.46723i −0.264888 + 0.458800i
\(143\) 3.37935 0.282596
\(144\) −2.60100 + 4.50506i −0.216750 + 0.375421i
\(145\) −9.89204 17.1335i −0.821489 1.42286i
\(146\) 17.4988 + 30.3088i 1.44821 + 2.50837i
\(147\) 1.90375 + 3.29740i 0.157019 + 0.271965i
\(148\) −6.37200 + 11.0366i −0.523775 + 0.907205i
\(149\) −18.4925 −1.51496 −0.757480 0.652858i \(-0.773570\pi\)
−0.757480 + 0.652858i \(0.773570\pi\)
\(150\) 24.1479 1.97167
\(151\) 7.85088 + 13.5981i 0.638895 + 1.10660i 0.985676 + 0.168653i \(0.0539417\pi\)
−0.346780 + 0.937946i \(0.612725\pi\)
\(152\) 17.7382 + 30.7235i 1.43876 + 2.49200i
\(153\) 2.90813 0.235108
\(154\) −23.4566 40.6280i −1.89018 3.27390i
\(155\) −18.5401 −1.48918
\(156\) 2.47186 0.197907
\(157\) −12.3818 + 1.92102i −0.988178 + 0.153314i
\(158\) −5.04583 −0.401424
\(159\) 8.64550 0.685632
\(160\) 3.88344 + 6.72632i 0.307013 + 0.531762i
\(161\) 14.0165 1.10465
\(162\) 1.24439 + 2.15535i 0.0977687 + 0.169340i
\(163\) 5.50827 + 9.54060i 0.431441 + 0.747278i 0.996998 0.0774318i \(-0.0246720\pi\)
−0.565557 + 0.824709i \(0.691339\pi\)
\(164\) 23.2884 1.81852
\(165\) 21.9858 1.71159
\(166\) −13.7807 + 23.8689i −1.06959 + 1.85258i
\(167\) 0.551802 + 0.955750i 0.0426998 + 0.0739581i 0.886585 0.462565i \(-0.153071\pi\)
−0.843886 + 0.536523i \(0.819737\pi\)
\(168\) −8.97569 15.5464i −0.692490 1.19943i
\(169\) 6.32632 + 10.9575i 0.486640 + 0.842885i
\(170\) 13.8762 24.0342i 1.06425 1.84334i
\(171\) 6.49687 0.496828
\(172\) 5.02716 8.70730i 0.383317 0.663925i
\(173\) −16.1574 −1.22842 −0.614211 0.789142i \(-0.710526\pi\)
−0.614211 + 0.789142i \(0.710526\pi\)
\(174\) −6.42059 11.1208i −0.486744 0.843065i
\(175\) −15.9487 + 27.6239i −1.20561 + 2.08817i
\(176\) 14.9137 + 25.8312i 1.12416 + 1.94710i
\(177\) −3.94543 6.83369i −0.296557 0.513651i
\(178\) −11.6365 20.1550i −0.872193 1.51068i
\(179\) 3.49081 + 6.04626i 0.260916 + 0.451919i 0.966485 0.256721i \(-0.0826422\pi\)
−0.705570 + 0.708640i \(0.749309\pi\)
\(180\) 16.0817 1.19866
\(181\) 5.35794 + 9.28023i 0.398253 + 0.689794i 0.993510 0.113741i \(-0.0362834\pi\)
−0.595258 + 0.803535i \(0.702950\pi\)
\(182\) −2.41107 + 4.17609i −0.178720 + 0.309553i
\(183\) −7.10113 + 12.2995i −0.524931 + 0.909207i
\(184\) −23.2816 −1.71634
\(185\) 11.6512 0.856612
\(186\) −12.0338 −0.882358
\(187\) 8.33735 14.4407i 0.609687 1.05601i
\(188\) 13.0355 22.5782i 0.950712 1.64668i
\(189\) −3.28748 −0.239129
\(190\) 30.9999 53.6934i 2.24897 3.89533i
\(191\) 1.25436 + 2.17262i 0.0907624 + 0.157205i 0.907832 0.419334i \(-0.137736\pi\)
−0.817070 + 0.576539i \(0.804403\pi\)
\(192\) −2.68138 4.64429i −0.193512 0.335173i
\(193\) 0.445945 0.772400i 0.0320998 0.0555985i −0.849529 0.527542i \(-0.823114\pi\)
0.881629 + 0.471943i \(0.156447\pi\)
\(194\) −19.8688 + 34.4138i −1.42650 + 2.47077i
\(195\) −1.12995 1.95712i −0.0809171 0.140153i
\(196\) 15.9689 1.14064
\(197\) 2.34936 + 4.06922i 0.167385 + 0.289920i 0.937500 0.347986i \(-0.113134\pi\)
−0.770114 + 0.637906i \(0.779801\pi\)
\(198\) 14.2703 1.01414
\(199\) −8.91188 15.4358i −0.631746 1.09422i −0.987195 0.159521i \(-0.949005\pi\)
0.355448 0.934696i \(-0.384328\pi\)
\(200\) 26.4910 45.8837i 1.87319 3.24447i
\(201\) 5.73900 + 9.94024i 0.404798 + 0.701131i
\(202\) 22.1003 1.55497
\(203\) 16.9621 1.19051
\(204\) 6.09843 10.5628i 0.426975 0.739543i
\(205\) −10.6457 18.4389i −0.743526 1.28783i
\(206\) 3.00888 0.209639
\(207\) −2.13180 + 3.69239i −0.148170 + 0.256639i
\(208\) 1.53295 2.65515i 0.106291 0.184102i
\(209\) 18.6260 32.2611i 1.28838 2.23155i
\(210\) −15.6862 + 27.1694i −1.08245 + 1.87486i
\(211\) −19.3188 −1.32996 −0.664980 0.746861i \(-0.731560\pi\)
−0.664980 + 0.746861i \(0.731560\pi\)
\(212\) 18.1298 31.4018i 1.24516 2.15669i
\(213\) 2.53658 0.173804
\(214\) 11.6500 20.1783i 0.796376 1.37936i
\(215\) −9.19215 −0.626899
\(216\) 5.46054 0.371542
\(217\) 7.94780 13.7660i 0.539532 0.934496i
\(218\) −2.99652 5.19012i −0.202950 0.351519i
\(219\) 7.03106 12.1781i 0.475115 0.822923i
\(220\) 46.1049 79.8560i 3.10839 5.38389i
\(221\) −1.71397 −0.115294
\(222\) 7.56239 0.507555
\(223\) −4.66315 + 8.07682i −0.312268 + 0.540864i −0.978853 0.204565i \(-0.934422\pi\)
0.666585 + 0.745429i \(0.267755\pi\)
\(224\) −6.65903 −0.444925
\(225\) −4.85135 8.40278i −0.323423 0.560185i
\(226\) 20.9819 + 36.3418i 1.39570 + 2.41742i
\(227\) 2.40625 + 4.16774i 0.159708 + 0.276623i 0.934763 0.355271i \(-0.115611\pi\)
−0.775055 + 0.631894i \(0.782278\pi\)
\(228\) 13.6241 23.5977i 0.902280 1.56279i
\(229\) 4.17311 7.22803i 0.275767 0.477642i −0.694562 0.719433i \(-0.744402\pi\)
0.970328 + 0.241791i \(0.0777350\pi\)
\(230\) 20.3438 + 35.2366i 1.34143 + 2.32343i
\(231\) −9.42491 + 16.3244i −0.620113 + 1.07407i
\(232\) −28.1743 −1.84973
\(233\) 7.23733 + 12.5354i 0.474133 + 0.821223i 0.999561 0.0296153i \(-0.00942822\pi\)
−0.525428 + 0.850838i \(0.676095\pi\)
\(234\) −0.733410 1.27030i −0.0479445 0.0830423i
\(235\) −23.8354 −1.55485
\(236\) −33.0947 −2.15428
\(237\) 1.01371 + 1.75580i 0.0658477 + 0.114052i
\(238\) 11.8969 + 20.6060i 0.771162 + 1.33569i
\(239\) −3.57167 −0.231032 −0.115516 0.993306i \(-0.536852\pi\)
−0.115516 + 0.993306i \(0.536852\pi\)
\(240\) 9.97328 17.2742i 0.643773 1.11505i
\(241\) 13.3312 + 23.0902i 0.858735 + 1.48737i 0.873136 + 0.487476i \(0.162082\pi\)
−0.0144011 + 0.999896i \(0.504584\pi\)
\(242\) 27.2233 47.1521i 1.74998 3.03105i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 29.7825 + 51.5849i 1.90663 + 3.30238i
\(245\) −7.29977 12.6436i −0.466365 0.807768i
\(246\) −6.90975 11.9680i −0.440550 0.763054i
\(247\) −3.82907 −0.243638
\(248\) −13.2014 + 22.8655i −0.838288 + 1.45196i
\(249\) 11.0742 0.701801
\(250\) −44.8779 −2.83833
\(251\) 5.01215 8.68130i 0.316364 0.547959i −0.663362 0.748298i \(-0.730871\pi\)
0.979727 + 0.200339i \(0.0642045\pi\)
\(252\) −6.89393 + 11.9406i −0.434277 + 0.752190i
\(253\) 12.2234 + 21.1715i 0.768477 + 1.33104i
\(254\) −11.2694 + 19.5192i −0.707104 + 1.22474i
\(255\) −11.1510 −0.698300
\(256\) −32.5742 −2.03589
\(257\) −2.77874 + 4.81291i −0.173333 + 0.300221i −0.939583 0.342321i \(-0.888787\pi\)
0.766250 + 0.642542i \(0.222120\pi\)
\(258\) −5.96631 −0.371446
\(259\) −4.99464 + 8.65097i −0.310352 + 0.537545i
\(260\) −9.47811 −0.587808
\(261\) −2.57981 + 4.46836i −0.159686 + 0.276584i
\(262\) 8.45288 14.6408i 0.522221 0.904513i
\(263\) −3.93830 + 6.82133i −0.242846 + 0.420621i −0.961524 0.274722i \(-0.911414\pi\)
0.718678 + 0.695343i \(0.244748\pi\)
\(264\) 15.6549 27.1150i 0.963491 1.66882i
\(265\) −33.1504 −2.03641
\(266\) 26.5781 + 46.0347i 1.62961 + 2.82257i
\(267\) −4.67557 + 8.09833i −0.286140 + 0.495610i
\(268\) 48.1394 2.94058
\(269\) −27.3968 −1.67041 −0.835206 0.549937i \(-0.814652\pi\)
−0.835206 + 0.549937i \(0.814652\pi\)
\(270\) −4.77151 8.26450i −0.290385 0.502962i
\(271\) −6.74815 + 11.6881i −0.409921 + 0.710004i −0.994880 0.101058i \(-0.967777\pi\)
0.584959 + 0.811063i \(0.301110\pi\)
\(272\) −7.56403 13.1013i −0.458637 0.794382i
\(273\) 1.93755 0.117266
\(274\) −10.5402 18.2562i −0.636759 1.10290i
\(275\) −55.6335 −3.35483
\(276\) 8.94090 + 15.4861i 0.538179 + 0.932153i
\(277\) −5.13464 + 8.89345i −0.308511 + 0.534356i −0.978037 0.208433i \(-0.933164\pi\)
0.669526 + 0.742788i \(0.266497\pi\)
\(278\) 7.13028 12.3500i 0.427645 0.740704i
\(279\) 2.41760 + 4.18740i 0.144738 + 0.250693i
\(280\) 34.4165 + 59.6111i 2.05678 + 3.56244i
\(281\) 4.06455 7.04000i 0.242470 0.419971i −0.718947 0.695065i \(-0.755376\pi\)
0.961417 + 0.275094i \(0.0887089\pi\)
\(282\) −15.4707 −0.921269
\(283\) −7.65842 + 13.2648i −0.455246 + 0.788508i −0.998702 0.0509287i \(-0.983782\pi\)
0.543457 + 0.839437i \(0.317115\pi\)
\(284\) 5.31928 9.21327i 0.315641 0.546707i
\(285\) −24.9117 −1.47564
\(286\) −8.41049 −0.497322
\(287\) 18.2544 1.07752
\(288\) 1.01279 1.75420i 0.0596791 0.103367i
\(289\) 4.27139 7.39827i 0.251258 0.435192i
\(290\) 24.6192 + 42.6416i 1.44569 + 2.50400i
\(291\) 15.9667 0.935983
\(292\) −29.4886 51.0758i −1.72569 2.98899i
\(293\) 9.43404 + 16.3402i 0.551142 + 0.954606i 0.998193 + 0.0600975i \(0.0191412\pi\)
−0.447050 + 0.894509i \(0.647526\pi\)
\(294\) −4.73803 8.20652i −0.276328 0.478614i
\(295\) 15.1284 + 26.2032i 0.880809 + 1.52561i
\(296\) 8.29616 14.3694i 0.482204 0.835202i
\(297\) −2.86691 4.96564i −0.166355 0.288135i
\(298\) 46.0238 2.66608
\(299\) 1.25642 2.17619i 0.0726608 0.125852i
\(300\) −40.6936 −2.34945
\(301\) 3.94050 6.82515i 0.227127 0.393395i
\(302\) −19.5392 33.8428i −1.12435 1.94744i
\(303\) −4.43997 7.69026i −0.255070 0.441794i
\(304\) −16.8983 29.2688i −0.969186 1.67868i
\(305\) 27.2286 47.1614i 1.55911 2.70045i
\(306\) −7.23771 −0.413752
\(307\) −14.1069 −0.805126 −0.402563 0.915392i \(-0.631881\pi\)
−0.402563 + 0.915392i \(0.631881\pi\)
\(308\) 39.5286 + 68.4655i 2.25235 + 3.90119i
\(309\) −0.604487 1.04700i −0.0343881 0.0595619i
\(310\) 46.1424 2.62071
\(311\) 11.8967 + 20.6058i 0.674602 + 1.16845i 0.976585 + 0.215132i \(0.0690182\pi\)
−0.301983 + 0.953313i \(0.597648\pi\)
\(312\) −3.21828 −0.182199
\(313\) −18.6516 −1.05425 −0.527125 0.849788i \(-0.676730\pi\)
−0.527125 + 0.849788i \(0.676730\pi\)
\(314\) 30.8157 4.78101i 1.73903 0.269808i
\(315\) 12.6055 0.710241
\(316\) 8.50313 0.478338
\(317\) 8.28354 + 14.3475i 0.465250 + 0.805836i 0.999213 0.0396716i \(-0.0126312\pi\)
−0.533963 + 0.845508i \(0.679298\pi\)
\(318\) −21.5168 −1.20660
\(319\) 14.7922 + 25.6208i 0.828202 + 1.43449i
\(320\) 10.2815 + 17.8081i 0.574754 + 0.995503i
\(321\) −9.36197 −0.522534
\(322\) −34.8841 −1.94401
\(323\) −9.44687 + 16.3625i −0.525638 + 0.910432i
\(324\) −2.09703 3.63216i −0.116502 0.201787i
\(325\) 2.85925 + 4.95236i 0.158602 + 0.274707i
\(326\) −13.7089 23.7445i −0.759266 1.31509i
\(327\) −1.20401 + 2.08540i −0.0665817 + 0.115323i
\(328\) −30.3208 −1.67418
\(329\) 10.2178 17.6977i 0.563324 0.975706i
\(330\) −54.7180 −3.01213
\(331\) −12.6550 21.9190i −0.695579 1.20478i −0.969985 0.243164i \(-0.921815\pi\)
0.274406 0.961614i \(-0.411519\pi\)
\(332\) 23.2230 40.2234i 1.27453 2.20755i
\(333\) −1.51929 2.63149i −0.0832568 0.144205i
\(334\) −1.37332 2.37866i −0.0751446 0.130154i
\(335\) −22.0057 38.1150i −1.20230 2.08244i
\(336\) 8.55071 + 14.8103i 0.466480 + 0.807967i
\(337\) 6.34464 0.345614 0.172807 0.984956i \(-0.444716\pi\)
0.172807 + 0.984956i \(0.444716\pi\)
\(338\) −15.7449 27.2709i −0.856407 1.48334i
\(339\) 8.43059 14.6022i 0.457887 0.793083i
\(340\) −23.3839 + 40.5020i −1.26817 + 2.19653i
\(341\) 27.7242 1.50135
\(342\) −16.1693 −0.874337
\(343\) −10.4952 −0.566690
\(344\) −6.54521 + 11.3366i −0.352894 + 0.611231i
\(345\) 8.17420 14.1581i 0.440084 0.762248i
\(346\) 40.2122 2.16182
\(347\) −14.7283 + 25.5102i −0.790657 + 1.36946i 0.134904 + 0.990859i \(0.456927\pi\)
−0.925561 + 0.378599i \(0.876406\pi\)
\(348\) 10.8199 + 18.7405i 0.580005 + 1.00460i
\(349\) 5.61868 + 9.73184i 0.300761 + 0.520934i 0.976309 0.216383i \(-0.0694260\pi\)
−0.675547 + 0.737317i \(0.736093\pi\)
\(350\) 39.6929 68.7501i 2.12167 3.67485i
\(351\) −0.294686 + 0.510411i −0.0157292 + 0.0272437i
\(352\) −5.80714 10.0583i −0.309522 0.536107i
\(353\) −9.75310 −0.519105 −0.259553 0.965729i \(-0.583575\pi\)
−0.259553 + 0.965729i \(0.583575\pi\)
\(354\) 9.81933 + 17.0076i 0.521892 + 0.903943i
\(355\) −9.72630 −0.516218
\(356\) 19.6096 + 33.9648i 1.03931 + 1.80013i
\(357\) 4.78020 8.27956i 0.252995 0.438201i
\(358\) −8.68789 15.0479i −0.459169 0.795304i
\(359\) 14.1939 0.749124 0.374562 0.927202i \(-0.377793\pi\)
0.374562 + 0.927202i \(0.377793\pi\)
\(360\) −20.9379 −1.10353
\(361\) −11.6047 + 20.0999i −0.610772 + 1.05789i
\(362\) −13.3348 23.0965i −0.700860 1.21393i
\(363\) −21.8767 −1.14823
\(364\) 4.06309 7.03747i 0.212964 0.368864i
\(365\) −26.9599 + 46.6960i −1.41115 + 2.44418i
\(366\) 17.6732 30.6109i 0.923793 1.60006i
\(367\) 6.68889 11.5855i 0.349157 0.604758i −0.636943 0.770911i \(-0.719801\pi\)
0.986100 + 0.166153i \(0.0531347\pi\)
\(368\) 22.1792 1.15617
\(369\) −2.77635 + 4.80879i −0.144531 + 0.250335i
\(370\) −28.9973 −1.50750
\(371\) 14.2109 24.6141i 0.737795 1.27790i
\(372\) 20.2791 1.05142
\(373\) 33.6429 1.74196 0.870981 0.491316i \(-0.163484\pi\)
0.870981 + 0.491316i \(0.163484\pi\)
\(374\) −20.7499 + 35.9398i −1.07295 + 1.85840i
\(375\) 9.01603 + 15.6162i 0.465586 + 0.806418i
\(376\) −16.9718 + 29.3961i −0.875256 + 1.51599i
\(377\) 1.52047 2.63352i 0.0783079 0.135633i
\(378\) 8.18183 0.420828
\(379\) 23.2927 1.19646 0.598232 0.801323i \(-0.295870\pi\)
0.598232 + 0.801323i \(0.295870\pi\)
\(380\) −52.2405 + 90.4831i −2.67988 + 4.64169i
\(381\) 9.05614 0.463960
\(382\) −3.12184 5.40718i −0.159727 0.276655i
\(383\) 1.07467 + 1.86138i 0.0549130 + 0.0951121i 0.892175 0.451690i \(-0.149179\pi\)
−0.837262 + 0.546802i \(0.815845\pi\)
\(384\) 8.69896 + 15.0670i 0.443917 + 0.768887i
\(385\) 36.1390 62.5945i 1.84181 3.19011i
\(386\) −1.10986 + 1.92234i −0.0564905 + 0.0978444i
\(387\) 1.19864 + 2.07610i 0.0609303 + 0.105534i
\(388\) 33.4826 57.9935i 1.69982 2.94417i
\(389\) −22.3660 −1.13400 −0.567002 0.823717i \(-0.691897\pi\)
−0.567002 + 0.823717i \(0.691897\pi\)
\(390\) 2.81219 + 4.87086i 0.142401 + 0.246646i
\(391\) −6.19955 10.7379i −0.313525 0.543041i
\(392\) −20.7910 −1.05011
\(393\) −6.79278 −0.342650
\(394\) −5.84707 10.1274i −0.294571 0.510212i
\(395\) −3.88699 6.73246i −0.195576 0.338747i
\(396\) −24.0480 −1.20846
\(397\) 12.1086 20.9727i 0.607713 1.05259i −0.383904 0.923373i \(-0.625421\pi\)
0.991616 0.129216i \(-0.0412461\pi\)
\(398\) 22.1798 + 38.4165i 1.11177 + 1.92564i
\(399\) 10.6792 18.4968i 0.534627 0.926001i
\(400\) −25.2367 + 43.7112i −1.26183 + 2.18556i
\(401\) −9.72418 16.8428i −0.485602 0.841088i 0.514261 0.857634i \(-0.328066\pi\)
−0.999863 + 0.0165459i \(0.994733\pi\)
\(402\) −14.2832 24.7391i −0.712379 1.23388i
\(403\) −1.42486 2.46794i −0.0709775 0.122937i
\(404\) −37.2430 −1.85291
\(405\) −1.91720 + 3.32070i −0.0952667 + 0.165007i
\(406\) −42.2151 −2.09510
\(407\) −17.4227 −0.863612
\(408\) −7.93997 + 13.7524i −0.393087 + 0.680847i
\(409\) 11.0695 19.1730i 0.547353 0.948044i −0.451101 0.892473i \(-0.648969\pi\)
0.998455 0.0555710i \(-0.0176979\pi\)
\(410\) 26.4948 + 45.8904i 1.30849 + 2.26636i
\(411\) −4.23509 + 7.33539i −0.208902 + 0.361828i
\(412\) −5.07051 −0.249806
\(413\) −25.9410 −1.27647
\(414\) 5.30560 9.18957i 0.260756 0.451643i
\(415\) −42.4632 −2.08443
\(416\) −0.596908 + 1.03387i −0.0292658 + 0.0506899i
\(417\) −5.72992 −0.280595
\(418\) −46.3560 + 80.2910i −2.26735 + 3.92716i
\(419\) 19.3914 33.5869i 0.947331 1.64083i 0.196317 0.980540i \(-0.437102\pi\)
0.751015 0.660286i \(-0.229565\pi\)
\(420\) 26.4342 45.7853i 1.28985 2.23409i
\(421\) −13.0515 + 22.6059i −0.636091 + 1.10174i 0.350192 + 0.936678i \(0.386116\pi\)
−0.986283 + 0.165064i \(0.947217\pi\)
\(422\) 48.0803 2.34051
\(423\) 3.10809 + 5.38337i 0.151121 + 0.261748i
\(424\) −23.6045 + 40.8842i −1.14634 + 1.98551i
\(425\) 28.2167 1.36871
\(426\) −6.31301 −0.305866
\(427\) 23.3448 + 40.4344i 1.12973 + 1.95676i
\(428\) −19.6323 + 34.0042i −0.948964 + 1.64365i
\(429\) 1.68968 + 2.92661i 0.0815783 + 0.141298i
\(430\) 22.8773 1.10324
\(431\) −2.71856 4.70868i −0.130948 0.226809i 0.793094 0.609099i \(-0.208469\pi\)
−0.924042 + 0.382290i \(0.875136\pi\)
\(432\) −5.20199 −0.250281
\(433\) −11.1341 19.2848i −0.535070 0.926768i −0.999160 0.0409798i \(-0.986952\pi\)
0.464090 0.885788i \(-0.346381\pi\)
\(434\) −19.7804 + 34.2606i −0.949488 + 1.64456i
\(435\) 9.89204 17.1335i 0.474287 0.821489i
\(436\) 5.04967 + 8.74629i 0.241835 + 0.418871i
\(437\) −13.8500 23.9890i −0.662537 1.14755i
\(438\) −17.4988 + 30.3088i −0.836125 + 1.44821i
\(439\) 35.3580 1.68754 0.843772 0.536701i \(-0.180330\pi\)
0.843772 + 0.536701i \(0.180330\pi\)
\(440\) −60.0272 + 103.970i −2.86168 + 4.95658i
\(441\) −1.90375 + 3.29740i −0.0906549 + 0.157019i
\(442\) 4.26570 0.202899
\(443\) −9.82780 −0.466933 −0.233466 0.972365i \(-0.575007\pi\)
−0.233466 + 0.972365i \(0.575007\pi\)
\(444\) −12.7440 −0.604804
\(445\) 17.9281 31.0523i 0.849872 1.47202i
\(446\) 11.6056 20.1015i 0.549540 0.951832i
\(447\) −9.24623 16.0149i −0.437331 0.757480i
\(448\) −17.6300 −0.832937
\(449\) −3.48340 6.03342i −0.164392 0.284735i 0.772047 0.635565i \(-0.219233\pi\)
−0.936439 + 0.350830i \(0.885899\pi\)
\(450\) 12.0740 + 20.9127i 0.569172 + 0.985835i
\(451\) 15.9191 + 27.5727i 0.749602 + 1.29835i
\(452\) −35.3584 61.2425i −1.66312 2.88060i
\(453\) −7.85088 + 13.5981i −0.368866 + 0.638895i
\(454\) −5.98863 10.3726i −0.281061 0.486811i
\(455\) −7.42934 −0.348293
\(456\) −17.7382 + 30.7235i −0.830667 + 1.43876i
\(457\) −2.17767 −0.101867 −0.0509336 0.998702i \(-0.516220\pi\)
−0.0509336 + 0.998702i \(0.516220\pi\)
\(458\) −10.3860 + 17.9890i −0.485304 + 0.840572i
\(459\) 1.45406 + 2.51851i 0.0678699 + 0.117554i
\(460\) −34.2831 59.3800i −1.59846 2.76861i
\(461\) 8.88563 + 15.3904i 0.413845 + 0.716801i 0.995306 0.0967733i \(-0.0308522\pi\)
−0.581461 + 0.813574i \(0.697519\pi\)
\(462\) 23.4566 40.6280i 1.09130 1.89018i
\(463\) 23.6891 1.10093 0.550463 0.834860i \(-0.314451\pi\)
0.550463 + 0.834860i \(0.314451\pi\)
\(464\) 26.8403 1.24603
\(465\) −9.27006 16.0562i −0.429889 0.744589i
\(466\) −18.0122 31.1980i −0.834397 1.44522i
\(467\) −23.0629 −1.06722 −0.533611 0.845730i \(-0.679165\pi\)
−0.533611 + 0.845730i \(0.679165\pi\)
\(468\) 1.23593 + 2.14069i 0.0571308 + 0.0989535i
\(469\) 37.7337 1.74238
\(470\) 59.3212 2.73628
\(471\) −7.85457 9.76247i −0.361919 0.449831i
\(472\) 43.0883 1.98330
\(473\) 13.7456 0.632022
\(474\) −2.52291 4.36981i −0.115881 0.200712i
\(475\) 63.0372 2.89234
\(476\) −20.0484 34.7249i −0.918919 1.59161i
\(477\) 4.32275 + 7.48722i 0.197925 + 0.342816i
\(478\) 8.88913 0.406579
\(479\) −36.9952 −1.69035 −0.845177 0.534487i \(-0.820505\pi\)
−0.845177 + 0.534487i \(0.820505\pi\)
\(480\) −3.88344 + 6.72632i −0.177254 + 0.307013i
\(481\) 0.895428 + 1.55093i 0.0408280 + 0.0707162i
\(482\) −33.1784 57.4666i −1.51123 2.61753i
\(483\) 7.00825 + 12.1386i 0.318886 + 0.552327i
\(484\) −45.8761 + 79.4598i −2.08528 + 3.61181i
\(485\) −61.2228 −2.77998
\(486\) −1.24439 + 2.15535i −0.0564468 + 0.0977687i
\(487\) −13.0169 −0.589850 −0.294925 0.955520i \(-0.595295\pi\)
−0.294925 + 0.955520i \(0.595295\pi\)
\(488\) −38.7760 67.1620i −1.75531 3.04028i
\(489\) −5.50827 + 9.54060i −0.249093 + 0.431441i
\(490\) 18.1676 + 31.4671i 0.820727 + 1.42154i
\(491\) 17.0799 + 29.5833i 0.770805 + 1.33507i 0.937122 + 0.349001i \(0.113479\pi\)
−0.166317 + 0.986072i \(0.553187\pi\)
\(492\) 11.6442 + 20.1683i 0.524960 + 0.909258i
\(493\) −7.50241 12.9946i −0.337892 0.585245i
\(494\) 9.52974 0.428763
\(495\) 10.9929 + 19.0403i 0.494095 + 0.855797i
\(496\) 12.5763 21.7828i 0.564694 0.978078i
\(497\) 4.16948 7.22175i 0.187027 0.323940i
\(498\) −27.5614 −1.23506
\(499\) −18.3704 −0.822370 −0.411185 0.911552i \(-0.634885\pi\)
−0.411185 + 0.911552i \(0.634885\pi\)
\(500\) 75.6274 3.38216
\(501\) −0.551802 + 0.955750i −0.0246527 + 0.0426998i
\(502\) −12.4742 + 21.6059i −0.556750 + 0.964319i
\(503\) 1.56322 0.0697006 0.0348503 0.999393i \(-0.488905\pi\)
0.0348503 + 0.999393i \(0.488905\pi\)
\(504\) 8.97569 15.5464i 0.399809 0.692490i
\(505\) 17.0247 + 29.4876i 0.757588 + 1.31218i
\(506\) −30.4214 52.6914i −1.35239 2.34242i
\(507\) −6.32632 + 10.9575i −0.280962 + 0.486640i
\(508\) 18.9910 32.8933i 0.842588 1.45941i
\(509\) −3.15901 5.47156i −0.140021 0.242523i 0.787484 0.616336i \(-0.211384\pi\)
−0.927504 + 0.373813i \(0.878050\pi\)
\(510\) 27.7523 1.22889
\(511\) −23.1144 40.0354i −1.02252 1.77106i
\(512\) 46.2743 2.04505
\(513\) 3.24844 + 5.62646i 0.143422 + 0.248414i
\(514\) 6.91568 11.9783i 0.305037 0.528340i
\(515\) 2.31785 + 4.01464i 0.102137 + 0.176906i
\(516\) 10.0543 0.442617
\(517\) 35.6425 1.56755
\(518\) 12.4306 21.5304i 0.546169 0.945993i
\(519\) −8.07868 13.9927i −0.354615 0.614211i
\(520\) 12.3402 0.541154
\(521\) −3.69810 + 6.40529i −0.162017 + 0.280621i −0.935592 0.353084i \(-0.885133\pi\)
0.773575 + 0.633704i \(0.218466\pi\)
\(522\) 6.42059 11.1208i 0.281022 0.486744i
\(523\) −1.92776 + 3.33899i −0.0842953 + 0.146004i −0.905091 0.425219i \(-0.860197\pi\)
0.820795 + 0.571222i \(0.193531\pi\)
\(524\) −14.2446 + 24.6724i −0.622280 + 1.07782i
\(525\) −31.8974 −1.39212
\(526\) 9.80158 16.9768i 0.427369 0.740225i
\(527\) −14.0614 −0.612523
\(528\) −14.9137 + 25.8312i −0.649033 + 1.12416i
\(529\) −4.82168 −0.209638
\(530\) 82.5042 3.58375
\(531\) 3.94543 6.83369i 0.171217 0.296557i
\(532\) −44.7890 77.5768i −1.94185 3.36338i
\(533\) 1.63630 2.83416i 0.0708762 0.122761i
\(534\) 11.6365 20.1550i 0.503561 0.872193i
\(535\) 35.8976 1.55199
\(536\) −62.6761 −2.70719
\(537\) −3.49081 + 6.04626i −0.150640 + 0.260916i
\(538\) 68.1848 2.93965
\(539\) 10.9158 + 18.9067i 0.470176 + 0.814369i
\(540\) 8.04086 + 13.9272i 0.346024 + 0.599331i
\(541\) 12.9904 + 22.5001i 0.558502 + 0.967354i 0.997622 + 0.0689253i \(0.0219570\pi\)
−0.439120 + 0.898429i \(0.644710\pi\)
\(542\) 16.7947 29.0893i 0.721394 1.24949i
\(543\) −5.35794 + 9.28023i −0.229931 + 0.398253i
\(544\) 2.94532 + 5.10144i 0.126279 + 0.218722i
\(545\) 4.61665 7.99628i 0.197756 0.342523i
\(546\) −4.82214 −0.206368
\(547\) 3.57210 + 6.18706i 0.152732 + 0.264540i 0.932231 0.361864i \(-0.117860\pi\)
−0.779499 + 0.626404i \(0.784526\pi\)
\(548\) 17.7622 + 30.7650i 0.758764 + 1.31422i
\(549\) −14.2023 −0.606138
\(550\) 138.460 5.90395
\(551\) −16.7607 29.0303i −0.714029 1.23673i
\(552\) −11.6408 20.1624i −0.495464 0.858170i
\(553\) 6.66511 0.283429
\(554\) 12.7790 22.1339i 0.542928 0.940380i
\(555\) 5.82559 + 10.0902i 0.247283 + 0.428306i
\(556\) −12.0158 + 20.8120i −0.509584 + 0.882625i
\(557\) −4.99582 + 8.65302i −0.211680 + 0.366640i −0.952240 0.305349i \(-0.901227\pi\)
0.740561 + 0.671990i \(0.234560\pi\)
\(558\) −6.01688 10.4215i −0.254715 0.441179i
\(559\) −0.706444 1.22360i −0.0298794 0.0517526i
\(560\) −32.7869 56.7886i −1.38550 2.39976i
\(561\) 16.6747 0.704006
\(562\) −10.1158 + 17.5210i −0.426709 + 0.739081i
\(563\) −17.6613 −0.744334 −0.372167 0.928166i \(-0.621385\pi\)
−0.372167 + 0.928166i \(0.621385\pi\)
\(564\) 26.0710 1.09779
\(565\) −32.3263 + 55.9908i −1.35998 + 2.35555i
\(566\) 19.0602 33.0132i 0.801158 1.38765i
\(567\) −1.64374 2.84704i −0.0690305 0.119564i
\(568\) −6.92555 + 11.9954i −0.290590 + 0.503316i
\(569\) 39.5299 1.65718 0.828591 0.559855i \(-0.189143\pi\)
0.828591 + 0.559855i \(0.189143\pi\)
\(570\) 61.9998 2.59689
\(571\) −8.62894 + 14.9458i −0.361110 + 0.625461i −0.988144 0.153531i \(-0.950935\pi\)
0.627034 + 0.778992i \(0.284269\pi\)
\(572\) 14.1732 0.592611
\(573\) −1.25436 + 2.17262i −0.0524017 + 0.0907624i
\(574\) −45.4313 −1.89627
\(575\) −20.6842 + 35.8261i −0.862592 + 1.49405i
\(576\) 2.68138 4.64429i 0.111724 0.193512i
\(577\) −4.78704 + 8.29139i −0.199287 + 0.345175i −0.948297 0.317383i \(-0.897196\pi\)
0.749010 + 0.662558i \(0.230529\pi\)
\(578\) −10.6306 + 18.4127i −0.442174 + 0.765868i
\(579\) 0.891890 0.0370657
\(580\) −41.4878 71.8589i −1.72269 2.98378i
\(581\) 18.2032 31.5288i 0.755194 1.30803i
\(582\) −39.7376 −1.64718
\(583\) 49.5717 2.05305
\(584\) 38.3933 + 66.4992i 1.58873 + 2.75176i
\(585\) 1.12995 1.95712i 0.0467175 0.0809171i
\(586\) −23.4793 40.6673i −0.969921 1.67995i
\(587\) −7.51888 −0.310337 −0.155169 0.987888i \(-0.549592\pi\)
−0.155169 + 0.987888i \(0.549592\pi\)
\(588\) 7.98445 + 13.8295i 0.329273 + 0.570318i
\(589\) −31.4136 −1.29438
\(590\) −37.6513 65.2140i −1.55008 2.68482i
\(591\) −2.34936 + 4.06922i −0.0966400 + 0.167385i
\(592\) −7.90335 + 13.6890i −0.324826 + 0.562615i
\(593\) 11.1514 + 19.3148i 0.457934 + 0.793166i 0.998852 0.0479102i \(-0.0152561\pi\)
−0.540917 + 0.841076i \(0.681923\pi\)
\(594\) 7.13513 + 12.3584i 0.292758 + 0.507072i
\(595\) −18.3293 + 31.7472i −0.751426 + 1.30151i
\(596\) −77.5584 −3.17691
\(597\) 8.91188 15.4358i 0.364739 0.631746i
\(598\) −3.12697 + 5.41607i −0.127871 + 0.221480i
\(599\) −25.0601 −1.02393 −0.511963 0.859007i \(-0.671082\pi\)
−0.511963 + 0.859007i \(0.671082\pi\)
\(600\) 52.9819 2.16298
\(601\) −41.5483 −1.69479 −0.847395 0.530962i \(-0.821831\pi\)
−0.847395 + 0.530962i \(0.821831\pi\)
\(602\) −9.80706 + 16.9863i −0.399706 + 0.692311i
\(603\) −5.73900 + 9.94024i −0.233710 + 0.404798i
\(604\) 32.9270 + 57.0313i 1.33978 + 2.32057i
\(605\) 83.8844 3.41038
\(606\) 11.0501 + 19.1394i 0.448881 + 0.777485i
\(607\) −0.316472 0.548146i −0.0128452 0.0222485i 0.859531 0.511083i \(-0.170756\pi\)
−0.872377 + 0.488834i \(0.837422\pi\)
\(608\) 6.57995 + 11.3968i 0.266852 + 0.462201i
\(609\) 8.48106 + 14.6896i 0.343670 + 0.595254i
\(610\) −67.7663 + 117.375i −2.74378 + 4.75236i
\(611\) −1.83182 3.17281i −0.0741075 0.128358i
\(612\) 12.1969 0.493029
\(613\) −5.44772 + 9.43572i −0.220031 + 0.381105i −0.954817 0.297194i \(-0.903949\pi\)
0.734786 + 0.678299i \(0.237283\pi\)
\(614\) 35.1092 1.41689
\(615\) 10.6457 18.4389i 0.429275 0.743526i
\(616\) −51.4650 89.1401i −2.07359 3.59156i
\(617\) −3.80760 6.59495i −0.153288 0.265503i 0.779146 0.626842i \(-0.215653\pi\)
−0.932434 + 0.361339i \(0.882320\pi\)
\(618\) 1.50444 + 2.60577i 0.0605175 + 0.104819i
\(619\) −0.481687 + 0.834306i −0.0193606 + 0.0335336i −0.875543 0.483139i \(-0.839496\pi\)
0.856183 + 0.516673i \(0.172830\pi\)
\(620\) −77.7583 −3.12285
\(621\) −4.26360 −0.171093
\(622\) −29.6084 51.2833i −1.18719 2.05627i
\(623\) 15.3708 + 26.6231i 0.615820 + 1.06663i
\(624\) 3.06591 0.122734
\(625\) −10.3144 17.8651i −0.412576 0.714603i
\(626\) 46.4198 1.85531
\(627\) 37.2519 1.48770
\(628\) −51.9301 + 8.05687i −2.07224 + 0.321504i
\(629\) 8.83660 0.352338
\(630\) −31.3725 −1.24991
\(631\) −2.58795 4.48247i −0.103025 0.178444i 0.809905 0.586562i \(-0.199519\pi\)
−0.912930 + 0.408117i \(0.866185\pi\)
\(632\) −11.0708 −0.440374
\(633\) −9.65939 16.7306i −0.383926 0.664980i
\(634\) −20.6160 35.7079i −0.818764 1.41814i
\(635\) −34.7249 −1.37802
\(636\) 36.2597 1.43779
\(637\) 1.12202 1.94339i 0.0444560 0.0770000i
\(638\) −36.8145 63.7646i −1.45750 2.52447i
\(639\) 1.26829 + 2.19675i 0.0501728 + 0.0869019i
\(640\) −33.3554 57.7732i −1.31849 2.28369i
\(641\) 5.43538 9.41436i 0.214685 0.371845i −0.738490 0.674264i \(-0.764461\pi\)
0.953175 + 0.302419i \(0.0977943\pi\)
\(642\) 23.2999 0.919575
\(643\) 1.21577 2.10577i 0.0479452 0.0830435i −0.841057 0.540947i \(-0.818066\pi\)
0.889002 + 0.457903i \(0.151399\pi\)
\(644\) 58.7860 2.31649
\(645\) −4.59607 7.96063i −0.180970 0.313450i
\(646\) 23.5112 40.7227i 0.925037 1.60221i
\(647\) 11.0196 + 19.0866i 0.433227 + 0.750371i 0.997149 0.0754572i \(-0.0240416\pi\)
−0.563922 + 0.825828i \(0.690708\pi\)
\(648\) 2.73027 + 4.72896i 0.107255 + 0.185771i
\(649\) −22.6224 39.1832i −0.888007 1.53807i
\(650\) −7.11605 12.3254i −0.279114 0.483440i
\(651\) 15.8956 0.622997
\(652\) 23.1020 + 40.0138i 0.904744 + 1.56706i
\(653\) 18.4465 31.9502i 0.721866 1.25031i −0.238386 0.971171i \(-0.576618\pi\)
0.960251 0.279137i \(-0.0900485\pi\)
\(654\) 2.99652 5.19012i 0.117173 0.202950i
\(655\) 26.0463 1.01771
\(656\) 28.8851 1.12778
\(657\) 14.0621 0.548615
\(658\) −25.4299 + 44.0458i −0.991359 + 1.71708i
\(659\) 5.16026 8.93784i 0.201015 0.348169i −0.747841 0.663878i \(-0.768909\pi\)
0.948856 + 0.315710i \(0.102243\pi\)
\(660\) 92.2098 3.58926
\(661\) 18.5193 32.0764i 0.720319 1.24763i −0.240553 0.970636i \(-0.577329\pi\)
0.960872 0.276993i \(-0.0893379\pi\)
\(662\) 31.4955 + 54.5518i 1.22411 + 2.12021i
\(663\) −0.856984 1.48434i −0.0332825 0.0576470i
\(664\) −30.2356 + 52.3697i −1.17337 + 2.03234i
\(665\) −40.9483 + 70.9245i −1.58791 + 2.75033i
\(666\) 3.78120 + 6.54922i 0.146518 + 0.253777i
\(667\) 21.9986 0.851787
\(668\) 2.31429 + 4.00847i 0.0895426 + 0.155092i
\(669\) −9.32630 −0.360576
\(670\) 54.7674 + 94.8600i 2.11585 + 3.66476i
\(671\) −40.7166 + 70.5233i −1.57185 + 2.72252i
\(672\) −3.32951 5.76689i −0.128439 0.222463i
\(673\) −32.9404 −1.26976 −0.634879 0.772612i \(-0.718950\pi\)
−0.634879 + 0.772612i \(0.718950\pi\)
\(674\) −15.7904 −0.608225
\(675\) 4.85135 8.40278i 0.186728 0.323423i
\(676\) 26.5329 + 45.9564i 1.02050 + 1.76755i
\(677\) 3.52049 0.135303 0.0676517 0.997709i \(-0.478449\pi\)
0.0676517 + 0.997709i \(0.478449\pi\)
\(678\) −20.9819 + 36.3418i −0.805806 + 1.39570i
\(679\) 26.2450 45.4578i 1.00719 1.74451i
\(680\) 30.4451 52.7324i 1.16752 2.02220i
\(681\) −2.40625 + 4.16774i −0.0922076 + 0.159708i
\(682\) −68.9995 −2.64213
\(683\) 14.5295 25.1658i 0.555955 0.962942i −0.441874 0.897077i \(-0.645686\pi\)
0.997829 0.0658648i \(-0.0209806\pi\)
\(684\) 27.2482 1.04186
\(685\) 16.2391 28.1269i 0.620463 1.07467i
\(686\) 26.1204 0.997283
\(687\) 8.34621 0.318428
\(688\) 6.23531 10.7999i 0.237719 0.411741i
\(689\) −2.54770 4.41275i −0.0970598 0.168113i
\(690\) −20.3438 + 35.2366i −0.774477 + 1.34143i
\(691\) −4.25610 + 7.37178i −0.161910 + 0.280436i −0.935554 0.353185i \(-0.885099\pi\)
0.773644 + 0.633621i \(0.218432\pi\)
\(692\) −67.7649 −2.57603
\(693\) −18.8498 −0.716045
\(694\) 36.6556 63.4893i 1.39143 2.41002i
\(695\) 21.9709 0.833402
\(696\) −14.0871 24.3996i −0.533971 0.924865i
\(697\) −8.07400 13.9846i −0.305824 0.529703i
\(698\) −13.9837 24.2205i −0.529291 0.916759i
\(699\) −7.23733 + 12.5354i −0.273741 + 0.474133i
\(700\) −66.8897 + 115.856i −2.52819 + 4.37896i
\(701\) −0.0191693 0.0332021i −0.000724013 0.00125403i 0.865663 0.500627i \(-0.166897\pi\)
−0.866387 + 0.499373i \(0.833564\pi\)
\(702\) 0.733410 1.27030i 0.0276808 0.0479445i
\(703\) 19.7413 0.744558
\(704\) −15.3746 26.6295i −0.579451 1.00364i
\(705\) −11.9177 20.6420i −0.448846 0.777424i
\(706\) 24.2734 0.913541
\(707\) −29.1926 −1.09790
\(708\) −16.5474 28.6609i −0.621888 1.07714i
\(709\) −11.0409 19.1235i −0.414651 0.718197i 0.580741 0.814089i \(-0.302763\pi\)
−0.995392 + 0.0958918i \(0.969430\pi\)
\(710\) 24.2067 0.908460
\(711\) −1.01371 + 1.75580i −0.0380172 + 0.0658477i
\(712\) −25.5311 44.2212i −0.956820 1.65726i
\(713\) 10.3077 17.8534i 0.386026 0.668616i
\(714\) −11.8969 + 20.6060i −0.445230 + 0.771162i
\(715\) −6.47891 11.2218i −0.242298 0.419672i
\(716\) 14.6407 + 25.3584i 0.547147 + 0.947687i
\(717\) −1.78584 3.09316i −0.0666933 0.115516i
\(718\) −35.3255 −1.31834
\(719\) −0.812483 + 1.40726i −0.0303005 + 0.0524820i −0.880778 0.473529i \(-0.842980\pi\)
0.850478 + 0.526011i \(0.176313\pi\)
\(720\) 19.9466 0.743365
\(721\) −3.97448 −0.148017
\(722\) 28.8816 50.0243i 1.07486 1.86171i
\(723\) −13.3312 + 23.0902i −0.495791 + 0.858735i
\(724\) 22.4715 + 38.9218i 0.835147 + 1.44652i
\(725\) −25.0311 + 43.3551i −0.929631 + 1.61017i
\(726\) 54.4465 2.02070
\(727\) −39.1375 −1.45153 −0.725765 0.687943i \(-0.758514\pi\)
−0.725765 + 0.687943i \(0.758514\pi\)
\(728\) −5.29002 + 9.16258i −0.196061 + 0.339588i
\(729\) 1.00000 0.0370370
\(730\) 67.0975 116.216i 2.48339 4.30136i
\(731\) −6.97159 −0.257854
\(732\) −29.7825 + 51.5849i −1.10079 + 1.90663i
\(733\) −10.9521 + 18.9696i −0.404525 + 0.700658i −0.994266 0.106935i \(-0.965896\pi\)
0.589741 + 0.807592i \(0.299230\pi\)
\(734\) −16.6472 + 28.8338i −0.614460 + 1.06428i
\(735\) 7.29977 12.6436i 0.269256 0.466365i
\(736\) −8.63625 −0.318336
\(737\) 32.9064 + 56.9956i 1.21212 + 2.09946i
\(738\) 6.90975 11.9680i 0.254351 0.440550i
\(739\) −38.0764 −1.40066 −0.700332 0.713817i \(-0.746965\pi\)
−0.700332 + 0.713817i \(0.746965\pi\)
\(740\) 48.8657 1.79634
\(741\) −1.91454 3.31607i −0.0703322 0.121819i
\(742\) −35.3680 + 61.2591i −1.29840 + 2.24889i
\(743\) −5.24336 9.08176i −0.192360 0.333178i 0.753672 0.657251i \(-0.228281\pi\)
−0.946032 + 0.324073i \(0.894948\pi\)
\(744\) −26.4028 −0.967972
\(745\) 35.4538 + 61.4078i 1.29893 + 2.24981i
\(746\) −83.7299 −3.06557
\(747\) 5.53712 + 9.59057i 0.202593 + 0.350901i
\(748\) 34.9673 60.5651i 1.27853 2.21448i
\(749\) −15.3886 + 26.6539i −0.562288 + 0.973912i
\(750\) −22.4390 38.8654i −0.819355 1.41916i
\(751\) −3.38405 5.86134i −0.123486 0.213883i 0.797654 0.603115i \(-0.206074\pi\)
−0.921140 + 0.389231i \(0.872741\pi\)
\(752\) 16.1683 28.0042i 0.589596 1.02121i
\(753\) 10.0243 0.365306
\(754\) −3.78411 + 6.55427i −0.137809 + 0.238693i
\(755\) 30.1035 52.1408i 1.09558 1.89760i
\(756\) −13.7879 −0.501460
\(757\) −12.8960 −0.468713 −0.234357 0.972151i \(-0.575298\pi\)
−0.234357 + 0.972151i \(0.575298\pi\)
\(758\) −57.9705 −2.10558
\(759\) −12.2234 + 21.1715i −0.443680 + 0.768477i
\(760\) 68.0155 117.806i 2.46718 4.27328i
\(761\) 6.98423 + 12.0970i 0.253178 + 0.438518i 0.964399 0.264451i \(-0.0851908\pi\)
−0.711221 + 0.702969i \(0.751857\pi\)
\(762\) −22.5388 −0.816494
\(763\) 3.95814 + 6.85571i 0.143294 + 0.248193i
\(764\) 5.26086 + 9.11208i 0.190331 + 0.329664i
\(765\) −5.57548 9.65701i −0.201582 0.349150i
\(766\) −2.67462 4.63258i −0.0966379 0.167382i
\(767\) −2.32533 + 4.02758i −0.0839626 + 0.145428i
\(768\) −16.2871 28.2101i −0.587710 1.01794i
\(769\) 16.3346 0.589041 0.294521 0.955645i \(-0.404840\pi\)
0.294521 + 0.955645i \(0.404840\pi\)
\(770\) −89.9421 + 155.784i −3.24129 + 5.61408i
\(771\) −5.55747 −0.200147
\(772\) 1.87032 3.23949i 0.0673143 0.116592i
\(773\) 12.7482 + 22.0805i 0.458521 + 0.794181i 0.998883 0.0472511i \(-0.0150461\pi\)
−0.540362 + 0.841433i \(0.681713\pi\)
\(774\) −2.98316 5.16698i −0.107227 0.185723i
\(775\) 23.4572 + 40.6291i 0.842608 + 1.45944i
\(776\) −43.5933 + 75.5058i −1.56491 + 2.71050i
\(777\) −9.98929 −0.358364
\(778\) 55.6643 1.99566
\(779\) −18.0376 31.2421i −0.646265 1.11936i
\(780\) −4.73906 8.20829i −0.169685 0.293904i
\(781\) 14.5443 0.520437
\(782\) 15.4294 + 26.7244i 0.551753 + 0.955664i
\(783\) −5.15961 −0.184390
\(784\) 19.8066 0.707379
\(785\) 30.1176 + 37.4333i 1.07494 + 1.33605i
\(786\) 16.9058 0.603009
\(787\) −28.4468 −1.01402 −0.507010 0.861940i \(-0.669249\pi\)
−0.507010 + 0.861940i \(0.669249\pi\)
\(788\) 9.85337 + 17.0665i 0.351012 + 0.607970i
\(789\) −7.87660 −0.280414
\(790\) 9.67388 + 16.7557i 0.344181 + 0.596139i
\(791\) −27.7154 48.0044i −0.985445 1.70684i
\(792\) 31.3097 1.11254
\(793\) 8.37041 0.297242
\(794\) −30.1357 + 52.1965i −1.06948 + 1.85239i
\(795\) −16.5752 28.7091i −0.587861 1.01821i
\(796\) −37.3769 64.7387i −1.32479 2.29460i
\(797\) 9.78759 + 16.9526i 0.346694 + 0.600492i 0.985660 0.168743i \(-0.0539709\pi\)
−0.638966 + 0.769235i \(0.720638\pi\)
\(798\) −26.5781 + 46.0347i −0.940856 + 1.62961i
\(799\) −18.0775 −0.639534
\(800\) 9.82676 17.0205i 0.347429 0.601764i
\(801\) −9.35115 −0.330407
\(802\) 24.2014 + 41.9181i 0.854581 + 1.48018i
\(803\) 40.3148 69.8273i 1.42268 2.46415i
\(804\) 24.0697 + 41.6899i 0.848873 + 1.47029i
\(805\) −26.8725 46.5445i −0.947131 1.64048i
\(806\) 3.54618 + 6.14216i 0.124909 + 0.216348i
\(807\) −13.6984 23.7263i −0.482207 0.835206i
\(808\) 48.4893 1.70585
\(809\) −4.91749 8.51735i −0.172890 0.299454i 0.766539 0.642198i \(-0.221977\pi\)
−0.939429 + 0.342744i \(0.888644\pi\)
\(810\) 4.77151 8.26450i 0.167654 0.290385i
\(811\) −8.00283 + 13.8613i −0.281017 + 0.486736i −0.971636 0.236483i \(-0.924005\pi\)
0.690618 + 0.723220i \(0.257339\pi\)
\(812\) 71.1401 2.49653
\(813\) −13.4963 −0.473336
\(814\) 43.3614 1.51982
\(815\) 21.1210 36.5826i 0.739835 1.28143i
\(816\) 7.56403 13.1013i 0.264794 0.458637i
\(817\) −15.5748 −0.544894
\(818\) −27.5497 + 47.7175i −0.963253 + 1.66840i
\(819\) 0.968773 + 1.67796i 0.0338517 + 0.0586328i
\(820\) −44.6486 77.3336i −1.55920 2.70061i
\(821\) 3.61979 6.26965i 0.126331 0.218812i −0.795921 0.605400i \(-0.793013\pi\)
0.922253 + 0.386588i \(0.126346\pi\)
\(822\) 10.5402 18.2562i 0.367633 0.636759i
\(823\) −18.6356 32.2779i −0.649598 1.12514i −0.983219 0.182429i \(-0.941604\pi\)
0.333621 0.942707i \(-0.391729\pi\)
\(824\) 6.60165 0.229979
\(825\) −27.8168 48.1801i −0.968456 1.67741i
\(826\) 64.5617 2.24639
\(827\) −18.5756 32.1739i −0.645937 1.11879i −0.984084 0.177702i \(-0.943134\pi\)
0.338148 0.941093i \(-0.390200\pi\)
\(828\) −8.94090 + 15.4861i −0.310718 + 0.538179i
\(829\) 1.45917 + 2.52735i 0.0506789 + 0.0877785i 0.890252 0.455468i \(-0.150528\pi\)
−0.839573 + 0.543247i \(0.817195\pi\)
\(830\) 105.682 3.66827
\(831\) −10.2693 −0.356237
\(832\) −1.58033 + 2.73721i −0.0547881 + 0.0948957i
\(833\) −5.53636 9.58926i −0.191823 0.332248i
\(834\) 14.2606 0.493802
\(835\) 2.11584 3.66474i 0.0732215 0.126823i
\(836\) 78.1183 135.305i 2.70178 4.67962i
\(837\) −2.41760 + 4.18740i −0.0835644 + 0.144738i
\(838\) −48.2610 + 83.5905i −1.66715 + 2.88759i
\(839\) 14.9309 0.515472 0.257736 0.966215i \(-0.417023\pi\)
0.257736 + 0.966215i \(0.417023\pi\)
\(840\) −34.4165 + 59.6111i −1.18748 + 2.05678i
\(841\) −2.37837 −0.0820129
\(842\) 32.4824 56.2611i 1.11942 1.93889i
\(843\) 8.12909 0.279981
\(844\) −81.0240 −2.78896
\(845\) 24.2577 42.0156i 0.834490 1.44538i
\(846\) −7.73537 13.3981i −0.265948 0.460635i
\(847\) −35.9596 + 62.2839i −1.23559 + 2.14010i
\(848\) 22.4869 38.9485i 0.772203 1.33750i
\(849\) −15.3168 −0.525672
\(850\) −70.2253 −2.40871
\(851\) −6.47767 + 11.2196i −0.222052 + 0.384604i
\(852\) 10.6386 0.364471
\(853\) −3.19989 5.54238i −0.109562 0.189767i 0.806031 0.591874i \(-0.201612\pi\)
−0.915593 + 0.402106i \(0.868278\pi\)
\(854\) −58.1002 100.633i −1.98815 3.44357i
\(855\) −12.4558 21.5741i −0.425981 0.737820i
\(856\) 25.5607 44.2724i 0.873646 1.51320i
\(857\) 22.7409 39.3884i 0.776814 1.34548i −0.156956 0.987606i \(-0.550168\pi\)
0.933769 0.357875i \(-0.116499\pi\)
\(858\) −4.20524 7.28369i −0.143565 0.248661i
\(859\) −15.0402 + 26.0504i −0.513165 + 0.888828i 0.486718 + 0.873559i \(0.338194\pi\)
−0.999883 + 0.0152691i \(0.995139\pi\)
\(860\) −38.5524 −1.31463
\(861\) 9.12720 + 15.8088i 0.311054 + 0.538762i
\(862\) 6.76590 + 11.7189i 0.230448 + 0.399147i
\(863\) 55.0453 1.87376 0.936882 0.349645i \(-0.113698\pi\)
0.936882 + 0.349645i \(0.113698\pi\)
\(864\) 2.02557 0.0689114
\(865\) 30.9770 + 53.6537i 1.05325 + 1.82428i
\(866\) 27.7103 + 47.9957i 0.941635 + 1.63096i
\(867\) 8.54279 0.290128
\(868\) 33.3335 57.7353i 1.13141 1.95966i
\(869\) 5.81245 + 10.0675i 0.197174 + 0.341515i
\(870\) −24.6192 + 42.6416i −0.834668 + 1.44569i
\(871\) 3.38241 5.85850i 0.114608 0.198508i
\(872\) −6.57452 11.3874i −0.222641 0.385626i
\(873\) 7.98334 + 13.8275i 0.270195 + 0.467992i
\(874\) 34.4698 + 59.7034i 1.16596 + 2.01950i
\(875\) 59.2800 2.00403
\(876\) 29.4886 51.0758i 0.996329 1.72569i
\(877\) 26.9421 0.909770 0.454885 0.890550i \(-0.349680\pi\)
0.454885 + 0.890550i \(0.349680\pi\)
\(878\) −87.9985 −2.96980
\(879\) −9.43404 + 16.3402i −0.318202 + 0.551142i
\(880\) 57.1850 99.0474i 1.92771 3.33889i
\(881\) 11.3162 + 19.6002i 0.381251 + 0.660347i 0.991241 0.132062i \(-0.0421599\pi\)
−0.609990 + 0.792409i \(0.708827\pi\)
\(882\) 4.73803 8.20652i 0.159538 0.276328i
\(883\) 0.709122 0.0238638 0.0119319 0.999929i \(-0.496202\pi\)
0.0119319 + 0.999929i \(0.496202\pi\)
\(884\) −7.18848 −0.241775
\(885\) −15.1284 + 26.2032i −0.508536 + 0.880809i
\(886\) 24.4593 0.821726
\(887\) 14.5252 25.1584i 0.487709 0.844737i −0.512191 0.858872i \(-0.671166\pi\)
0.999900 + 0.0141344i \(0.00449927\pi\)
\(888\) 16.5923 0.556801
\(889\) 14.8859 25.7832i 0.499258 0.864740i
\(890\) −44.6191 + 77.2826i −1.49564 + 2.59052i
\(891\) 2.86691 4.96564i 0.0960452 0.166355i
\(892\) −19.5575 + 33.8746i −0.654834 + 1.13421i
\(893\) −40.3857 −1.35146
\(894\) 23.0119 + 39.8577i 0.769632 + 1.33304i
\(895\) 13.3852 23.1839i 0.447418 0.774951i
\(896\) 57.1953 1.91076
\(897\) 2.51285 0.0839015
\(898\) 8.66944 + 15.0159i 0.289303 + 0.501087i
\(899\) 12.4739 21.6054i 0.416027 0.720580i
\(900\) −20.3468 35.2417i −0.678227 1.17472i
\(901\) −25.1422 −0.837609
\(902\) −39.6193 68.6226i −1.31918 2.28488i
\(903\) 7.88100 0.262263
\(904\) 46.0355 + 79.7359i 1.53112 + 2.65198i
\(905\) 20.5445 35.5842i 0.682924 1.18286i
\(906\) 19.5392 33.8428i 0.649145 1.12435i
\(907\) −4.45082 7.70904i −0.147787 0.255975i 0.782622 0.622497i \(-0.213882\pi\)
−0.930409 + 0.366522i \(0.880548\pi\)
\(908\) 10.0919 + 17.4797i 0.334913 + 0.580086i
\(909\) 4.43997 7.69026i 0.147265 0.255070i
\(910\) 18.4900 0.612939
\(911\) 14.4457 25.0206i 0.478606 0.828970i −0.521093 0.853500i \(-0.674476\pi\)
0.999699 + 0.0245298i \(0.00780887\pi\)
\(912\) 16.8983 29.2688i 0.559560 0.969186i
\(913\) 63.4977 2.10147
\(914\) 5.41976 0.179270
\(915\) 54.4573 1.80030
\(916\) 17.5022 30.3148i 0.578290 1.00163i
\(917\) −11.1655 + 19.3393i −0.368719 + 0.638640i
\(918\) −3.61885 6.26804i −0.119440 0.206876i
\(919\) 55.2168 1.82143 0.910716 0.413032i \(-0.135530\pi\)
0.910716 + 0.413032i \(0.135530\pi\)
\(920\) 44.6355 + 77.3110i 1.47159 + 2.54887i
\(921\) −7.05347 12.2170i −0.232420 0.402563i
\(922\) −22.1144 38.3033i −0.728300 1.26145i
\(923\) −0.747495 1.29470i −0.0246041 0.0426155i
\(924\) −39.5286 + 68.4655i −1.30040 + 2.25235i
\(925\) −14.7412 25.5326i −0.484689 0.839506i
\(926\) −58.9571 −1.93745
\(927\) 0.604487 1.04700i 0.0198540 0.0343881i
\(928\) −10.4512 −0.343077
\(929\) −3.56227 + 6.17003i −0.116874 + 0.202432i −0.918527 0.395357i \(-0.870621\pi\)
0.801653 + 0.597789i \(0.203954\pi\)
\(930\) 23.0712 + 39.9605i 0.756534 + 1.31036i
\(931\) −12.3684 21.4228i −0.405359 0.702103i
\(932\) 30.3538 + 52.5742i 0.994270 + 1.72213i
\(933\) −11.8967 + 20.6058i −0.389482 + 0.674602i
\(934\) 57.3985 1.87814
\(935\) −63.9376 −2.09098
\(936\) −1.60914 2.78712i −0.0525965 0.0910997i
\(937\) −1.02546 1.77615i −0.0335004 0.0580243i 0.848789 0.528732i \(-0.177332\pi\)
−0.882289 + 0.470707i \(0.843999\pi\)
\(938\) −93.9111 −3.06630
\(939\) −9.32579 16.1527i −0.304336 0.527125i
\(940\) −99.9669 −3.26056
\(941\) −1.79663 −0.0585685 −0.0292842 0.999571i \(-0.509323\pi\)
−0.0292842 + 0.999571i \(0.509323\pi\)
\(942\) 19.5483 + 24.2967i 0.636919 + 0.791629i
\(943\) 23.6746 0.770949
\(944\) −41.0482 −1.33601
\(945\) 6.30277 + 10.9167i 0.205029 + 0.355121i
\(946\) −34.2098 −1.11226
\(947\) −8.31990 14.4105i −0.270361 0.468278i 0.698594 0.715519i \(-0.253810\pi\)
−0.968954 + 0.247240i \(0.920476\pi\)
\(948\) 4.25157 + 7.36393i 0.138084 + 0.239169i
\(949\) −8.28781 −0.269034
\(950\) −156.886 −5.09005
\(951\) −8.28354 + 14.3475i −0.268612 + 0.465250i
\(952\) 26.1025 + 45.2108i 0.845986 + 1.46529i
\(953\) 20.4041 + 35.3409i 0.660953 + 1.14480i 0.980366 + 0.197188i \(0.0631811\pi\)
−0.319413 + 0.947616i \(0.603486\pi\)
\(954\) −10.7584 18.6341i −0.348316 0.603301i
\(955\) 4.80974 8.33071i 0.155639 0.269575i
\(956\) −14.9798 −0.484481
\(957\) −14.7922 + 25.6208i −0.478163 + 0.828202i
\(958\) 92.0731 2.97475
\(959\) 13.9228 + 24.1149i 0.449589 + 0.778712i
\(960\) −10.2815 + 17.8081i −0.331834 + 0.574754i
\(961\) 3.81045 + 6.59989i 0.122918 + 0.212900i
\(962\) −2.22853 3.85993i −0.0718507 0.124449i
\(963\) −4.68099 8.10771i −0.150843 0.261267i
\(964\) 55.9116 + 96.8417i 1.80079 + 3.11906i
\(965\) −3.41987 −0.110090
\(966\) −17.4420 30.2105i −0.561188 0.972007i
\(967\) 0.469200 0.812678i 0.0150884 0.0261339i −0.858383 0.513010i \(-0.828530\pi\)
0.873471 + 0.486876i \(0.161864\pi\)
\(968\) 59.7293 103.454i 1.91977 3.32515i
\(969\) −18.8937 −0.606954
\(970\) 152.370 4.89232
\(971\) 32.9863 1.05858 0.529290 0.848441i \(-0.322459\pi\)
0.529290 + 0.848441i \(0.322459\pi\)
\(972\) 2.09703 3.63216i 0.0672622 0.116502i
\(973\) −9.41849 + 16.3133i −0.301943 + 0.522981i
\(974\) 32.3962 1.03804
\(975\) −2.85925 + 4.95236i −0.0915692 + 0.158602i
\(976\) 36.9400 + 63.9820i 1.18242 + 2.04801i
\(977\) 8.17558 + 14.1605i 0.261560 + 0.453035i 0.966657 0.256076i \(-0.0824297\pi\)
−0.705097 + 0.709111i \(0.749096\pi\)
\(978\) 13.7089 23.7445i 0.438362 0.759266i
\(979\) −26.8089 + 46.4344i −0.856817 + 1.48405i
\(980\) −30.6156 53.0278i −0.977981 1.69391i
\(981\) −2.40801 −0.0768820
\(982\) −42.5082 73.6264i −1.35649 2.34951i
\(983\) −20.7375 −0.661423 −0.330712 0.943732i \(-0.607289\pi\)
−0.330712 + 0.943732i \(0.607289\pi\)
\(984\) −15.1604 26.2585i −0.483295 0.837092i
\(985\) 9.00843 15.6031i 0.287032 0.497155i
\(986\) 18.6719 + 32.3407i 0.594634 + 1.02994i
\(987\) 20.4356 0.650471
\(988\) −16.0593 −0.510916
\(989\) 5.11052 8.85169i 0.162505 0.281467i
\(990\) −27.3590 47.3872i −0.869526 1.50606i
\(991\) −5.41424 −0.171989 −0.0859946 0.996296i \(-0.527407\pi\)
−0.0859946 + 0.996296i \(0.527407\pi\)
\(992\) −4.89702 + 8.48189i −0.155481 + 0.269300i
\(993\) 12.6550 21.9190i 0.401593 0.695579i
\(994\) −10.3769 + 17.9734i −0.329137 + 0.570081i
\(995\) −34.1718 + 59.1873i −1.08332 + 1.87636i
\(996\) 46.4460 1.47170
\(997\) −25.3391 + 43.8886i −0.802497 + 1.38997i 0.115471 + 0.993311i \(0.463162\pi\)
−0.917968 + 0.396655i \(0.870171\pi\)
\(998\) 45.7199 1.44724
\(999\) 1.51929 2.63149i 0.0480683 0.0832568i
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 471.2.e.b.169.1 22
157.144 even 3 inner 471.2.e.b.301.1 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.e.b.169.1 22 1.1 even 1 trivial
471.2.e.b.301.1 yes 22 157.144 even 3 inner