Properties

Label 429.2.i.c.100.5
Level $429$
Weight $2$
Character 429.100
Analytic conductor $3.426$
Analytic rank $0$
Dimension $10$
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] = [429,2,Mod(100,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.i (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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.7965937851507.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 8x^{8} - 6x^{7} + 28x^{6} - 23x^{5} + 51x^{4} - 10x^{3} + 25x^{2} - 6x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.5
Root \(-0.893322 - 1.54728i\) of defining polynomial
Character \(\chi\) \(=\) 429.100
Dual form 429.2.i.c.133.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.893322 - 1.54728i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.596049 - 1.03239i) q^{4} -0.535309 q^{5} +(0.893322 + 1.54728i) q^{6} +(-2.30994 - 4.00094i) q^{7} +1.44343 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.893322 - 1.54728i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.596049 - 1.03239i) q^{4} -0.535309 q^{5} +(0.893322 + 1.54728i) q^{6} +(-2.30994 - 4.00094i) q^{7} +1.44343 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.478203 + 0.828272i) q^{10} +(0.500000 - 0.866025i) q^{11} +1.19210 q^{12} +(1.10471 - 3.43214i) q^{13} -8.25410 q^{14} +(0.267654 - 0.463591i) q^{15} +(2.48155 - 4.29817i) q^{16} +(-2.01117 - 3.48345i) q^{17} -1.78664 q^{18} +(3.75422 + 6.50250i) q^{19} +(0.319070 + 0.552646i) q^{20} +4.61989 q^{21} +(-0.893322 - 1.54728i) q^{22} +(2.59408 - 4.49308i) q^{23} +(-0.721717 + 1.25005i) q^{24} -4.71344 q^{25} +(-4.32362 - 4.77531i) q^{26} +1.00000 q^{27} +(-2.75368 + 4.76951i) q^{28} +(2.41231 - 4.17825i) q^{29} +(-0.478203 - 0.828272i) q^{30} -3.58893 q^{31} +(-2.99021 - 5.17920i) q^{32} +(0.500000 + 0.866025i) q^{33} -7.18648 q^{34} +(1.23653 + 2.14174i) q^{35} +(-0.596049 + 1.03239i) q^{36} +(-1.99803 + 3.46070i) q^{37} +13.4149 q^{38} +(2.41997 + 2.67278i) q^{39} -0.772682 q^{40} +(-4.70959 + 8.15724i) q^{41} +(4.12705 - 7.14826i) q^{42} +(3.90683 + 6.76683i) q^{43} -1.19210 q^{44} +(0.267654 + 0.463591i) q^{45} +(-4.63470 - 8.02754i) q^{46} +9.31634 q^{47} +(2.48155 + 4.29817i) q^{48} +(-7.17168 + 12.4217i) q^{49} +(-4.21062 + 7.29302i) q^{50} +4.02234 q^{51} +(-4.20176 + 0.905235i) q^{52} +7.61596 q^{53} +(0.893322 - 1.54728i) q^{54} +(-0.267654 + 0.463591i) q^{55} +(-3.33425 - 5.77509i) q^{56} -7.50844 q^{57} +(-4.30994 - 7.46504i) q^{58} +(-2.07790 - 3.59903i) q^{59} -0.638140 q^{60} +(4.87922 + 8.45107i) q^{61} +(-3.20607 + 5.55308i) q^{62} +(-2.30994 + 4.00094i) q^{63} -0.758694 q^{64} +(-0.591362 + 1.83726i) q^{65} +1.78664 q^{66} +(-3.91130 + 6.77458i) q^{67} +(-2.39751 + 4.15261i) q^{68} +(2.59408 + 4.49308i) q^{69} +4.41849 q^{70} +(-5.18779 - 8.98551i) q^{71} +(-0.721717 - 1.25005i) q^{72} +1.96904 q^{73} +(3.56978 + 6.18303i) q^{74} +(2.35672 - 4.08196i) q^{75} +(4.47540 - 7.75161i) q^{76} -4.61989 q^{77} +(6.29735 - 1.35671i) q^{78} +8.39852 q^{79} +(-1.32839 + 2.30085i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.41435 + 14.5741i) q^{82} +7.36522 q^{83} +(-2.75368 - 4.76951i) q^{84} +(1.07660 + 1.86472i) q^{85} +13.9602 q^{86} +(2.41231 + 4.17825i) q^{87} +(0.721717 - 1.25005i) q^{88} +(-1.68762 + 2.92305i) q^{89} +0.956406 q^{90} +(-16.2836 + 3.50817i) q^{91} -6.18480 q^{92} +(1.79447 - 3.10811i) q^{93} +(8.32249 - 14.4150i) q^{94} +(-2.00967 - 3.48084i) q^{95} +5.98042 q^{96} +(-5.95675 - 10.3174i) q^{97} +(12.8132 + 22.1932i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.893322 1.54728i 0.631674 1.09409i −0.355535 0.934663i \(-0.615701\pi\)
0.987209 0.159429i \(-0.0509653\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.596049 1.03239i −0.298024 0.516194i
\(5\) −0.535309 −0.239397 −0.119699 0.992810i \(-0.538193\pi\)
−0.119699 + 0.992810i \(0.538193\pi\)
\(6\) 0.893322 + 1.54728i 0.364697 + 0.631674i
\(7\) −2.30994 4.00094i −0.873077 1.51221i −0.858798 0.512315i \(-0.828788\pi\)
−0.0142792 0.999898i \(-0.504545\pi\)
\(8\) 1.44343 0.510331
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.478203 + 0.828272i −0.151221 + 0.261923i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 1.19210 0.344129
\(13\) 1.10471 3.43214i 0.306392 0.951905i
\(14\) −8.25410 −2.20600
\(15\) 0.267654 0.463591i 0.0691080 0.119699i
\(16\) 2.48155 4.29817i 0.620387 1.07454i
\(17\) −2.01117 3.48345i −0.487780 0.844860i 0.512121 0.858913i \(-0.328860\pi\)
−0.999901 + 0.0140535i \(0.995526\pi\)
\(18\) −1.78664 −0.421116
\(19\) 3.75422 + 6.50250i 0.861277 + 1.49178i 0.870697 + 0.491820i \(0.163668\pi\)
−0.00942037 + 0.999956i \(0.502999\pi\)
\(20\) 0.319070 + 0.552646i 0.0713463 + 0.123575i
\(21\) 4.61989 1.00814
\(22\) −0.893322 1.54728i −0.190457 0.329881i
\(23\) 2.59408 4.49308i 0.540904 0.936873i −0.457949 0.888979i \(-0.651416\pi\)
0.998852 0.0478941i \(-0.0152510\pi\)
\(24\) −0.721717 + 1.25005i −0.147320 + 0.255165i
\(25\) −4.71344 −0.942689
\(26\) −4.32362 4.77531i −0.847932 0.936515i
\(27\) 1.00000 0.192450
\(28\) −2.75368 + 4.76951i −0.520396 + 0.901353i
\(29\) 2.41231 4.17825i 0.447955 0.775881i −0.550298 0.834969i \(-0.685486\pi\)
0.998253 + 0.0590875i \(0.0188191\pi\)
\(30\) −0.478203 0.828272i −0.0873075 0.151221i
\(31\) −3.58893 −0.644591 −0.322296 0.946639i \(-0.604455\pi\)
−0.322296 + 0.946639i \(0.604455\pi\)
\(32\) −2.99021 5.17920i −0.528600 0.915562i
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) −7.18648 −1.23247
\(35\) 1.23653 + 2.14174i 0.209012 + 0.362020i
\(36\) −0.596049 + 1.03239i −0.0993415 + 0.172065i
\(37\) −1.99803 + 3.46070i −0.328475 + 0.568935i −0.982209 0.187789i \(-0.939868\pi\)
0.653735 + 0.756724i \(0.273201\pi\)
\(38\) 13.4149 2.17619
\(39\) 2.41997 + 2.67278i 0.387505 + 0.427987i
\(40\) −0.772682 −0.122172
\(41\) −4.70959 + 8.15724i −0.735514 + 1.27395i 0.218984 + 0.975728i \(0.429726\pi\)
−0.954498 + 0.298219i \(0.903608\pi\)
\(42\) 4.12705 7.14826i 0.636817 1.10300i
\(43\) 3.90683 + 6.76683i 0.595787 + 1.03193i 0.993435 + 0.114395i \(0.0364929\pi\)
−0.397649 + 0.917538i \(0.630174\pi\)
\(44\) −1.19210 −0.179716
\(45\) 0.267654 + 0.463591i 0.0398995 + 0.0691080i
\(46\) −4.63470 8.02754i −0.683350 1.18360i
\(47\) 9.31634 1.35893 0.679464 0.733709i \(-0.262212\pi\)
0.679464 + 0.733709i \(0.262212\pi\)
\(48\) 2.48155 + 4.29817i 0.358181 + 0.620387i
\(49\) −7.17168 + 12.4217i −1.02453 + 1.77453i
\(50\) −4.21062 + 7.29302i −0.595472 + 1.03139i
\(51\) 4.02234 0.563240
\(52\) −4.20176 + 0.905235i −0.582680 + 0.125534i
\(53\) 7.61596 1.04613 0.523066 0.852292i \(-0.324788\pi\)
0.523066 + 0.852292i \(0.324788\pi\)
\(54\) 0.893322 1.54728i 0.121566 0.210558i
\(55\) −0.267654 + 0.463591i −0.0360905 + 0.0625106i
\(56\) −3.33425 5.77509i −0.445558 0.771729i
\(57\) −7.50844 −0.994517
\(58\) −4.30994 7.46504i −0.565923 0.980208i
\(59\) −2.07790 3.59903i −0.270520 0.468554i 0.698475 0.715634i \(-0.253862\pi\)
−0.968995 + 0.247080i \(0.920529\pi\)
\(60\) −0.638140 −0.0823836
\(61\) 4.87922 + 8.45107i 0.624721 + 1.08205i 0.988595 + 0.150600i \(0.0481205\pi\)
−0.363874 + 0.931448i \(0.618546\pi\)
\(62\) −3.20607 + 5.55308i −0.407172 + 0.705242i
\(63\) −2.30994 + 4.00094i −0.291026 + 0.504071i
\(64\) −0.758694 −0.0948368
\(65\) −0.591362 + 1.83726i −0.0733494 + 0.227884i
\(66\) 1.78664 0.219921
\(67\) −3.91130 + 6.77458i −0.477842 + 0.827647i −0.999677 0.0253997i \(-0.991914\pi\)
0.521835 + 0.853046i \(0.325248\pi\)
\(68\) −2.39751 + 4.15261i −0.290741 + 0.503578i
\(69\) 2.59408 + 4.49308i 0.312291 + 0.540904i
\(70\) 4.41849 0.528110
\(71\) −5.18779 8.98551i −0.615677 1.06638i −0.990265 0.139193i \(-0.955549\pi\)
0.374588 0.927191i \(-0.377784\pi\)
\(72\) −0.721717 1.25005i −0.0850551 0.147320i
\(73\) 1.96904 0.230459 0.115230 0.993339i \(-0.463240\pi\)
0.115230 + 0.993339i \(0.463240\pi\)
\(74\) 3.56978 + 6.18303i 0.414978 + 0.718763i
\(75\) 2.35672 4.08196i 0.272131 0.471344i
\(76\) 4.47540 7.75161i 0.513363 0.889171i
\(77\) −4.61989 −0.526485
\(78\) 6.29735 1.35671i 0.713034 0.153617i
\(79\) 8.39852 0.944907 0.472453 0.881356i \(-0.343368\pi\)
0.472453 + 0.881356i \(0.343368\pi\)
\(80\) −1.32839 + 2.30085i −0.148519 + 0.257243i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 8.41435 + 14.5741i 0.929210 + 1.60944i
\(83\) 7.36522 0.808438 0.404219 0.914662i \(-0.367543\pi\)
0.404219 + 0.914662i \(0.367543\pi\)
\(84\) −2.75368 4.76951i −0.300451 0.520396i
\(85\) 1.07660 + 1.86472i 0.116773 + 0.202257i
\(86\) 13.9602 1.50537
\(87\) 2.41231 + 4.17825i 0.258627 + 0.447955i
\(88\) 0.721717 1.25005i 0.0769353 0.133256i
\(89\) −1.68762 + 2.92305i −0.178888 + 0.309842i −0.941500 0.337014i \(-0.890583\pi\)
0.762612 + 0.646856i \(0.223917\pi\)
\(90\) 0.956406 0.100814
\(91\) −16.2836 + 3.50817i −1.70699 + 0.367757i
\(92\) −6.18480 −0.644810
\(93\) 1.79447 3.10811i 0.186077 0.322296i
\(94\) 8.32249 14.4150i 0.858400 1.48679i
\(95\) −2.00967 3.48084i −0.206187 0.357127i
\(96\) 5.98042 0.610374
\(97\) −5.95675 10.3174i −0.604816 1.04757i −0.992081 0.125603i \(-0.959913\pi\)
0.387264 0.921969i \(-0.373420\pi\)
\(98\) 12.8132 + 22.1932i 1.29433 + 2.24185i
\(99\) −1.00000 −0.100504
\(100\) 2.80944 + 4.86610i 0.280944 + 0.486610i
\(101\) −5.61321 + 9.72236i −0.558535 + 0.967411i 0.439084 + 0.898446i \(0.355303\pi\)
−0.997619 + 0.0689652i \(0.978030\pi\)
\(102\) 3.59324 6.22368i 0.355784 0.616236i
\(103\) 7.92989 0.781356 0.390678 0.920527i \(-0.372241\pi\)
0.390678 + 0.920527i \(0.372241\pi\)
\(104\) 1.59458 4.95407i 0.156361 0.485787i
\(105\) −2.47307 −0.241346
\(106\) 6.80350 11.7840i 0.660815 1.14456i
\(107\) 6.35241 11.0027i 0.614111 1.06367i −0.376429 0.926446i \(-0.622848\pi\)
0.990540 0.137226i \(-0.0438186\pi\)
\(108\) −0.596049 1.03239i −0.0573548 0.0993415i
\(109\) −3.62992 −0.347683 −0.173842 0.984774i \(-0.555618\pi\)
−0.173842 + 0.984774i \(0.555618\pi\)
\(110\) 0.478203 + 0.828272i 0.0455949 + 0.0789726i
\(111\) −1.99803 3.46070i −0.189645 0.328475i
\(112\) −22.9290 −2.16658
\(113\) −6.87759 11.9123i −0.646989 1.12062i −0.983838 0.179059i \(-0.942695\pi\)
0.336849 0.941559i \(-0.390639\pi\)
\(114\) −6.70745 + 11.6176i −0.628211 + 1.08809i
\(115\) −1.38863 + 2.40519i −0.129491 + 0.224285i
\(116\) −5.75142 −0.534006
\(117\) −3.52468 + 0.759363i −0.325857 + 0.0702032i
\(118\) −7.42494 −0.683521
\(119\) −9.29137 + 16.0931i −0.851739 + 1.47525i
\(120\) 0.386341 0.669163i 0.0352680 0.0610859i
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 17.4349 1.57848
\(123\) −4.70959 8.15724i −0.424649 0.735514i
\(124\) 2.13918 + 3.70517i 0.192104 + 0.332734i
\(125\) 5.19969 0.465074
\(126\) 4.12705 + 7.14826i 0.367667 + 0.636817i
\(127\) 0.0993951 0.172157i 0.00881989 0.0152765i −0.861582 0.507619i \(-0.830526\pi\)
0.870402 + 0.492342i \(0.163859\pi\)
\(128\) 5.30267 9.18449i 0.468694 0.811802i
\(129\) −7.81367 −0.687955
\(130\) 2.31447 + 2.55626i 0.202993 + 0.224199i
\(131\) 21.7985 1.90454 0.952272 0.305251i \(-0.0987405\pi\)
0.952272 + 0.305251i \(0.0987405\pi\)
\(132\) 0.596049 1.03239i 0.0518794 0.0898578i
\(133\) 17.3441 30.0408i 1.50392 2.60487i
\(134\) 6.98811 + 12.1038i 0.603681 + 1.04561i
\(135\) −0.535309 −0.0460720
\(136\) −2.90299 5.02812i −0.248929 0.431158i
\(137\) 7.24914 + 12.5559i 0.619336 + 1.07272i 0.989607 + 0.143798i \(0.0459315\pi\)
−0.370271 + 0.928924i \(0.620735\pi\)
\(138\) 9.26941 0.789064
\(139\) 0.615714 + 1.06645i 0.0522242 + 0.0904549i 0.890956 0.454090i \(-0.150036\pi\)
−0.838732 + 0.544545i \(0.816702\pi\)
\(140\) 1.47407 2.55316i 0.124582 0.215781i
\(141\) −4.65817 + 8.06819i −0.392289 + 0.679464i
\(142\) −18.5375 −1.55563
\(143\) −2.41997 2.67278i −0.202368 0.223509i
\(144\) −4.96310 −0.413592
\(145\) −1.29133 + 2.23665i −0.107239 + 0.185744i
\(146\) 1.75899 3.04666i 0.145575 0.252144i
\(147\) −7.17168 12.4217i −0.591510 1.02453i
\(148\) 4.76370 0.391574
\(149\) −2.96573 5.13679i −0.242962 0.420822i 0.718595 0.695429i \(-0.244786\pi\)
−0.961557 + 0.274607i \(0.911452\pi\)
\(150\) −4.21062 7.29302i −0.343796 0.595472i
\(151\) 19.7316 1.60573 0.802867 0.596159i \(-0.203307\pi\)
0.802867 + 0.596159i \(0.203307\pi\)
\(152\) 5.41897 + 9.38592i 0.439536 + 0.761299i
\(153\) −2.01117 + 3.48345i −0.162593 + 0.281620i
\(154\) −4.12705 + 7.14826i −0.332567 + 0.576023i
\(155\) 1.92119 0.154313
\(156\) 1.31692 4.09145i 0.105438 0.327578i
\(157\) −21.5886 −1.72296 −0.861480 0.507791i \(-0.830462\pi\)
−0.861480 + 0.507791i \(0.830462\pi\)
\(158\) 7.50258 12.9949i 0.596873 1.03381i
\(159\) −3.80798 + 6.59561i −0.301992 + 0.523066i
\(160\) 1.60069 + 2.77247i 0.126545 + 0.219183i
\(161\) −23.9687 −1.88900
\(162\) 0.893322 + 1.54728i 0.0701860 + 0.121566i
\(163\) 3.24389 + 5.61858i 0.254081 + 0.440081i 0.964645 0.263551i \(-0.0848937\pi\)
−0.710565 + 0.703632i \(0.751560\pi\)
\(164\) 11.2286 0.876804
\(165\) −0.267654 0.463591i −0.0208369 0.0360905i
\(166\) 6.57952 11.3961i 0.510670 0.884506i
\(167\) −12.4782 + 21.6128i −0.965589 + 1.67245i −0.257564 + 0.966261i \(0.582920\pi\)
−0.708025 + 0.706187i \(0.750414\pi\)
\(168\) 6.66850 0.514486
\(169\) −10.5592 7.58306i −0.812248 0.583312i
\(170\) 3.84699 0.295050
\(171\) 3.75422 6.50250i 0.287092 0.497258i
\(172\) 4.65733 8.06673i 0.355118 0.615082i
\(173\) −1.29597 2.24468i −0.0985307 0.170660i 0.812546 0.582897i \(-0.198081\pi\)
−0.911077 + 0.412237i \(0.864748\pi\)
\(174\) 8.61989 0.653472
\(175\) 10.8878 + 18.8582i 0.823040 + 1.42555i
\(176\) −2.48155 4.29817i −0.187054 0.323987i
\(177\) 4.15580 0.312369
\(178\) 3.01518 + 5.22245i 0.225997 + 0.391439i
\(179\) 6.47062 11.2074i 0.483637 0.837683i −0.516187 0.856476i \(-0.672649\pi\)
0.999823 + 0.0187927i \(0.00598226\pi\)
\(180\) 0.319070 0.552646i 0.0237821 0.0411918i
\(181\) 10.6703 0.793119 0.396560 0.918009i \(-0.370204\pi\)
0.396560 + 0.918009i \(0.370204\pi\)
\(182\) −9.11840 + 28.3292i −0.675901 + 2.09990i
\(183\) −9.75845 −0.721365
\(184\) 3.74439 6.48547i 0.276040 0.478115i
\(185\) 1.06956 1.85254i 0.0786360 0.136201i
\(186\) −3.20607 5.55308i −0.235081 0.407172i
\(187\) −4.02234 −0.294142
\(188\) −5.55299 9.61807i −0.404994 0.701470i
\(189\) −2.30994 4.00094i −0.168024 0.291026i
\(190\) −7.18111 −0.520973
\(191\) −3.47247 6.01449i −0.251259 0.435193i 0.712614 0.701557i \(-0.247511\pi\)
−0.963873 + 0.266363i \(0.914178\pi\)
\(192\) 0.379347 0.657049i 0.0273770 0.0474184i
\(193\) −2.01255 + 3.48584i −0.144866 + 0.250916i −0.929323 0.369268i \(-0.879609\pi\)
0.784457 + 0.620184i \(0.212942\pi\)
\(194\) −21.2852 −1.52819
\(195\) −1.29543 1.43076i −0.0927676 0.102459i
\(196\) 17.0987 1.22134
\(197\) 3.59923 6.23405i 0.256434 0.444157i −0.708850 0.705360i \(-0.750786\pi\)
0.965284 + 0.261202i \(0.0841189\pi\)
\(198\) −0.893322 + 1.54728i −0.0634856 + 0.109960i
\(199\) 3.90499 + 6.76363i 0.276817 + 0.479461i 0.970592 0.240731i \(-0.0773871\pi\)
−0.693775 + 0.720192i \(0.744054\pi\)
\(200\) −6.80354 −0.481083
\(201\) −3.91130 6.77458i −0.275882 0.477842i
\(202\) 10.0288 + 17.3704i 0.705624 + 1.22218i
\(203\) −22.2892 −1.56440
\(204\) −2.39751 4.15261i −0.167859 0.290741i
\(205\) 2.52108 4.36664i 0.176080 0.304979i
\(206\) 7.08395 12.2698i 0.493562 0.854875i
\(207\) −5.18817 −0.360602
\(208\) −12.0105 13.2653i −0.832781 0.919781i
\(209\) 7.50844 0.519369
\(210\) −2.20924 + 3.82652i −0.152452 + 0.264055i
\(211\) −13.4909 + 23.3669i −0.928750 + 1.60864i −0.143333 + 0.989674i \(0.545782\pi\)
−0.785417 + 0.618967i \(0.787551\pi\)
\(212\) −4.53948 7.86261i −0.311773 0.540007i
\(213\) 10.3756 0.710923
\(214\) −11.3495 19.6579i −0.775836 1.34379i
\(215\) −2.09136 3.62234i −0.142630 0.247042i
\(216\) 1.44343 0.0982132
\(217\) 8.29023 + 14.3591i 0.562778 + 0.974759i
\(218\) −3.24269 + 5.61650i −0.219622 + 0.380397i
\(219\) −0.984522 + 1.70524i −0.0665279 + 0.115230i
\(220\) 0.638140 0.0430234
\(221\) −14.1774 + 3.05441i −0.953678 + 0.205462i
\(222\) −7.13955 −0.479175
\(223\) −11.5140 + 19.9428i −0.771032 + 1.33547i 0.165966 + 0.986131i \(0.446926\pi\)
−0.936998 + 0.349335i \(0.886408\pi\)
\(224\) −13.8144 + 23.9273i −0.923016 + 1.59871i
\(225\) 2.35672 + 4.08196i 0.157115 + 0.272131i
\(226\) −24.5756 −1.63475
\(227\) 1.56880 + 2.71724i 0.104125 + 0.180350i 0.913380 0.407107i \(-0.133462\pi\)
−0.809255 + 0.587457i \(0.800129\pi\)
\(228\) 4.47540 + 7.75161i 0.296390 + 0.513363i
\(229\) −9.84336 −0.650468 −0.325234 0.945634i \(-0.605443\pi\)
−0.325234 + 0.945634i \(0.605443\pi\)
\(230\) 2.48100 + 4.29721i 0.163592 + 0.283350i
\(231\) 2.30994 4.00094i 0.151983 0.263243i
\(232\) 3.48201 6.03102i 0.228605 0.395956i
\(233\) −1.00285 −0.0656991 −0.0328496 0.999460i \(-0.510458\pi\)
−0.0328496 + 0.999460i \(0.510458\pi\)
\(234\) −1.97373 + 6.13202i −0.129027 + 0.400863i
\(235\) −4.98712 −0.325324
\(236\) −2.47706 + 4.29039i −0.161243 + 0.279281i
\(237\) −4.19926 + 7.27333i −0.272771 + 0.472453i
\(238\) 16.6004 + 28.7527i 1.07604 + 1.86376i
\(239\) −4.57272 −0.295785 −0.147892 0.989003i \(-0.547249\pi\)
−0.147892 + 0.989003i \(0.547249\pi\)
\(240\) −1.32839 2.30085i −0.0857475 0.148519i
\(241\) −12.3916 21.4629i −0.798214 1.38255i −0.920778 0.390086i \(-0.872445\pi\)
0.122564 0.992461i \(-0.460888\pi\)
\(242\) −1.78664 −0.114850
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 5.81651 10.0745i 0.372364 0.644954i
\(245\) 3.83906 6.64945i 0.245269 0.424818i
\(246\) −16.8287 −1.07296
\(247\) 26.4648 5.70163i 1.68392 0.362786i
\(248\) −5.18039 −0.328955
\(249\) −3.68261 + 6.37847i −0.233376 + 0.404219i
\(250\) 4.64500 8.04537i 0.293776 0.508834i
\(251\) −0.255317 0.442223i −0.0161155 0.0279128i 0.857855 0.513891i \(-0.171797\pi\)
−0.873971 + 0.485979i \(0.838463\pi\)
\(252\) 5.50736 0.346931
\(253\) −2.59408 4.49308i −0.163089 0.282478i
\(254\) −0.177584 0.307584i −0.0111426 0.0192995i
\(255\) −2.15319 −0.134838
\(256\) −10.2327 17.7235i −0.639542 1.10772i
\(257\) 4.02806 6.97680i 0.251263 0.435201i −0.712611 0.701560i \(-0.752487\pi\)
0.963874 + 0.266359i \(0.0858207\pi\)
\(258\) −6.98012 + 12.0899i −0.434563 + 0.752686i
\(259\) 18.4614 1.14713
\(260\) 2.24924 0.484580i 0.139492 0.0300524i
\(261\) −4.82462 −0.298637
\(262\) 19.4731 33.7284i 1.20305 2.08375i
\(263\) −0.208161 + 0.360546i −0.0128358 + 0.0222322i −0.872372 0.488843i \(-0.837419\pi\)
0.859536 + 0.511075i \(0.170753\pi\)
\(264\) 0.721717 + 1.25005i 0.0444186 + 0.0769353i
\(265\) −4.07689 −0.250441
\(266\) −30.9877 53.6722i −1.89998 3.29086i
\(267\) −1.68762 2.92305i −0.103281 0.178888i
\(268\) 9.32532 0.569634
\(269\) 0.458296 + 0.793792i 0.0279428 + 0.0483984i 0.879659 0.475606i \(-0.157771\pi\)
−0.851716 + 0.524004i \(0.824438\pi\)
\(270\) −0.478203 + 0.828272i −0.0291025 + 0.0504070i
\(271\) 4.04304 7.00275i 0.245597 0.425387i −0.716702 0.697379i \(-0.754349\pi\)
0.962299 + 0.271993i \(0.0876826\pi\)
\(272\) −19.9633 −1.21045
\(273\) 5.10364 15.8561i 0.308887 0.959656i
\(274\) 25.9033 1.56487
\(275\) −2.35672 + 4.08196i −0.142116 + 0.246152i
\(276\) 3.09240 5.35620i 0.186141 0.322405i
\(277\) −4.67288 8.09367i −0.280766 0.486301i 0.690807 0.723039i \(-0.257255\pi\)
−0.971574 + 0.236737i \(0.923922\pi\)
\(278\) 2.20012 0.131955
\(279\) 1.79447 + 3.10811i 0.107432 + 0.186077i
\(280\) 1.78485 + 3.09146i 0.106665 + 0.184750i
\(281\) 9.89315 0.590176 0.295088 0.955470i \(-0.404651\pi\)
0.295088 + 0.955470i \(0.404651\pi\)
\(282\) 8.32249 + 14.4150i 0.495597 + 0.858400i
\(283\) −1.83539 + 3.17899i −0.109103 + 0.188971i −0.915407 0.402530i \(-0.868131\pi\)
0.806304 + 0.591501i \(0.201464\pi\)
\(284\) −6.18435 + 10.7116i −0.366974 + 0.635617i
\(285\) 4.01933 0.238085
\(286\) −6.29735 + 1.35671i −0.372370 + 0.0802241i
\(287\) 43.5155 2.56864
\(288\) −2.99021 + 5.17920i −0.176200 + 0.305187i
\(289\) 0.410406 0.710844i 0.0241415 0.0418143i
\(290\) 2.30715 + 3.99610i 0.135481 + 0.234659i
\(291\) 11.9135 0.698381
\(292\) −1.17365 2.03282i −0.0686825 0.118962i
\(293\) 7.06601 + 12.2387i 0.412800 + 0.714991i 0.995195 0.0979150i \(-0.0312173\pi\)
−0.582394 + 0.812906i \(0.697884\pi\)
\(294\) −25.6265 −1.49457
\(295\) 1.11232 + 1.92659i 0.0647616 + 0.112170i
\(296\) −2.88403 + 4.99529i −0.167631 + 0.290345i
\(297\) 0.500000 0.866025i 0.0290129 0.0502519i
\(298\) −10.5974 −0.613891
\(299\) −12.5552 13.8668i −0.726086 0.801939i
\(300\) −5.61889 −0.324407
\(301\) 18.0491 31.2620i 1.04033 1.80191i
\(302\) 17.6267 30.5303i 1.01430 1.75682i
\(303\) −5.61321 9.72236i −0.322470 0.558535i
\(304\) 37.2651 2.13730
\(305\) −2.61189 4.52393i −0.149556 0.259039i
\(306\) 3.59324 + 6.22368i 0.205412 + 0.355784i
\(307\) 3.45187 0.197009 0.0985044 0.995137i \(-0.468594\pi\)
0.0985044 + 0.995137i \(0.468594\pi\)
\(308\) 2.75368 + 4.76951i 0.156905 + 0.271768i
\(309\) −3.96495 + 6.86749i −0.225558 + 0.390678i
\(310\) 1.71624 2.97261i 0.0974758 0.168833i
\(311\) 29.0347 1.64640 0.823202 0.567748i \(-0.192185\pi\)
0.823202 + 0.567748i \(0.192185\pi\)
\(312\) 3.49306 + 3.85798i 0.197756 + 0.218415i
\(313\) 13.2960 0.751537 0.375768 0.926714i \(-0.377379\pi\)
0.375768 + 0.926714i \(0.377379\pi\)
\(314\) −19.2856 + 33.4036i −1.08835 + 1.88508i
\(315\) 1.23653 2.14174i 0.0696707 0.120673i
\(316\) −5.00593 8.67052i −0.281605 0.487755i
\(317\) −10.4283 −0.585710 −0.292855 0.956157i \(-0.594605\pi\)
−0.292855 + 0.956157i \(0.594605\pi\)
\(318\) 6.80350 + 11.7840i 0.381521 + 0.660815i
\(319\) −2.41231 4.17825i −0.135064 0.233937i
\(320\) 0.406136 0.0227037
\(321\) 6.35241 + 11.0027i 0.354557 + 0.614111i
\(322\) −21.4118 + 37.0863i −1.19323 + 2.06674i
\(323\) 15.1007 26.1552i 0.840227 1.45532i
\(324\) 1.19210 0.0662277
\(325\) −5.20700 + 16.1772i −0.288832 + 0.897351i
\(326\) 11.5913 0.641985
\(327\) 1.81496 3.14360i 0.100367 0.173842i
\(328\) −6.79797 + 11.7744i −0.375355 + 0.650134i
\(329\) −21.5202 37.2741i −1.18645 2.05499i
\(330\) −0.956406 −0.0526484
\(331\) 7.31168 + 12.6642i 0.401886 + 0.696088i 0.993954 0.109801i \(-0.0350213\pi\)
−0.592067 + 0.805889i \(0.701688\pi\)
\(332\) −4.39003 7.60376i −0.240934 0.417311i
\(333\) 3.99607 0.218983
\(334\) 22.2940 + 38.6144i 1.21987 + 2.11289i
\(335\) 2.09376 3.62649i 0.114394 0.198136i
\(336\) 11.4645 19.8571i 0.625439 1.08329i
\(337\) 4.53149 0.246846 0.123423 0.992354i \(-0.460613\pi\)
0.123423 + 0.992354i \(0.460613\pi\)
\(338\) −21.1659 + 9.56395i −1.15127 + 0.520210i
\(339\) 13.7552 0.747079
\(340\) 1.28341 2.22293i 0.0696025 0.120555i
\(341\) −1.79447 + 3.10811i −0.0971758 + 0.168313i
\(342\) −6.70745 11.6176i −0.362698 0.628211i
\(343\) 33.9255 1.83181
\(344\) 5.63926 + 9.76748i 0.304048 + 0.526627i
\(345\) −1.38863 2.40519i −0.0747616 0.129491i
\(346\) −4.63087 −0.248957
\(347\) −13.0510 22.6049i −0.700612 1.21350i −0.968252 0.249977i \(-0.919577\pi\)
0.267639 0.963519i \(-0.413756\pi\)
\(348\) 2.87571 4.98088i 0.154154 0.267003i
\(349\) 2.45211 4.24718i 0.131258 0.227346i −0.792904 0.609347i \(-0.791432\pi\)
0.924162 + 0.382001i \(0.124765\pi\)
\(350\) 38.9052 2.07957
\(351\) 1.10471 3.43214i 0.0589652 0.183194i
\(352\) −5.98042 −0.318758
\(353\) −12.7908 + 22.1543i −0.680784 + 1.17915i 0.293958 + 0.955818i \(0.405027\pi\)
−0.974742 + 0.223334i \(0.928306\pi\)
\(354\) 3.71247 6.43018i 0.197315 0.341760i
\(355\) 2.77707 + 4.81002i 0.147391 + 0.255289i
\(356\) 4.02362 0.213252
\(357\) −9.29137 16.0931i −0.491751 0.851739i
\(358\) −11.5607 20.0237i −0.611002 1.05829i
\(359\) −18.9318 −0.999180 −0.499590 0.866262i \(-0.666516\pi\)
−0.499590 + 0.866262i \(0.666516\pi\)
\(360\) 0.386341 + 0.669163i 0.0203620 + 0.0352680i
\(361\) −18.6883 + 32.3691i −0.983595 + 1.70364i
\(362\) 9.53204 16.5100i 0.500993 0.867745i
\(363\) 1.00000 0.0524864
\(364\) 13.3276 + 14.7200i 0.698558 + 0.771536i
\(365\) −1.05405 −0.0551713
\(366\) −8.71744 + 15.0990i −0.455668 + 0.789240i
\(367\) 18.3510 31.7848i 0.957914 1.65916i 0.230359 0.973106i \(-0.426010\pi\)
0.727555 0.686049i \(-0.240657\pi\)
\(368\) −12.8747 22.2996i −0.671140 1.16245i
\(369\) 9.41917 0.490342
\(370\) −1.91093 3.30983i −0.0993446 0.172070i
\(371\) −17.5924 30.4710i −0.913353 1.58197i
\(372\) −4.27836 −0.221823
\(373\) −0.346728 0.600550i −0.0179529 0.0310953i 0.856909 0.515467i \(-0.172382\pi\)
−0.874862 + 0.484372i \(0.839048\pi\)
\(374\) −3.59324 + 6.22368i −0.185802 + 0.321819i
\(375\) −2.59985 + 4.50306i −0.134255 + 0.232537i
\(376\) 13.4475 0.693503
\(377\) −11.6754 12.8952i −0.601316 0.664135i
\(378\) −8.25410 −0.424545
\(379\) −2.27022 + 3.93214i −0.116613 + 0.201980i −0.918424 0.395598i \(-0.870537\pi\)
0.801810 + 0.597579i \(0.203871\pi\)
\(380\) −2.39572 + 4.14951i −0.122898 + 0.212865i
\(381\) 0.0993951 + 0.172157i 0.00509217 + 0.00881989i
\(382\) −12.4081 −0.634855
\(383\) 10.0957 + 17.4863i 0.515868 + 0.893509i 0.999830 + 0.0184206i \(0.00586378\pi\)
−0.483962 + 0.875089i \(0.660803\pi\)
\(384\) 5.30267 + 9.18449i 0.270601 + 0.468694i
\(385\) 2.47307 0.126039
\(386\) 3.59571 + 6.22795i 0.183017 + 0.316994i
\(387\) 3.90683 6.76683i 0.198596 0.343978i
\(388\) −7.10103 + 12.2993i −0.360500 + 0.624404i
\(389\) −20.8841 −1.05887 −0.529434 0.848351i \(-0.677596\pi\)
−0.529434 + 0.848351i \(0.677596\pi\)
\(390\) −3.37103 + 0.726260i −0.170698 + 0.0367756i
\(391\) −20.8685 −1.05537
\(392\) −10.3518 + 17.9299i −0.522847 + 0.905598i
\(393\) −10.8992 + 18.8781i −0.549794 + 0.952272i
\(394\) −6.43054 11.1380i −0.323966 0.561126i
\(395\) −4.49580 −0.226208
\(396\) 0.596049 + 1.03239i 0.0299526 + 0.0518794i
\(397\) 6.70535 + 11.6140i 0.336532 + 0.582890i 0.983778 0.179391i \(-0.0574127\pi\)
−0.647246 + 0.762281i \(0.724079\pi\)
\(398\) 13.9536 0.699433
\(399\) 17.3441 + 30.0408i 0.868289 + 1.50392i
\(400\) −11.6966 + 20.2592i −0.584832 + 1.01296i
\(401\) 8.03094 13.9100i 0.401046 0.694632i −0.592806 0.805345i \(-0.701980\pi\)
0.993852 + 0.110713i \(0.0353134\pi\)
\(402\) −13.9762 −0.697071
\(403\) −3.96474 + 12.3177i −0.197498 + 0.613590i
\(404\) 13.3830 0.665829
\(405\) 0.267654 0.463591i 0.0132998 0.0230360i
\(406\) −19.9115 + 34.4877i −0.988189 + 1.71159i
\(407\) 1.99803 + 3.46070i 0.0990389 + 0.171540i
\(408\) 5.80598 0.287439
\(409\) 10.3126 + 17.8619i 0.509924 + 0.883214i 0.999934 + 0.0114971i \(0.00365971\pi\)
−0.490010 + 0.871717i \(0.663007\pi\)
\(410\) −4.50428 7.80164i −0.222450 0.385295i
\(411\) −14.4983 −0.715148
\(412\) −4.72660 8.18672i −0.232863 0.403331i
\(413\) −9.59966 + 16.6271i −0.472369 + 0.818166i
\(414\) −4.63470 + 8.02754i −0.227783 + 0.394532i
\(415\) −3.94267 −0.193538
\(416\) −21.0791 + 4.54132i −1.03349 + 0.222656i
\(417\) −1.23143 −0.0603033
\(418\) 6.70745 11.6176i 0.328072 0.568238i
\(419\) −2.47998 + 4.29544i −0.121155 + 0.209846i −0.920223 0.391394i \(-0.871993\pi\)
0.799069 + 0.601240i \(0.205326\pi\)
\(420\) 1.47407 + 2.55316i 0.0719272 + 0.124582i
\(421\) −4.21892 −0.205617 −0.102809 0.994701i \(-0.532783\pi\)
−0.102809 + 0.994701i \(0.532783\pi\)
\(422\) 24.1034 + 41.7483i 1.17333 + 2.03228i
\(423\) −4.65817 8.06819i −0.226488 0.392289i
\(424\) 10.9931 0.533873
\(425\) 9.47953 + 16.4190i 0.459825 + 0.796440i
\(426\) 9.26873 16.0539i 0.449072 0.777815i
\(427\) 22.5415 39.0430i 1.09086 1.88942i
\(428\) −15.1454 −0.732080
\(429\) 3.52468 0.759363i 0.170173 0.0366624i
\(430\) −7.47304 −0.360382
\(431\) 1.88481 3.26459i 0.0907882 0.157250i −0.817055 0.576560i \(-0.804395\pi\)
0.907843 + 0.419310i \(0.137728\pi\)
\(432\) 2.48155 4.29817i 0.119394 0.206796i
\(433\) 8.32647 + 14.4219i 0.400145 + 0.693071i 0.993743 0.111690i \(-0.0356265\pi\)
−0.593598 + 0.804761i \(0.702293\pi\)
\(434\) 29.6234 1.42197
\(435\) −1.29133 2.23665i −0.0619146 0.107239i
\(436\) 2.16361 + 3.74748i 0.103618 + 0.179472i
\(437\) 38.9550 1.86347
\(438\) 1.75899 + 3.04666i 0.0840479 + 0.145575i
\(439\) −14.8257 + 25.6789i −0.707592 + 1.22559i 0.258156 + 0.966103i \(0.416885\pi\)
−0.965748 + 0.259482i \(0.916448\pi\)
\(440\) −0.386341 + 0.669163i −0.0184181 + 0.0319011i
\(441\) 14.3434 0.683017
\(442\) −7.93899 + 24.6650i −0.377619 + 1.17320i
\(443\) 10.3758 0.492971 0.246486 0.969146i \(-0.420724\pi\)
0.246486 + 0.969146i \(0.420724\pi\)
\(444\) −2.38185 + 4.12549i −0.113038 + 0.195787i
\(445\) 0.903399 1.56473i 0.0428252 0.0741754i
\(446\) 20.5714 + 35.6306i 0.974082 + 1.68716i
\(447\) 5.93145 0.280548
\(448\) 1.75254 + 3.03549i 0.0827998 + 0.143413i
\(449\) 3.55561 + 6.15849i 0.167800 + 0.290637i 0.937646 0.347592i \(-0.113001\pi\)
−0.769846 + 0.638229i \(0.779667\pi\)
\(450\) 8.42125 0.396981
\(451\) 4.70959 + 8.15724i 0.221766 + 0.384109i
\(452\) −8.19876 + 14.2007i −0.385637 + 0.667943i
\(453\) −9.86579 + 17.0880i −0.463535 + 0.802867i
\(454\) 5.60577 0.263092
\(455\) 8.71676 1.87796i 0.408648 0.0880399i
\(456\) −10.8379 −0.507533
\(457\) 10.2724 17.7924i 0.480525 0.832293i −0.519226 0.854637i \(-0.673780\pi\)
0.999750 + 0.0223441i \(0.00711293\pi\)
\(458\) −8.79329 + 15.2304i −0.410884 + 0.711671i
\(459\) −2.01117 3.48345i −0.0938733 0.162593i
\(460\) 3.31078 0.154366
\(461\) −0.938105 1.62485i −0.0436919 0.0756766i 0.843352 0.537361i \(-0.180579\pi\)
−0.887044 + 0.461684i \(0.847245\pi\)
\(462\) −4.12705 7.14826i −0.192008 0.332567i
\(463\) −4.84844 −0.225326 −0.112663 0.993633i \(-0.535938\pi\)
−0.112663 + 0.993633i \(0.535938\pi\)
\(464\) −11.9725 20.7371i −0.555811 0.962693i
\(465\) −0.960593 + 1.66380i −0.0445464 + 0.0771567i
\(466\) −0.895871 + 1.55169i −0.0415004 + 0.0718809i
\(467\) −7.31136 −0.338330 −0.169165 0.985588i \(-0.554107\pi\)
−0.169165 + 0.985588i \(0.554107\pi\)
\(468\) 2.88484 + 3.18622i 0.133352 + 0.147283i
\(469\) 36.1396 1.66877
\(470\) −4.45510 + 7.71646i −0.205499 + 0.355934i
\(471\) 10.7943 18.6963i 0.497376 0.861480i
\(472\) −2.99931 5.19496i −0.138054 0.239117i
\(473\) 7.81367 0.359273
\(474\) 7.50258 + 12.9949i 0.344605 + 0.596873i
\(475\) −17.6953 30.6492i −0.811916 1.40628i
\(476\) 22.1524 1.01536
\(477\) −3.80798 6.59561i −0.174355 0.301992i
\(478\) −4.08491 + 7.07528i −0.186840 + 0.323616i
\(479\) −2.70089 + 4.67808i −0.123407 + 0.213747i −0.921109 0.389305i \(-0.872715\pi\)
0.797702 + 0.603052i \(0.206049\pi\)
\(480\) −3.20137 −0.146122
\(481\) 9.67036 + 10.6806i 0.440930 + 0.486994i
\(482\) −44.2788 −2.01684
\(483\) 11.9844 20.7575i 0.545308 0.944501i
\(484\) −0.596049 + 1.03239i −0.0270931 + 0.0469267i
\(485\) 3.18870 + 5.52299i 0.144791 + 0.250786i
\(486\) −1.78664 −0.0810438
\(487\) −4.80532 8.32306i −0.217750 0.377154i 0.736370 0.676579i \(-0.236538\pi\)
−0.954120 + 0.299425i \(0.903205\pi\)
\(488\) 7.04284 + 12.1986i 0.318814 + 0.552202i
\(489\) −6.48777 −0.293387
\(490\) −6.85904 11.8802i −0.309860 0.536693i
\(491\) 4.75881 8.24250i 0.214762 0.371979i −0.738437 0.674323i \(-0.764436\pi\)
0.953199 + 0.302344i \(0.0977691\pi\)
\(492\) −5.61429 + 9.72423i −0.253112 + 0.438402i
\(493\) −19.4063 −0.874014
\(494\) 14.8196 46.0419i 0.666766 2.07152i
\(495\) 0.535309 0.0240603
\(496\) −8.90611 + 15.4258i −0.399896 + 0.692641i
\(497\) −23.9670 + 41.5121i −1.07507 + 1.86207i
\(498\) 6.57952 + 11.3961i 0.294835 + 0.510670i
\(499\) −25.6619 −1.14879 −0.574393 0.818580i \(-0.694762\pi\)
−0.574393 + 0.818580i \(0.694762\pi\)
\(500\) −3.09927 5.36809i −0.138604 0.240068i
\(501\) −12.4782 21.6128i −0.557483 0.965589i
\(502\) −0.912323 −0.0407190
\(503\) 10.0579 + 17.4208i 0.448460 + 0.776756i 0.998286 0.0585234i \(-0.0186392\pi\)
−0.549826 + 0.835279i \(0.685306\pi\)
\(504\) −3.33425 + 5.77509i −0.148519 + 0.257243i
\(505\) 3.00480 5.20446i 0.133712 0.231596i
\(506\) −9.26941 −0.412075
\(507\) 11.8467 5.35303i 0.526132 0.237736i
\(508\) −0.236977 −0.0105142
\(509\) −9.89193 + 17.1333i −0.438452 + 0.759421i −0.997570 0.0696668i \(-0.977806\pi\)
0.559118 + 0.829088i \(0.311140\pi\)
\(510\) −1.92349 + 3.33159i −0.0851737 + 0.147525i
\(511\) −4.54838 7.87803i −0.201209 0.348504i
\(512\) −15.3536 −0.678541
\(513\) 3.75422 + 6.50250i 0.165753 + 0.287092i
\(514\) −7.19671 12.4651i −0.317433 0.549810i
\(515\) −4.24494 −0.187054
\(516\) 4.65733 + 8.06673i 0.205027 + 0.355118i
\(517\) 4.65817 8.06819i 0.204866 0.354838i
\(518\) 16.4920 28.5649i 0.724615 1.25507i
\(519\) 2.59194 0.113773
\(520\) −0.853592 + 2.65196i −0.0374325 + 0.116296i
\(521\) −7.29955 −0.319799 −0.159900 0.987133i \(-0.551117\pi\)
−0.159900 + 0.987133i \(0.551117\pi\)
\(522\) −4.30994 + 7.46504i −0.188641 + 0.326736i
\(523\) 15.3646 26.6122i 0.671846 1.16367i −0.305534 0.952181i \(-0.598835\pi\)
0.977380 0.211491i \(-0.0678318\pi\)
\(524\) −12.9930 22.5045i −0.567601 0.983113i
\(525\) −21.7756 −0.950364
\(526\) 0.371910 + 0.644167i 0.0162161 + 0.0280870i
\(527\) 7.21795 + 12.5019i 0.314419 + 0.544589i
\(528\) 4.96310 0.215991
\(529\) −1.95853 3.39228i −0.0851536 0.147490i
\(530\) −3.64197 + 6.30808i −0.158197 + 0.274006i
\(531\) −2.07790 + 3.59903i −0.0901732 + 0.156185i
\(532\) −41.3517 −1.79282
\(533\) 22.7941 + 25.1754i 0.987322 + 1.09047i
\(534\) −6.03036 −0.260959
\(535\) −3.40050 + 5.88984i −0.147016 + 0.254640i
\(536\) −5.64571 + 9.77865i −0.243857 + 0.422374i
\(537\) 6.47062 + 11.2074i 0.279228 + 0.483637i
\(538\) 1.63762 0.0706030
\(539\) 7.17168 + 12.4217i 0.308906 + 0.535041i
\(540\) 0.319070 + 0.552646i 0.0137306 + 0.0237821i
\(541\) −1.87138 −0.0804568 −0.0402284 0.999191i \(-0.512809\pi\)
−0.0402284 + 0.999191i \(0.512809\pi\)
\(542\) −7.22347 12.5114i −0.310275 0.537412i
\(543\) −5.33516 + 9.24077i −0.228954 + 0.396560i
\(544\) −12.0276 + 20.8325i −0.515681 + 0.893185i
\(545\) 1.94313 0.0832344
\(546\) −19.9746 22.0614i −0.854836 0.944140i
\(547\) 24.7950 1.06016 0.530078 0.847949i \(-0.322163\pi\)
0.530078 + 0.847949i \(0.322163\pi\)
\(548\) 8.64169 14.9678i 0.369155 0.639395i
\(549\) 4.87922 8.45107i 0.208240 0.360683i
\(550\) 4.21062 + 7.29302i 0.179542 + 0.310975i
\(551\) 36.2254 1.54325
\(552\) 3.74439 + 6.48547i 0.159372 + 0.276040i
\(553\) −19.4001 33.6020i −0.824976 1.42890i
\(554\) −16.6976 −0.709411
\(555\) 1.06956 + 1.85254i 0.0454005 + 0.0786360i
\(556\) 0.733991 1.27131i 0.0311282 0.0539155i
\(557\) 2.94986 5.10930i 0.124989 0.216488i −0.796739 0.604323i \(-0.793444\pi\)
0.921729 + 0.387835i \(0.126777\pi\)
\(558\) 6.41215 0.271448
\(559\) 27.5407 5.93341i 1.16485 0.250957i
\(560\) 12.2741 0.518674
\(561\) 2.01117 3.48345i 0.0849116 0.147071i
\(562\) 8.83777 15.3075i 0.372799 0.645706i
\(563\) 11.2847 + 19.5457i 0.475595 + 0.823754i 0.999609 0.0279551i \(-0.00889955\pi\)
−0.524014 + 0.851709i \(0.675566\pi\)
\(564\) 11.1060 0.467646
\(565\) 3.68163 + 6.37677i 0.154887 + 0.268273i
\(566\) 3.27919 + 5.67972i 0.137835 + 0.238736i
\(567\) 4.61989 0.194017
\(568\) −7.48823 12.9700i −0.314199 0.544209i
\(569\) 7.96900 13.8027i 0.334078 0.578640i −0.649229 0.760593i \(-0.724908\pi\)
0.983307 + 0.181953i \(0.0582418\pi\)
\(570\) 3.59056 6.21903i 0.150392 0.260486i
\(571\) −40.2086 −1.68268 −0.841339 0.540508i \(-0.818232\pi\)
−0.841339 + 0.540508i \(0.818232\pi\)
\(572\) −1.31692 + 4.09145i −0.0550634 + 0.171072i
\(573\) 6.94493 0.290129
\(574\) 38.8734 67.3307i 1.62254 2.81033i
\(575\) −12.2271 + 21.1779i −0.509904 + 0.883180i
\(576\) 0.379347 + 0.657049i 0.0158061 + 0.0273770i
\(577\) −32.5372 −1.35454 −0.677271 0.735734i \(-0.736838\pi\)
−0.677271 + 0.735734i \(0.736838\pi\)
\(578\) −0.733249 1.27003i −0.0304992 0.0528261i
\(579\) −2.01255 3.48584i −0.0836387 0.144866i
\(580\) 3.07879 0.127840
\(581\) −17.0133 29.4678i −0.705829 1.22253i
\(582\) 10.6426 18.4335i 0.441149 0.764093i
\(583\) 3.80798 6.59561i 0.157710 0.273162i
\(584\) 2.84219 0.117610
\(585\) 1.88679 0.406494i 0.0780092 0.0168064i
\(586\) 25.2489 1.04302
\(587\) −11.7315 + 20.3195i −0.484209 + 0.838675i −0.999835 0.0181386i \(-0.994226\pi\)
0.515626 + 0.856814i \(0.327559\pi\)
\(588\) −8.54935 + 14.8079i −0.352569 + 0.610668i
\(589\) −13.4736 23.3370i −0.555172 0.961585i
\(590\) 3.97463 0.163633
\(591\) 3.59923 + 6.23405i 0.148052 + 0.256434i
\(592\) 9.91644 + 17.1758i 0.407563 + 0.705920i
\(593\) −28.1332 −1.15529 −0.577646 0.816288i \(-0.696028\pi\)
−0.577646 + 0.816288i \(0.696028\pi\)
\(594\) −0.893322 1.54728i −0.0366535 0.0634856i
\(595\) 4.97375 8.61479i 0.203904 0.353172i
\(596\) −3.53544 + 6.12355i −0.144817 + 0.250831i
\(597\) −7.80997 −0.319641
\(598\) −32.6717 + 7.03885i −1.33604 + 0.287840i
\(599\) −24.4419 −0.998668 −0.499334 0.866410i \(-0.666422\pi\)
−0.499334 + 0.866410i \(0.666422\pi\)
\(600\) 3.40177 5.89204i 0.138877 0.240542i
\(601\) −11.8039 + 20.4450i −0.481492 + 0.833969i −0.999774 0.0212408i \(-0.993238\pi\)
0.518282 + 0.855210i \(0.326572\pi\)
\(602\) −32.2474 55.8541i −1.31431 2.27644i
\(603\) 7.82261 0.318561
\(604\) −11.7610 20.3706i −0.478548 0.828869i
\(605\) 0.267654 + 0.463591i 0.0108817 + 0.0188476i
\(606\) −20.0576 −0.814785
\(607\) −15.9891 27.6940i −0.648978 1.12406i −0.983367 0.181628i \(-0.941863\pi\)
0.334389 0.942435i \(-0.391470\pi\)
\(608\) 22.4518 38.8877i 0.910542 1.57710i
\(609\) 11.1446 19.3030i 0.451602 0.782198i
\(610\) −9.33304 −0.377884
\(611\) 10.2919 31.9750i 0.416365 1.29357i
\(612\) 4.79502 0.193827
\(613\) 6.74245 11.6783i 0.272325 0.471680i −0.697132 0.716943i \(-0.745541\pi\)
0.969457 + 0.245262i \(0.0788741\pi\)
\(614\) 3.08363 5.34101i 0.124445 0.215546i
\(615\) 2.52108 + 4.36664i 0.101660 + 0.176080i
\(616\) −6.66850 −0.268682
\(617\) 10.6931 + 18.5209i 0.430487 + 0.745625i 0.996915 0.0784862i \(-0.0250087\pi\)
−0.566429 + 0.824111i \(0.691675\pi\)
\(618\) 7.08395 + 12.2698i 0.284958 + 0.493562i
\(619\) 1.22293 0.0491539 0.0245769 0.999698i \(-0.492176\pi\)
0.0245769 + 0.999698i \(0.492176\pi\)
\(620\) −1.14512 1.98341i −0.0459892 0.0796556i
\(621\) 2.59408 4.49308i 0.104097 0.180301i
\(622\) 25.9373 44.9247i 1.03999 1.80132i
\(623\) 15.5932 0.624730
\(624\) 17.4933 3.76880i 0.700294 0.150873i
\(625\) 20.7838 0.831351
\(626\) 11.8777 20.5727i 0.474726 0.822250i
\(627\) −3.75422 + 6.50250i −0.149929 + 0.259685i
\(628\) 12.8679 + 22.2878i 0.513484 + 0.889381i
\(629\) 16.0735 0.640894
\(630\) −2.20924 3.82652i −0.0880184 0.152452i
\(631\) −9.16247 15.8699i −0.364752 0.631770i 0.623984 0.781437i \(-0.285513\pi\)
−0.988736 + 0.149667i \(0.952180\pi\)
\(632\) 12.1227 0.482215
\(633\) −13.4909 23.3669i −0.536214 0.928750i
\(634\) −9.31580 + 16.1354i −0.369978 + 0.640820i
\(635\) −0.0532071 + 0.0921573i −0.00211146 + 0.00365715i
\(636\) 9.07897 0.360004
\(637\) 34.7105 + 38.3367i 1.37528 + 1.51895i
\(638\) −8.61989 −0.341265
\(639\) −5.18779 + 8.98551i −0.205226 + 0.355461i
\(640\) −2.83856 + 4.91653i −0.112204 + 0.194343i
\(641\) 5.78650 + 10.0225i 0.228553 + 0.395866i 0.957380 0.288833i \(-0.0932672\pi\)
−0.728826 + 0.684699i \(0.759934\pi\)
\(642\) 22.6990 0.895858
\(643\) 4.71459 + 8.16590i 0.185925 + 0.322032i 0.943888 0.330266i \(-0.107138\pi\)
−0.757963 + 0.652298i \(0.773805\pi\)
\(644\) 14.2865 + 24.7450i 0.562969 + 0.975090i
\(645\) 4.18272 0.164695
\(646\) −26.9796 46.7301i −1.06150 1.83857i
\(647\) 5.17601 8.96512i 0.203490 0.352455i −0.746161 0.665766i \(-0.768105\pi\)
0.949651 + 0.313311i \(0.101438\pi\)
\(648\) −0.721717 + 1.25005i −0.0283517 + 0.0491066i
\(649\) −4.15580 −0.163129
\(650\) 20.3792 + 22.5082i 0.799336 + 0.882842i
\(651\) −16.5805 −0.649840
\(652\) 3.86703 6.69789i 0.151445 0.262310i
\(653\) 1.03022 1.78439i 0.0403155 0.0698286i −0.845164 0.534508i \(-0.820497\pi\)
0.885479 + 0.464679i \(0.153830\pi\)
\(654\) −3.24269 5.61650i −0.126799 0.219622i
\(655\) −11.6689 −0.455943
\(656\) 23.3741 + 40.4852i 0.912607 + 1.58068i
\(657\) −0.984522 1.70524i −0.0384099 0.0665279i
\(658\) −76.8980 −2.99779
\(659\) 9.78831 + 16.9539i 0.381299 + 0.660428i 0.991248 0.132012i \(-0.0421437\pi\)
−0.609950 + 0.792440i \(0.708810\pi\)
\(660\) −0.319070 + 0.552646i −0.0124198 + 0.0215117i
\(661\) −13.8637 + 24.0126i −0.539236 + 0.933983i 0.459710 + 0.888069i \(0.347953\pi\)
−0.998945 + 0.0459141i \(0.985380\pi\)
\(662\) 26.1268 1.01545
\(663\) 4.44352 13.8052i 0.172572 0.536151i
\(664\) 10.6312 0.412571
\(665\) −9.28443 + 16.0811i −0.360035 + 0.623598i
\(666\) 3.56978 6.18303i 0.138326 0.239588i
\(667\) −12.5155 21.6774i −0.484601 0.839354i
\(668\) 29.7504 1.15108
\(669\) −11.5140 19.9428i −0.445155 0.771032i
\(670\) −3.74080 6.47925i −0.144520 0.250315i
\(671\) 9.75845 0.376721
\(672\) −13.8144 23.9273i −0.532904 0.923016i
\(673\) −17.6580 + 30.5846i −0.680667 + 1.17895i 0.294110 + 0.955771i \(0.404977\pi\)
−0.974778 + 0.223179i \(0.928357\pi\)
\(674\) 4.04808 7.01149i 0.155926 0.270072i
\(675\) −4.71344 −0.181421
\(676\) −1.53484 + 15.4211i −0.0590323 + 0.593119i
\(677\) −10.2365 −0.393421 −0.196710 0.980462i \(-0.563026\pi\)
−0.196710 + 0.980462i \(0.563026\pi\)
\(678\) 12.2878 21.2831i 0.471910 0.817373i
\(679\) −27.5195 + 47.6652i −1.05610 + 1.82922i
\(680\) 1.55399 + 2.69160i 0.0595930 + 0.103218i
\(681\) −3.13760 −0.120233
\(682\) 3.20607 + 5.55308i 0.122767 + 0.212638i
\(683\) −12.7476 22.0795i −0.487774 0.844849i 0.512127 0.858910i \(-0.328858\pi\)
−0.999901 + 0.0140606i \(0.995524\pi\)
\(684\) −8.95079 −0.342242
\(685\) −3.88053 6.72127i −0.148267 0.256807i
\(686\) 30.3064 52.4922i 1.15710 2.00416i
\(687\) 4.92168 8.52460i 0.187774 0.325234i
\(688\) 38.7800 1.47847
\(689\) 8.41344 26.1391i 0.320526 0.995819i
\(690\) −4.96199 −0.188900
\(691\) −15.4711 + 26.7967i −0.588547 + 1.01939i 0.405876 + 0.913928i \(0.366966\pi\)
−0.994423 + 0.105465i \(0.966367\pi\)
\(692\) −1.54492 + 2.67588i −0.0587291 + 0.101722i
\(693\) 2.30994 + 4.00094i 0.0877475 + 0.151983i
\(694\) −46.6349 −1.77024
\(695\) −0.329597 0.570878i −0.0125023 0.0216547i
\(696\) 3.48201 + 6.03102i 0.131985 + 0.228605i
\(697\) 37.8871 1.43508
\(698\) −4.38105 7.58820i −0.165825 0.287218i
\(699\) 0.501427 0.868497i 0.0189657 0.0328496i
\(700\) 12.9793 22.4808i 0.490572 0.849696i
\(701\) 2.39678 0.0905252 0.0452626 0.998975i \(-0.485588\pi\)
0.0452626 + 0.998975i \(0.485588\pi\)
\(702\) −4.32362 4.77531i −0.163185 0.180232i
\(703\) −30.0042 −1.13163
\(704\) −0.379347 + 0.657049i −0.0142972 + 0.0247634i
\(705\) 2.49356 4.31897i 0.0939128 0.162662i
\(706\) 22.8526 + 39.5818i 0.860067 + 1.48968i
\(707\) 51.8648 1.95058
\(708\) −2.47706 4.29039i −0.0930936 0.161243i
\(709\) −10.3136 17.8637i −0.387336 0.670886i 0.604754 0.796412i \(-0.293271\pi\)
−0.992090 + 0.125526i \(0.959938\pi\)
\(710\) 9.92326 0.372413
\(711\) −4.19926 7.27333i −0.157484 0.272771i
\(712\) −2.43597 + 4.21922i −0.0912919 + 0.158122i
\(713\) −9.30999 + 16.1254i −0.348662 + 0.603900i
\(714\) −33.2007 −1.24251
\(715\) 1.29543 + 1.43076i 0.0484463 + 0.0535075i
\(716\) −15.4272 −0.576542
\(717\) 2.28636 3.96009i 0.0853857 0.147892i
\(718\) −16.9122 + 29.2927i −0.631156 + 1.09319i
\(719\) −6.73768 11.6700i −0.251273 0.435217i 0.712604 0.701567i \(-0.247516\pi\)
−0.963877 + 0.266349i \(0.914182\pi\)
\(720\) 2.65679 0.0990127
\(721\) −18.3176 31.7270i −0.682183 1.18158i
\(722\) 33.3894 + 57.8321i 1.24262 + 2.15229i
\(723\) 24.7832 0.921698
\(724\) −6.36004 11.0159i −0.236369 0.409403i
\(725\) −11.3703 + 19.6939i −0.422282 + 0.731414i
\(726\) 0.893322 1.54728i 0.0331543 0.0574249i
\(727\) −44.9188 −1.66594 −0.832972 0.553315i \(-0.813363\pi\)
−0.832972 + 0.553315i \(0.813363\pi\)
\(728\) −23.5043 + 5.06382i −0.871128 + 0.187677i
\(729\) 1.00000 0.0370370
\(730\) −0.941603 + 1.63090i −0.0348503 + 0.0603625i
\(731\) 15.7146 27.2185i 0.581225 1.00671i
\(732\) 5.81651 + 10.0745i 0.214985 + 0.372364i
\(733\) 7.31571 0.270212 0.135106 0.990831i \(-0.456863\pi\)
0.135106 + 0.990831i \(0.456863\pi\)
\(734\) −32.7867 56.7882i −1.21018 2.09609i
\(735\) 3.83906 + 6.64945i 0.141606 + 0.245269i
\(736\) −31.0274 −1.14369
\(737\) 3.91130 + 6.77458i 0.144075 + 0.249545i
\(738\) 8.41435 14.5741i 0.309737 0.536480i
\(739\) −17.6096 + 30.5008i −0.647781 + 1.12199i 0.335871 + 0.941908i \(0.390969\pi\)
−0.983652 + 0.180081i \(0.942364\pi\)
\(740\) −2.55005 −0.0937418
\(741\) −8.29466 + 25.7700i −0.304712 + 0.946686i
\(742\) −62.8628 −2.30777
\(743\) −3.98545 + 6.90300i −0.146212 + 0.253247i −0.929824 0.368003i \(-0.880041\pi\)
0.783613 + 0.621250i \(0.213375\pi\)
\(744\) 2.59019 4.48635i 0.0949611 0.164477i
\(745\) 1.58758 + 2.74977i 0.0581644 + 0.100744i
\(746\) −1.23896 −0.0453615
\(747\) −3.68261 6.37847i −0.134740 0.233376i
\(748\) 2.39751 + 4.15261i 0.0876616 + 0.151834i
\(749\) −58.6949 −2.14466
\(750\) 4.64500 + 8.04537i 0.169611 + 0.293776i
\(751\) 17.1442 29.6946i 0.625601 1.08357i −0.362824 0.931858i \(-0.618187\pi\)
0.988424 0.151714i \(-0.0484793\pi\)
\(752\) 23.1190 40.0432i 0.843061 1.46023i
\(753\) 0.510635 0.0186086
\(754\) −30.3823 + 6.54563i −1.10646 + 0.238378i
\(755\) −10.5625 −0.384408
\(756\) −2.75368 + 4.76951i −0.100150 + 0.173465i
\(757\) 20.7720 35.9781i 0.754970 1.30765i −0.190419 0.981703i \(-0.560985\pi\)
0.945389 0.325944i \(-0.105682\pi\)
\(758\) 4.05608 + 7.02534i 0.147323 + 0.255172i
\(759\) 5.18817 0.188318
\(760\) −2.90082 5.02437i −0.105224 0.182253i
\(761\) −16.3870 28.3832i −0.594029 1.02889i −0.993683 0.112223i \(-0.964203\pi\)
0.399654 0.916666i \(-0.369130\pi\)
\(762\) 0.355167 0.0128664
\(763\) 8.38491 + 14.5231i 0.303554 + 0.525771i
\(764\) −4.13952 + 7.16986i −0.149763 + 0.259396i
\(765\) 1.07660 1.86472i 0.0389244 0.0674190i
\(766\) 36.0750 1.30344
\(767\) −14.6479 + 3.15576i −0.528904 + 0.113948i
\(768\) 20.4653 0.738479
\(769\) 19.3953 33.5936i 0.699412 1.21142i −0.269258 0.963068i \(-0.586778\pi\)
0.968670 0.248350i \(-0.0798882\pi\)
\(770\) 2.20924 3.82652i 0.0796156 0.137898i
\(771\) 4.02806 + 6.97680i 0.145067 + 0.251263i
\(772\) 4.79831 0.172695
\(773\) −18.4521 31.9600i −0.663676 1.14952i −0.979642 0.200751i \(-0.935662\pi\)
0.315966 0.948770i \(-0.397671\pi\)
\(774\) −6.98012 12.0899i −0.250895 0.434563i
\(775\) 16.9162 0.607649
\(776\) −8.59817 14.8925i −0.308656 0.534608i
\(777\) −9.23069 + 15.9880i −0.331149 + 0.573567i
\(778\) −18.6563 + 32.3136i −0.668859 + 1.15850i
\(779\) −70.7233 −2.53392
\(780\) −0.704961 + 2.19019i −0.0252417 + 0.0784214i
\(781\) −10.3756 −0.371267
\(782\) −18.6423 + 32.2895i −0.666649 + 1.15467i
\(783\) 2.41231 4.17825i 0.0862090 0.149318i
\(784\) 35.5938 + 61.6502i 1.27121 + 2.20179i
\(785\) 11.5566 0.412472
\(786\) 19.4731 + 33.7284i 0.694582 + 1.20305i
\(787\) 4.08771 + 7.08013i 0.145711 + 0.252379i 0.929638 0.368474i \(-0.120120\pi\)
−0.783927 + 0.620853i \(0.786786\pi\)
\(788\) −8.58127 −0.305695
\(789\) −0.208161 0.360546i −0.00741074 0.0128358i
\(790\) −4.01620 + 6.95626i −0.142890 + 0.247492i
\(791\) −31.7737 + 55.0336i −1.12974 + 1.95677i
\(792\) −1.44343 −0.0512902
\(793\) 34.3954 7.41021i 1.22142 0.263144i
\(794\) 23.9602 0.850314
\(795\) 2.03844 3.53069i 0.0722961 0.125221i
\(796\) 4.65513 8.06291i 0.164997 0.285782i
\(797\) −6.50600 11.2687i −0.230454 0.399159i 0.727487 0.686121i \(-0.240688\pi\)
−0.957942 + 0.286962i \(0.907355\pi\)
\(798\) 61.9754 2.19390
\(799\) −18.7367 32.4530i −0.662858 1.14810i
\(800\) 14.0942 + 24.4119i 0.498305 + 0.863090i
\(801\) 3.37524 0.119258
\(802\) −14.3484 24.8522i −0.506661 0.877562i
\(803\) 0.984522 1.70524i 0.0347430 0.0601767i
\(804\) −4.66266 + 8.07596i −0.164439 + 0.284817i
\(805\) 12.8307 0.452222
\(806\) 15.5172 + 17.1383i 0.546570 + 0.603669i
\(807\) −0.916592 −0.0322656
\(808\) −8.10229 + 14.0336i −0.285038 + 0.493700i
\(809\) −20.9034 + 36.2057i −0.734923 + 1.27292i 0.219834 + 0.975537i \(0.429448\pi\)
−0.954757 + 0.297387i \(0.903885\pi\)
\(810\) −0.478203 0.828272i −0.0168023 0.0291025i
\(811\) −32.7280 −1.14924 −0.574618 0.818422i \(-0.694849\pi\)
−0.574618 + 0.818422i \(0.694849\pi\)
\(812\) 13.2855 + 23.0111i 0.466229 + 0.807532i
\(813\) 4.04304 + 7.00275i 0.141796 + 0.245597i
\(814\) 7.13955 0.250241
\(815\) −1.73648 3.00767i −0.0608263 0.105354i
\(816\) 9.98163 17.2887i 0.349427 0.605225i
\(817\) −29.3342 + 50.8084i −1.02627 + 1.77756i
\(818\) 36.8498 1.28842
\(819\) 11.1800 + 12.3479i 0.390660 + 0.431472i
\(820\) −6.01075 −0.209905
\(821\) −14.4593 + 25.0443i −0.504634 + 0.874053i 0.495351 + 0.868693i \(0.335039\pi\)
−0.999986 + 0.00535974i \(0.998294\pi\)
\(822\) −12.9516 + 22.4329i −0.451740 + 0.782437i
\(823\) 17.6582 + 30.5849i 0.615527 + 1.06612i 0.990292 + 0.139004i \(0.0443900\pi\)
−0.374765 + 0.927120i \(0.622277\pi\)
\(824\) 11.4463 0.398750
\(825\) −2.35672 4.08196i −0.0820505 0.142116i
\(826\) 17.1512 + 29.7067i 0.596766 + 1.03363i
\(827\) 50.2296 1.74665 0.873327 0.487135i \(-0.161958\pi\)
0.873327 + 0.487135i \(0.161958\pi\)
\(828\) 3.09240 + 5.35620i 0.107468 + 0.186141i
\(829\) 5.23523 9.06768i 0.181827 0.314934i −0.760676 0.649132i \(-0.775132\pi\)
0.942503 + 0.334198i \(0.108466\pi\)
\(830\) −3.52207 + 6.10041i −0.122253 + 0.211748i
\(831\) 9.34576 0.324201
\(832\) −0.838139 + 2.60395i −0.0290572 + 0.0902757i
\(833\) 57.6938 1.99897
\(834\) −1.10006 + 1.90536i −0.0380920 + 0.0659773i
\(835\) 6.67966 11.5695i 0.231159 0.400380i
\(836\) −4.47540 7.75161i −0.154785 0.268095i
\(837\) −3.58893 −0.124052
\(838\) 4.43083 + 7.67443i 0.153061 + 0.265109i
\(839\) −8.28161 14.3442i −0.285913 0.495216i 0.686917 0.726736i \(-0.258964\pi\)
−0.972830 + 0.231520i \(0.925630\pi\)
\(840\) −3.56971 −0.123167
\(841\) 2.86150 + 4.95626i 0.0986724 + 0.170906i
\(842\) −3.76885 + 6.52784i −0.129883 + 0.224964i
\(843\) −4.94657 + 8.56772i −0.170369 + 0.295088i
\(844\) 32.1649 1.10716
\(845\) 5.65244 + 4.05928i 0.194450 + 0.139643i
\(846\) −16.6450 −0.572266
\(847\) −2.30994 + 4.00094i −0.0793706 + 0.137474i
\(848\) 18.8994 32.7347i 0.649007 1.12411i
\(849\) −1.83539 3.17899i −0.0629904 0.109103i
\(850\) 33.8731 1.16184
\(851\) 10.3661 + 17.9547i 0.355346 + 0.615478i
\(852\) −6.18435 10.7116i −0.211872 0.366974i
\(853\) 21.1084 0.722736 0.361368 0.932423i \(-0.382310\pi\)
0.361368 + 0.932423i \(0.382310\pi\)
\(854\) −40.2736 69.7559i −1.37813 2.38700i
\(855\) −2.00967 + 3.48084i −0.0687291 + 0.119042i
\(856\) 9.16929 15.8817i 0.313400 0.542824i
\(857\) 32.6369 1.11485 0.557427 0.830226i \(-0.311789\pi\)
0.557427 + 0.830226i \(0.311789\pi\)
\(858\) 1.97373 6.13202i 0.0673819 0.209344i
\(859\) 15.0101 0.512137 0.256068 0.966659i \(-0.417573\pi\)
0.256068 + 0.966659i \(0.417573\pi\)
\(860\) −2.49311 + 4.31819i −0.0850143 + 0.147249i
\(861\) −21.7578 + 37.6855i −0.741502 + 1.28432i
\(862\) −3.36749 5.83266i −0.114697 0.198661i
\(863\) −20.5468 −0.699423 −0.349711 0.936858i \(-0.613720\pi\)
−0.349711 + 0.936858i \(0.613720\pi\)
\(864\) −2.99021 5.17920i −0.101729 0.176200i
\(865\) 0.693743 + 1.20160i 0.0235880 + 0.0408556i
\(866\) 29.7529 1.01104
\(867\) 0.410406 + 0.710844i 0.0139381 + 0.0241415i
\(868\) 9.88277 17.1175i 0.335443 0.581004i
\(869\) 4.19926 7.27333i 0.142450 0.246731i
\(870\) −4.61430 −0.156439
\(871\) 18.9305 + 20.9081i 0.641434 + 0.708445i
\(872\) −5.23955 −0.177433
\(873\) −5.95675 + 10.3174i −0.201605 + 0.349191i
\(874\) 34.7994 60.2743i 1.17711 2.03881i
\(875\) −12.0110 20.8037i −0.406046 0.703292i
\(876\) 2.34729 0.0793077
\(877\) 18.3606 + 31.8015i 0.619994 + 1.07386i 0.989486 + 0.144627i \(0.0461984\pi\)
−0.369492 + 0.929234i \(0.620468\pi\)
\(878\) 26.4883 + 45.8790i 0.893935 + 1.54834i
\(879\) −14.1320 −0.476661
\(880\) 1.32839 + 2.30085i 0.0447802 + 0.0775615i
\(881\) −21.6593 + 37.5150i −0.729721 + 1.26391i 0.227281 + 0.973829i \(0.427016\pi\)
−0.957001 + 0.290084i \(0.906317\pi\)
\(882\) 12.8132 22.1932i 0.431444 0.747284i
\(883\) −23.4531 −0.789261 −0.394630 0.918840i \(-0.629127\pi\)
−0.394630 + 0.918840i \(0.629127\pi\)
\(884\) 11.6038 + 12.8160i 0.390278 + 0.431050i
\(885\) −2.22464 −0.0747803
\(886\) 9.26897 16.0543i 0.311397 0.539356i
\(887\) −12.3370 + 21.3683i −0.414235 + 0.717477i −0.995348 0.0963466i \(-0.969284\pi\)
0.581113 + 0.813823i \(0.302618\pi\)
\(888\) −2.88403 4.99529i −0.0967817 0.167631i
\(889\) −0.918388 −0.0308018
\(890\) −1.61405 2.79562i −0.0541031 0.0937094i
\(891\) 0.500000 + 0.866025i 0.0167506 + 0.0290129i
\(892\) 27.4515 0.919145
\(893\) 34.9756 + 60.5795i 1.17041 + 2.02721i
\(894\) 5.29870 9.17761i 0.177215 0.306945i
\(895\) −3.46378 + 5.99944i −0.115781 + 0.200539i
\(896\) −48.9954 −1.63682
\(897\) 18.2866 3.93970i 0.610573 0.131543i
\(898\) 12.7052 0.423978
\(899\) −8.65763 + 14.9954i −0.288748 + 0.500126i
\(900\) 2.80944 4.86610i 0.0936481 0.162203i
\(901\) −15.3170 26.5298i −0.510282 0.883835i
\(902\) 16.8287 0.560335
\(903\) 18.0491 + 31.2620i 0.600638 + 1.04033i
\(904\) −9.92734 17.1947i −0.330178 0.571886i
\(905\) −5.71192 −0.189871
\(906\) 17.6267 + 30.5303i 0.585606 + 1.01430i
\(907\) −4.82458 + 8.35642i −0.160198 + 0.277470i −0.934939 0.354807i \(-0.884546\pi\)
0.774742 + 0.632278i \(0.217880\pi\)
\(908\) 1.87016 3.23922i 0.0620635 0.107497i
\(909\) 11.2264 0.372357
\(910\) 4.88116 15.1649i 0.161809 0.502711i
\(911\) −9.69851 −0.321326 −0.160663 0.987009i \(-0.551363\pi\)
−0.160663 + 0.987009i \(0.551363\pi\)
\(912\) −18.6326 + 32.2725i −0.616986 + 1.06865i
\(913\) 3.68261 6.37847i 0.121877 0.211097i
\(914\) −18.3532 31.7887i −0.607070 1.05148i
\(915\) 5.22378 0.172693
\(916\) 5.86713 + 10.1622i 0.193855 + 0.335767i
\(917\) −50.3533 87.2145i −1.66281 2.88008i
\(918\) −7.18648 −0.237189
\(919\) 27.1078 + 46.9520i 0.894202 + 1.54880i 0.834789 + 0.550570i \(0.185590\pi\)
0.0594134 + 0.998233i \(0.481077\pi\)
\(920\) −2.00440 + 3.47173i −0.0660832 + 0.114459i
\(921\) −1.72594 + 2.98941i −0.0568715 + 0.0985044i
\(922\) −3.35212 −0.110396
\(923\) −36.5706 + 7.87883i −1.20374 + 0.259335i
\(924\) −5.50736 −0.181179
\(925\) 9.41762 16.3118i 0.309650 0.536329i
\(926\) −4.33121 + 7.50188i −0.142333 + 0.246527i
\(927\) −3.96495 6.86749i −0.130226 0.225558i
\(928\) −28.8533 −0.947156
\(929\) −0.617623 1.06975i −0.0202635 0.0350975i 0.855716 0.517446i \(-0.173117\pi\)
−0.875979 + 0.482349i \(0.839784\pi\)
\(930\) 1.71624 + 2.97261i 0.0562777 + 0.0974758i
\(931\) −107.696 −3.52960
\(932\) 0.597750 + 1.03533i 0.0195799 + 0.0339135i
\(933\) −14.5173 + 25.1448i −0.475276 + 0.823202i
\(934\) −6.53140 + 11.3127i −0.213714 + 0.370164i
\(935\) 2.15319 0.0704169
\(936\) −5.08764 + 1.09609i −0.166295 + 0.0358268i
\(937\) 39.1734 1.27974 0.639869 0.768484i \(-0.278989\pi\)
0.639869 + 0.768484i \(0.278989\pi\)
\(938\) 32.2843 55.9180i 1.05412 1.82579i
\(939\) −6.64802 + 11.5147i −0.216950 + 0.375768i
\(940\) 2.97257 + 5.14863i 0.0969544 + 0.167930i
\(941\) −1.34392 −0.0438107 −0.0219053 0.999760i \(-0.506973\pi\)
−0.0219053 + 0.999760i \(0.506973\pi\)
\(942\) −19.2856 33.4036i −0.628359 1.08835i
\(943\) 24.4341 + 42.3211i 0.795684 + 1.37817i
\(944\) −20.6256 −0.671308
\(945\) 1.23653 + 2.14174i 0.0402244 + 0.0696707i
\(946\) 6.98012 12.0899i 0.226943 0.393077i
\(947\) −9.31931 + 16.1415i −0.302837 + 0.524529i −0.976777 0.214257i \(-0.931267\pi\)
0.673940 + 0.738786i \(0.264600\pi\)
\(948\) 10.0119 0.325170
\(949\) 2.17523 6.75805i 0.0706109 0.219375i
\(950\) −63.2304 −2.05147
\(951\) 5.21413 9.03114i 0.169080 0.292855i
\(952\) −13.4115 + 23.2294i −0.434668 + 0.752868i
\(953\) 27.5812 + 47.7721i 0.893443 + 1.54749i 0.835720 + 0.549156i \(0.185051\pi\)
0.0577236 + 0.998333i \(0.481616\pi\)
\(954\) −13.6070 −0.440543
\(955\) 1.85884 + 3.21961i 0.0601507 + 0.104184i
\(956\) 2.72557 + 4.72082i 0.0881511 + 0.152682i
\(957\) 4.82462 0.155958
\(958\) 4.82553 + 8.35807i 0.155906 + 0.270037i
\(959\) 33.4902 58.0068i 1.08146 1.87314i
\(960\) −0.203068 + 0.351724i −0.00655398 + 0.0113518i
\(961\) −18.1196 −0.584502
\(962\) 25.1646 5.42151i 0.811340 0.174797i
\(963\) −12.7048 −0.409407
\(964\) −14.7720 + 25.5859i −0.475775 + 0.824066i
\(965\) 1.07733 1.86600i 0.0346806 0.0600686i
\(966\) −21.4118 37.0863i −0.688914 1.19323i
\(967\) −17.8380 −0.573631 −0.286816 0.957986i \(-0.592597\pi\)
−0.286816 + 0.957986i \(0.592597\pi\)
\(968\) −0.721717 1.25005i −0.0231969 0.0401781i
\(969\) 15.1007 + 26.1552i 0.485105 + 0.840227i
\(970\) 11.3941 0.365844
\(971\) −19.2134 33.2786i −0.616587 1.06796i −0.990104 0.140337i \(-0.955182\pi\)
0.373517 0.927623i \(-0.378152\pi\)
\(972\) −0.596049 + 1.03239i −0.0191183 + 0.0331138i
\(973\) 2.84453 4.92687i 0.0911914 0.157948i
\(974\) −17.1708 −0.550188
\(975\) −11.4064 12.5980i −0.365297 0.403459i
\(976\) 48.4321 1.55028
\(977\) 11.3263 19.6177i 0.362360 0.627627i −0.625988 0.779832i \(-0.715304\pi\)
0.988349 + 0.152206i \(0.0486376\pi\)
\(978\) −5.79567 + 10.0384i −0.185325 + 0.320993i
\(979\) 1.68762 + 2.92305i 0.0539366 + 0.0934210i
\(980\) −9.15308 −0.292384
\(981\) 1.81496 + 3.14360i 0.0579472 + 0.100367i
\(982\) −8.50230 14.7264i −0.271319 0.469939i
\(983\) 18.4666 0.588993 0.294496 0.955653i \(-0.404848\pi\)
0.294496 + 0.955653i \(0.404848\pi\)
\(984\) −6.79797 11.7744i −0.216711 0.375355i
\(985\) −1.92670 + 3.33714i −0.0613897 + 0.106330i
\(986\) −17.3360 + 30.0269i −0.552092 + 0.956252i
\(987\) 43.0404 1.36999
\(988\) −21.6606 23.9235i −0.689116 0.761108i
\(989\) 40.5386 1.28905
\(990\) 0.478203 0.828272i 0.0151983 0.0263242i
\(991\) 11.7661 20.3795i 0.373763 0.647376i −0.616378 0.787450i \(-0.711401\pi\)
0.990141 + 0.140074i \(0.0447341\pi\)
\(992\) 10.7317 + 18.5878i 0.340731 + 0.590163i
\(993\) −14.6234 −0.464059
\(994\) 42.8205 + 74.1673i 1.35818 + 2.35244i
\(995\) −2.09037 3.62063i −0.0662693 0.114782i
\(996\) 8.78007 0.278207
\(997\) −11.8933 20.5998i −0.376664 0.652401i 0.613910 0.789376i \(-0.289596\pi\)
−0.990575 + 0.136974i \(0.956262\pi\)
\(998\) −22.9244 + 39.7061i −0.725658 + 1.25688i
\(999\) −1.99803 + 3.46070i −0.0632150 + 0.109492i
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 429.2.i.c.100.5 10
13.3 even 3 inner 429.2.i.c.133.5 yes 10
13.4 even 6 5577.2.a.p.1.5 5
13.9 even 3 5577.2.a.v.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.i.c.100.5 10 1.1 even 1 trivial
429.2.i.c.133.5 yes 10 13.3 even 3 inner
5577.2.a.p.1.5 5 13.4 even 6
5577.2.a.v.1.1 5 13.9 even 3