Properties

Label 168.2.v.a.11.12
Level $168$
Weight $2$
Character 168.11
Analytic conductor $1.341$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [168,2,Mod(11,168)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(168, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("168.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.v (of order \(6\), 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: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.12
Character \(\chi\) \(=\) 168.11
Dual form 168.2.v.a.107.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.389211 - 1.35960i) q^{2} +(1.72608 + 0.143748i) q^{3} +(-1.69703 + 1.05834i) q^{4} +(1.77783 + 3.07929i) q^{5} +(-0.476367 - 2.40272i) q^{6} +(-0.793456 - 2.52397i) q^{7} +(2.09943 + 1.89537i) q^{8} +(2.95867 + 0.496241i) q^{9} +O(q^{10})\) \(q+(-0.389211 - 1.35960i) q^{2} +(1.72608 + 0.143748i) q^{3} +(-1.69703 + 1.05834i) q^{4} +(1.77783 + 3.07929i) q^{5} +(-0.476367 - 2.40272i) q^{6} +(-0.793456 - 2.52397i) q^{7} +(2.09943 + 1.89537i) q^{8} +(2.95867 + 0.496241i) q^{9} +(3.49466 - 3.61563i) q^{10} +(0.396703 + 0.229036i) q^{11} +(-3.08134 + 1.58283i) q^{12} +0.799063i q^{13} +(-3.12277 + 2.06114i) q^{14} +(2.62603 + 5.57065i) q^{15} +(1.75982 - 3.59208i) q^{16} +(-5.48456 - 3.16651i) q^{17} +(-0.476858 - 4.21576i) q^{18} +(-2.61696 - 4.53272i) q^{19} +(-6.27598 - 3.34410i) q^{20} +(-1.00675 - 4.47062i) q^{21} +(0.156997 - 0.628501i) q^{22} +(1.55053 + 2.68559i) q^{23} +(3.35131 + 3.57333i) q^{24} +(-3.82137 + 6.61880i) q^{25} +(1.08641 - 0.311004i) q^{26} +(5.03556 + 1.28185i) q^{27} +(4.01774 + 3.44351i) q^{28} -2.60340 q^{29} +(6.55179 - 5.73851i) q^{30} +(-4.42520 - 2.55489i) q^{31} +(-5.56873 - 0.994581i) q^{32} +(0.651815 + 0.452359i) q^{33} +(-2.17055 + 8.68926i) q^{34} +(6.36142 - 6.93048i) q^{35} +(-5.54615 + 2.28915i) q^{36} +(2.89424 - 1.67099i) q^{37} +(-5.14413 + 5.32221i) q^{38} +(-0.114864 + 1.37924i) q^{39} +(-2.10396 + 9.83439i) q^{40} +10.1452i q^{41} +(-5.68643 + 3.10879i) q^{42} +3.56359 q^{43} +(-0.915615 + 0.0311657i) q^{44} +(3.73195 + 9.99285i) q^{45} +(3.04785 - 3.15336i) q^{46} +(-2.15923 - 3.73989i) q^{47} +(3.55394 - 5.94723i) q^{48} +(-5.74086 + 4.00532i) q^{49} +(10.4862 + 2.61943i) q^{50} +(-9.01159 - 6.25404i) q^{51} +(-0.845682 - 1.35603i) q^{52} +(1.16913 - 2.02499i) q^{53} +(-0.217084 - 7.34526i) q^{54} +1.62875i q^{55} +(3.11805 - 6.80278i) q^{56} +(-3.86551 - 8.19999i) q^{57} +(1.01327 + 3.53959i) q^{58} +(1.49741 + 0.864528i) q^{59} +(-10.3521 - 6.67433i) q^{60} +(-4.60841 + 2.66067i) q^{61} +(-1.75130 + 7.01090i) q^{62} +(-1.09508 - 7.86135i) q^{63} +(0.815178 + 7.95836i) q^{64} +(-2.46055 + 1.42060i) q^{65} +(0.361335 - 1.06227i) q^{66} +(0.00979145 - 0.0169593i) q^{67} +(12.6587 - 0.430877i) q^{68} +(2.29028 + 4.85842i) q^{69} +(-11.8986 - 5.95157i) q^{70} -9.04022 q^{71} +(5.27096 + 6.64959i) q^{72} +(4.15674 - 7.19969i) q^{73} +(-3.39835 - 3.28465i) q^{74} +(-7.54741 + 10.8752i) q^{75} +(9.23823 + 4.92251i) q^{76} +(0.263315 - 1.18300i) q^{77} +(1.91993 - 0.380647i) q^{78} +(10.8825 - 6.28304i) q^{79} +(14.1897 - 0.967099i) q^{80} +(8.50749 + 2.93643i) q^{81} +(13.7934 - 3.94861i) q^{82} +0.694004i q^{83} +(6.43993 + 6.52130i) q^{84} -22.5181i q^{85} +(-1.38699 - 4.84506i) q^{86} +(-4.49367 - 0.374235i) q^{87} +(0.398740 + 1.23274i) q^{88} +(-7.02189 + 4.05409i) q^{89} +(12.1338 - 8.96329i) q^{90} +(2.01681 - 0.634021i) q^{91} +(-5.47357 - 2.91654i) q^{92} +(-7.27097 - 5.04605i) q^{93} +(-4.24437 + 4.39129i) q^{94} +(9.30504 - 16.1168i) q^{95} +(-9.46909 - 2.51722i) q^{96} +7.05333 q^{97} +(7.68004 + 6.24636i) q^{98} +(1.06006 + 0.874504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36} + 14 q^{40} - 8 q^{42} - 16 q^{43} - 12 q^{46} + 64 q^{48} - 16 q^{49} - 34 q^{51} - 8 q^{52} + 32 q^{54} + 4 q^{57} - 18 q^{58} + 40 q^{60} + 4 q^{64} - 20 q^{66} - 36 q^{67} - 42 q^{70} + 22 q^{72} + 4 q^{73} + 104 q^{76} + 28 q^{78} - 10 q^{81} + 52 q^{82} + 4 q^{84} + 46 q^{88} + 140 q^{90} + 72 q^{91} - 46 q^{96} - 32 q^{97} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.389211 1.35960i −0.275214 0.961383i
\(3\) 1.72608 + 0.143748i 0.996550 + 0.0829931i
\(4\) −1.69703 + 1.05834i −0.848515 + 0.529171i
\(5\) 1.77783 + 3.07929i 0.795070 + 1.37710i 0.922795 + 0.385292i \(0.125899\pi\)
−0.127724 + 0.991810i \(0.540767\pi\)
\(6\) −0.476367 2.40272i −0.194476 0.980907i
\(7\) −0.793456 2.52397i −0.299898 0.953971i
\(8\) 2.09943 + 1.89537i 0.742259 + 0.670113i
\(9\) 2.95867 + 0.496241i 0.986224 + 0.165414i
\(10\) 3.49466 3.61563i 1.10511 1.14336i
\(11\) 0.396703 + 0.229036i 0.119610 + 0.0690571i 0.558612 0.829429i \(-0.311334\pi\)
−0.439001 + 0.898486i \(0.644668\pi\)
\(12\) −3.08134 + 1.58283i −0.889505 + 0.456925i
\(13\) 0.799063i 0.221620i 0.993842 + 0.110810i \(0.0353445\pi\)
−0.993842 + 0.110810i \(0.964655\pi\)
\(14\) −3.12277 + 2.06114i −0.834596 + 0.550863i
\(15\) 2.62603 + 5.57065i 0.678037 + 1.43834i
\(16\) 1.75982 3.59208i 0.439956 0.898020i
\(17\) −5.48456 3.16651i −1.33020 0.767993i −0.344872 0.938650i \(-0.612078\pi\)
−0.985330 + 0.170657i \(0.945411\pi\)
\(18\) −0.476858 4.21576i −0.112396 0.993663i
\(19\) −2.61696 4.53272i −0.600373 1.03988i −0.992764 0.120078i \(-0.961686\pi\)
0.392392 0.919798i \(-0.371648\pi\)
\(20\) −6.27598 3.34410i −1.40335 0.747763i
\(21\) −1.00675 4.47062i −0.219690 0.975570i
\(22\) 0.156997 0.628501i 0.0334719 0.133997i
\(23\) 1.55053 + 2.68559i 0.323307 + 0.559985i 0.981168 0.193155i \(-0.0618719\pi\)
−0.657861 + 0.753139i \(0.728539\pi\)
\(24\) 3.35131 + 3.57333i 0.684084 + 0.729404i
\(25\) −3.82137 + 6.61880i −0.764273 + 1.32376i
\(26\) 1.08641 0.311004i 0.213062 0.0609928i
\(27\) 5.03556 + 1.28185i 0.969094 + 0.246693i
\(28\) 4.01774 + 3.44351i 0.759282 + 0.650762i
\(29\) −2.60340 −0.483440 −0.241720 0.970346i \(-0.577712\pi\)
−0.241720 + 0.970346i \(0.577712\pi\)
\(30\) 6.55179 5.73851i 1.19619 1.04770i
\(31\) −4.42520 2.55489i −0.794790 0.458872i 0.0468563 0.998902i \(-0.485080\pi\)
−0.841646 + 0.540030i \(0.818413\pi\)
\(32\) −5.56873 0.994581i −0.984423 0.175819i
\(33\) 0.651815 + 0.452359i 0.113466 + 0.0787457i
\(34\) −2.17055 + 8.68926i −0.372245 + 1.49020i
\(35\) 6.36142 6.93048i 1.07528 1.17146i
\(36\) −5.54615 + 2.28915i −0.924358 + 0.381526i
\(37\) 2.89424 1.67099i 0.475810 0.274709i −0.242859 0.970062i \(-0.578085\pi\)
0.718669 + 0.695352i \(0.244752\pi\)
\(38\) −5.14413 + 5.32221i −0.834489 + 0.863376i
\(39\) −0.114864 + 1.37924i −0.0183929 + 0.220856i
\(40\) −2.10396 + 9.83439i −0.332666 + 1.55495i
\(41\) 10.1452i 1.58441i 0.610256 + 0.792205i \(0.291067\pi\)
−0.610256 + 0.792205i \(0.708933\pi\)
\(42\) −5.68643 + 3.10879i −0.877434 + 0.479697i
\(43\) 3.56359 0.543442 0.271721 0.962376i \(-0.412407\pi\)
0.271721 + 0.962376i \(0.412407\pi\)
\(44\) −0.915615 + 0.0311657i −0.138034 + 0.00469840i
\(45\) 3.73195 + 9.99285i 0.556326 + 1.48965i
\(46\) 3.04785 3.15336i 0.449381 0.464937i
\(47\) −2.15923 3.73989i −0.314956 0.545519i 0.664472 0.747313i \(-0.268656\pi\)
−0.979428 + 0.201794i \(0.935323\pi\)
\(48\) 3.55394 5.94723i 0.512967 0.858408i
\(49\) −5.74086 + 4.00532i −0.820122 + 0.572188i
\(50\) 10.4862 + 2.61943i 1.48298 + 0.370443i
\(51\) −9.01159 6.25404i −1.26188 0.875741i
\(52\) −0.845682 1.35603i −0.117275 0.188048i
\(53\) 1.16913 2.02499i 0.160592 0.278154i −0.774489 0.632587i \(-0.781993\pi\)
0.935081 + 0.354433i \(0.115326\pi\)
\(54\) −0.217084 7.34526i −0.0295414 0.999564i
\(55\) 1.62875i 0.219621i
\(56\) 3.11805 6.80278i 0.416666 0.909059i
\(57\) −3.86551 8.19999i −0.511999 1.08612i
\(58\) 1.01327 + 3.53959i 0.133049 + 0.464771i
\(59\) 1.49741 + 0.864528i 0.194946 + 0.112552i 0.594296 0.804247i \(-0.297431\pi\)
−0.399350 + 0.916798i \(0.630764\pi\)
\(60\) −10.3521 6.67433i −1.33645 0.861652i
\(61\) −4.60841 + 2.66067i −0.590047 + 0.340664i −0.765116 0.643892i \(-0.777318\pi\)
0.175069 + 0.984556i \(0.443985\pi\)
\(62\) −1.75130 + 7.01090i −0.222415 + 0.890385i
\(63\) −1.09508 7.86135i −0.137967 0.990437i
\(64\) 0.815178 + 7.95836i 0.101897 + 0.994795i
\(65\) −2.46055 + 1.42060i −0.305193 + 0.176204i
\(66\) 0.361335 1.06227i 0.0444773 0.130757i
\(67\) 0.00979145 0.0169593i 0.00119622 0.00207191i −0.865427 0.501036i \(-0.832953\pi\)
0.866623 + 0.498964i \(0.166286\pi\)
\(68\) 12.6587 0.430877i 1.53510 0.0522515i
\(69\) 2.29028 + 4.85842i 0.275717 + 0.584885i
\(70\) −11.8986 5.95157i −1.42216 0.711349i
\(71\) −9.04022 −1.07288 −0.536439 0.843939i \(-0.680231\pi\)
−0.536439 + 0.843939i \(0.680231\pi\)
\(72\) 5.27096 + 6.64959i 0.621188 + 0.783661i
\(73\) 4.15674 7.19969i 0.486510 0.842660i −0.513370 0.858167i \(-0.671603\pi\)
0.999880 + 0.0155078i \(0.00493650\pi\)
\(74\) −3.39835 3.28465i −0.395050 0.381832i
\(75\) −7.54741 + 10.8752i −0.871499 + 1.25576i
\(76\) 9.23823 + 4.92251i 1.05970 + 0.564651i
\(77\) 0.263315 1.18300i 0.0300076 0.134815i
\(78\) 1.91993 0.380647i 0.217389 0.0430998i
\(79\) 10.8825 6.28304i 1.22438 0.706897i 0.258533 0.966003i \(-0.416761\pi\)
0.965849 + 0.259105i \(0.0834277\pi\)
\(80\) 14.1897 0.967099i 1.58646 0.108125i
\(81\) 8.50749 + 2.93643i 0.945277 + 0.326270i
\(82\) 13.7934 3.94861i 1.52322 0.436051i
\(83\) 0.694004i 0.0761768i 0.999274 + 0.0380884i \(0.0121268\pi\)
−0.999274 + 0.0380884i \(0.987873\pi\)
\(84\) 6.43993 + 6.52130i 0.702654 + 0.711532i
\(85\) 22.5181i 2.44243i
\(86\) −1.38699 4.84506i −0.149563 0.522456i
\(87\) −4.49367 0.374235i −0.481772 0.0401222i
\(88\) 0.398740 + 1.23274i 0.0425058 + 0.131411i
\(89\) −7.02189 + 4.05409i −0.744319 + 0.429733i −0.823638 0.567116i \(-0.808059\pi\)
0.0793185 + 0.996849i \(0.474726\pi\)
\(90\) 12.1338 8.96329i 1.27901 0.944814i
\(91\) 2.01681 0.634021i 0.211419 0.0664634i
\(92\) −5.47357 2.91654i −0.570659 0.304070i
\(93\) −7.27097 5.04605i −0.753965 0.523251i
\(94\) −4.24437 + 4.39129i −0.437773 + 0.452927i
\(95\) 9.30504 16.1168i 0.954677 1.65355i
\(96\) −9.46909 2.51722i −0.966435 0.256912i
\(97\) 7.05333 0.716157 0.358078 0.933692i \(-0.383432\pi\)
0.358078 + 0.933692i \(0.383432\pi\)
\(98\) 7.68004 + 6.24636i 0.775801 + 0.630978i
\(99\) 1.06006 + 0.874504i 0.106540 + 0.0878909i
\(100\) −0.519985 15.2766i −0.0519985 1.52766i
\(101\) 3.34348 5.79108i 0.332689 0.576234i −0.650349 0.759635i \(-0.725378\pi\)
0.983038 + 0.183402i \(0.0587108\pi\)
\(102\) −4.99559 + 14.6863i −0.494637 + 1.45416i
\(103\) −5.48751 + 3.16822i −0.540701 + 0.312174i −0.745363 0.666659i \(-0.767724\pi\)
0.204662 + 0.978833i \(0.434390\pi\)
\(104\) −1.51452 + 1.67757i −0.148510 + 0.164500i
\(105\) 11.9765 11.0481i 1.16879 1.07818i
\(106\) −3.20822 0.801402i −0.311610 0.0778390i
\(107\) 3.09681 1.78795i 0.299380 0.172847i −0.342784 0.939414i \(-0.611370\pi\)
0.642164 + 0.766567i \(0.278037\pi\)
\(108\) −9.90213 + 3.15400i −0.952833 + 0.303494i
\(109\) −0.488061 0.281782i −0.0467478 0.0269899i 0.476444 0.879205i \(-0.341926\pi\)
−0.523192 + 0.852215i \(0.675259\pi\)
\(110\) 2.21445 0.633928i 0.211140 0.0604426i
\(111\) 5.23588 2.46821i 0.496968 0.234273i
\(112\) −10.4626 1.59159i −0.988627 0.150391i
\(113\) 1.41462i 0.133076i −0.997784 0.0665381i \(-0.978805\pi\)
0.997784 0.0665381i \(-0.0211954\pi\)
\(114\) −9.64422 + 8.44707i −0.903264 + 0.791141i
\(115\) −5.51315 + 9.54906i −0.514104 + 0.890454i
\(116\) 4.41805 2.75529i 0.410206 0.255822i
\(117\) −0.396527 + 2.36416i −0.0366590 + 0.218567i
\(118\) 0.592606 2.37236i 0.0545538 0.218393i
\(119\) −3.64043 + 16.3554i −0.333718 + 1.49929i
\(120\) −5.04527 + 16.6725i −0.460568 + 1.52198i
\(121\) −5.39508 9.34456i −0.490462 0.849506i
\(122\) 5.41109 + 5.23004i 0.489897 + 0.473506i
\(123\) −1.45835 + 17.5113i −0.131495 + 1.57894i
\(124\) 10.2137 0.347652i 0.917213 0.0312200i
\(125\) −9.39666 −0.840463
\(126\) −10.2621 + 4.54859i −0.914219 + 0.405221i
\(127\) 15.7043i 1.39353i 0.717299 + 0.696766i \(0.245378\pi\)
−0.717299 + 0.696766i \(0.754622\pi\)
\(128\) 10.5029 4.20580i 0.928336 0.371743i
\(129\) 6.15102 + 0.512260i 0.541567 + 0.0451019i
\(130\) 2.88912 + 2.79245i 0.253392 + 0.244914i
\(131\) −1.16617 + 0.673290i −0.101889 + 0.0588256i −0.550079 0.835113i \(-0.685402\pi\)
0.448190 + 0.893938i \(0.352069\pi\)
\(132\) −1.58490 0.0778238i −0.137948 0.00677370i
\(133\) −9.36400 + 10.2016i −0.811961 + 0.884595i
\(134\) −0.0268688 0.00671173i −0.00232111 0.000579805i
\(135\) 5.00517 + 17.7849i 0.430776 + 1.53068i
\(136\) −5.51273 17.0431i −0.472713 1.46144i
\(137\) 7.79136 + 4.49834i 0.665661 + 0.384320i 0.794431 0.607355i \(-0.207769\pi\)
−0.128770 + 0.991675i \(0.541103\pi\)
\(138\) 5.71411 5.00481i 0.486417 0.426038i
\(139\) −16.0176 −1.35859 −0.679296 0.733864i \(-0.737715\pi\)
−0.679296 + 0.733864i \(0.737715\pi\)
\(140\) −3.46070 + 18.4938i −0.292482 + 1.56301i
\(141\) −3.18939 6.76572i −0.268595 0.569777i
\(142\) 3.51855 + 12.2911i 0.295270 + 1.03145i
\(143\) −0.183014 + 0.316990i −0.0153044 + 0.0265081i
\(144\) 6.98927 9.75449i 0.582439 0.812874i
\(145\) −4.62841 8.01664i −0.384369 0.665746i
\(146\) −11.4065 2.84931i −0.944013 0.235811i
\(147\) −10.4849 + 6.08824i −0.864781 + 0.502150i
\(148\) −3.14313 + 5.89882i −0.258364 + 0.484880i
\(149\) 3.34348 + 5.79108i 0.273909 + 0.474424i 0.969859 0.243666i \(-0.0783501\pi\)
−0.695951 + 0.718090i \(0.745017\pi\)
\(150\) 17.7235 + 6.02871i 1.44712 + 0.492242i
\(151\) −3.66278 2.11471i −0.298073 0.172093i 0.343504 0.939151i \(-0.388386\pi\)
−0.641577 + 0.767059i \(0.721719\pi\)
\(152\) 3.09703 14.4762i 0.251202 1.17418i
\(153\) −14.6557 12.0903i −1.18484 0.977446i
\(154\) −1.71089 + 0.102431i −0.137867 + 0.00825413i
\(155\) 18.1687i 1.45934i
\(156\) −1.26478 2.46218i −0.101264 0.197132i
\(157\) 19.9382 + 11.5113i 1.59124 + 0.918702i 0.993095 + 0.117313i \(0.0374281\pi\)
0.598144 + 0.801389i \(0.295905\pi\)
\(158\) −12.7780 12.3505i −1.01657 0.982552i
\(159\) 2.30910 3.32723i 0.183123 0.263866i
\(160\) −6.83766 18.9160i −0.540565 1.49544i
\(161\) 5.54808 6.04438i 0.437250 0.476364i
\(162\) 0.681165 12.7097i 0.0535174 0.998567i
\(163\) 10.4009 + 18.0148i 0.814658 + 1.41103i 0.909573 + 0.415544i \(0.136409\pi\)
−0.0949145 + 0.995485i \(0.530258\pi\)
\(164\) −10.7371 17.2167i −0.838424 1.34440i
\(165\) −0.234130 + 2.81135i −0.0182270 + 0.218863i
\(166\) 0.943568 0.270114i 0.0732351 0.0209649i
\(167\) 7.53905 0.583390 0.291695 0.956511i \(-0.405781\pi\)
0.291695 + 0.956511i \(0.405781\pi\)
\(168\) 6.35987 11.2939i 0.490675 0.871343i
\(169\) 12.3615 0.950885
\(170\) −30.6156 + 8.76429i −2.34811 + 0.672190i
\(171\) −5.49342 14.7095i −0.420093 1.12486i
\(172\) −6.04751 + 3.77150i −0.461119 + 0.287574i
\(173\) 7.77603 + 13.4685i 0.591201 + 1.02399i 0.994071 + 0.108733i \(0.0346793\pi\)
−0.402870 + 0.915257i \(0.631987\pi\)
\(174\) 1.24017 + 6.25526i 0.0940174 + 0.474210i
\(175\) 19.7377 + 4.39329i 1.49203 + 0.332102i
\(176\) 1.52084 1.02192i 0.114638 0.0770304i
\(177\) 2.46036 + 1.70749i 0.184932 + 0.128343i
\(178\) 8.24494 + 7.96908i 0.617985 + 0.597308i
\(179\) 7.81218 + 4.51037i 0.583910 + 0.337121i 0.762686 0.646769i \(-0.223880\pi\)
−0.178776 + 0.983890i \(0.557214\pi\)
\(180\) −16.9091 13.0085i −1.26033 0.969596i
\(181\) 10.4041i 0.773330i 0.922220 + 0.386665i \(0.126373\pi\)
−0.922220 + 0.386665i \(0.873627\pi\)
\(182\) −1.64698 2.49529i −0.122082 0.184963i
\(183\) −8.33693 + 3.93006i −0.616284 + 0.290519i
\(184\) −1.83496 + 8.57702i −0.135275 + 0.632306i
\(185\) 10.2909 + 5.94148i 0.756605 + 0.436826i
\(186\) −4.03068 + 11.8496i −0.295543 + 0.868855i
\(187\) −1.45049 2.51233i −0.106071 0.183720i
\(188\) 7.62236 + 4.06151i 0.555918 + 0.296216i
\(189\) −0.760132 13.7267i −0.0552915 0.998470i
\(190\) −25.5340 6.37831i −1.85243 0.462731i
\(191\) −7.33838 12.7104i −0.530986 0.919695i −0.999346 0.0361574i \(-0.988488\pi\)
0.468360 0.883538i \(-0.344845\pi\)
\(192\) 0.263059 + 13.8539i 0.0189846 + 0.999820i
\(193\) 8.06569 13.9702i 0.580581 1.00560i −0.414829 0.909899i \(-0.636159\pi\)
0.995411 0.0956969i \(-0.0305080\pi\)
\(194\) −2.74523 9.58971i −0.197096 0.688501i
\(195\) −4.45130 + 2.09836i −0.318764 + 0.150267i
\(196\) 5.50341 12.8729i 0.393101 0.919495i
\(197\) 21.9480 1.56373 0.781863 0.623450i \(-0.214269\pi\)
0.781863 + 0.623450i \(0.214269\pi\)
\(198\) 0.776391 1.78162i 0.0551757 0.126614i
\(199\) −13.8171 7.97732i −0.979470 0.565497i −0.0773599 0.997003i \(-0.524649\pi\)
−0.902110 + 0.431506i \(0.857982\pi\)
\(200\) −20.5677 + 6.65279i −1.45436 + 0.470424i
\(201\) 0.0193387 0.0278655i 0.00136404 0.00196548i
\(202\) −9.17487 2.29185i −0.645542 0.161254i
\(203\) 2.06568 + 6.57091i 0.144983 + 0.461188i
\(204\) 21.9119 + 1.07594i 1.53414 + 0.0753311i
\(205\) −31.2400 + 18.0364i −2.18189 + 1.25972i
\(206\) 6.44331 + 6.22773i 0.448927 + 0.433906i
\(207\) 3.25480 + 8.71522i 0.226224 + 0.605750i
\(208\) 2.87030 + 1.40621i 0.199019 + 0.0975030i
\(209\) 2.39752i 0.165840i
\(210\) −19.6824 11.9833i −1.35821 0.826924i
\(211\) 20.9923 1.44517 0.722586 0.691281i \(-0.242953\pi\)
0.722586 + 0.691281i \(0.242953\pi\)
\(212\) 0.159087 + 4.67381i 0.0109261 + 0.320999i
\(213\) −15.6041 1.29952i −1.06918 0.0890414i
\(214\) −3.63621 3.51454i −0.248566 0.240249i
\(215\) 6.33546 + 10.9733i 0.432074 + 0.748375i
\(216\) 8.14220 + 12.2354i 0.554007 + 0.832512i
\(217\) −2.93727 + 13.1963i −0.199395 + 0.895821i
\(218\) −0.193153 + 0.773241i −0.0130820 + 0.0523705i
\(219\) 8.20979 11.8297i 0.554766 0.799375i
\(220\) −1.72378 2.76404i −0.116217 0.186352i
\(221\) 2.53024 4.38251i 0.170203 0.294800i
\(222\) −5.39365 6.15805i −0.361998 0.413302i
\(223\) 7.05072i 0.472151i −0.971735 0.236075i \(-0.924139\pi\)
0.971735 0.236075i \(-0.0758613\pi\)
\(224\) 1.90825 + 14.8445i 0.127500 + 0.991839i
\(225\) −14.5907 + 17.6865i −0.972713 + 1.17910i
\(226\) −1.92332 + 0.550585i −0.127937 + 0.0366244i
\(227\) −17.9681 10.3739i −1.19258 0.688539i −0.233693 0.972310i \(-0.575081\pi\)
−0.958892 + 0.283771i \(0.908414\pi\)
\(228\) 15.2383 + 9.82460i 1.00918 + 0.650650i
\(229\) 19.0453 10.9958i 1.25855 0.726623i 0.285756 0.958302i \(-0.407755\pi\)
0.972792 + 0.231680i \(0.0744221\pi\)
\(230\) 15.1287 + 3.77909i 0.997556 + 0.249186i
\(231\) 0.624556 2.00409i 0.0410927 0.131859i
\(232\) −5.46565 4.93440i −0.358838 0.323959i
\(233\) −15.1401 + 8.74112i −0.991858 + 0.572650i −0.905829 0.423643i \(-0.860751\pi\)
−0.0860289 + 0.996293i \(0.527418\pi\)
\(234\) 3.36865 0.381039i 0.220216 0.0249093i
\(235\) 7.67748 13.2978i 0.500824 0.867452i
\(236\) −3.45611 + 0.117639i −0.224974 + 0.00765764i
\(237\) 19.6873 9.28065i 1.27883 0.602843i
\(238\) 23.6537 1.41615i 1.53324 0.0917953i
\(239\) −6.60546 −0.427271 −0.213636 0.976913i \(-0.568531\pi\)
−0.213636 + 0.976913i \(0.568531\pi\)
\(240\) 24.6316 + 0.370463i 1.58996 + 0.0239133i
\(241\) −5.27959 + 9.14453i −0.340089 + 0.589051i −0.984449 0.175671i \(-0.943790\pi\)
0.644360 + 0.764722i \(0.277124\pi\)
\(242\) −10.6051 + 10.9722i −0.681718 + 0.705318i
\(243\) 14.2625 + 6.29143i 0.914937 + 0.403596i
\(244\) 5.00472 9.39251i 0.320394 0.601294i
\(245\) −22.5398 10.5570i −1.44002 0.674462i
\(246\) 24.3760 4.83282i 1.55416 0.308129i
\(247\) 3.62192 2.09112i 0.230457 0.133055i
\(248\) −4.44793 13.7512i −0.282444 0.873201i
\(249\) −0.0997618 + 1.19790i −0.00632215 + 0.0759140i
\(250\) 3.65728 + 12.7757i 0.231307 + 0.808007i
\(251\) 6.66647i 0.420784i 0.977617 + 0.210392i \(0.0674741\pi\)
−0.977617 + 0.210392i \(0.932526\pi\)
\(252\) 10.1784 + 12.1820i 0.641178 + 0.767392i
\(253\) 1.42051i 0.0893066i
\(254\) 21.3516 6.11228i 1.33972 0.383519i
\(255\) 3.23694 38.8680i 0.202705 2.43401i
\(256\) −9.80605 12.6428i −0.612878 0.790177i
\(257\) 0.887844 0.512597i 0.0553822 0.0319749i −0.472053 0.881570i \(-0.656487\pi\)
0.527435 + 0.849595i \(0.323154\pi\)
\(258\) −1.69757 8.56231i −0.105686 0.533066i
\(259\) −6.51398 5.97912i −0.404759 0.371525i
\(260\) 2.67214 5.01490i 0.165719 0.311011i
\(261\) −7.70262 1.29191i −0.476780 0.0799675i
\(262\) 1.36929 + 1.32348i 0.0845952 + 0.0817647i
\(263\) −8.60208 + 14.8992i −0.530427 + 0.918726i 0.468943 + 0.883228i \(0.344635\pi\)
−0.999370 + 0.0354978i \(0.988698\pi\)
\(264\) 0.511051 + 2.18512i 0.0314530 + 0.134485i
\(265\) 8.31406 0.510729
\(266\) 17.5147 + 8.76071i 1.07390 + 0.537153i
\(267\) −12.7031 + 5.98828i −0.777416 + 0.366477i
\(268\) 0.00133235 + 0.0391431i 8.13864e−5 + 0.00239105i
\(269\) −3.92637 + 6.80068i −0.239395 + 0.414644i −0.960541 0.278139i \(-0.910282\pi\)
0.721146 + 0.692783i \(0.243616\pi\)
\(270\) 22.2323 13.7271i 1.35301 0.835405i
\(271\) −15.7096 + 9.06993i −0.954289 + 0.550959i −0.894411 0.447247i \(-0.852405\pi\)
−0.0598783 + 0.998206i \(0.519071\pi\)
\(272\) −21.0262 + 14.1285i −1.27490 + 0.856665i
\(273\) 3.57231 0.804454i 0.216206 0.0486878i
\(274\) 3.08347 12.3439i 0.186279 0.745725i
\(275\) −3.03189 + 1.75046i −0.182830 + 0.105557i
\(276\) −9.02854 5.82099i −0.543454 0.350382i
\(277\) 19.2898 + 11.1370i 1.15901 + 0.669157i 0.951067 0.308983i \(-0.0999888\pi\)
0.207946 + 0.978140i \(0.433322\pi\)
\(278\) 6.23421 + 21.7775i 0.373903 + 1.30613i
\(279\) −11.8249 9.75505i −0.707937 0.584020i
\(280\) 26.4911 2.49281i 1.58315 0.148974i
\(281\) 17.9109i 1.06847i −0.845335 0.534236i \(-0.820599\pi\)
0.845335 0.534236i \(-0.179401\pi\)
\(282\) −7.95734 + 6.96959i −0.473853 + 0.415033i
\(283\) −2.24283 + 3.88469i −0.133322 + 0.230921i −0.924955 0.380076i \(-0.875898\pi\)
0.791633 + 0.610997i \(0.209231\pi\)
\(284\) 15.3415 9.56765i 0.910352 0.567736i
\(285\) 18.3780 26.4812i 1.08862 1.56861i
\(286\) 0.502211 + 0.125451i 0.0296964 + 0.00741805i
\(287\) 25.6061 8.04974i 1.51148 0.475161i
\(288\) −15.9825 5.70607i −0.941779 0.336234i
\(289\) 11.5536 + 20.0115i 0.679625 + 1.17715i
\(290\) −9.09801 + 9.41296i −0.534254 + 0.552748i
\(291\) 12.1746 + 1.01390i 0.713686 + 0.0594361i
\(292\) 0.565620 + 16.6173i 0.0331004 + 0.972456i
\(293\) −24.7711 −1.44714 −0.723570 0.690251i \(-0.757500\pi\)
−0.723570 + 0.690251i \(0.757500\pi\)
\(294\) 12.3584 + 11.8857i 0.720758 + 0.693187i
\(295\) 6.14794i 0.357947i
\(296\) 9.24338 + 1.97752i 0.537261 + 0.114941i
\(297\) 1.70403 + 1.66184i 0.0988778 + 0.0964298i
\(298\) 6.57224 6.79975i 0.380719 0.393899i
\(299\) −2.14596 + 1.23897i −0.124104 + 0.0716514i
\(300\) 1.29845 26.4433i 0.0749663 1.52671i
\(301\) −2.82755 8.99439i −0.162977 0.518428i
\(302\) −1.44957 + 5.80299i −0.0834131 + 0.333925i
\(303\) 6.60356 9.51522i 0.379364 0.546635i
\(304\) −20.8873 + 1.42357i −1.19797 + 0.0816473i
\(305\) −16.3860 9.46044i −0.938257 0.541703i
\(306\) −10.7339 + 24.6316i −0.613616 + 1.40809i
\(307\) 7.72188 0.440711 0.220355 0.975420i \(-0.429278\pi\)
0.220355 + 0.975420i \(0.429278\pi\)
\(308\) 0.805161 + 2.28626i 0.0458783 + 0.130272i
\(309\) −9.92729 + 4.67976i −0.564744 + 0.266222i
\(310\) −24.7021 + 7.07144i −1.40299 + 0.401631i
\(311\) −10.0093 + 17.3367i −0.567577 + 0.983072i 0.429228 + 0.903196i \(0.358786\pi\)
−0.996805 + 0.0798757i \(0.974548\pi\)
\(312\) −2.85532 + 2.67791i −0.161650 + 0.151607i
\(313\) −8.54501 14.8004i −0.482993 0.836568i 0.516817 0.856096i \(-0.327117\pi\)
−0.999809 + 0.0195284i \(0.993784\pi\)
\(314\) 7.89063 31.5883i 0.445294 1.78263i
\(315\) 22.2605 17.3482i 1.25424 0.977461i
\(316\) −11.8184 + 22.1800i −0.664837 + 1.24772i
\(317\) −7.67062 13.2859i −0.430825 0.746210i 0.566120 0.824323i \(-0.308444\pi\)
−0.996945 + 0.0781127i \(0.975111\pi\)
\(318\) −5.42243 1.84446i −0.304075 0.103432i
\(319\) −1.03278 0.596274i −0.0578244 0.0333849i
\(320\) −23.0569 + 16.6588i −1.28892 + 0.931255i
\(321\) 5.60235 2.64097i 0.312693 0.147405i
\(322\) −10.3773 5.19064i −0.578305 0.289263i
\(323\) 33.1466i 1.84433i
\(324\) −17.5452 + 4.02063i −0.974734 + 0.223368i
\(325\) −5.28884 3.05351i −0.293372 0.169378i
\(326\) 20.4448 21.1526i 1.13234 1.17153i
\(327\) −0.801925 0.556536i −0.0443465 0.0307765i
\(328\) −19.2288 + 21.2990i −1.06173 + 1.17604i
\(329\) −7.72613 + 8.41727i −0.425955 + 0.464059i
\(330\) 3.91344 0.775883i 0.215428 0.0427110i
\(331\) −6.86143 11.8844i −0.377138 0.653223i 0.613506 0.789690i \(-0.289759\pi\)
−0.990645 + 0.136467i \(0.956425\pi\)
\(332\) −0.734493 1.17774i −0.0403106 0.0646371i
\(333\) 9.39233 3.50768i 0.514696 0.192219i
\(334\) −2.93428 10.2501i −0.160557 0.560861i
\(335\) 0.0696302 0.00380430
\(336\) −17.8305 4.25118i −0.972735 0.231921i
\(337\) −15.7338 −0.857074 −0.428537 0.903524i \(-0.640971\pi\)
−0.428537 + 0.903524i \(0.640971\pi\)
\(338\) −4.81123 16.8067i −0.261696 0.914164i
\(339\) 0.203349 2.44174i 0.0110444 0.132617i
\(340\) 23.8319 + 38.2139i 1.29246 + 2.07244i
\(341\) −1.17033 2.02706i −0.0633767 0.109772i
\(342\) −17.8609 + 13.1939i −0.965807 + 0.713447i
\(343\) 14.6644 + 11.3117i 0.791804 + 0.610775i
\(344\) 7.48149 + 6.75430i 0.403375 + 0.364167i
\(345\) −10.8888 + 15.6899i −0.586232 + 0.844715i
\(346\) 15.2853 15.8144i 0.821740 0.850187i
\(347\) −18.5301 10.6984i −0.994748 0.574318i −0.0880576 0.996115i \(-0.528066\pi\)
−0.906690 + 0.421798i \(0.861399\pi\)
\(348\) 8.02196 4.12076i 0.430022 0.220896i
\(349\) 15.7266i 0.841826i −0.907101 0.420913i \(-0.861710\pi\)
0.907101 0.420913i \(-0.138290\pi\)
\(350\) −1.70901 28.5454i −0.0913507 1.52581i
\(351\) −1.02428 + 4.02373i −0.0546721 + 0.214771i
\(352\) −1.98134 1.67000i −0.105606 0.0890111i
\(353\) −10.1824 5.87883i −0.541956 0.312898i 0.203915 0.978989i \(-0.434633\pi\)
−0.745871 + 0.666090i \(0.767967\pi\)
\(354\) 1.36391 4.00968i 0.0724908 0.213112i
\(355\) −16.0720 27.8375i −0.853013 1.47746i
\(356\) 7.62574 14.3115i 0.404164 0.758507i
\(357\) −8.63472 + 27.7073i −0.456998 + 1.46643i
\(358\) 3.09171 12.3769i 0.163402 0.654141i
\(359\) −10.2639 17.7776i −0.541709 0.938268i −0.998806 0.0488509i \(-0.984444\pi\)
0.457097 0.889417i \(-0.348889\pi\)
\(360\) −11.1052 + 28.0527i −0.585293 + 1.47851i
\(361\) −4.19701 + 7.26943i −0.220895 + 0.382601i
\(362\) 14.1454 4.04938i 0.743466 0.212831i
\(363\) −7.96906 16.9050i −0.418267 0.887280i
\(364\) −2.75158 + 3.21043i −0.144222 + 0.168272i
\(365\) 29.5599 1.54724
\(366\) 8.58814 + 9.80528i 0.448909 + 0.512530i
\(367\) 19.9290 + 11.5060i 1.04029 + 0.600609i 0.919914 0.392120i \(-0.128258\pi\)
0.120372 + 0.992729i \(0.461591\pi\)
\(368\) 12.3755 0.843451i 0.645118 0.0439679i
\(369\) −5.03445 + 30.0162i −0.262083 + 1.56258i
\(370\) 4.07270 16.3041i 0.211729 0.847608i
\(371\) −6.03867 1.34411i −0.313512 0.0697826i
\(372\) 17.6795 + 0.868122i 0.916640 + 0.0450100i
\(373\) 21.6640 12.5077i 1.12172 0.647624i 0.179878 0.983689i \(-0.442430\pi\)
0.941839 + 0.336065i \(0.109096\pi\)
\(374\) −2.85122 + 2.94992i −0.147433 + 0.152537i
\(375\) −16.2193 1.35075i −0.837563 0.0697526i
\(376\) 2.55532 11.9442i 0.131781 0.615973i
\(377\) 2.08028i 0.107140i
\(378\) −18.3670 + 6.37605i −0.944696 + 0.327949i
\(379\) −11.7405 −0.603071 −0.301535 0.953455i \(-0.597499\pi\)
−0.301535 + 0.953455i \(0.597499\pi\)
\(380\) 1.26616 + 37.1986i 0.0649529 + 1.90825i
\(381\) −2.25747 + 27.1068i −0.115653 + 1.38872i
\(382\) −14.4250 + 14.9243i −0.738045 + 0.763594i
\(383\) −8.93250 15.4715i −0.456430 0.790559i 0.542340 0.840159i \(-0.317539\pi\)
−0.998769 + 0.0496002i \(0.984205\pi\)
\(384\) 18.7334 5.74974i 0.955985 0.293415i
\(385\) 4.11092 1.29234i 0.209512 0.0658639i
\(386\) −22.1331 5.52878i −1.12655 0.281407i
\(387\) 10.5435 + 1.76840i 0.535956 + 0.0898927i
\(388\) −11.9697 + 7.46484i −0.607670 + 0.378970i
\(389\) −12.9460 + 22.4231i −0.656386 + 1.13689i 0.325158 + 0.945660i \(0.394582\pi\)
−0.981544 + 0.191235i \(0.938751\pi\)
\(390\) 4.58543 + 5.23529i 0.232192 + 0.265099i
\(391\) 19.6391i 0.993190i
\(392\) −19.6440 2.47216i −0.992174 0.124863i
\(393\) −2.10969 + 0.994514i −0.106420 + 0.0501666i
\(394\) −8.54238 29.8405i −0.430359 1.50334i
\(395\) 38.6946 + 22.3404i 1.94694 + 1.12407i
\(396\) −2.72447 0.362157i −0.136910 0.0181991i
\(397\) −17.5040 + 10.1060i −0.878502 + 0.507203i −0.870164 0.492762i \(-0.835987\pi\)
−0.00833784 + 0.999965i \(0.502654\pi\)
\(398\) −5.46820 + 21.8906i −0.274096 + 1.09728i
\(399\) −17.6294 + 16.2628i −0.882576 + 0.814156i
\(400\) 17.0503 + 25.3746i 0.852516 + 1.26873i
\(401\) 32.0937 18.5293i 1.60268 0.925309i 0.611735 0.791063i \(-0.290472\pi\)
0.990948 0.134247i \(-0.0428615\pi\)
\(402\) −0.0454128 0.0154473i −0.00226498 0.000770441i
\(403\) 2.04152 3.53601i 0.101695 0.176141i
\(404\) 0.454957 + 13.3662i 0.0226350 + 0.664992i
\(405\) 6.08275 + 31.4175i 0.302255 + 1.56115i
\(406\) 8.12983 5.36598i 0.403477 0.266309i
\(407\) 1.53087 0.0758825
\(408\) −7.06547 30.2102i −0.349793 1.49563i
\(409\) −14.5304 + 25.1675i −0.718484 + 1.24445i 0.243117 + 0.969997i \(0.421830\pi\)
−0.961600 + 0.274453i \(0.911503\pi\)
\(410\) 36.6812 + 35.4539i 1.81156 + 1.75094i
\(411\) 12.8018 + 8.88448i 0.631469 + 0.438239i
\(412\) 5.95942 11.1842i 0.293599 0.551008i
\(413\) 0.993917 4.46537i 0.0489075 0.219727i
\(414\) 10.5824 7.81729i 0.520098 0.384199i
\(415\) −2.13704 + 1.23382i −0.104903 + 0.0605659i
\(416\) 0.794732 4.44977i 0.0389650 0.218168i
\(417\) −27.6475 2.30250i −1.35391 0.112754i
\(418\) −3.25967 + 0.933141i −0.159436 + 0.0456414i
\(419\) 1.27248i 0.0621647i −0.999517 0.0310823i \(-0.990105\pi\)
0.999517 0.0310823i \(-0.00989541\pi\)
\(420\) −8.63188 + 31.4242i −0.421192 + 1.53334i
\(421\) 12.1006i 0.589749i −0.955536 0.294875i \(-0.904722\pi\)
0.955536 0.294875i \(-0.0952779\pi\)
\(422\) −8.17044 28.5412i −0.397731 1.38936i
\(423\) −4.53256 12.1366i −0.220381 0.590102i
\(424\) 6.29260 2.03539i 0.305596 0.0988474i
\(425\) 41.9171 24.2008i 2.03328 1.17391i
\(426\) 4.30646 + 21.7211i 0.208649 + 1.05239i
\(427\) 10.3720 + 9.52038i 0.501937 + 0.460723i
\(428\) −3.36313 + 6.31169i −0.162563 + 0.305087i
\(429\) −0.361463 + 0.520841i −0.0174516 + 0.0251464i
\(430\) 12.4535 12.8846i 0.600562 0.621352i
\(431\) 8.36354 14.4861i 0.402858 0.697770i −0.591212 0.806516i \(-0.701350\pi\)
0.994070 + 0.108746i \(0.0346837\pi\)
\(432\) 13.4662 15.8323i 0.647893 0.761731i
\(433\) −14.1708 −0.681007 −0.340503 0.940243i \(-0.610597\pi\)
−0.340503 + 0.940243i \(0.610597\pi\)
\(434\) 19.0849 1.14261i 0.916104 0.0548472i
\(435\) −6.83661 14.5027i −0.327790 0.695349i
\(436\) 1.12648 0.0383430i 0.0539485 0.00183630i
\(437\) 8.11535 14.0562i 0.388210 0.672399i
\(438\) −19.2790 6.55780i −0.921185 0.313344i
\(439\) −22.3364 + 12.8959i −1.06606 + 0.615489i −0.927102 0.374809i \(-0.877708\pi\)
−0.138957 + 0.990298i \(0.544375\pi\)
\(440\) −3.08708 + 3.41944i −0.147171 + 0.163016i
\(441\) −18.9729 + 9.00158i −0.903472 + 0.428646i
\(442\) −6.94326 1.73440i −0.330257 0.0824971i
\(443\) −30.3993 + 17.5510i −1.44431 + 0.833875i −0.998134 0.0610673i \(-0.980550\pi\)
−0.446181 + 0.894943i \(0.647216\pi\)
\(444\) −6.27323 + 9.72999i −0.297714 + 0.461765i
\(445\) −24.9675 14.4150i −1.18357 0.683336i
\(446\) −9.58616 + 2.74421i −0.453918 + 0.129942i
\(447\) 4.93864 + 10.4765i 0.233590 + 0.495519i
\(448\) 19.4399 8.37209i 0.918447 0.395544i
\(449\) 13.8891i 0.655467i 0.944770 + 0.327733i \(0.106285\pi\)
−0.944770 + 0.327733i \(0.893715\pi\)
\(450\) 29.7255 + 12.9537i 1.40127 + 0.610644i
\(451\) −2.32361 + 4.02462i −0.109415 + 0.189512i
\(452\) 1.49715 + 2.40065i 0.0704201 + 0.112917i
\(453\) −6.01825 4.17667i −0.282762 0.196237i
\(454\) −7.11097 + 28.4671i −0.333734 + 1.33603i
\(455\) 5.53788 + 5.08317i 0.259620 + 0.238303i
\(456\) 7.42664 24.5418i 0.347784 1.14928i
\(457\) 3.77280 + 6.53468i 0.176484 + 0.305679i 0.940674 0.339312i \(-0.110194\pi\)
−0.764190 + 0.644991i \(0.776861\pi\)
\(458\) −22.3625 21.6143i −1.04493 1.00997i
\(459\) −23.5588 22.9756i −1.09963 1.07241i
\(460\) −0.750191 22.0398i −0.0349778 1.02761i
\(461\) 17.6339 0.821292 0.410646 0.911795i \(-0.365303\pi\)
0.410646 + 0.911795i \(0.365303\pi\)
\(462\) −2.96785 0.0691334i −0.138077 0.00321638i
\(463\) 29.5192i 1.37187i −0.727661 0.685937i \(-0.759393\pi\)
0.727661 0.685937i \(-0.240607\pi\)
\(464\) −4.58153 + 9.35163i −0.212692 + 0.434138i
\(465\) 2.61171 31.3605i 0.121115 1.45431i
\(466\) 17.7771 + 17.1823i 0.823508 + 0.795955i
\(467\) 26.4319 15.2605i 1.22312 0.706170i 0.257539 0.966268i \(-0.417088\pi\)
0.965582 + 0.260098i \(0.0837549\pi\)
\(468\) −1.82918 4.43172i −0.0845537 0.204856i
\(469\) −0.0505738 0.0112569i −0.00233528 0.000519795i
\(470\) −21.0679 5.26267i −0.971788 0.242749i
\(471\) 32.7600 + 22.7355i 1.50950 + 1.04759i
\(472\) 1.50510 + 4.65314i 0.0692777 + 0.214178i
\(473\) 1.41368 + 0.816191i 0.0650013 + 0.0375285i
\(474\) −20.2805 23.1547i −0.931513 1.06353i
\(475\) 40.0015 1.83540
\(476\) −11.1317 31.6084i −0.510219 1.44877i
\(477\) 4.46396 5.41112i 0.204391 0.247758i
\(478\) 2.57091 + 8.98079i 0.117591 + 0.410772i
\(479\) 0.0969618 0.167943i 0.00443030 0.00767350i −0.863802 0.503832i \(-0.831923\pi\)
0.868232 + 0.496158i \(0.165256\pi\)
\(480\) −9.08319 33.6333i −0.414589 1.53514i
\(481\) 1.33523 + 2.31268i 0.0608811 + 0.105449i
\(482\) 14.4878 + 3.61899i 0.659900 + 0.164841i
\(483\) 10.4453 9.63553i 0.475276 0.438432i
\(484\) 19.0454 + 10.1482i 0.865699 + 0.461280i
\(485\) 12.5396 + 21.7193i 0.569395 + 0.986221i
\(486\) 3.00274 21.8400i 0.136207 0.990680i
\(487\) −17.4486 10.0740i −0.790673 0.456496i 0.0495261 0.998773i \(-0.484229\pi\)
−0.840200 + 0.542277i \(0.817562\pi\)
\(488\) −14.7180 3.14875i −0.666251 0.142537i
\(489\) 15.3631 + 32.5900i 0.694742 + 1.47377i
\(490\) −5.58058 + 34.7541i −0.252105 + 1.57003i
\(491\) 4.30244i 0.194167i 0.995276 + 0.0970833i \(0.0309513\pi\)
−0.995276 + 0.0970833i \(0.969049\pi\)
\(492\) −16.0581 31.2607i −0.723956 1.40934i
\(493\) 14.2785 + 8.24371i 0.643073 + 0.371278i
\(494\) −4.25278 4.11048i −0.191342 0.184939i
\(495\) −0.808253 + 4.81894i −0.0363283 + 0.216595i
\(496\) −16.9649 + 11.3995i −0.761748 + 0.511853i
\(497\) 7.17302 + 22.8173i 0.321754 + 1.02349i
\(498\) 1.66750 0.330600i 0.0747224 0.0148145i
\(499\) −13.0198 22.5510i −0.582848 1.00952i −0.995140 0.0984710i \(-0.968605\pi\)
0.412292 0.911052i \(-0.364728\pi\)
\(500\) 15.9464 9.94489i 0.713145 0.444749i
\(501\) 13.0130 + 1.08373i 0.581377 + 0.0484173i
\(502\) 9.06375 2.59466i 0.404535 0.115805i
\(503\) 22.7182 1.01295 0.506476 0.862254i \(-0.330948\pi\)
0.506476 + 0.862254i \(0.330948\pi\)
\(504\) 12.6011 18.5799i 0.561297 0.827614i
\(505\) 23.7766 1.05804
\(506\) 1.93132 0.552877i 0.0858578 0.0245784i
\(507\) 21.3369 + 1.77694i 0.947604 + 0.0789169i
\(508\) −16.6205 26.6507i −0.737417 1.18243i
\(509\) −18.1915 31.5087i −0.806326 1.39660i −0.915392 0.402563i \(-0.868120\pi\)
0.109067 0.994034i \(-0.465214\pi\)
\(510\) −54.1048 + 10.7269i −2.39580 + 0.474994i
\(511\) −21.4700 4.77886i −0.949776 0.211404i
\(512\) −13.3726 + 18.2530i −0.590991 + 0.806678i
\(513\) −7.36760 26.1793i −0.325288 1.15585i
\(514\) −1.04249 1.00761i −0.0459821 0.0444436i
\(515\) −19.5117 11.2651i −0.859790 0.496400i
\(516\) −10.9806 + 5.64057i −0.483395 + 0.248312i
\(517\) 1.97817i 0.0869997i
\(518\) −5.59391 + 11.1836i −0.245782 + 0.491377i
\(519\) 11.4860 + 24.3654i 0.504177 + 1.06952i
\(520\) −7.85829 1.68120i −0.344609 0.0737254i
\(521\) −4.25083 2.45422i −0.186232 0.107521i 0.403985 0.914765i \(-0.367625\pi\)
−0.590218 + 0.807244i \(0.700958\pi\)
\(522\) 1.24145 + 10.9753i 0.0543369 + 0.480377i
\(523\) 20.4680 + 35.4516i 0.895002 + 1.55019i 0.833802 + 0.552064i \(0.186159\pi\)
0.0612000 + 0.998126i \(0.480507\pi\)
\(524\) 1.26646 2.37680i 0.0553255 0.103831i
\(525\) 33.4373 + 10.4204i 1.45932 + 0.454784i
\(526\) 23.6050 + 5.89645i 1.02923 + 0.257098i
\(527\) 16.1802 + 28.0249i 0.704821 + 1.22079i
\(528\) 2.77199 1.54530i 0.120635 0.0672505i
\(529\) 6.69173 11.5904i 0.290945 0.503931i
\(530\) −3.23592 11.3038i −0.140559 0.491006i
\(531\) 4.00132 + 3.30093i 0.173642 + 0.143248i
\(532\) 5.09414 27.2228i 0.220859 1.18026i
\(533\) −8.10662 −0.351137
\(534\) 13.0859 + 14.9404i 0.566280 + 0.646535i
\(535\) 11.0112 + 6.35733i 0.476057 + 0.274852i
\(536\) 0.0527005 0.0170464i 0.00227631 0.000736292i
\(537\) 12.8361 + 8.90822i 0.553917 + 0.384418i
\(538\) 10.7744 + 2.69140i 0.464517 + 0.116035i
\(539\) −3.19478 + 0.274055i −0.137609 + 0.0118044i
\(540\) −27.3164 24.8843i −1.17551 1.07085i
\(541\) −7.39731 + 4.27084i −0.318035 + 0.183618i −0.650517 0.759492i \(-0.725448\pi\)
0.332481 + 0.943110i \(0.392114\pi\)
\(542\) 18.4458 + 17.8286i 0.792316 + 0.765806i
\(543\) −1.49557 + 17.9582i −0.0641810 + 0.770662i
\(544\) 27.3927 + 23.0883i 1.17445 + 0.989904i
\(545\) 2.00385i 0.0858353i
\(546\) −2.48412 4.54381i −0.106310 0.194457i
\(547\) −0.501652 −0.0214491 −0.0107245 0.999942i \(-0.503414\pi\)
−0.0107245 + 0.999942i \(0.503414\pi\)
\(548\) −17.9830 + 0.612103i −0.768194 + 0.0261478i
\(549\) −14.9551 + 5.58516i −0.638269 + 0.238369i
\(550\) 3.55998 + 3.44086i 0.151798 + 0.146719i
\(551\) 6.81301 + 11.8005i 0.290244 + 0.502718i
\(552\) −4.40021 + 14.5408i −0.187285 + 0.618898i
\(553\) −24.4930 22.4819i −1.04155 0.956028i
\(554\) 7.63405 30.5611i 0.324340 1.29842i
\(555\) 16.9089 + 11.7347i 0.717741 + 0.498112i
\(556\) 27.1823 16.9521i 1.15279 0.718928i
\(557\) −8.85048 + 15.3295i −0.375007 + 0.649531i −0.990328 0.138745i \(-0.955693\pi\)
0.615321 + 0.788277i \(0.289026\pi\)
\(558\) −8.66061 + 19.8739i −0.366633 + 0.841329i
\(559\) 2.84753i 0.120438i
\(560\) −13.6998 35.0471i −0.578924 1.48101i
\(561\) −2.14252 4.54498i −0.0904572 0.191889i
\(562\) −24.3516 + 6.97110i −1.02721 + 0.294058i
\(563\) 0.214083 + 0.123601i 0.00902251 + 0.00520915i 0.504504 0.863409i \(-0.331675\pi\)
−0.495482 + 0.868618i \(0.665009\pi\)
\(564\) 12.5729 + 8.10617i 0.529416 + 0.341331i
\(565\) 4.35603 2.51495i 0.183260 0.105805i
\(566\) 6.15456 + 1.53739i 0.258696 + 0.0646212i
\(567\) 0.661144 23.8026i 0.0277654 0.999614i
\(568\) −18.9793 17.1345i −0.796353 0.718949i
\(569\) 22.8950 13.2184i 0.959809 0.554146i 0.0636947 0.997969i \(-0.479712\pi\)
0.896114 + 0.443824i \(0.146378\pi\)
\(570\) −43.1568 14.6799i −1.80764 0.614874i
\(571\) −16.4357 + 28.4675i −0.687814 + 1.19133i 0.284730 + 0.958608i \(0.408096\pi\)
−0.972544 + 0.232721i \(0.925237\pi\)
\(572\) −0.0249033 0.731634i −0.00104126 0.0305912i
\(573\) −10.8395 22.9941i −0.452826 0.960591i
\(574\) −20.9106 31.6810i −0.872792 1.32234i
\(575\) −23.7005 −0.988380
\(576\) −1.53742 + 23.9507i −0.0640590 + 0.997946i
\(577\) 13.3055 23.0459i 0.553917 0.959413i −0.444070 0.895992i \(-0.646466\pi\)
0.997987 0.0634205i \(-0.0202009\pi\)
\(578\) 22.7108 23.4970i 0.944646 0.977347i
\(579\) 15.9302 22.9542i 0.662036 0.953943i
\(580\) 16.3389 + 8.70604i 0.678436 + 0.361499i
\(581\) 1.75164 0.550661i 0.0726705 0.0228453i
\(582\) −3.35997 16.9472i −0.139275 0.702484i
\(583\) 0.927594 0.535547i 0.0384170 0.0221801i
\(584\) 22.3728 7.23666i 0.925793 0.299455i
\(585\) −7.98492 + 2.98206i −0.330136 + 0.123293i
\(586\) 9.64116 + 33.6788i 0.398273 + 1.39126i
\(587\) 23.5447i 0.971792i −0.874017 0.485896i \(-0.838493\pi\)
0.874017 0.485896i \(-0.161507\pi\)
\(588\) 11.3498 21.4286i 0.468056 0.883699i
\(589\) 26.7442i 1.10198i
\(590\) 8.35874 2.39284i 0.344124 0.0985118i
\(591\) 37.8838 + 3.15498i 1.55833 + 0.129779i
\(592\) −0.908981 13.3370i −0.0373589 0.548147i
\(593\) −4.37266 + 2.52456i −0.179564 + 0.103671i −0.587088 0.809523i \(-0.699726\pi\)
0.407524 + 0.913195i \(0.366392\pi\)
\(594\) 1.59621 2.96361i 0.0654935 0.121598i
\(595\) −56.8351 + 17.8671i −2.33001 + 0.732480i
\(596\) −11.8029 6.28908i −0.483467 0.257611i
\(597\) −22.7027 15.7556i −0.929159 0.644836i
\(598\) 2.51973 + 2.43542i 0.103039 + 0.0995919i
\(599\) −7.88687 + 13.6605i −0.322249 + 0.558151i −0.980952 0.194252i \(-0.937772\pi\)
0.658703 + 0.752403i \(0.271105\pi\)
\(600\) −36.4578 + 8.52665i −1.48838 + 0.348099i
\(601\) −3.65359 −0.149033 −0.0745165 0.997220i \(-0.523741\pi\)
−0.0745165 + 0.997220i \(0.523741\pi\)
\(602\) −11.1283 + 7.34505i −0.453554 + 0.299362i
\(603\) 0.0373856 0.0453181i 0.00152246 0.00184550i
\(604\) 8.45394 0.287755i 0.343986 0.0117086i
\(605\) 19.1831 33.2261i 0.779904 1.35083i
\(606\) −15.5071 5.27478i −0.629932 0.214273i
\(607\) 40.3527 23.2976i 1.63786 0.945622i 0.656298 0.754502i \(-0.272122\pi\)
0.981567 0.191120i \(-0.0612118\pi\)
\(608\) 10.0650 + 27.8443i 0.408191 + 1.12923i
\(609\) 2.62097 + 11.6388i 0.106207 + 0.471629i
\(610\) −6.48483 + 25.9605i −0.262563 + 1.05111i
\(611\) 2.98841 1.72536i 0.120898 0.0698005i
\(612\) 37.6669 + 5.00695i 1.52259 + 0.202394i
\(613\) −18.5964 10.7366i −0.751102 0.433649i 0.0749902 0.997184i \(-0.476107\pi\)
−0.826092 + 0.563536i \(0.809441\pi\)
\(614\) −3.00544 10.4987i −0.121290 0.423692i
\(615\) −56.5152 + 26.6415i −2.27891 + 1.07429i
\(616\) 2.79502 1.98453i 0.112615 0.0799592i
\(617\) 23.7350i 0.955536i −0.878486 0.477768i \(-0.841446\pi\)
0.878486 0.477768i \(-0.158554\pi\)
\(618\) 10.2264 + 11.6757i 0.411367 + 0.469667i
\(619\) −10.3184 + 17.8719i −0.414730 + 0.718334i −0.995400 0.0958052i \(-0.969457\pi\)
0.580670 + 0.814139i \(0.302791\pi\)
\(620\) 19.2287 + 30.8328i 0.772242 + 1.23827i
\(621\) 4.36524 + 15.5110i 0.175171 + 0.622435i
\(622\) 27.4667 + 6.86108i 1.10131 + 0.275104i
\(623\) 15.8040 + 14.5063i 0.633173 + 0.581183i
\(624\) 4.75221 + 2.83982i 0.190241 + 0.113684i
\(625\) 2.40116 + 4.15892i 0.0960462 + 0.166357i
\(626\) −16.7968 + 17.3783i −0.671336 + 0.694576i
\(627\) 0.344639 4.13830i 0.0137636 0.165268i
\(628\) −46.0186 + 1.56638i −1.83634 + 0.0625053i
\(629\) −21.1649 −0.843899
\(630\) −32.2507 23.5133i −1.28490 0.936794i
\(631\) 1.83946i 0.0732279i 0.999329 + 0.0366139i \(0.0116572\pi\)
−0.999329 + 0.0366139i \(0.988343\pi\)
\(632\) 34.7557 + 7.43562i 1.38251 + 0.295773i
\(633\) 36.2343 + 3.01761i 1.44019 + 0.119939i
\(634\) −15.0780 + 15.6000i −0.598825 + 0.619555i
\(635\) −48.3581 + 27.9196i −1.91903 + 1.10796i
\(636\) −0.397256 + 8.09022i −0.0157522 + 0.320798i
\(637\) −3.20050 4.58730i −0.126808 0.181756i
\(638\) −0.408727 + 1.63624i −0.0161817 + 0.0647794i
\(639\) −26.7471 4.48613i −1.05810 0.177468i
\(640\) 31.6233 + 24.8644i 1.25002 + 0.982851i
\(641\) 21.1148 + 12.1906i 0.833983 + 0.481500i 0.855214 0.518274i \(-0.173425\pi\)
−0.0212316 + 0.999775i \(0.506759\pi\)
\(642\) −5.77116 6.58907i −0.227769 0.260050i
\(643\) −7.88201 −0.310836 −0.155418 0.987849i \(-0.549672\pi\)
−0.155418 + 0.987849i \(0.549672\pi\)
\(644\) −3.01823 + 16.1293i −0.118935 + 0.635582i
\(645\) 9.35808 + 19.8515i 0.368474 + 0.781652i
\(646\) 45.0662 12.9010i 1.77311 0.507584i
\(647\) −2.44506 + 4.23496i −0.0961251 + 0.166494i −0.910078 0.414438i \(-0.863978\pi\)
0.813953 + 0.580931i \(0.197312\pi\)
\(648\) 12.2952 + 22.2896i 0.483003 + 0.875619i
\(649\) 0.396017 + 0.685921i 0.0155450 + 0.0269247i
\(650\) −2.09308 + 8.37916i −0.0820975 + 0.328658i
\(651\) −6.96689 + 22.3555i −0.273054 + 0.876182i
\(652\) −36.7164 19.5640i −1.43793 0.766186i
\(653\) 21.3381 + 36.9587i 0.835024 + 1.44630i 0.894011 + 0.448045i \(0.147880\pi\)
−0.0589868 + 0.998259i \(0.518787\pi\)
\(654\) −0.444549 + 1.30691i −0.0173832 + 0.0511041i
\(655\) −4.14651 2.39399i −0.162018 0.0935410i
\(656\) 36.4422 + 17.8537i 1.42283 + 0.697070i
\(657\) 15.8712 19.2388i 0.619195 0.750576i
\(658\) 14.4512 + 7.22836i 0.563367 + 0.281791i
\(659\) 33.4550i 1.30322i 0.758553 + 0.651611i \(0.225907\pi\)
−0.758553 + 0.651611i \(0.774093\pi\)
\(660\) −2.57804 5.01873i −0.100350 0.195354i
\(661\) −11.2595 6.50067i −0.437944 0.252847i 0.264781 0.964308i \(-0.414700\pi\)
−0.702725 + 0.711462i \(0.748034\pi\)
\(662\) −13.4874 + 13.9543i −0.524204 + 0.542350i
\(663\) 4.99737 7.20082i 0.194082 0.279657i
\(664\) −1.31539 + 1.45701i −0.0510470 + 0.0565429i
\(665\) −48.0615 10.6977i −1.86374 0.414838i
\(666\) −8.42463 11.4046i −0.326448 0.441919i
\(667\) −4.03665 6.99168i −0.156300 0.270719i
\(668\) −12.7940 + 7.97890i −0.495015 + 0.308713i
\(669\) 1.01353 12.1701i 0.0391853 0.470522i
\(670\) −0.0271008 0.0946693i −0.00104700 0.00365739i
\(671\) −2.43756 −0.0941009
\(672\) 1.15992 + 25.8970i 0.0447448 + 0.998998i
\(673\) −12.3531 −0.476179 −0.238089 0.971243i \(-0.576521\pi\)
−0.238089 + 0.971243i \(0.576521\pi\)
\(674\) 6.12376 + 21.3917i 0.235878 + 0.823977i
\(675\) −27.7270 + 28.4309i −1.06721 + 1.09431i
\(676\) −20.9778 + 13.0827i −0.806840 + 0.503181i
\(677\) 2.07866 + 3.60034i 0.0798894 + 0.138372i 0.903202 0.429216i \(-0.141210\pi\)
−0.823313 + 0.567588i \(0.807877\pi\)
\(678\) −3.39894 + 0.673878i −0.130535 + 0.0258801i
\(679\) −5.59650 17.8024i −0.214774 0.683193i
\(680\) 42.6801 47.2751i 1.63671 1.81292i
\(681\) −29.5231 20.4890i −1.13133 0.785140i
\(682\) −2.30050 + 2.38013i −0.0880905 + 0.0911400i
\(683\) 11.5310 + 6.65741i 0.441221 + 0.254739i 0.704115 0.710086i \(-0.251344\pi\)
−0.262895 + 0.964825i \(0.584677\pi\)
\(684\) 24.8902 + 19.1485i 0.951699 + 0.732161i
\(685\) 31.9892i 1.22224i
\(686\) 9.67187 24.3404i 0.369274 0.929321i
\(687\) 34.4542 16.2419i 1.31451 0.619665i
\(688\) 6.27128 12.8007i 0.239090 0.488022i
\(689\) 1.61810 + 0.934208i 0.0616445 + 0.0355905i
\(690\) 25.5700 + 8.69772i 0.973434 + 0.331116i
\(691\) 7.57239 + 13.1158i 0.288067 + 0.498947i 0.973348 0.229332i \(-0.0736540\pi\)
−0.685281 + 0.728279i \(0.740321\pi\)
\(692\) −27.4504 14.6267i −1.04351 0.556024i
\(693\) 1.36611 3.36943i 0.0518944 0.127994i
\(694\) −7.33338 + 29.3575i −0.278371 + 1.11439i
\(695\) −28.4765 49.3228i −1.08018 1.87092i
\(696\) −8.72482 9.30283i −0.330713 0.352623i
\(697\) 32.1248 55.6418i 1.21681 2.10758i
\(698\) −21.3819 + 6.12096i −0.809317 + 0.231682i
\(699\) −27.3894 + 12.9115i −1.03596 + 0.488357i
\(700\) −38.1451 + 13.4337i −1.44175 + 0.507748i
\(701\) −51.6538 −1.95094 −0.975468 0.220142i \(-0.929348\pi\)
−0.975468 + 0.220142i \(0.929348\pi\)
\(702\) 5.86932 0.173464i 0.221523 0.00654698i
\(703\) −15.1483 8.74585i −0.571327 0.329856i
\(704\) −1.49937 + 3.34381i −0.0565096 + 0.126024i
\(705\) 15.1635 21.8494i 0.571089 0.822895i
\(706\) −4.02975 + 16.1321i −0.151662 + 0.607141i
\(707\) −17.2694 3.84388i −0.649483 0.144564i
\(708\) −5.98241 0.293756i −0.224833 0.0110400i
\(709\) 44.7941 25.8619i 1.68228 0.971263i 0.722134 0.691753i \(-0.243161\pi\)
0.960143 0.279510i \(-0.0901719\pi\)
\(710\) −31.5925 + 32.6861i −1.18565 + 1.22669i
\(711\) 35.3158 13.1891i 1.32445 0.494630i
\(712\) −22.4259 4.79779i −0.840447 0.179805i
\(713\) 15.8457i 0.593427i
\(714\) 41.0316 + 0.955796i 1.53557 + 0.0357698i
\(715\) −1.30147 −0.0486724
\(716\) −18.0310 + 0.613739i −0.673851 + 0.0229365i
\(717\) −11.4015 0.949523i −0.425797 0.0354606i
\(718\) −20.1757 + 20.8741i −0.752949 + 0.779014i
\(719\) −18.9896 32.8909i −0.708191 1.22662i −0.965527 0.260302i \(-0.916178\pi\)
0.257336 0.966322i \(-0.417155\pi\)
\(720\) 42.4627 + 4.18019i 1.58249 + 0.155787i
\(721\) 12.3506 + 11.3365i 0.459960 + 0.422193i
\(722\) 11.5170 + 2.87691i 0.428620 + 0.107068i
\(723\) −10.4275 + 15.0252i −0.387802 + 0.558794i
\(724\) −11.0111 17.6560i −0.409224 0.656182i
\(725\) 9.94856 17.2314i 0.369480 0.639958i
\(726\) −19.8823 + 17.4143i −0.737903 + 0.646306i
\(727\) 15.9886i 0.592984i 0.955035 + 0.296492i \(0.0958167\pi\)
−0.955035 + 0.296492i \(0.904183\pi\)
\(728\) 5.43585 + 2.49151i 0.201466 + 0.0923417i
\(729\) 23.7137 + 12.9097i 0.878285 + 0.478137i
\(730\) −11.5050 40.1897i −0.425821 1.48749i
\(731\) −19.5447 11.2842i −0.722888 0.417359i
\(732\) 9.98868 15.4928i 0.369192 0.572629i
\(733\) −10.1169 + 5.84098i −0.373675 + 0.215741i −0.675063 0.737760i \(-0.735883\pi\)
0.301388 + 0.953502i \(0.402550\pi\)
\(734\) 7.88701 31.5738i 0.291115 1.16541i
\(735\) −37.3879 21.4623i −1.37907 0.791647i
\(736\) −5.96344 16.4975i −0.219815 0.608105i
\(737\) 0.00776859 0.00448520i 0.000286160 0.000165214i
\(738\) 42.7696 4.83780i 1.57437 0.178082i
\(739\) 8.47946 14.6869i 0.311922 0.540265i −0.666857 0.745186i \(-0.732361\pi\)
0.978778 + 0.204922i \(0.0656939\pi\)
\(740\) −23.7522 + 0.808475i −0.873147 + 0.0297201i
\(741\) 6.55231 3.08878i 0.240705 0.113469i
\(742\) 0.522866 + 8.73333i 0.0191950 + 0.320611i
\(743\) 14.5437 0.533558 0.266779 0.963758i \(-0.414041\pi\)
0.266779 + 0.963758i \(0.414041\pi\)
\(744\) −5.70075 24.3750i −0.209000 0.893629i
\(745\) −11.8883 + 20.5911i −0.435553 + 0.754400i
\(746\) −25.4373 24.5862i −0.931326 0.900165i
\(747\) −0.344393 + 2.05333i −0.0126007 + 0.0751274i
\(748\) 5.12044 + 2.72838i 0.187222 + 0.0997594i
\(749\) −6.96991 6.39761i −0.254675 0.233764i
\(750\) 4.47626 + 22.5776i 0.163450 + 0.824416i
\(751\) −9.37421 + 5.41220i −0.342070 + 0.197494i −0.661187 0.750221i \(-0.729947\pi\)
0.319117 + 0.947715i \(0.396614\pi\)
\(752\) −17.2338 + 1.17457i −0.628454 + 0.0428322i
\(753\) −0.958294 + 11.5068i −0.0349222 + 0.419333i
\(754\) −2.82835 + 0.809668i −0.103003 + 0.0294864i
\(755\) 15.0384i 0.547303i
\(756\) 15.8175 + 22.4901i 0.575277 + 0.817958i
\(757\) 13.5121i 0.491105i −0.969383 0.245552i \(-0.921031\pi\)
0.969383 0.245552i \(-0.0789694\pi\)
\(758\) 4.56954 + 15.9624i 0.165973 + 0.579782i
\(759\) −0.204196 + 2.45190i −0.00741183 + 0.0889985i
\(760\) 50.0825 16.1996i 1.81668 0.587621i
\(761\) −22.5165 + 12.9999i −0.816221 + 0.471245i −0.849111 0.528214i \(-0.822862\pi\)
0.0328907 + 0.999459i \(0.489529\pi\)
\(762\) 37.7331 7.48100i 1.36692 0.271008i
\(763\) −0.323955 + 1.45543i −0.0117280 + 0.0526903i
\(764\) 25.9054 + 13.8035i 0.937226 + 0.499393i
\(765\) 11.1744 66.6237i 0.404011 2.40879i
\(766\) −17.5585 + 18.1663i −0.634415 + 0.656376i
\(767\) −0.690812 + 1.19652i −0.0249438 + 0.0432039i
\(768\) −15.1086 23.2321i −0.545185 0.838316i
\(769\) 3.84206 0.138548 0.0692741 0.997598i \(-0.477932\pi\)
0.0692741 + 0.997598i \(0.477932\pi\)
\(770\) −3.35708 5.08622i −0.120981 0.183295i
\(771\) 1.60617 0.757155i 0.0578449 0.0272683i
\(772\) 1.09752 + 32.2441i 0.0395007 + 1.16049i
\(773\) 18.3710 31.8195i 0.660760 1.14447i −0.319657 0.947533i \(-0.603568\pi\)
0.980416 0.196936i \(-0.0630991\pi\)
\(774\) −1.69932 15.0232i −0.0610809 0.539998i
\(775\) 33.8206 19.5263i 1.21487 0.701407i
\(776\) 14.8079 + 13.3686i 0.531574 + 0.479906i
\(777\) −10.3841 11.2568i −0.372529 0.403835i
\(778\) 35.5251 + 8.87405i 1.27364 + 0.318150i
\(779\) 45.9852 26.5495i 1.64759 0.951236i
\(780\) 5.33321 8.27198i 0.190959 0.296184i
\(781\) −3.58628 2.07054i −0.128327 0.0740897i
\(782\) −26.7013 + 7.64373i −0.954836 + 0.273339i
\(783\) −13.1096 3.33718i −0.468499 0.119261i
\(784\) 4.28453 + 27.6703i 0.153019 + 0.988223i
\(785\) 81.8606i 2.92173i
\(786\) 2.17325 + 2.48126i 0.0775174 + 0.0885035i
\(787\) 19.1854 33.2301i 0.683886 1.18453i −0.289899 0.957057i \(-0.593622\pi\)
0.973785 0.227469i \(-0.0730450\pi\)
\(788\) −37.2463 + 23.2285i −1.32685 + 0.827479i
\(789\) −16.9896 + 24.4807i −0.604845 + 0.871535i
\(790\) 15.3136 61.3044i 0.544834 2.18111i
\(791\) −3.57046 + 1.12244i −0.126951 + 0.0399093i
\(792\) 0.568005 + 3.84515i 0.0201832 + 0.136631i
\(793\) −2.12604 3.68241i −0.0754979 0.130766i
\(794\) 20.5528 + 19.8652i 0.729392 + 0.704988i
\(795\) 14.3507 + 1.19513i 0.508967 + 0.0423870i
\(796\) 31.8908 1.08550i 1.13034 0.0384745i
\(797\) −25.0108 −0.885927 −0.442964 0.896540i \(-0.646073\pi\)
−0.442964 + 0.896540i \(0.646073\pi\)
\(798\) 28.9724 + 17.6394i 1.02561 + 0.624426i
\(799\) 27.3489i 0.967535i
\(800\) 27.8631 33.0577i 0.985109 1.16877i
\(801\) −22.7873 + 8.51018i −0.805149 + 0.300692i
\(802\) −37.6837 36.4228i −1.33066 1.28613i
\(803\) 3.29798 1.90409i 0.116383 0.0671939i
\(804\) −0.00332702 + 0.0677555i −0.000117335 + 0.00238955i
\(805\) 28.4760 + 6.33828i 1.00365 + 0.223395i
\(806\) −5.60215 1.39940i −0.197327 0.0492916i
\(807\) −7.75480 + 11.1741i −0.272982 + 0.393346i
\(808\) 17.9956 5.82082i 0.633083 0.204776i
\(809\) −32.0756 18.5188i −1.12772 0.651087i −0.184357 0.982859i \(-0.559020\pi\)
−0.943360 + 0.331772i \(0.892354\pi\)
\(810\) 40.3478 20.4982i 1.41768 0.720232i
\(811\) 1.97747 0.0694383 0.0347192 0.999397i \(-0.488946\pi\)
0.0347192 + 0.999397i \(0.488946\pi\)
\(812\) −10.4598 8.96484i −0.367067 0.314604i
\(813\) −28.4197 + 13.3972i −0.996722 + 0.469859i
\(814\) −0.595831 2.08137i −0.0208839 0.0729521i
\(815\) −36.9820 + 64.0546i −1.29542 + 2.24374i
\(816\) −38.3238 + 21.3643i −1.34160 + 0.747902i
\(817\) −9.32578 16.1527i −0.326268 0.565112i
\(818\) 39.8731 + 9.96015i 1.39413 + 0.348249i
\(819\) 6.28171 0.875036i 0.219501 0.0305762i
\(820\) 33.9265 63.6709i 1.18476 2.22348i
\(821\) 6.85902 + 11.8802i 0.239382 + 0.414621i 0.960537 0.278152i \(-0.0897220\pi\)
−0.721155 + 0.692773i \(0.756389\pi\)
\(822\) 7.09673 20.8633i 0.247527 0.727693i
\(823\) 34.0169 + 19.6397i 1.18575 + 0.684596i 0.957339 0.288968i \(-0.0933122\pi\)
0.228416 + 0.973564i \(0.426646\pi\)
\(824\) −17.5256 3.74941i −0.610532 0.130617i
\(825\) −5.48490 + 2.58560i −0.190960 + 0.0900191i
\(826\) −6.45797 + 0.386639i −0.224701 + 0.0134529i
\(827\) 26.9376i 0.936713i −0.883540 0.468356i \(-0.844846\pi\)
0.883540 0.468356i \(-0.155154\pi\)
\(828\) −14.7472 11.3453i −0.512500 0.394276i
\(829\) −17.5320 10.1221i −0.608910 0.351554i 0.163629 0.986522i \(-0.447680\pi\)
−0.772539 + 0.634968i \(0.781013\pi\)
\(830\) 2.50926 + 2.42531i 0.0870978 + 0.0841836i
\(831\) 31.6948 + 21.9962i 1.09948 + 0.763038i
\(832\) −6.35923 + 0.651378i −0.220467 + 0.0225825i
\(833\) 44.1690 3.78891i 1.53036 0.131278i
\(834\) 7.63024 + 38.4858i 0.264213 + 1.33265i
\(835\) 13.4032 + 23.2150i 0.463836 + 0.803387i
\(836\) 2.53740 + 4.06866i 0.0877577 + 0.140718i
\(837\) −19.0084 18.5378i −0.657025 0.640759i
\(838\) −1.73006 + 0.495263i −0.0597641 + 0.0171086i
\(839\) 45.3448 1.56548 0.782738 0.622352i \(-0.213823\pi\)
0.782738 + 0.622352i \(0.213823\pi\)
\(840\) 46.0840 0.494725i 1.59005 0.0170696i
\(841\) −22.2223 −0.766286
\(842\) −16.4521 + 4.70970i −0.566975 + 0.162307i
\(843\) 2.57466 30.9155i 0.0886758 1.06479i
\(844\) −35.6246 + 22.2171i −1.22625 + 0.764743i
\(845\) 21.9767 + 38.0647i 0.756020 + 1.30946i
\(846\) −14.7368 + 10.8862i −0.506663 + 0.374274i
\(847\) −19.3046 + 21.0315i −0.663315 + 0.722652i
\(848\) −5.21647 7.76323i −0.179134 0.266591i
\(849\) −4.42971 + 6.38287i −0.152027 + 0.219059i
\(850\) −49.2180 47.5712i −1.68816 1.63168i
\(851\) 8.97520 + 5.18183i 0.307666 + 0.177631i
\(852\) 27.8560 14.3092i 0.954330 0.490224i
\(853\) 37.8961i 1.29754i −0.760986 0.648769i \(-0.775284\pi\)
0.760986 0.648769i \(-0.224716\pi\)
\(854\) 8.90701 17.8072i 0.304792 0.609351i
\(855\) 35.5284 43.0668i 1.21505 1.47285i
\(856\) 9.89035 + 2.11593i 0.338045 + 0.0723211i
\(857\) 30.1090 + 17.3834i 1.02850 + 0.593806i 0.916555 0.399908i \(-0.130958\pi\)
0.111947 + 0.993714i \(0.464291\pi\)
\(858\) 0.848822 + 0.288729i 0.0289783 + 0.00985705i
\(859\) −17.5062 30.3217i −0.597305 1.03456i −0.993217 0.116274i \(-0.962905\pi\)
0.395912 0.918288i \(-0.370428\pi\)
\(860\) −22.3650 11.9170i −0.762640 0.406366i
\(861\) 45.3552 10.2136i 1.54570 0.348079i
\(862\) −22.9505 5.73294i −0.781696 0.195265i
\(863\) 11.8510 + 20.5265i 0.403413 + 0.698732i 0.994135 0.108143i \(-0.0344905\pi\)
−0.590722 + 0.806875i \(0.701157\pi\)
\(864\) −26.7668 12.1466i −0.910625 0.413235i
\(865\) −27.6490 + 47.8894i −0.940093 + 1.62829i
\(866\) 5.51544 + 19.2667i 0.187422 + 0.654708i
\(867\) 17.0658 + 36.2021i 0.579586 + 1.22949i
\(868\) −8.98154 25.5031i −0.304853 0.865632i
\(869\) 5.75618 0.195265
\(870\) −17.0569 + 14.9396i −0.578285 + 0.506502i
\(871\) 0.0135515 + 0.00782398i 0.000459176 + 0.000265106i
\(872\) −0.490568 1.51664i −0.0166127 0.0513598i
\(873\) 20.8685 + 3.50015i 0.706291 + 0.118462i
\(874\) −22.2694 5.56281i −0.753274 0.188165i
\(875\) 7.45583 + 23.7169i 0.252053 + 0.801777i
\(876\) −1.41241 + 28.7641i −0.0477209 + 0.971848i
\(877\) −6.02275 + 3.47724i −0.203374 + 0.117418i −0.598228 0.801326i \(-0.704128\pi\)
0.394854 + 0.918744i \(0.370795\pi\)
\(878\) 26.2269 + 25.3494i 0.885115 + 0.855500i
\(879\) −42.7567 3.56080i −1.44215 0.120103i
\(880\) 5.85060 + 2.86631i 0.197224 + 0.0966234i
\(881\) 23.8500i 0.803528i −0.915743 0.401764i \(-0.868397\pi\)
0.915743 0.401764i \(-0.131603\pi\)
\(882\) 19.6230 + 22.2921i 0.660741 + 0.750614i
\(883\) 32.0357 1.07809 0.539044 0.842278i \(-0.318786\pi\)
0.539044 + 0.842278i \(0.318786\pi\)
\(884\) 0.344298 + 10.1151i 0.0115800 + 0.340208i
\(885\) −0.883755 + 10.6118i −0.0297071 + 0.356712i
\(886\) 35.6942 + 34.4999i 1.19917 + 1.15905i
\(887\) −25.4399 44.0633i −0.854190 1.47950i −0.877395 0.479769i \(-0.840720\pi\)
0.0232053 0.999731i \(-0.492613\pi\)
\(888\) 15.6705 + 4.74208i 0.525868 + 0.159134i
\(889\) 39.6372 12.4607i 1.32939 0.417917i
\(890\) −9.88101 + 39.5563i −0.331212 + 1.32593i
\(891\) 2.70239 + 3.11341i 0.0905336 + 0.104303i
\(892\) 7.46207 + 11.9653i 0.249849 + 0.400627i
\(893\) −11.3012 + 19.5743i −0.378182 + 0.655030i
\(894\) 12.3216 10.7921i 0.412097 0.360943i
\(895\) 32.0747i 1.07214i
\(896\) −18.9489 23.1719i −0.633038 0.774120i
\(897\) −3.88218 + 1.83007i −0.129622 + 0.0611044i
\(898\) 18.8836 5.40578i 0.630155 0.180393i
\(899\) 11.5206 + 6.65141i 0.384233 + 0.221837i
\(900\) 6.04242 45.4565i 0.201414 1.51522i
\(901\) −12.8243 + 7.40413i −0.427241 + 0.246667i
\(902\) 6.37625 + 1.59276i 0.212306 + 0.0530332i
\(903\) −3.58763 15.9315i −0.119389 0.530165i
\(904\) 2.68122 2.96989i 0.0891761 0.0987770i
\(905\) −32.0372 + 18.4967i −1.06495 + 0.614851i
\(906\) −3.33623 + 9.80803i −0.110839 + 0.325850i
\(907\) 5.21438 9.03157i 0.173141 0.299888i −0.766376 0.642393i \(-0.777942\pi\)
0.939516 + 0.342504i \(0.111275\pi\)
\(908\) 41.4715 1.41161i 1.37628 0.0468458i
\(909\) 12.7660 15.4747i 0.423423 0.513264i
\(910\) 4.75568 9.50774i 0.157649 0.315178i
\(911\) 9.95365 0.329779 0.164889 0.986312i \(-0.447273\pi\)
0.164889 + 0.986312i \(0.447273\pi\)
\(912\) −36.2576 0.545321i −1.20061 0.0180574i
\(913\) −0.158952 + 0.275313i −0.00526055 + 0.00911153i
\(914\) 7.41614 7.67287i 0.245304 0.253796i
\(915\) −26.9235 18.6849i −0.890063 0.617703i
\(916\) −20.6831 + 38.8166i −0.683389 + 1.28254i
\(917\) 2.62467 + 2.40916i 0.0866742 + 0.0795574i
\(918\) −22.0683 + 40.9730i −0.728361 + 1.35231i
\(919\) −7.23519 + 4.17724i −0.238667 + 0.137794i −0.614564 0.788867i \(-0.710668\pi\)
0.375897 + 0.926661i \(0.377335\pi\)
\(920\) −29.6734 + 9.59810i −0.978303 + 0.316440i
\(921\) 13.3285 + 1.11001i 0.439190 + 0.0365760i
\(922\) −6.86329 23.9750i −0.226031 0.789576i
\(923\) 7.22370i 0.237771i
\(924\) 1.06112 + 4.06199i 0.0349084 + 0.133630i
\(925\) 25.5419i 0.839812i
\(926\) −40.1343 + 11.4892i −1.31890 + 0.377558i
\(927\) −17.8080 + 6.65059i −0.584890 + 0.218434i
\(928\) 14.4977 + 2.58929i 0.475909 + 0.0849978i
\(929\) −45.0777 + 26.0256i −1.47895 + 0.853872i −0.999716 0.0238151i \(-0.992419\pi\)
−0.479234 + 0.877687i \(0.659085\pi\)
\(930\) −43.6542 + 8.65494i −1.43148 + 0.283807i
\(931\) 33.1786 + 15.5399i 1.08738 + 0.509300i
\(932\) 16.4420 30.8573i 0.538577 1.01076i
\(933\) −19.7690 + 28.4856i −0.647207 + 0.932575i
\(934\) −31.0357 29.9973i −1.01552 0.981541i
\(935\) 5.15747 8.93299i 0.168667 0.292140i
\(936\) −5.31344 + 4.21182i −0.173675 + 0.137668i
\(937\) −35.8998 −1.17280 −0.586398 0.810023i \(-0.699455\pi\)
−0.586398 + 0.810023i \(0.699455\pi\)
\(938\) 0.00437899 + 0.0731416i 0.000142979 + 0.00238816i
\(939\) −12.6218 26.7749i −0.411897 0.873767i
\(940\) 1.04470 + 30.6922i 0.0340743 + 1.00107i
\(941\) −2.74621 + 4.75657i −0.0895238 + 0.155060i −0.907310 0.420462i \(-0.861868\pi\)
0.817786 + 0.575522i \(0.195201\pi\)
\(942\) 18.1606 53.3895i 0.591704 1.73952i
\(943\) −27.2458 + 15.7304i −0.887245 + 0.512251i
\(944\) 5.74062 3.85738i 0.186841 0.125547i
\(945\) 40.9171 26.7444i 1.33103 0.869996i
\(946\) 0.559473 2.23972i 0.0181900 0.0728195i
\(947\) −1.99491 + 1.15176i −0.0648257 + 0.0374272i −0.532063 0.846705i \(-0.678583\pi\)
0.467237 + 0.884132i \(0.345250\pi\)
\(948\) −23.5878 + 36.5854i −0.766095 + 1.18824i
\(949\) 5.75300 + 3.32150i 0.186750 + 0.107820i
\(950\) −15.5690 54.3861i −0.505126 1.76452i
\(951\) −11.3302 24.0351i −0.367408 0.779391i
\(952\) −38.6422 + 27.4369i −1.25240 + 0.889236i
\(953\) 27.0751i 0.877047i −0.898720 0.438524i \(-0.855502\pi\)
0.898720 0.438524i \(-0.144498\pi\)
\(954\) −9.09439 3.96313i −0.294442 0.128311i
\(955\) 26.0928 45.1940i 0.844343 1.46244i
\(956\) 11.2097 6.99084i 0.362546 0.226100i
\(957\) −1.69694 1.17767i −0.0548542 0.0380688i
\(958\) −0.266074 0.0664643i −0.00859646 0.00214736i
\(959\) 5.17159 23.2344i 0.166999 0.750278i
\(960\) −42.1926 + 25.4399i −1.36176 + 0.821071i
\(961\) −2.44506 4.23497i −0.0788729 0.136612i
\(962\) 2.62464 2.71549i 0.0846217 0.0875511i
\(963\) 10.0497 3.75318i 0.323847 0.120945i
\(964\) −0.718410 21.1062i −0.0231384 0.679783i
\(965\) 57.3577 1.84641
\(966\) −17.1659 10.4512i −0.552304 0.336260i
\(967\) 33.0009i 1.06124i −0.847611 0.530618i \(-0.821960\pi\)
0.847611 0.530618i \(-0.178040\pi\)
\(968\) 6.38478 29.8439i 0.205215 0.959218i
\(969\) −4.76477 + 57.2136i −0.153066 + 1.83796i
\(970\) 24.6490 25.5023i 0.791431 0.818828i
\(971\) 31.6718 18.2857i 1.01640 0.586817i 0.103339 0.994646i \(-0.467047\pi\)
0.913058 + 0.407829i \(0.133714\pi\)
\(972\) −30.8623 + 4.41782i −0.989909 + 0.141702i
\(973\) 12.7092 + 40.4279i 0.407439 + 1.29606i
\(974\) −6.90539 + 27.6441i −0.221263 + 0.885774i
\(975\) −8.68999 6.03085i −0.278302 0.193142i
\(976\) 1.44734 + 21.2361i 0.0463283 + 0.679750i
\(977\) 2.71660 + 1.56843i 0.0869117 + 0.0501785i 0.542826 0.839845i \(-0.317354\pi\)
−0.455914 + 0.890024i \(0.650688\pi\)
\(978\) 38.3300 33.5720i 1.22566 1.07352i
\(979\) −3.71414 −0.118704
\(980\) 49.4237 5.93929i 1.57878 0.189724i
\(981\) −1.30418 1.07590i −0.0416393 0.0343508i
\(982\) 5.84961 1.67456i 0.186668 0.0534373i
\(983\) 5.06871 8.77927i 0.161667 0.280015i −0.773800 0.633430i \(-0.781646\pi\)
0.935467 + 0.353415i \(0.114980\pi\)
\(984\) −36.2521 + 33.9996i −1.15567 + 1.08387i
\(985\) 39.0197 + 67.5842i 1.24327 + 2.15341i
\(986\) 5.65081 22.6216i 0.179958 0.720420i
\(987\) −14.5458 + 13.4182i −0.462999 + 0.427107i
\(988\) −3.93339 + 7.38193i −0.125138 + 0.234850i
\(989\) 5.52544 + 9.57034i 0.175699 + 0.304319i
\(990\) 6.86642 0.776683i 0.218229 0.0246846i
\(991\) 22.8644 + 13.2008i 0.726313 + 0.419337i 0.817072 0.576536i \(-0.195596\pi\)
−0.0907589 + 0.995873i \(0.528929\pi\)
\(992\) 22.1017 + 18.6287i 0.701731 + 0.591463i
\(993\) −10.1350 21.4996i −0.321624 0.682269i
\(994\) 28.2306 18.6332i 0.895419 0.591008i
\(995\) 56.7293i 1.79844i
\(996\) −1.09849 2.13846i −0.0348071 0.0677597i
\(997\) −0.842124 0.486200i −0.0266703 0.0153981i 0.486606 0.873622i \(-0.338235\pi\)
−0.513276 + 0.858224i \(0.671568\pi\)
\(998\) −25.5929 + 26.4789i −0.810131 + 0.838175i
\(999\) 16.7161 4.70438i 0.528874 0.148840i
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 168.2.v.a.11.12 yes 56
3.2 odd 2 inner 168.2.v.a.11.17 yes 56
4.3 odd 2 672.2.bd.a.431.2 56
7.2 even 3 inner 168.2.v.a.107.7 yes 56
8.3 odd 2 inner 168.2.v.a.11.22 yes 56
8.5 even 2 672.2.bd.a.431.1 56
12.11 even 2 672.2.bd.a.431.19 56
21.2 odd 6 inner 168.2.v.a.107.22 yes 56
24.5 odd 2 672.2.bd.a.431.20 56
24.11 even 2 inner 168.2.v.a.11.7 56
28.23 odd 6 672.2.bd.a.527.20 56
56.37 even 6 672.2.bd.a.527.19 56
56.51 odd 6 inner 168.2.v.a.107.17 yes 56
84.23 even 6 672.2.bd.a.527.1 56
168.107 even 6 inner 168.2.v.a.107.12 yes 56
168.149 odd 6 672.2.bd.a.527.2 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.2.v.a.11.7 56 24.11 even 2 inner
168.2.v.a.11.12 yes 56 1.1 even 1 trivial
168.2.v.a.11.17 yes 56 3.2 odd 2 inner
168.2.v.a.11.22 yes 56 8.3 odd 2 inner
168.2.v.a.107.7 yes 56 7.2 even 3 inner
168.2.v.a.107.12 yes 56 168.107 even 6 inner
168.2.v.a.107.17 yes 56 56.51 odd 6 inner
168.2.v.a.107.22 yes 56 21.2 odd 6 inner
672.2.bd.a.431.1 56 8.5 even 2
672.2.bd.a.431.2 56 4.3 odd 2
672.2.bd.a.431.19 56 12.11 even 2
672.2.bd.a.431.20 56 24.5 odd 2
672.2.bd.a.527.1 56 84.23 even 6
672.2.bd.a.527.2 56 168.149 odd 6
672.2.bd.a.527.19 56 56.37 even 6
672.2.bd.a.527.20 56 28.23 odd 6