Properties

Label 273.2.bv.b.2.19
Level $273$
Weight $2$
Character 273.2
Analytic conductor $2.180$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(2,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bv (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 2.19
Character \(\chi\) \(=\) 273.2
Dual form 273.2.bv.b.137.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.397102 + 0.397102i) q^{2} +(-0.160369 - 1.72461i) q^{3} -1.68462i q^{4} +(3.29155 - 0.881968i) q^{5} +(0.621163 - 0.748529i) q^{6} +(-2.64283 + 0.124223i) q^{7} +(1.46317 - 1.46317i) q^{8} +(-2.94856 + 0.553150i) q^{9} +O(q^{10})\) \(q+(0.397102 + 0.397102i) q^{2} +(-0.160369 - 1.72461i) q^{3} -1.68462i q^{4} +(3.29155 - 0.881968i) q^{5} +(0.621163 - 0.748529i) q^{6} +(-2.64283 + 0.124223i) q^{7} +(1.46317 - 1.46317i) q^{8} +(-2.94856 + 0.553150i) q^{9} +(1.65731 + 0.956850i) q^{10} +(1.17323 + 4.37855i) q^{11} +(-2.90531 + 0.270162i) q^{12} +(-1.88678 - 3.07247i) q^{13} +(-1.09880 - 1.00015i) q^{14} +(-2.04891 - 5.53520i) q^{15} -2.20718 q^{16} -2.97397 q^{17} +(-1.39054 - 0.951224i) q^{18} +(6.44064 + 1.72576i) q^{19} +(-1.48578 - 5.54501i) q^{20} +(0.638066 + 4.53794i) q^{21} +(-1.27284 + 2.20463i) q^{22} +3.72097 q^{23} +(-2.75805 - 2.28875i) q^{24} +(5.72630 - 3.30608i) q^{25} +(0.470839 - 1.96933i) q^{26} +(1.42683 + 4.99642i) q^{27} +(0.209269 + 4.45217i) q^{28} +(0.0674871 - 0.0389637i) q^{29} +(1.38441 - 3.01167i) q^{30} +(6.13896 + 1.64493i) q^{31} +(-3.80282 - 3.80282i) q^{32} +(7.36315 - 2.72555i) q^{33} +(-1.18097 - 1.18097i) q^{34} +(-8.58945 + 2.73978i) q^{35} +(0.931847 + 4.96721i) q^{36} +(-1.05987 - 1.05987i) q^{37} +(1.87229 + 3.24289i) q^{38} +(-4.99623 + 3.74669i) q^{39} +(3.52563 - 6.10657i) q^{40} +(0.861677 - 3.21582i) q^{41} +(-1.54865 + 2.05540i) q^{42} +(-4.85881 - 2.80523i) q^{43} +(7.37620 - 1.97645i) q^{44} +(-9.21748 + 4.42126i) q^{45} +(1.47761 + 1.47761i) q^{46} +(2.87335 + 10.7235i) q^{47} +(0.353965 + 3.80653i) q^{48} +(6.96914 - 0.656602i) q^{49} +(3.58678 + 0.961074i) q^{50} +(0.476934 + 5.12894i) q^{51} +(-5.17594 + 3.17851i) q^{52} +(-2.45164 + 1.41545i) q^{53} +(-1.41749 + 2.55068i) q^{54} +(7.72349 + 13.3775i) q^{55} +(-3.68516 + 4.04867i) q^{56} +(1.94339 - 11.3843i) q^{57} +(0.0422718 + 0.0113267i) q^{58} +(-1.11593 + 1.11593i) q^{59} +(-9.32471 + 3.45164i) q^{60} +(2.93034 + 5.07550i) q^{61} +(1.78459 + 3.09100i) q^{62} +(7.72385 - 1.82816i) q^{63} +1.39415i q^{64} +(-8.92025 - 8.44910i) q^{65} +(4.00625 + 1.84160i) q^{66} +(-1.75293 - 6.54202i) q^{67} +5.01001i q^{68} +(-0.596730 - 6.41723i) q^{69} +(-4.49886 - 2.32292i) q^{70} +(-12.1333 + 3.25110i) q^{71} +(-3.50490 + 5.12360i) q^{72} +(0.803695 - 2.99943i) q^{73} -0.841749i q^{74} +(-6.62003 - 9.34544i) q^{75} +(2.90725 - 10.8500i) q^{76} +(-3.64457 - 11.4260i) q^{77} +(-3.47183 - 0.496195i) q^{78} +(-5.07964 + 8.79819i) q^{79} +(-7.26505 + 1.94667i) q^{80} +(8.38805 - 3.26199i) q^{81} +(1.61918 - 0.934836i) q^{82} +(5.49809 + 5.49809i) q^{83} +(7.64470 - 1.07490i) q^{84} +(-9.78897 + 2.62295i) q^{85} +(-0.815478 - 3.04341i) q^{86} +(-0.0780201 - 0.110140i) q^{87} +(8.12321 + 4.68994i) q^{88} +(5.27498 - 5.27498i) q^{89} +(-5.41597 - 1.90459i) q^{90} +(5.36812 + 7.88564i) q^{91} -6.26842i q^{92} +(1.85236 - 10.8511i) q^{93} +(-3.11730 + 5.39933i) q^{94} +22.7217 q^{95} +(-5.94852 + 7.16824i) q^{96} +(1.54966 + 5.78341i) q^{97} +(3.02820 + 2.50672i) q^{98} +(-5.88134 - 12.2615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q + 2 q^{3} - 4 q^{6} - 16 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 2 q^{3} - 4 q^{6} - 16 q^{7} + 8 q^{9} - 12 q^{10} + 48 q^{12} - 16 q^{13} - 6 q^{15} - 64 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{21} - 8 q^{22} + 2 q^{24} - 40 q^{27} + 68 q^{28} + 18 q^{30} + 20 q^{31} - 16 q^{33} - 48 q^{34} - 60 q^{36} - 8 q^{37} + 4 q^{39} + 44 q^{40} + 2 q^{42} - 144 q^{43} - 2 q^{45} - 24 q^{46} - 64 q^{48} - 60 q^{49} - 36 q^{51} + 48 q^{52} + 14 q^{54} - 16 q^{55} + 40 q^{57} + 44 q^{58} - 58 q^{60} + 20 q^{61} + 14 q^{63} - 34 q^{66} - 84 q^{67} - 54 q^{69} - 104 q^{70} + 46 q^{72} - 48 q^{73} + 144 q^{76} + 82 q^{78} - 24 q^{79} + 24 q^{81} + 36 q^{82} + 184 q^{84} + 56 q^{85} + 4 q^{87} + 132 q^{88} + 24 q^{91} + 16 q^{93} - 16 q^{94} - 90 q^{96} + 52 q^{97} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.397102 + 0.397102i 0.280794 + 0.280794i 0.833425 0.552632i \(-0.186376\pi\)
−0.552632 + 0.833425i \(0.686376\pi\)
\(3\) −0.160369 1.72461i −0.0925893 0.995704i
\(4\) 1.68462i 0.842310i
\(5\) 3.29155 0.881968i 1.47203 0.394428i 0.568400 0.822752i \(-0.307563\pi\)
0.903625 + 0.428324i \(0.140896\pi\)
\(6\) 0.621163 0.748529i 0.253589 0.305586i
\(7\) −2.64283 + 0.124223i −0.998897 + 0.0469520i
\(8\) 1.46317 1.46317i 0.517309 0.517309i
\(9\) −2.94856 + 0.553150i −0.982854 + 0.184383i
\(10\) 1.65731 + 0.956850i 0.524088 + 0.302582i
\(11\) 1.17323 + 4.37855i 0.353742 + 1.32018i 0.882060 + 0.471137i \(0.156156\pi\)
−0.528318 + 0.849047i \(0.677177\pi\)
\(12\) −2.90531 + 0.270162i −0.838692 + 0.0779889i
\(13\) −1.88678 3.07247i −0.523299 0.852149i
\(14\) −1.09880 1.00015i −0.293668 0.267300i
\(15\) −2.04891 5.53520i −0.529028 1.42918i
\(16\) −2.20718 −0.551796
\(17\) −2.97397 −0.721294 −0.360647 0.932702i \(-0.617444\pi\)
−0.360647 + 0.932702i \(0.617444\pi\)
\(18\) −1.39054 0.951224i −0.327753 0.224206i
\(19\) 6.44064 + 1.72576i 1.47758 + 0.395917i 0.905524 0.424295i \(-0.139478\pi\)
0.572059 + 0.820212i \(0.306145\pi\)
\(20\) −1.48578 5.54501i −0.332231 1.23990i
\(21\) 0.638066 + 4.53794i 0.139237 + 0.990259i
\(22\) −1.27284 + 2.20463i −0.271371 + 0.470028i
\(23\) 3.72097 0.775876 0.387938 0.921685i \(-0.373187\pi\)
0.387938 + 0.921685i \(0.373187\pi\)
\(24\) −2.75805 2.28875i −0.562984 0.467189i
\(25\) 5.72630 3.30608i 1.14526 0.661216i
\(26\) 0.470839 1.96933i 0.0923392 0.386217i
\(27\) 1.42683 + 4.99642i 0.274593 + 0.961561i
\(28\) 0.209269 + 4.45217i 0.0395481 + 0.841381i
\(29\) 0.0674871 0.0389637i 0.0125320 0.00723538i −0.493721 0.869620i \(-0.664364\pi\)
0.506253 + 0.862385i \(0.331030\pi\)
\(30\) 1.38441 3.01167i 0.252758 0.549853i
\(31\) 6.13896 + 1.64493i 1.10259 + 0.295438i 0.763819 0.645431i \(-0.223322\pi\)
0.338771 + 0.940869i \(0.389989\pi\)
\(32\) −3.80282 3.80282i −0.672250 0.672250i
\(33\) 7.36315 2.72555i 1.28176 0.474458i
\(34\) −1.18097 1.18097i −0.202535 0.202535i
\(35\) −8.58945 + 2.73978i −1.45188 + 0.463108i
\(36\) 0.931847 + 4.96721i 0.155308 + 0.827868i
\(37\) −1.05987 1.05987i −0.174241 0.174241i 0.614599 0.788840i \(-0.289318\pi\)
−0.788840 + 0.614599i \(0.789318\pi\)
\(38\) 1.87229 + 3.24289i 0.303725 + 0.526067i
\(39\) −4.99623 + 3.74669i −0.800037 + 0.599951i
\(40\) 3.52563 6.10657i 0.557451 0.965533i
\(41\) 0.861677 3.21582i 0.134571 0.502227i −0.865428 0.501033i \(-0.832953\pi\)
0.999999 0.00119364i \(-0.000379946\pi\)
\(42\) −1.54865 + 2.05540i −0.238961 + 0.317155i
\(43\) −4.85881 2.80523i −0.740961 0.427794i 0.0814574 0.996677i \(-0.474043\pi\)
−0.822419 + 0.568883i \(0.807376\pi\)
\(44\) 7.37620 1.97645i 1.11200 0.297961i
\(45\) −9.21748 + 4.42126i −1.37406 + 0.659082i
\(46\) 1.47761 + 1.47761i 0.217861 + 0.217861i
\(47\) 2.87335 + 10.7235i 0.419121 + 1.56418i 0.776436 + 0.630196i \(0.217026\pi\)
−0.357315 + 0.933984i \(0.616308\pi\)
\(48\) 0.353965 + 3.80653i 0.0510904 + 0.549426i
\(49\) 6.96914 0.656602i 0.995591 0.0938003i
\(50\) 3.58678 + 0.961074i 0.507247 + 0.135916i
\(51\) 0.476934 + 5.12894i 0.0667841 + 0.718195i
\(52\) −5.17594 + 3.17851i −0.717774 + 0.440780i
\(53\) −2.45164 + 1.41545i −0.336758 + 0.194428i −0.658838 0.752285i \(-0.728952\pi\)
0.322079 + 0.946713i \(0.395618\pi\)
\(54\) −1.41749 + 2.55068i −0.192896 + 0.347104i
\(55\) 7.72349 + 13.3775i 1.04144 + 1.80382i
\(56\) −3.68516 + 4.04867i −0.492450 + 0.541027i
\(57\) 1.94339 11.3843i 0.257408 1.50789i
\(58\) 0.0422718 + 0.0113267i 0.00555056 + 0.00148727i
\(59\) −1.11593 + 1.11593i −0.145282 + 0.145282i −0.776007 0.630725i \(-0.782758\pi\)
0.630725 + 0.776007i \(0.282758\pi\)
\(60\) −9.32471 + 3.45164i −1.20381 + 0.445605i
\(61\) 2.93034 + 5.07550i 0.375192 + 0.649852i 0.990356 0.138548i \(-0.0442435\pi\)
−0.615164 + 0.788399i \(0.710910\pi\)
\(62\) 1.78459 + 3.09100i 0.226643 + 0.392557i
\(63\) 7.72385 1.82816i 0.973113 0.230327i
\(64\) 1.39415i 0.174269i
\(65\) −8.92025 8.44910i −1.10642 1.04798i
\(66\) 4.00625 + 1.84160i 0.493135 + 0.226685i
\(67\) −1.75293 6.54202i −0.214154 0.799235i −0.986462 0.163987i \(-0.947564\pi\)
0.772308 0.635248i \(-0.219102\pi\)
\(68\) 5.01001i 0.607553i
\(69\) −0.596730 6.41723i −0.0718379 0.772543i
\(70\) −4.49886 2.32292i −0.537717 0.277642i
\(71\) −12.1333 + 3.25110i −1.43995 + 0.385835i −0.892518 0.451013i \(-0.851063\pi\)
−0.547437 + 0.836847i \(0.684396\pi\)
\(72\) −3.50490 + 5.12360i −0.413056 + 0.603822i
\(73\) 0.803695 2.99943i 0.0940654 0.351057i −0.902811 0.430038i \(-0.858500\pi\)
0.996876 + 0.0789814i \(0.0251668\pi\)
\(74\) 0.841749i 0.0978514i
\(75\) −6.62003 9.34544i −0.764415 1.07912i
\(76\) 2.90725 10.8500i 0.333485 1.24458i
\(77\) −3.64457 11.4260i −0.415337 1.30212i
\(78\) −3.47183 0.496195i −0.393108 0.0561830i
\(79\) −5.07964 + 8.79819i −0.571504 + 0.989874i 0.424908 + 0.905237i \(0.360307\pi\)
−0.996412 + 0.0846374i \(0.973027\pi\)
\(80\) −7.26505 + 1.94667i −0.812258 + 0.217644i
\(81\) 8.38805 3.26199i 0.932006 0.362444i
\(82\) 1.61918 0.934836i 0.178809 0.103235i
\(83\) 5.49809 + 5.49809i 0.603494 + 0.603494i 0.941238 0.337744i \(-0.109664\pi\)
−0.337744 + 0.941238i \(0.609664\pi\)
\(84\) 7.64470 1.07490i 0.834105 0.117281i
\(85\) −9.78897 + 2.62295i −1.06176 + 0.284499i
\(86\) −0.815478 3.04341i −0.0879353 0.328179i
\(87\) −0.0780201 0.110140i −0.00836463 0.0118083i
\(88\) 8.12321 + 4.68994i 0.865937 + 0.499949i
\(89\) 5.27498 5.27498i 0.559147 0.559147i −0.369918 0.929065i \(-0.620614\pi\)
0.929065 + 0.369918i \(0.120614\pi\)
\(90\) −5.41597 1.90459i −0.570893 0.200761i
\(91\) 5.36812 + 7.88564i 0.562732 + 0.826640i
\(92\) 6.26842i 0.653528i
\(93\) 1.85236 10.8511i 0.192081 1.12521i
\(94\) −3.11730 + 5.39933i −0.321525 + 0.556898i
\(95\) 22.7217 2.33120
\(96\) −5.94852 + 7.16824i −0.607119 + 0.731605i
\(97\) 1.54966 + 5.78341i 0.157344 + 0.587216i 0.998893 + 0.0470356i \(0.0149774\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(98\) 3.02820 + 2.50672i 0.305894 + 0.253217i
\(99\) −5.88134 12.2615i −0.591097 1.23232i
\(100\) −5.56949 9.64664i −0.556949 0.964664i
\(101\) −3.83092 + 6.63535i −0.381191 + 0.660242i −0.991233 0.132127i \(-0.957819\pi\)
0.610042 + 0.792369i \(0.291153\pi\)
\(102\) −1.84732 + 2.22610i −0.182912 + 0.220417i
\(103\) 4.87851 + 2.81661i 0.480694 + 0.277529i 0.720706 0.693241i \(-0.243818\pi\)
−0.240012 + 0.970770i \(0.577151\pi\)
\(104\) −7.25622 1.73486i −0.711531 0.170117i
\(105\) 6.10254 + 14.3741i 0.595547 + 1.40277i
\(106\) −1.53563 0.411471i −0.149154 0.0399656i
\(107\) 2.41600i 0.233563i −0.993158 0.116782i \(-0.962742\pi\)
0.993158 0.116782i \(-0.0372577\pi\)
\(108\) 8.41706 2.40366i 0.809932 0.231292i
\(109\) −13.6211 3.64976i −1.30466 0.349583i −0.461451 0.887166i \(-0.652671\pi\)
−0.843211 + 0.537582i \(0.819338\pi\)
\(110\) −2.24521 + 8.37924i −0.214072 + 0.798929i
\(111\) −1.65788 + 1.99782i −0.157359 + 0.189625i
\(112\) 5.83322 0.274183i 0.551187 0.0259079i
\(113\) 3.89443 + 2.24845i 0.366357 + 0.211517i 0.671866 0.740673i \(-0.265493\pi\)
−0.305508 + 0.952189i \(0.598826\pi\)
\(114\) 5.29247 3.74902i 0.495685 0.351128i
\(115\) 12.2478 3.28178i 1.14211 0.306027i
\(116\) −0.0656390 0.113690i −0.00609443 0.0105559i
\(117\) 7.26282 + 8.01570i 0.671448 + 0.741051i
\(118\) −0.886278 −0.0815885
\(119\) 7.85971 0.369436i 0.720498 0.0338662i
\(120\) −11.0969 5.10103i −1.01300 0.465658i
\(121\) −8.26899 + 4.77411i −0.751727 + 0.434010i
\(122\) −0.851847 + 3.17914i −0.0771226 + 0.287826i
\(123\) −5.68423 0.970338i −0.512529 0.0874924i
\(124\) 2.77108 10.3418i 0.248850 0.928722i
\(125\) 3.88464 3.88464i 0.347452 0.347452i
\(126\) 3.79312 + 2.34119i 0.337918 + 0.208570i
\(127\) 3.39968 1.96281i 0.301673 0.174171i −0.341521 0.939874i \(-0.610942\pi\)
0.643194 + 0.765703i \(0.277609\pi\)
\(128\) −8.15926 + 8.15926i −0.721183 + 0.721183i
\(129\) −4.05873 + 8.82943i −0.357351 + 0.777388i
\(130\) −0.187093 6.89740i −0.0164091 0.604942i
\(131\) −9.63155 5.56078i −0.841512 0.485847i 0.0162657 0.999868i \(-0.494822\pi\)
−0.857778 + 0.514020i \(0.828156\pi\)
\(132\) −4.59152 12.4041i −0.399640 1.07964i
\(133\) −17.2359 3.76083i −1.49454 0.326105i
\(134\) 1.90176 3.29394i 0.164287 0.284553i
\(135\) 9.10315 + 15.1875i 0.783474 + 1.30713i
\(136\) −4.35143 + 4.35143i −0.373132 + 0.373132i
\(137\) 6.21082 6.21082i 0.530626 0.530626i −0.390132 0.920759i \(-0.627571\pi\)
0.920759 + 0.390132i \(0.127571\pi\)
\(138\) 2.31133 2.78526i 0.196754 0.237097i
\(139\) −0.542340 + 0.939360i −0.0460007 + 0.0796755i −0.888109 0.459633i \(-0.847981\pi\)
0.842108 + 0.539308i \(0.181314\pi\)
\(140\) 4.61549 + 14.4700i 0.390080 + 1.22294i
\(141\) 18.0330 6.67512i 1.51865 0.562147i
\(142\) −6.10916 3.52713i −0.512670 0.295990i
\(143\) 11.2393 11.8661i 0.939881 0.992292i
\(144\) 6.50802 1.22090i 0.542335 0.101742i
\(145\) 0.187772 0.187772i 0.0155936 0.0155936i
\(146\) 1.51023 0.871931i 0.124987 0.0721615i
\(147\) −2.25002 11.9137i −0.185579 0.982629i
\(148\) −1.78547 + 1.78547i −0.146765 + 0.146765i
\(149\) −2.11277 + 7.88496i −0.173085 + 0.645961i 0.823785 + 0.566902i \(0.191858\pi\)
−0.996870 + 0.0790591i \(0.974808\pi\)
\(150\) 1.08227 6.33992i 0.0883669 0.517652i
\(151\) 4.16672 15.5504i 0.339083 1.26547i −0.560292 0.828295i \(-0.689311\pi\)
0.899375 0.437179i \(-0.144022\pi\)
\(152\) 11.9488 6.89866i 0.969178 0.559555i
\(153\) 8.76894 1.64505i 0.708927 0.132994i
\(154\) 3.09004 5.98457i 0.249003 0.482251i
\(155\) 21.6575 1.73957
\(156\) 6.31175 + 8.41675i 0.505344 + 0.673879i
\(157\) −4.64883 8.05201i −0.371017 0.642620i 0.618705 0.785623i \(-0.287658\pi\)
−0.989722 + 0.143003i \(0.954324\pi\)
\(158\) −5.51092 + 1.47665i −0.438425 + 0.117476i
\(159\) 2.83428 + 4.00113i 0.224773 + 0.317310i
\(160\) −15.8711 9.16320i −1.25472 0.724414i
\(161\) −9.83391 + 0.462231i −0.775021 + 0.0364289i
\(162\) 4.62626 + 2.03557i 0.363473 + 0.159929i
\(163\) −1.62077 + 6.04881i −0.126949 + 0.473779i −0.999902 0.0140252i \(-0.995535\pi\)
0.872953 + 0.487805i \(0.162202\pi\)
\(164\) −5.41744 1.45160i −0.423031 0.113351i
\(165\) 21.8323 15.4654i 1.69964 1.20398i
\(166\) 4.36661i 0.338914i
\(167\) −23.7884 6.37407i −1.84080 0.493240i −0.841877 0.539670i \(-0.818549\pi\)
−0.998922 + 0.0464293i \(0.985216\pi\)
\(168\) 7.57337 + 5.70617i 0.584298 + 0.440241i
\(169\) −5.88012 + 11.5941i −0.452317 + 0.891857i
\(170\) −4.92880 2.84564i −0.378022 0.218251i
\(171\) −19.9452 1.52589i −1.52525 0.116687i
\(172\) −4.72575 + 8.18524i −0.360335 + 0.624119i
\(173\) −5.75244 9.96352i −0.437350 0.757512i 0.560134 0.828402i \(-0.310750\pi\)
−0.997484 + 0.0708895i \(0.977416\pi\)
\(174\) 0.0127550 0.0747189i 0.000966957 0.00566443i
\(175\) −14.7230 + 9.44876i −1.11295 + 0.714259i
\(176\) −2.58953 9.66428i −0.195194 0.728472i
\(177\) 2.10351 + 1.74559i 0.158109 + 0.131206i
\(178\) 4.18941 0.314010
\(179\) −4.67043 + 8.08942i −0.349084 + 0.604632i −0.986087 0.166230i \(-0.946841\pi\)
0.637003 + 0.770862i \(0.280174\pi\)
\(180\) 7.44814 + 15.5280i 0.555151 + 1.15739i
\(181\) 14.9370i 1.11026i −0.831764 0.555129i \(-0.812669\pi\)
0.831764 0.555129i \(-0.187331\pi\)
\(182\) −0.999714 + 5.26309i −0.0741037 + 0.390127i
\(183\) 8.28333 5.86766i 0.612321 0.433750i
\(184\) 5.44442 5.44442i 0.401368 0.401368i
\(185\) −4.42337 2.55383i −0.325212 0.187761i
\(186\) 5.04458 3.57342i 0.369886 0.262016i
\(187\) −3.48915 13.0217i −0.255152 0.952241i
\(188\) 18.0650 4.84050i 1.31752 0.353030i
\(189\) −4.39154 13.0274i −0.319437 0.947607i
\(190\) 9.02285 + 9.02285i 0.654586 + 0.654586i
\(191\) 3.46331 1.99954i 0.250596 0.144682i −0.369441 0.929254i \(-0.620451\pi\)
0.620037 + 0.784572i \(0.287117\pi\)
\(192\) 2.40437 0.223580i 0.173521 0.0161355i
\(193\) −15.6641 + 4.19719i −1.12753 + 0.302120i −0.773926 0.633276i \(-0.781710\pi\)
−0.353602 + 0.935396i \(0.615043\pi\)
\(194\) −1.68123 + 2.91198i −0.120705 + 0.209068i
\(195\) −13.1409 + 16.7389i −0.941038 + 1.19870i
\(196\) −1.10613 11.7403i −0.0790090 0.838596i
\(197\) −0.792333 + 2.95703i −0.0564514 + 0.210679i −0.988390 0.151936i \(-0.951449\pi\)
0.931939 + 0.362615i \(0.118116\pi\)
\(198\) 2.53356 7.20455i 0.180053 0.512005i
\(199\) 8.54936i 0.606048i 0.952983 + 0.303024i \(0.0979963\pi\)
−0.952983 + 0.303024i \(0.902004\pi\)
\(200\) 3.54119 13.2159i 0.250400 0.934506i
\(201\) −11.0013 + 4.07226i −0.775974 + 0.287235i
\(202\) −4.15618 + 1.11364i −0.292428 + 0.0783558i
\(203\) −0.173517 + 0.111358i −0.0121785 + 0.00781580i
\(204\) 8.64032 0.803452i 0.604943 0.0562529i
\(205\) 11.3450i 0.792370i
\(206\) 0.818785 + 3.05575i 0.0570474 + 0.212904i
\(207\) −10.9715 + 2.05825i −0.762573 + 0.143059i
\(208\) 4.16447 + 6.78150i 0.288754 + 0.470213i
\(209\) 30.2254i 2.09073i
\(210\) −3.28465 + 8.13131i −0.226662 + 0.561114i
\(211\) 6.42430 + 11.1272i 0.442267 + 0.766029i 0.997857 0.0654271i \(-0.0208410\pi\)
−0.555590 + 0.831456i \(0.687508\pi\)
\(212\) 2.38450 + 4.13008i 0.163768 + 0.283655i
\(213\) 7.55269 + 20.4038i 0.517502 + 1.39804i
\(214\) 0.959397 0.959397i 0.0655830 0.0655830i
\(215\) −18.4671 4.94825i −1.25945 0.337468i
\(216\) 9.39830 + 5.22292i 0.639473 + 0.355374i
\(217\) −16.4286 3.58467i −1.11525 0.243344i
\(218\) −3.95963 6.85828i −0.268180 0.464502i
\(219\) −5.30174 0.905044i −0.358258 0.0611572i
\(220\) 22.5360 13.0111i 1.51937 0.877211i
\(221\) 5.61123 + 9.13743i 0.377452 + 0.614650i
\(222\) −1.45169 + 0.134991i −0.0974311 + 0.00905999i
\(223\) −11.4905 3.07886i −0.769458 0.206176i −0.147326 0.989088i \(-0.547067\pi\)
−0.622132 + 0.782912i \(0.713733\pi\)
\(224\) 10.5226 + 9.57782i 0.703072 + 0.639945i
\(225\) −15.0556 + 12.9157i −1.00371 + 0.861046i
\(226\) 0.653623 + 2.43935i 0.0434783 + 0.162263i
\(227\) −17.6200 17.6200i −1.16948 1.16948i −0.982332 0.187146i \(-0.940076\pi\)
−0.187146 0.982332i \(-0.559924\pi\)
\(228\) −19.1783 3.27387i −1.27011 0.216817i
\(229\) −0.758454 + 0.203227i −0.0501200 + 0.0134296i −0.283792 0.958886i \(-0.591593\pi\)
0.233672 + 0.972316i \(0.424926\pi\)
\(230\) 6.16681 + 3.56041i 0.406628 + 0.234767i
\(231\) −19.1210 + 8.11785i −1.25807 + 0.534116i
\(232\) 0.0417346 0.155756i 0.00274001 0.0102259i
\(233\) 0.106730 0.184861i 0.00699209 0.0121107i −0.862508 0.506043i \(-0.831108\pi\)
0.869500 + 0.493932i \(0.164441\pi\)
\(234\) −0.298967 + 6.06713i −0.0195441 + 0.396621i
\(235\) 18.9155 + 32.7627i 1.23391 + 2.13720i
\(236\) 1.87992 + 1.87992i 0.122372 + 0.122372i
\(237\) 15.9881 + 7.34944i 1.03854 + 0.477397i
\(238\) 3.26781 + 2.97440i 0.211821 + 0.192802i
\(239\) 0.442912 + 0.442912i 0.0286496 + 0.0286496i 0.721286 0.692637i \(-0.243551\pi\)
−0.692637 + 0.721286i \(0.743551\pi\)
\(240\) 4.52233 + 12.2172i 0.291915 + 0.788617i
\(241\) 5.78592 + 5.78592i 0.372704 + 0.372704i 0.868461 0.495757i \(-0.165109\pi\)
−0.495757 + 0.868461i \(0.665109\pi\)
\(242\) −5.17944 1.38783i −0.332947 0.0892129i
\(243\) −6.97085 13.9430i −0.447181 0.894444i
\(244\) 8.55029 4.93651i 0.547376 0.316028i
\(245\) 22.3602 8.30779i 1.42854 0.530766i
\(246\) −1.87190 2.64254i −0.119348 0.168482i
\(247\) −6.84971 23.0448i −0.435836 1.46630i
\(248\) 11.3892 6.57553i 0.723212 0.417547i
\(249\) 8.60034 10.3638i 0.545024 0.656779i
\(250\) 3.08519 0.195125
\(251\) 4.77301 8.26709i 0.301270 0.521814i −0.675154 0.737677i \(-0.735923\pi\)
0.976424 + 0.215862i \(0.0692563\pi\)
\(252\) −3.07976 13.0117i −0.194007 0.819663i
\(253\) 4.36556 + 16.2925i 0.274460 + 1.02430i
\(254\) 2.12946 + 0.570586i 0.133614 + 0.0358018i
\(255\) 6.09341 + 16.4615i 0.381584 + 1.03086i
\(256\) −3.69181 −0.230738
\(257\) 12.6285 0.787746 0.393873 0.919165i \(-0.371135\pi\)
0.393873 + 0.919165i \(0.371135\pi\)
\(258\) −5.11791 + 1.89445i −0.318627 + 0.117943i
\(259\) 2.93271 + 2.66939i 0.182230 + 0.165868i
\(260\) −14.2335 + 15.0272i −0.882726 + 0.931949i
\(261\) −0.177437 + 0.152217i −0.0109831 + 0.00942202i
\(262\) −1.61651 6.03290i −0.0998684 0.372714i
\(263\) −27.1512 15.6758i −1.67422 0.966610i −0.965235 0.261383i \(-0.915821\pi\)
−0.708982 0.705227i \(-0.750845\pi\)
\(264\) 6.78560 14.7615i 0.417625 0.908507i
\(265\) −6.82130 + 6.82130i −0.419029 + 0.419029i
\(266\) −5.35098 8.33785i −0.328090 0.511226i
\(267\) −9.94323 8.25134i −0.608516 0.504974i
\(268\) −11.0208 + 2.95302i −0.673204 + 0.180384i
\(269\) 18.1615i 1.10733i −0.832740 0.553664i \(-0.813229\pi\)
0.832740 0.553664i \(-0.186771\pi\)
\(270\) −2.41612 + 9.64588i −0.147040 + 0.587030i
\(271\) 11.3142 + 11.3142i 0.687288 + 0.687288i 0.961632 0.274344i \(-0.0884607\pi\)
−0.274344 + 0.961632i \(0.588461\pi\)
\(272\) 6.56410 0.398007
\(273\) 12.7388 10.5225i 0.770986 0.636852i
\(274\) 4.93266 0.297993
\(275\) 21.1941 + 21.1941i 1.27805 + 1.27805i
\(276\) −10.8106 + 1.00526i −0.650721 + 0.0605097i
\(277\) 9.36646i 0.562776i −0.959594 0.281388i \(-0.909205\pi\)
0.959594 0.281388i \(-0.0907948\pi\)
\(278\) −0.588386 + 0.157658i −0.0352891 + 0.00945567i
\(279\) −19.0110 1.45442i −1.13816 0.0870736i
\(280\) −8.55907 + 16.5766i −0.511502 + 0.990641i
\(281\) −9.37899 + 9.37899i −0.559504 + 0.559504i −0.929166 0.369662i \(-0.879473\pi\)
0.369662 + 0.929166i \(0.379473\pi\)
\(282\) 9.81166 + 4.51025i 0.584276 + 0.268581i
\(283\) 8.46019 + 4.88449i 0.502906 + 0.290353i 0.729913 0.683540i \(-0.239561\pi\)
−0.227007 + 0.973893i \(0.572894\pi\)
\(284\) 5.47687 + 20.4399i 0.324992 + 1.21289i
\(285\) −3.64387 39.1861i −0.215844 2.32119i
\(286\) 9.17521 0.248878i 0.542542 0.0147165i
\(287\) −1.87779 + 8.60592i −0.110842 + 0.507992i
\(288\) 13.3164 + 9.10932i 0.784675 + 0.536772i
\(289\) −8.15550 −0.479735
\(290\) 0.149130 0.00875719
\(291\) 9.72561 3.60004i 0.570125 0.211038i
\(292\) −5.05290 1.35392i −0.295699 0.0792322i
\(293\) 5.69235 + 21.2441i 0.332551 + 1.24110i 0.906500 + 0.422206i \(0.138744\pi\)
−0.573949 + 0.818891i \(0.694589\pi\)
\(294\) 3.83749 5.62446i 0.223807 0.328025i
\(295\) −2.68893 + 4.65736i −0.156555 + 0.271162i
\(296\) −3.10153 −0.180273
\(297\) −20.2031 + 12.1094i −1.17230 + 0.702658i
\(298\) −3.97012 + 2.29215i −0.229983 + 0.132781i
\(299\) −7.02065 11.4326i −0.406015 0.661163i
\(300\) −15.7435 + 11.1522i −0.908953 + 0.643874i
\(301\) 13.1895 + 6.81019i 0.760230 + 0.392533i
\(302\) 7.82971 4.52048i 0.450549 0.260125i
\(303\) 12.0578 + 5.54274i 0.692700 + 0.318422i
\(304\) −14.2157 3.80908i −0.815324 0.218466i
\(305\) 14.1218 + 14.1218i 0.808612 + 0.808612i
\(306\) 4.13542 + 2.82891i 0.236406 + 0.161718i
\(307\) 13.2557 + 13.2557i 0.756542 + 0.756542i 0.975691 0.219150i \(-0.0703283\pi\)
−0.219150 + 0.975691i \(0.570328\pi\)
\(308\) −19.2485 + 6.13972i −1.09679 + 0.349843i
\(309\) 4.07519 8.86523i 0.231829 0.504325i
\(310\) 8.60022 + 8.60022i 0.488460 + 0.488460i
\(311\) 12.1397 + 21.0265i 0.688378 + 1.19230i 0.972363 + 0.233476i \(0.0750101\pi\)
−0.283985 + 0.958829i \(0.591657\pi\)
\(312\) −1.82829 + 12.7924i −0.103506 + 0.724226i
\(313\) −5.34817 + 9.26331i −0.302297 + 0.523593i −0.976656 0.214810i \(-0.931087\pi\)
0.674359 + 0.738403i \(0.264420\pi\)
\(314\) 1.35141 5.04353i 0.0762645 0.284623i
\(315\) 23.8110 12.8297i 1.34160 0.722870i
\(316\) 14.8216 + 8.55726i 0.833781 + 0.481384i
\(317\) −8.82386 + 2.36434i −0.495597 + 0.132795i −0.497956 0.867202i \(-0.665916\pi\)
0.00235877 + 0.999997i \(0.499249\pi\)
\(318\) −0.463359 + 2.71435i −0.0259839 + 0.152213i
\(319\) 0.249783 + 0.249783i 0.0139851 + 0.0139851i
\(320\) 1.22960 + 4.58893i 0.0687367 + 0.256529i
\(321\) −4.16665 + 0.387452i −0.232560 + 0.0216255i
\(322\) −4.08862 3.72151i −0.227850 0.207392i
\(323\) −19.1543 5.13237i −1.06577 0.285573i
\(324\) −5.49522 14.1307i −0.305290 0.785038i
\(325\) −20.9621 11.3560i −1.16277 0.629919i
\(326\) −3.04561 + 1.75838i −0.168681 + 0.0973878i
\(327\) −4.11000 + 24.0764i −0.227284 + 1.33143i
\(328\) −3.44451 5.96607i −0.190192 0.329421i
\(329\) −8.92588 27.9834i −0.492100 1.54278i
\(330\) 14.8110 + 2.52834i 0.815318 + 0.139181i
\(331\) 23.0901 + 6.18697i 1.26915 + 0.340066i 0.829703 0.558205i \(-0.188510\pi\)
0.439442 + 0.898271i \(0.355176\pi\)
\(332\) 9.26219 9.26219i 0.508329 0.508329i
\(333\) 3.71134 + 2.53882i 0.203380 + 0.139126i
\(334\) −6.91525 11.9776i −0.378386 0.655383i
\(335\) −11.5397 19.9874i −0.630482 1.09203i
\(336\) −1.40833 10.0161i −0.0768307 0.546421i
\(337\) 13.3669i 0.728144i −0.931371 0.364072i \(-0.881386\pi\)
0.931371 0.364072i \(-0.118614\pi\)
\(338\) −6.93907 + 2.26905i −0.377436 + 0.123420i
\(339\) 3.25316 7.07696i 0.176687 0.384368i
\(340\) 4.41867 + 16.4907i 0.239636 + 0.894333i
\(341\) 28.8097i 1.56013i
\(342\) −7.31436 8.52622i −0.395515 0.461045i
\(343\) −18.3367 + 2.60102i −0.990089 + 0.140442i
\(344\) −11.2138 + 3.00473i −0.604607 + 0.162004i
\(345\) −7.62396 20.5963i −0.410460 1.10887i
\(346\) 1.67223 6.24084i 0.0898996 0.335510i
\(347\) 30.7736i 1.65201i 0.563661 + 0.826006i \(0.309392\pi\)
−0.563661 + 0.826006i \(0.690608\pi\)
\(348\) −0.185545 + 0.131434i −0.00994624 + 0.00704561i
\(349\) 3.59684 13.4236i 0.192534 0.718548i −0.800357 0.599524i \(-0.795357\pi\)
0.992891 0.119024i \(-0.0379766\pi\)
\(350\) −9.59864 2.09440i −0.513069 0.111950i
\(351\) 12.6592 13.8110i 0.675699 0.737177i
\(352\) 12.1893 21.1124i 0.649690 1.12530i
\(353\) 31.5979 8.46662i 1.68178 0.450633i 0.713535 0.700620i \(-0.247093\pi\)
0.968249 + 0.249987i \(0.0804264\pi\)
\(354\) 0.142132 + 1.52848i 0.00755422 + 0.0812380i
\(355\) −37.0699 + 21.4023i −1.96747 + 1.13592i
\(356\) −8.88634 8.88634i −0.470975 0.470975i
\(357\) −1.89759 13.4957i −0.100431 0.714268i
\(358\) −5.06696 + 1.35769i −0.267797 + 0.0717561i
\(359\) −5.25960 19.6291i −0.277591 1.03598i −0.954085 0.299535i \(-0.903168\pi\)
0.676494 0.736448i \(-0.263498\pi\)
\(360\) −7.01769 + 19.9558i −0.369865 + 1.05176i
\(361\) 22.0490 + 12.7300i 1.16048 + 0.670001i
\(362\) 5.93151 5.93151i 0.311753 0.311753i
\(363\) 9.55957 + 13.4952i 0.501747 + 0.708313i
\(364\) 13.2843 9.04324i 0.696287 0.473994i
\(365\) 10.5816i 0.553866i
\(366\) 5.61939 + 0.959269i 0.293730 + 0.0501418i
\(367\) 11.7724 20.3905i 0.614516 1.06437i −0.375953 0.926639i \(-0.622685\pi\)
0.990469 0.137735i \(-0.0439821\pi\)
\(368\) −8.21287 −0.428125
\(369\) −0.761878 + 9.95869i −0.0396618 + 0.518429i
\(370\) −0.742396 2.77066i −0.0385953 0.144040i
\(371\) 6.30344 4.04536i 0.327258 0.210025i
\(372\) −18.2800 3.12052i −0.947774 0.161792i
\(373\) 2.76000 + 4.78046i 0.142907 + 0.247523i 0.928590 0.371107i \(-0.121022\pi\)
−0.785683 + 0.618629i \(0.787688\pi\)
\(374\) 3.78539 6.55649i 0.195738 0.339028i
\(375\) −7.32246 6.07651i −0.378130 0.313789i
\(376\) 19.8945 + 11.4861i 1.02598 + 0.592349i
\(377\) −0.247048 0.133836i −0.0127236 0.00689291i
\(378\) 3.42934 6.91712i 0.176386 0.355778i
\(379\) −3.81746 1.02289i −0.196090 0.0525421i 0.159437 0.987208i \(-0.449032\pi\)
−0.355527 + 0.934666i \(0.615699\pi\)
\(380\) 38.2775i 1.96359i
\(381\) −3.93028 5.54836i −0.201355 0.284251i
\(382\) 2.16931 + 0.581265i 0.110992 + 0.0297401i
\(383\) 9.64207 35.9847i 0.492687 1.83873i −0.0499301 0.998753i \(-0.515900\pi\)
0.542617 0.839980i \(-0.317433\pi\)
\(384\) 15.3800 + 12.7630i 0.784859 + 0.651311i
\(385\) −22.0737 34.3950i −1.12498 1.75293i
\(386\) −7.88697 4.55354i −0.401436 0.231769i
\(387\) 15.8782 + 5.58376i 0.807135 + 0.283839i
\(388\) 9.74285 2.61059i 0.494618 0.132533i
\(389\) −8.36934 14.4961i −0.424342 0.734982i 0.572017 0.820242i \(-0.306161\pi\)
−0.996359 + 0.0852599i \(0.972828\pi\)
\(390\) −11.8653 + 1.42879i −0.600824 + 0.0723498i
\(391\) −11.0661 −0.559635
\(392\) 9.23631 11.1578i 0.466504 0.563552i
\(393\) −8.04557 + 17.5024i −0.405845 + 0.882882i
\(394\) −1.48888 + 0.859604i −0.0750086 + 0.0433062i
\(395\) −8.96016 + 33.4398i −0.450834 + 1.68254i
\(396\) −20.6559 + 9.90782i −1.03800 + 0.497887i
\(397\) 1.20999 4.51574i 0.0607276 0.226639i −0.928892 0.370351i \(-0.879237\pi\)
0.989619 + 0.143712i \(0.0459040\pi\)
\(398\) −3.39497 + 3.39497i −0.170174 + 0.170174i
\(399\) −3.72185 + 30.3283i −0.186326 + 1.51832i
\(400\) −12.6390 + 7.29713i −0.631950 + 0.364856i
\(401\) −8.11133 + 8.11133i −0.405060 + 0.405060i −0.880012 0.474952i \(-0.842466\pi\)
0.474952 + 0.880012i \(0.342466\pi\)
\(402\) −5.98575 2.75155i −0.298542 0.137235i
\(403\) −6.52887 21.9654i −0.325226 1.09417i
\(404\) 11.1780 + 6.45365i 0.556128 + 0.321081i
\(405\) 24.7327 18.1350i 1.22898 0.901135i
\(406\) −0.113124 0.0246835i −0.00561427 0.00122502i
\(407\) 3.39721 5.88414i 0.168394 0.291666i
\(408\) 8.20235 + 6.80668i 0.406077 + 0.336981i
\(409\) 24.1858 24.1858i 1.19591 1.19591i 0.220529 0.975380i \(-0.429222\pi\)
0.975380 0.220529i \(-0.0707783\pi\)
\(410\) 4.50513 4.50513i 0.222492 0.222492i
\(411\) −11.7073 9.71522i −0.577477 0.479217i
\(412\) 4.74491 8.21843i 0.233765 0.404893i
\(413\) 2.81060 3.08785i 0.138300 0.151943i
\(414\) −5.17415 3.53948i −0.254296 0.173956i
\(415\) 22.9464 + 13.2481i 1.12639 + 0.650323i
\(416\) −4.50896 + 18.8591i −0.221070 + 0.924644i
\(417\) 1.70701 + 0.784680i 0.0835924 + 0.0384260i
\(418\) −12.0026 + 12.0026i −0.587065 + 0.587065i
\(419\) −15.7912 + 9.11707i −0.771452 + 0.445398i −0.833392 0.552682i \(-0.813604\pi\)
0.0619404 + 0.998080i \(0.480271\pi\)
\(420\) 24.2149 10.2805i 1.18156 0.501635i
\(421\) 17.0106 17.0106i 0.829045 0.829045i −0.158340 0.987385i \(-0.550614\pi\)
0.987385 + 0.158340i \(0.0506142\pi\)
\(422\) −1.86754 + 6.96974i −0.0909103 + 0.339282i
\(423\) −14.4039 30.0295i −0.700343 1.46008i
\(424\) −1.51611 + 5.65822i −0.0736290 + 0.274787i
\(425\) −17.0298 + 9.83219i −0.826069 + 0.476931i
\(426\) −5.10320 + 11.1016i −0.247251 + 0.537873i
\(427\) −8.37490 13.0497i −0.405290 0.631519i
\(428\) −4.07003 −0.196733
\(429\) −22.2668 17.4805i −1.07505 0.843968i
\(430\) −5.36837 9.29830i −0.258886 0.448404i
\(431\) −28.4763 + 7.63021i −1.37166 + 0.367534i −0.868084 0.496418i \(-0.834648\pi\)
−0.503573 + 0.863952i \(0.667982\pi\)
\(432\) −3.14927 11.0280i −0.151519 0.530585i
\(433\) 15.1309 + 8.73583i 0.727145 + 0.419817i 0.817377 0.576103i \(-0.195427\pi\)
−0.0902317 + 0.995921i \(0.528761\pi\)
\(434\) −5.10035 7.94731i −0.244824 0.381483i
\(435\) −0.353947 0.293721i −0.0169705 0.0140829i
\(436\) −6.14845 + 22.9463i −0.294457 + 1.09893i
\(437\) 23.9654 + 6.42152i 1.14642 + 0.307183i
\(438\) −1.74594 2.46473i −0.0834240 0.117769i
\(439\) 16.3826i 0.781901i 0.920412 + 0.390950i \(0.127854\pi\)
−0.920412 + 0.390950i \(0.872146\pi\)
\(440\) 30.8743 + 8.27275i 1.47187 + 0.394388i
\(441\) −20.1857 + 5.79101i −0.961226 + 0.275762i
\(442\) −1.40026 + 5.85672i −0.0666037 + 0.278576i
\(443\) 17.0034 + 9.81693i 0.807857 + 0.466416i 0.846211 0.532848i \(-0.178878\pi\)
−0.0383541 + 0.999264i \(0.512211\pi\)
\(444\) 3.36558 + 2.79291i 0.159723 + 0.132545i
\(445\) 12.7105 22.0152i 0.602535 1.04362i
\(446\) −3.34026 5.78551i −0.158166 0.273952i
\(447\) 13.9373 + 2.37920i 0.659212 + 0.112532i
\(448\) −0.173186 3.68452i −0.00818228 0.174077i
\(449\) 3.09336 + 11.5446i 0.145984 + 0.544821i 0.999710 + 0.0240976i \(0.00767124\pi\)
−0.853725 + 0.520724i \(0.825662\pi\)
\(450\) −11.1075 0.849763i −0.523611 0.0400582i
\(451\) 15.0916 0.710636
\(452\) 3.78779 6.56064i 0.178163 0.308587i
\(453\) −27.4866 4.69216i −1.29143 0.220457i
\(454\) 13.9939i 0.656764i
\(455\) 24.6243 + 21.2215i 1.15440 + 0.994878i
\(456\) −13.8137 19.5007i −0.646887 0.913206i
\(457\) 6.28317 6.28317i 0.293914 0.293914i −0.544710 0.838624i \(-0.683360\pi\)
0.838624 + 0.544710i \(0.183360\pi\)
\(458\) −0.381886 0.220482i −0.0178443 0.0103024i
\(459\) −4.24334 14.8592i −0.198062 0.693568i
\(460\) −5.52855 20.6328i −0.257770 0.962010i
\(461\) 25.7182 6.89117i 1.19782 0.320954i 0.395845 0.918317i \(-0.370452\pi\)
0.801970 + 0.597364i \(0.203785\pi\)
\(462\) −10.8166 4.36938i −0.503234 0.203282i
\(463\) −1.52114 1.52114i −0.0706936 0.0706936i 0.670876 0.741570i \(-0.265918\pi\)
−0.741570 + 0.670876i \(0.765918\pi\)
\(464\) −0.148956 + 0.0860000i −0.00691513 + 0.00399245i
\(465\) −3.47320 37.3507i −0.161066 1.73210i
\(466\) 0.115791 0.0310262i 0.00536393 0.00143726i
\(467\) −6.28892 + 10.8927i −0.291017 + 0.504056i −0.974050 0.226331i \(-0.927327\pi\)
0.683034 + 0.730387i \(0.260660\pi\)
\(468\) 13.5034 12.2351i 0.624195 0.565568i
\(469\) 5.44537 + 17.0717i 0.251444 + 0.788299i
\(470\) −5.49872 + 20.5215i −0.253637 + 0.946587i
\(471\) −13.1411 + 9.30872i −0.605508 + 0.428923i
\(472\) 3.26560i 0.150311i
\(473\) 6.58237 24.5657i 0.302658 1.12953i
\(474\) 3.43042 + 9.26738i 0.157564 + 0.425665i
\(475\) 42.5865 11.4110i 1.95400 0.523574i
\(476\) −0.622359 13.2406i −0.0285258 0.606883i
\(477\) 6.44585 5.52968i 0.295135 0.253187i
\(478\) 0.351763i 0.0160893i
\(479\) −3.54058 13.2136i −0.161773 0.603746i −0.998430 0.0560179i \(-0.982160\pi\)
0.836657 0.547728i \(-0.184507\pi\)
\(480\) −13.2577 + 28.8410i −0.605129 + 1.31641i
\(481\) −1.25667 + 5.25614i −0.0572992 + 0.239659i
\(482\) 4.59520i 0.209306i
\(483\) 2.37423 + 16.8855i 0.108031 + 0.768318i
\(484\) 8.04255 + 13.9301i 0.365571 + 0.633187i
\(485\) 10.2016 + 17.6696i 0.463229 + 0.802336i
\(486\) 2.76865 8.30493i 0.125589 0.376719i
\(487\) 5.32968 5.32968i 0.241511 0.241511i −0.575964 0.817475i \(-0.695373\pi\)
0.817475 + 0.575964i \(0.195373\pi\)
\(488\) 11.7139 + 3.13873i 0.530264 + 0.142084i
\(489\) 10.6918 + 1.82516i 0.483498 + 0.0825366i
\(490\) 12.1783 + 5.58022i 0.550160 + 0.252089i
\(491\) 16.5182 + 28.6104i 0.745457 + 1.29117i 0.949981 + 0.312308i \(0.101102\pi\)
−0.204523 + 0.978862i \(0.565564\pi\)
\(492\) −1.63465 + 9.57576i −0.0736957 + 0.431709i
\(493\) −0.200705 + 0.115877i −0.00903928 + 0.00521883i
\(494\) 6.43110 11.8712i 0.289349 0.534109i
\(495\) −30.1729 35.1721i −1.35617 1.58087i
\(496\) −13.5498 3.63066i −0.608405 0.163022i
\(497\) 31.6623 10.0993i 1.42025 0.453018i
\(498\) 7.53070 0.700270i 0.337459 0.0313799i
\(499\) −4.39571 16.4050i −0.196779 0.734390i −0.991799 0.127807i \(-0.959206\pi\)
0.795020 0.606583i \(-0.207460\pi\)
\(500\) −6.54413 6.54413i −0.292663 0.292663i
\(501\) −7.17787 + 42.0479i −0.320683 + 1.87856i
\(502\) 5.17825 1.38751i 0.231117 0.0619275i
\(503\) −9.32997 5.38666i −0.416003 0.240179i 0.277363 0.960765i \(-0.410540\pi\)
−0.693366 + 0.720586i \(0.743873\pi\)
\(504\) 8.62639 13.9762i 0.384250 0.622550i
\(505\) −6.75750 + 25.2193i −0.300705 + 1.12225i
\(506\) −4.73621 + 8.20335i −0.210550 + 0.364683i
\(507\) 20.9384 + 8.28158i 0.929906 + 0.367798i
\(508\) −3.30659 5.72717i −0.146706 0.254102i
\(509\) −12.8219 12.8219i −0.568322 0.568322i 0.363336 0.931658i \(-0.381638\pi\)
−0.931658 + 0.363336i \(0.881638\pi\)
\(510\) −4.11720 + 8.95661i −0.182313 + 0.396605i
\(511\) −1.75143 + 8.02683i −0.0774788 + 0.355086i
\(512\) 14.8525 + 14.8525i 0.656393 + 0.656393i
\(513\) 0.567044 + 34.6425i 0.0250356 + 1.52950i
\(514\) 5.01481 + 5.01481i 0.221194 + 0.221194i
\(515\) 18.5420 + 4.96832i 0.817059 + 0.218930i
\(516\) 14.8742 + 6.83742i 0.654801 + 0.301001i
\(517\) −43.5822 + 25.1622i −1.91674 + 1.10663i
\(518\) 0.104565 + 2.22460i 0.00459431 + 0.0977435i
\(519\) −16.2607 + 11.5186i −0.713764 + 0.505609i
\(520\) −25.4143 + 0.689366i −1.11449 + 0.0302307i
\(521\) 13.5307 7.81195i 0.592790 0.342248i −0.173410 0.984850i \(-0.555479\pi\)
0.766200 + 0.642602i \(0.222145\pi\)
\(522\) −0.130907 0.0100149i −0.00572962 0.000438338i
\(523\) −23.9138 −1.04568 −0.522840 0.852431i \(-0.675127\pi\)
−0.522840 + 0.852431i \(0.675127\pi\)
\(524\) −9.36780 + 16.2255i −0.409234 + 0.708814i
\(525\) 18.6565 + 23.8761i 0.814238 + 1.04204i
\(526\) −4.55693 17.0067i −0.198692 0.741527i
\(527\) −18.2571 4.89197i −0.795291 0.213098i
\(528\) −16.2518 + 6.01579i −0.707270 + 0.261804i
\(529\) −9.15437 −0.398016
\(530\) −5.41751 −0.235322
\(531\) 2.67312 3.90767i 0.116003 0.169579i
\(532\) −6.33557 + 29.0359i −0.274682 + 1.25887i
\(533\) −11.5063 + 3.42007i −0.498393 + 0.148140i
\(534\) −0.671853 7.22510i −0.0290739 0.312661i
\(535\) −2.13083 7.95237i −0.0921238 0.343811i
\(536\) −12.1369 7.00726i −0.524236 0.302668i
\(537\) 14.7001 + 6.75738i 0.634356 + 0.291602i
\(538\) 7.21198 7.21198i 0.310930 0.310930i
\(539\) 11.0514 + 29.7444i 0.476016 + 1.28118i
\(540\) 25.5852 15.3353i 1.10101 0.659928i
\(541\) 26.2082 7.02248i 1.12678 0.301920i 0.353156 0.935564i \(-0.385109\pi\)
0.773624 + 0.633645i \(0.218442\pi\)
\(542\) 8.98577i 0.385972i
\(543\) −25.7605 + 2.39544i −1.10549 + 0.102798i
\(544\) 11.3095 + 11.3095i 0.484889 + 0.484889i
\(545\) −48.0534 −2.05838
\(546\) 9.23711 + 0.880078i 0.395312 + 0.0376639i
\(547\) 19.3833 0.828770 0.414385 0.910102i \(-0.363997\pi\)
0.414385 + 0.910102i \(0.363997\pi\)
\(548\) −10.4629 10.4629i −0.446952 0.446952i
\(549\) −11.4478 13.3445i −0.488581 0.569530i
\(550\) 16.8325i 0.717739i
\(551\) 0.501902 0.134484i 0.0213817 0.00572922i
\(552\) −10.2626 8.51638i −0.436806 0.362481i
\(553\) 12.3317 23.8832i 0.524397 1.01562i
\(554\) 3.71944 3.71944i 0.158024 0.158024i
\(555\) −3.69499 + 8.03814i −0.156844 + 0.341200i
\(556\) 1.58246 + 0.913636i 0.0671115 + 0.0387468i
\(557\) −5.55919 20.7472i −0.235551 0.879087i −0.977900 0.209074i \(-0.932955\pi\)
0.742349 0.670013i \(-0.233712\pi\)
\(558\) −6.97176 8.12686i −0.295138 0.344038i
\(559\) 0.548507 + 20.2214i 0.0231994 + 0.855274i
\(560\) 18.9585 6.04720i 0.801143 0.255541i
\(561\) −21.8978 + 8.10571i −0.924526 + 0.342223i
\(562\) −7.44883 −0.314210
\(563\) −36.6784 −1.54581 −0.772906 0.634521i \(-0.781198\pi\)
−0.772906 + 0.634521i \(0.781198\pi\)
\(564\) −11.2450 30.3788i −0.473502 1.27918i
\(565\) 14.8018 + 3.96613i 0.622716 + 0.166856i
\(566\) 1.41992 + 5.29920i 0.0596836 + 0.222742i
\(567\) −21.7630 + 9.66290i −0.913960 + 0.405803i
\(568\) −12.9961 + 22.5099i −0.545305 + 0.944497i
\(569\) 4.46811 0.187313 0.0936565 0.995605i \(-0.470144\pi\)
0.0936565 + 0.995605i \(0.470144\pi\)
\(570\) 14.1139 17.0079i 0.591167 0.712382i
\(571\) −7.70795 + 4.45018i −0.322567 + 0.186234i −0.652536 0.757757i \(-0.726295\pi\)
0.329969 + 0.943992i \(0.392962\pi\)
\(572\) −19.9898 18.9340i −0.835817 0.791671i
\(573\) −4.00384 5.65219i −0.167263 0.236124i
\(574\) −4.16310 + 2.67176i −0.173765 + 0.111517i
\(575\) 21.3074 12.3018i 0.888580 0.513022i
\(576\) −0.771176 4.11075i −0.0321323 0.171281i
\(577\) 20.7772 + 5.56723i 0.864965 + 0.231767i 0.663909 0.747813i \(-0.268896\pi\)
0.201056 + 0.979580i \(0.435563\pi\)
\(578\) −3.23857 3.23857i −0.134707 0.134707i
\(579\) 9.75056 + 26.3414i 0.405220 + 1.09471i
\(580\) −0.316325 0.316325i −0.0131347 0.0131347i
\(581\) −15.2135 13.8475i −0.631164 0.574493i
\(582\) 5.29164 + 2.43248i 0.219346 + 0.100829i
\(583\) −9.07398 9.07398i −0.375806 0.375806i
\(584\) −3.21273 5.56462i −0.132944 0.230266i
\(585\) 30.9755 + 19.9785i 1.28068 + 0.826008i
\(586\) −6.17565 + 10.6965i −0.255114 + 0.441870i
\(587\) 6.43634 24.0207i 0.265656 0.991442i −0.696191 0.717856i \(-0.745123\pi\)
0.961848 0.273586i \(-0.0882099\pi\)
\(588\) −20.0701 + 3.79043i −0.827679 + 0.156315i
\(589\) 36.7001 + 21.1888i 1.51220 + 0.873069i
\(590\) −2.91723 + 0.781668i −0.120100 + 0.0321808i
\(591\) 5.22678 + 0.892249i 0.215001 + 0.0367022i
\(592\) 2.33932 + 2.33932i 0.0961454 + 0.0961454i
\(593\) −2.51968 9.40359i −0.103471 0.386159i 0.894696 0.446675i \(-0.147392\pi\)
−0.998167 + 0.0605161i \(0.980725\pi\)
\(594\) −12.8313 3.21402i −0.526477 0.131873i
\(595\) 25.5448 8.14803i 1.04723 0.334037i
\(596\) 13.2832 + 3.55921i 0.544100 + 0.145791i
\(597\) 14.7443 1.37106i 0.603445 0.0561136i
\(598\) 1.75198 7.32781i 0.0716438 0.299657i
\(599\) −22.5356 + 13.0110i −0.920781 + 0.531613i −0.883884 0.467706i \(-0.845081\pi\)
−0.0368968 + 0.999319i \(0.511747\pi\)
\(600\) −23.3602 3.98775i −0.953676 0.162799i
\(601\) 14.4909 + 25.0989i 0.591094 + 1.02381i 0.994085 + 0.108602i \(0.0346373\pi\)
−0.402991 + 0.915204i \(0.632029\pi\)
\(602\) 2.53324 + 7.94192i 0.103247 + 0.323688i
\(603\) 8.78734 + 18.3199i 0.357848 + 0.746046i
\(604\) −26.1965 7.01933i −1.06592 0.285613i
\(605\) −23.0072 + 23.0072i −0.935375 + 0.935375i
\(606\) 2.58713 + 6.98919i 0.105095 + 0.283917i
\(607\) 1.73922 + 3.01242i 0.0705928 + 0.122270i 0.899161 0.437617i \(-0.144178\pi\)
−0.828568 + 0.559888i \(0.810844\pi\)
\(608\) −17.9298 31.0553i −0.727149 1.25946i
\(609\) 0.219876 + 0.281391i 0.00890983 + 0.0114025i
\(610\) 11.2156i 0.454106i
\(611\) 27.5262 29.0611i 1.11359 1.17569i
\(612\) −2.77128 14.7723i −0.112023 0.597136i
\(613\) 4.59569 + 17.1513i 0.185618 + 0.692736i 0.994497 + 0.104761i \(0.0334079\pi\)
−0.808879 + 0.587975i \(0.799925\pi\)
\(614\) 10.5277i 0.424864i
\(615\) −19.5657 + 1.81939i −0.788966 + 0.0733650i
\(616\) −22.0509 11.3856i −0.888455 0.458740i
\(617\) 29.4261 7.88471i 1.18465 0.317427i 0.387882 0.921709i \(-0.373207\pi\)
0.796770 + 0.604282i \(0.206540\pi\)
\(618\) 5.13867 1.90213i 0.206707 0.0765150i
\(619\) 3.21905 12.0137i 0.129385 0.482870i −0.870573 0.492039i \(-0.836252\pi\)
0.999958 + 0.00916885i \(0.00291858\pi\)
\(620\) 36.4846i 1.46526i
\(621\) 5.30918 + 18.5915i 0.213050 + 0.746052i
\(622\) −3.52899 + 13.1704i −0.141500 + 0.528084i
\(623\) −13.2856 + 14.5962i −0.532277 + 0.584783i
\(624\) 11.0276 8.26963i 0.441457 0.331050i
\(625\) −7.17006 + 12.4189i −0.286802 + 0.496756i
\(626\) −5.80225 + 1.55471i −0.231905 + 0.0621386i
\(627\) 52.1270 4.84723i 2.08175 0.193580i
\(628\) −13.5646 + 7.83151i −0.541286 + 0.312511i
\(629\) 3.15201 + 3.15201i 0.125679 + 0.125679i
\(630\) 14.5501 + 4.36073i 0.579690 + 0.173735i
\(631\) 9.15432 2.45289i 0.364428 0.0976481i −0.0719584 0.997408i \(-0.522925\pi\)
0.436386 + 0.899760i \(0.356258\pi\)
\(632\) 5.44088 + 20.3056i 0.216426 + 0.807715i
\(633\) 18.1599 12.8639i 0.721789 0.511293i
\(634\) −4.44286 2.56509i −0.176448 0.101873i
\(635\) 9.45909 9.45909i 0.375373 0.375373i
\(636\) 6.74038 4.77468i 0.267273 0.189328i
\(637\) −15.1666 20.1736i −0.600923 0.799307i
\(638\) 0.198378i 0.00785388i
\(639\) 33.9774 16.2976i 1.34412 0.644723i
\(640\) −19.6604 + 34.0528i −0.777145 + 1.34605i
\(641\) −3.21821 −0.127112 −0.0635558 0.997978i \(-0.520244\pi\)
−0.0635558 + 0.997978i \(0.520244\pi\)
\(642\) −1.80844 1.50073i −0.0713736 0.0592290i
\(643\) −7.26853 27.1265i −0.286643 1.06977i −0.947630 0.319369i \(-0.896529\pi\)
0.660987 0.750397i \(-0.270138\pi\)
\(644\) 0.778684 + 16.5664i 0.0306844 + 0.652808i
\(645\) −5.57225 + 32.6422i −0.219407 + 1.28528i
\(646\) −5.56812 9.64427i −0.219075 0.379449i
\(647\) −0.520734 + 0.901937i −0.0204722 + 0.0354588i −0.876080 0.482166i \(-0.839850\pi\)
0.855608 + 0.517625i \(0.173184\pi\)
\(648\) 7.50030 17.0460i 0.294639 0.669630i
\(649\) −6.19541 3.57692i −0.243191 0.140407i
\(650\) −3.81459 12.8336i −0.149620 0.503375i
\(651\) −3.54752 + 28.9078i −0.139038 + 1.13299i
\(652\) 10.1899 + 2.73039i 0.399069 + 0.106930i
\(653\) 33.4930i 1.31068i 0.755334 + 0.655341i \(0.227475\pi\)
−0.755334 + 0.655341i \(0.772525\pi\)
\(654\) −11.1929 + 7.92868i −0.437676 + 0.310036i
\(655\) −36.6071 9.80885i −1.43036 0.383264i
\(656\) −1.90188 + 7.09791i −0.0742559 + 0.277127i
\(657\) −0.710612 + 9.28857i −0.0277236 + 0.362382i
\(658\) 7.56779 14.6568i 0.295023 0.571380i
\(659\) −2.89696 1.67256i −0.112850 0.0651537i 0.442513 0.896762i \(-0.354087\pi\)
−0.555362 + 0.831608i \(0.687420\pi\)
\(660\) −26.0532 36.7792i −1.01412 1.43163i
\(661\) −39.4613 + 10.5736i −1.53486 + 0.411266i −0.924602 0.380934i \(-0.875603\pi\)
−0.610262 + 0.792199i \(0.708936\pi\)
\(662\) 6.71226 + 11.6260i 0.260879 + 0.451856i
\(663\) 14.8586 11.1425i 0.577062 0.432741i
\(664\) 16.0893 0.624385
\(665\) −60.0498 + 2.82257i −2.32863 + 0.109454i
\(666\) 0.465613 + 2.48195i 0.0180422 + 0.0961737i
\(667\) 0.251118 0.144983i 0.00972331 0.00561376i
\(668\) −10.7379 + 40.0743i −0.415461 + 1.55052i
\(669\) −3.46712 + 20.3103i −0.134046 + 0.785243i
\(670\) 3.35458 12.5195i 0.129599 0.483669i
\(671\) −18.7854 + 18.7854i −0.725202 + 0.725202i
\(672\) 14.8305 19.6834i 0.572099 0.759304i
\(673\) −18.4345 + 10.6432i −0.710599 + 0.410265i −0.811283 0.584654i \(-0.801230\pi\)
0.100683 + 0.994919i \(0.467897\pi\)
\(674\) 5.30804 5.30804i 0.204458 0.204458i
\(675\) 24.6890 + 23.8938i 0.950280 + 0.919672i
\(676\) 19.5317 + 9.90577i 0.751220 + 0.380991i
\(677\) −8.11505 4.68523i −0.311887 0.180068i 0.335884 0.941903i \(-0.390965\pi\)
−0.647771 + 0.761836i \(0.724298\pi\)
\(678\) 4.10211 1.51844i 0.157541 0.0583154i
\(679\) −4.81393 15.0921i −0.184742 0.579181i
\(680\) −10.4851 + 18.1607i −0.402086 + 0.696433i
\(681\) −27.5619 + 33.2133i −1.05617 + 1.27274i
\(682\) −11.4404 + 11.4404i −0.438075 + 0.438075i
\(683\) 24.8855 24.8855i 0.952217 0.952217i −0.0466920 0.998909i \(-0.514868\pi\)
0.998909 + 0.0466920i \(0.0148679\pi\)
\(684\) −2.57054 + 33.6001i −0.0982870 + 1.28473i
\(685\) 14.9655 25.9210i 0.571802 0.990389i
\(686\) −8.31441 6.24867i −0.317446 0.238575i
\(687\) 0.472120 + 1.27545i 0.0180125 + 0.0486613i
\(688\) 10.7243 + 6.19167i 0.408859 + 0.236055i
\(689\) 8.97464 + 4.86193i 0.341907 + 0.185225i
\(690\) 5.15135 11.2063i 0.196109 0.426618i
\(691\) 23.6749 23.6749i 0.900637 0.900637i −0.0948540 0.995491i \(-0.530238\pi\)
0.995491 + 0.0948540i \(0.0302384\pi\)
\(692\) −16.7847 + 9.69068i −0.638060 + 0.368384i
\(693\) 17.0666 + 31.6744i 0.648305 + 1.20321i
\(694\) −12.2202 + 12.2202i −0.463874 + 0.463874i
\(695\) −0.956653 + 3.57028i −0.0362879 + 0.135428i
\(696\) −0.275311 0.0469975i −0.0104356 0.00178144i
\(697\) −2.56260 + 9.56376i −0.0970655 + 0.362253i
\(698\) 6.75884 3.90222i 0.255826 0.147701i
\(699\) −0.335930 0.154421i −0.0127060 0.00584074i
\(700\) 15.9176 + 24.8026i 0.601628 + 0.937450i
\(701\) 15.1881 0.573647 0.286823 0.957984i \(-0.407401\pi\)
0.286823 + 0.957984i \(0.407401\pi\)
\(702\) 10.5114 0.457381i 0.396727 0.0172627i
\(703\) −4.99713 8.65528i −0.188470 0.326440i
\(704\) −6.10438 + 1.63566i −0.230067 + 0.0616464i
\(705\) 53.4694 37.8760i 2.01377 1.42649i
\(706\) 15.9097 + 9.18546i 0.598769 + 0.345699i
\(707\) 9.30022 18.0120i 0.349771 0.677411i
\(708\) 2.94065 3.54361i 0.110516 0.133177i
\(709\) −10.3698 + 38.7006i −0.389446 + 1.45343i 0.441591 + 0.897216i \(0.354414\pi\)
−0.831037 + 0.556217i \(0.812252\pi\)
\(710\) −23.2194 6.22163i −0.871410 0.233494i
\(711\) 10.1109 28.7518i 0.379189 1.07828i
\(712\) 15.4364i 0.578503i
\(713\) 22.8429 + 6.12074i 0.855473 + 0.229223i
\(714\) 4.60563 6.11270i 0.172361 0.228762i
\(715\) 26.5294 48.9705i 0.992141 1.83139i
\(716\) 13.6276 + 7.86790i 0.509287 + 0.294037i
\(717\) 0.692821 0.834881i 0.0258739 0.0311792i
\(718\) 5.70615 9.88334i 0.212952 0.368843i
\(719\) 22.8854 + 39.6387i 0.853483 + 1.47828i 0.878045 + 0.478577i \(0.158847\pi\)
−0.0245625 + 0.999698i \(0.507819\pi\)
\(720\) 20.3447 9.75853i 0.758201 0.363679i
\(721\) −13.2430 6.83780i −0.493194 0.254653i
\(722\) 3.70060 + 13.8108i 0.137722 + 0.513986i
\(723\) 9.05057 10.9063i 0.336594 0.405611i
\(724\) −25.1632 −0.935182
\(725\) 0.257634 0.446236i 0.00956830 0.0165728i
\(726\) −1.56284 + 9.15509i −0.0580023 + 0.339777i
\(727\) 33.7767i 1.25271i 0.779538 + 0.626355i \(0.215454\pi\)
−0.779538 + 0.626355i \(0.784546\pi\)
\(728\) 19.3925 + 3.68357i 0.718734 + 0.136522i
\(729\) −22.9283 + 14.2580i −0.849197 + 0.528076i
\(730\) 4.20198 4.20198i 0.155522 0.155522i
\(731\) 14.4500 + 8.34268i 0.534451 + 0.308565i
\(732\) −9.88477 13.9543i −0.365352 0.515764i
\(733\) −0.224901 0.839342i −0.00830691 0.0310018i 0.961648 0.274287i \(-0.0884417\pi\)
−0.969955 + 0.243285i \(0.921775\pi\)
\(734\) 12.7720 3.42224i 0.471421 0.126317i
\(735\) −17.9136 37.2302i −0.660753 1.37326i
\(736\) −14.1502 14.1502i −0.521582 0.521582i
\(737\) 26.5880 15.3506i 0.979382 0.565447i
\(738\) −4.25716 + 3.65207i −0.156708 + 0.134435i
\(739\) −23.5059 + 6.29839i −0.864678 + 0.231690i −0.663785 0.747923i \(-0.731051\pi\)
−0.200893 + 0.979613i \(0.564384\pi\)
\(740\) −4.30224 + 7.45169i −0.158153 + 0.273930i
\(741\) −38.6448 + 15.5088i −1.41965 + 0.569728i
\(742\) 4.10953 + 0.896688i 0.150866 + 0.0329185i
\(743\) 11.4882 42.8747i 0.421462 1.57292i −0.350066 0.936725i \(-0.613841\pi\)
0.771529 0.636194i \(-0.219492\pi\)
\(744\) −13.1667 18.5873i −0.482715 0.681445i
\(745\) 27.8171i 1.01914i
\(746\) −0.802329 + 2.99433i −0.0293753 + 0.109630i
\(747\) −19.2527 13.1702i −0.704421 0.481873i
\(748\) −21.9366 + 5.87790i −0.802082 + 0.214917i
\(749\) 0.300123 + 6.38507i 0.0109662 + 0.233306i
\(750\) −0.494771 5.32076i −0.0180665 0.194287i
\(751\) 39.6555i 1.44705i −0.690299 0.723525i \(-0.742521\pi\)
0.690299 0.723525i \(-0.257479\pi\)
\(752\) −6.34201 23.6687i −0.231269 0.863108i
\(753\) −15.0230 6.90579i −0.547467 0.251661i
\(754\) −0.0449567 0.151250i −0.00163723 0.00550820i
\(755\) 54.8598i 1.99655i
\(756\) −21.9463 + 7.39807i −0.798179 + 0.269065i
\(757\) −25.9265 44.9060i −0.942315 1.63214i −0.761040 0.648705i \(-0.775311\pi\)
−0.181276 0.983432i \(-0.558023\pi\)
\(758\) −1.10973 1.92211i −0.0403073 0.0698142i
\(759\) 27.3981 10.1417i 0.994487 0.368120i
\(760\) 33.2458 33.2458i 1.20595 1.20595i
\(761\) −6.84207 1.83333i −0.248025 0.0664580i 0.132665 0.991161i \(-0.457647\pi\)
−0.380689 + 0.924703i \(0.624313\pi\)
\(762\) 0.642539 3.76399i 0.0232767 0.136355i
\(763\) 36.4516 + 7.95364i 1.31964 + 0.287941i
\(764\) −3.36847 5.83436i −0.121867 0.211080i
\(765\) 27.4125 13.1487i 0.991102 0.475392i
\(766\) 18.1185 10.4607i 0.654648 0.377961i
\(767\) 5.53418 + 1.32315i 0.199828 + 0.0477761i
\(768\) 0.592053 + 6.36693i 0.0213639 + 0.229747i
\(769\) −48.7154 13.0533i −1.75672 0.470712i −0.770683 0.637219i \(-0.780085\pi\)
−0.986040 + 0.166507i \(0.946751\pi\)
\(770\) 4.89282 22.4238i 0.176325 0.808099i
\(771\) −2.02523 21.7793i −0.0729369 0.784362i
\(772\) 7.07067 + 26.3881i 0.254479 + 0.949728i
\(773\) 8.40190 + 8.40190i 0.302195 + 0.302195i 0.841872 0.539677i \(-0.181454\pi\)
−0.539677 + 0.841872i \(0.681454\pi\)
\(774\) 4.08795 + 8.52260i 0.146938 + 0.306338i
\(775\) 40.5918 10.8765i 1.45810 0.390697i
\(776\) 10.7295 + 6.19470i 0.385168 + 0.222377i
\(777\) 4.13334 5.48587i 0.148283 0.196804i
\(778\) 2.43296 9.07992i 0.0872257 0.325531i
\(779\) 11.0995 19.2249i 0.397681 0.688803i
\(780\) 28.1987 + 22.1374i 1.00968 + 0.792645i
\(781\) −28.4702 49.3119i −1.01875 1.76452i
\(782\) −4.39436 4.39436i −0.157142 0.157142i
\(783\) 0.290971 + 0.281599i 0.0103985 + 0.0100635i
\(784\) −15.3822 + 1.44924i −0.549363 + 0.0517587i
\(785\) −22.4035 22.4035i −0.799614 0.799614i
\(786\) −10.1452 + 3.75535i −0.361866 + 0.133949i
\(787\) 28.3986 + 28.3986i 1.01230 + 1.01230i 0.999923 + 0.0123764i \(0.00393964\pi\)
0.0123764 + 0.999923i \(0.496060\pi\)
\(788\) 4.98146 + 1.33478i 0.177457 + 0.0475495i
\(789\) −22.6804 + 49.3392i −0.807443 + 1.75652i
\(790\) −16.8371 + 9.72090i −0.599037 + 0.345854i
\(791\) −10.5716 5.45851i −0.375885 0.194082i
\(792\) −26.5460 9.33522i −0.943272 0.331713i
\(793\) 10.0654 18.5797i 0.357433 0.659786i
\(794\) 2.27370 1.31272i 0.0806906 0.0465867i
\(795\) 12.8580 + 10.6702i 0.456027 + 0.378432i
\(796\) 14.4024 0.510481
\(797\) 5.98314 10.3631i 0.211934 0.367080i −0.740386 0.672182i \(-0.765357\pi\)
0.952320 + 0.305102i \(0.0986906\pi\)
\(798\) −13.5214 + 10.5655i −0.478653 + 0.374014i
\(799\) −8.54525 31.8913i −0.302309 1.12823i
\(800\) −34.3485 9.20365i −1.21440 0.325398i
\(801\) −12.6358 + 18.4715i −0.446463 + 0.652657i
\(802\) −6.44205 −0.227477
\(803\) 14.0761 0.496734
\(804\) 6.86021 + 18.5331i 0.241941 + 0.653610i
\(805\) −31.9611 + 10.1946i −1.12648 + 0.359314i
\(806\) 6.12987 11.3151i 0.215915 0.398558i
\(807\) −31.3215 + 2.91255i −1.10257 + 0.102527i
\(808\) 4.10336 + 15.3139i 0.144356 + 0.538742i
\(809\) 29.6819 + 17.1369i 1.04356 + 0.602500i 0.920840 0.389942i \(-0.127505\pi\)
0.122721 + 0.992441i \(0.460838\pi\)
\(810\) 17.0229 + 2.61996i 0.598122 + 0.0920561i
\(811\) 13.0348 13.0348i 0.457713 0.457713i −0.440191 0.897904i \(-0.645089\pi\)
0.897904 + 0.440191i \(0.145089\pi\)
\(812\) 0.187596 + 0.292310i 0.00658333 + 0.0102581i
\(813\) 17.6981 21.3270i 0.620700 0.747971i
\(814\) 3.68565 0.987566i 0.129182 0.0346142i
\(815\) 21.3394i 0.747488i
\(816\) −1.05268 11.3205i −0.0368512 0.396297i
\(817\) −26.4526 26.4526i −0.925461 0.925461i
\(818\) 19.2084 0.671607
\(819\) −20.1902 20.2819i −0.705502 0.708708i
\(820\) −19.1120 −0.667421
\(821\) 23.8891 + 23.8891i 0.833735 + 0.833735i 0.988025 0.154291i \(-0.0493093\pi\)
−0.154291 + 0.988025i \(0.549309\pi\)
\(822\) −0.791048 8.50692i −0.0275910 0.296713i
\(823\) 48.4392i 1.68848i 0.535961 + 0.844242i \(0.319949\pi\)
−0.535961 + 0.844242i \(0.680051\pi\)
\(824\) 11.2593 3.01691i 0.392235 0.105099i
\(825\) 33.1527 39.9505i 1.15423 1.39090i
\(826\) 2.34228 0.110096i 0.0814985 0.00383074i
\(827\) −20.1765 + 20.1765i −0.701605 + 0.701605i −0.964755 0.263150i \(-0.915239\pi\)
0.263150 + 0.964755i \(0.415239\pi\)
\(828\) 3.46738 + 18.4828i 0.120500 + 0.642323i
\(829\) −36.0814 20.8316i −1.25316 0.723512i −0.281423 0.959584i \(-0.590807\pi\)
−0.971736 + 0.236072i \(0.924140\pi\)
\(830\) 3.85121 + 14.3729i 0.133677 + 0.498891i
\(831\) −16.1535 + 1.50209i −0.560359 + 0.0521071i
\(832\) 4.28349 2.63046i 0.148503 0.0911948i
\(833\) −20.7260 + 1.95272i −0.718114 + 0.0676576i
\(834\) 0.366257 + 0.989453i 0.0126824 + 0.0342620i
\(835\) −83.9223 −2.90425
\(836\) 50.9183 1.76105
\(837\) 0.540484 + 33.0198i 0.0186819 + 1.14133i
\(838\) −9.89114 2.65032i −0.341684 0.0915538i
\(839\) 0.811595 + 3.02891i 0.0280194 + 0.104570i 0.978519 0.206155i \(-0.0660950\pi\)
−0.950500 + 0.310724i \(0.899428\pi\)
\(840\) 29.9608 + 12.1027i 1.03375 + 0.417582i
\(841\) −14.4970 + 25.1095i −0.499895 + 0.865844i
\(842\) 13.5099 0.465581
\(843\) 17.6792 + 14.6710i 0.608904 + 0.505296i
\(844\) 18.7451 10.8225i 0.645234 0.372526i
\(845\) −9.12906 + 43.3488i −0.314049 + 1.49124i
\(846\) 6.20493 17.6446i 0.213330 0.606634i
\(847\) 21.2605 13.6444i 0.730520 0.468826i
\(848\) 5.41122 3.12417i 0.185822 0.107284i
\(849\) 7.06709 15.3739i 0.242542 0.527630i
\(850\) −10.6670 2.85821i −0.365874 0.0980357i
\(851\) −3.94373 3.94373i −0.135189 0.135189i
\(852\) 34.3726 12.7234i 1.17759 0.435897i
\(853\) −11.1030 11.1030i −0.380158 0.380158i 0.491001 0.871159i \(-0.336631\pi\)
−0.871159 + 0.491001i \(0.836631\pi\)
\(854\) 1.85637 8.50775i 0.0635236 0.291129i
\(855\) −66.9965 + 12.5685i −2.29123 + 0.429834i
\(856\) −3.53501 3.53501i −0.120824 0.120824i
\(857\) −17.9037 31.0101i −0.611577 1.05928i −0.990975 0.134049i \(-0.957202\pi\)
0.379397 0.925234i \(-0.376131\pi\)
\(858\) −1.90064 15.7838i −0.0648868 0.538849i
\(859\) −11.7731 + 20.3916i −0.401692 + 0.695751i −0.993930 0.110012i \(-0.964911\pi\)
0.592238 + 0.805763i \(0.298244\pi\)
\(860\) −8.33593 + 31.1101i −0.284253 + 1.06085i
\(861\) 15.1430 + 1.85833i 0.516072 + 0.0633316i
\(862\) −14.3380 8.27804i −0.488354 0.281951i
\(863\) −14.3250 + 3.83837i −0.487628 + 0.130660i −0.494252 0.869318i \(-0.664558\pi\)
0.00662411 + 0.999978i \(0.497891\pi\)
\(864\) 13.5745 24.4264i 0.461814 0.831004i
\(865\) −27.7219 27.7219i −0.942574 0.942574i
\(866\) 2.53950 + 9.47753i 0.0862956 + 0.322060i
\(867\) 1.30789 + 14.0651i 0.0444184 + 0.477674i
\(868\) −6.03881 + 27.6759i −0.204971 + 0.939382i
\(869\) −44.4830 11.9192i −1.50898 0.404330i
\(870\) −0.0239158 0.257191i −0.000810823 0.00871957i
\(871\) −16.7928 + 17.7292i −0.569001 + 0.600730i
\(872\) −25.2702 + 14.5897i −0.855756 + 0.494071i
\(873\) −7.76836 16.1956i −0.262919 0.548137i
\(874\) 6.96672 + 12.0667i 0.235653 + 0.408163i
\(875\) −9.78388 + 10.7490i −0.330756 + 0.363383i
\(876\) −1.52465 + 8.93141i −0.0515133 + 0.301764i
\(877\) 45.5542 + 12.2062i 1.53826 + 0.412174i 0.925702 0.378254i \(-0.123475\pi\)
0.612554 + 0.790429i \(0.290142\pi\)
\(878\) −6.50558 + 6.50558i −0.219553 + 0.219553i
\(879\) 35.7250 13.2240i 1.20497 0.446035i
\(880\) −17.0472 29.5266i −0.574660 0.995340i
\(881\) 1.74590 + 3.02399i 0.0588209 + 0.101881i 0.893936 0.448194i \(-0.147933\pi\)
−0.835115 + 0.550075i \(0.814599\pi\)
\(882\) −10.3154 5.71618i −0.347338 0.192474i
\(883\) 52.2309i 1.75771i −0.477090 0.878855i \(-0.658308\pi\)
0.477090 0.878855i \(-0.341692\pi\)
\(884\) 15.3931 9.45279i 0.517726 0.317932i
\(885\) 8.46335 + 3.89046i 0.284493 + 0.130776i
\(886\) 2.85377 + 10.6504i 0.0958743 + 0.357808i
\(887\) 1.47235i 0.0494367i −0.999694 0.0247183i \(-0.992131\pi\)
0.999694 0.0247183i \(-0.00786889\pi\)
\(888\) 0.497390 + 5.34893i 0.0166913 + 0.179498i
\(889\) −8.74097 + 5.60969i −0.293163 + 0.188143i
\(890\) 13.7897 3.69493i 0.462230 0.123854i
\(891\) 24.1239 + 32.9005i 0.808182 + 1.10221i
\(892\) −5.18671 + 19.3571i −0.173664 + 0.648122i
\(893\) 74.0247i 2.47714i
\(894\) 4.58975 + 6.47932i 0.153504 + 0.216701i
\(895\) −8.23834 + 30.7459i −0.275377 + 1.02772i
\(896\) 20.5500 22.5771i 0.686527 0.754249i
\(897\) −18.5908 + 13.9413i −0.620730 + 0.465487i
\(898\) −3.35599 + 5.81275i −0.111991 + 0.193974i
\(899\) 0.478393 0.128185i 0.0159553 0.00427521i
\(900\) 21.7580 + 25.3630i 0.725268 + 0.845432i
\(901\) 7.29110 4.20952i 0.242902 0.140239i
\(902\) 5.99290 + 5.99290i 0.199542 + 0.199542i
\(903\) 9.62973 23.8389i 0.320457 0.793309i
\(904\) 8.98809 2.40835i 0.298939 0.0801006i
\(905\) −13.1740 49.1659i −0.437917 1.63433i
\(906\) −9.05172 12.7783i −0.300723 0.424529i
\(907\) 34.6454 + 20.0025i 1.15038 + 0.664173i 0.948980 0.315336i \(-0.102117\pi\)
0.201401 + 0.979509i \(0.435451\pi\)
\(908\) −29.6830 + 29.6830i −0.985063 + 0.985063i
\(909\) 7.62537 21.6838i 0.252918 0.719207i
\(910\) 1.35127 + 18.2054i 0.0447942 + 0.603505i
\(911\) 40.8487i 1.35338i −0.736269 0.676689i \(-0.763414\pi\)
0.736269 0.676689i \(-0.236586\pi\)
\(912\) −4.28942 + 25.1273i −0.142037 + 0.832050i
\(913\) −17.6232 + 30.5242i −0.583242 + 1.01020i
\(914\) 4.99012 0.165058
\(915\) 22.0899 26.6193i 0.730269 0.880007i
\(916\) 0.342360 + 1.27771i 0.0113119 + 0.0422166i
\(917\) 26.1454 + 13.4997i 0.863396 + 0.445801i
\(918\) 4.21558 7.58566i 0.139135 0.250364i
\(919\) −18.4596 31.9729i −0.608926 1.05469i −0.991418 0.130731i \(-0.958267\pi\)
0.382492 0.923959i \(-0.375066\pi\)
\(920\) 13.1188 22.7224i 0.432513 0.749134i
\(921\) 20.7351 24.9867i 0.683244 0.823340i
\(922\) 12.9492 + 7.47625i 0.426460 + 0.246217i
\(923\) 32.8817 + 31.1450i 1.08231 + 1.02515i
\(924\) 13.6755 + 32.2116i 0.449891 + 1.05968i
\(925\) −9.57311 2.56511i −0.314762 0.0843402i
\(926\) 1.20810i 0.0397006i
\(927\) −15.9426 5.60640i −0.523624 0.184138i
\(928\) −0.404813 0.108469i −0.0132886 0.00356068i
\(929\) 1.86510 6.96066i 0.0611920 0.228372i −0.928557 0.371190i \(-0.878950\pi\)
0.989749 + 0.142818i \(0.0456165\pi\)
\(930\) 13.4528 16.2113i 0.441136 0.531588i
\(931\) 46.0188 + 7.79814i 1.50821 + 0.255574i
\(932\) −0.311421 0.179799i −0.0102009 0.00588951i
\(933\) 34.3157 24.3082i 1.12345 0.795815i
\(934\) −6.82287 + 1.82818i −0.223251 + 0.0598200i
\(935\) −22.9694 39.7842i −0.751181 1.30108i
\(936\) 22.3551 + 1.10158i 0.730699 + 0.0360063i
\(937\) −20.3231 −0.663928 −0.331964 0.943292i \(-0.607711\pi\)
−0.331964 + 0.943292i \(0.607711\pi\)
\(938\) −4.61685 + 8.94159i −0.150745 + 0.291953i
\(939\) 16.8333 + 7.73796i 0.549333 + 0.252519i
\(940\) 55.1926 31.8655i 1.80018 1.03934i
\(941\) 11.0104 41.0914i 0.358929 1.33954i −0.516539 0.856264i \(-0.672780\pi\)
0.875468 0.483276i \(-0.160553\pi\)
\(942\) −8.91485 1.52183i −0.290462 0.0495838i
\(943\) 3.20628 11.9660i 0.104411 0.389666i
\(944\) 2.46307 2.46307i 0.0801660 0.0801660i
\(945\) −25.9447 39.0073i −0.843983 1.26891i
\(946\) 12.3690 7.14123i 0.402150 0.232182i
\(947\) −28.0164 + 28.0164i −0.910410 + 0.910410i −0.996304 0.0858945i \(-0.972625\pi\)
0.0858945 + 0.996304i \(0.472625\pi\)
\(948\) 12.3810 26.9338i 0.402116 0.874770i
\(949\) −10.7320 + 3.18994i −0.348377 + 0.103550i
\(950\) 21.4425 + 12.3799i 0.695688 + 0.401656i
\(951\) 5.49265 + 14.8385i 0.178111 + 0.481173i
\(952\) 10.9595 12.0406i 0.355201 0.390239i
\(953\) −9.75016 + 16.8878i −0.315839 + 0.547048i −0.979615 0.200882i \(-0.935619\pi\)
0.663777 + 0.747931i \(0.268952\pi\)
\(954\) 4.75551 + 0.363815i 0.153965 + 0.0117789i
\(955\) 9.63612 9.63612i 0.311817 0.311817i
\(956\) 0.746139 0.746139i 0.0241318 0.0241318i
\(957\) 0.390720 0.470835i 0.0126302 0.0152199i
\(958\) 3.84118 6.65313i 0.124103 0.214953i
\(959\) −15.6426 + 17.1857i −0.505127 + 0.554955i
\(960\) 7.71692 2.85650i 0.249063 0.0921932i
\(961\) 8.13426 + 4.69632i 0.262396 + 0.151494i
\(962\) −2.58625 + 1.58820i −0.0833840 + 0.0512055i
\(963\) 1.33641 + 7.12372i 0.0430651 + 0.229559i
\(964\) 9.74708 9.74708i 0.313932 0.313932i
\(965\) −47.8574 + 27.6305i −1.54059 + 0.889457i
\(966\) −5.76247 + 7.64809i −0.185404 + 0.246073i
\(967\) 14.5491 14.5491i 0.467869 0.467869i −0.433354 0.901224i \(-0.642670\pi\)
0.901224 + 0.433354i \(0.142670\pi\)
\(968\) −5.11362 + 19.0843i −0.164358 + 0.613392i
\(969\) −5.77958 + 33.8567i −0.185667 + 1.08763i
\(970\) −2.96558 + 11.0677i −0.0952191 + 0.355363i
\(971\) 48.3453 27.9121i 1.55147 0.895743i 0.553451 0.832882i \(-0.313311\pi\)
0.998022 0.0628617i \(-0.0200227\pi\)
\(972\) −23.4887 + 11.7432i −0.753399 + 0.376665i
\(973\) 1.31662 2.54994i 0.0422090 0.0817474i
\(974\) 4.23285 0.135629
\(975\) −16.2231 + 37.9726i −0.519553 + 1.21610i
\(976\) −6.46781 11.2026i −0.207029 0.358585i
\(977\) 4.36439 1.16943i 0.139629 0.0374135i −0.188328 0.982106i \(-0.560307\pi\)
0.327957 + 0.944693i \(0.393640\pi\)
\(978\) 3.52095 + 4.97050i 0.112587 + 0.158939i
\(979\) 29.2856 + 16.9080i 0.935970 + 0.540383i
\(980\) −13.9955 37.6684i −0.447069 1.20327i
\(981\) 42.1815 + 3.22704i 1.34675 + 0.103032i
\(982\) −4.80183 + 17.9207i −0.153233 + 0.571872i
\(983\) 29.3716 + 7.87010i 0.936809 + 0.251017i 0.694756 0.719246i \(-0.255512\pi\)
0.242053 + 0.970263i \(0.422179\pi\)
\(984\) −9.73676 + 6.89722i −0.310397 + 0.219875i
\(985\) 10.4320i 0.332391i
\(986\) −0.125715 0.0336853i −0.00400359 0.00107276i
\(987\) −46.8291 + 19.8814i −1.49059 + 0.632831i
\(988\) −38.8217 + 11.5392i −1.23508 + 0.367109i
\(989\) −18.0795 10.4382i −0.574894 0.331915i
\(990\) 1.98517 25.9486i 0.0630929 0.824702i
\(991\) 9.16702 15.8777i 0.291200 0.504373i −0.682894 0.730518i \(-0.739279\pi\)
0.974094 + 0.226144i \(0.0726121\pi\)
\(992\) −17.0900 29.6007i −0.542607 0.939824i
\(993\) 6.96717 40.8136i 0.221096 1.29518i
\(994\) 16.5837 + 8.56271i 0.526002 + 0.271593i
\(995\) 7.54026 + 28.1407i 0.239042 + 0.892119i
\(996\) −17.4590 14.4883i −0.553211 0.459079i
\(997\) −2.21851 −0.0702608 −0.0351304 0.999383i \(-0.511185\pi\)
−0.0351304 + 0.999383i \(0.511185\pi\)
\(998\) 4.76892 8.26002i 0.150958 0.261466i
\(999\) 3.78328 6.80777i 0.119698 0.215388i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 273.2.bv.b.2.19 yes 128
3.2 odd 2 inner 273.2.bv.b.2.14 128
7.4 even 3 273.2.bw.b.158.14 yes 128
13.7 odd 12 273.2.bw.b.254.19 yes 128
21.11 odd 6 273.2.bw.b.158.19 yes 128
39.20 even 12 273.2.bw.b.254.14 yes 128
91.46 odd 12 inner 273.2.bv.b.137.14 yes 128
273.137 even 12 inner 273.2.bv.b.137.19 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bv.b.2.14 128 3.2 odd 2 inner
273.2.bv.b.2.19 yes 128 1.1 even 1 trivial
273.2.bv.b.137.14 yes 128 91.46 odd 12 inner
273.2.bv.b.137.19 yes 128 273.137 even 12 inner
273.2.bw.b.158.14 yes 128 7.4 even 3
273.2.bw.b.158.19 yes 128 21.11 odd 6
273.2.bw.b.254.14 yes 128 39.20 even 12
273.2.bw.b.254.19 yes 128 13.7 odd 12