Properties

Label 252.2.bi.c.139.19
Level $252$
Weight $2$
Character 252.139
Analytic conductor $2.012$
Analytic rank $0$
Dimension $80$
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] = [252,2,Mod(139,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.139");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bi (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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 139.19
Character \(\chi\) \(=\) 252.139
Dual form 252.2.bi.c.223.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.161186 - 1.40500i) q^{2} +(-1.59413 - 0.677299i) q^{3} +(-1.94804 + 0.452933i) q^{4} +(-1.43245 - 0.827025i) q^{5} +(-0.694651 + 2.34893i) q^{6} +(0.0302588 - 2.64558i) q^{7} +(0.950366 + 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +O(q^{10})\) \(q+(-0.161186 - 1.40500i) q^{2} +(-1.59413 - 0.677299i) q^{3} +(-1.94804 + 0.452933i) q^{4} +(-1.43245 - 0.827025i) q^{5} +(-0.694651 + 2.34893i) q^{6} +(0.0302588 - 2.64558i) q^{7} +(0.950366 + 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +(-0.931077 + 2.14589i) q^{10} +(-4.24842 + 2.45282i) q^{11} +(3.41221 + 0.597369i) q^{12} +(0.876334 + 0.505952i) q^{13} +(-3.72191 + 0.383917i) q^{14} +(1.72337 + 2.28859i) q^{15} +(3.58970 - 1.76466i) q^{16} +7.66107i q^{17} +(2.69829 - 3.27402i) q^{18} -2.85119 q^{19} +(3.16505 + 0.962273i) q^{20} +(-1.84008 + 4.19691i) q^{21} +(4.13100 + 5.57365i) q^{22} +(-1.98118 - 1.14384i) q^{23} +(0.289302 - 4.89043i) q^{24} +(-1.13206 - 1.96079i) q^{25} +(0.569608 - 1.31280i) q^{26} +(-1.85727 - 4.85289i) q^{27} +(1.13932 + 5.16739i) q^{28} +(-4.19857 - 7.27213i) q^{29} +(2.93767 - 2.79022i) q^{30} +(0.348784 - 0.604112i) q^{31} +(-3.05795 - 4.75909i) q^{32} +(8.43384 - 1.03268i) q^{33} +(10.7638 - 1.23486i) q^{34} +(-2.23130 + 3.76463i) q^{35} +(-5.03492 - 3.26337i) q^{36} +3.97490 q^{37} +(0.459573 + 4.00592i) q^{38} +(-1.05431 - 1.40010i) q^{39} +(0.841829 - 4.60200i) q^{40} +(-6.69947 - 3.86794i) q^{41} +(6.19325 + 1.90883i) q^{42} +(-6.70811 + 3.87293i) q^{43} +(7.16511 - 6.70244i) q^{44} +(-1.19723 - 4.81555i) q^{45} +(-1.28775 + 2.96793i) q^{46} +(3.70722 + 6.42109i) q^{47} +(-6.91767 + 0.381802i) q^{48} +(-6.99817 - 0.160104i) q^{49} +(-2.57243 + 1.90659i) q^{50} +(5.18884 - 12.2128i) q^{51} +(-1.93629 - 0.588693i) q^{52} -8.61878 q^{53} +(-6.51894 + 3.39168i) q^{54} +8.11418 q^{55} +(7.07653 - 2.43366i) q^{56} +(4.54518 + 1.93111i) q^{57} +(-9.54058 + 7.07115i) q^{58} +(2.54378 - 4.40596i) q^{59} +(-4.39377 - 3.67768i) q^{60} +(-5.12759 + 2.96042i) q^{61} +(-0.904996 - 0.392667i) q^{62} +(5.77591 - 5.44416i) q^{63} +(-6.19361 + 5.06352i) q^{64} +(-0.836869 - 1.44950i) q^{65} +(-2.81034 - 11.6831i) q^{66} +(2.18590 + 1.26203i) q^{67} +(-3.46995 - 14.9241i) q^{68} +(2.38355 + 3.16528i) q^{69} +(5.64895 + 2.52817i) q^{70} +1.00362i q^{71} +(-3.77347 + 7.60006i) q^{72} -5.89658i q^{73} +(-0.640700 - 5.58473i) q^{74} +(0.476618 + 3.89250i) q^{75} +(5.55423 - 1.29140i) q^{76} +(6.36058 + 11.3137i) q^{77} +(-1.79719 + 1.70698i) q^{78} +(4.90752 - 2.83336i) q^{79} +(-6.60149 - 0.440989i) q^{80} +(-0.326126 + 8.99409i) q^{81} +(-4.35458 + 10.0362i) q^{82} +(-1.20736 - 2.09120i) q^{83} +(1.68364 - 9.00918i) q^{84} +(6.33589 - 10.9741i) q^{85} +(6.52272 + 8.80062i) q^{86} +(1.76767 + 14.4364i) q^{87} +(-10.5718 - 8.98662i) q^{88} -8.19734i q^{89} +(-6.57286 + 2.45831i) q^{90} +(1.36505 - 2.30310i) q^{91} +(4.37750 + 1.33089i) q^{92} +(-0.965174 + 0.726805i) q^{93} +(8.42407 - 6.24363i) q^{94} +(4.08418 + 2.35800i) q^{95} +(1.65146 + 9.65778i) q^{96} +(8.82136 - 5.09301i) q^{97} +(0.903062 + 9.85822i) q^{98} +(-14.1441 - 4.06600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.161186 1.40500i −0.113976 0.993484i
\(3\) −1.59413 0.677299i −0.920374 0.391039i
\(4\) −1.94804 + 0.452933i −0.974019 + 0.226466i
\(5\) −1.43245 0.827025i −0.640611 0.369857i 0.144239 0.989543i \(-0.453927\pi\)
−0.784850 + 0.619686i \(0.787260\pi\)
\(6\) −0.694651 + 2.34893i −0.283590 + 0.958946i
\(7\) 0.0302588 2.64558i 0.0114368 0.999935i
\(8\) 0.950366 + 2.66398i 0.336005 + 0.941860i
\(9\) 2.08253 + 2.15941i 0.694177 + 0.719804i
\(10\) −0.931077 + 2.14589i −0.294432 + 0.678591i
\(11\) −4.24842 + 2.45282i −1.28095 + 0.739554i −0.977021 0.213142i \(-0.931630\pi\)
−0.303924 + 0.952696i \(0.598297\pi\)
\(12\) 3.41221 + 0.597369i 0.985019 + 0.172446i
\(13\) 0.876334 + 0.505952i 0.243051 + 0.140326i 0.616578 0.787294i \(-0.288518\pi\)
−0.373527 + 0.927619i \(0.621852\pi\)
\(14\) −3.72191 + 0.383917i −0.994722 + 0.102606i
\(15\) 1.72337 + 2.28859i 0.444973 + 0.590910i
\(16\) 3.58970 1.76466i 0.897426 0.441165i
\(17\) 7.66107i 1.85808i 0.369976 + 0.929041i \(0.379366\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(18\) 2.69829 3.27402i 0.635994 0.771694i
\(19\) −2.85119 −0.654108 −0.327054 0.945006i \(-0.606056\pi\)
−0.327054 + 0.945006i \(0.606056\pi\)
\(20\) 3.16505 + 0.962273i 0.707727 + 0.215171i
\(21\) −1.84008 + 4.19691i −0.401539 + 0.915842i
\(22\) 4.13100 + 5.57365i 0.880732 + 1.18831i
\(23\) −1.98118 1.14384i −0.413105 0.238506i 0.279018 0.960286i \(-0.409991\pi\)
−0.692123 + 0.721780i \(0.743324\pi\)
\(24\) 0.289302 4.89043i 0.0590534 0.998255i
\(25\) −1.13206 1.96079i −0.226412 0.392157i
\(26\) 0.569608 1.31280i 0.111709 0.257461i
\(27\) −1.85727 4.85289i −0.357431 0.933939i
\(28\) 1.13932 + 5.16739i 0.215312 + 0.976545i
\(29\) −4.19857 7.27213i −0.779654 1.35040i −0.932141 0.362096i \(-0.882061\pi\)
0.152486 0.988306i \(-0.451272\pi\)
\(30\) 2.93767 2.79022i 0.536343 0.509423i
\(31\) 0.348784 0.604112i 0.0626435 0.108502i −0.833003 0.553269i \(-0.813380\pi\)
0.895646 + 0.444767i \(0.146714\pi\)
\(32\) −3.05795 4.75909i −0.540575 0.841296i
\(33\) 8.43384 1.03268i 1.46814 0.179767i
\(34\) 10.7638 1.23486i 1.84597 0.211777i
\(35\) −2.23130 + 3.76463i −0.377159 + 0.636339i
\(36\) −5.03492 3.26337i −0.839153 0.543895i
\(37\) 3.97490 0.653470 0.326735 0.945116i \(-0.394051\pi\)
0.326735 + 0.945116i \(0.394051\pi\)
\(38\) 0.459573 + 4.00592i 0.0745525 + 0.649845i
\(39\) −1.05431 1.40010i −0.168825 0.224195i
\(40\) 0.841829 4.60200i 0.133105 0.727639i
\(41\) −6.69947 3.86794i −1.04628 0.604071i −0.124675 0.992198i \(-0.539789\pi\)
−0.921606 + 0.388127i \(0.873122\pi\)
\(42\) 6.19325 + 1.90883i 0.955639 + 0.294539i
\(43\) −6.70811 + 3.87293i −1.02298 + 0.590617i −0.914965 0.403533i \(-0.867782\pi\)
−0.108013 + 0.994150i \(0.534449\pi\)
\(44\) 7.16511 6.70244i 1.08018 1.01043i
\(45\) −1.19723 4.81555i −0.178473 0.717860i
\(46\) −1.28775 + 2.96793i −0.189868 + 0.437597i
\(47\) 3.70722 + 6.42109i 0.540754 + 0.936613i 0.998861 + 0.0477158i \(0.0151942\pi\)
−0.458107 + 0.888897i \(0.651472\pi\)
\(48\) −6.91767 + 0.381802i −0.998480 + 0.0551084i
\(49\) −6.99817 0.160104i −0.999738 0.0228720i
\(50\) −2.57243 + 1.90659i −0.363796 + 0.269633i
\(51\) 5.18884 12.2128i 0.726582 1.71013i
\(52\) −1.93629 0.588693i −0.268516 0.0816370i
\(53\) −8.61878 −1.18388 −0.591940 0.805982i \(-0.701638\pi\)
−0.591940 + 0.805982i \(0.701638\pi\)
\(54\) −6.51894 + 3.39168i −0.887115 + 0.461549i
\(55\) 8.11418 1.09412
\(56\) 7.07653 2.43366i 0.945641 0.325211i
\(57\) 4.54518 + 1.93111i 0.602024 + 0.255782i
\(58\) −9.54058 + 7.07115i −1.25274 + 0.928487i
\(59\) 2.54378 4.40596i 0.331172 0.573607i −0.651570 0.758589i \(-0.725889\pi\)
0.982742 + 0.184981i \(0.0592225\pi\)
\(60\) −4.39377 3.67768i −0.567234 0.474786i
\(61\) −5.12759 + 2.96042i −0.656521 + 0.379042i −0.790950 0.611881i \(-0.790413\pi\)
0.134429 + 0.990923i \(0.457080\pi\)
\(62\) −0.904996 0.392667i −0.114935 0.0498687i
\(63\) 5.77591 5.44416i 0.727696 0.685900i
\(64\) −6.19361 + 5.06352i −0.774201 + 0.632940i
\(65\) −0.836869 1.44950i −0.103801 0.179788i
\(66\) −2.81034 11.6831i −0.345929 1.43809i
\(67\) 2.18590 + 1.26203i 0.267051 + 0.154182i 0.627547 0.778579i \(-0.284059\pi\)
−0.360496 + 0.932761i \(0.617393\pi\)
\(68\) −3.46995 14.9241i −0.420793 1.80981i
\(69\) 2.38355 + 3.16528i 0.286946 + 0.381055i
\(70\) 5.64895 + 2.52817i 0.675179 + 0.302174i
\(71\) 1.00362i 0.119108i 0.998225 + 0.0595539i \(0.0189678\pi\)
−0.998225 + 0.0595539i \(0.981032\pi\)
\(72\) −3.77347 + 7.60006i −0.444708 + 0.895676i
\(73\) 5.89658i 0.690142i −0.938577 0.345071i \(-0.887855\pi\)
0.938577 0.345071i \(-0.112145\pi\)
\(74\) −0.640700 5.58473i −0.0744799 0.649212i
\(75\) 0.476618 + 3.89250i 0.0550351 + 0.449467i
\(76\) 5.55423 1.29140i 0.637113 0.148133i
\(77\) 6.36058 + 11.3137i 0.724856 + 1.28932i
\(78\) −1.79719 + 1.70698i −0.203492 + 0.193278i
\(79\) 4.90752 2.83336i 0.552139 0.318778i −0.197845 0.980233i \(-0.563394\pi\)
0.749984 + 0.661456i \(0.230061\pi\)
\(80\) −6.60149 0.440989i −0.738069 0.0493041i
\(81\) −0.326126 + 8.99409i −0.0362362 + 0.999343i
\(82\) −4.35458 + 10.0362i −0.480883 + 1.10831i
\(83\) −1.20736 2.09120i −0.132525 0.229539i 0.792125 0.610359i \(-0.208975\pi\)
−0.924649 + 0.380820i \(0.875642\pi\)
\(84\) 1.68364 9.00918i 0.183700 0.982982i
\(85\) 6.33589 10.9741i 0.687224 1.19031i
\(86\) 6.52272 + 8.80062i 0.703363 + 0.948996i
\(87\) 1.76767 + 14.4364i 0.189514 + 1.54775i
\(88\) −10.5718 8.98662i −1.12696 0.957977i
\(89\) 8.19734i 0.868916i −0.900692 0.434458i \(-0.856940\pi\)
0.900692 0.434458i \(-0.143060\pi\)
\(90\) −6.57286 + 2.45831i −0.692841 + 0.259129i
\(91\) 1.36505 2.30310i 0.143096 0.241431i
\(92\) 4.37750 + 1.33089i 0.456386 + 0.138755i
\(93\) −0.965174 + 0.726805i −0.100084 + 0.0753662i
\(94\) 8.42407 6.24363i 0.868876 0.643981i
\(95\) 4.08418 + 2.35800i 0.419028 + 0.241926i
\(96\) 1.65146 + 9.65778i 0.168552 + 0.985693i
\(97\) 8.82136 5.09301i 0.895673 0.517117i 0.0198794 0.999802i \(-0.493672\pi\)
0.875794 + 0.482685i \(0.160338\pi\)
\(98\) 0.903062 + 9.85822i 0.0912231 + 0.995830i
\(99\) −14.1441 4.06600i −1.42154 0.408648i
\(100\) 3.09340 + 3.30694i 0.309340 + 0.330694i
\(101\) −0.846450 + 0.488698i −0.0842249 + 0.0486273i −0.541521 0.840687i \(-0.682151\pi\)
0.457296 + 0.889315i \(0.348818\pi\)
\(102\) −17.9953 5.32177i −1.78180 0.526934i
\(103\) −6.53514 + 11.3192i −0.643926 + 1.11531i 0.340622 + 0.940200i \(0.389362\pi\)
−0.984548 + 0.175113i \(0.943971\pi\)
\(104\) −0.515008 + 2.81538i −0.0505007 + 0.276071i
\(105\) 6.10678 4.49007i 0.595961 0.438186i
\(106\) 1.38923 + 12.1094i 0.134934 + 1.17617i
\(107\) 1.03143i 0.0997116i 0.998756 + 0.0498558i \(0.0158762\pi\)
−0.998756 + 0.0498558i \(0.984124\pi\)
\(108\) 5.81606 + 8.61240i 0.559651 + 0.828729i
\(109\) −0.842410 −0.0806882 −0.0403441 0.999186i \(-0.512845\pi\)
−0.0403441 + 0.999186i \(0.512845\pi\)
\(110\) −1.30789 11.4004i −0.124703 1.08699i
\(111\) −6.33653 2.69220i −0.601437 0.255532i
\(112\) −4.55993 9.55024i −0.430872 0.902413i
\(113\) 3.19162 5.52804i 0.300242 0.520035i −0.675949 0.736949i \(-0.736266\pi\)
0.976191 + 0.216914i \(0.0695992\pi\)
\(114\) 1.98058 6.69724i 0.185499 0.627254i
\(115\) 1.89196 + 3.27697i 0.176426 + 0.305579i
\(116\) 11.4728 + 12.2647i 1.06522 + 1.13875i
\(117\) 0.732435 + 2.94603i 0.0677136 + 0.272360i
\(118\) −6.60039 2.86383i −0.607615 0.263637i
\(119\) 20.2680 + 0.231815i 1.85796 + 0.0212505i
\(120\) −4.45892 + 6.76603i −0.407042 + 0.617651i
\(121\) 6.53269 11.3149i 0.593881 1.02863i
\(122\) 4.98587 + 6.72707i 0.451400 + 0.609041i
\(123\) 8.06010 + 10.7036i 0.726755 + 0.965108i
\(124\) −0.405823 + 1.33481i −0.0364440 + 0.119869i
\(125\) 12.0152i 1.07467i
\(126\) −8.58003 7.23762i −0.764370 0.644778i
\(127\) 17.9070i 1.58899i −0.607272 0.794494i \(-0.707736\pi\)
0.607272 0.794494i \(-0.292264\pi\)
\(128\) 8.11256 + 7.88584i 0.717056 + 0.697016i
\(129\) 13.3168 1.63057i 1.17248 0.143564i
\(130\) −1.90165 + 1.40944i −0.166786 + 0.123616i
\(131\) 5.02346 8.70089i 0.438902 0.760200i −0.558703 0.829368i \(-0.688701\pi\)
0.997605 + 0.0691675i \(0.0220343\pi\)
\(132\) −15.9617 + 5.83167i −1.38929 + 0.507582i
\(133\) −0.0862737 + 7.54305i −0.00748088 + 0.654065i
\(134\) 1.42081 3.27461i 0.122740 0.282883i
\(135\) −1.35302 + 8.48753i −0.116450 + 0.730490i
\(136\) −20.4090 + 7.28082i −1.75005 + 0.624325i
\(137\) 1.97707 + 3.42439i 0.168913 + 0.292566i 0.938038 0.346533i \(-0.112641\pi\)
−0.769125 + 0.639098i \(0.779308\pi\)
\(138\) 4.06302 3.85909i 0.345867 0.328507i
\(139\) −4.85060 + 8.40148i −0.411422 + 0.712605i −0.995046 0.0994201i \(-0.968301\pi\)
0.583623 + 0.812025i \(0.301635\pi\)
\(140\) 2.64154 8.34427i 0.223251 0.705220i
\(141\) −1.56081 12.7470i −0.131444 1.07349i
\(142\) 1.41008 0.161770i 0.118332 0.0135754i
\(143\) −4.96404 −0.415114
\(144\) 11.2863 + 4.07669i 0.940525 + 0.339724i
\(145\) 13.8893i 1.15344i
\(146\) −8.28468 + 0.950447i −0.685645 + 0.0786596i
\(147\) 11.0476 + 4.99508i 0.911190 + 0.411987i
\(148\) −7.74327 + 1.80036i −0.636493 + 0.147989i
\(149\) −3.46856 + 6.00773i −0.284156 + 0.492172i −0.972404 0.233303i \(-0.925047\pi\)
0.688248 + 0.725475i \(0.258380\pi\)
\(150\) 5.39213 1.29706i 0.440266 0.105905i
\(151\) −10.8500 + 6.26427i −0.882964 + 0.509779i −0.871635 0.490156i \(-0.836940\pi\)
−0.0113294 + 0.999936i \(0.503606\pi\)
\(152\) −2.70967 7.59552i −0.219784 0.616078i
\(153\) −16.5434 + 15.9544i −1.33746 + 1.28984i
\(154\) 14.8705 10.7602i 1.19830 0.867084i
\(155\) −0.999232 + 0.576907i −0.0802602 + 0.0463383i
\(156\) 2.68799 + 2.24991i 0.215212 + 0.180137i
\(157\) −1.44619 0.834956i −0.115418 0.0666367i 0.441180 0.897419i \(-0.354560\pi\)
−0.556598 + 0.830782i \(0.687894\pi\)
\(158\) −4.77189 6.43836i −0.379631 0.512208i
\(159\) 13.7395 + 5.83749i 1.08961 + 0.462943i
\(160\) 0.444480 + 9.34615i 0.0351392 + 0.738878i
\(161\) −3.08606 + 5.20676i −0.243215 + 0.410350i
\(162\) 12.6892 0.991517i 0.996961 0.0779010i
\(163\) 7.06914i 0.553698i 0.960913 + 0.276849i \(0.0892901\pi\)
−0.960913 + 0.276849i \(0.910710\pi\)
\(164\) 14.8027 + 4.50048i 1.15590 + 0.351429i
\(165\) −12.9351 5.49573i −1.00700 0.427842i
\(166\) −2.74352 + 2.03341i −0.212939 + 0.157823i
\(167\) −0.578614 + 1.00219i −0.0447745 + 0.0775518i −0.887544 0.460723i \(-0.847590\pi\)
0.842770 + 0.538274i \(0.180924\pi\)
\(168\) −12.9293 0.913349i −0.997514 0.0704664i
\(169\) −5.98803 10.3716i −0.460617 0.797813i
\(170\) −16.4398 7.13305i −1.26088 0.547080i
\(171\) −5.93769 6.15689i −0.454067 0.470830i
\(172\) 11.3135 10.5829i 0.862645 0.806942i
\(173\) 1.30347 0.752561i 0.0991013 0.0572162i −0.449630 0.893215i \(-0.648444\pi\)
0.548732 + 0.835999i \(0.315111\pi\)
\(174\) 19.9983 4.81053i 1.51606 0.364686i
\(175\) −5.22167 + 2.93562i −0.394721 + 0.221912i
\(176\) −10.9222 + 16.3019i −0.823288 + 1.22880i
\(177\) −7.03929 + 5.30080i −0.529105 + 0.398432i
\(178\) −11.5172 + 1.32130i −0.863254 + 0.0990355i
\(179\) 1.28088i 0.0957374i 0.998854 + 0.0478687i \(0.0152429\pi\)
−0.998854 + 0.0478687i \(0.984757\pi\)
\(180\) 4.51338 + 8.83862i 0.336407 + 0.658792i
\(181\) 26.6202i 1.97866i −0.145683 0.989331i \(-0.546538\pi\)
0.145683 0.989331i \(-0.453462\pi\)
\(182\) −3.45588 1.54667i −0.256167 0.114647i
\(183\) 10.1792 1.24639i 0.752465 0.0921357i
\(184\) 1.16431 6.36490i 0.0858341 0.469227i
\(185\) −5.69385 3.28734i −0.418620 0.241690i
\(186\) 1.17673 + 1.23892i 0.0862822 + 0.0908418i
\(187\) −18.7913 32.5474i −1.37415 2.38010i
\(188\) −10.1301 10.8294i −0.738815 0.789816i
\(189\) −12.8949 + 4.76670i −0.937966 + 0.346727i
\(190\) 2.65468 6.11835i 0.192591 0.443872i
\(191\) −7.44229 + 4.29681i −0.538506 + 0.310906i −0.744473 0.667653i \(-0.767299\pi\)
0.205968 + 0.978559i \(0.433966\pi\)
\(192\) 13.3030 3.87701i 0.960059 0.279799i
\(193\) −3.80654 + 6.59312i −0.274001 + 0.474583i −0.969882 0.243573i \(-0.921680\pi\)
0.695882 + 0.718156i \(0.255014\pi\)
\(194\) −8.57756 11.5731i −0.615833 0.830898i
\(195\) 0.352337 + 2.87751i 0.0252314 + 0.206063i
\(196\) 13.7052 2.85781i 0.978944 0.204129i
\(197\) 14.3946 1.02557 0.512786 0.858517i \(-0.328614\pi\)
0.512786 + 0.858517i \(0.328614\pi\)
\(198\) −3.43288 + 20.5278i −0.243964 + 1.45885i
\(199\) 21.9194 1.55382 0.776911 0.629610i \(-0.216785\pi\)
0.776911 + 0.629610i \(0.216785\pi\)
\(200\) 4.14763 4.87925i 0.293282 0.345015i
\(201\) −2.62985 3.49236i −0.185495 0.246332i
\(202\) 0.823056 + 1.11049i 0.0579100 + 0.0781337i
\(203\) −19.3660 + 10.8876i −1.35923 + 0.764159i
\(204\) −4.57649 + 26.1411i −0.320418 + 1.83025i
\(205\) 6.39776 + 11.0813i 0.446839 + 0.773948i
\(206\) 16.9568 + 7.35736i 1.18144 + 0.512611i
\(207\) −1.65586 6.66026i −0.115090 0.462920i
\(208\) 4.03861 + 0.269785i 0.280027 + 0.0187062i
\(209\) 12.1130 6.99347i 0.837876 0.483748i
\(210\) −7.29287 7.85627i −0.503256 0.542134i
\(211\) 1.45464 + 0.839838i 0.100142 + 0.0578168i 0.549234 0.835668i \(-0.314919\pi\)
−0.449093 + 0.893485i \(0.648253\pi\)
\(212\) 16.7897 3.90373i 1.15312 0.268109i
\(213\) 0.679751 1.59991i 0.0465758 0.109624i
\(214\) 1.44915 0.166252i 0.0990619 0.0113647i
\(215\) 12.8120 0.873774
\(216\) 11.1629 9.55975i 0.759542 0.650459i
\(217\) −1.58767 0.941016i −0.107778 0.0638803i
\(218\) 0.135785 + 1.18358i 0.00919651 + 0.0801624i
\(219\) −3.99375 + 9.39994i −0.269873 + 0.635189i
\(220\) −15.8067 + 3.67518i −1.06569 + 0.247780i
\(221\) −3.87613 + 6.71366i −0.260737 + 0.451609i
\(222\) −2.76117 + 9.33676i −0.185318 + 0.626642i
\(223\) 4.09002 + 7.08413i 0.273888 + 0.474388i 0.969854 0.243687i \(-0.0783568\pi\)
−0.695966 + 0.718075i \(0.745023\pi\)
\(224\) −12.6831 + 7.94605i −0.847423 + 0.530918i
\(225\) 1.87659 6.52798i 0.125106 0.435199i
\(226\) −8.28133 3.59317i −0.550866 0.239014i
\(227\) −13.5064 23.3937i −0.896450 1.55270i −0.832000 0.554776i \(-0.812804\pi\)
−0.0644498 0.997921i \(-0.520529\pi\)
\(228\) −9.72885 1.70321i −0.644309 0.112798i
\(229\) 10.4216 + 6.01689i 0.688677 + 0.397608i 0.803116 0.595823i \(-0.203174\pi\)
−0.114439 + 0.993430i \(0.536507\pi\)
\(230\) 4.29918 3.18640i 0.283480 0.210105i
\(231\) −2.47685 22.3436i −0.162964 1.47010i
\(232\) 15.3827 18.0961i 1.00992 1.18807i
\(233\) 12.9746 0.849992 0.424996 0.905195i \(-0.360276\pi\)
0.424996 + 0.905195i \(0.360276\pi\)
\(234\) 4.02110 1.50393i 0.262868 0.0983148i
\(235\) 12.2639i 0.800005i
\(236\) −2.95978 + 9.73514i −0.192665 + 0.633704i
\(237\) −9.74228 + 1.19290i −0.632829 + 0.0774869i
\(238\) −2.94122 28.5138i −0.190651 1.84828i
\(239\) −5.65067 3.26242i −0.365512 0.211028i 0.305984 0.952037i \(-0.401015\pi\)
−0.671496 + 0.741008i \(0.734348\pi\)
\(240\) 10.2250 + 5.17418i 0.660019 + 0.333992i
\(241\) −20.0162 + 11.5564i −1.28936 + 0.744410i −0.978539 0.206059i \(-0.933936\pi\)
−0.310817 + 0.950470i \(0.600603\pi\)
\(242\) −16.9505 7.35460i −1.08962 0.472772i
\(243\) 6.61158 14.1169i 0.424133 0.905600i
\(244\) 8.64787 8.08945i 0.553623 0.517874i
\(245\) 9.89211 + 6.01700i 0.631984 + 0.384412i
\(246\) 13.7393 13.0497i 0.875986 0.832018i
\(247\) −2.49859 1.44256i −0.158982 0.0917881i
\(248\) 1.94082 + 0.355028i 0.123242 + 0.0225443i
\(249\) 0.508319 + 4.15140i 0.0322134 + 0.263084i
\(250\) 16.8814 1.93669i 1.06767 0.122487i
\(251\) −5.55147 −0.350406 −0.175203 0.984532i \(-0.556058\pi\)
−0.175203 + 0.984532i \(0.556058\pi\)
\(252\) −8.78586 + 13.2215i −0.553457 + 0.832878i
\(253\) 11.2225 0.705553
\(254\) −25.1593 + 2.88636i −1.57863 + 0.181106i
\(255\) −17.5330 + 13.2029i −1.09796 + 0.826797i
\(256\) 9.77195 12.6692i 0.610747 0.791826i
\(257\) −16.9652 9.79486i −1.05826 0.610987i −0.133309 0.991074i \(-0.542560\pi\)
−0.924950 + 0.380088i \(0.875894\pi\)
\(258\) −4.43743 18.4472i −0.276263 1.14847i
\(259\) 0.120276 10.5159i 0.00747359 0.653428i
\(260\) 2.28678 + 2.44464i 0.141820 + 0.151610i
\(261\) 6.95989 24.2109i 0.430806 1.49862i
\(262\) −13.0344 5.65549i −0.805270 0.349397i
\(263\) 11.4745 6.62480i 0.707548 0.408503i −0.102605 0.994722i \(-0.532718\pi\)
0.810152 + 0.586219i \(0.199384\pi\)
\(264\) 10.7663 + 21.4862i 0.662619 + 1.32238i
\(265\) 12.3460 + 7.12794i 0.758406 + 0.437866i
\(266\) 10.6119 1.09462i 0.650655 0.0671155i
\(267\) −5.55205 + 13.0677i −0.339780 + 0.799728i
\(268\) −4.82984 1.46842i −0.295029 0.0896980i
\(269\) 23.5318i 1.43476i −0.696683 0.717379i \(-0.745342\pi\)
0.696683 0.717379i \(-0.254658\pi\)
\(270\) 12.1430 + 0.532920i 0.739002 + 0.0324325i
\(271\) −20.2947 −1.23281 −0.616406 0.787428i \(-0.711412\pi\)
−0.616406 + 0.787428i \(0.711412\pi\)
\(272\) 13.5192 + 27.5010i 0.819721 + 1.66749i
\(273\) −3.73596 + 2.74690i −0.226111 + 0.166250i
\(274\) 4.49259 3.32975i 0.271407 0.201157i
\(275\) 9.61892 + 5.55349i 0.580043 + 0.334888i
\(276\) −6.07691 5.08650i −0.365787 0.306171i
\(277\) 9.44902 + 16.3662i 0.567736 + 0.983348i 0.996789 + 0.0800689i \(0.0255140\pi\)
−0.429053 + 0.903279i \(0.641153\pi\)
\(278\) 12.5859 + 5.46088i 0.754853 + 0.327522i
\(279\) 2.03088 0.504913i 0.121586 0.0302284i
\(280\) −12.1495 2.36637i −0.726070 0.141418i
\(281\) −1.06714 1.84834i −0.0636602 0.110263i 0.832439 0.554117i \(-0.186944\pi\)
−0.896099 + 0.443854i \(0.853611\pi\)
\(282\) −17.6579 + 4.24757i −1.05151 + 0.252939i
\(283\) −0.122715 + 0.212549i −0.00729468 + 0.0126347i −0.869650 0.493669i \(-0.835655\pi\)
0.862355 + 0.506304i \(0.168989\pi\)
\(284\) −0.454572 1.95509i −0.0269739 0.116013i
\(285\) −4.91366 6.52519i −0.291060 0.386519i
\(286\) 0.800135 + 6.97447i 0.0473130 + 0.412409i
\(287\) −10.4357 + 17.6069i −0.615997 + 1.03930i
\(288\) 3.90855 16.5143i 0.230313 0.973117i
\(289\) −41.6920 −2.45247
\(290\) 19.5144 2.23876i 1.14593 0.131465i
\(291\) −17.5119 + 2.14425i −1.02657 + 0.125698i
\(292\) 2.67075 + 11.4868i 0.156294 + 0.672212i
\(293\) 9.64296 + 5.56736i 0.563347 + 0.325249i 0.754488 0.656314i \(-0.227885\pi\)
−0.191141 + 0.981563i \(0.561219\pi\)
\(294\) 5.23736 16.3270i 0.305449 0.952208i
\(295\) −7.28768 + 4.20754i −0.424305 + 0.244973i
\(296\) 3.77762 + 10.5891i 0.219569 + 0.615478i
\(297\) 19.7937 + 16.0616i 1.14855 + 0.931986i
\(298\) 8.99993 + 3.90496i 0.521352 + 0.226208i
\(299\) −1.15745 2.00476i −0.0669371 0.115939i
\(300\) −2.69151 7.36686i −0.155394 0.425326i
\(301\) 10.0432 + 17.8640i 0.578878 + 1.02967i
\(302\) 10.5502 + 14.2346i 0.607094 + 0.819108i
\(303\) 1.68035 0.205751i 0.0965336 0.0118201i
\(304\) −10.2349 + 5.03138i −0.587013 + 0.288569i
\(305\) 9.79335 0.560765
\(306\) 25.0825 + 20.6718i 1.43387 + 1.18173i
\(307\) 23.3864 1.33473 0.667366 0.744730i \(-0.267422\pi\)
0.667366 + 0.744730i \(0.267422\pi\)
\(308\) −17.5150 19.1587i −0.998011 1.09167i
\(309\) 18.0844 13.6181i 1.02878 0.774705i
\(310\) 0.971615 + 1.31093i 0.0551840 + 0.0744558i
\(311\) 15.3325 26.5567i 0.869428 1.50589i 0.00684678 0.999977i \(-0.497821\pi\)
0.862582 0.505918i \(-0.168846\pi\)
\(312\) 2.72785 4.13928i 0.154434 0.234340i
\(313\) −13.6566 + 7.88467i −0.771919 + 0.445668i −0.833559 0.552431i \(-0.813700\pi\)
0.0616396 + 0.998098i \(0.480367\pi\)
\(314\) −0.940006 + 2.16647i −0.0530476 + 0.122261i
\(315\) −12.7762 + 3.02166i −0.719855 + 0.170251i
\(316\) −8.27672 + 7.74227i −0.465602 + 0.435537i
\(317\) −3.31354 5.73923i −0.186107 0.322347i 0.757842 0.652438i \(-0.226254\pi\)
−0.943949 + 0.330091i \(0.892920\pi\)
\(318\) 5.98705 20.2449i 0.335737 1.13528i
\(319\) 35.6745 + 20.5967i 1.99739 + 1.15319i
\(320\) 13.0597 2.13096i 0.730058 0.119125i
\(321\) 0.698583 1.64423i 0.0389911 0.0917720i
\(322\) 7.81292 + 3.49664i 0.435397 + 0.194860i
\(323\) 21.8432i 1.21539i
\(324\) −3.43841 17.6685i −0.191023 0.981586i
\(325\) 2.29107i 0.127086i
\(326\) 9.93212 1.13945i 0.550089 0.0631082i
\(327\) 1.34291 + 0.570563i 0.0742633 + 0.0315522i
\(328\) 3.93718 21.5232i 0.217394 1.18842i
\(329\) 17.0997 9.61345i 0.942736 0.530006i
\(330\) −5.63653 + 19.0596i −0.310281 + 1.04920i
\(331\) −6.89178 + 3.97897i −0.378807 + 0.218704i −0.677299 0.735708i \(-0.736850\pi\)
0.298492 + 0.954412i \(0.403516\pi\)
\(332\) 3.29915 + 3.52689i 0.181064 + 0.193563i
\(333\) 8.27786 + 8.58346i 0.453624 + 0.470371i
\(334\) 1.50134 + 0.651413i 0.0821496 + 0.0356437i
\(335\) −2.08746 3.61559i −0.114050 0.197541i
\(336\) 0.800766 + 18.3128i 0.0436854 + 0.999045i
\(337\) −16.0246 + 27.7555i −0.872918 + 1.51194i −0.0139542 + 0.999903i \(0.504442\pi\)
−0.858964 + 0.512036i \(0.828891\pi\)
\(338\) −13.6068 + 10.0849i −0.740114 + 0.548547i
\(339\) −8.83201 + 6.65077i −0.479689 + 0.361220i
\(340\) −7.37204 + 24.2477i −0.399805 + 1.31502i
\(341\) 3.42203i 0.185313i
\(342\) −7.69335 + 9.33485i −0.416009 + 0.504771i
\(343\) −0.635325 + 18.5094i −0.0343043 + 0.999411i
\(344\) −16.6926 14.1896i −0.900004 0.765052i
\(345\) −0.796550 6.50536i −0.0428848 0.350237i
\(346\) −1.26745 1.71008i −0.0681385 0.0919343i
\(347\) −2.35072 1.35719i −0.126193 0.0728576i 0.435575 0.900153i \(-0.356545\pi\)
−0.561768 + 0.827295i \(0.689879\pi\)
\(348\) −9.98223 27.3221i −0.535104 1.46462i
\(349\) −0.192902 + 0.111372i −0.0103258 + 0.00596160i −0.505154 0.863029i \(-0.668564\pi\)
0.494828 + 0.868991i \(0.335231\pi\)
\(350\) 4.96620 + 6.86325i 0.265455 + 0.366856i
\(351\) 0.827742 5.19244i 0.0441816 0.277152i
\(352\) 24.6647 + 12.7180i 1.31463 + 0.677869i
\(353\) −24.5385 + 14.1673i −1.30605 + 0.754049i −0.981435 0.191796i \(-0.938569\pi\)
−0.324617 + 0.945846i \(0.605235\pi\)
\(354\) 8.58224 + 9.03577i 0.456141 + 0.480246i
\(355\) 0.830019 1.43763i 0.0440528 0.0763017i
\(356\) 3.71284 + 15.9687i 0.196780 + 0.846341i
\(357\) −32.1529 14.0970i −1.70171 0.746093i
\(358\) 1.79963 0.206460i 0.0951135 0.0109117i
\(359\) 21.8680i 1.15415i −0.816691 0.577075i \(-0.804194\pi\)
0.816691 0.577075i \(-0.195806\pi\)
\(360\) 11.6907 7.76595i 0.616156 0.409301i
\(361\) −10.8707 −0.572143
\(362\) −37.4013 + 4.29081i −1.96577 + 0.225520i
\(363\) −18.0776 + 13.6130i −0.948827 + 0.714495i
\(364\) −1.61602 + 5.10480i −0.0847026 + 0.267564i
\(365\) −4.87662 + 8.44655i −0.255254 + 0.442113i
\(366\) −3.39191 14.1008i −0.177298 0.737060i
\(367\) 3.75833 + 6.50962i 0.196183 + 0.339800i 0.947288 0.320384i \(-0.103812\pi\)
−0.751104 + 0.660183i \(0.770479\pi\)
\(368\) −9.13034 0.609920i −0.475952 0.0317943i
\(369\) −5.59937 22.5220i −0.291492 1.17245i
\(370\) −3.70094 + 8.52972i −0.192403 + 0.443439i
\(371\) −0.260794 + 22.8017i −0.0135398 + 1.18380i
\(372\) 1.55100 1.85300i 0.0804157 0.0960737i
\(373\) 5.04377 8.73606i 0.261156 0.452336i −0.705393 0.708816i \(-0.749230\pi\)
0.966549 + 0.256480i \(0.0825629\pi\)
\(374\) −42.7001 + 31.6479i −2.20797 + 1.63647i
\(375\) 8.13790 19.1539i 0.420239 0.989102i
\(376\) −13.5825 + 15.9784i −0.700462 + 0.824021i
\(377\) 8.49709i 0.437622i
\(378\) 8.77569 + 17.3490i 0.451373 + 0.892336i
\(379\) 20.7129i 1.06395i 0.846761 + 0.531974i \(0.178550\pi\)
−0.846761 + 0.531974i \(0.821450\pi\)
\(380\) −9.02416 2.74362i −0.462930 0.140745i
\(381\) −12.1284 + 28.5462i −0.621356 + 1.46246i
\(382\) 7.23661 + 9.76382i 0.370257 + 0.499561i
\(383\) −12.6923 + 21.9837i −0.648545 + 1.12331i 0.334926 + 0.942245i \(0.391289\pi\)
−0.983471 + 0.181068i \(0.942045\pi\)
\(384\) −7.59144 18.0657i −0.387399 0.921912i
\(385\) 0.245526 21.4667i 0.0125132 1.09404i
\(386\) 9.87688 + 4.28546i 0.502720 + 0.218124i
\(387\) −22.3331 6.42009i −1.13526 0.326351i
\(388\) −14.8776 + 13.9169i −0.755293 + 0.706522i
\(389\) 15.9336 + 27.5978i 0.807865 + 1.39926i 0.914340 + 0.404947i \(0.132710\pi\)
−0.106475 + 0.994315i \(0.533957\pi\)
\(390\) 3.98610 0.958848i 0.201844 0.0485531i
\(391\) 8.76301 15.1780i 0.443164 0.767583i
\(392\) −6.22431 18.7952i −0.314375 0.949299i
\(393\) −13.9012 + 10.4680i −0.701222 + 0.528041i
\(394\) −2.32021 20.2244i −0.116890 1.01889i
\(395\) −9.37303 −0.471608
\(396\) 29.3949 + 1.51439i 1.47715 + 0.0761009i
\(397\) 10.3571i 0.519806i 0.965635 + 0.259903i \(0.0836906\pi\)
−0.965635 + 0.259903i \(0.916309\pi\)
\(398\) −3.53310 30.7967i −0.177098 1.54370i
\(399\) 5.24643 11.9662i 0.262650 0.599059i
\(400\) −7.52388 5.04094i −0.376194 0.252047i
\(401\) 9.69923 16.7996i 0.484356 0.838930i −0.515482 0.856900i \(-0.672387\pi\)
0.999839 + 0.0179704i \(0.00572046\pi\)
\(402\) −4.48286 + 4.25785i −0.223585 + 0.212362i
\(403\) 0.611303 0.352936i 0.0304512 0.0175810i
\(404\) 1.42757 1.33539i 0.0710242 0.0664380i
\(405\) 7.90549 12.6139i 0.392827 0.626788i
\(406\) 18.4186 + 25.4543i 0.914099 + 1.26328i
\(407\) −16.8870 + 9.74974i −0.837060 + 0.483277i
\(408\) 37.4659 + 2.21636i 1.85484 + 0.109726i
\(409\) 14.1825 + 8.18830i 0.701282 + 0.404885i 0.807825 0.589423i \(-0.200645\pi\)
−0.106543 + 0.994308i \(0.533978\pi\)
\(410\) 14.5379 10.7750i 0.717976 0.532139i
\(411\) −0.832384 6.79801i −0.0410585 0.335321i
\(412\) 7.60387 25.0102i 0.374616 1.23216i
\(413\) −11.5793 6.86310i −0.569782 0.337711i
\(414\) −9.09076 + 3.40002i −0.446786 + 0.167102i
\(415\) 3.99405i 0.196060i
\(416\) −0.271921 5.71773i −0.0133320 0.280335i
\(417\) 13.4228 10.1078i 0.657319 0.494981i
\(418\) −11.7783 15.8915i −0.576093 0.777281i
\(419\) −10.4437 + 18.0890i −0.510209 + 0.883707i 0.489722 + 0.871879i \(0.337098\pi\)
−0.999930 + 0.0118282i \(0.996235\pi\)
\(420\) −9.86254 + 11.5128i −0.481243 + 0.561766i
\(421\) −2.68795 4.65567i −0.131003 0.226904i 0.793061 0.609143i \(-0.208486\pi\)
−0.924063 + 0.382239i \(0.875153\pi\)
\(422\) 0.945502 2.17914i 0.0460263 0.106079i
\(423\) −6.14539 + 21.3775i −0.298799 + 1.03941i
\(424\) −8.19100 22.9603i −0.397790 1.11505i
\(425\) 15.0217 8.67279i 0.728660 0.420692i
\(426\) −2.35743 0.697166i −0.114218 0.0337778i
\(427\) 7.67685 + 13.6550i 0.371509 + 0.660813i
\(428\) −0.467166 2.00926i −0.0225813 0.0971210i
\(429\) 7.91335 + 3.36214i 0.382060 + 0.162326i
\(430\) −2.06512 18.0009i −0.0995892 0.868080i
\(431\) 0.569062i 0.0274108i −0.999906 0.0137054i \(-0.995637\pi\)
0.999906 0.0137054i \(-0.00436270\pi\)
\(432\) −15.2307 14.1430i −0.732789 0.680455i
\(433\) 29.1119i 1.39903i 0.714619 + 0.699514i \(0.246600\pi\)
−0.714619 + 0.699514i \(0.753400\pi\)
\(434\) −1.06621 + 2.38236i −0.0511799 + 0.114357i
\(435\) 9.40720 22.1414i 0.451041 1.06160i
\(436\) 1.64105 0.381555i 0.0785919 0.0182732i
\(437\) 5.64873 + 3.26129i 0.270215 + 0.156009i
\(438\) 13.8506 + 4.09607i 0.661809 + 0.195718i
\(439\) 0.679870 + 1.17757i 0.0324484 + 0.0562023i 0.881794 0.471636i \(-0.156336\pi\)
−0.849345 + 0.527838i \(0.823003\pi\)
\(440\) 7.71145 + 21.6160i 0.367629 + 1.03050i
\(441\) −14.2282 15.4454i −0.677532 0.735493i
\(442\) 10.0575 + 4.36381i 0.478384 + 0.207565i
\(443\) −3.04716 + 1.75928i −0.144775 + 0.0835858i −0.570638 0.821202i \(-0.693304\pi\)
0.425863 + 0.904788i \(0.359971\pi\)
\(444\) 13.5632 + 2.37449i 0.643681 + 0.112688i
\(445\) −6.77940 + 11.7423i −0.321374 + 0.556637i
\(446\) 9.29393 6.88834i 0.440080 0.326172i
\(447\) 9.59839 7.22787i 0.453988 0.341867i
\(448\) 13.2085 + 16.5389i 0.624044 + 0.781389i
\(449\) 13.2772 0.626591 0.313295 0.949656i \(-0.398567\pi\)
0.313295 + 0.949656i \(0.398567\pi\)
\(450\) −9.47428 1.58439i −0.446622 0.0746889i
\(451\) 37.9495 1.78697
\(452\) −3.71356 + 12.2144i −0.174671 + 0.574518i
\(453\) 21.5392 2.63737i 1.01200 0.123915i
\(454\) −30.6911 + 22.7472i −1.44040 + 1.06758i
\(455\) −3.86009 + 2.17014i −0.180964 + 0.101738i
\(456\) −0.824854 + 13.9435i −0.0386273 + 0.652966i
\(457\) 11.7494 + 20.3506i 0.549614 + 0.951959i 0.998301 + 0.0582701i \(0.0185584\pi\)
−0.448687 + 0.893689i \(0.648108\pi\)
\(458\) 6.77391 15.6121i 0.316524 0.729507i
\(459\) 37.1783 14.2287i 1.73534 0.664137i
\(460\) −5.16986 5.52674i −0.241046 0.257685i
\(461\) −13.3984 + 7.73555i −0.624024 + 0.360280i −0.778434 0.627726i \(-0.783986\pi\)
0.154410 + 0.988007i \(0.450652\pi\)
\(462\) −30.9935 + 7.08145i −1.44195 + 0.329459i
\(463\) 18.2044 + 10.5103i 0.846031 + 0.488456i 0.859310 0.511456i \(-0.170894\pi\)
−0.0132786 + 0.999912i \(0.504227\pi\)
\(464\) −27.9045 18.6958i −1.29543 0.867929i
\(465\) 1.98365 0.242888i 0.0919895 0.0112637i
\(466\) −2.09132 18.2292i −0.0968786 0.844453i
\(467\) 29.6578 1.37240 0.686199 0.727414i \(-0.259278\pi\)
0.686199 + 0.727414i \(0.259278\pi\)
\(468\) −2.76116 5.40723i −0.127635 0.249949i
\(469\) 3.40495 5.74479i 0.157226 0.265270i
\(470\) −17.2307 + 1.97676i −0.794792 + 0.0911813i
\(471\) 1.73990 + 2.31053i 0.0801703 + 0.106464i
\(472\) 14.1549 + 2.58932i 0.651534 + 0.119183i
\(473\) 18.9992 32.9076i 0.873586 1.51310i
\(474\) 3.24634 + 13.4956i 0.149109 + 0.619874i
\(475\) 3.22772 + 5.59057i 0.148098 + 0.256513i
\(476\) −39.5878 + 8.72844i −1.81450 + 0.400067i
\(477\) −17.9489 18.6115i −0.821823 0.852162i
\(478\) −3.67288 + 8.46504i −0.167994 + 0.387182i
\(479\) −2.16539 3.75057i −0.0989393 0.171368i 0.812307 0.583231i \(-0.198212\pi\)
−0.911246 + 0.411863i \(0.864878\pi\)
\(480\) 5.62158 15.2001i 0.256589 0.693785i
\(481\) 3.48334 + 2.01111i 0.158827 + 0.0916987i
\(482\) 19.4630 + 26.2600i 0.886515 + 1.19611i
\(483\) 8.44612 6.21010i 0.384312 0.282569i
\(484\) −7.60102 + 25.0008i −0.345501 + 1.13640i
\(485\) −16.8482 −0.765037
\(486\) −20.8999 7.01380i −0.948040 0.318153i
\(487\) 33.3117i 1.50950i −0.656015 0.754748i \(-0.727759\pi\)
0.656015 0.754748i \(-0.272241\pi\)
\(488\) −12.7596 10.8463i −0.577599 0.490990i
\(489\) 4.78792 11.2692i 0.216517 0.509609i
\(490\) 6.85940 14.8683i 0.309876 0.671679i
\(491\) 27.8604 + 16.0852i 1.25732 + 0.725916i 0.972553 0.232680i \(-0.0747495\pi\)
0.284770 + 0.958596i \(0.408083\pi\)
\(492\) −20.5494 17.2003i −0.926437 0.775448i
\(493\) 55.7123 32.1655i 2.50916 1.44866i
\(494\) −1.62406 + 3.74304i −0.0730699 + 0.168407i
\(495\) 16.8980 + 17.5219i 0.759511 + 0.787550i
\(496\) 0.185980 2.78407i 0.00835075 0.125008i
\(497\) 2.65516 + 0.0303684i 0.119100 + 0.00136221i
\(498\) 5.75077 1.38333i 0.257698 0.0619887i
\(499\) −29.5577 17.0652i −1.32319 0.763941i −0.338950 0.940805i \(-0.610072\pi\)
−0.984235 + 0.176863i \(0.943405\pi\)
\(500\) −5.44208 23.4061i −0.243377 1.04675i
\(501\) 1.60117 1.20573i 0.0715351 0.0538681i
\(502\) 0.894821 + 7.79980i 0.0399378 + 0.348122i
\(503\) −9.76180 −0.435257 −0.217629 0.976032i \(-0.569832\pi\)
−0.217629 + 0.976032i \(0.569832\pi\)
\(504\) 19.9924 + 10.2130i 0.890531 + 0.454922i
\(505\) 1.61666 0.0719405
\(506\) −1.80891 15.7676i −0.0804161 0.700956i
\(507\) 2.52107 + 20.5894i 0.111965 + 0.914405i
\(508\) 8.11066 + 34.8835i 0.359852 + 1.54770i
\(509\) 12.0256 + 6.94300i 0.533027 + 0.307743i 0.742248 0.670125i \(-0.233760\pi\)
−0.209221 + 0.977868i \(0.567093\pi\)
\(510\) 21.3761 + 22.5057i 0.946550 + 0.996570i
\(511\) −15.5999 0.178424i −0.690097 0.00789300i
\(512\) −19.3753 11.6875i −0.856276 0.516518i
\(513\) 5.29542 + 13.8365i 0.233799 + 0.610897i
\(514\) −11.0272 + 25.4149i −0.486389 + 1.12100i
\(515\) 18.7225 10.8094i 0.825012 0.476321i
\(516\) −25.2030 + 9.20802i −1.10950 + 0.405361i
\(517\) −31.4996 18.1863i −1.38535 0.799833i
\(518\) −14.7942 + 1.52603i −0.650021 + 0.0670501i
\(519\) −2.58762 + 0.316842i −0.113584 + 0.0139078i
\(520\) 3.06611 3.60696i 0.134458 0.158176i
\(521\) 15.9160i 0.697291i −0.937255 0.348646i \(-0.886642\pi\)
0.937255 0.348646i \(-0.113358\pi\)
\(522\) −35.1381 5.87616i −1.53795 0.257193i
\(523\) −28.0511 −1.22659 −0.613294 0.789855i \(-0.710156\pi\)
−0.613294 + 0.789855i \(0.710156\pi\)
\(524\) −5.84497 + 19.2249i −0.255339 + 0.839846i
\(525\) 10.3123 1.14315i 0.450067 0.0498910i
\(526\) −11.1574 15.0538i −0.486484 0.656378i
\(527\) 4.62815 + 2.67206i 0.201605 + 0.116397i
\(528\) 28.4527 18.5899i 1.23824 0.809021i
\(529\) −8.88328 15.3863i −0.386229 0.668969i
\(530\) 8.02475 18.4950i 0.348573 0.803370i
\(531\) 14.8118 3.68248i 0.642777 0.159806i
\(532\) −3.24843 14.7332i −0.140837 0.638766i
\(533\) −3.91398 6.77921i −0.169533 0.293640i
\(534\) 19.2549 + 5.69429i 0.833243 + 0.246416i
\(535\) 0.853014 1.47746i 0.0368790 0.0638763i
\(536\) −1.28462 + 7.02260i −0.0554872 + 0.303330i
\(537\) 0.867538 2.04189i 0.0374370 0.0881142i
\(538\) −33.0621 + 3.79300i −1.42541 + 0.163528i
\(539\) 30.1238 16.4851i 1.29753 0.710063i
\(540\) −1.20854 17.1469i −0.0520073 0.737883i
\(541\) 4.98478 0.214313 0.107156 0.994242i \(-0.465825\pi\)
0.107156 + 0.994242i \(0.465825\pi\)
\(542\) 3.27122 + 28.5140i 0.140511 + 1.22478i
\(543\) −18.0298 + 42.4362i −0.773734 + 1.82111i
\(544\) 36.4597 23.4272i 1.56320 1.00443i
\(545\) 1.20671 + 0.696694i 0.0516897 + 0.0298431i
\(546\) 4.46158 + 4.80626i 0.190938 + 0.205689i
\(547\) 24.9146 14.3844i 1.06527 0.615034i 0.138384 0.990379i \(-0.455809\pi\)
0.926885 + 0.375345i \(0.122476\pi\)
\(548\) −5.40243 5.77536i −0.230780 0.246711i
\(549\) −17.0711 4.90742i −0.728578 0.209444i
\(550\) 6.25220 14.4097i 0.266595 0.614432i
\(551\) 11.9709 + 20.7342i 0.509978 + 0.883308i
\(552\) −6.16701 + 9.35792i −0.262485 + 0.398299i
\(553\) −7.34738 13.0690i −0.312442 0.555749i
\(554\) 21.4714 15.9139i 0.912232 0.676115i
\(555\) 6.85025 + 9.09691i 0.290777 + 0.386142i
\(556\) 5.64384 18.5634i 0.239352 0.787264i
\(557\) −24.8923 −1.05472 −0.527360 0.849642i \(-0.676818\pi\)
−0.527360 + 0.849642i \(0.676818\pi\)
\(558\) −1.03675 2.77200i −0.0438892 0.117348i
\(559\) −7.83806 −0.331515
\(560\) −1.36642 + 17.4514i −0.0577420 + 0.737456i
\(561\) 7.91146 + 64.6123i 0.334022 + 2.72793i
\(562\) −2.42491 + 1.79726i −0.102289 + 0.0758127i
\(563\) 5.94575 10.2983i 0.250584 0.434024i −0.713103 0.701059i \(-0.752711\pi\)
0.963687 + 0.267036i \(0.0860442\pi\)
\(564\) 8.81404 + 24.1247i 0.371138 + 1.01583i
\(565\) −9.14366 + 5.27909i −0.384677 + 0.222093i
\(566\) 0.318411 + 0.138155i 0.0133838 + 0.00580708i
\(567\) 23.7847 + 1.13494i 0.998863 + 0.0476631i
\(568\) −2.67363 + 0.953807i −0.112183 + 0.0400208i
\(569\) 2.96159 + 5.12962i 0.124156 + 0.215045i 0.921403 0.388609i \(-0.127044\pi\)
−0.797247 + 0.603654i \(0.793711\pi\)
\(570\) −8.37586 + 7.95546i −0.350826 + 0.333218i
\(571\) −28.8922 16.6809i −1.20910 0.698074i −0.246537 0.969133i \(-0.579293\pi\)
−0.962563 + 0.271059i \(0.912626\pi\)
\(572\) 9.67014 2.24838i 0.404329 0.0940093i
\(573\) 14.7742 1.80903i 0.617203 0.0755735i
\(574\) 26.4198 + 11.8241i 1.10274 + 0.493527i
\(575\) 5.17956i 0.216003i
\(576\) −23.8326 2.82962i −0.993025 0.117901i
\(577\) 29.0803i 1.21063i −0.795987 0.605314i \(-0.793048\pi\)
0.795987 0.605314i \(-0.206952\pi\)
\(578\) 6.72017 + 58.5772i 0.279522 + 2.43649i
\(579\) 10.5336 7.93215i 0.437763 0.329649i
\(580\) −6.29091 27.0568i −0.261216 1.12347i
\(581\) −5.56897 + 3.13088i −0.231040 + 0.129891i
\(582\) 5.83535 + 24.2586i 0.241883 + 1.00555i
\(583\) 36.6162 21.1403i 1.51649 0.875544i
\(584\) 15.7084 5.60391i 0.650018 0.231891i
\(585\) 1.38726 4.82577i 0.0573562 0.199521i
\(586\) 6.26782 14.4457i 0.258921 0.596747i
\(587\) −7.47781 12.9519i −0.308642 0.534584i 0.669423 0.742881i \(-0.266541\pi\)
−0.978066 + 0.208297i \(0.933208\pi\)
\(588\) −23.7836 4.72680i −0.980817 0.194930i
\(589\) −0.994450 + 1.72244i −0.0409756 + 0.0709718i
\(590\) 7.08626 + 9.56098i 0.291737 + 0.393619i
\(591\) −22.9469 9.74944i −0.943910 0.401038i
\(592\) 14.2687 7.01436i 0.586441 0.288288i
\(593\) 15.6604i 0.643096i −0.946893 0.321548i \(-0.895797\pi\)
0.946893 0.321548i \(-0.104203\pi\)
\(594\) 19.3760 30.3990i 0.795006 1.24729i
\(595\) −28.8411 17.0942i −1.18237 0.700793i
\(596\) 4.03580 13.2743i 0.165313 0.543737i
\(597\) −34.9424 14.8460i −1.43010 0.607605i
\(598\) −2.63012 + 1.94936i −0.107554 + 0.0797151i
\(599\) −33.5225 19.3542i −1.36969 0.790791i −0.378803 0.925477i \(-0.623664\pi\)
−0.990888 + 0.134686i \(0.956997\pi\)
\(600\) −9.91659 + 4.96900i −0.404843 + 0.202859i
\(601\) −22.3109 + 12.8812i −0.910081 + 0.525435i −0.880457 0.474126i \(-0.842764\pi\)
−0.0296235 + 0.999561i \(0.509431\pi\)
\(602\) 23.4801 16.9901i 0.956978 0.692463i
\(603\) 1.82696 + 7.34849i 0.0743997 + 0.299254i
\(604\) 18.2990 17.1174i 0.744576 0.696496i
\(605\) −18.7155 + 10.8054i −0.760893 + 0.439302i
\(606\) −0.559928 2.32772i −0.0227455 0.0945573i
\(607\) −3.14595 + 5.44895i −0.127690 + 0.221166i −0.922781 0.385324i \(-0.874090\pi\)
0.795091 + 0.606490i \(0.207423\pi\)
\(608\) 8.71881 + 13.5691i 0.353594 + 0.550298i
\(609\) 38.2462 4.23969i 1.54982 0.171801i
\(610\) −1.57855 13.7596i −0.0639137 0.557111i
\(611\) 7.50270i 0.303527i
\(612\) 25.0009 38.5729i 1.01060 1.55922i
\(613\) 22.1645 0.895217 0.447608 0.894230i \(-0.352276\pi\)
0.447608 + 0.894230i \(0.352276\pi\)
\(614\) −3.76957 32.8579i −0.152127 1.32604i
\(615\) −2.69357 21.9982i −0.108615 0.887053i
\(616\) −24.0947 + 27.6967i −0.970803 + 1.11593i
\(617\) −20.1769 + 34.9474i −0.812291 + 1.40693i 0.0989666 + 0.995091i \(0.468446\pi\)
−0.911257 + 0.411838i \(0.864887\pi\)
\(618\) −22.0483 23.2135i −0.886913 0.933782i
\(619\) 19.4800 + 33.7403i 0.782966 + 1.35614i 0.930207 + 0.367035i \(0.119627\pi\)
−0.147241 + 0.989101i \(0.547039\pi\)
\(620\) 1.68524 1.57642i 0.0676809 0.0633106i
\(621\) −1.87133 + 11.7389i −0.0750938 + 0.471065i
\(622\) −39.7836 17.2616i −1.59518 0.692127i
\(623\) −21.6867 0.248042i −0.868859 0.00993759i
\(624\) −6.25537 3.16542i −0.250415 0.126718i
\(625\) 4.27658 7.40725i 0.171063 0.296290i
\(626\) 13.2792 + 17.9167i 0.530744 + 0.716094i
\(627\) −24.0465 + 2.94438i −0.960324 + 0.117587i
\(628\) 3.19540 + 0.971501i 0.127510 + 0.0387671i
\(629\) 30.4520i 1.21420i
\(630\) 6.30476 + 17.4634i 0.251188 + 0.695759i
\(631\) 1.06032i 0.0422108i −0.999777 0.0211054i \(-0.993281\pi\)
0.999777 0.0211054i \(-0.00671856\pi\)
\(632\) 12.2120 + 10.3808i 0.485766 + 0.412927i
\(633\) −1.75007 2.32404i −0.0695592 0.0923724i
\(634\) −7.52950 + 5.58061i −0.299035 + 0.221634i
\(635\) −14.8095 + 25.6508i −0.587698 + 1.01792i
\(636\) −29.4091 5.14859i −1.16614 0.204155i
\(637\) −6.05173 3.68104i −0.239778 0.145848i
\(638\) 23.1881 53.4425i 0.918024 2.11581i
\(639\) −2.16723 + 2.09007i −0.0857343 + 0.0826819i
\(640\) −5.09904 18.0053i −0.201557 0.711724i
\(641\) −13.7294 23.7800i −0.542278 0.939253i −0.998773 0.0495272i \(-0.984229\pi\)
0.456495 0.889726i \(-0.349105\pi\)
\(642\) −2.42274 0.716481i −0.0956180 0.0282772i
\(643\) 0.0203966 0.0353280i 0.000804364 0.00139320i −0.865623 0.500696i \(-0.833077\pi\)
0.866427 + 0.499303i \(0.166411\pi\)
\(644\) 3.65344 11.5407i 0.143966 0.454769i
\(645\) −20.4241 8.67759i −0.804199 0.341680i
\(646\) −30.6896 + 3.52082i −1.20747 + 0.138525i
\(647\) 12.6901 0.498899 0.249449 0.968388i \(-0.419750\pi\)
0.249449 + 0.968388i \(0.419750\pi\)
\(648\) −24.2700 + 7.67889i −0.953417 + 0.301655i
\(649\) 24.9578i 0.979680i
\(650\) −3.21895 + 0.369289i −0.126258 + 0.0144847i
\(651\) 1.89361 + 2.57544i 0.0742166 + 0.100939i
\(652\) −3.20184 13.7709i −0.125394 0.539312i
\(653\) −3.40787 + 5.90260i −0.133360 + 0.230987i −0.924970 0.380041i \(-0.875910\pi\)
0.791610 + 0.611027i \(0.209243\pi\)
\(654\) 0.585181 1.97876i 0.0228824 0.0773756i
\(655\) −14.3917 + 8.30905i −0.562330 + 0.324661i
\(656\) −30.8747 2.06248i −1.20545 0.0805261i
\(657\) 12.7331 12.2798i 0.496767 0.479081i
\(658\) −16.2631 22.4755i −0.634002 0.876185i
\(659\) −21.9583 + 12.6776i −0.855375 + 0.493851i −0.862461 0.506124i \(-0.831078\pi\)
0.00708581 + 0.999975i \(0.497744\pi\)
\(660\) 27.6873 + 4.84716i 1.07773 + 0.188676i
\(661\) −27.4120 15.8263i −1.06620 0.615572i −0.139061 0.990284i \(-0.544408\pi\)
−0.927141 + 0.374712i \(0.877742\pi\)
\(662\) 6.70131 + 9.04158i 0.260454 + 0.351411i
\(663\) 10.7262 8.07717i 0.416572 0.313691i
\(664\) 4.42349 5.20378i 0.171665 0.201946i
\(665\) 6.36187 10.7337i 0.246703 0.416234i
\(666\) 10.7255 13.0139i 0.415603 0.504279i
\(667\) 19.2099i 0.743810i
\(668\) 0.673239 2.21438i 0.0260484 0.0856768i
\(669\) −1.72197 14.0632i −0.0665754 0.543716i
\(670\) −4.74343 + 3.51566i −0.183255 + 0.135822i
\(671\) 14.5228 25.1541i 0.560645 0.971065i
\(672\) 25.6004 4.07685i 0.987556 0.157268i
\(673\) −2.22066 3.84630i −0.0856002 0.148264i 0.820047 0.572297i \(-0.193947\pi\)
−0.905647 + 0.424033i \(0.860614\pi\)
\(674\) 41.5794 + 18.0408i 1.60158 + 0.694905i
\(675\) −7.41294 + 9.13547i −0.285324 + 0.351624i
\(676\) 16.3625 + 17.4920i 0.629328 + 0.672770i
\(677\) 5.61421 3.24137i 0.215772 0.124576i −0.388219 0.921567i \(-0.626910\pi\)
0.603991 + 0.796991i \(0.293576\pi\)
\(678\) 10.7679 + 11.3369i 0.413539 + 0.435393i
\(679\) −13.2070 23.4917i −0.506840 0.901529i
\(680\) 35.2562 + 6.44931i 1.35201 + 0.247320i
\(681\) 5.68643 + 46.4406i 0.217904 + 1.77961i
\(682\) 4.80794 0.551583i 0.184106 0.0211212i
\(683\) 28.5921i 1.09405i 0.837117 + 0.547024i \(0.184239\pi\)
−0.837117 + 0.547024i \(0.815761\pi\)
\(684\) 14.3555 + 9.30449i 0.548897 + 0.355766i
\(685\) 6.54035i 0.249894i
\(686\) 26.1080 2.09082i 0.996809 0.0798280i
\(687\) −12.5381 16.6503i −0.478360 0.635247i
\(688\) −17.2457 + 25.7402i −0.657488 + 0.981337i
\(689\) −7.55293 4.36069i −0.287744 0.166129i
\(690\) −9.01163 + 2.16773i −0.343067 + 0.0825239i
\(691\) 4.98156 + 8.62831i 0.189507 + 0.328236i 0.945086 0.326822i \(-0.105978\pi\)
−0.755579 + 0.655058i \(0.772644\pi\)
\(692\) −2.19836 + 2.05640i −0.0835690 + 0.0781728i
\(693\) −11.1849 + 37.2963i −0.424879 + 1.41677i
\(694\) −1.52794 + 3.52151i −0.0579999 + 0.133675i
\(695\) 13.8965 8.02313i 0.527123 0.304335i
\(696\) −36.7785 + 18.4290i −1.39409 + 0.698548i
\(697\) 29.6326 51.3251i 1.12241 1.94408i
\(698\) 0.187570 + 0.253075i 0.00709964 + 0.00957902i
\(699\) −20.6832 8.78766i −0.782311 0.332380i
\(700\) 8.84236 8.08377i 0.334210 0.305538i
\(701\) −13.0365 −0.492382 −0.246191 0.969221i \(-0.579179\pi\)
−0.246191 + 0.969221i \(0.579179\pi\)
\(702\) −7.42879 0.326026i −0.280382 0.0123051i
\(703\) −11.3332 −0.427440
\(704\) 13.8931 36.7038i 0.523616 1.38332i
\(705\) −8.30630 + 19.5502i −0.312833 + 0.736304i
\(706\) 23.8603 + 32.1929i 0.897994 + 1.21160i
\(707\) 1.26728 + 2.25414i 0.0476608 + 0.0847755i
\(708\) 11.3119 13.5145i 0.425127 0.507905i
\(709\) −1.46945 2.54516i −0.0551862 0.0955853i 0.837113 0.547031i \(-0.184242\pi\)
−0.892299 + 0.451445i \(0.850909\pi\)
\(710\) −2.15366 0.934447i −0.0808254 0.0350692i
\(711\) 16.3385 + 4.69680i 0.612740 + 0.176144i
\(712\) 21.8376 7.79047i 0.818397 0.291960i
\(713\) −1.38201 + 0.797904i −0.0517567 + 0.0298817i
\(714\) −14.6237 + 47.4469i −0.547278 + 1.77566i
\(715\) 7.11073 + 4.10538i 0.265926 + 0.153533i
\(716\) −0.580152 2.49520i −0.0216813 0.0932500i
\(717\) 6.79830 + 9.02793i 0.253887 + 0.337154i
\(718\) −30.7245 + 3.52482i −1.14663 + 0.131545i
\(719\) −52.8108 −1.96951 −0.984754 0.173951i \(-0.944347\pi\)
−0.984754 + 0.173951i \(0.944347\pi\)
\(720\) −12.7955 15.1737i −0.476861 0.565491i
\(721\) 29.7481 + 17.6317i 1.10788 + 0.656640i
\(722\) 1.75221 + 15.2733i 0.0652105 + 0.568415i
\(723\) 39.7356 4.86543i 1.47778 0.180947i
\(724\) 12.0571 + 51.8571i 0.448100 + 1.92726i
\(725\) −9.50606 + 16.4650i −0.353046 + 0.611494i
\(726\) 22.0400 + 23.2048i 0.817983 + 0.861209i
\(727\) −13.3309 23.0897i −0.494414 0.856351i 0.505565 0.862789i \(-0.331284\pi\)
−0.999979 + 0.00643778i \(0.997951\pi\)
\(728\) 7.43272 + 1.44768i 0.275475 + 0.0536548i
\(729\) −20.1011 + 18.0262i −0.744486 + 0.667638i
\(730\) 12.6534 + 5.49017i 0.468324 + 0.203200i
\(731\) −29.6708 51.3913i −1.09741 1.90078i
\(732\) −19.2649 + 7.03848i −0.712049 + 0.260150i
\(733\) −23.6033 13.6274i −0.871807 0.503338i −0.00385894 0.999993i \(-0.501228\pi\)
−0.867948 + 0.496654i \(0.834562\pi\)
\(734\) 8.54021 6.32971i 0.315225 0.233634i
\(735\) −11.6940 16.2918i −0.431341 0.600933i
\(736\) 0.614749 + 12.9264i 0.0226599 + 0.476474i
\(737\) −12.3822 −0.456103
\(738\) −30.7408 + 11.4973i −1.13159 + 0.423223i
\(739\) 42.7029i 1.57085i 0.618957 + 0.785425i \(0.287556\pi\)
−0.618957 + 0.785425i \(0.712444\pi\)
\(740\) 12.5808 + 3.82494i 0.462479 + 0.140608i
\(741\) 3.00605 + 3.99194i 0.110430 + 0.146647i
\(742\) 32.0783 3.30890i 1.17763 0.121473i
\(743\) 31.9011 + 18.4181i 1.17034 + 0.675695i 0.953760 0.300571i \(-0.0971772\pi\)
0.216578 + 0.976265i \(0.430510\pi\)
\(744\) −2.85346 1.88048i −0.104613 0.0689416i
\(745\) 9.93708 5.73718i 0.364067 0.210194i
\(746\) −13.0871 5.67835i −0.479154 0.207899i
\(747\) 2.00141 6.96217i 0.0732278 0.254733i
\(748\) 51.3479 + 54.8924i 1.87746 + 2.00707i
\(749\) 2.72872 + 0.0312097i 0.0997051 + 0.00114038i
\(750\) −28.2229 8.34639i −1.03055 0.304767i
\(751\) −20.8062 12.0125i −0.759228 0.438341i 0.0697904 0.997562i \(-0.477767\pi\)
−0.829019 + 0.559221i \(0.811100\pi\)
\(752\) 24.6389 + 16.5078i 0.898487 + 0.601979i
\(753\) 8.84979 + 3.76001i 0.322504 + 0.137022i
\(754\) −11.9384 + 1.36961i −0.434771 + 0.0498784i
\(755\) 20.7228 0.754181
\(756\) 22.9608 15.1262i 0.835075 0.550136i
\(757\) 45.4741 1.65279 0.826393 0.563094i \(-0.190389\pi\)
0.826393 + 0.563094i \(0.190389\pi\)
\(758\) 29.1015 3.33863i 1.05701 0.121264i
\(759\) −17.8902 7.60100i −0.649373 0.275899i
\(760\) −2.40021 + 13.1212i −0.0870649 + 0.475955i
\(761\) 33.8844 + 19.5632i 1.22831 + 0.709164i 0.966676 0.256003i \(-0.0824057\pi\)
0.261633 + 0.965167i \(0.415739\pi\)
\(762\) 42.0622 + 12.4391i 1.52375 + 0.450622i
\(763\) −0.0254903 + 2.22866i −0.000922812 + 0.0806829i
\(764\) 12.5517 11.7412i 0.454105 0.424782i
\(765\) 36.8923 9.17208i 1.33384 0.331617i
\(766\) 32.9328 + 14.2892i 1.18991 + 0.516288i
\(767\) 4.45841 2.57406i 0.160984 0.0929440i
\(768\) −24.1587 + 13.5779i −0.871750 + 0.489950i
\(769\) −14.2130 8.20587i −0.512534 0.295911i 0.221341 0.975196i \(-0.428957\pi\)
−0.733874 + 0.679285i \(0.762290\pi\)
\(770\) −30.2003 + 3.11517i −1.08834 + 0.112263i
\(771\) 20.4108 + 27.1048i 0.735075 + 0.976157i
\(772\) 4.42904 14.5677i 0.159405 0.524305i
\(773\) 43.6024i 1.56827i 0.620591 + 0.784134i \(0.286893\pi\)
−0.620591 + 0.784134i \(0.713107\pi\)
\(774\) −5.42042 + 32.4128i −0.194833 + 1.16505i
\(775\) −1.57938 −0.0567330
\(776\) 21.9512 + 18.6597i 0.788003 + 0.669845i
\(777\) −7.31416 + 16.6823i −0.262394 + 0.598475i
\(778\) 36.2065 26.8350i 1.29807 0.962082i
\(779\) 19.1015 + 11.0282i 0.684380 + 0.395127i
\(780\) −1.98968 5.44591i −0.0712421 0.194995i
\(781\) −2.46170 4.26379i −0.0880866 0.152571i
\(782\) −22.7375 9.86553i −0.813091 0.352790i
\(783\) −27.4930 + 33.8815i −0.982520 + 1.21083i
\(784\) −25.4039 + 11.7747i −0.907282 + 0.420524i
\(785\) 1.38106 + 2.39206i 0.0492921 + 0.0853764i
\(786\) 16.9482 + 17.8438i 0.604522 + 0.636468i
\(787\) −2.89125 + 5.00779i −0.103062 + 0.178508i −0.912945 0.408083i \(-0.866197\pi\)
0.809883 + 0.586592i \(0.199531\pi\)
\(788\) −28.0412 + 6.51978i −0.998926 + 0.232257i
\(789\) −22.7789 + 2.78916i −0.810949 + 0.0992968i
\(790\) 1.51080 + 13.1691i 0.0537520 + 0.468535i
\(791\) −14.5283 8.61095i −0.516567 0.306170i
\(792\) −2.61034 41.5439i −0.0927544 1.47620i
\(793\) −5.99131 −0.212758
\(794\) 14.5517 1.66942i 0.516419 0.0592454i
\(795\) −14.8534 19.7248i −0.526795 0.699567i
\(796\) −42.6997 + 9.92799i −1.51345 + 0.351888i
\(797\) 11.1404 + 6.43191i 0.394613 + 0.227830i 0.684157 0.729335i \(-0.260170\pi\)
−0.289544 + 0.957165i \(0.593504\pi\)
\(798\) −17.6581 5.44244i −0.625091 0.192660i
\(799\) −49.1924 + 28.4013i −1.74030 + 1.00476i
\(800\) −5.86976 + 11.3836i −0.207527 + 0.402470i
\(801\) 17.7014 17.0712i 0.625449 0.603182i
\(802\) −25.1667 10.9195i −0.888668 0.385582i
\(803\) 14.4633 + 25.0511i 0.510398 + 0.884035i
\(804\) 6.70485 + 5.61210i 0.236462 + 0.197924i
\(805\) 8.72674 4.90617i 0.307577 0.172920i
\(806\) −0.594408 0.801991i −0.0209371 0.0282489i
\(807\) −15.9381 + 37.5128i −0.561046 + 1.32051i
\(808\) −2.10632 1.79049i −0.0741001 0.0629890i
\(809\) 11.6895 0.410980 0.205490 0.978659i \(-0.434121\pi\)
0.205490 + 0.978659i \(0.434121\pi\)
\(810\) −18.9967 9.07402i −0.667476 0.318829i
\(811\) −23.0355 −0.808885 −0.404443 0.914563i \(-0.632534\pi\)
−0.404443 + 0.914563i \(0.632534\pi\)
\(812\) 32.7944 29.9810i 1.15086 1.05213i
\(813\) 32.3524 + 13.7456i 1.13465 + 0.482078i
\(814\) 16.4203 + 22.1547i 0.575532 + 0.776523i
\(815\) 5.84635 10.1262i 0.204789 0.354705i
\(816\) −2.92501 52.9968i −0.102396 1.85526i
\(817\) 19.1261 11.0425i 0.669138 0.386327i
\(818\) 9.21851 21.2463i 0.322318 0.742859i
\(819\) 7.81611 1.84857i 0.273117 0.0645943i
\(820\) −17.4821 18.6889i −0.610503 0.652646i
\(821\) 5.85488 + 10.1410i 0.204337 + 0.353922i 0.949921 0.312489i \(-0.101163\pi\)
−0.745584 + 0.666411i \(0.767830\pi\)
\(822\) −9.41702 + 2.26524i −0.328456 + 0.0790094i
\(823\) −30.7319 17.7431i −1.07125 0.618484i −0.142724 0.989763i \(-0.545586\pi\)
−0.928521 + 0.371279i \(0.878919\pi\)
\(824\) −36.3649 6.65212i −1.26683 0.231737i
\(825\) −11.5725 15.3679i −0.402902 0.535041i
\(826\) −7.77621 + 17.3752i −0.270569 + 0.604560i
\(827\) 28.8739i 1.00405i −0.864854 0.502023i \(-0.832589\pi\)
0.864854 0.502023i \(-0.167411\pi\)
\(828\) 6.24233 + 12.2245i 0.216936 + 0.424829i
\(829\) 31.4981i 1.09397i 0.837141 + 0.546987i \(0.184225\pi\)
−0.837141 + 0.546987i \(0.815775\pi\)
\(830\) 5.61164 0.643786i 0.194783 0.0223461i
\(831\) −3.97821 32.4897i −0.138002 1.12706i
\(832\) −7.98956 + 1.30367i −0.276988 + 0.0451965i
\(833\) 1.22657 53.6135i 0.0424981 1.85760i
\(834\) −16.3650 17.2298i −0.566674 0.596619i
\(835\) 1.65767 0.957057i 0.0573661 0.0331203i
\(836\) −20.4291 + 19.1099i −0.706555 + 0.660931i
\(837\) −3.57948 0.570615i −0.123725 0.0197233i
\(838\) 27.0984 + 11.7577i 0.936100 + 0.406162i
\(839\) −7.70959 13.3534i −0.266165 0.461011i 0.701703 0.712469i \(-0.252423\pi\)
−0.967868 + 0.251458i \(0.919090\pi\)
\(840\) 17.7651 + 12.0011i 0.612956 + 0.414079i
\(841\) −20.7559 + 35.9503i −0.715722 + 1.23967i
\(842\) −6.10795 + 4.52700i −0.210494 + 0.156011i
\(843\) 0.449285 + 3.66928i 0.0154742 + 0.126377i
\(844\) −3.21409 0.977182i −0.110633 0.0336360i
\(845\) 19.8090i 0.681450i
\(846\) 31.0260 + 5.18849i 1.06669 + 0.178384i
\(847\) −29.7369 17.6251i −1.02177 0.605606i
\(848\) −30.9389 + 15.2092i −1.06245 + 0.522287i
\(849\) 0.339584 0.255717i 0.0116545 0.00877619i
\(850\) −14.6065 19.7075i −0.501000 0.675963i
\(851\) −7.87501 4.54664i −0.269952 0.155857i
\(852\) −0.599531 + 3.42456i −0.0205396 + 0.117323i
\(853\) 9.82218 5.67084i 0.336305 0.194166i −0.322332 0.946627i \(-0.604467\pi\)
0.658637 + 0.752461i \(0.271133\pi\)
\(854\) 17.9479 12.9870i 0.614163 0.444405i
\(855\) 3.41354 + 13.7301i 0.116740 + 0.469558i
\(856\) −2.74770 + 0.980232i −0.0939144 + 0.0335036i
\(857\) −0.268417 + 0.154971i −0.00916895 + 0.00529370i −0.504577 0.863366i \(-0.668352\pi\)
0.495409 + 0.868660i \(0.335018\pi\)
\(858\) 3.44828 11.6602i 0.117722 0.398072i
\(859\) 9.88124 17.1148i 0.337144 0.583950i −0.646751 0.762702i \(-0.723873\pi\)
0.983894 + 0.178752i \(0.0572059\pi\)
\(860\) −24.9583 + 5.80299i −0.851073 + 0.197880i
\(861\) 28.5610 20.9998i 0.973356 0.715670i
\(862\) −0.799531 + 0.0917250i −0.0272321 + 0.00312417i
\(863\) 23.9730i 0.816051i 0.912970 + 0.408026i \(0.133783\pi\)
−0.912970 + 0.408026i \(0.866217\pi\)
\(864\) −17.4159 + 23.6788i −0.592501 + 0.805570i
\(865\) −2.48955 −0.0846472
\(866\) 40.9021 4.69244i 1.38991 0.159455i
\(867\) 66.4626 + 28.2380i 2.25719 + 0.959011i
\(868\) 3.51906 + 1.11403i 0.119445 + 0.0378125i
\(869\) −13.8995 + 24.0746i −0.471507 + 0.816674i
\(870\) −32.6249 9.64821i −1.10609 0.327105i
\(871\) 1.27705 + 2.21192i 0.0432713 + 0.0749481i
\(872\) −0.800598 2.24416i −0.0271117 0.0759970i
\(873\) 29.3687 + 8.44259i 0.993979 + 0.285738i
\(874\) 3.67161 8.46212i 0.124194 0.286236i
\(875\) 31.7872 + 0.363567i 1.07460 + 0.0122908i
\(876\) 3.52243 20.1203i 0.119012 0.679803i
\(877\) 15.6916 27.1787i 0.529868 0.917759i −0.469524 0.882919i \(-0.655575\pi\)
0.999393 0.0348396i \(-0.0110920\pi\)
\(878\) 1.54490 1.14502i 0.0521377 0.0386427i
\(879\) −11.6014 15.4063i −0.391305 0.519641i
\(880\) 29.1275 14.3188i 0.981888 0.482686i
\(881\) 2.85106i 0.0960548i 0.998846 + 0.0480274i \(0.0152935\pi\)
−0.998846 + 0.0480274i \(0.984707\pi\)
\(882\) −19.4073 + 22.4801i −0.653478 + 0.756946i
\(883\) 58.5844i 1.97152i −0.168153 0.985761i \(-0.553780\pi\)
0.168153 0.985761i \(-0.446220\pi\)
\(884\) 4.51002 14.8341i 0.151688 0.498924i
\(885\) 14.4673 1.77145i 0.486313 0.0595467i
\(886\) 2.96294 + 3.99768i 0.0995419 + 0.134305i
\(887\) 11.7716 20.3891i 0.395253 0.684598i −0.597881 0.801585i \(-0.703990\pi\)
0.993133 + 0.116987i \(0.0373237\pi\)
\(888\) 1.14995 19.4390i 0.0385897 0.652330i
\(889\) −47.3743 0.541845i −1.58888 0.0181729i
\(890\) 17.5906 + 7.63235i 0.589638 + 0.255837i
\(891\) −20.6754 39.0106i −0.692652 1.30690i
\(892\) −11.1762 11.9476i −0.374205 0.400037i
\(893\) −10.5700 18.3078i −0.353711 0.612646i
\(894\) −11.7023 12.3207i −0.391383 0.412065i
\(895\) 1.05932 1.83479i 0.0354091 0.0613304i
\(896\) 21.1081 21.2238i 0.705171 0.709037i
\(897\) 0.487308 + 3.97981i 0.0162707 + 0.132882i
\(898\) −2.14010 18.6545i −0.0714162 0.622508i
\(899\) −5.85758 −0.195361
\(900\) −0.698941 + 13.5667i −0.0232980 + 0.452224i
\(901\) 66.0291i 2.19975i
\(902\) −6.11694 53.3190i −0.203672 1.77533i
\(903\) −3.91086 35.2799i −0.130145 1.17404i
\(904\) 17.7598 + 3.24875i 0.590683 + 0.108052i
\(905\) −22.0156 + 38.1321i −0.731822 + 1.26755i
\(906\) −7.17733 29.8374i −0.238451 0.991283i
\(907\) 16.2312 9.37107i 0.538947 0.311161i −0.205705 0.978614i \(-0.565949\pi\)
0.744652 + 0.667453i \(0.232615\pi\)
\(908\) 36.9067 + 39.4544i 1.22479 + 1.30934i
\(909\) −2.81806 0.810105i −0.0934691 0.0268695i
\(910\) 3.67124 + 5.07362i 0.121700 + 0.168189i
\(911\) 27.7633 16.0291i 0.919838 0.531069i 0.0362544 0.999343i \(-0.488457\pi\)
0.883583 + 0.468274i \(0.155124\pi\)
\(912\) 19.7236 1.08859i 0.653114 0.0360468i
\(913\) 10.2587 + 5.92286i 0.339513 + 0.196018i
\(914\) 26.6987 19.7881i 0.883113 0.654533i
\(915\) −15.6119 6.63303i −0.516114 0.219281i
\(916\) −23.0269 7.00087i −0.760829 0.231315i
\(917\) −22.8669 13.5532i −0.755131 0.447567i
\(918\) −25.9839 49.9420i −0.857595 1.64833i
\(919\) 40.9560i 1.35101i 0.737354 + 0.675507i \(0.236075\pi\)
−0.737354 + 0.675507i \(0.763925\pi\)
\(920\) −6.93174 + 8.15448i −0.228533 + 0.268845i
\(921\) −37.2811 15.8396i −1.22845 0.521932i
\(922\) 13.0281 + 17.5778i 0.429056 + 0.578894i
\(923\) −0.507783 + 0.879506i −0.0167139 + 0.0289493i
\(924\) 14.9452 + 42.4044i 0.491659 + 1.39500i
\(925\) −4.49983 7.79394i −0.147954 0.256263i
\(926\) 11.8327 27.2713i 0.388846 0.896190i
\(927\) −38.0524 + 9.46051i −1.24981 + 0.310724i
\(928\) −21.7697 + 42.2192i −0.714625 + 1.38591i
\(929\) −20.6442 + 11.9189i −0.677314 + 0.391047i −0.798842 0.601540i \(-0.794554\pi\)
0.121528 + 0.992588i \(0.461221\pi\)
\(930\) −0.660994 2.74787i −0.0216748 0.0901062i
\(931\) 19.9531 + 0.456488i 0.653937 + 0.0149608i
\(932\) −25.2749 + 5.87660i −0.827908 + 0.192495i
\(933\) −42.4290 + 31.9503i −1.38906 + 1.04601i
\(934\) −4.78042 41.6691i −0.156420 1.36345i
\(935\) 62.1633i 2.03296i
\(936\) −7.15208 + 4.75100i −0.233773 + 0.155291i
\(937\) 28.7675i 0.939794i −0.882721 0.469897i \(-0.844291\pi\)
0.882721 0.469897i \(-0.155709\pi\)
\(938\) −8.62025 3.85796i −0.281461 0.125967i
\(939\) 27.1108 3.31959i 0.884728 0.108331i
\(940\) 5.55470 + 23.8904i 0.181174 + 0.779220i
\(941\) −35.9743 20.7698i −1.17273 0.677075i −0.218407 0.975858i \(-0.570086\pi\)
−0.954321 + 0.298783i \(0.903419\pi\)
\(942\) 2.96584 2.81698i 0.0966324 0.0917822i
\(943\) 8.84858 + 15.3262i 0.288149 + 0.499089i
\(944\) 1.35640 20.3050i 0.0441472 0.660872i
\(945\) 22.4135 + 3.83635i 0.729110 + 0.124796i
\(946\) −49.2976 21.3896i −1.60280 0.695437i
\(947\) −11.5666 + 6.67800i −0.375865 + 0.217006i −0.676018 0.736885i \(-0.736296\pi\)
0.300152 + 0.953891i \(0.402962\pi\)
\(948\) 18.4380 6.73640i 0.598840 0.218788i
\(949\) 2.98338 5.16737i 0.0968447 0.167740i
\(950\) 7.33448 5.43606i 0.237962 0.176369i
\(951\) 1.39506 + 11.3934i 0.0452380 + 0.369455i
\(952\) 18.6444 + 54.2138i 0.604270 + 1.75708i
\(953\) −6.70188 −0.217095 −0.108548 0.994091i \(-0.534620\pi\)
−0.108548 + 0.994091i \(0.534620\pi\)
\(954\) −23.2560 + 28.2181i −0.752941 + 0.913593i
\(955\) 14.2143 0.459963
\(956\) 12.4854 + 3.79594i 0.403806 + 0.122769i
\(957\) −42.9199 56.9962i −1.38740 1.84243i
\(958\) −4.92051 + 3.64691i −0.158975 + 0.117826i
\(959\) 9.11932 5.12688i 0.294478 0.165556i
\(960\) −22.2622 5.44827i −0.718509 0.175842i
\(961\) 15.2567 + 26.4254i 0.492152 + 0.852432i
\(962\) 2.26414 5.21825i 0.0729987 0.168243i
\(963\) −2.22727 + 2.14798i −0.0717729 + 0.0692175i
\(964\) 33.7581 31.5782i 1.08727 1.01707i
\(965\) 10.9053 6.29620i 0.351055 0.202682i
\(966\) −10.0866 10.8658i −0.324530 0.349602i
\(967\) −18.7298 10.8137i −0.602311 0.347744i 0.167639 0.985848i \(-0.446386\pi\)
−0.769950 + 0.638104i \(0.779719\pi\)
\(968\) 36.3513 + 6.64962i 1.16837 + 0.213727i
\(969\) −14.7944 + 34.8209i −0.475263 + 1.11861i
\(970\) 2.71570 + 23.6717i 0.0871958 + 0.760052i
\(971\) 25.7885 0.827592 0.413796 0.910370i \(-0.364203\pi\)
0.413796 + 0.910370i \(0.364203\pi\)
\(972\) −6.48560 + 30.4949i −0.208026 + 0.978123i
\(973\) 22.0800 + 13.0869i 0.707853 + 0.419545i
\(974\) −46.8028 + 5.36938i −1.49966 + 0.172046i
\(975\) −1.55174 + 3.65228i −0.0496955 + 0.116966i
\(976\) −13.1824 + 19.6755i −0.421958 + 0.629796i
\(977\) 18.8498 32.6488i 0.603058 1.04453i −0.389298 0.921112i \(-0.627282\pi\)
0.992355 0.123414i \(-0.0393844\pi\)
\(978\) −16.6049 4.91059i −0.530966 0.157023i
\(979\) 20.1066 + 34.8257i 0.642610 + 1.11303i
\(980\) −21.9955 7.24089i −0.702620 0.231302i
\(981\) −1.75434 1.81911i −0.0560119 0.0580797i
\(982\) 18.1090 41.7365i 0.577881 1.33187i
\(983\) 23.1492 + 40.0956i 0.738345 + 1.27885i 0.953240 + 0.302214i \(0.0977258\pi\)
−0.214895 + 0.976637i \(0.568941\pi\)
\(984\) −20.8541 + 31.6443i −0.664803 + 1.00878i
\(985\) −20.6195 11.9047i −0.656992 0.379315i
\(986\) −54.1725 73.0910i −1.72521 2.32769i
\(987\) −33.7704 + 3.74353i −1.07492 + 0.119158i
\(988\) 5.52074 + 1.67847i 0.175638 + 0.0533994i
\(989\) 17.7200 0.563463
\(990\) 21.8945 26.5660i 0.695852 0.844323i
\(991\) 12.6519i 0.401900i 0.979602 + 0.200950i \(0.0644028\pi\)
−0.979602 + 0.200950i \(0.935597\pi\)
\(992\) −3.94159 + 0.187452i −0.125146 + 0.00595162i
\(993\) 13.6814 1.67522i 0.434166 0.0531615i
\(994\) −0.385307 3.73538i −0.0122212 0.118479i
\(995\) −31.3984 18.1279i −0.995395 0.574692i
\(996\) −2.87053 7.85685i −0.0909561 0.248954i
\(997\) −12.9778 + 7.49276i −0.411012 + 0.237298i −0.691225 0.722640i \(-0.742928\pi\)
0.280212 + 0.959938i \(0.409595\pi\)
\(998\) −19.2122 + 44.2792i −0.608152 + 1.40163i
\(999\) −7.38246 19.2898i −0.233571 0.610302i
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 252.2.bi.c.139.19 yes 80
3.2 odd 2 756.2.bi.c.307.22 80
4.3 odd 2 inner 252.2.bi.c.139.10 yes 80
7.6 odd 2 inner 252.2.bi.c.139.20 yes 80
9.2 odd 6 756.2.bi.c.559.31 80
9.7 even 3 inner 252.2.bi.c.223.9 yes 80
12.11 even 2 756.2.bi.c.307.32 80
21.20 even 2 756.2.bi.c.307.21 80
28.27 even 2 inner 252.2.bi.c.139.9 80
36.7 odd 6 inner 252.2.bi.c.223.20 yes 80
36.11 even 6 756.2.bi.c.559.21 80
63.20 even 6 756.2.bi.c.559.32 80
63.34 odd 6 inner 252.2.bi.c.223.10 yes 80
84.83 odd 2 756.2.bi.c.307.31 80
252.83 odd 6 756.2.bi.c.559.22 80
252.223 even 6 inner 252.2.bi.c.223.19 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.bi.c.139.9 80 28.27 even 2 inner
252.2.bi.c.139.10 yes 80 4.3 odd 2 inner
252.2.bi.c.139.19 yes 80 1.1 even 1 trivial
252.2.bi.c.139.20 yes 80 7.6 odd 2 inner
252.2.bi.c.223.9 yes 80 9.7 even 3 inner
252.2.bi.c.223.10 yes 80 63.34 odd 6 inner
252.2.bi.c.223.19 yes 80 252.223 even 6 inner
252.2.bi.c.223.20 yes 80 36.7 odd 6 inner
756.2.bi.c.307.21 80 21.20 even 2
756.2.bi.c.307.22 80 3.2 odd 2
756.2.bi.c.307.31 80 84.83 odd 2
756.2.bi.c.307.32 80 12.11 even 2
756.2.bi.c.559.21 80 36.11 even 6
756.2.bi.c.559.22 80 252.83 odd 6
756.2.bi.c.559.31 80 9.2 odd 6
756.2.bi.c.559.32 80 63.20 even 6