Properties

Label 336.2.bq.a.277.2
Level $336$
Weight $2$
Character 336.277
Analytic conductor $2.683$
Analytic rank $0$
Dimension $8$
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] = [336,2,Mod(37,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bq (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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 277.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 336.277
Dual form 336.2.bq.a.205.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(0.258819 + 0.965926i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.990870 + 3.69798i) q^{5} +(1.00000 + 1.00000i) q^{6} +(-0.358719 + 2.62132i) q^{7} -2.82843i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(0.258819 + 0.965926i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.990870 + 3.69798i) q^{5} +(1.00000 + 1.00000i) q^{6} +(-0.358719 + 2.62132i) q^{7} -2.82843i q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.40130 + 5.22973i) q^{10} +(2.33195 - 0.624844i) q^{11} +(1.93185 + 0.517638i) q^{12} +(-2.41421 + 2.41421i) q^{13} +(1.41421 + 3.46410i) q^{14} -3.82843 q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.41421 - 5.91359i) q^{17} +(-0.707107 + 1.22474i) q^{18} +(2.73205 + 0.732051i) q^{19} +(5.41421 + 5.41421i) q^{20} +(-2.62484 + 0.331951i) q^{21} +(2.41421 - 2.41421i) q^{22} +(-0.210133 + 0.121320i) q^{23} +(2.73205 - 0.732051i) q^{24} +(-8.36308 - 4.82843i) q^{25} +(-1.24969 + 4.66390i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(4.18154 + 3.24264i) q^{28} +(6.12132 - 6.12132i) q^{29} +(-4.68885 + 2.70711i) q^{30} +(-0.207107 + 0.358719i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(1.20711 + 2.09077i) q^{33} -9.65685i q^{34} +(-9.33814 - 3.92392i) q^{35} +2.00000i q^{36} +(0.732051 - 2.73205i) q^{37} +(3.86370 - 1.03528i) q^{38} +(-2.95680 - 1.70711i) q^{39} +(10.4595 + 2.80260i) q^{40} -3.41421i q^{41} +(-2.98004 + 2.26260i) q^{42} +(7.41421 + 7.41421i) q^{43} +(1.24969 - 4.66390i) q^{44} +(-0.990870 - 3.69798i) q^{45} +(-0.171573 + 0.297173i) q^{46} +(-1.12132 - 1.94218i) q^{47} +(2.82843 - 2.82843i) q^{48} +(-6.74264 - 1.88064i) q^{49} -13.6569 q^{50} +(6.59575 + 1.76733i) q^{51} +(1.76733 + 6.59575i) q^{52} +(-2.56632 + 0.687644i) q^{53} +(-1.36603 - 0.366025i) q^{54} +9.24264i q^{55} +(7.41421 + 1.01461i) q^{56} +2.82843i q^{57} +(3.16863 - 11.8255i) q^{58} +(-11.6598 + 3.12422i) q^{59} +(-3.82843 + 6.63103i) q^{60} +(2.49768 + 0.669251i) q^{61} +0.585786i q^{62} +(-1.00000 - 2.44949i) q^{63} -8.00000 q^{64} +(-6.53553 - 11.3199i) q^{65} +(2.95680 + 1.70711i) q^{66} +(2.41057 + 8.99635i) q^{67} +(-6.82843 - 11.8272i) q^{68} +(-0.171573 - 0.171573i) q^{69} +(-14.2115 + 1.79725i) q^{70} +3.89949i q^{71} +(1.41421 + 2.44949i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(-1.03528 - 3.86370i) q^{74} +(2.49938 - 9.32780i) q^{75} +(4.00000 - 4.00000i) q^{76} +(0.801401 + 6.33694i) q^{77} -4.82843 q^{78} +(-1.37868 - 2.38794i) q^{79} +(14.7919 - 3.96348i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.41421 - 4.18154i) q^{82} +(6.77817 - 6.77817i) q^{83} +(-2.04989 + 4.87832i) q^{84} +(18.4853 + 18.4853i) q^{85} +(14.3232 + 3.83788i) q^{86} +(7.49706 + 4.32843i) q^{87} +(-1.76733 - 6.59575i) q^{88} +(13.4722 - 7.77817i) q^{89} +(-3.82843 - 3.82843i) q^{90} +(-5.46240 - 7.19445i) q^{91} +0.485281i q^{92} +(-0.400100 - 0.107206i) q^{93} +(-2.74666 - 1.58579i) q^{94} +(-5.41421 + 9.37769i) q^{95} +(1.46410 - 5.46410i) q^{96} -14.3137 q^{97} +(-9.58783 + 2.46447i) q^{98} +(-1.70711 + 1.70711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 8 q^{13} - 8 q^{15} - 16 q^{16} + 16 q^{17} + 8 q^{19} + 32 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 8 q^{26} + 32 q^{29} + 4 q^{31} + 4 q^{33} - 16 q^{35} - 8 q^{37} + 8 q^{40} - 4 q^{42} + 48 q^{43} - 8 q^{44} + 8 q^{45} - 24 q^{46} + 8 q^{47} - 20 q^{49} - 64 q^{50} + 8 q^{51} - 8 q^{52} - 16 q^{53} - 4 q^{54} + 48 q^{56} - 12 q^{58} - 20 q^{59} - 8 q^{60} - 4 q^{61} - 8 q^{63} - 64 q^{64} - 24 q^{65} - 32 q^{67} - 32 q^{68} - 24 q^{69} - 44 q^{70} - 16 q^{75} + 32 q^{76} - 8 q^{77} - 16 q^{78} - 28 q^{79} + 32 q^{80} + 4 q^{81} - 8 q^{82} - 8 q^{83} + 80 q^{85} + 8 q^{86} + 8 q^{88} - 8 q^{90} - 28 q^{91} - 4 q^{93} - 32 q^{95} - 16 q^{96} - 24 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.866025 0.500000i
\(3\) 0.258819 + 0.965926i 0.149429 + 0.557678i
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) −0.990870 + 3.69798i −0.443130 + 1.65379i 0.277695 + 0.960669i \(0.410429\pi\)
−0.720826 + 0.693116i \(0.756237\pi\)
\(6\) 1.00000 + 1.00000i 0.408248 + 0.408248i
\(7\) −0.358719 + 2.62132i −0.135583 + 0.990766i
\(8\) 2.82843i 1.00000i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) 1.40130 + 5.22973i 0.443130 + 1.65379i
\(11\) 2.33195 0.624844i 0.703110 0.188398i 0.110487 0.993878i \(-0.464759\pi\)
0.592623 + 0.805480i \(0.298092\pi\)
\(12\) 1.93185 + 0.517638i 0.557678 + 0.149429i
\(13\) −2.41421 + 2.41421i −0.669582 + 0.669582i −0.957619 0.288037i \(-0.906997\pi\)
0.288037 + 0.957619i \(0.406997\pi\)
\(14\) 1.41421 + 3.46410i 0.377964 + 0.925820i
\(15\) −3.82843 −0.988496
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 3.41421 5.91359i 0.828068 1.43426i −0.0714831 0.997442i \(-0.522773\pi\)
0.899551 0.436815i \(-0.143893\pi\)
\(18\) −0.707107 + 1.22474i −0.166667 + 0.288675i
\(19\) 2.73205 + 0.732051i 0.626775 + 0.167944i 0.558206 0.829702i \(-0.311490\pi\)
0.0685694 + 0.997646i \(0.478157\pi\)
\(20\) 5.41421 + 5.41421i 1.21065 + 1.21065i
\(21\) −2.62484 + 0.331951i −0.572788 + 0.0724377i
\(22\) 2.41421 2.41421i 0.514712 0.514712i
\(23\) −0.210133 + 0.121320i −0.0438158 + 0.0252970i −0.521748 0.853100i \(-0.674720\pi\)
0.477932 + 0.878397i \(0.341386\pi\)
\(24\) 2.73205 0.732051i 0.557678 0.149429i
\(25\) −8.36308 4.82843i −1.67262 0.965685i
\(26\) −1.24969 + 4.66390i −0.245084 + 0.914667i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 4.18154 + 3.24264i 0.790237 + 0.612801i
\(29\) 6.12132 6.12132i 1.13670 1.13670i 0.147663 0.989038i \(-0.452825\pi\)
0.989038 0.147663i \(-0.0471751\pi\)
\(30\) −4.68885 + 2.70711i −0.856062 + 0.494248i
\(31\) −0.207107 + 0.358719i −0.0371975 + 0.0644279i −0.884025 0.467440i \(-0.845176\pi\)
0.846827 + 0.531868i \(0.178510\pi\)
\(32\) −4.89898 2.82843i −0.866025 0.500000i
\(33\) 1.20711 + 2.09077i 0.210130 + 0.363956i
\(34\) 9.65685i 1.65614i
\(35\) −9.33814 3.92392i −1.57843 0.663264i
\(36\) 2.00000i 0.333333i
\(37\) 0.732051 2.73205i 0.120348 0.449146i −0.879283 0.476300i \(-0.841978\pi\)
0.999631 + 0.0271536i \(0.00864431\pi\)
\(38\) 3.86370 1.03528i 0.626775 0.167944i
\(39\) −2.95680 1.70711i −0.473466 0.273356i
\(40\) 10.4595 + 2.80260i 1.65379 + 0.443130i
\(41\) 3.41421i 0.533211i −0.963806 0.266605i \(-0.914098\pi\)
0.963806 0.266605i \(-0.0859020\pi\)
\(42\) −2.98004 + 2.26260i −0.459830 + 0.349127i
\(43\) 7.41421 + 7.41421i 1.13066 + 1.13066i 0.990068 + 0.140589i \(0.0448996\pi\)
0.140589 + 0.990068i \(0.455100\pi\)
\(44\) 1.24969 4.66390i 0.188398 0.703110i
\(45\) −0.990870 3.69798i −0.147710 0.551262i
\(46\) −0.171573 + 0.297173i −0.0252970 + 0.0438158i
\(47\) −1.12132 1.94218i −0.163561 0.283297i 0.772582 0.634915i \(-0.218965\pi\)
−0.936143 + 0.351618i \(0.885632\pi\)
\(48\) 2.82843 2.82843i 0.408248 0.408248i
\(49\) −6.74264 1.88064i −0.963234 0.268662i
\(50\) −13.6569 −1.93137
\(51\) 6.59575 + 1.76733i 0.923590 + 0.247475i
\(52\) 1.76733 + 6.59575i 0.245084 + 0.914667i
\(53\) −2.56632 + 0.687644i −0.352512 + 0.0944552i −0.430730 0.902481i \(-0.641744\pi\)
0.0782178 + 0.996936i \(0.475077\pi\)
\(54\) −1.36603 0.366025i −0.185893 0.0498097i
\(55\) 9.24264i 1.24628i
\(56\) 7.41421 + 1.01461i 0.990766 + 0.135583i
\(57\) 2.82843i 0.374634i
\(58\) 3.16863 11.8255i 0.416061 1.55276i
\(59\) −11.6598 + 3.12422i −1.51797 + 0.406739i −0.919073 0.394087i \(-0.871061\pi\)
−0.598898 + 0.800826i \(0.704394\pi\)
\(60\) −3.82843 + 6.63103i −0.494248 + 0.856062i
\(61\) 2.49768 + 0.669251i 0.319795 + 0.0856888i 0.415146 0.909755i \(-0.363731\pi\)
−0.0953508 + 0.995444i \(0.530397\pi\)
\(62\) 0.585786i 0.0743950i
\(63\) −1.00000 2.44949i −0.125988 0.308607i
\(64\) −8.00000 −1.00000
\(65\) −6.53553 11.3199i −0.810633 1.40406i
\(66\) 2.95680 + 1.70711i 0.363956 + 0.210130i
\(67\) 2.41057 + 8.99635i 0.294497 + 1.09908i 0.941616 + 0.336690i \(0.109307\pi\)
−0.647118 + 0.762390i \(0.724026\pi\)
\(68\) −6.82843 11.8272i −0.828068 1.43426i
\(69\) −0.171573 0.171573i −0.0206549 0.0206549i
\(70\) −14.2115 + 1.79725i −1.69860 + 0.214813i
\(71\) 3.89949i 0.462785i 0.972860 + 0.231392i \(0.0743281\pi\)
−0.972860 + 0.231392i \(0.925672\pi\)
\(72\) 1.41421 + 2.44949i 0.166667 + 0.288675i
\(73\) −3.46410 2.00000i −0.405442 0.234082i 0.283387 0.959006i \(-0.408542\pi\)
−0.688830 + 0.724923i \(0.741875\pi\)
\(74\) −1.03528 3.86370i −0.120348 0.449146i
\(75\) 2.49938 9.32780i 0.288603 1.07708i
\(76\) 4.00000 4.00000i 0.458831 0.458831i
\(77\) 0.801401 + 6.33694i 0.0913281 + 0.722161i
\(78\) −4.82843 −0.546712
\(79\) −1.37868 2.38794i −0.155114 0.268665i 0.777987 0.628281i \(-0.216241\pi\)
−0.933100 + 0.359616i \(0.882908\pi\)
\(80\) 14.7919 3.96348i 1.65379 0.443130i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) −2.41421 4.18154i −0.266605 0.461774i
\(83\) 6.77817 6.77817i 0.744001 0.744001i −0.229344 0.973345i \(-0.573658\pi\)
0.973345 + 0.229344i \(0.0736581\pi\)
\(84\) −2.04989 + 4.87832i −0.223661 + 0.532268i
\(85\) 18.4853 + 18.4853i 2.00501 + 2.00501i
\(86\) 14.3232 + 3.83788i 1.54451 + 0.413849i
\(87\) 7.49706 + 4.32843i 0.803769 + 0.464056i
\(88\) −1.76733 6.59575i −0.188398 0.703110i
\(89\) 13.4722 7.77817i 1.42805 0.824485i 0.431083 0.902312i \(-0.358132\pi\)
0.996967 + 0.0778275i \(0.0247983\pi\)
\(90\) −3.82843 3.82843i −0.403552 0.403552i
\(91\) −5.46240 7.19445i −0.572615 0.754184i
\(92\) 0.485281i 0.0505941i
\(93\) −0.400100 0.107206i −0.0414884 0.0111168i
\(94\) −2.74666 1.58579i −0.283297 0.163561i
\(95\) −5.41421 + 9.37769i −0.555487 + 0.962131i
\(96\) 1.46410 5.46410i 0.149429 0.557678i
\(97\) −14.3137 −1.45334 −0.726668 0.686988i \(-0.758932\pi\)
−0.726668 + 0.686988i \(0.758932\pi\)
\(98\) −9.58783 + 2.46447i −0.968517 + 0.248949i
\(99\) −1.70711 + 1.70711i −0.171571 + 0.171571i
\(100\) −16.7262 + 9.65685i −1.67262 + 0.965685i
\(101\) −3.53225 + 0.946464i −0.351472 + 0.0941766i −0.430235 0.902717i \(-0.641569\pi\)
0.0787635 + 0.996893i \(0.474903\pi\)
\(102\) 9.32780 2.49938i 0.923590 0.247475i
\(103\) −5.49333 + 3.17157i −0.541273 + 0.312504i −0.745595 0.666399i \(-0.767835\pi\)
0.204321 + 0.978904i \(0.434501\pi\)
\(104\) 6.82843 + 6.82843i 0.669582 + 0.669582i
\(105\) 1.37333 10.0355i 0.134023 0.979368i
\(106\) −2.65685 + 2.65685i −0.258056 + 0.258056i
\(107\) −0.499244 + 1.86321i −0.0482638 + 0.180123i −0.985850 0.167630i \(-0.946389\pi\)
0.937586 + 0.347753i \(0.113055\pi\)
\(108\) −1.93185 + 0.517638i −0.185893 + 0.0498097i
\(109\) −4.78434 17.8554i −0.458257 1.71024i −0.678332 0.734755i \(-0.737297\pi\)
0.220075 0.975483i \(-0.429370\pi\)
\(110\) 6.53553 + 11.3199i 0.623139 + 1.07931i
\(111\) 2.82843 0.268462
\(112\) 9.79796 4.00000i 0.925820 0.377964i
\(113\) −15.8995 −1.49570 −0.747849 0.663868i \(-0.768913\pi\)
−0.747849 + 0.663868i \(0.768913\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) −0.240425 0.897280i −0.0224198 0.0836718i
\(116\) −4.48112 16.7238i −0.416061 1.55276i
\(117\) 0.883663 3.29788i 0.0816947 0.304889i
\(118\) −12.0711 + 12.0711i −1.11123 + 1.11123i
\(119\) 14.2767 + 11.0711i 1.30874 + 1.01488i
\(120\) 10.8284i 0.988496i
\(121\) −4.47871 + 2.58579i −0.407156 + 0.235071i
\(122\) 3.53225 0.946464i 0.319795 0.0856888i
\(123\) 3.29788 0.883663i 0.297360 0.0796773i
\(124\) 0.414214 + 0.717439i 0.0371975 + 0.0644279i
\(125\) 12.6066 12.6066i 1.12757 1.12757i
\(126\) −2.95680 2.29289i −0.263412 0.204267i
\(127\) 2.75736 0.244676 0.122338 0.992488i \(-0.460961\pi\)
0.122338 + 0.992488i \(0.460961\pi\)
\(128\) −9.79796 + 5.65685i −0.866025 + 0.500000i
\(129\) −5.24264 + 9.08052i −0.461589 + 0.799495i
\(130\) −16.0087 9.24264i −1.40406 0.810633i
\(131\) 19.0557 + 5.10596i 1.66491 + 0.446110i 0.963730 0.266879i \(-0.0859925\pi\)
0.701175 + 0.712989i \(0.252659\pi\)
\(132\) 4.82843 0.420261
\(133\) −2.89898 + 6.89898i −0.251373 + 0.598217i
\(134\) 9.31371 + 9.31371i 0.804582 + 0.804582i
\(135\) 3.31552 1.91421i 0.285354 0.164749i
\(136\) −16.7262 9.65685i −1.43426 0.828068i
\(137\) 6.21076 + 3.58579i 0.530621 + 0.306354i 0.741269 0.671208i \(-0.234224\pi\)
−0.210648 + 0.977562i \(0.567557\pi\)
\(138\) −0.331453 0.0888127i −0.0282152 0.00756024i
\(139\) −6.89949 6.89949i −0.585208 0.585208i 0.351122 0.936330i \(-0.385800\pi\)
−0.936330 + 0.351122i \(0.885800\pi\)
\(140\) −16.1346 + 12.2502i −1.36362 + 1.03533i
\(141\) 1.58579 1.58579i 0.133547 0.133547i
\(142\) 2.75736 + 4.77589i 0.231392 + 0.400783i
\(143\) −4.12132 + 7.13834i −0.344642 + 0.596938i
\(144\) 3.46410 + 2.00000i 0.288675 + 0.166667i
\(145\) 16.5711 + 28.7019i 1.37615 + 2.38357i
\(146\) −5.65685 −0.468165
\(147\) 0.0714323 6.99964i 0.00589164 0.577320i
\(148\) −4.00000 4.00000i −0.328798 0.328798i
\(149\) 2.37378 8.85906i 0.194467 0.725762i −0.797937 0.602741i \(-0.794075\pi\)
0.992404 0.123021i \(-0.0392583\pi\)
\(150\) −3.53465 13.1915i −0.288603 1.07708i
\(151\) 10.7510 + 6.20711i 0.874906 + 0.505127i 0.868975 0.494855i \(-0.164779\pi\)
0.00593052 + 0.999982i \(0.498112\pi\)
\(152\) 2.07055 7.72741i 0.167944 0.626775i
\(153\) 6.82843i 0.552046i
\(154\) 5.46240 + 7.19445i 0.440173 + 0.579746i
\(155\) −1.12132 1.12132i −0.0900666 0.0900666i
\(156\) −5.91359 + 3.41421i −0.473466 + 0.273356i
\(157\) 3.35703 + 12.5286i 0.267920 + 0.999891i 0.960439 + 0.278491i \(0.0898343\pi\)
−0.692519 + 0.721400i \(0.743499\pi\)
\(158\) −3.37706 1.94975i −0.268665 0.155114i
\(159\) −1.32843 2.30090i −0.105351 0.182473i
\(160\) 15.3137 15.3137i 1.21065 1.21065i
\(161\) −0.242641 0.594346i −0.0191228 0.0468410i
\(162\) 1.41421i 0.111111i
\(163\) 15.6892 + 4.20390i 1.22887 + 0.329275i 0.814140 0.580668i \(-0.197209\pi\)
0.414732 + 0.909944i \(0.363875\pi\)
\(164\) −5.91359 3.41421i −0.461774 0.266605i
\(165\) −8.92771 + 2.39217i −0.695021 + 0.186230i
\(166\) 3.50864 13.0944i 0.272323 1.01632i
\(167\) 6.00000i 0.464294i −0.972681 0.232147i \(-0.925425\pi\)
0.972681 0.232147i \(-0.0745750\pi\)
\(168\) 0.938900 + 7.42418i 0.0724377 + 0.572788i
\(169\) 1.34315i 0.103319i
\(170\) 35.7108 + 9.56869i 2.73889 + 0.733885i
\(171\) −2.73205 + 0.732051i −0.208925 + 0.0559813i
\(172\) 20.2560 5.42758i 1.54451 0.413849i
\(173\) −16.3923 4.39230i −1.24628 0.333941i −0.425384 0.905013i \(-0.639861\pi\)
−0.820900 + 0.571072i \(0.806528\pi\)
\(174\) 12.2426 0.928112
\(175\) 15.6569 20.1903i 1.18355 1.52624i
\(176\) −6.82843 6.82843i −0.514712 0.514712i
\(177\) −6.03553 10.4539i −0.453659 0.785760i
\(178\) 11.0000 19.0526i 0.824485 1.42805i
\(179\) −6.89168 25.7201i −0.515109 1.92241i −0.352930 0.935650i \(-0.614814\pi\)
−0.162179 0.986761i \(-0.551852\pi\)
\(180\) −7.39595 1.98174i −0.551262 0.147710i
\(181\) 9.72792 + 9.72792i 0.723071 + 0.723071i 0.969230 0.246159i \(-0.0791685\pi\)
−0.246159 + 0.969230i \(0.579168\pi\)
\(182\) −11.7773 4.94887i −0.872991 0.366834i
\(183\) 2.58579i 0.191147i
\(184\) 0.343146 + 0.594346i 0.0252970 + 0.0438158i
\(185\) 9.37769 + 5.41421i 0.689462 + 0.398061i
\(186\) −0.565826 + 0.151613i −0.0414884 + 0.0111168i
\(187\) 4.26670 15.9236i 0.312012 1.16445i
\(188\) −4.48528 −0.327123
\(189\) 2.10721 1.59990i 0.153277 0.116376i
\(190\) 15.3137i 1.11097i
\(191\) 1.65685 + 2.86976i 0.119886 + 0.207648i 0.919722 0.392570i \(-0.128414\pi\)
−0.799836 + 0.600218i \(0.795081\pi\)
\(192\) −2.07055 7.72741i −0.149429 0.557678i
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) −17.5306 + 10.1213i −1.25863 + 0.726668i
\(195\) 9.24264 9.24264i 0.661879 0.661879i
\(196\) −10.0000 + 9.79796i −0.714286 + 0.699854i
\(197\) 8.82843 + 8.82843i 0.628999 + 0.628999i 0.947816 0.318817i \(-0.103286\pi\)
−0.318817 + 0.947816i \(0.603286\pi\)
\(198\) −0.883663 + 3.29788i −0.0627992 + 0.234370i
\(199\) −11.4069 6.58579i −0.808615 0.466854i 0.0378598 0.999283i \(-0.487946\pi\)
−0.846475 + 0.532429i \(0.821279\pi\)
\(200\) −13.6569 + 23.6544i −0.965685 + 1.67262i
\(201\) −8.06591 + 4.65685i −0.568925 + 0.328469i
\(202\) −3.65685 + 3.65685i −0.257295 + 0.257295i
\(203\) 13.8501 + 18.2418i 0.972087 + 1.28032i
\(204\) 9.65685 9.65685i 0.676115 0.676115i
\(205\) 12.6257 + 3.38304i 0.881816 + 0.236282i
\(206\) −4.48528 + 7.76874i −0.312504 + 0.541273i
\(207\) 0.121320 0.210133i 0.00843235 0.0146053i
\(208\) 13.1915 + 3.53465i 0.914667 + 0.245084i
\(209\) 6.82843 0.472332
\(210\) −5.41421 13.2621i −0.373616 0.915169i
\(211\) −5.58579 + 5.58579i −0.384541 + 0.384541i −0.872735 0.488194i \(-0.837656\pi\)
0.488194 + 0.872735i \(0.337656\pi\)
\(212\) −1.37529 + 5.13265i −0.0944552 + 0.352512i
\(213\) −3.76662 + 1.00926i −0.258085 + 0.0691536i
\(214\) 0.706038 + 2.63497i 0.0482638 + 0.180123i
\(215\) −34.7641 + 20.0711i −2.37089 + 1.36884i
\(216\) −2.00000 + 2.00000i −0.136083 + 0.136083i
\(217\) −0.866025 0.671573i −0.0587896 0.0455893i
\(218\) −18.4853 18.4853i −1.25198 1.25198i
\(219\) 1.03528 3.86370i 0.0699575 0.261085i
\(220\) 16.0087 + 9.24264i 1.07931 + 0.623139i
\(221\) 6.03403 + 22.5193i 0.405893 + 1.51481i
\(222\) 3.46410 2.00000i 0.232495 0.134231i
\(223\) −10.5563 −0.706905 −0.353453 0.935452i \(-0.614992\pi\)
−0.353453 + 0.935452i \(0.614992\pi\)
\(224\) 9.17157 11.8272i 0.612801 0.790237i
\(225\) 9.65685 0.643790
\(226\) −19.4728 + 11.2426i −1.29531 + 0.747849i
\(227\) 4.98036 + 18.5870i 0.330558 + 1.23366i 0.908605 + 0.417656i \(0.137148\pi\)
−0.578047 + 0.816004i \(0.696185\pi\)
\(228\) 4.89898 + 2.82843i 0.324443 + 0.187317i
\(229\) 3.20542 11.9628i 0.211820 0.790522i −0.775442 0.631419i \(-0.782473\pi\)
0.987262 0.159104i \(-0.0508604\pi\)
\(230\) −0.928932 0.928932i −0.0612520 0.0612520i
\(231\) −5.91359 + 2.41421i −0.389086 + 0.158844i
\(232\) −17.3137 17.3137i −1.13670 1.13670i
\(233\) 9.37769 5.41421i 0.614353 0.354697i −0.160314 0.987066i \(-0.551251\pi\)
0.774667 + 0.632369i \(0.217917\pi\)
\(234\) −1.24969 4.66390i −0.0816947 0.304889i
\(235\) 8.29323 2.22217i 0.540991 0.144958i
\(236\) −6.24844 + 23.3195i −0.406739 + 1.51797i
\(237\) 1.94975 1.94975i 0.126650 0.126650i
\(238\) 25.3137 + 3.46410i 1.64084 + 0.224544i
\(239\) −3.07107 −0.198651 −0.0993254 0.995055i \(-0.531668\pi\)
−0.0993254 + 0.995055i \(0.531668\pi\)
\(240\) 7.65685 + 13.2621i 0.494248 + 0.856062i
\(241\) 2.57107 4.45322i 0.165617 0.286857i −0.771257 0.636524i \(-0.780372\pi\)
0.936874 + 0.349667i \(0.113705\pi\)
\(242\) −3.65685 + 6.33386i −0.235071 + 0.407156i
\(243\) 0.965926 + 0.258819i 0.0619642 + 0.0166032i
\(244\) 3.65685 3.65685i 0.234106 0.234106i
\(245\) 13.6356 23.0707i 0.871149 1.47393i
\(246\) 3.41421 3.41421i 0.217682 0.217682i
\(247\) −8.36308 + 4.82843i −0.532130 + 0.307225i
\(248\) 1.01461 + 0.585786i 0.0644279 + 0.0371975i
\(249\) 8.30153 + 4.79289i 0.526088 + 0.303737i
\(250\) 6.52566 24.3541i 0.412719 1.54029i
\(251\) −13.9497 13.9497i −0.880500 0.880500i 0.113085 0.993585i \(-0.463927\pi\)
−0.993585 + 0.113085i \(0.963927\pi\)
\(252\) −5.24264 0.717439i −0.330255 0.0451944i
\(253\) −0.414214 + 0.414214i −0.0260414 + 0.0260414i
\(254\) 3.37706 1.94975i 0.211896 0.122338i
\(255\) −13.0711 + 22.6398i −0.818542 + 1.41776i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 5.87868 + 10.1822i 0.366702 + 0.635146i 0.989048 0.147596i \(-0.0471535\pi\)
−0.622346 + 0.782742i \(0.713820\pi\)
\(258\) 14.8284i 0.923178i
\(259\) 6.89898 + 2.89898i 0.428682 + 0.180134i
\(260\) −26.1421 −1.62127
\(261\) −2.24056 + 8.36188i −0.138687 + 0.517587i
\(262\) 26.9488 7.22092i 1.66491 0.446110i
\(263\) −16.0087 9.24264i −0.987140 0.569926i −0.0827219 0.996573i \(-0.526361\pi\)
−0.904418 + 0.426647i \(0.859695\pi\)
\(264\) 5.91359 3.41421i 0.363956 0.210130i
\(265\) 10.1716i 0.624835i
\(266\) 1.32780 + 10.4994i 0.0814129 + 0.643758i
\(267\) 11.0000 + 11.0000i 0.673189 + 0.673189i
\(268\) 17.9927 + 4.82113i 1.09908 + 0.294497i
\(269\) 7.54254 + 28.1491i 0.459877 + 1.71628i 0.673341 + 0.739332i \(0.264859\pi\)
−0.213464 + 0.976951i \(0.568475\pi\)
\(270\) 2.70711 4.68885i 0.164749 0.285354i
\(271\) −0.136039 0.235626i −0.00826378 0.0143133i 0.861864 0.507140i \(-0.169297\pi\)
−0.870128 + 0.492826i \(0.835964\pi\)
\(272\) −27.3137 −1.65614
\(273\) 5.53553 7.13834i 0.335026 0.432032i
\(274\) 10.1421 0.612709
\(275\) −22.5193 6.03403i −1.35797 0.363866i
\(276\) −0.468746 + 0.125600i −0.0282152 + 0.00756024i
\(277\) −20.9189 + 5.60521i −1.25690 + 0.336784i −0.824997 0.565138i \(-0.808823\pi\)
−0.431899 + 0.901922i \(0.642156\pi\)
\(278\) −13.3288 3.57144i −0.799408 0.214201i
\(279\) 0.414214i 0.0247983i
\(280\) −11.0985 + 26.4122i −0.663264 + 1.57843i
\(281\) 0.828427i 0.0494198i −0.999695 0.0247099i \(-0.992134\pi\)
0.999695 0.0247099i \(-0.00786621\pi\)
\(282\) 0.820863 3.06350i 0.0488817 0.182429i
\(283\) −26.5203 + 7.10610i −1.57647 + 0.422414i −0.937830 0.347094i \(-0.887169\pi\)
−0.638638 + 0.769507i \(0.720502\pi\)
\(284\) 6.75412 + 3.89949i 0.400783 + 0.231392i
\(285\) −10.4595 2.80260i −0.619565 0.166012i
\(286\) 11.6569i 0.689284i
\(287\) 8.94975 + 1.22474i 0.528287 + 0.0722944i
\(288\) 5.65685 0.333333
\(289\) −14.8137 25.6581i −0.871395 1.50930i
\(290\) 40.5907 + 23.4350i 2.38357 + 1.37615i
\(291\) −3.70466 13.8260i −0.217171 0.810493i
\(292\) −6.92820 + 4.00000i −0.405442 + 0.234082i
\(293\) −1.05025 1.05025i −0.0613564 0.0613564i 0.675763 0.737119i \(-0.263814\pi\)
−0.737119 + 0.675763i \(0.763814\pi\)
\(294\) −4.86200 8.62328i −0.283558 0.502920i
\(295\) 46.2132i 2.69064i
\(296\) −7.72741 2.07055i −0.449146 0.120348i
\(297\) −2.09077 1.20711i −0.121319 0.0700434i
\(298\) −3.35703 12.5286i −0.194467 0.725762i
\(299\) 0.214413 0.800199i 0.0123998 0.0462767i
\(300\) −13.6569 13.6569i −0.788479 0.788479i
\(301\) −22.0947 + 16.7754i −1.27351 + 0.966918i
\(302\) 17.5563 1.01025
\(303\) −1.82843 3.16693i −0.105040 0.181935i
\(304\) −2.92820 10.9282i −0.167944 0.626775i
\(305\) −4.94975 + 8.57321i −0.283422 + 0.490901i
\(306\) 4.82843 + 8.36308i 0.276023 + 0.478086i
\(307\) −16.3137 + 16.3137i −0.931073 + 0.931073i −0.997773 0.0667005i \(-0.978753\pi\)
0.0667005 + 0.997773i \(0.478753\pi\)
\(308\) 11.7773 + 4.94887i 0.671074 + 0.281988i
\(309\) −4.48528 4.48528i −0.255159 0.255159i
\(310\) −2.16622 0.580438i −0.123033 0.0329667i
\(311\) −16.9363 9.77817i −0.960369 0.554469i −0.0640825 0.997945i \(-0.520412\pi\)
−0.896287 + 0.443475i \(0.853745\pi\)
\(312\) −4.82843 + 8.36308i −0.273356 + 0.473466i
\(313\) 3.61269 2.08579i 0.204201 0.117896i −0.394412 0.918934i \(-0.629052\pi\)
0.598614 + 0.801038i \(0.295719\pi\)
\(314\) 12.9706 + 12.9706i 0.731971 + 0.731971i
\(315\) 10.0490 1.27085i 0.566198 0.0716043i
\(316\) −5.51472 −0.310227
\(317\) −21.8848 5.86403i −1.22918 0.329356i −0.414917 0.909859i \(-0.636189\pi\)
−0.814258 + 0.580503i \(0.802856\pi\)
\(318\) −3.25397 1.87868i −0.182473 0.105351i
\(319\) 10.4497 18.0995i 0.585074 1.01338i
\(320\) 7.92696 29.5838i 0.443130 1.65379i
\(321\) −1.92893 −0.107662
\(322\) −0.717439 0.556349i −0.0399813 0.0310041i
\(323\) 13.6569 13.6569i 0.759888 0.759888i
\(324\) −1.00000 1.73205i −0.0555556 0.0962250i
\(325\) 31.8471 8.53341i 1.76656 0.473348i
\(326\) 22.1879 5.94522i 1.22887 0.329275i
\(327\) 16.0087 9.24264i 0.885284 0.511119i
\(328\) −9.65685 −0.533211
\(329\) 5.49333 2.24264i 0.302857 0.123641i
\(330\) −9.24264 + 9.24264i −0.508791 + 0.508791i
\(331\) −2.07055 + 7.72741i −0.113808 + 0.424737i −0.999195 0.0401178i \(-0.987227\pi\)
0.885387 + 0.464854i \(0.153893\pi\)
\(332\) −4.96197 18.5183i −0.272323 1.01632i
\(333\) 0.732051 + 2.73205i 0.0401161 + 0.149715i
\(334\) −4.24264 7.34847i −0.232147 0.402090i
\(335\) −35.6569 −1.94814
\(336\) 6.39960 + 8.42883i 0.349127 + 0.459830i
\(337\) −7.34315 −0.400007 −0.200003 0.979795i \(-0.564095\pi\)
−0.200003 + 0.979795i \(0.564095\pi\)
\(338\) 0.949747 + 1.64501i 0.0516595 + 0.0894768i
\(339\) −4.11509 15.3577i −0.223501 0.834118i
\(340\) 50.5027 13.5322i 2.73889 0.733885i
\(341\) −0.258819 + 0.965926i −0.0140158 + 0.0523078i
\(342\) −2.82843 + 2.82843i −0.152944 + 0.152944i
\(343\) 7.34847 17.0000i 0.396780 0.917914i
\(344\) 20.9706 20.9706i 1.13066 1.13066i
\(345\) 0.804479 0.464466i 0.0433117 0.0250060i
\(346\) −23.1822 + 6.21166i −1.24628 + 0.333941i
\(347\) 7.25866 1.94495i 0.389665 0.104411i −0.0586667 0.998278i \(-0.518685\pi\)
0.448332 + 0.893867i \(0.352018\pi\)
\(348\) 14.9941 8.65685i 0.803769 0.464056i
\(349\) −0.585786 + 0.585786i −0.0313564 + 0.0313564i −0.722611 0.691255i \(-0.757058\pi\)
0.691255 + 0.722611i \(0.257058\pi\)
\(350\) 4.89898 35.7990i 0.261861 1.91354i
\(351\) 3.41421 0.182237
\(352\) −13.1915 3.53465i −0.703110 0.188398i
\(353\) 1.65685 2.86976i 0.0881855 0.152742i −0.818559 0.574423i \(-0.805227\pi\)
0.906744 + 0.421681i \(0.138560\pi\)
\(354\) −14.7840 8.53553i −0.785760 0.453659i
\(355\) −14.4202 3.86389i −0.765347 0.205074i
\(356\) 31.1127i 1.64897i
\(357\) −6.99876 + 16.6556i −0.370413 + 0.881508i
\(358\) −26.6274 26.6274i −1.40730 1.40730i
\(359\) −6.63103 + 3.82843i −0.349972 + 0.202057i −0.664673 0.747134i \(-0.731429\pi\)
0.314701 + 0.949191i \(0.398096\pi\)
\(360\) −10.4595 + 2.80260i −0.551262 + 0.147710i
\(361\) −9.52628 5.50000i −0.501383 0.289474i
\(362\) 18.7929 + 5.03554i 0.987733 + 0.264662i
\(363\) −3.65685 3.65685i −0.191935 0.191935i
\(364\) −17.9236 + 2.26670i −0.939450 + 0.118808i
\(365\) 10.8284 10.8284i 0.566786 0.566786i
\(366\) 1.82843 + 3.16693i 0.0955734 + 0.165538i
\(367\) 12.6924 21.9839i 0.662537 1.14755i −0.317409 0.948289i \(-0.602813\pi\)
0.979947 0.199260i \(-0.0638537\pi\)
\(368\) 0.840532 + 0.485281i 0.0438158 + 0.0252970i
\(369\) 1.70711 + 2.95680i 0.0888684 + 0.153925i
\(370\) 15.3137 0.796122
\(371\) −0.881946 6.97383i −0.0457884 0.362063i
\(372\) −0.585786 + 0.585786i −0.0303716 + 0.0303716i
\(373\) −0.0260126 + 0.0970804i −0.00134688 + 0.00502663i −0.966596 0.256305i \(-0.917495\pi\)
0.965249 + 0.261331i \(0.0841616\pi\)
\(374\) −6.03403 22.5193i −0.312012 1.16445i
\(375\) 15.4399 + 8.91421i 0.797311 + 0.460328i
\(376\) −5.49333 + 3.17157i −0.283297 + 0.163561i
\(377\) 29.5563i 1.52223i
\(378\) 1.44949 3.44949i 0.0745537 0.177423i
\(379\) 6.65685 + 6.65685i 0.341940 + 0.341940i 0.857096 0.515156i \(-0.172266\pi\)
−0.515156 + 0.857096i \(0.672266\pi\)
\(380\) 10.8284 + 18.7554i 0.555487 + 0.962131i
\(381\) 0.713657 + 2.66340i 0.0365618 + 0.136450i
\(382\) 4.05845 + 2.34315i 0.207648 + 0.119886i
\(383\) 7.46447 + 12.9288i 0.381416 + 0.660633i 0.991265 0.131885i \(-0.0421031\pi\)
−0.609849 + 0.792518i \(0.708770\pi\)
\(384\) −8.00000 8.00000i −0.408248 0.408248i
\(385\) −24.2279 3.31552i −1.23477 0.168974i
\(386\) 9.89949i 0.503871i
\(387\) −10.1280 2.71379i −0.514835 0.137950i
\(388\) −14.3137 + 24.7921i −0.726668 + 1.25863i
\(389\) −34.5792 + 9.26546i −1.75323 + 0.469777i −0.985312 0.170766i \(-0.945376\pi\)
−0.767922 + 0.640544i \(0.778709\pi\)
\(390\) 4.78434 17.8554i 0.242265 0.904144i
\(391\) 1.65685i 0.0837907i
\(392\) −5.31925 + 19.0711i −0.268662 + 0.963234i
\(393\) 19.7279i 0.995142i
\(394\) 17.0552 + 4.56993i 0.859229 + 0.230230i
\(395\) 10.1967 2.73218i 0.513049 0.137471i
\(396\) 1.24969 + 4.66390i 0.0627992 + 0.234370i
\(397\) 0.937492 + 0.251200i 0.0470514 + 0.0126074i 0.282268 0.959336i \(-0.408913\pi\)
−0.235217 + 0.971943i \(0.575580\pi\)
\(398\) −18.6274 −0.933708
\(399\) −7.41421 1.01461i −0.371175 0.0507941i
\(400\) 38.6274i 1.93137i
\(401\) 12.0000 + 20.7846i 0.599251 + 1.03793i 0.992932 + 0.118686i \(0.0378683\pi\)
−0.393680 + 0.919247i \(0.628798\pi\)
\(402\) −6.58579 + 11.4069i −0.328469 + 0.568925i
\(403\) −0.366025 1.36603i −0.0182330 0.0680466i
\(404\) −1.89293 + 7.06450i −0.0941766 + 0.351472i
\(405\) 2.70711 + 2.70711i 0.134517 + 0.134517i
\(406\) 29.8617 + 12.5480i 1.48201 + 0.622748i
\(407\) 6.82843i 0.338473i
\(408\) 4.99876 18.6556i 0.247475 0.923590i
\(409\) −28.2817 16.3284i −1.39844 0.807389i −0.404209 0.914667i \(-0.632453\pi\)
−0.994229 + 0.107278i \(0.965787\pi\)
\(410\) 17.8554 4.78434i 0.881816 0.236282i
\(411\) −1.85614 + 6.92721i −0.0915566 + 0.341694i
\(412\) 12.6863i 0.625009i
\(413\) −4.00701 31.6847i −0.197172 1.55910i
\(414\) 0.343146i 0.0168647i
\(415\) 18.3492 + 31.7818i 0.900729 + 1.56011i
\(416\) 18.6556 4.99876i 0.914667 0.245084i
\(417\) 4.87868 8.45012i 0.238910 0.413804i
\(418\) 8.36308 4.82843i 0.409052 0.236166i
\(419\) −13.7990 + 13.7990i −0.674125 + 0.674125i −0.958664 0.284540i \(-0.908159\pi\)
0.284540 + 0.958664i \(0.408159\pi\)
\(420\) −16.0087 12.4142i −0.781146 0.605752i
\(421\) −1.48528 1.48528i −0.0723882 0.0723882i 0.669986 0.742374i \(-0.266300\pi\)
−0.742374 + 0.669986i \(0.766300\pi\)
\(422\) −2.89142 + 10.7909i −0.140752 + 0.525293i
\(423\) 1.94218 + 1.12132i 0.0944322 + 0.0545205i
\(424\) 1.94495 + 7.25866i 0.0944552 + 0.352512i
\(425\) −57.1067 + 32.9706i −2.77008 + 1.59931i
\(426\) −3.89949 + 3.89949i −0.188931 + 0.188931i
\(427\) −2.65029 + 6.30714i −0.128256 + 0.305224i
\(428\) 2.72792 + 2.72792i 0.131859 + 0.131859i
\(429\) −7.96178 2.13335i −0.384398 0.102999i
\(430\) −28.3848 + 49.1639i −1.36884 + 2.37089i
\(431\) 11.1924 19.3858i 0.539118 0.933780i −0.459833 0.888005i \(-0.652091\pi\)
0.998952 0.0457752i \(-0.0145758\pi\)
\(432\) −1.03528 + 3.86370i −0.0498097 + 0.185893i
\(433\) 16.9706 0.815553 0.407777 0.913082i \(-0.366304\pi\)
0.407777 + 0.913082i \(0.366304\pi\)
\(434\) −1.53553 0.210133i −0.0737080 0.0100867i
\(435\) −23.4350 + 23.4350i −1.12362 + 1.12362i
\(436\) −35.7108 9.56869i −1.71024 0.458257i
\(437\) −0.662907 + 0.177625i −0.0317111 + 0.00849697i
\(438\) −1.46410 5.46410i −0.0699575 0.261085i
\(439\) 3.94591 2.27817i 0.188328 0.108731i −0.402871 0.915257i \(-0.631988\pi\)
0.591200 + 0.806525i \(0.298655\pi\)
\(440\) 26.1421 1.24628
\(441\) 6.77962 1.74264i 0.322839 0.0829829i
\(442\) 23.3137 + 23.3137i 1.10892 + 1.10892i
\(443\) −3.21303 + 11.9912i −0.152656 + 0.569720i 0.846639 + 0.532168i \(0.178623\pi\)
−0.999295 + 0.0375516i \(0.988044\pi\)
\(444\) 2.82843 4.89898i 0.134231 0.232495i
\(445\) 15.4143 + 57.5270i 0.730709 + 2.72704i
\(446\) −12.9288 + 7.46447i −0.612198 + 0.353453i
\(447\) 9.17157 0.433801
\(448\) 2.86976 20.9706i 0.135583 0.990766i
\(449\) −1.75736 −0.0829349 −0.0414675 0.999140i \(-0.513203\pi\)
−0.0414675 + 0.999140i \(0.513203\pi\)
\(450\) 11.8272 6.82843i 0.557539 0.321895i
\(451\) −2.13335 7.96178i −0.100456 0.374906i
\(452\) −15.8995 + 27.5387i −0.747849 + 1.29531i
\(453\) −3.21303 + 11.9912i −0.150962 + 0.563396i
\(454\) 19.2426 + 19.2426i 0.903102 + 0.903102i
\(455\) 32.0174 13.0711i 1.50100 0.612781i
\(456\) 8.00000 0.374634
\(457\) 20.4619 11.8137i 0.957169 0.552622i 0.0618687 0.998084i \(-0.480294\pi\)
0.895301 + 0.445462i \(0.146961\pi\)
\(458\) −4.53314 16.9179i −0.211820 0.790522i
\(459\) −6.59575 + 1.76733i −0.307863 + 0.0824918i
\(460\) −1.79456 0.480851i −0.0836718 0.0224198i
\(461\) 8.00000 8.00000i 0.372597 0.372597i −0.495825 0.868422i \(-0.665134\pi\)
0.868422 + 0.495825i \(0.165134\pi\)
\(462\) −5.53553 + 7.13834i −0.257536 + 0.332105i
\(463\) 35.7990 1.66372 0.831860 0.554985i \(-0.187276\pi\)
0.831860 + 0.554985i \(0.187276\pi\)
\(464\) −33.4475 8.96224i −1.55276 0.416061i
\(465\) 0.792893 1.37333i 0.0367695 0.0636867i
\(466\) 7.65685 13.2621i 0.354697 0.614353i
\(467\) 17.5240 + 4.69553i 0.810912 + 0.217283i 0.640369 0.768067i \(-0.278781\pi\)
0.170543 + 0.985350i \(0.445448\pi\)
\(468\) −4.82843 4.82843i −0.223194 0.223194i
\(469\) −24.4470 + 3.09170i −1.12886 + 0.142761i
\(470\) 8.58579 8.58579i 0.396033 0.396033i
\(471\) −11.2328 + 6.48528i −0.517582 + 0.298826i
\(472\) 8.83663 + 32.9788i 0.406739 + 1.51797i
\(473\) 21.9223 + 12.6569i 1.00799 + 0.581963i
\(474\) 1.00926 3.76662i 0.0463570 0.173007i
\(475\) −19.3137 19.3137i −0.886174 0.886174i
\(476\) 33.4523 13.6569i 1.53328 0.625961i
\(477\) 1.87868 1.87868i 0.0860188 0.0860188i
\(478\) −3.76127 + 2.17157i −0.172037 + 0.0993254i
\(479\) 10.4142 18.0379i 0.475838 0.824175i −0.523779 0.851854i \(-0.675478\pi\)
0.999617 + 0.0276792i \(0.00881168\pi\)
\(480\) 18.7554 + 10.8284i 0.856062 + 0.494248i
\(481\) 4.82843 + 8.36308i 0.220157 + 0.381324i
\(482\) 7.27208i 0.331234i
\(483\) 0.511294 0.388201i 0.0232647 0.0176638i
\(484\) 10.3431i 0.470143i
\(485\) 14.1830 52.9318i 0.644018 2.40351i
\(486\) 1.36603 0.366025i 0.0619642 0.0166032i
\(487\) 26.4626 + 15.2782i 1.19913 + 0.692320i 0.960362 0.278756i \(-0.0899219\pi\)
0.238772 + 0.971076i \(0.423255\pi\)
\(488\) 1.89293 7.06450i 0.0856888 0.319795i
\(489\) 16.2426i 0.734518i
\(490\) 0.386750 37.8975i 0.0174716 1.71204i
\(491\) 6.05025 + 6.05025i 0.273044 + 0.273044i 0.830324 0.557280i \(-0.188155\pi\)
−0.557280 + 0.830324i \(0.688155\pi\)
\(492\) 1.76733 6.59575i 0.0796773 0.297360i
\(493\) −15.2995 57.0985i −0.689054 2.57159i
\(494\) −6.82843 + 11.8272i −0.307225 + 0.532130i
\(495\) −4.62132 8.00436i −0.207713 0.359769i
\(496\) 1.65685 0.0743950
\(497\) −10.2218 1.39882i −0.458512 0.0627459i
\(498\) 13.5563 0.607475
\(499\) 23.0851 + 6.18564i 1.03343 + 0.276907i 0.735389 0.677645i \(-0.236999\pi\)
0.298043 + 0.954552i \(0.403666\pi\)
\(500\) −9.22867 34.4419i −0.412719 1.54029i
\(501\) 5.79555 1.55291i 0.258926 0.0693791i
\(502\) −26.9488 7.22092i −1.20279 0.322285i
\(503\) 23.5147i 1.04847i 0.851574 + 0.524235i \(0.175649\pi\)
−0.851574 + 0.524235i \(0.824351\pi\)
\(504\) −6.92820 + 2.82843i −0.308607 + 0.125988i
\(505\) 14.0000i 0.622992i
\(506\) −0.214413 + 0.800199i −0.00953181 + 0.0355732i
\(507\) −1.29738 + 0.347632i −0.0576186 + 0.0154389i
\(508\) 2.75736 4.77589i 0.122338 0.211896i
\(509\) −18.8213 5.04316i −0.834241 0.223534i −0.183678 0.982986i \(-0.558800\pi\)
−0.650563 + 0.759452i \(0.725467\pi\)
\(510\) 36.9706i 1.63708i
\(511\) 6.48528 8.36308i 0.286892 0.369961i
\(512\) 22.6274i 1.00000i
\(513\) −1.41421 2.44949i −0.0624391 0.108148i
\(514\) 14.3998 + 8.31371i 0.635146 + 0.366702i
\(515\) −6.28523 23.4568i −0.276960 1.03363i
\(516\) 10.4853 + 18.1610i 0.461589 + 0.799495i
\(517\) −3.82843 3.82843i −0.168374 0.168374i
\(518\) 10.4994 1.32780i 0.461316 0.0583404i
\(519\) 16.9706i 0.744925i
\(520\) −32.0174 + 18.4853i −1.40406 + 0.810633i
\(521\) 10.0951 + 5.82843i 0.442276 + 0.255348i 0.704562 0.709642i \(-0.251143\pi\)
−0.262287 + 0.964990i \(0.584477\pi\)
\(522\) 3.16863 + 11.8255i 0.138687 + 0.517587i
\(523\) −7.13211 + 26.6174i −0.311865 + 1.16390i 0.615007 + 0.788521i \(0.289153\pi\)
−0.926873 + 0.375376i \(0.877514\pi\)
\(524\) 27.8995 27.8995i 1.21880 1.21880i
\(525\) 23.5546 + 9.89774i 1.02801 + 0.431973i
\(526\) −26.1421 −1.13985
\(527\) 1.41421 + 2.44949i 0.0616041 + 0.106701i
\(528\) 4.82843 8.36308i 0.210130 0.363956i
\(529\) −11.4706 + 19.8676i −0.498720 + 0.863809i
\(530\) −7.19239 12.4576i −0.312417 0.541123i
\(531\) 8.53553 8.53553i 0.370411 0.370411i
\(532\) 9.05040 + 11.9202i 0.392385 + 0.516804i
\(533\) 8.24264 + 8.24264i 0.357028 + 0.357028i
\(534\) 21.2504 + 5.69402i 0.919593 + 0.246404i
\(535\) −6.39540 3.69239i −0.276497 0.159636i
\(536\) 25.4455 6.81811i 1.09908 0.294497i
\(537\) 23.0600 13.3137i 0.995113 0.574529i
\(538\) 29.1421 + 29.1421i 1.25641 + 1.25641i
\(539\) −16.8986 0.172453i −0.727875 0.00742807i
\(540\) 7.65685i 0.329499i
\(541\) 4.19516 + 1.12409i 0.180364 + 0.0483284i 0.347870 0.937543i \(-0.386905\pi\)
−0.167507 + 0.985871i \(0.553572\pi\)
\(542\) −0.333226 0.192388i −0.0143133 0.00826378i
\(543\) −6.87868 + 11.9142i −0.295192 + 0.511288i
\(544\) −33.4523 + 19.3137i −1.43426 + 0.828068i
\(545\) 70.7696 3.03143
\(546\) 1.73205 12.6569i 0.0741249 0.541663i
\(547\) −3.17157 + 3.17157i −0.135607 + 0.135607i −0.771652 0.636045i \(-0.780569\pi\)
0.636045 + 0.771652i \(0.280569\pi\)
\(548\) 12.4215 7.17157i 0.530621 0.306354i
\(549\) −2.49768 + 0.669251i −0.106598 + 0.0285629i
\(550\) −31.8471 + 8.53341i −1.35797 + 0.363866i
\(551\) 21.2049 12.2426i 0.903358 0.521554i
\(552\) −0.485281 + 0.485281i −0.0206549 + 0.0206549i
\(553\) 6.75412 2.75736i 0.287215 0.117255i
\(554\) −21.6569 + 21.6569i −0.920112 + 0.920112i
\(555\) −2.80260 + 10.4595i −0.118964 + 0.443979i
\(556\) −18.8498 + 5.05078i −0.799408 + 0.214201i
\(557\) 2.58057 + 9.63082i 0.109342 + 0.408071i 0.998802 0.0489434i \(-0.0155854\pi\)
−0.889459 + 0.457015i \(0.848919\pi\)
\(558\) −0.292893 0.507306i −0.0123992 0.0214760i
\(559\) −35.7990 −1.51414
\(560\) 5.08340 + 40.1961i 0.214813 + 1.69860i
\(561\) 16.4853 0.696009
\(562\) −0.585786 1.01461i −0.0247099 0.0427988i
\(563\) 5.19477 + 19.3872i 0.218934 + 0.817071i 0.984745 + 0.174006i \(0.0556711\pi\)
−0.765811 + 0.643066i \(0.777662\pi\)
\(564\) −1.16088 4.33245i −0.0488817 0.182429i
\(565\) 15.7543 58.7960i 0.662790 2.47356i
\(566\) −27.4558 + 27.4558i −1.15406 + 1.15406i
\(567\) 2.09077 + 1.62132i 0.0878041 + 0.0680891i
\(568\) 11.0294 0.462785
\(569\) 5.91359 3.41421i 0.247911 0.143131i −0.370897 0.928674i \(-0.620950\pi\)
0.618807 + 0.785543i \(0.287616\pi\)
\(570\) −14.7919 + 3.96348i −0.619565 + 0.166012i
\(571\) −5.83577 + 1.56369i −0.244219 + 0.0654384i −0.378852 0.925457i \(-0.623681\pi\)
0.134633 + 0.990896i \(0.457014\pi\)
\(572\) 8.24264 + 14.2767i 0.344642 + 0.596938i
\(573\) −2.34315 + 2.34315i −0.0978863 + 0.0978863i
\(574\) 11.8272 4.82843i 0.493657 0.201535i
\(575\) 2.34315 0.0977159
\(576\) 6.92820 4.00000i 0.288675 0.166667i
\(577\) −10.2574 + 17.7663i −0.427019 + 0.739619i −0.996607 0.0823115i \(-0.973770\pi\)
0.569587 + 0.821931i \(0.307103\pi\)
\(578\) −36.2860 20.9497i −1.50930 0.871395i
\(579\) 6.76148 + 1.81173i 0.280998 + 0.0752931i
\(580\) 66.2843 2.75230
\(581\) 15.3363 + 20.1992i 0.636257 + 0.838005i
\(582\) −14.3137 14.3137i −0.593322 0.593322i
\(583\) −5.55487 + 3.20711i −0.230059 + 0.132825i
\(584\) −5.65685 + 9.79796i −0.234082 + 0.405442i
\(585\) 11.3199 + 6.53553i 0.468019 + 0.270211i
\(586\) −2.02893 0.543651i −0.0838144 0.0224580i
\(587\) 2.87868 + 2.87868i 0.118816 + 0.118816i 0.764015 0.645199i \(-0.223225\pi\)
−0.645199 + 0.764015i \(0.723225\pi\)
\(588\) −12.0523 7.12336i −0.497028 0.293762i
\(589\) −0.828427 + 0.828427i −0.0341347 + 0.0341347i
\(590\) −32.6777 56.5994i −1.34532 2.33016i
\(591\) −6.24264 + 10.8126i −0.256788 + 0.444770i
\(592\) −10.9282 + 2.92820i −0.449146 + 0.120348i
\(593\) −8.29289 14.3637i −0.340548 0.589847i 0.643986 0.765037i \(-0.277279\pi\)
−0.984535 + 0.175190i \(0.943946\pi\)
\(594\) −3.41421 −0.140087
\(595\) −55.0869 + 41.8248i −2.25834 + 1.71465i
\(596\) −12.9706 12.9706i −0.531295 0.531295i
\(597\) 3.40905 12.7228i 0.139523 0.520708i
\(598\) −0.303225 1.13165i −0.0123998 0.0462767i
\(599\) 16.1828 + 9.34315i 0.661211 + 0.381751i 0.792738 0.609562i \(-0.208655\pi\)
−0.131527 + 0.991313i \(0.541988\pi\)
\(600\) −26.3830 7.06931i −1.07708 0.288603i
\(601\) 3.34315i 0.136370i 0.997673 + 0.0681849i \(0.0217208\pi\)
−0.997673 + 0.0681849i \(0.978279\pi\)
\(602\) −15.1983 + 36.1689i −0.619437 + 1.47413i
\(603\) −6.58579 6.58579i −0.268194 0.268194i
\(604\) 21.5020 12.4142i 0.874906 0.505127i
\(605\) −5.12436 19.1244i −0.208335 0.777516i
\(606\) −4.47871 2.58579i −0.181935 0.105040i
\(607\) −7.96447 13.7949i −0.323268 0.559916i 0.657893 0.753112i \(-0.271448\pi\)
−0.981160 + 0.193196i \(0.938115\pi\)
\(608\) −11.3137 11.3137i −0.458831 0.458831i
\(609\) −14.0355 + 18.0995i −0.568749 + 0.733428i
\(610\) 14.0000i 0.566843i
\(611\) 7.39595 + 1.98174i 0.299208 + 0.0801726i
\(612\) 11.8272 + 6.82843i 0.478086 + 0.276023i
\(613\) 22.6164 6.06004i 0.913468 0.244763i 0.228677 0.973502i \(-0.426560\pi\)
0.684791 + 0.728740i \(0.259894\pi\)
\(614\) −8.44460 + 31.5157i −0.340796 + 1.27187i
\(615\) 13.0711i 0.527076i
\(616\) 17.9236 2.26670i 0.722161 0.0913281i
\(617\) 32.2426i 1.29804i −0.760771 0.649020i \(-0.775179\pi\)
0.760771 0.649020i \(-0.224821\pi\)
\(618\) −8.66490 2.32175i −0.348553 0.0933946i
\(619\) 24.0226 6.43684i 0.965551 0.258719i 0.258603 0.965984i \(-0.416738\pi\)
0.706948 + 0.707265i \(0.250071\pi\)
\(620\) −3.06350 + 0.820863i −0.123033 + 0.0329667i
\(621\) 0.234373 + 0.0628000i 0.00940506 + 0.00252008i
\(622\) −27.6569 −1.10894
\(623\) 15.5563 + 38.1051i 0.623252 + 1.52665i
\(624\) 13.6569i 0.546712i
\(625\) 9.98528 + 17.2950i 0.399411 + 0.691801i
\(626\) 2.94975 5.10911i 0.117896 0.204201i
\(627\) 1.76733 + 6.59575i 0.0705802 + 0.263409i
\(628\) 25.0572 + 6.71406i 0.999891 + 0.267920i
\(629\) −13.6569 13.6569i −0.544534 0.544534i
\(630\) 11.4089 8.66220i 0.454540 0.345110i
\(631\) 8.75736i 0.348625i 0.984690 + 0.174312i \(0.0557703\pi\)
−0.984690 + 0.174312i \(0.944230\pi\)
\(632\) −6.75412 + 3.89949i −0.268665 + 0.155114i
\(633\) −6.84116 3.94975i −0.271912 0.156988i
\(634\) −30.9498 + 8.29298i −1.22918 + 0.329356i
\(635\) −2.73218 + 10.1967i −0.108423 + 0.404642i
\(636\) −5.31371 −0.210702
\(637\) 20.8184 11.7379i 0.824856 0.465073i
\(638\) 29.5563i 1.17015i
\(639\) −1.94975 3.37706i −0.0771308 0.133594i
\(640\) −11.2104 41.8378i −0.443130 1.65379i
\(641\) 20.2635 35.0973i 0.800358 1.38626i −0.119022 0.992892i \(-0.537976\pi\)
0.919380 0.393370i \(-0.128691\pi\)
\(642\) −2.36245 + 1.36396i −0.0932385 + 0.0538312i
\(643\) 16.9289 16.9289i 0.667612 0.667612i −0.289551 0.957163i \(-0.593506\pi\)
0.957163 + 0.289551i \(0.0935059\pi\)
\(644\) −1.27208 0.174080i −0.0501269 0.00685971i
\(645\) −28.3848 28.3848i −1.11765 1.11765i
\(646\) 7.06931 26.3830i 0.278138 1.03803i
\(647\) 9.88500 + 5.70711i 0.388619 + 0.224370i 0.681562 0.731761i \(-0.261301\pi\)
−0.292942 + 0.956130i \(0.594634\pi\)
\(648\) −2.44949 1.41421i −0.0962250 0.0555556i
\(649\) −25.2378 + 14.5711i −0.990671 + 0.571964i
\(650\) 32.9706 32.9706i 1.29321 1.29321i
\(651\) 0.424546 1.01033i 0.0166393 0.0395980i
\(652\) 22.9706 22.9706i 0.899597 0.899597i
\(653\) 16.8895 + 4.52552i 0.660937 + 0.177097i 0.573669 0.819087i \(-0.305520\pi\)
0.0872679 + 0.996185i \(0.472186\pi\)
\(654\) 13.0711 22.6398i 0.511119 0.885284i
\(655\) −37.7635 + 65.4082i −1.47554 + 2.55571i
\(656\) −11.8272 + 6.82843i −0.461774 + 0.266605i
\(657\) 4.00000 0.156055
\(658\) 5.14214 6.63103i 0.200461 0.258504i
\(659\) −21.4142 + 21.4142i −0.834179 + 0.834179i −0.988085 0.153906i \(-0.950815\pi\)
0.153906 + 0.988085i \(0.450815\pi\)
\(660\) −4.78434 + 17.8554i −0.186230 + 0.695021i
\(661\) −0.331453 + 0.0888127i −0.0128920 + 0.00345441i −0.265259 0.964177i \(-0.585458\pi\)
0.252367 + 0.967632i \(0.418791\pi\)
\(662\) 2.92820 + 10.9282i 0.113808 + 0.424737i
\(663\) −20.1903 + 11.6569i −0.784125 + 0.452715i
\(664\) −19.1716 19.1716i −0.744001 0.744001i
\(665\) −22.6398 17.5563i −0.877932 0.680806i
\(666\) 2.82843 + 2.82843i 0.109599 + 0.109599i
\(667\) −0.543651 + 2.02893i −0.0210502 + 0.0785606i
\(668\) −10.3923 6.00000i −0.402090 0.232147i
\(669\) −2.73218 10.1967i −0.105632 0.394225i
\(670\) −43.6705 + 25.2132i −1.68714 + 0.974071i
\(671\) 6.24264 0.240994
\(672\) 13.7980 + 5.79796i 0.532268 + 0.223661i
\(673\) 36.9411 1.42398 0.711988 0.702192i \(-0.247795\pi\)
0.711988 + 0.702192i \(0.247795\pi\)
\(674\) −8.99348 + 5.19239i −0.346416 + 0.200003i
\(675\) 2.49938 + 9.32780i 0.0962011 + 0.359027i
\(676\) 2.32640 + 1.34315i 0.0894768 + 0.0516595i
\(677\) −8.11220 + 30.2752i −0.311777 + 1.16357i 0.615175 + 0.788390i \(0.289085\pi\)
−0.926953 + 0.375178i \(0.877581\pi\)
\(678\) −15.8995 15.8995i −0.610616 0.610616i
\(679\) 5.13461 37.5208i 0.197048 1.43992i
\(680\) 52.2843 52.2843i 2.00501 2.00501i
\(681\) −16.6646 + 9.62132i −0.638589 + 0.368690i
\(682\) 0.366025 + 1.36603i 0.0140158 + 0.0523078i
\(683\) 13.1229 3.51626i 0.502132 0.134546i 0.00114290 0.999999i \(-0.499636\pi\)
0.500989 + 0.865453i \(0.332970\pi\)
\(684\) −1.46410 + 5.46410i −0.0559813 + 0.208925i
\(685\) −19.4142 + 19.4142i −0.741779 + 0.741779i
\(686\) −3.02082 26.0168i −0.115335 0.993327i
\(687\) 12.3848 0.472509
\(688\) 10.8552 40.5120i 0.413849 1.54451i
\(689\) 4.53553 7.85578i 0.172790 0.299281i
\(690\) 0.656854 1.13770i 0.0250060 0.0433117i
\(691\) −14.7517 3.95270i −0.561181 0.150368i −0.0329321 0.999458i \(-0.510485\pi\)
−0.528249 + 0.849090i \(0.677151\pi\)
\(692\) −24.0000 + 24.0000i −0.912343 + 0.912343i
\(693\) −3.86250 5.08725i −0.146724 0.193249i
\(694\) 7.51472 7.51472i 0.285255 0.285255i
\(695\) 32.3507 18.6777i 1.22713 0.708484i
\(696\) 12.2426 21.2049i 0.464056 0.803769i
\(697\) −20.1903 11.6569i −0.764761 0.441535i
\(698\) −0.303225 + 1.13165i −0.0114772 + 0.0428337i
\(699\) 7.65685 + 7.65685i 0.289609 + 0.289609i
\(700\) −19.3137 47.3087i −0.729990 1.78810i
\(701\) −20.1213 + 20.1213i −0.759972 + 0.759972i −0.976317 0.216345i \(-0.930586\pi\)
0.216345 + 0.976317i \(0.430586\pi\)
\(702\) 4.18154 2.41421i 0.157822 0.0911186i
\(703\) 4.00000 6.92820i 0.150863 0.261302i
\(704\) −18.6556 + 4.99876i −0.703110 + 0.188398i
\(705\) 4.29289 + 7.43551i 0.161680 + 0.280037i
\(706\) 4.68629i 0.176371i
\(707\) −1.21390 9.59867i −0.0456533 0.360995i
\(708\) −24.1421 −0.907317
\(709\) 3.59745 13.4259i 0.135105 0.504220i −0.864892 0.501958i \(-0.832613\pi\)
0.999997 0.00226194i \(-0.000719997\pi\)
\(710\) −20.3933 + 5.46437i −0.765347 + 0.205074i
\(711\) 2.38794 + 1.37868i 0.0895549 + 0.0517045i
\(712\) −22.0000 38.1051i −0.824485 1.42805i
\(713\) 0.100505i 0.00376394i
\(714\) 3.20560 + 25.3477i 0.119967 + 0.948615i
\(715\) −22.3137 22.3137i −0.834485 0.834485i
\(716\) −51.4402 13.7834i −1.92241 0.515109i
\(717\) −0.794851 2.96642i −0.0296842 0.110783i
\(718\) −5.41421 + 9.37769i −0.202057 + 0.349972i
\(719\) −16.4350 28.4663i −0.612923 1.06161i −0.990745 0.135736i \(-0.956660\pi\)
0.377822 0.925878i \(-0.376673\pi\)
\(720\) −10.8284 + 10.8284i −0.403552 + 0.403552i
\(721\) −6.34315 15.5375i −0.236231 0.578646i
\(722\) −15.5563 −0.578947
\(723\) 4.96692 + 1.33088i 0.184722 + 0.0494961i
\(724\) 26.5772 7.12133i 0.987733 0.264662i
\(725\) −80.7494 + 21.6367i −2.99896 + 0.803569i
\(726\) −7.06450 1.89293i −0.262188 0.0702531i
\(727\) 14.5563i 0.539865i −0.962879 0.269933i \(-0.912999\pi\)
0.962879 0.269933i \(-0.0870014\pi\)
\(728\) −20.3490 + 15.4500i −0.754184 + 0.572615i
\(729\) 1.00000i 0.0370370i
\(730\) 5.60521 20.9189i 0.207458 0.774244i
\(731\) 69.1583 18.5309i 2.55791 0.685391i
\(732\) 4.47871 + 2.58579i 0.165538 + 0.0955734i
\(733\) 40.5689 + 10.8704i 1.49845 + 0.401507i 0.912579 0.408900i \(-0.134088\pi\)
0.585867 + 0.810407i \(0.300754\pi\)
\(734\) 35.8995i 1.32507i
\(735\) 25.8137 + 7.19988i 0.952153 + 0.265572i
\(736\) 1.37258 0.0505941
\(737\) 11.2426 + 19.4728i 0.414128 + 0.717291i
\(738\) 4.18154 + 2.41421i 0.153925 + 0.0888684i
\(739\) 3.43507 + 12.8198i 0.126361 + 0.471586i 0.999885 0.0151963i \(-0.00483733\pi\)
−0.873524 + 0.486782i \(0.838171\pi\)
\(740\) 18.7554 10.8284i 0.689462 0.398061i
\(741\) −6.82843 6.82843i −0.250849 0.250849i
\(742\) −6.01140 7.91753i −0.220685 0.290662i
\(743\) 5.31371i 0.194941i 0.995238 + 0.0974705i \(0.0310752\pi\)
−0.995238 + 0.0974705i \(0.968925\pi\)
\(744\) −0.303225 + 1.13165i −0.0111168 + 0.0414884i
\(745\) 30.4085 + 17.5563i 1.11408 + 0.643215i
\(746\) 0.0367874 + 0.137292i 0.00134688 + 0.00502663i
\(747\) −2.48098 + 9.25916i −0.0907745 + 0.338775i
\(748\) −23.3137 23.3137i −0.852434 0.852434i
\(749\) −4.70497 1.97705i −0.171916 0.0722397i
\(750\) 25.2132 0.920656
\(751\) −15.0355 26.0423i −0.548654 0.950297i −0.998367 0.0571241i \(-0.981807\pi\)
0.449713 0.893173i \(-0.351526\pi\)
\(752\) −4.48528 + 7.76874i −0.163561 + 0.283297i
\(753\) 9.86396 17.0849i 0.359463 0.622608i
\(754\) 20.8995 + 36.1990i 0.761115 + 1.31829i
\(755\) −33.6066 + 33.6066i −1.22307 + 1.22307i
\(756\) −0.663902 5.24969i −0.0241459 0.190929i
\(757\) 12.3137 + 12.3137i 0.447549 + 0.447549i 0.894539 0.446990i \(-0.147504\pi\)
−0.446990 + 0.894539i \(0.647504\pi\)
\(758\) 12.8601 + 3.44584i 0.467098 + 0.125159i
\(759\) −0.507306 0.292893i −0.0184140 0.0106314i
\(760\) 26.5241 + 15.3137i 0.962131 + 0.555487i
\(761\) 30.9158 17.8492i 1.12070 0.647035i 0.179118 0.983828i \(-0.442676\pi\)
0.941579 + 0.336793i \(0.109342\pi\)
\(762\) 2.75736 + 2.75736i 0.0998886 + 0.0998886i
\(763\) 48.5210 6.13621i 1.75658 0.222146i
\(764\) 6.62742 0.239772
\(765\) −25.2514 6.76608i −0.912965 0.244628i
\(766\) 18.2841 + 10.5563i 0.660633 + 0.381416i
\(767\) 20.6066 35.6917i 0.744061 1.28875i
\(768\) −15.4548 4.14110i −0.557678 0.149429i
\(769\) 14.1716 0.511040 0.255520 0.966804i \(-0.417753\pi\)
0.255520 + 0.966804i \(0.417753\pi\)
\(770\) −32.0174 + 13.0711i −1.15383 + 0.471049i
\(771\) −8.31371 + 8.31371i −0.299411 + 0.299411i
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) −25.2514 + 6.76608i −0.908228 + 0.243359i −0.682547 0.730842i \(-0.739128\pi\)
−0.225682 + 0.974201i \(0.572461\pi\)
\(774\) −14.3232 + 3.83788i −0.514835 + 0.137950i
\(775\) 3.46410 2.00000i 0.124434 0.0718421i
\(776\) 40.4853i 1.45334i
\(777\) −1.01461 + 7.41421i −0.0363990 + 0.265983i
\(778\) −35.7990 + 35.7990i −1.28346 + 1.28346i
\(779\) 2.49938 9.32780i 0.0895495 0.334203i
\(780\) −6.76608 25.2514i −0.242265 0.904144i
\(781\) 2.43658 + 9.09343i 0.0871876 + 0.325389i
\(782\) 1.17157 + 2.02922i 0.0418954 + 0.0725649i
\(783\) −8.65685 −0.309371
\(784\) 6.97056 + 27.1185i 0.248949 + 0.968517i
\(785\) −49.6569 −1.77233
\(786\) 13.9497 + 24.1617i 0.497571 + 0.861818i
\(787\) 13.3285 + 49.7427i 0.475111 + 1.77314i 0.620973 + 0.783832i \(0.286738\pi\)
−0.145862 + 0.989305i \(0.546596\pi\)
\(788\) 24.1197 6.46286i 0.859229 0.230230i
\(789\) 4.78434 17.8554i 0.170327 0.635669i
\(790\) 10.5563 10.5563i 0.375578 0.375578i
\(791\) 5.70346 41.6777i 0.202792 1.48189i
\(792\) 4.82843 + 4.82843i 0.171571 + 0.171571i
\(793\) −7.64564 + 4.41421i −0.271505 + 0.156753i
\(794\) 1.32581 0.355251i 0.0470514 0.0126074i
\(795\) 9.82498 2.63260i 0.348456 0.0933686i
\(796\) −22.8138 + 13.1716i −0.808615 + 0.466854i
\(797\) −2.26346 + 2.26346i −0.0801757 + 0.0801757i −0.746057 0.665882i \(-0.768056\pi\)
0.665882 + 0.746057i \(0.268056\pi\)
\(798\) −9.79796 + 4.00000i −0.346844 + 0.141598i
\(799\) −15.3137 −0.541760
\(800\) 27.3137 + 47.3087i 0.965685 + 1.67262i
\(801\) −7.77817 + 13.4722i −0.274828 + 0.476017i
\(802\) 29.3939 + 16.9706i 1.03793 + 0.599251i
\(803\) −9.32780 2.49938i −0.329171 0.0882011i
\(804\) 18.6274i 0.656938i
\(805\) 2.43830 0.308360i 0.0859389 0.0108683i
\(806\) −1.41421 1.41421i −0.0498135 0.0498135i
\(807\) −25.2378 + 14.5711i −0.888414 + 0.512926i
\(808\) 2.67700 + 9.99071i 0.0941766 + 0.351472i
\(809\) −15.2913 8.82843i −0.537613 0.310391i 0.206498 0.978447i \(-0.433793\pi\)
−0.744111 + 0.668056i \(0.767127\pi\)
\(810\) 5.22973 + 1.40130i 0.183754 + 0.0492367i
\(811\) 15.5563 + 15.5563i 0.546257 + 0.546257i 0.925356 0.379099i \(-0.123766\pi\)
−0.379099 + 0.925356i \(0.623766\pi\)
\(812\) 45.4458 5.74731i 1.59483 0.201691i
\(813\) 0.192388 0.192388i 0.00674735 0.00674735i
\(814\) −4.82843 8.36308i −0.169236 0.293126i
\(815\) −31.0919 + 53.8527i −1.08910 + 1.88638i
\(816\) −7.06931 26.3830i −0.247475 0.923590i
\(817\) 14.8284 + 25.6836i 0.518781 + 0.898555i
\(818\) −46.1838 −1.61478
\(819\) 8.32780 + 3.49938i 0.290997 + 0.122278i
\(820\) 18.4853 18.4853i 0.645534 0.645534i
\(821\) 1.29410 4.82963i 0.0451642 0.168555i −0.939660 0.342110i \(-0.888859\pi\)
0.984824 + 0.173554i \(0.0555252\pi\)
\(822\) 2.62498 + 9.79655i 0.0915566 + 0.341694i
\(823\) 15.8856 + 9.17157i 0.553738 + 0.319701i 0.750628 0.660725i \(-0.229751\pi\)
−0.196890 + 0.980426i \(0.563084\pi\)
\(824\) 8.97056 + 15.5375i 0.312504 + 0.541273i
\(825\) 23.3137i 0.811679i
\(826\) −27.3120 35.9723i −0.950306 1.25164i
\(827\) −29.9497 29.9497i −1.04145 1.04145i −0.999103 0.0423520i \(-0.986515\pi\)
−0.0423520 0.999103i \(-0.513485\pi\)
\(828\) −0.242641 0.420266i −0.00843235 0.0146053i
\(829\) −10.9072 40.7062i −0.378822 1.41378i −0.847679 0.530510i \(-0.822001\pi\)
0.468857 0.883274i \(-0.344666\pi\)
\(830\) 44.9463 + 25.9497i 1.56011 + 0.900729i
\(831\) −10.8284 18.7554i −0.375634 0.650617i
\(832\) 19.3137 19.3137i 0.669582 0.669582i
\(833\) −34.1421 + 33.4523i −1.18295 + 1.15905i
\(834\) 13.7990i 0.477820i
\(835\) 22.1879 + 5.94522i 0.767843 + 0.205743i
\(836\) 6.82843 11.8272i 0.236166 0.409052i
\(837\) 0.400100 0.107206i 0.0138295 0.00370559i
\(838\) −7.14288 + 26.6576i −0.246747 + 0.920872i
\(839\) 19.7990i 0.683537i −0.939784 0.341769i \(-0.888974\pi\)
0.939784 0.341769i \(-0.111026\pi\)
\(840\) −28.3848 3.88437i −0.979368 0.134023i
\(841\) 45.9411i 1.58418i
\(842\) −2.86934 0.768838i −0.0988841 0.0264959i
\(843\) 0.800199 0.214413i 0.0275603 0.00738477i
\(844\) 4.08908 + 15.2607i 0.140752 + 0.525293i
\(845\) −4.96692 1.33088i −0.170867 0.0457838i
\(846\) 3.17157 0.109041
\(847\) −5.17157 12.6677i −0.177697 0.435268i
\(848\) 7.51472 + 7.51472i 0.258056 + 0.258056i
\(849\) −13.7279 23.7775i −0.471141 0.816040i
\(850\) −46.6274 + 80.7611i −1.59931 + 2.77008i
\(851\) 0.177625 + 0.662907i 0.00608892 + 0.0227241i
\(852\) −2.01853 + 7.53325i −0.0691536 + 0.258085i
\(853\) 5.07107 + 5.07107i 0.173630 + 0.173630i 0.788572 0.614942i \(-0.210821\pi\)
−0.614942 + 0.788572i \(0.710821\pi\)
\(854\) 1.21390 + 9.59867i 0.0415387 + 0.328460i
\(855\) 10.8284i 0.370324i
\(856\) 5.26994 + 1.41208i 0.180123 + 0.0482638i
\(857\) −6.71807 3.87868i −0.229485 0.132493i 0.380850 0.924637i \(-0.375632\pi\)
−0.610334 + 0.792144i \(0.708965\pi\)
\(858\) −11.2597 + 3.01702i −0.384398 + 0.102999i
\(859\) 11.2472 41.9751i 0.383750 1.43217i −0.456379 0.889785i \(-0.650854\pi\)
0.840129 0.542387i \(-0.182479\pi\)
\(860\) 80.2843i 2.73767i
\(861\) 1.13335 + 8.96178i 0.0386245 + 0.305417i
\(862\) 31.6569i 1.07824i
\(863\) 18.1924 + 31.5101i 0.619276 + 1.07262i 0.989618 + 0.143722i \(0.0459072\pi\)
−0.370342 + 0.928895i \(0.620759\pi\)
\(864\) 1.46410 + 5.46410i 0.0498097 + 0.185893i
\(865\) 32.4853 56.2662i 1.10453 1.91311i
\(866\) 20.7846 12.0000i 0.706290 0.407777i
\(867\) 20.9497 20.9497i 0.711491 0.711491i
\(868\) −2.02922 + 0.828427i −0.0688763 + 0.0281186i
\(869\) −4.70711 4.70711i −0.159678 0.159678i
\(870\) −12.1309 + 45.2730i −0.411275 + 1.53490i
\(871\) −27.5387 15.8995i −0.933114 0.538734i
\(872\) −50.5027 + 13.5322i −1.71024 + 0.458257i
\(873\) 12.3960 7.15685i 0.419542 0.242223i
\(874\) −0.686292 + 0.686292i −0.0232142 + 0.0232142i
\(875\) 28.5237 + 37.5682i 0.964277 + 1.27004i
\(876\) −5.65685 5.65685i −0.191127 0.191127i
\(877\) −42.7753 11.4616i −1.44442 0.387031i −0.550341 0.834940i \(-0.685502\pi\)
−0.894079 + 0.447909i \(0.852169\pi\)
\(878\) 3.22183 5.58037i 0.108731 0.188328i
\(879\) 0.742641 1.28629i 0.0250486 0.0433855i
\(880\) 32.0174 18.4853i 1.07931 0.623139i
\(881\) 33.5147 1.12914 0.564570 0.825385i \(-0.309042\pi\)
0.564570 + 0.825385i \(0.309042\pi\)
\(882\) 7.07107 6.92820i 0.238095 0.233285i
\(883\) −19.0000 + 19.0000i −0.639401 + 0.639401i −0.950408 0.311007i \(-0.899334\pi\)
0.311007 + 0.950408i \(0.399334\pi\)
\(884\) 45.0386 + 12.0681i 1.51481 + 0.405893i
\(885\) 44.6385 11.9609i 1.50051 0.402060i
\(886\) 4.54392 + 16.9581i 0.152656 + 0.569720i
\(887\) 12.0373 6.94975i 0.404174 0.233350i −0.284110 0.958792i \(-0.591698\pi\)
0.688283 + 0.725442i \(0.258365\pi\)
\(888\) 8.00000i 0.268462i
\(889\) −0.989118 + 7.22792i −0.0331740 + 0.242417i
\(890\) 59.5563 + 59.5563i 1.99633 + 1.99633i
\(891\) 0.624844 2.33195i 0.0209331 0.0781233i
\(892\) −10.5563 + 18.2841i −0.353453 + 0.612198i
\(893\) −1.64173 6.12701i −0.0549383 0.205033i
\(894\) 11.2328 6.48528i 0.375682 0.216900i
\(895\) 101.941 3.40752
\(896\) −11.3137 27.7128i −0.377964 0.925820i
\(897\) 0.828427 0.0276604
\(898\) −2.15232 + 1.24264i −0.0718237 + 0.0414675i
\(899\) 0.928070 + 3.46360i 0.0309529 + 0.115518i
\(900\) 9.65685 16.7262i 0.321895 0.557539i
\(901\) −4.69553 + 17.5240i −0.156431 + 0.583808i
\(902\) −8.24264 8.24264i −0.274450 0.274450i
\(903\) −21.9223 17.0000i −0.729529 0.565725i
\(904\) 44.9706i 1.49570i
\(905\) −45.6127 + 26.3345i −1.51622 + 0.875389i
\(906\) 4.54392 + 16.9581i 0.150962 + 0.563396i
\(907\) −27.2803 + 7.30973i −0.905827 + 0.242716i −0.681517 0.731802i \(-0.738680\pi\)
−0.224310 + 0.974518i \(0.572013\pi\)
\(908\) 37.1739 + 9.96072i 1.23366 + 0.330558i
\(909\) 2.58579 2.58579i 0.0857651 0.0857651i
\(910\) 29.9706 38.6485i 0.993514 1.28118i
\(911\) −38.7279 −1.28311 −0.641557 0.767076i \(-0.721711\pi\)
−0.641557 + 0.767076i \(0.721711\pi\)
\(912\) 9.79796 5.65685i 0.324443 0.187317i
\(913\) 11.5711 20.0417i 0.382946 0.663283i
\(914\) 16.7071 28.9376i 0.552622 0.957169i
\(915\) −9.56218 2.56218i −0.316116 0.0847030i
\(916\) −17.5147 17.5147i −0.578703 0.578703i
\(917\) −20.2200 + 48.1195i −0.667724 + 1.58905i
\(918\) −6.82843 + 6.82843i −0.225372 + 0.225372i
\(919\) −47.3087 + 27.3137i −1.56057 + 0.900996i −0.563372 + 0.826203i \(0.690496\pi\)
−0.997199 + 0.0747927i \(0.976170\pi\)
\(920\) −2.53789 + 0.680026i −0.0836718 + 0.0224198i
\(921\) −19.9801 11.5355i −0.658368 0.380109i
\(922\) 4.14110 15.4548i 0.136380 0.508977i
\(923\) −9.41421 9.41421i −0.309873 0.309873i
\(924\) −1.73205 + 12.6569i −0.0569803 + 0.416380i
\(925\) −19.3137 + 19.3137i −0.635031 + 0.635031i
\(926\) 43.8446 25.3137i 1.44082 0.831860i
\(927\) 3.17157 5.49333i 0.104168 0.180424i
\(928\) −47.3019 + 12.6745i −1.55276 + 0.416061i
\(929\) −11.8284 20.4874i −0.388078 0.672171i 0.604113 0.796899i \(-0.293528\pi\)
−0.992191 + 0.124728i \(0.960194\pi\)
\(930\) 2.24264i 0.0735391i
\(931\) −17.0445 10.0740i −0.558611 0.330160i
\(932\) 21.6569i 0.709394i
\(933\) 5.06156 18.8900i 0.165708 0.618430i
\(934\) 24.7826 6.64048i 0.810912 0.217283i
\(935\) 54.6572 + 31.5563i 1.78748 + 1.03200i
\(936\) −9.32780 2.49938i −0.304889 0.0816947i
\(937\) 27.0000i 0.882052i 0.897494 + 0.441026i \(0.145385\pi\)
−0.897494 + 0.441026i \(0.854615\pi\)
\(938\) −27.7552 + 21.0732i −0.906240 + 0.688065i
\(939\) 2.94975 + 2.94975i 0.0962614 + 0.0962614i
\(940\) 4.44433 16.5865i 0.144958 0.540991i
\(941\) 4.79196 + 17.8838i 0.156213 + 0.582997i 0.998998 + 0.0447462i \(0.0142479\pi\)
−0.842785 + 0.538251i \(0.819085\pi\)
\(942\) −9.17157 + 15.8856i −0.298826 + 0.517582i
\(943\) 0.414214 + 0.717439i 0.0134886 + 0.0233630i
\(944\) 34.1421 + 34.1421i 1.11123 + 1.11123i
\(945\) 3.82843 + 9.37769i 0.124539 + 0.305056i
\(946\) 35.7990 1.16393
\(947\) −43.9070 11.7648i −1.42678 0.382306i −0.538899 0.842370i \(-0.681160\pi\)
−0.887886 + 0.460064i \(0.847826\pi\)
\(948\) −1.42731 5.32681i −0.0463570 0.173007i
\(949\) 13.1915 3.53465i 0.428214 0.114740i
\(950\) −37.3112 9.99751i −1.21054 0.324362i
\(951\) 22.6569i 0.734699i
\(952\) 31.3137 40.3805i 1.01488 1.30874i
\(953\) 35.2548i 1.14202i 0.820944 + 0.571008i \(0.193447\pi\)
−0.820944 + 0.571008i \(0.806553\pi\)
\(954\) 0.972476 3.62933i 0.0314851 0.117504i
\(955\) −12.2540 + 3.28345i −0.396531 + 0.106250i
\(956\) −3.07107 + 5.31925i −0.0993254 + 0.172037i
\(957\) 20.1874 + 5.40919i 0.652565 + 0.174854i
\(958\) 29.4558i 0.951675i
\(959\) −11.6274 + 14.9941i −0.375469 + 0.484185i
\(960\) 30.6274 0.988496
\(961\) 15.4142 + 26.6982i 0.497233 + 0.861232i
\(962\) 11.8272 + 6.82843i 0.381324 + 0.220157i
\(963\) −0.499244 1.86321i −0.0160879 0.0600410i
\(964\) −5.14214 8.90644i −0.165617 0.286857i
\(965\) 18.9497 + 18.9497i 0.610014 + 0.610014i
\(966\) 0.351705 0.836987i 0.0113159 0.0269296i
\(967\) 41.1838i 1.32438i 0.749336 + 0.662190i \(0.230373\pi\)
−0.749336 + 0.662190i \(0.769627\pi\)
\(968\) 7.31371 + 12.6677i 0.235071 + 0.407156i
\(969\) 16.7262 + 9.65685i 0.537322 + 0.310223i
\(970\) −20.0578 74.8568i −0.644018 2.40351i
\(971\) 2.99862 11.1910i 0.0962304 0.359137i −0.900973 0.433876i \(-0.857146\pi\)
0.997203 + 0.0747390i \(0.0238124\pi\)
\(972\) 1.41421 1.41421i 0.0453609 0.0453609i
\(973\) 20.5608 15.6108i 0.659148 0.500459i
\(974\) 43.2132 1.38464
\(975\) 16.4853 + 28.5533i 0.527952 + 0.914439i
\(976\) −2.67700 9.99071i −0.0856888 0.319795i
\(977\) 5.34315 9.25460i 0.170942 0.296081i −0.767807 0.640681i \(-0.778652\pi\)
0.938750 + 0.344600i \(0.111985\pi\)
\(978\) 11.4853 + 19.8931i 0.367259 + 0.636111i
\(979\) 26.5563 26.5563i 0.848745 0.848745i
\(980\) −26.3239 46.6883i −0.840887 1.49140i
\(981\) 13.0711 + 13.0711i 0.417327 + 0.417327i
\(982\) 11.6882 + 3.13184i 0.372985 + 0.0999411i
\(983\) −28.9376 16.7071i −0.922965 0.532874i −0.0383851 0.999263i \(-0.512221\pi\)
−0.884580 + 0.466389i \(0.845555\pi\)
\(984\) −2.49938 9.32780i −0.0796773 0.297360i
\(985\) −41.3951 + 23.8995i −1.31896 + 0.761501i
\(986\) −59.1127 59.1127i −1.88253 1.88253i
\(987\) 3.58800 + 4.72571i 0.114207 + 0.150421i
\(988\) 19.3137i 0.614451i
\(989\) −2.45747 0.658476i −0.0781429 0.0209383i
\(990\) −11.3199 6.53553i −0.359769 0.207713i
\(991\) −0.278175 + 0.481813i −0.00883651 + 0.0153053i −0.870410 0.492328i \(-0.836146\pi\)
0.861573 + 0.507633i \(0.169479\pi\)
\(992\) 2.02922 1.17157i 0.0644279 0.0371975i
\(993\) −8.00000 −0.253872
\(994\) −13.5082 + 5.51472i −0.428456 + 0.174916i
\(995\) 35.6569 35.6569i 1.13040 1.13040i
\(996\) 16.6031 9.58579i 0.526088 0.303737i
\(997\) 9.46510 2.53617i 0.299763 0.0803212i −0.105803 0.994387i \(-0.533741\pi\)
0.405566 + 0.914066i \(0.367075\pi\)
\(998\) 32.6473 8.74782i 1.03343 0.276907i
\(999\) −2.44949 + 1.41421i −0.0774984 + 0.0447437i
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 336.2.bq.a.277.2 yes 8
7.2 even 3 inner 336.2.bq.a.37.1 8
16.13 even 4 inner 336.2.bq.a.109.1 yes 8
112.93 even 12 inner 336.2.bq.a.205.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.bq.a.37.1 8 7.2 even 3 inner
336.2.bq.a.109.1 yes 8 16.13 even 4 inner
336.2.bq.a.205.2 yes 8 112.93 even 12 inner
336.2.bq.a.277.2 yes 8 1.1 even 1 trivial