Properties

Label 756.2.bb.a.611.14
Level $756$
Weight $2$
Character 756.611
Analytic conductor $6.037$
Analytic rank $0$
Dimension $88$
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] = [756,2,Mod(611,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.611");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bb (of order \(6\), degree \(2\), not 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(44\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 611.14
Character \(\chi\) \(=\) 756.611
Dual form 756.2.bb.a.683.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.801193 + 1.16537i) q^{2} +(-0.716179 - 1.86737i) q^{4} +(-2.71842 + 1.56948i) q^{5} +(-2.39714 - 1.11970i) q^{7} +(2.74998 + 0.661514i) q^{8} +O(q^{10})\) \(q+(-0.801193 + 1.16537i) q^{2} +(-0.716179 - 1.86737i) q^{4} +(-2.71842 + 1.56948i) q^{5} +(-2.39714 - 1.11970i) q^{7} +(2.74998 + 0.661514i) q^{8} +(0.348953 - 4.42542i) q^{10} +(1.84616 - 3.19765i) q^{11} +(0.398951 - 0.691003i) q^{13} +(3.22543 - 1.89646i) q^{14} +(-2.97418 + 2.67475i) q^{16} +(2.63178 - 1.51946i) q^{17} +(3.92177 + 2.26423i) q^{19} +(4.87768 + 3.95228i) q^{20} +(2.24731 + 4.71340i) q^{22} +(1.10618 + 1.91595i) q^{23} +(2.42653 - 4.20287i) q^{25} +(0.485638 + 1.01855i) q^{26} +(-0.374113 + 5.27826i) q^{28} +(-8.16616 + 4.71474i) q^{29} +2.16508i q^{31} +(-0.734183 - 5.60901i) q^{32} +(-0.337832 + 4.28438i) q^{34} +(8.27376 - 0.718458i) q^{35} +(-2.94414 + 5.09940i) q^{37} +(-5.78077 + 2.75622i) q^{38} +(-8.51383 + 2.51777i) q^{40} +(9.25469 + 5.34320i) q^{41} +(4.01769 - 2.31962i) q^{43} +(-7.29339 - 1.15739i) q^{44} +(-3.11906 - 0.245944i) q^{46} +10.6006 q^{47} +(4.49256 + 5.36814i) q^{49} +(2.95378 + 6.19511i) q^{50} +(-1.57608 - 0.250109i) q^{52} +(6.12081 - 3.53385i) q^{53} +11.5900i q^{55} +(-5.85140 - 4.66489i) q^{56} +(1.04826 - 13.2940i) q^{58} -0.509408 q^{59} +9.56150 q^{61} +(-2.52312 - 1.73465i) q^{62} +(7.12480 + 3.63830i) q^{64} +2.50458i q^{65} -7.45608i q^{67} +(-4.72223 - 3.82632i) q^{68} +(-5.79162 + 10.2176i) q^{70} -2.15661 q^{71} +(1.27196 + 2.20310i) q^{73} +(-3.58387 - 7.51662i) q^{74} +(1.41949 - 8.94500i) q^{76} +(-8.00590 + 5.59807i) q^{77} -10.3964i q^{79} +(3.88709 - 11.9390i) q^{80} +(-13.6416 + 6.50421i) q^{82} +(-0.812599 - 1.40746i) q^{83} +(-4.76952 + 8.26105i) q^{85} +(-0.515736 + 6.54057i) q^{86} +(7.19220 - 7.57221i) q^{88} +(1.73558 + 1.00204i) q^{89} +(-1.73006 + 1.20973i) q^{91} +(2.78558 - 3.43781i) q^{92} +(-8.49313 + 12.3536i) q^{94} -14.2147 q^{95} +(-1.88309 - 3.26161i) q^{97} +(-9.85528 + 0.934580i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.801193 + 1.16537i −0.566529 + 0.824042i
\(3\) 0 0
\(4\) −0.716179 1.86737i −0.358089 0.933687i
\(5\) −2.71842 + 1.56948i −1.21571 + 0.701892i −0.963998 0.265909i \(-0.914328\pi\)
−0.251715 + 0.967801i \(0.580995\pi\)
\(6\) 0 0
\(7\) −2.39714 1.11970i −0.906034 0.423206i
\(8\) 2.74998 + 0.661514i 0.972265 + 0.233881i
\(9\) 0 0
\(10\) 0.348953 4.42542i 0.110348 1.39944i
\(11\) 1.84616 3.19765i 0.556639 0.964127i −0.441135 0.897441i \(-0.645424\pi\)
0.997774 0.0666862i \(-0.0212426\pi\)
\(12\) 0 0
\(13\) 0.398951 0.691003i 0.110649 0.191650i −0.805383 0.592755i \(-0.798040\pi\)
0.916032 + 0.401105i \(0.131374\pi\)
\(14\) 3.22543 1.89646i 0.862034 0.506851i
\(15\) 0 0
\(16\) −2.97418 + 2.67475i −0.743544 + 0.668687i
\(17\) 2.63178 1.51946i 0.638301 0.368523i −0.145659 0.989335i \(-0.546530\pi\)
0.783960 + 0.620812i \(0.213197\pi\)
\(18\) 0 0
\(19\) 3.92177 + 2.26423i 0.899715 + 0.519451i 0.877108 0.480294i \(-0.159470\pi\)
0.0226074 + 0.999744i \(0.492803\pi\)
\(20\) 4.87768 + 3.95228i 1.09068 + 0.883756i
\(21\) 0 0
\(22\) 2.24731 + 4.71340i 0.479129 + 1.00490i
\(23\) 1.10618 + 1.91595i 0.230654 + 0.399504i 0.958001 0.286766i \(-0.0925802\pi\)
−0.727347 + 0.686270i \(0.759247\pi\)
\(24\) 0 0
\(25\) 2.42653 4.20287i 0.485305 0.840573i
\(26\) 0.485638 + 1.01855i 0.0952415 + 0.199755i
\(27\) 0 0
\(28\) −0.374113 + 5.27826i −0.0707007 + 0.997498i
\(29\) −8.16616 + 4.71474i −1.51642 + 0.875505i −0.516604 + 0.856224i \(0.672804\pi\)
−0.999814 + 0.0192805i \(0.993862\pi\)
\(30\) 0 0
\(31\) 2.16508i 0.388860i 0.980916 + 0.194430i \(0.0622858\pi\)
−0.980916 + 0.194430i \(0.937714\pi\)
\(32\) −0.734183 5.60901i −0.129786 0.991542i
\(33\) 0 0
\(34\) −0.337832 + 4.28438i −0.0579377 + 0.734766i
\(35\) 8.27376 0.718458i 1.39852 0.121441i
\(36\) 0 0
\(37\) −2.94414 + 5.09940i −0.484013 + 0.838336i −0.999831 0.0183623i \(-0.994155\pi\)
0.515818 + 0.856698i \(0.327488\pi\)
\(38\) −5.78077 + 2.75622i −0.937764 + 0.447119i
\(39\) 0 0
\(40\) −8.51383 + 2.51777i −1.34615 + 0.398094i
\(41\) 9.25469 + 5.34320i 1.44534 + 0.834467i 0.998199 0.0599959i \(-0.0191088\pi\)
0.447141 + 0.894463i \(0.352442\pi\)
\(42\) 0 0
\(43\) 4.01769 2.31962i 0.612693 0.353738i −0.161326 0.986901i \(-0.551577\pi\)
0.774019 + 0.633163i \(0.218244\pi\)
\(44\) −7.29339 1.15739i −1.09952 0.174483i
\(45\) 0 0
\(46\) −3.11906 0.245944i −0.459880 0.0362624i
\(47\) 10.6006 1.54626 0.773128 0.634250i \(-0.218691\pi\)
0.773128 + 0.634250i \(0.218691\pi\)
\(48\) 0 0
\(49\) 4.49256 + 5.36814i 0.641794 + 0.766877i
\(50\) 2.95378 + 6.19511i 0.417728 + 0.876121i
\(51\) 0 0
\(52\) −1.57608 0.250109i −0.218563 0.0346839i
\(53\) 6.12081 3.53385i 0.840758 0.485412i −0.0167637 0.999859i \(-0.505336\pi\)
0.857522 + 0.514447i \(0.172003\pi\)
\(54\) 0 0
\(55\) 11.5900i 1.56280i
\(56\) −5.85140 4.66489i −0.781926 0.623372i
\(57\) 0 0
\(58\) 1.04826 13.2940i 0.137643 1.74559i
\(59\) −0.509408 −0.0663192 −0.0331596 0.999450i \(-0.510557\pi\)
−0.0331596 + 0.999450i \(0.510557\pi\)
\(60\) 0 0
\(61\) 9.56150 1.22422 0.612112 0.790771i \(-0.290320\pi\)
0.612112 + 0.790771i \(0.290320\pi\)
\(62\) −2.52312 1.73465i −0.320437 0.220301i
\(63\) 0 0
\(64\) 7.12480 + 3.63830i 0.890600 + 0.454788i
\(65\) 2.50458i 0.310655i
\(66\) 0 0
\(67\) 7.45608i 0.910906i −0.890260 0.455453i \(-0.849477\pi\)
0.890260 0.455453i \(-0.150523\pi\)
\(68\) −4.72223 3.82632i −0.572654 0.464009i
\(69\) 0 0
\(70\) −5.79162 + 10.2176i −0.692230 + 1.22124i
\(71\) −2.15661 −0.255942 −0.127971 0.991778i \(-0.540847\pi\)
−0.127971 + 0.991778i \(0.540847\pi\)
\(72\) 0 0
\(73\) 1.27196 + 2.20310i 0.148871 + 0.257853i 0.930811 0.365502i \(-0.119103\pi\)
−0.781939 + 0.623355i \(0.785769\pi\)
\(74\) −3.58387 7.51662i −0.416616 0.873789i
\(75\) 0 0
\(76\) 1.41949 8.94500i 0.162826 1.02606i
\(77\) −8.00590 + 5.59807i −0.912357 + 0.637959i
\(78\) 0 0
\(79\) 10.3964i 1.16969i −0.811145 0.584846i \(-0.801155\pi\)
0.811145 0.584846i \(-0.198845\pi\)
\(80\) 3.88709 11.9390i 0.434590 1.33482i
\(81\) 0 0
\(82\) −13.6416 + 6.50421i −1.50646 + 0.718270i
\(83\) −0.812599 1.40746i −0.0891943 0.154489i 0.817976 0.575252i \(-0.195096\pi\)
−0.907171 + 0.420763i \(0.861763\pi\)
\(84\) 0 0
\(85\) −4.76952 + 8.26105i −0.517327 + 0.896037i
\(86\) −0.515736 + 6.54057i −0.0556132 + 0.705287i
\(87\) 0 0
\(88\) 7.19220 7.57221i 0.766691 0.807200i
\(89\) 1.73558 + 1.00204i 0.183971 + 0.106216i 0.589157 0.808019i \(-0.299460\pi\)
−0.405186 + 0.914234i \(0.632793\pi\)
\(90\) 0 0
\(91\) −1.73006 + 1.20973i −0.181359 + 0.126814i
\(92\) 2.78558 3.43781i 0.290417 0.358417i
\(93\) 0 0
\(94\) −8.49313 + 12.3536i −0.876000 + 1.27418i
\(95\) −14.2147 −1.45839
\(96\) 0 0
\(97\) −1.88309 3.26161i −0.191199 0.331167i 0.754449 0.656359i \(-0.227904\pi\)
−0.945648 + 0.325192i \(0.894571\pi\)
\(98\) −9.85528 + 0.934580i −0.995534 + 0.0944069i
\(99\) 0 0
\(100\) −9.58615 1.52123i −0.958615 0.152123i
\(101\) 14.8471 + 8.57197i 1.47734 + 0.852943i 0.999672 0.0255972i \(-0.00814873\pi\)
0.477668 + 0.878540i \(0.341482\pi\)
\(102\) 0 0
\(103\) 2.78573 1.60834i 0.274486 0.158475i −0.356438 0.934319i \(-0.616009\pi\)
0.630925 + 0.775844i \(0.282676\pi\)
\(104\) 1.55422 1.63634i 0.152403 0.160456i
\(105\) 0 0
\(106\) −0.785705 + 9.96432i −0.0763144 + 0.967820i
\(107\) −1.77960 + 3.08236i −0.172041 + 0.297983i −0.939133 0.343553i \(-0.888369\pi\)
0.767092 + 0.641537i \(0.221703\pi\)
\(108\) 0 0
\(109\) 2.56961 + 4.45070i 0.246124 + 0.426300i 0.962447 0.271469i \(-0.0875095\pi\)
−0.716323 + 0.697769i \(0.754176\pi\)
\(110\) −13.5067 9.28587i −1.28781 0.885373i
\(111\) 0 0
\(112\) 10.1244 3.08157i 0.956668 0.291181i
\(113\) 7.11141 + 4.10577i 0.668985 + 0.386239i 0.795692 0.605701i \(-0.207107\pi\)
−0.126707 + 0.991940i \(0.540441\pi\)
\(114\) 0 0
\(115\) −6.01410 3.47224i −0.560818 0.323788i
\(116\) 14.6526 + 11.8727i 1.36046 + 1.10235i
\(117\) 0 0
\(118\) 0.408134 0.593649i 0.0375718 0.0546498i
\(119\) −8.01009 + 0.695561i −0.734283 + 0.0637620i
\(120\) 0 0
\(121\) −1.31663 2.28047i −0.119694 0.207316i
\(122\) −7.66061 + 11.1427i −0.693559 + 1.00881i
\(123\) 0 0
\(124\) 4.04302 1.55059i 0.363074 0.139247i
\(125\) 0.461263i 0.0412566i
\(126\) 0 0
\(127\) 16.6020i 1.47319i −0.676333 0.736596i \(-0.736432\pi\)
0.676333 0.736596i \(-0.263568\pi\)
\(128\) −9.94831 + 5.38805i −0.879315 + 0.476241i
\(129\) 0 0
\(130\) −2.91877 2.00665i −0.255993 0.175995i
\(131\) 5.74553 + 9.95156i 0.501990 + 0.869471i 0.999997 + 0.00229890i \(0.000731762\pi\)
−0.498008 + 0.867173i \(0.665935\pi\)
\(132\) 0 0
\(133\) −6.86577 9.81887i −0.595338 0.851404i
\(134\) 8.68910 + 5.97377i 0.750624 + 0.516055i
\(135\) 0 0
\(136\) 8.24250 2.43753i 0.706789 0.209016i
\(137\) −12.0589 6.96218i −1.03026 0.594819i −0.113199 0.993572i \(-0.536110\pi\)
−0.917058 + 0.398753i \(0.869443\pi\)
\(138\) 0 0
\(139\) −13.1223 7.57615i −1.11302 0.642601i −0.173408 0.984850i \(-0.555478\pi\)
−0.939609 + 0.342249i \(0.888811\pi\)
\(140\) −7.26712 14.9357i −0.614184 1.26229i
\(141\) 0 0
\(142\) 1.72786 2.51325i 0.144999 0.210907i
\(143\) −1.47306 2.55141i −0.123183 0.213360i
\(144\) 0 0
\(145\) 14.7994 25.6332i 1.22902 2.12872i
\(146\) −3.58651 0.282803i −0.296822 0.0234049i
\(147\) 0 0
\(148\) 11.6310 + 1.84573i 0.956064 + 0.151718i
\(149\) −15.6827 + 9.05441i −1.28478 + 0.741766i −0.977718 0.209924i \(-0.932678\pi\)
−0.307059 + 0.951690i \(0.599345\pi\)
\(150\) 0 0
\(151\) 17.0993 + 9.87226i 1.39152 + 0.803393i 0.993483 0.113977i \(-0.0363590\pi\)
0.398035 + 0.917370i \(0.369692\pi\)
\(152\) 9.28697 + 8.82091i 0.753272 + 0.715470i
\(153\) 0 0
\(154\) −0.109546 13.8150i −0.00882743 1.11324i
\(155\) −3.39805 5.88560i −0.272938 0.472743i
\(156\) 0 0
\(157\) −5.62102 −0.448606 −0.224303 0.974519i \(-0.572011\pi\)
−0.224303 + 0.974519i \(0.572011\pi\)
\(158\) 12.1157 + 8.32956i 0.963874 + 0.662664i
\(159\) 0 0
\(160\) 10.7990 + 14.0953i 0.853739 + 1.11433i
\(161\) −0.506373 5.83139i −0.0399078 0.459578i
\(162\) 0 0
\(163\) 3.24708 + 1.87470i 0.254331 + 0.146838i 0.621746 0.783219i \(-0.286424\pi\)
−0.367415 + 0.930057i \(0.619757\pi\)
\(164\) 3.34974 21.1087i 0.261571 1.64831i
\(165\) 0 0
\(166\) 2.29126 + 0.180670i 0.177837 + 0.0140227i
\(167\) 0.739116 1.28019i 0.0571945 0.0990638i −0.836011 0.548713i \(-0.815118\pi\)
0.893205 + 0.449650i \(0.148451\pi\)
\(168\) 0 0
\(169\) 6.18168 + 10.7070i 0.475514 + 0.823614i
\(170\) −5.80588 12.1770i −0.445291 0.933930i
\(171\) 0 0
\(172\) −7.20898 5.84128i −0.549680 0.445393i
\(173\) 6.91237i 0.525537i −0.964859 0.262769i \(-0.915364\pi\)
0.964859 0.262769i \(-0.0846356\pi\)
\(174\) 0 0
\(175\) −10.5227 + 7.35789i −0.795438 + 0.556204i
\(176\) 3.06209 + 14.4484i 0.230813 + 1.08909i
\(177\) 0 0
\(178\) −2.55828 + 1.21977i −0.191751 + 0.0914254i
\(179\) −1.52346 2.63872i −0.113869 0.197227i 0.803458 0.595361i \(-0.202991\pi\)
−0.917327 + 0.398134i \(0.869658\pi\)
\(180\) 0 0
\(181\) −2.27649 −0.169210 −0.0846049 0.996415i \(-0.526963\pi\)
−0.0846049 + 0.996415i \(0.526963\pi\)
\(182\) −0.0236725 2.98538i −0.00175472 0.221291i
\(183\) 0 0
\(184\) 1.77453 + 6.00059i 0.130820 + 0.442369i
\(185\) 18.4831i 1.35890i
\(186\) 0 0
\(187\) 11.2207i 0.820538i
\(188\) −7.59192 19.7953i −0.553698 1.44372i
\(189\) 0 0
\(190\) 11.3887 16.5654i 0.826223 1.20178i
\(191\) −8.64042 −0.625199 −0.312599 0.949885i \(-0.601200\pi\)
−0.312599 + 0.949885i \(0.601200\pi\)
\(192\) 0 0
\(193\) 22.9563 1.65243 0.826215 0.563355i \(-0.190490\pi\)
0.826215 + 0.563355i \(0.190490\pi\)
\(194\) 5.30971 + 0.418681i 0.381215 + 0.0300595i
\(195\) 0 0
\(196\) 6.80685 12.2338i 0.486204 0.873845i
\(197\) 6.30658i 0.449325i −0.974437 0.224663i \(-0.927872\pi\)
0.974437 0.224663i \(-0.0721280\pi\)
\(198\) 0 0
\(199\) 11.1317 6.42691i 0.789108 0.455592i −0.0505404 0.998722i \(-0.516094\pi\)
0.839648 + 0.543130i \(0.182761\pi\)
\(200\) 9.45316 9.95262i 0.668439 0.703757i
\(201\) 0 0
\(202\) −21.8849 + 10.4346i −1.53982 + 0.734173i
\(203\) 24.8545 2.15826i 1.74444 0.151480i
\(204\) 0 0
\(205\) −33.5441 −2.34282
\(206\) −0.357594 + 4.53501i −0.0249147 + 0.315969i
\(207\) 0 0
\(208\) 0.661709 + 3.12226i 0.0458813 + 0.216490i
\(209\) 14.4804 8.36029i 1.00163 0.578293i
\(210\) 0 0
\(211\) −12.3528 7.13189i −0.850402 0.490980i 0.0103847 0.999946i \(-0.496694\pi\)
−0.860786 + 0.508966i \(0.830028\pi\)
\(212\) −10.9826 8.89898i −0.754290 0.611184i
\(213\) 0 0
\(214\) −2.16629 4.54347i −0.148085 0.310585i
\(215\) −7.28118 + 12.6114i −0.496572 + 0.860088i
\(216\) 0 0
\(217\) 2.42424 5.19001i 0.164568 0.352321i
\(218\) −7.24547 0.571319i −0.490725 0.0386946i
\(219\) 0 0
\(220\) 21.6430 8.30055i 1.45917 0.559623i
\(221\) 2.42476i 0.163107i
\(222\) 0 0
\(223\) 3.96034 2.28651i 0.265204 0.153116i −0.361502 0.932371i \(-0.617736\pi\)
0.626706 + 0.779256i \(0.284403\pi\)
\(224\) −4.52045 + 14.2676i −0.302035 + 0.953297i
\(225\) 0 0
\(226\) −10.4824 + 4.99791i −0.697276 + 0.332456i
\(227\) −3.22107 + 5.57906i −0.213790 + 0.370295i −0.952898 0.303292i \(-0.901914\pi\)
0.739108 + 0.673587i \(0.235247\pi\)
\(228\) 0 0
\(229\) 3.29989 + 5.71557i 0.218063 + 0.377696i 0.954216 0.299120i \(-0.0966930\pi\)
−0.736153 + 0.676815i \(0.763360\pi\)
\(230\) 8.86491 4.22672i 0.584535 0.278702i
\(231\) 0 0
\(232\) −25.5757 + 7.56341i −1.67912 + 0.496562i
\(233\) 4.20962 + 2.43043i 0.275781 + 0.159222i 0.631512 0.775366i \(-0.282435\pi\)
−0.355731 + 0.934589i \(0.615768\pi\)
\(234\) 0 0
\(235\) −28.8169 + 16.6374i −1.87980 + 1.08531i
\(236\) 0.364827 + 0.951255i 0.0237482 + 0.0619214i
\(237\) 0 0
\(238\) 5.60704 9.89200i 0.363451 0.641203i
\(239\) 7.00661 12.1358i 0.453220 0.785000i −0.545364 0.838199i \(-0.683608\pi\)
0.998584 + 0.0531992i \(0.0169418\pi\)
\(240\) 0 0
\(241\) 2.09728 3.63260i 0.135098 0.233997i −0.790537 0.612414i \(-0.790198\pi\)
0.925635 + 0.378418i \(0.123532\pi\)
\(242\) 3.71247 + 0.292735i 0.238647 + 0.0188177i
\(243\) 0 0
\(244\) −6.84774 17.8549i −0.438382 1.14304i
\(245\) −20.6378 7.54186i −1.31850 0.481832i
\(246\) 0 0
\(247\) 3.12919 1.80664i 0.199105 0.114954i
\(248\) −1.43223 + 5.95394i −0.0909469 + 0.378075i
\(249\) 0 0
\(250\) 0.537542 + 0.369561i 0.0339972 + 0.0233731i
\(251\) −4.07143 −0.256986 −0.128493 0.991710i \(-0.541014\pi\)
−0.128493 + 0.991710i \(0.541014\pi\)
\(252\) 0 0
\(253\) 8.16873 0.513564
\(254\) 19.3475 + 13.3014i 1.21397 + 0.834606i
\(255\) 0 0
\(256\) 1.69145 15.9103i 0.105716 0.994396i
\(257\) 22.8777 13.2084i 1.42707 0.823920i 0.430183 0.902742i \(-0.358449\pi\)
0.996889 + 0.0788211i \(0.0251156\pi\)
\(258\) 0 0
\(259\) 12.7673 8.92743i 0.793321 0.554723i
\(260\) 4.67699 1.79373i 0.290055 0.111242i
\(261\) 0 0
\(262\) −16.2005 1.27744i −1.00087 0.0789206i
\(263\) 1.36934 2.37177i 0.0844373 0.146250i −0.820714 0.571339i \(-0.806424\pi\)
0.905151 + 0.425090i \(0.139757\pi\)
\(264\) 0 0
\(265\) −11.0926 + 19.2130i −0.681414 + 1.18024i
\(266\) 16.9434 0.134353i 1.03887 0.00823769i
\(267\) 0 0
\(268\) −13.9233 + 5.33989i −0.850501 + 0.326186i
\(269\) −11.0850 + 6.39993i −0.675865 + 0.390211i −0.798295 0.602266i \(-0.794265\pi\)
0.122430 + 0.992477i \(0.460931\pi\)
\(270\) 0 0
\(271\) 19.3102 + 11.1488i 1.17301 + 0.677240i 0.954388 0.298569i \(-0.0965093\pi\)
0.218626 + 0.975809i \(0.429843\pi\)
\(272\) −3.76321 + 11.5585i −0.228178 + 0.700837i
\(273\) 0 0
\(274\) 17.7750 8.47498i 1.07383 0.511992i
\(275\) −8.95952 15.5183i −0.540280 0.935792i
\(276\) 0 0
\(277\) −9.01753 + 15.6188i −0.541811 + 0.938444i 0.456989 + 0.889472i \(0.348928\pi\)
−0.998800 + 0.0489717i \(0.984406\pi\)
\(278\) 19.3425 9.22236i 1.16009 0.553121i
\(279\) 0 0
\(280\) 23.2280 + 3.49747i 1.38814 + 0.209014i
\(281\) −6.29086 + 3.63203i −0.375281 + 0.216669i −0.675763 0.737119i \(-0.736186\pi\)
0.300482 + 0.953788i \(0.402853\pi\)
\(282\) 0 0
\(283\) 9.99707i 0.594264i 0.954836 + 0.297132i \(0.0960302\pi\)
−0.954836 + 0.297132i \(0.903970\pi\)
\(284\) 1.54452 + 4.02720i 0.0916503 + 0.238970i
\(285\) 0 0
\(286\) 4.15354 + 0.327514i 0.245604 + 0.0193663i
\(287\) −16.2020 23.1708i −0.956375 1.36773i
\(288\) 0 0
\(289\) −3.88248 + 6.72465i −0.228381 + 0.395568i
\(290\) 18.0151 + 37.7839i 1.05788 + 2.21875i
\(291\) 0 0
\(292\) 3.20306 3.95303i 0.187445 0.231334i
\(293\) 20.0527 + 11.5774i 1.17149 + 0.676361i 0.954031 0.299708i \(-0.0968893\pi\)
0.217460 + 0.976069i \(0.430223\pi\)
\(294\) 0 0
\(295\) 1.38478 0.799505i 0.0806252 0.0465490i
\(296\) −11.4697 + 12.0757i −0.666660 + 0.701884i
\(297\) 0 0
\(298\) 2.01313 25.5305i 0.116617 1.47894i
\(299\) 1.76524 0.102087
\(300\) 0 0
\(301\) −12.2282 + 1.06185i −0.704824 + 0.0612038i
\(302\) −25.2047 + 12.0174i −1.45037 + 0.691523i
\(303\) 0 0
\(304\) −17.7203 + 3.75551i −1.01633 + 0.215393i
\(305\) −25.9921 + 15.0066i −1.48831 + 0.859273i
\(306\) 0 0
\(307\) 28.4146i 1.62171i 0.585250 + 0.810853i \(0.300996\pi\)
−0.585250 + 0.810853i \(0.699004\pi\)
\(308\) 16.1873 + 10.9408i 0.922359 + 0.623410i
\(309\) 0 0
\(310\) 9.58140 + 0.755511i 0.544187 + 0.0429102i
\(311\) −4.59925 −0.260799 −0.130400 0.991462i \(-0.541626\pi\)
−0.130400 + 0.991462i \(0.541626\pi\)
\(312\) 0 0
\(313\) −21.3503 −1.20679 −0.603395 0.797442i \(-0.706186\pi\)
−0.603395 + 0.797442i \(0.706186\pi\)
\(314\) 4.50352 6.55057i 0.254149 0.369670i
\(315\) 0 0
\(316\) −19.4141 + 7.44571i −1.09213 + 0.418854i
\(317\) 2.13460i 0.119891i −0.998202 0.0599457i \(-0.980907\pi\)
0.998202 0.0599457i \(-0.0190927\pi\)
\(318\) 0 0
\(319\) 34.8167i 1.94936i
\(320\) −25.0784 + 1.29179i −1.40193 + 0.0722132i
\(321\) 0 0
\(322\) 7.20144 + 4.08196i 0.401320 + 0.227479i
\(323\) 13.7617 0.765719
\(324\) 0 0
\(325\) −1.93613 3.35348i −0.107397 0.186017i
\(326\) −4.78626 + 2.28205i −0.265086 + 0.126391i
\(327\) 0 0
\(328\) 21.9156 + 20.8158i 1.21009 + 1.14936i
\(329\) −25.4111 11.8695i −1.40096 0.654384i
\(330\) 0 0
\(331\) 29.0079i 1.59442i 0.603704 + 0.797209i \(0.293691\pi\)
−0.603704 + 0.797209i \(0.706309\pi\)
\(332\) −2.04629 + 2.52542i −0.112305 + 0.138600i
\(333\) 0 0
\(334\) 0.899717 + 1.88702i 0.0492303 + 0.103253i
\(335\) 11.7022 + 20.2687i 0.639358 + 1.10740i
\(336\) 0 0
\(337\) 6.37475 11.0414i 0.347255 0.601463i −0.638506 0.769617i \(-0.720447\pi\)
0.985761 + 0.168154i \(0.0537807\pi\)
\(338\) −17.4303 1.37441i −0.948084 0.0747582i
\(339\) 0 0
\(340\) 18.8423 + 2.99009i 1.02187 + 0.162161i
\(341\) 6.92317 + 3.99709i 0.374911 + 0.216455i
\(342\) 0 0
\(343\) −4.75860 17.8985i −0.256940 0.966427i
\(344\) 12.5830 3.72114i 0.678432 0.200630i
\(345\) 0 0
\(346\) 8.05547 + 5.53814i 0.433065 + 0.297732i
\(347\) −31.5387 −1.69308 −0.846542 0.532322i \(-0.821319\pi\)
−0.846542 + 0.532322i \(0.821319\pi\)
\(348\) 0 0
\(349\) 4.19035 + 7.25790i 0.224304 + 0.388507i 0.956111 0.293006i \(-0.0946557\pi\)
−0.731806 + 0.681513i \(0.761322\pi\)
\(350\) −0.143983 18.1579i −0.00769619 0.970580i
\(351\) 0 0
\(352\) −19.2911 8.00748i −1.02822 0.426800i
\(353\) −9.89067 5.71038i −0.526427 0.303933i 0.213133 0.977023i \(-0.431633\pi\)
−0.739560 + 0.673090i \(0.764967\pi\)
\(354\) 0 0
\(355\) 5.86256 3.38475i 0.311153 0.179644i
\(356\) 0.628193 3.95861i 0.0332942 0.209806i
\(357\) 0 0
\(358\) 4.29567 + 0.338722i 0.227033 + 0.0179020i
\(359\) 1.41558 2.45186i 0.0747117 0.129404i −0.826249 0.563305i \(-0.809530\pi\)
0.900961 + 0.433900i \(0.142863\pi\)
\(360\) 0 0
\(361\) 0.753506 + 1.30511i 0.0396582 + 0.0686900i
\(362\) 1.82391 2.65295i 0.0958623 0.139436i
\(363\) 0 0
\(364\) 3.49804 + 2.36428i 0.183347 + 0.123922i
\(365\) −6.91543 3.99262i −0.361970 0.208983i
\(366\) 0 0
\(367\) −24.0829 13.9043i −1.25712 0.725797i −0.284604 0.958645i \(-0.591862\pi\)
−0.972513 + 0.232848i \(0.925195\pi\)
\(368\) −8.41466 2.73964i −0.438644 0.142814i
\(369\) 0 0
\(370\) 21.5396 + 14.8085i 1.11979 + 0.769857i
\(371\) −18.6293 + 1.61769i −0.967184 + 0.0839861i
\(372\) 0 0
\(373\) −15.6595 27.1231i −0.810821 1.40438i −0.912290 0.409544i \(-0.865688\pi\)
0.101470 0.994839i \(-0.467645\pi\)
\(374\) 13.0763 + 8.98994i 0.676157 + 0.464859i
\(375\) 0 0
\(376\) 29.1515 + 7.01245i 1.50337 + 0.361639i
\(377\) 7.52380i 0.387495i
\(378\) 0 0
\(379\) 26.7198i 1.37250i 0.727364 + 0.686252i \(0.240745\pi\)
−0.727364 + 0.686252i \(0.759255\pi\)
\(380\) 10.1802 + 26.5441i 0.522235 + 1.36168i
\(381\) 0 0
\(382\) 6.92264 10.0693i 0.354193 0.515190i
\(383\) 3.72138 + 6.44562i 0.190154 + 0.329356i 0.945301 0.326199i \(-0.105768\pi\)
−0.755147 + 0.655555i \(0.772435\pi\)
\(384\) 0 0
\(385\) 12.9773 27.7830i 0.661386 1.41595i
\(386\) −18.3924 + 26.7526i −0.936150 + 1.36167i
\(387\) 0 0
\(388\) −4.74202 + 5.85234i −0.240740 + 0.297108i
\(389\) 26.6043 + 15.3600i 1.34889 + 0.778784i 0.988093 0.153859i \(-0.0491701\pi\)
0.360801 + 0.932643i \(0.382503\pi\)
\(390\) 0 0
\(391\) 5.82243 + 3.36158i 0.294453 + 0.170003i
\(392\) 8.80335 + 17.7342i 0.444636 + 0.895711i
\(393\) 0 0
\(394\) 7.34950 + 5.05279i 0.370263 + 0.254556i
\(395\) 16.3170 + 28.2619i 0.820997 + 1.42201i
\(396\) 0 0
\(397\) −2.16714 + 3.75359i −0.108765 + 0.188387i −0.915270 0.402840i \(-0.868023\pi\)
0.806505 + 0.591227i \(0.201356\pi\)
\(398\) −1.42894 + 18.1218i −0.0716262 + 0.908364i
\(399\) 0 0
\(400\) 4.02469 + 18.9904i 0.201235 + 0.949521i
\(401\) 11.4437 6.60702i 0.571471 0.329939i −0.186266 0.982499i \(-0.559639\pi\)
0.757737 + 0.652560i \(0.226305\pi\)
\(402\) 0 0
\(403\) 1.49608 + 0.863762i 0.0745250 + 0.0430271i
\(404\) 5.37391 33.8641i 0.267362 1.68480i
\(405\) 0 0
\(406\) −17.3981 + 30.6939i −0.863453 + 1.52331i
\(407\) 10.8707 + 18.8286i 0.538841 + 0.933301i
\(408\) 0 0
\(409\) −23.9859 −1.18603 −0.593014 0.805192i \(-0.702062\pi\)
−0.593014 + 0.805192i \(0.702062\pi\)
\(410\) 26.8753 39.0914i 1.32728 1.93058i
\(411\) 0 0
\(412\) −4.99846 4.05015i −0.246257 0.199536i
\(413\) 1.22112 + 0.570382i 0.0600875 + 0.0280667i
\(414\) 0 0
\(415\) 4.41796 + 2.55071i 0.216869 + 0.125210i
\(416\) −4.16875 1.73040i −0.204390 0.0848397i
\(417\) 0 0
\(418\) −1.85880 + 23.5733i −0.0909167 + 1.15301i
\(419\) −9.47883 + 16.4178i −0.463071 + 0.802063i −0.999112 0.0421291i \(-0.986586\pi\)
0.536041 + 0.844192i \(0.319919\pi\)
\(420\) 0 0
\(421\) −6.69978 11.6044i −0.326527 0.565562i 0.655293 0.755375i \(-0.272545\pi\)
−0.981820 + 0.189813i \(0.939212\pi\)
\(422\) 18.2083 8.68157i 0.886365 0.422612i
\(423\) 0 0
\(424\) 19.1698 5.66902i 0.930969 0.275312i
\(425\) 14.7480i 0.715385i
\(426\) 0 0
\(427\) −22.9202 10.7060i −1.10919 0.518098i
\(428\) 7.03044 + 1.11566i 0.339829 + 0.0539276i
\(429\) 0 0
\(430\) −8.86329 18.5894i −0.427426 0.896461i
\(431\) 8.82760 + 15.2899i 0.425211 + 0.736486i 0.996440 0.0843040i \(-0.0268667\pi\)
−0.571229 + 0.820790i \(0.693533\pi\)
\(432\) 0 0
\(433\) 22.5556 1.08395 0.541976 0.840394i \(-0.317676\pi\)
0.541976 + 0.840394i \(0.317676\pi\)
\(434\) 4.10600 + 6.98333i 0.197094 + 0.335211i
\(435\) 0 0
\(436\) 6.47082 7.98593i 0.309896 0.382456i
\(437\) 10.0186i 0.479253i
\(438\) 0 0
\(439\) 33.5109i 1.59939i 0.600408 + 0.799694i \(0.295005\pi\)
−0.600408 + 0.799694i \(0.704995\pi\)
\(440\) −7.66698 + 31.8724i −0.365509 + 1.51946i
\(441\) 0 0
\(442\) 2.82575 + 1.94270i 0.134407 + 0.0924049i
\(443\) 2.98342 0.141747 0.0708733 0.997485i \(-0.477421\pi\)
0.0708733 + 0.997485i \(0.477421\pi\)
\(444\) 0 0
\(445\) −6.29069 −0.298208
\(446\) −0.508374 + 6.44720i −0.0240722 + 0.305284i
\(447\) 0 0
\(448\) −13.0053 16.6991i −0.614444 0.788960i
\(449\) 39.5688i 1.86737i −0.358099 0.933684i \(-0.616575\pi\)
0.358099 0.933684i \(-0.383425\pi\)
\(450\) 0 0
\(451\) 34.1713 19.7288i 1.60906 0.928994i
\(452\) 2.57398 16.2201i 0.121070 0.762931i
\(453\) 0 0
\(454\) −3.92097 8.22364i −0.184020 0.385955i
\(455\) 2.80437 6.00383i 0.131471 0.281464i
\(456\) 0 0
\(457\) 29.2088 1.36633 0.683165 0.730264i \(-0.260603\pi\)
0.683165 + 0.730264i \(0.260603\pi\)
\(458\) −9.30461 0.733686i −0.434776 0.0342829i
\(459\) 0 0
\(460\) −2.17681 + 13.7173i −0.101494 + 0.639573i
\(461\) 1.80514 1.04220i 0.0840737 0.0485400i −0.457374 0.889275i \(-0.651210\pi\)
0.541447 + 0.840735i \(0.317877\pi\)
\(462\) 0 0
\(463\) −17.8405 10.3002i −0.829118 0.478692i 0.0244325 0.999701i \(-0.492222\pi\)
−0.853551 + 0.521010i \(0.825555\pi\)
\(464\) 11.6769 35.8649i 0.542086 1.66499i
\(465\) 0 0
\(466\) −6.20507 + 2.95853i −0.287444 + 0.137051i
\(467\) 7.00189 12.1276i 0.324009 0.561199i −0.657303 0.753627i \(-0.728303\pi\)
0.981311 + 0.192427i \(0.0616360\pi\)
\(468\) 0 0
\(469\) −8.34855 + 17.8733i −0.385500 + 0.825311i
\(470\) 3.69911 46.9121i 0.170627 2.16389i
\(471\) 0 0
\(472\) −1.40086 0.336981i −0.0644799 0.0155108i
\(473\) 17.1296i 0.787618i
\(474\) 0 0
\(475\) 19.0325 10.9884i 0.873273 0.504184i
\(476\) 7.03553 + 14.4597i 0.322473 + 0.662759i
\(477\) 0 0
\(478\) 8.52907 + 17.8884i 0.390110 + 0.818198i
\(479\) 18.7706 32.5116i 0.857650 1.48549i −0.0165142 0.999864i \(-0.505257\pi\)
0.874164 0.485630i \(-0.161410\pi\)
\(480\) 0 0
\(481\) 2.34913 + 4.06882i 0.107111 + 0.185522i
\(482\) 2.55300 + 5.35453i 0.116286 + 0.243892i
\(483\) 0 0
\(484\) −3.31555 + 4.09187i −0.150707 + 0.185994i
\(485\) 10.2381 + 5.91095i 0.464887 + 0.268402i
\(486\) 0 0
\(487\) 0.414665 0.239407i 0.0187903 0.0108486i −0.490575 0.871399i \(-0.663213\pi\)
0.509366 + 0.860550i \(0.329880\pi\)
\(488\) 26.2939 + 6.32507i 1.19027 + 0.286322i
\(489\) 0 0
\(490\) 25.3240 18.0082i 1.14402 0.813529i
\(491\) −1.44107 + 2.49601i −0.0650346 + 0.112643i −0.896709 0.442620i \(-0.854049\pi\)
0.831675 + 0.555263i \(0.187382\pi\)
\(492\) 0 0
\(493\) −14.3277 + 24.8163i −0.645288 + 1.11767i
\(494\) −0.401681 + 5.09413i −0.0180725 + 0.229196i
\(495\) 0 0
\(496\) −5.79105 6.43934i −0.260026 0.289135i
\(497\) 5.16969 + 2.41475i 0.231893 + 0.108316i
\(498\) 0 0
\(499\) 15.0701 8.70073i 0.674631 0.389498i −0.123198 0.992382i \(-0.539315\pi\)
0.797829 + 0.602884i \(0.205982\pi\)
\(500\) −0.861351 + 0.330347i −0.0385208 + 0.0147736i
\(501\) 0 0
\(502\) 3.26200 4.74473i 0.145590 0.211768i
\(503\) −22.3882 −0.998240 −0.499120 0.866533i \(-0.666343\pi\)
−0.499120 + 0.866533i \(0.666343\pi\)
\(504\) 0 0
\(505\) −53.8141 −2.39470
\(506\) −6.54473 + 9.51960i −0.290949 + 0.423198i
\(507\) 0 0
\(508\) −31.0022 + 11.8900i −1.37550 + 0.527534i
\(509\) −9.84296 + 5.68284i −0.436282 + 0.251887i −0.702019 0.712158i \(-0.747718\pi\)
0.265738 + 0.964045i \(0.414385\pi\)
\(510\) 0 0
\(511\) −0.582262 6.70534i −0.0257578 0.296627i
\(512\) 17.1863 + 14.7184i 0.759533 + 0.650469i
\(513\) 0 0
\(514\) −2.93672 + 37.2435i −0.129533 + 1.64274i
\(515\) −5.04852 + 8.74430i −0.222464 + 0.385320i
\(516\) 0 0
\(517\) 19.5704 33.8970i 0.860707 1.49079i
\(518\) 0.174696 + 22.0312i 0.00767571 + 0.967997i
\(519\) 0 0
\(520\) −1.65682 + 6.88755i −0.0726562 + 0.302039i
\(521\) −21.0799 + 12.1705i −0.923529 + 0.533200i −0.884759 0.466049i \(-0.845677\pi\)
−0.0387695 + 0.999248i \(0.512344\pi\)
\(522\) 0 0
\(523\) −36.0137 20.7925i −1.57477 0.909194i −0.995571 0.0940077i \(-0.970032\pi\)
−0.579199 0.815186i \(-0.696634\pi\)
\(524\) 14.4685 17.8562i 0.632057 0.780050i
\(525\) 0 0
\(526\) 1.66689 + 3.49604i 0.0726797 + 0.152435i
\(527\) 3.28976 + 5.69803i 0.143304 + 0.248210i
\(528\) 0 0
\(529\) 9.05275 15.6798i 0.393598 0.681731i
\(530\) −13.5029 28.3203i −0.586529 1.23016i
\(531\) 0 0
\(532\) −13.4184 + 19.8530i −0.581761 + 0.860738i
\(533\) 7.38434 4.26335i 0.319851 0.184666i
\(534\) 0 0
\(535\) 11.1722i 0.483016i
\(536\) 4.93231 20.5041i 0.213043 0.885642i
\(537\) 0 0
\(538\) 1.42294 18.0457i 0.0613473 0.778007i
\(539\) 25.4594 4.45516i 1.09661 0.191897i
\(540\) 0 0
\(541\) 9.99498 17.3118i 0.429718 0.744293i −0.567130 0.823628i \(-0.691946\pi\)
0.996848 + 0.0793350i \(0.0252797\pi\)
\(542\) −28.4637 + 13.5713i −1.22262 + 0.582936i
\(543\) 0 0
\(544\) −10.4549 13.6461i −0.448249 0.585073i
\(545\) −13.9706 8.06590i −0.598433 0.345505i
\(546\) 0 0
\(547\) −10.5952 + 6.11715i −0.453019 + 0.261551i −0.709104 0.705104i \(-0.750900\pi\)
0.256085 + 0.966654i \(0.417567\pi\)
\(548\) −4.36471 + 27.5046i −0.186451 + 1.17494i
\(549\) 0 0
\(550\) 25.2629 + 1.99203i 1.07722 + 0.0849404i
\(551\) −42.7011 −1.81913
\(552\) 0 0
\(553\) −11.6409 + 24.9217i −0.495020 + 1.05978i
\(554\) −10.9769 23.0225i −0.466365 0.978131i
\(555\) 0 0
\(556\) −4.74962 + 29.9301i −0.201429 + 1.26932i
\(557\) −6.58200 + 3.80012i −0.278888 + 0.161016i −0.632920 0.774217i \(-0.718144\pi\)
0.354032 + 0.935233i \(0.384810\pi\)
\(558\) 0 0
\(559\) 3.70165i 0.156563i
\(560\) −22.6859 + 24.2671i −0.958656 + 1.02547i
\(561\) 0 0
\(562\) 0.807534 10.2411i 0.0340637 0.431997i
\(563\) 17.0080 0.716801 0.358401 0.933568i \(-0.383322\pi\)
0.358401 + 0.933568i \(0.383322\pi\)
\(564\) 0 0
\(565\) −25.7757 −1.08439
\(566\) −11.6503 8.00959i −0.489699 0.336668i
\(567\) 0 0
\(568\) −5.93064 1.42663i −0.248844 0.0598600i
\(569\) 4.41762i 0.185196i −0.995704 0.0925982i \(-0.970483\pi\)
0.995704 0.0925982i \(-0.0295172\pi\)
\(570\) 0 0
\(571\) 0.912274i 0.0381775i −0.999818 0.0190887i \(-0.993923\pi\)
0.999818 0.0190887i \(-0.00607651\pi\)
\(572\) −3.70947 + 4.57801i −0.155101 + 0.191416i
\(573\) 0 0
\(574\) 39.9836 0.317049i 1.66888 0.0132334i
\(575\) 10.7367 0.447750
\(576\) 0 0
\(577\) 4.46070 + 7.72616i 0.185701 + 0.321644i 0.943813 0.330481i \(-0.107211\pi\)
−0.758111 + 0.652125i \(0.773878\pi\)
\(578\) −4.72610 9.91227i −0.196580 0.412296i
\(579\) 0 0
\(580\) −58.4658 9.27797i −2.42766 0.385247i
\(581\) 0.371982 + 4.28375i 0.0154324 + 0.177720i
\(582\) 0 0
\(583\) 26.0963i 1.08080i
\(584\) 2.04048 + 6.89989i 0.0844358 + 0.285520i
\(585\) 0 0
\(586\) −29.5581 + 14.0931i −1.22103 + 0.582180i
\(587\) 6.93517 + 12.0121i 0.286245 + 0.495791i 0.972910 0.231183i \(-0.0742596\pi\)
−0.686665 + 0.726974i \(0.740926\pi\)
\(588\) 0 0
\(589\) −4.90225 + 8.49095i −0.201994 + 0.349864i
\(590\) −0.177759 + 2.25434i −0.00731823 + 0.0928098i
\(591\) 0 0
\(592\) −4.88322 23.0413i −0.200699 0.946993i
\(593\) 14.8781 + 8.58990i 0.610972 + 0.352745i 0.773346 0.633984i \(-0.218582\pi\)
−0.162374 + 0.986729i \(0.551915\pi\)
\(594\) 0 0
\(595\) 20.6831 14.4625i 0.847924 0.592904i
\(596\) 28.1396 + 22.8009i 1.15264 + 0.933961i
\(597\) 0 0
\(598\) −1.41430 + 2.05716i −0.0578350 + 0.0841236i
\(599\) −10.4271 −0.426039 −0.213020 0.977048i \(-0.568330\pi\)
−0.213020 + 0.977048i \(0.568330\pi\)
\(600\) 0 0
\(601\) 13.3792 + 23.1735i 0.545750 + 0.945267i 0.998559 + 0.0536595i \(0.0170885\pi\)
−0.452809 + 0.891607i \(0.649578\pi\)
\(602\) 8.55974 15.1012i 0.348869 0.615478i
\(603\) 0 0
\(604\) 6.18909 39.0010i 0.251830 1.58693i
\(605\) 7.15831 + 4.13285i 0.291026 + 0.168024i
\(606\) 0 0
\(607\) 26.0574 15.0442i 1.05764 0.610626i 0.132858 0.991135i \(-0.457585\pi\)
0.924777 + 0.380509i \(0.124251\pi\)
\(608\) 9.82081 23.6596i 0.398286 0.959523i
\(609\) 0 0
\(610\) 3.33651 42.3136i 0.135091 1.71323i
\(611\) 4.22912 7.32505i 0.171092 0.296340i
\(612\) 0 0
\(613\) 3.42095 + 5.92526i 0.138171 + 0.239319i 0.926804 0.375545i \(-0.122544\pi\)
−0.788633 + 0.614864i \(0.789211\pi\)
\(614\) −33.1135 22.7656i −1.33635 0.918744i
\(615\) 0 0
\(616\) −25.7193 + 10.0986i −1.03626 + 0.406882i
\(617\) −3.69878 2.13549i −0.148907 0.0859716i 0.423695 0.905805i \(-0.360733\pi\)
−0.572602 + 0.819833i \(0.694066\pi\)
\(618\) 0 0
\(619\) 19.4075 + 11.2049i 0.780055 + 0.450365i 0.836450 0.548044i \(-0.184627\pi\)
−0.0563948 + 0.998409i \(0.517961\pi\)
\(620\) −8.55700 + 10.5606i −0.343658 + 0.424123i
\(621\) 0 0
\(622\) 3.68488 5.35983i 0.147750 0.214909i
\(623\) −3.03844 4.34534i −0.121733 0.174092i
\(624\) 0 0
\(625\) 12.8566 + 22.2682i 0.514263 + 0.890729i
\(626\) 17.1057 24.8810i 0.683682 0.994445i
\(627\) 0 0
\(628\) 4.02565 + 10.4966i 0.160641 + 0.418858i
\(629\) 17.8940i 0.713481i
\(630\) 0 0
\(631\) 5.90962i 0.235258i −0.993058 0.117629i \(-0.962471\pi\)
0.993058 0.117629i \(-0.0375294\pi\)
\(632\) 6.87740 28.5900i 0.273568 1.13725i
\(633\) 0 0
\(634\) 2.48761 + 1.71023i 0.0987955 + 0.0679219i
\(635\) 26.0565 + 45.1312i 1.03402 + 1.79098i
\(636\) 0 0
\(637\) 5.50171 0.962749i 0.217986 0.0381455i
\(638\) −40.5743 27.8949i −1.60635 1.10437i
\(639\) 0 0
\(640\) 18.5872 30.2606i 0.734725 1.19616i
\(641\) 6.47169 + 3.73643i 0.255616 + 0.147580i 0.622333 0.782752i \(-0.286185\pi\)
−0.366717 + 0.930333i \(0.619518\pi\)
\(642\) 0 0
\(643\) 15.9307 + 9.19760i 0.628246 + 0.362718i 0.780073 0.625689i \(-0.215182\pi\)
−0.151826 + 0.988407i \(0.548515\pi\)
\(644\) −10.5267 + 5.12191i −0.414812 + 0.201831i
\(645\) 0 0
\(646\) −11.0257 + 16.0374i −0.433802 + 0.630984i
\(647\) −1.76191 3.05173i −0.0692680 0.119976i 0.829311 0.558787i \(-0.188733\pi\)
−0.898579 + 0.438811i \(0.855400\pi\)
\(648\) 0 0
\(649\) −0.940449 + 1.62891i −0.0369159 + 0.0639402i
\(650\) 5.45926 + 0.430473i 0.214130 + 0.0168845i
\(651\) 0 0
\(652\) 1.17528 7.40613i 0.0460276 0.290047i
\(653\) 6.32176 3.64987i 0.247390 0.142830i −0.371179 0.928561i \(-0.621046\pi\)
0.618568 + 0.785731i \(0.287713\pi\)
\(654\) 0 0
\(655\) −31.2375 18.0350i −1.22055 0.704685i
\(656\) −41.8168 + 8.86235i −1.63267 + 0.346017i
\(657\) 0 0
\(658\) 34.1915 20.1037i 1.33293 0.783722i
\(659\) −21.3105 36.9109i −0.830139 1.43784i −0.897927 0.440144i \(-0.854927\pi\)
0.0677880 0.997700i \(-0.478406\pi\)
\(660\) 0 0
\(661\) 14.9175 0.580225 0.290113 0.956992i \(-0.406307\pi\)
0.290113 + 0.956992i \(0.406307\pi\)
\(662\) −33.8050 23.2409i −1.31387 0.903284i
\(663\) 0 0
\(664\) −1.30358 4.40804i −0.0505885 0.171065i
\(665\) 34.0745 + 15.9161i 1.32135 + 0.617200i
\(666\) 0 0
\(667\) −18.0664 10.4307i −0.699535 0.403877i
\(668\) −2.91993 0.463364i −0.112975 0.0179281i
\(669\) 0 0
\(670\) −32.9963 2.60182i −1.27476 0.100517i
\(671\) 17.6521 30.5743i 0.681451 1.18031i
\(672\) 0 0
\(673\) 9.11649 + 15.7902i 0.351415 + 0.608668i 0.986498 0.163776i \(-0.0523673\pi\)
−0.635083 + 0.772444i \(0.719034\pi\)
\(674\) 7.75990 + 16.2752i 0.298900 + 0.626898i
\(675\) 0 0
\(676\) 15.5668 19.2116i 0.598721 0.738908i
\(677\) 24.2358i 0.931456i 0.884928 + 0.465728i \(0.154208\pi\)
−0.884928 + 0.465728i \(0.845792\pi\)
\(678\) 0 0
\(679\) 0.862021 + 9.92704i 0.0330813 + 0.380965i
\(680\) −18.5809 + 19.5626i −0.712545 + 0.750193i
\(681\) 0 0
\(682\) −10.2049 + 4.86562i −0.390766 + 0.186314i
\(683\) −17.8152 30.8568i −0.681678 1.18070i −0.974468 0.224524i \(-0.927917\pi\)
0.292790 0.956177i \(-0.405416\pi\)
\(684\) 0 0
\(685\) 43.7080 1.67000
\(686\) 24.6709 + 8.79461i 0.941941 + 0.335780i
\(687\) 0 0
\(688\) −5.74494 + 17.6453i −0.219024 + 0.672720i
\(689\) 5.63934i 0.214842i
\(690\) 0 0
\(691\) 9.77976i 0.372039i 0.982546 + 0.186020i \(0.0595588\pi\)
−0.982546 + 0.186020i \(0.940441\pi\)
\(692\) −12.9080 + 4.95049i −0.490688 + 0.188189i
\(693\) 0 0
\(694\) 25.2686 36.7542i 0.959181 1.39517i
\(695\) 47.5624 1.80415
\(696\) 0 0
\(697\) 32.4751 1.23008
\(698\) −11.8154 0.931668i −0.447221 0.0352642i
\(699\) 0 0
\(700\) 21.2760 + 14.3802i 0.804158 + 0.543520i
\(701\) 13.9885i 0.528337i 0.964476 + 0.264169i \(0.0850976\pi\)
−0.964476 + 0.264169i \(0.914902\pi\)
\(702\) 0 0
\(703\) −23.0925 + 13.3324i −0.870949 + 0.502842i
\(704\) 24.7875 16.0657i 0.934216 0.605498i
\(705\) 0 0
\(706\) 14.5791 6.95118i 0.548690 0.261611i
\(707\) −25.9925 37.1725i −0.977550 1.39801i
\(708\) 0 0
\(709\) 38.5365 1.44727 0.723633 0.690184i \(-0.242471\pi\)
0.723633 + 0.690184i \(0.242471\pi\)
\(710\) −0.752554 + 9.54390i −0.0282429 + 0.358176i
\(711\) 0 0
\(712\) 4.10994 + 3.90369i 0.154027 + 0.146297i
\(713\) −4.14820 + 2.39496i −0.155351 + 0.0896921i
\(714\) 0 0
\(715\) 8.00876 + 4.62386i 0.299511 + 0.172923i
\(716\) −3.83640 + 4.73467i −0.143373 + 0.176943i
\(717\) 0 0
\(718\) 1.72317 + 3.61410i 0.0643083 + 0.134877i
\(719\) −11.8394 + 20.5064i −0.441534 + 0.764760i −0.997804 0.0662424i \(-0.978899\pi\)
0.556269 + 0.831002i \(0.312232\pi\)
\(720\) 0 0
\(721\) −8.47865 + 0.736249i −0.315761 + 0.0274193i
\(722\) −2.12464 0.167532i −0.0790710 0.00623489i
\(723\) 0 0
\(724\) 1.63037 + 4.25105i 0.0605922 + 0.157989i
\(725\) 45.7617i 1.69955i
\(726\) 0 0
\(727\) −23.5627 + 13.6039i −0.873892 + 0.504542i −0.868640 0.495444i \(-0.835005\pi\)
−0.00525253 + 0.999986i \(0.501672\pi\)
\(728\) −5.55787 + 2.18227i −0.205989 + 0.0808804i
\(729\) 0 0
\(730\) 10.1935 4.86017i 0.377278 0.179883i
\(731\) 7.04913 12.2095i 0.260722 0.451583i
\(732\) 0 0
\(733\) −5.77399 10.0008i −0.213267 0.369390i 0.739468 0.673192i \(-0.235077\pi\)
−0.952735 + 0.303802i \(0.901744\pi\)
\(734\) 35.4987 16.9255i 1.31028 0.624732i
\(735\) 0 0
\(736\) 9.93447 7.61122i 0.366189 0.280553i
\(737\) −23.8419 13.7651i −0.878229 0.507046i
\(738\) 0 0
\(739\) −8.71192 + 5.02983i −0.320473 + 0.185025i −0.651603 0.758560i \(-0.725903\pi\)
0.331130 + 0.943585i \(0.392570\pi\)
\(740\) −34.5148 + 13.2372i −1.26879 + 0.486608i
\(741\) 0 0
\(742\) 13.0405 23.0061i 0.478730 0.844581i
\(743\) 22.8644 39.6022i 0.838812 1.45286i −0.0520771 0.998643i \(-0.516584\pi\)
0.890889 0.454221i \(-0.150082\pi\)
\(744\) 0 0
\(745\) 28.4214 49.2273i 1.04128 1.80355i
\(746\) 44.1548 + 3.48169i 1.61662 + 0.127474i
\(747\) 0 0
\(748\) −20.9532 + 8.03601i −0.766126 + 0.293826i
\(749\) 7.71727 5.39624i 0.281983 0.197174i
\(750\) 0 0
\(751\) −6.42335 + 3.70852i −0.234391 + 0.135326i −0.612596 0.790396i \(-0.709875\pi\)
0.378205 + 0.925722i \(0.376541\pi\)
\(752\) −31.5281 + 28.3539i −1.14971 + 1.03396i
\(753\) 0 0
\(754\) −8.76801 6.02802i −0.319312 0.219527i
\(755\) −61.9772 −2.25558
\(756\) 0 0
\(757\) −30.6722 −1.11480 −0.557401 0.830244i \(-0.688201\pi\)
−0.557401 + 0.830244i \(0.688201\pi\)
\(758\) −31.1385 21.4077i −1.13100 0.777563i
\(759\) 0 0
\(760\) −39.0901 9.40320i −1.41795 0.341090i
\(761\) 4.88598 2.82092i 0.177117 0.102258i −0.408821 0.912615i \(-0.634060\pi\)
0.585937 + 0.810356i \(0.300726\pi\)
\(762\) 0 0
\(763\) −1.17629 13.5461i −0.0425845 0.490403i
\(764\) 6.18808 + 16.1349i 0.223877 + 0.583740i
\(765\) 0 0
\(766\) −10.4931 0.827399i −0.379130 0.0298951i
\(767\) −0.203229 + 0.352003i −0.00733816 + 0.0127101i
\(768\) 0 0
\(769\) −3.33932 + 5.78387i −0.120419 + 0.208572i −0.919933 0.392076i \(-0.871757\pi\)
0.799514 + 0.600647i \(0.205090\pi\)
\(770\) 21.9801 + 37.3829i 0.792108 + 1.34719i
\(771\) 0 0
\(772\) −16.4408 42.8680i −0.591718 1.54285i
\(773\) 11.7948 6.80973i 0.424230 0.244929i −0.272656 0.962112i \(-0.587902\pi\)
0.696885 + 0.717183i \(0.254569\pi\)
\(774\) 0 0
\(775\) 9.09955 + 5.25363i 0.326866 + 0.188716i
\(776\) −3.02087 10.2151i −0.108443 0.366700i
\(777\) 0 0
\(778\) −39.2153 + 18.6976i −1.40594 + 0.670341i
\(779\) 24.1965 + 41.9096i 0.866929 + 1.50157i
\(780\) 0 0
\(781\) −3.98145 + 6.89608i −0.142468 + 0.246761i
\(782\) −8.58239 + 4.09202i −0.306906 + 0.146330i
\(783\) 0 0
\(784\) −27.7201 3.94933i −0.990003 0.141048i
\(785\) 15.2803 8.82207i 0.545376 0.314873i
\(786\) 0 0
\(787\) 18.7977i 0.670065i 0.942207 + 0.335032i \(0.108747\pi\)
−0.942207 + 0.335032i \(0.891253\pi\)
\(788\) −11.7767 + 4.51664i −0.419529 + 0.160898i
\(789\) 0 0
\(790\) −46.0086 3.62787i −1.63691 0.129074i
\(791\) −12.4498 17.8047i −0.442665 0.633064i
\(792\) 0 0
\(793\) 3.81457 6.60703i 0.135459 0.234622i
\(794\) −2.63803 5.53287i −0.0936202 0.196354i
\(795\) 0 0
\(796\) −19.9738 16.1843i −0.707951 0.573638i
\(797\) −26.5106 15.3059i −0.939054 0.542163i −0.0493904 0.998780i \(-0.515728\pi\)
−0.889664 + 0.456616i \(0.849061\pi\)
\(798\) 0 0
\(799\) 27.8985 16.1072i 0.986977 0.569832i
\(800\) −25.3554 10.5247i −0.896450 0.372105i
\(801\) 0 0
\(802\) −1.46898 + 18.6297i −0.0518716 + 0.657836i
\(803\) 9.39297 0.331471
\(804\) 0 0
\(805\) 10.5288 + 15.0574i 0.371091 + 0.530704i
\(806\) −2.20525 + 1.05145i −0.0776767 + 0.0370357i
\(807\) 0 0
\(808\) 35.1587 + 33.3943i 1.23688 + 1.17481i
\(809\) 0.871099 0.502929i 0.0306262 0.0176821i −0.484609 0.874731i \(-0.661038\pi\)
0.515235 + 0.857049i \(0.327705\pi\)
\(810\) 0 0
\(811\) 37.9915i 1.33406i −0.745030 0.667031i \(-0.767565\pi\)
0.745030 0.667031i \(-0.232435\pi\)
\(812\) −21.8305 44.8670i −0.766102 1.57452i
\(813\) 0 0
\(814\) −30.6519 2.41696i −1.07435 0.0847143i
\(815\) −11.7692 −0.412258
\(816\) 0 0
\(817\) 21.0086 0.734998
\(818\) 19.2174 27.9525i 0.671919 0.977336i
\(819\) 0 0
\(820\) 24.0236 + 62.6395i 0.838940 + 2.18747i
\(821\) 53.1065i 1.85343i 0.375767 + 0.926714i \(0.377379\pi\)
−0.375767 + 0.926714i \(0.622621\pi\)
\(822\) 0 0
\(823\) 4.76362i 0.166049i −0.996547 0.0830247i \(-0.973542\pi\)
0.996547 0.0830247i \(-0.0264580\pi\)
\(824\) 8.72466 2.58011i 0.303938 0.0898825i
\(825\) 0 0
\(826\) −1.64306 + 0.966073i −0.0571694 + 0.0336140i
\(827\) −2.02105 −0.0702787 −0.0351393 0.999382i \(-0.511188\pi\)
−0.0351393 + 0.999382i \(0.511188\pi\)
\(828\) 0 0
\(829\) −1.51810 2.62943i −0.0527259 0.0913240i 0.838458 0.544967i \(-0.183458\pi\)
−0.891184 + 0.453643i \(0.850124\pi\)
\(830\) −6.51217 + 3.10495i −0.226041 + 0.107774i
\(831\) 0 0
\(832\) 5.35653 3.47175i 0.185704 0.120361i
\(833\) 19.9801 + 7.30151i 0.692270 + 0.252982i
\(834\) 0 0
\(835\) 4.64011i 0.160577i
\(836\) −25.9824 21.0529i −0.898619 0.728131i
\(837\) 0 0
\(838\) −11.5385 24.2002i −0.398590 0.835982i
\(839\) 14.7757 + 25.5923i 0.510114 + 0.883543i 0.999931 + 0.0117180i \(0.00373004\pi\)
−0.489818 + 0.871825i \(0.662937\pi\)
\(840\) 0 0
\(841\) 29.9575 51.8879i 1.03302 1.78924i
\(842\) 18.8912 + 1.48961i 0.651034 + 0.0513352i
\(843\) 0 0
\(844\) −4.47110 + 28.1750i −0.153902 + 0.969824i
\(845\) −33.6087 19.4040i −1.15618 0.667518i
\(846\) 0 0
\(847\) 0.602712 + 6.94084i 0.0207094 + 0.238490i
\(848\) −8.75221 + 26.8819i −0.300552 + 0.923129i
\(849\) 0 0
\(850\) 17.1869 + 11.8160i 0.589507 + 0.405287i
\(851\) −13.0270 −0.446558
\(852\) 0 0
\(853\) −10.4280 18.0618i −0.357048 0.618426i 0.630418 0.776256i \(-0.282884\pi\)
−0.987466 + 0.157830i \(0.949550\pi\)
\(854\) 30.8400 18.1330i 1.05532 0.620499i
\(855\) 0 0
\(856\) −6.93290 + 7.29921i −0.236962 + 0.249482i
\(857\) −19.1033 11.0293i −0.652557 0.376754i 0.136878 0.990588i \(-0.456293\pi\)
−0.789435 + 0.613834i \(0.789626\pi\)
\(858\) 0 0
\(859\) 46.7963 27.0178i 1.59667 0.921836i 0.604544 0.796572i \(-0.293355\pi\)
0.992123 0.125265i \(-0.0399781\pi\)
\(860\) 28.7648 + 4.56469i 0.980871 + 0.155655i
\(861\) 0 0
\(862\) −24.8910 1.96270i −0.847790 0.0668498i
\(863\) −14.8916 + 25.7931i −0.506917 + 0.878007i 0.493051 + 0.870001i \(0.335882\pi\)
−0.999968 + 0.00800595i \(0.997452\pi\)
\(864\) 0 0
\(865\) 10.8488 + 18.7907i 0.368871 + 0.638903i
\(866\) −18.0714 + 26.2856i −0.614091 + 0.893222i
\(867\) 0 0
\(868\) −11.4279 0.809985i −0.387887 0.0274927i
\(869\) −33.2442 19.1935i −1.12773 0.651096i
\(870\) 0 0
\(871\) −5.15218 2.97461i −0.174575 0.100791i
\(872\) 4.12219 + 13.9392i 0.139595 + 0.472040i
\(873\) 0 0
\(874\) −11.6754 8.02681i −0.394925 0.271511i
\(875\) −0.516475 + 1.10571i −0.0174600 + 0.0373799i
\(876\) 0 0
\(877\) −5.43528 9.41418i −0.183536 0.317894i 0.759546 0.650454i \(-0.225421\pi\)
−0.943082 + 0.332559i \(0.892088\pi\)
\(878\) −39.0526 26.8487i −1.31796 0.906100i
\(879\) 0 0
\(880\) −31.0005 34.4709i −1.04503 1.16201i
\(881\) 40.5406i 1.36585i −0.730490 0.682923i \(-0.760708\pi\)
0.730490 0.682923i \(-0.239292\pi\)
\(882\) 0 0
\(883\) 18.8427i 0.634106i −0.948408 0.317053i \(-0.897307\pi\)
0.948408 0.317053i \(-0.102693\pi\)
\(884\) −4.52794 + 1.73656i −0.152291 + 0.0584069i
\(885\) 0 0
\(886\) −2.39030 + 3.47679i −0.0803035 + 0.116805i
\(887\) −1.05971 1.83546i −0.0355814 0.0616289i 0.847686 0.530498i \(-0.177995\pi\)
−0.883268 + 0.468869i \(0.844662\pi\)
\(888\) 0 0
\(889\) −18.5892 + 39.7974i −0.623463 + 1.33476i
\(890\) 5.04006 7.33099i 0.168943 0.245735i
\(891\) 0 0
\(892\) −7.10608 5.75790i −0.237929 0.192789i
\(893\) 41.5731 + 24.0022i 1.39119 + 0.803204i
\(894\) 0 0
\(895\) 8.28282 + 4.78209i 0.276864 + 0.159848i
\(896\) 29.8805 1.77681i 0.998237 0.0593590i
\(897\) 0 0
\(898\) 46.1123 + 31.7023i 1.53879 + 1.05792i
\(899\) −10.2078 17.6804i −0.340449 0.589675i
\(900\) 0 0
\(901\) 10.7391 18.6007i 0.357771 0.619678i
\(902\) −4.38644 + 55.6289i −0.146052 + 1.85224i
\(903\) 0 0
\(904\) 16.8402 + 15.9951i 0.560097 + 0.531989i
\(905\) 6.18844 3.57290i 0.205711 0.118767i
\(906\) 0 0
\(907\) −16.4300 9.48585i −0.545548 0.314972i 0.201776 0.979432i \(-0.435329\pi\)
−0.747324 + 0.664459i \(0.768662\pi\)
\(908\) 12.7250 + 2.01934i 0.422296 + 0.0670143i
\(909\) 0 0
\(910\) 4.74985 + 8.07836i 0.157456 + 0.267795i
\(911\) 7.63448 + 13.2233i 0.252942 + 0.438108i 0.964334 0.264687i \(-0.0852686\pi\)
−0.711393 + 0.702795i \(0.751935\pi\)
\(912\) 0 0
\(913\) −6.00076 −0.198596
\(914\) −23.4019 + 34.0391i −0.774066 + 1.12591i
\(915\) 0 0
\(916\) 8.30980 10.2555i 0.274564 0.338851i
\(917\) −2.63012 30.2885i −0.0868543 1.00022i
\(918\) 0 0
\(919\) −11.7046 6.75766i −0.386099 0.222914i 0.294369 0.955692i \(-0.404890\pi\)
−0.680469 + 0.732777i \(0.738224\pi\)
\(920\) −14.2417 13.5270i −0.469536 0.445972i
\(921\) 0 0
\(922\) −0.231719 + 2.93866i −0.00763125 + 0.0967796i
\(923\) −0.860382 + 1.49022i −0.0283198 + 0.0490513i
\(924\) 0 0
\(925\) 14.2881 + 24.7476i 0.469789 + 0.813698i
\(926\) 26.2973 12.5383i 0.864181 0.412035i
\(927\) 0 0
\(928\) 32.4405 + 42.3426i 1.06491 + 1.38996i
\(929\) 3.85010i 0.126318i −0.998003 0.0631589i \(-0.979883\pi\)
0.998003 0.0631589i \(-0.0201175\pi\)
\(930\) 0 0
\(931\) 5.46405 + 31.2248i 0.179077 + 1.02335i
\(932\) 1.52367 9.60156i 0.0499096 0.314509i
\(933\) 0 0
\(934\) 8.52331 + 17.8764i 0.278891 + 0.584932i
\(935\) 17.6106 + 30.5025i 0.575929 + 0.997538i
\(936\) 0 0
\(937\) −54.7523 −1.78868 −0.894340 0.447389i \(-0.852354\pi\)
−0.894340 + 0.447389i \(0.852354\pi\)
\(938\) −14.1402 24.0491i −0.461694 0.785231i
\(939\) 0 0
\(940\) 51.7063 + 41.8965i 1.68647 + 1.36651i
\(941\) 0.543104i 0.0177047i −0.999961 0.00885234i \(-0.997182\pi\)
0.999961 0.00885234i \(-0.00281783\pi\)
\(942\) 0 0
\(943\) 23.6421i 0.769892i
\(944\) 1.51507 1.36254i 0.0493113 0.0443468i
\(945\) 0 0
\(946\) 19.9623 + 13.7241i 0.649030 + 0.446209i
\(947\) −37.8464 −1.22984 −0.614921 0.788589i \(-0.710812\pi\)
−0.614921 + 0.788589i \(0.710812\pi\)
\(948\) 0 0
\(949\) 2.02980 0.0658900
\(950\) −2.44313 + 30.9838i −0.0792657 + 1.00525i
\(951\) 0 0
\(952\) −22.4877 3.38601i −0.728831 0.109741i
\(953\) 55.2382i 1.78934i 0.446726 + 0.894671i \(0.352590\pi\)
−0.446726 + 0.894671i \(0.647410\pi\)
\(954\) 0 0
\(955\) 23.4883 13.5609i 0.760062 0.438822i
\(956\) −27.6801 4.39256i −0.895238 0.142066i
\(957\) 0 0
\(958\) 22.8492 + 47.9228i 0.738225 + 1.54832i
\(959\) 21.1112 + 30.1916i 0.681717 + 0.974937i
\(960\) 0 0
\(961\) 26.3124 0.848788
\(962\) −6.62380 0.522299i −0.213560 0.0168396i
\(963\) 0 0
\(964\) −8.28546 1.31482i −0.266857 0.0423476i
\(965\) −62.4048 + 36.0294i −2.00888 + 1.15983i
\(966\) 0 0
\(967\) −13.0909 7.55803i −0.420975 0.243050i 0.274519 0.961582i \(-0.411481\pi\)
−0.695494 + 0.718532i \(0.744815\pi\)
\(968\) −2.11215 7.14223i −0.0678870 0.229560i
\(969\) 0 0
\(970\) −15.0911 + 7.19533i −0.484547 + 0.231028i
\(971\) 24.1097 41.7592i 0.773716 1.34012i −0.161797 0.986824i \(-0.551729\pi\)
0.935513 0.353292i \(-0.114938\pi\)
\(972\) 0 0
\(973\) 22.9730 + 32.8541i 0.736479 + 1.05325i
\(974\) −0.0532289 + 0.675049i −0.00170556 + 0.0216300i
\(975\) 0 0
\(976\) −28.4376 + 25.5746i −0.910265 + 0.818623i
\(977\) 37.7372i 1.20732i 0.797242 + 0.603660i \(0.206292\pi\)
−0.797242 + 0.603660i \(0.793708\pi\)
\(978\) 0 0
\(979\) 6.40831 3.69984i 0.204811 0.118247i
\(980\) 0.696884 + 43.9399i 0.0222612 + 1.40361i
\(981\) 0 0
\(982\) −1.75420 3.67917i −0.0559787 0.117407i
\(983\) −19.0627 + 33.0176i −0.608006 + 1.05310i 0.383563 + 0.923515i \(0.374697\pi\)
−0.991569 + 0.129582i \(0.958636\pi\)
\(984\) 0 0
\(985\) 9.89804 + 17.1439i 0.315378 + 0.546250i
\(986\) −17.4410 36.5798i −0.555433 1.16494i
\(987\) 0 0
\(988\) −5.61472 4.54949i −0.178628 0.144739i
\(989\) 8.88856 + 5.13181i 0.282640 + 0.163182i
\(990\) 0 0
\(991\) −32.4040 + 18.7085i −1.02935 + 0.594294i −0.916798 0.399352i \(-0.869235\pi\)
−0.112550 + 0.993646i \(0.535902\pi\)
\(992\) 12.1440 1.58957i 0.385571 0.0504688i
\(993\) 0 0
\(994\) −6.95600 + 4.08993i −0.220631 + 0.129725i
\(995\) −20.1738 + 34.9421i −0.639553 + 1.10774i
\(996\) 0 0
\(997\) 2.33397 4.04255i 0.0739174 0.128029i −0.826698 0.562647i \(-0.809783\pi\)
0.900615 + 0.434618i \(0.143117\pi\)
\(998\) −1.93449 + 24.5332i −0.0612353 + 0.776586i
\(999\) 0 0
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 756.2.bb.a.611.14 88
3.2 odd 2 252.2.bb.a.23.31 yes 88
4.3 odd 2 inner 756.2.bb.a.611.31 88
7.4 even 3 756.2.o.a.179.16 88
9.2 odd 6 756.2.o.a.359.3 88
9.7 even 3 252.2.o.a.191.42 yes 88
12.11 even 2 252.2.bb.a.23.14 yes 88
21.11 odd 6 252.2.o.a.95.29 88
28.11 odd 6 756.2.o.a.179.3 88
36.7 odd 6 252.2.o.a.191.29 yes 88
36.11 even 6 756.2.o.a.359.16 88
63.11 odd 6 inner 756.2.bb.a.683.31 88
63.25 even 3 252.2.bb.a.11.14 yes 88
84.11 even 6 252.2.o.a.95.42 yes 88
252.11 even 6 inner 756.2.bb.a.683.14 88
252.151 odd 6 252.2.bb.a.11.31 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.o.a.95.29 88 21.11 odd 6
252.2.o.a.95.42 yes 88 84.11 even 6
252.2.o.a.191.29 yes 88 36.7 odd 6
252.2.o.a.191.42 yes 88 9.7 even 3
252.2.bb.a.11.14 yes 88 63.25 even 3
252.2.bb.a.11.31 yes 88 252.151 odd 6
252.2.bb.a.23.14 yes 88 12.11 even 2
252.2.bb.a.23.31 yes 88 3.2 odd 2
756.2.o.a.179.3 88 28.11 odd 6
756.2.o.a.179.16 88 7.4 even 3
756.2.o.a.359.3 88 9.2 odd 6
756.2.o.a.359.16 88 36.11 even 6
756.2.bb.a.611.14 88 1.1 even 1 trivial
756.2.bb.a.611.31 88 4.3 odd 2 inner
756.2.bb.a.683.14 88 252.11 even 6 inner
756.2.bb.a.683.31 88 63.11 odd 6 inner