Properties

Label 504.2.ch.b.269.1
Level $504$
Weight $2$
Character 504.269
Analytic conductor $4.024$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(269,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.269");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.ch (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.1
Character \(\chi\) \(=\) 504.269
Dual form 504.2.ch.b.341.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41410 + 0.0182389i) q^{2} +(1.99933 - 0.0515832i) q^{4} +(-0.785247 + 0.453362i) q^{5} +(-2.47043 - 0.947077i) q^{7} +(-2.82631 + 0.109409i) q^{8} +O(q^{10})\) \(q+(-1.41410 + 0.0182389i) q^{2} +(1.99933 - 0.0515832i) q^{4} +(-0.785247 + 0.453362i) q^{5} +(-2.47043 - 0.947077i) q^{7} +(-2.82631 + 0.109409i) q^{8} +(1.10215 - 0.655420i) q^{10} +(-0.0729337 + 0.126325i) q^{11} +6.12830 q^{13} +(3.51070 + 1.29420i) q^{14} +(3.99468 - 0.206264i) q^{16} +(-3.00430 + 5.20361i) q^{17} +(2.10516 + 3.64625i) q^{19} +(-1.54658 + 0.946928i) q^{20} +(0.100831 - 0.179966i) q^{22} +(3.20566 - 1.85079i) q^{23} +(-2.08893 + 3.61812i) q^{25} +(-8.66600 + 0.111774i) q^{26} +(-4.98808 - 1.76609i) q^{28} +10.2484 q^{29} +(-3.54741 - 2.04810i) q^{31} +(-5.64510 + 0.364536i) q^{32} +(4.15347 - 7.41320i) q^{34} +(2.36927 - 0.376312i) q^{35} +(-2.51971 + 1.45475i) q^{37} +(-3.04340 - 5.11775i) q^{38} +(2.16975 - 1.36726i) q^{40} +2.26244 q^{41} +8.73882i q^{43} +(-0.139303 + 0.256328i) q^{44} +(-4.49935 + 2.67566i) q^{46} +(3.58285 + 6.20567i) q^{47} +(5.20609 + 4.67938i) q^{49} +(2.88795 - 5.15448i) q^{50} +(12.2525 - 0.316117i) q^{52} +(-1.86849 + 3.23632i) q^{53} -0.132262i q^{55} +(7.08583 + 2.40645i) q^{56} +(-14.4923 + 0.186920i) q^{58} +(6.35100 + 3.66675i) q^{59} +(3.41070 + 5.90751i) q^{61} +(5.05374 + 2.83151i) q^{62} +(7.97606 - 0.618449i) q^{64} +(-4.81223 + 2.77834i) q^{65} +(-2.66978 - 1.54140i) q^{67} +(-5.73819 + 10.5587i) q^{68} +(-3.34351 + 0.575355i) q^{70} -4.91850i q^{71} +(2.67843 + 1.54639i) q^{73} +(3.53658 - 2.10312i) q^{74} +(4.39701 + 7.18148i) q^{76} +(0.299817 - 0.243004i) q^{77} +(-5.41731 - 9.38305i) q^{79} +(-3.04329 + 1.97300i) q^{80} +(-3.19931 + 0.0412645i) q^{82} -12.8534i q^{83} -5.44815i q^{85} +(-0.159387 - 12.3575i) q^{86} +(0.192312 - 0.365013i) q^{88} +(1.55708 + 2.69694i) q^{89} +(-15.1396 - 5.80397i) q^{91} +(6.31372 - 3.86570i) q^{92} +(-5.17967 - 8.71007i) q^{94} +(-3.30614 - 1.90880i) q^{95} -0.593803i q^{97} +(-7.44726 - 6.52214i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41410 + 0.0182389i −0.999917 + 0.0128969i
\(3\) 0 0
\(4\) 1.99933 0.0515832i 0.999667 0.0257916i
\(5\) −0.785247 + 0.453362i −0.351173 + 0.202750i −0.665202 0.746664i \(-0.731654\pi\)
0.314029 + 0.949413i \(0.398321\pi\)
\(6\) 0 0
\(7\) −2.47043 0.947077i −0.933736 0.357962i
\(8\) −2.82631 + 0.109409i −0.999252 + 0.0386820i
\(9\) 0 0
\(10\) 1.10215 0.655420i 0.348529 0.207262i
\(11\) −0.0729337 + 0.126325i −0.0219903 + 0.0380884i −0.876811 0.480835i \(-0.840334\pi\)
0.854821 + 0.518923i \(0.173667\pi\)
\(12\) 0 0
\(13\) 6.12830 1.69968 0.849842 0.527037i \(-0.176697\pi\)
0.849842 + 0.527037i \(0.176697\pi\)
\(14\) 3.51070 + 1.29420i 0.938275 + 0.345890i
\(15\) 0 0
\(16\) 3.99468 0.206264i 0.998670 0.0515660i
\(17\) −3.00430 + 5.20361i −0.728651 + 1.26206i 0.228803 + 0.973473i \(0.426519\pi\)
−0.957454 + 0.288587i \(0.906814\pi\)
\(18\) 0 0
\(19\) 2.10516 + 3.64625i 0.482957 + 0.836506i 0.999809 0.0195688i \(-0.00622934\pi\)
−0.516851 + 0.856075i \(0.672896\pi\)
\(20\) −1.54658 + 0.946928i −0.345827 + 0.211740i
\(21\) 0 0
\(22\) 0.100831 0.179966i 0.0214973 0.0383688i
\(23\) 3.20566 1.85079i 0.668426 0.385916i −0.127054 0.991896i \(-0.540552\pi\)
0.795480 + 0.605980i \(0.207219\pi\)
\(24\) 0 0
\(25\) −2.08893 + 3.61812i −0.417785 + 0.723625i
\(26\) −8.66600 + 0.111774i −1.69954 + 0.0219206i
\(27\) 0 0
\(28\) −4.98808 1.76609i −0.942658 0.333760i
\(29\) 10.2484 1.90309 0.951543 0.307515i \(-0.0994973\pi\)
0.951543 + 0.307515i \(0.0994973\pi\)
\(30\) 0 0
\(31\) −3.54741 2.04810i −0.637134 0.367849i 0.146376 0.989229i \(-0.453239\pi\)
−0.783510 + 0.621380i \(0.786572\pi\)
\(32\) −5.64510 + 0.364536i −0.997921 + 0.0644414i
\(33\) 0 0
\(34\) 4.15347 7.41320i 0.712314 1.27135i
\(35\) 2.36927 0.376312i 0.400480 0.0636084i
\(36\) 0 0
\(37\) −2.51971 + 1.45475i −0.414238 + 0.239160i −0.692609 0.721313i \(-0.743539\pi\)
0.278371 + 0.960474i \(0.410205\pi\)
\(38\) −3.04340 5.11775i −0.493705 0.830208i
\(39\) 0 0
\(40\) 2.16975 1.36726i 0.343067 0.216182i
\(41\) 2.26244 0.353334 0.176667 0.984271i \(-0.443468\pi\)
0.176667 + 0.984271i \(0.443468\pi\)
\(42\) 0 0
\(43\) 8.73882i 1.33266i 0.745658 + 0.666329i \(0.232135\pi\)
−0.745658 + 0.666329i \(0.767865\pi\)
\(44\) −0.139303 + 0.256328i −0.0210007 + 0.0386429i
\(45\) 0 0
\(46\) −4.49935 + 2.67566i −0.663393 + 0.394505i
\(47\) 3.58285 + 6.20567i 0.522612 + 0.905190i 0.999654 + 0.0263098i \(0.00837564\pi\)
−0.477042 + 0.878881i \(0.658291\pi\)
\(48\) 0 0
\(49\) 5.20609 + 4.67938i 0.743727 + 0.668483i
\(50\) 2.88795 5.15448i 0.408418 0.728953i
\(51\) 0 0
\(52\) 12.2525 0.316117i 1.69912 0.0438376i
\(53\) −1.86849 + 3.23632i −0.256657 + 0.444543i −0.965344 0.260980i \(-0.915954\pi\)
0.708687 + 0.705523i \(0.249288\pi\)
\(54\) 0 0
\(55\) 0.132262i 0.0178342i
\(56\) 7.08583 + 2.40645i 0.946884 + 0.321575i
\(57\) 0 0
\(58\) −14.4923 + 0.186920i −1.90293 + 0.0245439i
\(59\) 6.35100 + 3.66675i 0.826829 + 0.477370i 0.852766 0.522293i \(-0.174923\pi\)
−0.0259364 + 0.999664i \(0.508257\pi\)
\(60\) 0 0
\(61\) 3.41070 + 5.90751i 0.436696 + 0.756379i 0.997432 0.0716150i \(-0.0228153\pi\)
−0.560737 + 0.827994i \(0.689482\pi\)
\(62\) 5.05374 + 2.83151i 0.641825 + 0.359602i
\(63\) 0 0
\(64\) 7.97606 0.618449i 0.997007 0.0773061i
\(65\) −4.81223 + 2.77834i −0.596883 + 0.344611i
\(66\) 0 0
\(67\) −2.66978 1.54140i −0.326166 0.188312i 0.327972 0.944688i \(-0.393635\pi\)
−0.654138 + 0.756376i \(0.726968\pi\)
\(68\) −5.73819 + 10.5587i −0.695858 + 1.28043i
\(69\) 0 0
\(70\) −3.34351 + 0.575355i −0.399626 + 0.0687681i
\(71\) 4.91850i 0.583719i −0.956461 0.291859i \(-0.905726\pi\)
0.956461 0.291859i \(-0.0942739\pi\)
\(72\) 0 0
\(73\) 2.67843 + 1.54639i 0.313486 + 0.180991i 0.648485 0.761227i \(-0.275403\pi\)
−0.334999 + 0.942218i \(0.608736\pi\)
\(74\) 3.53658 2.10312i 0.411119 0.244483i
\(75\) 0 0
\(76\) 4.39701 + 7.18148i 0.504371 + 0.823772i
\(77\) 0.299817 0.243004i 0.0341674 0.0276928i
\(78\) 0 0
\(79\) −5.41731 9.38305i −0.609495 1.05568i −0.991324 0.131443i \(-0.958039\pi\)
0.381829 0.924233i \(-0.375294\pi\)
\(80\) −3.04329 + 1.97300i −0.340251 + 0.220589i
\(81\) 0 0
\(82\) −3.19931 + 0.0412645i −0.353305 + 0.00455691i
\(83\) 12.8534i 1.41085i −0.708785 0.705424i \(-0.750756\pi\)
0.708785 0.705424i \(-0.249244\pi\)
\(84\) 0 0
\(85\) 5.44815i 0.590935i
\(86\) −0.159387 12.3575i −0.0171871 1.33255i
\(87\) 0 0
\(88\) 0.192312 0.365013i 0.0205006 0.0389105i
\(89\) 1.55708 + 2.69694i 0.165050 + 0.285875i 0.936673 0.350205i \(-0.113888\pi\)
−0.771623 + 0.636080i \(0.780555\pi\)
\(90\) 0 0
\(91\) −15.1396 5.80397i −1.58706 0.608422i
\(92\) 6.31372 3.86570i 0.658250 0.403027i
\(93\) 0 0
\(94\) −5.17967 8.71007i −0.534243 0.898375i
\(95\) −3.30614 1.90880i −0.339203 0.195839i
\(96\) 0 0
\(97\) 0.593803i 0.0602915i −0.999546 0.0301458i \(-0.990403\pi\)
0.999546 0.0301458i \(-0.00959715\pi\)
\(98\) −7.44726 6.52214i −0.752286 0.658836i
\(99\) 0 0
\(100\) −3.98983 + 7.34160i −0.398983 + 0.734160i
\(101\) 9.65297 + 5.57314i 0.960506 + 0.554549i 0.896329 0.443390i \(-0.146224\pi\)
0.0641776 + 0.997938i \(0.479558\pi\)
\(102\) 0 0
\(103\) −1.41603 + 0.817548i −0.139526 + 0.0805554i −0.568138 0.822933i \(-0.692336\pi\)
0.428612 + 0.903489i \(0.359003\pi\)
\(104\) −17.3205 + 0.670493i −1.69841 + 0.0657472i
\(105\) 0 0
\(106\) 2.58320 4.61055i 0.250903 0.447816i
\(107\) −7.12074 12.3335i −0.688387 1.19232i −0.972359 0.233489i \(-0.924986\pi\)
0.283972 0.958833i \(-0.408348\pi\)
\(108\) 0 0
\(109\) −5.88150 3.39568i −0.563345 0.325247i 0.191142 0.981562i \(-0.438781\pi\)
−0.754487 + 0.656315i \(0.772114\pi\)
\(110\) 0.00241231 + 0.187031i 0.000230005 + 0.0178327i
\(111\) 0 0
\(112\) −10.0639 3.27371i −0.950953 0.309336i
\(113\) 8.54183i 0.803548i 0.915739 + 0.401774i \(0.131606\pi\)
−0.915739 + 0.401774i \(0.868394\pi\)
\(114\) 0 0
\(115\) −1.67816 + 2.90665i −0.156489 + 0.271046i
\(116\) 20.4901 0.528647i 1.90245 0.0490836i
\(117\) 0 0
\(118\) −9.04780 5.06930i −0.832917 0.466667i
\(119\) 12.3502 10.0099i 1.13214 0.917602i
\(120\) 0 0
\(121\) 5.48936 + 9.50785i 0.499033 + 0.864350i
\(122\) −4.93081 8.29158i −0.446414 0.750684i
\(123\) 0 0
\(124\) −7.19811 3.91185i −0.646409 0.351294i
\(125\) 8.32178i 0.744323i
\(126\) 0 0
\(127\) −18.0974 −1.60589 −0.802944 0.596054i \(-0.796734\pi\)
−0.802944 + 0.596054i \(0.796734\pi\)
\(128\) −11.2676 + 1.02002i −0.995927 + 0.0901580i
\(129\) 0 0
\(130\) 6.75428 4.01661i 0.592389 0.352280i
\(131\) −8.38458 + 4.84084i −0.732564 + 0.422946i −0.819359 0.573280i \(-0.805671\pi\)
0.0867954 + 0.996226i \(0.472337\pi\)
\(132\) 0 0
\(133\) −1.74739 11.0016i −0.151518 0.953957i
\(134\) 3.80344 + 2.13099i 0.328568 + 0.184090i
\(135\) 0 0
\(136\) 7.92177 15.0357i 0.679286 1.28930i
\(137\) −9.11532 5.26273i −0.778774 0.449625i 0.0572215 0.998362i \(-0.481776\pi\)
−0.835996 + 0.548736i \(0.815109\pi\)
\(138\) 0 0
\(139\) 15.8152 1.34143 0.670715 0.741715i \(-0.265987\pi\)
0.670715 + 0.741715i \(0.265987\pi\)
\(140\) 4.71755 0.874589i 0.398706 0.0739163i
\(141\) 0 0
\(142\) 0.0897082 + 6.95523i 0.00752814 + 0.583670i
\(143\) −0.446960 + 0.774157i −0.0373767 + 0.0647383i
\(144\) 0 0
\(145\) −8.04755 + 4.64625i −0.668312 + 0.385850i
\(146\) −3.81576 2.13789i −0.315794 0.176933i
\(147\) 0 0
\(148\) −4.96270 + 3.03852i −0.407931 + 0.249764i
\(149\) −5.79849 10.0433i −0.475031 0.822777i 0.524560 0.851373i \(-0.324230\pi\)
−0.999591 + 0.0285960i \(0.990896\pi\)
\(150\) 0 0
\(151\) 7.79321 13.4982i 0.634202 1.09847i −0.352481 0.935819i \(-0.614662\pi\)
0.986684 0.162652i \(-0.0520047\pi\)
\(152\) −6.34877 10.0751i −0.514953 0.817199i
\(153\) 0 0
\(154\) −0.419538 + 0.349099i −0.0338074 + 0.0281312i
\(155\) 3.71412 0.298326
\(156\) 0 0
\(157\) 6.66733 11.5482i 0.532111 0.921643i −0.467186 0.884159i \(-0.654732\pi\)
0.999297 0.0374841i \(-0.0119344\pi\)
\(158\) 7.83173 + 13.1697i 0.623059 + 1.04773i
\(159\) 0 0
\(160\) 4.26753 2.84552i 0.337378 0.224958i
\(161\) −9.67221 + 1.53624i −0.762277 + 0.121073i
\(162\) 0 0
\(163\) −14.7888 + 8.53830i −1.15835 + 0.668771i −0.950907 0.309477i \(-0.899846\pi\)
−0.207439 + 0.978248i \(0.566513\pi\)
\(164\) 4.52338 0.116704i 0.353217 0.00911305i
\(165\) 0 0
\(166\) 0.234433 + 18.1760i 0.0181955 + 1.41073i
\(167\) −1.64523 −0.127312 −0.0636558 0.997972i \(-0.520276\pi\)
−0.0636558 + 0.997972i \(0.520276\pi\)
\(168\) 0 0
\(169\) 24.5561 1.88893
\(170\) 0.0993685 + 7.70421i 0.00762121 + 0.590886i
\(171\) 0 0
\(172\) 0.450776 + 17.4718i 0.0343714 + 1.33221i
\(173\) −7.80851 + 4.50825i −0.593670 + 0.342756i −0.766547 0.642188i \(-0.778027\pi\)
0.172877 + 0.984943i \(0.444694\pi\)
\(174\) 0 0
\(175\) 8.58720 6.95996i 0.649131 0.526124i
\(176\) −0.265290 + 0.519671i −0.0199970 + 0.0391717i
\(177\) 0 0
\(178\) −2.25105 3.78533i −0.168723 0.283723i
\(179\) −7.30700 + 12.6561i −0.546151 + 0.945961i 0.452383 + 0.891824i \(0.350574\pi\)
−0.998534 + 0.0541368i \(0.982759\pi\)
\(180\) 0 0
\(181\) 0.198456 0.0147511 0.00737556 0.999973i \(-0.497652\pi\)
0.00737556 + 0.999973i \(0.497652\pi\)
\(182\) 21.5147 + 7.93125i 1.59477 + 0.587903i
\(183\) 0 0
\(184\) −8.85769 + 5.58163i −0.652998 + 0.411483i
\(185\) 1.31906 2.28468i 0.0969793 0.167973i
\(186\) 0 0
\(187\) −0.438230 0.759037i −0.0320466 0.0555063i
\(188\) 7.48342 + 12.2224i 0.545784 + 0.891410i
\(189\) 0 0
\(190\) 4.71002 + 2.63893i 0.341700 + 0.191448i
\(191\) −0.169619 + 0.0979296i −0.0122732 + 0.00708594i −0.506124 0.862461i \(-0.668922\pi\)
0.493851 + 0.869547i \(0.335589\pi\)
\(192\) 0 0
\(193\) 5.03614 8.72285i 0.362509 0.627884i −0.625864 0.779932i \(-0.715254\pi\)
0.988373 + 0.152048i \(0.0485868\pi\)
\(194\) 0.0108303 + 0.839694i 0.000777572 + 0.0602865i
\(195\) 0 0
\(196\) 10.6501 + 9.08711i 0.760721 + 0.649079i
\(197\) −0.981430 −0.0699240 −0.0349620 0.999389i \(-0.511131\pi\)
−0.0349620 + 0.999389i \(0.511131\pi\)
\(198\) 0 0
\(199\) −1.90703 1.10102i −0.135185 0.0780494i 0.430882 0.902408i \(-0.358203\pi\)
−0.566067 + 0.824359i \(0.691536\pi\)
\(200\) 5.50809 10.4545i 0.389481 0.739244i
\(201\) 0 0
\(202\) −13.7519 7.70490i −0.967578 0.542115i
\(203\) −25.3181 9.70606i −1.77698 0.681232i
\(204\) 0 0
\(205\) −1.77658 + 1.02571i −0.124081 + 0.0716385i
\(206\) 1.98750 1.18192i 0.138476 0.0823482i
\(207\) 0 0
\(208\) 24.4806 1.26405i 1.69742 0.0876460i
\(209\) −0.614149 −0.0424816
\(210\) 0 0
\(211\) 17.7696i 1.22331i −0.791125 0.611654i \(-0.790504\pi\)
0.791125 0.611654i \(-0.209496\pi\)
\(212\) −3.56880 + 6.56688i −0.245106 + 0.451015i
\(213\) 0 0
\(214\) 10.2944 + 17.3108i 0.703707 + 1.18334i
\(215\) −3.96185 6.86213i −0.270196 0.467993i
\(216\) 0 0
\(217\) 6.82394 + 8.41937i 0.463239 + 0.571544i
\(218\) 8.37893 + 4.69455i 0.567493 + 0.317955i
\(219\) 0 0
\(220\) −0.00682247 0.264435i −0.000459971 0.0178282i
\(221\) −18.4113 + 31.8893i −1.23848 + 2.14510i
\(222\) 0 0
\(223\) 20.7181i 1.38738i 0.720271 + 0.693692i \(0.244017\pi\)
−0.720271 + 0.693692i \(0.755983\pi\)
\(224\) 14.2911 + 4.44578i 0.954863 + 0.297046i
\(225\) 0 0
\(226\) −0.155794 12.0790i −0.0103633 0.803481i
\(227\) 17.3954 + 10.0432i 1.15457 + 0.666593i 0.949997 0.312258i \(-0.101085\pi\)
0.204575 + 0.978851i \(0.434419\pi\)
\(228\) 0 0
\(229\) 9.68640 + 16.7773i 0.640095 + 1.10868i 0.985411 + 0.170191i \(0.0544385\pi\)
−0.345316 + 0.938487i \(0.612228\pi\)
\(230\) 2.32006 4.14089i 0.152980 0.273042i
\(231\) 0 0
\(232\) −28.9653 + 1.12127i −1.90166 + 0.0736152i
\(233\) 22.4100 12.9384i 1.46813 0.847625i 0.468768 0.883322i \(-0.344698\pi\)
0.999363 + 0.0356961i \(0.0113649\pi\)
\(234\) 0 0
\(235\) −5.62684 3.24866i −0.367054 0.211919i
\(236\) 12.8869 + 7.00346i 0.838867 + 0.455886i
\(237\) 0 0
\(238\) −17.2817 + 14.3802i −1.12021 + 0.932127i
\(239\) 11.2007i 0.724512i −0.932079 0.362256i \(-0.882007\pi\)
0.932079 0.362256i \(-0.117993\pi\)
\(240\) 0 0
\(241\) −23.6842 13.6741i −1.52563 0.880825i −0.999538 0.0303997i \(-0.990322\pi\)
−0.526096 0.850425i \(-0.676345\pi\)
\(242\) −7.93590 13.3449i −0.510139 0.857842i
\(243\) 0 0
\(244\) 7.12386 + 11.6352i 0.456059 + 0.744865i
\(245\) −6.20952 1.31423i −0.396712 0.0839628i
\(246\) 0 0
\(247\) 12.9011 + 22.3453i 0.820875 + 1.42180i
\(248\) 10.2502 + 5.40044i 0.650886 + 0.342929i
\(249\) 0 0
\(250\) 0.151780 + 11.7678i 0.00959943 + 0.744261i
\(251\) 29.0073i 1.83092i 0.402407 + 0.915461i \(0.368174\pi\)
−0.402407 + 0.915461i \(0.631826\pi\)
\(252\) 0 0
\(253\) 0.539939i 0.0339457i
\(254\) 25.5915 0.330078i 1.60575 0.0207109i
\(255\) 0 0
\(256\) 15.9149 1.64792i 0.994682 0.102995i
\(257\) −6.02554 10.4365i −0.375863 0.651014i 0.614593 0.788845i \(-0.289320\pi\)
−0.990456 + 0.137831i \(0.955987\pi\)
\(258\) 0 0
\(259\) 7.60254 1.20752i 0.472399 0.0750314i
\(260\) −9.47794 + 5.80306i −0.587797 + 0.359891i
\(261\) 0 0
\(262\) 11.7683 6.99834i 0.727048 0.432359i
\(263\) 2.36800 + 1.36716i 0.146017 + 0.0843029i 0.571229 0.820791i \(-0.306467\pi\)
−0.425212 + 0.905094i \(0.639800\pi\)
\(264\) 0 0
\(265\) 3.38842i 0.208149i
\(266\) 2.67163 + 15.5254i 0.163808 + 0.951923i
\(267\) 0 0
\(268\) −5.41730 2.94406i −0.330914 0.179837i
\(269\) 4.45879 + 2.57428i 0.271857 + 0.156957i 0.629731 0.776813i \(-0.283165\pi\)
−0.357874 + 0.933770i \(0.616498\pi\)
\(270\) 0 0
\(271\) 21.0489 12.1526i 1.27863 0.738216i 0.302031 0.953298i \(-0.402335\pi\)
0.976596 + 0.215082i \(0.0690020\pi\)
\(272\) −10.9279 + 21.4064i −0.662602 + 1.29795i
\(273\) 0 0
\(274\) 12.9859 + 7.27575i 0.784508 + 0.439544i
\(275\) −0.304706 0.527767i −0.0183745 0.0318255i
\(276\) 0 0
\(277\) 0.705869 + 0.407533i 0.0424115 + 0.0244863i 0.521056 0.853523i \(-0.325538\pi\)
−0.478644 + 0.878009i \(0.658872\pi\)
\(278\) −22.3642 + 0.288453i −1.34132 + 0.0173002i
\(279\) 0 0
\(280\) −6.65512 + 1.32280i −0.397719 + 0.0790522i
\(281\) 1.06599i 0.0635918i 0.999494 + 0.0317959i \(0.0101227\pi\)
−0.999494 + 0.0317959i \(0.989877\pi\)
\(282\) 0 0
\(283\) 3.14663 5.45012i 0.187048 0.323976i −0.757217 0.653164i \(-0.773441\pi\)
0.944265 + 0.329187i \(0.106775\pi\)
\(284\) −0.253712 9.83373i −0.0150550 0.583525i
\(285\) 0 0
\(286\) 0.617924 1.10288i 0.0365386 0.0652149i
\(287\) −5.58922 2.14271i −0.329921 0.126480i
\(288\) 0 0
\(289\) −9.55169 16.5440i −0.561864 0.973177i
\(290\) 11.2953 6.71703i 0.663281 0.394437i
\(291\) 0 0
\(292\) 5.43484 + 2.95359i 0.318050 + 0.172846i
\(293\) 17.9687i 1.04974i −0.851181 0.524872i \(-0.824113\pi\)
0.851181 0.524872i \(-0.175887\pi\)
\(294\) 0 0
\(295\) −6.64946 −0.387147
\(296\) 6.96232 4.38727i 0.404676 0.255005i
\(297\) 0 0
\(298\) 8.38280 + 14.0964i 0.485602 + 0.816582i
\(299\) 19.6452 11.3422i 1.13611 0.655936i
\(300\) 0 0
\(301\) 8.27634 21.5887i 0.477040 1.24435i
\(302\) −10.7742 + 19.2299i −0.619983 + 1.10656i
\(303\) 0 0
\(304\) 9.16153 + 14.1314i 0.525450 + 0.810489i
\(305\) −5.35648 3.09257i −0.306711 0.177080i
\(306\) 0 0
\(307\) 27.7008 1.58097 0.790485 0.612481i \(-0.209829\pi\)
0.790485 + 0.612481i \(0.209829\pi\)
\(308\) 0.586900 0.501311i 0.0334418 0.0285648i
\(309\) 0 0
\(310\) −5.25213 + 0.0677416i −0.298301 + 0.00384747i
\(311\) −12.7971 + 22.1653i −0.725658 + 1.25688i 0.233045 + 0.972466i \(0.425131\pi\)
−0.958703 + 0.284410i \(0.908202\pi\)
\(312\) 0 0
\(313\) −14.9541 + 8.63375i −0.845255 + 0.488008i −0.859047 0.511897i \(-0.828943\pi\)
0.0137920 + 0.999905i \(0.495610\pi\)
\(314\) −9.21762 + 16.4518i −0.520180 + 0.928429i
\(315\) 0 0
\(316\) −11.3150 18.4804i −0.636520 1.03961i
\(317\) −2.17346 3.76454i −0.122074 0.211438i 0.798512 0.601979i \(-0.205621\pi\)
−0.920585 + 0.390542i \(0.872288\pi\)
\(318\) 0 0
\(319\) −0.747457 + 1.29463i −0.0418495 + 0.0724855i
\(320\) −5.98279 + 4.10168i −0.334448 + 0.229291i
\(321\) 0 0
\(322\) 13.6494 2.34881i 0.760652 0.130894i
\(323\) −25.2982 −1.40763
\(324\) 0 0
\(325\) −12.8016 + 22.1730i −0.710103 + 1.22993i
\(326\) 20.7570 12.3437i 1.14962 0.683655i
\(327\) 0 0
\(328\) −6.39437 + 0.247532i −0.353070 + 0.0136677i
\(329\) −2.97393 18.7239i −0.163958 1.03228i
\(330\) 0 0
\(331\) 15.0111 8.66665i 0.825084 0.476362i −0.0270828 0.999633i \(-0.508622\pi\)
0.852166 + 0.523271i \(0.175288\pi\)
\(332\) −0.663022 25.6983i −0.0363880 1.41038i
\(333\) 0 0
\(334\) 2.32651 0.0300072i 0.127301 0.00164192i
\(335\) 2.79525 0.152721
\(336\) 0 0
\(337\) −0.659592 −0.0359303 −0.0179651 0.999839i \(-0.505719\pi\)
−0.0179651 + 0.999839i \(0.505719\pi\)
\(338\) −34.7246 + 0.447876i −1.88877 + 0.0243613i
\(339\) 0 0
\(340\) −0.281033 10.8927i −0.0152412 0.590739i
\(341\) 0.517452 0.298751i 0.0280216 0.0161783i
\(342\) 0 0
\(343\) −8.42956 16.4907i −0.455154 0.890413i
\(344\) −0.956108 24.6986i −0.0515499 1.33166i
\(345\) 0 0
\(346\) 10.9598 6.51751i 0.589200 0.350384i
\(347\) −3.49897 + 6.06039i −0.187834 + 0.325339i −0.944528 0.328431i \(-0.893480\pi\)
0.756694 + 0.653770i \(0.226813\pi\)
\(348\) 0 0
\(349\) −20.2632 −1.08467 −0.542333 0.840164i \(-0.682459\pi\)
−0.542333 + 0.840164i \(0.682459\pi\)
\(350\) −12.0162 + 9.99868i −0.642292 + 0.534452i
\(351\) 0 0
\(352\) 0.365668 0.739703i 0.0194902 0.0394263i
\(353\) −5.18465 + 8.98008i −0.275951 + 0.477962i −0.970375 0.241605i \(-0.922326\pi\)
0.694423 + 0.719567i \(0.255659\pi\)
\(354\) 0 0
\(355\) 2.22986 + 3.86224i 0.118349 + 0.204986i
\(356\) 3.25224 + 5.31177i 0.172368 + 0.281523i
\(357\) 0 0
\(358\) 10.1020 18.0302i 0.533905 0.952926i
\(359\) −17.5691 + 10.1436i −0.927264 + 0.535356i −0.885945 0.463790i \(-0.846489\pi\)
−0.0413188 + 0.999146i \(0.513156\pi\)
\(360\) 0 0
\(361\) 0.636589 1.10261i 0.0335047 0.0580319i
\(362\) −0.280636 + 0.00361962i −0.0147499 + 0.000190243i
\(363\) 0 0
\(364\) −30.5684 10.8231i −1.60222 0.567287i
\(365\) −2.80430 −0.146784
\(366\) 0 0
\(367\) 21.6024 + 12.4722i 1.12764 + 0.651042i 0.943340 0.331829i \(-0.107666\pi\)
0.184298 + 0.982870i \(0.440999\pi\)
\(368\) 12.4238 8.05452i 0.647637 0.419871i
\(369\) 0 0
\(370\) −1.82361 + 3.25482i −0.0948050 + 0.169210i
\(371\) 7.68104 6.22552i 0.398780 0.323213i
\(372\) 0 0
\(373\) −4.26886 + 2.46463i −0.221033 + 0.127614i −0.606429 0.795138i \(-0.707398\pi\)
0.385395 + 0.922752i \(0.374065\pi\)
\(374\) 0.633544 + 1.06536i 0.0327598 + 0.0550884i
\(375\) 0 0
\(376\) −10.8052 17.1472i −0.557235 0.884297i
\(377\) 62.8055 3.23465
\(378\) 0 0
\(379\) 25.1007i 1.28934i 0.764462 + 0.644669i \(0.223005\pi\)
−0.764462 + 0.644669i \(0.776995\pi\)
\(380\) −6.70855 3.64579i −0.344141 0.187025i
\(381\) 0 0
\(382\) 0.238071 0.141575i 0.0121808 0.00724363i
\(383\) 14.0619 + 24.3560i 0.718531 + 1.24453i 0.961582 + 0.274519i \(0.0885185\pi\)
−0.243051 + 0.970014i \(0.578148\pi\)
\(384\) 0 0
\(385\) −0.125262 + 0.326744i −0.00638394 + 0.0166524i
\(386\) −6.96249 + 12.4268i −0.354381 + 0.632507i
\(387\) 0 0
\(388\) −0.0306302 1.18721i −0.00155501 0.0602715i
\(389\) 3.82681 6.62822i 0.194027 0.336064i −0.752554 0.658530i \(-0.771178\pi\)
0.946581 + 0.322466i \(0.104512\pi\)
\(390\) 0 0
\(391\) 22.2413i 1.12479i
\(392\) −15.2260 12.6558i −0.769029 0.639214i
\(393\) 0 0
\(394\) 1.38784 0.0179002i 0.0699182 0.000901800i
\(395\) 8.50785 + 4.91201i 0.428076 + 0.247150i
\(396\) 0 0
\(397\) 6.22748 + 10.7863i 0.312548 + 0.541350i 0.978913 0.204276i \(-0.0654841\pi\)
−0.666365 + 0.745626i \(0.732151\pi\)
\(398\) 2.71680 + 1.52217i 0.136181 + 0.0762994i
\(399\) 0 0
\(400\) −7.59830 + 14.8841i −0.379915 + 0.744206i
\(401\) −18.1682 + 10.4894i −0.907279 + 0.523818i −0.879555 0.475798i \(-0.842159\pi\)
−0.0277241 + 0.999616i \(0.508826\pi\)
\(402\) 0 0
\(403\) −21.7396 12.5514i −1.08293 0.625228i
\(404\) 19.5870 + 10.6447i 0.974490 + 0.529591i
\(405\) 0 0
\(406\) 35.9792 + 13.2635i 1.78562 + 0.658258i
\(407\) 0.424403i 0.0210369i
\(408\) 0 0
\(409\) 0.456865 + 0.263771i 0.0225905 + 0.0130426i 0.511253 0.859430i \(-0.329182\pi\)
−0.488662 + 0.872473i \(0.662515\pi\)
\(410\) 2.49354 1.48285i 0.123147 0.0732328i
\(411\) 0 0
\(412\) −2.78896 + 1.70760i −0.137402 + 0.0841272i
\(413\) −12.2170 15.0733i −0.601160 0.741711i
\(414\) 0 0
\(415\) 5.82727 + 10.0931i 0.286049 + 0.495452i
\(416\) −34.5948 + 2.23399i −1.69615 + 0.109530i
\(417\) 0 0
\(418\) 0.868466 0.0112014i 0.0424780 0.000547879i
\(419\) 22.0482i 1.07713i −0.842585 0.538564i \(-0.818967\pi\)
0.842585 0.538564i \(-0.181033\pi\)
\(420\) 0 0
\(421\) 18.2360i 0.888771i −0.895836 0.444385i \(-0.853422\pi\)
0.895836 0.444385i \(-0.146578\pi\)
\(422\) 0.324098 + 25.1279i 0.0157768 + 1.22321i
\(423\) 0 0
\(424\) 4.92686 9.35129i 0.239269 0.454139i
\(425\) −12.5515 21.7399i −0.608839 1.05454i
\(426\) 0 0
\(427\) −2.83105 17.8243i −0.137004 0.862579i
\(428\) −14.8729 24.2914i −0.718910 1.17417i
\(429\) 0 0
\(430\) 5.72760 + 9.63145i 0.276209 + 0.464470i
\(431\) −24.8419 14.3425i −1.19659 0.690854i −0.236799 0.971559i \(-0.576098\pi\)
−0.959794 + 0.280705i \(0.909432\pi\)
\(432\) 0 0
\(433\) 37.7023i 1.81186i −0.423429 0.905929i \(-0.639174\pi\)
0.423429 0.905929i \(-0.360826\pi\)
\(434\) −9.80326 11.7813i −0.470572 0.565522i
\(435\) 0 0
\(436\) −11.9342 6.48572i −0.571546 0.310610i
\(437\) 13.4969 + 7.79242i 0.645642 + 0.372762i
\(438\) 0 0
\(439\) −7.68790 + 4.43861i −0.366924 + 0.211843i −0.672114 0.740448i \(-0.734613\pi\)
0.305190 + 0.952291i \(0.401280\pi\)
\(440\) 0.0144706 + 0.373812i 0.000689861 + 0.0178208i
\(441\) 0 0
\(442\) 25.4537 45.4303i 1.21071 2.16090i
\(443\) 0.209480 + 0.362830i 0.00995270 + 0.0172386i 0.870959 0.491356i \(-0.163499\pi\)
−0.861006 + 0.508595i \(0.830165\pi\)
\(444\) 0 0
\(445\) −2.44538 1.41184i −0.115922 0.0669278i
\(446\) −0.377875 29.2973i −0.0178929 1.38727i
\(447\) 0 0
\(448\) −20.2900 6.02611i −0.958615 0.284707i
\(449\) 39.4411i 1.86134i 0.365861 + 0.930670i \(0.380775\pi\)
−0.365861 + 0.930670i \(0.619225\pi\)
\(450\) 0 0
\(451\) −0.165008 + 0.285803i −0.00776994 + 0.0134579i
\(452\) 0.440615 + 17.0780i 0.0207248 + 0.803281i
\(453\) 0 0
\(454\) −24.7819 13.8848i −1.16307 0.651647i
\(455\) 14.5196 2.30616i 0.680689 0.108114i
\(456\) 0 0
\(457\) −5.94479 10.2967i −0.278085 0.481658i 0.692823 0.721107i \(-0.256367\pi\)
−0.970909 + 0.239449i \(0.923033\pi\)
\(458\) −14.0035 23.5481i −0.654341 1.10033i
\(459\) 0 0
\(460\) −3.20526 + 5.89793i −0.149446 + 0.274992i
\(461\) 0.217896i 0.0101484i −0.999987 0.00507422i \(-0.998385\pi\)
0.999987 0.00507422i \(-0.00161518\pi\)
\(462\) 0 0
\(463\) −9.13271 −0.424433 −0.212216 0.977223i \(-0.568068\pi\)
−0.212216 + 0.977223i \(0.568068\pi\)
\(464\) 40.9392 2.11388i 1.90055 0.0981346i
\(465\) 0 0
\(466\) −31.4540 + 18.7049i −1.45708 + 0.866489i
\(467\) 23.4188 13.5208i 1.08369 0.625670i 0.151802 0.988411i \(-0.451492\pi\)
0.931890 + 0.362741i \(0.118159\pi\)
\(468\) 0 0
\(469\) 5.13570 + 6.33642i 0.237145 + 0.292589i
\(470\) 8.01614 + 4.49128i 0.369757 + 0.207167i
\(471\) 0 0
\(472\) −18.3511 9.66852i −0.844676 0.445029i
\(473\) −1.10393 0.637355i −0.0507588 0.0293056i
\(474\) 0 0
\(475\) −17.5901 −0.807089
\(476\) 24.1758 20.6501i 1.10809 0.946497i
\(477\) 0 0
\(478\) 0.204289 + 15.8388i 0.00934394 + 0.724452i
\(479\) −5.06539 + 8.77352i −0.231444 + 0.400872i −0.958233 0.285988i \(-0.907678\pi\)
0.726789 + 0.686860i \(0.241012\pi\)
\(480\) 0 0
\(481\) −15.4415 + 8.91517i −0.704073 + 0.406497i
\(482\) 33.7411 + 18.9045i 1.53687 + 0.861076i
\(483\) 0 0
\(484\) 11.4655 + 18.7262i 0.521160 + 0.851192i
\(485\) 0.269208 + 0.466281i 0.0122241 + 0.0211728i
\(486\) 0 0
\(487\) 5.08735 8.81155i 0.230530 0.399290i −0.727434 0.686177i \(-0.759287\pi\)
0.957964 + 0.286888i \(0.0926207\pi\)
\(488\) −10.2860 16.3233i −0.465627 0.738921i
\(489\) 0 0
\(490\) 8.80483 + 1.74519i 0.397762 + 0.0788395i
\(491\) 24.6642 1.11308 0.556540 0.830821i \(-0.312129\pi\)
0.556540 + 0.830821i \(0.312129\pi\)
\(492\) 0 0
\(493\) −30.7894 + 53.3288i −1.38669 + 2.40181i
\(494\) −18.6509 31.3631i −0.839143 1.41109i
\(495\) 0 0
\(496\) −14.5932 7.44979i −0.655255 0.334506i
\(497\) −4.65820 + 12.1508i −0.208949 + 0.545039i
\(498\) 0 0
\(499\) 12.8103 7.39603i 0.573468 0.331092i −0.185065 0.982726i \(-0.559250\pi\)
0.758533 + 0.651634i \(0.225916\pi\)
\(500\) −0.429264 16.6380i −0.0191973 0.744075i
\(501\) 0 0
\(502\) −0.529061 41.0190i −0.0236132 1.83077i
\(503\) −34.7978 −1.55156 −0.775778 0.631006i \(-0.782642\pi\)
−0.775778 + 0.631006i \(0.782642\pi\)
\(504\) 0 0
\(505\) −10.1066 −0.449738
\(506\) −0.00984792 0.763526i −0.000437793 0.0339429i
\(507\) 0 0
\(508\) −36.1828 + 0.933524i −1.60535 + 0.0414184i
\(509\) 30.0509 17.3499i 1.33198 0.769021i 0.346381 0.938094i \(-0.387411\pi\)
0.985604 + 0.169073i \(0.0540772\pi\)
\(510\) 0 0
\(511\) −5.15233 6.35693i −0.227926 0.281214i
\(512\) −22.4752 + 2.62058i −0.993271 + 0.115815i
\(513\) 0 0
\(514\) 8.71105 + 14.6484i 0.384228 + 0.646112i
\(515\) 0.741291 1.28395i 0.0326652 0.0565778i
\(516\) 0 0
\(517\) −1.04524 −0.0459697
\(518\) −10.7287 + 1.84621i −0.471392 + 0.0811176i
\(519\) 0 0
\(520\) 13.2969 8.37895i 0.583106 0.367441i
\(521\) 19.9658 34.5818i 0.874718 1.51506i 0.0176549 0.999844i \(-0.494380\pi\)
0.857063 0.515212i \(-0.172287\pi\)
\(522\) 0 0
\(523\) −3.77245 6.53407i −0.164958 0.285715i 0.771683 0.636008i \(-0.219415\pi\)
−0.936640 + 0.350293i \(0.886082\pi\)
\(524\) −16.5139 + 10.1110i −0.721412 + 0.441699i
\(525\) 0 0
\(526\) −3.37351 1.89011i −0.147092 0.0824127i
\(527\) 21.3150 12.3062i 0.928496 0.536068i
\(528\) 0 0
\(529\) −4.64917 + 8.05259i −0.202138 + 0.350113i
\(530\) 0.0618011 + 4.79155i 0.00268447 + 0.208131i
\(531\) 0 0
\(532\) −4.06110 21.9057i −0.176071 0.949731i
\(533\) 13.8649 0.600557
\(534\) 0 0
\(535\) 11.1831 + 6.45655i 0.483486 + 0.279141i
\(536\) 7.71428 + 4.06438i 0.333206 + 0.175554i
\(537\) 0 0
\(538\) −6.35210 3.55896i −0.273859 0.153438i
\(539\) −0.970822 + 0.316374i −0.0418163 + 0.0136272i
\(540\) 0 0
\(541\) −14.8073 + 8.54900i −0.636616 + 0.367550i −0.783310 0.621632i \(-0.786470\pi\)
0.146694 + 0.989182i \(0.453137\pi\)
\(542\) −29.5435 + 17.5688i −1.26900 + 0.754645i
\(543\) 0 0
\(544\) 15.0627 30.4700i 0.645807 1.30639i
\(545\) 6.15790 0.263775
\(546\) 0 0
\(547\) 26.4723i 1.13187i 0.824449 + 0.565936i \(0.191485\pi\)
−0.824449 + 0.565936i \(0.808515\pi\)
\(548\) −18.4960 10.0518i −0.790112 0.429390i
\(549\) 0 0
\(550\) 0.440510 + 0.740755i 0.0187834 + 0.0315859i
\(551\) 21.5746 + 37.3683i 0.919109 + 1.59194i
\(552\) 0 0
\(553\) 4.49663 + 28.3108i 0.191216 + 1.20390i
\(554\) −1.00560 0.563417i −0.0427238 0.0239373i
\(555\) 0 0
\(556\) 31.6199 0.815799i 1.34098 0.0345976i
\(557\) 21.9010 37.9337i 0.927976 1.60730i 0.141273 0.989971i \(-0.454881\pi\)
0.786703 0.617331i \(-0.211786\pi\)
\(558\) 0 0
\(559\) 53.5541i 2.26510i
\(560\) 9.38685 1.99194i 0.396667 0.0841749i
\(561\) 0 0
\(562\) −0.0194426 1.50742i −0.000820135 0.0635865i
\(563\) 30.7646 + 17.7620i 1.29657 + 0.748578i 0.979811 0.199927i \(-0.0640705\pi\)
0.316764 + 0.948505i \(0.397404\pi\)
\(564\) 0 0
\(565\) −3.87254 6.70744i −0.162919 0.282184i
\(566\) −4.35023 + 7.76439i −0.182854 + 0.326362i
\(567\) 0 0
\(568\) 0.538130 + 13.9012i 0.0225794 + 0.583282i
\(569\) 22.4782 12.9778i 0.942334 0.544057i 0.0516428 0.998666i \(-0.483554\pi\)
0.890691 + 0.454609i \(0.150221\pi\)
\(570\) 0 0
\(571\) 13.6202 + 7.86364i 0.569989 + 0.329083i 0.757145 0.653247i \(-0.226594\pi\)
−0.187156 + 0.982330i \(0.559927\pi\)
\(572\) −0.853689 + 1.57085i −0.0356945 + 0.0656807i
\(573\) 0 0
\(574\) 7.94277 + 2.92805i 0.331525 + 0.122215i
\(575\) 15.4646i 0.644920i
\(576\) 0 0
\(577\) −31.0772 17.9424i −1.29376 0.746953i −0.314441 0.949277i \(-0.601817\pi\)
−0.979319 + 0.202324i \(0.935150\pi\)
\(578\) 13.8087 + 23.2206i 0.574368 + 0.965850i
\(579\) 0 0
\(580\) −15.8501 + 9.70453i −0.658138 + 0.402959i
\(581\) −12.1732 + 31.7536i −0.505030 + 1.31736i
\(582\) 0 0
\(583\) −0.272552 0.472074i −0.0112880 0.0195513i
\(584\) −7.73926 4.07754i −0.320253 0.168730i
\(585\) 0 0
\(586\) 0.327730 + 25.4095i 0.0135384 + 1.04966i
\(587\) 3.78446i 0.156201i 0.996945 + 0.0781007i \(0.0248856\pi\)
−0.996945 + 0.0781007i \(0.975114\pi\)
\(588\) 0 0
\(589\) 17.2463i 0.710622i
\(590\) 9.40298 0.121279i 0.387115 0.00499298i
\(591\) 0 0
\(592\) −9.76536 + 6.33100i −0.401354 + 0.260203i
\(593\) 11.6115 + 20.1117i 0.476826 + 0.825887i 0.999647 0.0265552i \(-0.00845376\pi\)
−0.522821 + 0.852442i \(0.675120\pi\)
\(594\) 0 0
\(595\) −5.15982 + 13.4593i −0.211532 + 0.551778i
\(596\) −12.1112 19.7808i −0.496093 0.810252i
\(597\) 0 0
\(598\) −27.5734 + 16.3972i −1.12756 + 0.670533i
\(599\) 13.4585 + 7.77024i 0.549898 + 0.317484i 0.749081 0.662479i \(-0.230496\pi\)
−0.199183 + 0.979962i \(0.563829\pi\)
\(600\) 0 0
\(601\) 23.5188i 0.959354i −0.877445 0.479677i \(-0.840754\pi\)
0.877445 0.479677i \(-0.159246\pi\)
\(602\) −11.3098 + 30.6794i −0.460952 + 1.25040i
\(603\) 0 0
\(604\) 14.8850 27.3895i 0.605660 1.11446i
\(605\) −8.62100 4.97734i −0.350494 0.202358i
\(606\) 0 0
\(607\) 29.9332 17.2819i 1.21495 0.701452i 0.251117 0.967957i \(-0.419202\pi\)
0.963834 + 0.266505i \(0.0858687\pi\)
\(608\) −13.2130 19.8160i −0.535859 0.803645i
\(609\) 0 0
\(610\) 7.63099 + 4.27549i 0.308970 + 0.173110i
\(611\) 21.9568 + 38.0302i 0.888275 + 1.53854i
\(612\) 0 0
\(613\) −7.20869 4.16194i −0.291156 0.168099i 0.347307 0.937752i \(-0.387096\pi\)
−0.638463 + 0.769652i \(0.720430\pi\)
\(614\) −39.1716 + 0.505233i −1.58084 + 0.0203896i
\(615\) 0 0
\(616\) −0.820790 + 0.719606i −0.0330706 + 0.0289938i
\(617\) 9.28453i 0.373781i −0.982381 0.186891i \(-0.940159\pi\)
0.982381 0.186891i \(-0.0598410\pi\)
\(618\) 0 0
\(619\) −12.0804 + 20.9238i −0.485551 + 0.840999i −0.999862 0.0166047i \(-0.994714\pi\)
0.514311 + 0.857604i \(0.328048\pi\)
\(620\) 7.42578 0.191586i 0.298226 0.00769429i
\(621\) 0 0
\(622\) 17.6921 31.5772i 0.709388 1.26613i
\(623\) −1.29245 8.13729i −0.0517810 0.326014i
\(624\) 0 0
\(625\) −6.67184 11.5560i −0.266874 0.462239i
\(626\) 20.9890 12.4817i 0.838891 0.498869i
\(627\) 0 0
\(628\) 12.7345 23.4325i 0.508163 0.935060i
\(629\) 17.4821i 0.697057i
\(630\) 0 0
\(631\) −10.8391 −0.431498 −0.215749 0.976449i \(-0.569219\pi\)
−0.215749 + 0.976449i \(0.569219\pi\)
\(632\) 16.3376 + 25.9267i 0.649874 + 1.03131i
\(633\) 0 0
\(634\) 3.14214 + 5.28378i 0.124790 + 0.209846i
\(635\) 14.2110 8.20470i 0.563944 0.325593i
\(636\) 0 0
\(637\) 31.9045 + 28.6767i 1.26410 + 1.13621i
\(638\) 1.03336 1.84437i 0.0409112 0.0730192i
\(639\) 0 0
\(640\) 8.38543 5.90929i 0.331463 0.233585i
\(641\) −32.0492 18.5036i −1.26587 0.730849i −0.291664 0.956521i \(-0.594209\pi\)
−0.974203 + 0.225672i \(0.927542\pi\)
\(642\) 0 0
\(643\) 24.9620 0.984405 0.492203 0.870481i \(-0.336192\pi\)
0.492203 + 0.870481i \(0.336192\pi\)
\(644\) −19.2587 + 3.57039i −0.758901 + 0.140693i
\(645\) 0 0
\(646\) 35.7741 0.461412i 1.40751 0.0181540i
\(647\) −15.6875 + 27.1715i −0.616738 + 1.06822i 0.373339 + 0.927695i \(0.378213\pi\)
−0.990077 + 0.140527i \(0.955120\pi\)
\(648\) 0 0
\(649\) −0.926404 + 0.534859i −0.0363645 + 0.0209951i
\(650\) 17.6982 31.5882i 0.694182 1.23899i
\(651\) 0 0
\(652\) −29.1273 + 17.8338i −1.14071 + 0.698424i
\(653\) −3.95300 6.84679i −0.154693 0.267936i 0.778254 0.627949i \(-0.216105\pi\)
−0.932947 + 0.360014i \(0.882772\pi\)
\(654\) 0 0
\(655\) 4.38931 7.60250i 0.171504 0.297054i
\(656\) 9.03773 0.466661i 0.352864 0.0182200i
\(657\) 0 0
\(658\) 4.54693 + 26.4232i 0.177258 + 1.03008i
\(659\) −32.9121 −1.28207 −0.641036 0.767510i \(-0.721495\pi\)
−0.641036 + 0.767510i \(0.721495\pi\)
\(660\) 0 0
\(661\) 2.37104 4.10677i 0.0922230 0.159735i −0.816223 0.577737i \(-0.803936\pi\)
0.908446 + 0.418002i \(0.137269\pi\)
\(662\) −21.0690 + 12.5293i −0.818871 + 0.486964i
\(663\) 0 0
\(664\) 1.40629 + 36.3278i 0.0545745 + 1.40979i
\(665\) 6.35982 + 7.84674i 0.246623 + 0.304284i
\(666\) 0 0
\(667\) 32.8530 18.9677i 1.27207 0.734432i
\(668\) −3.28936 + 0.0848662i −0.127269 + 0.00328357i
\(669\) 0 0
\(670\) −3.95275 + 0.0509824i −0.152708 + 0.00196962i
\(671\) −0.995021 −0.0384124
\(672\) 0 0
\(673\) 12.7891 0.492983 0.246492 0.969145i \(-0.420722\pi\)
0.246492 + 0.969145i \(0.420722\pi\)
\(674\) 0.932727 0.0120303i 0.0359273 0.000463388i
\(675\) 0 0
\(676\) 49.0958 1.26668i 1.88830 0.0487185i
\(677\) −19.9765 + 11.5334i −0.767759 + 0.443266i −0.832075 0.554664i \(-0.812847\pi\)
0.0643155 + 0.997930i \(0.479514\pi\)
\(678\) 0 0
\(679\) −0.562377 + 1.46695i −0.0215820 + 0.0562964i
\(680\) 0.596079 + 15.3982i 0.0228586 + 0.590493i
\(681\) 0 0
\(682\) −0.726278 + 0.431900i −0.0278106 + 0.0165383i
\(683\) −3.40643 + 5.90011i −0.130343 + 0.225761i −0.923809 0.382854i \(-0.874941\pi\)
0.793466 + 0.608615i \(0.208275\pi\)
\(684\) 0 0
\(685\) 9.54370 0.364646
\(686\) 12.2210 + 23.1657i 0.466599 + 0.884469i
\(687\) 0 0
\(688\) 1.80250 + 34.9088i 0.0687199 + 1.33088i
\(689\) −11.4507 + 19.8332i −0.436236 + 0.755583i
\(690\) 0 0
\(691\) −14.9637 25.9178i −0.569245 0.985961i −0.996641 0.0818962i \(-0.973902\pi\)
0.427396 0.904064i \(-0.359431\pi\)
\(692\) −15.3793 + 9.41628i −0.584633 + 0.357953i
\(693\) 0 0
\(694\) 4.83734 8.63379i 0.183623 0.327734i
\(695\) −12.4188 + 7.17002i −0.471074 + 0.271975i
\(696\) 0 0
\(697\) −6.79707 + 11.7729i −0.257457 + 0.445929i
\(698\) 28.6541 0.369579i 1.08458 0.0139888i
\(699\) 0 0
\(700\) 16.8097 14.3583i 0.635345 0.542691i
\(701\) 18.0414 0.681415 0.340707 0.940169i \(-0.389333\pi\)
0.340707 + 0.940169i \(0.389333\pi\)
\(702\) 0 0
\(703\) −10.6088 6.12499i −0.400118 0.231008i
\(704\) −0.503598 + 1.05268i −0.0189801 + 0.0396744i
\(705\) 0 0
\(706\) 7.16781 12.7933i 0.269764 0.481481i
\(707\) −18.5688 22.9102i −0.698353 0.861627i
\(708\) 0 0
\(709\) 29.1885 16.8520i 1.09620 0.632889i 0.160977 0.986958i \(-0.448536\pi\)
0.935219 + 0.354069i \(0.115202\pi\)
\(710\) −3.22368 5.42090i −0.120983 0.203443i
\(711\) 0 0
\(712\) −4.69586 7.45203i −0.175985 0.279277i
\(713\) −15.1624 −0.567836
\(714\) 0 0
\(715\) 0.810539i 0.0303124i
\(716\) −13.9563 + 25.6807i −0.521571 + 0.959732i
\(717\) 0 0
\(718\) 24.6595 14.6644i 0.920283 0.547270i
\(719\) −24.8458 43.0342i −0.926592 1.60490i −0.788981 0.614418i \(-0.789391\pi\)
−0.137611 0.990486i \(-0.543942\pi\)
\(720\) 0 0
\(721\) 4.27250 0.678604i 0.159116 0.0252725i
\(722\) −0.880088 + 1.57080i −0.0327535 + 0.0584591i
\(723\) 0 0
\(724\) 0.396780 0.0102370i 0.0147462 0.000380455i
\(725\) −21.4082 + 37.0801i −0.795081 + 1.37712i
\(726\) 0 0
\(727\) 5.49208i 0.203690i −0.994800 0.101845i \(-0.967525\pi\)
0.994800 0.101845i \(-0.0324746\pi\)
\(728\) 43.4241 + 14.7474i 1.60940 + 0.546576i
\(729\) 0 0
\(730\) 3.96555 0.0511474i 0.146772 0.00189305i
\(731\) −45.4734 26.2541i −1.68189 0.971042i
\(732\) 0 0
\(733\) 0.176068 + 0.304959i 0.00650322 + 0.0112639i 0.869259 0.494357i \(-0.164597\pi\)
−0.862755 + 0.505621i \(0.831263\pi\)
\(734\) −30.7754 17.2428i −1.13594 0.636445i
\(735\) 0 0
\(736\) −17.4216 + 11.6165i −0.642168 + 0.428188i
\(737\) 0.389435 0.224840i 0.0143450 0.00828209i
\(738\) 0 0
\(739\) −13.2521 7.65108i −0.487485 0.281450i 0.236045 0.971742i \(-0.424149\pi\)
−0.723531 + 0.690292i \(0.757482\pi\)
\(740\) 2.51939 4.63589i 0.0926148 0.170419i
\(741\) 0 0
\(742\) −10.7482 + 8.94357i −0.394578 + 0.328329i
\(743\) 41.8196i 1.53421i −0.641520 0.767106i \(-0.721696\pi\)
0.641520 0.767106i \(-0.278304\pi\)
\(744\) 0 0
\(745\) 9.10648 + 5.25763i 0.333636 + 0.192625i
\(746\) 5.99163 3.56308i 0.219369 0.130454i
\(747\) 0 0
\(748\) −0.915322 1.49496i −0.0334675 0.0546613i
\(749\) 5.91055 + 37.2129i 0.215967 + 1.35973i
\(750\) 0 0
\(751\) 0.457654 + 0.792680i 0.0167000 + 0.0289253i 0.874255 0.485468i \(-0.161351\pi\)
−0.857555 + 0.514393i \(0.828017\pi\)
\(752\) 15.5923 + 24.0507i 0.568594 + 0.877037i
\(753\) 0 0
\(754\) −88.8130 + 1.14550i −3.23438 + 0.0417168i
\(755\) 14.1326i 0.514338i
\(756\) 0 0
\(757\) 20.2296i 0.735257i 0.929973 + 0.367628i \(0.119830\pi\)
−0.929973 + 0.367628i \(0.880170\pi\)
\(758\) −0.457810 35.4949i −0.0166284 1.28923i
\(759\) 0 0
\(760\) 9.55302 + 5.03314i 0.346525 + 0.182571i
\(761\) −5.53329 9.58394i −0.200582 0.347417i 0.748134 0.663547i \(-0.230950\pi\)
−0.948716 + 0.316130i \(0.897616\pi\)
\(762\) 0 0
\(763\) 11.3139 + 13.9590i 0.409590 + 0.505351i
\(764\) −0.334074 + 0.204544i −0.0120864 + 0.00740012i
\(765\) 0 0
\(766\) −20.3291 34.1852i −0.734522 1.23516i
\(767\) 38.9208 + 22.4709i 1.40535 + 0.811379i
\(768\) 0 0
\(769\) 20.8715i 0.752646i −0.926489 0.376323i \(-0.877188\pi\)
0.926489 0.376323i \(-0.122812\pi\)
\(770\) 0.171173 0.464331i 0.00616865 0.0167333i
\(771\) 0 0
\(772\) 9.61897 17.6997i 0.346194 0.637025i
\(773\) −25.3570 14.6399i −0.912030 0.526561i −0.0309460 0.999521i \(-0.509852\pi\)
−0.881084 + 0.472961i \(0.843185\pi\)
\(774\) 0 0
\(775\) 14.8206 8.55665i 0.532370 0.307364i
\(776\) 0.0649675 + 1.67827i 0.00233220 + 0.0602464i
\(777\) 0 0
\(778\) −5.29058 + 9.44274i −0.189676 + 0.338539i
\(779\) 4.76281 + 8.24943i 0.170645 + 0.295566i
\(780\) 0 0
\(781\) 0.621329 + 0.358725i 0.0222329 + 0.0128362i
\(782\) −0.405658 31.4514i −0.0145063 1.12470i
\(783\) 0 0
\(784\) 21.7618 + 17.6188i 0.777209 + 0.629243i
\(785\) 12.0909i 0.431541i
\(786\) 0 0
\(787\) 10.4134 18.0366i 0.371199 0.642935i −0.618551 0.785744i \(-0.712280\pi\)
0.989750 + 0.142809i \(0.0456135\pi\)
\(788\) −1.96221 + 0.0506253i −0.0699007 + 0.00180345i
\(789\) 0 0
\(790\) −12.1205 6.79088i −0.431228 0.241608i
\(791\) 8.08977 21.1020i 0.287639 0.750302i
\(792\) 0 0
\(793\) 20.9018 + 36.2030i 0.742245 + 1.28561i
\(794\) −9.00299 15.1393i −0.319504 0.537274i
\(795\) 0 0
\(796\) −3.86958 2.10294i −0.137154 0.0745368i
\(797\) 28.8543i 1.02207i −0.859559 0.511036i \(-0.829262\pi\)
0.859559 0.511036i \(-0.170738\pi\)
\(798\) 0 0
\(799\) −43.0558 −1.52321
\(800\) 10.4732 21.1862i 0.370285 0.749044i
\(801\) 0 0
\(802\) 25.5003 15.1644i 0.900448 0.535475i
\(803\) −0.390695 + 0.225568i −0.0137873 + 0.00796013i
\(804\) 0 0
\(805\) 6.89859 5.59134i 0.243143 0.197069i
\(806\) 30.9708 + 17.3523i 1.09090 + 0.611210i
\(807\) 0 0
\(808\) −27.8920 14.6953i −0.981239 0.516979i
\(809\) 32.6025 + 18.8231i 1.14624 + 0.661784i 0.947969 0.318362i \(-0.103133\pi\)
0.198275 + 0.980146i \(0.436466\pi\)
\(810\) 0 0
\(811\) −11.3863 −0.399827 −0.199913 0.979814i \(-0.564066\pi\)
−0.199913 + 0.979814i \(0.564066\pi\)
\(812\) −51.1200 18.0997i −1.79396 0.635174i
\(813\) 0 0
\(814\) 0.00774065 + 0.600146i 0.000271310 + 0.0210351i
\(815\) 7.74189 13.4093i 0.271186 0.469709i
\(816\) 0 0
\(817\) −31.8639 + 18.3966i −1.11478 + 0.643617i
\(818\) −0.650862 0.364665i −0.0227568 0.0127502i
\(819\) 0 0
\(820\) −3.49906 + 2.14237i −0.122192 + 0.0748149i
\(821\) 6.92169 + 11.9887i 0.241569 + 0.418409i 0.961161 0.275987i \(-0.0890048\pi\)
−0.719593 + 0.694396i \(0.755671\pi\)
\(822\) 0 0
\(823\) −6.60648 + 11.4428i −0.230287 + 0.398869i −0.957893 0.287127i \(-0.907300\pi\)
0.727605 + 0.685996i \(0.240633\pi\)
\(824\) 3.91271 2.46557i 0.136306 0.0858923i
\(825\) 0 0
\(826\) 17.5510 + 21.0923i 0.610676 + 0.733896i
\(827\) 12.2445 0.425784 0.212892 0.977076i \(-0.431712\pi\)
0.212892 + 0.977076i \(0.431712\pi\)
\(828\) 0 0
\(829\) 21.1084 36.5609i 0.733126 1.26981i −0.222415 0.974952i \(-0.571394\pi\)
0.955541 0.294859i \(-0.0952728\pi\)
\(830\) −8.42440 14.1664i −0.292415 0.491722i
\(831\) 0 0
\(832\) 48.8797 3.79004i 1.69460 0.131396i
\(833\) −39.9904 + 13.0322i −1.38558 + 0.451537i
\(834\) 0 0
\(835\) 1.29191 0.745885i 0.0447084 0.0258124i
\(836\) −1.22789 + 0.0316798i −0.0424674 + 0.00109567i
\(837\) 0 0
\(838\) 0.402136 + 31.1783i 0.0138916 + 1.07704i
\(839\) −4.30094 −0.148485 −0.0742424 0.997240i \(-0.523654\pi\)
−0.0742424 + 0.997240i \(0.523654\pi\)
\(840\) 0 0
\(841\) 76.0304 2.62174
\(842\) 0.332606 + 25.7875i 0.0114624 + 0.888697i
\(843\) 0 0
\(844\) −0.916612 35.5273i −0.0315511 1.22290i
\(845\) −19.2826 + 11.1328i −0.663340 + 0.382980i
\(846\) 0 0
\(847\) −4.55643 28.6874i −0.156561 0.985710i
\(848\) −6.79649 + 13.3135i −0.233392 + 0.457187i
\(849\) 0 0
\(850\) 18.1456 + 30.5134i 0.622388 + 1.04660i
\(851\) −5.38488 + 9.32689i −0.184591 + 0.319722i
\(852\) 0 0
\(853\) −28.0209 −0.959416 −0.479708 0.877428i \(-0.659257\pi\)
−0.479708 + 0.877428i \(0.659257\pi\)
\(854\) 4.32847 + 25.1537i 0.148117 + 0.860740i
\(855\) 0 0
\(856\) 21.4748 + 34.0792i 0.733994 + 1.16480i
\(857\) 6.76275 11.7134i 0.231011 0.400123i −0.727095 0.686537i \(-0.759130\pi\)
0.958106 + 0.286414i \(0.0924632\pi\)
\(858\) 0 0
\(859\) −9.51823 16.4861i −0.324758 0.562497i 0.656705 0.754147i \(-0.271950\pi\)
−0.981463 + 0.191650i \(0.938616\pi\)
\(860\) −8.27504 13.5153i −0.282176 0.460869i
\(861\) 0 0
\(862\) 35.3905 + 19.8286i 1.20540 + 0.675364i
\(863\) −14.7548 + 8.51871i −0.502260 + 0.289980i −0.729646 0.683825i \(-0.760315\pi\)
0.227386 + 0.973805i \(0.426982\pi\)
\(864\) 0 0
\(865\) 4.08774 7.08017i 0.138987 0.240733i
\(866\) 0.687650 + 53.3147i 0.0233673 + 1.81171i
\(867\) 0 0
\(868\) 14.0776 + 16.4811i 0.477826 + 0.559406i
\(869\) 1.58042 0.0536120
\(870\) 0 0
\(871\) −16.3612 9.44617i −0.554379 0.320071i
\(872\) 16.9944 + 8.95376i 0.575505 + 0.303213i
\(873\) 0 0
\(874\) −19.2280 10.7731i −0.650396 0.364404i
\(875\) −7.88137 + 20.5584i −0.266439 + 0.695001i
\(876\) 0 0
\(877\) 39.7587 22.9547i 1.34255 0.775124i 0.355373 0.934725i \(-0.384354\pi\)
0.987182 + 0.159600i \(0.0510205\pi\)
\(878\) 10.7905 6.41684i 0.364161 0.216558i
\(879\) 0 0
\(880\) −0.0272808 0.528343i −0.000919636 0.0178104i
\(881\) −12.9601 −0.436638 −0.218319 0.975877i \(-0.570057\pi\)
−0.218319 + 0.975877i \(0.570057\pi\)
\(882\) 0 0
\(883\) 53.9117i 1.81427i 0.420835 + 0.907137i \(0.361737\pi\)
−0.420835 + 0.907137i \(0.638263\pi\)
\(884\) −35.1654 + 64.7070i −1.18274 + 2.17633i
\(885\) 0 0
\(886\) −0.302843 0.509256i −0.0101742 0.0171088i
\(887\) 8.11124 + 14.0491i 0.272349 + 0.471722i 0.969463 0.245238i \(-0.0788662\pi\)
−0.697114 + 0.716960i \(0.745533\pi\)
\(888\) 0 0
\(889\) 44.7085 + 17.1397i 1.49948 + 0.574846i
\(890\) 3.48376 + 1.95188i 0.116776 + 0.0654272i
\(891\) 0 0
\(892\) 1.06870 + 41.4224i 0.0357829 + 1.38692i
\(893\) −15.0849 + 26.1279i −0.504798 + 0.874336i
\(894\) 0 0
\(895\) 13.2509i 0.442928i
\(896\) 28.8020 + 8.15142i 0.962207 + 0.272320i
\(897\) 0 0
\(898\) −0.719363 55.7735i −0.0240054 1.86118i
\(899\) −36.3554 20.9898i −1.21252 0.700049i
\(900\) 0 0
\(901\) −11.2270 19.4458i −0.374027 0.647834i
\(902\) 0.228125 0.407162i 0.00759573 0.0135570i
\(903\) 0 0
\(904\) −0.934556 24.1419i −0.0310829 0.802946i
\(905\) −0.155837 + 0.0899725i −0.00518019 + 0.00299079i
\(906\) 0 0
\(907\) 6.60352 + 3.81255i 0.219266 + 0.126594i 0.605611 0.795761i \(-0.292929\pi\)
−0.386344 + 0.922355i \(0.626262\pi\)
\(908\) 35.2973 + 19.1825i 1.17138 + 0.636593i
\(909\) 0 0
\(910\) −20.4900 + 3.52595i −0.679238 + 0.116884i
\(911\) 33.1109i 1.09701i −0.836146 0.548507i \(-0.815196\pi\)
0.836146 0.548507i \(-0.184804\pi\)
\(912\) 0 0
\(913\) 1.62371 + 0.937450i 0.0537370 + 0.0310251i
\(914\) 8.59430 + 14.4521i 0.284274 + 0.478032i
\(915\) 0 0
\(916\) 20.2318 + 33.0439i 0.668477 + 1.09180i
\(917\) 25.2982 4.01813i 0.835420 0.132690i
\(918\) 0 0
\(919\) −16.2880 28.2116i −0.537291 0.930616i −0.999049 0.0436094i \(-0.986114\pi\)
0.461758 0.887006i \(-0.347219\pi\)
\(920\) 4.42497 8.39870i 0.145887 0.276897i
\(921\) 0 0
\(922\) 0.00397420 + 0.308126i 0.000130883 + 0.0101476i
\(923\) 30.1421i 0.992138i
\(924\) 0 0
\(925\) 12.1555i 0.399670i
\(926\) 12.9145 0.166571i 0.424398 0.00547385i
\(927\) 0 0
\(928\) −57.8534 + 3.73592i −1.89913 + 0.122638i
\(929\) −7.81822 13.5416i −0.256507 0.444284i 0.708796 0.705413i \(-0.249238\pi\)
−0.965304 + 0.261129i \(0.915905\pi\)
\(930\) 0 0
\(931\) −6.10253 + 28.8335i −0.200002 + 0.944981i
\(932\) 44.1378 27.0243i 1.44578 0.885209i
\(933\) 0 0
\(934\) −32.8698 + 19.5469i −1.07553 + 0.639594i
\(935\) 0.688237 + 0.397354i 0.0225078 + 0.0129949i
\(936\) 0 0
\(937\) 49.5708i 1.61941i 0.586839 + 0.809704i \(0.300372\pi\)
−0.586839 + 0.809704i \(0.699628\pi\)
\(938\) −7.37794 8.86664i −0.240898 0.289506i
\(939\) 0 0
\(940\) −11.4175 6.20490i −0.372398 0.202381i
\(941\) 10.5801 + 6.10840i 0.344900 + 0.199128i 0.662437 0.749118i \(-0.269522\pi\)
−0.317537 + 0.948246i \(0.602856\pi\)
\(942\) 0 0
\(943\) 7.25262 4.18730i 0.236178 0.136357i
\(944\) 26.1265 + 13.3375i 0.850345 + 0.434099i
\(945\) 0 0
\(946\) 1.57269 + 0.881146i 0.0511325 + 0.0286485i
\(947\) −11.4761 19.8772i −0.372923 0.645921i 0.617091 0.786892i \(-0.288311\pi\)
−0.990014 + 0.140971i \(0.954978\pi\)
\(948\) 0 0
\(949\) 16.4142 + 9.47675i 0.532828 + 0.307628i
\(950\) 24.8741 0.320825i 0.807022 0.0104089i
\(951\) 0 0
\(952\) −33.8102 + 29.6422i −1.09579 + 0.960709i
\(953\) 10.7450i 0.348063i −0.984740 0.174032i \(-0.944321\pi\)
0.984740 0.174032i \(-0.0556795\pi\)
\(954\) 0 0
\(955\) 0.0887952 0.153798i 0.00287334 0.00497678i
\(956\) −0.577767 22.3939i −0.0186863 0.724271i
\(957\) 0 0
\(958\) 7.00293 12.4990i 0.226254 0.403824i
\(959\) 17.5346 + 21.6341i 0.566221 + 0.698603i
\(960\) 0 0
\(961\) −7.11058 12.3159i −0.229374 0.397287i
\(962\) 21.6732 12.8885i 0.698772 0.415543i
\(963\) 0 0
\(964\) −48.0580 26.1174i −1.54784 0.841183i
\(965\) 9.13278i 0.293995i
\(966\) 0 0
\(967\) −7.48832 −0.240808 −0.120404 0.992725i \(-0.538419\pi\)
−0.120404 + 0.992725i \(0.538419\pi\)
\(968\) −16.5549 26.2716i −0.532094 0.844400i
\(969\) 0 0
\(970\) −0.389190 0.654457i −0.0124961 0.0210133i
\(971\) −45.0252 + 25.9953i −1.44493 + 0.834229i −0.998173 0.0604275i \(-0.980754\pi\)
−0.446755 + 0.894657i \(0.647420\pi\)
\(972\) 0 0
\(973\) −39.0705 14.9782i −1.25254 0.480180i
\(974\) −7.03329 + 12.5532i −0.225361 + 0.402229i
\(975\) 0 0
\(976\) 14.8432 + 22.8951i 0.475118 + 0.732854i
\(977\) −17.3850 10.0372i −0.556196 0.321120i 0.195421 0.980719i \(-0.437393\pi\)
−0.751617 + 0.659600i \(0.770726\pi\)
\(978\) 0 0
\(979\) −0.454255 −0.0145180
\(980\) −12.4827 2.30727i −0.398745 0.0737030i
\(981\) 0 0
\(982\) −34.8776 + 0.449849i −1.11299 + 0.0143552i
\(983\) 30.7294 53.2249i 0.980115 1.69761i 0.318214 0.948019i \(-0.396917\pi\)
0.661902 0.749591i \(-0.269750\pi\)
\(984\) 0 0
\(985\) 0.770664 0.444943i 0.0245554 0.0141771i
\(986\) 42.5665 75.9737i 1.35559 2.41949i
\(987\) 0 0
\(988\) 26.9462 + 44.0102i 0.857272 + 1.40015i
\(989\) 16.1737 + 28.0137i 0.514294 + 0.890783i
\(990\) 0 0
\(991\) 9.87483 17.1037i 0.313684 0.543317i −0.665473 0.746422i \(-0.731770\pi\)
0.979157 + 0.203105i \(0.0651033\pi\)
\(992\) 20.7721 + 10.2686i 0.659514 + 0.326027i
\(993\) 0 0
\(994\) 6.36552 17.2674i 0.201902 0.547689i
\(995\) 1.99665 0.0632980
\(996\) 0 0
\(997\) 1.94579 3.37021i 0.0616239 0.106736i −0.833568 0.552418i \(-0.813705\pi\)
0.895191 + 0.445682i \(0.147039\pi\)
\(998\) −17.9801 + 10.6923i −0.569150 + 0.338460i
\(999\) 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 504.2.ch.b.269.1 56
3.2 odd 2 inner 504.2.ch.b.269.28 yes 56
4.3 odd 2 2016.2.cp.b.17.11 56
7.5 odd 6 inner 504.2.ch.b.341.20 yes 56
8.3 odd 2 2016.2.cp.b.17.18 56
8.5 even 2 inner 504.2.ch.b.269.9 yes 56
12.11 even 2 2016.2.cp.b.17.17 56
21.5 even 6 inner 504.2.ch.b.341.9 yes 56
24.5 odd 2 inner 504.2.ch.b.269.20 yes 56
24.11 even 2 2016.2.cp.b.17.12 56
28.19 even 6 2016.2.cp.b.593.12 56
56.5 odd 6 inner 504.2.ch.b.341.28 yes 56
56.19 even 6 2016.2.cp.b.593.17 56
84.47 odd 6 2016.2.cp.b.593.18 56
168.5 even 6 inner 504.2.ch.b.341.1 yes 56
168.131 odd 6 2016.2.cp.b.593.11 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.ch.b.269.1 56 1.1 even 1 trivial
504.2.ch.b.269.9 yes 56 8.5 even 2 inner
504.2.ch.b.269.20 yes 56 24.5 odd 2 inner
504.2.ch.b.269.28 yes 56 3.2 odd 2 inner
504.2.ch.b.341.1 yes 56 168.5 even 6 inner
504.2.ch.b.341.9 yes 56 21.5 even 6 inner
504.2.ch.b.341.20 yes 56 7.5 odd 6 inner
504.2.ch.b.341.28 yes 56 56.5 odd 6 inner
2016.2.cp.b.17.11 56 4.3 odd 2
2016.2.cp.b.17.12 56 24.11 even 2
2016.2.cp.b.17.17 56 12.11 even 2
2016.2.cp.b.17.18 56 8.3 odd 2
2016.2.cp.b.593.11 56 168.131 odd 6
2016.2.cp.b.593.12 56 28.19 even 6
2016.2.cp.b.593.17 56 56.19 even 6
2016.2.cp.b.593.18 56 84.47 odd 6