Properties

Label 819.2.s.d.802.5
Level $819$
Weight $2$
Character 819.802
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(289,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.s (of order \(3\), 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: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 802.5
Root \(1.16700 + 2.02131i\) of defining polynomial
Character \(\chi\) \(=\) 819.802
Dual form 819.2.s.d.289.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.90556 q^{2} +1.63116 q^{4} +(-0.736565 - 1.27577i) q^{5} +(1.58334 - 2.11968i) q^{7} -0.702849 q^{8} +O(q^{10})\) \(q+1.90556 q^{2} +1.63116 q^{4} +(-0.736565 - 1.27577i) q^{5} +(1.58334 - 2.11968i) q^{7} -0.702849 q^{8} +(-1.40357 - 2.43105i) q^{10} +(-2.19681 - 3.80498i) q^{11} +(2.69752 - 2.39236i) q^{13} +(3.01715 - 4.03917i) q^{14} -4.60164 q^{16} +1.20271 q^{17} +(-1.62105 + 2.80773i) q^{19} +(-1.20145 - 2.08098i) q^{20} +(-4.18615 - 7.25062i) q^{22} +4.43710 q^{23} +(1.41494 - 2.45075i) q^{25} +(5.14029 - 4.55878i) q^{26} +(2.58268 - 3.45753i) q^{28} +(0.0837807 - 0.145112i) q^{29} +(-2.62272 + 4.54268i) q^{31} -7.36300 q^{32} +2.29184 q^{34} +(-3.87045 - 0.458697i) q^{35} +7.05055 q^{37} +(-3.08900 + 5.35031i) q^{38} +(0.517694 + 0.896672i) q^{40} +(2.58195 - 4.47206i) q^{41} +(-0.0113752 - 0.0197024i) q^{43} +(-3.58334 - 6.20653i) q^{44} +8.45516 q^{46} +(5.84178 + 10.1183i) q^{47} +(-1.98606 - 6.71235i) q^{49} +(2.69626 - 4.67006i) q^{50} +(4.40009 - 3.90231i) q^{52} +(-0.0708929 + 0.122790i) q^{53} +(-3.23618 + 5.60523i) q^{55} +(-1.11285 + 1.48981i) q^{56} +(0.159649 - 0.276520i) q^{58} +5.34354 q^{59} +(-5.77287 + 9.99891i) q^{61} +(-4.99774 + 8.65635i) q^{62} -4.82736 q^{64} +(-5.03899 - 1.67929i) q^{65} +(-2.06773 - 3.58141i) q^{67} +1.96181 q^{68} +(-7.37537 - 0.874075i) q^{70} +(-4.98486 - 8.63403i) q^{71} +(-7.62080 + 13.1996i) q^{73} +13.4352 q^{74} +(-2.64418 + 4.57986i) q^{76} +(-11.5436 - 1.36807i) q^{77} +(-0.387251 - 0.670738i) q^{79} +(3.38941 + 5.87062i) q^{80} +(4.92006 - 8.52179i) q^{82} +16.0186 q^{83} +(-0.885875 - 1.53438i) q^{85} +(-0.0216761 - 0.0375441i) q^{86} +(1.54402 + 2.67433i) q^{88} -6.55760 q^{89} +(-0.799921 - 9.50579i) q^{91} +7.23762 q^{92} +(11.1319 + 19.2809i) q^{94} +4.77602 q^{95} +(-1.74583 - 3.02387i) q^{97} +(-3.78455 - 12.7908i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} + 16 q^{32} + 32 q^{34} - 20 q^{35} + 26 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} - 32 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} + 41 q^{52} + 2 q^{53} + 9 q^{55} - 9 q^{56} - 8 q^{58} + 26 q^{59} - 5 q^{61} - 5 q^{62} - 30 q^{64} + 5 q^{65} - 11 q^{67} + 58 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} - 6 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} + 7 q^{80} + q^{82} + 54 q^{83} - q^{85} + 7 q^{86} + 8 q^{89} - 23 q^{91} - 54 q^{92} + 45 q^{94} - 12 q^{95} - 35 q^{97} - 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90556 1.34743 0.673717 0.738989i \(-0.264697\pi\)
0.673717 + 0.738989i \(0.264697\pi\)
\(3\) 0 0
\(4\) 1.63116 0.815580
\(5\) −0.736565 1.27577i −0.329402 0.570541i 0.652991 0.757365i \(-0.273514\pi\)
−0.982393 + 0.186825i \(0.940180\pi\)
\(6\) 0 0
\(7\) 1.58334 2.11968i 0.598447 0.801162i
\(8\) −0.702849 −0.248495
\(9\) 0 0
\(10\) −1.40357 2.43105i −0.443847 0.768766i
\(11\) −2.19681 3.80498i −0.662362 1.14725i −0.979993 0.199031i \(-0.936221\pi\)
0.317631 0.948214i \(-0.397113\pi\)
\(12\) 0 0
\(13\) 2.69752 2.39236i 0.748158 0.663520i
\(14\) 3.01715 4.03917i 0.806368 1.07951i
\(15\) 0 0
\(16\) −4.60164 −1.15041
\(17\) 1.20271 0.291700 0.145850 0.989307i \(-0.453408\pi\)
0.145850 + 0.989307i \(0.453408\pi\)
\(18\) 0 0
\(19\) −1.62105 + 2.80773i −0.371893 + 0.644138i −0.989857 0.142068i \(-0.954625\pi\)
0.617963 + 0.786207i \(0.287958\pi\)
\(20\) −1.20145 2.08098i −0.268653 0.465321i
\(21\) 0 0
\(22\) −4.18615 7.25062i −0.892490 1.54584i
\(23\) 4.43710 0.925200 0.462600 0.886567i \(-0.346917\pi\)
0.462600 + 0.886567i \(0.346917\pi\)
\(24\) 0 0
\(25\) 1.41494 2.45075i 0.282989 0.490151i
\(26\) 5.14029 4.55878i 1.00809 0.894050i
\(27\) 0 0
\(28\) 2.58268 3.45753i 0.488081 0.653412i
\(29\) 0.0837807 0.145112i 0.0155577 0.0269467i −0.858142 0.513413i \(-0.828381\pi\)
0.873699 + 0.486466i \(0.161714\pi\)
\(30\) 0 0
\(31\) −2.62272 + 4.54268i −0.471054 + 0.815889i −0.999452 0.0331076i \(-0.989460\pi\)
0.528398 + 0.848997i \(0.322793\pi\)
\(32\) −7.36300 −1.30161
\(33\) 0 0
\(34\) 2.29184 0.393047
\(35\) −3.87045 0.458697i −0.654225 0.0775340i
\(36\) 0 0
\(37\) 7.05055 1.15910 0.579552 0.814936i \(-0.303228\pi\)
0.579552 + 0.814936i \(0.303228\pi\)
\(38\) −3.08900 + 5.35031i −0.501102 + 0.867934i
\(39\) 0 0
\(40\) 0.517694 + 0.896672i 0.0818546 + 0.141776i
\(41\) 2.58195 4.47206i 0.403233 0.698419i −0.590881 0.806758i \(-0.701220\pi\)
0.994114 + 0.108339i \(0.0345533\pi\)
\(42\) 0 0
\(43\) −0.0113752 0.0197024i −0.00173470 0.00300459i 0.865157 0.501502i \(-0.167219\pi\)
−0.866891 + 0.498497i \(0.833886\pi\)
\(44\) −3.58334 6.20653i −0.540209 0.935670i
\(45\) 0 0
\(46\) 8.45516 1.24665
\(47\) 5.84178 + 10.1183i 0.852111 + 1.47590i 0.879300 + 0.476269i \(0.158011\pi\)
−0.0271891 + 0.999630i \(0.508656\pi\)
\(48\) 0 0
\(49\) −1.98606 6.71235i −0.283722 0.958906i
\(50\) 2.69626 4.67006i 0.381309 0.660446i
\(51\) 0 0
\(52\) 4.40009 3.90231i 0.610183 0.541154i
\(53\) −0.0708929 + 0.122790i −0.00973788 + 0.0168665i −0.870853 0.491543i \(-0.836433\pi\)
0.861115 + 0.508410i \(0.169766\pi\)
\(54\) 0 0
\(55\) −3.23618 + 5.60523i −0.436367 + 0.755809i
\(56\) −1.11285 + 1.48981i −0.148711 + 0.199084i
\(57\) 0 0
\(58\) 0.159649 0.276520i 0.0209630 0.0363089i
\(59\) 5.34354 0.695670 0.347835 0.937556i \(-0.386917\pi\)
0.347835 + 0.937556i \(0.386917\pi\)
\(60\) 0 0
\(61\) −5.77287 + 9.99891i −0.739141 + 1.28023i 0.213742 + 0.976890i \(0.431435\pi\)
−0.952883 + 0.303339i \(0.901898\pi\)
\(62\) −4.99774 + 8.65635i −0.634714 + 1.09936i
\(63\) 0 0
\(64\) −4.82736 −0.603420
\(65\) −5.03899 1.67929i −0.625010 0.208290i
\(66\) 0 0
\(67\) −2.06773 3.58141i −0.252613 0.437539i 0.711631 0.702553i \(-0.247957\pi\)
−0.964245 + 0.265014i \(0.914623\pi\)
\(68\) 1.96181 0.237905
\(69\) 0 0
\(70\) −7.37537 0.874075i −0.881526 0.104472i
\(71\) −4.98486 8.63403i −0.591594 1.02467i −0.994018 0.109217i \(-0.965166\pi\)
0.402424 0.915453i \(-0.368168\pi\)
\(72\) 0 0
\(73\) −7.62080 + 13.1996i −0.891947 + 1.54490i −0.0544080 + 0.998519i \(0.517327\pi\)
−0.837539 + 0.546378i \(0.816006\pi\)
\(74\) 13.4352 1.56182
\(75\) 0 0
\(76\) −2.64418 + 4.57986i −0.303309 + 0.525346i
\(77\) −11.5436 1.36807i −1.31552 0.155906i
\(78\) 0 0
\(79\) −0.387251 0.670738i −0.0435691 0.0754639i 0.843418 0.537257i \(-0.180540\pi\)
−0.886988 + 0.461793i \(0.847206\pi\)
\(80\) 3.38941 + 5.87062i 0.378947 + 0.656356i
\(81\) 0 0
\(82\) 4.92006 8.52179i 0.543329 0.941074i
\(83\) 16.0186 1.75827 0.879136 0.476571i \(-0.158121\pi\)
0.879136 + 0.476571i \(0.158121\pi\)
\(84\) 0 0
\(85\) −0.885875 1.53438i −0.0960866 0.166427i
\(86\) −0.0216761 0.0375441i −0.00233740 0.00404849i
\(87\) 0 0
\(88\) 1.54402 + 2.67433i 0.164593 + 0.285084i
\(89\) −6.55760 −0.695104 −0.347552 0.937661i \(-0.612987\pi\)
−0.347552 + 0.937661i \(0.612987\pi\)
\(90\) 0 0
\(91\) −0.799921 9.50579i −0.0838545 0.996478i
\(92\) 7.23762 0.754574
\(93\) 0 0
\(94\) 11.1319 + 19.2809i 1.14816 + 1.98868i
\(95\) 4.77602 0.490010
\(96\) 0 0
\(97\) −1.74583 3.02387i −0.177262 0.307027i 0.763680 0.645595i \(-0.223391\pi\)
−0.940942 + 0.338568i \(0.890057\pi\)
\(98\) −3.78455 12.7908i −0.382297 1.29206i
\(99\) 0 0
\(100\) 2.30800 3.99757i 0.230800 0.399757i
\(101\) 1.28890 + 2.23244i 0.128250 + 0.222136i 0.922999 0.384803i \(-0.125731\pi\)
−0.794749 + 0.606939i \(0.792397\pi\)
\(102\) 0 0
\(103\) 8.43173 + 14.6042i 0.830803 + 1.43899i 0.897402 + 0.441213i \(0.145452\pi\)
−0.0665997 + 0.997780i \(0.521215\pi\)
\(104\) −1.89595 + 1.68146i −0.185913 + 0.164881i
\(105\) 0 0
\(106\) −0.135091 + 0.233984i −0.0131212 + 0.0227265i
\(107\) −8.68265 −0.839383 −0.419692 0.907667i \(-0.637862\pi\)
−0.419692 + 0.907667i \(0.637862\pi\)
\(108\) 0 0
\(109\) 6.02026 10.4274i 0.576637 0.998764i −0.419225 0.907882i \(-0.637698\pi\)
0.995862 0.0908816i \(-0.0289685\pi\)
\(110\) −6.16674 + 10.6811i −0.587976 + 1.01840i
\(111\) 0 0
\(112\) −7.28597 + 9.75398i −0.688459 + 0.921665i
\(113\) 4.68616 + 8.11667i 0.440837 + 0.763552i 0.997752 0.0670176i \(-0.0213484\pi\)
−0.556915 + 0.830570i \(0.688015\pi\)
\(114\) 0 0
\(115\) −3.26821 5.66071i −0.304763 0.527864i
\(116\) 0.136660 0.236701i 0.0126885 0.0219772i
\(117\) 0 0
\(118\) 10.1824 0.937369
\(119\) 1.90430 2.54936i 0.174567 0.233699i
\(120\) 0 0
\(121\) −4.15192 + 7.19134i −0.377448 + 0.653758i
\(122\) −11.0006 + 19.0535i −0.995944 + 1.72503i
\(123\) 0 0
\(124\) −4.27807 + 7.40983i −0.384182 + 0.665423i
\(125\) −11.5344 −1.03167
\(126\) 0 0
\(127\) −7.94269 + 13.7571i −0.704800 + 1.22075i 0.261964 + 0.965078i \(0.415630\pi\)
−0.966764 + 0.255672i \(0.917703\pi\)
\(128\) 5.52717 0.488537
\(129\) 0 0
\(130\) −9.60210 3.19998i −0.842160 0.280657i
\(131\) 0.928725 + 1.60860i 0.0811430 + 0.140544i 0.903741 0.428079i \(-0.140810\pi\)
−0.822598 + 0.568623i \(0.807476\pi\)
\(132\) 0 0
\(133\) 3.38482 + 7.88170i 0.293501 + 0.683430i
\(134\) −3.94018 6.82459i −0.340380 0.589555i
\(135\) 0 0
\(136\) −0.845324 −0.0724859
\(137\) 12.8002 1.09360 0.546798 0.837264i \(-0.315847\pi\)
0.546798 + 0.837264i \(0.315847\pi\)
\(138\) 0 0
\(139\) 0.169365 + 0.293348i 0.0143653 + 0.0248815i 0.873119 0.487508i \(-0.162094\pi\)
−0.858753 + 0.512389i \(0.828761\pi\)
\(140\) −6.31332 0.748208i −0.533573 0.0632351i
\(141\) 0 0
\(142\) −9.49894 16.4527i −0.797134 1.38068i
\(143\) −15.0288 5.00848i −1.25677 0.418830i
\(144\) 0 0
\(145\) −0.246840 −0.0204989
\(146\) −14.5219 + 25.1526i −1.20184 + 2.08165i
\(147\) 0 0
\(148\) 11.5006 0.945341
\(149\) 1.96158 3.39756i 0.160699 0.278339i −0.774421 0.632671i \(-0.781959\pi\)
0.935120 + 0.354332i \(0.115292\pi\)
\(150\) 0 0
\(151\) 1.05939 1.83492i 0.0862122 0.149324i −0.819695 0.572800i \(-0.805857\pi\)
0.905907 + 0.423476i \(0.139190\pi\)
\(152\) 1.13935 1.97341i 0.0924135 0.160065i
\(153\) 0 0
\(154\) −21.9971 2.60693i −1.77257 0.210073i
\(155\) 7.72721 0.620664
\(156\) 0 0
\(157\) 11.0564 19.1502i 0.882397 1.52836i 0.0337285 0.999431i \(-0.489262\pi\)
0.848668 0.528925i \(-0.177405\pi\)
\(158\) −0.737929 1.27813i −0.0587065 0.101683i
\(159\) 0 0
\(160\) 5.42333 + 9.39348i 0.428752 + 0.742620i
\(161\) 7.02545 9.40522i 0.553683 0.741235i
\(162\) 0 0
\(163\) −1.92607 + 3.33605i −0.150861 + 0.261299i −0.931544 0.363628i \(-0.881538\pi\)
0.780683 + 0.624927i \(0.214871\pi\)
\(164\) 4.21157 7.29465i 0.328868 0.569616i
\(165\) 0 0
\(166\) 30.5244 2.36916
\(167\) 1.06947 1.85238i 0.0827582 0.143341i −0.821676 0.569956i \(-0.806960\pi\)
0.904434 + 0.426614i \(0.140294\pi\)
\(168\) 0 0
\(169\) 1.55326 12.9069i 0.119482 0.992836i
\(170\) −1.68809 2.92385i −0.129470 0.224249i
\(171\) 0 0
\(172\) −0.0185547 0.0321378i −0.00141479 0.00245048i
\(173\) −8.30664 + 14.3875i −0.631542 + 1.09386i 0.355695 + 0.934602i \(0.384244\pi\)
−0.987237 + 0.159260i \(0.949089\pi\)
\(174\) 0 0
\(175\) −2.95447 6.87961i −0.223337 0.520049i
\(176\) 10.1089 + 17.5091i 0.761988 + 1.31980i
\(177\) 0 0
\(178\) −12.4959 −0.936607
\(179\) −0.269748 0.467217i −0.0201619 0.0349214i 0.855768 0.517359i \(-0.173085\pi\)
−0.875930 + 0.482438i \(0.839752\pi\)
\(180\) 0 0
\(181\) 2.77164 0.206014 0.103007 0.994681i \(-0.467154\pi\)
0.103007 + 0.994681i \(0.467154\pi\)
\(182\) −1.52430 18.1139i −0.112988 1.34269i
\(183\) 0 0
\(184\) −3.11861 −0.229907
\(185\) −5.19319 8.99486i −0.381811 0.661316i
\(186\) 0 0
\(187\) −2.64213 4.57629i −0.193211 0.334652i
\(188\) 9.52887 + 16.5045i 0.694964 + 1.20371i
\(189\) 0 0
\(190\) 9.10100 0.660256
\(191\) −10.1204 + 17.5290i −0.732284 + 1.26835i 0.223621 + 0.974676i \(0.428212\pi\)
−0.955905 + 0.293677i \(0.905121\pi\)
\(192\) 0 0
\(193\) 8.18856 + 14.1830i 0.589425 + 1.02091i 0.994308 + 0.106546i \(0.0339791\pi\)
−0.404882 + 0.914369i \(0.632688\pi\)
\(194\) −3.32678 5.76216i −0.238849 0.413699i
\(195\) 0 0
\(196\) −3.23958 10.9489i −0.231398 0.782064i
\(197\) 9.86676 17.0897i 0.702977 1.21759i −0.264439 0.964402i \(-0.585187\pi\)
0.967417 0.253190i \(-0.0814798\pi\)
\(198\) 0 0
\(199\) −14.1175 −1.00076 −0.500380 0.865806i \(-0.666806\pi\)
−0.500380 + 0.865806i \(0.666806\pi\)
\(200\) −0.994491 + 1.72251i −0.0703212 + 0.121800i
\(201\) 0 0
\(202\) 2.45607 + 4.25404i 0.172809 + 0.299313i
\(203\) −0.174938 0.407351i −0.0122782 0.0285904i
\(204\) 0 0
\(205\) −7.60709 −0.531302
\(206\) 16.0672 + 27.8291i 1.11945 + 1.93895i
\(207\) 0 0
\(208\) −12.4130 + 11.0088i −0.860688 + 0.763320i
\(209\) 14.2445 0.985313
\(210\) 0 0
\(211\) 2.31317 4.00652i 0.159245 0.275820i −0.775352 0.631530i \(-0.782427\pi\)
0.934597 + 0.355709i \(0.115761\pi\)
\(212\) −0.115638 + 0.200290i −0.00794202 + 0.0137560i
\(213\) 0 0
\(214\) −16.5453 −1.13101
\(215\) −0.0167571 + 0.0290242i −0.00114283 + 0.00197943i
\(216\) 0 0
\(217\) 5.47635 + 12.7519i 0.371759 + 0.865657i
\(218\) 11.4720 19.8700i 0.776980 1.34577i
\(219\) 0 0
\(220\) −5.27873 + 9.14303i −0.355892 + 0.616423i
\(221\) 3.24434 2.87731i 0.218238 0.193549i
\(222\) 0 0
\(223\) 10.6761 18.4916i 0.714926 1.23829i −0.248061 0.968744i \(-0.579793\pi\)
0.962988 0.269545i \(-0.0868732\pi\)
\(224\) −11.6581 + 15.6072i −0.778943 + 1.04280i
\(225\) 0 0
\(226\) 8.92976 + 15.4668i 0.593999 + 1.02884i
\(227\) 10.4490 0.693526 0.346763 0.937953i \(-0.387281\pi\)
0.346763 + 0.937953i \(0.387281\pi\)
\(228\) 0 0
\(229\) −7.22901 12.5210i −0.477706 0.827412i 0.521967 0.852966i \(-0.325198\pi\)
−0.999673 + 0.0255538i \(0.991865\pi\)
\(230\) −6.22778 10.7868i −0.410648 0.711262i
\(231\) 0 0
\(232\) −0.0588852 + 0.101992i −0.00386600 + 0.00669611i
\(233\) −4.64413 8.04388i −0.304247 0.526972i 0.672846 0.739783i \(-0.265072\pi\)
−0.977093 + 0.212811i \(0.931738\pi\)
\(234\) 0 0
\(235\) 8.60570 14.9055i 0.561374 0.972328i
\(236\) 8.71616 0.567374
\(237\) 0 0
\(238\) 3.62876 4.85796i 0.235218 0.314895i
\(239\) −19.6332 −1.26997 −0.634983 0.772526i \(-0.718993\pi\)
−0.634983 + 0.772526i \(0.718993\pi\)
\(240\) 0 0
\(241\) 7.31105 0.470946 0.235473 0.971881i \(-0.424336\pi\)
0.235473 + 0.971881i \(0.424336\pi\)
\(242\) −7.91174 + 13.7035i −0.508586 + 0.880897i
\(243\) 0 0
\(244\) −9.41648 + 16.3098i −0.602828 + 1.04413i
\(245\) −7.10053 + 7.47783i −0.453637 + 0.477741i
\(246\) 0 0
\(247\) 2.34429 + 11.4520i 0.149164 + 0.728676i
\(248\) 1.84337 3.19282i 0.117054 0.202744i
\(249\) 0 0
\(250\) −21.9796 −1.39011
\(251\) −5.93191 10.2744i −0.374419 0.648512i 0.615821 0.787886i \(-0.288824\pi\)
−0.990240 + 0.139374i \(0.955491\pi\)
\(252\) 0 0
\(253\) −9.74746 16.8831i −0.612817 1.06143i
\(254\) −15.1353 + 26.2151i −0.949672 + 1.64488i
\(255\) 0 0
\(256\) 20.1871 1.26169
\(257\) 15.1722 0.946413 0.473206 0.880952i \(-0.343096\pi\)
0.473206 + 0.880952i \(0.343096\pi\)
\(258\) 0 0
\(259\) 11.1634 14.9449i 0.693662 0.928630i
\(260\) −8.21940 2.73919i −0.509745 0.169877i
\(261\) 0 0
\(262\) 1.76974 + 3.06528i 0.109335 + 0.189374i
\(263\) 8.59820 + 14.8925i 0.530187 + 0.918312i 0.999380 + 0.0352156i \(0.0112118\pi\)
−0.469192 + 0.883096i \(0.655455\pi\)
\(264\) 0 0
\(265\) 0.208869 0.0128307
\(266\) 6.44997 + 15.0190i 0.395473 + 0.920877i
\(267\) 0 0
\(268\) −3.37279 5.84185i −0.206026 0.356848i
\(269\) −18.9220 −1.15370 −0.576849 0.816851i \(-0.695718\pi\)
−0.576849 + 0.816851i \(0.695718\pi\)
\(270\) 0 0
\(271\) 32.1334 1.95196 0.975982 0.217853i \(-0.0699054\pi\)
0.975982 + 0.217853i \(0.0699054\pi\)
\(272\) −5.53444 −0.335575
\(273\) 0 0
\(274\) 24.3916 1.47355
\(275\) −12.4334 −0.749764
\(276\) 0 0
\(277\) 18.4054 1.10587 0.552936 0.833224i \(-0.313507\pi\)
0.552936 + 0.833224i \(0.313507\pi\)
\(278\) 0.322734 + 0.558992i 0.0193563 + 0.0335261i
\(279\) 0 0
\(280\) 2.72034 + 0.322395i 0.162571 + 0.0192668i
\(281\) 14.2252 0.848603 0.424302 0.905521i \(-0.360520\pi\)
0.424302 + 0.905521i \(0.360520\pi\)
\(282\) 0 0
\(283\) 5.71446 + 9.89773i 0.339689 + 0.588359i 0.984374 0.176089i \(-0.0563448\pi\)
−0.644685 + 0.764448i \(0.723011\pi\)
\(284\) −8.13109 14.0835i −0.482492 0.835700i
\(285\) 0 0
\(286\) −28.6383 9.54396i −1.69342 0.564346i
\(287\) −5.39123 12.5537i −0.318234 0.741022i
\(288\) 0 0
\(289\) −15.5535 −0.914911
\(290\) −0.470368 −0.0276210
\(291\) 0 0
\(292\) −12.4307 + 21.5307i −0.727453 + 1.25999i
\(293\) −6.60231 11.4355i −0.385711 0.668071i 0.606156 0.795345i \(-0.292711\pi\)
−0.991868 + 0.127274i \(0.959377\pi\)
\(294\) 0 0
\(295\) −3.93586 6.81712i −0.229155 0.396908i
\(296\) −4.95547 −0.288031
\(297\) 0 0
\(298\) 3.73791 6.47425i 0.216531 0.375043i
\(299\) 11.9692 10.6151i 0.692196 0.613889i
\(300\) 0 0
\(301\) −0.0597736 0.00708392i −0.00344529 0.000408310i
\(302\) 2.01874 3.49656i 0.116165 0.201204i
\(303\) 0 0
\(304\) 7.45947 12.9202i 0.427830 0.741023i
\(305\) 17.0084 0.973898
\(306\) 0 0
\(307\) −6.65903 −0.380051 −0.190026 0.981779i \(-0.560857\pi\)
−0.190026 + 0.981779i \(0.560857\pi\)
\(308\) −18.8295 2.23153i −1.07291 0.127153i
\(309\) 0 0
\(310\) 14.7247 0.836304
\(311\) −1.02298 + 1.77186i −0.0580081 + 0.100473i −0.893571 0.448922i \(-0.851808\pi\)
0.835563 + 0.549395i \(0.185142\pi\)
\(312\) 0 0
\(313\) −4.70883 8.15594i −0.266159 0.461001i 0.701708 0.712465i \(-0.252421\pi\)
−0.967867 + 0.251464i \(0.919088\pi\)
\(314\) 21.0686 36.4919i 1.18897 2.05936i
\(315\) 0 0
\(316\) −0.631667 1.09408i −0.0355341 0.0615468i
\(317\) −16.6856 28.9004i −0.937159 1.62321i −0.770738 0.637153i \(-0.780112\pi\)
−0.166421 0.986055i \(-0.553221\pi\)
\(318\) 0 0
\(319\) −0.736200 −0.0412193
\(320\) 3.55567 + 6.15860i 0.198768 + 0.344276i
\(321\) 0 0
\(322\) 13.3874 17.9222i 0.746051 0.998766i
\(323\) −1.94965 + 3.37689i −0.108481 + 0.187895i
\(324\) 0 0
\(325\) −2.04624 9.99602i −0.113505 0.554479i
\(326\) −3.67024 + 6.35704i −0.203276 + 0.352084i
\(327\) 0 0
\(328\) −1.81472 + 3.14318i −0.100201 + 0.173553i
\(329\) 30.6970 + 3.63798i 1.69238 + 0.200568i
\(330\) 0 0
\(331\) −9.53298 + 16.5116i −0.523980 + 0.907560i 0.475631 + 0.879645i \(0.342220\pi\)
−0.999610 + 0.0279144i \(0.991113\pi\)
\(332\) 26.1289 1.43401
\(333\) 0 0
\(334\) 2.03794 3.52982i 0.111511 0.193143i
\(335\) −3.04603 + 5.27588i −0.166423 + 0.288252i
\(336\) 0 0
\(337\) −31.2849 −1.70420 −0.852098 0.523382i \(-0.824670\pi\)
−0.852098 + 0.523382i \(0.824670\pi\)
\(338\) 2.95983 24.5948i 0.160994 1.33778i
\(339\) 0 0
\(340\) −1.44500 2.50282i −0.0783663 0.135734i
\(341\) 23.0464 1.24803
\(342\) 0 0
\(343\) −17.3726 6.41814i −0.938033 0.346547i
\(344\) 0.00799504 + 0.0138478i 0.000431064 + 0.000746624i
\(345\) 0 0
\(346\) −15.8288 + 27.4163i −0.850961 + 1.47391i
\(347\) −11.6752 −0.626757 −0.313378 0.949628i \(-0.601461\pi\)
−0.313378 + 0.949628i \(0.601461\pi\)
\(348\) 0 0
\(349\) −11.9952 + 20.7763i −0.642089 + 1.11213i 0.342877 + 0.939380i \(0.388599\pi\)
−0.984966 + 0.172750i \(0.944735\pi\)
\(350\) −5.62992 13.1095i −0.300932 0.700732i
\(351\) 0 0
\(352\) 16.1751 + 28.0161i 0.862135 + 1.49326i
\(353\) 6.39668 + 11.0794i 0.340461 + 0.589696i 0.984518 0.175282i \(-0.0560836\pi\)
−0.644057 + 0.764977i \(0.722750\pi\)
\(354\) 0 0
\(355\) −7.34334 + 12.7190i −0.389744 + 0.675057i
\(356\) −10.6965 −0.566912
\(357\) 0 0
\(358\) −0.514021 0.890310i −0.0271668 0.0470544i
\(359\) 6.16986 + 10.6865i 0.325633 + 0.564012i 0.981640 0.190742i \(-0.0610894\pi\)
−0.656008 + 0.754754i \(0.727756\pi\)
\(360\) 0 0
\(361\) 4.24442 + 7.35155i 0.223390 + 0.386924i
\(362\) 5.28152 0.277591
\(363\) 0 0
\(364\) −1.30480 15.5055i −0.0683900 0.812707i
\(365\) 22.4528 1.17524
\(366\) 0 0
\(367\) −1.01538 1.75870i −0.0530026 0.0918032i 0.838307 0.545199i \(-0.183546\pi\)
−0.891309 + 0.453396i \(0.850212\pi\)
\(368\) −20.4179 −1.06436
\(369\) 0 0
\(370\) −9.89593 17.1403i −0.514465 0.891079i
\(371\) 0.148028 + 0.344689i 0.00768521 + 0.0178953i
\(372\) 0 0
\(373\) 1.93700 3.35498i 0.100294 0.173714i −0.811512 0.584336i \(-0.801355\pi\)
0.911806 + 0.410622i \(0.134688\pi\)
\(374\) −5.03473 8.72040i −0.260340 0.450921i
\(375\) 0 0
\(376\) −4.10588 7.11160i −0.211745 0.366753i
\(377\) −0.121160 0.591877i −0.00624007 0.0304832i
\(378\) 0 0
\(379\) 7.28396 12.6162i 0.374152 0.648050i −0.616048 0.787709i \(-0.711267\pi\)
0.990200 + 0.139659i \(0.0446006\pi\)
\(380\) 7.79045 0.399642
\(381\) 0 0
\(382\) −19.2850 + 33.4025i −0.986705 + 1.70902i
\(383\) −13.3909 + 23.1937i −0.684243 + 1.18514i 0.289430 + 0.957199i \(0.406534\pi\)
−0.973674 + 0.227945i \(0.926799\pi\)
\(384\) 0 0
\(385\) 6.75730 + 15.7347i 0.344384 + 0.801912i
\(386\) 15.6038 + 27.0266i 0.794212 + 1.37562i
\(387\) 0 0
\(388\) −2.84773 4.93241i −0.144571 0.250405i
\(389\) 6.00738 10.4051i 0.304586 0.527559i −0.672583 0.740022i \(-0.734815\pi\)
0.977169 + 0.212463i \(0.0681485\pi\)
\(390\) 0 0
\(391\) 5.33655 0.269881
\(392\) 1.39590 + 4.71776i 0.0705035 + 0.238283i
\(393\) 0 0
\(394\) 18.8017 32.5655i 0.947216 1.64063i
\(395\) −0.570470 + 0.988084i −0.0287035 + 0.0497159i
\(396\) 0 0
\(397\) 0.828825 1.43557i 0.0415975 0.0720491i −0.844477 0.535592i \(-0.820089\pi\)
0.886075 + 0.463543i \(0.153422\pi\)
\(398\) −26.9017 −1.34846
\(399\) 0 0
\(400\) −6.51106 + 11.2775i −0.325553 + 0.563874i
\(401\) 20.4828 1.02286 0.511430 0.859325i \(-0.329116\pi\)
0.511430 + 0.859325i \(0.329116\pi\)
\(402\) 0 0
\(403\) 3.79287 + 18.5285i 0.188936 + 0.922968i
\(404\) 2.10240 + 3.64146i 0.104598 + 0.181169i
\(405\) 0 0
\(406\) −0.333355 0.776231i −0.0165441 0.0385237i
\(407\) −15.4887 26.8272i −0.767746 1.32978i
\(408\) 0 0
\(409\) 14.8659 0.735070 0.367535 0.930010i \(-0.380202\pi\)
0.367535 + 0.930010i \(0.380202\pi\)
\(410\) −14.4958 −0.715895
\(411\) 0 0
\(412\) 13.7535 + 23.8217i 0.677586 + 1.17361i
\(413\) 8.46065 11.3266i 0.416321 0.557344i
\(414\) 0 0
\(415\) −11.7988 20.4360i −0.579178 1.00317i
\(416\) −19.8619 + 17.6149i −0.973808 + 0.863643i
\(417\) 0 0
\(418\) 27.1438 1.32764
\(419\) −11.8087 + 20.4533i −0.576895 + 0.999211i 0.418938 + 0.908015i \(0.362402\pi\)
−0.995833 + 0.0911962i \(0.970931\pi\)
\(420\) 0 0
\(421\) 26.0822 1.27117 0.635585 0.772031i \(-0.280759\pi\)
0.635585 + 0.772031i \(0.280759\pi\)
\(422\) 4.40788 7.63467i 0.214572 0.371650i
\(423\) 0 0
\(424\) 0.0498269 0.0863028i 0.00241981 0.00419123i
\(425\) 1.70177 2.94755i 0.0825479 0.142977i
\(426\) 0 0
\(427\) 12.0540 + 28.0683i 0.583335 + 1.35832i
\(428\) −14.1628 −0.684584
\(429\) 0 0
\(430\) −0.0319317 + 0.0553074i −0.00153988 + 0.00266716i
\(431\) −6.65859 11.5330i −0.320733 0.555526i 0.659906 0.751348i \(-0.270596\pi\)
−0.980640 + 0.195822i \(0.937263\pi\)
\(432\) 0 0
\(433\) −10.2110 17.6860i −0.490711 0.849937i 0.509232 0.860629i \(-0.329930\pi\)
−0.999943 + 0.0106929i \(0.996596\pi\)
\(434\) 10.4355 + 24.2996i 0.500921 + 1.16642i
\(435\) 0 0
\(436\) 9.82001 17.0087i 0.470293 0.814571i
\(437\) −7.19275 + 12.4582i −0.344076 + 0.595957i
\(438\) 0 0
\(439\) −9.77074 −0.466332 −0.233166 0.972437i \(-0.574909\pi\)
−0.233166 + 0.972437i \(0.574909\pi\)
\(440\) 2.27455 3.93963i 0.108435 0.187814i
\(441\) 0 0
\(442\) 6.18229 5.48290i 0.294061 0.260795i
\(443\) 10.5819 + 18.3285i 0.502763 + 0.870811i 0.999995 + 0.00319331i \(0.00101646\pi\)
−0.497232 + 0.867618i \(0.665650\pi\)
\(444\) 0 0
\(445\) 4.83010 + 8.36597i 0.228968 + 0.396585i
\(446\) 20.3440 35.2368i 0.963317 1.66851i
\(447\) 0 0
\(448\) −7.64337 + 10.2324i −0.361115 + 0.483438i
\(449\) −9.07320 15.7152i −0.428191 0.741648i 0.568522 0.822668i \(-0.307516\pi\)
−0.996712 + 0.0810200i \(0.974182\pi\)
\(450\) 0 0
\(451\) −22.6882 −1.06834
\(452\) 7.64387 + 13.2396i 0.359538 + 0.622737i
\(453\) 0 0
\(454\) 19.9112 0.934480
\(455\) −11.5380 + 8.02215i −0.540910 + 0.376084i
\(456\) 0 0
\(457\) −18.0198 −0.842932 −0.421466 0.906844i \(-0.638484\pi\)
−0.421466 + 0.906844i \(0.638484\pi\)
\(458\) −13.7753 23.8595i −0.643678 1.11488i
\(459\) 0 0
\(460\) −5.33098 9.23352i −0.248558 0.430515i
\(461\) −14.8873 25.7855i −0.693370 1.20095i −0.970727 0.240185i \(-0.922792\pi\)
0.277357 0.960767i \(-0.410542\pi\)
\(462\) 0 0
\(463\) 17.7067 0.822900 0.411450 0.911432i \(-0.365023\pi\)
0.411450 + 0.911432i \(0.365023\pi\)
\(464\) −0.385529 + 0.667755i −0.0178977 + 0.0309997i
\(465\) 0 0
\(466\) −8.84968 15.3281i −0.409953 0.710060i
\(467\) −2.91461 5.04825i −0.134872 0.233605i 0.790677 0.612234i \(-0.209729\pi\)
−0.925549 + 0.378629i \(0.876396\pi\)
\(468\) 0 0
\(469\) −10.8654 1.28768i −0.501715 0.0594596i
\(470\) 16.3987 28.4033i 0.756414 1.31015i
\(471\) 0 0
\(472\) −3.75570 −0.172870
\(473\) −0.0499782 + 0.0865648i −0.00229800 + 0.00398025i
\(474\) 0 0
\(475\) 4.58738 + 7.94557i 0.210483 + 0.364568i
\(476\) 3.10622 4.15841i 0.142373 0.190600i
\(477\) 0 0
\(478\) −37.4122 −1.71120
\(479\) 7.24565 + 12.5498i 0.331062 + 0.573417i 0.982720 0.185096i \(-0.0592596\pi\)
−0.651658 + 0.758513i \(0.725926\pi\)
\(480\) 0 0
\(481\) 19.0190 16.8674i 0.867193 0.769088i
\(482\) 13.9316 0.634569
\(483\) 0 0
\(484\) −6.77245 + 11.7302i −0.307839 + 0.533192i
\(485\) −2.57183 + 4.45455i −0.116781 + 0.202271i
\(486\) 0 0
\(487\) −17.9601 −0.813851 −0.406926 0.913461i \(-0.633399\pi\)
−0.406926 + 0.913461i \(0.633399\pi\)
\(488\) 4.05746 7.02772i 0.183672 0.318130i
\(489\) 0 0
\(490\) −13.5305 + 14.2494i −0.611245 + 0.643724i
\(491\) −18.1505 + 31.4375i −0.819119 + 1.41876i 0.0872134 + 0.996190i \(0.472204\pi\)
−0.906332 + 0.422566i \(0.861130\pi\)
\(492\) 0 0
\(493\) 0.100764 0.174528i 0.00453818 0.00786036i
\(494\) 4.46719 + 21.8226i 0.200988 + 0.981844i
\(495\) 0 0
\(496\) 12.0688 20.9038i 0.541905 0.938607i
\(497\) −26.1941 3.10433i −1.17496 0.139248i
\(498\) 0 0
\(499\) −11.8538 20.5314i −0.530649 0.919112i −0.999360 0.0357602i \(-0.988615\pi\)
0.468711 0.883352i \(-0.344719\pi\)
\(500\) −18.8145 −0.841410
\(501\) 0 0
\(502\) −11.3036 19.5784i −0.504505 0.873828i
\(503\) 13.8876 + 24.0540i 0.619217 + 1.07252i 0.989629 + 0.143648i \(0.0458834\pi\)
−0.370411 + 0.928868i \(0.620783\pi\)
\(504\) 0 0
\(505\) 1.89871 3.28867i 0.0844916 0.146344i
\(506\) −18.5744 32.1717i −0.825731 1.43021i
\(507\) 0 0
\(508\) −12.9558 + 22.4401i −0.574820 + 0.995618i
\(509\) −8.70416 −0.385805 −0.192902 0.981218i \(-0.561790\pi\)
−0.192902 + 0.981218i \(0.561790\pi\)
\(510\) 0 0
\(511\) 15.9126 + 37.0531i 0.703931 + 1.63913i
\(512\) 27.4134 1.21151
\(513\) 0 0
\(514\) 28.9114 1.27523
\(515\) 12.4210 21.5139i 0.547336 0.948014i
\(516\) 0 0
\(517\) 25.6665 44.4557i 1.12881 1.95516i
\(518\) 21.2726 28.4784i 0.934664 1.25127i
\(519\) 0 0
\(520\) 3.54165 + 1.18028i 0.155312 + 0.0517589i
\(521\) −4.28573 + 7.42310i −0.187761 + 0.325212i −0.944504 0.328501i \(-0.893456\pi\)
0.756742 + 0.653713i \(0.226790\pi\)
\(522\) 0 0
\(523\) 29.9493 1.30959 0.654796 0.755806i \(-0.272755\pi\)
0.654796 + 0.755806i \(0.272755\pi\)
\(524\) 1.51490 + 2.62388i 0.0661786 + 0.114625i
\(525\) 0 0
\(526\) 16.3844 + 28.3786i 0.714393 + 1.23736i
\(527\) −3.15437 + 5.46353i −0.137407 + 0.237995i
\(528\) 0 0
\(529\) −3.31212 −0.144005
\(530\) 0.398012 0.0172885
\(531\) 0 0
\(532\) 5.52118 + 12.8563i 0.239373 + 0.557391i
\(533\) −3.73391 18.2404i −0.161734 0.790081i
\(534\) 0 0
\(535\) 6.39534 + 11.0770i 0.276494 + 0.478902i
\(536\) 1.45330 + 2.51719i 0.0627730 + 0.108726i
\(537\) 0 0
\(538\) −36.0571 −1.55453
\(539\) −21.1774 + 22.3026i −0.912174 + 0.960643i
\(540\) 0 0
\(541\) −5.24095 9.07760i −0.225326 0.390276i 0.731091 0.682280i \(-0.239011\pi\)
−0.956417 + 0.292003i \(0.905678\pi\)
\(542\) 61.2321 2.63014
\(543\) 0 0
\(544\) −8.85557 −0.379679
\(545\) −17.7373 −0.759781
\(546\) 0 0
\(547\) 15.2216 0.650829 0.325415 0.945571i \(-0.394496\pi\)
0.325415 + 0.945571i \(0.394496\pi\)
\(548\) 20.8792 0.891915
\(549\) 0 0
\(550\) −23.6927 −1.01026
\(551\) 0.271625 + 0.470468i 0.0115716 + 0.0200426i
\(552\) 0 0
\(553\) −2.03490 0.241161i −0.0865326 0.0102552i
\(554\) 35.0726 1.49009
\(555\) 0 0
\(556\) 0.276261 + 0.478497i 0.0117161 + 0.0202928i
\(557\) 5.92986 + 10.2708i 0.251256 + 0.435189i 0.963872 0.266366i \(-0.0858230\pi\)
−0.712616 + 0.701555i \(0.752490\pi\)
\(558\) 0 0
\(559\) −0.0778200 0.0259342i −0.00329144 0.00109690i
\(560\) 17.8104 + 2.11076i 0.752627 + 0.0891958i
\(561\) 0 0
\(562\) 27.1069 1.14344
\(563\) −7.69349 −0.324242 −0.162121 0.986771i \(-0.551834\pi\)
−0.162121 + 0.986771i \(0.551834\pi\)
\(564\) 0 0
\(565\) 6.90332 11.9569i 0.290425 0.503031i
\(566\) 10.8892 + 18.8607i 0.457709 + 0.792775i
\(567\) 0 0
\(568\) 3.50360 + 6.06841i 0.147008 + 0.254625i
\(569\) −37.4196 −1.56871 −0.784355 0.620312i \(-0.787006\pi\)
−0.784355 + 0.620312i \(0.787006\pi\)
\(570\) 0 0
\(571\) −7.08285 + 12.2679i −0.296408 + 0.513394i −0.975311 0.220834i \(-0.929122\pi\)
0.678903 + 0.734228i \(0.262456\pi\)
\(572\) −24.5144 8.16963i −1.02500 0.341589i
\(573\) 0 0
\(574\) −10.2733 23.9218i −0.428799 0.998478i
\(575\) 6.27825 10.8742i 0.261821 0.453488i
\(576\) 0 0
\(577\) 7.48776 12.9692i 0.311720 0.539914i −0.667015 0.745044i \(-0.732428\pi\)
0.978735 + 0.205130i \(0.0657617\pi\)
\(578\) −29.6381 −1.23278
\(579\) 0 0
\(580\) −0.402635 −0.0167185
\(581\) 25.3629 33.9543i 1.05223 1.40866i
\(582\) 0 0
\(583\) 0.622952 0.0258000
\(584\) 5.35627 9.27732i 0.221644 0.383898i
\(585\) 0 0
\(586\) −12.5811 21.7911i −0.519720 0.900182i
\(587\) −6.58821 + 11.4111i −0.271925 + 0.470987i −0.969355 0.245666i \(-0.920993\pi\)
0.697430 + 0.716653i \(0.254327\pi\)
\(588\) 0 0
\(589\) −8.50309 14.7278i −0.350364 0.606848i
\(590\) −7.50003 12.9904i −0.308771 0.534807i
\(591\) 0 0
\(592\) −32.4441 −1.33344
\(593\) −22.0663 38.2200i −0.906156 1.56951i −0.819357 0.573283i \(-0.805670\pi\)
−0.0867989 0.996226i \(-0.527664\pi\)
\(594\) 0 0
\(595\) −4.65503 0.551680i −0.190838 0.0226167i
\(596\) 3.19965 5.54195i 0.131063 0.227007i
\(597\) 0 0
\(598\) 22.8080 20.2278i 0.932689 0.827175i
\(599\) −3.01349 + 5.21952i −0.123128 + 0.213264i −0.921000 0.389564i \(-0.872626\pi\)
0.797872 + 0.602827i \(0.205959\pi\)
\(600\) 0 0
\(601\) −1.86260 + 3.22612i −0.0759770 + 0.131596i −0.901511 0.432757i \(-0.857541\pi\)
0.825534 + 0.564353i \(0.190874\pi\)
\(602\) −0.113902 0.0134988i −0.00464230 0.000550172i
\(603\) 0 0
\(604\) 1.72804 2.99305i 0.0703129 0.121786i
\(605\) 12.2326 0.497328
\(606\) 0 0
\(607\) 3.00825 5.21045i 0.122101 0.211486i −0.798495 0.602002i \(-0.794370\pi\)
0.920596 + 0.390516i \(0.127703\pi\)
\(608\) 11.9358 20.6733i 0.484059 0.838415i
\(609\) 0 0
\(610\) 32.4105 1.31226
\(611\) 39.9648 + 13.3186i 1.61680 + 0.538813i
\(612\) 0 0
\(613\) −4.90413 8.49420i −0.198076 0.343077i 0.749829 0.661632i \(-0.230136\pi\)
−0.947904 + 0.318555i \(0.896803\pi\)
\(614\) −12.6892 −0.512094
\(615\) 0 0
\(616\) 8.11342 + 0.961543i 0.326899 + 0.0387417i
\(617\) 16.8838 + 29.2436i 0.679716 + 1.17730i 0.975066 + 0.221914i \(0.0712304\pi\)
−0.295350 + 0.955389i \(0.595436\pi\)
\(618\) 0 0
\(619\) −2.04671 + 3.54501i −0.0822644 + 0.142486i −0.904222 0.427062i \(-0.859549\pi\)
0.821958 + 0.569548i \(0.192882\pi\)
\(620\) 12.6043 0.506201
\(621\) 0 0
\(622\) −1.94936 + 3.37639i −0.0781621 + 0.135381i
\(623\) −10.3829 + 13.9000i −0.415983 + 0.556891i
\(624\) 0 0
\(625\) 1.42115 + 2.46150i 0.0568459 + 0.0984599i
\(626\) −8.97297 15.5416i −0.358632 0.621169i
\(627\) 0 0
\(628\) 18.0347 31.2371i 0.719665 1.24650i
\(629\) 8.47978 0.338111
\(630\) 0 0
\(631\) 13.3868 + 23.1866i 0.532921 + 0.923046i 0.999261 + 0.0384402i \(0.0122389\pi\)
−0.466340 + 0.884605i \(0.654428\pi\)
\(632\) 0.272179 + 0.471427i 0.0108267 + 0.0187524i
\(633\) 0 0
\(634\) −31.7955 55.0714i −1.26276 2.18717i
\(635\) 23.4012 0.928650
\(636\) 0 0
\(637\) −21.4158 13.3553i −0.848523 0.529158i
\(638\) −1.40287 −0.0555403
\(639\) 0 0
\(640\) −4.07112 7.05139i −0.160925 0.278731i
\(641\) 18.5722 0.733558 0.366779 0.930308i \(-0.380461\pi\)
0.366779 + 0.930308i \(0.380461\pi\)
\(642\) 0 0
\(643\) 1.96695 + 3.40686i 0.0775690 + 0.134353i 0.902201 0.431317i \(-0.141951\pi\)
−0.824632 + 0.565670i \(0.808618\pi\)
\(644\) 11.4596 15.3414i 0.451572 0.604536i
\(645\) 0 0
\(646\) −3.71518 + 6.43487i −0.146172 + 0.253177i
\(647\) −0.0985378 0.170672i −0.00387392 0.00670983i 0.864082 0.503351i \(-0.167900\pi\)
−0.867956 + 0.496641i \(0.834566\pi\)
\(648\) 0 0
\(649\) −11.7387 20.3321i −0.460785 0.798104i
\(650\) −3.89922 19.0480i −0.152940 0.747125i
\(651\) 0 0
\(652\) −3.14172 + 5.44163i −0.123039 + 0.213110i
\(653\) 14.4673 0.566148 0.283074 0.959098i \(-0.408646\pi\)
0.283074 + 0.959098i \(0.408646\pi\)
\(654\) 0 0
\(655\) 1.36813 2.36967i 0.0534573 0.0925908i
\(656\) −11.8812 + 20.5788i −0.463883 + 0.803468i
\(657\) 0 0
\(658\) 58.4949 + 6.93238i 2.28037 + 0.270252i
\(659\) −11.7066 20.2764i −0.456024 0.789857i 0.542722 0.839912i \(-0.317394\pi\)
−0.998746 + 0.0500552i \(0.984060\pi\)
\(660\) 0 0
\(661\) 2.02409 + 3.50582i 0.0787278 + 0.136361i 0.902701 0.430268i \(-0.141581\pi\)
−0.823973 + 0.566628i \(0.808248\pi\)
\(662\) −18.1657 + 31.4638i −0.706028 + 1.22288i
\(663\) 0 0
\(664\) −11.2587 −0.436921
\(665\) 7.56208 10.1236i 0.293245 0.392577i
\(666\) 0 0
\(667\) 0.371744 0.643879i 0.0143940 0.0249311i
\(668\) 1.74448 3.02153i 0.0674959 0.116906i
\(669\) 0 0
\(670\) −5.80440 + 10.0535i −0.224243 + 0.388401i
\(671\) 50.7276 1.95832
\(672\) 0 0
\(673\) −3.64704 + 6.31685i −0.140583 + 0.243497i −0.927716 0.373286i \(-0.878231\pi\)
0.787133 + 0.616783i \(0.211564\pi\)
\(674\) −59.6152 −2.29629
\(675\) 0 0
\(676\) 2.53362 21.0532i 0.0974468 0.809737i
\(677\) −7.87553 13.6408i −0.302681 0.524259i 0.674061 0.738676i \(-0.264548\pi\)
−0.976742 + 0.214416i \(0.931215\pi\)
\(678\) 0 0
\(679\) −9.17387 1.08722i −0.352061 0.0417236i
\(680\) 0.622636 + 1.07844i 0.0238770 + 0.0413562i
\(681\) 0 0
\(682\) 43.9163 1.68164
\(683\) −41.4854 −1.58739 −0.793697 0.608314i \(-0.791846\pi\)
−0.793697 + 0.608314i \(0.791846\pi\)
\(684\) 0 0
\(685\) −9.42819 16.3301i −0.360233 0.623941i
\(686\) −33.1045 12.2301i −1.26394 0.466949i
\(687\) 0 0
\(688\) 0.0523445 + 0.0906634i 0.00199562 + 0.00345651i
\(689\) 0.102522 + 0.500830i 0.00390579 + 0.0190801i
\(690\) 0 0
\(691\) −46.8216 −1.78118 −0.890589 0.454809i \(-0.849708\pi\)
−0.890589 + 0.454809i \(0.849708\pi\)
\(692\) −13.5494 + 23.4683i −0.515073 + 0.892132i
\(693\) 0 0
\(694\) −22.2478 −0.844514
\(695\) 0.249496 0.432140i 0.00946392 0.0163920i
\(696\) 0 0
\(697\) 3.10534 5.37860i 0.117623 0.203729i
\(698\) −22.8576 + 39.5905i −0.865172 + 1.49852i
\(699\) 0 0
\(700\) −4.81921 11.2217i −0.182149 0.424142i
\(701\) −29.8626 −1.12790 −0.563948 0.825810i \(-0.690718\pi\)
−0.563948 + 0.825810i \(0.690718\pi\)
\(702\) 0 0
\(703\) −11.4293 + 19.7961i −0.431063 + 0.746623i
\(704\) 10.6048 + 18.3680i 0.399683 + 0.692271i
\(705\) 0 0
\(706\) 12.1893 + 21.1124i 0.458749 + 0.794576i
\(707\) 6.77281 + 0.802663i 0.254718 + 0.0301873i
\(708\) 0 0
\(709\) −13.4666 + 23.3249i −0.505750 + 0.875984i 0.494228 + 0.869332i \(0.335451\pi\)
−0.999978 + 0.00665185i \(0.997883\pi\)
\(710\) −13.9932 + 24.2369i −0.525155 + 0.909595i
\(711\) 0 0
\(712\) 4.60900 0.172729
\(713\) −11.6373 + 20.1563i −0.435819 + 0.754861i
\(714\) 0 0
\(715\) 4.68004 + 22.8623i 0.175023 + 0.855003i
\(716\) −0.440002 0.762105i −0.0164436 0.0284812i
\(717\) 0 0
\(718\) 11.7570 + 20.3638i 0.438769 + 0.759969i
\(719\) −7.24938 + 12.5563i −0.270356 + 0.468271i −0.968953 0.247245i \(-0.920475\pi\)
0.698597 + 0.715516i \(0.253808\pi\)
\(720\) 0 0
\(721\) 44.3064 + 5.25087i 1.65006 + 0.195553i
\(722\) 8.08799 + 14.0088i 0.301004 + 0.521354i
\(723\) 0 0
\(724\) 4.52098 0.168021
\(725\) −0.237090 0.410652i −0.00880530 0.0152512i
\(726\) 0 0
\(727\) −6.26424 −0.232328 −0.116164 0.993230i \(-0.537060\pi\)
−0.116164 + 0.993230i \(0.537060\pi\)
\(728\) 0.562223 + 6.68113i 0.0208374 + 0.247619i
\(729\) 0 0
\(730\) 42.7852 1.58355
\(731\) −0.0136811 0.0236963i −0.000506013 0.000876440i
\(732\) 0 0
\(733\) 5.99189 + 10.3783i 0.221316 + 0.383330i 0.955208 0.295936i \(-0.0956316\pi\)
−0.733892 + 0.679266i \(0.762298\pi\)
\(734\) −1.93487 3.35130i −0.0714175 0.123699i
\(735\) 0 0
\(736\) −32.6704 −1.20425
\(737\) −9.08480 + 15.7353i −0.334643 + 0.579619i
\(738\) 0 0
\(739\) −6.76269 11.7133i −0.248770 0.430882i 0.714415 0.699722i \(-0.246693\pi\)
−0.963185 + 0.268840i \(0.913360\pi\)
\(740\) −8.47091 14.6721i −0.311397 0.539355i
\(741\) 0 0
\(742\) 0.282075 + 0.656825i 0.0103553 + 0.0241128i
\(743\) −19.2299 + 33.3072i −0.705477 + 1.22192i 0.261043 + 0.965327i \(0.415934\pi\)
−0.966519 + 0.256594i \(0.917400\pi\)
\(744\) 0 0
\(745\) −5.77932 −0.211738
\(746\) 3.69107 6.39312i 0.135140 0.234069i
\(747\) 0 0
\(748\) −4.30973 7.46466i −0.157579 0.272935i
\(749\) −13.7476 + 18.4044i −0.502326 + 0.672482i
\(750\) 0 0
\(751\) 11.7115 0.427357 0.213679 0.976904i \(-0.431455\pi\)
0.213679 + 0.976904i \(0.431455\pi\)
\(752\) −26.8817 46.5605i −0.980276 1.69789i
\(753\) 0 0
\(754\) −0.230878 1.12786i −0.00840809 0.0410742i
\(755\) −3.12125 −0.113594
\(756\) 0 0
\(757\) −4.65791 + 8.06773i −0.169295 + 0.293227i −0.938172 0.346169i \(-0.887482\pi\)
0.768877 + 0.639396i \(0.220816\pi\)
\(758\) 13.8800 24.0409i 0.504145 0.873205i
\(759\) 0 0
\(760\) −3.35682 −0.121765
\(761\) −21.9691 + 38.0515i −0.796378 + 1.37937i 0.125582 + 0.992083i \(0.459920\pi\)
−0.921960 + 0.387284i \(0.873413\pi\)
\(762\) 0 0
\(763\) −12.5706 29.2712i −0.455086 1.05969i
\(764\) −16.5079 + 28.5926i −0.597236 + 1.03444i
\(765\) 0 0
\(766\) −25.5172 + 44.1971i −0.921973 + 1.59690i
\(767\) 14.4143 12.7837i 0.520471 0.461591i
\(768\) 0 0
\(769\) −12.6771 + 21.9573i −0.457147 + 0.791802i −0.998809 0.0487946i \(-0.984462\pi\)
0.541662 + 0.840597i \(0.317795\pi\)
\(770\) 12.8764 + 29.9833i 0.464035 + 1.08052i
\(771\) 0 0
\(772\) 13.3568 + 23.1347i 0.480723 + 0.832637i
\(773\) 23.1084 0.831152 0.415576 0.909559i \(-0.363580\pi\)
0.415576 + 0.909559i \(0.363580\pi\)
\(774\) 0 0
\(775\) 7.42200 + 12.8553i 0.266606 + 0.461775i
\(776\) 1.22705 + 2.12532i 0.0440487 + 0.0762946i
\(777\) 0 0
\(778\) 11.4474 19.8275i 0.410410 0.710851i
\(779\) 8.37091 + 14.4988i 0.299919 + 0.519475i
\(780\) 0 0
\(781\) −21.9015 + 37.9346i −0.783699 + 1.35741i
\(782\) 10.1691 0.363647
\(783\) 0 0
\(784\) 9.13912 + 30.8878i 0.326397 + 1.10314i
\(785\) −32.5750 −1.16265
\(786\) 0 0
\(787\) −24.6692 −0.879364 −0.439682 0.898154i \(-0.644909\pi\)
−0.439682 + 0.898154i \(0.644909\pi\)
\(788\) 16.0943 27.8761i 0.573334 0.993044i
\(789\) 0 0
\(790\) −1.08707 + 1.88285i −0.0386761 + 0.0669889i
\(791\) 24.6245 + 2.91832i 0.875547 + 0.103763i
\(792\) 0 0
\(793\) 8.34850 + 40.7831i 0.296464 + 1.44825i
\(794\) 1.57938 2.73556i 0.0560500 0.0970814i
\(795\) 0 0
\(796\) −23.0278 −0.816199
\(797\) 5.65686 + 9.79797i 0.200376 + 0.347062i 0.948650 0.316329i \(-0.102450\pi\)
−0.748273 + 0.663390i \(0.769117\pi\)
\(798\) 0 0
\(799\) 7.02597 + 12.1693i 0.248561 + 0.430520i
\(800\) −10.4182 + 18.0449i −0.368340 + 0.637984i
\(801\) 0 0
\(802\) 39.0311 1.37824
\(803\) 66.9657 2.36317
\(804\) 0 0
\(805\) −17.1736 2.03529i −0.605289 0.0717344i
\(806\) 7.22754 + 35.3071i 0.254579 + 1.24364i
\(807\) 0 0
\(808\) −0.905900 1.56906i −0.0318694 0.0551995i
\(809\) 8.18540 + 14.1775i 0.287783 + 0.498455i 0.973280 0.229620i \(-0.0737484\pi\)
−0.685497 + 0.728075i \(0.740415\pi\)
\(810\) 0 0
\(811\) −29.0412 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(812\) −0.285352 0.664454i −0.0100139 0.0233178i
\(813\) 0 0
\(814\) −29.5146 51.1209i −1.03449 1.79179i
\(815\) 5.67470 0.198776
\(816\) 0 0
\(817\) 0.0737588 0.00258050
\(818\) 28.3278 0.990458
\(819\) 0 0
\(820\) −12.4084 −0.433319
\(821\) 13.7518 0.479940 0.239970 0.970780i \(-0.422862\pi\)
0.239970 + 0.970780i \(0.422862\pi\)
\(822\) 0 0
\(823\) −29.1153 −1.01490 −0.507448 0.861682i \(-0.669411\pi\)
−0.507448 + 0.861682i \(0.669411\pi\)
\(824\) −5.92623 10.2645i −0.206450 0.357582i
\(825\) 0 0
\(826\) 16.1223 21.5835i 0.560966 0.750985i
\(827\) 22.9118 0.796722 0.398361 0.917229i \(-0.369579\pi\)
0.398361 + 0.917229i \(0.369579\pi\)
\(828\) 0 0
\(829\) 11.6914 + 20.2502i 0.406061 + 0.703317i 0.994444 0.105264i \(-0.0335689\pi\)
−0.588384 + 0.808582i \(0.700236\pi\)
\(830\) −22.4832 38.9421i −0.780404 1.35170i
\(831\) 0 0
\(832\) −13.0219 + 11.5488i −0.451454 + 0.400382i
\(833\) −2.38865 8.07301i −0.0827620 0.279713i
\(834\) 0 0
\(835\) −3.15094 −0.109043
\(836\) 23.2350 0.803601
\(837\) 0 0
\(838\) −22.5023 + 38.9751i −0.777328 + 1.34637i
\(839\) 0.367168 + 0.635954i 0.0126761 + 0.0219556i 0.872294 0.488982i \(-0.162632\pi\)
−0.859618 + 0.510938i \(0.829298\pi\)
\(840\) 0 0
\(841\) 14.4860 + 25.0904i 0.499516 + 0.865187i
\(842\) 49.7013 1.71282
\(843\) 0 0
\(844\) 3.77314 6.53528i 0.129877 0.224954i
\(845\) −17.6103 + 7.52515i −0.605811 + 0.258873i
\(846\) 0 0
\(847\) 8.66941 + 20.1871i 0.297884 + 0.693637i
\(848\) 0.326223 0.565035i 0.0112026 0.0194034i
\(849\) 0 0
\(850\) 3.24282 5.61674i 0.111228 0.192652i
\(851\) 31.2840 1.07240
\(852\) 0 0
\(853\) 54.3567 1.86114 0.930569 0.366118i \(-0.119313\pi\)
0.930569 + 0.366118i \(0.119313\pi\)
\(854\) 22.9697 + 53.4859i 0.786006 + 1.83025i
\(855\) 0 0
\(856\) 6.10259 0.208582
\(857\) −10.5106 + 18.2048i −0.359034 + 0.621864i −0.987800 0.155730i \(-0.950227\pi\)
0.628766 + 0.777595i \(0.283560\pi\)
\(858\) 0 0
\(859\) 25.6814 + 44.4816i 0.876240 + 1.51769i 0.855436 + 0.517908i \(0.173289\pi\)
0.0208035 + 0.999784i \(0.493378\pi\)
\(860\) −0.0273336 + 0.0473431i −0.000932066 + 0.00161439i
\(861\) 0 0
\(862\) −12.6884 21.9769i −0.432167 0.748535i
\(863\) 3.55660 + 6.16021i 0.121068 + 0.209696i 0.920189 0.391474i \(-0.128035\pi\)
−0.799121 + 0.601170i \(0.794701\pi\)
\(864\) 0 0
\(865\) 24.4735 0.832124
\(866\) −19.4577 33.7018i −0.661201 1.14523i
\(867\) 0 0
\(868\) 8.93280 + 20.8004i 0.303199 + 0.706012i
\(869\) −1.70143 + 2.94696i −0.0577171 + 0.0999689i
\(870\) 0 0
\(871\) −14.1458 4.71419i −0.479311 0.159734i
\(872\) −4.23133 + 7.32888i −0.143291 + 0.248187i
\(873\) 0 0
\(874\) −13.7062 + 23.7399i −0.463620 + 0.803013i
\(875\) −18.2630 + 24.4493i −0.617401 + 0.826537i
\(876\) 0 0
\(877\) −0.256238 + 0.443818i −0.00865255 + 0.0149867i −0.870319 0.492488i \(-0.836088\pi\)
0.861667 + 0.507475i \(0.169421\pi\)
\(878\) −18.6187 −0.628352
\(879\) 0 0
\(880\) 14.8917 25.7933i 0.502000 0.869490i
\(881\) −18.5464 + 32.1232i −0.624843 + 1.08226i 0.363729 + 0.931505i \(0.381503\pi\)
−0.988571 + 0.150754i \(0.951830\pi\)
\(882\) 0 0
\(883\) −15.5667 −0.523860 −0.261930 0.965087i \(-0.584359\pi\)
−0.261930 + 0.965087i \(0.584359\pi\)
\(884\) 5.29204 4.69336i 0.177990 0.157855i
\(885\) 0 0
\(886\) 20.1645 + 34.9260i 0.677440 + 1.17336i
\(887\) −27.5799 −0.926043 −0.463022 0.886347i \(-0.653235\pi\)
−0.463022 + 0.886347i \(0.653235\pi\)
\(888\) 0 0
\(889\) 16.5847 + 38.6182i 0.556233 + 1.29521i
\(890\) 9.20404 + 15.9419i 0.308520 + 0.534372i
\(891\) 0 0
\(892\) 17.4145 30.1627i 0.583079 1.00992i
\(893\) −37.8792 −1.26758
\(894\) 0 0
\(895\) −0.397374 + 0.688272i −0.0132827 + 0.0230064i
\(896\) 8.75140 11.7158i 0.292364 0.391398i
\(897\) 0 0
\(898\) −17.2895 29.9463i −0.576959 0.999323i
\(899\) 0.439466 + 0.761178i 0.0146570 + 0.0253867i
\(900\) 0 0
\(901\) −0.0852637 + 0.147681i −0.00284054 + 0.00491997i
\(902\) −43.2337 −1.43952
\(903\) 0 0
\(904\) −3.29366 5.70479i −0.109546 0.189738i
\(905\) −2.04149 3.53597i −0.0678615 0.117539i
\(906\) 0 0
\(907\) 22.5236 + 39.0119i 0.747882 + 1.29537i 0.948836 + 0.315769i \(0.102263\pi\)
−0.200954 + 0.979601i \(0.564404\pi\)
\(908\) 17.0440 0.565625
\(909\) 0 0
\(910\) −21.9863 + 15.2867i −0.728840 + 0.506749i
\(911\) −35.4678 −1.17510 −0.587550 0.809188i \(-0.699907\pi\)
−0.587550 + 0.809188i \(0.699907\pi\)
\(912\) 0 0
\(913\) −35.1898 60.9505i −1.16461 2.01717i
\(914\) −34.3379 −1.13580
\(915\) 0 0
\(916\) −11.7917 20.4238i −0.389608 0.674820i
\(917\) 4.88020 + 0.578365i 0.161158 + 0.0190993i
\(918\) 0 0
\(919\) −8.68622 + 15.0450i −0.286532 + 0.496288i −0.972980 0.230891i \(-0.925836\pi\)
0.686447 + 0.727179i \(0.259169\pi\)
\(920\) 2.29706 + 3.97862i 0.0757318 + 0.131171i
\(921\) 0 0
\(922\) −28.3686 49.1359i −0.934271 1.61820i
\(923\) −34.1024 11.3649i −1.12250 0.374081i
\(924\) 0 0
\(925\) 9.97613 17.2792i 0.328013 0.568136i
\(926\) 33.7412 1.10880
\(927\) 0 0
\(928\) −0.616877 + 1.06846i −0.0202500 + 0.0350740i
\(929\) 5.38001 9.31845i 0.176512 0.305729i −0.764171 0.645013i \(-0.776852\pi\)
0.940684 + 0.339285i \(0.110185\pi\)
\(930\) 0 0
\(931\) 22.0660 + 5.30470i 0.723183 + 0.173854i
\(932\) −7.57532 13.1208i −0.248138 0.429788i
\(933\) 0 0
\(934\) −5.55396 9.61975i −0.181731 0.314768i
\(935\) −3.89219 + 6.74148i −0.127288 + 0.220470i
\(936\) 0 0
\(937\) −10.9816 −0.358755 −0.179377 0.983780i \(-0.557408\pi\)
−0.179377 + 0.983780i \(0.557408\pi\)
\(938\) −20.7046 2.45375i −0.676029 0.0801179i
\(939\) 0 0
\(940\) 14.0373 24.3132i 0.457845 0.793011i
\(941\) 4.08897 7.08231i 0.133297 0.230877i −0.791649 0.610976i \(-0.790777\pi\)
0.924946 + 0.380100i \(0.124110\pi\)
\(942\) 0 0
\(943\) 11.4564 19.8430i 0.373071 0.646177i
\(944\) −24.5890 −0.800305
\(945\) 0 0
\(946\) −0.0952365 + 0.164954i −0.00309640 + 0.00536313i
\(947\) 4.59378 0.149278 0.0746389 0.997211i \(-0.476220\pi\)
0.0746389 + 0.997211i \(0.476220\pi\)
\(948\) 0 0
\(949\) 11.0209 + 53.8379i 0.357753 + 1.74765i
\(950\) 8.74153 + 15.1408i 0.283613 + 0.491231i
\(951\) 0 0
\(952\) −1.33844 + 1.79181i −0.0433790 + 0.0580730i
\(953\) 10.5714 + 18.3102i 0.342442 + 0.593126i 0.984886 0.173206i \(-0.0554128\pi\)
−0.642444 + 0.766333i \(0.722079\pi\)
\(954\) 0 0
\(955\) 29.8172 0.964863
\(956\) −32.0249 −1.03576
\(957\) 0 0
\(958\) 13.8070 + 23.9145i 0.446085 + 0.772641i
\(959\) 20.2671 27.1323i 0.654459 0.876148i
\(960\) 0 0
\(961\) 1.74271 + 3.01846i 0.0562164 + 0.0973697i
\(962\) 36.2419 32.1419i 1.16849 1.03630i
\(963\) 0 0
\(964\) 11.9255 0.384094
\(965\) 12.0628 20.8934i 0.388316 0.672582i
\(966\) 0 0
\(967\) −32.0750 −1.03146 −0.515731 0.856750i \(-0.672480\pi\)
−0.515731 + 0.856750i \(0.672480\pi\)
\(968\) 2.91817 5.05442i 0.0937936 0.162455i
\(969\) 0 0
\(970\) −4.90079 + 8.48841i −0.157355 + 0.272546i
\(971\) −26.0417 + 45.1056i −0.835719 + 1.44751i 0.0577245 + 0.998333i \(0.481616\pi\)
−0.893444 + 0.449175i \(0.851718\pi\)
\(972\) 0 0
\(973\) 0.889965 + 0.105472i 0.0285310 + 0.00338128i
\(974\) −34.2241 −1.09661
\(975\) 0 0
\(976\) 26.5647 46.0114i 0.850315 1.47279i
\(977\) 9.62898 + 16.6779i 0.308058 + 0.533573i 0.977938 0.208897i \(-0.0669874\pi\)
−0.669879 + 0.742470i \(0.733654\pi\)
\(978\) 0 0
\(979\) 14.4058 + 24.9515i 0.460410 + 0.797454i
\(980\) −11.5821 + 12.1975i −0.369977 + 0.389636i
\(981\) 0 0
\(982\) −34.5868 + 59.9061i −1.10371 + 1.91168i
\(983\) −8.03657 + 13.9197i −0.256327 + 0.443971i −0.965255 0.261310i \(-0.915846\pi\)
0.708928 + 0.705280i \(0.249179\pi\)
\(984\) 0 0
\(985\) −29.0700 −0.926248
\(986\) 0.192012 0.332574i 0.00611490 0.0105913i
\(987\) 0 0
\(988\) 3.82391 + 18.6801i 0.121655 + 0.594294i
\(989\) −0.0504729 0.0874216i −0.00160494 0.00277985i
\(990\) 0 0
\(991\) −10.7132 18.5559i −0.340317 0.589447i 0.644174 0.764879i \(-0.277201\pi\)
−0.984492 + 0.175432i \(0.943868\pi\)
\(992\) 19.3111 33.4478i 0.613127 1.06197i
\(993\) 0 0
\(994\) −49.9144 5.91549i −1.58319 0.187628i
\(995\) 10.3984 + 18.0106i 0.329652 + 0.570974i
\(996\) 0 0
\(997\) −16.9537 −0.536931 −0.268465 0.963289i \(-0.586516\pi\)
−0.268465 + 0.963289i \(0.586516\pi\)
\(998\) −22.5881 39.1238i −0.715015 1.23844i
\(999\) 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 819.2.s.d.802.5 12
3.2 odd 2 91.2.h.b.74.2 yes 12
7.2 even 3 819.2.n.d.100.2 12
13.3 even 3 819.2.n.d.172.2 12
21.2 odd 6 91.2.g.b.9.5 12
21.5 even 6 637.2.g.l.373.5 12
21.11 odd 6 637.2.f.k.295.5 12
21.17 even 6 637.2.f.j.295.5 12
21.20 even 2 637.2.h.l.165.2 12
39.17 odd 6 1183.2.e.g.508.2 12
39.29 odd 6 91.2.g.b.81.5 yes 12
39.35 odd 6 1183.2.e.h.508.5 12
91.16 even 3 inner 819.2.s.d.289.5 12
273.17 even 6 8281.2.a.cf.1.5 6
273.68 even 6 637.2.h.l.471.2 12
273.74 odd 6 8281.2.a.bz.1.2 6
273.95 odd 6 8281.2.a.ce.1.5 6
273.107 odd 6 91.2.h.b.16.2 yes 12
273.146 even 6 637.2.g.l.263.5 12
273.185 even 6 637.2.f.j.393.5 12
273.191 odd 6 1183.2.e.h.170.5 12
273.212 odd 6 1183.2.e.g.170.2 12
273.263 odd 6 637.2.f.k.393.5 12
273.269 even 6 8281.2.a.ca.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.5 12 21.2 odd 6
91.2.g.b.81.5 yes 12 39.29 odd 6
91.2.h.b.16.2 yes 12 273.107 odd 6
91.2.h.b.74.2 yes 12 3.2 odd 2
637.2.f.j.295.5 12 21.17 even 6
637.2.f.j.393.5 12 273.185 even 6
637.2.f.k.295.5 12 21.11 odd 6
637.2.f.k.393.5 12 273.263 odd 6
637.2.g.l.263.5 12 273.146 even 6
637.2.g.l.373.5 12 21.5 even 6
637.2.h.l.165.2 12 21.20 even 2
637.2.h.l.471.2 12 273.68 even 6
819.2.n.d.100.2 12 7.2 even 3
819.2.n.d.172.2 12 13.3 even 3
819.2.s.d.289.5 12 91.16 even 3 inner
819.2.s.d.802.5 12 1.1 even 1 trivial
1183.2.e.g.170.2 12 273.212 odd 6
1183.2.e.g.508.2 12 39.17 odd 6
1183.2.e.h.170.5 12 273.191 odd 6
1183.2.e.h.508.5 12 39.35 odd 6
8281.2.a.bz.1.2 6 273.74 odd 6
8281.2.a.ca.1.2 6 273.269 even 6
8281.2.a.ce.1.5 6 273.95 odd 6
8281.2.a.cf.1.5 6 273.17 even 6