Properties

Label 1110.2.e.c.739.14
Level $1110$
Weight $2$
Character 1110.739
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
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] = [1110,2,Mod(739,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.739");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.e (of order \(2\), degree \(1\), 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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} - 3018 x^{7} + 658 x^{6} - 1584 x^{5} + 16372 x^{4} - 18840 x^{3} + 10952 x^{2} + \cdots + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 739.14
Root \(-1.28817 - 1.28817i\) of defining polynomial
Character \(\chi\) \(=\) 1110.739
Dual form 1110.2.e.c.739.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.28817 - 1.82773i) q^{5} -1.00000i q^{6} -1.25548i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.28817 - 1.82773i) q^{5} -1.00000i q^{6} -1.25548i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-1.28817 + 1.82773i) q^{10} -5.46829 q^{11} +1.00000i q^{12} +4.70887 q^{13} +1.25548i q^{14} +(1.82773 + 1.28817i) q^{15} +1.00000 q^{16} +1.19309 q^{17} +1.00000 q^{18} -1.22179i q^{19} +(1.28817 - 1.82773i) q^{20} +1.25548 q^{21} +5.46829 q^{22} +1.91577 q^{23} -1.00000i q^{24} +(-1.68122 - 4.70887i) q^{25} -4.70887 q^{26} -1.00000i q^{27} -1.25548i q^{28} -5.08822i q^{29} +(-1.82773 - 1.28817i) q^{30} -3.43275i q^{31} -1.00000 q^{32} -5.46829i q^{33} -1.19309 q^{34} +(-2.29468 - 1.61728i) q^{35} -1.00000 q^{36} +(-4.58473 - 3.99753i) q^{37} +1.22179i q^{38} +4.70887i q^{39} +(-1.28817 + 1.82773i) q^{40} -4.46326 q^{41} -1.25548 q^{42} +1.34271 q^{43} -5.46829 q^{44} +(-1.28817 + 1.82773i) q^{45} -1.91577 q^{46} +1.90301i q^{47} +1.00000i q^{48} +5.42377 q^{49} +(1.68122 + 4.70887i) q^{50} +1.19309i q^{51} +4.70887 q^{52} -1.11671i q^{53} +1.00000i q^{54} +(-7.04410 + 9.99458i) q^{55} +1.25548i q^{56} +1.22179 q^{57} +5.08822i q^{58} -8.99577i q^{59} +(1.82773 + 1.28817i) q^{60} -6.21190i q^{61} +3.43275i q^{62} +1.25548i q^{63} +1.00000 q^{64} +(6.06585 - 8.60657i) q^{65} +5.46829i q^{66} +4.21117i q^{67} +1.19309 q^{68} +1.91577i q^{69} +(2.29468 + 1.61728i) q^{70} -12.4170 q^{71} +1.00000 q^{72} -10.2834i q^{73} +(4.58473 + 3.99753i) q^{74} +(4.70887 - 1.68122i) q^{75} -1.22179i q^{76} +6.86533i q^{77} -4.70887i q^{78} +1.00691i q^{79} +(1.28817 - 1.82773i) q^{80} +1.00000 q^{81} +4.46326 q^{82} -0.754493i q^{83} +1.25548 q^{84} +(1.53691 - 2.18065i) q^{85} -1.34271 q^{86} +5.08822 q^{87} +5.46829 q^{88} -11.4743i q^{89} +(1.28817 - 1.82773i) q^{90} -5.91190i q^{91} +1.91577 q^{92} +3.43275 q^{93} -1.90301i q^{94} +(-2.23311 - 1.57388i) q^{95} -1.00000i q^{96} +16.6814 q^{97} -5.42377 q^{98} +5.46829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} + 6 q^{15} + 16 q^{16} - 38 q^{17} + 16 q^{18} - 2 q^{20} + 6 q^{21} - 2 q^{22} - 20 q^{23} - 4 q^{25} - 6 q^{30} - 16 q^{32} + 38 q^{34} - 10 q^{35} - 16 q^{36} - 4 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 2 q^{44} + 2 q^{45} + 20 q^{46} - 18 q^{49} + 4 q^{50} + 20 q^{55} + 16 q^{57} + 6 q^{60} + 16 q^{64} + 12 q^{65} - 38 q^{68} + 10 q^{70} - 24 q^{71} + 16 q^{72} + 4 q^{74} - 2 q^{80} + 16 q^{81} + 6 q^{82} + 6 q^{84} + 2 q^{86} + 2 q^{87} - 2 q^{88} - 2 q^{90} - 20 q^{92} + 22 q^{93} - 16 q^{95} + 38 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) 1.28817 1.82773i 0.576089 0.817387i
\(6\) 1.00000i 0.408248i
\(7\) 1.25548i 0.474527i −0.971445 0.237263i \(-0.923750\pi\)
0.971445 0.237263i \(-0.0762505\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) −1.28817 + 1.82773i −0.407356 + 0.577980i
\(11\) −5.46829 −1.64875 −0.824376 0.566043i \(-0.808474\pi\)
−0.824376 + 0.566043i \(0.808474\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 4.70887 1.30601 0.653003 0.757355i \(-0.273509\pi\)
0.653003 + 0.757355i \(0.273509\pi\)
\(14\) 1.25548i 0.335541i
\(15\) 1.82773 + 1.28817i 0.471919 + 0.332605i
\(16\) 1.00000 0.250000
\(17\) 1.19309 0.289367 0.144684 0.989478i \(-0.453784\pi\)
0.144684 + 0.989478i \(0.453784\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.22179i 0.280298i −0.990130 0.140149i \(-0.955242\pi\)
0.990130 0.140149i \(-0.0447582\pi\)
\(20\) 1.28817 1.82773i 0.288044 0.408694i
\(21\) 1.25548 0.273968
\(22\) 5.46829 1.16584
\(23\) 1.91577 0.399466 0.199733 0.979850i \(-0.435993\pi\)
0.199733 + 0.979850i \(0.435993\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −1.68122 4.70887i −0.336244 0.941775i
\(26\) −4.70887 −0.923486
\(27\) 1.00000i 0.192450i
\(28\) 1.25548i 0.237263i
\(29\) 5.08822i 0.944858i −0.881369 0.472429i \(-0.843377\pi\)
0.881369 0.472429i \(-0.156623\pi\)
\(30\) −1.82773 1.28817i −0.333697 0.235187i
\(31\) 3.43275i 0.616540i −0.951299 0.308270i \(-0.900250\pi\)
0.951299 0.308270i \(-0.0997501\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.46829i 0.951907i
\(34\) −1.19309 −0.204613
\(35\) −2.29468 1.61728i −0.387872 0.273370i
\(36\) −1.00000 −0.166667
\(37\) −4.58473 3.99753i −0.753725 0.657190i
\(38\) 1.22179i 0.198201i
\(39\) 4.70887i 0.754023i
\(40\) −1.28817 + 1.82773i −0.203678 + 0.288990i
\(41\) −4.46326 −0.697043 −0.348522 0.937301i \(-0.613316\pi\)
−0.348522 + 0.937301i \(0.613316\pi\)
\(42\) −1.25548 −0.193725
\(43\) 1.34271 0.204761 0.102380 0.994745i \(-0.467354\pi\)
0.102380 + 0.994745i \(0.467354\pi\)
\(44\) −5.46829 −0.824376
\(45\) −1.28817 + 1.82773i −0.192030 + 0.272462i
\(46\) −1.91577 −0.282465
\(47\) 1.90301i 0.277583i 0.990322 + 0.138791i \(0.0443217\pi\)
−0.990322 + 0.138791i \(0.955678\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 5.42377 0.774824
\(50\) 1.68122 + 4.70887i 0.237760 + 0.665935i
\(51\) 1.19309i 0.167066i
\(52\) 4.70887 0.653003
\(53\) 1.11671i 0.153392i −0.997055 0.0766959i \(-0.975563\pi\)
0.997055 0.0766959i \(-0.0244370\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −7.04410 + 9.99458i −0.949827 + 1.34767i
\(56\) 1.25548i 0.167771i
\(57\) 1.22179 0.161830
\(58\) 5.08822i 0.668116i
\(59\) 8.99577i 1.17115i −0.810618 0.585575i \(-0.800869\pi\)
0.810618 0.585575i \(-0.199131\pi\)
\(60\) 1.82773 + 1.28817i 0.235959 + 0.166302i
\(61\) 6.21190i 0.795352i −0.917526 0.397676i \(-0.869817\pi\)
0.917526 0.397676i \(-0.130183\pi\)
\(62\) 3.43275i 0.435960i
\(63\) 1.25548i 0.158176i
\(64\) 1.00000 0.125000
\(65\) 6.06585 8.60657i 0.752376 1.06751i
\(66\) 5.46829i 0.673100i
\(67\) 4.21117i 0.514476i 0.966348 + 0.257238i \(0.0828125\pi\)
−0.966348 + 0.257238i \(0.917188\pi\)
\(68\) 1.19309 0.144684
\(69\) 1.91577i 0.230632i
\(70\) 2.29468 + 1.61728i 0.274267 + 0.193301i
\(71\) −12.4170 −1.47363 −0.736815 0.676094i \(-0.763671\pi\)
−0.736815 + 0.676094i \(0.763671\pi\)
\(72\) 1.00000 0.117851
\(73\) 10.2834i 1.20359i −0.798652 0.601793i \(-0.794453\pi\)
0.798652 0.601793i \(-0.205547\pi\)
\(74\) 4.58473 + 3.99753i 0.532964 + 0.464703i
\(75\) 4.70887 1.68122i 0.543734 0.194130i
\(76\) 1.22179i 0.140149i
\(77\) 6.86533i 0.782377i
\(78\) 4.70887i 0.533175i
\(79\) 1.00691i 0.113286i 0.998394 + 0.0566431i \(0.0180397\pi\)
−0.998394 + 0.0566431i \(0.981960\pi\)
\(80\) 1.28817 1.82773i 0.144022 0.204347i
\(81\) 1.00000 0.111111
\(82\) 4.46326 0.492884
\(83\) 0.754493i 0.0828164i −0.999142 0.0414082i \(-0.986816\pi\)
0.999142 0.0414082i \(-0.0131844\pi\)
\(84\) 1.25548 0.136984
\(85\) 1.53691 2.18065i 0.166701 0.236525i
\(86\) −1.34271 −0.144788
\(87\) 5.08822 0.545514
\(88\) 5.46829 0.582922
\(89\) 11.4743i 1.21627i −0.793832 0.608137i \(-0.791917\pi\)
0.793832 0.608137i \(-0.208083\pi\)
\(90\) 1.28817 1.82773i 0.135785 0.192660i
\(91\) 5.91190i 0.619735i
\(92\) 1.91577 0.199733
\(93\) 3.43275 0.355960
\(94\) 1.90301i 0.196281i
\(95\) −2.23311 1.57388i −0.229112 0.161477i
\(96\) 1.00000i 0.102062i
\(97\) 16.6814 1.69374 0.846868 0.531803i \(-0.178485\pi\)
0.846868 + 0.531803i \(0.178485\pi\)
\(98\) −5.42377 −0.547883
\(99\) 5.46829 0.549584
\(100\) −1.68122 4.70887i −0.168122 0.470887i
\(101\) 3.26214 0.324595 0.162298 0.986742i \(-0.448110\pi\)
0.162298 + 0.986742i \(0.448110\pi\)
\(102\) 1.19309i 0.118134i
\(103\) 5.19330 0.511711 0.255856 0.966715i \(-0.417643\pi\)
0.255856 + 0.966715i \(0.417643\pi\)
\(104\) −4.70887 −0.461743
\(105\) 1.61728 2.29468i 0.157830 0.223938i
\(106\) 1.11671i 0.108464i
\(107\) 8.65950i 0.837146i −0.908183 0.418573i \(-0.862530\pi\)
0.908183 0.418573i \(-0.137470\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 2.54677i 0.243936i 0.992534 + 0.121968i \(0.0389205\pi\)
−0.992534 + 0.121968i \(0.961079\pi\)
\(110\) 7.04410 9.99458i 0.671629 0.952945i
\(111\) 3.99753 4.58473i 0.379429 0.435164i
\(112\) 1.25548i 0.118632i
\(113\) −4.72781 −0.444755 −0.222378 0.974961i \(-0.571382\pi\)
−0.222378 + 0.974961i \(0.571382\pi\)
\(114\) −1.22179 −0.114431
\(115\) 2.46784 3.50152i 0.230128 0.326518i
\(116\) 5.08822i 0.472429i
\(117\) −4.70887 −0.435336
\(118\) 8.99577i 0.828128i
\(119\) 1.49790i 0.137312i
\(120\) −1.82773 1.28817i −0.166848 0.117594i
\(121\) 18.9022 1.71838
\(122\) 6.21190i 0.562399i
\(123\) 4.46326i 0.402438i
\(124\) 3.43275i 0.308270i
\(125\) −10.7723 2.99303i −0.963501 0.267704i
\(126\) 1.25548i 0.111847i
\(127\) 8.05067i 0.714381i 0.934031 + 0.357191i \(0.116265\pi\)
−0.934031 + 0.357191i \(0.883735\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.34271i 0.118219i
\(130\) −6.06585 + 8.60657i −0.532010 + 0.754846i
\(131\) 12.9999i 1.13581i −0.823094 0.567905i \(-0.807754\pi\)
0.823094 0.567905i \(-0.192246\pi\)
\(132\) 5.46829i 0.475954i
\(133\) −1.53393 −0.133009
\(134\) 4.21117i 0.363790i
\(135\) −1.82773 1.28817i −0.157306 0.110868i
\(136\) −1.19309 −0.102307
\(137\) 13.5487i 1.15754i 0.815490 + 0.578772i \(0.196468\pi\)
−0.815490 + 0.578772i \(0.803532\pi\)
\(138\) 1.91577i 0.163081i
\(139\) 15.3257 1.29991 0.649955 0.759972i \(-0.274788\pi\)
0.649955 + 0.759972i \(0.274788\pi\)
\(140\) −2.29468 1.61728i −0.193936 0.136685i
\(141\) −1.90301 −0.160262
\(142\) 12.4170 1.04201
\(143\) −25.7495 −2.15328
\(144\) −1.00000 −0.0833333
\(145\) −9.29991 6.55451i −0.772315 0.544322i
\(146\) 10.2834i 0.851064i
\(147\) 5.42377i 0.447345i
\(148\) −4.58473 3.99753i −0.376863 0.328595i
\(149\) 13.4684 1.10337 0.551686 0.834052i \(-0.313985\pi\)
0.551686 + 0.834052i \(0.313985\pi\)
\(150\) −4.70887 + 1.68122i −0.384478 + 0.137271i
\(151\) −10.3930 −0.845767 −0.422883 0.906184i \(-0.638982\pi\)
−0.422883 + 0.906184i \(0.638982\pi\)
\(152\) 1.22179i 0.0991003i
\(153\) −1.19309 −0.0964557
\(154\) 6.86533i 0.553224i
\(155\) −6.27415 4.42198i −0.503952 0.355182i
\(156\) 4.70887i 0.377012i
\(157\) 14.2297i 1.13565i 0.823148 + 0.567827i \(0.192216\pi\)
−0.823148 + 0.567827i \(0.807784\pi\)
\(158\) 1.00691i 0.0801054i
\(159\) 1.11671 0.0885608
\(160\) −1.28817 + 1.82773i −0.101839 + 0.144495i
\(161\) 2.40521i 0.189557i
\(162\) −1.00000 −0.0785674
\(163\) 0.455364 0.0356669 0.0178334 0.999841i \(-0.494323\pi\)
0.0178334 + 0.999841i \(0.494323\pi\)
\(164\) −4.46326 −0.348522
\(165\) −9.99458 7.04410i −0.778077 0.548383i
\(166\) 0.754493i 0.0585600i
\(167\) 0.755752 0.0584819 0.0292409 0.999572i \(-0.490691\pi\)
0.0292409 + 0.999572i \(0.490691\pi\)
\(168\) −1.25548 −0.0968624
\(169\) 9.17350 0.705654
\(170\) −1.53691 + 2.18065i −0.117875 + 0.167248i
\(171\) 1.22179i 0.0934327i
\(172\) 1.34271 0.102380
\(173\) 4.41375i 0.335571i 0.985823 + 0.167786i \(0.0536617\pi\)
−0.985823 + 0.167786i \(0.946338\pi\)
\(174\) −5.08822 −0.385737
\(175\) −5.91190 + 2.11074i −0.446898 + 0.159557i
\(176\) −5.46829 −0.412188
\(177\) 8.99577 0.676164
\(178\) 11.4743i 0.860036i
\(179\) 12.6883i 0.948368i 0.880426 + 0.474184i \(0.157257\pi\)
−0.880426 + 0.474184i \(0.842743\pi\)
\(180\) −1.28817 + 1.82773i −0.0960148 + 0.136231i
\(181\) 13.2444 0.984445 0.492223 0.870469i \(-0.336185\pi\)
0.492223 + 0.870469i \(0.336185\pi\)
\(182\) 5.91190i 0.438219i
\(183\) 6.21190 0.459197
\(184\) −1.91577 −0.141233
\(185\) −13.2123 + 3.23016i −0.971391 + 0.237486i
\(186\) −3.43275 −0.251702
\(187\) −6.52417 −0.477094
\(188\) 1.90301i 0.138791i
\(189\) −1.25548 −0.0913227
\(190\) 2.23311 + 1.57388i 0.162007 + 0.114181i
\(191\) 7.03990i 0.509389i −0.967022 0.254695i \(-0.918025\pi\)
0.967022 0.254695i \(-0.0819749\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −0.635749 −0.0457622 −0.0228811 0.999738i \(-0.507284\pi\)
−0.0228811 + 0.999738i \(0.507284\pi\)
\(194\) −16.6814 −1.19765
\(195\) 8.60657 + 6.06585i 0.616329 + 0.434384i
\(196\) 5.42377 0.387412
\(197\) 5.18937i 0.369727i 0.982764 + 0.184864i \(0.0591843\pi\)
−0.982764 + 0.184864i \(0.940816\pi\)
\(198\) −5.46829 −0.388614
\(199\) 23.8852i 1.69318i 0.532247 + 0.846589i \(0.321348\pi\)
−0.532247 + 0.846589i \(0.678652\pi\)
\(200\) 1.68122 + 4.70887i 0.118880 + 0.332968i
\(201\) −4.21117 −0.297033
\(202\) −3.26214 −0.229523
\(203\) −6.38816 −0.448361
\(204\) 1.19309i 0.0835331i
\(205\) −5.74945 + 8.15764i −0.401559 + 0.569754i
\(206\) −5.19330 −0.361834
\(207\) −1.91577 −0.133155
\(208\) 4.70887 0.326502
\(209\) 6.68111i 0.462142i
\(210\) −1.61728 + 2.29468i −0.111603 + 0.158348i
\(211\) −26.6260 −1.83301 −0.916505 0.400022i \(-0.869002\pi\)
−0.916505 + 0.400022i \(0.869002\pi\)
\(212\) 1.11671i 0.0766959i
\(213\) 12.4170i 0.850801i
\(214\) 8.65950i 0.591952i
\(215\) 1.72964 2.45411i 0.117960 0.167369i
\(216\) 1.00000i 0.0680414i
\(217\) −4.30975 −0.292565
\(218\) 2.54677i 0.172489i
\(219\) 10.2834 0.694891
\(220\) −7.04410 + 9.99458i −0.474913 + 0.673834i
\(221\) 5.61812 0.377915
\(222\) −3.99753 + 4.58473i −0.268297 + 0.307707i
\(223\) 20.0982i 1.34588i −0.739698 0.672938i \(-0.765032\pi\)
0.739698 0.672938i \(-0.234968\pi\)
\(224\) 1.25548i 0.0838853i
\(225\) 1.68122 + 4.70887i 0.112081 + 0.313925i
\(226\) 4.72781 0.314489
\(227\) 15.1621 1.00635 0.503173 0.864186i \(-0.332166\pi\)
0.503173 + 0.864186i \(0.332166\pi\)
\(228\) 1.22179 0.0809151
\(229\) −2.54527 −0.168196 −0.0840980 0.996457i \(-0.526801\pi\)
−0.0840980 + 0.996457i \(0.526801\pi\)
\(230\) −2.46784 + 3.50152i −0.162725 + 0.230883i
\(231\) −6.86533 −0.451705
\(232\) 5.08822i 0.334058i
\(233\) 13.9212i 0.912008i −0.889978 0.456004i \(-0.849280\pi\)
0.889978 0.456004i \(-0.150720\pi\)
\(234\) 4.70887 0.307829
\(235\) 3.47820 + 2.45141i 0.226892 + 0.159912i
\(236\) 8.99577i 0.585575i
\(237\) −1.00691 −0.0654058
\(238\) 1.49790i 0.0970945i
\(239\) 28.8753i 1.86779i 0.357546 + 0.933895i \(0.383613\pi\)
−0.357546 + 0.933895i \(0.616387\pi\)
\(240\) 1.82773 + 1.28817i 0.117980 + 0.0831512i
\(241\) 6.84853i 0.441152i −0.975370 0.220576i \(-0.929206\pi\)
0.975370 0.220576i \(-0.0707938\pi\)
\(242\) −18.9022 −1.21508
\(243\) 1.00000i 0.0641500i
\(244\) 6.21190i 0.397676i
\(245\) 6.98676 9.91321i 0.446367 0.633331i
\(246\) 4.46326i 0.284567i
\(247\) 5.75326i 0.366071i
\(248\) 3.43275i 0.217980i
\(249\) 0.754493 0.0478141
\(250\) 10.7723 + 2.99303i 0.681298 + 0.189296i
\(251\) 18.7459i 1.18323i −0.806221 0.591615i \(-0.798491\pi\)
0.806221 0.591615i \(-0.201509\pi\)
\(252\) 1.25548i 0.0790878i
\(253\) −10.4760 −0.658620
\(254\) 8.05067i 0.505144i
\(255\) 2.18065 + 1.53691i 0.136558 + 0.0962449i
\(256\) 1.00000 0.0625000
\(257\) 17.3509 1.08232 0.541158 0.840921i \(-0.317986\pi\)
0.541158 + 0.840921i \(0.317986\pi\)
\(258\) 1.34271i 0.0835933i
\(259\) −5.01882 + 5.75604i −0.311854 + 0.357663i
\(260\) 6.06585 8.60657i 0.376188 0.533757i
\(261\) 5.08822i 0.314953i
\(262\) 12.9999i 0.803139i
\(263\) 31.3436i 1.93273i 0.257176 + 0.966364i \(0.417208\pi\)
−0.257176 + 0.966364i \(0.582792\pi\)
\(264\) 5.46829i 0.336550i
\(265\) −2.04105 1.43851i −0.125380 0.0883672i
\(266\) 1.53393 0.0940516
\(267\) 11.4743 0.702217
\(268\) 4.21117i 0.257238i
\(269\) 20.8503 1.27126 0.635631 0.771993i \(-0.280740\pi\)
0.635631 + 0.771993i \(0.280740\pi\)
\(270\) 1.82773 + 1.28817i 0.111232 + 0.0783957i
\(271\) −0.977182 −0.0593596 −0.0296798 0.999559i \(-0.509449\pi\)
−0.0296798 + 0.999559i \(0.509449\pi\)
\(272\) 1.19309 0.0723418
\(273\) 5.91190 0.357804
\(274\) 13.5487i 0.818507i
\(275\) 9.19339 + 25.7495i 0.554383 + 1.55275i
\(276\) 1.91577i 0.115316i
\(277\) −28.0775 −1.68701 −0.843506 0.537120i \(-0.819512\pi\)
−0.843506 + 0.537120i \(0.819512\pi\)
\(278\) −15.3257 −0.919176
\(279\) 3.43275i 0.205513i
\(280\) 2.29468 + 1.61728i 0.137134 + 0.0966507i
\(281\) 20.9112i 1.24746i 0.781640 + 0.623730i \(0.214383\pi\)
−0.781640 + 0.623730i \(0.785617\pi\)
\(282\) 1.90301 0.113323
\(283\) −11.7273 −0.697116 −0.348558 0.937287i \(-0.613329\pi\)
−0.348558 + 0.937287i \(0.613329\pi\)
\(284\) −12.4170 −0.736815
\(285\) 1.57388 2.23311i 0.0932285 0.132278i
\(286\) 25.7495 1.52260
\(287\) 5.60353i 0.330766i
\(288\) 1.00000 0.0589256
\(289\) −15.5765 −0.916267
\(290\) 9.29991 + 6.55451i 0.546109 + 0.384894i
\(291\) 16.6814i 0.977879i
\(292\) 10.2834i 0.601793i
\(293\) 19.0944i 1.11550i 0.830007 + 0.557752i \(0.188336\pi\)
−0.830007 + 0.557752i \(0.811664\pi\)
\(294\) 5.42377i 0.316321i
\(295\) −16.4419 11.5881i −0.957283 0.674686i
\(296\) 4.58473 + 3.99753i 0.266482 + 0.232352i
\(297\) 5.46829i 0.317302i
\(298\) −13.4684 −0.780202
\(299\) 9.02113 0.521705
\(300\) 4.70887 1.68122i 0.271867 0.0970652i
\(301\) 1.68574i 0.0971645i
\(302\) 10.3930 0.598048
\(303\) 3.26214i 0.187405i
\(304\) 1.22179i 0.0700745i
\(305\) −11.3537 8.00200i −0.650111 0.458193i
\(306\) 1.19309 0.0682045
\(307\) 31.2854i 1.78555i 0.450500 + 0.892777i \(0.351246\pi\)
−0.450500 + 0.892777i \(0.648754\pi\)
\(308\) 6.86533i 0.391188i
\(309\) 5.19330i 0.295437i
\(310\) 6.27415 + 4.42198i 0.356348 + 0.251151i
\(311\) 7.52409i 0.426652i −0.976981 0.213326i \(-0.931570\pi\)
0.976981 0.213326i \(-0.0684296\pi\)
\(312\) 4.70887i 0.266588i
\(313\) −0.0900227 −0.00508838 −0.00254419 0.999997i \(-0.500810\pi\)
−0.00254419 + 0.999997i \(0.500810\pi\)
\(314\) 14.2297i 0.803029i
\(315\) 2.29468 + 1.61728i 0.129291 + 0.0911232i
\(316\) 1.00691i 0.0566431i
\(317\) 7.86659i 0.441832i 0.975293 + 0.220916i \(0.0709046\pi\)
−0.975293 + 0.220916i \(0.929095\pi\)
\(318\) −1.11671 −0.0626219
\(319\) 27.8239i 1.55784i
\(320\) 1.28817 1.82773i 0.0720111 0.102173i
\(321\) 8.65950 0.483326
\(322\) 2.40521i 0.134037i
\(323\) 1.45771i 0.0811090i
\(324\) 1.00000 0.0555556
\(325\) −7.91665 22.1735i −0.439137 1.22996i
\(326\) −0.455364 −0.0252203
\(327\) −2.54677 −0.140836
\(328\) 4.46326 0.246442
\(329\) 2.38919 0.131720
\(330\) 9.99458 + 7.04410i 0.550183 + 0.387765i
\(331\) 21.5849i 1.18641i 0.805051 + 0.593205i \(0.202138\pi\)
−0.805051 + 0.593205i \(0.797862\pi\)
\(332\) 0.754493i 0.0414082i
\(333\) 4.58473 + 3.99753i 0.251242 + 0.219063i
\(334\) −0.755752 −0.0413529
\(335\) 7.69690 + 5.42472i 0.420526 + 0.296384i
\(336\) 1.25548 0.0684921
\(337\) 24.3782i 1.32796i 0.747748 + 0.663982i \(0.231135\pi\)
−0.747748 + 0.663982i \(0.768865\pi\)
\(338\) −9.17350 −0.498973
\(339\) 4.72781i 0.256779i
\(340\) 1.53691 2.18065i 0.0833505 0.118262i
\(341\) 18.7713i 1.01652i
\(342\) 1.22179i 0.0660669i
\(343\) 15.5978i 0.842202i
\(344\) −1.34271 −0.0723939
\(345\) 3.50152 + 2.46784i 0.188515 + 0.132864i
\(346\) 4.41375i 0.237285i
\(347\) 25.4950 1.36864 0.684321 0.729181i \(-0.260099\pi\)
0.684321 + 0.729181i \(0.260099\pi\)
\(348\) 5.08822 0.272757
\(349\) 2.69761 0.144400 0.0721999 0.997390i \(-0.476998\pi\)
0.0721999 + 0.997390i \(0.476998\pi\)
\(350\) 5.91190 2.11074i 0.316004 0.112824i
\(351\) 4.70887i 0.251341i
\(352\) 5.46829 0.291461
\(353\) −21.7179 −1.15592 −0.577962 0.816063i \(-0.696152\pi\)
−0.577962 + 0.816063i \(0.696152\pi\)
\(354\) −8.99577 −0.478120
\(355\) −15.9953 + 22.6950i −0.848942 + 1.20453i
\(356\) 11.4743i 0.608137i
\(357\) 1.49790 0.0792774
\(358\) 12.6883i 0.670597i
\(359\) −20.3716 −1.07517 −0.537585 0.843210i \(-0.680663\pi\)
−0.537585 + 0.843210i \(0.680663\pi\)
\(360\) 1.28817 1.82773i 0.0678927 0.0963300i
\(361\) 17.5072 0.921433
\(362\) −13.2444 −0.696108
\(363\) 18.9022i 0.992108i
\(364\) 5.91190i 0.309868i
\(365\) −18.7954 13.2469i −0.983796 0.693372i
\(366\) −6.21190 −0.324701
\(367\) 31.0972i 1.62326i −0.584172 0.811630i \(-0.698581\pi\)
0.584172 0.811630i \(-0.301419\pi\)
\(368\) 1.91577 0.0998665
\(369\) 4.46326 0.232348
\(370\) 13.2123 3.23016i 0.686877 0.167928i
\(371\) −1.40201 −0.0727885
\(372\) 3.43275 0.177980
\(373\) 33.4131i 1.73006i −0.501716 0.865032i \(-0.667298\pi\)
0.501716 0.865032i \(-0.332702\pi\)
\(374\) 6.52417 0.337357
\(375\) 2.99303 10.7723i 0.154559 0.556278i
\(376\) 1.90301i 0.0981403i
\(377\) 23.9598i 1.23399i
\(378\) 1.25548 0.0645749
\(379\) −24.6191 −1.26460 −0.632298 0.774725i \(-0.717888\pi\)
−0.632298 + 0.774725i \(0.717888\pi\)
\(380\) −2.23311 1.57388i −0.114556 0.0807383i
\(381\) −8.05067 −0.412448
\(382\) 7.03990i 0.360192i
\(383\) 17.5596 0.897252 0.448626 0.893720i \(-0.351914\pi\)
0.448626 + 0.893720i \(0.351914\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 12.5480 + 8.84373i 0.639505 + 0.450718i
\(386\) 0.635749 0.0323587
\(387\) −1.34271 −0.0682536
\(388\) 16.6814 0.846868
\(389\) 19.6417i 0.995875i −0.867213 0.497937i \(-0.834091\pi\)
0.867213 0.497937i \(-0.165909\pi\)
\(390\) −8.60657 6.06585i −0.435811 0.307156i
\(391\) 2.28569 0.115592
\(392\) −5.42377 −0.273942
\(393\) 12.9999 0.655760
\(394\) 5.18937i 0.261437i
\(395\) 1.84036 + 1.29707i 0.0925987 + 0.0652629i
\(396\) 5.46829 0.274792
\(397\) 4.31480i 0.216554i −0.994121 0.108277i \(-0.965467\pi\)
0.994121 0.108277i \(-0.0345333\pi\)
\(398\) 23.8852i 1.19726i
\(399\) 1.53393i 0.0767928i
\(400\) −1.68122 4.70887i −0.0840610 0.235444i
\(401\) 9.64980i 0.481888i 0.970539 + 0.240944i \(0.0774570\pi\)
−0.970539 + 0.240944i \(0.922543\pi\)
\(402\) 4.21117 0.210034
\(403\) 16.1644i 0.805206i
\(404\) 3.26214 0.162298
\(405\) 1.28817 1.82773i 0.0640098 0.0908208i
\(406\) 6.38816 0.317039
\(407\) 25.0706 + 21.8596i 1.24271 + 1.08354i
\(408\) 1.19309i 0.0590668i
\(409\) 25.5235i 1.26206i −0.775760 0.631029i \(-0.782633\pi\)
0.775760 0.631029i \(-0.217367\pi\)
\(410\) 5.74945 8.15764i 0.283945 0.402877i
\(411\) −13.5487 −0.668308
\(412\) 5.19330 0.255856
\(413\) −11.2940 −0.555742
\(414\) 1.91577 0.0941550
\(415\) −1.37901 0.971918i −0.0676930 0.0477096i
\(416\) −4.70887 −0.230872
\(417\) 15.3257i 0.750504i
\(418\) 6.68111i 0.326784i
\(419\) −22.0969 −1.07950 −0.539751 0.841824i \(-0.681482\pi\)
−0.539751 + 0.841824i \(0.681482\pi\)
\(420\) 1.61728 2.29468i 0.0789150 0.111969i
\(421\) 8.20101i 0.399693i −0.979827 0.199846i \(-0.935956\pi\)
0.979827 0.199846i \(-0.0640443\pi\)
\(422\) 26.6260 1.29613
\(423\) 1.90301i 0.0925275i
\(424\) 1.11671i 0.0542322i
\(425\) −2.00585 5.61812i −0.0972979 0.272519i
\(426\) 12.4170i 0.601607i
\(427\) −7.79891 −0.377416
\(428\) 8.65950i 0.418573i
\(429\) 25.7495i 1.24320i
\(430\) −1.72964 + 2.45411i −0.0834106 + 0.118348i
\(431\) 9.83076i 0.473531i 0.971567 + 0.236765i \(0.0760873\pi\)
−0.971567 + 0.236765i \(0.923913\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 1.61024i 0.0773832i 0.999251 + 0.0386916i \(0.0123190\pi\)
−0.999251 + 0.0386916i \(0.987681\pi\)
\(434\) 4.30975 0.206875
\(435\) 6.55451 9.29991i 0.314265 0.445896i
\(436\) 2.54677i 0.121968i
\(437\) 2.34067i 0.111970i
\(438\) −10.2834 −0.491362
\(439\) 32.2443i 1.53894i 0.638684 + 0.769469i \(0.279479\pi\)
−0.638684 + 0.769469i \(0.720521\pi\)
\(440\) 7.04410 9.99458i 0.335815 0.476473i
\(441\) −5.42377 −0.258275
\(442\) −5.61812 −0.267226
\(443\) 19.0730i 0.906186i 0.891463 + 0.453093i \(0.149679\pi\)
−0.891463 + 0.453093i \(0.850321\pi\)
\(444\) 3.99753 4.58473i 0.189714 0.217582i
\(445\) −20.9720 14.7809i −0.994168 0.700682i
\(446\) 20.0982i 0.951679i
\(447\) 13.4684i 0.637032i
\(448\) 1.25548i 0.0593159i
\(449\) 30.6914i 1.44841i 0.689582 + 0.724207i \(0.257794\pi\)
−0.689582 + 0.724207i \(0.742206\pi\)
\(450\) −1.68122 4.70887i −0.0792534 0.221978i
\(451\) 24.4064 1.14925
\(452\) −4.72781 −0.222378
\(453\) 10.3930i 0.488304i
\(454\) −15.1621 −0.711593
\(455\) −10.8054 7.61555i −0.506564 0.357022i
\(456\) −1.22179 −0.0572156
\(457\) 22.4560 1.05045 0.525223 0.850965i \(-0.323982\pi\)
0.525223 + 0.850965i \(0.323982\pi\)
\(458\) 2.54527 0.118932
\(459\) 1.19309i 0.0556887i
\(460\) 2.46784 3.50152i 0.115064 0.163259i
\(461\) 7.37800i 0.343628i −0.985129 0.171814i \(-0.945037\pi\)
0.985129 0.171814i \(-0.0549628\pi\)
\(462\) 6.86533 0.319404
\(463\) −6.16145 −0.286347 −0.143173 0.989698i \(-0.545731\pi\)
−0.143173 + 0.989698i \(0.545731\pi\)
\(464\) 5.08822i 0.236215i
\(465\) 4.42198 6.27415i 0.205064 0.290957i
\(466\) 13.9212i 0.644887i
\(467\) 5.37297 0.248631 0.124316 0.992243i \(-0.460326\pi\)
0.124316 + 0.992243i \(0.460326\pi\)
\(468\) −4.70887 −0.217668
\(469\) 5.28704 0.244133
\(470\) −3.47820 2.45141i −0.160437 0.113075i
\(471\) −14.2297 −0.655670
\(472\) 8.99577i 0.414064i
\(473\) −7.34231 −0.337600
\(474\) 1.00691 0.0462489
\(475\) −5.75326 + 2.05410i −0.263978 + 0.0942485i
\(476\) 1.49790i 0.0686562i
\(477\) 1.11671i 0.0511306i
\(478\) 28.8753i 1.32073i
\(479\) 21.5810i 0.986062i −0.870012 0.493031i \(-0.835889\pi\)
0.870012 0.493031i \(-0.164111\pi\)
\(480\) −1.82773 1.28817i −0.0834242 0.0587968i
\(481\) −21.5889 18.8239i −0.984370 0.858294i
\(482\) 6.84853i 0.311942i
\(483\) 2.40521 0.109441
\(484\) 18.9022 0.859191
\(485\) 21.4885 30.4891i 0.975742 1.38444i
\(486\) 1.00000i 0.0453609i
\(487\) −0.346315 −0.0156930 −0.00784652 0.999969i \(-0.502498\pi\)
−0.00784652 + 0.999969i \(0.502498\pi\)
\(488\) 6.21190i 0.281199i
\(489\) 0.455364i 0.0205923i
\(490\) −6.98676 + 9.91321i −0.315629 + 0.447833i
\(491\) 10.6278 0.479624 0.239812 0.970819i \(-0.422914\pi\)
0.239812 + 0.970819i \(0.422914\pi\)
\(492\) 4.46326i 0.201219i
\(493\) 6.07071i 0.273411i
\(494\) 5.75326i 0.258851i
\(495\) 7.04410 9.99458i 0.316609 0.449223i
\(496\) 3.43275i 0.154135i
\(497\) 15.5893i 0.699277i
\(498\) −0.754493 −0.0338096
\(499\) 12.0121i 0.537736i −0.963177 0.268868i \(-0.913350\pi\)
0.963177 0.268868i \(-0.0866496\pi\)
\(500\) −10.7723 2.99303i −0.481751 0.133852i
\(501\) 0.755752i 0.0337645i
\(502\) 18.7459i 0.836669i
\(503\) −4.15447 −0.185239 −0.0926194 0.995702i \(-0.529524\pi\)
−0.0926194 + 0.995702i \(0.529524\pi\)
\(504\) 1.25548i 0.0559235i
\(505\) 4.20220 5.96232i 0.186996 0.265320i
\(506\) 10.4760 0.465715
\(507\) 9.17350i 0.407410i
\(508\) 8.05067i 0.357191i
\(509\) −8.30223 −0.367990 −0.183995 0.982927i \(-0.558903\pi\)
−0.183995 + 0.982927i \(0.558903\pi\)
\(510\) −2.18065 1.53691i −0.0965609 0.0680554i
\(511\) −12.9107 −0.571134
\(512\) −1.00000 −0.0441942
\(513\) −1.22179 −0.0539434
\(514\) −17.3509 −0.765313
\(515\) 6.68987 9.49197i 0.294791 0.418266i
\(516\) 1.34271i 0.0591094i
\(517\) 10.4062i 0.457665i
\(518\) 5.01882 5.75604i 0.220514 0.252906i
\(519\) −4.41375 −0.193742
\(520\) −6.06585 + 8.60657i −0.266005 + 0.377423i
\(521\) 14.0992 0.617698 0.308849 0.951111i \(-0.400056\pi\)
0.308849 + 0.951111i \(0.400056\pi\)
\(522\) 5.08822i 0.222705i
\(523\) 29.0802 1.27159 0.635794 0.771858i \(-0.280673\pi\)
0.635794 + 0.771858i \(0.280673\pi\)
\(524\) 12.9999i 0.567905i
\(525\) −2.11074 5.91190i −0.0921201 0.258016i
\(526\) 31.3436i 1.36665i
\(527\) 4.09558i 0.178406i
\(528\) 5.46829i 0.237977i
\(529\) −19.3298 −0.840427
\(530\) 2.04105 + 1.43851i 0.0886574 + 0.0624851i
\(531\) 8.99577i 0.390383i
\(532\) −1.53393 −0.0665045
\(533\) −21.0169 −0.910344
\(534\) −11.4743 −0.496542
\(535\) −15.8273 11.1549i −0.684272 0.482270i
\(536\) 4.21117i 0.181895i
\(537\) −12.6883 −0.547540
\(538\) −20.8503 −0.898918
\(539\) −29.6587 −1.27749
\(540\) −1.82773 1.28817i −0.0786531 0.0554342i
\(541\) 10.2446i 0.440450i 0.975449 + 0.220225i \(0.0706791\pi\)
−0.975449 + 0.220225i \(0.929321\pi\)
\(542\) 0.977182 0.0419736
\(543\) 13.2444i 0.568370i
\(544\) −1.19309 −0.0511533
\(545\) 4.65481 + 3.28068i 0.199390 + 0.140529i
\(546\) −5.91190 −0.253006
\(547\) 36.6360 1.56644 0.783220 0.621744i \(-0.213576\pi\)
0.783220 + 0.621744i \(0.213576\pi\)
\(548\) 13.5487i 0.578772i
\(549\) 6.21190i 0.265117i
\(550\) −9.19339 25.7495i −0.392008 1.09796i
\(551\) −6.21674 −0.264842
\(552\) 1.91577i 0.0815406i
\(553\) 1.26415 0.0537573
\(554\) 28.0775 1.19290
\(555\) −3.23016 13.2123i −0.137113 0.560833i
\(556\) 15.3257 0.649955
\(557\) −3.19892 −0.135543 −0.0677714 0.997701i \(-0.521589\pi\)
−0.0677714 + 0.997701i \(0.521589\pi\)
\(558\) 3.43275i 0.145320i
\(559\) 6.32264 0.267419
\(560\) −2.29468 1.61728i −0.0969680 0.0683424i
\(561\) 6.52417i 0.275451i
\(562\) 20.9112i 0.882087i
\(563\) 43.0080 1.81257 0.906285 0.422668i \(-0.138906\pi\)
0.906285 + 0.422668i \(0.138906\pi\)
\(564\) −1.90301 −0.0801312
\(565\) −6.09024 + 8.64118i −0.256218 + 0.363537i
\(566\) 11.7273 0.492936
\(567\) 1.25548i 0.0527252i
\(568\) 12.4170 0.521007
\(569\) 19.8692i 0.832960i 0.909145 + 0.416480i \(0.136736\pi\)
−0.909145 + 0.416480i \(0.863264\pi\)
\(570\) −1.57388 + 2.23311i −0.0659225 + 0.0935346i
\(571\) −16.6100 −0.695105 −0.347553 0.937660i \(-0.612987\pi\)
−0.347553 + 0.937660i \(0.612987\pi\)
\(572\) −25.7495 −1.07664
\(573\) 7.03990 0.294096
\(574\) 5.60353i 0.233887i
\(575\) −3.22083 9.02113i −0.134318 0.376207i
\(576\) −1.00000 −0.0416667
\(577\) −36.4851 −1.51890 −0.759448 0.650568i \(-0.774531\pi\)
−0.759448 + 0.650568i \(0.774531\pi\)
\(578\) 15.5765 0.647898
\(579\) 0.635749i 0.0264208i
\(580\) −9.29991 6.55451i −0.386158 0.272161i
\(581\) −0.947251 −0.0392986
\(582\) 16.6814i 0.691465i
\(583\) 6.10649i 0.252905i
\(584\) 10.2834i 0.425532i
\(585\) −6.06585 + 8.60657i −0.250792 + 0.355838i
\(586\) 19.0944i 0.788781i
\(587\) 14.3652 0.592917 0.296458 0.955046i \(-0.404194\pi\)
0.296458 + 0.955046i \(0.404194\pi\)
\(588\) 5.42377i 0.223673i
\(589\) −4.19411 −0.172815
\(590\) 16.4419 + 11.5881i 0.676901 + 0.477075i
\(591\) −5.18937 −0.213462
\(592\) −4.58473 3.99753i −0.188431 0.164297i
\(593\) 19.6724i 0.807850i −0.914792 0.403925i \(-0.867646\pi\)
0.914792 0.403925i \(-0.132354\pi\)
\(594\) 5.46829i 0.224367i
\(595\) −2.73777 1.92956i −0.112237 0.0791041i
\(596\) 13.4684 0.551686
\(597\) −23.8852 −0.977557
\(598\) −9.02113 −0.368901
\(599\) 32.9039 1.34442 0.672208 0.740362i \(-0.265346\pi\)
0.672208 + 0.740362i \(0.265346\pi\)
\(600\) −4.70887 + 1.68122i −0.192239 + 0.0686355i
\(601\) 43.6508 1.78055 0.890276 0.455422i \(-0.150512\pi\)
0.890276 + 0.455422i \(0.150512\pi\)
\(602\) 1.68574i 0.0687057i
\(603\) 4.21117i 0.171492i
\(604\) −10.3930 −0.422883
\(605\) 24.3493 34.5482i 0.989940 1.40458i
\(606\) 3.26214i 0.132515i
\(607\) 15.4852 0.628523 0.314262 0.949336i \(-0.398243\pi\)
0.314262 + 0.949336i \(0.398243\pi\)
\(608\) 1.22179i 0.0495502i
\(609\) 6.38816i 0.258861i
\(610\) 11.3537 + 8.00200i 0.459698 + 0.323992i
\(611\) 8.96104i 0.362525i
\(612\) −1.19309 −0.0482278
\(613\) 47.5322i 1.91981i 0.280329 + 0.959904i \(0.409556\pi\)
−0.280329 + 0.959904i \(0.590444\pi\)
\(614\) 31.2854i 1.26258i
\(615\) −8.15764 5.74945i −0.328948 0.231840i
\(616\) 6.86533i 0.276612i
\(617\) 31.3888i 1.26367i −0.775105 0.631833i \(-0.782303\pi\)
0.775105 0.631833i \(-0.217697\pi\)
\(618\) 5.19330i 0.208905i
\(619\) 8.12905 0.326734 0.163367 0.986565i \(-0.447765\pi\)
0.163367 + 0.986565i \(0.447765\pi\)
\(620\) −6.27415 4.42198i −0.251976 0.177591i
\(621\) 1.91577i 0.0768772i
\(622\) 7.52409i 0.301688i
\(623\) −14.4058 −0.577155
\(624\) 4.70887i 0.188506i
\(625\) −19.3470 + 15.8333i −0.773880 + 0.633332i
\(626\) 0.0900227 0.00359803
\(627\) −6.68111 −0.266818
\(628\) 14.2297i 0.567827i
\(629\) −5.47000 4.76941i −0.218103 0.190169i
\(630\) −2.29468 1.61728i −0.0914224 0.0644338i
\(631\) 37.9315i 1.51003i −0.655709 0.755014i \(-0.727630\pi\)
0.655709 0.755014i \(-0.272370\pi\)
\(632\) 1.00691i 0.0400527i
\(633\) 26.6260i 1.05829i
\(634\) 7.86659i 0.312422i
\(635\) 14.7145 + 10.3707i 0.583926 + 0.411547i
\(636\) 1.11671 0.0442804
\(637\) 25.5399 1.01193
\(638\) 27.8239i 1.10156i
\(639\) 12.4170 0.491210
\(640\) −1.28817 + 1.82773i −0.0509195 + 0.0722475i
\(641\) −36.9793 −1.46059 −0.730296 0.683130i \(-0.760618\pi\)
−0.730296 + 0.683130i \(0.760618\pi\)
\(642\) −8.65950 −0.341763
\(643\) −8.44944 −0.333213 −0.166607 0.986023i \(-0.553281\pi\)
−0.166607 + 0.986023i \(0.553281\pi\)
\(644\) 2.40521i 0.0947786i
\(645\) 2.45411 + 1.72964i 0.0966305 + 0.0681045i
\(646\) 1.45771i 0.0573527i
\(647\) 4.22924 0.166269 0.0831343 0.996538i \(-0.473507\pi\)
0.0831343 + 0.996538i \(0.473507\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 49.1915i 1.93093i
\(650\) 7.91665 + 22.1735i 0.310517 + 0.869716i
\(651\) 4.30975i 0.168912i
\(652\) 0.455364 0.0178334
\(653\) 40.2219 1.57400 0.787002 0.616951i \(-0.211632\pi\)
0.787002 + 0.616951i \(0.211632\pi\)
\(654\) 2.54677 0.0995864
\(655\) −23.7604 16.7462i −0.928397 0.654327i
\(656\) −4.46326 −0.174261
\(657\) 10.2834i 0.401195i
\(658\) −2.38919 −0.0931404
\(659\) 20.4172 0.795341 0.397670 0.917528i \(-0.369819\pi\)
0.397670 + 0.917528i \(0.369819\pi\)
\(660\) −9.99458 7.04410i −0.389038 0.274191i
\(661\) 49.8075i 1.93729i −0.248454 0.968644i \(-0.579923\pi\)
0.248454 0.968644i \(-0.420077\pi\)
\(662\) 21.5849i 0.838919i
\(663\) 5.61812i 0.218190i
\(664\) 0.754493i 0.0292800i
\(665\) −1.97597 + 2.80362i −0.0766250 + 0.108720i
\(666\) −4.58473 3.99753i −0.177655 0.154901i
\(667\) 9.74786i 0.377439i
\(668\) 0.755752 0.0292409
\(669\) 20.0982 0.777042
\(670\) −7.69690 5.42472i −0.297357 0.209575i
\(671\) 33.9685i 1.31134i
\(672\) −1.25548 −0.0484312
\(673\) 30.7799i 1.18648i 0.805026 + 0.593239i \(0.202151\pi\)
−0.805026 + 0.593239i \(0.797849\pi\)
\(674\) 24.3782i 0.939013i
\(675\) −4.70887 + 1.68122i −0.181245 + 0.0647102i
\(676\) 9.17350 0.352827
\(677\) 36.8784i 1.41735i −0.705533 0.708677i \(-0.749292\pi\)
0.705533 0.708677i \(-0.250708\pi\)
\(678\) 4.72781i 0.181571i
\(679\) 20.9431i 0.803723i
\(680\) −1.53691 + 2.18065i −0.0589377 + 0.0836242i
\(681\) 15.1621i 0.581014i
\(682\) 18.7713i 0.718789i
\(683\) 22.1763 0.848552 0.424276 0.905533i \(-0.360529\pi\)
0.424276 + 0.905533i \(0.360529\pi\)
\(684\) 1.22179i 0.0467164i
\(685\) 24.7634 + 17.4531i 0.946161 + 0.666848i
\(686\) 15.5978i 0.595527i
\(687\) 2.54527i 0.0971080i
\(688\) 1.34271 0.0511902
\(689\) 5.25844i 0.200331i
\(690\) −3.50152 2.46784i −0.133301 0.0939492i
\(691\) 15.0935 0.574185 0.287093 0.957903i \(-0.407311\pi\)
0.287093 + 0.957903i \(0.407311\pi\)
\(692\) 4.41375i 0.167786i
\(693\) 6.86533i 0.260792i
\(694\) −25.4950 −0.967776
\(695\) 19.7422 28.0113i 0.748864 1.06253i
\(696\) −5.08822 −0.192868
\(697\) −5.32507 −0.201701
\(698\) −2.69761 −0.102106
\(699\) 13.9212 0.526548
\(700\) −5.91190 + 2.11074i −0.223449 + 0.0797784i
\(701\) 31.2390i 1.17988i 0.807447 + 0.589941i \(0.200849\pi\)
−0.807447 + 0.589941i \(0.799151\pi\)
\(702\) 4.70887i 0.177725i
\(703\) −4.88414 + 5.60159i −0.184209 + 0.211268i
\(704\) −5.46829 −0.206094
\(705\) −2.45141 + 3.47820i −0.0923253 + 0.130996i
\(706\) 21.7179 0.817362
\(707\) 4.09555i 0.154029i
\(708\) 8.99577 0.338082
\(709\) 23.2007i 0.871322i −0.900111 0.435661i \(-0.856515\pi\)
0.900111 0.435661i \(-0.143485\pi\)
\(710\) 15.9953 22.6950i 0.600293 0.851729i
\(711\) 1.00691i 0.0377621i
\(712\) 11.4743i 0.430018i
\(713\) 6.57636i 0.246287i
\(714\) −1.49790 −0.0560576
\(715\) −33.1698 + 47.0632i −1.24048 + 1.76006i
\(716\) 12.6883i 0.474184i
\(717\) −28.8753 −1.07837
\(718\) 20.3716 0.760260
\(719\) 41.3863 1.54345 0.771724 0.635958i \(-0.219395\pi\)
0.771724 + 0.635958i \(0.219395\pi\)
\(720\) −1.28817 + 1.82773i −0.0480074 + 0.0681156i
\(721\) 6.52009i 0.242821i
\(722\) −17.5072 −0.651552
\(723\) 6.84853 0.254699
\(724\) 13.2444 0.492223
\(725\) −23.9598 + 8.55441i −0.889844 + 0.317703i
\(726\) 18.9022i 0.701526i
\(727\) −8.02093 −0.297480 −0.148740 0.988876i \(-0.547522\pi\)
−0.148740 + 0.988876i \(0.547522\pi\)
\(728\) 5.91190i 0.219110i
\(729\) −1.00000 −0.0370370
\(730\) 18.7954 + 13.2469i 0.695649 + 0.490288i
\(731\) 1.60197 0.0592510
\(732\) 6.21190 0.229598
\(733\) 43.5044i 1.60687i 0.595391 + 0.803436i \(0.296997\pi\)
−0.595391 + 0.803436i \(0.703003\pi\)
\(734\) 31.0972i 1.14782i
\(735\) 9.91321 + 6.98676i 0.365654 + 0.257710i
\(736\) −1.91577 −0.0706163
\(737\) 23.0279i 0.848244i
\(738\) −4.46326 −0.164295
\(739\) −40.4960 −1.48967 −0.744834 0.667249i \(-0.767472\pi\)
−0.744834 + 0.667249i \(0.767472\pi\)
\(740\) −13.2123 + 3.23016i −0.485695 + 0.118743i
\(741\) 5.75326 0.211351
\(742\) 1.40201 0.0514692
\(743\) 33.7617i 1.23860i −0.785156 0.619298i \(-0.787417\pi\)
0.785156 0.619298i \(-0.212583\pi\)
\(744\) −3.43275 −0.125851
\(745\) 17.3496 24.6166i 0.635640 0.901882i
\(746\) 33.4131i 1.22334i
\(747\) 0.754493i 0.0276055i
\(748\) −6.52417 −0.238547
\(749\) −10.8718 −0.397248
\(750\) −2.99303 + 10.7723i −0.109290 + 0.393348i
\(751\) −16.9597 −0.618867 −0.309434 0.950921i \(-0.600139\pi\)
−0.309434 + 0.950921i \(0.600139\pi\)
\(752\) 1.90301i 0.0693956i
\(753\) 18.7459 0.683138
\(754\) 23.9598i 0.872564i
\(755\) −13.3879 + 18.9956i −0.487237 + 0.691319i
\(756\) −1.25548 −0.0456614
\(757\) 10.2892 0.373969 0.186984 0.982363i \(-0.440129\pi\)
0.186984 + 0.982363i \(0.440129\pi\)
\(758\) 24.6191 0.894204
\(759\) 10.4760i 0.380254i
\(760\) 2.23311 + 1.57388i 0.0810034 + 0.0570906i
\(761\) −30.3977 −1.10192 −0.550959 0.834533i \(-0.685738\pi\)
−0.550959 + 0.834533i \(0.685738\pi\)
\(762\) 8.05067 0.291645
\(763\) 3.19741 0.115754
\(764\) 7.03990i 0.254695i
\(765\) −1.53691 + 2.18065i −0.0555670 + 0.0788416i
\(766\) −17.5596 −0.634453
\(767\) 42.3600i 1.52953i
\(768\) 1.00000i 0.0360844i
\(769\) 46.4643i 1.67554i 0.546019 + 0.837772i \(0.316142\pi\)
−0.546019 + 0.837772i \(0.683858\pi\)
\(770\) −12.5480 8.84373i −0.452198 0.318706i
\(771\) 17.3509i 0.624876i
\(772\) −0.635749 −0.0228811
\(773\) 30.6420i 1.10212i −0.834467 0.551058i \(-0.814224\pi\)
0.834467 0.551058i \(-0.185776\pi\)
\(774\) 1.34271 0.0482626
\(775\) −16.1644 + 5.77121i −0.580642 + 0.207308i
\(776\) −16.6814 −0.598826
\(777\) −5.75604 5.01882i −0.206497 0.180049i
\(778\) 19.6417i 0.704190i
\(779\) 5.45317i 0.195380i
\(780\) 8.60657 + 6.06585i 0.308165 + 0.217192i
\(781\) 67.8999 2.42965
\(782\) −2.28569 −0.0817361
\(783\) −5.08822 −0.181838
\(784\) 5.42377 0.193706
\(785\) 26.0081 + 18.3303i 0.928270 + 0.654238i
\(786\) −12.9999 −0.463693
\(787\) 8.65409i 0.308485i 0.988033 + 0.154243i \(0.0492937\pi\)
−0.988033 + 0.154243i \(0.950706\pi\)
\(788\) 5.18937i 0.184864i
\(789\) −31.3436 −1.11586
\(790\) −1.84036 1.29707i −0.0654772 0.0461478i
\(791\) 5.93567i 0.211048i
\(792\) −5.46829 −0.194307
\(793\) 29.2511i 1.03874i
\(794\) 4.31480i 0.153127i
\(795\) 1.43851 2.04105i 0.0510188 0.0723884i
\(796\) 23.8852i 0.846589i
\(797\) −25.1436 −0.890634 −0.445317 0.895373i \(-0.646909\pi\)
−0.445317 + 0.895373i \(0.646909\pi\)
\(798\) 1.53393i 0.0543007i
\(799\) 2.27046i 0.0803232i
\(800\) 1.68122 + 4.70887i 0.0594401 + 0.166484i
\(801\) 11.4743i 0.405425i
\(802\) 9.64980i 0.340746i
\(803\) 56.2328i 1.98441i
\(804\) −4.21117 −0.148517
\(805\) −4.39609 3.09833i −0.154942 0.109202i
\(806\) 16.1644i 0.569367i
\(807\) 20.8503i 0.733964i
\(808\) −3.26214 −0.114762
\(809\) 54.4206i 1.91333i 0.291199 + 0.956663i \(0.405946\pi\)
−0.291199 + 0.956663i \(0.594054\pi\)
\(810\) −1.28817 + 1.82773i −0.0452618 + 0.0642200i
\(811\) 32.8378 1.15309 0.576546 0.817065i \(-0.304400\pi\)
0.576546 + 0.817065i \(0.304400\pi\)
\(812\) −6.38816 −0.224180
\(813\) 0.977182i 0.0342713i
\(814\) −25.0706 21.8596i −0.878726 0.766180i
\(815\) 0.586588 0.832284i 0.0205473 0.0291536i
\(816\) 1.19309i 0.0417665i
\(817\) 1.64051i 0.0573941i
\(818\) 25.5235i 0.892409i
\(819\) 5.91190i 0.206578i
\(820\) −5.74945 + 8.15764i −0.200779 + 0.284877i
\(821\) 25.1041 0.876138 0.438069 0.898941i \(-0.355663\pi\)
0.438069 + 0.898941i \(0.355663\pi\)
\(822\) 13.5487 0.472565
\(823\) 11.1202i 0.387627i 0.981038 + 0.193814i \(0.0620857\pi\)
−0.981038 + 0.193814i \(0.937914\pi\)
\(824\) −5.19330 −0.180917
\(825\) −25.7495 + 9.19339i −0.896482 + 0.320073i
\(826\) 11.2940 0.392969
\(827\) 7.01483 0.243930 0.121965 0.992534i \(-0.461080\pi\)
0.121965 + 0.992534i \(0.461080\pi\)
\(828\) −1.91577 −0.0665776
\(829\) 12.5028i 0.434240i −0.976145 0.217120i \(-0.930334\pi\)
0.976145 0.217120i \(-0.0696662\pi\)
\(830\) 1.37901 + 0.971918i 0.0478662 + 0.0337358i
\(831\) 28.0775i 0.973997i
\(832\) 4.70887 0.163251
\(833\) 6.47105 0.224209
\(834\) 15.3257i 0.530686i
\(835\) 0.973540 1.38131i 0.0336907 0.0478023i
\(836\) 6.68111i 0.231071i
\(837\) −3.43275 −0.118653
\(838\) 22.0969 0.763324
\(839\) 44.6267 1.54069 0.770343 0.637630i \(-0.220085\pi\)
0.770343 + 0.637630i \(0.220085\pi\)
\(840\) −1.61728 + 2.29468i −0.0558013 + 0.0791741i
\(841\) 3.11004 0.107243
\(842\) 8.20101i 0.282626i
\(843\) −20.9112 −0.720221
\(844\) −26.6260 −0.916505
\(845\) 11.8171 16.7667i 0.406519 0.576793i
\(846\) 1.90301i 0.0654268i
\(847\) 23.7313i 0.815418i
\(848\) 1.11671i 0.0383479i
\(849\) 11.7273i 0.402480i
\(850\) 2.00585 + 5.61812i 0.0688000 + 0.192700i
\(851\) −8.78330 7.65835i −0.301088 0.262525i
\(852\) 12.4170i 0.425401i
\(853\) 3.59757 0.123178 0.0615892 0.998102i \(-0.480383\pi\)
0.0615892 + 0.998102i \(0.480383\pi\)
\(854\) 7.79891 0.266873
\(855\) 2.23311 + 1.57388i 0.0763707 + 0.0538255i
\(856\) 8.65950i 0.295976i
\(857\) 7.66263 0.261750 0.130875 0.991399i \(-0.458221\pi\)
0.130875 + 0.991399i \(0.458221\pi\)
\(858\) 25.7495i 0.879073i
\(859\) 56.3900i 1.92400i −0.273046 0.962001i \(-0.588031\pi\)
0.273046 0.962001i \(-0.411969\pi\)
\(860\) 1.72964 2.45411i 0.0589802 0.0836844i
\(861\) −5.60353 −0.190968
\(862\) 9.83076i 0.334837i
\(863\) 12.7800i 0.435037i 0.976056 + 0.217518i \(0.0697962\pi\)
−0.976056 + 0.217518i \(0.930204\pi\)
\(864\) 1.00000i 0.0340207i
\(865\) 8.06716 + 5.68568i 0.274292 + 0.193319i
\(866\) 1.61024i 0.0547182i
\(867\) 15.5765i 0.529007i
\(868\) −4.30975 −0.146282
\(869\) 5.50607i 0.186781i
\(870\) −6.55451 + 9.29991i −0.222219 + 0.315296i
\(871\) 19.8299i 0.671910i
\(872\) 2.54677i 0.0862444i
\(873\) −16.6814 −0.564579
\(874\) 2.34067i 0.0791744i
\(875\) −3.75768 + 13.5244i −0.127033 + 0.457207i
\(876\) 10.2834 0.347445
\(877\) 40.4607i 1.36626i −0.730297 0.683130i \(-0.760618\pi\)
0.730297 0.683130i \(-0.239382\pi\)
\(878\) 32.2443i 1.08819i
\(879\) −19.0944 −0.644037
\(880\) −7.04410 + 9.99458i −0.237457 + 0.336917i
\(881\) −48.2664 −1.62614 −0.813069 0.582168i \(-0.802205\pi\)
−0.813069 + 0.582168i \(0.802205\pi\)
\(882\) 5.42377 0.182628
\(883\) −7.33442 −0.246823 −0.123411 0.992356i \(-0.539383\pi\)
−0.123411 + 0.992356i \(0.539383\pi\)
\(884\) 5.61812 0.188958
\(885\) 11.5881 16.4419i 0.389530 0.552687i
\(886\) 19.0730i 0.640770i
\(887\) 28.5353i 0.958120i 0.877782 + 0.479060i \(0.159022\pi\)
−0.877782 + 0.479060i \(0.840978\pi\)
\(888\) −3.99753 + 4.58473i −0.134148 + 0.153854i
\(889\) 10.1075 0.338993
\(890\) 20.9720 + 14.7809i 0.702983 + 0.495457i
\(891\) −5.46829 −0.183195
\(892\) 20.0982i 0.672938i
\(893\) 2.32508 0.0778059
\(894\) 13.4684i 0.450450i
\(895\) 23.1908 + 16.3447i 0.775184 + 0.546344i
\(896\) 1.25548i 0.0419426i
\(897\) 9.02113i 0.301207i
\(898\) 30.6914i 1.02418i
\(899\) −17.4666 −0.582543
\(900\) 1.68122 + 4.70887i 0.0560406 + 0.156962i
\(901\) 1.33233i 0.0443865i
\(902\) −24.4064 −0.812643
\(903\) 1.68574 0.0560980
\(904\) 4.72781 0.157245
\(905\) 17.0610 24.2072i 0.567128 0.804673i
\(906\) 10.3930i 0.345283i
\(907\) −31.6207 −1.04995 −0.524974 0.851118i \(-0.675925\pi\)
−0.524974 + 0.851118i \(0.675925\pi\)
\(908\) 15.1621 0.503173
\(909\) −3.26214 −0.108198
\(910\) 10.8054 + 7.61555i 0.358195 + 0.252453i
\(911\) 2.67057i 0.0884800i −0.999021 0.0442400i \(-0.985913\pi\)
0.999021 0.0442400i \(-0.0140866\pi\)
\(912\) 1.22179 0.0404575
\(913\) 4.12579i 0.136544i
\(914\) −22.4560 −0.742777
\(915\) 8.00200 11.3537i 0.264538 0.375342i
\(916\) −2.54527 −0.0840980
\(917\) −16.3212 −0.538972
\(918\) 1.19309i 0.0393779i
\(919\) 40.0514i 1.32117i 0.750750 + 0.660587i \(0.229692\pi\)
−0.750750 + 0.660587i \(0.770308\pi\)
\(920\) −2.46784 + 3.50152i −0.0813624 + 0.115442i
\(921\) −31.2854 −1.03089
\(922\) 7.37800i 0.242981i
\(923\) −58.4703 −1.92457
\(924\) −6.86533 −0.225853
\(925\) −11.1159 + 28.3097i −0.365489 + 0.930816i
\(926\) 6.16145 0.202478
\(927\) −5.19330 −0.170570
\(928\) 5.08822i 0.167029i
\(929\) 47.8279 1.56918 0.784592 0.620013i \(-0.212873\pi\)
0.784592 + 0.620013i \(0.212873\pi\)
\(930\) −4.42198 + 6.27415i −0.145002 + 0.205738i
\(931\) 6.62671i 0.217182i
\(932\) 13.9212i 0.456004i
\(933\) 7.52409 0.246328
\(934\) −5.37297 −0.175809
\(935\) −8.40426 + 11.9244i −0.274849 + 0.389971i
\(936\) 4.70887 0.153914
\(937\) 44.7707i 1.46260i 0.682058 + 0.731298i \(0.261085\pi\)
−0.682058 + 0.731298i \(0.738915\pi\)
\(938\) −5.28704 −0.172628
\(939\) 0.0900227i 0.00293778i
\(940\) 3.47820 + 2.45141i 0.113446 + 0.0799561i
\(941\) 38.1052 1.24219 0.621097 0.783734i \(-0.286687\pi\)
0.621097 + 0.783734i \(0.286687\pi\)
\(942\) 14.2297 0.463629
\(943\) −8.55058 −0.278445
\(944\) 8.99577i 0.292787i
\(945\) −1.61728 + 2.29468i −0.0526100 + 0.0746460i
\(946\) 7.34231 0.238719
\(947\) 53.7661 1.74716 0.873582 0.486678i \(-0.161791\pi\)
0.873582 + 0.486678i \(0.161791\pi\)
\(948\) −1.00691 −0.0327029
\(949\) 48.4234i 1.57189i
\(950\) 5.75326 2.05410i 0.186660 0.0666438i
\(951\) −7.86659 −0.255092
\(952\) 1.49790i 0.0485473i
\(953\) 12.7882i 0.414252i 0.978314 + 0.207126i \(0.0664109\pi\)
−0.978314 + 0.207126i \(0.933589\pi\)
\(954\) 1.11671i 0.0361548i
\(955\) −12.8671 9.06861i −0.416368 0.293453i
\(956\) 28.8753i 0.933895i
\(957\) −27.8239 −0.899417
\(958\) 21.5810i 0.697251i
\(959\) 17.0101 0.549286
\(960\) 1.82773 + 1.28817i 0.0589898 + 0.0415756i
\(961\) 19.2162 0.619878
\(962\) 21.5889 + 18.8239i 0.696055 + 0.606906i
\(963\) 8.65950i 0.279049i
\(964\) 6.84853i 0.220576i
\(965\) −0.818954 + 1.16198i −0.0263631 + 0.0374054i
\(966\) −2.40521 −0.0773864
\(967\) −49.4979 −1.59175 −0.795873 0.605463i \(-0.792988\pi\)
−0.795873 + 0.605463i \(0.792988\pi\)
\(968\) −18.9022 −0.607540
\(969\) 1.45771 0.0468283
\(970\) −21.4885 + 30.4891i −0.689954 + 0.978946i
\(971\) −22.7751 −0.730887 −0.365444 0.930834i \(-0.619083\pi\)
−0.365444 + 0.930834i \(0.619083\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 19.2411i 0.616843i
\(974\) 0.346315 0.0110967
\(975\) 22.1735 7.91665i 0.710120 0.253536i
\(976\) 6.21190i 0.198838i
\(977\) 7.08386 0.226633 0.113316 0.993559i \(-0.463853\pi\)
0.113316 + 0.993559i \(0.463853\pi\)
\(978\) 0.455364i 0.0145609i
\(979\) 62.7449i 2.00534i
\(980\) 6.98676 9.91321i 0.223184 0.316666i
\(981\) 2.54677i 0.0813120i
\(982\) −10.6278 −0.339146
\(983\) 50.8277i 1.62115i 0.585634 + 0.810576i \(0.300846\pi\)
−0.585634 + 0.810576i \(0.699154\pi\)
\(984\) 4.46326i 0.142283i
\(985\) 9.48478 + 6.68481i 0.302210 + 0.212996i
\(986\) 6.07071i 0.193331i
\(987\) 2.38919i 0.0760488i
\(988\) 5.75326i 0.183036i
\(989\) 2.57232 0.0817949
\(990\) −7.04410 + 9.99458i −0.223876 + 0.317648i
\(991\) 42.8852i 1.36229i −0.732146 0.681147i \(-0.761481\pi\)
0.732146 0.681147i \(-0.238519\pi\)
\(992\) 3.43275i 0.108990i
\(993\) −21.5849 −0.684975
\(994\) 15.5893i 0.494464i
\(995\) 43.6558 + 30.7683i 1.38398 + 0.975421i
\(996\) 0.754493 0.0239070
\(997\) 6.15244 0.194850 0.0974248 0.995243i \(-0.468939\pi\)
0.0974248 + 0.995243i \(0.468939\pi\)
\(998\) 12.0121i 0.380237i
\(999\) −3.99753 + 4.58473i −0.126476 + 0.145055i
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 1110.2.e.c.739.14 yes 16
3.2 odd 2 3330.2.e.f.739.6 16
5.4 even 2 1110.2.e.d.739.3 yes 16
15.14 odd 2 3330.2.e.e.739.12 16
37.36 even 2 1110.2.e.d.739.11 yes 16
111.110 odd 2 3330.2.e.e.739.11 16
185.184 even 2 inner 1110.2.e.c.739.6 16
555.554 odd 2 3330.2.e.f.739.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.e.c.739.6 16 185.184 even 2 inner
1110.2.e.c.739.14 yes 16 1.1 even 1 trivial
1110.2.e.d.739.3 yes 16 5.4 even 2
1110.2.e.d.739.11 yes 16 37.36 even 2
3330.2.e.e.739.11 16 111.110 odd 2
3330.2.e.e.739.12 16 15.14 odd 2
3330.2.e.f.739.5 16 555.554 odd 2
3330.2.e.f.739.6 16 3.2 odd 2