Properties

Label 1134.2.h.t.109.1
Level $1134$
Weight $2$
Character 1134.109
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
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] = [1134,2,Mod(109,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(1.32288 + 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 1134.109
Dual form 1134.2.h.t.541.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.64575 q^{5} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.64575 q^{5} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.822876 + 1.42526i) q^{10} +1.64575 q^{11} +(-0.322876 + 0.559237i) q^{13} -2.64575 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.822876 + 1.42526i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(0.822876 + 1.42526i) q^{20} +(0.822876 - 1.42526i) q^{22} -9.29150 q^{23} -2.29150 q^{25} +(0.322876 + 0.559237i) q^{26} +(-1.32288 + 2.29129i) q^{28} +(3.82288 + 6.62141i) q^{29} +(-0.322876 - 0.559237i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.822876 + 1.42526i) q^{34} +(2.17712 + 3.77089i) q^{35} +(-1.96863 - 3.40976i) q^{37} -2.00000 q^{38} +1.64575 q^{40} +(-2.46863 + 4.27579i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(-0.822876 - 1.42526i) q^{44} +(-4.64575 + 8.04668i) q^{46} +(-5.46863 + 9.47194i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-1.14575 + 1.98450i) q^{50} +0.645751 q^{52} +(3.00000 - 5.19615i) q^{53} -2.70850 q^{55} +(1.32288 + 2.29129i) q^{56} +7.64575 q^{58} +(6.82288 + 11.8176i) q^{59} +(-6.32288 + 10.9515i) q^{61} -0.645751 q^{62} +1.00000 q^{64} +(0.531373 - 0.920365i) q^{65} +(-4.14575 - 7.18065i) q^{67} +1.64575 q^{68} +4.35425 q^{70} -10.3542 q^{71} +(5.29150 - 9.16515i) q^{73} -3.93725 q^{74} +(-1.00000 + 1.73205i) q^{76} +(-2.17712 - 3.77089i) q^{77} +(7.61438 - 13.1885i) q^{79} +(0.822876 - 1.42526i) q^{80} +(2.46863 + 4.27579i) q^{82} +(-1.35425 - 2.34563i) q^{83} +(1.35425 - 2.34563i) q^{85} -5.00000 q^{86} -1.64575 q^{88} +(-5.46863 - 9.47194i) q^{89} +1.70850 q^{91} +(4.64575 + 8.04668i) q^{92} +(5.46863 + 9.47194i) q^{94} +(1.64575 + 2.85052i) q^{95} +(3.79150 + 6.56708i) q^{97} +(3.50000 + 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8} + 2 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{16} + 2 q^{17} - 4 q^{19} - 2 q^{20} - 2 q^{22} - 16 q^{23} + 12 q^{25} - 4 q^{26} + 10 q^{29} + 4 q^{31} + 2 q^{32} - 2 q^{34} + 14 q^{35} + 8 q^{37} - 8 q^{38} - 4 q^{40} + 6 q^{41} - 10 q^{43} + 2 q^{44} - 8 q^{46} - 6 q^{47} - 14 q^{49} + 6 q^{50} - 8 q^{52} + 12 q^{53} - 32 q^{55} + 20 q^{58} + 22 q^{59} - 20 q^{61} + 8 q^{62} + 4 q^{64} + 18 q^{65} - 6 q^{67} - 4 q^{68} + 28 q^{70} - 52 q^{71} + 16 q^{74} - 4 q^{76} - 14 q^{77} + 4 q^{79} - 2 q^{80} - 6 q^{82} - 16 q^{83} + 16 q^{85} - 20 q^{86} + 4 q^{88} - 6 q^{89} + 28 q^{91} + 8 q^{92} + 6 q^{94} - 4 q^{95} - 6 q^{97} + 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.64575 −0.736002 −0.368001 0.929825i \(-0.619958\pi\)
−0.368001 + 0.929825i \(0.619958\pi\)
\(6\) 0 0
\(7\) −1.32288 2.29129i −0.500000 0.866025i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.822876 + 1.42526i −0.260216 + 0.450708i
\(11\) 1.64575 0.496213 0.248106 0.968733i \(-0.420192\pi\)
0.248106 + 0.968733i \(0.420192\pi\)
\(12\) 0 0
\(13\) −0.322876 + 0.559237i −0.0895496 + 0.155104i −0.907321 0.420439i \(-0.861876\pi\)
0.817771 + 0.575543i \(0.195209\pi\)
\(14\) −2.64575 −0.707107
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.822876 + 1.42526i −0.199577 + 0.345677i −0.948391 0.317103i \(-0.897290\pi\)
0.748815 + 0.662780i \(0.230623\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0.822876 + 1.42526i 0.184001 + 0.318698i
\(21\) 0 0
\(22\) 0.822876 1.42526i 0.175438 0.303867i
\(23\) −9.29150 −1.93741 −0.968706 0.248211i \(-0.920158\pi\)
−0.968706 + 0.248211i \(0.920158\pi\)
\(24\) 0 0
\(25\) −2.29150 −0.458301
\(26\) 0.322876 + 0.559237i 0.0633211 + 0.109675i
\(27\) 0 0
\(28\) −1.32288 + 2.29129i −0.250000 + 0.433013i
\(29\) 3.82288 + 6.62141i 0.709890 + 1.22957i 0.964898 + 0.262627i \(0.0845888\pi\)
−0.255007 + 0.966939i \(0.582078\pi\)
\(30\) 0 0
\(31\) −0.322876 0.559237i −0.0579902 0.100442i 0.835573 0.549380i \(-0.185136\pi\)
−0.893563 + 0.448938i \(0.851803\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 0.822876 + 1.42526i 0.141122 + 0.244430i
\(35\) 2.17712 + 3.77089i 0.368001 + 0.637397i
\(36\) 0 0
\(37\) −1.96863 3.40976i −0.323640 0.560561i 0.657596 0.753371i \(-0.271573\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) −2.00000 −0.324443
\(39\) 0 0
\(40\) 1.64575 0.260216
\(41\) −2.46863 + 4.27579i −0.385535 + 0.667766i −0.991843 0.127464i \(-0.959316\pi\)
0.606308 + 0.795230i \(0.292650\pi\)
\(42\) 0 0
\(43\) −2.50000 4.33013i −0.381246 0.660338i 0.609994 0.792406i \(-0.291172\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) −0.822876 1.42526i −0.124053 0.214866i
\(45\) 0 0
\(46\) −4.64575 + 8.04668i −0.684979 + 1.18642i
\(47\) −5.46863 + 9.47194i −0.797681 + 1.38162i 0.123441 + 0.992352i \(0.460607\pi\)
−0.921123 + 0.389273i \(0.872726\pi\)
\(48\) 0 0
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) −1.14575 + 1.98450i −0.162034 + 0.280651i
\(51\) 0 0
\(52\) 0.645751 0.0895496
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) −2.70850 −0.365214
\(56\) 1.32288 + 2.29129i 0.176777 + 0.306186i
\(57\) 0 0
\(58\) 7.64575 1.00394
\(59\) 6.82288 + 11.8176i 0.888263 + 1.53852i 0.841928 + 0.539590i \(0.181421\pi\)
0.0463350 + 0.998926i \(0.485246\pi\)
\(60\) 0 0
\(61\) −6.32288 + 10.9515i −0.809561 + 1.40220i 0.103607 + 0.994618i \(0.466962\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(62\) −0.645751 −0.0820105
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.531373 0.920365i 0.0659087 0.114157i
\(66\) 0 0
\(67\) −4.14575 7.18065i −0.506484 0.877256i −0.999972 0.00750349i \(-0.997612\pi\)
0.493488 0.869753i \(-0.335722\pi\)
\(68\) 1.64575 0.199577
\(69\) 0 0
\(70\) 4.35425 0.520432
\(71\) −10.3542 −1.22882 −0.614412 0.788986i \(-0.710607\pi\)
−0.614412 + 0.788986i \(0.710607\pi\)
\(72\) 0 0
\(73\) 5.29150 9.16515i 0.619324 1.07270i −0.370286 0.928918i \(-0.620740\pi\)
0.989609 0.143782i \(-0.0459264\pi\)
\(74\) −3.93725 −0.457696
\(75\) 0 0
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) −2.17712 3.77089i −0.248106 0.429733i
\(78\) 0 0
\(79\) 7.61438 13.1885i 0.856684 1.48382i −0.0183890 0.999831i \(-0.505854\pi\)
0.875073 0.483990i \(-0.160813\pi\)
\(80\) 0.822876 1.42526i 0.0920003 0.159349i
\(81\) 0 0
\(82\) 2.46863 + 4.27579i 0.272614 + 0.472182i
\(83\) −1.35425 2.34563i −0.148648 0.257466i 0.782080 0.623178i \(-0.214159\pi\)
−0.930728 + 0.365712i \(0.880826\pi\)
\(84\) 0 0
\(85\) 1.35425 2.34563i 0.146889 0.254419i
\(86\) −5.00000 −0.539164
\(87\) 0 0
\(88\) −1.64575 −0.175438
\(89\) −5.46863 9.47194i −0.579673 1.00402i −0.995517 0.0945873i \(-0.969847\pi\)
0.415843 0.909436i \(-0.363486\pi\)
\(90\) 0 0
\(91\) 1.70850 0.179099
\(92\) 4.64575 + 8.04668i 0.484353 + 0.838924i
\(93\) 0 0
\(94\) 5.46863 + 9.47194i 0.564046 + 0.976956i
\(95\) 1.64575 + 2.85052i 0.168851 + 0.292458i
\(96\) 0 0
\(97\) 3.79150 + 6.56708i 0.384969 + 0.666785i 0.991765 0.128072i \(-0.0408789\pi\)
−0.606796 + 0.794858i \(0.707546\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) 0 0
\(100\) 1.14575 + 1.98450i 0.114575 + 0.198450i
\(101\) −13.6458 −1.35780 −0.678902 0.734229i \(-0.737544\pi\)
−0.678902 + 0.734229i \(0.737544\pi\)
\(102\) 0 0
\(103\) −11.9373 −1.17621 −0.588106 0.808784i \(-0.700126\pi\)
−0.588106 + 0.808784i \(0.700126\pi\)
\(104\) 0.322876 0.559237i 0.0316606 0.0548377i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 0 0
\(109\) 4.32288 7.48744i 0.414056 0.717167i −0.581272 0.813709i \(-0.697445\pi\)
0.995329 + 0.0965423i \(0.0307783\pi\)
\(110\) −1.35425 + 2.34563i −0.129123 + 0.223647i
\(111\) 0 0
\(112\) 2.64575 0.250000
\(113\) 3.82288 6.62141i 0.359626 0.622890i −0.628272 0.777993i \(-0.716238\pi\)
0.987898 + 0.155103i \(0.0495710\pi\)
\(114\) 0 0
\(115\) 15.2915 1.42594
\(116\) 3.82288 6.62141i 0.354945 0.614783i
\(117\) 0 0
\(118\) 13.6458 1.25619
\(119\) 4.35425 0.399153
\(120\) 0 0
\(121\) −8.29150 −0.753773
\(122\) 6.32288 + 10.9515i 0.572446 + 0.991506i
\(123\) 0 0
\(124\) −0.322876 + 0.559237i −0.0289951 + 0.0502210i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 6.64575 0.589715 0.294858 0.955541i \(-0.404728\pi\)
0.294858 + 0.955541i \(0.404728\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −0.531373 0.920365i −0.0466045 0.0807214i
\(131\) −6.58301 −0.575160 −0.287580 0.957757i \(-0.592851\pi\)
−0.287580 + 0.957757i \(0.592851\pi\)
\(132\) 0 0
\(133\) −2.64575 + 4.58258i −0.229416 + 0.397360i
\(134\) −8.29150 −0.716277
\(135\) 0 0
\(136\) 0.822876 1.42526i 0.0705610 0.122215i
\(137\) 9.29150 0.793827 0.396913 0.917856i \(-0.370081\pi\)
0.396913 + 0.917856i \(0.370081\pi\)
\(138\) 0 0
\(139\) 9.79150 16.9594i 0.830504 1.43848i −0.0671344 0.997744i \(-0.521386\pi\)
0.897639 0.440732i \(-0.145281\pi\)
\(140\) 2.17712 3.77089i 0.184001 0.318698i
\(141\) 0 0
\(142\) −5.17712 + 8.96704i −0.434455 + 0.752497i
\(143\) −0.531373 + 0.920365i −0.0444356 + 0.0769648i
\(144\) 0 0
\(145\) −6.29150 10.8972i −0.522481 0.904963i
\(146\) −5.29150 9.16515i −0.437928 0.758513i
\(147\) 0 0
\(148\) −1.96863 + 3.40976i −0.161820 + 0.280281i
\(149\) −7.06275 −0.578603 −0.289301 0.957238i \(-0.593423\pi\)
−0.289301 + 0.957238i \(0.593423\pi\)
\(150\) 0 0
\(151\) 7.22876 0.588268 0.294134 0.955764i \(-0.404969\pi\)
0.294134 + 0.955764i \(0.404969\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) 0 0
\(154\) −4.35425 −0.350875
\(155\) 0.531373 + 0.920365i 0.0426809 + 0.0739255i
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) −7.61438 13.1885i −0.605767 1.04922i
\(159\) 0 0
\(160\) −0.822876 1.42526i −0.0650540 0.112677i
\(161\) 12.2915 + 21.2895i 0.968706 + 1.67785i
\(162\) 0 0
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) 4.93725 0.385535
\(165\) 0 0
\(166\) −2.70850 −0.210220
\(167\) 6.29150 10.8972i 0.486851 0.843251i −0.513035 0.858368i \(-0.671479\pi\)
0.999886 + 0.0151171i \(0.00481210\pi\)
\(168\) 0 0
\(169\) 6.29150 + 10.8972i 0.483962 + 0.838246i
\(170\) −1.35425 2.34563i −0.103866 0.179901i
\(171\) 0 0
\(172\) −2.50000 + 4.33013i −0.190623 + 0.330169i
\(173\) 3.29150 5.70105i 0.250248 0.433443i −0.713346 0.700812i \(-0.752821\pi\)
0.963594 + 0.267369i \(0.0861544\pi\)
\(174\) 0 0
\(175\) 3.03137 + 5.25049i 0.229150 + 0.396900i
\(176\) −0.822876 + 1.42526i −0.0620266 + 0.107433i
\(177\) 0 0
\(178\) −10.9373 −0.819782
\(179\) 0.531373 0.920365i 0.0397167 0.0687913i −0.845484 0.534001i \(-0.820688\pi\)
0.885200 + 0.465210i \(0.154021\pi\)
\(180\) 0 0
\(181\) −13.2915 −0.987950 −0.493975 0.869476i \(-0.664457\pi\)
−0.493975 + 0.869476i \(0.664457\pi\)
\(182\) 0.854249 1.47960i 0.0633211 0.109675i
\(183\) 0 0
\(184\) 9.29150 0.684979
\(185\) 3.23987 + 5.61162i 0.238200 + 0.412575i
\(186\) 0 0
\(187\) −1.35425 + 2.34563i −0.0990325 + 0.171529i
\(188\) 10.9373 0.797681
\(189\) 0 0
\(190\) 3.29150 0.238791
\(191\) 13.4059 23.2197i 0.970015 1.68012i 0.274526 0.961580i \(-0.411479\pi\)
0.695489 0.718537i \(-0.255188\pi\)
\(192\) 0 0
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) 7.58301 0.544428
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) −15.2915 −1.08947 −0.544737 0.838607i \(-0.683371\pi\)
−0.544737 + 0.838607i \(0.683371\pi\)
\(198\) 0 0
\(199\) −10.9686 + 18.9982i −0.777545 + 1.34675i 0.155807 + 0.987787i \(0.450202\pi\)
−0.933353 + 0.358961i \(0.883131\pi\)
\(200\) 2.29150 0.162034
\(201\) 0 0
\(202\) −6.82288 + 11.8176i −0.480056 + 0.831481i
\(203\) 10.1144 17.5186i 0.709890 1.22957i
\(204\) 0 0
\(205\) 4.06275 7.03688i 0.283754 0.491477i
\(206\) −5.96863 + 10.3380i −0.415854 + 0.720280i
\(207\) 0 0
\(208\) −0.322876 0.559237i −0.0223874 0.0387761i
\(209\) −1.64575 2.85052i −0.113839 0.197175i
\(210\) 0 0
\(211\) 8.43725 14.6138i 0.580845 1.00605i −0.414535 0.910033i \(-0.636056\pi\)
0.995380 0.0960188i \(-0.0306109\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) −6.00000 −0.410152
\(215\) 4.11438 + 7.12631i 0.280598 + 0.486010i
\(216\) 0 0
\(217\) −0.854249 + 1.47960i −0.0579902 + 0.100442i
\(218\) −4.32288 7.48744i −0.292782 0.507113i
\(219\) 0 0
\(220\) 1.35425 + 2.34563i 0.0913034 + 0.158142i
\(221\) −0.531373 0.920365i −0.0357440 0.0619105i
\(222\) 0 0
\(223\) −8.93725 15.4798i −0.598483 1.03660i −0.993045 0.117733i \(-0.962437\pi\)
0.394562 0.918869i \(-0.370896\pi\)
\(224\) 1.32288 2.29129i 0.0883883 0.153093i
\(225\) 0 0
\(226\) −3.82288 6.62141i −0.254294 0.440450i
\(227\) −6.00000 −0.398234 −0.199117 0.979976i \(-0.563807\pi\)
−0.199117 + 0.979976i \(0.563807\pi\)
\(228\) 0 0
\(229\) −14.6458 −0.967818 −0.483909 0.875118i \(-0.660784\pi\)
−0.483909 + 0.875118i \(0.660784\pi\)
\(230\) 7.64575 13.2428i 0.504146 0.873206i
\(231\) 0 0
\(232\) −3.82288 6.62141i −0.250984 0.434717i
\(233\) −4.35425 7.54178i −0.285256 0.494078i 0.687415 0.726265i \(-0.258745\pi\)
−0.972671 + 0.232186i \(0.925412\pi\)
\(234\) 0 0
\(235\) 9.00000 15.5885i 0.587095 1.01688i
\(236\) 6.82288 11.8176i 0.444131 0.769258i
\(237\) 0 0
\(238\) 2.17712 3.77089i 0.141122 0.244430i
\(239\) 2.46863 4.27579i 0.159682 0.276578i −0.775072 0.631873i \(-0.782286\pi\)
0.934754 + 0.355295i \(0.115620\pi\)
\(240\) 0 0
\(241\) 5.00000 0.322078 0.161039 0.986948i \(-0.448515\pi\)
0.161039 + 0.986948i \(0.448515\pi\)
\(242\) −4.14575 + 7.18065i −0.266499 + 0.461590i
\(243\) 0 0
\(244\) 12.6458 0.809561
\(245\) 5.76013 9.97684i 0.368001 0.637397i
\(246\) 0 0
\(247\) 1.29150 0.0821763
\(248\) 0.322876 + 0.559237i 0.0205026 + 0.0355116i
\(249\) 0 0
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 0 0
\(253\) −15.2915 −0.961369
\(254\) 3.32288 5.75539i 0.208496 0.361125i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.8745 0.990225 0.495112 0.868829i \(-0.335127\pi\)
0.495112 + 0.868829i \(0.335127\pi\)
\(258\) 0 0
\(259\) −5.20850 + 9.02138i −0.323640 + 0.560561i
\(260\) −1.06275 −0.0659087
\(261\) 0 0
\(262\) −3.29150 + 5.70105i −0.203350 + 0.352212i
\(263\) −10.9373 −0.674420 −0.337210 0.941429i \(-0.609483\pi\)
−0.337210 + 0.941429i \(0.609483\pi\)
\(264\) 0 0
\(265\) −4.93725 + 8.55157i −0.303293 + 0.525319i
\(266\) 2.64575 + 4.58258i 0.162221 + 0.280976i
\(267\) 0 0
\(268\) −4.14575 + 7.18065i −0.253242 + 0.438628i
\(269\) −13.6458 + 23.6351i −0.831996 + 1.44106i 0.0644567 + 0.997921i \(0.479469\pi\)
−0.896453 + 0.443139i \(0.853865\pi\)
\(270\) 0 0
\(271\) 10.6144 + 18.3846i 0.644778 + 1.11679i 0.984353 + 0.176209i \(0.0563833\pi\)
−0.339575 + 0.940579i \(0.610283\pi\)
\(272\) −0.822876 1.42526i −0.0498942 0.0864192i
\(273\) 0 0
\(274\) 4.64575 8.04668i 0.280660 0.486118i
\(275\) −3.77124 −0.227415
\(276\) 0 0
\(277\) −17.9373 −1.07775 −0.538873 0.842387i \(-0.681150\pi\)
−0.538873 + 0.842387i \(0.681150\pi\)
\(278\) −9.79150 16.9594i −0.587255 1.01716i
\(279\) 0 0
\(280\) −2.17712 3.77089i −0.130108 0.225354i
\(281\) −8.76013 15.1730i −0.522586 0.905145i −0.999655 0.0262789i \(-0.991634\pi\)
0.477069 0.878866i \(-0.341699\pi\)
\(282\) 0 0
\(283\) −4.14575 7.18065i −0.246439 0.426845i 0.716096 0.698002i \(-0.245927\pi\)
−0.962535 + 0.271156i \(0.912594\pi\)
\(284\) 5.17712 + 8.96704i 0.307206 + 0.532096i
\(285\) 0 0
\(286\) 0.531373 + 0.920365i 0.0314207 + 0.0544223i
\(287\) 13.0627 0.771070
\(288\) 0 0
\(289\) 7.14575 + 12.3768i 0.420338 + 0.728047i
\(290\) −12.5830 −0.738900
\(291\) 0 0
\(292\) −10.5830 −0.619324
\(293\) 11.4686 19.8642i 0.670004 1.16048i −0.307898 0.951419i \(-0.599626\pi\)
0.977902 0.209062i \(-0.0670411\pi\)
\(294\) 0 0
\(295\) −11.2288 19.4488i −0.653763 1.13235i
\(296\) 1.96863 + 3.40976i 0.114424 + 0.198188i
\(297\) 0 0
\(298\) −3.53137 + 6.11652i −0.204567 + 0.354320i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) −6.61438 + 11.4564i −0.381246 + 0.660338i
\(302\) 3.61438 6.26029i 0.207984 0.360239i
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) 10.4059 18.0235i 0.595839 1.03202i
\(306\) 0 0
\(307\) −13.5830 −0.775223 −0.387612 0.921823i \(-0.626700\pi\)
−0.387612 + 0.921823i \(0.626700\pi\)
\(308\) −2.17712 + 3.77089i −0.124053 + 0.214866i
\(309\) 0 0
\(310\) 1.06275 0.0603599
\(311\) 11.7601 + 20.3691i 0.666856 + 1.15503i 0.978779 + 0.204921i \(0.0656936\pi\)
−0.311923 + 0.950107i \(0.600973\pi\)
\(312\) 0 0
\(313\) −11.6458 + 20.1710i −0.658257 + 1.14013i 0.322810 + 0.946464i \(0.395373\pi\)
−0.981067 + 0.193670i \(0.937961\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −15.2288 −0.856684
\(317\) −10.4059 + 18.0235i −0.584452 + 1.01230i 0.410491 + 0.911865i \(0.365357\pi\)
−0.994943 + 0.100437i \(0.967976\pi\)
\(318\) 0 0
\(319\) 6.29150 + 10.8972i 0.352257 + 0.610126i
\(320\) −1.64575 −0.0920003
\(321\) 0 0
\(322\) 24.5830 1.36996
\(323\) 3.29150 0.183144
\(324\) 0 0
\(325\) 0.739870 1.28149i 0.0410406 0.0710844i
\(326\) 1.00000 0.0553849
\(327\) 0 0
\(328\) 2.46863 4.27579i 0.136307 0.236091i
\(329\) 28.9373 1.59536
\(330\) 0 0
\(331\) 0.0627461 0.108679i 0.00344884 0.00597356i −0.864296 0.502984i \(-0.832236\pi\)
0.867745 + 0.497010i \(0.165569\pi\)
\(332\) −1.35425 + 2.34563i −0.0743241 + 0.128733i
\(333\) 0 0
\(334\) −6.29150 10.8972i −0.344256 0.596268i
\(335\) 6.82288 + 11.8176i 0.372774 + 0.645663i
\(336\) 0 0
\(337\) 4.70850 8.15536i 0.256488 0.444251i −0.708810 0.705399i \(-0.750768\pi\)
0.965299 + 0.261148i \(0.0841012\pi\)
\(338\) 12.5830 0.684425
\(339\) 0 0
\(340\) −2.70850 −0.146889
\(341\) −0.531373 0.920365i −0.0287755 0.0498406i
\(342\) 0 0
\(343\) 18.5203 1.00000
\(344\) 2.50000 + 4.33013i 0.134791 + 0.233465i
\(345\) 0 0
\(346\) −3.29150 5.70105i −0.176952 0.306490i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) −12.6144 21.8487i −0.675232 1.16954i −0.976401 0.215966i \(-0.930710\pi\)
0.301169 0.953571i \(-0.402623\pi\)
\(350\) 6.06275 0.324067
\(351\) 0 0
\(352\) 0.822876 + 1.42526i 0.0438594 + 0.0759667i
\(353\) 12.0000 0.638696 0.319348 0.947638i \(-0.396536\pi\)
0.319348 + 0.947638i \(0.396536\pi\)
\(354\) 0 0
\(355\) 17.0405 0.904417
\(356\) −5.46863 + 9.47194i −0.289837 + 0.502012i
\(357\) 0 0
\(358\) −0.531373 0.920365i −0.0280839 0.0486428i
\(359\) −15.5830 26.9906i −0.822440 1.42451i −0.903860 0.427827i \(-0.859279\pi\)
0.0814209 0.996680i \(-0.474054\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −6.64575 + 11.5108i −0.349293 + 0.604993i
\(363\) 0 0
\(364\) −0.854249 1.47960i −0.0447748 0.0775522i
\(365\) −8.70850 + 15.0836i −0.455824 + 0.789510i
\(366\) 0 0
\(367\) −1.87451 −0.0978485 −0.0489243 0.998802i \(-0.515579\pi\)
−0.0489243 + 0.998802i \(0.515579\pi\)
\(368\) 4.64575 8.04668i 0.242177 0.419462i
\(369\) 0 0
\(370\) 6.47974 0.336866
\(371\) −15.8745 −0.824163
\(372\) 0 0
\(373\) −16.5830 −0.858635 −0.429318 0.903154i \(-0.641246\pi\)
−0.429318 + 0.903154i \(0.641246\pi\)
\(374\) 1.35425 + 2.34563i 0.0700265 + 0.121290i
\(375\) 0 0
\(376\) 5.46863 9.47194i 0.282023 0.488478i
\(377\) −4.93725 −0.254282
\(378\) 0 0
\(379\) 4.41699 0.226886 0.113443 0.993545i \(-0.463812\pi\)
0.113443 + 0.993545i \(0.463812\pi\)
\(380\) 1.64575 2.85052i 0.0844253 0.146229i
\(381\) 0 0
\(382\) −13.4059 23.2197i −0.685905 1.18802i
\(383\) 0.583005 0.0297902 0.0148951 0.999889i \(-0.495259\pi\)
0.0148951 + 0.999889i \(0.495259\pi\)
\(384\) 0 0
\(385\) 3.58301 + 6.20595i 0.182607 + 0.316284i
\(386\) 7.00000 0.356291
\(387\) 0 0
\(388\) 3.79150 6.56708i 0.192484 0.333393i
\(389\) −8.70850 −0.441538 −0.220769 0.975326i \(-0.570857\pi\)
−0.220769 + 0.975326i \(0.570857\pi\)
\(390\) 0 0
\(391\) 7.64575 13.2428i 0.386662 0.669719i
\(392\) 3.50000 6.06218i 0.176777 0.306186i
\(393\) 0 0
\(394\) −7.64575 + 13.2428i −0.385187 + 0.667164i
\(395\) −12.5314 + 21.7050i −0.630522 + 1.09210i
\(396\) 0 0
\(397\) 5.67712 + 9.83307i 0.284927 + 0.493508i 0.972591 0.232521i \(-0.0746974\pi\)
−0.687665 + 0.726028i \(0.741364\pi\)
\(398\) 10.9686 + 18.9982i 0.549808 + 0.952295i
\(399\) 0 0
\(400\) 1.14575 1.98450i 0.0572876 0.0992250i
\(401\) −26.8118 −1.33892 −0.669458 0.742850i \(-0.733473\pi\)
−0.669458 + 0.742850i \(0.733473\pi\)
\(402\) 0 0
\(403\) 0.416995 0.0207720
\(404\) 6.82288 + 11.8176i 0.339451 + 0.587946i
\(405\) 0 0
\(406\) −10.1144 17.5186i −0.501968 0.869434i
\(407\) −3.23987 5.61162i −0.160594 0.278158i
\(408\) 0 0
\(409\) 8.43725 + 14.6138i 0.417195 + 0.722604i 0.995656 0.0931066i \(-0.0296798\pi\)
−0.578461 + 0.815710i \(0.696346\pi\)
\(410\) −4.06275 7.03688i −0.200645 0.347527i
\(411\) 0 0
\(412\) 5.96863 + 10.3380i 0.294053 + 0.509315i
\(413\) 18.0516 31.2663i 0.888263 1.53852i
\(414\) 0 0
\(415\) 2.22876 + 3.86032i 0.109405 + 0.189496i
\(416\) −0.645751 −0.0316606
\(417\) 0 0
\(418\) −3.29150 −0.160993
\(419\) 6.53137 11.3127i 0.319078 0.552660i −0.661218 0.750194i \(-0.729960\pi\)
0.980296 + 0.197534i \(0.0632933\pi\)
\(420\) 0 0
\(421\) 12.6458 + 21.9031i 0.616316 + 1.06749i 0.990152 + 0.139996i \(0.0447090\pi\)
−0.373836 + 0.927495i \(0.621958\pi\)
\(422\) −8.43725 14.6138i −0.410719 0.711386i
\(423\) 0 0
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 1.88562 3.26599i 0.0914661 0.158424i
\(426\) 0 0
\(427\) 33.4575 1.61912
\(428\) −3.00000 + 5.19615i −0.145010 + 0.251166i
\(429\) 0 0
\(430\) 8.22876 0.396826
\(431\) −4.40588 + 7.63121i −0.212224 + 0.367582i −0.952410 0.304819i \(-0.901404\pi\)
0.740186 + 0.672402i \(0.234737\pi\)
\(432\) 0 0
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) 0.854249 + 1.47960i 0.0410052 + 0.0710232i
\(435\) 0 0
\(436\) −8.64575 −0.414056
\(437\) 9.29150 + 16.0934i 0.444473 + 0.769850i
\(438\) 0 0
\(439\) 8.58301 14.8662i 0.409644 0.709525i −0.585205 0.810885i \(-0.698986\pi\)
0.994850 + 0.101360i \(0.0323194\pi\)
\(440\) 2.70850 0.129123
\(441\) 0 0
\(442\) −1.06275 −0.0505497
\(443\) −4.35425 + 7.54178i −0.206877 + 0.358321i −0.950729 0.310023i \(-0.899663\pi\)
0.743852 + 0.668344i \(0.232997\pi\)
\(444\) 0 0
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) −17.8745 −0.846382
\(447\) 0 0
\(448\) −1.32288 2.29129i −0.0625000 0.108253i
\(449\) −7.64575 −0.360825 −0.180413 0.983591i \(-0.557743\pi\)
−0.180413 + 0.983591i \(0.557743\pi\)
\(450\) 0 0
\(451\) −4.06275 + 7.03688i −0.191307 + 0.331354i
\(452\) −7.64575 −0.359626
\(453\) 0 0
\(454\) −3.00000 + 5.19615i −0.140797 + 0.243868i
\(455\) −2.81176 −0.131817
\(456\) 0 0
\(457\) −1.14575 + 1.98450i −0.0535960 + 0.0928310i −0.891579 0.452866i \(-0.850402\pi\)
0.837983 + 0.545697i \(0.183735\pi\)
\(458\) −7.32288 + 12.6836i −0.342176 + 0.592665i
\(459\) 0 0
\(460\) −7.64575 13.2428i −0.356485 0.617450i
\(461\) −1.11438 1.93016i −0.0519018 0.0898965i 0.838907 0.544274i \(-0.183195\pi\)
−0.890809 + 0.454378i \(0.849862\pi\)
\(462\) 0 0
\(463\) −14.6458 + 25.3672i −0.680646 + 1.17891i 0.294138 + 0.955763i \(0.404967\pi\)
−0.974784 + 0.223150i \(0.928366\pi\)
\(464\) −7.64575 −0.354945
\(465\) 0 0
\(466\) −8.70850 −0.403413
\(467\) −13.1144 22.7148i −0.606861 1.05111i −0.991754 0.128153i \(-0.959095\pi\)
0.384893 0.922961i \(-0.374238\pi\)
\(468\) 0 0
\(469\) −10.9686 + 18.9982i −0.506484 + 0.877256i
\(470\) −9.00000 15.5885i −0.415139 0.719042i
\(471\) 0 0
\(472\) −6.82288 11.8176i −0.314048 0.543948i
\(473\) −4.11438 7.12631i −0.189179 0.327668i
\(474\) 0 0
\(475\) 2.29150 + 3.96900i 0.105141 + 0.182110i
\(476\) −2.17712 3.77089i −0.0997883 0.172838i
\(477\) 0 0
\(478\) −2.46863 4.27579i −0.112912 0.195570i
\(479\) 1.64575 0.0751963 0.0375981 0.999293i \(-0.488029\pi\)
0.0375981 + 0.999293i \(0.488029\pi\)
\(480\) 0 0
\(481\) 2.54249 0.115927
\(482\) 2.50000 4.33013i 0.113872 0.197232i
\(483\) 0 0
\(484\) 4.14575 + 7.18065i 0.188443 + 0.326393i
\(485\) −6.23987 10.8078i −0.283338 0.490756i
\(486\) 0 0
\(487\) 3.93725 6.81952i 0.178414 0.309022i −0.762923 0.646489i \(-0.776237\pi\)
0.941337 + 0.337467i \(0.109570\pi\)
\(488\) 6.32288 10.9515i 0.286223 0.495753i
\(489\) 0 0
\(490\) −5.76013 9.97684i −0.260216 0.450708i
\(491\) −18.8745 + 32.6916i −0.851795 + 1.47535i 0.0277925 + 0.999614i \(0.491152\pi\)
−0.879587 + 0.475738i \(0.842181\pi\)
\(492\) 0 0
\(493\) −12.5830 −0.566710
\(494\) 0.645751 1.11847i 0.0290537 0.0503225i
\(495\) 0 0
\(496\) 0.645751 0.0289951
\(497\) 13.6974 + 23.7246i 0.614412 + 1.06419i
\(498\) 0 0
\(499\) 36.1660 1.61901 0.809506 0.587111i \(-0.199735\pi\)
0.809506 + 0.587111i \(0.199735\pi\)
\(500\) −6.00000 10.3923i −0.268328 0.464758i
\(501\) 0 0
\(502\) 9.00000 15.5885i 0.401690 0.695747i
\(503\) 27.8745 1.24286 0.621431 0.783469i \(-0.286551\pi\)
0.621431 + 0.783469i \(0.286551\pi\)
\(504\) 0 0
\(505\) 22.4575 0.999346
\(506\) −7.64575 + 13.2428i −0.339895 + 0.588716i
\(507\) 0 0
\(508\) −3.32288 5.75539i −0.147429 0.255354i
\(509\) −39.8745 −1.76741 −0.883703 0.468048i \(-0.844958\pi\)
−0.883703 + 0.468048i \(0.844958\pi\)
\(510\) 0 0
\(511\) −28.0000 −1.23865
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 7.93725 13.7477i 0.350097 0.606386i
\(515\) 19.6458 0.865695
\(516\) 0 0
\(517\) −9.00000 + 15.5885i −0.395820 + 0.685580i
\(518\) 5.20850 + 9.02138i 0.228848 + 0.396377i
\(519\) 0 0
\(520\) −0.531373 + 0.920365i −0.0233022 + 0.0403607i
\(521\) −19.9373 + 34.5323i −0.873467 + 1.51289i −0.0150801 + 0.999886i \(0.504800\pi\)
−0.858387 + 0.513003i \(0.828533\pi\)
\(522\) 0 0
\(523\) 0.500000 + 0.866025i 0.0218635 + 0.0378686i 0.876750 0.480946i \(-0.159707\pi\)
−0.854887 + 0.518815i \(0.826373\pi\)
\(524\) 3.29150 + 5.70105i 0.143790 + 0.249052i
\(525\) 0 0
\(526\) −5.46863 + 9.47194i −0.238443 + 0.412996i
\(527\) 1.06275 0.0462939
\(528\) 0 0
\(529\) 63.3320 2.75357
\(530\) 4.93725 + 8.55157i 0.214461 + 0.371457i
\(531\) 0 0
\(532\) 5.29150 0.229416
\(533\) −1.59412 2.76110i −0.0690490 0.119596i
\(534\) 0 0
\(535\) 4.93725 + 8.55157i 0.213456 + 0.369717i
\(536\) 4.14575 + 7.18065i 0.179069 + 0.310157i
\(537\) 0 0
\(538\) 13.6458 + 23.6351i 0.588310 + 1.01898i
\(539\) −5.76013 + 9.97684i −0.248106 + 0.429733i
\(540\) 0 0
\(541\) 20.5830 + 35.6508i 0.884933 + 1.53275i 0.845791 + 0.533514i \(0.179129\pi\)
0.0391415 + 0.999234i \(0.487538\pi\)
\(542\) 21.2288 0.911853
\(543\) 0 0
\(544\) −1.64575 −0.0705610
\(545\) −7.11438 + 12.3225i −0.304746 + 0.527836i
\(546\) 0 0
\(547\) −3.85425 6.67575i −0.164796 0.285435i 0.771787 0.635881i \(-0.219363\pi\)
−0.936583 + 0.350447i \(0.886030\pi\)
\(548\) −4.64575 8.04668i −0.198457 0.343737i
\(549\) 0 0
\(550\) −1.88562 + 3.26599i −0.0804032 + 0.139262i
\(551\) 7.64575 13.2428i 0.325720 0.564164i
\(552\) 0 0
\(553\) −40.2915 −1.71337
\(554\) −8.96863 + 15.5341i −0.381040 + 0.659981i
\(555\) 0 0
\(556\) −19.5830 −0.830504
\(557\) −16.1144 + 27.9109i −0.682788 + 1.18262i 0.291338 + 0.956620i \(0.405899\pi\)
−0.974126 + 0.226004i \(0.927434\pi\)
\(558\) 0 0
\(559\) 3.22876 0.136562
\(560\) −4.35425 −0.184001
\(561\) 0 0
\(562\) −17.5203 −0.739048
\(563\) −17.2288 29.8411i −0.726106 1.25765i −0.958517 0.285034i \(-0.907995\pi\)
0.232412 0.972617i \(-0.425338\pi\)
\(564\) 0 0
\(565\) −6.29150 + 10.8972i −0.264686 + 0.458449i
\(566\) −8.29150 −0.348518
\(567\) 0 0
\(568\) 10.3542 0.434455
\(569\) −0.531373 + 0.920365i −0.0222763 + 0.0385837i −0.876949 0.480584i \(-0.840425\pi\)
0.854672 + 0.519168i \(0.173758\pi\)
\(570\) 0 0
\(571\) 0.645751 + 1.11847i 0.0270239 + 0.0468067i 0.879221 0.476414i \(-0.158064\pi\)
−0.852197 + 0.523221i \(0.824730\pi\)
\(572\) 1.06275 0.0444356
\(573\) 0 0
\(574\) 6.53137 11.3127i 0.272614 0.472182i
\(575\) 21.2915 0.887917
\(576\) 0 0
\(577\) 10.8542 18.8001i 0.451868 0.782659i −0.546634 0.837372i \(-0.684091\pi\)
0.998502 + 0.0547129i \(0.0174244\pi\)
\(578\) 14.2915 0.594448
\(579\) 0 0
\(580\) −6.29150 + 10.8972i −0.261240 + 0.452482i
\(581\) −3.58301 + 6.20595i −0.148648 + 0.257466i
\(582\) 0 0
\(583\) 4.93725 8.55157i 0.204480 0.354170i
\(584\) −5.29150 + 9.16515i −0.218964 + 0.379257i
\(585\) 0 0
\(586\) −11.4686 19.8642i −0.473765 0.820584i
\(587\) 19.1144 + 33.1071i 0.788935 + 1.36648i 0.926620 + 0.375999i \(0.122700\pi\)
−0.137685 + 0.990476i \(0.543966\pi\)
\(588\) 0 0
\(589\) −0.645751 + 1.11847i −0.0266077 + 0.0460859i
\(590\) −22.4575 −0.924561
\(591\) 0 0
\(592\) 3.93725 0.161820
\(593\) 12.5314 + 21.7050i 0.514602 + 0.891316i 0.999856 + 0.0169436i \(0.00539357\pi\)
−0.485255 + 0.874373i \(0.661273\pi\)
\(594\) 0 0
\(595\) −7.16601 −0.293778
\(596\) 3.53137 + 6.11652i 0.144651 + 0.250542i
\(597\) 0 0
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) −10.9373 18.9439i −0.446884 0.774026i 0.551297 0.834309i \(-0.314133\pi\)
−0.998181 + 0.0602830i \(0.980800\pi\)
\(600\) 0 0
\(601\) 2.43725 + 4.22145i 0.0994177 + 0.172196i 0.911444 0.411425i \(-0.134969\pi\)
−0.812026 + 0.583621i \(0.801635\pi\)
\(602\) 6.61438 + 11.4564i 0.269582 + 0.466930i
\(603\) 0 0
\(604\) −3.61438 6.26029i −0.147067 0.254727i
\(605\) 13.6458 0.554779
\(606\) 0 0
\(607\) 26.5830 1.07897 0.539485 0.841995i \(-0.318619\pi\)
0.539485 + 0.841995i \(0.318619\pi\)
\(608\) 1.00000 1.73205i 0.0405554 0.0702439i
\(609\) 0 0
\(610\) −10.4059 18.0235i −0.421322 0.729751i
\(611\) −3.53137 6.11652i −0.142864 0.247448i
\(612\) 0 0
\(613\) −13.1974 + 22.8585i −0.533037 + 0.923248i 0.466218 + 0.884670i \(0.345616\pi\)
−0.999256 + 0.0385780i \(0.987717\pi\)
\(614\) −6.79150 + 11.7632i −0.274083 + 0.474725i
\(615\) 0 0
\(616\) 2.17712 + 3.77089i 0.0877188 + 0.151933i
\(617\) −17.7601 + 30.7614i −0.714996 + 1.23841i 0.247965 + 0.968769i \(0.420238\pi\)
−0.962961 + 0.269640i \(0.913095\pi\)
\(618\) 0 0
\(619\) 2.29150 0.0921033 0.0460516 0.998939i \(-0.485336\pi\)
0.0460516 + 0.998939i \(0.485336\pi\)
\(620\) 0.531373 0.920365i 0.0213405 0.0369628i
\(621\) 0 0
\(622\) 23.5203 0.943076
\(623\) −14.4686 + 25.0604i −0.579673 + 1.00402i
\(624\) 0 0
\(625\) −8.29150 −0.331660
\(626\) 11.6458 + 20.1710i 0.465458 + 0.806197i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 6.47974 0.258364
\(630\) 0 0
\(631\) 21.9373 0.873308 0.436654 0.899629i \(-0.356163\pi\)
0.436654 + 0.899629i \(0.356163\pi\)
\(632\) −7.61438 + 13.1885i −0.302884 + 0.524610i
\(633\) 0 0
\(634\) 10.4059 + 18.0235i 0.413270 + 0.715805i
\(635\) −10.9373 −0.434032
\(636\) 0 0
\(637\) −2.26013 3.91466i −0.0895496 0.155104i
\(638\) 12.5830 0.498166
\(639\) 0 0
\(640\) −0.822876 + 1.42526i −0.0325270 + 0.0563384i
\(641\) −8.22876 −0.325016 −0.162508 0.986707i \(-0.551958\pi\)
−0.162508 + 0.986707i \(0.551958\pi\)
\(642\) 0 0
\(643\) 17.4373 30.2022i 0.687658 1.19106i −0.284935 0.958547i \(-0.591972\pi\)
0.972593 0.232512i \(-0.0746945\pi\)
\(644\) 12.2915 21.2895i 0.484353 0.838924i
\(645\) 0 0
\(646\) 1.64575 2.85052i 0.0647512 0.112152i
\(647\) −10.9373 + 18.9439i −0.429988 + 0.744761i −0.996872 0.0790370i \(-0.974815\pi\)
0.566884 + 0.823798i \(0.308149\pi\)
\(648\) 0 0
\(649\) 11.2288 + 19.4488i 0.440767 + 0.763431i
\(650\) −0.739870 1.28149i −0.0290201 0.0502643i
\(651\) 0 0
\(652\) 0.500000 0.866025i 0.0195815 0.0339162i
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 10.8340 0.423319
\(656\) −2.46863 4.27579i −0.0963837 0.166941i
\(657\) 0 0
\(658\) 14.4686 25.0604i 0.564046 0.976956i
\(659\) 1.11438 + 1.93016i 0.0434100 + 0.0751884i 0.886914 0.461934i \(-0.152844\pi\)
−0.843504 + 0.537123i \(0.819511\pi\)
\(660\) 0 0
\(661\) −19.5830 33.9188i −0.761691 1.31929i −0.941979 0.335673i \(-0.891036\pi\)
0.180288 0.983614i \(-0.442297\pi\)
\(662\) −0.0627461 0.108679i −0.00243870 0.00422394i
\(663\) 0 0
\(664\) 1.35425 + 2.34563i 0.0525550 + 0.0910280i
\(665\) 4.35425 7.54178i 0.168851 0.292458i
\(666\) 0 0
\(667\) −35.5203 61.5229i −1.37535 2.38218i
\(668\) −12.5830 −0.486851
\(669\) 0 0
\(670\) 13.6458 0.527181
\(671\) −10.4059 + 18.0235i −0.401715 + 0.695790i
\(672\) 0 0
\(673\) 23.8745 + 41.3519i 0.920295 + 1.59400i 0.798959 + 0.601386i \(0.205384\pi\)
0.121336 + 0.992612i \(0.461282\pi\)
\(674\) −4.70850 8.15536i −0.181365 0.314133i
\(675\) 0 0
\(676\) 6.29150 10.8972i 0.241981 0.419123i
\(677\) −7.06275 + 12.2330i −0.271443 + 0.470154i −0.969232 0.246150i \(-0.920834\pi\)
0.697788 + 0.716304i \(0.254168\pi\)
\(678\) 0 0
\(679\) 10.0314 17.3748i 0.384969 0.666785i
\(680\) −1.35425 + 2.34563i −0.0519331 + 0.0899507i
\(681\) 0 0
\(682\) −1.06275 −0.0406947
\(683\) 10.4059 18.0235i 0.398170 0.689651i −0.595330 0.803481i \(-0.702979\pi\)
0.993500 + 0.113831i \(0.0363121\pi\)
\(684\) 0 0
\(685\) −15.2915 −0.584258
\(686\) 9.26013 16.0390i 0.353553 0.612372i
\(687\) 0 0
\(688\) 5.00000 0.190623
\(689\) 1.93725 + 3.35542i 0.0738035 + 0.127831i
\(690\) 0 0
\(691\) −12.3745 + 21.4333i −0.470748 + 0.815360i −0.999440 0.0334536i \(-0.989349\pi\)
0.528692 + 0.848814i \(0.322683\pi\)
\(692\) −6.58301 −0.250248
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −16.1144 + 27.9109i −0.611253 + 1.05872i
\(696\) 0 0
\(697\) −4.06275 7.03688i −0.153887 0.266541i
\(698\) −25.2288 −0.954923
\(699\) 0 0
\(700\) 3.03137 5.25049i 0.114575 0.198450i
\(701\) 5.41699 0.204597 0.102299 0.994754i \(-0.467380\pi\)
0.102299 + 0.994754i \(0.467380\pi\)
\(702\) 0 0
\(703\) −3.93725 + 6.81952i −0.148496 + 0.257203i
\(704\) 1.64575 0.0620266
\(705\) 0 0
\(706\) 6.00000 10.3923i 0.225813 0.391120i
\(707\) 18.0516 + 31.2663i 0.678902 + 1.17589i
\(708\) 0 0
\(709\) 4.90588 8.49723i 0.184244 0.319120i −0.759077 0.651000i \(-0.774350\pi\)
0.943322 + 0.331880i \(0.107683\pi\)
\(710\) 8.52026 14.7575i 0.319760 0.553840i
\(711\) 0 0
\(712\) 5.46863 + 9.47194i 0.204945 + 0.354976i
\(713\) 3.00000 + 5.19615i 0.112351 + 0.194597i
\(714\) 0 0
\(715\) 0.874508 1.51469i 0.0327047 0.0566463i
\(716\) −1.06275 −0.0397167
\(717\) 0 0
\(718\) −31.1660 −1.16311
\(719\) 3.53137 + 6.11652i 0.131698 + 0.228108i 0.924331 0.381591i \(-0.124624\pi\)
−0.792633 + 0.609699i \(0.791290\pi\)
\(720\) 0 0
\(721\) 15.7915 + 27.3517i 0.588106 + 1.01863i
\(722\) −7.50000 12.9904i −0.279121 0.483452i
\(723\) 0 0
\(724\) 6.64575 + 11.5108i 0.246987 + 0.427795i
\(725\) −8.76013 15.1730i −0.325343 0.563511i
\(726\) 0 0
\(727\) −12.6144 21.8487i −0.467841 0.810325i 0.531483 0.847069i \(-0.321635\pi\)
−0.999325 + 0.0367437i \(0.988301\pi\)
\(728\) −1.70850 −0.0633211
\(729\) 0 0
\(730\) 8.70850 + 15.0836i 0.322316 + 0.558268i
\(731\) 8.22876 0.304352
\(732\) 0 0
\(733\) 8.77124 0.323973 0.161987 0.986793i \(-0.448210\pi\)
0.161987 + 0.986793i \(0.448210\pi\)
\(734\) −0.937254 + 1.62337i −0.0345947 + 0.0599197i
\(735\) 0 0
\(736\) −4.64575 8.04668i −0.171245 0.296604i
\(737\) −6.82288 11.8176i −0.251324 0.435306i
\(738\) 0 0
\(739\) −10.7288 + 18.5828i −0.394664 + 0.683578i −0.993058 0.117624i \(-0.962472\pi\)
0.598395 + 0.801202i \(0.295806\pi\)
\(740\) 3.23987 5.61162i 0.119100 0.206287i
\(741\) 0 0
\(742\) −7.93725 + 13.7477i −0.291386 + 0.504695i
\(743\) −6.53137 + 11.3127i −0.239613 + 0.415022i −0.960603 0.277923i \(-0.910354\pi\)
0.720990 + 0.692945i \(0.243687\pi\)
\(744\) 0 0
\(745\) 11.6235 0.425853
\(746\) −8.29150 + 14.3613i −0.303573 + 0.525805i
\(747\) 0 0
\(748\) 2.70850 0.0990325
\(749\) −7.93725 + 13.7477i −0.290021 + 0.502331i
\(750\) 0 0
\(751\) 0.457513 0.0166949 0.00834745 0.999965i \(-0.497343\pi\)
0.00834745 + 0.999965i \(0.497343\pi\)
\(752\) −5.46863 9.47194i −0.199420 0.345406i
\(753\) 0 0
\(754\) −2.46863 + 4.27579i −0.0899021 + 0.155715i
\(755\) −11.8967 −0.432967
\(756\) 0 0
\(757\) −40.9778 −1.48936 −0.744681 0.667420i \(-0.767398\pi\)
−0.744681 + 0.667420i \(0.767398\pi\)
\(758\) 2.20850 3.82523i 0.0802162 0.138939i
\(759\) 0 0
\(760\) −1.64575 2.85052i −0.0596977 0.103399i
\(761\) 18.5830 0.673633 0.336817 0.941570i \(-0.390650\pi\)
0.336817 + 0.941570i \(0.390650\pi\)
\(762\) 0 0
\(763\) −22.8745 −0.828113
\(764\) −26.8118 −0.970015
\(765\) 0 0
\(766\) 0.291503 0.504897i 0.0105324 0.0182427i
\(767\) −8.81176 −0.318174
\(768\) 0 0
\(769\) −9.70850 + 16.8156i −0.350097 + 0.606386i −0.986266 0.165163i \(-0.947185\pi\)
0.636169 + 0.771550i \(0.280518\pi\)
\(770\) 7.16601 0.258245
\(771\) 0 0
\(772\) 3.50000 6.06218i 0.125968 0.218183i
\(773\) 19.1660 33.1965i 0.689353 1.19400i −0.282694 0.959210i \(-0.591228\pi\)
0.972047 0.234785i \(-0.0754386\pi\)
\(774\) 0 0
\(775\) 0.739870 + 1.28149i 0.0265769 + 0.0460326i
\(776\) −3.79150 6.56708i −0.136107 0.235744i
\(777\) 0 0
\(778\) −4.35425 + 7.54178i −0.156107 + 0.270386i
\(779\) 9.87451 0.353791
\(780\) 0 0
\(781\) −17.0405 −0.609758
\(782\) −7.64575 13.2428i −0.273412 0.473563i
\(783\) 0 0
\(784\) −3.50000 6.06218i −0.125000 0.216506i
\(785\) −3.29150 5.70105i −0.117479 0.203479i
\(786\) 0 0
\(787\) 11.1458 + 19.3050i 0.397303 + 0.688149i 0.993392 0.114769i \(-0.0366128\pi\)
−0.596089 + 0.802918i \(0.703279\pi\)
\(788\) 7.64575 + 13.2428i 0.272369 + 0.471756i
\(789\) 0 0
\(790\) 12.5314 + 21.7050i 0.445846 + 0.772228i
\(791\) −20.2288 −0.719252
\(792\) 0 0
\(793\) −4.08301 7.07197i −0.144992 0.251133i
\(794\) 11.3542 0.402947
\(795\) 0 0
\(796\) 21.9373 0.777545
\(797\) 16.4059 28.4158i 0.581126 1.00654i −0.414220 0.910177i \(-0.635946\pi\)
0.995346 0.0963632i \(-0.0307210\pi\)
\(798\) 0 0
\(799\) −9.00000 15.5885i −0.318397 0.551480i
\(800\) −1.14575 1.98450i −0.0405084 0.0701627i
\(801\) 0 0
\(802\) −13.4059 + 23.2197i −0.473378 + 0.819915i
\(803\) 8.70850 15.0836i 0.307316 0.532287i
\(804\) 0 0
\(805\) −20.2288 35.0372i −0.712970 1.23490i
\(806\) 0.208497 0.361128i 0.00734401 0.0127202i
\(807\) 0 0
\(808\) 13.6458 0.480056
\(809\) 18.2915 31.6818i 0.643095 1.11387i −0.341643 0.939830i \(-0.610983\pi\)
0.984738 0.174043i \(-0.0556833\pi\)
\(810\) 0 0
\(811\) −18.7085 −0.656944 −0.328472 0.944514i \(-0.606534\pi\)
−0.328472 + 0.944514i \(0.606534\pi\)
\(812\) −20.2288 −0.709890
\(813\) 0 0
\(814\) −6.47974 −0.227115
\(815\) −0.822876 1.42526i −0.0288241 0.0499248i
\(816\) 0 0
\(817\) −5.00000 + 8.66025i −0.174928 + 0.302984i
\(818\) 16.8745 0.590003
\(819\) 0 0
\(820\) −8.12549 −0.283754
\(821\) −0.291503 + 0.504897i −0.0101735 + 0.0176210i −0.871067 0.491164i \(-0.836572\pi\)
0.860894 + 0.508785i \(0.169905\pi\)
\(822\) 0 0
\(823\) −11.5516 20.0080i −0.402665 0.697436i 0.591382 0.806392i \(-0.298583\pi\)
−0.994047 + 0.108956i \(0.965249\pi\)
\(824\) 11.9373 0.415854
\(825\) 0 0
\(826\) −18.0516 31.2663i −0.628097 1.08790i
\(827\) −19.7490 −0.686741 −0.343370 0.939200i \(-0.611569\pi\)
−0.343370 + 0.939200i \(0.611569\pi\)
\(828\) 0 0
\(829\) 9.35425 16.2020i 0.324886 0.562720i −0.656603 0.754236i \(-0.728007\pi\)
0.981489 + 0.191517i \(0.0613406\pi\)
\(830\) 4.45751 0.154723
\(831\) 0 0
\(832\) −0.322876 + 0.559237i −0.0111937 + 0.0193881i
\(833\) −5.76013 9.97684i −0.199577 0.345677i
\(834\) 0 0
\(835\) −10.3542 + 17.9341i −0.358324 + 0.620635i
\(836\) −1.64575 + 2.85052i −0.0569195 + 0.0985875i
\(837\) 0 0
\(838\) −6.53137 11.3127i −0.225623 0.390790i
\(839\) −19.3542 33.5225i −0.668183 1.15733i −0.978412 0.206665i \(-0.933739\pi\)
0.310229 0.950662i \(-0.399594\pi\)
\(840\) 0 0
\(841\) −14.7288 + 25.5110i −0.507888 + 0.879688i
\(842\) 25.2915 0.871603
\(843\) 0 0
\(844\) −16.8745 −0.580845
\(845\) −10.3542 17.9341i −0.356197 0.616951i
\(846\) 0 0
\(847\) 10.9686 + 18.9982i 0.376886 + 0.652787i
\(848\) 3.00000 + 5.19615i 0.103020 + 0.178437i
\(849\) 0 0
\(850\) −1.88562 3.26599i −0.0646763 0.112023i
\(851\) 18.2915 + 31.6818i 0.627025 + 1.08604i
\(852\) 0 0
\(853\) −8.06275 13.9651i −0.276063 0.478155i 0.694340 0.719647i \(-0.255697\pi\)
−0.970403 + 0.241492i \(0.922363\pi\)
\(854\) 16.7288 28.9751i 0.572446 0.991506i
\(855\) 0 0
\(856\) 3.00000 + 5.19615i 0.102538 + 0.177601i
\(857\) −20.8118 −0.710916 −0.355458 0.934692i \(-0.615675\pi\)
−0.355458 + 0.934692i \(0.615675\pi\)
\(858\) 0 0
\(859\) −7.00000 −0.238837 −0.119418 0.992844i \(-0.538103\pi\)
−0.119418 + 0.992844i \(0.538103\pi\)
\(860\) 4.11438 7.12631i 0.140299 0.243005i
\(861\) 0 0
\(862\) 4.40588 + 7.63121i 0.150065 + 0.259920i
\(863\) −6.58301 11.4021i −0.224088 0.388132i 0.731957 0.681350i \(-0.238607\pi\)
−0.956045 + 0.293218i \(0.905274\pi\)
\(864\) 0 0
\(865\) −5.41699 + 9.38251i −0.184183 + 0.319015i
\(866\) −9.50000 + 16.4545i −0.322823 + 0.559146i
\(867\) 0 0
\(868\) 1.70850 0.0579902
\(869\) 12.5314 21.7050i 0.425098 0.736291i
\(870\) 0 0
\(871\) 5.35425 0.181422
\(872\) −4.32288 + 7.48744i −0.146391 + 0.253557i
\(873\) 0 0
\(874\) 18.5830 0.628580
\(875\) −15.8745 27.4955i −0.536656 0.929516i
\(876\) 0 0
\(877\) 21.3542 0.721082 0.360541 0.932743i \(-0.382592\pi\)
0.360541 + 0.932743i \(0.382592\pi\)
\(878\) −8.58301 14.8662i −0.289662 0.501710i
\(879\) 0 0
\(880\) 1.35425 2.34563i 0.0456517 0.0790711i
\(881\) −27.8745 −0.939116 −0.469558 0.882902i \(-0.655587\pi\)
−0.469558 + 0.882902i \(0.655587\pi\)
\(882\) 0 0
\(883\) 11.8745 0.399609 0.199805 0.979836i \(-0.435969\pi\)
0.199805 + 0.979836i \(0.435969\pi\)
\(884\) −0.531373 + 0.920365i −0.0178720 + 0.0309552i
\(885\) 0 0
\(886\) 4.35425 + 7.54178i 0.146284 + 0.253371i
\(887\) 15.8745 0.533014 0.266507 0.963833i \(-0.414130\pi\)
0.266507 + 0.963833i \(0.414130\pi\)
\(888\) 0 0
\(889\) −8.79150 15.2273i −0.294858 0.510708i
\(890\) 18.0000 0.603361
\(891\) 0 0
\(892\) −8.93725 + 15.4798i −0.299241 + 0.518301i
\(893\) 21.8745 0.732002
\(894\) 0 0
\(895\) −0.874508 + 1.51469i −0.0292316 + 0.0506306i
\(896\) −2.64575 −0.0883883
\(897\) 0 0
\(898\) −3.82288 + 6.62141i −0.127571 + 0.220959i
\(899\) 2.46863 4.27579i 0.0823333 0.142605i
\(900\) 0 0
\(901\) 4.93725 + 8.55157i 0.164484 + 0.284894i
\(902\) 4.06275 + 7.03688i 0.135275 + 0.234303i
\(903\) 0 0
\(904\) −3.82288 + 6.62141i −0.127147 + 0.220225i
\(905\) 21.8745 0.727133
\(906\) 0 0
\(907\) 25.7085 0.853637 0.426818 0.904337i \(-0.359634\pi\)
0.426818 + 0.904337i \(0.359634\pi\)
\(908\) 3.00000 + 5.19615i 0.0995585 + 0.172440i
\(909\) 0 0
\(910\) −1.40588 + 2.43506i −0.0466045 + 0.0807214i
\(911\) 6.53137 + 11.3127i 0.216394 + 0.374805i 0.953703 0.300750i \(-0.0972371\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(912\) 0 0
\(913\) −2.22876 3.86032i −0.0737611 0.127758i
\(914\) 1.14575 + 1.98450i 0.0378981 + 0.0656414i
\(915\) 0 0
\(916\) 7.32288 + 12.6836i 0.241955 + 0.419078i
\(917\) 8.70850 + 15.0836i 0.287580 + 0.498103i
\(918\) 0 0
\(919\) −27.6144 47.8295i −0.910914 1.57775i −0.812775 0.582577i \(-0.802044\pi\)
−0.0981388 0.995173i \(-0.531289\pi\)
\(920\) −15.2915 −0.504146
\(921\) 0 0
\(922\) −2.22876 −0.0734002
\(923\) 3.34313 5.79048i 0.110041 0.190596i
\(924\) 0 0
\(925\) 4.51111 + 7.81348i 0.148325 + 0.256906i
\(926\) 14.6458 + 25.3672i 0.481289 + 0.833617i
\(927\) 0 0
\(928\) −3.82288 + 6.62141i −0.125492 + 0.217359i
\(929\) −0.531373 + 0.920365i −0.0174338 + 0.0301962i −0.874611 0.484826i \(-0.838883\pi\)
0.857177 + 0.515022i \(0.172216\pi\)
\(930\) 0 0
\(931\) 14.0000 0.458831
\(932\) −4.35425 + 7.54178i −0.142628 + 0.247039i
\(933\) 0 0
\(934\) −26.2288 −0.858231
\(935\) 2.22876 3.86032i 0.0728881 0.126246i
\(936\) 0 0
\(937\) 18.7490 0.612504 0.306252 0.951951i \(-0.400925\pi\)
0.306252 + 0.951951i \(0.400925\pi\)
\(938\) 10.9686 + 18.9982i 0.358138 + 0.620314i
\(939\) 0 0
\(940\) −18.0000 −0.587095
\(941\) 7.69738 + 13.3323i 0.250928 + 0.434619i 0.963781 0.266693i \(-0.0859311\pi\)
−0.712854 + 0.701313i \(0.752598\pi\)
\(942\) 0 0
\(943\) 22.9373 39.7285i 0.746940 1.29374i
\(944\) −13.6458 −0.444131
\(945\) 0 0
\(946\) −8.22876 −0.267540
\(947\) 23.7601 41.1538i 0.772100 1.33732i −0.164309 0.986409i \(-0.552540\pi\)
0.936410 0.350908i \(-0.114127\pi\)
\(948\) 0 0
\(949\) 3.41699 + 5.91841i 0.110920 + 0.192120i
\(950\) 4.58301 0.148692
\(951\) 0 0
\(952\) −4.35425 −0.141122
\(953\) 32.3320 1.04734 0.523668 0.851922i \(-0.324563\pi\)
0.523668 + 0.851922i \(0.324563\pi\)
\(954\) 0 0
\(955\) −22.0627 + 38.2138i −0.713934 + 1.23657i
\(956\) −4.93725 −0.159682
\(957\) 0 0
\(958\) 0.822876 1.42526i 0.0265859 0.0460481i
\(959\) −12.2915 21.2895i −0.396913 0.687474i
\(960\) 0 0
\(961\) 15.2915 26.4857i 0.493274 0.854376i
\(962\) 1.27124 2.20186i 0.0409865 0.0709908i
\(963\) 0 0
\(964\) −2.50000 4.33013i −0.0805196 0.139464i
\(965\) −5.76013 9.97684i −0.185425 0.321166i
\(966\) 0 0
\(967\) −25.9686 + 44.9790i −0.835095 + 1.44643i 0.0588585 + 0.998266i \(0.481254\pi\)
−0.893953 + 0.448160i \(0.852079\pi\)
\(968\) 8.29150 0.266499
\(969\) 0 0
\(970\) −12.4797 −0.400700
\(971\) 10.9373 + 18.9439i 0.350993 + 0.607938i 0.986424 0.164220i \(-0.0525107\pi\)
−0.635431 + 0.772158i \(0.719177\pi\)
\(972\) 0 0
\(973\) −51.8118 −1.66101
\(974\) −3.93725 6.81952i −0.126158 0.218512i
\(975\) 0 0
\(976\) −6.32288 10.9515i −0.202390 0.350550i
\(977\) −10.0627 17.4292i −0.321936 0.557609i 0.658952 0.752185i \(-0.271000\pi\)
−0.980887 + 0.194576i \(0.937667\pi\)
\(978\) 0 0
\(979\) −9.00000 15.5885i −0.287641 0.498209i
\(980\) −11.5203 −0.368001
\(981\) 0 0
\(982\) 18.8745 + 32.6916i 0.602310 + 1.04323i
\(983\) 26.8118 0.855162 0.427581 0.903977i \(-0.359366\pi\)
0.427581 + 0.903977i \(0.359366\pi\)
\(984\) 0 0
\(985\) 25.1660 0.801856
\(986\) −6.29150 + 10.8972i −0.200362 + 0.347038i
\(987\) 0 0
\(988\) −0.645751 1.11847i −0.0205441 0.0355834i
\(989\) 23.2288 + 40.2334i 0.738631 + 1.27935i
\(990\) 0 0
\(991\) 20.9686 36.3187i 0.666090 1.15370i −0.312898 0.949787i \(-0.601300\pi\)
0.978988 0.203916i \(-0.0653668\pi\)
\(992\) 0.322876 0.559237i 0.0102513 0.0177558i
\(993\) 0 0
\(994\) 27.3948 0.868909
\(995\) 18.0516 31.2663i 0.572275 0.991210i
\(996\) 0 0
\(997\) −55.6863 −1.76360 −0.881801 0.471622i \(-0.843669\pi\)
−0.881801 + 0.471622i \(0.843669\pi\)
\(998\) 18.0830 31.3207i 0.572408 0.991439i
\(999\) 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 1134.2.h.t.109.1 4
3.2 odd 2 1134.2.h.q.109.2 4
7.2 even 3 1134.2.e.q.919.2 4
9.2 odd 6 1134.2.e.t.865.1 4
9.4 even 3 378.2.g.h.109.2 yes 4
9.5 odd 6 378.2.g.g.109.1 4
9.7 even 3 1134.2.e.q.865.2 4
21.2 odd 6 1134.2.e.t.919.1 4
63.2 odd 6 1134.2.h.q.541.2 4
63.4 even 3 2646.2.a.bi.1.1 2
63.16 even 3 inner 1134.2.h.t.541.1 4
63.23 odd 6 378.2.g.g.163.1 yes 4
63.31 odd 6 2646.2.a.bf.1.2 2
63.32 odd 6 2646.2.a.bl.1.2 2
63.58 even 3 378.2.g.h.163.2 yes 4
63.59 even 6 2646.2.a.bo.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.g.g.109.1 4 9.5 odd 6
378.2.g.g.163.1 yes 4 63.23 odd 6
378.2.g.h.109.2 yes 4 9.4 even 3
378.2.g.h.163.2 yes 4 63.58 even 3
1134.2.e.q.865.2 4 9.7 even 3
1134.2.e.q.919.2 4 7.2 even 3
1134.2.e.t.865.1 4 9.2 odd 6
1134.2.e.t.919.1 4 21.2 odd 6
1134.2.h.q.109.2 4 3.2 odd 2
1134.2.h.q.541.2 4 63.2 odd 6
1134.2.h.t.109.1 4 1.1 even 1 trivial
1134.2.h.t.541.1 4 63.16 even 3 inner
2646.2.a.bf.1.2 2 63.31 odd 6
2646.2.a.bi.1.1 2 63.4 even 3
2646.2.a.bl.1.2 2 63.32 odd 6
2646.2.a.bo.1.1 2 63.59 even 6