Properties

Label 1134.2.l.f.215.4
Level $1134$
Weight $2$
Character 1134.215
Analytic conductor $9.055$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(215,1134)]
 
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([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.215");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.4
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1134.215
Dual form 1134.2.l.f.269.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(0.358719 + 0.621320i) q^{5} +(-1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(0.358719 + 0.621320i) q^{5} +(-1.62132 - 2.09077i) q^{7} -1.00000i q^{8} +(-0.621320 + 0.358719i) q^{10} +(-2.59808 - 1.50000i) q^{11} +(2.12132 + 1.22474i) q^{13} +(2.09077 - 1.62132i) q^{14} +1.00000 q^{16} +(2.95680 + 5.12132i) q^{17} +(-5.12132 - 2.95680i) q^{19} +(-0.358719 - 0.621320i) q^{20} +(1.50000 - 2.59808i) q^{22} +(3.67423 - 2.12132i) q^{23} +(2.24264 - 3.88437i) q^{25} +(-1.22474 + 2.12132i) q^{26} +(1.62132 + 2.09077i) q^{28} +(6.27231 - 3.62132i) q^{29} -9.08052i q^{31} +1.00000i q^{32} +(-5.12132 + 2.95680i) q^{34} +(0.717439 - 1.75736i) q^{35} +(0.121320 - 0.210133i) q^{37} +(2.95680 - 5.12132i) q^{38} +(0.621320 - 0.358719i) q^{40} +(5.91359 - 10.2426i) q^{41} +(0.121320 + 0.210133i) q^{43} +(2.59808 + 1.50000i) q^{44} +(2.12132 + 3.67423i) q^{46} -5.91359 q^{47} +(-1.74264 + 6.77962i) q^{49} +(3.88437 + 2.24264i) q^{50} +(-2.12132 - 1.22474i) q^{52} +(6.27231 - 3.62132i) q^{53} -2.15232i q^{55} +(-2.09077 + 1.62132i) q^{56} +(3.62132 + 6.27231i) q^{58} +8.06591 q^{59} -1.01461i q^{61} +9.08052 q^{62} -1.00000 q^{64} +1.75736i q^{65} -10.0000 q^{67} +(-2.95680 - 5.12132i) q^{68} +(1.75736 + 0.717439i) q^{70} -1.75736i q^{71} +(-1.24264 + 0.717439i) q^{73} +(0.210133 + 0.121320i) q^{74} +(5.12132 + 2.95680i) q^{76} +(1.07616 + 7.86396i) q^{77} -2.75736 q^{79} +(0.358719 + 0.621320i) q^{80} +(10.2426 + 5.91359i) q^{82} +(3.31552 + 5.74264i) q^{83} +(-2.12132 + 3.67423i) q^{85} +(-0.210133 + 0.121320i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(-0.878680 - 6.42090i) q^{91} +(-3.67423 + 2.12132i) q^{92} -5.91359i q^{94} -4.24264i q^{95} +(11.7426 - 6.77962i) q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 4 q^{7} + 12 q^{10} + 8 q^{16} - 24 q^{19} + 12 q^{22} - 16 q^{25} - 4 q^{28} - 24 q^{34} - 16 q^{37} - 12 q^{40} - 16 q^{43} + 20 q^{49} + 12 q^{58} - 8 q^{64} - 80 q^{67} + 48 q^{70} + 24 q^{73} + 24 q^{76} - 56 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 0.358719 + 0.621320i 0.160424 + 0.277863i 0.935021 0.354593i \(-0.115380\pi\)
−0.774597 + 0.632456i \(0.782047\pi\)
\(6\) 0 0
\(7\) −1.62132 2.09077i −0.612801 0.790237i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.621320 + 0.358719i −0.196479 + 0.113437i
\(11\) −2.59808 1.50000i −0.783349 0.452267i 0.0542666 0.998526i \(-0.482718\pi\)
−0.837616 + 0.546259i \(0.816051\pi\)
\(12\) 0 0
\(13\) 2.12132 + 1.22474i 0.588348 + 0.339683i 0.764444 0.644690i \(-0.223014\pi\)
−0.176096 + 0.984373i \(0.556347\pi\)
\(14\) 2.09077 1.62132i 0.558782 0.433316i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.95680 + 5.12132i 0.717128 + 1.24210i 0.962133 + 0.272581i \(0.0878772\pi\)
−0.245005 + 0.969522i \(0.578789\pi\)
\(18\) 0 0
\(19\) −5.12132 2.95680i −1.17491 0.678335i −0.220080 0.975482i \(-0.570632\pi\)
−0.954832 + 0.297146i \(0.903965\pi\)
\(20\) −0.358719 0.621320i −0.0802121 0.138931i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) 3.67423 2.12132i 0.766131 0.442326i −0.0653618 0.997862i \(-0.520820\pi\)
0.831493 + 0.555536i \(0.187487\pi\)
\(24\) 0 0
\(25\) 2.24264 3.88437i 0.448528 0.776874i
\(26\) −1.22474 + 2.12132i −0.240192 + 0.416025i
\(27\) 0 0
\(28\) 1.62132 + 2.09077i 0.306401 + 0.395118i
\(29\) 6.27231 3.62132i 1.16474 0.672462i 0.212304 0.977204i \(-0.431903\pi\)
0.952435 + 0.304741i \(0.0985700\pi\)
\(30\) 0 0
\(31\) 9.08052i 1.63091i −0.578821 0.815455i \(-0.696487\pi\)
0.578821 0.815455i \(-0.303513\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −5.12132 + 2.95680i −0.878299 + 0.507086i
\(35\) 0.717439 1.75736i 0.121269 0.297048i
\(36\) 0 0
\(37\) 0.121320 0.210133i 0.0199449 0.0345457i −0.855881 0.517173i \(-0.826984\pi\)
0.875826 + 0.482628i \(0.160318\pi\)
\(38\) 2.95680 5.12132i 0.479656 0.830788i
\(39\) 0 0
\(40\) 0.621320 0.358719i 0.0982394 0.0567185i
\(41\) 5.91359 10.2426i 0.923548 1.59963i 0.129668 0.991558i \(-0.458609\pi\)
0.793880 0.608074i \(-0.208058\pi\)
\(42\) 0 0
\(43\) 0.121320 + 0.210133i 0.0185012 + 0.0320450i 0.875128 0.483892i \(-0.160777\pi\)
−0.856627 + 0.515937i \(0.827444\pi\)
\(44\) 2.59808 + 1.50000i 0.391675 + 0.226134i
\(45\) 0 0
\(46\) 2.12132 + 3.67423i 0.312772 + 0.541736i
\(47\) −5.91359 −0.862586 −0.431293 0.902212i \(-0.641942\pi\)
−0.431293 + 0.902212i \(0.641942\pi\)
\(48\) 0 0
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 3.88437 + 2.24264i 0.549333 + 0.317157i
\(51\) 0 0
\(52\) −2.12132 1.22474i −0.294174 0.169842i
\(53\) 6.27231 3.62132i 0.861568 0.497427i −0.00296896 0.999996i \(-0.500945\pi\)
0.864537 + 0.502569i \(0.167612\pi\)
\(54\) 0 0
\(55\) 2.15232i 0.290218i
\(56\) −2.09077 + 1.62132i −0.279391 + 0.216658i
\(57\) 0 0
\(58\) 3.62132 + 6.27231i 0.475503 + 0.823595i
\(59\) 8.06591 1.05009 0.525046 0.851074i \(-0.324048\pi\)
0.525046 + 0.851074i \(0.324048\pi\)
\(60\) 0 0
\(61\) 1.01461i 0.129908i −0.997888 0.0649539i \(-0.979310\pi\)
0.997888 0.0649539i \(-0.0206900\pi\)
\(62\) 9.08052 1.15323
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.75736i 0.217974i
\(66\) 0 0
\(67\) −10.0000 −1.22169 −0.610847 0.791748i \(-0.709171\pi\)
−0.610847 + 0.791748i \(0.709171\pi\)
\(68\) −2.95680 5.12132i −0.358564 0.621051i
\(69\) 0 0
\(70\) 1.75736 + 0.717439i 0.210045 + 0.0857504i
\(71\) 1.75736i 0.208560i −0.994548 0.104280i \(-0.966746\pi\)
0.994548 0.104280i \(-0.0332538\pi\)
\(72\) 0 0
\(73\) −1.24264 + 0.717439i −0.145440 + 0.0839699i −0.570954 0.820982i \(-0.693427\pi\)
0.425514 + 0.904952i \(0.360093\pi\)
\(74\) 0.210133 + 0.121320i 0.0244275 + 0.0141032i
\(75\) 0 0
\(76\) 5.12132 + 2.95680i 0.587456 + 0.339168i
\(77\) 1.07616 + 7.86396i 0.122640 + 0.896182i
\(78\) 0 0
\(79\) −2.75736 −0.310227 −0.155114 0.987897i \(-0.549574\pi\)
−0.155114 + 0.987897i \(0.549574\pi\)
\(80\) 0.358719 + 0.621320i 0.0401061 + 0.0694657i
\(81\) 0 0
\(82\) 10.2426 + 5.91359i 1.13111 + 0.653047i
\(83\) 3.31552 + 5.74264i 0.363925 + 0.630337i 0.988603 0.150546i \(-0.0481031\pi\)
−0.624678 + 0.780882i \(0.714770\pi\)
\(84\) 0 0
\(85\) −2.12132 + 3.67423i −0.230089 + 0.398527i
\(86\) −0.210133 + 0.121320i −0.0226592 + 0.0130823i
\(87\) 0 0
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) −5.19615 + 9.00000i −0.550791 + 0.953998i 0.447427 + 0.894321i \(0.352341\pi\)
−0.998218 + 0.0596775i \(0.980993\pi\)
\(90\) 0 0
\(91\) −0.878680 6.42090i −0.0921107 0.673093i
\(92\) −3.67423 + 2.12132i −0.383065 + 0.221163i
\(93\) 0 0
\(94\) 5.91359i 0.609940i
\(95\) 4.24264i 0.435286i
\(96\) 0 0
\(97\) 11.7426 6.77962i 1.19228 0.688366i 0.233460 0.972366i \(-0.424995\pi\)
0.958824 + 0.284001i \(0.0916617\pi\)
\(98\) −6.77962 1.74264i −0.684845 0.176033i
\(99\) 0 0
\(100\) −2.24264 + 3.88437i −0.224264 + 0.388437i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 4.75736 2.74666i 0.468757 0.270637i −0.246963 0.969025i \(-0.579432\pi\)
0.715719 + 0.698388i \(0.246099\pi\)
\(104\) 1.22474 2.12132i 0.120096 0.208013i
\(105\) 0 0
\(106\) 3.62132 + 6.27231i 0.351734 + 0.609221i
\(107\) 9.94655 + 5.74264i 0.961569 + 0.555162i 0.896656 0.442729i \(-0.145990\pi\)
0.0649133 + 0.997891i \(0.479323\pi\)
\(108\) 0 0
\(109\) −9.24264 16.0087i −0.885284 1.53336i −0.845387 0.534154i \(-0.820630\pi\)
−0.0398971 0.999204i \(-0.512703\pi\)
\(110\) 2.15232 0.205215
\(111\) 0 0
\(112\) −1.62132 2.09077i −0.153200 0.197559i
\(113\) −7.34847 4.24264i −0.691286 0.399114i 0.112808 0.993617i \(-0.464016\pi\)
−0.804094 + 0.594503i \(0.797349\pi\)
\(114\) 0 0
\(115\) 2.63604 + 1.52192i 0.245812 + 0.141920i
\(116\) −6.27231 + 3.62132i −0.582369 + 0.336231i
\(117\) 0 0
\(118\) 8.06591i 0.742527i
\(119\) 5.91359 14.4853i 0.542098 1.32786i
\(120\) 0 0
\(121\) −1.00000 1.73205i −0.0909091 0.157459i
\(122\) 1.01461 0.0918586
\(123\) 0 0
\(124\) 9.08052i 0.815455i
\(125\) 6.80511 0.608668
\(126\) 0 0
\(127\) 3.24264 0.287738 0.143869 0.989597i \(-0.454046\pi\)
0.143869 + 0.989597i \(0.454046\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −1.75736 −0.154131
\(131\) 2.59808 + 4.50000i 0.226995 + 0.393167i 0.956916 0.290365i \(-0.0937766\pi\)
−0.729921 + 0.683531i \(0.760443\pi\)
\(132\) 0 0
\(133\) 2.12132 + 15.5014i 0.183942 + 1.34414i
\(134\) 10.0000i 0.863868i
\(135\) 0 0
\(136\) 5.12132 2.95680i 0.439150 0.253543i
\(137\) −2.15232 1.24264i −0.183885 0.106166i 0.405232 0.914214i \(-0.367191\pi\)
−0.589117 + 0.808048i \(0.700524\pi\)
\(138\) 0 0
\(139\) 0.514719 + 0.297173i 0.0436579 + 0.0252059i 0.521670 0.853147i \(-0.325309\pi\)
−0.478012 + 0.878353i \(0.658643\pi\)
\(140\) −0.717439 + 1.75736i −0.0606347 + 0.148524i
\(141\) 0 0
\(142\) 1.75736 0.147474
\(143\) −3.67423 6.36396i −0.307255 0.532181i
\(144\) 0 0
\(145\) 4.50000 + 2.59808i 0.373705 + 0.215758i
\(146\) −0.717439 1.24264i −0.0593757 0.102842i
\(147\) 0 0
\(148\) −0.121320 + 0.210133i −0.00997247 + 0.0172728i
\(149\) −3.04384 + 1.75736i −0.249361 + 0.143968i −0.619472 0.785019i \(-0.712653\pi\)
0.370111 + 0.928988i \(0.379320\pi\)
\(150\) 0 0
\(151\) −2.62132 + 4.54026i −0.213320 + 0.369481i −0.952752 0.303751i \(-0.901761\pi\)
0.739432 + 0.673232i \(0.235094\pi\)
\(152\) −2.95680 + 5.12132i −0.239828 + 0.415394i
\(153\) 0 0
\(154\) −7.86396 + 1.07616i −0.633696 + 0.0867193i
\(155\) 5.64191 3.25736i 0.453169 0.261637i
\(156\) 0 0
\(157\) 14.6969i 1.17294i 0.809970 + 0.586472i \(0.199483\pi\)
−0.809970 + 0.586472i \(0.800517\pi\)
\(158\) 2.75736i 0.219364i
\(159\) 0 0
\(160\) −0.621320 + 0.358719i −0.0491197 + 0.0283593i
\(161\) −10.3923 4.24264i −0.819028 0.334367i
\(162\) 0 0
\(163\) 1.12132 1.94218i 0.0878286 0.152124i −0.818764 0.574130i \(-0.805341\pi\)
0.906593 + 0.422006i \(0.138674\pi\)
\(164\) −5.91359 + 10.2426i −0.461774 + 0.799816i
\(165\) 0 0
\(166\) −5.74264 + 3.31552i −0.445715 + 0.257334i
\(167\) −8.06591 + 13.9706i −0.624159 + 1.08107i 0.364544 + 0.931186i \(0.381225\pi\)
−0.988703 + 0.149889i \(0.952109\pi\)
\(168\) 0 0
\(169\) −3.50000 6.06218i −0.269231 0.466321i
\(170\) −3.67423 2.12132i −0.281801 0.162698i
\(171\) 0 0
\(172\) −0.121320 0.210133i −0.00925059 0.0160225i
\(173\) −20.7846 −1.58022 −0.790112 0.612962i \(-0.789978\pi\)
−0.790112 + 0.612962i \(0.789978\pi\)
\(174\) 0 0
\(175\) −11.7574 + 1.60896i −0.888773 + 0.121626i
\(176\) −2.59808 1.50000i −0.195837 0.113067i
\(177\) 0 0
\(178\) −9.00000 5.19615i −0.674579 0.389468i
\(179\) −22.9369 + 13.2426i −1.71439 + 0.989801i −0.785966 + 0.618269i \(0.787834\pi\)
−0.928420 + 0.371532i \(0.878833\pi\)
\(180\) 0 0
\(181\) 11.8272i 0.879108i 0.898216 + 0.439554i \(0.144863\pi\)
−0.898216 + 0.439554i \(0.855137\pi\)
\(182\) 6.42090 0.878680i 0.475949 0.0651321i
\(183\) 0 0
\(184\) −2.12132 3.67423i −0.156386 0.270868i
\(185\) 0.174080 0.0127986
\(186\) 0 0
\(187\) 17.7408i 1.29733i
\(188\) 5.91359 0.431293
\(189\) 0 0
\(190\) 4.24264 0.307794
\(191\) 8.48528i 0.613973i 0.951714 + 0.306987i \(0.0993207\pi\)
−0.951714 + 0.306987i \(0.900679\pi\)
\(192\) 0 0
\(193\) 9.48528 0.682765 0.341383 0.939924i \(-0.389105\pi\)
0.341383 + 0.939924i \(0.389105\pi\)
\(194\) 6.77962 + 11.7426i 0.486748 + 0.843072i
\(195\) 0 0
\(196\) 1.74264 6.77962i 0.124474 0.484258i
\(197\) 26.4853i 1.88700i −0.331375 0.943499i \(-0.607513\pi\)
0.331375 0.943499i \(-0.392487\pi\)
\(198\) 0 0
\(199\) 19.9706 11.5300i 1.41568 0.817341i 0.419761 0.907635i \(-0.362114\pi\)
0.995915 + 0.0902942i \(0.0287807\pi\)
\(200\) −3.88437 2.24264i −0.274666 0.158579i
\(201\) 0 0
\(202\) 0 0
\(203\) −17.7408 7.24264i −1.24516 0.508334i
\(204\) 0 0
\(205\) 8.48528 0.592638
\(206\) 2.74666 + 4.75736i 0.191369 + 0.331461i
\(207\) 0 0
\(208\) 2.12132 + 1.22474i 0.147087 + 0.0849208i
\(209\) 8.87039 + 15.3640i 0.613578 + 1.06275i
\(210\) 0 0
\(211\) 0.121320 0.210133i 0.00835204 0.0144662i −0.861819 0.507216i \(-0.830675\pi\)
0.870171 + 0.492749i \(0.164008\pi\)
\(212\) −6.27231 + 3.62132i −0.430784 + 0.248713i
\(213\) 0 0
\(214\) −5.74264 + 9.94655i −0.392559 + 0.679932i
\(215\) −0.0870399 + 0.150758i −0.00593607 + 0.0102816i
\(216\) 0 0
\(217\) −18.9853 + 14.7224i −1.28880 + 0.999424i
\(218\) 16.0087 9.24264i 1.08425 0.625991i
\(219\) 0 0
\(220\) 2.15232i 0.145109i
\(221\) 14.4853i 0.974385i
\(222\) 0 0
\(223\) 1.86396 1.07616i 0.124820 0.0720649i −0.436290 0.899806i \(-0.643708\pi\)
0.561110 + 0.827741i \(0.310374\pi\)
\(224\) 2.09077 1.62132i 0.139695 0.108329i
\(225\) 0 0
\(226\) 4.24264 7.34847i 0.282216 0.488813i
\(227\) −7.79423 + 13.5000i −0.517321 + 0.896026i 0.482476 + 0.875909i \(0.339737\pi\)
−0.999798 + 0.0201176i \(0.993596\pi\)
\(228\) 0 0
\(229\) 12.0000 6.92820i 0.792982 0.457829i −0.0480291 0.998846i \(-0.515294\pi\)
0.841011 + 0.541017i \(0.181961\pi\)
\(230\) −1.52192 + 2.63604i −0.100352 + 0.173815i
\(231\) 0 0
\(232\) −3.62132 6.27231i −0.237751 0.411797i
\(233\) −16.2189 9.36396i −1.06253 0.613453i −0.136401 0.990654i \(-0.543554\pi\)
−0.926132 + 0.377200i \(0.876887\pi\)
\(234\) 0 0
\(235\) −2.12132 3.67423i −0.138380 0.239681i
\(236\) −8.06591 −0.525046
\(237\) 0 0
\(238\) 14.4853 + 5.91359i 0.938941 + 0.383321i
\(239\) −11.0227 6.36396i −0.712999 0.411650i 0.0991712 0.995070i \(-0.468381\pi\)
−0.812171 + 0.583420i \(0.801714\pi\)
\(240\) 0 0
\(241\) −6.25736 3.61269i −0.403072 0.232714i 0.284737 0.958606i \(-0.408094\pi\)
−0.687809 + 0.725892i \(0.741427\pi\)
\(242\) 1.73205 1.00000i 0.111340 0.0642824i
\(243\) 0 0
\(244\) 1.01461i 0.0649539i
\(245\) −4.83743 + 1.34924i −0.309052 + 0.0861999i
\(246\) 0 0
\(247\) −7.24264 12.5446i −0.460838 0.798195i
\(248\) −9.08052 −0.576614
\(249\) 0 0
\(250\) 6.80511i 0.430393i
\(251\) 27.4156 1.73046 0.865230 0.501375i \(-0.167172\pi\)
0.865230 + 0.501375i \(0.167172\pi\)
\(252\) 0 0
\(253\) −12.7279 −0.800198
\(254\) 3.24264i 0.203461i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −2.15232 3.72792i −0.134258 0.232541i 0.791056 0.611744i \(-0.209532\pi\)
−0.925314 + 0.379203i \(0.876198\pi\)
\(258\) 0 0
\(259\) −0.636039 + 0.0870399i −0.0395215 + 0.00540840i
\(260\) 1.75736i 0.108987i
\(261\) 0 0
\(262\) −4.50000 + 2.59808i −0.278011 + 0.160510i
\(263\) 13.1750 + 7.60660i 0.812407 + 0.469043i 0.847791 0.530331i \(-0.177932\pi\)
−0.0353843 + 0.999374i \(0.511266\pi\)
\(264\) 0 0
\(265\) 4.50000 + 2.59808i 0.276433 + 0.159599i
\(266\) −15.5014 + 2.12132i −0.950453 + 0.130066i
\(267\) 0 0
\(268\) 10.0000 0.610847
\(269\) 6.98975 + 12.1066i 0.426173 + 0.738153i 0.996529 0.0832447i \(-0.0265283\pi\)
−0.570357 + 0.821397i \(0.693195\pi\)
\(270\) 0 0
\(271\) −5.37868 3.10538i −0.326732 0.188639i 0.327658 0.944797i \(-0.393741\pi\)
−0.654389 + 0.756158i \(0.727074\pi\)
\(272\) 2.95680 + 5.12132i 0.179282 + 0.310526i
\(273\) 0 0
\(274\) 1.24264 2.15232i 0.0750707 0.130026i
\(275\) −11.6531 + 6.72792i −0.702709 + 0.405709i
\(276\) 0 0
\(277\) −6.48528 + 11.2328i −0.389663 + 0.674916i −0.992404 0.123021i \(-0.960742\pi\)
0.602741 + 0.797937i \(0.294075\pi\)
\(278\) −0.297173 + 0.514719i −0.0178232 + 0.0308708i
\(279\) 0 0
\(280\) −1.75736 0.717439i −0.105022 0.0428752i
\(281\) 5.19615 3.00000i 0.309976 0.178965i −0.336939 0.941526i \(-0.609392\pi\)
0.646916 + 0.762561i \(0.276058\pi\)
\(282\) 0 0
\(283\) 21.2049i 1.26050i −0.776393 0.630250i \(-0.782953\pi\)
0.776393 0.630250i \(-0.217047\pi\)
\(284\) 1.75736i 0.104280i
\(285\) 0 0
\(286\) 6.36396 3.67423i 0.376309 0.217262i
\(287\) −31.0028 + 4.24264i −1.83004 + 0.250435i
\(288\) 0 0
\(289\) −8.98528 + 15.5630i −0.528546 + 0.915468i
\(290\) −2.59808 + 4.50000i −0.152564 + 0.264249i
\(291\) 0 0
\(292\) 1.24264 0.717439i 0.0727200 0.0419849i
\(293\) −0.358719 + 0.621320i −0.0209566 + 0.0362979i −0.876314 0.481741i \(-0.840005\pi\)
0.855357 + 0.518039i \(0.173338\pi\)
\(294\) 0 0
\(295\) 2.89340 + 5.01151i 0.168460 + 0.291782i
\(296\) −0.210133 0.121320i −0.0122137 0.00705160i
\(297\) 0 0
\(298\) −1.75736 3.04384i −0.101801 0.176325i
\(299\) 10.3923 0.601003
\(300\) 0 0
\(301\) 0.242641 0.594346i 0.0139856 0.0342575i
\(302\) −4.54026 2.62132i −0.261263 0.150840i
\(303\) 0 0
\(304\) −5.12132 2.95680i −0.293728 0.169584i
\(305\) 0.630399 0.363961i 0.0360965 0.0208403i
\(306\) 0 0
\(307\) 9.97204i 0.569134i −0.958656 0.284567i \(-0.908150\pi\)
0.958656 0.284567i \(-0.0918499\pi\)
\(308\) −1.07616 7.86396i −0.0613198 0.448091i
\(309\) 0 0
\(310\) 3.25736 + 5.64191i 0.185006 + 0.320439i
\(311\) −8.95743 −0.507929 −0.253965 0.967214i \(-0.581735\pi\)
−0.253965 + 0.967214i \(0.581735\pi\)
\(312\) 0 0
\(313\) 18.4582i 1.04332i −0.853154 0.521660i \(-0.825313\pi\)
0.853154 0.521660i \(-0.174687\pi\)
\(314\) −14.6969 −0.829396
\(315\) 0 0
\(316\) 2.75736 0.155114
\(317\) 1.24264i 0.0697937i 0.999391 + 0.0348968i \(0.0111103\pi\)
−0.999391 + 0.0348968i \(0.988890\pi\)
\(318\) 0 0
\(319\) −21.7279 −1.21653
\(320\) −0.358719 0.621320i −0.0200530 0.0347329i
\(321\) 0 0
\(322\) 4.24264 10.3923i 0.236433 0.579141i
\(323\) 34.9706i 1.94581i
\(324\) 0 0
\(325\) 9.51472 5.49333i 0.527782 0.304715i
\(326\) 1.94218 + 1.12132i 0.107568 + 0.0621042i
\(327\) 0 0
\(328\) −10.2426 5.91359i −0.565555 0.326523i
\(329\) 9.58783 + 12.3640i 0.528594 + 0.681647i
\(330\) 0 0
\(331\) −33.4558 −1.83890 −0.919450 0.393208i \(-0.871365\pi\)
−0.919450 + 0.393208i \(0.871365\pi\)
\(332\) −3.31552 5.74264i −0.181963 0.315168i
\(333\) 0 0
\(334\) −13.9706 8.06591i −0.764435 0.441347i
\(335\) −3.58719 6.21320i −0.195989 0.339464i
\(336\) 0 0
\(337\) 2.50000 4.33013i 0.136184 0.235877i −0.789865 0.613280i \(-0.789850\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 6.06218 3.50000i 0.329739 0.190375i
\(339\) 0 0
\(340\) 2.12132 3.67423i 0.115045 0.199263i
\(341\) −13.6208 + 23.5919i −0.737607 + 1.27757i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 0.210133 0.121320i 0.0113296 0.00654115i
\(345\) 0 0
\(346\) 20.7846i 1.11739i
\(347\) 2.48528i 0.133417i −0.997773 0.0667084i \(-0.978750\pi\)
0.997773 0.0667084i \(-0.0212497\pi\)
\(348\) 0 0
\(349\) −1.97056 + 1.13770i −0.105482 + 0.0608999i −0.551813 0.833968i \(-0.686064\pi\)
0.446331 + 0.894868i \(0.352730\pi\)
\(350\) −1.60896 11.7574i −0.0860024 0.628457i
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) 4.47871 7.75736i 0.238378 0.412883i −0.721871 0.692028i \(-0.756718\pi\)
0.960249 + 0.279145i \(0.0900510\pi\)
\(354\) 0 0
\(355\) 1.09188 0.630399i 0.0579511 0.0334581i
\(356\) 5.19615 9.00000i 0.275396 0.476999i
\(357\) 0 0
\(358\) −13.2426 22.9369i −0.699895 1.21225i
\(359\) 15.5885 + 9.00000i 0.822727 + 0.475002i 0.851356 0.524588i \(-0.175781\pi\)
−0.0286287 + 0.999590i \(0.509114\pi\)
\(360\) 0 0
\(361\) 7.98528 + 13.8309i 0.420278 + 0.727943i
\(362\) −11.8272 −0.621623
\(363\) 0 0
\(364\) 0.878680 + 6.42090i 0.0460553 + 0.336546i
\(365\) −0.891519 0.514719i −0.0466642 0.0269416i
\(366\) 0 0
\(367\) 13.3492 + 7.70719i 0.696825 + 0.402312i 0.806164 0.591693i \(-0.201540\pi\)
−0.109339 + 0.994005i \(0.534873\pi\)
\(368\) 3.67423 2.12132i 0.191533 0.110581i
\(369\) 0 0
\(370\) 0.174080i 0.00904998i
\(371\) −17.7408 7.24264i −0.921055 0.376019i
\(372\) 0 0
\(373\) 14.7279 + 25.5095i 0.762583 + 1.32083i 0.941515 + 0.336971i \(0.109402\pi\)
−0.178932 + 0.983861i \(0.557264\pi\)
\(374\) 17.7408 0.917354
\(375\) 0 0
\(376\) 5.91359i 0.304970i
\(377\) 17.7408 0.913696
\(378\) 0 0
\(379\) 12.4853 0.641326 0.320663 0.947193i \(-0.396094\pi\)
0.320663 + 0.947193i \(0.396094\pi\)
\(380\) 4.24264i 0.217643i
\(381\) 0 0
\(382\) −8.48528 −0.434145
\(383\) 11.1097 + 19.2426i 0.567681 + 0.983253i 0.996795 + 0.0800023i \(0.0254928\pi\)
−0.429113 + 0.903251i \(0.641174\pi\)
\(384\) 0 0
\(385\) −4.50000 + 3.48960i −0.229341 + 0.177846i
\(386\) 9.48528i 0.482788i
\(387\) 0 0
\(388\) −11.7426 + 6.77962i −0.596142 + 0.344183i
\(389\) −27.2416 15.7279i −1.38120 0.797437i −0.388900 0.921280i \(-0.627145\pi\)
−0.992302 + 0.123843i \(0.960478\pi\)
\(390\) 0 0
\(391\) 21.7279 + 12.5446i 1.09883 + 0.634409i
\(392\) 6.77962 + 1.74264i 0.342422 + 0.0880166i
\(393\) 0 0
\(394\) 26.4853 1.33431
\(395\) −0.989118 1.71320i −0.0497680 0.0862006i
\(396\) 0 0
\(397\) 12.0000 + 6.92820i 0.602263 + 0.347717i 0.769931 0.638127i \(-0.220290\pi\)
−0.167668 + 0.985843i \(0.553624\pi\)
\(398\) 11.5300 + 19.9706i 0.577947 + 1.00103i
\(399\) 0 0
\(400\) 2.24264 3.88437i 0.112132 0.194218i
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) 11.1213 19.2627i 0.553992 0.959543i
\(404\) 0 0
\(405\) 0 0
\(406\) 7.24264 17.7408i 0.359446 0.880460i
\(407\) −0.630399 + 0.363961i −0.0312477 + 0.0180409i
\(408\) 0 0
\(409\) 14.9941i 0.741411i 0.928750 + 0.370706i \(0.120884\pi\)
−0.928750 + 0.370706i \(0.879116\pi\)
\(410\) 8.48528i 0.419058i
\(411\) 0 0
\(412\) −4.75736 + 2.74666i −0.234378 + 0.135318i
\(413\) −13.0774 16.8640i −0.643498 0.829821i
\(414\) 0 0
\(415\) −2.37868 + 4.11999i −0.116765 + 0.202243i
\(416\) −1.22474 + 2.12132i −0.0600481 + 0.104006i
\(417\) 0 0
\(418\) −15.3640 + 8.87039i −0.751476 + 0.433865i
\(419\) 11.8272 20.4853i 0.577796 1.00077i −0.417936 0.908476i \(-0.637246\pi\)
0.995732 0.0922950i \(-0.0294203\pi\)
\(420\) 0 0
\(421\) 7.12132 + 12.3345i 0.347072 + 0.601146i 0.985728 0.168346i \(-0.0538426\pi\)
−0.638656 + 0.769492i \(0.720509\pi\)
\(422\) 0.210133 + 0.121320i 0.0102291 + 0.00590578i
\(423\) 0 0
\(424\) −3.62132 6.27231i −0.175867 0.304610i
\(425\) 26.5241 1.28661
\(426\) 0 0
\(427\) −2.12132 + 1.64501i −0.102658 + 0.0796077i
\(428\) −9.94655 5.74264i −0.480784 0.277581i
\(429\) 0 0
\(430\) −0.150758 0.0870399i −0.00727018 0.00419744i
\(431\) 3.04384 1.75736i 0.146616 0.0846490i −0.424897 0.905242i \(-0.639690\pi\)
0.571514 + 0.820593i \(0.306356\pi\)
\(432\) 0 0
\(433\) 3.46410i 0.166474i −0.996530 0.0832370i \(-0.973474\pi\)
0.996530 0.0832370i \(-0.0265259\pi\)
\(434\) −14.7224 18.9853i −0.706699 0.911323i
\(435\) 0 0
\(436\) 9.24264 + 16.0087i 0.442642 + 0.766679i
\(437\) −25.0892 −1.20018
\(438\) 0 0
\(439\) 16.8493i 0.804171i 0.915602 + 0.402086i \(0.131715\pi\)
−0.915602 + 0.402086i \(0.868285\pi\)
\(440\) −2.15232 −0.102608
\(441\) 0 0
\(442\) −14.4853 −0.688995
\(443\) 16.4558i 0.781841i −0.920425 0.390920i \(-0.872157\pi\)
0.920425 0.390920i \(-0.127843\pi\)
\(444\) 0 0
\(445\) −7.45584 −0.353441
\(446\) 1.07616 + 1.86396i 0.0509576 + 0.0882611i
\(447\) 0 0
\(448\) 1.62132 + 2.09077i 0.0766002 + 0.0987796i
\(449\) 1.75736i 0.0829349i −0.999140 0.0414675i \(-0.986797\pi\)
0.999140 0.0414675i \(-0.0132033\pi\)
\(450\) 0 0
\(451\) −30.7279 + 17.7408i −1.44692 + 0.835380i
\(452\) 7.34847 + 4.24264i 0.345643 + 0.199557i
\(453\) 0 0
\(454\) −13.5000 7.79423i −0.633586 0.365801i
\(455\) 3.67423 2.84924i 0.172251 0.133575i
\(456\) 0 0
\(457\) −23.0000 −1.07589 −0.537947 0.842978i \(-0.680800\pi\)
−0.537947 + 0.842978i \(0.680800\pi\)
\(458\) 6.92820 + 12.0000i 0.323734 + 0.560723i
\(459\) 0 0
\(460\) −2.63604 1.52192i −0.122906 0.0709598i
\(461\) 16.3059 + 28.2426i 0.759441 + 1.31539i 0.943136 + 0.332408i \(0.107861\pi\)
−0.183695 + 0.982983i \(0.558806\pi\)
\(462\) 0 0
\(463\) 14.7279 25.5095i 0.684465 1.18553i −0.289140 0.957287i \(-0.593369\pi\)
0.973605 0.228241i \(-0.0732973\pi\)
\(464\) 6.27231 3.62132i 0.291185 0.168116i
\(465\) 0 0
\(466\) 9.36396 16.2189i 0.433777 0.751324i
\(467\) −19.8931 + 34.4558i −0.920542 + 1.59443i −0.121965 + 0.992534i \(0.538920\pi\)
−0.798578 + 0.601892i \(0.794414\pi\)
\(468\) 0 0
\(469\) 16.2132 + 20.9077i 0.748656 + 0.965428i
\(470\) 3.67423 2.12132i 0.169480 0.0978492i
\(471\) 0 0
\(472\) 8.06591i 0.371264i
\(473\) 0.727922i 0.0334699i
\(474\) 0 0
\(475\) −22.9706 + 13.2621i −1.05396 + 0.608505i
\(476\) −5.91359 + 14.4853i −0.271049 + 0.663932i
\(477\) 0 0
\(478\) 6.36396 11.0227i 0.291081 0.504167i
\(479\) −6.00063 + 10.3934i −0.274176 + 0.474886i −0.969927 0.243397i \(-0.921738\pi\)
0.695751 + 0.718283i \(0.255072\pi\)
\(480\) 0 0
\(481\) 0.514719 0.297173i 0.0234691 0.0135499i
\(482\) 3.61269 6.25736i 0.164553 0.285015i
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 8.42463 + 4.86396i 0.382543 + 0.220861i
\(486\) 0 0
\(487\) 7.10660 + 12.3090i 0.322031 + 0.557774i 0.980907 0.194478i \(-0.0623012\pi\)
−0.658876 + 0.752251i \(0.728968\pi\)
\(488\) −1.01461 −0.0459293
\(489\) 0 0
\(490\) −1.34924 4.83743i −0.0609526 0.218533i
\(491\) 12.0989 + 6.98528i 0.546014 + 0.315241i 0.747513 0.664247i \(-0.231248\pi\)
−0.201499 + 0.979489i \(0.564581\pi\)
\(492\) 0 0
\(493\) 37.0919 + 21.4150i 1.67053 + 0.964483i
\(494\) 12.5446 7.24264i 0.564409 0.325862i
\(495\) 0 0
\(496\) 9.08052i 0.407727i
\(497\) −3.67423 + 2.84924i −0.164812 + 0.127806i
\(498\) 0 0
\(499\) −15.9706 27.6618i −0.714941 1.23831i −0.962982 0.269564i \(-0.913120\pi\)
0.248042 0.968749i \(-0.420213\pi\)
\(500\) −6.80511 −0.304334
\(501\) 0 0
\(502\) 27.4156i 1.22362i
\(503\) 31.0028 1.38235 0.691174 0.722688i \(-0.257094\pi\)
0.691174 + 0.722688i \(0.257094\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 12.7279i 0.565825i
\(507\) 0 0
\(508\) −3.24264 −0.143869
\(509\) −8.59871 14.8934i −0.381131 0.660138i 0.610093 0.792330i \(-0.291132\pi\)
−0.991224 + 0.132191i \(0.957799\pi\)
\(510\) 0 0
\(511\) 3.51472 + 1.43488i 0.155482 + 0.0634753i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.72792 2.15232i 0.164432 0.0949346i
\(515\) 3.41311 + 1.97056i 0.150400 + 0.0868334i
\(516\) 0 0
\(517\) 15.3640 + 8.87039i 0.675706 + 0.390119i
\(518\) −0.0870399 0.636039i −0.00382432 0.0279459i
\(519\) 0 0
\(520\) 1.75736 0.0770653
\(521\) 16.9363 + 29.3345i 0.741993 + 1.28517i 0.951587 + 0.307380i \(0.0994524\pi\)
−0.209594 + 0.977788i \(0.567214\pi\)
\(522\) 0 0
\(523\) 5.84924 + 3.37706i 0.255770 + 0.147669i 0.622403 0.782697i \(-0.286156\pi\)
−0.366634 + 0.930365i \(0.619490\pi\)
\(524\) −2.59808 4.50000i −0.113497 0.196583i
\(525\) 0 0
\(526\) −7.60660 + 13.1750i −0.331664 + 0.574458i
\(527\) 46.5043 26.8492i 2.02576 1.16957i
\(528\) 0 0
\(529\) −2.50000 + 4.33013i −0.108696 + 0.188266i
\(530\) −2.59808 + 4.50000i −0.112853 + 0.195468i
\(531\) 0 0
\(532\) −2.12132 15.5014i −0.0919709 0.672072i
\(533\) 25.0892 14.4853i 1.08674 0.627427i
\(534\) 0 0
\(535\) 8.23999i 0.356246i
\(536\) 10.0000i 0.431934i
\(537\) 0 0
\(538\) −12.1066 + 6.98975i −0.521953 + 0.301350i
\(539\) 14.6969 15.0000i 0.633042 0.646096i
\(540\) 0 0
\(541\) −7.36396 + 12.7548i −0.316601 + 0.548370i −0.979777 0.200094i \(-0.935875\pi\)
0.663175 + 0.748464i \(0.269208\pi\)
\(542\) 3.10538 5.37868i 0.133388 0.231034i
\(543\) 0 0
\(544\) −5.12132 + 2.95680i −0.219575 + 0.126772i
\(545\) 6.63103 11.4853i 0.284042 0.491975i
\(546\) 0 0
\(547\) 19.8492 + 34.3799i 0.848692 + 1.46998i 0.882376 + 0.470546i \(0.155943\pi\)
−0.0336833 + 0.999433i \(0.510724\pi\)
\(548\) 2.15232 + 1.24264i 0.0919424 + 0.0530830i
\(549\) 0 0
\(550\) −6.72792 11.6531i −0.286880 0.496890i
\(551\) −42.8300 −1.82462
\(552\) 0 0
\(553\) 4.47056 + 5.76500i 0.190108 + 0.245153i
\(554\) −11.2328 6.48528i −0.477238 0.275533i
\(555\) 0 0
\(556\) −0.514719 0.297173i −0.0218289 0.0126029i
\(557\) −8.42463 + 4.86396i −0.356963 + 0.206093i −0.667748 0.744388i \(-0.732741\pi\)
0.310785 + 0.950480i \(0.399408\pi\)
\(558\) 0 0
\(559\) 0.594346i 0.0251382i
\(560\) 0.717439 1.75736i 0.0303173 0.0742620i
\(561\) 0 0
\(562\) 3.00000 + 5.19615i 0.126547 + 0.219186i
\(563\) 34.5900 1.45780 0.728898 0.684622i \(-0.240033\pi\)
0.728898 + 0.684622i \(0.240033\pi\)
\(564\) 0 0
\(565\) 6.08767i 0.256110i
\(566\) 21.2049 0.891307
\(567\) 0 0
\(568\) −1.75736 −0.0737372
\(569\) 10.2426i 0.429394i −0.976681 0.214697i \(-0.931124\pi\)
0.976681 0.214697i \(-0.0688764\pi\)
\(570\) 0 0
\(571\) 8.72792 0.365252 0.182626 0.983182i \(-0.441540\pi\)
0.182626 + 0.983182i \(0.441540\pi\)
\(572\) 3.67423 + 6.36396i 0.153627 + 0.266091i
\(573\) 0 0
\(574\) −4.24264 31.0028i −0.177084 1.29403i
\(575\) 19.0294i 0.793582i
\(576\) 0 0
\(577\) 9.25736 5.34474i 0.385389 0.222504i −0.294771 0.955568i \(-0.595243\pi\)
0.680160 + 0.733063i \(0.261910\pi\)
\(578\) −15.5630 8.98528i −0.647334 0.373738i
\(579\) 0 0
\(580\) −4.50000 2.59808i −0.186852 0.107879i
\(581\) 6.63103 16.2426i 0.275101 0.673858i
\(582\) 0 0
\(583\) −21.7279 −0.899879
\(584\) 0.717439 + 1.24264i 0.0296878 + 0.0514208i
\(585\) 0 0
\(586\) −0.621320 0.358719i −0.0256665 0.0148186i
\(587\) 2.59808 + 4.50000i 0.107234 + 0.185735i 0.914649 0.404249i \(-0.132467\pi\)
−0.807415 + 0.589984i \(0.799134\pi\)
\(588\) 0 0
\(589\) −26.8492 + 46.5043i −1.10630 + 1.91617i
\(590\) −5.01151 + 2.89340i −0.206321 + 0.119119i
\(591\) 0 0
\(592\) 0.121320 0.210133i 0.00498624 0.00863641i
\(593\) 11.7401 20.3345i 0.482110 0.835039i −0.517679 0.855575i \(-0.673204\pi\)
0.999789 + 0.0205360i \(0.00653726\pi\)
\(594\) 0 0
\(595\) 11.1213 1.52192i 0.455930 0.0623925i
\(596\) 3.04384 1.75736i 0.124680 0.0719842i
\(597\) 0 0
\(598\) 10.3923i 0.424973i
\(599\) 7.45584i 0.304638i 0.988331 + 0.152319i \(0.0486740\pi\)
−0.988331 + 0.152319i \(0.951326\pi\)
\(600\) 0 0
\(601\) 20.2279 11.6786i 0.825114 0.476380i −0.0270627 0.999634i \(-0.508615\pi\)
0.852177 + 0.523254i \(0.175282\pi\)
\(602\) 0.594346 + 0.242641i 0.0242237 + 0.00988930i
\(603\) 0 0
\(604\) 2.62132 4.54026i 0.106660 0.184741i
\(605\) 0.717439 1.24264i 0.0291680 0.0505205i
\(606\) 0 0
\(607\) 17.3787 10.0336i 0.705379 0.407251i −0.103969 0.994581i \(-0.533154\pi\)
0.809348 + 0.587330i \(0.199821\pi\)
\(608\) 2.95680 5.12132i 0.119914 0.207697i
\(609\) 0 0
\(610\) 0.363961 + 0.630399i 0.0147364 + 0.0255241i
\(611\) −12.5446 7.24264i −0.507501 0.293006i
\(612\) 0 0
\(613\) 18.6066 + 32.2276i 0.751514 + 1.30166i 0.947089 + 0.320971i \(0.104009\pi\)
−0.195575 + 0.980689i \(0.562657\pi\)
\(614\) 9.97204 0.402439
\(615\) 0 0
\(616\) 7.86396 1.07616i 0.316848 0.0433597i
\(617\) 15.3273 + 8.84924i 0.617055 + 0.356257i 0.775722 0.631075i \(-0.217386\pi\)
−0.158666 + 0.987332i \(0.550719\pi\)
\(618\) 0 0
\(619\) −5.33452 3.07989i −0.214413 0.123791i 0.388948 0.921260i \(-0.372839\pi\)
−0.603360 + 0.797469i \(0.706172\pi\)
\(620\) −5.64191 + 3.25736i −0.226585 + 0.130819i
\(621\) 0 0
\(622\) 8.95743i 0.359160i
\(623\) 27.2416 3.72792i 1.09141 0.149356i
\(624\) 0 0
\(625\) −8.77208 15.1937i −0.350883 0.607747i
\(626\) 18.4582 0.737739
\(627\) 0 0
\(628\) 14.6969i 0.586472i
\(629\) 1.43488 0.0572123
\(630\) 0 0
\(631\) 24.7574 0.985575 0.492787 0.870150i \(-0.335978\pi\)
0.492787 + 0.870150i \(0.335978\pi\)
\(632\) 2.75736i 0.109682i
\(633\) 0 0
\(634\) −1.24264 −0.0493516
\(635\) 1.16320 + 2.01472i 0.0461601 + 0.0799517i
\(636\) 0 0
\(637\) −12.0000 + 12.2474i −0.475457 + 0.485262i
\(638\) 21.7279i 0.860217i
\(639\) 0 0
\(640\) 0.621320 0.358719i 0.0245598 0.0141796i
\(641\) −15.3273 8.84924i −0.605393 0.349524i 0.165767 0.986165i \(-0.446990\pi\)
−0.771160 + 0.636641i \(0.780323\pi\)
\(642\) 0 0
\(643\) −27.7279 16.0087i −1.09348 0.631322i −0.158981 0.987282i \(-0.550821\pi\)
−0.934501 + 0.355959i \(0.884154\pi\)
\(644\) 10.3923 + 4.24264i 0.409514 + 0.167183i
\(645\) 0 0
\(646\) 34.9706 1.37590
\(647\) 16.2189 + 28.0919i 0.637629 + 1.10441i 0.985952 + 0.167031i \(0.0534180\pi\)
−0.348323 + 0.937375i \(0.613249\pi\)
\(648\) 0 0
\(649\) −20.9558 12.0989i −0.822589 0.474922i
\(650\) 5.49333 + 9.51472i 0.215466 + 0.373198i
\(651\) 0 0
\(652\) −1.12132 + 1.94218i −0.0439143 + 0.0760618i
\(653\) 16.6646 9.62132i 0.652137 0.376511i −0.137138 0.990552i \(-0.543790\pi\)
0.789274 + 0.614041i \(0.210457\pi\)
\(654\) 0 0
\(655\) −1.86396 + 3.22848i −0.0728310 + 0.126147i
\(656\) 5.91359 10.2426i 0.230887 0.399908i
\(657\) 0 0
\(658\) −12.3640 + 9.58783i −0.481997 + 0.373772i
\(659\) 5.19615 3.00000i 0.202413 0.116863i −0.395367 0.918523i \(-0.629383\pi\)
0.597781 + 0.801660i \(0.296049\pi\)
\(660\) 0 0
\(661\) 35.6556i 1.38684i 0.720532 + 0.693422i \(0.243898\pi\)
−0.720532 + 0.693422i \(0.756102\pi\)
\(662\) 33.4558i 1.30030i
\(663\) 0 0
\(664\) 5.74264 3.31552i 0.222858 0.128667i
\(665\) −8.87039 + 6.87868i −0.343979 + 0.266744i
\(666\) 0 0
\(667\) 15.3640 26.6112i 0.594895 1.03039i
\(668\) 8.06591 13.9706i 0.312079 0.540537i
\(669\) 0 0
\(670\) 6.21320 3.58719i 0.240037 0.138585i
\(671\) −1.52192 + 2.63604i −0.0587530 + 0.101763i
\(672\) 0 0
\(673\) −8.98528 15.5630i −0.346357 0.599908i 0.639242 0.769005i \(-0.279248\pi\)
−0.985599 + 0.169097i \(0.945915\pi\)
\(674\) 4.33013 + 2.50000i 0.166790 + 0.0962964i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) 2.15232 0.0827203 0.0413601 0.999144i \(-0.486831\pi\)
0.0413601 + 0.999144i \(0.486831\pi\)
\(678\) 0 0
\(679\) −33.2132 13.5592i −1.27461 0.520356i
\(680\) 3.67423 + 2.12132i 0.140900 + 0.0813489i
\(681\) 0 0
\(682\) −23.5919 13.6208i −0.903380 0.521567i
\(683\) 6.90271 3.98528i 0.264125 0.152493i −0.362090 0.932143i \(-0.617937\pi\)
0.626215 + 0.779651i \(0.284603\pi\)
\(684\) 0 0
\(685\) 1.78304i 0.0681264i
\(686\) 7.34847 + 17.0000i 0.280566 + 0.649063i
\(687\) 0 0
\(688\) 0.121320 + 0.210133i 0.00462529 + 0.00801125i
\(689\) 17.7408 0.675870
\(690\) 0 0
\(691\) 28.5533i 1.08622i −0.839661 0.543110i \(-0.817247\pi\)
0.839661 0.543110i \(-0.182753\pi\)
\(692\) 20.7846 0.790112
\(693\) 0 0
\(694\) 2.48528 0.0943400
\(695\) 0.426407i 0.0161745i
\(696\) 0 0
\(697\) 69.9411 2.64921
\(698\) −1.13770 1.97056i −0.0430628 0.0745869i
\(699\) 0 0
\(700\) 11.7574 1.60896i 0.444386 0.0608129i
\(701\) 20.6985i 0.781771i 0.920439 + 0.390885i \(0.127831\pi\)
−0.920439 + 0.390885i \(0.872169\pi\)
\(702\) 0 0
\(703\) −1.24264 + 0.717439i −0.0468671 + 0.0270587i
\(704\) 2.59808 + 1.50000i 0.0979187 + 0.0565334i
\(705\) 0 0
\(706\) 7.75736 + 4.47871i 0.291952 + 0.168559i
\(707\) 0 0
\(708\) 0 0
\(709\) 26.9706 1.01290 0.506450 0.862269i \(-0.330957\pi\)
0.506450 + 0.862269i \(0.330957\pi\)
\(710\) 0.630399 + 1.09188i 0.0236585 + 0.0409776i
\(711\) 0 0
\(712\) 9.00000 + 5.19615i 0.337289 + 0.194734i
\(713\) −19.2627 33.3640i −0.721393 1.24949i
\(714\) 0 0
\(715\) 2.63604 4.56575i 0.0985823 0.170749i
\(716\) 22.9369 13.2426i 0.857193 0.494901i
\(717\) 0 0
\(718\) −9.00000 + 15.5885i −0.335877 + 0.581756i
\(719\) 8.06591 13.9706i 0.300808 0.521014i −0.675511 0.737349i \(-0.736077\pi\)
0.976319 + 0.216335i \(0.0694105\pi\)
\(720\) 0 0
\(721\) −13.4558 5.49333i −0.501122 0.204582i
\(722\) −13.8309 + 7.98528i −0.514733 + 0.297181i
\(723\) 0 0
\(724\) 11.8272i 0.439554i
\(725\) 32.4853i 1.20647i
\(726\) 0 0
\(727\) −10.1360 + 5.85204i −0.375925 + 0.217040i −0.676044 0.736861i \(-0.736307\pi\)
0.300119 + 0.953902i \(0.402974\pi\)
\(728\) −6.42090 + 0.878680i −0.237974 + 0.0325660i
\(729\) 0 0
\(730\) 0.514719 0.891519i 0.0190506 0.0329966i
\(731\) −0.717439 + 1.24264i −0.0265354 + 0.0459607i
\(732\) 0 0
\(733\) −4.09188 + 2.36245i −0.151137 + 0.0872591i −0.573661 0.819093i \(-0.694477\pi\)
0.422524 + 0.906352i \(0.361144\pi\)
\(734\) −7.70719 + 13.3492i −0.284478 + 0.492730i
\(735\) 0 0
\(736\) 2.12132 + 3.67423i 0.0781929 + 0.135434i
\(737\) 25.9808 + 15.0000i 0.957014 + 0.552532i
\(738\) 0 0
\(739\) −7.72792 13.3852i −0.284276 0.492381i 0.688157 0.725562i \(-0.258420\pi\)
−0.972433 + 0.233181i \(0.925087\pi\)
\(740\) −0.174080 −0.00639930
\(741\) 0 0
\(742\) 7.24264 17.7408i 0.265886 0.651284i
\(743\) −33.3292 19.2426i −1.22273 0.705944i −0.257232 0.966350i \(-0.582810\pi\)
−0.965499 + 0.260406i \(0.916144\pi\)
\(744\) 0 0
\(745\) −2.18377 1.26080i −0.0800070 0.0461921i
\(746\) −25.5095 + 14.7279i −0.933969 + 0.539228i
\(747\) 0 0
\(748\) 17.7408i 0.648667i
\(749\) −4.11999 30.1066i −0.150541 1.10007i
\(750\) 0 0
\(751\) −17.6213 30.5210i −0.643011 1.11373i −0.984757 0.173936i \(-0.944352\pi\)
0.341746 0.939792i \(-0.388982\pi\)
\(752\) −5.91359 −0.215646
\(753\) 0 0
\(754\) 17.7408i 0.646081i
\(755\) −3.76127 −0.136887
\(756\) 0 0
\(757\) −33.7574 −1.22693 −0.613466 0.789721i \(-0.710225\pi\)
−0.613466 + 0.789721i \(0.710225\pi\)
\(758\) 12.4853i 0.453486i
\(759\) 0 0
\(760\) −4.24264 −0.153897
\(761\) 14.7840 + 25.6066i 0.535919 + 0.928239i 0.999118 + 0.0419845i \(0.0133680\pi\)
−0.463199 + 0.886254i \(0.653299\pi\)
\(762\) 0 0
\(763\) −18.4853 + 45.2795i −0.669212 + 1.63923i
\(764\) 8.48528i 0.306987i
\(765\) 0 0
\(766\) −19.2426 + 11.1097i −0.695265 + 0.401411i
\(767\) 17.1104 + 9.87868i 0.617820 + 0.356698i
\(768\) 0 0
\(769\) −8.52944 4.92447i −0.307579 0.177581i 0.338263 0.941051i \(-0.390161\pi\)
−0.645843 + 0.763470i \(0.723494\pi\)
\(770\) −3.48960 4.50000i −0.125756 0.162169i
\(771\) 0 0
\(772\) −9.48528 −0.341383
\(773\) −8.06591 13.9706i −0.290111 0.502486i 0.683725 0.729740i \(-0.260359\pi\)
−0.973836 + 0.227253i \(0.927025\pi\)
\(774\) 0 0
\(775\) −35.2721 20.3643i −1.26701 0.731509i
\(776\) −6.77962 11.7426i −0.243374 0.421536i
\(777\) 0 0
\(778\) 15.7279 27.2416i 0.563873 0.976657i
\(779\) −60.5708 + 34.9706i −2.17017 + 1.25295i
\(780\) 0 0
\(781\) −2.63604 + 4.56575i −0.0943249 + 0.163376i
\(782\) −12.5446 + 21.7279i −0.448595 + 0.776989i
\(783\) 0 0
\(784\) −1.74264 + 6.77962i −0.0622372 + 0.242129i
\(785\) −9.13151 + 5.27208i −0.325917 + 0.188169i
\(786\) 0 0
\(787\) 32.1915i 1.14750i 0.819029 + 0.573752i \(0.194513\pi\)
−0.819029 + 0.573752i \(0.805487\pi\)
\(788\) 26.4853i 0.943499i
\(789\) 0 0
\(790\) 1.71320 0.989118i 0.0609530 0.0351913i
\(791\) 3.04384 + 22.2426i 0.108226 + 0.790857i
\(792\) 0 0
\(793\) 1.24264 2.15232i 0.0441275 0.0764310i
\(794\) −6.92820 + 12.0000i −0.245873 + 0.425864i
\(795\) 0 0
\(796\) −19.9706 + 11.5300i −0.707838 + 0.408670i
\(797\) 3.22848 5.59188i 0.114358 0.198075i −0.803165 0.595757i \(-0.796852\pi\)
0.917523 + 0.397682i \(0.130185\pi\)
\(798\) 0 0
\(799\) −17.4853 30.2854i −0.618585 1.07142i
\(800\) 3.88437 + 2.24264i 0.137333 + 0.0792893i
\(801\) 0 0
\(802\) 0 0
\(803\) 4.30463 0.151907
\(804\) 0 0
\(805\) −1.09188 7.97887i −0.0384838 0.281218i
\(806\) 19.2627 + 11.1213i 0.678499 + 0.391732i
\(807\) 0 0
\(808\) 0 0
\(809\) 6.08767 3.51472i 0.214031 0.123571i −0.389152 0.921173i \(-0.627232\pi\)
0.603183 + 0.797602i \(0.293899\pi\)
\(810\) 0 0
\(811\) 31.1769i 1.09477i 0.836881 + 0.547385i \(0.184377\pi\)
−0.836881 + 0.547385i \(0.815623\pi\)
\(812\) 17.7408 + 7.24264i 0.622579 + 0.254167i
\(813\) 0 0
\(814\) −0.363961 0.630399i −0.0127568 0.0220955i
\(815\) 1.60896 0.0563593
\(816\) 0 0
\(817\) 1.43488i 0.0502000i
\(818\) −14.9941 −0.524257
\(819\) 0 0
\(820\) −8.48528 −0.296319
\(821\) 40.7574i 1.42244i 0.702969 + 0.711221i \(0.251857\pi\)
−0.702969 + 0.711221i \(0.748143\pi\)
\(822\) 0 0
\(823\) 29.9411 1.04368 0.521841 0.853043i \(-0.325245\pi\)
0.521841 + 0.853043i \(0.325245\pi\)
\(824\) −2.74666 4.75736i −0.0956845 0.165730i
\(825\) 0 0
\(826\) 16.8640 13.0774i 0.586772 0.455022i
\(827\) 37.9706i 1.32037i 0.751105 + 0.660183i \(0.229521\pi\)
−0.751105 + 0.660183i \(0.770479\pi\)
\(828\) 0 0
\(829\) 11.3345 6.54399i 0.393664 0.227282i −0.290082 0.957002i \(-0.593683\pi\)
0.683747 + 0.729720i \(0.260349\pi\)
\(830\) −4.11999 2.37868i −0.143007 0.0825652i
\(831\) 0 0
\(832\) −2.12132 1.22474i −0.0735436 0.0424604i
\(833\) −39.8732 + 11.1213i −1.38153 + 0.385331i
\(834\) 0 0
\(835\) −11.5736 −0.400521
\(836\) −8.87039 15.3640i −0.306789 0.531374i
\(837\) 0 0
\(838\) 20.4853 + 11.8272i 0.707652 + 0.408563i
\(839\) 5.10911 + 8.84924i 0.176386 + 0.305510i 0.940640 0.339406i \(-0.110226\pi\)
−0.764254 + 0.644915i \(0.776893\pi\)
\(840\) 0 0
\(841\) 11.7279 20.3134i 0.404411 0.700461i
\(842\) −12.3345 + 7.12132i −0.425075 + 0.245417i
\(843\) 0 0
\(844\) −0.121320 + 0.210133i −0.00417602 + 0.00723308i
\(845\) 2.51104 4.34924i 0.0863823 0.149618i
\(846\) 0 0
\(847\) −2.00000 + 4.89898i −0.0687208 + 0.168331i
\(848\) 6.27231 3.62132i 0.215392 0.124357i
\(849\) 0 0
\(850\) 26.5241i 0.909770i
\(851\) 1.02944i 0.0352887i
\(852\) 0 0
\(853\) 31.9706 18.4582i 1.09465 0.631997i 0.159840 0.987143i \(-0.448902\pi\)
0.934811 + 0.355146i \(0.115569\pi\)
\(854\) −1.64501 2.12132i −0.0562911 0.0725901i
\(855\) 0 0
\(856\) 5.74264 9.94655i 0.196279 0.339966i
\(857\) −16.9363 + 29.3345i −0.578533 + 1.00205i 0.417115 + 0.908854i \(0.363041\pi\)
−0.995648 + 0.0931946i \(0.970292\pi\)
\(858\) 0 0
\(859\) −8.12132 + 4.68885i −0.277096 + 0.159981i −0.632108 0.774880i \(-0.717810\pi\)
0.355012 + 0.934862i \(0.384477\pi\)
\(860\) 0.0870399 0.150758i 0.00296804 0.00514079i
\(861\) 0 0
\(862\) 1.75736 + 3.04384i 0.0598559 + 0.103673i
\(863\) −29.0246 16.7574i −0.988009 0.570427i −0.0833303 0.996522i \(-0.526556\pi\)
−0.904679 + 0.426095i \(0.859889\pi\)
\(864\) 0 0
\(865\) −7.45584 12.9139i −0.253506 0.439086i
\(866\) 3.46410 0.117715
\(867\) 0 0
\(868\) 18.9853 14.7224i 0.644402 0.499712i
\(869\) 7.16383 + 4.13604i 0.243016 + 0.140306i
\(870\) 0 0
\(871\) −21.2132 12.2474i −0.718782 0.414989i
\(872\) −16.0087 + 9.24264i −0.542124 + 0.312995i
\(873\) 0 0
\(874\) 25.0892i 0.848656i
\(875\) −11.0333 14.2279i −0.372992 0.480992i
\(876\) 0 0
\(877\) −2.24264 3.88437i −0.0757286 0.131166i 0.825674 0.564147i \(-0.190795\pi\)
−0.901403 + 0.432981i \(0.857462\pi\)
\(878\) −16.8493 −0.568635
\(879\) 0 0
\(880\) 2.15232i 0.0725546i
\(881\) −19.0016 −0.640179 −0.320090 0.947387i \(-0.603713\pi\)
−0.320090 + 0.947387i \(0.603713\pi\)
\(882\) 0 0
\(883\) 41.4558 1.39510 0.697550 0.716536i \(-0.254273\pi\)
0.697550 + 0.716536i \(0.254273\pi\)
\(884\) 14.4853i 0.487193i
\(885\) 0 0
\(886\) 16.4558 0.552845
\(887\) −5.28319 9.15076i −0.177392 0.307252i 0.763594 0.645696i \(-0.223433\pi\)
−0.940987 + 0.338444i \(0.890099\pi\)
\(888\) 0 0
\(889\) −5.25736 6.77962i −0.176326 0.227381i
\(890\) 7.45584i 0.249920i
\(891\) 0 0
\(892\) −1.86396 + 1.07616i −0.0624100 + 0.0360324i
\(893\) 30.2854 + 17.4853i 1.01346 + 0.585123i
\(894\) 0 0
\(895\) −16.4558 9.50079i −0.550058 0.317576i
\(896\) −2.09077 + 1.62132i −0.0698477 + 0.0541645i
\(897\) 0 0
\(898\) 1.75736 0.0586438
\(899\) −32.8835 56.9558i −1.09673 1.89958i
\(900\) 0 0
\(901\) 37.0919 + 21.4150i 1.23571 + 0.713437i
\(902\) −17.7408 30.7279i −0.590703 1.02313i
\(903\) 0 0
\(904\) −4.24264 + 7.34847i −0.141108 + 0.244406i
\(905\) −7.34847 + 4.24264i −0.244271 + 0.141030i
\(906\) 0 0
\(907\) 15.8492 27.4517i 0.526265 0.911519i −0.473266 0.880919i \(-0.656925\pi\)
0.999532 0.0305991i \(-0.00974151\pi\)
\(908\) 7.79423 13.5000i 0.258661 0.448013i
\(909\) 0 0
\(910\) 2.84924 + 3.67423i 0.0944515 + 0.121800i
\(911\) −5.82655 + 3.36396i −0.193042 + 0.111453i −0.593406 0.804903i \(-0.702217\pi\)
0.400364 + 0.916356i \(0.368884\pi\)
\(912\) 0 0
\(913\) 19.8931i 0.658365i
\(914\) 23.0000i 0.760772i
\(915\) 0 0
\(916\) −12.0000 + 6.92820i −0.396491 + 0.228914i
\(917\) 5.19615 12.7279i 0.171592 0.420313i
\(918\) 0 0
\(919\) −18.2426 + 31.5972i −0.601769 + 1.04229i 0.390784 + 0.920482i \(0.372204\pi\)
−0.992553 + 0.121812i \(0.961129\pi\)
\(920\) 1.52192 2.63604i 0.0501761 0.0869076i
\(921\) 0 0
\(922\) −28.2426 + 16.3059i −0.930122 + 0.537006i
\(923\) 2.15232 3.72792i 0.0708444 0.122706i
\(924\) 0 0
\(925\) −0.544156 0.942506i −0.0178917 0.0309894i
\(926\) 25.5095 + 14.7279i 0.838294 + 0.483990i
\(927\) 0 0
\(928\) 3.62132 + 6.27231i 0.118876 + 0.205899i
\(929\) −31.0028 −1.01717 −0.508585 0.861012i \(-0.669831\pi\)
−0.508585 + 0.861012i \(0.669831\pi\)
\(930\) 0 0
\(931\) 28.9706 29.5680i 0.949472 0.969051i
\(932\) 16.2189 + 9.36396i 0.531266 + 0.306727i
\(933\) 0 0
\(934\) −34.4558 19.8931i −1.12743 0.650922i
\(935\) 11.0227 6.36396i 0.360481 0.208124i
\(936\) 0 0
\(937\) 35.1844i 1.14942i −0.818356 0.574712i \(-0.805114\pi\)
0.818356 0.574712i \(-0.194886\pi\)
\(938\) −20.9077 + 16.2132i −0.682661 + 0.529380i
\(939\) 0 0
\(940\) 2.12132 + 3.67423i 0.0691898 + 0.119840i
\(941\) 27.5897 0.899399 0.449700 0.893180i \(-0.351531\pi\)
0.449700 + 0.893180i \(0.351531\pi\)
\(942\) 0 0
\(943\) 50.1785i 1.63404i
\(944\) 8.06591 0.262523
\(945\) 0 0
\(946\) 0.727922 0.0236668
\(947\) 10.9706i 0.356495i −0.983986 0.178248i \(-0.942957\pi\)
0.983986 0.178248i \(-0.0570428\pi\)
\(948\) 0 0
\(949\) −3.51472 −0.114093
\(950\) −13.2621 22.9706i −0.430278 0.745263i
\(951\) 0 0
\(952\) −14.4853 5.91359i −0.469471 0.191661i
\(953\) 17.6985i 0.573310i −0.958034 0.286655i \(-0.907457\pi\)
0.958034 0.286655i \(-0.0925434\pi\)
\(954\) 0 0
\(955\) −5.27208 + 3.04384i −0.170600 + 0.0984962i
\(956\) 11.0227 + 6.36396i 0.356500 + 0.205825i
\(957\) 0 0
\(958\) −10.3934 6.00063i −0.335795 0.193872i
\(959\) 0.891519 + 6.51472i 0.0287886 + 0.210371i
\(960\) 0 0
\(961\) −51.4558 −1.65987
\(962\) 0.297173 + 0.514719i 0.00958124 + 0.0165952i
\(963\) 0 0
\(964\) 6.25736 + 3.61269i 0.201536 + 0.116357i
\(965\) 3.40256 + 5.89340i 0.109532 + 0.189715i
\(966\) 0 0
\(967\) −23.8640 + 41.3336i −0.767413 + 1.32920i 0.171548 + 0.985176i \(0.445123\pi\)
−0.938961 + 0.344023i \(0.888210\pi\)
\(968\) −1.73205 + 1.00000i −0.0556702 + 0.0321412i
\(969\) 0 0
\(970\) −4.86396 + 8.42463i −0.156172 + 0.270498i
\(971\) −13.5337 + 23.4411i −0.434318 + 0.752262i −0.997240 0.0742490i \(-0.976344\pi\)
0.562921 + 0.826510i \(0.309677\pi\)
\(972\) 0 0
\(973\) −0.213203 1.55797i −0.00683499 0.0499463i
\(974\) −12.3090 + 7.10660i −0.394406 + 0.227710i
\(975\) 0 0
\(976\) 1.01461i 0.0324769i
\(977\) 40.2426i 1.28748i 0.765246 + 0.643738i \(0.222617\pi\)
−0.765246 + 0.643738i \(0.777383\pi\)
\(978\) 0 0
\(979\) 27.0000 15.5885i 0.862924 0.498209i
\(980\) 4.83743 1.34924i 0.154526 0.0431000i
\(981\) 0 0
\(982\) −6.98528 + 12.0989i −0.222909 + 0.386090i
\(983\) 23.6544 40.9706i 0.754457 1.30676i −0.191187 0.981554i \(-0.561234\pi\)
0.945644 0.325204i \(-0.105433\pi\)
\(984\) 0 0
\(985\) 16.4558 9.50079i 0.524327 0.302720i
\(986\) −21.4150 + 37.0919i −0.681993 + 1.18125i
\(987\) 0 0
\(988\) 7.24264 + 12.5446i 0.230419 + 0.399098i
\(989\) 0.891519 + 0.514719i 0.0283486 + 0.0163671i
\(990\) 0 0
\(991\) −26.1066 45.2180i −0.829304 1.43640i −0.898585 0.438799i \(-0.855404\pi\)
0.0692818 0.997597i \(-0.477929\pi\)
\(992\) 9.08052 0.288307
\(993\) 0 0
\(994\) −2.84924 3.67423i −0.0903725 0.116540i
\(995\) 14.3277 + 8.27208i 0.454217 + 0.262243i
\(996\) 0 0
\(997\) 33.7279 + 19.4728i 1.06817 + 0.616711i 0.927682 0.373371i \(-0.121798\pi\)
0.140492 + 0.990082i \(0.455132\pi\)
\(998\) 27.6618 15.9706i 0.875620 0.505539i
\(999\) 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.l.f.215.4 8
3.2 odd 2 inner 1134.2.l.f.215.1 8
7.3 odd 6 1134.2.t.e.1025.2 8
9.2 odd 6 1134.2.t.e.593.2 8
9.4 even 3 126.2.k.a.89.2 yes 8
9.5 odd 6 126.2.k.a.89.3 yes 8
9.7 even 3 1134.2.t.e.593.3 8
21.17 even 6 1134.2.t.e.1025.3 8
36.23 even 6 1008.2.bt.c.593.2 8
36.31 odd 6 1008.2.bt.c.593.3 8
45.4 even 6 3150.2.bf.a.1601.3 8
45.13 odd 12 3150.2.bp.b.1349.2 8
45.14 odd 6 3150.2.bf.a.1601.1 8
45.22 odd 12 3150.2.bp.e.1349.3 8
45.23 even 12 3150.2.bp.e.1349.2 8
45.32 even 12 3150.2.bp.b.1349.3 8
63.4 even 3 882.2.k.a.521.4 8
63.5 even 6 882.2.d.a.881.2 8
63.13 odd 6 882.2.k.a.215.1 8
63.23 odd 6 882.2.d.a.881.3 8
63.31 odd 6 126.2.k.a.17.3 yes 8
63.32 odd 6 882.2.k.a.521.1 8
63.38 even 6 inner 1134.2.l.f.269.2 8
63.40 odd 6 882.2.d.a.881.7 8
63.41 even 6 882.2.k.a.215.4 8
63.52 odd 6 inner 1134.2.l.f.269.3 8
63.58 even 3 882.2.d.a.881.6 8
63.59 even 6 126.2.k.a.17.2 8
252.23 even 6 7056.2.k.f.881.6 8
252.31 even 6 1008.2.bt.c.17.2 8
252.59 odd 6 1008.2.bt.c.17.3 8
252.103 even 6 7056.2.k.f.881.5 8
252.131 odd 6 7056.2.k.f.881.4 8
252.247 odd 6 7056.2.k.f.881.3 8
315.59 even 6 3150.2.bf.a.1151.3 8
315.94 odd 6 3150.2.bf.a.1151.1 8
315.122 odd 12 3150.2.bp.b.899.2 8
315.157 even 12 3150.2.bp.e.899.2 8
315.248 odd 12 3150.2.bp.e.899.3 8
315.283 even 12 3150.2.bp.b.899.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.k.a.17.2 8 63.59 even 6
126.2.k.a.17.3 yes 8 63.31 odd 6
126.2.k.a.89.2 yes 8 9.4 even 3
126.2.k.a.89.3 yes 8 9.5 odd 6
882.2.d.a.881.2 8 63.5 even 6
882.2.d.a.881.3 8 63.23 odd 6
882.2.d.a.881.6 8 63.58 even 3
882.2.d.a.881.7 8 63.40 odd 6
882.2.k.a.215.1 8 63.13 odd 6
882.2.k.a.215.4 8 63.41 even 6
882.2.k.a.521.1 8 63.32 odd 6
882.2.k.a.521.4 8 63.4 even 3
1008.2.bt.c.17.2 8 252.31 even 6
1008.2.bt.c.17.3 8 252.59 odd 6
1008.2.bt.c.593.2 8 36.23 even 6
1008.2.bt.c.593.3 8 36.31 odd 6
1134.2.l.f.215.1 8 3.2 odd 2 inner
1134.2.l.f.215.4 8 1.1 even 1 trivial
1134.2.l.f.269.2 8 63.38 even 6 inner
1134.2.l.f.269.3 8 63.52 odd 6 inner
1134.2.t.e.593.2 8 9.2 odd 6
1134.2.t.e.593.3 8 9.7 even 3
1134.2.t.e.1025.2 8 7.3 odd 6
1134.2.t.e.1025.3 8 21.17 even 6
3150.2.bf.a.1151.1 8 315.94 odd 6
3150.2.bf.a.1151.3 8 315.59 even 6
3150.2.bf.a.1601.1 8 45.14 odd 6
3150.2.bf.a.1601.3 8 45.4 even 6
3150.2.bp.b.899.2 8 315.122 odd 12
3150.2.bp.b.899.3 8 315.283 even 12
3150.2.bp.b.1349.2 8 45.13 odd 12
3150.2.bp.b.1349.3 8 45.32 even 12
3150.2.bp.e.899.2 8 315.157 even 12
3150.2.bp.e.899.3 8 315.248 odd 12
3150.2.bp.e.1349.2 8 45.23 even 12
3150.2.bp.e.1349.3 8 45.22 odd 12
7056.2.k.f.881.3 8 252.247 odd 6
7056.2.k.f.881.4 8 252.131 odd 6
7056.2.k.f.881.5 8 252.103 even 6
7056.2.k.f.881.6 8 252.23 even 6