Properties

Label 1155.2.c.c.694.6
Level $1155$
Weight $2$
Character 1155.694
Analytic conductor $9.223$
Analytic rank $0$
Dimension $6$
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] = [1155,2,Mod(694,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.694");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 694.6
Root \(1.45161 - 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 1155.694
Dual form 1155.2.c.c.694.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.21432i q^{2} +1.00000i q^{3} -2.90321 q^{4} +(0.311108 + 2.21432i) q^{5} -2.21432 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+2.21432i q^{2} +1.00000i q^{3} -2.90321 q^{4} +(0.311108 + 2.21432i) q^{5} -2.21432 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(-4.90321 + 0.688892i) q^{10} -1.00000 q^{11} -2.90321i q^{12} +1.31111i q^{13} -2.21432 q^{14} +(-2.21432 + 0.311108i) q^{15} -1.37778 q^{16} -1.90321i q^{17} -2.21432i q^{18} -0.377784 q^{19} +(-0.903212 - 6.42864i) q^{20} -1.00000 q^{21} -2.21432i q^{22} +2.52543i q^{23} +2.00000 q^{24} +(-4.80642 + 1.37778i) q^{25} -2.90321 q^{26} -1.00000i q^{27} -2.90321i q^{28} +6.11753 q^{29} +(-0.688892 - 4.90321i) q^{30} -4.96989 q^{31} -7.05086i q^{32} -1.00000i q^{33} +4.21432 q^{34} +(-2.21432 + 0.311108i) q^{35} +2.90321 q^{36} +1.31111i q^{37} -0.836535i q^{38} -1.31111 q^{39} +(4.42864 - 0.622216i) q^{40} -2.68889 q^{41} -2.21432i q^{42} +6.11753i q^{43} +2.90321 q^{44} +(-0.311108 - 2.21432i) q^{45} -5.59210 q^{46} +1.59210i q^{47} -1.37778i q^{48} -1.00000 q^{49} +(-3.05086 - 10.6430i) q^{50} +1.90321 q^{51} -3.80642i q^{52} -11.4286i q^{53} +2.21432 q^{54} +(-0.311108 - 2.21432i) q^{55} +2.00000 q^{56} -0.377784i q^{57} +13.5462i q^{58} +7.21432 q^{59} +(6.42864 - 0.903212i) q^{60} -1.04593 q^{61} -11.0049i q^{62} -1.00000i q^{63} +12.8573 q^{64} +(-2.90321 + 0.407896i) q^{65} +2.21432 q^{66} +2.00000i q^{67} +5.52543i q^{68} -2.52543 q^{69} +(-0.688892 - 4.90321i) q^{70} +4.92396 q^{71} +2.00000i q^{72} +12.4286i q^{73} -2.90321 q^{74} +(-1.37778 - 4.80642i) q^{75} +1.09679 q^{76} -1.00000i q^{77} -2.90321i q^{78} +0.969888 q^{79} +(-0.428639 - 3.05086i) q^{80} +1.00000 q^{81} -5.95407i q^{82} -6.71900i q^{83} +2.90321 q^{84} +(4.21432 - 0.592104i) q^{85} -13.5462 q^{86} +6.11753i q^{87} +2.00000i q^{88} +11.3620 q^{89} +(4.90321 - 0.688892i) q^{90} -1.31111 q^{91} -7.33185i q^{92} -4.96989i q^{93} -3.52543 q^{94} +(-0.117532 - 0.836535i) q^{95} +7.05086 q^{96} -8.54617i q^{97} -2.21432i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} - 16 q^{10} - 6 q^{11} - 8 q^{16} - 2 q^{19} + 8 q^{20} - 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 10 q^{29} - 4 q^{30} - 16 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} + 4 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{49} + 8 q^{50} - 2 q^{51} - 2 q^{55} + 12 q^{56} + 30 q^{59} + 12 q^{60} - 46 q^{61} + 24 q^{64} - 4 q^{65} - 2 q^{69} - 4 q^{70} - 24 q^{71} - 4 q^{74} - 8 q^{75} + 20 q^{76} - 8 q^{79} + 24 q^{80} + 6 q^{81} + 4 q^{84} + 12 q^{85} - 28 q^{86} + 42 q^{89} + 16 q^{90} - 8 q^{91} - 8 q^{94} + 26 q^{95} + 16 q^{96} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.21432i 1.56576i 0.622172 + 0.782880i \(0.286250\pi\)
−0.622172 + 0.782880i \(0.713750\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −2.90321 −1.45161
\(5\) 0.311108 + 2.21432i 0.139132 + 0.990274i
\(6\) −2.21432 −0.903992
\(7\) 1.00000i 0.377964i
\(8\) 2.00000i 0.707107i
\(9\) −1.00000 −0.333333
\(10\) −4.90321 + 0.688892i −1.55053 + 0.217847i
\(11\) −1.00000 −0.301511
\(12\) 2.90321i 0.838085i
\(13\) 1.31111i 0.363636i 0.983332 + 0.181818i \(0.0581982\pi\)
−0.983332 + 0.181818i \(0.941802\pi\)
\(14\) −2.21432 −0.591802
\(15\) −2.21432 + 0.311108i −0.571735 + 0.0803277i
\(16\) −1.37778 −0.344446
\(17\) 1.90321i 0.461597i −0.973002 0.230798i \(-0.925866\pi\)
0.973002 0.230798i \(-0.0741338\pi\)
\(18\) 2.21432i 0.521920i
\(19\) −0.377784 −0.0866697 −0.0433348 0.999061i \(-0.513798\pi\)
−0.0433348 + 0.999061i \(0.513798\pi\)
\(20\) −0.903212 6.42864i −0.201964 1.43749i
\(21\) −1.00000 −0.218218
\(22\) 2.21432i 0.472095i
\(23\) 2.52543i 0.526588i 0.964716 + 0.263294i \(0.0848089\pi\)
−0.964716 + 0.263294i \(0.915191\pi\)
\(24\) 2.00000 0.408248
\(25\) −4.80642 + 1.37778i −0.961285 + 0.275557i
\(26\) −2.90321 −0.569367
\(27\) 1.00000i 0.192450i
\(28\) 2.90321i 0.548655i
\(29\) 6.11753 1.13600 0.567999 0.823030i \(-0.307718\pi\)
0.567999 + 0.823030i \(0.307718\pi\)
\(30\) −0.688892 4.90321i −0.125774 0.895200i
\(31\) −4.96989 −0.892618 −0.446309 0.894879i \(-0.647262\pi\)
−0.446309 + 0.894879i \(0.647262\pi\)
\(32\) 7.05086i 1.24643i
\(33\) 1.00000i 0.174078i
\(34\) 4.21432 0.722750
\(35\) −2.21432 + 0.311108i −0.374288 + 0.0525868i
\(36\) 2.90321 0.483869
\(37\) 1.31111i 0.215545i 0.994176 + 0.107772i \(0.0343718\pi\)
−0.994176 + 0.107772i \(0.965628\pi\)
\(38\) 0.836535i 0.135704i
\(39\) −1.31111 −0.209945
\(40\) 4.42864 0.622216i 0.700229 0.0983809i
\(41\) −2.68889 −0.419934 −0.209967 0.977708i \(-0.567336\pi\)
−0.209967 + 0.977708i \(0.567336\pi\)
\(42\) 2.21432i 0.341677i
\(43\) 6.11753i 0.932915i 0.884544 + 0.466457i \(0.154470\pi\)
−0.884544 + 0.466457i \(0.845530\pi\)
\(44\) 2.90321 0.437676
\(45\) −0.311108 2.21432i −0.0463772 0.330091i
\(46\) −5.59210 −0.824511
\(47\) 1.59210i 0.232232i 0.993236 + 0.116116i \(0.0370445\pi\)
−0.993236 + 0.116116i \(0.962956\pi\)
\(48\) 1.37778i 0.198866i
\(49\) −1.00000 −0.142857
\(50\) −3.05086 10.6430i −0.431456 1.50514i
\(51\) 1.90321 0.266503
\(52\) 3.80642i 0.527856i
\(53\) 11.4286i 1.56984i −0.619594 0.784922i \(-0.712703\pi\)
0.619594 0.784922i \(-0.287297\pi\)
\(54\) 2.21432 0.301331
\(55\) −0.311108 2.21432i −0.0419498 0.298579i
\(56\) 2.00000 0.267261
\(57\) 0.377784i 0.0500388i
\(58\) 13.5462i 1.77870i
\(59\) 7.21432 0.939224 0.469612 0.882873i \(-0.344394\pi\)
0.469612 + 0.882873i \(0.344394\pi\)
\(60\) 6.42864 0.903212i 0.829934 0.116604i
\(61\) −1.04593 −0.133918 −0.0669590 0.997756i \(-0.521330\pi\)
−0.0669590 + 0.997756i \(0.521330\pi\)
\(62\) 11.0049i 1.39763i
\(63\) 1.00000i 0.125988i
\(64\) 12.8573 1.60716
\(65\) −2.90321 + 0.407896i −0.360099 + 0.0505933i
\(66\) 2.21432 0.272564
\(67\) 2.00000i 0.244339i 0.992509 + 0.122169i \(0.0389851\pi\)
−0.992509 + 0.122169i \(0.961015\pi\)
\(68\) 5.52543i 0.670057i
\(69\) −2.52543 −0.304026
\(70\) −0.688892 4.90321i −0.0823384 0.586046i
\(71\) 4.92396 0.584366 0.292183 0.956362i \(-0.405618\pi\)
0.292183 + 0.956362i \(0.405618\pi\)
\(72\) 2.00000i 0.235702i
\(73\) 12.4286i 1.45466i 0.686287 + 0.727331i \(0.259240\pi\)
−0.686287 + 0.727331i \(0.740760\pi\)
\(74\) −2.90321 −0.337492
\(75\) −1.37778 4.80642i −0.159093 0.554998i
\(76\) 1.09679 0.125810
\(77\) 1.00000i 0.113961i
\(78\) 2.90321i 0.328724i
\(79\) 0.969888 0.109121 0.0545605 0.998510i \(-0.482624\pi\)
0.0545605 + 0.998510i \(0.482624\pi\)
\(80\) −0.428639 3.05086i −0.0479234 0.341096i
\(81\) 1.00000 0.111111
\(82\) 5.95407i 0.657517i
\(83\) 6.71900i 0.737506i −0.929527 0.368753i \(-0.879785\pi\)
0.929527 0.368753i \(-0.120215\pi\)
\(84\) 2.90321 0.316766
\(85\) 4.21432 0.592104i 0.457107 0.0642227i
\(86\) −13.5462 −1.46072
\(87\) 6.11753i 0.655868i
\(88\) 2.00000i 0.213201i
\(89\) 11.3620 1.20437 0.602183 0.798358i \(-0.294298\pi\)
0.602183 + 0.798358i \(0.294298\pi\)
\(90\) 4.90321 0.688892i 0.516844 0.0726156i
\(91\) −1.31111 −0.137441
\(92\) 7.33185i 0.764398i
\(93\) 4.96989i 0.515353i
\(94\) −3.52543 −0.363620
\(95\) −0.117532 0.836535i −0.0120585 0.0858267i
\(96\) 7.05086 0.719625
\(97\) 8.54617i 0.867732i −0.900977 0.433866i \(-0.857149\pi\)
0.900977 0.433866i \(-0.142851\pi\)
\(98\) 2.21432i 0.223680i
\(99\) 1.00000 0.100504
\(100\) 13.9541 4.00000i 1.39541 0.400000i
\(101\) −4.75557 −0.473197 −0.236598 0.971608i \(-0.576033\pi\)
−0.236598 + 0.971608i \(0.576033\pi\)
\(102\) 4.21432i 0.417280i
\(103\) 11.3017i 1.11359i 0.830649 + 0.556797i \(0.187970\pi\)
−0.830649 + 0.556797i \(0.812030\pi\)
\(104\) 2.62222 0.257129
\(105\) −0.311108 2.21432i −0.0303610 0.216095i
\(106\) 25.3067 2.45800
\(107\) 8.83654i 0.854260i 0.904190 + 0.427130i \(0.140475\pi\)
−0.904190 + 0.427130i \(0.859525\pi\)
\(108\) 2.90321i 0.279362i
\(109\) −3.39853 −0.325520 −0.162760 0.986666i \(-0.552040\pi\)
−0.162760 + 0.986666i \(0.552040\pi\)
\(110\) 4.90321 0.688892i 0.467503 0.0656833i
\(111\) −1.31111 −0.124445
\(112\) 1.37778i 0.130188i
\(113\) 2.76049i 0.259685i 0.991535 + 0.129843i \(0.0414472\pi\)
−0.991535 + 0.129843i \(0.958553\pi\)
\(114\) 0.836535 0.0783487
\(115\) −5.59210 + 0.785680i −0.521466 + 0.0732651i
\(116\) −17.7605 −1.64902
\(117\) 1.31111i 0.121212i
\(118\) 15.9748i 1.47060i
\(119\) 1.90321 0.174467
\(120\) 0.622216 + 4.42864i 0.0568003 + 0.404278i
\(121\) 1.00000 0.0909091
\(122\) 2.31603i 0.209684i
\(123\) 2.68889i 0.242449i
\(124\) 14.4286 1.29573
\(125\) −4.54617 10.2143i −0.406622 0.913597i
\(126\) 2.21432 0.197267
\(127\) 2.45875i 0.218179i 0.994032 + 0.109089i \(0.0347935\pi\)
−0.994032 + 0.109089i \(0.965207\pi\)
\(128\) 14.3684i 1.27000i
\(129\) −6.11753 −0.538619
\(130\) −0.903212 6.42864i −0.0792169 0.563829i
\(131\) −5.73975 −0.501484 −0.250742 0.968054i \(-0.580675\pi\)
−0.250742 + 0.968054i \(0.580675\pi\)
\(132\) 2.90321i 0.252692i
\(133\) 0.377784i 0.0327581i
\(134\) −4.42864 −0.382576
\(135\) 2.21432 0.311108i 0.190578 0.0267759i
\(136\) −3.80642 −0.326398
\(137\) 13.5669i 1.15910i 0.814937 + 0.579550i \(0.196772\pi\)
−0.814937 + 0.579550i \(0.803228\pi\)
\(138\) 5.59210i 0.476032i
\(139\) −6.01429 −0.510125 −0.255063 0.966925i \(-0.582096\pi\)
−0.255063 + 0.966925i \(0.582096\pi\)
\(140\) 6.42864 0.903212i 0.543319 0.0763353i
\(141\) −1.59210 −0.134079
\(142\) 10.9032i 0.914977i
\(143\) 1.31111i 0.109640i
\(144\) 1.37778 0.114815
\(145\) 1.90321 + 13.5462i 0.158053 + 1.12495i
\(146\) −27.5210 −2.27765
\(147\) 1.00000i 0.0824786i
\(148\) 3.80642i 0.312886i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 10.6430 3.05086i 0.868994 0.249101i
\(151\) −5.05086 −0.411033 −0.205516 0.978654i \(-0.565887\pi\)
−0.205516 + 0.978654i \(0.565887\pi\)
\(152\) 0.755569i 0.0612847i
\(153\) 1.90321i 0.153866i
\(154\) 2.21432 0.178435
\(155\) −1.54617 11.0049i −0.124191 0.883937i
\(156\) 3.80642 0.304758
\(157\) 8.88739i 0.709291i 0.935001 + 0.354645i \(0.115398\pi\)
−0.935001 + 0.354645i \(0.884602\pi\)
\(158\) 2.14764i 0.170857i
\(159\) 11.4286 0.906350
\(160\) 15.6128 2.19358i 1.23430 0.173417i
\(161\) −2.52543 −0.199032
\(162\) 2.21432i 0.173973i
\(163\) 1.31111i 0.102694i 0.998681 + 0.0513469i \(0.0163514\pi\)
−0.998681 + 0.0513469i \(0.983649\pi\)
\(164\) 7.80642 0.609579
\(165\) 2.21432 0.311108i 0.172385 0.0242197i
\(166\) 14.8780 1.15476
\(167\) 15.1383i 1.17143i 0.810515 + 0.585717i \(0.199187\pi\)
−0.810515 + 0.585717i \(0.800813\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 11.2810 0.867769
\(170\) 1.31111 + 9.33185i 0.100557 + 0.715720i
\(171\) 0.377784 0.0288899
\(172\) 17.7605i 1.35422i
\(173\) 21.8622i 1.66215i 0.556159 + 0.831076i \(0.312275\pi\)
−0.556159 + 0.831076i \(0.687725\pi\)
\(174\) −13.5462 −1.02693
\(175\) −1.37778 4.80642i −0.104151 0.363331i
\(176\) 1.37778 0.103854
\(177\) 7.21432i 0.542261i
\(178\) 25.1590i 1.88575i
\(179\) 15.8129 1.18191 0.590955 0.806705i \(-0.298751\pi\)
0.590955 + 0.806705i \(0.298751\pi\)
\(180\) 0.903212 + 6.42864i 0.0673214 + 0.479162i
\(181\) −21.5812 −1.60412 −0.802059 0.597245i \(-0.796262\pi\)
−0.802059 + 0.597245i \(0.796262\pi\)
\(182\) 2.90321i 0.215200i
\(183\) 1.04593i 0.0773176i
\(184\) 5.05086 0.372354
\(185\) −2.90321 + 0.407896i −0.213448 + 0.0299891i
\(186\) 11.0049 0.806920
\(187\) 1.90321i 0.139177i
\(188\) 4.62222i 0.337110i
\(189\) 1.00000 0.0727393
\(190\) 1.85236 0.260253i 0.134384 0.0188807i
\(191\) −5.53972 −0.400840 −0.200420 0.979710i \(-0.564231\pi\)
−0.200420 + 0.979710i \(0.564231\pi\)
\(192\) 12.8573i 0.927894i
\(193\) 9.31756i 0.670693i −0.942095 0.335346i \(-0.891147\pi\)
0.942095 0.335346i \(-0.108853\pi\)
\(194\) 18.9240 1.35866
\(195\) −0.407896 2.90321i −0.0292100 0.207903i
\(196\) 2.90321 0.207372
\(197\) 27.0321i 1.92596i −0.269575 0.962979i \(-0.586883\pi\)
0.269575 0.962979i \(-0.413117\pi\)
\(198\) 2.21432i 0.157365i
\(199\) 4.06022 0.287822 0.143911 0.989591i \(-0.454032\pi\)
0.143911 + 0.989591i \(0.454032\pi\)
\(200\) 2.75557 + 9.61285i 0.194848 + 0.679731i
\(201\) −2.00000 −0.141069
\(202\) 10.5303i 0.740913i
\(203\) 6.11753i 0.429367i
\(204\) −5.52543 −0.386857
\(205\) −0.836535 5.95407i −0.0584262 0.415850i
\(206\) −25.0257 −1.74362
\(207\) 2.52543i 0.175529i
\(208\) 1.80642i 0.125253i
\(209\) 0.377784 0.0261319
\(210\) 4.90321 0.688892i 0.338354 0.0475381i
\(211\) 5.41927 0.373078 0.186539 0.982448i \(-0.440273\pi\)
0.186539 + 0.982448i \(0.440273\pi\)
\(212\) 33.1798i 2.27880i
\(213\) 4.92396i 0.337384i
\(214\) −19.5669 −1.33757
\(215\) −13.5462 + 1.90321i −0.923841 + 0.129798i
\(216\) −2.00000 −0.136083
\(217\) 4.96989i 0.337378i
\(218\) 7.52543i 0.509686i
\(219\) −12.4286 −0.839850
\(220\) 0.903212 + 6.42864i 0.0608945 + 0.433419i
\(221\) 2.49532 0.167853
\(222\) 2.90321i 0.194851i
\(223\) 18.2924i 1.22495i 0.790491 + 0.612474i \(0.209826\pi\)
−0.790491 + 0.612474i \(0.790174\pi\)
\(224\) 7.05086 0.471105
\(225\) 4.80642 1.37778i 0.320428 0.0918523i
\(226\) −6.11261 −0.406605
\(227\) 9.17484i 0.608956i 0.952519 + 0.304478i \(0.0984819\pi\)
−0.952519 + 0.304478i \(0.901518\pi\)
\(228\) 1.09679i 0.0726366i
\(229\) −0.112610 −0.00744145 −0.00372072 0.999993i \(-0.501184\pi\)
−0.00372072 + 0.999993i \(0.501184\pi\)
\(230\) −1.73975 12.3827i −0.114716 0.816491i
\(231\) 1.00000 0.0657952
\(232\) 12.2351i 0.803271i
\(233\) 20.3892i 1.33574i −0.744279 0.667869i \(-0.767207\pi\)
0.744279 0.667869i \(-0.232793\pi\)
\(234\) 2.90321 0.189789
\(235\) −3.52543 + 0.495316i −0.229974 + 0.0323109i
\(236\) −20.9447 −1.36338
\(237\) 0.969888i 0.0630010i
\(238\) 4.21432i 0.273174i
\(239\) −25.0207 −1.61846 −0.809229 0.587494i \(-0.800115\pi\)
−0.809229 + 0.587494i \(0.800115\pi\)
\(240\) 3.05086 0.428639i 0.196932 0.0276686i
\(241\) −1.18865 −0.0765679 −0.0382840 0.999267i \(-0.512189\pi\)
−0.0382840 + 0.999267i \(0.512189\pi\)
\(242\) 2.21432i 0.142342i
\(243\) 1.00000i 0.0641500i
\(244\) 3.03657 0.194396
\(245\) −0.311108 2.21432i −0.0198759 0.141468i
\(246\) 5.95407 0.379617
\(247\) 0.495316i 0.0315162i
\(248\) 9.93978i 0.631176i
\(249\) 6.71900 0.425800
\(250\) 22.6178 10.0667i 1.43047 0.636673i
\(251\) −27.8163 −1.75575 −0.877874 0.478892i \(-0.841038\pi\)
−0.877874 + 0.478892i \(0.841038\pi\)
\(252\) 2.90321i 0.182885i
\(253\) 2.52543i 0.158772i
\(254\) −5.44446 −0.341616
\(255\) 0.592104 + 4.21432i 0.0370790 + 0.263911i
\(256\) −6.10171 −0.381357
\(257\) 31.6336i 1.97325i 0.163009 + 0.986625i \(0.447880\pi\)
−0.163009 + 0.986625i \(0.552120\pi\)
\(258\) 13.5462i 0.843348i
\(259\) −1.31111 −0.0814683
\(260\) 8.42864 1.18421i 0.522722 0.0734415i
\(261\) −6.11753 −0.378666
\(262\) 12.7096i 0.785204i
\(263\) 22.8573i 1.40944i −0.709485 0.704720i \(-0.751073\pi\)
0.709485 0.704720i \(-0.248927\pi\)
\(264\) −2.00000 −0.123091
\(265\) 25.3067 3.55554i 1.55458 0.218415i
\(266\) 0.836535 0.0512913
\(267\) 11.3620i 0.695341i
\(268\) 5.80642i 0.354684i
\(269\) −1.48103 −0.0902997 −0.0451499 0.998980i \(-0.514377\pi\)
−0.0451499 + 0.998980i \(0.514377\pi\)
\(270\) 0.688892 + 4.90321i 0.0419246 + 0.298400i
\(271\) −25.4844 −1.54807 −0.774034 0.633144i \(-0.781764\pi\)
−0.774034 + 0.633144i \(0.781764\pi\)
\(272\) 2.62222i 0.158995i
\(273\) 1.31111i 0.0793519i
\(274\) −30.0415 −1.81487
\(275\) 4.80642 1.37778i 0.289838 0.0830835i
\(276\) 7.33185 0.441326
\(277\) 14.2395i 0.855569i −0.903881 0.427785i \(-0.859294\pi\)
0.903881 0.427785i \(-0.140706\pi\)
\(278\) 13.3176i 0.798734i
\(279\) 4.96989 0.297539
\(280\) 0.622216 + 4.42864i 0.0371845 + 0.264662i
\(281\) −2.23951 −0.133598 −0.0667990 0.997766i \(-0.521279\pi\)
−0.0667990 + 0.997766i \(0.521279\pi\)
\(282\) 3.52543i 0.209936i
\(283\) 24.8321i 1.47611i 0.674738 + 0.738057i \(0.264257\pi\)
−0.674738 + 0.738057i \(0.735743\pi\)
\(284\) −14.2953 −0.848269
\(285\) 0.836535 0.117532i 0.0495521 0.00696198i
\(286\) 2.90321 0.171671
\(287\) 2.68889i 0.158720i
\(288\) 7.05086i 0.415476i
\(289\) 13.3778 0.786928
\(290\) −29.9956 + 4.21432i −1.76140 + 0.247473i
\(291\) 8.54617 0.500985
\(292\) 36.0830i 2.11160i
\(293\) 25.6035i 1.49577i 0.663828 + 0.747886i \(0.268931\pi\)
−0.663828 + 0.747886i \(0.731069\pi\)
\(294\) 2.21432 0.129142
\(295\) 2.24443 + 15.9748i 0.130676 + 0.930089i
\(296\) 2.62222 0.152413
\(297\) 1.00000i 0.0580259i
\(298\) 22.1432i 1.28272i
\(299\) −3.31111 −0.191486
\(300\) 4.00000 + 13.9541i 0.230940 + 0.805638i
\(301\) −6.11753 −0.352609
\(302\) 11.1842i 0.643579i
\(303\) 4.75557i 0.273200i
\(304\) 0.520505 0.0298530
\(305\) −0.325398 2.31603i −0.0186322 0.132615i
\(306\) −4.21432 −0.240917
\(307\) 5.09234i 0.290635i 0.989385 + 0.145318i \(0.0464204\pi\)
−0.989385 + 0.145318i \(0.953580\pi\)
\(308\) 2.90321i 0.165426i
\(309\) −11.3017 −0.642934
\(310\) 24.3684 3.42372i 1.38403 0.194454i
\(311\) 17.3274 0.982547 0.491274 0.871005i \(-0.336532\pi\)
0.491274 + 0.871005i \(0.336532\pi\)
\(312\) 2.62222i 0.148454i
\(313\) 15.4909i 0.875596i −0.899073 0.437798i \(-0.855759\pi\)
0.899073 0.437798i \(-0.144241\pi\)
\(314\) −19.6795 −1.11058
\(315\) 2.21432 0.311108i 0.124763 0.0175289i
\(316\) −2.81579 −0.158401
\(317\) 12.4143i 0.697259i −0.937261 0.348630i \(-0.886647\pi\)
0.937261 0.348630i \(-0.113353\pi\)
\(318\) 25.3067i 1.41913i
\(319\) −6.11753 −0.342516
\(320\) 4.00000 + 28.4701i 0.223607 + 1.59153i
\(321\) −8.83654 −0.493207
\(322\) 5.59210i 0.311636i
\(323\) 0.719004i 0.0400064i
\(324\) −2.90321 −0.161290
\(325\) −1.80642 6.30174i −0.100202 0.349558i
\(326\) −2.90321 −0.160794
\(327\) 3.39853i 0.187939i
\(328\) 5.37778i 0.296938i
\(329\) −1.59210 −0.0877755
\(330\) 0.688892 + 4.90321i 0.0379223 + 0.269913i
\(331\) 32.5210 1.78751 0.893757 0.448551i \(-0.148060\pi\)
0.893757 + 0.448551i \(0.148060\pi\)
\(332\) 19.5067i 1.07057i
\(333\) 1.31111i 0.0718483i
\(334\) −33.5210 −1.83419
\(335\) −4.42864 + 0.622216i −0.241962 + 0.0339953i
\(336\) 1.37778 0.0751643
\(337\) 3.06668i 0.167053i −0.996506 0.0835263i \(-0.973382\pi\)
0.996506 0.0835263i \(-0.0266182\pi\)
\(338\) 24.9797i 1.35872i
\(339\) −2.76049 −0.149929
\(340\) −12.2351 + 1.71900i −0.663539 + 0.0932261i
\(341\) 4.96989 0.269135
\(342\) 0.836535i 0.0452347i
\(343\) 1.00000i 0.0539949i
\(344\) 12.2351 0.659670
\(345\) −0.785680 5.59210i −0.0422996 0.301069i
\(346\) −48.4099 −2.60253
\(347\) 23.7146i 1.27306i 0.771250 + 0.636532i \(0.219632\pi\)
−0.771250 + 0.636532i \(0.780368\pi\)
\(348\) 17.7605i 0.952062i
\(349\) −21.8385 −1.16899 −0.584495 0.811397i \(-0.698707\pi\)
−0.584495 + 0.811397i \(0.698707\pi\)
\(350\) 10.6430 3.05086i 0.568890 0.163075i
\(351\) 1.31111 0.0699818
\(352\) 7.05086i 0.375812i
\(353\) 31.1941i 1.66029i −0.557546 0.830146i \(-0.688257\pi\)
0.557546 0.830146i \(-0.311743\pi\)
\(354\) −15.9748 −0.849052
\(355\) 1.53188 + 10.9032i 0.0813038 + 0.578682i
\(356\) −32.9862 −1.74826
\(357\) 1.90321i 0.100729i
\(358\) 35.0148i 1.85059i
\(359\) 7.16839 0.378333 0.189166 0.981945i \(-0.439421\pi\)
0.189166 + 0.981945i \(0.439421\pi\)
\(360\) −4.42864 + 0.622216i −0.233410 + 0.0327936i
\(361\) −18.8573 −0.992488
\(362\) 47.7877i 2.51167i
\(363\) 1.00000i 0.0524864i
\(364\) 3.80642 0.199511
\(365\) −27.5210 + 3.86665i −1.44051 + 0.202390i
\(366\) 2.31603 0.121061
\(367\) 17.9195i 0.935391i 0.883890 + 0.467695i \(0.154916\pi\)
−0.883890 + 0.467695i \(0.845084\pi\)
\(368\) 3.47949i 0.181381i
\(369\) 2.68889 0.139978
\(370\) −0.903212 6.42864i −0.0469558 0.334209i
\(371\) 11.4286 0.593345
\(372\) 14.4286i 0.748090i
\(373\) 2.22369i 0.115138i 0.998342 + 0.0575691i \(0.0183349\pi\)
−0.998342 + 0.0575691i \(0.981665\pi\)
\(374\) −4.21432 −0.217917
\(375\) 10.2143 4.54617i 0.527465 0.234763i
\(376\) 3.18421 0.164213
\(377\) 8.02074i 0.413089i
\(378\) 2.21432i 0.113892i
\(379\) −17.6780 −0.908058 −0.454029 0.890987i \(-0.650014\pi\)
−0.454029 + 0.890987i \(0.650014\pi\)
\(380\) 0.341219 + 2.42864i 0.0175042 + 0.124587i
\(381\) −2.45875 −0.125966
\(382\) 12.2667i 0.627619i
\(383\) 16.8365i 0.860307i 0.902756 + 0.430153i \(0.141541\pi\)
−0.902756 + 0.430153i \(0.858459\pi\)
\(384\) −14.3684 −0.733235
\(385\) 2.21432 0.311108i 0.112852 0.0158555i
\(386\) 20.6321 1.05014
\(387\) 6.11753i 0.310972i
\(388\) 24.8113i 1.25961i
\(389\) 15.4859 0.785169 0.392584 0.919716i \(-0.371581\pi\)
0.392584 + 0.919716i \(0.371581\pi\)
\(390\) 6.42864 0.903212i 0.325527 0.0457359i
\(391\) 4.80642 0.243071
\(392\) 2.00000i 0.101015i
\(393\) 5.73975i 0.289532i
\(394\) 59.8578 3.01559
\(395\) 0.301740 + 2.14764i 0.0151822 + 0.108060i
\(396\) −2.90321 −0.145892
\(397\) 16.9032i 0.848348i 0.905581 + 0.424174i \(0.139435\pi\)
−0.905581 + 0.424174i \(0.860565\pi\)
\(398\) 8.99063i 0.450660i
\(399\) 0.377784 0.0189129
\(400\) 6.62222 1.89829i 0.331111 0.0949145i
\(401\) 23.3210 1.16459 0.582296 0.812977i \(-0.302154\pi\)
0.582296 + 0.812977i \(0.302154\pi\)
\(402\) 4.42864i 0.220880i
\(403\) 6.51606i 0.324588i
\(404\) 13.8064 0.686895
\(405\) 0.311108 + 2.21432i 0.0154591 + 0.110030i
\(406\) −13.5462 −0.672285
\(407\) 1.31111i 0.0649892i
\(408\) 3.80642i 0.188446i
\(409\) 2.60793 0.128954 0.0644768 0.997919i \(-0.479462\pi\)
0.0644768 + 0.997919i \(0.479462\pi\)
\(410\) 13.1842 1.85236i 0.651122 0.0914814i
\(411\) −13.5669 −0.669207
\(412\) 32.8113i 1.61650i
\(413\) 7.21432i 0.354993i
\(414\) 5.59210 0.274837
\(415\) 14.8780 2.09033i 0.730333 0.102610i
\(416\) 9.24443 0.453246
\(417\) 6.01429i 0.294521i
\(418\) 0.836535i 0.0409163i
\(419\) 15.4222 0.753423 0.376712 0.926331i \(-0.377055\pi\)
0.376712 + 0.926331i \(0.377055\pi\)
\(420\) 0.903212 + 6.42864i 0.0440722 + 0.313685i
\(421\) 6.28592 0.306357 0.153178 0.988199i \(-0.451049\pi\)
0.153178 + 0.988199i \(0.451049\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 1.59210i 0.0774108i
\(424\) −22.8573 −1.11005
\(425\) 2.62222 + 9.14764i 0.127196 + 0.443726i
\(426\) −10.9032 −0.528262
\(427\) 1.04593i 0.0506162i
\(428\) 25.6543i 1.24005i
\(429\) 1.31111 0.0633009
\(430\) −4.21432 29.9956i −0.203233 1.44651i
\(431\) 16.3082 0.785538 0.392769 0.919637i \(-0.371517\pi\)
0.392769 + 0.919637i \(0.371517\pi\)
\(432\) 1.37778i 0.0662887i
\(433\) 14.8859i 0.715369i −0.933843 0.357684i \(-0.883566\pi\)
0.933843 0.357684i \(-0.116434\pi\)
\(434\) 11.0049 0.528253
\(435\) −13.5462 + 1.90321i −0.649489 + 0.0912520i
\(436\) 9.86665 0.472527
\(437\) 0.954067i 0.0456392i
\(438\) 27.5210i 1.31500i
\(439\) −10.3176 −0.492430 −0.246215 0.969215i \(-0.579187\pi\)
−0.246215 + 0.969215i \(0.579187\pi\)
\(440\) −4.42864 + 0.622216i −0.211127 + 0.0296630i
\(441\) 1.00000 0.0476190
\(442\) 5.52543i 0.262818i
\(443\) 4.17929i 0.198564i −0.995059 0.0992819i \(-0.968345\pi\)
0.995059 0.0992819i \(-0.0316546\pi\)
\(444\) 3.80642 0.180645
\(445\) 3.53480 + 25.1590i 0.167565 + 1.19265i
\(446\) −40.5052 −1.91797
\(447\) 10.0000i 0.472984i
\(448\) 12.8573i 0.607449i
\(449\) 25.2192 1.19017 0.595085 0.803663i \(-0.297118\pi\)
0.595085 + 0.803663i \(0.297118\pi\)
\(450\) 3.05086 + 10.6430i 0.143819 + 0.501714i
\(451\) 2.68889 0.126615
\(452\) 8.01429i 0.376960i
\(453\) 5.05086i 0.237310i
\(454\) −20.3160 −0.953479
\(455\) −0.407896 2.90321i −0.0191225 0.136105i
\(456\) −0.755569 −0.0353827
\(457\) 27.5970i 1.29093i 0.763788 + 0.645467i \(0.223337\pi\)
−0.763788 + 0.645467i \(0.776663\pi\)
\(458\) 0.249353i 0.0116515i
\(459\) −1.90321 −0.0888343
\(460\) 16.2351 2.28100i 0.756964 0.106352i
\(461\) 33.5812 1.56403 0.782016 0.623258i \(-0.214191\pi\)
0.782016 + 0.623258i \(0.214191\pi\)
\(462\) 2.21432i 0.103019i
\(463\) 22.8889i 1.06374i 0.846827 + 0.531869i \(0.178510\pi\)
−0.846827 + 0.531869i \(0.821490\pi\)
\(464\) −8.42864 −0.391290
\(465\) 11.0049 1.54617i 0.510341 0.0717020i
\(466\) 45.1481 2.09145
\(467\) 6.38715i 0.295562i −0.989020 0.147781i \(-0.952787\pi\)
0.989020 0.147781i \(-0.0472131\pi\)
\(468\) 3.80642i 0.175952i
\(469\) −2.00000 −0.0923514
\(470\) −1.09679 7.80642i −0.0505911 0.360083i
\(471\) −8.88739 −0.409509
\(472\) 14.4286i 0.664132i
\(473\) 6.11753i 0.281284i
\(474\) −2.14764 −0.0986445
\(475\) 1.81579 0.520505i 0.0833142 0.0238824i
\(476\) −5.52543 −0.253258
\(477\) 11.4286i 0.523281i
\(478\) 55.4039i 2.53412i
\(479\) 34.5970 1.58078 0.790389 0.612605i \(-0.209878\pi\)
0.790389 + 0.612605i \(0.209878\pi\)
\(480\) 2.19358 + 15.6128i 0.100123 + 0.712626i
\(481\) −1.71900 −0.0783798
\(482\) 2.63206i 0.119887i
\(483\) 2.52543i 0.114911i
\(484\) −2.90321 −0.131964
\(485\) 18.9240 2.65878i 0.859293 0.120729i
\(486\) −2.21432 −0.100444
\(487\) 12.4572i 0.564491i −0.959342 0.282245i \(-0.908921\pi\)
0.959342 0.282245i \(-0.0910792\pi\)
\(488\) 2.09187i 0.0946943i
\(489\) −1.31111 −0.0592903
\(490\) 4.90321 0.688892i 0.221505 0.0311210i
\(491\) 16.4271 0.741345 0.370673 0.928764i \(-0.379127\pi\)
0.370673 + 0.928764i \(0.379127\pi\)
\(492\) 7.80642i 0.351941i
\(493\) 11.6430i 0.524373i
\(494\) 1.09679 0.0493468
\(495\) 0.311108 + 2.21432i 0.0139833 + 0.0995263i
\(496\) 6.84743 0.307459
\(497\) 4.92396i 0.220870i
\(498\) 14.8780i 0.666700i
\(499\) 37.2623 1.66809 0.834044 0.551698i \(-0.186020\pi\)
0.834044 + 0.551698i \(0.186020\pi\)
\(500\) 13.1985 + 29.6543i 0.590255 + 1.32618i
\(501\) −15.1383 −0.676328
\(502\) 61.5941i 2.74908i
\(503\) 9.23506i 0.411771i −0.978576 0.205886i \(-0.933993\pi\)
0.978576 0.205886i \(-0.0660075\pi\)
\(504\) −2.00000 −0.0890871
\(505\) −1.47949 10.5303i −0.0658366 0.468594i
\(506\) 5.59210 0.248599
\(507\) 11.2810i 0.501007i
\(508\) 7.13828i 0.316710i
\(509\) 43.3847 1.92299 0.961497 0.274816i \(-0.0886170\pi\)
0.961497 + 0.274816i \(0.0886170\pi\)
\(510\) −9.33185 + 1.31111i −0.413221 + 0.0580568i
\(511\) −12.4286 −0.549811
\(512\) 15.2257i 0.672887i
\(513\) 0.377784i 0.0166796i
\(514\) −70.0469 −3.08964
\(515\) −25.0257 + 3.51606i −1.10276 + 0.154936i
\(516\) 17.7605 0.781862
\(517\) 1.59210i 0.0700207i
\(518\) 2.90321i 0.127560i
\(519\) −21.8622 −0.959644
\(520\) 0.815792 + 5.80642i 0.0357748 + 0.254629i
\(521\) 33.9195 1.48604 0.743020 0.669269i \(-0.233393\pi\)
0.743020 + 0.669269i \(0.233393\pi\)
\(522\) 13.5462i 0.592900i
\(523\) 19.6731i 0.860243i 0.902771 + 0.430122i \(0.141529\pi\)
−0.902771 + 0.430122i \(0.858471\pi\)
\(524\) 16.6637 0.727957
\(525\) 4.80642 1.37778i 0.209770 0.0601314i
\(526\) 50.6133 2.20685
\(527\) 9.45875i 0.412030i
\(528\) 1.37778i 0.0599604i
\(529\) 16.6222 0.722705
\(530\) 7.87310 + 56.0370i 0.341986 + 2.43409i
\(531\) −7.21432 −0.313075
\(532\) 1.09679i 0.0475518i
\(533\) 3.52543i 0.152703i
\(534\) −25.1590 −1.08874
\(535\) −19.5669 + 2.74912i −0.845951 + 0.118855i
\(536\) 4.00000 0.172774
\(537\) 15.8129i 0.682376i
\(538\) 3.27946i 0.141388i
\(539\) 1.00000 0.0430730
\(540\) −6.42864 + 0.903212i −0.276645 + 0.0388681i
\(541\) −26.2844 −1.13005 −0.565027 0.825072i \(-0.691134\pi\)
−0.565027 + 0.825072i \(0.691134\pi\)
\(542\) 56.4306i 2.42390i
\(543\) 21.5812i 0.926138i
\(544\) −13.4193 −0.575347
\(545\) −1.05731 7.52543i −0.0452901 0.322354i
\(546\) 2.90321 0.124246
\(547\) 3.43648i 0.146933i −0.997298 0.0734666i \(-0.976594\pi\)
0.997298 0.0734666i \(-0.0234062\pi\)
\(548\) 39.3876i 1.68256i
\(549\) 1.04593 0.0446393
\(550\) 3.05086 + 10.6430i 0.130089 + 0.453817i
\(551\) −2.31111 −0.0984565
\(552\) 5.05086i 0.214979i
\(553\) 0.969888i 0.0412439i
\(554\) 31.5308 1.33962
\(555\) −0.407896 2.90321i −0.0173142 0.123234i
\(556\) 17.4608 0.740501
\(557\) 35.1941i 1.49122i 0.666383 + 0.745610i \(0.267842\pi\)
−0.666383 + 0.745610i \(0.732158\pi\)
\(558\) 11.0049i 0.465876i
\(559\) −8.02074 −0.339241
\(560\) 3.05086 0.428639i 0.128922 0.0181133i
\(561\) −1.90321 −0.0803537
\(562\) 4.95899i 0.209182i
\(563\) 16.6780i 0.702894i −0.936208 0.351447i \(-0.885690\pi\)
0.936208 0.351447i \(-0.114310\pi\)
\(564\) 4.62222 0.194630
\(565\) −6.11261 + 0.858810i −0.257159 + 0.0361304i
\(566\) −54.9862 −2.31124
\(567\) 1.00000i 0.0419961i
\(568\) 9.84791i 0.413209i
\(569\) 41.9481 1.75856 0.879278 0.476309i \(-0.158026\pi\)
0.879278 + 0.476309i \(0.158026\pi\)
\(570\) 0.260253 + 1.85236i 0.0109008 + 0.0775867i
\(571\) −3.76694 −0.157642 −0.0788209 0.996889i \(-0.525116\pi\)
−0.0788209 + 0.996889i \(0.525116\pi\)
\(572\) 3.80642i 0.159155i
\(573\) 5.53972i 0.231425i
\(574\) 5.95407 0.248518
\(575\) −3.47949 12.1383i −0.145105 0.506201i
\(576\) −12.8573 −0.535720
\(577\) 43.5812i 1.81431i −0.420797 0.907155i \(-0.638250\pi\)
0.420797 0.907155i \(-0.361750\pi\)
\(578\) 29.6227i 1.23214i
\(579\) 9.31756 0.387225
\(580\) −5.52543 39.3274i −0.229431 1.63298i
\(581\) 6.71900 0.278751
\(582\) 18.9240i 0.784423i
\(583\) 11.4286i 0.473326i
\(584\) 24.8573 1.02860
\(585\) 2.90321 0.407896i 0.120033 0.0168644i
\(586\) −56.6943 −2.34202
\(587\) 20.6015i 0.850314i 0.905120 + 0.425157i \(0.139781\pi\)
−0.905120 + 0.425157i \(0.860219\pi\)
\(588\) 2.90321i 0.119726i
\(589\) 1.87755 0.0773629
\(590\) −35.3733 + 4.96989i −1.45630 + 0.204607i
\(591\) 27.0321 1.11195
\(592\) 1.80642i 0.0742436i
\(593\) 7.33185i 0.301083i −0.988604 0.150542i \(-0.951898\pi\)
0.988604 0.150542i \(-0.0481017\pi\)
\(594\) −2.21432 −0.0908546
\(595\) 0.592104 + 4.21432i 0.0242739 + 0.172770i
\(596\) 29.0321 1.18920
\(597\) 4.06022i 0.166174i
\(598\) 7.33185i 0.299822i
\(599\) 2.16193 0.0883342 0.0441671 0.999024i \(-0.485937\pi\)
0.0441671 + 0.999024i \(0.485937\pi\)
\(600\) −9.61285 + 2.75557i −0.392443 + 0.112496i
\(601\) −3.51606 −0.143423 −0.0717115 0.997425i \(-0.522846\pi\)
−0.0717115 + 0.997425i \(0.522846\pi\)
\(602\) 13.5462i 0.552101i
\(603\) 2.00000i 0.0814463i
\(604\) 14.6637 0.596658
\(605\) 0.311108 + 2.21432i 0.0126483 + 0.0900249i
\(606\) 10.5303 0.427766
\(607\) 43.2958i 1.75732i 0.477447 + 0.878660i \(0.341562\pi\)
−0.477447 + 0.878660i \(0.658438\pi\)
\(608\) 2.66370i 0.108027i
\(609\) −6.11753 −0.247895
\(610\) 5.12843 0.720535i 0.207644 0.0291736i
\(611\) −2.08742 −0.0844480
\(612\) 5.52543i 0.223352i
\(613\) 36.3466i 1.46803i −0.679135 0.734013i \(-0.737645\pi\)
0.679135 0.734013i \(-0.262355\pi\)
\(614\) −11.2761 −0.455065
\(615\) 5.95407 0.836535i 0.240091 0.0337324i
\(616\) −2.00000 −0.0805823
\(617\) 31.1896i 1.25565i −0.778356 0.627823i \(-0.783946\pi\)
0.778356 0.627823i \(-0.216054\pi\)
\(618\) 25.0257i 1.00668i
\(619\) −14.5906 −0.586445 −0.293222 0.956044i \(-0.594728\pi\)
−0.293222 + 0.956044i \(0.594728\pi\)
\(620\) 4.48886 + 31.9496i 0.180277 + 1.28313i
\(621\) 2.52543 0.101342
\(622\) 38.3684i 1.53843i
\(623\) 11.3620i 0.455207i
\(624\) 1.80642 0.0723148
\(625\) 21.2034 13.2444i 0.848137 0.529777i
\(626\) 34.3017 1.37097
\(627\) 0.377784i 0.0150873i
\(628\) 25.8020i 1.02961i
\(629\) 2.49532 0.0994948
\(630\) 0.688892 + 4.90321i 0.0274461 + 0.195349i
\(631\) 21.6365 0.861336 0.430668 0.902511i \(-0.358278\pi\)
0.430668 + 0.902511i \(0.358278\pi\)
\(632\) 1.93978i 0.0771602i
\(633\) 5.41927i 0.215397i
\(634\) 27.4893 1.09174
\(635\) −5.44446 + 0.764937i −0.216057 + 0.0303556i
\(636\) −33.1798 −1.31566
\(637\) 1.31111i 0.0519480i
\(638\) 13.5462i 0.536298i
\(639\) −4.92396 −0.194789
\(640\) −31.8163 + 4.47013i −1.25765 + 0.176697i
\(641\) −4.78415 −0.188963 −0.0944813 0.995527i \(-0.530119\pi\)
−0.0944813 + 0.995527i \(0.530119\pi\)
\(642\) 19.5669i 0.772245i
\(643\) 24.5832i 0.969467i −0.874662 0.484734i \(-0.838917\pi\)
0.874662 0.484734i \(-0.161083\pi\)
\(644\) 7.33185 0.288915
\(645\) −1.90321 13.5462i −0.0749389 0.533380i
\(646\) −1.59210 −0.0626405
\(647\) 19.0638i 0.749474i −0.927131 0.374737i \(-0.877733\pi\)
0.927131 0.374737i \(-0.122267\pi\)
\(648\) 2.00000i 0.0785674i
\(649\) −7.21432 −0.283187
\(650\) 13.9541 4.00000i 0.547324 0.156893i
\(651\) 4.96989 0.194785
\(652\) 3.80642i 0.149071i
\(653\) 25.7654i 1.00828i −0.863622 0.504139i \(-0.831810\pi\)
0.863622 0.504139i \(-0.168190\pi\)
\(654\) 7.52543 0.294268
\(655\) −1.78568 12.7096i −0.0697723 0.496607i
\(656\) 3.70471 0.144645
\(657\) 12.4286i 0.484887i
\(658\) 3.52543i 0.137435i
\(659\) −50.0212 −1.94855 −0.974275 0.225362i \(-0.927643\pi\)
−0.974275 + 0.225362i \(0.927643\pi\)
\(660\) −6.42864 + 0.903212i −0.250234 + 0.0351575i
\(661\) 36.5195 1.42044 0.710221 0.703979i \(-0.248595\pi\)
0.710221 + 0.703979i \(0.248595\pi\)
\(662\) 72.0119i 2.79882i
\(663\) 2.49532i 0.0969100i
\(664\) −13.4380 −0.521496
\(665\) 0.836535 0.117532i 0.0324395 0.00455768i
\(666\) 2.90321 0.112497
\(667\) 15.4494i 0.598203i
\(668\) 43.9496i 1.70046i
\(669\) −18.2924 −0.707224
\(670\) −1.37778 9.80642i −0.0532285 0.378855i
\(671\) 1.04593 0.0403778
\(672\) 7.05086i 0.271993i
\(673\) 27.5926i 1.06362i −0.846865 0.531808i \(-0.821513\pi\)
0.846865 0.531808i \(-0.178487\pi\)
\(674\) 6.79060 0.261564
\(675\) 1.37778 + 4.80642i 0.0530309 + 0.184999i
\(676\) −32.7511 −1.25966
\(677\) 17.3511i 0.666856i 0.942776 + 0.333428i \(0.108205\pi\)
−0.942776 + 0.333428i \(0.891795\pi\)
\(678\) 6.11261i 0.234753i
\(679\) 8.54617 0.327972
\(680\) −1.18421 8.42864i −0.0454123 0.323224i
\(681\) −9.17484 −0.351581
\(682\) 11.0049i 0.421400i
\(683\) 21.8983i 0.837915i −0.908006 0.418957i \(-0.862396\pi\)
0.908006 0.418957i \(-0.137604\pi\)
\(684\) −1.09679 −0.0419367
\(685\) −30.0415 + 4.22077i −1.14783 + 0.161267i
\(686\) 2.21432 0.0845431
\(687\) 0.112610i 0.00429632i
\(688\) 8.42864i 0.321339i
\(689\) 14.9842 0.570852
\(690\) 12.3827 1.73975i 0.471402 0.0662310i
\(691\) −0.726989 −0.0276559 −0.0138280 0.999904i \(-0.504402\pi\)
−0.0138280 + 0.999904i \(0.504402\pi\)
\(692\) 63.4706i 2.41279i
\(693\) 1.00000i 0.0379869i
\(694\) −52.5116 −1.99331
\(695\) −1.87109 13.3176i −0.0709746 0.505164i
\(696\) 12.2351 0.463769
\(697\) 5.11753i 0.193840i
\(698\) 48.3575i 1.83036i
\(699\) 20.3892 0.771189
\(700\) 4.00000 + 13.9541i 0.151186 + 0.527414i
\(701\) 27.9940 1.05732 0.528660 0.848834i \(-0.322695\pi\)
0.528660 + 0.848834i \(0.322695\pi\)
\(702\) 2.90321i 0.109575i
\(703\) 0.495316i 0.0186812i
\(704\) −12.8573 −0.484577
\(705\) −0.495316 3.52543i −0.0186547 0.132775i
\(706\) 69.0736 2.59962
\(707\) 4.75557i 0.178852i
\(708\) 20.9447i 0.787150i
\(709\) 40.3319 1.51469 0.757347 0.653012i \(-0.226495\pi\)
0.757347 + 0.653012i \(0.226495\pi\)
\(710\) −24.1432 + 3.39207i −0.906078 + 0.127302i
\(711\) −0.969888 −0.0363737
\(712\) 22.7239i 0.851615i
\(713\) 12.5511i 0.470042i
\(714\) −4.21432 −0.157717
\(715\) 2.90321 0.407896i 0.108574 0.0152544i
\(716\) −45.9081 −1.71567
\(717\) 25.0207i 0.934417i
\(718\) 15.8731i 0.592379i
\(719\) 40.9418 1.52687 0.763435 0.645884i \(-0.223511\pi\)
0.763435 + 0.645884i \(0.223511\pi\)
\(720\) 0.428639 + 3.05086i 0.0159745 + 0.113699i
\(721\) −11.3017 −0.420899
\(722\) 41.7560i 1.55400i
\(723\) 1.18865i 0.0442065i
\(724\) 62.6548 2.32855
\(725\) −29.4035 + 8.42864i −1.09202 + 0.313032i
\(726\) −2.21432 −0.0821811
\(727\) 26.2464i 0.973427i 0.873562 + 0.486713i \(0.161804\pi\)
−0.873562 + 0.486713i \(0.838196\pi\)
\(728\) 2.62222i 0.0971858i
\(729\) −1.00000 −0.0370370
\(730\) −8.56199 60.9403i −0.316894 2.25550i
\(731\) 11.6430 0.430630
\(732\) 3.03657i 0.112235i
\(733\) 24.0129i 0.886937i −0.896290 0.443468i \(-0.853748\pi\)
0.896290 0.443468i \(-0.146252\pi\)
\(734\) −39.6795 −1.46460
\(735\) 2.21432 0.311108i 0.0816764 0.0114754i
\(736\) 17.8064 0.656353
\(737\) 2.00000i 0.0736709i
\(738\) 5.95407i 0.219172i
\(739\) 29.2958 1.07766 0.538831 0.842414i \(-0.318866\pi\)
0.538831 + 0.842414i \(0.318866\pi\)
\(740\) 8.42864 1.18421i 0.309843 0.0435324i
\(741\) 0.495316 0.0181959
\(742\) 25.3067i 0.929037i
\(743\) 40.0830i 1.47050i 0.677795 + 0.735251i \(0.262936\pi\)
−0.677795 + 0.735251i \(0.737064\pi\)
\(744\) −9.93978 −0.364410
\(745\) −3.11108 22.1432i −0.113981 0.811264i
\(746\) −4.92396 −0.180279
\(747\) 6.71900i 0.245835i
\(748\) 5.52543i 0.202030i
\(749\) −8.83654 −0.322880
\(750\) 10.0667 + 22.6178i 0.367583 + 0.825884i
\(751\) −12.2444 −0.446806 −0.223403 0.974726i \(-0.571717\pi\)
−0.223403 + 0.974726i \(0.571717\pi\)
\(752\) 2.19358i 0.0799915i
\(753\) 27.8163i 1.01368i
\(754\) −17.7605 −0.646799
\(755\) −1.57136 11.1842i −0.0571877 0.407035i
\(756\) −2.90321 −0.105589
\(757\) 49.1655i 1.78695i 0.449113 + 0.893475i \(0.351740\pi\)
−0.449113 + 0.893475i \(0.648260\pi\)
\(758\) 39.1447i 1.42180i
\(759\) 2.52543 0.0916672
\(760\) −1.67307 + 0.235063i −0.0606887 + 0.00852664i
\(761\) −37.6860 −1.36612 −0.683058 0.730364i \(-0.739350\pi\)
−0.683058 + 0.730364i \(0.739350\pi\)
\(762\) 5.44446i 0.197232i
\(763\) 3.39853i 0.123035i
\(764\) 16.0830 0.581862
\(765\) −4.21432 + 0.592104i −0.152369 + 0.0214076i
\(766\) −37.2815 −1.34703
\(767\) 9.45875i 0.341536i
\(768\) 6.10171i 0.220177i
\(769\) 7.78415 0.280704 0.140352 0.990102i \(-0.455177\pi\)
0.140352 + 0.990102i \(0.455177\pi\)
\(770\) 0.688892 + 4.90321i 0.0248260 + 0.176699i
\(771\) −31.6336 −1.13926
\(772\) 27.0509i 0.973582i
\(773\) 43.0450i 1.54822i −0.633050 0.774111i \(-0.718197\pi\)
0.633050 0.774111i \(-0.281803\pi\)
\(774\) 13.5462 0.486907
\(775\) 23.8874 6.84743i 0.858060 0.245967i
\(776\) −17.0923 −0.613579
\(777\) 1.31111i 0.0470357i
\(778\) 34.2908i 1.22939i
\(779\) 1.01582 0.0363956
\(780\) 1.18421 + 8.42864i 0.0424015 + 0.301794i
\(781\) −4.92396 −0.176193
\(782\) 10.6430i 0.380591i
\(783\) 6.11753i 0.218623i
\(784\) 1.37778 0.0492066
\(785\) −19.6795 + 2.76494i −0.702392 + 0.0986848i
\(786\) 12.7096 0.453338
\(787\) 9.21585i 0.328510i −0.986418 0.164255i \(-0.947478\pi\)
0.986418 0.164255i \(-0.0525219\pi\)
\(788\) 78.4800i 2.79573i
\(789\) 22.8573 0.813741
\(790\) −4.75557 + 0.668149i −0.169196 + 0.0237717i
\(791\) −2.76049 −0.0981518
\(792\) 2.00000i 0.0710669i
\(793\) 1.37133i 0.0486974i
\(794\) −37.4291 −1.32831
\(795\) 3.55554 + 25.3067i 0.126102 + 0.897535i
\(796\) −11.7877 −0.417804
\(797\) 15.4982i 0.548975i 0.961591 + 0.274488i \(0.0885083\pi\)
−0.961591 + 0.274488i \(0.911492\pi\)
\(798\) 0.836535i 0.0296130i
\(799\) 3.03011 0.107198
\(800\) 9.71456 + 33.8894i 0.343461 + 1.19817i
\(801\) −11.3620 −0.401455
\(802\) 51.6400i 1.82347i
\(803\) 12.4286i 0.438597i
\(804\) 5.80642 0.204777
\(805\) −0.785680 5.59210i −0.0276916 0.197096i
\(806\) 14.4286 0.508227
\(807\) 1.48103i 0.0521346i
\(808\) 9.51114i 0.334601i
\(809\) 20.9304 0.735874 0.367937 0.929851i \(-0.380064\pi\)
0.367937 + 0.929851i \(0.380064\pi\)
\(810\) −4.90321 + 0.688892i −0.172281 + 0.0242052i
\(811\) −49.2770 −1.73035 −0.865175 0.501470i \(-0.832793\pi\)
−0.865175 + 0.501470i \(0.832793\pi\)
\(812\) 17.7605i 0.623271i
\(813\) 25.4844i 0.893778i
\(814\) 2.90321 0.101758
\(815\) −2.90321 + 0.407896i −0.101695 + 0.0142880i
\(816\) −2.62222 −0.0917959
\(817\) 2.31111i 0.0808554i
\(818\) 5.77478i 0.201910i
\(819\) 1.31111 0.0458138
\(820\) 2.42864 + 17.2859i 0.0848118 + 0.603650i
\(821\) −44.1862 −1.54211 −0.771055 0.636769i \(-0.780271\pi\)
−0.771055 + 0.636769i \(0.780271\pi\)
\(822\) 30.0415i 1.04782i
\(823\) 7.10462i 0.247652i 0.992304 + 0.123826i \(0.0395164\pi\)
−0.992304 + 0.123826i \(0.960484\pi\)
\(824\) 22.6035 0.787430
\(825\) 1.37778 + 4.80642i 0.0479683 + 0.167338i
\(826\) −15.9748 −0.555835
\(827\) 41.3461i 1.43775i 0.695141 + 0.718873i \(0.255342\pi\)
−0.695141 + 0.718873i \(0.744658\pi\)
\(828\) 7.33185i 0.254799i
\(829\) 3.40943 0.118414 0.0592072 0.998246i \(-0.481143\pi\)
0.0592072 + 0.998246i \(0.481143\pi\)
\(830\) 4.62867 + 32.9447i 0.160663 + 1.14353i
\(831\) 14.2395 0.493963
\(832\) 16.8573i 0.584421i
\(833\) 1.90321i 0.0659424i
\(834\) 13.3176 0.461149
\(835\) −33.5210 + 4.70964i −1.16004 + 0.162984i
\(836\) −1.09679 −0.0379332
\(837\) 4.96989i 0.171784i
\(838\) 34.1497i 1.17968i
\(839\) −5.09526 −0.175908 −0.0879539 0.996125i \(-0.528033\pi\)
−0.0879539 + 0.996125i \(0.528033\pi\)
\(840\) −4.42864 + 0.622216i −0.152803 + 0.0214685i
\(841\) 8.42419 0.290489
\(842\) 13.9190i 0.479682i
\(843\) 2.23951i 0.0771328i
\(844\) −15.7333 −0.541562
\(845\) 3.50961 + 24.9797i 0.120734 + 0.859329i
\(846\) 3.52543 0.121207
\(847\) 1.00000i 0.0343604i
\(848\) 15.7462i 0.540727i
\(849\) −24.8321 −0.852235
\(850\) −20.2558 + 5.80642i −0.694768 + 0.199159i
\(851\) −3.31111 −0.113503
\(852\) 14.2953i 0.489748i
\(853\) 23.0257i 0.788384i 0.919028 + 0.394192i \(0.128975\pi\)
−0.919028 + 0.394192i \(0.871025\pi\)
\(854\) 2.31603 0.0792529
\(855\) 0.117532 + 0.836535i 0.00401950 + 0.0286089i
\(856\) 17.6731 0.604053
\(857\) 12.6923i 0.433560i 0.976220 + 0.216780i \(0.0695554\pi\)
−0.976220 + 0.216780i \(0.930445\pi\)
\(858\) 2.90321i 0.0991140i
\(859\) −41.9418 −1.43104 −0.715518 0.698595i \(-0.753809\pi\)
−0.715518 + 0.698595i \(0.753809\pi\)
\(860\) 39.3274 5.52543i 1.34105 0.188416i
\(861\) 2.68889 0.0916372
\(862\) 36.1116i 1.22996i
\(863\) 45.1659i 1.53747i −0.639569 0.768733i \(-0.720887\pi\)
0.639569 0.768733i \(-0.279113\pi\)
\(864\) −7.05086 −0.239875
\(865\) −48.4099 + 6.80150i −1.64599 + 0.231258i
\(866\) 32.9621 1.12010
\(867\) 13.3778i 0.454333i
\(868\) 14.4286i 0.489740i
\(869\) −0.969888 −0.0329012
\(870\) −4.21432 29.9956i −0.142879 1.01694i
\(871\) −2.62222 −0.0888504
\(872\) 6.79706i 0.230177i
\(873\) 8.54617i 0.289244i
\(874\) 2.11261 0.0714601
\(875\) 10.2143 4.54617i 0.345307 0.153689i
\(876\) 36.0830 1.21913
\(877\) 47.6671i 1.60960i −0.593544 0.804802i \(-0.702272\pi\)
0.593544 0.804802i \(-0.297728\pi\)
\(878\) 22.8464i 0.771028i
\(879\) −25.6035 −0.863584
\(880\) 0.428639 + 3.05086i 0.0144494 + 0.102844i
\(881\) −8.53633 −0.287596 −0.143798 0.989607i \(-0.545932\pi\)
−0.143798 + 0.989607i \(0.545932\pi\)
\(882\) 2.21432i 0.0745600i
\(883\) 17.6258i 0.593154i 0.955009 + 0.296577i \(0.0958451\pi\)
−0.955009 + 0.296577i \(0.904155\pi\)
\(884\) −7.24443 −0.243657
\(885\) −15.9748 + 2.24443i −0.536987 + 0.0754457i
\(886\) 9.25428 0.310903
\(887\) 14.2761i 0.479344i −0.970854 0.239672i \(-0.922960\pi\)
0.970854 0.239672i \(-0.0770398\pi\)
\(888\) 2.62222i 0.0879958i
\(889\) −2.45875 −0.0824639
\(890\) −55.7101 + 7.82717i −1.86741 + 0.262367i
\(891\) −1.00000 −0.0335013
\(892\) 53.1066i 1.77814i
\(893\) 0.601472i 0.0201275i
\(894\) 22.1432 0.740579
\(895\) 4.91951 + 35.0148i 0.164441 + 1.17041i
\(896\) −14.3684 −0.480015
\(897\) 3.31111i 0.110555i
\(898\) 55.8435i 1.86352i
\(899\) −30.4035 −1.01401
\(900\) −13.9541 + 4.00000i −0.465136 + 0.133333i
\(901\) −21.7511 −0.724635
\(902\) 5.95407i 0.198249i
\(903\) 6.11753i 0.203579i
\(904\) 5.52098 0.183625
\(905\) −6.71408 47.7877i −0.223184 1.58852i
\(906\) 11.1842 0.371570
\(907\) 46.8736i 1.55641i 0.628009 + 0.778206i \(0.283870\pi\)
−0.628009 + 0.778206i \(0.716130\pi\)
\(908\) 26.6365i 0.883963i
\(909\) 4.75557 0.157732
\(910\) 6.42864 0.903212i 0.213107 0.0299412i
\(911\) −14.5018 −0.480465 −0.240233 0.970715i \(-0.577224\pi\)
−0.240233 + 0.970715i \(0.577224\pi\)
\(912\) 0.520505i 0.0172357i
\(913\) 6.71900i 0.222367i
\(914\) −61.1086 −2.02129
\(915\) 2.31603 0.325398i 0.0765656 0.0107573i
\(916\) 0.326929 0.0108020
\(917\) 5.73975i 0.189543i
\(918\) 4.21432i 0.139093i
\(919\) −0.990632 −0.0326779 −0.0163390 0.999867i \(-0.505201\pi\)
−0.0163390 + 0.999867i \(0.505201\pi\)
\(920\) 1.57136 + 11.1842i 0.0518062 + 0.368732i
\(921\) −5.09234 −0.167798
\(922\) 74.3595i 2.44890i
\(923\) 6.45584i 0.212496i
\(924\) −2.90321 −0.0955087
\(925\) −1.80642 6.30174i −0.0593949 0.207200i
\(926\) −50.6834 −1.66556
\(927\) 11.3017i 0.371198i
\(928\) 43.1338i 1.41594i
\(929\) 40.8943 1.34170 0.670850 0.741593i \(-0.265930\pi\)
0.670850 + 0.741593i \(0.265930\pi\)
\(930\) 3.42372 + 24.3684i 0.112268 + 0.799072i
\(931\) 0.377784 0.0123814
\(932\) 59.1941i 1.93897i
\(933\) 17.3274i 0.567274i
\(934\) 14.1432 0.462780
\(935\) −4.21432 + 0.592104i −0.137823 + 0.0193639i
\(936\) −2.62222 −0.0857098
\(937\) 16.5872i 0.541880i −0.962596 0.270940i \(-0.912666\pi\)
0.962596 0.270940i \(-0.0873344\pi\)
\(938\) 4.42864i 0.144600i
\(939\) 15.4909 0.505525
\(940\) 10.2351 1.43801i 0.333831 0.0469026i
\(941\) 35.9561 1.17213 0.586067 0.810262i \(-0.300675\pi\)
0.586067 + 0.810262i \(0.300675\pi\)
\(942\) 19.6795i 0.641194i
\(943\) 6.79060i 0.221132i
\(944\) −9.93978 −0.323512
\(945\) 0.311108 + 2.21432i 0.0101203 + 0.0720318i
\(946\) 13.5462 0.440424
\(947\) 41.9675i 1.36376i −0.731465 0.681879i \(-0.761163\pi\)
0.731465 0.681879i \(-0.238837\pi\)
\(948\) 2.81579i 0.0914527i
\(949\) −16.2953 −0.528967
\(950\) 1.15257 + 4.02074i 0.0373942 + 0.130450i
\(951\) 12.4143 0.402563
\(952\) 3.80642i 0.123367i
\(953\) 7.83500i 0.253801i 0.991915 + 0.126900i \(0.0405028\pi\)
−0.991915 + 0.126900i \(0.959497\pi\)
\(954\) −25.3067 −0.819333
\(955\) −1.72345 12.2667i −0.0557695 0.396941i
\(956\) 72.6405 2.34936
\(957\) 6.11753i 0.197752i
\(958\) 76.6089i 2.47512i
\(959\) −13.5669 −0.438099
\(960\) −28.4701 + 4.00000i −0.918869 + 0.129099i
\(961\) −6.30021 −0.203233
\(962\) 3.80642i 0.122724i
\(963\) 8.83654i 0.284753i
\(964\) 3.45091 0.111146
\(965\) 20.6321 2.89877i 0.664170 0.0933146i
\(966\) 5.59210 0.179923
\(967\) 29.5783i 0.951174i 0.879669 + 0.475587i \(0.157764\pi\)
−0.879669 + 0.475587i \(0.842236\pi\)
\(968\) 2.00000i 0.0642824i
\(969\) −0.719004 −0.0230977
\(970\) 5.88739 + 41.9037i 0.189033 + 1.34545i
\(971\) 13.3749 0.429220 0.214610 0.976700i \(-0.431152\pi\)
0.214610 + 0.976700i \(0.431152\pi\)
\(972\) 2.90321i 0.0931206i
\(973\) 6.01429i 0.192809i
\(974\) 27.5843 0.883857
\(975\) 6.30174 1.80642i 0.201817 0.0578519i
\(976\) 1.44107 0.0461275
\(977\) 57.1245i 1.82757i −0.406194 0.913787i \(-0.633144\pi\)
0.406194 0.913787i \(-0.366856\pi\)
\(978\) 2.90321i 0.0928345i
\(979\) −11.3620 −0.363130
\(980\) 0.903212 + 6.42864i 0.0288520 + 0.205355i
\(981\) 3.39853 0.108507
\(982\) 36.3749i 1.16077i
\(983\) 11.4924i 0.366551i −0.983062 0.183275i \(-0.941330\pi\)
0.983062 0.183275i \(-0.0586700\pi\)
\(984\) −5.37778 −0.171438
\(985\) 59.8578 8.40990i 1.90723 0.267962i
\(986\) 25.7812 0.821042
\(987\) 1.59210i 0.0506772i
\(988\) 1.43801i 0.0457491i
\(989\) −15.4494 −0.491262
\(990\) −4.90321 + 0.688892i −0.155834 + 0.0218944i
\(991\) 23.4987 0.746461 0.373231 0.927739i \(-0.378250\pi\)
0.373231 + 0.927739i \(0.378250\pi\)
\(992\) 35.0420i 1.11258i
\(993\) 32.5210i 1.03202i
\(994\) −10.9032 −0.345829
\(995\) 1.26317 + 8.99063i 0.0400451 + 0.285022i
\(996\) −19.5067 −0.618093
\(997\) 24.3970i 0.772661i −0.922360 0.386330i \(-0.873742\pi\)
0.922360 0.386330i \(-0.126258\pi\)
\(998\) 82.5106i 2.61183i
\(999\) 1.31111 0.0414816
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 1155.2.c.c.694.6 yes 6
5.2 odd 4 5775.2.a.bu.1.1 3
5.3 odd 4 5775.2.a.bt.1.3 3
5.4 even 2 inner 1155.2.c.c.694.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.c.c.694.1 6 5.4 even 2 inner
1155.2.c.c.694.6 yes 6 1.1 even 1 trivial
5775.2.a.bt.1.3 3 5.3 odd 4
5775.2.a.bu.1.1 3 5.2 odd 4