Properties

Label 170.2.c.b.69.4
Level $170$
Weight $2$
Character 170.69
Analytic conductor $1.357$
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] = [170,2,Mod(69,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.69");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.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: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 69.4
Root \(-1.75233 + 1.75233i\) of defining polynomial
Character \(\chi\) \(=\) 170.69
Dual form 170.2.c.b.69.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -3.14134i q^{3} -1.00000 q^{4} +(1.38900 + 1.75233i) q^{5} +3.14134 q^{6} -3.50466i q^{7} -1.00000i q^{8} -6.86799 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -3.14134i q^{3} -1.00000 q^{4} +(1.38900 + 1.75233i) q^{5} +3.14134 q^{6} -3.50466i q^{7} -1.00000i q^{8} -6.86799 q^{9} +(-1.75233 + 1.38900i) q^{10} +2.00000 q^{11} +3.14134i q^{12} -3.14134i q^{13} +3.50466 q^{14} +(5.50466 - 4.36333i) q^{15} +1.00000 q^{16} +1.00000i q^{17} -6.86799i q^{18} +3.86799 q^{19} +(-1.38900 - 1.75233i) q^{20} -11.0093 q^{21} +2.00000i q^{22} +7.50466i q^{23} -3.14134 q^{24} +(-1.14134 + 4.86799i) q^{25} +3.14134 q^{26} +12.1507i q^{27} +3.50466i q^{28} +0.646000 q^{29} +(4.36333 + 5.50466i) q^{30} -3.91934 q^{31} +1.00000i q^{32} -6.28267i q^{33} -1.00000 q^{34} +(6.14134 - 4.86799i) q^{35} +6.86799 q^{36} +8.95798i q^{37} +3.86799i q^{38} -9.86799 q^{39} +(1.75233 - 1.38900i) q^{40} +6.72666 q^{41} -11.0093i q^{42} +4.28267i q^{43} -2.00000 q^{44} +(-9.53967 - 12.0350i) q^{45} -7.50466 q^{46} -10.5946i q^{47} -3.14134i q^{48} -5.28267 q^{49} +(-4.86799 - 1.14134i) q^{50} +3.14134 q^{51} +3.14134i q^{52} +8.69735i q^{53} -12.1507 q^{54} +(2.77801 + 3.50466i) q^{55} -3.50466 q^{56} -12.1507i q^{57} +0.646000i q^{58} -4.41468 q^{59} +(-5.50466 + 4.36333i) q^{60} -0.910015 q^{61} -3.91934i q^{62} +24.0700i q^{63} -1.00000 q^{64} +(5.50466 - 4.36333i) q^{65} +6.28267 q^{66} -10.2827i q^{67} -1.00000i q^{68} +23.5747 q^{69} +(4.86799 + 6.14134i) q^{70} +3.19269 q^{71} +6.86799i q^{72} -3.14134i q^{73} -8.95798 q^{74} +(15.2920 + 3.58532i) q^{75} -3.86799 q^{76} -7.00933i q^{77} -9.86799i q^{78} -2.05135 q^{79} +(1.38900 + 1.75233i) q^{80} +17.5653 q^{81} +6.72666i q^{82} -1.73599i q^{83} +11.0093 q^{84} +(-1.75233 + 1.38900i) q^{85} -4.28267 q^{86} -2.02930i q^{87} -2.00000i q^{88} +4.41468 q^{89} +(12.0350 - 9.53967i) q^{90} -11.0093 q^{91} -7.50466i q^{92} +12.3120i q^{93} +10.5946 q^{94} +(5.37266 + 6.77801i) q^{95} +3.14134 q^{96} +2.41468i q^{97} -5.28267i q^{98} -13.7360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{9} + 12 q^{11} + 12 q^{15} + 6 q^{16} - 2 q^{19} - 2 q^{20} - 24 q^{21} - 2 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{29} + 22 q^{30} + 6 q^{31} - 6 q^{34} + 20 q^{35} + 16 q^{36} - 34 q^{39} + 32 q^{41} - 12 q^{44} + 8 q^{45} - 24 q^{46} + 2 q^{49} - 4 q^{50} + 2 q^{51} - 14 q^{54} + 4 q^{55} - 18 q^{59} - 12 q^{60} - 18 q^{61} - 6 q^{64} + 12 q^{65} + 4 q^{66} + 32 q^{69} + 4 q^{70} - 2 q^{71} - 16 q^{74} + 16 q^{75} + 2 q^{76} - 8 q^{79} + 2 q^{80} + 38 q^{81} + 24 q^{84} + 8 q^{86} + 18 q^{89} + 28 q^{90} - 24 q^{91} + 30 q^{94} - 14 q^{95} + 2 q^{96} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 3.14134i 1.81365i −0.421506 0.906826i \(-0.638498\pi\)
0.421506 0.906826i \(-0.361502\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.38900 + 1.75233i 0.621181 + 0.783667i
\(6\) 3.14134 1.28245
\(7\) 3.50466i 1.32464i −0.749222 0.662319i \(-0.769572\pi\)
0.749222 0.662319i \(-0.230428\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −6.86799 −2.28933
\(10\) −1.75233 + 1.38900i −0.554136 + 0.439242i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 3.14134i 0.906826i
\(13\) 3.14134i 0.871250i −0.900128 0.435625i \(-0.856527\pi\)
0.900128 0.435625i \(-0.143473\pi\)
\(14\) 3.50466 0.936661
\(15\) 5.50466 4.36333i 1.42130 1.12661i
\(16\) 1.00000 0.250000
\(17\) 1.00000i 0.242536i
\(18\) 6.86799i 1.61880i
\(19\) 3.86799 0.887378 0.443689 0.896181i \(-0.353669\pi\)
0.443689 + 0.896181i \(0.353669\pi\)
\(20\) −1.38900 1.75233i −0.310591 0.391833i
\(21\) −11.0093 −2.40243
\(22\) 2.00000i 0.426401i
\(23\) 7.50466i 1.56483i 0.622757 + 0.782415i \(0.286013\pi\)
−0.622757 + 0.782415i \(0.713987\pi\)
\(24\) −3.14134 −0.641223
\(25\) −1.14134 + 4.86799i −0.228267 + 0.973599i
\(26\) 3.14134 0.616067
\(27\) 12.1507i 2.33840i
\(28\) 3.50466i 0.662319i
\(29\) 0.646000 0.119959 0.0599796 0.998200i \(-0.480896\pi\)
0.0599796 + 0.998200i \(0.480896\pi\)
\(30\) 4.36333 + 5.50466i 0.796631 + 1.00501i
\(31\) −3.91934 −0.703935 −0.351967 0.936012i \(-0.614487\pi\)
−0.351967 + 0.936012i \(0.614487\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 6.28267i 1.09367i
\(34\) −1.00000 −0.171499
\(35\) 6.14134 4.86799i 1.03808 0.822841i
\(36\) 6.86799 1.14467
\(37\) 8.95798i 1.47268i 0.676610 + 0.736341i \(0.263448\pi\)
−0.676610 + 0.736341i \(0.736552\pi\)
\(38\) 3.86799i 0.627471i
\(39\) −9.86799 −1.58014
\(40\) 1.75233 1.38900i 0.277068 0.219621i
\(41\) 6.72666 1.05053 0.525264 0.850940i \(-0.323967\pi\)
0.525264 + 0.850940i \(0.323967\pi\)
\(42\) 11.0093i 1.69878i
\(43\) 4.28267i 0.653101i 0.945180 + 0.326551i \(0.105886\pi\)
−0.945180 + 0.326551i \(0.894114\pi\)
\(44\) −2.00000 −0.301511
\(45\) −9.53967 12.0350i −1.42209 1.79407i
\(46\) −7.50466 −1.10650
\(47\) 10.5946i 1.54539i −0.634778 0.772694i \(-0.718909\pi\)
0.634778 0.772694i \(-0.281091\pi\)
\(48\) 3.14134i 0.453413i
\(49\) −5.28267 −0.754667
\(50\) −4.86799 1.14134i −0.688438 0.161409i
\(51\) 3.14134 0.439875
\(52\) 3.14134i 0.435625i
\(53\) 8.69735i 1.19467i 0.801991 + 0.597337i \(0.203774\pi\)
−0.801991 + 0.597337i \(0.796226\pi\)
\(54\) −12.1507 −1.65350
\(55\) 2.77801 + 3.50466i 0.374587 + 0.472569i
\(56\) −3.50466 −0.468330
\(57\) 12.1507i 1.60939i
\(58\) 0.646000i 0.0848240i
\(59\) −4.41468 −0.574742 −0.287371 0.957819i \(-0.592781\pi\)
−0.287371 + 0.957819i \(0.592781\pi\)
\(60\) −5.50466 + 4.36333i −0.710649 + 0.563303i
\(61\) −0.910015 −0.116516 −0.0582578 0.998302i \(-0.518555\pi\)
−0.0582578 + 0.998302i \(0.518555\pi\)
\(62\) 3.91934i 0.497757i
\(63\) 24.0700i 3.03254i
\(64\) −1.00000 −0.125000
\(65\) 5.50466 4.36333i 0.682770 0.541204i
\(66\) 6.28267 0.773343
\(67\) 10.2827i 1.25623i −0.778121 0.628114i \(-0.783827\pi\)
0.778121 0.628114i \(-0.216173\pi\)
\(68\) 1.00000i 0.121268i
\(69\) 23.5747 2.83806
\(70\) 4.86799 + 6.14134i 0.581836 + 0.734030i
\(71\) 3.19269 0.378902 0.189451 0.981890i \(-0.439329\pi\)
0.189451 + 0.981890i \(0.439329\pi\)
\(72\) 6.86799i 0.809401i
\(73\) 3.14134i 0.367666i −0.982958 0.183833i \(-0.941150\pi\)
0.982958 0.183833i \(-0.0588505\pi\)
\(74\) −8.95798 −1.04134
\(75\) 15.2920 + 3.58532i 1.76577 + 0.413997i
\(76\) −3.86799 −0.443689
\(77\) 7.00933i 0.798787i
\(78\) 9.86799i 1.11733i
\(79\) −2.05135 −0.230795 −0.115398 0.993319i \(-0.536814\pi\)
−0.115398 + 0.993319i \(0.536814\pi\)
\(80\) 1.38900 + 1.75233i 0.155295 + 0.195917i
\(81\) 17.5653 1.95170
\(82\) 6.72666i 0.742835i
\(83\) 1.73599i 0.190549i −0.995451 0.0952746i \(-0.969627\pi\)
0.995451 0.0952746i \(-0.0303729\pi\)
\(84\) 11.0093 1.20122
\(85\) −1.75233 + 1.38900i −0.190067 + 0.150659i
\(86\) −4.28267 −0.461812
\(87\) 2.02930i 0.217564i
\(88\) 2.00000i 0.213201i
\(89\) 4.41468 0.467955 0.233978 0.972242i \(-0.424826\pi\)
0.233978 + 0.972242i \(0.424826\pi\)
\(90\) 12.0350 9.53967i 1.26860 1.00557i
\(91\) −11.0093 −1.15409
\(92\) 7.50466i 0.782415i
\(93\) 12.3120i 1.27669i
\(94\) 10.5946 1.09275
\(95\) 5.37266 + 6.77801i 0.551223 + 0.695409i
\(96\) 3.14134 0.320611
\(97\) 2.41468i 0.245174i 0.992458 + 0.122587i \(0.0391190\pi\)
−0.992458 + 0.122587i \(0.960881\pi\)
\(98\) 5.28267i 0.533630i
\(99\) −13.7360 −1.38052
\(100\) 1.14134 4.86799i 0.114134 0.486799i
\(101\) −5.73599 −0.570752 −0.285376 0.958416i \(-0.592118\pi\)
−0.285376 + 0.958416i \(0.592118\pi\)
\(102\) 3.14134i 0.311039i
\(103\) 9.55602i 0.941582i 0.882245 + 0.470791i \(0.156031\pi\)
−0.882245 + 0.470791i \(0.843969\pi\)
\(104\) −3.14134 −0.308033
\(105\) −15.2920 19.2920i −1.49235 1.88271i
\(106\) −8.69735 −0.844761
\(107\) 10.8294i 1.04691i −0.852052 0.523457i \(-0.824642\pi\)
0.852052 0.523457i \(-0.175358\pi\)
\(108\) 12.1507i 1.16920i
\(109\) −10.0993 −0.967339 −0.483669 0.875251i \(-0.660696\pi\)
−0.483669 + 0.875251i \(0.660696\pi\)
\(110\) −3.50466 + 2.77801i −0.334157 + 0.264873i
\(111\) 28.1400 2.67093
\(112\) 3.50466i 0.331160i
\(113\) 4.85866i 0.457065i −0.973536 0.228532i \(-0.926607\pi\)
0.973536 0.228532i \(-0.0733927\pi\)
\(114\) 12.1507 1.13801
\(115\) −13.1507 + 10.4240i −1.22631 + 0.972044i
\(116\) −0.646000 −0.0599796
\(117\) 21.5747i 1.99458i
\(118\) 4.41468i 0.406404i
\(119\) 3.50466 0.321272
\(120\) −4.36333 5.50466i −0.398316 0.502505i
\(121\) −7.00000 −0.636364
\(122\) 0.910015i 0.0823889i
\(123\) 21.1307i 1.90529i
\(124\) 3.91934 0.351967
\(125\) −10.1157 + 4.76166i −0.904772 + 0.425896i
\(126\) −24.0700 −2.14433
\(127\) 0.150665i 0.0133693i 0.999978 + 0.00668467i \(0.00212781\pi\)
−0.999978 + 0.00668467i \(0.997872\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 13.4533 1.18450
\(130\) 4.36333 + 5.50466i 0.382689 + 0.482791i
\(131\) 11.4533 1.00068 0.500340 0.865829i \(-0.333208\pi\)
0.500340 + 0.865829i \(0.333208\pi\)
\(132\) 6.28267i 0.546836i
\(133\) 13.5560i 1.17546i
\(134\) 10.2827 0.888288
\(135\) −21.2920 + 16.8773i −1.83252 + 1.45257i
\(136\) 1.00000 0.0857493
\(137\) 8.56534i 0.731787i −0.930657 0.365893i \(-0.880763\pi\)
0.930657 0.365893i \(-0.119237\pi\)
\(138\) 23.5747i 2.00681i
\(139\) −14.3013 −1.21302 −0.606511 0.795075i \(-0.707432\pi\)
−0.606511 + 0.795075i \(0.707432\pi\)
\(140\) −6.14134 + 4.86799i −0.519038 + 0.411420i
\(141\) −33.2814 −2.80280
\(142\) 3.19269i 0.267924i
\(143\) 6.28267i 0.525383i
\(144\) −6.86799 −0.572333
\(145\) 0.897297 + 1.13201i 0.0745165 + 0.0940081i
\(146\) 3.14134 0.259979
\(147\) 16.5946i 1.36870i
\(148\) 8.95798i 0.736341i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −3.58532 + 15.2920i −0.292740 + 1.24859i
\(151\) 21.0280 1.71123 0.855617 0.517610i \(-0.173178\pi\)
0.855617 + 0.517610i \(0.173178\pi\)
\(152\) 3.86799i 0.313736i
\(153\) 6.86799i 0.555244i
\(154\) 7.00933 0.564828
\(155\) −5.44398 6.86799i −0.437271 0.551650i
\(156\) 9.86799 0.790072
\(157\) 21.5747i 1.72185i −0.508735 0.860923i \(-0.669887\pi\)
0.508735 0.860923i \(-0.330113\pi\)
\(158\) 2.05135i 0.163197i
\(159\) 27.3213 2.16672
\(160\) −1.75233 + 1.38900i −0.138534 + 0.109810i
\(161\) 26.3013 2.07284
\(162\) 17.5653i 1.38006i
\(163\) 9.27334i 0.726344i −0.931722 0.363172i \(-0.881694\pi\)
0.931722 0.363172i \(-0.118306\pi\)
\(164\) −6.72666 −0.525264
\(165\) 11.0093 8.72666i 0.857075 0.679369i
\(166\) 1.73599 0.134739
\(167\) 20.7967i 1.60929i 0.593753 + 0.804647i \(0.297646\pi\)
−0.593753 + 0.804647i \(0.702354\pi\)
\(168\) 11.0093i 0.849388i
\(169\) 3.13201 0.240924
\(170\) −1.38900 1.75233i −0.106532 0.134398i
\(171\) −26.5653 −2.03150
\(172\) 4.28267i 0.326551i
\(173\) 13.9486i 1.06050i 0.847843 + 0.530248i \(0.177901\pi\)
−0.847843 + 0.530248i \(0.822099\pi\)
\(174\) 2.02930 0.153841
\(175\) 17.0607 + 4.00000i 1.28967 + 0.302372i
\(176\) 2.00000 0.150756
\(177\) 13.8680i 1.04238i
\(178\) 4.41468i 0.330894i
\(179\) −14.3013 −1.06893 −0.534466 0.845190i \(-0.679487\pi\)
−0.534466 + 0.845190i \(0.679487\pi\)
\(180\) 9.53967 + 12.0350i 0.711045 + 0.897036i
\(181\) −10.6753 −0.793489 −0.396745 0.917929i \(-0.629860\pi\)
−0.396745 + 0.917929i \(0.629860\pi\)
\(182\) 11.0093i 0.816066i
\(183\) 2.85866i 0.211319i
\(184\) 7.50466 0.553251
\(185\) −15.6974 + 12.4427i −1.15409 + 0.914803i
\(186\) −12.3120 −0.902758
\(187\) 2.00000i 0.146254i
\(188\) 10.5946i 0.772694i
\(189\) 42.5840 3.09753
\(190\) −6.77801 + 5.37266i −0.491728 + 0.389774i
\(191\) −4.56534 −0.330337 −0.165168 0.986265i \(-0.552817\pi\)
−0.165168 + 0.986265i \(0.552817\pi\)
\(192\) 3.14134i 0.226706i
\(193\) 12.0187i 0.865122i 0.901605 + 0.432561i \(0.142390\pi\)
−0.901605 + 0.432561i \(0.857610\pi\)
\(194\) −2.41468 −0.173364
\(195\) −13.7067 17.2920i −0.981556 1.23831i
\(196\) 5.28267 0.377334
\(197\) 21.8900i 1.55960i 0.626028 + 0.779800i \(0.284679\pi\)
−0.626028 + 0.779800i \(0.715321\pi\)
\(198\) 13.7360i 0.976174i
\(199\) 7.08998 0.502596 0.251298 0.967910i \(-0.419143\pi\)
0.251298 + 0.967910i \(0.419143\pi\)
\(200\) 4.86799 + 1.14134i 0.344219 + 0.0807047i
\(201\) −32.3013 −2.27836
\(202\) 5.73599i 0.403583i
\(203\) 2.26401i 0.158903i
\(204\) −3.14134 −0.219938
\(205\) 9.34335 + 11.7873i 0.652568 + 0.823263i
\(206\) −9.55602 −0.665799
\(207\) 51.5420i 3.58242i
\(208\) 3.14134i 0.217812i
\(209\) 7.73599 0.535109
\(210\) 19.2920 15.2920i 1.33127 1.05525i
\(211\) −15.1893 −1.04567 −0.522837 0.852433i \(-0.675126\pi\)
−0.522837 + 0.852433i \(0.675126\pi\)
\(212\) 8.69735i 0.597337i
\(213\) 10.0293i 0.687197i
\(214\) 10.8294 0.740280
\(215\) −7.50466 + 5.94865i −0.511814 + 0.405694i
\(216\) 12.1507 0.826748
\(217\) 13.7360i 0.932459i
\(218\) 10.0993i 0.684012i
\(219\) −9.86799 −0.666817
\(220\) −2.77801 3.50466i −0.187293 0.236284i
\(221\) 3.14134 0.211309
\(222\) 28.1400i 1.88863i
\(223\) 5.60398i 0.375270i −0.982239 0.187635i \(-0.939918\pi\)
0.982239 0.187635i \(-0.0600822\pi\)
\(224\) 3.50466 0.234165
\(225\) 7.83869 33.4333i 0.522579 2.22889i
\(226\) 4.85866 0.323194
\(227\) 7.76529i 0.515400i 0.966225 + 0.257700i \(0.0829647\pi\)
−0.966225 + 0.257700i \(0.917035\pi\)
\(228\) 12.1507i 0.804697i
\(229\) −13.0093 −0.859681 −0.429840 0.902905i \(-0.641430\pi\)
−0.429840 + 0.902905i \(0.641430\pi\)
\(230\) −10.4240 13.1507i −0.687339 0.867129i
\(231\) −22.0187 −1.44872
\(232\) 0.646000i 0.0424120i
\(233\) 10.8773i 0.712597i −0.934372 0.356299i \(-0.884039\pi\)
0.934372 0.356299i \(-0.115961\pi\)
\(234\) −21.5747 −1.41038
\(235\) 18.5653 14.7160i 1.21107 0.959967i
\(236\) 4.41468 0.287371
\(237\) 6.44398i 0.418582i
\(238\) 3.50466i 0.227174i
\(239\) −24.3013 −1.57192 −0.785961 0.618276i \(-0.787831\pi\)
−0.785961 + 0.618276i \(0.787831\pi\)
\(240\) 5.50466 4.36333i 0.355325 0.281652i
\(241\) 19.8573 1.27912 0.639562 0.768739i \(-0.279116\pi\)
0.639562 + 0.768739i \(0.279116\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 18.7267i 1.20132i
\(244\) 0.910015 0.0582578
\(245\) −7.33765 9.25700i −0.468785 0.591408i
\(246\) 21.1307 1.34724
\(247\) 12.1507i 0.773128i
\(248\) 3.91934i 0.248879i
\(249\) −5.45331 −0.345590
\(250\) −4.76166 10.1157i −0.301154 0.639771i
\(251\) 10.8294 0.683543 0.341772 0.939783i \(-0.388973\pi\)
0.341772 + 0.939783i \(0.388973\pi\)
\(252\) 24.0700i 1.51627i
\(253\) 15.0093i 0.943628i
\(254\) −0.150665 −0.00945355
\(255\) 4.36333 + 5.50466i 0.273242 + 0.344715i
\(256\) 1.00000 0.0625000
\(257\) 24.5653i 1.53234i 0.642636 + 0.766172i \(0.277841\pi\)
−0.642636 + 0.766172i \(0.722159\pi\)
\(258\) 13.4533i 0.837567i
\(259\) 31.3947 1.95077
\(260\) −5.50466 + 4.36333i −0.341385 + 0.270602i
\(261\) −4.43673 −0.274626
\(262\) 11.4533i 0.707588i
\(263\) 7.32131i 0.451451i −0.974191 0.225726i \(-0.927525\pi\)
0.974191 0.225726i \(-0.0724752\pi\)
\(264\) −6.28267 −0.386672
\(265\) −15.2406 + 12.0807i −0.936226 + 0.742109i
\(266\) 13.5560 0.831173
\(267\) 13.8680i 0.848707i
\(268\) 10.2827i 0.628114i
\(269\) 5.37266 0.327577 0.163788 0.986496i \(-0.447629\pi\)
0.163788 + 0.986496i \(0.447629\pi\)
\(270\) −16.8773 21.2920i −1.02712 1.29579i
\(271\) 9.18930 0.558210 0.279105 0.960261i \(-0.409962\pi\)
0.279105 + 0.960261i \(0.409962\pi\)
\(272\) 1.00000i 0.0606339i
\(273\) 34.5840i 2.09312i
\(274\) 8.56534 0.517451
\(275\) −2.28267 + 9.73599i −0.137650 + 0.587102i
\(276\) −23.5747 −1.41903
\(277\) 4.79667i 0.288204i −0.989563 0.144102i \(-0.953971\pi\)
0.989563 0.144102i \(-0.0460293\pi\)
\(278\) 14.3013i 0.857737i
\(279\) 26.9180 1.61154
\(280\) −4.86799 6.14134i −0.290918 0.367015i
\(281\) 31.2627 1.86498 0.932488 0.361201i \(-0.117633\pi\)
0.932488 + 0.361201i \(0.117633\pi\)
\(282\) 33.2814i 1.98188i
\(283\) 17.0573i 1.01395i 0.861961 + 0.506975i \(0.169236\pi\)
−0.861961 + 0.506975i \(0.830764\pi\)
\(284\) −3.19269 −0.189451
\(285\) 21.2920 16.8773i 1.26123 0.999726i
\(286\) 6.28267 0.371502
\(287\) 23.5747i 1.39157i
\(288\) 6.86799i 0.404700i
\(289\) −1.00000 −0.0588235
\(290\) −1.13201 + 0.897297i −0.0664738 + 0.0526911i
\(291\) 7.58532 0.444659
\(292\) 3.14134i 0.183833i
\(293\) 22.2534i 1.30006i 0.759910 + 0.650028i \(0.225243\pi\)
−0.759910 + 0.650028i \(0.774757\pi\)
\(294\) −16.5946 −0.967820
\(295\) −6.13201 7.73599i −0.357019 0.450406i
\(296\) 8.95798 0.520672
\(297\) 24.3013i 1.41011i
\(298\) 10.0000i 0.579284i
\(299\) 23.5747 1.36336
\(300\) −15.2920 3.58532i −0.882884 0.206999i
\(301\) 15.0093 0.865123
\(302\) 21.0280i 1.21002i
\(303\) 18.0187i 1.03514i
\(304\) 3.86799 0.221845
\(305\) −1.26401 1.59465i −0.0723773 0.0913093i
\(306\) 6.86799 0.392617
\(307\) 29.7360i 1.69712i −0.529097 0.848561i \(-0.677469\pi\)
0.529097 0.848561i \(-0.322531\pi\)
\(308\) 7.00933i 0.399394i
\(309\) 30.0187 1.70770
\(310\) 6.86799 5.44398i 0.390076 0.309198i
\(311\) −23.1820 −1.31453 −0.657266 0.753658i \(-0.728287\pi\)
−0.657266 + 0.753658i \(0.728287\pi\)
\(312\) 9.86799i 0.558665i
\(313\) 23.4533i 1.32566i −0.748770 0.662830i \(-0.769355\pi\)
0.748770 0.662830i \(-0.230645\pi\)
\(314\) 21.5747 1.21753
\(315\) −42.1787 + 33.4333i −2.37650 + 1.88376i
\(316\) 2.05135 0.115398
\(317\) 3.60737i 0.202610i 0.994855 + 0.101305i \(0.0323018\pi\)
−0.994855 + 0.101305i \(0.967698\pi\)
\(318\) 27.3213i 1.53210i
\(319\) 1.29200 0.0723382
\(320\) −1.38900 1.75233i −0.0776477 0.0979583i
\(321\) −34.0187 −1.89874
\(322\) 26.3013i 1.46572i
\(323\) 3.86799i 0.215221i
\(324\) −17.5653 −0.975852
\(325\) 15.2920 + 3.58532i 0.848248 + 0.198878i
\(326\) 9.27334 0.513603
\(327\) 31.7253i 1.75442i
\(328\) 6.72666i 0.371417i
\(329\) −37.1307 −2.04708
\(330\) 8.72666 + 11.0093i 0.480387 + 0.606044i
\(331\) −33.9053 −1.86360 −0.931802 0.362967i \(-0.881764\pi\)
−0.931802 + 0.362967i \(0.881764\pi\)
\(332\) 1.73599i 0.0952746i
\(333\) 61.5233i 3.37146i
\(334\) −20.7967 −1.13794
\(335\) 18.0187 14.2827i 0.984464 0.780346i
\(336\) −11.0093 −0.600608
\(337\) 8.33063i 0.453799i −0.973918 0.226899i \(-0.927141\pi\)
0.973918 0.226899i \(-0.0728588\pi\)
\(338\) 3.13201i 0.170359i
\(339\) −15.2627 −0.828956
\(340\) 1.75233 1.38900i 0.0950336 0.0753293i
\(341\) −7.83869 −0.424489
\(342\) 26.5653i 1.43649i
\(343\) 6.01866i 0.324977i
\(344\) 4.28267 0.230906
\(345\) 32.7453 + 41.3107i 1.76295 + 2.22409i
\(346\) −13.9486 −0.749884
\(347\) 7.14134i 0.383367i 0.981457 + 0.191684i \(0.0613947\pi\)
−0.981457 + 0.191684i \(0.938605\pi\)
\(348\) 2.02930i 0.108782i
\(349\) −4.64939 −0.248876 −0.124438 0.992227i \(-0.539713\pi\)
−0.124438 + 0.992227i \(0.539713\pi\)
\(350\) −4.00000 + 17.0607i −0.213809 + 0.911932i
\(351\) 38.1693 2.03733
\(352\) 2.00000i 0.106600i
\(353\) 20.8480i 1.10963i 0.831974 + 0.554814i \(0.187211\pi\)
−0.831974 + 0.554814i \(0.812789\pi\)
\(354\) −13.8680 −0.737075
\(355\) 4.43466 + 5.59465i 0.235367 + 0.296933i
\(356\) −4.41468 −0.233978
\(357\) 11.0093i 0.582675i
\(358\) 14.3013i 0.755849i
\(359\) −12.4626 −0.657753 −0.328877 0.944373i \(-0.606670\pi\)
−0.328877 + 0.944373i \(0.606670\pi\)
\(360\) −12.0350 + 9.53967i −0.634300 + 0.502785i
\(361\) −4.03863 −0.212560
\(362\) 10.6753i 0.561082i
\(363\) 21.9894i 1.15414i
\(364\) 11.0093 0.577046
\(365\) 5.50466 4.36333i 0.288127 0.228387i
\(366\) −2.85866 −0.149425
\(367\) 5.22199i 0.272586i −0.990669 0.136293i \(-0.956481\pi\)
0.990669 0.136293i \(-0.0435188\pi\)
\(368\) 7.50466i 0.391208i
\(369\) −46.1986 −2.40500
\(370\) −12.4427 15.6974i −0.646863 0.816066i
\(371\) 30.4813 1.58251
\(372\) 12.3120i 0.638346i
\(373\) 26.4626i 1.37018i −0.728457 0.685092i \(-0.759762\pi\)
0.728457 0.685092i \(-0.240238\pi\)
\(374\) −2.00000 −0.103418
\(375\) 14.9580 + 31.7767i 0.772427 + 1.64094i
\(376\) −10.5946 −0.546377
\(377\) 2.02930i 0.104515i
\(378\) 42.5840i 2.19028i
\(379\) −8.70800 −0.447300 −0.223650 0.974670i \(-0.571797\pi\)
−0.223650 + 0.974670i \(0.571797\pi\)
\(380\) −5.37266 6.77801i −0.275611 0.347704i
\(381\) 0.473289 0.0242473
\(382\) 4.56534i 0.233583i
\(383\) 33.8094i 1.72758i −0.503853 0.863789i \(-0.668085\pi\)
0.503853 0.863789i \(-0.331915\pi\)
\(384\) −3.14134 −0.160306
\(385\) 12.2827 9.73599i 0.625983 0.496192i
\(386\) −12.0187 −0.611734
\(387\) 29.4134i 1.49517i
\(388\) 2.41468i 0.122587i
\(389\) 22.4626 1.13890 0.569451 0.822026i \(-0.307156\pi\)
0.569451 + 0.822026i \(0.307156\pi\)
\(390\) 17.2920 13.7067i 0.875615 0.694065i
\(391\) −7.50466 −0.379527
\(392\) 5.28267i 0.266815i
\(393\) 35.9787i 1.81489i
\(394\) −21.8900 −1.10280
\(395\) −2.84934 3.59465i −0.143366 0.180866i
\(396\) 13.7360 0.690259
\(397\) 23.8060i 1.19479i 0.801948 + 0.597394i \(0.203797\pi\)
−0.801948 + 0.597394i \(0.796203\pi\)
\(398\) 7.08998i 0.355389i
\(399\) −42.5840 −2.13187
\(400\) −1.14134 + 4.86799i −0.0570668 + 0.243400i
\(401\) 14.4626 0.722230 0.361115 0.932521i \(-0.382396\pi\)
0.361115 + 0.932521i \(0.382396\pi\)
\(402\) 32.3013i 1.61104i
\(403\) 12.3120i 0.613303i
\(404\) 5.73599 0.285376
\(405\) 24.3983 + 30.7803i 1.21236 + 1.52949i
\(406\) 2.26401 0.112361
\(407\) 17.9160i 0.888061i
\(408\) 3.14134i 0.155519i
\(409\) 6.13201 0.303208 0.151604 0.988441i \(-0.451556\pi\)
0.151604 + 0.988441i \(0.451556\pi\)
\(410\) −11.7873 + 9.34335i −0.582135 + 0.461435i
\(411\) −26.9066 −1.32721
\(412\) 9.55602i 0.470791i
\(413\) 15.4720i 0.761326i
\(414\) 51.5420 2.53315
\(415\) 3.04202 2.41129i 0.149327 0.118366i
\(416\) 3.14134 0.154017
\(417\) 44.9253i 2.20000i
\(418\) 7.73599i 0.378379i
\(419\) −21.8387 −1.06689 −0.533445 0.845835i \(-0.679103\pi\)
−0.533445 + 0.845835i \(0.679103\pi\)
\(420\) 15.2920 + 19.2920i 0.746173 + 0.941353i
\(421\) 3.71733 0.181171 0.0905857 0.995889i \(-0.471126\pi\)
0.0905857 + 0.995889i \(0.471126\pi\)
\(422\) 15.1893i 0.739403i
\(423\) 72.7640i 3.53791i
\(424\) 8.69735 0.422381
\(425\) −4.86799 1.14134i −0.236132 0.0553629i
\(426\) 10.0293 0.485921
\(427\) 3.18930i 0.154341i
\(428\) 10.8294i 0.523457i
\(429\) −19.7360 −0.952862
\(430\) −5.94865 7.50466i −0.286869 0.361907i
\(431\) −11.9673 −0.576445 −0.288222 0.957563i \(-0.593064\pi\)
−0.288222 + 0.957563i \(0.593064\pi\)
\(432\) 12.1507i 0.584599i
\(433\) 18.3013i 0.879506i −0.898119 0.439753i \(-0.855066\pi\)
0.898119 0.439753i \(-0.144934\pi\)
\(434\) −13.7360 −0.659348
\(435\) 3.55602 2.81871i 0.170498 0.135147i
\(436\) 10.0993 0.483669
\(437\) 29.0280i 1.38860i
\(438\) 9.86799i 0.471511i
\(439\) 31.0793 1.48334 0.741668 0.670767i \(-0.234035\pi\)
0.741668 + 0.670767i \(0.234035\pi\)
\(440\) 3.50466 2.77801i 0.167078 0.132436i
\(441\) 36.2814 1.72768
\(442\) 3.14134i 0.149418i
\(443\) 29.3947i 1.39658i −0.715813 0.698292i \(-0.753944\pi\)
0.715813 0.698292i \(-0.246056\pi\)
\(444\) −28.1400 −1.33547
\(445\) 6.13201 + 7.73599i 0.290685 + 0.366721i
\(446\) 5.60398 0.265356
\(447\) 31.4134i 1.48580i
\(448\) 3.50466i 0.165580i
\(449\) −14.1027 −0.665548 −0.332774 0.943007i \(-0.607985\pi\)
−0.332774 + 0.943007i \(0.607985\pi\)
\(450\) 33.4333 + 7.83869i 1.57606 + 0.369519i
\(451\) 13.4533 0.633492
\(452\) 4.85866i 0.228532i
\(453\) 66.0560i 3.10358i
\(454\) −7.76529 −0.364443
\(455\) −15.2920 19.2920i −0.716900 0.904423i
\(456\) −12.1507 −0.569007
\(457\) 30.8294i 1.44214i −0.692864 0.721068i \(-0.743651\pi\)
0.692864 0.721068i \(-0.256349\pi\)
\(458\) 13.0093i 0.607886i
\(459\) −12.1507 −0.567144
\(460\) 13.1507 10.4240i 0.613153 0.486022i
\(461\) 4.38538 0.204247 0.102124 0.994772i \(-0.467436\pi\)
0.102124 + 0.994772i \(0.467436\pi\)
\(462\) 22.0187i 1.02440i
\(463\) 2.55733i 0.118849i 0.998233 + 0.0594247i \(0.0189266\pi\)
−0.998233 + 0.0594247i \(0.981073\pi\)
\(464\) 0.646000 0.0299898
\(465\) −21.5747 + 17.1014i −1.00050 + 0.793058i
\(466\) 10.8773 0.503882
\(467\) 12.6240i 0.584167i −0.956393 0.292083i \(-0.905651\pi\)
0.956393 0.292083i \(-0.0943485\pi\)
\(468\) 21.5747i 0.997290i
\(469\) −36.0373 −1.66405
\(470\) 14.7160 + 18.5653i 0.678799 + 0.856355i
\(471\) −67.7733 −3.12283
\(472\) 4.41468i 0.203202i
\(473\) 8.56534i 0.393835i
\(474\) −6.44398 −0.295982
\(475\) −4.41468 + 18.8294i −0.202559 + 0.863950i
\(476\) −3.50466 −0.160636
\(477\) 59.7333i 2.73500i
\(478\) 24.3013i 1.11152i
\(479\) 7.75803 0.354474 0.177237 0.984168i \(-0.443284\pi\)
0.177237 + 0.984168i \(0.443284\pi\)
\(480\) 4.36333 + 5.50466i 0.199158 + 0.251252i
\(481\) 28.1400 1.28307
\(482\) 19.8573i 0.904477i
\(483\) 82.6213i 3.75940i
\(484\) 7.00000 0.318182
\(485\) −4.23132 + 3.35400i −0.192134 + 0.152297i
\(486\) 18.7267 0.849458
\(487\) 8.33402i 0.377651i 0.982011 + 0.188825i \(0.0604680\pi\)
−0.982011 + 0.188825i \(0.939532\pi\)
\(488\) 0.910015i 0.0411945i
\(489\) −29.1307 −1.31734
\(490\) 9.25700 7.33765i 0.418188 0.331481i
\(491\) 9.84934 0.444494 0.222247 0.974990i \(-0.428661\pi\)
0.222247 + 0.974990i \(0.428661\pi\)
\(492\) 21.1307i 0.952645i
\(493\) 0.646000i 0.0290944i
\(494\) 12.1507 0.546684
\(495\) −19.0793 24.0700i −0.857552 1.08187i
\(496\) −3.91934 −0.175984
\(497\) 11.1893i 0.501909i
\(498\) 5.45331i 0.244369i
\(499\) 21.4134 0.958594 0.479297 0.877653i \(-0.340892\pi\)
0.479297 + 0.877653i \(0.340892\pi\)
\(500\) 10.1157 4.76166i 0.452386 0.212948i
\(501\) 65.3293 2.91870
\(502\) 10.8294i 0.483338i
\(503\) 5.36201i 0.239080i 0.992829 + 0.119540i \(0.0381420\pi\)
−0.992829 + 0.119540i \(0.961858\pi\)
\(504\) 24.0700 1.07216
\(505\) −7.96731 10.0514i −0.354540 0.447279i
\(506\) −15.0093 −0.667246
\(507\) 9.83869i 0.436951i
\(508\) 0.150665i 0.00668467i
\(509\) 18.8294 0.834597 0.417298 0.908770i \(-0.362977\pi\)
0.417298 + 0.908770i \(0.362977\pi\)
\(510\) −5.50466 + 4.36333i −0.243751 + 0.193211i
\(511\) −11.0093 −0.487024
\(512\) 1.00000i 0.0441942i
\(513\) 46.9987i 2.07504i
\(514\) −24.5653 −1.08353
\(515\) −16.7453 + 13.2733i −0.737887 + 0.584893i
\(516\) −13.4533 −0.592249
\(517\) 21.1893i 0.931904i
\(518\) 31.3947i 1.37940i
\(519\) 43.8174 1.92337
\(520\) −4.36333 5.50466i −0.191345 0.241396i
\(521\) 23.2920 1.02044 0.510221 0.860044i \(-0.329564\pi\)
0.510221 + 0.860044i \(0.329564\pi\)
\(522\) 4.43673i 0.194190i
\(523\) 11.7360i 0.513179i −0.966521 0.256589i \(-0.917401\pi\)
0.966521 0.256589i \(-0.0825988\pi\)
\(524\) −11.4533 −0.500340
\(525\) 12.5653 53.5933i 0.548397 2.33900i
\(526\) 7.32131 0.319224
\(527\) 3.91934i 0.170729i
\(528\) 6.28267i 0.273418i
\(529\) −33.3200 −1.44870
\(530\) −12.0807 15.2406i −0.524750 0.662012i
\(531\) 30.3200 1.31578
\(532\) 13.5560i 0.587728i
\(533\) 21.1307i 0.915272i
\(534\) 13.8680 0.600127
\(535\) 18.9766 15.0420i 0.820431 0.650323i
\(536\) −10.2827 −0.444144
\(537\) 44.9253i 1.93867i
\(538\) 5.37266i 0.231632i
\(539\) −10.5653 −0.455082
\(540\) 21.2920 16.8773i 0.916262 0.726284i
\(541\) −36.2686 −1.55931 −0.779655 0.626209i \(-0.784606\pi\)
−0.779655 + 0.626209i \(0.784606\pi\)
\(542\) 9.18930i 0.394714i
\(543\) 33.5347i 1.43911i
\(544\) −1.00000 −0.0428746
\(545\) −14.0280 17.6974i −0.600893 0.758071i
\(546\) −34.5840 −1.48006
\(547\) 33.8280i 1.44638i 0.690648 + 0.723191i \(0.257326\pi\)
−0.690648 + 0.723191i \(0.742674\pi\)
\(548\) 8.56534i 0.365893i
\(549\) 6.24998 0.266743
\(550\) −9.73599 2.28267i −0.415144 0.0973335i
\(551\) 2.49873 0.106449
\(552\) 23.5747i 1.00340i
\(553\) 7.18930i 0.305720i
\(554\) 4.79667 0.203791
\(555\) 39.0866 + 49.3107i 1.65913 + 2.09312i
\(556\) 14.3013 0.606511
\(557\) 0.0293046i 0.00124168i 1.00000 0.000620838i \(0.000197619\pi\)
−1.00000 0.000620838i \(0.999802\pi\)
\(558\) 26.9180i 1.13953i
\(559\) 13.4533 0.569015
\(560\) 6.14134 4.86799i 0.259519 0.205710i
\(561\) 6.28267 0.265255
\(562\) 31.2627i 1.31874i
\(563\) 12.6426i 0.532823i 0.963859 + 0.266411i \(0.0858379\pi\)
−0.963859 + 0.266411i \(0.914162\pi\)
\(564\) 33.2814 1.40140
\(565\) 8.51399 6.74870i 0.358186 0.283920i
\(566\) −17.0573 −0.716971
\(567\) 61.5606i 2.58530i
\(568\) 3.19269i 0.133962i
\(569\) 2.15066 0.0901606 0.0450803 0.998983i \(-0.485646\pi\)
0.0450803 + 0.998983i \(0.485646\pi\)
\(570\) 16.8773 + 21.2920i 0.706913 + 0.891824i
\(571\) −30.4626 −1.27482 −0.637411 0.770524i \(-0.719995\pi\)
−0.637411 + 0.770524i \(0.719995\pi\)
\(572\) 6.28267i 0.262692i
\(573\) 14.3413i 0.599116i
\(574\) 23.5747 0.983988
\(575\) −36.5327 8.56534i −1.52352 0.357200i
\(576\) 6.86799 0.286166
\(577\) 16.9253i 0.704609i −0.935885 0.352304i \(-0.885398\pi\)
0.935885 0.352304i \(-0.114602\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 37.7546 1.56903
\(580\) −0.897297 1.13201i −0.0372582 0.0470040i
\(581\) −6.08405 −0.252409
\(582\) 7.58532i 0.314422i
\(583\) 17.3947i 0.720415i
\(584\) −3.14134 −0.129989
\(585\) −37.8060 + 29.9673i −1.56309 + 1.23900i
\(586\) −22.2534 −0.919278
\(587\) 30.0560i 1.24054i −0.784387 0.620271i \(-0.787022\pi\)
0.784387 0.620271i \(-0.212978\pi\)
\(588\) 16.5946i 0.684352i
\(589\) −15.1600 −0.624657
\(590\) 7.73599 6.13201i 0.318485 0.252451i
\(591\) 68.7640 2.82857
\(592\) 8.95798i 0.368171i
\(593\) 34.3200i 1.40935i −0.709529 0.704676i \(-0.751092\pi\)
0.709529 0.704676i \(-0.248908\pi\)
\(594\) −24.3013 −0.997096
\(595\) 4.86799 + 6.14134i 0.199568 + 0.251770i
\(596\) 10.0000 0.409616
\(597\) 22.2720i 0.911533i
\(598\) 23.5747i 0.964040i
\(599\) 8.35994 0.341578 0.170789 0.985308i \(-0.445368\pi\)
0.170789 + 0.985308i \(0.445368\pi\)
\(600\) 3.58532 15.2920i 0.146370 0.624293i
\(601\) 18.5653 0.757296 0.378648 0.925541i \(-0.376389\pi\)
0.378648 + 0.925541i \(0.376389\pi\)
\(602\) 15.0093i 0.611735i
\(603\) 70.6213i 2.87592i
\(604\) −21.0280 −0.855617
\(605\) −9.72303 12.2663i −0.395297 0.498697i
\(606\) −18.0187 −0.731958
\(607\) 17.9860i 0.730028i 0.931002 + 0.365014i \(0.118936\pi\)
−0.931002 + 0.365014i \(0.881064\pi\)
\(608\) 3.86799i 0.156868i
\(609\) −7.11203 −0.288194
\(610\) 1.59465 1.26401i 0.0645655 0.0511785i
\(611\) −33.2814 −1.34642
\(612\) 6.86799i 0.277622i
\(613\) 2.04796i 0.0827164i −0.999144 0.0413582i \(-0.986832\pi\)
0.999144 0.0413582i \(-0.0131685\pi\)
\(614\) 29.7360 1.20005
\(615\) 37.0280 29.3506i 1.49311 1.18353i
\(616\) −7.00933 −0.282414
\(617\) 1.74663i 0.0703168i 0.999382 + 0.0351584i \(0.0111936\pi\)
−0.999382 + 0.0351584i \(0.988806\pi\)
\(618\) 30.0187i 1.20753i
\(619\) 13.0093 0.522889 0.261445 0.965219i \(-0.415801\pi\)
0.261445 + 0.965219i \(0.415801\pi\)
\(620\) 5.44398 + 6.86799i 0.218636 + 0.275825i
\(621\) −91.1867 −3.65919
\(622\) 23.1820i 0.929515i
\(623\) 15.4720i 0.619871i
\(624\) −9.86799 −0.395036
\(625\) −22.3947 11.1120i −0.895788 0.444481i
\(626\) 23.4533 0.937383
\(627\) 24.3013i 0.970502i
\(628\) 21.5747i 0.860923i
\(629\) −8.95798 −0.357178
\(630\) −33.4333 42.1787i −1.33202 1.68044i
\(631\) 0.161312 0.00642173 0.00321086 0.999995i \(-0.498978\pi\)
0.00321086 + 0.999995i \(0.498978\pi\)
\(632\) 2.05135i 0.0815984i
\(633\) 47.7147i 1.89649i
\(634\) −3.60737 −0.143267
\(635\) −0.264015 + 0.209274i −0.0104771 + 0.00830479i
\(636\) −27.3213 −1.08336
\(637\) 16.5946i 0.657504i
\(638\) 1.29200i 0.0511508i
\(639\) −21.9274 −0.867433
\(640\) 1.75233 1.38900i 0.0692670 0.0549052i
\(641\) 9.53736 0.376703 0.188352 0.982102i \(-0.439686\pi\)
0.188352 + 0.982102i \(0.439686\pi\)
\(642\) 34.0187i 1.34261i
\(643\) 34.1986i 1.34866i −0.738429 0.674331i \(-0.764432\pi\)
0.738429 0.674331i \(-0.235568\pi\)
\(644\) −26.3013 −1.03642
\(645\) 18.6867 + 23.5747i 0.735788 + 0.928252i
\(646\) −3.86799 −0.152184
\(647\) 1.61076i 0.0633254i −0.999499 0.0316627i \(-0.989920\pi\)
0.999499 0.0316627i \(-0.0100802\pi\)
\(648\) 17.5653i 0.690032i
\(649\) −8.82936 −0.346583
\(650\) −3.58532 + 15.2920i −0.140628 + 0.599802i
\(651\) 43.1493 1.69116
\(652\) 9.27334i 0.363172i
\(653\) 37.3993i 1.46355i 0.681547 + 0.731774i \(0.261307\pi\)
−0.681547 + 0.731774i \(0.738693\pi\)
\(654\) −31.7253 −1.24056
\(655\) 15.9087 + 20.0700i 0.621604 + 0.784200i
\(656\) 6.72666 0.262632
\(657\) 21.5747i 0.841708i
\(658\) 37.1307i 1.44750i
\(659\) 2.07340 0.0807681 0.0403841 0.999184i \(-0.487142\pi\)
0.0403841 + 0.999184i \(0.487142\pi\)
\(660\) −11.0093 + 8.72666i −0.428538 + 0.339685i
\(661\) −46.4040 −1.80491 −0.902454 0.430787i \(-0.858236\pi\)
−0.902454 + 0.430787i \(0.858236\pi\)
\(662\) 33.9053i 1.31777i
\(663\) 9.86799i 0.383241i
\(664\) −1.73599 −0.0673693
\(665\) 23.7546 18.8294i 0.921166 0.730171i
\(666\) 61.5233 2.38398
\(667\) 4.84802i 0.187716i
\(668\) 20.7967i 0.804647i
\(669\) −17.6040 −0.680609
\(670\) 14.2827 + 18.0187i 0.551788 + 0.696121i
\(671\) −1.82003 −0.0702615
\(672\) 11.0093i 0.424694i
\(673\) 17.6812i 0.681562i 0.940143 + 0.340781i \(0.110691\pi\)
−0.940143 + 0.340781i \(0.889309\pi\)
\(674\) 8.33063 0.320884
\(675\) −59.1493 13.8680i −2.27666 0.533779i
\(676\) −3.13201 −0.120462
\(677\) 29.2007i 1.12227i 0.827723 + 0.561137i \(0.189636\pi\)
−0.827723 + 0.561137i \(0.810364\pi\)
\(678\) 15.2627i 0.586160i
\(679\) 8.46264 0.324766
\(680\) 1.38900 + 1.75233i 0.0532659 + 0.0671989i
\(681\) 24.3934 0.934757
\(682\) 7.83869i 0.300159i
\(683\) 2.04796i 0.0783631i −0.999232 0.0391815i \(-0.987525\pi\)
0.999232 0.0391815i \(-0.0124751\pi\)
\(684\) 26.5653 1.01575
\(685\) 15.0093 11.8973i 0.573477 0.454572i
\(686\) 6.01866 0.229793
\(687\) 40.8667i 1.55916i
\(688\) 4.28267i 0.163275i
\(689\) 27.3213 1.04086
\(690\) −41.3107 + 32.7453i −1.57267 + 1.24659i
\(691\) −24.4881 −0.931570 −0.465785 0.884898i \(-0.654228\pi\)
−0.465785 + 0.884898i \(0.654228\pi\)
\(692\) 13.9486i 0.530248i
\(693\) 48.1400i 1.82869i
\(694\) −7.14134 −0.271081
\(695\) −19.8646 25.0607i −0.753507 0.950606i
\(696\) −2.02930 −0.0769206
\(697\) 6.72666i 0.254790i
\(698\) 4.64939i 0.175982i
\(699\) −34.1693 −1.29240
\(700\) −17.0607 4.00000i −0.644833 0.151186i
\(701\) 29.7360 1.12311 0.561556 0.827439i \(-0.310203\pi\)
0.561556 + 0.827439i \(0.310203\pi\)
\(702\) 38.1693i 1.44061i
\(703\) 34.6494i 1.30683i
\(704\) −2.00000 −0.0753778
\(705\) −46.2279 58.3200i −1.74104 2.19646i
\(706\) −20.8480 −0.784625
\(707\) 20.1027i 0.756040i
\(708\) 13.8680i 0.521191i
\(709\) 4.08066 0.153252 0.0766261 0.997060i \(-0.475585\pi\)
0.0766261 + 0.997060i \(0.475585\pi\)
\(710\) −5.59465 + 4.43466i −0.209963 + 0.166430i
\(711\) 14.0887 0.528366
\(712\) 4.41468i 0.165447i
\(713\) 29.4134i 1.10154i
\(714\) 11.0093 0.412014
\(715\) 11.0093 8.72666i 0.411726 0.326358i
\(716\) 14.3013 0.534466
\(717\) 76.3386i 2.85092i
\(718\) 12.4626i 0.465102i
\(719\) −38.7020 −1.44334 −0.721670 0.692237i \(-0.756625\pi\)
−0.721670 + 0.692237i \(0.756625\pi\)
\(720\) −9.53967 12.0350i −0.355522 0.448518i
\(721\) 33.4906 1.24726
\(722\) 4.03863i 0.150302i
\(723\) 62.3786i 2.31988i
\(724\) 10.6753 0.396745
\(725\) −0.737304 + 3.14473i −0.0273828 + 0.116792i
\(726\) −21.9894 −0.816101
\(727\) 11.9894i 0.444660i 0.974971 + 0.222330i \(0.0713663\pi\)
−0.974971 + 0.222330i \(0.928634\pi\)
\(728\) 11.0093i 0.408033i
\(729\) −6.13069 −0.227063
\(730\) 4.36333 + 5.50466i 0.161494 + 0.203737i
\(731\) −4.28267 −0.158400
\(732\) 2.85866i 0.105659i
\(733\) 46.3973i 1.71372i 0.515548 + 0.856861i \(0.327588\pi\)
−0.515548 + 0.856861i \(0.672412\pi\)
\(734\) 5.22199 0.192747
\(735\) −29.0793 + 23.0500i −1.07261 + 0.850213i
\(736\) −7.50466 −0.276626
\(737\) 20.5653i 0.757534i
\(738\) 46.1986i 1.70059i
\(739\) 43.6413 1.60537 0.802685 0.596403i \(-0.203404\pi\)
0.802685 + 0.596403i \(0.203404\pi\)
\(740\) 15.6974 12.4427i 0.577046 0.457401i
\(741\) −38.1693 −1.40219
\(742\) 30.4813i 1.11900i
\(743\) 11.6447i 0.427202i −0.976921 0.213601i \(-0.931481\pi\)
0.976921 0.213601i \(-0.0685192\pi\)
\(744\) 12.3120 0.451379
\(745\) −13.8900 17.5233i −0.508892 0.642005i
\(746\) 26.4626 0.968866
\(747\) 11.9227i 0.436230i
\(748\) 2.00000i 0.0731272i
\(749\) −37.9533 −1.38678
\(750\) −31.7767 + 14.9580i −1.16032 + 0.546188i
\(751\) −3.72072 −0.135771 −0.0678854 0.997693i \(-0.521625\pi\)
−0.0678854 + 0.997693i \(0.521625\pi\)
\(752\) 10.5946i 0.386347i
\(753\) 34.0187i 1.23971i
\(754\) 2.02930 0.0739029
\(755\) 29.2080 + 36.8480i 1.06299 + 1.34104i
\(756\) −42.5840 −1.54877
\(757\) 38.7533i 1.40851i 0.709945 + 0.704257i \(0.248720\pi\)
−0.709945 + 0.704257i \(0.751280\pi\)
\(758\) 8.70800i 0.316289i
\(759\) 47.1493 1.71141
\(760\) 6.77801 5.37266i 0.245864 0.194887i
\(761\) −46.6027 −1.68935 −0.844673 0.535283i \(-0.820205\pi\)
−0.844673 + 0.535283i \(0.820205\pi\)
\(762\) 0.473289i 0.0171454i
\(763\) 35.3947i 1.28137i
\(764\) 4.56534 0.165168
\(765\) 12.0350 9.53967i 0.435127 0.344907i
\(766\) 33.8094 1.22158
\(767\) 13.8680i 0.500744i
\(768\) 3.14134i 0.113353i
\(769\) 36.9987 1.33421 0.667103 0.744965i \(-0.267534\pi\)
0.667103 + 0.744965i \(0.267534\pi\)
\(770\) 9.73599 + 12.2827i 0.350861 + 0.442637i
\(771\) 77.1680 2.77914
\(772\) 12.0187i 0.432561i
\(773\) 19.9813i 0.718679i 0.933207 + 0.359339i \(0.116998\pi\)
−0.933207 + 0.359339i \(0.883002\pi\)
\(774\) 29.4134 1.05724
\(775\) 4.47329 19.0793i 0.160685 0.685350i
\(776\) 2.41468 0.0866819
\(777\) 98.6213i 3.53802i
\(778\) 22.4626i 0.805325i
\(779\) 26.0187 0.932215
\(780\) 13.7067 + 17.2920i 0.490778 + 0.619153i
\(781\) 6.38538 0.228487
\(782\) 7.50466i 0.268366i
\(783\) 7.84934i 0.280512i
\(784\) −5.28267 −0.188667
\(785\) 37.8060 29.9673i 1.34935 1.06958i
\(786\) 35.9787 1.28332
\(787\) 18.4520i 0.657743i −0.944375 0.328871i \(-0.893332\pi\)
0.944375 0.328871i \(-0.106668\pi\)
\(788\) 21.8900i 0.779800i
\(789\) −22.9987 −0.818775
\(790\) 3.59465 2.84934i 0.127892 0.101375i
\(791\) −17.0280 −0.605445
\(792\) 13.7360i 0.488087i
\(793\) 2.85866i 0.101514i
\(794\) −23.8060 −0.844843
\(795\) 37.9494 + 47.8760i 1.34593 + 1.69799i
\(796\) −7.08998 −0.251298
\(797\) 9.11203i 0.322765i −0.986892 0.161382i \(-0.948405\pi\)
0.986892 0.161382i \(-0.0515952\pi\)
\(798\) 42.5840i 1.50746i
\(799\) 10.5946 0.374812
\(800\) −4.86799 1.14134i −0.172110 0.0403523i
\(801\) −30.3200 −1.07130
\(802\) 14.4626i 0.510694i
\(803\) 6.28267i 0.221711i
\(804\) 32.3013 1.13918
\(805\) 36.5327 + 46.0887i 1.28761 + 1.62441i
\(806\) −12.3120 −0.433671
\(807\) 16.8773i 0.594110i
\(808\) 5.73599i 0.201791i
\(809\) 52.1587 1.83380 0.916901 0.399115i \(-0.130683\pi\)
0.916901 + 0.399115i \(0.130683\pi\)
\(810\) −30.7803 + 24.3983i −1.08151 + 0.857270i
\(811\) 31.6519 1.11145 0.555725 0.831366i \(-0.312441\pi\)
0.555725 + 0.831366i \(0.312441\pi\)
\(812\) 2.26401i 0.0794513i
\(813\) 28.8667i 1.01240i
\(814\) −17.9160 −0.627954
\(815\) 16.2500 12.8807i 0.569212 0.451192i
\(816\) 3.14134 0.109969
\(817\) 16.5653i 0.579548i
\(818\) 6.13201i 0.214401i
\(819\) 75.6120 2.64210
\(820\) −9.34335 11.7873i −0.326284 0.411632i
\(821\) 19.3327 0.674716 0.337358 0.941376i \(-0.390467\pi\)
0.337358 + 0.941376i \(0.390467\pi\)
\(822\) 26.9066i 0.938476i
\(823\) 11.5633i 0.403070i 0.979481 + 0.201535i \(0.0645930\pi\)
−0.979481 + 0.201535i \(0.935407\pi\)
\(824\) 9.55602 0.332900
\(825\) 30.5840 + 7.17064i 1.06480 + 0.249650i
\(826\) −15.4720 −0.538339
\(827\) 35.4320i 1.23209i 0.787710 + 0.616046i \(0.211266\pi\)
−0.787710 + 0.616046i \(0.788734\pi\)
\(828\) 51.5420i 1.79121i
\(829\) 23.1307 0.803362 0.401681 0.915780i \(-0.368426\pi\)
0.401681 + 0.915780i \(0.368426\pi\)
\(830\) 2.41129 + 3.04202i 0.0836971 + 0.105590i
\(831\) −15.0679 −0.522701
\(832\) 3.14134i 0.108906i
\(833\) 5.28267i 0.183034i
\(834\) −44.9253 −1.55564
\(835\) −36.4427 + 28.8867i −1.26115 + 0.999664i
\(836\) −7.73599 −0.267555
\(837\) 47.6226i 1.64608i
\(838\) 21.8387i 0.754405i
\(839\) −7.28861 −0.251631 −0.125815 0.992054i \(-0.540155\pi\)
−0.125815 + 0.992054i \(0.540155\pi\)
\(840\) −19.2920 + 15.2920i −0.665637 + 0.527624i
\(841\) −28.5827 −0.985610
\(842\) 3.71733i 0.128108i
\(843\) 98.2066i 3.38242i
\(844\) 15.1893 0.522837
\(845\) 4.35037 + 5.48832i 0.149657 + 0.188804i
\(846\) −72.7640 −2.50168
\(847\) 24.5327i 0.842952i
\(848\) 8.69735i 0.298668i
\(849\) 53.5827 1.83895
\(850\) 1.14134 4.86799i 0.0391475 0.166971i
\(851\) −67.2266 −2.30450
\(852\) 10.0293i 0.343598i
\(853\) 15.7033i 0.537670i −0.963186 0.268835i \(-0.913361\pi\)
0.963186 0.268835i \(-0.0866387\pi\)
\(854\) −3.18930 −0.109136
\(855\) −36.8994 46.5513i −1.26193 1.59202i
\(856\) −10.8294 −0.370140
\(857\) 36.7347i 1.25483i −0.778684 0.627416i \(-0.784113\pi\)
0.778684 0.627416i \(-0.215887\pi\)
\(858\) 19.7360i 0.673775i
\(859\) −6.99868 −0.238792 −0.119396 0.992847i \(-0.538096\pi\)
−0.119396 + 0.992847i \(0.538096\pi\)
\(860\) 7.50466 5.94865i 0.255907 0.202847i
\(861\) −74.0560 −2.52382
\(862\) 11.9673i 0.407608i
\(863\) 21.2334i 0.722793i −0.932412 0.361397i \(-0.882300\pi\)
0.932412 0.361397i \(-0.117700\pi\)
\(864\) −12.1507 −0.413374
\(865\) −24.4427 + 19.3747i −0.831076 + 0.658761i
\(866\) 18.3013 0.621904
\(867\) 3.14134i 0.106685i
\(868\) 13.7360i 0.466230i
\(869\) −4.10270 −0.139175
\(870\) 2.81871 + 3.55602i 0.0955633 + 0.120560i
\(871\) −32.3013 −1.09449
\(872\) 10.0993i 0.342006i
\(873\) 16.5840i 0.561283i
\(874\) −29.0280 −0.981886
\(875\) 16.6880 + 35.4520i 0.564158 + 1.19850i
\(876\) 9.86799 0.333409
\(877\) 6.31537i 0.213255i −0.994299 0.106627i \(-0.965995\pi\)
0.994299 0.106627i \(-0.0340052\pi\)
\(878\) 31.0793i 1.04888i
\(879\) 69.9053 2.35785
\(880\) 2.77801 + 3.50466i 0.0936466 + 0.118142i
\(881\) 14.0373 0.472929 0.236465 0.971640i \(-0.424011\pi\)
0.236465 + 0.971640i \(0.424011\pi\)
\(882\) 36.2814i 1.22166i
\(883\) 42.8853i 1.44321i 0.692307 + 0.721603i \(0.256594\pi\)
−0.692307 + 0.721603i \(0.743406\pi\)
\(884\) −3.14134 −0.105655
\(885\) −24.3013 + 19.2627i −0.816880 + 0.647508i
\(886\) 29.3947 0.987534
\(887\) 7.66598i 0.257398i 0.991684 + 0.128699i \(0.0410802\pi\)
−0.991684 + 0.128699i \(0.958920\pi\)
\(888\) 28.1400i 0.944317i
\(889\) 0.528030 0.0177095
\(890\) −7.73599 + 6.13201i −0.259311 + 0.205545i
\(891\) 35.1307 1.17692
\(892\) 5.60398i 0.187635i
\(893\) 40.9800i 1.37134i
\(894\) −31.4134 −1.05062
\(895\) −19.8646 25.0607i −0.664000 0.837686i
\(896\) −3.50466 −0.117083
\(897\) 74.0560i 2.47266i
\(898\) 14.1027i 0.470613i
\(899\) −2.53190 −0.0844435
\(900\) −7.83869 + 33.4333i −0.261290 + 1.11444i
\(901\) −8.69735 −0.289751
\(902\) 13.4533i 0.447946i
\(903\) 47.1493i 1.56903i
\(904\) −4.85866 −0.161597
\(905\) −14.8280 18.7067i −0.492901 0.621831i
\(906\) 66.0560 2.19456
\(907\) 49.6226i 1.64769i −0.566813 0.823846i \(-0.691824\pi\)
0.566813 0.823846i \(-0.308176\pi\)
\(908\) 7.76529i 0.257700i
\(909\) 39.3947 1.30664
\(910\) 19.2920 15.2920i 0.639524 0.506925i
\(911\) −16.4953 −0.546515 −0.273257 0.961941i \(-0.588101\pi\)
−0.273257 + 0.961941i \(0.588101\pi\)
\(912\) 12.1507i 0.402349i
\(913\) 3.47197i 0.114905i
\(914\) 30.8294 1.01974
\(915\) −5.00933 + 3.97070i −0.165603 + 0.131267i
\(916\) 13.0093 0.429840
\(917\) 40.1400i 1.32554i
\(918\) 12.1507i 0.401032i
\(919\) −12.2640 −0.404553 −0.202276 0.979329i \(-0.564834\pi\)
−0.202276 + 0.979329i \(0.564834\pi\)
\(920\) 10.4240 + 13.1507i 0.343669 + 0.433565i
\(921\) −93.4107 −3.07799
\(922\) 4.38538i 0.144425i
\(923\) 10.0293i 0.330119i
\(924\) 22.0187 0.724361
\(925\) −43.6074 10.2241i −1.43380 0.336165i
\(926\) −2.55733 −0.0840392
\(927\) 65.6306i 2.15559i
\(928\) 0.646000i 0.0212060i
\(929\) 20.1214 0.660160 0.330080 0.943953i \(-0.392924\pi\)
0.330080 + 0.943953i \(0.392924\pi\)
\(930\) −17.1014 21.5747i −0.560776 0.707461i
\(931\) −20.4333 −0.669676
\(932\) 10.8773i 0.356299i
\(933\) 72.8226i 2.38410i
\(934\) 12.6240 0.413068
\(935\) −3.50466 + 2.77801i −0.114615 + 0.0908506i
\(936\) 21.5747 0.705190
\(937\) 33.1706i 1.08364i −0.840495 0.541819i \(-0.817736\pi\)
0.840495 0.541819i \(-0.182264\pi\)
\(938\) 36.0373i 1.17666i
\(939\) −73.6747 −2.40428
\(940\) −18.5653 + 14.7160i −0.605535 + 0.479983i
\(941\) 24.9100 0.812043 0.406022 0.913863i \(-0.366916\pi\)
0.406022 + 0.913863i \(0.366916\pi\)
\(942\) 67.7733i 2.20817i
\(943\) 50.4813i 1.64390i
\(944\) −4.41468 −0.143686
\(945\) 59.1493 + 74.6213i 1.92413 + 2.42743i
\(946\) −8.56534 −0.278483
\(947\) 11.8680i 0.385658i 0.981232 + 0.192829i \(0.0617663\pi\)
−0.981232 + 0.192829i \(0.938234\pi\)
\(948\) 6.44398i 0.209291i
\(949\) −9.86799 −0.320329
\(950\) −18.8294 4.41468i −0.610905 0.143231i
\(951\) 11.3320 0.367464
\(952\) 3.50466i 0.113587i
\(953\) 34.8667i 1.12944i −0.825282 0.564721i \(-0.808984\pi\)
0.825282 0.564721i \(-0.191016\pi\)
\(954\) 59.7333 1.93394
\(955\) −6.34128 8.00000i −0.205199 0.258874i
\(956\) 24.3013 0.785961
\(957\) 4.05861i 0.131196i
\(958\) 7.75803i 0.250651i
\(959\) −30.0187 −0.969353
\(960\) −5.50466 + 4.36333i −0.177662 + 0.140826i
\(961\) −15.6387 −0.504476
\(962\) 28.1400i 0.907271i
\(963\) 74.3760i 2.39673i
\(964\) −19.8573 −0.639562
\(965\) −21.0607 + 16.6940i −0.677967 + 0.537398i
\(966\) 82.6213 2.65830
\(967\) 13.0934i 0.421055i −0.977588 0.210527i \(-0.932482\pi\)
0.977588 0.210527i \(-0.0675181\pi\)
\(968\) 7.00000i 0.224989i
\(969\) 12.1507 0.390336
\(970\) −3.35400 4.23132i −0.107690 0.135860i
\(971\) 27.3586 0.877980 0.438990 0.898492i \(-0.355336\pi\)
0.438990 + 0.898492i \(0.355336\pi\)
\(972\) 18.7267i 0.600658i
\(973\) 50.1214i 1.60682i
\(974\) −8.33402 −0.267039
\(975\) 11.2627 48.0373i 0.360695 1.53843i
\(976\) −0.910015 −0.0291289
\(977\) 52.5441i 1.68103i 0.541786 + 0.840517i \(0.317748\pi\)
−0.541786 + 0.840517i \(0.682252\pi\)
\(978\) 29.1307i 0.931497i
\(979\) 8.82936 0.282188
\(980\) 7.33765 + 9.25700i 0.234393 + 0.295704i
\(981\) 69.3620 2.21456
\(982\) 9.84934i 0.314305i
\(983\) 25.7873i 0.822488i 0.911525 + 0.411244i \(0.134906\pi\)
−0.911525 + 0.411244i \(0.865094\pi\)
\(984\) −21.1307 −0.673622
\(985\) −38.3586 + 30.4054i −1.22221 + 0.968795i
\(986\) −0.646000 −0.0205728
\(987\) 116.640i 3.71269i
\(988\) 12.1507i 0.386564i
\(989\) −32.1400 −1.02199
\(990\) 24.0700 19.0793i 0.764995 0.606381i
\(991\) 55.8980 1.77566 0.887830 0.460172i \(-0.152212\pi\)
0.887830 + 0.460172i \(0.152212\pi\)
\(992\) 3.91934i 0.124439i
\(993\) 106.508i 3.37993i
\(994\) 11.1893 0.354903
\(995\) 9.84802 + 12.4240i 0.312203 + 0.393868i
\(996\) 5.45331 0.172795
\(997\) 33.6260i 1.06495i −0.846447 0.532473i \(-0.821263\pi\)
0.846447 0.532473i \(-0.178737\pi\)
\(998\) 21.4134i 0.677828i
\(999\) −108.845 −3.44372
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 170.2.c.b.69.4 yes 6
3.2 odd 2 1530.2.d.g.919.2 6
4.3 odd 2 1360.2.e.c.1089.6 6
5.2 odd 4 850.2.a.p.1.1 3
5.3 odd 4 850.2.a.q.1.3 3
5.4 even 2 inner 170.2.c.b.69.3 6
15.2 even 4 7650.2.a.do.1.3 3
15.8 even 4 7650.2.a.dj.1.1 3
15.14 odd 2 1530.2.d.g.919.5 6
20.3 even 4 6800.2.a.bk.1.1 3
20.7 even 4 6800.2.a.bp.1.3 3
20.19 odd 2 1360.2.e.c.1089.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.c.b.69.3 6 5.4 even 2 inner
170.2.c.b.69.4 yes 6 1.1 even 1 trivial
850.2.a.p.1.1 3 5.2 odd 4
850.2.a.q.1.3 3 5.3 odd 4
1360.2.e.c.1089.1 6 20.19 odd 2
1360.2.e.c.1089.6 6 4.3 odd 2
1530.2.d.g.919.2 6 3.2 odd 2
1530.2.d.g.919.5 6 15.14 odd 2
6800.2.a.bk.1.1 3 20.3 even 4
6800.2.a.bp.1.3 3 20.7 even 4
7650.2.a.dj.1.1 3 15.8 even 4
7650.2.a.do.1.3 3 15.2 even 4