Properties

Label 170.2.c.b.69.2
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 69.2
Root \(1.32001 + 1.32001i\) of defining polynomial
Character \(\chi\) \(=\) 170.69
Dual form 170.2.c.b.69.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +0.484862i q^{3} -1.00000 q^{4} +(1.80487 + 1.32001i) q^{5} +0.484862 q^{6} -2.64002i q^{7} +1.00000i q^{8} +2.76491 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +0.484862i q^{3} -1.00000 q^{4} +(1.80487 + 1.32001i) q^{5} +0.484862 q^{6} -2.64002i q^{7} +1.00000i q^{8} +2.76491 q^{9} +(1.32001 - 1.80487i) q^{10} +2.00000 q^{11} -0.484862i q^{12} +0.484862i q^{13} -2.64002 q^{14} +(-0.640023 + 0.875115i) q^{15} +1.00000 q^{16} -1.00000i q^{17} -2.76491i q^{18} -5.76491 q^{19} +(-1.80487 - 1.32001i) q^{20} +1.28005 q^{21} -2.00000i q^{22} -1.35998i q^{23} -0.484862 q^{24} +(1.51514 + 4.76491i) q^{25} +0.484862 q^{26} +2.79518i q^{27} +2.64002i q^{28} -8.15516 q^{29} +(0.875115 + 0.640023i) q^{30} -2.09461 q^{31} -1.00000i q^{32} +0.969724i q^{33} -1.00000 q^{34} +(3.48486 - 4.76491i) q^{35} -2.76491 q^{36} +11.1396i q^{37} +5.76491i q^{38} -0.235091 q^{39} +(-1.32001 + 1.80487i) q^{40} -0.249771 q^{41} -1.28005i q^{42} +1.03028i q^{43} -2.00000 q^{44} +(4.99031 + 3.64971i) q^{45} -1.35998 q^{46} -6.01468i q^{47} +0.484862i q^{48} +0.0302761 q^{49} +(4.76491 - 1.51514i) q^{50} +0.484862 q^{51} -0.484862i q^{52} -7.70436i q^{53} +2.79518 q^{54} +(3.60975 + 2.64002i) q^{55} +2.64002 q^{56} -2.79518i q^{57} +8.15516i q^{58} -8.73463 q^{59} +(0.640023 - 0.875115i) q^{60} -11.3747 q^{61} +2.09461i q^{62} -7.29942i q^{63} -1.00000 q^{64} +(-0.640023 + 0.875115i) q^{65} +0.969724 q^{66} +4.96972i q^{67} +1.00000i q^{68} +0.659401 q^{69} +(-4.76491 - 3.48486i) q^{70} +8.34438 q^{71} +2.76491i q^{72} +0.484862i q^{73} +11.1396 q^{74} +(-2.31032 + 0.734633i) q^{75} +5.76491 q^{76} -5.28005i q^{77} +0.235091i q^{78} -9.85952 q^{79} +(1.80487 + 1.32001i) q^{80} +6.93945 q^{81} +0.249771i q^{82} -17.5298i q^{83} -1.28005 q^{84} +(1.32001 - 1.80487i) q^{85} +1.03028 q^{86} -3.95413i q^{87} +2.00000i q^{88} +8.73463 q^{89} +(3.64971 - 4.99031i) q^{90} +1.28005 q^{91} +1.35998i q^{92} -1.01560i q^{93} -6.01468 q^{94} +(-10.4049 - 7.60975i) q^{95} +0.484862 q^{96} -6.73463i q^{97} -0.0302761i q^{98} +5.52982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{9}+O(q^{10}) \) 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
\(3\) 0.484862i 0.279935i 0.990156 + 0.139968i \(0.0446998\pi\)
−0.990156 + 0.139968i \(0.955300\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.80487 + 1.32001i 0.807164 + 0.590327i
\(6\) 0.484862 0.197944
\(7\) 2.64002i 0.997835i −0.866649 0.498918i \(-0.833731\pi\)
0.866649 0.498918i \(-0.166269\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.76491 0.921636
\(10\) 1.32001 1.80487i 0.417424 0.570751i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0.484862i 0.139968i
\(13\) 0.484862i 0.134477i 0.997737 + 0.0672383i \(0.0214188\pi\)
−0.997737 + 0.0672383i \(0.978581\pi\)
\(14\) −2.64002 −0.705576
\(15\) −0.640023 + 0.875115i −0.165253 + 0.225954i
\(16\) 1.00000 0.250000
\(17\) 1.00000i 0.242536i
\(18\) 2.76491i 0.651695i
\(19\) −5.76491 −1.32256 −0.661280 0.750139i \(-0.729987\pi\)
−0.661280 + 0.750139i \(0.729987\pi\)
\(20\) −1.80487 1.32001i −0.403582 0.295164i
\(21\) 1.28005 0.279329
\(22\) 2.00000i 0.426401i
\(23\) 1.35998i 0.283575i −0.989897 0.141787i \(-0.954715\pi\)
0.989897 0.141787i \(-0.0452849\pi\)
\(24\) −0.484862 −0.0989720
\(25\) 1.51514 + 4.76491i 0.303028 + 0.952982i
\(26\) 0.484862 0.0950893
\(27\) 2.79518i 0.537934i
\(28\) 2.64002i 0.498918i
\(29\) −8.15516 −1.51438 −0.757188 0.653197i \(-0.773427\pi\)
−0.757188 + 0.653197i \(0.773427\pi\)
\(30\) 0.875115 + 0.640023i 0.159773 + 0.116852i
\(31\) −2.09461 −0.376203 −0.188101 0.982150i \(-0.560233\pi\)
−0.188101 + 0.982150i \(0.560233\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.969724i 0.168807i
\(34\) −1.00000 −0.171499
\(35\) 3.48486 4.76491i 0.589049 0.805417i
\(36\) −2.76491 −0.460818
\(37\) 11.1396i 1.83133i 0.401939 + 0.915667i \(0.368337\pi\)
−0.401939 + 0.915667i \(0.631663\pi\)
\(38\) 5.76491i 0.935192i
\(39\) −0.235091 −0.0376447
\(40\) −1.32001 + 1.80487i −0.208712 + 0.285376i
\(41\) −0.249771 −0.0390077 −0.0195038 0.999810i \(-0.506209\pi\)
−0.0195038 + 0.999810i \(0.506209\pi\)
\(42\) 1.28005i 0.197516i
\(43\) 1.03028i 0.157116i 0.996910 + 0.0785578i \(0.0250315\pi\)
−0.996910 + 0.0785578i \(0.974968\pi\)
\(44\) −2.00000 −0.301511
\(45\) 4.99031 + 3.64971i 0.743912 + 0.544067i
\(46\) −1.35998 −0.200518
\(47\) 6.01468i 0.877331i −0.898650 0.438666i \(-0.855451\pi\)
0.898650 0.438666i \(-0.144549\pi\)
\(48\) 0.484862i 0.0699838i
\(49\) 0.0302761 0.00432516
\(50\) 4.76491 1.51514i 0.673860 0.214273i
\(51\) 0.484862 0.0678943
\(52\) 0.484862i 0.0672383i
\(53\) 7.70436i 1.05827i −0.848536 0.529137i \(-0.822516\pi\)
0.848536 0.529137i \(-0.177484\pi\)
\(54\) 2.79518 0.380376
\(55\) 3.60975 + 2.64002i 0.486738 + 0.355981i
\(56\) 2.64002 0.352788
\(57\) 2.79518i 0.370231i
\(58\) 8.15516i 1.07083i
\(59\) −8.73463 −1.13715 −0.568576 0.822631i \(-0.692506\pi\)
−0.568576 + 0.822631i \(0.692506\pi\)
\(60\) 0.640023 0.875115i 0.0826267 0.112977i
\(61\) −11.3747 −1.45638 −0.728188 0.685378i \(-0.759637\pi\)
−0.728188 + 0.685378i \(0.759637\pi\)
\(62\) 2.09461i 0.266016i
\(63\) 7.29942i 0.919641i
\(64\) −1.00000 −0.125000
\(65\) −0.640023 + 0.875115i −0.0793851 + 0.108545i
\(66\) 0.969724 0.119365
\(67\) 4.96972i 0.607148i 0.952808 + 0.303574i \(0.0981800\pi\)
−0.952808 + 0.303574i \(0.901820\pi\)
\(68\) 1.00000i 0.121268i
\(69\) 0.659401 0.0793825
\(70\) −4.76491 3.48486i −0.569516 0.416521i
\(71\) 8.34438 0.990296 0.495148 0.868809i \(-0.335114\pi\)
0.495148 + 0.868809i \(0.335114\pi\)
\(72\) 2.76491i 0.325848i
\(73\) 0.484862i 0.0567488i 0.999597 + 0.0283744i \(0.00903306\pi\)
−0.999597 + 0.0283744i \(0.990967\pi\)
\(74\) 11.1396 1.29495
\(75\) −2.31032 + 0.734633i −0.266773 + 0.0848281i
\(76\) 5.76491 0.661280
\(77\) 5.28005i 0.601717i
\(78\) 0.235091i 0.0266188i
\(79\) −9.85952 −1.10928 −0.554641 0.832090i \(-0.687144\pi\)
−0.554641 + 0.832090i \(0.687144\pi\)
\(80\) 1.80487 + 1.32001i 0.201791 + 0.147582i
\(81\) 6.93945 0.771050
\(82\) 0.249771i 0.0275826i
\(83\) 17.5298i 1.92415i −0.272790 0.962074i \(-0.587946\pi\)
0.272790 0.962074i \(-0.412054\pi\)
\(84\) −1.28005 −0.139665
\(85\) 1.32001 1.80487i 0.143175 0.195766i
\(86\) 1.03028 0.111098
\(87\) 3.95413i 0.423927i
\(88\) 2.00000i 0.213201i
\(89\) 8.73463 0.925869 0.462935 0.886392i \(-0.346796\pi\)
0.462935 + 0.886392i \(0.346796\pi\)
\(90\) 3.64971 4.99031i 0.384713 0.526025i
\(91\) 1.28005 0.134185
\(92\) 1.35998i 0.141787i
\(93\) 1.01560i 0.105312i
\(94\) −6.01468 −0.620367
\(95\) −10.4049 7.60975i −1.06752 0.780744i
\(96\) 0.484862 0.0494860
\(97\) 6.73463i 0.683798i −0.939737 0.341899i \(-0.888930\pi\)
0.939737 0.341899i \(-0.111070\pi\)
\(98\) 0.0302761i 0.00305835i
\(99\) 5.52982 0.555768
\(100\) −1.51514 4.76491i −0.151514 0.476491i
\(101\) 13.5298 1.34627 0.673134 0.739521i \(-0.264948\pi\)
0.673134 + 0.739521i \(0.264948\pi\)
\(102\) 0.484862i 0.0480085i
\(103\) 11.2195i 1.10549i −0.833351 0.552745i \(-0.813580\pi\)
0.833351 0.552745i \(-0.186420\pi\)
\(104\) −0.484862 −0.0475446
\(105\) 2.31032 + 1.68968i 0.225464 + 0.164896i
\(106\) −7.70436 −0.748313
\(107\) 19.4693i 1.88216i 0.338177 + 0.941082i \(0.390190\pi\)
−0.338177 + 0.941082i \(0.609810\pi\)
\(108\) 2.79518i 0.268967i
\(109\) 12.6547 1.21210 0.606050 0.795426i \(-0.292753\pi\)
0.606050 + 0.795426i \(0.292753\pi\)
\(110\) 2.64002 3.60975i 0.251716 0.344176i
\(111\) −5.40115 −0.512655
\(112\) 2.64002i 0.249459i
\(113\) 7.51514i 0.706965i 0.935441 + 0.353482i \(0.115003\pi\)
−0.935441 + 0.353482i \(0.884997\pi\)
\(114\) −2.79518 −0.261793
\(115\) 1.79518 2.45459i 0.167402 0.228891i
\(116\) 8.15516 0.757188
\(117\) 1.34060i 0.123938i
\(118\) 8.73463i 0.804088i
\(119\) −2.64002 −0.242011
\(120\) −0.875115 0.640023i −0.0798867 0.0584259i
\(121\) −7.00000 −0.636364
\(122\) 11.3747i 1.02981i
\(123\) 0.121104i 0.0109196i
\(124\) 2.09461 0.188101
\(125\) −3.55510 + 10.6001i −0.317978 + 0.948098i
\(126\) −7.29942 −0.650284
\(127\) 14.7952i 1.31286i 0.754387 + 0.656430i \(0.227934\pi\)
−0.754387 + 0.656430i \(0.772066\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −0.499542 −0.0439822
\(130\) 0.875115 + 0.640023i 0.0767526 + 0.0561338i
\(131\) −2.49954 −0.218386 −0.109193 0.994021i \(-0.534827\pi\)
−0.109193 + 0.994021i \(0.534827\pi\)
\(132\) 0.969724i 0.0844036i
\(133\) 15.2195i 1.31970i
\(134\) 4.96972 0.429319
\(135\) −3.68968 + 5.04496i −0.317557 + 0.434201i
\(136\) 1.00000 0.0857493
\(137\) 2.06055i 0.176045i −0.996118 0.0880224i \(-0.971945\pi\)
0.996118 0.0880224i \(-0.0280547\pi\)
\(138\) 0.659401i 0.0561319i
\(139\) 15.5904 1.32236 0.661179 0.750228i \(-0.270056\pi\)
0.661179 + 0.750228i \(0.270056\pi\)
\(140\) −3.48486 + 4.76491i −0.294525 + 0.402708i
\(141\) 2.91629 0.245596
\(142\) 8.34438i 0.700245i
\(143\) 0.969724i 0.0810924i
\(144\) 2.76491 0.230409
\(145\) −14.7190 10.7649i −1.22235 0.893977i
\(146\) 0.484862 0.0401275
\(147\) 0.0146797i 0.00121076i
\(148\) 11.1396i 0.915667i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0.734633 + 2.31032i 0.0599825 + 0.188637i
\(151\) −15.8401 −1.28905 −0.644526 0.764582i \(-0.722945\pi\)
−0.644526 + 0.764582i \(0.722945\pi\)
\(152\) 5.76491i 0.467596i
\(153\) 2.76491i 0.223530i
\(154\) −5.28005 −0.425478
\(155\) −3.78051 2.76491i −0.303657 0.222083i
\(156\) 0.235091 0.0188224
\(157\) 1.34060i 0.106991i −0.998568 0.0534957i \(-0.982964\pi\)
0.998568 0.0534957i \(-0.0170364\pi\)
\(158\) 9.85952i 0.784381i
\(159\) 3.73555 0.296248
\(160\) 1.32001 1.80487i 0.104356 0.142688i
\(161\) −3.59037 −0.282961
\(162\) 6.93945i 0.545215i
\(163\) 16.2498i 1.27278i 0.771367 + 0.636390i \(0.219573\pi\)
−0.771367 + 0.636390i \(0.780427\pi\)
\(164\) 0.249771 0.0195038
\(165\) −1.28005 + 1.75023i −0.0996515 + 0.136255i
\(166\) −17.5298 −1.36058
\(167\) 2.95035i 0.228305i 0.993463 + 0.114152i \(0.0364152\pi\)
−0.993463 + 0.114152i \(0.963585\pi\)
\(168\) 1.28005i 0.0987578i
\(169\) 12.7649 0.981916
\(170\) −1.80487 1.32001i −0.138427 0.101240i
\(171\) −15.9394 −1.21892
\(172\) 1.03028i 0.0785578i
\(173\) 6.14048i 0.466852i −0.972375 0.233426i \(-0.925006\pi\)
0.972375 0.233426i \(-0.0749937\pi\)
\(174\) −3.95413 −0.299762
\(175\) 12.5795 4.00000i 0.950919 0.302372i
\(176\) 2.00000 0.150756
\(177\) 4.23509i 0.318329i
\(178\) 8.73463i 0.654688i
\(179\) 15.5904 1.16528 0.582639 0.812731i \(-0.302020\pi\)
0.582639 + 0.812731i \(0.302020\pi\)
\(180\) −4.99031 3.64971i −0.371956 0.272033i
\(181\) 4.10929 0.305441 0.152721 0.988269i \(-0.451197\pi\)
0.152721 + 0.988269i \(0.451197\pi\)
\(182\) 1.28005i 0.0948834i
\(183\) 5.51514i 0.407691i
\(184\) 1.35998 0.100259
\(185\) −14.7044 + 20.1055i −1.08109 + 1.47819i
\(186\) −1.01560 −0.0744671
\(187\) 2.00000i 0.146254i
\(188\) 6.01468i 0.438666i
\(189\) 7.37935 0.536769
\(190\) −7.60975 + 10.4049i −0.552069 + 0.754853i
\(191\) 6.06055 0.438526 0.219263 0.975666i \(-0.429635\pi\)
0.219263 + 0.975666i \(0.429635\pi\)
\(192\) 0.484862i 0.0349919i
\(193\) 12.5601i 0.904095i 0.891994 + 0.452048i \(0.149306\pi\)
−0.891994 + 0.452048i \(0.850694\pi\)
\(194\) −6.73463 −0.483518
\(195\) −0.424310 0.310323i −0.0303855 0.0222227i
\(196\) −0.0302761 −0.00216258
\(197\) 26.0487i 1.85590i −0.372710 0.927948i \(-0.621571\pi\)
0.372710 0.927948i \(-0.378429\pi\)
\(198\) 5.52982i 0.392987i
\(199\) −3.37466 −0.239223 −0.119612 0.992821i \(-0.538165\pi\)
−0.119612 + 0.992821i \(0.538165\pi\)
\(200\) −4.76491 + 1.51514i −0.336930 + 0.107136i
\(201\) −2.40963 −0.169962
\(202\) 13.5298i 0.951955i
\(203\) 21.5298i 1.51110i
\(204\) −0.484862 −0.0339471
\(205\) −0.450805 0.329700i −0.0314856 0.0230273i
\(206\) −11.2195 −0.781699
\(207\) 3.76021i 0.261353i
\(208\) 0.484862i 0.0336191i
\(209\) −11.5298 −0.797534
\(210\) 1.68968 2.31032i 0.116599 0.159427i
\(211\) 18.0294 1.24119 0.620596 0.784130i \(-0.286891\pi\)
0.620596 + 0.784130i \(0.286891\pi\)
\(212\) 7.70436i 0.529137i
\(213\) 4.04587i 0.277219i
\(214\) 19.4693 1.33089
\(215\) −1.35998 + 1.85952i −0.0927496 + 0.126818i
\(216\) −2.79518 −0.190188
\(217\) 5.52982i 0.375388i
\(218\) 12.6547i 0.857085i
\(219\) −0.235091 −0.0158860
\(220\) −3.60975 2.64002i −0.243369 0.177990i
\(221\) 0.484862 0.0326153
\(222\) 5.40115i 0.362502i
\(223\) 23.2947i 1.55993i −0.625823 0.779965i \(-0.715237\pi\)
0.625823 0.779965i \(-0.284763\pi\)
\(224\) −2.64002 −0.176394
\(225\) 4.18922 + 13.1745i 0.279281 + 0.878303i
\(226\) 7.51514 0.499900
\(227\) 17.4839i 1.16045i 0.814456 + 0.580225i \(0.197035\pi\)
−0.814456 + 0.580225i \(0.802965\pi\)
\(228\) 2.79518i 0.185116i
\(229\) −0.719953 −0.0475758 −0.0237879 0.999717i \(-0.507573\pi\)
−0.0237879 + 0.999717i \(0.507573\pi\)
\(230\) −2.45459 1.79518i −0.161851 0.118371i
\(231\) 2.56009 0.168442
\(232\) 8.15516i 0.535413i
\(233\) 11.0450i 0.723579i −0.932260 0.361790i \(-0.882166\pi\)
0.932260 0.361790i \(-0.117834\pi\)
\(234\) 1.34060 0.0876377
\(235\) 7.93945 10.8557i 0.517912 0.708150i
\(236\) 8.73463 0.568576
\(237\) 4.78051i 0.310527i
\(238\) 2.64002i 0.171127i
\(239\) 5.59037 0.361611 0.180805 0.983519i \(-0.442130\pi\)
0.180805 + 0.983519i \(0.442130\pi\)
\(240\) −0.640023 + 0.875115i −0.0413133 + 0.0564884i
\(241\) −8.37088 −0.539215 −0.269608 0.962970i \(-0.586894\pi\)
−0.269608 + 0.962970i \(0.586894\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 11.7502i 0.753778i
\(244\) 11.3747 0.728188
\(245\) 0.0546445 + 0.0399648i 0.00349111 + 0.00255326i
\(246\) −0.121104 −0.00772133
\(247\) 2.79518i 0.177853i
\(248\) 2.09461i 0.133008i
\(249\) 8.49954 0.538637
\(250\) 10.6001 + 3.55510i 0.670407 + 0.224844i
\(251\) 19.4693 1.22889 0.614445 0.788960i \(-0.289380\pi\)
0.614445 + 0.788960i \(0.289380\pi\)
\(252\) 7.29942i 0.459821i
\(253\) 2.71995i 0.171002i
\(254\) 14.7952 0.928332
\(255\) 0.875115 + 0.640023i 0.0548018 + 0.0400798i
\(256\) 1.00000 0.0625000
\(257\) 13.9394i 0.869519i −0.900547 0.434759i \(-0.856833\pi\)
0.900547 0.434759i \(-0.143167\pi\)
\(258\) 0.499542i 0.0311001i
\(259\) 29.4087 1.82737
\(260\) 0.640023 0.875115i 0.0396926 0.0542723i
\(261\) −22.5483 −1.39570
\(262\) 2.49954i 0.154422i
\(263\) 16.2645i 1.00291i −0.865184 0.501454i \(-0.832798\pi\)
0.865184 0.501454i \(-0.167202\pi\)
\(264\) −0.969724 −0.0596824
\(265\) 10.1698 13.9054i 0.624728 0.854201i
\(266\) 15.2195 0.933167
\(267\) 4.23509i 0.259183i
\(268\) 4.96972i 0.303574i
\(269\) −10.4049 −0.634400 −0.317200 0.948359i \(-0.602743\pi\)
−0.317200 + 0.948359i \(0.602743\pi\)
\(270\) 5.04496 + 3.68968i 0.307026 + 0.224547i
\(271\) −24.0294 −1.45968 −0.729840 0.683618i \(-0.760405\pi\)
−0.729840 + 0.683618i \(0.760405\pi\)
\(272\) 1.00000i 0.0606339i
\(273\) 0.620646i 0.0375632i
\(274\) −2.06055 −0.124483
\(275\) 3.03028 + 9.52982i 0.182733 + 0.574670i
\(276\) −0.659401 −0.0396913
\(277\) 18.9503i 1.13862i −0.822124 0.569308i \(-0.807211\pi\)
0.822124 0.569308i \(-0.192789\pi\)
\(278\) 15.5904i 0.935048i
\(279\) −5.79140 −0.346722
\(280\) 4.76491 + 3.48486i 0.284758 + 0.208260i
\(281\) 19.6438 1.17185 0.585926 0.810365i \(-0.300731\pi\)
0.585926 + 0.810365i \(0.300731\pi\)
\(282\) 2.91629i 0.173663i
\(283\) 25.7943i 1.53331i 0.642059 + 0.766655i \(0.278080\pi\)
−0.642059 + 0.766655i \(0.721920\pi\)
\(284\) −8.34438 −0.495148
\(285\) 3.68968 5.04496i 0.218558 0.298837i
\(286\) 0.969724 0.0573410
\(287\) 0.659401i 0.0389232i
\(288\) 2.76491i 0.162924i
\(289\) −1.00000 −0.0588235
\(290\) −10.7649 + 14.7190i −0.632137 + 0.864332i
\(291\) 3.26537 0.191419
\(292\) 0.484862i 0.0283744i
\(293\) 22.9239i 1.33923i −0.742710 0.669613i \(-0.766460\pi\)
0.742710 0.669613i \(-0.233540\pi\)
\(294\) 0.0146797 0.000856139
\(295\) −15.7649 11.5298i −0.917868 0.671292i
\(296\) −11.1396 −0.647474
\(297\) 5.59037i 0.324386i
\(298\) 10.0000i 0.579284i
\(299\) 0.659401 0.0381341
\(300\) 2.31032 0.734633i 0.133387 0.0424140i
\(301\) 2.71995 0.156775
\(302\) 15.8401i 0.911498i
\(303\) 6.56009i 0.376868i
\(304\) −5.76491 −0.330640
\(305\) −20.5298 15.0147i −1.17553 0.859738i
\(306\) −2.76491 −0.158059
\(307\) 10.4702i 0.597565i 0.954321 + 0.298782i \(0.0965805\pi\)
−0.954321 + 0.298782i \(0.903420\pi\)
\(308\) 5.28005i 0.300859i
\(309\) 5.43991 0.309465
\(310\) −2.76491 + 3.78051i −0.157036 + 0.214718i
\(311\) −9.73841 −0.552215 −0.276107 0.961127i \(-0.589045\pi\)
−0.276107 + 0.961127i \(0.589045\pi\)
\(312\) 0.235091i 0.0133094i
\(313\) 9.50046i 0.536998i 0.963280 + 0.268499i \(0.0865275\pi\)
−0.963280 + 0.268499i \(0.913472\pi\)
\(314\) −1.34060 −0.0756544
\(315\) 9.63533 13.1745i 0.542889 0.742301i
\(316\) 9.85952 0.554641
\(317\) 13.0790i 0.734591i −0.930104 0.367295i \(-0.880284\pi\)
0.930104 0.367295i \(-0.119716\pi\)
\(318\) 3.73555i 0.209479i
\(319\) −16.3103 −0.913203
\(320\) −1.80487 1.32001i −0.100896 0.0737909i
\(321\) −9.43991 −0.526884
\(322\) 3.59037i 0.200083i
\(323\) 5.76491i 0.320768i
\(324\) −6.93945 −0.385525
\(325\) −2.31032 + 0.734633i −0.128154 + 0.0407501i
\(326\) 16.2498 0.899992
\(327\) 6.13578i 0.339310i
\(328\) 0.249771i 0.0137913i
\(329\) −15.8789 −0.875432
\(330\) 1.75023 + 1.28005i 0.0963469 + 0.0704643i
\(331\) 24.8851 1.36781 0.683904 0.729572i \(-0.260281\pi\)
0.683904 + 0.729572i \(0.260281\pi\)
\(332\) 17.5298i 0.962074i
\(333\) 30.7999i 1.68782i
\(334\) 2.95035 0.161436
\(335\) −6.56009 + 8.96972i −0.358416 + 0.490068i
\(336\) 1.28005 0.0698323
\(337\) 27.5445i 1.50044i −0.661186 0.750222i \(-0.729947\pi\)
0.661186 0.750222i \(-0.270053\pi\)
\(338\) 12.7649i 0.694320i
\(339\) −3.64380 −0.197904
\(340\) −1.32001 + 1.80487i −0.0715877 + 0.0978830i
\(341\) −4.18922 −0.226859
\(342\) 15.9394i 0.861907i
\(343\) 18.5601i 1.00215i
\(344\) −1.03028 −0.0555488
\(345\) 1.19014 + 0.870417i 0.0640747 + 0.0468617i
\(346\) −6.14048 −0.330114
\(347\) 4.48486i 0.240760i −0.992728 0.120380i \(-0.961589\pi\)
0.992728 0.120380i \(-0.0384113\pi\)
\(348\) 3.95413i 0.211963i
\(349\) −34.2186 −1.83168 −0.915839 0.401545i \(-0.868473\pi\)
−0.915839 + 0.401545i \(0.868473\pi\)
\(350\) −4.00000 12.5795i −0.213809 0.672401i
\(351\) −1.35528 −0.0723394
\(352\) 2.00000i 0.106600i
\(353\) 4.90917i 0.261289i −0.991429 0.130644i \(-0.958295\pi\)
0.991429 0.130644i \(-0.0417046\pi\)
\(354\) −4.23509 −0.225093
\(355\) 15.0606 + 11.0147i 0.799331 + 0.584599i
\(356\) −8.73463 −0.462935
\(357\) 1.28005i 0.0677473i
\(358\) 15.5904i 0.823977i
\(359\) 13.7796 0.727259 0.363629 0.931544i \(-0.381537\pi\)
0.363629 + 0.931544i \(0.381537\pi\)
\(360\) −3.64971 + 4.99031i −0.192357 + 0.263012i
\(361\) 14.2342 0.749167
\(362\) 4.10929i 0.215979i
\(363\) 3.39403i 0.178141i
\(364\) −1.28005 −0.0670927
\(365\) −0.640023 + 0.875115i −0.0335004 + 0.0458056i
\(366\) −5.51514 −0.288281
\(367\) 4.39025i 0.229169i 0.993413 + 0.114585i \(0.0365537\pi\)
−0.993413 + 0.114585i \(0.963446\pi\)
\(368\) 1.35998i 0.0708937i
\(369\) −0.690594 −0.0359509
\(370\) 20.1055 + 14.7044i 1.04524 + 0.764443i
\(371\) −20.3397 −1.05598
\(372\) 1.01560i 0.0526562i
\(373\) 0.220411i 0.0114125i 0.999984 + 0.00570623i \(0.00181636\pi\)
−0.999984 + 0.00570623i \(0.998184\pi\)
\(374\) −2.00000 −0.103418
\(375\) −5.13957 1.72373i −0.265406 0.0890132i
\(376\) 6.01468 0.310183
\(377\) 3.95413i 0.203648i
\(378\) 7.37935i 0.379553i
\(379\) −26.3103 −1.35147 −0.675735 0.737144i \(-0.736174\pi\)
−0.675735 + 0.737144i \(0.736174\pi\)
\(380\) 10.4049 + 7.60975i 0.533762 + 0.390372i
\(381\) −7.17362 −0.367516
\(382\) 6.06055i 0.310085i
\(383\) 36.1433i 1.84684i 0.383793 + 0.923419i \(0.374618\pi\)
−0.383793 + 0.923419i \(0.625382\pi\)
\(384\) −0.484862 −0.0247430
\(385\) 6.96972 9.52982i 0.355210 0.485684i
\(386\) 12.5601 0.639292
\(387\) 2.84862i 0.144803i
\(388\) 6.73463i 0.341899i
\(389\) −3.77959 −0.191633 −0.0958164 0.995399i \(-0.530546\pi\)
−0.0958164 + 0.995399i \(0.530546\pi\)
\(390\) −0.310323 + 0.424310i −0.0157138 + 0.0214858i
\(391\) −1.35998 −0.0687770
\(392\) 0.0302761i 0.00152917i
\(393\) 1.21193i 0.0611339i
\(394\) −26.0487 −1.31232
\(395\) −17.7952 13.0147i −0.895373 0.654840i
\(396\) −5.52982 −0.277884
\(397\) 12.2304i 0.613826i 0.951738 + 0.306913i \(0.0992960\pi\)
−0.951738 + 0.306913i \(0.900704\pi\)
\(398\) 3.37466i 0.169156i
\(399\) −7.37935 −0.369430
\(400\) 1.51514 + 4.76491i 0.0757569 + 0.238245i
\(401\) −11.7796 −0.588245 −0.294122 0.955768i \(-0.595027\pi\)
−0.294122 + 0.955768i \(0.595027\pi\)
\(402\) 2.40963i 0.120181i
\(403\) 1.01560i 0.0505905i
\(404\) −13.5298 −0.673134
\(405\) 12.5248 + 9.16015i 0.622364 + 0.455172i
\(406\) 21.5298 1.06851
\(407\) 22.2791i 1.10434i
\(408\) 0.484862i 0.0240042i
\(409\) 15.7649 0.779525 0.389762 0.920916i \(-0.372557\pi\)
0.389762 + 0.920916i \(0.372557\pi\)
\(410\) −0.329700 + 0.450805i −0.0162827 + 0.0222637i
\(411\) 0.999083 0.0492811
\(412\) 11.2195i 0.552745i
\(413\) 23.0596i 1.13469i
\(414\) −3.76021 −0.184804
\(415\) 23.1396 31.6391i 1.13588 1.55310i
\(416\) 0.484862 0.0237723
\(417\) 7.55918i 0.370175i
\(418\) 11.5298i 0.563942i
\(419\) −18.1892 −0.888601 −0.444301 0.895878i \(-0.646548\pi\)
−0.444301 + 0.895878i \(0.646548\pi\)
\(420\) −2.31032 1.68968i −0.112732 0.0824478i
\(421\) 9.03028 0.440109 0.220054 0.975488i \(-0.429377\pi\)
0.220054 + 0.975488i \(0.429377\pi\)
\(422\) 18.0294i 0.877655i
\(423\) 16.6300i 0.808580i
\(424\) 7.70436 0.374157
\(425\) 4.76491 1.51514i 0.231132 0.0734950i
\(426\) 4.04587 0.196023
\(427\) 30.0294i 1.45322i
\(428\) 19.4693i 0.941082i
\(429\) −0.470182 −0.0227006
\(430\) 1.85952 + 1.35998i 0.0896739 + 0.0655839i
\(431\) 20.4196 0.983578 0.491789 0.870714i \(-0.336343\pi\)
0.491789 + 0.870714i \(0.336343\pi\)
\(432\) 2.79518i 0.134483i
\(433\) 11.5904i 0.556998i −0.960437 0.278499i \(-0.910163\pi\)
0.960437 0.278499i \(-0.0898368\pi\)
\(434\) 5.52982 0.265440
\(435\) 5.21949 7.13670i 0.250256 0.342179i
\(436\) −12.6547 −0.606050
\(437\) 7.84014i 0.375045i
\(438\) 0.235091i 0.0112331i
\(439\) 2.01938 0.0963796 0.0481898 0.998838i \(-0.484655\pi\)
0.0481898 + 0.998838i \(0.484655\pi\)
\(440\) −2.64002 + 3.60975i −0.125858 + 0.172088i
\(441\) 0.0837106 0.00398622
\(442\) 0.484862i 0.0230625i
\(443\) 27.4087i 1.30223i 0.758980 + 0.651114i \(0.225698\pi\)
−0.758980 + 0.651114i \(0.774302\pi\)
\(444\) 5.40115 0.256327
\(445\) 15.7649 + 11.5298i 0.747328 + 0.546566i
\(446\) −23.2947 −1.10304
\(447\) 4.84862i 0.229332i
\(448\) 2.64002i 0.124729i
\(449\) −29.7190 −1.40253 −0.701264 0.712902i \(-0.747381\pi\)
−0.701264 + 0.712902i \(0.747381\pi\)
\(450\) 13.1745 4.18922i 0.621054 0.197482i
\(451\) −0.499542 −0.0235225
\(452\) 7.51514i 0.353482i
\(453\) 7.68028i 0.360851i
\(454\) 17.4839 0.820562
\(455\) 2.31032 + 1.68968i 0.108310 + 0.0792133i
\(456\) 2.79518 0.130897
\(457\) 39.4693i 1.84629i 0.384447 + 0.923147i \(0.374392\pi\)
−0.384447 + 0.923147i \(0.625608\pi\)
\(458\) 0.719953i 0.0336412i
\(459\) 2.79518 0.130468
\(460\) −1.79518 + 2.45459i −0.0837009 + 0.114446i
\(461\) 14.6888 0.684124 0.342062 0.939677i \(-0.388875\pi\)
0.342062 + 0.939677i \(0.388875\pi\)
\(462\) 2.56009i 0.119106i
\(463\) 35.1055i 1.63149i −0.578411 0.815746i \(-0.696327\pi\)
0.578411 0.815746i \(-0.303673\pi\)
\(464\) −8.15516 −0.378594
\(465\) 1.34060 1.83302i 0.0621688 0.0850044i
\(466\) −11.0450 −0.511648
\(467\) 9.96881i 0.461301i −0.973037 0.230651i \(-0.925915\pi\)
0.973037 0.230651i \(-0.0740855\pi\)
\(468\) 1.34060i 0.0619692i
\(469\) 13.1202 0.605834
\(470\) −10.8557 7.93945i −0.500738 0.366219i
\(471\) 0.650006 0.0299507
\(472\) 8.73463i 0.402044i
\(473\) 2.06055i 0.0947443i
\(474\) −4.78051 −0.219576
\(475\) −8.73463 27.4693i −0.400772 1.26038i
\(476\) 2.64002 0.121005
\(477\) 21.3018i 0.975344i
\(478\) 5.59037i 0.255698i
\(479\) 2.28383 0.104351 0.0521754 0.998638i \(-0.483385\pi\)
0.0521754 + 0.998638i \(0.483385\pi\)
\(480\) 0.875115 + 0.640023i 0.0399433 + 0.0292129i
\(481\) −5.40115 −0.246271
\(482\) 8.37088i 0.381283i
\(483\) 1.74083i 0.0792107i
\(484\) 7.00000 0.318182
\(485\) 8.88979 12.1552i 0.403665 0.551937i
\(486\) 11.7502 0.533001
\(487\) 10.8292i 0.490720i −0.969432 0.245360i \(-0.921094\pi\)
0.969432 0.245360i \(-0.0789061\pi\)
\(488\) 11.3747i 0.514906i
\(489\) −7.87890 −0.356296
\(490\) 0.0399648 0.0546445i 0.00180543 0.00246859i
\(491\) 24.7952 1.11899 0.559496 0.828833i \(-0.310995\pi\)
0.559496 + 0.828833i \(0.310995\pi\)
\(492\) 0.121104i 0.00545981i
\(493\) 8.15516i 0.367290i
\(494\) −2.79518 −0.125761
\(495\) 9.98062 + 7.29942i 0.448596 + 0.328085i
\(496\) −2.09461 −0.0940507
\(497\) 22.0294i 0.988152i
\(498\) 8.49954i 0.380874i
\(499\) −5.15138 −0.230607 −0.115304 0.993330i \(-0.536784\pi\)
−0.115304 + 0.993330i \(0.536784\pi\)
\(500\) 3.55510 10.6001i 0.158989 0.474049i
\(501\) −1.43051 −0.0639105
\(502\) 19.4693i 0.868956i
\(503\) 29.0109i 1.29353i 0.762688 + 0.646766i \(0.223879\pi\)
−0.762688 + 0.646766i \(0.776121\pi\)
\(504\) 7.29942 0.325142
\(505\) 24.4196 + 17.8595i 1.08666 + 0.794738i
\(506\) −2.71995 −0.120917
\(507\) 6.18922i 0.274873i
\(508\) 14.7952i 0.656430i
\(509\) 27.4693 1.21755 0.608777 0.793341i \(-0.291660\pi\)
0.608777 + 0.793341i \(0.291660\pi\)
\(510\) 0.640023 0.875115i 0.0283407 0.0387507i
\(511\) 1.28005 0.0566259
\(512\) 1.00000i 0.0441942i
\(513\) 16.1140i 0.711450i
\(514\) −13.9394 −0.614843
\(515\) 14.8099 20.2498i 0.652601 0.892312i
\(516\) 0.499542 0.0219911
\(517\) 12.0294i 0.529051i
\(518\) 29.4087i 1.29214i
\(519\) 2.97729 0.130688
\(520\) −0.875115 0.640023i −0.0383763 0.0280669i
\(521\) 5.68968 0.249269 0.124635 0.992203i \(-0.460224\pi\)
0.124635 + 0.992203i \(0.460224\pi\)
\(522\) 22.5483i 0.986911i
\(523\) 7.52982i 0.329256i −0.986356 0.164628i \(-0.947358\pi\)
0.986356 0.164628i \(-0.0526424\pi\)
\(524\) 2.49954 0.109193
\(525\) 1.93945 + 6.09931i 0.0846444 + 0.266196i
\(526\) −16.2645 −0.709164
\(527\) 2.09461i 0.0912426i
\(528\) 0.969724i 0.0422018i
\(529\) 21.1505 0.919585
\(530\) −13.9054 10.1698i −0.604012 0.441750i
\(531\) −24.1505 −1.04804
\(532\) 15.2195i 0.659849i
\(533\) 0.121104i 0.00524561i
\(534\) 4.23509 0.183270
\(535\) −25.6997 + 35.1396i −1.11109 + 1.51922i
\(536\) −4.96972 −0.214659
\(537\) 7.55918i 0.326203i
\(538\) 10.4049i 0.448588i
\(539\) 0.0605522 0.00260817
\(540\) 3.68968 5.04496i 0.158778 0.217100i
\(541\) 26.0100 1.11826 0.559128 0.829081i \(-0.311136\pi\)
0.559128 + 0.829081i \(0.311136\pi\)
\(542\) 24.0294i 1.03215i
\(543\) 1.99244i 0.0855037i
\(544\) −1.00000 −0.0428746
\(545\) 22.8401 + 16.7044i 0.978364 + 0.715536i
\(546\) 0.620646 0.0265612
\(547\) 11.5833i 0.495264i −0.968854 0.247632i \(-0.920348\pi\)
0.968854 0.247632i \(-0.0796524\pi\)
\(548\) 2.06055i 0.0880224i
\(549\) −31.4499 −1.34225
\(550\) 9.52982 3.03028i 0.406353 0.129211i
\(551\) 47.0138 2.00285
\(552\) 0.659401i 0.0280660i
\(553\) 26.0294i 1.10688i
\(554\) −18.9503 −0.805123
\(555\) −9.74840 7.12958i −0.413796 0.302634i
\(556\) −15.5904 −0.661179
\(557\) 5.95413i 0.252284i 0.992012 + 0.126142i \(0.0402596\pi\)
−0.992012 + 0.126142i \(0.959740\pi\)
\(558\) 5.79140i 0.245170i
\(559\) −0.499542 −0.0211284
\(560\) 3.48486 4.76491i 0.147262 0.201354i
\(561\) 0.969724 0.0409418
\(562\) 19.6438i 0.828624i
\(563\) 34.5289i 1.45522i 0.685991 + 0.727610i \(0.259369\pi\)
−0.685991 + 0.727610i \(0.740631\pi\)
\(564\) −2.91629 −0.122798
\(565\) −9.92007 + 13.5639i −0.417340 + 0.570637i
\(566\) 25.7943 1.08421
\(567\) 18.3203i 0.769380i
\(568\) 8.34438i 0.350122i
\(569\) −12.7952 −0.536402 −0.268201 0.963363i \(-0.586429\pi\)
−0.268201 + 0.963363i \(0.586429\pi\)
\(570\) −5.04496 3.68968i −0.211310 0.154544i
\(571\) −4.22041 −0.176619 −0.0883094 0.996093i \(-0.528146\pi\)
−0.0883094 + 0.996093i \(0.528146\pi\)
\(572\) 0.969724i 0.0405462i
\(573\) 2.93853i 0.122759i
\(574\) 0.659401 0.0275229
\(575\) 6.48016 2.06055i 0.270242 0.0859310i
\(576\) −2.76491 −0.115205
\(577\) 35.5592i 1.48035i −0.672415 0.740174i \(-0.734743\pi\)
0.672415 0.740174i \(-0.265257\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) −6.08991 −0.253088
\(580\) 14.7190 + 10.7649i 0.611175 + 0.446989i
\(581\) −46.2791 −1.91998
\(582\) 3.26537i 0.135354i
\(583\) 15.4087i 0.638164i
\(584\) −0.484862 −0.0200637
\(585\) −1.76961 + 2.41961i −0.0731642 + 0.100039i
\(586\) −22.9239 −0.946976
\(587\) 43.6803i 1.80288i −0.432906 0.901439i \(-0.642512\pi\)
0.432906 0.901439i \(-0.357488\pi\)
\(588\) 0.0146797i 0.000605382i
\(589\) 12.0752 0.497551
\(590\) −11.5298 + 15.7649i −0.474675 + 0.649031i
\(591\) 12.6300 0.519530
\(592\) 11.1396i 0.457833i
\(593\) 20.1505i 0.827480i −0.910395 0.413740i \(-0.864222\pi\)
0.910395 0.413740i \(-0.135778\pi\)
\(594\) 5.59037 0.229376
\(595\) −4.76491 3.48486i −0.195342 0.142865i
\(596\) 10.0000 0.409616
\(597\) 1.63624i 0.0669669i
\(598\) 0.659401i 0.0269649i
\(599\) −33.4986 −1.36872 −0.684358 0.729146i \(-0.739918\pi\)
−0.684358 + 0.729146i \(0.739918\pi\)
\(600\) −0.734633 2.31032i −0.0299913 0.0943185i
\(601\) 7.93945 0.323857 0.161928 0.986803i \(-0.448229\pi\)
0.161928 + 0.986803i \(0.448229\pi\)
\(602\) 2.71995i 0.110857i
\(603\) 13.7408i 0.559570i
\(604\) 15.8401 0.644526
\(605\) −12.6341 9.24008i −0.513650 0.375663i
\(606\) 6.56009 0.266486
\(607\) 38.9797i 1.58214i 0.611727 + 0.791069i \(0.290475\pi\)
−0.611727 + 0.791069i \(0.709525\pi\)
\(608\) 5.76491i 0.233798i
\(609\) −10.4390 −0.423009
\(610\) −15.0147 + 20.5298i −0.607927 + 0.831228i
\(611\) 2.91629 0.117980
\(612\) 2.76491i 0.111765i
\(613\) 28.5142i 1.15168i −0.817563 0.575839i \(-0.804675\pi\)
0.817563 0.575839i \(-0.195325\pi\)
\(614\) 10.4702 0.422542
\(615\) 0.159859 0.218578i 0.00644615 0.00881392i
\(616\) 5.28005 0.212739
\(617\) 1.07615i 0.0433241i −0.999765 0.0216621i \(-0.993104\pi\)
0.999765 0.0216621i \(-0.00689579\pi\)
\(618\) 5.43991i 0.218825i
\(619\) 0.719953 0.0289374 0.0144687 0.999895i \(-0.495394\pi\)
0.0144687 + 0.999895i \(0.495394\pi\)
\(620\) 3.78051 + 2.76491i 0.151829 + 0.111041i
\(621\) 3.80139 0.152544
\(622\) 9.73841i 0.390475i
\(623\) 23.0596i 0.923865i
\(624\) −0.235091 −0.00941118
\(625\) −20.4087 + 14.4390i −0.816349 + 0.577560i
\(626\) 9.50046 0.379715
\(627\) 5.59037i 0.223258i
\(628\) 1.34060i 0.0534957i
\(629\) 11.1396 0.444164
\(630\) −13.1745 9.63533i −0.524886 0.383881i
\(631\) 3.81078 0.151705 0.0758524 0.997119i \(-0.475832\pi\)
0.0758524 + 0.997119i \(0.475832\pi\)
\(632\) 9.85952i 0.392191i
\(633\) 8.74175i 0.347453i
\(634\) −13.0790 −0.519434
\(635\) −19.5298 + 26.7034i −0.775017 + 1.05969i
\(636\) −3.73555 −0.148124
\(637\) 0.0146797i 0.000581632i
\(638\) 16.3103i 0.645732i
\(639\) 23.0715 0.912692
\(640\) −1.32001 + 1.80487i −0.0521780 + 0.0713439i
\(641\) 35.7796 1.41321 0.706604 0.707609i \(-0.250226\pi\)
0.706604 + 0.707609i \(0.250226\pi\)
\(642\) 9.43991i 0.372563i
\(643\) 11.3094i 0.445999i −0.974819 0.223000i \(-0.928415\pi\)
0.974819 0.223000i \(-0.0715849\pi\)
\(644\) 3.59037 0.141480
\(645\) −0.901610 0.659401i −0.0355008 0.0259639i
\(646\) 5.76491 0.226817
\(647\) 49.4528i 1.94419i 0.234591 + 0.972094i \(0.424625\pi\)
−0.234591 + 0.972094i \(0.575375\pi\)
\(648\) 6.93945i 0.272607i
\(649\) −17.4693 −0.685729
\(650\) 0.734633 + 2.31032i 0.0288147 + 0.0906183i
\(651\) −2.68120 −0.105084
\(652\) 16.2498i 0.636390i
\(653\) 46.1311i 1.80525i 0.430429 + 0.902624i \(0.358362\pi\)
−0.430429 + 0.902624i \(0.641638\pi\)
\(654\) 6.13578 0.239928
\(655\) −4.51136 3.29942i −0.176273 0.128919i
\(656\) −0.249771 −0.00975191
\(657\) 1.34060i 0.0523018i
\(658\) 15.8789i 0.619024i
\(659\) 23.6732 0.922176 0.461088 0.887355i \(-0.347459\pi\)
0.461088 + 0.887355i \(0.347459\pi\)
\(660\) 1.28005 1.75023i 0.0498258 0.0681276i
\(661\) −32.1287 −1.24966 −0.624830 0.780761i \(-0.714832\pi\)
−0.624830 + 0.780761i \(0.714832\pi\)
\(662\) 24.8851i 0.967187i
\(663\) 0.235091i 0.00913018i
\(664\) 17.5298 0.680289
\(665\) −20.0899 + 27.4693i −0.779053 + 1.06521i
\(666\) 30.7999 1.19347
\(667\) 11.0908i 0.429439i
\(668\) 2.95035i 0.114152i
\(669\) 11.2947 0.436679
\(670\) 8.96972 + 6.56009i 0.346531 + 0.253439i
\(671\) −22.7493 −0.878227
\(672\) 1.28005i 0.0493789i
\(673\) 47.7631i 1.84113i 0.390588 + 0.920566i \(0.372272\pi\)
−0.390588 + 0.920566i \(0.627728\pi\)
\(674\) −27.5445 −1.06097
\(675\) −13.3188 + 4.23509i −0.512641 + 0.163009i
\(676\) −12.7649 −0.490958
\(677\) 8.82168i 0.339045i 0.985526 + 0.169522i \(0.0542225\pi\)
−0.985526 + 0.169522i \(0.945778\pi\)
\(678\) 3.64380i 0.139939i
\(679\) −17.7796 −0.682318
\(680\) 1.80487 + 1.32001i 0.0692137 + 0.0506201i
\(681\) −8.47730 −0.324851
\(682\) 4.18922i 0.160413i
\(683\) 28.5142i 1.09107i −0.838089 0.545533i \(-0.816327\pi\)
0.838089 0.545533i \(-0.183673\pi\)
\(684\) 15.9394 0.609460
\(685\) 2.71995 3.71904i 0.103924 0.142097i
\(686\) −18.5601 −0.708628
\(687\) 0.349078i 0.0133182i
\(688\) 1.03028i 0.0392789i
\(689\) 3.73555 0.142313
\(690\) 0.870417 1.19014i 0.0331362 0.0453077i
\(691\) −50.4078 −1.91760 −0.958801 0.284077i \(-0.908313\pi\)
−0.958801 + 0.284077i \(0.908313\pi\)
\(692\) 6.14048i 0.233426i
\(693\) 14.5988i 0.554564i
\(694\) −4.48486 −0.170243
\(695\) 28.1386 + 20.5795i 1.06736 + 0.780624i
\(696\) 3.95413 0.149881
\(697\) 0.249771i 0.00946075i
\(698\) 34.2186i 1.29519i
\(699\) 5.35528 0.202555
\(700\) −12.5795 + 4.00000i −0.475459 + 0.151186i
\(701\) 10.4702 0.395453 0.197727 0.980257i \(-0.436644\pi\)
0.197727 + 0.980257i \(0.436644\pi\)
\(702\) 1.35528i 0.0511517i
\(703\) 64.2186i 2.42205i
\(704\) −2.00000 −0.0753778
\(705\) 5.26353 + 3.84954i 0.198236 + 0.144982i
\(706\) −4.90917 −0.184759
\(707\) 35.7190i 1.34335i
\(708\) 4.23509i 0.159164i
\(709\) 5.90539 0.221782 0.110891 0.993833i \(-0.464630\pi\)
0.110891 + 0.993833i \(0.464630\pi\)
\(710\) 11.0147 15.0606i 0.413374 0.565212i
\(711\) −27.2607 −1.02235
\(712\) 8.73463i 0.327344i
\(713\) 2.84862i 0.106682i
\(714\) −1.28005 −0.0479046
\(715\) −1.28005 + 1.75023i −0.0478710 + 0.0654549i
\(716\) −15.5904 −0.582639
\(717\) 2.71056i 0.101228i
\(718\) 13.7796i 0.514250i
\(719\) 43.8354 1.63479 0.817393 0.576080i \(-0.195418\pi\)
0.817393 + 0.576080i \(0.195418\pi\)
\(720\) 4.99031 + 3.64971i 0.185978 + 0.136017i
\(721\) −29.6197 −1.10310
\(722\) 14.2342i 0.529741i
\(723\) 4.05872i 0.150945i
\(724\) −4.10929 −0.152721
\(725\) −12.3562 38.8586i −0.458898 1.44317i
\(726\) −3.39403 −0.125964
\(727\) 6.60597i 0.245002i 0.992468 + 0.122501i \(0.0390914\pi\)
−0.992468 + 0.122501i \(0.960909\pi\)
\(728\) 1.28005i 0.0474417i
\(729\) 15.1211 0.560041
\(730\) 0.875115 + 0.640023i 0.0323894 + 0.0236883i
\(731\) 1.03028 0.0381061
\(732\) 5.51514i 0.203845i
\(733\) 44.6188i 1.64803i 0.566565 + 0.824017i \(0.308272\pi\)
−0.566565 + 0.824017i \(0.691728\pi\)
\(734\) 4.39025 0.162047
\(735\) −0.0193774 + 0.0264951i −0.000714747 + 0.000977285i
\(736\) −1.35998 −0.0501294
\(737\) 9.93945i 0.366124i
\(738\) 0.690594i 0.0254211i
\(739\) −34.4149 −1.26597 −0.632987 0.774163i \(-0.718171\pi\)
−0.632987 + 0.774163i \(0.718171\pi\)
\(740\) 14.7044 20.1055i 0.540543 0.739093i
\(741\) 1.35528 0.0497874
\(742\) 20.3397i 0.746693i
\(743\) 28.0412i 1.02873i −0.857571 0.514365i \(-0.828027\pi\)
0.857571 0.514365i \(-0.171973\pi\)
\(744\) 1.01560 0.0372336
\(745\) −18.0487 13.2001i −0.661255 0.483615i
\(746\) 0.220411 0.00806983
\(747\) 48.4683i 1.77336i
\(748\) 2.00000i 0.0731272i
\(749\) 51.3993 1.87809
\(750\) −1.72373 + 5.13957i −0.0629419 + 0.187670i
\(751\) −47.4040 −1.72980 −0.864899 0.501947i \(-0.832617\pi\)
−0.864899 + 0.501947i \(0.832617\pi\)
\(752\) 6.01468i 0.219333i
\(753\) 9.43991i 0.344009i
\(754\) −3.95413 −0.144001
\(755\) −28.5895 20.9092i −1.04048 0.760963i
\(756\) −7.37935 −0.268385
\(757\) 35.9759i 1.30757i 0.756682 + 0.653784i \(0.226819\pi\)
−0.756682 + 0.653784i \(0.773181\pi\)
\(758\) 26.3103i 0.955634i
\(759\) 1.31880 0.0478695
\(760\) 7.60975 10.4049i 0.276035 0.377427i
\(761\) 13.1807 0.477801 0.238901 0.971044i \(-0.423213\pi\)
0.238901 + 0.971044i \(0.423213\pi\)
\(762\) 7.17362i 0.259873i
\(763\) 33.4087i 1.20948i
\(764\) −6.06055 −0.219263
\(765\) 3.64971 4.99031i 0.131956 0.180425i
\(766\) 36.1433 1.30591
\(767\) 4.23509i 0.152920i
\(768\) 0.484862i 0.0174959i
\(769\) 6.11399 0.220476 0.110238 0.993905i \(-0.464839\pi\)
0.110238 + 0.993905i \(0.464839\pi\)
\(770\) −9.52982 6.96972i −0.343431 0.251171i
\(771\) 6.75871 0.243409
\(772\) 12.5601i 0.452048i
\(773\) 44.5601i 1.60272i −0.598186 0.801358i \(-0.704111\pi\)
0.598186 0.801358i \(-0.295889\pi\)
\(774\) 2.84862 0.102392
\(775\) −3.17362 9.98062i −0.114000 0.358515i
\(776\) 6.73463 0.241759
\(777\) 14.2592i 0.511545i
\(778\) 3.77959i 0.135505i
\(779\) 1.43991 0.0515900
\(780\) 0.424310 + 0.310323i 0.0151927 + 0.0111113i
\(781\) 16.6888 0.597171
\(782\) 1.35998i 0.0486327i
\(783\) 22.7952i 0.814633i
\(784\) 0.0302761 0.00108129
\(785\) 1.76961 2.41961i 0.0631600 0.0863597i
\(786\) −1.21193 −0.0432282
\(787\) 26.3856i 0.940543i −0.882522 0.470272i \(-0.844156\pi\)
0.882522 0.470272i \(-0.155844\pi\)
\(788\) 26.0487i 0.927948i
\(789\) 7.88601 0.280750
\(790\) −13.0147 + 17.7952i −0.463042 + 0.633124i
\(791\) 19.8401 0.705434
\(792\) 5.52982i 0.196494i
\(793\) 5.51514i 0.195848i
\(794\) 12.2304 0.434040
\(795\) 6.74219 + 4.93097i 0.239121 + 0.174883i
\(796\) 3.37466 0.119612
\(797\) 12.4390i 0.440612i 0.975431 + 0.220306i \(0.0707055\pi\)
−0.975431 + 0.220306i \(0.929294\pi\)
\(798\) 7.37935i 0.261226i
\(799\) −6.01468 −0.212784
\(800\) 4.76491 1.51514i 0.168465 0.0535682i
\(801\) 24.1505 0.853315
\(802\) 11.7796i 0.415952i
\(803\) 0.969724i 0.0342208i
\(804\) 2.40963 0.0849811
\(805\) −6.48016 4.73933i −0.228396 0.167039i
\(806\) −1.01560 −0.0357729
\(807\) 5.04496i 0.177591i
\(808\) 13.5298i 0.475977i
\(809\) −5.96125 −0.209586 −0.104793 0.994494i \(-0.533418\pi\)
−0.104793 + 0.994494i \(0.533418\pi\)
\(810\) 9.16015 12.5248i 0.321855 0.440078i
\(811\) −27.8089 −0.976504 −0.488252 0.872703i \(-0.662365\pi\)
−0.488252 + 0.872703i \(0.662365\pi\)
\(812\) 21.5298i 0.755548i
\(813\) 11.6509i 0.408616i
\(814\) 22.2791 0.780883
\(815\) −21.4499 + 29.3288i −0.751357 + 1.02734i
\(816\) 0.484862 0.0169736
\(817\) 5.93945i 0.207795i
\(818\) 15.7649i 0.551207i
\(819\) 3.53921 0.123670
\(820\) 0.450805 + 0.329700i 0.0157428 + 0.0115136i
\(821\) −9.05677 −0.316083 −0.158042 0.987432i \(-0.550518\pi\)
−0.158042 + 0.987432i \(0.550518\pi\)
\(822\) 0.999083i 0.0348470i
\(823\) 6.54828i 0.228259i 0.993466 + 0.114129i \(0.0364078\pi\)
−0.993466 + 0.114129i \(0.963592\pi\)
\(824\) 11.2195 0.390850
\(825\) −4.62065 + 1.46927i −0.160870 + 0.0511533i
\(826\) 23.0596 0.802347
\(827\) 15.7115i 0.546341i 0.961966 + 0.273171i \(0.0880724\pi\)
−0.961966 + 0.273171i \(0.911928\pi\)
\(828\) 3.76021i 0.130676i
\(829\) 1.87890 0.0652567 0.0326284 0.999468i \(-0.489612\pi\)
0.0326284 + 0.999468i \(0.489612\pi\)
\(830\) −31.6391 23.1396i −1.09821 0.803186i
\(831\) 9.18830 0.318739
\(832\) 0.484862i 0.0168096i
\(833\) 0.0302761i 0.00104900i
\(834\) 7.55918 0.261753
\(835\) −3.89449 + 5.32500i −0.134774 + 0.184279i
\(836\) 11.5298 0.398767
\(837\) 5.85482i 0.202372i
\(838\) 18.1892i 0.628336i
\(839\) 48.6841 1.68076 0.840380 0.541997i \(-0.182332\pi\)
0.840380 + 0.541997i \(0.182332\pi\)
\(840\) −1.68968 + 2.31032i −0.0582994 + 0.0797137i
\(841\) 37.5067 1.29333
\(842\) 9.03028i 0.311204i
\(843\) 9.52453i 0.328042i
\(844\) −18.0294 −0.620596
\(845\) 23.0390 + 16.8498i 0.792567 + 0.579652i
\(846\) −16.6300 −0.571753
\(847\) 18.4802i 0.634986i
\(848\) 7.70436i 0.264569i
\(849\) −12.5067 −0.429227
\(850\) −1.51514 4.76491i −0.0519688 0.163435i
\(851\) 15.1495 0.519320
\(852\) 4.04587i 0.138609i
\(853\) 35.9494i 1.23089i −0.788182 0.615443i \(-0.788977\pi\)
0.788182 0.615443i \(-0.211023\pi\)
\(854\) 30.0294 1.02758
\(855\) −28.7687 21.0403i −0.983868 0.719562i
\(856\) −19.4693 −0.665446
\(857\) 13.4158i 0.458276i −0.973394 0.229138i \(-0.926409\pi\)
0.973394 0.229138i \(-0.0735907\pi\)
\(858\) 0.470182i 0.0160518i
\(859\) 23.8860 0.814980 0.407490 0.913210i \(-0.366404\pi\)
0.407490 + 0.913210i \(0.366404\pi\)
\(860\) 1.35998 1.85952i 0.0463748 0.0634090i
\(861\) −0.319718 −0.0108960
\(862\) 20.4196i 0.695495i
\(863\) 15.5979i 0.530960i 0.964116 + 0.265480i \(0.0855304\pi\)
−0.964116 + 0.265480i \(0.914470\pi\)
\(864\) 2.79518 0.0950941
\(865\) 8.10551 11.0828i 0.275596 0.376826i
\(866\) −11.5904 −0.393857
\(867\) 0.484862i 0.0164668i
\(868\) 5.52982i 0.187694i
\(869\) −19.7190 −0.668922
\(870\) −7.13670 5.21949i −0.241957 0.176957i
\(871\) −2.40963 −0.0816472
\(872\) 12.6547i 0.428542i
\(873\) 18.6206i 0.630213i
\(874\) 7.84014 0.265197
\(875\) 27.9844 + 9.38555i 0.946046 + 0.317290i
\(876\) 0.235091 0.00794299
\(877\) 33.3893i 1.12748i 0.825953 + 0.563739i \(0.190638\pi\)
−0.825953 + 0.563739i \(0.809362\pi\)
\(878\) 2.01938i 0.0681507i
\(879\) 11.1149 0.374896
\(880\) 3.60975 + 2.64002i 0.121685 + 0.0889952i
\(881\) −35.1202 −1.18323 −0.591615 0.806221i \(-0.701509\pi\)
−0.591615 + 0.806221i \(0.701509\pi\)
\(882\) 0.0837106i 0.00281868i
\(883\) 22.2110i 0.747460i 0.927537 + 0.373730i \(0.121921\pi\)
−0.927537 + 0.373730i \(0.878079\pi\)
\(884\) −0.484862 −0.0163077
\(885\) 5.59037 7.64380i 0.187918 0.256944i
\(886\) 27.4087 0.920814
\(887\) 5.17076i 0.173617i −0.996225 0.0868085i \(-0.972333\pi\)
0.996225 0.0868085i \(-0.0276668\pi\)
\(888\) 5.40115i 0.181251i
\(889\) 39.0596 1.31002
\(890\) 11.5298 15.7649i 0.386480 0.528441i
\(891\) 13.8789 0.464960
\(892\) 23.2947i 0.779965i
\(893\) 34.6741i 1.16032i
\(894\) −4.84862 −0.162162
\(895\) 28.1386 + 20.5795i 0.940571 + 0.687896i
\(896\) 2.64002 0.0881970
\(897\) 0.319718i 0.0106751i
\(898\) 29.7190i 0.991737i
\(899\) 17.0819 0.569713
\(900\) −4.18922 13.1745i −0.139641 0.439151i
\(901\) −7.70436 −0.256669
\(902\) 0.499542i 0.0166329i
\(903\) 1.31880i 0.0438870i
\(904\) −7.51514 −0.249950
\(905\) 7.41675 + 5.42431i 0.246541 + 0.180310i
\(906\) −7.68028 −0.255160
\(907\) 3.85482i 0.127997i −0.997950 0.0639986i \(-0.979615\pi\)
0.997950 0.0639986i \(-0.0203853\pi\)
\(908\) 17.4839i 0.580225i
\(909\) 37.4087 1.24077
\(910\) 1.68968 2.31032i 0.0560122 0.0765865i
\(911\) −22.6400 −0.750097 −0.375049 0.927005i \(-0.622374\pi\)
−0.375049 + 0.927005i \(0.622374\pi\)
\(912\) 2.79518i 0.0925578i
\(913\) 35.0596i 1.16030i
\(914\) 39.4693 1.30553
\(915\) 7.28005 9.95413i 0.240671 0.329073i
\(916\) 0.719953 0.0237879
\(917\) 6.59885i 0.217913i
\(918\) 2.79518i 0.0922549i
\(919\) −31.5298 −1.04007 −0.520036 0.854144i \(-0.674082\pi\)
−0.520036 + 0.854144i \(0.674082\pi\)
\(920\) 2.45459 + 1.79518i 0.0809253 + 0.0591855i
\(921\) −5.07659 −0.167279
\(922\) 14.6888i 0.483749i
\(923\) 4.04587i 0.133172i
\(924\) −2.56009 −0.0842209
\(925\) −53.0790 + 16.8780i −1.74523 + 0.554945i
\(926\) −35.1055 −1.15364
\(927\) 31.0209i 1.01886i
\(928\) 8.15516i 0.267706i
\(929\) 11.1589 0.366113 0.183057 0.983102i \(-0.441401\pi\)
0.183057 + 0.983102i \(0.441401\pi\)
\(930\) −1.83302 1.34060i −0.0601072 0.0439600i
\(931\) −0.174539 −0.00572028
\(932\) 11.0450i 0.361790i
\(933\) 4.72179i 0.154584i
\(934\) −9.96881 −0.326189
\(935\) 2.64002 3.60975i 0.0863380 0.118051i
\(936\) −1.34060 −0.0438189
\(937\) 24.5307i 0.801384i 0.916213 + 0.400692i \(0.131230\pi\)
−0.916213 + 0.400692i \(0.868770\pi\)
\(938\) 13.1202i 0.428389i
\(939\) −4.60641 −0.150325
\(940\) −7.93945 + 10.8557i −0.258956 + 0.354075i
\(941\) 35.3747 1.15318 0.576590 0.817033i \(-0.304383\pi\)
0.576590 + 0.817033i \(0.304383\pi\)
\(942\) 0.650006i 0.0211783i
\(943\) 0.339682i 0.0110616i
\(944\) −8.73463 −0.284288
\(945\) 13.3188 + 9.74083i 0.433261 + 0.316869i
\(946\) 2.06055 0.0669943
\(947\) 2.23509i 0.0726307i −0.999340 0.0363154i \(-0.988438\pi\)
0.999340 0.0363154i \(-0.0115621\pi\)
\(948\) 4.78051i 0.155264i
\(949\) −0.235091 −0.00763138
\(950\) −27.4693 + 8.73463i −0.891221 + 0.283389i
\(951\) 6.34152 0.205638
\(952\) 2.64002i 0.0855637i
\(953\) 5.65092i 0.183051i −0.995803 0.0915257i \(-0.970826\pi\)
0.995803 0.0915257i \(-0.0291744\pi\)
\(954\) −21.3018 −0.689673
\(955\) 10.9385 + 8.00000i 0.353963 + 0.258874i
\(956\) −5.59037 −0.180805
\(957\) 7.90826i 0.255638i
\(958\) 2.28383i 0.0737871i
\(959\) −5.43991 −0.175664
\(960\) 0.640023 0.875115i 0.0206567 0.0282442i
\(961\) −26.6126 −0.858471
\(962\) 5.40115i 0.174140i
\(963\) 53.8307i 1.73467i
\(964\) 8.37088 0.269608
\(965\) −16.5795 + 22.6694i −0.533712 + 0.729753i
\(966\) −1.74083 −0.0560104
\(967\) 40.9991i 1.31844i 0.751949 + 0.659221i \(0.229114\pi\)
−0.751949 + 0.659221i \(0.770886\pi\)
\(968\) 7.00000i 0.224989i
\(969\) −2.79518 −0.0897943
\(970\) −12.1552 8.88979i −0.390279 0.285434i
\(971\) −45.3846 −1.45646 −0.728231 0.685332i \(-0.759657\pi\)
−0.728231 + 0.685332i \(0.759657\pi\)
\(972\) 11.7502i 0.376889i
\(973\) 41.1589i 1.31950i
\(974\) −10.8292 −0.346991
\(975\) −0.356195 1.12019i −0.0114074 0.0358747i
\(976\) −11.3747 −0.364094
\(977\) 4.72752i 0.151247i −0.997136 0.0756233i \(-0.975905\pi\)
0.997136 0.0756233i \(-0.0240946\pi\)
\(978\) 7.87890i 0.251939i
\(979\) 17.4693 0.558320
\(980\) −0.0546445 0.0399648i −0.00174556 0.00127663i
\(981\) 34.9891 1.11712
\(982\) 24.7952i 0.791246i
\(983\) 14.3297i 0.457046i −0.973538 0.228523i \(-0.926610\pi\)
0.973538 0.228523i \(-0.0733897\pi\)
\(984\) 0.121104 0.00386067
\(985\) 34.3846 47.0147i 1.09559 1.49801i
\(986\) 8.15516 0.259713
\(987\) 7.69907i 0.245064i
\(988\) 2.79518i 0.0889267i
\(989\) 1.40115 0.0445540
\(990\) 7.29942 9.98062i 0.231991 0.317205i
\(991\) 16.8827 0.536296 0.268148 0.963378i \(-0.413588\pi\)
0.268148 + 0.963378i \(0.413588\pi\)
\(992\) 2.09461i 0.0665039i
\(993\) 12.0658i 0.382898i
\(994\) −22.0294 −0.698729
\(995\) −6.09083 4.45459i −0.193092 0.141220i
\(996\) −8.49954 −0.269318
\(997\) 18.5189i 0.586500i 0.956036 + 0.293250i \(0.0947368\pi\)
−0.956036 + 0.293250i \(0.905263\pi\)
\(998\) 5.15138i 0.163064i
\(999\) −31.1371 −0.985136
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.69.2 6
3.2 odd 2 1530.2.d.g.919.4 6
4.3 odd 2 1360.2.e.c.1089.3 6
5.2 odd 4 850.2.a.q.1.2 3
5.3 odd 4 850.2.a.p.1.2 3
5.4 even 2 inner 170.2.c.b.69.5 yes 6
15.2 even 4 7650.2.a.dj.1.3 3
15.8 even 4 7650.2.a.do.1.1 3
15.14 odd 2 1530.2.d.g.919.1 6
20.3 even 4 6800.2.a.bp.1.2 3
20.7 even 4 6800.2.a.bk.1.2 3
20.19 odd 2 1360.2.e.c.1089.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.c.b.69.2 6 1.1 even 1 trivial
170.2.c.b.69.5 yes 6 5.4 even 2 inner
850.2.a.p.1.2 3 5.3 odd 4
850.2.a.q.1.2 3 5.2 odd 4
1360.2.e.c.1089.3 6 4.3 odd 2
1360.2.e.c.1089.4 6 20.19 odd 2
1530.2.d.g.919.1 6 15.14 odd 2
1530.2.d.g.919.4 6 3.2 odd 2
6800.2.a.bk.1.2 3 20.7 even 4
6800.2.a.bp.1.2 3 20.3 even 4
7650.2.a.dj.1.3 3 15.2 even 4
7650.2.a.do.1.1 3 15.8 even 4