Properties

Label 1260.2.c.c.811.5
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1260,2,Mod(811,1260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1260, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1260.811");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.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: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.342102016.5
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.5
Root \(-1.17915 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.c.811.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.780776 - 1.17915i) q^{2} +(-0.780776 - 1.84130i) q^{4} -1.00000i q^{5} +(-2.17238 + 1.51022i) q^{7} +(-2.78078 - 0.516994i) q^{8} +O(q^{10})\) \(q+(0.780776 - 1.17915i) q^{2} +(-0.780776 - 1.84130i) q^{4} -1.00000i q^{5} +(-2.17238 + 1.51022i) q^{7} +(-2.78078 - 0.516994i) q^{8} +(-1.17915 - 0.780776i) q^{10} +4.71659i q^{11} +2.00000i q^{13} +(0.0846354 + 3.74070i) q^{14} +(-2.78078 + 2.87529i) q^{16} -1.12311i q^{17} -4.71659 q^{19} +(-1.84130 + 0.780776i) q^{20} +(5.56155 + 3.68260i) q^{22} +6.41273i q^{23} -1.00000 q^{25} +(2.35829 + 1.56155i) q^{26} +(4.47692 + 2.82085i) q^{28} +2.00000 q^{29} -3.39228 q^{31} +(1.21922 + 5.52390i) q^{32} +(-1.32431 - 0.876894i) q^{34} +(1.51022 + 2.17238i) q^{35} +2.00000 q^{37} +(-3.68260 + 5.56155i) q^{38} +(-0.516994 + 2.78078i) q^{40} +1.12311i q^{41} +0.371834i q^{43} +(8.68466 - 3.68260i) q^{44} +(7.56155 + 5.00691i) q^{46} -5.08842 q^{47} +(2.43845 - 6.56155i) q^{49} +(-0.780776 + 1.17915i) q^{50} +(3.68260 - 1.56155i) q^{52} -2.00000 q^{53} +4.71659 q^{55} +(6.82167 - 3.07649i) q^{56} +(1.56155 - 2.35829i) q^{58} +2.06798 q^{59} +2.00000i q^{61} +(-2.64861 + 4.00000i) q^{62} +(7.46543 + 2.87529i) q^{64} +2.00000 q^{65} +3.76412i q^{67} +(-2.06798 + 0.876894i) q^{68} +(3.74070 - 0.0846354i) q^{70} -7.36520i q^{71} +15.3693i q^{73} +(1.56155 - 2.35829i) q^{74} +(3.68260 + 8.68466i) q^{76} +(-7.12311 - 10.2462i) q^{77} -1.32431i q^{79} +(2.87529 + 2.78078i) q^{80} +(1.32431 + 0.876894i) q^{82} -3.02045 q^{83} -1.12311 q^{85} +(0.438447 + 0.290319i) q^{86} +(2.43845 - 13.1158i) q^{88} -12.0000i q^{89} +(-3.02045 - 4.34475i) q^{91} +(11.8078 - 5.00691i) q^{92} +(-3.97292 + 6.00000i) q^{94} +4.71659i q^{95} -1.12311i q^{97} +(-5.83315 - 7.99839i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 6 q^{14} - 14 q^{16} + 28 q^{22} - 8 q^{25} + 14 q^{28} + 16 q^{29} + 18 q^{32} + 16 q^{37} + 20 q^{44} + 44 q^{46} + 36 q^{49} + 2 q^{50} - 16 q^{53} - 2 q^{56} - 4 q^{58} + 2 q^{64} + 16 q^{65} + 4 q^{70} - 4 q^{74} - 24 q^{77} + 24 q^{85} + 20 q^{86} + 36 q^{88} + 12 q^{92} - 26 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.780776 1.17915i 0.552092 0.833783i
\(3\) 0 0
\(4\) −0.780776 1.84130i −0.390388 0.920650i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −2.17238 + 1.51022i −0.821081 + 0.570811i
\(8\) −2.78078 0.516994i −0.983153 0.182785i
\(9\) 0 0
\(10\) −1.17915 0.780776i −0.372879 0.246903i
\(11\) 4.71659i 1.42211i 0.703139 + 0.711053i \(0.251781\pi\)
−0.703139 + 0.711053i \(0.748219\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 0.0846354 + 3.74070i 0.0226198 + 0.999744i
\(15\) 0 0
\(16\) −2.78078 + 2.87529i −0.695194 + 0.718822i
\(17\) 1.12311i 0.272393i −0.990682 0.136197i \(-0.956512\pi\)
0.990682 0.136197i \(-0.0434879\pi\)
\(18\) 0 0
\(19\) −4.71659 −1.08206 −0.541030 0.841003i \(-0.681965\pi\)
−0.541030 + 0.841003i \(0.681965\pi\)
\(20\) −1.84130 + 0.780776i −0.411727 + 0.174587i
\(21\) 0 0
\(22\) 5.56155 + 3.68260i 1.18573 + 0.785133i
\(23\) 6.41273i 1.33715i 0.743646 + 0.668573i \(0.233095\pi\)
−0.743646 + 0.668573i \(0.766905\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 2.35829 + 1.56155i 0.462500 + 0.306246i
\(27\) 0 0
\(28\) 4.47692 + 2.82085i 0.846058 + 0.533091i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) −3.39228 −0.609272 −0.304636 0.952469i \(-0.598535\pi\)
−0.304636 + 0.952469i \(0.598535\pi\)
\(32\) 1.21922 + 5.52390i 0.215530 + 0.976497i
\(33\) 0 0
\(34\) −1.32431 0.876894i −0.227117 0.150386i
\(35\) 1.51022 + 2.17238i 0.255274 + 0.367199i
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −3.68260 + 5.56155i −0.597397 + 0.902203i
\(39\) 0 0
\(40\) −0.516994 + 2.78078i −0.0817439 + 0.439679i
\(41\) 1.12311i 0.175400i 0.996147 + 0.0876998i \(0.0279516\pi\)
−0.996147 + 0.0876998i \(0.972048\pi\)
\(42\) 0 0
\(43\) 0.371834i 0.0567042i 0.999598 + 0.0283521i \(0.00902596\pi\)
−0.999598 + 0.0283521i \(0.990974\pi\)
\(44\) 8.68466 3.68260i 1.30926 0.555173i
\(45\) 0 0
\(46\) 7.56155 + 5.00691i 1.11489 + 0.738228i
\(47\) −5.08842 −0.742223 −0.371111 0.928588i \(-0.621023\pi\)
−0.371111 + 0.928588i \(0.621023\pi\)
\(48\) 0 0
\(49\) 2.43845 6.56155i 0.348350 0.937365i
\(50\) −0.780776 + 1.17915i −0.110418 + 0.166757i
\(51\) 0 0
\(52\) 3.68260 1.56155i 0.510685 0.216548i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 4.71659 0.635985
\(56\) 6.82167 3.07649i 0.911584 0.411113i
\(57\) 0 0
\(58\) 1.56155 2.35829i 0.205042 0.309659i
\(59\) 2.06798 0.269227 0.134614 0.990898i \(-0.457021\pi\)
0.134614 + 0.990898i \(0.457021\pi\)
\(60\) 0 0
\(61\) 2.00000i 0.256074i 0.991769 + 0.128037i \(0.0408676\pi\)
−0.991769 + 0.128037i \(0.959132\pi\)
\(62\) −2.64861 + 4.00000i −0.336374 + 0.508001i
\(63\) 0 0
\(64\) 7.46543 + 2.87529i 0.933179 + 0.359411i
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 3.76412i 0.459860i 0.973207 + 0.229930i \(0.0738497\pi\)
−0.973207 + 0.229930i \(0.926150\pi\)
\(68\) −2.06798 + 0.876894i −0.250779 + 0.106339i
\(69\) 0 0
\(70\) 3.74070 0.0846354i 0.447099 0.0101159i
\(71\) 7.36520i 0.874089i −0.899440 0.437044i \(-0.856025\pi\)
0.899440 0.437044i \(-0.143975\pi\)
\(72\) 0 0
\(73\) 15.3693i 1.79884i 0.437083 + 0.899421i \(0.356012\pi\)
−0.437083 + 0.899421i \(0.643988\pi\)
\(74\) 1.56155 2.35829i 0.181527 0.274146i
\(75\) 0 0
\(76\) 3.68260 + 8.68466i 0.422423 + 0.996199i
\(77\) −7.12311 10.2462i −0.811753 1.16766i
\(78\) 0 0
\(79\) 1.32431i 0.148996i −0.997221 0.0744981i \(-0.976265\pi\)
0.997221 0.0744981i \(-0.0237355\pi\)
\(80\) 2.87529 + 2.78078i 0.321467 + 0.310900i
\(81\) 0 0
\(82\) 1.32431 + 0.876894i 0.146245 + 0.0968368i
\(83\) −3.02045 −0.331537 −0.165769 0.986165i \(-0.553010\pi\)
−0.165769 + 0.986165i \(0.553010\pi\)
\(84\) 0 0
\(85\) −1.12311 −0.121818
\(86\) 0.438447 + 0.290319i 0.0472790 + 0.0313059i
\(87\) 0 0
\(88\) 2.43845 13.1158i 0.259939 1.39815i
\(89\) 12.0000i 1.27200i −0.771690 0.635999i \(-0.780588\pi\)
0.771690 0.635999i \(-0.219412\pi\)
\(90\) 0 0
\(91\) −3.02045 4.34475i −0.316629 0.455454i
\(92\) 11.8078 5.00691i 1.23104 0.522006i
\(93\) 0 0
\(94\) −3.97292 + 6.00000i −0.409775 + 0.618853i
\(95\) 4.71659i 0.483912i
\(96\) 0 0
\(97\) 1.12311i 0.114034i −0.998373 0.0570170i \(-0.981841\pi\)
0.998373 0.0570170i \(-0.0181589\pi\)
\(98\) −5.83315 7.99839i −0.589238 0.807960i
\(99\) 0 0
\(100\) 0.780776 + 1.84130i 0.0780776 + 0.184130i
\(101\) 15.1231i 1.50481i 0.658703 + 0.752403i \(0.271105\pi\)
−0.658703 + 0.752403i \(0.728895\pi\)
\(102\) 0 0
\(103\) −7.73704 −0.762353 −0.381176 0.924502i \(-0.624481\pi\)
−0.381176 + 0.924502i \(0.624481\pi\)
\(104\) 1.03399 5.56155i 0.101391 0.545355i
\(105\) 0 0
\(106\) −1.56155 + 2.35829i −0.151671 + 0.229058i
\(107\) 5.66906i 0.548049i −0.961723 0.274024i \(-0.911645\pi\)
0.961723 0.274024i \(-0.0883549\pi\)
\(108\) 0 0
\(109\) −7.12311 −0.682270 −0.341135 0.940014i \(-0.610811\pi\)
−0.341135 + 0.940014i \(0.610811\pi\)
\(110\) 3.68260 5.56155i 0.351122 0.530273i
\(111\) 0 0
\(112\) 1.69857 10.4458i 0.160499 0.987036i
\(113\) −18.4924 −1.73962 −0.869810 0.493386i \(-0.835759\pi\)
−0.869810 + 0.493386i \(0.835759\pi\)
\(114\) 0 0
\(115\) 6.41273 0.597990
\(116\) −1.56155 3.68260i −0.144987 0.341921i
\(117\) 0 0
\(118\) 1.61463 2.43845i 0.148638 0.224477i
\(119\) 1.69614 + 2.43981i 0.155485 + 0.223657i
\(120\) 0 0
\(121\) −11.2462 −1.02238
\(122\) 2.35829 + 1.56155i 0.213510 + 0.141376i
\(123\) 0 0
\(124\) 2.64861 + 6.24621i 0.237853 + 0.560926i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 17.7509i 1.57513i 0.616229 + 0.787567i \(0.288659\pi\)
−0.616229 + 0.787567i \(0.711341\pi\)
\(128\) 9.21922 6.55789i 0.814872 0.579641i
\(129\) 0 0
\(130\) 1.56155 2.35829i 0.136957 0.206836i
\(131\) −17.5420 −1.53266 −0.766328 0.642450i \(-0.777918\pi\)
−0.766328 + 0.642450i \(0.777918\pi\)
\(132\) 0 0
\(133\) 10.2462 7.12311i 0.888459 0.617652i
\(134\) 4.43845 + 2.93893i 0.383423 + 0.253885i
\(135\) 0 0
\(136\) −0.580639 + 3.12311i −0.0497894 + 0.267804i
\(137\) 14.0000 1.19610 0.598050 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) 16.7984 1.42482 0.712410 0.701763i \(-0.247604\pi\)
0.712410 + 0.701763i \(0.247604\pi\)
\(140\) 2.82085 4.47692i 0.238406 0.378369i
\(141\) 0 0
\(142\) −8.68466 5.75058i −0.728800 0.482578i
\(143\) −9.43318 −0.788842
\(144\) 0 0
\(145\) 2.00000i 0.166091i
\(146\) 18.1227 + 12.0000i 1.49984 + 0.993127i
\(147\) 0 0
\(148\) −1.56155 3.68260i −0.128359 0.302708i
\(149\) −5.36932 −0.439872 −0.219936 0.975514i \(-0.570585\pi\)
−0.219936 + 0.975514i \(0.570585\pi\)
\(150\) 0 0
\(151\) 10.0138i 0.814913i 0.913225 + 0.407456i \(0.133584\pi\)
−0.913225 + 0.407456i \(0.866416\pi\)
\(152\) 13.1158 + 2.43845i 1.06383 + 0.197784i
\(153\) 0 0
\(154\) −17.6433 + 0.399190i −1.42174 + 0.0321677i
\(155\) 3.39228i 0.272475i
\(156\) 0 0
\(157\) 0.246211i 0.0196498i −0.999952 0.00982490i \(-0.996873\pi\)
0.999952 0.00982490i \(-0.00312741\pi\)
\(158\) −1.56155 1.03399i −0.124230 0.0822596i
\(159\) 0 0
\(160\) 5.52390 1.21922i 0.436703 0.0963881i
\(161\) −9.68466 13.9309i −0.763258 1.09791i
\(162\) 0 0
\(163\) 3.02045i 0.236580i −0.992979 0.118290i \(-0.962259\pi\)
0.992979 0.118290i \(-0.0377412\pi\)
\(164\) 2.06798 0.876894i 0.161482 0.0684739i
\(165\) 0 0
\(166\) −2.35829 + 3.56155i −0.183039 + 0.276430i
\(167\) 19.8188 1.53363 0.766813 0.641870i \(-0.221841\pi\)
0.766813 + 0.641870i \(0.221841\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −0.876894 + 1.32431i −0.0672547 + 0.101570i
\(171\) 0 0
\(172\) 0.684658 0.290319i 0.0522047 0.0221366i
\(173\) 16.2462i 1.23518i 0.786502 + 0.617588i \(0.211890\pi\)
−0.786502 + 0.617588i \(0.788110\pi\)
\(174\) 0 0
\(175\) 2.17238 1.51022i 0.164216 0.114162i
\(176\) −13.5616 13.1158i −1.02224 0.988639i
\(177\) 0 0
\(178\) −14.1498 9.36932i −1.06057 0.702260i
\(179\) 10.7575i 0.804052i −0.915628 0.402026i \(-0.868306\pi\)
0.915628 0.402026i \(-0.131694\pi\)
\(180\) 0 0
\(181\) 15.1231i 1.12409i −0.827106 0.562046i \(-0.810014\pi\)
0.827106 0.562046i \(-0.189986\pi\)
\(182\) −7.48140 + 0.169271i −0.554558 + 0.0125472i
\(183\) 0 0
\(184\) 3.31534 17.8324i 0.244410 1.31462i
\(185\) 2.00000i 0.147043i
\(186\) 0 0
\(187\) 5.29723 0.387372
\(188\) 3.97292 + 9.36932i 0.289755 + 0.683328i
\(189\) 0 0
\(190\) 5.56155 + 3.68260i 0.403477 + 0.267164i
\(191\) 16.7984i 1.21549i 0.794133 + 0.607744i \(0.207925\pi\)
−0.794133 + 0.607744i \(0.792075\pi\)
\(192\) 0 0
\(193\) −22.4924 −1.61904 −0.809520 0.587092i \(-0.800273\pi\)
−0.809520 + 0.587092i \(0.800273\pi\)
\(194\) −1.32431 0.876894i −0.0950797 0.0629573i
\(195\) 0 0
\(196\) −13.9857 + 0.633191i −0.998977 + 0.0452279i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −26.8122 −1.90067 −0.950333 0.311235i \(-0.899258\pi\)
−0.950333 + 0.311235i \(0.899258\pi\)
\(200\) 2.78078 + 0.516994i 0.196631 + 0.0365570i
\(201\) 0 0
\(202\) 17.8324 + 11.8078i 1.25468 + 0.830791i
\(203\) −4.34475 + 3.02045i −0.304942 + 0.211994i
\(204\) 0 0
\(205\) 1.12311 0.0784411
\(206\) −6.04090 + 9.12311i −0.420889 + 0.635637i
\(207\) 0 0
\(208\) −5.75058 5.56155i −0.398731 0.385624i
\(209\) 22.2462i 1.53880i
\(210\) 0 0
\(211\) 22.0956i 1.52112i −0.649265 0.760562i \(-0.724923\pi\)
0.649265 0.760562i \(-0.275077\pi\)
\(212\) 1.56155 + 3.68260i 0.107248 + 0.252922i
\(213\) 0 0
\(214\) −6.68466 4.42627i −0.456954 0.302574i
\(215\) 0.371834 0.0253589
\(216\) 0 0
\(217\) 7.36932 5.12311i 0.500262 0.347779i
\(218\) −5.56155 + 8.39919i −0.376676 + 0.568865i
\(219\) 0 0
\(220\) −3.68260 8.68466i −0.248281 0.585520i
\(221\) 2.24621 0.151097
\(222\) 0 0
\(223\) 20.5625 1.37697 0.688483 0.725252i \(-0.258277\pi\)
0.688483 + 0.725252i \(0.258277\pi\)
\(224\) −10.9909 10.1587i −0.734363 0.678757i
\(225\) 0 0
\(226\) −14.4384 + 21.8053i −0.960431 + 1.45047i
\(227\) 3.76412 0.249833 0.124917 0.992167i \(-0.460134\pi\)
0.124917 + 0.992167i \(0.460134\pi\)
\(228\) 0 0
\(229\) 12.8769i 0.850929i −0.904975 0.425465i \(-0.860111\pi\)
0.904975 0.425465i \(-0.139889\pi\)
\(230\) 5.00691 7.56155i 0.330146 0.498594i
\(231\) 0 0
\(232\) −5.56155 1.03399i −0.365134 0.0678846i
\(233\) −7.75379 −0.507968 −0.253984 0.967208i \(-0.581741\pi\)
−0.253984 + 0.967208i \(0.581741\pi\)
\(234\) 0 0
\(235\) 5.08842i 0.331932i
\(236\) −1.61463 3.80776i −0.105103 0.247864i
\(237\) 0 0
\(238\) 4.20120 0.0950545i 0.272323 0.00616147i
\(239\) 3.97292i 0.256987i 0.991710 + 0.128493i \(0.0410141\pi\)
−0.991710 + 0.128493i \(0.958986\pi\)
\(240\) 0 0
\(241\) 25.6155i 1.65004i −0.565103 0.825021i \(-0.691163\pi\)
0.565103 0.825021i \(-0.308837\pi\)
\(242\) −8.78078 + 13.2609i −0.564450 + 0.852445i
\(243\) 0 0
\(244\) 3.68260 1.56155i 0.235754 0.0999682i
\(245\) −6.56155 2.43845i −0.419202 0.155787i
\(246\) 0 0
\(247\) 9.43318i 0.600219i
\(248\) 9.43318 + 1.75379i 0.599007 + 0.111366i
\(249\) 0 0
\(250\) 1.17915 + 0.780776i 0.0745758 + 0.0493806i
\(251\) 16.0547 1.01336 0.506682 0.862133i \(-0.330872\pi\)
0.506682 + 0.862133i \(0.330872\pi\)
\(252\) 0 0
\(253\) −30.2462 −1.90156
\(254\) 20.9309 + 13.8594i 1.31332 + 0.869619i
\(255\) 0 0
\(256\) −0.534565 15.9911i −0.0334103 0.999442i
\(257\) 11.3693i 0.709199i 0.935018 + 0.354599i \(0.115383\pi\)
−0.935018 + 0.354599i \(0.884617\pi\)
\(258\) 0 0
\(259\) −4.34475 + 3.02045i −0.269970 + 0.187682i
\(260\) −1.56155 3.68260i −0.0968434 0.228385i
\(261\) 0 0
\(262\) −13.6964 + 20.6847i −0.846168 + 1.27790i
\(263\) 18.4945i 1.14042i −0.821499 0.570211i \(-0.806862\pi\)
0.821499 0.570211i \(-0.193138\pi\)
\(264\) 0 0
\(265\) 2.00000i 0.122859i
\(266\) −0.399190 17.6433i −0.0244759 1.08178i
\(267\) 0 0
\(268\) 6.93087 2.93893i 0.423370 0.179524i
\(269\) 0.246211i 0.0150118i 0.999972 + 0.00750588i \(0.00238922\pi\)
−0.999972 + 0.00750588i \(0.997611\pi\)
\(270\) 0 0
\(271\) 1.90495 0.115717 0.0578586 0.998325i \(-0.481573\pi\)
0.0578586 + 0.998325i \(0.481573\pi\)
\(272\) 3.22925 + 3.12311i 0.195802 + 0.189366i
\(273\) 0 0
\(274\) 10.9309 16.5081i 0.660358 0.997288i
\(275\) 4.71659i 0.284421i
\(276\) 0 0
\(277\) 12.2462 0.735804 0.367902 0.929865i \(-0.380076\pi\)
0.367902 + 0.929865i \(0.380076\pi\)
\(278\) 13.1158 19.8078i 0.786632 1.18799i
\(279\) 0 0
\(280\) −3.07649 6.82167i −0.183855 0.407673i
\(281\) 29.3693 1.75203 0.876013 0.482287i \(-0.160194\pi\)
0.876013 + 0.482287i \(0.160194\pi\)
\(282\) 0 0
\(283\) −4.92539 −0.292784 −0.146392 0.989227i \(-0.546766\pi\)
−0.146392 + 0.989227i \(0.546766\pi\)
\(284\) −13.5616 + 5.75058i −0.804730 + 0.341234i
\(285\) 0 0
\(286\) −7.36520 + 11.1231i −0.435514 + 0.657723i
\(287\) −1.69614 2.43981i −0.100120 0.144017i
\(288\) 0 0
\(289\) 15.7386 0.925802
\(290\) −2.35829 1.56155i −0.138484 0.0916975i
\(291\) 0 0
\(292\) 28.2995 12.0000i 1.65610 0.702247i
\(293\) 15.7538i 0.920346i 0.887829 + 0.460173i \(0.152213\pi\)
−0.887829 + 0.460173i \(0.847787\pi\)
\(294\) 0 0
\(295\) 2.06798i 0.120402i
\(296\) −5.56155 1.03399i −0.323259 0.0600993i
\(297\) 0 0
\(298\) −4.19224 + 6.33122i −0.242850 + 0.366757i
\(299\) −12.8255 −0.741715
\(300\) 0 0
\(301\) −0.561553 0.807764i −0.0323674 0.0465587i
\(302\) 11.8078 + 7.81855i 0.679460 + 0.449907i
\(303\) 0 0
\(304\) 13.1158 13.5616i 0.752242 0.777808i
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) 1.53311 0.0874993 0.0437496 0.999043i \(-0.486070\pi\)
0.0437496 + 0.999043i \(0.486070\pi\)
\(308\) −13.3048 + 21.1158i −0.758112 + 1.20318i
\(309\) 0 0
\(310\) 4.00000 + 2.64861i 0.227185 + 0.150431i
\(311\) −30.2045 −1.71274 −0.856369 0.516364i \(-0.827285\pi\)
−0.856369 + 0.516364i \(0.827285\pi\)
\(312\) 0 0
\(313\) 33.6155i 1.90006i 0.312156 + 0.950031i \(0.398949\pi\)
−0.312156 + 0.950031i \(0.601051\pi\)
\(314\) −0.290319 0.192236i −0.0163837 0.0108485i
\(315\) 0 0
\(316\) −2.43845 + 1.03399i −0.137173 + 0.0581663i
\(317\) −12.2462 −0.687816 −0.343908 0.939003i \(-0.611751\pi\)
−0.343908 + 0.939003i \(0.611751\pi\)
\(318\) 0 0
\(319\) 9.43318i 0.528157i
\(320\) 2.87529 7.46543i 0.160734 0.417330i
\(321\) 0 0
\(322\) −23.9881 + 0.542744i −1.33680 + 0.0302459i
\(323\) 5.29723i 0.294746i
\(324\) 0 0
\(325\) 2.00000i 0.110940i
\(326\) −3.56155 2.35829i −0.197256 0.130614i
\(327\) 0 0
\(328\) 0.580639 3.12311i 0.0320604 0.172445i
\(329\) 11.0540 7.68466i 0.609425 0.423669i
\(330\) 0 0
\(331\) 18.2857i 1.00507i −0.864556 0.502537i \(-0.832400\pi\)
0.864556 0.502537i \(-0.167600\pi\)
\(332\) 2.35829 + 5.56155i 0.129428 + 0.305230i
\(333\) 0 0
\(334\) 15.4741 23.3693i 0.846704 1.27871i
\(335\) 3.76412 0.205656
\(336\) 0 0
\(337\) −12.2462 −0.667094 −0.333547 0.942734i \(-0.608246\pi\)
−0.333547 + 0.942734i \(0.608246\pi\)
\(338\) 7.02699 10.6123i 0.382218 0.577234i
\(339\) 0 0
\(340\) 0.876894 + 2.06798i 0.0475563 + 0.112152i
\(341\) 16.0000i 0.866449i
\(342\) 0 0
\(343\) 4.61219 + 17.9368i 0.249035 + 0.968495i
\(344\) 0.192236 1.03399i 0.0103647 0.0557489i
\(345\) 0 0
\(346\) 19.1567 + 12.6847i 1.02987 + 0.681931i
\(347\) 5.66906i 0.304331i −0.988355 0.152166i \(-0.951375\pi\)
0.988355 0.152166i \(-0.0486247\pi\)
\(348\) 0 0
\(349\) 29.8617i 1.59846i 0.601024 + 0.799231i \(0.294760\pi\)
−0.601024 + 0.799231i \(0.705240\pi\)
\(350\) −0.0846354 3.74070i −0.00452395 0.199949i
\(351\) 0 0
\(352\) −26.0540 + 5.75058i −1.38868 + 0.306507i
\(353\) 19.3693i 1.03092i 0.856912 + 0.515462i \(0.172380\pi\)
−0.856912 + 0.515462i \(0.827620\pi\)
\(354\) 0 0
\(355\) −7.36520 −0.390904
\(356\) −22.0956 + 9.36932i −1.17106 + 0.496573i
\(357\) 0 0
\(358\) −12.6847 8.39919i −0.670405 0.443911i
\(359\) 16.0547i 0.847335i 0.905818 + 0.423668i \(0.139258\pi\)
−0.905818 + 0.423668i \(0.860742\pi\)
\(360\) 0 0
\(361\) 3.24621 0.170853
\(362\) −17.8324 11.8078i −0.937248 0.620602i
\(363\) 0 0
\(364\) −5.64171 + 8.95383i −0.295706 + 0.469308i
\(365\) 15.3693 0.804467
\(366\) 0 0
\(367\) −10.3857 −0.542127 −0.271063 0.962562i \(-0.587375\pi\)
−0.271063 + 0.962562i \(0.587375\pi\)
\(368\) −18.4384 17.8324i −0.961171 0.929576i
\(369\) 0 0
\(370\) −2.35829 1.56155i −0.122602 0.0811813i
\(371\) 4.34475 3.02045i 0.225568 0.156814i
\(372\) 0 0
\(373\) −10.4924 −0.543277 −0.271639 0.962399i \(-0.587566\pi\)
−0.271639 + 0.962399i \(0.587566\pi\)
\(374\) 4.13595 6.24621i 0.213865 0.322984i
\(375\) 0 0
\(376\) 14.1498 + 2.63068i 0.729719 + 0.135667i
\(377\) 4.00000i 0.206010i
\(378\) 0 0
\(379\) 14.8934i 0.765024i −0.923950 0.382512i \(-0.875059\pi\)
0.923950 0.382512i \(-0.124941\pi\)
\(380\) 8.68466 3.68260i 0.445514 0.188913i
\(381\) 0 0
\(382\) 19.8078 + 13.1158i 1.01345 + 0.671062i
\(383\) 19.0752 0.974695 0.487348 0.873208i \(-0.337964\pi\)
0.487348 + 0.873208i \(0.337964\pi\)
\(384\) 0 0
\(385\) −10.2462 + 7.12311i −0.522195 + 0.363027i
\(386\) −17.5616 + 26.5219i −0.893860 + 1.34993i
\(387\) 0 0
\(388\) −2.06798 + 0.876894i −0.104986 + 0.0445176i
\(389\) 7.12311 0.361156 0.180578 0.983561i \(-0.442203\pi\)
0.180578 + 0.983561i \(0.442203\pi\)
\(390\) 0 0
\(391\) 7.20217 0.364230
\(392\) −10.1731 + 16.9855i −0.513817 + 0.857900i
\(393\) 0 0
\(394\) −14.0540 + 21.2247i −0.708029 + 1.06928i
\(395\) −1.32431 −0.0666331
\(396\) 0 0
\(397\) 14.0000i 0.702640i −0.936255 0.351320i \(-0.885733\pi\)
0.936255 0.351320i \(-0.114267\pi\)
\(398\) −20.9343 + 31.6155i −1.04934 + 1.58474i
\(399\) 0 0
\(400\) 2.78078 2.87529i 0.139039 0.143764i
\(401\) −6.00000 −0.299626 −0.149813 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 0 0
\(403\) 6.78456i 0.337963i
\(404\) 27.8462 11.8078i 1.38540 0.587458i
\(405\) 0 0
\(406\) 0.169271 + 7.48140i 0.00840077 + 0.371296i
\(407\) 9.43318i 0.467585i
\(408\) 0 0
\(409\) 17.1231i 0.846683i −0.905970 0.423342i \(-0.860857\pi\)
0.905970 0.423342i \(-0.139143\pi\)
\(410\) 0.876894 1.32431i 0.0433067 0.0654029i
\(411\) 0 0
\(412\) 6.04090 + 14.2462i 0.297614 + 0.701860i
\(413\) −4.49242 + 3.12311i −0.221058 + 0.153678i
\(414\) 0 0
\(415\) 3.02045i 0.148268i
\(416\) −11.0478 + 2.43845i −0.541663 + 0.119555i
\(417\) 0 0
\(418\) −26.2316 17.3693i −1.28303 0.849561i
\(419\) 23.5829 1.15210 0.576051 0.817414i \(-0.304593\pi\)
0.576051 + 0.817414i \(0.304593\pi\)
\(420\) 0 0
\(421\) 23.6155 1.15095 0.575475 0.817819i \(-0.304817\pi\)
0.575475 + 0.817819i \(0.304817\pi\)
\(422\) −26.0540 17.2517i −1.26829 0.839801i
\(423\) 0 0
\(424\) 5.56155 + 1.03399i 0.270093 + 0.0502149i
\(425\) 1.12311i 0.0544786i
\(426\) 0 0
\(427\) −3.02045 4.34475i −0.146170 0.210257i
\(428\) −10.4384 + 4.42627i −0.504561 + 0.213952i
\(429\) 0 0
\(430\) 0.290319 0.438447i 0.0140004 0.0211438i
\(431\) 5.87787i 0.283127i 0.989929 + 0.141563i \(0.0452129\pi\)
−0.989929 + 0.141563i \(0.954787\pi\)
\(432\) 0 0
\(433\) 29.6155i 1.42323i 0.702569 + 0.711616i \(0.252036\pi\)
−0.702569 + 0.711616i \(0.747964\pi\)
\(434\) −0.287107 12.6895i −0.0137816 0.609116i
\(435\) 0 0
\(436\) 5.56155 + 13.1158i 0.266350 + 0.628132i
\(437\) 30.2462i 1.44687i
\(438\) 0 0
\(439\) 16.2177 0.774031 0.387015 0.922073i \(-0.373506\pi\)
0.387015 + 0.922073i \(0.373506\pi\)
\(440\) −13.1158 2.43845i −0.625270 0.116248i
\(441\) 0 0
\(442\) 1.75379 2.64861i 0.0834192 0.125982i
\(443\) 23.0481i 1.09505i −0.836790 0.547524i \(-0.815571\pi\)
0.836790 0.547524i \(-0.184429\pi\)
\(444\) 0 0
\(445\) −12.0000 −0.568855
\(446\) 16.0547 24.2462i 0.760213 1.14809i
\(447\) 0 0
\(448\) −20.5601 + 5.02827i −0.971372 + 0.237563i
\(449\) 15.6155 0.736942 0.368471 0.929639i \(-0.379881\pi\)
0.368471 + 0.929639i \(0.379881\pi\)
\(450\) 0 0
\(451\) −5.29723 −0.249437
\(452\) 14.4384 + 34.0501i 0.679127 + 1.60158i
\(453\) 0 0
\(454\) 2.93893 4.43845i 0.137931 0.208307i
\(455\) −4.34475 + 3.02045i −0.203685 + 0.141601i
\(456\) 0 0
\(457\) 6.00000 0.280668 0.140334 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) −15.1838 10.0540i −0.709490 0.469791i
\(459\) 0 0
\(460\) −5.00691 11.8078i −0.233448 0.550540i
\(461\) 3.61553i 0.168392i −0.996449 0.0841960i \(-0.973168\pi\)
0.996449 0.0841960i \(-0.0268322\pi\)
\(462\) 0 0
\(463\) 28.6714i 1.33247i 0.745741 + 0.666236i \(0.232096\pi\)
−0.745741 + 0.666236i \(0.767904\pi\)
\(464\) −5.56155 + 5.75058i −0.258189 + 0.266964i
\(465\) 0 0
\(466\) −6.05398 + 9.14286i −0.280445 + 0.423535i
\(467\) −18.4945 −0.855824 −0.427912 0.903820i \(-0.640751\pi\)
−0.427912 + 0.903820i \(0.640751\pi\)
\(468\) 0 0
\(469\) −5.68466 8.17708i −0.262493 0.377583i
\(470\) 6.00000 + 3.97292i 0.276759 + 0.183257i
\(471\) 0 0
\(472\) −5.75058 1.06913i −0.264692 0.0492107i
\(473\) −1.75379 −0.0806393
\(474\) 0 0
\(475\) 4.71659 0.216412
\(476\) 3.16812 5.02805i 0.145210 0.230460i
\(477\) 0 0
\(478\) 4.68466 + 3.10196i 0.214271 + 0.141880i
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 4.00000i 0.182384i
\(482\) −30.2045 20.0000i −1.37578 0.910975i
\(483\) 0 0
\(484\) 8.78078 + 20.7077i 0.399126 + 0.941257i
\(485\) −1.12311 −0.0509976
\(486\) 0 0
\(487\) 13.1973i 0.598026i −0.954249 0.299013i \(-0.903343\pi\)
0.954249 0.299013i \(-0.0966575\pi\)
\(488\) 1.03399 5.56155i 0.0468064 0.251760i
\(489\) 0 0
\(490\) −7.99839 + 5.83315i −0.361331 + 0.263515i
\(491\) 31.5288i 1.42287i −0.702750 0.711437i \(-0.748045\pi\)
0.702750 0.711437i \(-0.251955\pi\)
\(492\) 0 0
\(493\) 2.24621i 0.101164i
\(494\) −11.1231 7.36520i −0.500452 0.331376i
\(495\) 0 0
\(496\) 9.43318 9.75379i 0.423562 0.437958i
\(497\) 11.1231 + 16.0000i 0.498939 + 0.717698i
\(498\) 0 0
\(499\) 24.3266i 1.08901i 0.838758 + 0.544504i \(0.183282\pi\)
−0.838758 + 0.544504i \(0.816718\pi\)
\(500\) 1.84130 0.780776i 0.0823455 0.0349174i
\(501\) 0 0
\(502\) 12.5351 18.9309i 0.559471 0.844926i
\(503\) 17.9139 0.798741 0.399370 0.916790i \(-0.369229\pi\)
0.399370 + 0.916790i \(0.369229\pi\)
\(504\) 0 0
\(505\) 15.1231 0.672969
\(506\) −23.6155 + 35.6647i −1.04984 + 1.58549i
\(507\) 0 0
\(508\) 32.6847 13.8594i 1.45015 0.614914i
\(509\) 23.6155i 1.04674i 0.852106 + 0.523370i \(0.175325\pi\)
−0.852106 + 0.523370i \(0.824675\pi\)
\(510\) 0 0
\(511\) −23.2111 33.3880i −1.02680 1.47700i
\(512\) −19.2732 11.8551i −0.851763 0.523927i
\(513\) 0 0
\(514\) 13.4061 + 8.87689i 0.591318 + 0.391543i
\(515\) 7.73704i 0.340935i
\(516\) 0 0
\(517\) 24.0000i 1.05552i
\(518\) 0.169271 + 7.48140i 0.00743733 + 0.328714i
\(519\) 0 0
\(520\) −5.56155 1.03399i −0.243890 0.0453434i
\(521\) 9.75379i 0.427321i 0.976908 + 0.213661i \(0.0685387\pi\)
−0.976908 + 0.213661i \(0.931461\pi\)
\(522\) 0 0
\(523\) 19.2382 0.841227 0.420614 0.907240i \(-0.361815\pi\)
0.420614 + 0.907240i \(0.361815\pi\)
\(524\) 13.6964 + 32.3002i 0.598331 + 1.41104i
\(525\) 0 0
\(526\) −21.8078 14.4401i −0.950864 0.629618i
\(527\) 3.80989i 0.165961i
\(528\) 0 0
\(529\) −18.1231 −0.787961
\(530\) 2.35829 + 1.56155i 0.102438 + 0.0678295i
\(531\) 0 0
\(532\) −21.1158 13.3048i −0.915485 0.576836i
\(533\) −2.24621 −0.0972942
\(534\) 0 0
\(535\) −5.66906 −0.245095
\(536\) 1.94602 10.4672i 0.0840555 0.452113i
\(537\) 0 0
\(538\) 0.290319 + 0.192236i 0.0125166 + 0.00828788i
\(539\) 30.9481 + 11.5012i 1.33303 + 0.495390i
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 1.48734 2.24621i 0.0638866 0.0964830i
\(543\) 0 0
\(544\) 6.20393 1.36932i 0.265991 0.0587090i
\(545\) 7.12311i 0.305120i
\(546\) 0 0
\(547\) 30.5763i 1.30735i −0.756776 0.653674i \(-0.773227\pi\)
0.756776 0.653674i \(-0.226773\pi\)
\(548\) −10.9309 25.7782i −0.466944 1.10119i
\(549\) 0 0
\(550\) −5.56155 3.68260i −0.237145 0.157027i
\(551\) −9.43318 −0.401867
\(552\) 0 0
\(553\) 2.00000 + 2.87689i 0.0850487 + 0.122338i
\(554\) 9.56155 14.4401i 0.406231 0.613500i
\(555\) 0 0
\(556\) −13.1158 30.9309i −0.556233 1.31176i
\(557\) 26.4924 1.12252 0.561260 0.827640i \(-0.310317\pi\)
0.561260 + 0.827640i \(0.310317\pi\)
\(558\) 0 0
\(559\) −0.743668 −0.0314538
\(560\) −10.4458 1.69857i −0.441416 0.0717775i
\(561\) 0 0
\(562\) 22.9309 34.6307i 0.967280 1.46081i
\(563\) 38.1045 1.60592 0.802958 0.596036i \(-0.203259\pi\)
0.802958 + 0.596036i \(0.203259\pi\)
\(564\) 0 0
\(565\) 18.4924i 0.777982i
\(566\) −3.84563 + 5.80776i −0.161644 + 0.244119i
\(567\) 0 0
\(568\) −3.80776 + 20.4810i −0.159770 + 0.859363i
\(569\) 28.8769 1.21058 0.605291 0.796004i \(-0.293057\pi\)
0.605291 + 0.796004i \(0.293057\pi\)
\(570\) 0 0
\(571\) 3.22925i 0.135140i −0.997715 0.0675700i \(-0.978475\pi\)
0.997715 0.0675700i \(-0.0215246\pi\)
\(572\) 7.36520 + 17.3693i 0.307955 + 0.726248i
\(573\) 0 0
\(574\) −4.20120 + 0.0950545i −0.175355 + 0.00396750i
\(575\) 6.41273i 0.267429i
\(576\) 0 0
\(577\) 45.6155i 1.89900i 0.313768 + 0.949500i \(0.398409\pi\)
−0.313768 + 0.949500i \(0.601591\pi\)
\(578\) 12.2884 18.5582i 0.511128 0.771918i
\(579\) 0 0
\(580\) −3.68260 + 1.56155i −0.152912 + 0.0648400i
\(581\) 6.56155 4.56155i 0.272219 0.189245i
\(582\) 0 0
\(583\) 9.43318i 0.390682i
\(584\) 7.94584 42.7386i 0.328801 1.76854i
\(585\) 0 0
\(586\) 18.5760 + 12.3002i 0.767369 + 0.508116i
\(587\) 21.8868 0.903365 0.451683 0.892179i \(-0.350824\pi\)
0.451683 + 0.892179i \(0.350824\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) −2.43845 1.61463i −0.100389 0.0664731i
\(591\) 0 0
\(592\) −5.56155 + 5.75058i −0.228578 + 0.236347i
\(593\) 11.3693i 0.466882i 0.972371 + 0.233441i \(0.0749986\pi\)
−0.972371 + 0.233441i \(0.925001\pi\)
\(594\) 0 0
\(595\) 2.43981 1.69614i 0.100022 0.0695350i
\(596\) 4.19224 + 9.88653i 0.171721 + 0.404968i
\(597\) 0 0
\(598\) −10.0138 + 15.1231i −0.409495 + 0.618430i
\(599\) 29.6238i 1.21040i −0.796074 0.605199i \(-0.793094\pi\)
0.796074 0.605199i \(-0.206906\pi\)
\(600\) 0 0
\(601\) 17.1231i 0.698466i 0.937036 + 0.349233i \(0.113558\pi\)
−0.937036 + 0.349233i \(0.886442\pi\)
\(602\) −1.39092 + 0.0314703i −0.0566897 + 0.00128263i
\(603\) 0 0
\(604\) 18.4384 7.81855i 0.750250 0.318132i
\(605\) 11.2462i 0.457224i
\(606\) 0 0
\(607\) −37.9415 −1.54000 −0.769999 0.638045i \(-0.779743\pi\)
−0.769999 + 0.638045i \(0.779743\pi\)
\(608\) −5.75058 26.0540i −0.233217 1.05663i
\(609\) 0 0
\(610\) 1.56155 2.35829i 0.0632254 0.0954846i
\(611\) 10.1768i 0.411711i
\(612\) 0 0
\(613\) 28.2462 1.14085 0.570427 0.821348i \(-0.306778\pi\)
0.570427 + 0.821348i \(0.306778\pi\)
\(614\) 1.19702 1.80776i 0.0483077 0.0729554i
\(615\) 0 0
\(616\) 14.5105 + 32.1750i 0.584646 + 1.29637i
\(617\) 26.0000 1.04672 0.523360 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 0 0
\(619\) 20.6083 0.828316 0.414158 0.910205i \(-0.364076\pi\)
0.414158 + 0.910205i \(0.364076\pi\)
\(620\) 6.24621 2.64861i 0.250854 0.106371i
\(621\) 0 0
\(622\) −23.5829 + 35.6155i −0.945590 + 1.42805i
\(623\) 18.1227 + 26.0685i 0.726070 + 1.04441i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 39.6377 + 26.2462i 1.58424 + 1.04901i
\(627\) 0 0
\(628\) −0.453349 + 0.192236i −0.0180906 + 0.00767105i
\(629\) 2.24621i 0.0895623i
\(630\) 0 0
\(631\) 14.1498i 0.563293i 0.959518 + 0.281647i \(0.0908806\pi\)
−0.959518 + 0.281647i \(0.909119\pi\)
\(632\) −0.684658 + 3.68260i −0.0272343 + 0.146486i
\(633\) 0 0
\(634\) −9.56155 + 14.4401i −0.379738 + 0.573489i
\(635\) 17.7509 0.704421
\(636\) 0 0
\(637\) 13.1231 + 4.87689i 0.519956 + 0.193230i
\(638\) 11.1231 + 7.36520i 0.440368 + 0.291591i
\(639\) 0 0
\(640\) −6.55789 9.21922i −0.259223 0.364422i
\(641\) 7.12311 0.281346 0.140673 0.990056i \(-0.455073\pi\)
0.140673 + 0.990056i \(0.455073\pi\)
\(642\) 0 0
\(643\) 33.9686 1.33959 0.669795 0.742546i \(-0.266382\pi\)
0.669795 + 0.742546i \(0.266382\pi\)
\(644\) −18.0894 + 28.7093i −0.712821 + 1.13130i
\(645\) 0 0
\(646\) 6.24621 + 4.13595i 0.245754 + 0.162727i
\(647\) −40.1725 −1.57934 −0.789672 0.613529i \(-0.789749\pi\)
−0.789672 + 0.613529i \(0.789749\pi\)
\(648\) 0 0
\(649\) 9.75379i 0.382870i
\(650\) −2.35829 1.56155i −0.0924999 0.0612491i
\(651\) 0 0
\(652\) −5.56155 + 2.35829i −0.217807 + 0.0923579i
\(653\) 22.9848 0.899466 0.449733 0.893163i \(-0.351519\pi\)
0.449733 + 0.893163i \(0.351519\pi\)
\(654\) 0 0
\(655\) 17.5420i 0.685425i
\(656\) −3.22925 3.12311i −0.126081 0.121937i
\(657\) 0 0
\(658\) −0.430661 19.0343i −0.0167889 0.742033i
\(659\) 1.32431i 0.0515877i 0.999667 + 0.0257938i \(0.00821134\pi\)
−0.999667 + 0.0257938i \(0.991789\pi\)
\(660\) 0 0
\(661\) 12.2462i 0.476322i −0.971226 0.238161i \(-0.923455\pi\)
0.971226 0.238161i \(-0.0765447\pi\)
\(662\) −21.5616 14.2771i −0.838014 0.554894i
\(663\) 0 0
\(664\) 8.39919 + 1.56155i 0.325952 + 0.0606000i
\(665\) −7.12311 10.2462i −0.276222 0.397331i
\(666\) 0 0
\(667\) 12.8255i 0.496604i
\(668\) −15.4741 36.4924i −0.598710 1.41193i
\(669\) 0 0
\(670\) 2.93893 4.43845i 0.113541 0.171472i
\(671\) −9.43318 −0.364164
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −9.56155 + 14.4401i −0.368297 + 0.556211i
\(675\) 0 0
\(676\) −7.02699 16.5717i −0.270269 0.637373i
\(677\) 32.7386i 1.25825i 0.777305 + 0.629124i \(0.216586\pi\)
−0.777305 + 0.629124i \(0.783414\pi\)
\(678\) 0 0
\(679\) 1.69614 + 2.43981i 0.0650919 + 0.0936313i
\(680\) 3.12311 + 0.580639i 0.119766 + 0.0222665i
\(681\) 0 0
\(682\) −18.8664 12.4924i −0.722430 0.478360i
\(683\) 0.371834i 0.0142278i −0.999975 0.00711392i \(-0.997736\pi\)
0.999975 0.00711392i \(-0.00226445\pi\)
\(684\) 0 0
\(685\) 14.0000i 0.534913i
\(686\) 24.7512 + 8.56616i 0.945004 + 0.327058i
\(687\) 0 0
\(688\) −1.06913 1.03399i −0.0407602 0.0394204i
\(689\) 4.00000i 0.152388i
\(690\) 0 0
\(691\) −14.8934 −0.566573 −0.283286 0.959035i \(-0.591425\pi\)
−0.283286 + 0.959035i \(0.591425\pi\)
\(692\) 29.9142 12.6847i 1.13717 0.482198i
\(693\) 0 0
\(694\) −6.68466 4.42627i −0.253746 0.168019i
\(695\) 16.7984i 0.637199i
\(696\) 0 0
\(697\) 1.26137 0.0477777
\(698\) 35.2114 + 23.3153i 1.33277 + 0.882499i
\(699\) 0 0
\(700\) −4.47692 2.82085i −0.169212 0.106618i
\(701\) −11.1231 −0.420114 −0.210057 0.977689i \(-0.567365\pi\)
−0.210057 + 0.977689i \(0.567365\pi\)
\(702\) 0 0
\(703\) −9.43318 −0.355779
\(704\) −13.5616 + 35.2114i −0.511120 + 1.32708i
\(705\) 0 0
\(706\) 22.8393 + 15.1231i 0.859568 + 0.569166i
\(707\) −22.8393 32.8531i −0.858959 1.23557i
\(708\) 0 0
\(709\) 44.7386 1.68019 0.840097 0.542436i \(-0.182498\pi\)
0.840097 + 0.542436i \(0.182498\pi\)
\(710\) −5.75058 + 8.68466i −0.215815 + 0.325929i
\(711\) 0 0
\(712\) −6.20393 + 33.3693i −0.232502 + 1.25057i
\(713\) 21.7538i 0.814686i
\(714\) 0 0
\(715\) 9.43318i 0.352781i
\(716\) −19.8078 + 8.39919i −0.740251 + 0.313892i
\(717\) 0 0
\(718\) 18.9309 + 12.5351i 0.706494 + 0.467807i
\(719\) −22.6762 −0.845681 −0.422841 0.906204i \(-0.638967\pi\)
−0.422841 + 0.906204i \(0.638967\pi\)
\(720\) 0 0
\(721\) 16.8078 11.6847i 0.625954 0.435159i
\(722\) 2.53457 3.82776i 0.0943267 0.142455i
\(723\) 0 0
\(724\) −27.8462 + 11.8078i −1.03490 + 0.438832i
\(725\) −2.00000 −0.0742781
\(726\) 0 0
\(727\) −9.64198 −0.357601 −0.178801 0.983885i \(-0.557222\pi\)
−0.178801 + 0.983885i \(0.557222\pi\)
\(728\) 6.15298 + 13.6433i 0.228045 + 0.505656i
\(729\) 0 0
\(730\) 12.0000 18.1227i 0.444140 0.670751i
\(731\) 0.417609 0.0154458
\(732\) 0 0
\(733\) 0.738634i 0.0272821i 0.999907 + 0.0136410i \(0.00434221\pi\)
−0.999907 + 0.0136410i \(0.995658\pi\)
\(734\) −8.10887 + 12.2462i −0.299304 + 0.452016i
\(735\) 0 0
\(736\) −35.4233 + 7.81855i −1.30572 + 0.288196i
\(737\) −17.7538 −0.653969
\(738\) 0 0
\(739\) 37.5697i 1.38202i −0.722844 0.691012i \(-0.757165\pi\)
0.722844 0.691012i \(-0.242835\pi\)
\(740\) −3.68260 + 1.56155i −0.135375 + 0.0574038i
\(741\) 0 0
\(742\) −0.169271 7.48140i −0.00621413 0.274651i
\(743\) 23.7917i 0.872835i 0.899744 + 0.436417i \(0.143753\pi\)
−0.899744 + 0.436417i \(0.856247\pi\)
\(744\) 0 0
\(745\) 5.36932i 0.196717i
\(746\) −8.19224 + 12.3721i −0.299939 + 0.452975i
\(747\) 0 0
\(748\) −4.13595 9.75379i −0.151225 0.356634i
\(749\) 8.56155 + 12.3153i 0.312832 + 0.449993i
\(750\) 0 0
\(751\) 28.8802i 1.05385i 0.849911 + 0.526926i \(0.176656\pi\)
−0.849911 + 0.526926i \(0.823344\pi\)
\(752\) 14.1498 14.6307i 0.515989 0.533526i
\(753\) 0 0
\(754\) 4.71659 + 3.12311i 0.171768 + 0.113737i
\(755\) 10.0138 0.364440
\(756\) 0 0
\(757\) 4.24621 0.154331 0.0771656 0.997018i \(-0.475413\pi\)
0.0771656 + 0.997018i \(0.475413\pi\)
\(758\) −17.5616 11.6284i −0.637864 0.422364i
\(759\) 0 0
\(760\) 2.43845 13.1158i 0.0884518 0.475759i
\(761\) 47.2311i 1.71212i 0.516873 + 0.856062i \(0.327096\pi\)
−0.516873 + 0.856062i \(0.672904\pi\)
\(762\) 0 0
\(763\) 15.4741 10.7575i 0.560199 0.389447i
\(764\) 30.9309 13.1158i 1.11904 0.474512i
\(765\) 0 0
\(766\) 14.8934 22.4924i 0.538122 0.812684i
\(767\) 4.13595i 0.149341i
\(768\) 0 0
\(769\) 27.2311i 0.981977i −0.871166 0.490989i \(-0.836636\pi\)
0.871166 0.490989i \(-0.163364\pi\)
\(770\) 0.399190 + 17.6433i 0.0143858 + 0.635822i
\(771\) 0 0
\(772\) 17.5616 + 41.4153i 0.632054 + 1.49057i
\(773\) 32.7386i 1.17753i 0.808305 + 0.588763i \(0.200385\pi\)
−0.808305 + 0.588763i \(0.799615\pi\)
\(774\) 0 0
\(775\) 3.39228 0.121854
\(776\) −0.580639 + 3.12311i −0.0208437 + 0.112113i
\(777\) 0 0
\(778\) 5.56155 8.39919i 0.199391 0.301126i
\(779\) 5.29723i 0.189793i
\(780\) 0 0
\(781\) 34.7386 1.24305
\(782\) 5.62329 8.49242i 0.201088 0.303688i
\(783\) 0 0
\(784\) 12.0856 + 25.2574i 0.431628 + 0.902052i
\(785\) −0.246211 −0.00878766
\(786\) 0 0
\(787\) 3.02045 0.107667 0.0538337 0.998550i \(-0.482856\pi\)
0.0538337 + 0.998550i \(0.482856\pi\)
\(788\) 14.0540 + 33.1434i 0.500652 + 1.18069i
\(789\) 0 0
\(790\) −1.03399 + 1.56155i −0.0367876 + 0.0555576i
\(791\) 40.1725 27.9277i 1.42837 0.992995i
\(792\) 0 0
\(793\) −4.00000 −0.142044
\(794\) −16.5081 10.9309i −0.585849 0.387922i
\(795\) 0 0
\(796\) 20.9343 + 49.3693i 0.741998 + 1.74985i
\(797\) 3.75379i 0.132966i 0.997788 + 0.0664830i \(0.0211778\pi\)
−0.997788 + 0.0664830i \(0.978822\pi\)
\(798\) 0 0
\(799\) 5.71484i 0.202176i
\(800\) −1.21922 5.52390i −0.0431061 0.195299i
\(801\) 0 0
\(802\) −4.68466 + 7.07488i −0.165421 + 0.249823i
\(803\) −72.4908 −2.55814
\(804\) 0 0
\(805\) −13.9309 + 9.68466i −0.490999 + 0.341339i
\(806\) −8.00000 5.29723i −0.281788 0.186587i
\(807\) 0 0
\(808\) 7.81855 42.0540i 0.275056 1.47945i
\(809\) −46.9848 −1.65190 −0.825950 0.563744i \(-0.809360\pi\)
−0.825950 + 0.563744i \(0.809360\pi\)
\(810\) 0 0
\(811\) 8.10887 0.284741 0.142370 0.989813i \(-0.454528\pi\)
0.142370 + 0.989813i \(0.454528\pi\)
\(812\) 8.95383 + 5.64171i 0.314218 + 0.197985i
\(813\) 0 0
\(814\) 11.1231 + 7.36520i 0.389865 + 0.258150i
\(815\) −3.02045 −0.105802
\(816\) 0 0
\(817\) 1.75379i 0.0613573i
\(818\) −20.1907 13.3693i −0.705950 0.467447i
\(819\) 0 0
\(820\) −0.876894 2.06798i −0.0306225 0.0722168i
\(821\) −15.6155 −0.544986 −0.272493 0.962158i \(-0.587848\pi\)
−0.272493 + 0.962158i \(0.587848\pi\)
\(822\) 0 0
\(823\) 29.0890i 1.01398i 0.861953 + 0.506989i \(0.169242\pi\)
−0.861953 + 0.506989i \(0.830758\pi\)
\(824\) 21.5150 + 4.00000i 0.749509 + 0.139347i
\(825\) 0 0
\(826\) 0.175024 + 7.73567i 0.00608986 + 0.269159i
\(827\) 24.5354i 0.853180i −0.904445 0.426590i \(-0.859715\pi\)
0.904445 0.426590i \(-0.140285\pi\)
\(828\) 0 0
\(829\) 15.7538i 0.547152i 0.961850 + 0.273576i \(0.0882065\pi\)
−0.961850 + 0.273576i \(0.911794\pi\)
\(830\) 3.56155 + 2.35829i 0.123623 + 0.0818576i
\(831\) 0 0
\(832\) −5.75058 + 14.9309i −0.199365 + 0.517635i
\(833\) −7.36932 2.73863i −0.255332 0.0948880i
\(834\) 0 0
\(835\) 19.8188i 0.685859i
\(836\) −40.9620 + 17.3693i −1.41670 + 0.600730i
\(837\) 0 0
\(838\) 18.4130 27.8078i 0.636067 0.960603i
\(839\) −10.9205 −0.377018 −0.188509 0.982071i \(-0.560365\pi\)
−0.188509 + 0.982071i \(0.560365\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 18.4384 27.8462i 0.635431 0.959643i
\(843\) 0 0
\(844\) −40.6847 + 17.2517i −1.40042 + 0.593829i
\(845\) 9.00000i 0.309609i
\(846\) 0 0
\(847\) 24.4310 16.9843i 0.839460 0.583587i
\(848\) 5.56155 5.75058i 0.190985 0.197476i
\(849\) 0 0
\(850\) 1.32431 + 0.876894i 0.0454234 + 0.0300772i
\(851\) 12.8255i 0.439651i
\(852\) 0 0
\(853\) 24.2462i 0.830174i 0.909782 + 0.415087i \(0.136249\pi\)
−0.909782 + 0.415087i \(0.863751\pi\)
\(854\) −7.48140 + 0.169271i −0.256008 + 0.00579233i
\(855\) 0 0
\(856\) −2.93087 + 15.7644i −0.100175 + 0.538816i
\(857\) 25.6155i 0.875010i −0.899216 0.437505i \(-0.855862\pi\)
0.899216 0.437505i \(-0.144138\pi\)
\(858\) 0 0
\(859\) −3.55531 −0.121306 −0.0606528 0.998159i \(-0.519318\pi\)
−0.0606528 + 0.998159i \(0.519318\pi\)
\(860\) −0.290319 0.684658i −0.00989981 0.0233467i
\(861\) 0 0
\(862\) 6.93087 + 4.58930i 0.236066 + 0.156312i
\(863\) 10.2226i 0.347982i −0.984747 0.173991i \(-0.944334\pi\)
0.984747 0.173991i \(-0.0556664\pi\)
\(864\) 0 0
\(865\) 16.2462 0.552388
\(866\) 34.9211 + 23.1231i 1.18667 + 0.785755i
\(867\) 0 0
\(868\) −15.1870 9.56913i −0.515479 0.324797i
\(869\) 6.24621 0.211888
\(870\) 0 0
\(871\) −7.52823 −0.255084
\(872\) 19.8078 + 3.68260i 0.670776 + 0.124709i
\(873\) 0 0
\(874\) −35.6647 23.6155i −1.20638 0.798807i
\(875\) −1.51022 2.17238i −0.0510549 0.0734398i
\(876\) 0 0
\(877\) 0.738634 0.0249419 0.0124709 0.999922i \(-0.496030\pi\)
0.0124709 + 0.999922i \(0.496030\pi\)
\(878\) 12.6624 19.1231i 0.427336 0.645374i
\(879\) 0 0
\(880\) −13.1158 + 13.5616i −0.442133 + 0.457160i
\(881\) 31.3693i 1.05686i −0.848977 0.528430i \(-0.822781\pi\)
0.848977 0.528430i \(-0.177219\pi\)
\(882\) 0 0
\(883\) 31.3200i 1.05400i 0.849865 + 0.527001i \(0.176683\pi\)
−0.849865 + 0.527001i \(0.823317\pi\)
\(884\) −1.75379 4.13595i −0.0589863 0.139107i
\(885\) 0 0
\(886\) −27.1771 17.9954i −0.913032 0.604567i
\(887\) −29.9957 −1.00716 −0.503578 0.863950i \(-0.667983\pi\)
−0.503578 + 0.863950i \(0.667983\pi\)
\(888\) 0 0
\(889\) −26.8078 38.5616i −0.899104 1.29331i
\(890\) −9.36932 + 14.1498i −0.314060 + 0.474301i
\(891\) 0 0
\(892\) −16.0547 37.8617i −0.537552 1.26770i
\(893\) 24.0000 0.803129
\(894\) 0 0
\(895\) −10.7575 −0.359583
\(896\) −10.1238 + 28.1693i −0.338211 + 0.941070i
\(897\) 0 0
\(898\) 12.1922 18.4130i 0.406860 0.614450i
\(899\) −6.78456 −0.226278
\(900\) 0 0
\(901\) 2.24621i 0.0748321i
\(902\) −4.13595 + 6.24621i −0.137712 + 0.207976i
\(903\) 0 0
\(904\) 51.4233 + 9.56047i 1.71031 + 0.317976i
\(905\) −15.1231 −0.502709
\(906\) 0 0
\(907\) 52.8350i 1.75436i −0.480166 0.877178i \(-0.659423\pi\)
0.480166 0.877178i \(-0.340577\pi\)
\(908\) −2.93893 6.93087i −0.0975319 0.230009i
\(909\) 0 0
\(910\) 0.169271 + 7.48140i 0.00561127 + 0.248006i
\(911\) 2.06798i 0.0685151i 0.999413 + 0.0342575i \(0.0109066\pi\)
−0.999413 + 0.0342575i \(0.989093\pi\)
\(912\) 0 0
\(913\) 14.2462i 0.471481i
\(914\) 4.68466 7.07488i 0.154955 0.234016i
\(915\) 0 0
\(916\) −23.7102 + 10.0540i −0.783408 + 0.332193i
\(917\) 38.1080 26.4924i 1.25844 0.874857i
\(918\) 0 0
\(919\) 9.27015i 0.305794i 0.988242 + 0.152897i \(0.0488603\pi\)
−0.988242 + 0.152897i \(0.951140\pi\)
\(920\) −17.8324 3.31534i −0.587916 0.109304i
\(921\) 0 0
\(922\) −4.26324 2.82292i −0.140402 0.0929679i
\(923\) 14.7304 0.484857
\(924\) 0 0
\(925\) −2.00000 −0.0657596
\(926\) 33.8078 + 22.3859i 1.11099 + 0.735647i
\(927\) 0 0
\(928\) 2.43845 + 11.0478i 0.0800460 + 0.362662i
\(929\) 21.1231i 0.693027i 0.938045 + 0.346513i \(0.112634\pi\)
−0.938045 + 0.346513i \(0.887366\pi\)
\(930\) 0 0
\(931\) −11.5012 + 30.9481i −0.376935 + 1.01428i
\(932\) 6.05398 + 14.2771i 0.198305 + 0.467661i
\(933\) 0 0
\(934\) −14.4401 + 21.8078i −0.472494 + 0.713572i
\(935\) 5.29723i 0.173238i
\(936\) 0 0
\(937\) 38.1080i 1.24493i −0.782647 0.622466i \(-0.786131\pi\)
0.782647 0.622466i \(-0.213869\pi\)
\(938\) −14.0804 + 0.318577i −0.459742 + 0.0104019i
\(939\) 0 0
\(940\) 9.36932 3.97292i 0.305593 0.129582i
\(941\) 26.6307i 0.868135i −0.900880 0.434068i \(-0.857078\pi\)
0.900880 0.434068i \(-0.142922\pi\)
\(942\) 0 0
\(943\) −7.20217 −0.234535
\(944\) −5.75058 + 5.94602i −0.187165 + 0.193527i
\(945\) 0 0
\(946\) −1.36932 + 2.06798i −0.0445203 + 0.0672357i
\(947\) 35.8735i 1.16573i 0.812568 + 0.582867i \(0.198069\pi\)
−0.812568 + 0.582867i \(0.801931\pi\)
\(948\) 0 0
\(949\) −30.7386 −0.997818
\(950\) 3.68260 5.56155i 0.119479 0.180441i
\(951\) 0 0
\(952\) −3.45522 7.66146i −0.111984 0.248309i
\(953\) −28.2462 −0.914985 −0.457492 0.889214i \(-0.651252\pi\)
−0.457492 + 0.889214i \(0.651252\pi\)
\(954\) 0 0
\(955\) 16.7984 0.543583
\(956\) 7.31534 3.10196i 0.236595 0.100325i
\(957\) 0 0
\(958\) 0 0
\(959\) −30.4133 + 21.1431i −0.982096 + 0.682747i
\(960\) 0 0
\(961\) −19.4924 −0.628788
\(962\) 4.71659 + 3.12311i 0.152069 + 0.100693i
\(963\) 0 0
\(964\) −47.1659 + 20.0000i −1.51911 + 0.644157i
\(965\) 22.4924i 0.724057i
\(966\) 0 0
\(967\) 3.43806i 0.110560i −0.998471 0.0552802i \(-0.982395\pi\)
0.998471 0.0552802i \(-0.0176052\pi\)
\(968\) 31.2732 + 5.81422i 1.00516 + 0.186876i
\(969\) 0 0
\(970\) −0.876894 + 1.32431i −0.0281554 + 0.0425209i
\(971\) 10.7575 0.345224 0.172612 0.984990i \(-0.444779\pi\)
0.172612 + 0.984990i \(0.444779\pi\)
\(972\) 0 0
\(973\) −36.4924 + 25.3693i −1.16989 + 0.813303i
\(974\) −15.5616 10.3041i −0.498624 0.330166i
\(975\) 0 0
\(976\) −5.75058 5.56155i −0.184071 0.178021i
\(977\) −22.4924 −0.719596 −0.359798 0.933030i \(-0.617154\pi\)
−0.359798 + 0.933030i \(0.617154\pi\)
\(978\) 0 0
\(979\) 56.5991 1.80891
\(980\) 0.633191 + 13.9857i 0.0202265 + 0.446756i
\(981\) 0 0
\(982\) −37.1771 24.6169i −1.18637 0.785558i
\(983\) −28.5083 −0.909275 −0.454637 0.890677i \(-0.650231\pi\)
−0.454637 + 0.890677i \(0.650231\pi\)
\(984\) 0 0
\(985\) 18.0000i 0.573528i
\(986\) −2.64861 1.75379i −0.0843490 0.0558520i
\(987\) 0 0
\(988\) −17.3693 + 7.36520i −0.552592 + 0.234318i
\(989\) −2.38447 −0.0758218
\(990\) 0 0
\(991\) 48.9078i 1.55361i 0.629743 + 0.776804i \(0.283160\pi\)
−0.629743 + 0.776804i \(0.716840\pi\)
\(992\) −4.13595 18.7386i −0.131317 0.594952i
\(993\) 0 0
\(994\) 27.5510 0.623357i 0.873865 0.0197717i
\(995\) 26.8122i 0.850004i
\(996\) 0 0
\(997\) 5.50758i 0.174427i −0.996190 0.0872134i \(-0.972204\pi\)
0.996190 0.0872134i \(-0.0277962\pi\)
\(998\) 28.6847 + 18.9936i 0.907997 + 0.601233i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1260.2.c.c.811.5 8
3.2 odd 2 140.2.g.c.111.4 yes 8
4.3 odd 2 inner 1260.2.c.c.811.7 8
7.6 odd 2 inner 1260.2.c.c.811.6 8
12.11 even 2 140.2.g.c.111.1 8
15.2 even 4 700.2.c.j.699.1 8
15.8 even 4 700.2.c.i.699.8 8
15.14 odd 2 700.2.g.j.251.5 8
21.2 odd 6 980.2.o.e.31.7 16
21.5 even 6 980.2.o.e.31.8 16
21.11 odd 6 980.2.o.e.411.3 16
21.17 even 6 980.2.o.e.411.4 16
21.20 even 2 140.2.g.c.111.3 yes 8
24.5 odd 2 2240.2.k.e.1791.1 8
24.11 even 2 2240.2.k.e.1791.7 8
28.27 even 2 inner 1260.2.c.c.811.8 8
60.23 odd 4 700.2.c.i.699.2 8
60.47 odd 4 700.2.c.j.699.7 8
60.59 even 2 700.2.g.j.251.8 8
84.11 even 6 980.2.o.e.411.8 16
84.23 even 6 980.2.o.e.31.4 16
84.47 odd 6 980.2.o.e.31.3 16
84.59 odd 6 980.2.o.e.411.7 16
84.83 odd 2 140.2.g.c.111.2 yes 8
105.62 odd 4 700.2.c.i.699.1 8
105.83 odd 4 700.2.c.j.699.8 8
105.104 even 2 700.2.g.j.251.6 8
168.83 odd 2 2240.2.k.e.1791.2 8
168.125 even 2 2240.2.k.e.1791.8 8
420.83 even 4 700.2.c.j.699.2 8
420.167 even 4 700.2.c.i.699.7 8
420.419 odd 2 700.2.g.j.251.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.g.c.111.1 8 12.11 even 2
140.2.g.c.111.2 yes 8 84.83 odd 2
140.2.g.c.111.3 yes 8 21.20 even 2
140.2.g.c.111.4 yes 8 3.2 odd 2
700.2.c.i.699.1 8 105.62 odd 4
700.2.c.i.699.2 8 60.23 odd 4
700.2.c.i.699.7 8 420.167 even 4
700.2.c.i.699.8 8 15.8 even 4
700.2.c.j.699.1 8 15.2 even 4
700.2.c.j.699.2 8 420.83 even 4
700.2.c.j.699.7 8 60.47 odd 4
700.2.c.j.699.8 8 105.83 odd 4
700.2.g.j.251.5 8 15.14 odd 2
700.2.g.j.251.6 8 105.104 even 2
700.2.g.j.251.7 8 420.419 odd 2
700.2.g.j.251.8 8 60.59 even 2
980.2.o.e.31.3 16 84.47 odd 6
980.2.o.e.31.4 16 84.23 even 6
980.2.o.e.31.7 16 21.2 odd 6
980.2.o.e.31.8 16 21.5 even 6
980.2.o.e.411.3 16 21.11 odd 6
980.2.o.e.411.4 16 21.17 even 6
980.2.o.e.411.7 16 84.59 odd 6
980.2.o.e.411.8 16 84.11 even 6
1260.2.c.c.811.5 8 1.1 even 1 trivial
1260.2.c.c.811.6 8 7.6 odd 2 inner
1260.2.c.c.811.7 8 4.3 odd 2 inner
1260.2.c.c.811.8 8 28.27 even 2 inner
2240.2.k.e.1791.1 8 24.5 odd 2
2240.2.k.e.1791.2 8 168.83 odd 2
2240.2.k.e.1791.7 8 24.11 even 2
2240.2.k.e.1791.8 8 168.125 even 2