Properties

Label 121.2.c.d.81.1
Level $121$
Weight $2$
Character 121.81
Analytic conductor $0.966$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [121,2,Mod(3,121)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(121, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("121.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 121.c (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.966189864457\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 121.81
Dual form 121.2.c.d.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(0.618034 - 1.90211i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.61803 - 1.17557i) q^{6} +(0.618034 + 1.90211i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} -1.00000 q^{10} -2.00000 q^{12} +(0.809017 + 0.587785i) q^{13} +(-0.618034 + 1.90211i) q^{14} +(0.618034 + 1.90211i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-4.04508 + 2.93893i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-1.85410 + 5.70634i) q^{19} +(0.809017 + 0.587785i) q^{20} +4.00000 q^{21} +2.00000 q^{23} +(-4.85410 - 3.52671i) q^{24} +(-1.23607 + 3.80423i) q^{25} +(0.309017 + 0.951057i) q^{26} +(3.23607 - 2.35114i) q^{27} +(1.61803 - 1.17557i) q^{28} +(-2.78115 - 8.55951i) q^{29} +(-0.618034 + 1.90211i) q^{30} +(1.61803 + 1.17557i) q^{31} -5.00000 q^{32} -5.00000 q^{34} +(-1.61803 - 1.17557i) q^{35} +(-0.309017 + 0.951057i) q^{36} +(-0.927051 - 2.85317i) q^{37} +(-4.85410 + 3.52671i) q^{38} +(1.61803 - 1.17557i) q^{39} +(0.927051 + 2.85317i) q^{40} +(1.54508 - 4.75528i) q^{41} +(3.23607 + 2.35114i) q^{42} +1.00000 q^{45} +(1.61803 + 1.17557i) q^{46} +(0.618034 - 1.90211i) q^{47} +(-0.618034 - 1.90211i) q^{48} +(2.42705 - 1.76336i) q^{49} +(-3.23607 + 2.35114i) q^{50} +(3.09017 + 9.51057i) q^{51} +(0.309017 - 0.951057i) q^{52} +(-7.28115 - 5.29007i) q^{53} +4.00000 q^{54} +6.00000 q^{56} +(9.70820 + 7.05342i) q^{57} +(2.78115 - 8.55951i) q^{58} +(2.47214 + 7.60845i) q^{59} +(1.61803 - 1.17557i) q^{60} +(4.85410 - 3.52671i) q^{61} +(0.618034 + 1.90211i) q^{62} +(0.618034 - 1.90211i) q^{63} +(-5.66312 - 4.11450i) q^{64} -1.00000 q^{65} +2.00000 q^{67} +(4.04508 + 2.93893i) q^{68} +(1.23607 - 3.80423i) q^{69} +(-0.618034 - 1.90211i) q^{70} +(-9.70820 + 7.05342i) q^{71} +(-2.42705 + 1.76336i) q^{72} +(0.618034 + 1.90211i) q^{73} +(0.927051 - 2.85317i) q^{74} +(6.47214 + 4.70228i) q^{75} +6.00000 q^{76} +2.00000 q^{78} +(-8.09017 - 5.87785i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(-3.39919 - 10.4616i) q^{81} +(4.04508 - 2.93893i) q^{82} +(4.85410 - 3.52671i) q^{83} +(-1.23607 - 3.80423i) q^{84} +(1.54508 - 4.75528i) q^{85} -18.0000 q^{87} -9.00000 q^{89} +(0.809017 + 0.587785i) q^{90} +(-0.618034 + 1.90211i) q^{91} +(-0.618034 - 1.90211i) q^{92} +(3.23607 - 2.35114i) q^{93} +(1.61803 - 1.17557i) q^{94} +(-1.85410 - 5.70634i) q^{95} +(-3.09017 + 9.51057i) q^{96} +(10.5172 + 7.64121i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - 2 q^{7} - 3 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} + q^{13} + 2 q^{14} - 2 q^{15} + q^{16} - 5 q^{17} + q^{18} + 6 q^{19} + q^{20} + 16 q^{21} + 8 q^{23}+ \cdots + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i 0.835853 0.548953i \(-0.184973\pi\)
−0.263792 + 0.964580i \(0.584973\pi\)
\(3\) 0.618034 1.90211i 0.356822 1.09819i −0.598123 0.801404i \(-0.704087\pi\)
0.954945 0.296781i \(-0.0959133\pi\)
\(4\) −0.309017 0.951057i −0.154508 0.475528i
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i −0.753804 0.657099i \(-0.771783\pi\)
0.392000 + 0.919965i \(0.371783\pi\)
\(6\) 1.61803 1.17557i 0.660560 0.479925i
\(7\) 0.618034 + 1.90211i 0.233595 + 0.718931i 0.997305 + 0.0733714i \(0.0233759\pi\)
−0.763710 + 0.645560i \(0.776624\pi\)
\(8\) 0.927051 2.85317i 0.327762 1.00875i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) −2.00000 −0.577350
\(13\) 0.809017 + 0.587785i 0.224381 + 0.163022i 0.694297 0.719689i \(-0.255716\pi\)
−0.469916 + 0.882711i \(0.655716\pi\)
\(14\) −0.618034 + 1.90211i −0.165177 + 0.508361i
\(15\) 0.618034 + 1.90211i 0.159576 + 0.491123i
\(16\) 0.809017 0.587785i 0.202254 0.146946i
\(17\) −4.04508 + 2.93893i −0.981077 + 0.712794i −0.957949 0.286938i \(-0.907363\pi\)
−0.0231281 + 0.999733i \(0.507363\pi\)
\(18\) −0.309017 0.951057i −0.0728360 0.224166i
\(19\) −1.85410 + 5.70634i −0.425360 + 1.30912i 0.477289 + 0.878746i \(0.341620\pi\)
−0.902649 + 0.430377i \(0.858380\pi\)
\(20\) 0.809017 + 0.587785i 0.180902 + 0.131433i
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) −4.85410 3.52671i −0.990839 0.719887i
\(25\) −1.23607 + 3.80423i −0.247214 + 0.760845i
\(26\) 0.309017 + 0.951057i 0.0606032 + 0.186518i
\(27\) 3.23607 2.35114i 0.622782 0.452477i
\(28\) 1.61803 1.17557i 0.305780 0.222162i
\(29\) −2.78115 8.55951i −0.516447 1.58946i −0.780633 0.624989i \(-0.785103\pi\)
0.264186 0.964472i \(-0.414897\pi\)
\(30\) −0.618034 + 1.90211i −0.112837 + 0.347277i
\(31\) 1.61803 + 1.17557i 0.290607 + 0.211139i 0.723531 0.690292i \(-0.242518\pi\)
−0.432923 + 0.901431i \(0.642518\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) −5.00000 −0.857493
\(35\) −1.61803 1.17557i −0.273498 0.198708i
\(36\) −0.309017 + 0.951057i −0.0515028 + 0.158509i
\(37\) −0.927051 2.85317i −0.152406 0.469058i 0.845483 0.534003i \(-0.179313\pi\)
−0.997889 + 0.0649448i \(0.979313\pi\)
\(38\) −4.85410 + 3.52671i −0.787439 + 0.572108i
\(39\) 1.61803 1.17557i 0.259093 0.188242i
\(40\) 0.927051 + 2.85317i 0.146580 + 0.451126i
\(41\) 1.54508 4.75528i 0.241302 0.742650i −0.754921 0.655816i \(-0.772325\pi\)
0.996223 0.0868346i \(-0.0276752\pi\)
\(42\) 3.23607 + 2.35114i 0.499336 + 0.362789i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) 1.61803 + 1.17557i 0.238566 + 0.173328i
\(47\) 0.618034 1.90211i 0.0901495 0.277452i −0.895810 0.444438i \(-0.853403\pi\)
0.985959 + 0.166986i \(0.0534035\pi\)
\(48\) −0.618034 1.90211i −0.0892055 0.274546i
\(49\) 2.42705 1.76336i 0.346722 0.251908i
\(50\) −3.23607 + 2.35114i −0.457649 + 0.332502i
\(51\) 3.09017 + 9.51057i 0.432710 + 1.33175i
\(52\) 0.309017 0.951057i 0.0428529 0.131888i
\(53\) −7.28115 5.29007i −1.00014 0.726647i −0.0380244 0.999277i \(-0.512106\pi\)
−0.962119 + 0.272630i \(0.912106\pi\)
\(54\) 4.00000 0.544331
\(55\) 0 0
\(56\) 6.00000 0.801784
\(57\) 9.70820 + 7.05342i 1.28588 + 0.934249i
\(58\) 2.78115 8.55951i 0.365183 1.12392i
\(59\) 2.47214 + 7.60845i 0.321845 + 0.990536i 0.972845 + 0.231458i \(0.0743497\pi\)
−0.651000 + 0.759078i \(0.725650\pi\)
\(60\) 1.61803 1.17557i 0.208887 0.151765i
\(61\) 4.85410 3.52671i 0.621504 0.451549i −0.231942 0.972730i \(-0.574508\pi\)
0.853447 + 0.521180i \(0.174508\pi\)
\(62\) 0.618034 + 1.90211i 0.0784904 + 0.241569i
\(63\) 0.618034 1.90211i 0.0778650 0.239644i
\(64\) −5.66312 4.11450i −0.707890 0.514312i
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 4.04508 + 2.93893i 0.490539 + 0.356397i
\(69\) 1.23607 3.80423i 0.148805 0.457975i
\(70\) −0.618034 1.90211i −0.0738692 0.227346i
\(71\) −9.70820 + 7.05342i −1.15215 + 0.837087i −0.988766 0.149475i \(-0.952242\pi\)
−0.163386 + 0.986562i \(0.552242\pi\)
\(72\) −2.42705 + 1.76336i −0.286031 + 0.207813i
\(73\) 0.618034 + 1.90211i 0.0723354 + 0.222625i 0.980688 0.195580i \(-0.0626591\pi\)
−0.908352 + 0.418206i \(0.862659\pi\)
\(74\) 0.927051 2.85317i 0.107767 0.331674i
\(75\) 6.47214 + 4.70228i 0.747338 + 0.542973i
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) −8.09017 5.87785i −0.910215 0.661310i 0.0308541 0.999524i \(-0.490177\pi\)
−0.941069 + 0.338214i \(0.890177\pi\)
\(80\) −0.309017 + 0.951057i −0.0345492 + 0.106331i
\(81\) −3.39919 10.4616i −0.377687 1.16240i
\(82\) 4.04508 2.93893i 0.446705 0.324550i
\(83\) 4.85410 3.52671i 0.532807 0.387107i −0.288600 0.957450i \(-0.593190\pi\)
0.821407 + 0.570343i \(0.193190\pi\)
\(84\) −1.23607 3.80423i −0.134866 0.415075i
\(85\) 1.54508 4.75528i 0.167588 0.515783i
\(86\) 0 0
\(87\) −18.0000 −1.92980
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0.809017 + 0.587785i 0.0852779 + 0.0619580i
\(91\) −0.618034 + 1.90211i −0.0647876 + 0.199396i
\(92\) −0.618034 1.90211i −0.0644345 0.198309i
\(93\) 3.23607 2.35114i 0.335565 0.243802i
\(94\) 1.61803 1.17557i 0.166887 0.121251i
\(95\) −1.85410 5.70634i −0.190227 0.585458i
\(96\) −3.09017 + 9.51057i −0.315389 + 0.970668i
\(97\) 10.5172 + 7.64121i 1.06786 + 0.775847i 0.975527 0.219881i \(-0.0705669\pi\)
0.0923353 + 0.995728i \(0.470567\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −8.09017 5.87785i −0.805002 0.584868i 0.107375 0.994219i \(-0.465755\pi\)
−0.912377 + 0.409350i \(0.865755\pi\)
\(102\) −3.09017 + 9.51057i −0.305972 + 0.941686i
\(103\) 2.47214 + 7.60845i 0.243587 + 0.749683i 0.995866 + 0.0908382i \(0.0289546\pi\)
−0.752279 + 0.658845i \(0.771045\pi\)
\(104\) 2.42705 1.76336i 0.237992 0.172911i
\(105\) −3.23607 + 2.35114i −0.315808 + 0.229448i
\(106\) −2.78115 8.55951i −0.270129 0.831373i
\(107\) −1.85410 + 5.70634i −0.179243 + 0.551653i −0.999802 0.0199092i \(-0.993662\pi\)
0.820559 + 0.571562i \(0.193662\pi\)
\(108\) −3.23607 2.35114i −0.311391 0.226239i
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) 1.61803 + 1.17557i 0.152890 + 0.111081i
\(113\) −2.78115 + 8.55951i −0.261629 + 0.805211i 0.730822 + 0.682568i \(0.239137\pi\)
−0.992451 + 0.122643i \(0.960863\pi\)
\(114\) 3.70820 + 11.4127i 0.347305 + 1.06890i
\(115\) −1.61803 + 1.17557i −0.150882 + 0.109623i
\(116\) −7.28115 + 5.29007i −0.676038 + 0.491170i
\(117\) −0.309017 0.951057i −0.0285686 0.0879252i
\(118\) −2.47214 + 7.60845i −0.227579 + 0.700415i
\(119\) −8.09017 5.87785i −0.741625 0.538822i
\(120\) 6.00000 0.547723
\(121\) 0 0
\(122\) 6.00000 0.543214
\(123\) −8.09017 5.87785i −0.729466 0.529988i
\(124\) 0.618034 1.90211i 0.0555011 0.170815i
\(125\) −2.78115 8.55951i −0.248754 0.765586i
\(126\) 1.61803 1.17557i 0.144146 0.104728i
\(127\) −12.9443 + 9.40456i −1.14862 + 0.834520i −0.988297 0.152545i \(-0.951253\pi\)
−0.160322 + 0.987065i \(0.551253\pi\)
\(128\) 0.927051 + 2.85317i 0.0819405 + 0.252187i
\(129\) 0 0
\(130\) −0.809017 0.587785i −0.0709555 0.0515522i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −12.0000 −1.04053
\(134\) 1.61803 + 1.17557i 0.139777 + 0.101554i
\(135\) −1.23607 + 3.80423i −0.106384 + 0.327416i
\(136\) 4.63525 + 14.2658i 0.397470 + 1.22329i
\(137\) 8.09017 5.87785i 0.691190 0.502179i −0.185861 0.982576i \(-0.559507\pi\)
0.877051 + 0.480397i \(0.159507\pi\)
\(138\) 3.23607 2.35114i 0.275472 0.200142i
\(139\) 0.618034 + 1.90211i 0.0524210 + 0.161335i 0.973840 0.227236i \(-0.0729688\pi\)
−0.921419 + 0.388571i \(0.872969\pi\)
\(140\) −0.618034 + 1.90211i −0.0522334 + 0.160758i
\(141\) −3.23607 2.35114i −0.272526 0.198002i
\(142\) −12.0000 −1.00702
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) 7.28115 + 5.29007i 0.604667 + 0.439316i
\(146\) −0.618034 + 1.90211i −0.0511489 + 0.157420i
\(147\) −1.85410 5.70634i −0.152924 0.470651i
\(148\) −2.42705 + 1.76336i −0.199502 + 0.144947i
\(149\) 13.7533 9.99235i 1.12671 0.818605i 0.141500 0.989938i \(-0.454807\pi\)
0.985213 + 0.171333i \(0.0548074\pi\)
\(150\) 2.47214 + 7.60845i 0.201849 + 0.621228i
\(151\) 4.94427 15.2169i 0.402359 1.23833i −0.520721 0.853727i \(-0.674337\pi\)
0.923080 0.384607i \(-0.125663\pi\)
\(152\) 14.5623 + 10.5801i 1.18116 + 0.858162i
\(153\) 5.00000 0.404226
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) −1.61803 1.17557i −0.129546 0.0941210i
\(157\) 0.618034 1.90211i 0.0493245 0.151805i −0.923361 0.383934i \(-0.874569\pi\)
0.972685 + 0.232129i \(0.0745691\pi\)
\(158\) −3.09017 9.51057i −0.245841 0.756620i
\(159\) −14.5623 + 10.5801i −1.15487 + 0.839059i
\(160\) 4.04508 2.93893i 0.319792 0.232343i
\(161\) 1.23607 + 3.80423i 0.0974158 + 0.299815i
\(162\) 3.39919 10.4616i 0.267065 0.821943i
\(163\) 1.61803 + 1.17557i 0.126734 + 0.0920778i 0.649347 0.760493i \(-0.275042\pi\)
−0.522612 + 0.852570i \(0.675042\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) 9.70820 + 7.05342i 0.751243 + 0.545810i 0.896212 0.443626i \(-0.146308\pi\)
−0.144969 + 0.989436i \(0.546308\pi\)
\(168\) 3.70820 11.4127i 0.286094 0.880507i
\(169\) −3.70820 11.4127i −0.285246 0.877898i
\(170\) 4.04508 2.93893i 0.310244 0.225405i
\(171\) 4.85410 3.52671i 0.371202 0.269694i
\(172\) 0 0
\(173\) −1.85410 + 5.70634i −0.140965 + 0.433845i −0.996470 0.0839492i \(-0.973247\pi\)
0.855505 + 0.517794i \(0.173247\pi\)
\(174\) −14.5623 10.5801i −1.10397 0.802078i
\(175\) −8.00000 −0.604743
\(176\) 0 0
\(177\) 16.0000 1.20263
\(178\) −7.28115 5.29007i −0.545745 0.396507i
\(179\) 7.41641 22.8254i 0.554328 1.70605i −0.143382 0.989667i \(-0.545798\pi\)
0.697710 0.716380i \(-0.254202\pi\)
\(180\) −0.309017 0.951057i −0.0230328 0.0708876i
\(181\) −0.809017 + 0.587785i −0.0601338 + 0.0436897i −0.617446 0.786613i \(-0.711833\pi\)
0.557312 + 0.830303i \(0.311833\pi\)
\(182\) −1.61803 + 1.17557i −0.119937 + 0.0871391i
\(183\) −3.70820 11.4127i −0.274118 0.843649i
\(184\) 1.85410 5.70634i 0.136686 0.420677i
\(185\) 2.42705 + 1.76336i 0.178440 + 0.129644i
\(186\) 4.00000 0.293294
\(187\) 0 0
\(188\) −2.00000 −0.145865
\(189\) 6.47214 + 4.70228i 0.470779 + 0.342041i
\(190\) 1.85410 5.70634i 0.134511 0.413981i
\(191\) 2.47214 + 7.60845i 0.178877 + 0.550528i 0.999789 0.0205267i \(-0.00653431\pi\)
−0.820912 + 0.571055i \(0.806534\pi\)
\(192\) −11.3262 + 8.22899i −0.817401 + 0.593876i
\(193\) −4.04508 + 2.93893i −0.291172 + 0.211549i −0.723775 0.690036i \(-0.757595\pi\)
0.432604 + 0.901584i \(0.357595\pi\)
\(194\) 4.01722 + 12.3637i 0.288420 + 0.887664i
\(195\) −0.618034 + 1.90211i −0.0442583 + 0.136213i
\(196\) −2.42705 1.76336i −0.173361 0.125954i
\(197\) 11.0000 0.783718 0.391859 0.920025i \(-0.371832\pi\)
0.391859 + 0.920025i \(0.371832\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 9.70820 + 7.05342i 0.686474 + 0.498752i
\(201\) 1.23607 3.80423i 0.0871855 0.268329i
\(202\) −3.09017 9.51057i −0.217424 0.669161i
\(203\) 14.5623 10.5801i 1.02207 0.742580i
\(204\) 8.09017 5.87785i 0.566425 0.411532i
\(205\) 1.54508 + 4.75528i 0.107913 + 0.332123i
\(206\) −2.47214 + 7.60845i −0.172242 + 0.530106i
\(207\) −1.61803 1.17557i −0.112461 0.0817078i
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) −4.00000 −0.276026
\(211\) 9.70820 + 7.05342i 0.668340 + 0.485578i 0.869469 0.493987i \(-0.164461\pi\)
−0.201129 + 0.979565i \(0.564461\pi\)
\(212\) −2.78115 + 8.55951i −0.191010 + 0.587869i
\(213\) 7.41641 + 22.8254i 0.508164 + 1.56397i
\(214\) −4.85410 + 3.52671i −0.331820 + 0.241081i
\(215\) 0 0
\(216\) −3.70820 11.4127i −0.252311 0.776534i
\(217\) −1.23607 + 3.80423i −0.0839098 + 0.258248i
\(218\) 8.89919 + 6.46564i 0.602729 + 0.437908i
\(219\) 4.00000 0.270295
\(220\) 0 0
\(221\) −5.00000 −0.336336
\(222\) −4.85410 3.52671i −0.325786 0.236697i
\(223\) −6.18034 + 19.0211i −0.413866 + 1.27375i 0.499395 + 0.866374i \(0.333556\pi\)
−0.913261 + 0.407375i \(0.866444\pi\)
\(224\) −3.09017 9.51057i −0.206471 0.635451i
\(225\) 3.23607 2.35114i 0.215738 0.156743i
\(226\) −7.28115 + 5.29007i −0.484335 + 0.351890i
\(227\) 7.41641 + 22.8254i 0.492244 + 1.51497i 0.821208 + 0.570629i \(0.193301\pi\)
−0.328963 + 0.944343i \(0.606699\pi\)
\(228\) 3.70820 11.4127i 0.245582 0.755823i
\(229\) −7.28115 5.29007i −0.481152 0.349577i 0.320619 0.947208i \(-0.396109\pi\)
−0.801772 + 0.597631i \(0.796109\pi\)
\(230\) −2.00000 −0.131876
\(231\) 0 0
\(232\) −27.0000 −1.77264
\(233\) −16.9894 12.3435i −1.11301 0.808649i −0.129875 0.991530i \(-0.541458\pi\)
−0.983135 + 0.182881i \(0.941458\pi\)
\(234\) 0.309017 0.951057i 0.0202011 0.0621725i
\(235\) 0.618034 + 1.90211i 0.0403161 + 0.124080i
\(236\) 6.47214 4.70228i 0.421300 0.306092i
\(237\) −16.1803 + 11.7557i −1.05103 + 0.763615i
\(238\) −3.09017 9.51057i −0.200306 0.616478i
\(239\) −1.85410 + 5.70634i −0.119932 + 0.369112i −0.992944 0.118587i \(-0.962164\pi\)
0.873012 + 0.487699i \(0.162164\pi\)
\(240\) 1.61803 + 1.17557i 0.104444 + 0.0758827i
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 0 0
\(243\) −10.0000 −0.641500
\(244\) −4.85410 3.52671i −0.310752 0.225775i
\(245\) −0.927051 + 2.85317i −0.0592271 + 0.182282i
\(246\) −3.09017 9.51057i −0.197022 0.606371i
\(247\) −4.85410 + 3.52671i −0.308859 + 0.224399i
\(248\) 4.85410 3.52671i 0.308236 0.223946i
\(249\) −3.70820 11.4127i −0.234998 0.723249i
\(250\) 2.78115 8.55951i 0.175896 0.541351i
\(251\) 1.61803 + 1.17557i 0.102129 + 0.0742014i 0.637678 0.770303i \(-0.279895\pi\)
−0.535548 + 0.844504i \(0.679895\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) −16.0000 −1.00393
\(255\) −8.09017 5.87785i −0.506626 0.368085i
\(256\) −5.25329 + 16.1680i −0.328331 + 1.01050i
\(257\) 5.87132 + 18.0701i 0.366243 + 1.12718i 0.949199 + 0.314676i \(0.101896\pi\)
−0.582956 + 0.812504i \(0.698104\pi\)
\(258\) 0 0
\(259\) 4.85410 3.52671i 0.301619 0.219139i
\(260\) 0.309017 + 0.951057i 0.0191644 + 0.0589820i
\(261\) −2.78115 + 8.55951i −0.172149 + 0.529820i
\(262\) 0 0
\(263\) 22.0000 1.35658 0.678289 0.734795i \(-0.262722\pi\)
0.678289 + 0.734795i \(0.262722\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) −9.70820 7.05342i −0.595248 0.432473i
\(267\) −5.56231 + 17.1190i −0.340408 + 1.04767i
\(268\) −0.618034 1.90211i −0.0377524 0.116190i
\(269\) −0.809017 + 0.587785i −0.0493266 + 0.0358379i −0.612175 0.790722i \(-0.709705\pi\)
0.562849 + 0.826560i \(0.309705\pi\)
\(270\) −3.23607 + 2.35114i −0.196941 + 0.143086i
\(271\) −6.18034 19.0211i −0.375429 1.15545i −0.943189 0.332257i \(-0.892190\pi\)
0.567760 0.823194i \(-0.307810\pi\)
\(272\) −1.54508 + 4.75528i −0.0936845 + 0.288331i
\(273\) 3.23607 + 2.35114i 0.195856 + 0.142298i
\(274\) 10.0000 0.604122
\(275\) 0 0
\(276\) −4.00000 −0.240772
\(277\) 0.809017 + 0.587785i 0.0486091 + 0.0353166i 0.611825 0.790994i \(-0.290436\pi\)
−0.563215 + 0.826310i \(0.690436\pi\)
\(278\) −0.618034 + 1.90211i −0.0370672 + 0.114081i
\(279\) −0.618034 1.90211i −0.0370007 0.113877i
\(280\) −4.85410 + 3.52671i −0.290088 + 0.210761i
\(281\) 4.85410 3.52671i 0.289571 0.210386i −0.433510 0.901149i \(-0.642725\pi\)
0.723081 + 0.690763i \(0.242725\pi\)
\(282\) −1.23607 3.80423i −0.0736068 0.226538i
\(283\) −8.65248 + 26.6296i −0.514336 + 1.58296i 0.270150 + 0.962818i \(0.412927\pi\)
−0.784486 + 0.620146i \(0.787073\pi\)
\(284\) 9.70820 + 7.05342i 0.576076 + 0.418544i
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 10.0000 0.590281
\(288\) 4.04508 + 2.93893i 0.238359 + 0.173178i
\(289\) 2.47214 7.60845i 0.145420 0.447556i
\(290\) 2.78115 + 8.55951i 0.163315 + 0.502632i
\(291\) 21.0344 15.2824i 1.23306 0.895871i
\(292\) 1.61803 1.17557i 0.0946883 0.0687951i
\(293\) −2.78115 8.55951i −0.162477 0.500052i 0.836365 0.548173i \(-0.184677\pi\)
−0.998841 + 0.0481214i \(0.984677\pi\)
\(294\) 1.85410 5.70634i 0.108133 0.332800i
\(295\) −6.47214 4.70228i −0.376822 0.273777i
\(296\) −9.00000 −0.523114
\(297\) 0 0
\(298\) 17.0000 0.984784
\(299\) 1.61803 + 1.17557i 0.0935733 + 0.0679850i
\(300\) 2.47214 7.60845i 0.142729 0.439274i
\(301\) 0 0
\(302\) 12.9443 9.40456i 0.744859 0.541172i
\(303\) −16.1803 + 11.7557i −0.929536 + 0.675348i
\(304\) 1.85410 + 5.70634i 0.106340 + 0.327281i
\(305\) −1.85410 + 5.70634i −0.106166 + 0.326744i
\(306\) 4.04508 + 2.93893i 0.231242 + 0.168007i
\(307\) 22.0000 1.25561 0.627803 0.778372i \(-0.283954\pi\)
0.627803 + 0.778372i \(0.283954\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) −1.61803 1.17557i −0.0918982 0.0667679i
\(311\) 7.41641 22.8254i 0.420546 1.29431i −0.486649 0.873597i \(-0.661781\pi\)
0.907195 0.420710i \(-0.138219\pi\)
\(312\) −1.85410 5.70634i −0.104968 0.323058i
\(313\) −18.6074 + 13.5191i −1.05175 + 0.764142i −0.972545 0.232716i \(-0.925239\pi\)
−0.0792071 + 0.996858i \(0.525239\pi\)
\(314\) 1.61803 1.17557i 0.0913109 0.0663413i
\(315\) 0.618034 + 1.90211i 0.0348223 + 0.107172i
\(316\) −3.09017 + 9.51057i −0.173836 + 0.535011i
\(317\) 1.61803 + 1.17557i 0.0908778 + 0.0660266i 0.632296 0.774727i \(-0.282113\pi\)
−0.541418 + 0.840753i \(0.682113\pi\)
\(318\) −18.0000 −1.00939
\(319\) 0 0
\(320\) 7.00000 0.391312
\(321\) 9.70820 + 7.05342i 0.541859 + 0.393684i
\(322\) −1.23607 + 3.80423i −0.0688834 + 0.212001i
\(323\) −9.27051 28.5317i −0.515825 1.58755i
\(324\) −8.89919 + 6.46564i −0.494399 + 0.359202i
\(325\) −3.23607 + 2.35114i −0.179505 + 0.130418i
\(326\) 0.618034 + 1.90211i 0.0342297 + 0.105348i
\(327\) 6.79837 20.9232i 0.375951 1.15706i
\(328\) −12.1353 8.81678i −0.670057 0.486825i
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) −4.85410 3.52671i −0.266403 0.193553i
\(333\) −0.927051 + 2.85317i −0.0508021 + 0.156353i
\(334\) 3.70820 + 11.4127i 0.202904 + 0.624474i
\(335\) −1.61803 + 1.17557i −0.0884026 + 0.0642283i
\(336\) 3.23607 2.35114i 0.176542 0.128265i
\(337\) 4.01722 + 12.3637i 0.218832 + 0.673496i 0.998859 + 0.0477501i \(0.0152051\pi\)
−0.780027 + 0.625745i \(0.784795\pi\)
\(338\) 3.70820 11.4127i 0.201700 0.620768i
\(339\) 14.5623 + 10.5801i 0.790916 + 0.574634i
\(340\) −5.00000 −0.271163
\(341\) 0 0
\(342\) 6.00000 0.324443
\(343\) 16.1803 + 11.7557i 0.873656 + 0.634748i
\(344\) 0 0
\(345\) 1.23607 + 3.80423i 0.0665477 + 0.204813i
\(346\) −4.85410 + 3.52671i −0.260958 + 0.189597i
\(347\) 22.6525 16.4580i 1.21605 0.883511i 0.220283 0.975436i \(-0.429302\pi\)
0.995766 + 0.0919250i \(0.0293020\pi\)
\(348\) 5.56231 + 17.1190i 0.298171 + 0.917676i
\(349\) 8.34346 25.6785i 0.446615 1.37454i −0.434088 0.900871i \(-0.642929\pi\)
0.880703 0.473669i \(-0.157071\pi\)
\(350\) −6.47214 4.70228i −0.345950 0.251348i
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) −9.00000 −0.479022 −0.239511 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(354\) 12.9443 + 9.40456i 0.687980 + 0.499847i
\(355\) 3.70820 11.4127i 0.196811 0.605722i
\(356\) 2.78115 + 8.55951i 0.147401 + 0.453653i
\(357\) −16.1803 + 11.7557i −0.856354 + 0.622178i
\(358\) 19.4164 14.1068i 1.02619 0.745570i
\(359\) 0.618034 + 1.90211i 0.0326186 + 0.100390i 0.966040 0.258391i \(-0.0831924\pi\)
−0.933422 + 0.358781i \(0.883192\pi\)
\(360\) 0.927051 2.85317i 0.0488599 0.150375i
\(361\) −13.7533 9.99235i −0.723857 0.525913i
\(362\) −1.00000 −0.0525588
\(363\) 0 0
\(364\) 2.00000 0.104828
\(365\) −1.61803 1.17557i −0.0846918 0.0615322i
\(366\) 3.70820 11.4127i 0.193831 0.596550i
\(367\) −4.32624 13.3148i −0.225828 0.695026i −0.998207 0.0598642i \(-0.980933\pi\)
0.772379 0.635162i \(-0.219067\pi\)
\(368\) 1.61803 1.17557i 0.0843459 0.0612808i
\(369\) −4.04508 + 2.93893i −0.210579 + 0.152994i
\(370\) 0.927051 + 2.85317i 0.0481951 + 0.148329i
\(371\) 5.56231 17.1190i 0.288781 0.888775i
\(372\) −3.23607 2.35114i −0.167782 0.121901i
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) −18.0000 −0.929516
\(376\) −4.85410 3.52671i −0.250331 0.181876i
\(377\) 2.78115 8.55951i 0.143237 0.440837i
\(378\) 2.47214 + 7.60845i 0.127153 + 0.391337i
\(379\) 25.8885 18.8091i 1.32981 0.966160i 0.330052 0.943963i \(-0.392934\pi\)
0.999754 0.0221971i \(-0.00706614\pi\)
\(380\) −4.85410 + 3.52671i −0.249010 + 0.180916i
\(381\) 9.88854 + 30.4338i 0.506605 + 1.55917i
\(382\) −2.47214 + 7.60845i −0.126485 + 0.389282i
\(383\) −16.1803 11.7557i −0.826777 0.600688i 0.0918688 0.995771i \(-0.470716\pi\)
−0.918646 + 0.395083i \(0.870716\pi\)
\(384\) 6.00000 0.306186
\(385\) 0 0
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) 4.01722 12.3637i 0.203943 0.627674i
\(389\) −0.927051 2.85317i −0.0470034 0.144661i 0.924800 0.380453i \(-0.124232\pi\)
−0.971804 + 0.235791i \(0.924232\pi\)
\(390\) −1.61803 + 1.17557i −0.0819323 + 0.0595273i
\(391\) −8.09017 + 5.87785i −0.409137 + 0.297256i
\(392\) −2.78115 8.55951i −0.140469 0.432320i
\(393\) 0 0
\(394\) 8.89919 + 6.46564i 0.448335 + 0.325734i
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) 13.0000 0.652451 0.326226 0.945292i \(-0.394223\pi\)
0.326226 + 0.945292i \(0.394223\pi\)
\(398\) 19.4164 + 14.1068i 0.973257 + 0.707112i
\(399\) −7.41641 + 22.8254i −0.371285 + 1.14270i
\(400\) 1.23607 + 3.80423i 0.0618034 + 0.190211i
\(401\) −18.6074 + 13.5191i −0.929209 + 0.675110i −0.945799 0.324753i \(-0.894719\pi\)
0.0165902 + 0.999862i \(0.494719\pi\)
\(402\) 3.23607 2.35114i 0.161400 0.117264i
\(403\) 0.618034 + 1.90211i 0.0307865 + 0.0947510i
\(404\) −3.09017 + 9.51057i −0.153742 + 0.473168i
\(405\) 8.89919 + 6.46564i 0.442204 + 0.321280i
\(406\) 18.0000 0.893325
\(407\) 0 0
\(408\) 30.0000 1.48522
\(409\) −16.9894 12.3435i −0.840070 0.610346i 0.0823205 0.996606i \(-0.473767\pi\)
−0.922390 + 0.386260i \(0.873767\pi\)
\(410\) −1.54508 + 4.75528i −0.0763063 + 0.234847i
\(411\) −6.18034 19.0211i −0.304854 0.938243i
\(412\) 6.47214 4.70228i 0.318859 0.231665i
\(413\) −12.9443 + 9.40456i −0.636946 + 0.462768i
\(414\) −0.618034 1.90211i −0.0303747 0.0934838i
\(415\) −1.85410 + 5.70634i −0.0910143 + 0.280113i
\(416\) −4.04508 2.93893i −0.198327 0.144093i
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) 2.00000 0.0977064 0.0488532 0.998806i \(-0.484443\pi\)
0.0488532 + 0.998806i \(0.484443\pi\)
\(420\) 3.23607 + 2.35114i 0.157904 + 0.114724i
\(421\) 4.01722 12.3637i 0.195787 0.602572i −0.804179 0.594387i \(-0.797395\pi\)
0.999967 0.00818455i \(-0.00260525\pi\)
\(422\) 3.70820 + 11.4127i 0.180513 + 0.555560i
\(423\) −1.61803 + 1.17557i −0.0786715 + 0.0571582i
\(424\) −21.8435 + 15.8702i −1.06081 + 0.770725i
\(425\) −6.18034 19.0211i −0.299791 0.922660i
\(426\) −7.41641 + 22.8254i −0.359326 + 1.10589i
\(427\) 9.70820 + 7.05342i 0.469813 + 0.341339i
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) 0 0
\(431\) 9.70820 + 7.05342i 0.467628 + 0.339751i 0.796516 0.604617i \(-0.206674\pi\)
−0.328888 + 0.944369i \(0.606674\pi\)
\(432\) 1.23607 3.80423i 0.0594703 0.183031i
\(433\) 5.87132 + 18.0701i 0.282158 + 0.868392i 0.987236 + 0.159263i \(0.0509118\pi\)
−0.705078 + 0.709129i \(0.749088\pi\)
\(434\) −3.23607 + 2.35114i −0.155336 + 0.112858i
\(435\) 14.5623 10.5801i 0.698209 0.507279i
\(436\) −3.39919 10.4616i −0.162792 0.501021i
\(437\) −3.70820 + 11.4127i −0.177387 + 0.545942i
\(438\) 3.23607 + 2.35114i 0.154625 + 0.112342i
\(439\) −22.0000 −1.05000 −0.525001 0.851101i \(-0.675935\pi\)
−0.525001 + 0.851101i \(0.675935\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) −4.04508 2.93893i −0.192405 0.139790i
\(443\) −6.18034 + 19.0211i −0.293637 + 0.903721i 0.690039 + 0.723772i \(0.257593\pi\)
−0.983676 + 0.179949i \(0.942407\pi\)
\(444\) 1.85410 + 5.70634i 0.0879918 + 0.270811i
\(445\) 7.28115 5.29007i 0.345160 0.250773i
\(446\) −16.1803 + 11.7557i −0.766161 + 0.556649i
\(447\) −10.5066 32.3359i −0.496944 1.52944i
\(448\) 4.32624 13.3148i 0.204396 0.629065i
\(449\) 10.5172 + 7.64121i 0.496338 + 0.360611i 0.807617 0.589708i \(-0.200757\pi\)
−0.311278 + 0.950319i \(0.600757\pi\)
\(450\) 4.00000 0.188562
\(451\) 0 0
\(452\) 9.00000 0.423324
\(453\) −25.8885 18.8091i −1.21635 0.883730i
\(454\) −7.41641 + 22.8254i −0.348069 + 1.07125i
\(455\) −0.618034 1.90211i −0.0289739 0.0891724i
\(456\) 29.1246 21.1603i 1.36388 0.990920i
\(457\) 31.5517 22.9236i 1.47592 1.07232i 0.497083 0.867703i \(-0.334405\pi\)
0.978842 0.204619i \(-0.0655955\pi\)
\(458\) −2.78115 8.55951i −0.129955 0.399960i
\(459\) −6.18034 + 19.0211i −0.288474 + 0.887830i
\(460\) 1.61803 + 1.17557i 0.0754412 + 0.0548113i
\(461\) −33.0000 −1.53696 −0.768482 0.639872i \(-0.778987\pi\)
−0.768482 + 0.639872i \(0.778987\pi\)
\(462\) 0 0
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) −7.28115 5.29007i −0.338019 0.245585i
\(465\) −1.23607 + 3.80423i −0.0573213 + 0.176417i
\(466\) −6.48936 19.9722i −0.300614 0.925194i
\(467\) −9.70820 + 7.05342i −0.449242 + 0.326393i −0.789296 0.614012i \(-0.789555\pi\)
0.340054 + 0.940406i \(0.389555\pi\)
\(468\) −0.809017 + 0.587785i −0.0373968 + 0.0271704i
\(469\) 1.23607 + 3.80423i 0.0570763 + 0.175663i
\(470\) −0.618034 + 1.90211i −0.0285078 + 0.0877379i
\(471\) −3.23607 2.35114i −0.149110 0.108335i
\(472\) 24.0000 1.10469
\(473\) 0 0
\(474\) −20.0000 −0.918630
\(475\) −19.4164 14.1068i −0.890886 0.647266i
\(476\) −3.09017 + 9.51057i −0.141638 + 0.435916i
\(477\) 2.78115 + 8.55951i 0.127340 + 0.391913i
\(478\) −4.85410 + 3.52671i −0.222021 + 0.161308i
\(479\) −12.9443 + 9.40456i −0.591439 + 0.429705i −0.842830 0.538180i \(-0.819112\pi\)
0.251391 + 0.967886i \(0.419112\pi\)
\(480\) −3.09017 9.51057i −0.141046 0.434096i
\(481\) 0.927051 2.85317i 0.0422699 0.130093i
\(482\) −17.7984 12.9313i −0.810694 0.589003i
\(483\) 8.00000 0.364013
\(484\) 0 0
\(485\) −13.0000 −0.590300
\(486\) −8.09017 5.87785i −0.366978 0.266625i
\(487\) 0.618034 1.90211i 0.0280058 0.0861930i −0.936077 0.351796i \(-0.885571\pi\)
0.964082 + 0.265603i \(0.0855711\pi\)
\(488\) −5.56231 17.1190i −0.251794 0.774942i
\(489\) 3.23607 2.35114i 0.146340 0.106322i
\(490\) −2.42705 + 1.76336i −0.109643 + 0.0796603i
\(491\) 0.618034 + 1.90211i 0.0278915 + 0.0858412i 0.964033 0.265782i \(-0.0856300\pi\)
−0.936142 + 0.351623i \(0.885630\pi\)
\(492\) −3.09017 + 9.51057i −0.139316 + 0.428769i
\(493\) 36.4058 + 26.4503i 1.63963 + 1.19126i
\(494\) −6.00000 −0.269953
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) −19.4164 14.1068i −0.870945 0.632779i
\(498\) 3.70820 11.4127i 0.166169 0.511414i
\(499\) 2.47214 + 7.60845i 0.110668 + 0.340601i 0.991019 0.133722i \(-0.0426929\pi\)
−0.880351 + 0.474323i \(0.842693\pi\)
\(500\) −7.28115 + 5.29007i −0.325623 + 0.236579i
\(501\) 19.4164 14.1068i 0.867461 0.630247i
\(502\) 0.618034 + 1.90211i 0.0275842 + 0.0848955i
\(503\) 11.7426 36.1401i 0.523579 1.61141i −0.243531 0.969893i \(-0.578306\pi\)
0.767109 0.641516i \(-0.221694\pi\)
\(504\) −4.85410 3.52671i −0.216219 0.157092i
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) −24.0000 −1.06588
\(508\) 12.9443 + 9.40456i 0.574309 + 0.417260i
\(509\) −12.9787 + 39.9444i −0.575271 + 1.77050i 0.0599820 + 0.998199i \(0.480896\pi\)
−0.635253 + 0.772304i \(0.719104\pi\)
\(510\) −3.09017 9.51057i −0.136835 0.421135i
\(511\) −3.23607 + 2.35114i −0.143155 + 0.104008i
\(512\) −8.89919 + 6.46564i −0.393292 + 0.285744i
\(513\) 7.41641 + 22.8254i 0.327442 + 1.00776i
\(514\) −5.87132 + 18.0701i −0.258973 + 0.797037i
\(515\) −6.47214 4.70228i −0.285196 0.207207i
\(516\) 0 0
\(517\) 0 0
\(518\) 6.00000 0.263625
\(519\) 9.70820 + 7.05342i 0.426143 + 0.309611i
\(520\) −0.927051 + 2.85317i −0.0406539 + 0.125120i
\(521\) 9.27051 + 28.5317i 0.406148 + 1.25000i 0.919933 + 0.392077i \(0.128243\pi\)
−0.513784 + 0.857920i \(0.671757\pi\)
\(522\) −7.28115 + 5.29007i −0.318687 + 0.231540i
\(523\) −12.9443 + 9.40456i −0.566013 + 0.411233i −0.833655 0.552286i \(-0.813756\pi\)
0.267641 + 0.963519i \(0.413756\pi\)
\(524\) 0 0
\(525\) −4.94427 + 15.2169i −0.215786 + 0.664120i
\(526\) 17.7984 + 12.9313i 0.776046 + 0.563830i
\(527\) −10.0000 −0.435607
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 7.28115 + 5.29007i 0.316273 + 0.229786i
\(531\) 2.47214 7.60845i 0.107282 0.330179i
\(532\) 3.70820 + 11.4127i 0.160771 + 0.494802i
\(533\) 4.04508 2.93893i 0.175212 0.127299i
\(534\) −14.5623 + 10.5801i −0.630173 + 0.457847i
\(535\) −1.85410 5.70634i −0.0801598 0.246707i
\(536\) 1.85410 5.70634i 0.0800850 0.246476i
\(537\) −38.8328 28.2137i −1.67576 1.21751i
\(538\) −1.00000 −0.0431131
\(539\) 0 0
\(540\) 4.00000 0.172133
\(541\) 27.5066 + 19.9847i 1.18260 + 0.859209i 0.992463 0.122548i \(-0.0391066\pi\)
0.190138 + 0.981757i \(0.439107\pi\)
\(542\) 6.18034 19.0211i 0.265468 0.817028i
\(543\) 0.618034 + 1.90211i 0.0265224 + 0.0816275i
\(544\) 20.2254 14.6946i 0.867158 0.630027i
\(545\) −8.89919 + 6.46564i −0.381199 + 0.276957i
\(546\) 1.23607 + 3.80423i 0.0528988 + 0.162806i
\(547\) 4.94427 15.2169i 0.211402 0.650628i −0.787988 0.615691i \(-0.788877\pi\)
0.999390 0.0349369i \(-0.0111230\pi\)
\(548\) −8.09017 5.87785i −0.345595 0.251089i
\(549\) −6.00000 −0.256074
\(550\) 0 0
\(551\) 54.0000 2.30048
\(552\) −9.70820 7.05342i −0.413209 0.300214i
\(553\) 6.18034 19.0211i 0.262815 0.808861i
\(554\) 0.309017 + 0.951057i 0.0131289 + 0.0404065i
\(555\) 4.85410 3.52671i 0.206045 0.149701i
\(556\) 1.61803 1.17557i 0.0686199 0.0498553i
\(557\) 0.618034 + 1.90211i 0.0261869 + 0.0805951i 0.963296 0.268442i \(-0.0865087\pi\)
−0.937109 + 0.349037i \(0.886509\pi\)
\(558\) 0.618034 1.90211i 0.0261635 0.0805229i
\(559\) 0 0
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 27.5066 + 19.9847i 1.15926 + 0.842255i 0.989685 0.143262i \(-0.0457591\pi\)
0.169579 + 0.985517i \(0.445759\pi\)
\(564\) −1.23607 + 3.80423i −0.0520479 + 0.160187i
\(565\) −2.78115 8.55951i −0.117004 0.360101i
\(566\) −22.6525 + 16.4580i −0.952155 + 0.691781i
\(567\) 17.7984 12.9313i 0.747461 0.543063i
\(568\) 11.1246 + 34.2380i 0.466778 + 1.43660i
\(569\) −1.85410 + 5.70634i −0.0777280 + 0.239222i −0.982369 0.186952i \(-0.940139\pi\)
0.904641 + 0.426174i \(0.140139\pi\)
\(570\) −9.70820 7.05342i −0.406632 0.295435i
\(571\) 22.0000 0.920671 0.460336 0.887745i \(-0.347729\pi\)
0.460336 + 0.887745i \(0.347729\pi\)
\(572\) 0 0
\(573\) 16.0000 0.668410
\(574\) 8.09017 + 5.87785i 0.337677 + 0.245337i
\(575\) −2.47214 + 7.60845i −0.103095 + 0.317294i
\(576\) 2.16312 + 6.65740i 0.0901300 + 0.277391i
\(577\) 16.9894 12.3435i 0.707276 0.513866i −0.175018 0.984565i \(-0.555998\pi\)
0.882294 + 0.470699i \(0.155998\pi\)
\(578\) 6.47214 4.70228i 0.269205 0.195589i
\(579\) 3.09017 + 9.51057i 0.128423 + 0.395246i
\(580\) 2.78115 8.55951i 0.115481 0.355414i
\(581\) 9.70820 + 7.05342i 0.402764 + 0.292625i
\(582\) 26.0000 1.07773
\(583\) 0 0
\(584\) 6.00000 0.248282
\(585\) 0.809017 + 0.587785i 0.0334487 + 0.0243019i
\(586\) 2.78115 8.55951i 0.114888 0.353590i
\(587\) −4.32624 13.3148i −0.178563 0.549560i 0.821215 0.570618i \(-0.193296\pi\)
−0.999778 + 0.0210582i \(0.993296\pi\)
\(588\) −4.85410 + 3.52671i −0.200180 + 0.145439i
\(589\) −9.70820 + 7.05342i −0.400020 + 0.290631i
\(590\) −2.47214 7.60845i −0.101776 0.313235i
\(591\) 6.79837 20.9232i 0.279648 0.860667i
\(592\) −2.42705 1.76336i −0.0997512 0.0724735i
\(593\) −11.0000 −0.451716 −0.225858 0.974160i \(-0.572519\pi\)
−0.225858 + 0.974160i \(0.572519\pi\)
\(594\) 0 0
\(595\) 10.0000 0.409960
\(596\) −13.7533 9.99235i −0.563357 0.409303i
\(597\) 14.8328 45.6507i 0.607067 1.86836i
\(598\) 0.618034 + 1.90211i 0.0252733 + 0.0777832i
\(599\) −27.5066 + 19.9847i −1.12389 + 0.816553i −0.984794 0.173726i \(-0.944419\pi\)
−0.139094 + 0.990279i \(0.544419\pi\)
\(600\) 19.4164 14.1068i 0.792672 0.575910i
\(601\) 4.01722 + 12.3637i 0.163866 + 0.504327i 0.998951 0.0457936i \(-0.0145816\pi\)
−0.835085 + 0.550121i \(0.814582\pi\)
\(602\) 0 0
\(603\) −1.61803 1.17557i −0.0658914 0.0478729i
\(604\) −16.0000 −0.651031
\(605\) 0 0
\(606\) −20.0000 −0.812444
\(607\) −8.09017 5.87785i −0.328370 0.238575i 0.411369 0.911469i \(-0.365051\pi\)
−0.739739 + 0.672894i \(0.765051\pi\)
\(608\) 9.27051 28.5317i 0.375969 1.15711i
\(609\) −11.1246 34.2380i −0.450792 1.38740i
\(610\) −4.85410 + 3.52671i −0.196537 + 0.142792i
\(611\) 1.61803 1.17557i 0.0654586 0.0475585i
\(612\) −1.54508 4.75528i −0.0624564 0.192221i
\(613\) −5.25329 + 16.1680i −0.212178 + 0.653018i 0.787164 + 0.616744i \(0.211549\pi\)
−0.999342 + 0.0362735i \(0.988451\pi\)
\(614\) 17.7984 + 12.9313i 0.718284 + 0.521864i
\(615\) 10.0000 0.403239
\(616\) 0 0
\(617\) −9.00000 −0.362326 −0.181163 0.983453i \(-0.557986\pi\)
−0.181163 + 0.983453i \(0.557986\pi\)
\(618\) 12.9443 + 9.40456i 0.520695 + 0.378307i
\(619\) 0.618034 1.90211i 0.0248409 0.0764524i −0.937868 0.346993i \(-0.887203\pi\)
0.962708 + 0.270541i \(0.0872026\pi\)
\(620\) 0.618034 + 1.90211i 0.0248208 + 0.0763907i
\(621\) 6.47214 4.70228i 0.259718 0.188696i
\(622\) 19.4164 14.1068i 0.778527 0.565633i
\(623\) −5.56231 17.1190i −0.222849 0.685859i
\(624\) 0.618034 1.90211i 0.0247412 0.0761455i
\(625\) −8.89919 6.46564i −0.355967 0.258626i
\(626\) −23.0000 −0.919265
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) 12.1353 + 8.81678i 0.483864 + 0.351548i
\(630\) −0.618034 + 1.90211i −0.0246231 + 0.0757820i
\(631\) −4.32624 13.3148i −0.172225 0.530053i 0.827271 0.561803i \(-0.189892\pi\)
−0.999496 + 0.0317495i \(0.989892\pi\)
\(632\) −24.2705 + 17.6336i −0.965429 + 0.701425i
\(633\) 19.4164 14.1068i 0.771733 0.560697i
\(634\) 0.618034 + 1.90211i 0.0245453 + 0.0755426i
\(635\) 4.94427 15.2169i 0.196207 0.603864i
\(636\) 14.5623 + 10.5801i 0.577433 + 0.419530i
\(637\) 3.00000 0.118864
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) −2.42705 1.76336i −0.0959376 0.0697028i
\(641\) −2.78115 + 8.55951i −0.109849 + 0.338080i −0.990838 0.135057i \(-0.956878\pi\)
0.880989 + 0.473137i \(0.156878\pi\)
\(642\) 3.70820 + 11.4127i 0.146351 + 0.450422i
\(643\) 8.09017 5.87785i 0.319045 0.231800i −0.416723 0.909034i \(-0.636821\pi\)
0.735768 + 0.677234i \(0.236821\pi\)
\(644\) 3.23607 2.35114i 0.127519 0.0926479i
\(645\) 0 0
\(646\) 9.27051 28.5317i 0.364743 1.12256i
\(647\) −16.1803 11.7557i −0.636115 0.462164i 0.222398 0.974956i \(-0.428611\pi\)
−0.858513 + 0.512791i \(0.828611\pi\)
\(648\) −33.0000 −1.29636
\(649\) 0 0
\(650\) −4.00000 −0.156893
\(651\) 6.47214 + 4.70228i 0.253663 + 0.184297i
\(652\) 0.618034 1.90211i 0.0242041 0.0744925i
\(653\) −4.32624 13.3148i −0.169299 0.521048i 0.830029 0.557721i \(-0.188324\pi\)
−0.999327 + 0.0366729i \(0.988324\pi\)
\(654\) 17.7984 12.9313i 0.695971 0.505653i
\(655\) 0 0
\(656\) −1.54508 4.75528i −0.0603254 0.185663i
\(657\) 0.618034 1.90211i 0.0241118 0.0742085i
\(658\) 3.23607 + 2.35114i 0.126155 + 0.0916570i
\(659\) −22.0000 −0.856998 −0.428499 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) 0 0
\(661\) 13.0000 0.505641 0.252821 0.967513i \(-0.418642\pi\)
0.252821 + 0.967513i \(0.418642\pi\)
\(662\) −16.1803 11.7557i −0.628867 0.456898i
\(663\) −3.09017 + 9.51057i −0.120012 + 0.369360i
\(664\) −5.56231 17.1190i −0.215859 0.664347i
\(665\) 9.70820 7.05342i 0.376468 0.273520i
\(666\) −2.42705 + 1.76336i −0.0940463 + 0.0683286i
\(667\) −5.56231 17.1190i −0.215373 0.662851i
\(668\) 3.70820 11.4127i 0.143475 0.441570i
\(669\) 32.3607 + 23.5114i 1.25114 + 0.909004i
\(670\) −2.00000 −0.0772667
\(671\) 0 0
\(672\) −20.0000 −0.771517
\(673\) −8.09017 5.87785i −0.311853 0.226575i 0.420838 0.907136i \(-0.361736\pi\)
−0.732691 + 0.680561i \(0.761736\pi\)
\(674\) −4.01722 + 12.3637i −0.154738 + 0.476233i
\(675\) 4.94427 + 15.2169i 0.190305 + 0.585699i
\(676\) −9.70820 + 7.05342i −0.373392 + 0.271286i
\(677\) −21.8435 + 15.8702i −0.839512 + 0.609941i −0.922234 0.386631i \(-0.873639\pi\)
0.0827221 + 0.996573i \(0.473639\pi\)
\(678\) 5.56231 + 17.1190i 0.213619 + 0.657452i
\(679\) −8.03444 + 24.7275i −0.308334 + 0.948953i
\(680\) −12.1353 8.81678i −0.465366 0.338108i
\(681\) 48.0000 1.83936
\(682\) 0 0
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) −4.85410 3.52671i −0.185601 0.134847i
\(685\) −3.09017 + 9.51057i −0.118069 + 0.363380i
\(686\) 6.18034 + 19.0211i 0.235966 + 0.726230i
\(687\) −14.5623 + 10.5801i −0.555587 + 0.403657i
\(688\) 0 0
\(689\) −2.78115 8.55951i −0.105953 0.326091i
\(690\) −1.23607 + 3.80423i −0.0470563 + 0.144824i
\(691\) −16.1803 11.7557i −0.615529 0.447208i 0.235828 0.971795i \(-0.424220\pi\)
−0.851357 + 0.524587i \(0.824220\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) −1.61803 1.17557i −0.0613755 0.0445919i
\(696\) −16.6869 + 51.3571i −0.632516 + 1.94668i
\(697\) 7.72542 + 23.7764i 0.292621 + 0.900596i
\(698\) 21.8435 15.8702i 0.826787 0.600696i
\(699\) −33.9787 + 24.6870i −1.28519 + 0.933747i
\(700\) 2.47214 + 7.60845i 0.0934380 + 0.287572i
\(701\) −5.25329 + 16.1680i −0.198414 + 0.610655i 0.801506 + 0.597987i \(0.204033\pi\)
−0.999920 + 0.0126684i \(0.995967\pi\)
\(702\) 3.23607 + 2.35114i 0.122138 + 0.0887381i
\(703\) 18.0000 0.678883
\(704\) 0 0
\(705\) 4.00000 0.150649
\(706\) −7.28115 5.29007i −0.274030 0.199094i
\(707\) 6.18034 19.0211i 0.232436 0.715363i
\(708\) −4.94427 15.2169i −0.185817 0.571886i
\(709\) 8.09017 5.87785i 0.303833 0.220747i −0.425413 0.904999i \(-0.639871\pi\)
0.729246 + 0.684252i \(0.239871\pi\)
\(710\) 9.70820 7.05342i 0.364342 0.264710i
\(711\) 3.09017 + 9.51057i 0.115890 + 0.356674i
\(712\) −8.34346 + 25.6785i −0.312684 + 0.962343i
\(713\) 3.23607 + 2.35114i 0.121192 + 0.0880509i
\(714\) −20.0000 −0.748481
\(715\) 0 0
\(716\) −24.0000 −0.896922
\(717\) 9.70820 + 7.05342i 0.362560 + 0.263415i
\(718\) −0.618034 + 1.90211i −0.0230648 + 0.0709862i
\(719\) 9.27051 + 28.5317i 0.345732 + 1.06405i 0.961191 + 0.275884i \(0.0889706\pi\)
−0.615459 + 0.788169i \(0.711029\pi\)
\(720\) 0.809017 0.587785i 0.0301503 0.0219055i
\(721\) −12.9443 + 9.40456i −0.482070 + 0.350244i
\(722\) −5.25329 16.1680i −0.195507 0.601709i
\(723\) −13.5967 + 41.8465i −0.505668 + 1.55629i
\(724\) 0.809017 + 0.587785i 0.0300669 + 0.0218449i
\(725\) 36.0000 1.33701
\(726\) 0 0
\(727\) −42.0000 −1.55769 −0.778847 0.627214i \(-0.784195\pi\)
−0.778847 + 0.627214i \(0.784195\pi\)
\(728\) 4.85410 + 3.52671i 0.179905 + 0.130709i
\(729\) 4.01722 12.3637i 0.148786 0.457916i
\(730\) −0.618034 1.90211i −0.0228745 0.0704004i
\(731\) 0 0
\(732\) −9.70820 + 7.05342i −0.358826 + 0.260702i
\(733\) −2.78115 8.55951i −0.102724 0.316153i 0.886465 0.462795i \(-0.153153\pi\)
−0.989190 + 0.146642i \(0.953153\pi\)
\(734\) 4.32624 13.3148i 0.159684 0.491458i
\(735\) 4.85410 + 3.52671i 0.179046 + 0.130085i
\(736\) −10.0000 −0.368605
\(737\) 0 0
\(738\) −5.00000 −0.184053
\(739\) −8.09017 5.87785i −0.297602 0.216220i 0.428957 0.903325i \(-0.358881\pi\)
−0.726558 + 0.687105i \(0.758881\pi\)
\(740\) 0.927051 2.85317i 0.0340791 0.104885i
\(741\) 3.70820 + 11.4127i 0.136224 + 0.419255i
\(742\) 14.5623 10.5801i 0.534599 0.388409i
\(743\) −30.7426 + 22.3358i −1.12784 + 0.819422i −0.985379 0.170378i \(-0.945501\pi\)
−0.142460 + 0.989801i \(0.545501\pi\)
\(744\) −3.70820 11.4127i −0.135949 0.418409i
\(745\) −5.25329 + 16.1680i −0.192466 + 0.592348i
\(746\) −17.7984 12.9313i −0.651645 0.473448i
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) −14.5623 10.5801i −0.531740 0.386332i
\(751\) −6.18034 + 19.0211i −0.225524 + 0.694091i 0.772714 + 0.634754i \(0.218899\pi\)
−0.998238 + 0.0593368i \(0.981101\pi\)
\(752\) −0.618034 1.90211i −0.0225374 0.0693629i
\(753\) 3.23607 2.35114i 0.117929 0.0856803i
\(754\) 7.28115 5.29007i 0.265164 0.192653i
\(755\) 4.94427 + 15.2169i 0.179940 + 0.553800i
\(756\) 2.47214 7.60845i 0.0899107 0.276717i
\(757\) −42.8779 31.1526i −1.55842 1.13226i −0.937287 0.348559i \(-0.886671\pi\)
−0.621137 0.783702i \(-0.713329\pi\)
\(758\) 32.0000 1.16229
\(759\) 0 0
\(760\) −18.0000 −0.652929
\(761\) −16.9894 12.3435i −0.615864 0.447451i 0.235611 0.971848i \(-0.424291\pi\)
−0.851474 + 0.524396i \(0.824291\pi\)
\(762\) −9.88854 + 30.4338i −0.358224 + 1.10250i
\(763\) 6.79837 + 20.9232i 0.246118 + 0.757472i
\(764\) 6.47214 4.70228i 0.234154 0.170123i
\(765\) −4.04508 + 2.93893i −0.146250 + 0.106257i
\(766\) −6.18034 19.0211i −0.223305 0.687261i
\(767\) −2.47214 + 7.60845i −0.0892637 + 0.274725i
\(768\) 27.5066 + 19.9847i 0.992558 + 0.721136i
\(769\) −11.0000 −0.396670 −0.198335 0.980134i \(-0.563553\pi\)
−0.198335 + 0.980134i \(0.563553\pi\)
\(770\) 0 0
\(771\) 38.0000 1.36854
\(772\) 4.04508 + 2.93893i 0.145586 + 0.105774i
\(773\) −12.9787 + 39.9444i −0.466812 + 1.43670i 0.389878 + 0.920867i \(0.372517\pi\)
−0.856689 + 0.515833i \(0.827483\pi\)
\(774\) 0 0
\(775\) −6.47214 + 4.70228i −0.232486 + 0.168911i
\(776\) 31.5517 22.9236i 1.13264 0.822910i
\(777\) −3.70820 11.4127i −0.133031 0.409428i
\(778\) 0.927051 2.85317i 0.0332364 0.102291i
\(779\) 24.2705 + 17.6336i 0.869581 + 0.631788i
\(780\) 2.00000 0.0716115
\(781\) 0 0
\(782\) −10.0000 −0.357599
\(783\) −29.1246 21.1603i −1.04083 0.756206i
\(784\) 0.927051 2.85317i 0.0331090 0.101899i
\(785\) 0.618034 + 1.90211i 0.0220586 + 0.0678893i
\(786\) 0 0
\(787\) 22.6525 16.4580i 0.807474 0.586664i −0.105623 0.994406i \(-0.533684\pi\)
0.913097 + 0.407742i \(0.133684\pi\)
\(788\) −3.39919 10.4616i −0.121091 0.372680i
\(789\) 13.5967 41.8465i 0.484057 1.48977i
\(790\) 8.09017 + 5.87785i 0.287835 + 0.209125i
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 6.00000 0.213066
\(794\) 10.5172 + 7.64121i 0.373242 + 0.271176i
\(795\) 5.56231 17.1190i 0.197275 0.607149i
\(796\) −7.41641 22.8254i −0.262868 0.809023i
\(797\) 8.09017 5.87785i 0.286569 0.208204i −0.435209 0.900330i \(-0.643325\pi\)
0.721777 + 0.692125i \(0.243325\pi\)
\(798\) −19.4164 + 14.1068i −0.687333 + 0.499377i
\(799\) 3.09017 + 9.51057i 0.109322 + 0.336460i
\(800\) 6.18034 19.0211i 0.218508 0.672499i
\(801\) 7.28115 + 5.29007i 0.257267 + 0.186915i
\(802\) −23.0000 −0.812158
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) −3.23607 2.35114i −0.114056 0.0828668i
\(806\) −0.618034 + 1.90211i −0.0217693 + 0.0669991i
\(807\) 0.618034 + 1.90211i 0.0217558 + 0.0669575i
\(808\) −24.2705 + 17.6336i −0.853834 + 0.620346i
\(809\) 4.85410 3.52671i 0.170661 0.123993i −0.499176 0.866501i \(-0.666364\pi\)
0.669837 + 0.742508i \(0.266364\pi\)
\(810\) 3.39919 + 10.4616i 0.119435 + 0.367584i
\(811\) −8.65248 + 26.6296i −0.303830 + 0.935091i 0.676282 + 0.736643i \(0.263590\pi\)
−0.980111 + 0.198448i \(0.936410\pi\)
\(812\) −14.5623 10.5801i −0.511037 0.371290i
\(813\) −40.0000 −1.40286
\(814\) 0 0
\(815\) −2.00000 −0.0700569
\(816\) 8.09017 + 5.87785i 0.283213 + 0.205766i
\(817\) 0 0
\(818\) −6.48936 19.9722i −0.226895 0.698311i
\(819\) 1.61803 1.17557i 0.0565387 0.0410778i
\(820\) 4.04508 2.93893i 0.141260 0.102632i
\(821\) 0.618034 + 1.90211i 0.0215695 + 0.0663842i 0.961262 0.275637i \(-0.0888887\pi\)
−0.939692 + 0.342021i \(0.888889\pi\)
\(822\) 6.18034 19.0211i 0.215564 0.663438i
\(823\) 19.4164 + 14.1068i 0.676813 + 0.491734i 0.872299 0.488973i \(-0.162628\pi\)
−0.195486 + 0.980707i \(0.562628\pi\)
\(824\) 24.0000 0.836080
\(825\) 0 0
\(826\) −16.0000 −0.556711
\(827\) −8.09017 5.87785i −0.281323 0.204393i 0.438171 0.898891i \(-0.355626\pi\)
−0.719494 + 0.694498i \(0.755626\pi\)
\(828\) −0.618034 + 1.90211i −0.0214782 + 0.0661030i
\(829\) −14.5238 44.6997i −0.504432 1.55248i −0.801723 0.597696i \(-0.796083\pi\)
0.297290 0.954787i \(-0.403917\pi\)
\(830\) −4.85410 + 3.52671i −0.168488 + 0.122414i
\(831\) 1.61803 1.17557i 0.0561290 0.0407801i
\(832\) −2.16312 6.65740i −0.0749927 0.230804i
\(833\) −4.63525 + 14.2658i −0.160602 + 0.494282i
\(834\) 3.23607 + 2.35114i 0.112056 + 0.0814134i
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) 8.00000 0.276520
\(838\) 1.61803 + 1.17557i 0.0558941 + 0.0406094i
\(839\) 14.2148 43.7486i 0.490749 1.51037i −0.332730 0.943022i \(-0.607970\pi\)
0.823479 0.567347i \(-0.192030\pi\)
\(840\) 3.70820 + 11.4127i 0.127945 + 0.393775i
\(841\) −42.0689 + 30.5648i −1.45065 + 1.05396i
\(842\) 10.5172 7.64121i 0.362447 0.263333i
\(843\) −3.70820 11.4127i −0.127717 0.393074i
\(844\) 3.70820 11.4127i 0.127642 0.392841i
\(845\) 9.70820 + 7.05342i 0.333972 + 0.242645i
\(846\) −2.00000 −0.0687614
\(847\) 0 0
\(848\) −9.00000 −0.309061
\(849\) 45.3050 + 32.9160i 1.55486 + 1.12967i
\(850\) 6.18034 19.0211i 0.211984 0.652419i
\(851\) −1.85410 5.70634i −0.0635578 0.195611i
\(852\) 19.4164 14.1068i 0.665195 0.483293i
\(853\) 13.7533 9.99235i 0.470904 0.342132i −0.326890 0.945062i \(-0.606001\pi\)
0.797793 + 0.602931i \(0.206001\pi\)
\(854\) 3.70820 + 11.4127i 0.126892 + 0.390534i
\(855\) −1.85410 + 5.70634i −0.0634089 + 0.195153i
\(856\) 14.5623 + 10.5801i 0.497729 + 0.361622i
\(857\) 22.0000 0.751506 0.375753 0.926720i \(-0.377384\pi\)
0.375753 + 0.926720i \(0.377384\pi\)
\(858\) 0 0
\(859\) 24.0000 0.818869 0.409435 0.912339i \(-0.365726\pi\)
0.409435 + 0.912339i \(0.365726\pi\)
\(860\) 0 0
\(861\) 6.18034 19.0211i 0.210625 0.648238i
\(862\) 3.70820 + 11.4127i 0.126302 + 0.388717i
\(863\) 43.6869 31.7404i 1.48712 1.08046i 0.511946 0.859018i \(-0.328925\pi\)
0.975174 0.221438i \(-0.0710750\pi\)
\(864\) −16.1803 + 11.7557i −0.550466 + 0.399937i
\(865\) −1.85410 5.70634i −0.0630414 0.194021i
\(866\) −5.87132 + 18.0701i −0.199516 + 0.614046i
\(867\) −12.9443 9.40456i −0.439611 0.319396i
\(868\) 4.00000 0.135769
\(869\) 0 0
\(870\) 18.0000 0.610257
\(871\) 1.61803 + 1.17557i 0.0548250 + 0.0398327i
\(872\) 10.1976 31.3849i 0.345333 1.06283i
\(873\) −4.01722 12.3637i −0.135962 0.418449i
\(874\) −9.70820 + 7.05342i −0.328385 + 0.238586i
\(875\) 14.5623 10.5801i 0.492296 0.357674i
\(876\) −1.23607 3.80423i −0.0417629 0.128533i
\(877\) 8.34346 25.6785i 0.281739 0.867102i −0.705619 0.708592i \(-0.749331\pi\)
0.987357 0.158510i \(-0.0506692\pi\)
\(878\) −17.7984 12.9313i −0.600666 0.436409i
\(879\) −18.0000 −0.607125
\(880\) 0 0
\(881\) 35.0000 1.17918 0.589590 0.807703i \(-0.299289\pi\)
0.589590 + 0.807703i \(0.299289\pi\)
\(882\) −2.42705 1.76336i −0.0817231 0.0593753i
\(883\) −6.18034 + 19.0211i −0.207985 + 0.640112i 0.791593 + 0.611049i \(0.209252\pi\)
−0.999578 + 0.0290628i \(0.990748\pi\)
\(884\) 1.54508 + 4.75528i 0.0519668 + 0.159937i
\(885\) −12.9443 + 9.40456i −0.435117 + 0.316131i
\(886\) −16.1803 + 11.7557i −0.543589 + 0.394941i
\(887\) 14.2148 + 43.7486i 0.477286 + 1.46893i 0.842850 + 0.538148i \(0.180876\pi\)
−0.365565 + 0.930786i \(0.619124\pi\)
\(888\) −5.56231 + 17.1190i −0.186659 + 0.574477i
\(889\) −25.8885 18.8091i −0.868274 0.630838i
\(890\) 9.00000 0.301681
\(891\) 0 0
\(892\) 20.0000 0.669650
\(893\) 9.70820 + 7.05342i 0.324873 + 0.236034i
\(894\) 10.5066 32.3359i 0.351393 1.08147i
\(895\) 7.41641 + 22.8254i 0.247903 + 0.762968i
\(896\) −4.85410 + 3.52671i −0.162164 + 0.117819i
\(897\) 3.23607 2.35114i 0.108049 0.0785023i
\(898\) 4.01722 + 12.3637i 0.134056 + 0.412583i
\(899\) 5.56231 17.1190i 0.185513 0.570951i
\(900\) −3.23607 2.35114i −0.107869 0.0783714i
\(901\) 45.0000 1.49917
\(902\) 0 0
\(903\) 0 0
\(904\) 21.8435 + 15.8702i 0.726503 + 0.527835i
\(905\) 0.309017 0.951057i 0.0102721 0.0316142i
\(906\) −9.88854 30.4338i −0.328525 1.01110i
\(907\) −9.70820 + 7.05342i −0.322356 + 0.234205i −0.737180 0.675696i \(-0.763843\pi\)
0.414824 + 0.909902i \(0.363843\pi\)
\(908\) 19.4164 14.1068i 0.644356 0.468152i
\(909\) 3.09017 + 9.51057i 0.102494 + 0.315446i
\(910\) 0.618034 1.90211i 0.0204876 0.0630544i
\(911\) 19.4164 + 14.1068i 0.643294 + 0.467381i 0.860980 0.508638i \(-0.169851\pi\)
−0.217686 + 0.976019i \(0.569851\pi\)
\(912\) 12.0000 0.397360
\(913\) 0 0
\(914\) 39.0000 1.29001
\(915\) 9.70820 + 7.05342i 0.320943 + 0.233179i
\(916\) −2.78115 + 8.55951i −0.0918919 + 0.282814i
\(917\) 0 0
\(918\) −16.1803 + 11.7557i −0.534031 + 0.387996i
\(919\) 22.6525 16.4580i 0.747236 0.542899i −0.147733 0.989027i \(-0.547198\pi\)
0.894969 + 0.446128i \(0.147198\pi\)
\(920\) 1.85410 + 5.70634i 0.0611279 + 0.188132i
\(921\) 13.5967 41.8465i 0.448028 1.37889i
\(922\) −26.6976 19.3969i −0.879237 0.638803i
\(923\) −12.0000 −0.394985
\(924\) 0 0
\(925\) 12.0000 0.394558
\(926\) −16.1803 11.7557i −0.531719 0.386316i
\(927\) 2.47214 7.60845i 0.0811956 0.249894i
\(928\) 13.9058 + 42.7975i 0.456479 + 1.40490i
\(929\) 16.9894 12.3435i 0.557403 0.404977i −0.273105 0.961984i \(-0.588051\pi\)
0.830507 + 0.557008i \(0.188051\pi\)
\(930\) −3.23607 + 2.35114i −0.106115 + 0.0770970i
\(931\) 5.56231 + 17.1190i 0.182297 + 0.561053i
\(932\) −6.48936 + 19.9722i −0.212566 + 0.654211i
\(933\) −38.8328 28.2137i −1.27133 0.923675i
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −3.00000 −0.0980581
\(937\) 18.6074 + 13.5191i 0.607877 + 0.441648i 0.848666 0.528929i \(-0.177406\pi\)
−0.240789 + 0.970577i \(0.577406\pi\)
\(938\) −1.23607 + 3.80423i −0.0403591 + 0.124212i
\(939\) 14.2148 + 43.7486i 0.463882 + 1.42768i
\(940\) 1.61803 1.17557i 0.0527744 0.0383429i
\(941\) −21.8435 + 15.8702i −0.712076 + 0.517354i −0.883843 0.467784i \(-0.845053\pi\)
0.171766 + 0.985138i \(0.445053\pi\)
\(942\) −1.23607 3.80423i −0.0402733 0.123948i
\(943\) 3.09017 9.51057i 0.100630 0.309707i
\(944\) 6.47214 + 4.70228i 0.210650 + 0.153046i
\(945\) −8.00000 −0.260240
\(946\) 0 0
\(947\) −42.0000 −1.36482 −0.682408 0.730971i \(-0.739067\pi\)
−0.682408 + 0.730971i \(0.739067\pi\)
\(948\) 16.1803 + 11.7557i 0.525513 + 0.381808i
\(949\) −0.618034 + 1.90211i −0.0200622 + 0.0617452i
\(950\) −7.41641 22.8254i −0.240620 0.740552i
\(951\) 3.23607 2.35114i 0.104937 0.0762410i
\(952\) −24.2705 + 17.6336i −0.786612 + 0.571507i
\(953\) −9.57953 29.4828i −0.310311 0.955040i −0.977642 0.210278i \(-0.932563\pi\)
0.667330 0.744762i \(-0.267437\pi\)
\(954\) −2.78115 + 8.55951i −0.0900432 + 0.277124i
\(955\) −6.47214 4.70228i −0.209433 0.152162i
\(956\) 6.00000 0.194054
\(957\) 0 0
\(958\) −16.0000 −0.516937
\(959\) 16.1803 + 11.7557i 0.522490 + 0.379612i
\(960\) 4.32624 13.3148i 0.139629 0.429733i
\(961\) −8.34346 25.6785i −0.269144 0.828340i
\(962\) 2.42705 1.76336i 0.0782513 0.0568529i
\(963\) 4.85410 3.52671i 0.156421 0.113647i
\(964\) 6.79837 + 20.9232i 0.218961 + 0.673892i
\(965\) 1.54508 4.75528i 0.0497380 0.153078i
\(966\) 6.47214 + 4.70228i 0.208238 + 0.151293i
\(967\) −22.0000 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) 0 0
\(969\) −60.0000 −1.92748
\(970\) −10.5172 7.64121i −0.337688 0.245344i
\(971\) 0.618034 1.90211i 0.0198337 0.0610417i −0.940650 0.339379i \(-0.889783\pi\)
0.960483 + 0.278337i \(0.0897832\pi\)
\(972\) 3.09017 + 9.51057i 0.0991172 + 0.305052i
\(973\) −3.23607 + 2.35114i −0.103744 + 0.0753741i
\(974\) 1.61803 1.17557i 0.0518452 0.0376677i
\(975\) 2.47214 + 7.60845i 0.0791717 + 0.243665i
\(976\) 1.85410 5.70634i 0.0593484 0.182655i
\(977\) 46.1140 + 33.5038i 1.47532 + 1.07188i 0.979029 + 0.203722i \(0.0653039\pi\)
0.496288 + 0.868158i \(0.334696\pi\)
\(978\) 4.00000 0.127906
\(979\) 0 0
\(980\) 3.00000 0.0958315
\(981\) −8.89919 6.46564i −0.284129 0.206432i
\(982\) −0.618034 + 1.90211i −0.0197223 + 0.0606989i
\(983\) −11.1246 34.2380i −0.354820 1.09202i −0.956114 0.292996i \(-0.905348\pi\)
0.601294 0.799028i \(-0.294652\pi\)
\(984\) −24.2705 + 17.6336i −0.773716 + 0.562137i
\(985\) −8.89919 + 6.46564i −0.283552 + 0.206012i
\(986\) 13.9058 + 42.7975i 0.442850 + 1.36295i
\(987\) 2.47214 7.60845i 0.0786890 0.242180i
\(988\) 4.85410 + 3.52671i 0.154430 + 0.112200i
\(989\) 0 0
\(990\) 0 0
\(991\) −20.0000 −0.635321 −0.317660 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) −8.09017 5.87785i −0.256863 0.186622i
\(993\) −12.3607 + 38.0423i −0.392254 + 1.20723i
\(994\) −7.41641 22.8254i −0.235234 0.723976i
\(995\) −19.4164 + 14.1068i −0.615542 + 0.447217i
\(996\) −9.70820 + 7.05342i −0.307616 + 0.223496i
\(997\) −16.3779 50.4060i −0.518693 1.59637i −0.776460 0.630167i \(-0.782987\pi\)
0.257767 0.966207i \(-0.417013\pi\)
\(998\) −2.47214 + 7.60845i −0.0782541 + 0.240841i
\(999\) −9.70820 7.05342i −0.307154 0.223160i
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 121.2.c.d.81.1 4
11.2 odd 10 121.2.c.b.27.1 4
11.3 even 5 inner 121.2.c.d.3.1 4
11.4 even 5 inner 121.2.c.d.9.1 4
11.5 even 5 121.2.a.a.1.1 1
11.6 odd 10 121.2.a.c.1.1 yes 1
11.7 odd 10 121.2.c.b.9.1 4
11.8 odd 10 121.2.c.b.3.1 4
11.9 even 5 inner 121.2.c.d.27.1 4
11.10 odd 2 121.2.c.b.81.1 4
33.5 odd 10 1089.2.a.i.1.1 1
33.17 even 10 1089.2.a.c.1.1 1
44.27 odd 10 1936.2.a.a.1.1 1
44.39 even 10 1936.2.a.b.1.1 1
55.39 odd 10 3025.2.a.b.1.1 1
55.49 even 10 3025.2.a.e.1.1 1
77.6 even 10 5929.2.a.g.1.1 1
77.27 odd 10 5929.2.a.a.1.1 1
88.5 even 10 7744.2.a.f.1.1 1
88.27 odd 10 7744.2.a.be.1.1 1
88.61 odd 10 7744.2.a.c.1.1 1
88.83 even 10 7744.2.a.bf.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
121.2.a.a.1.1 1 11.5 even 5
121.2.a.c.1.1 yes 1 11.6 odd 10
121.2.c.b.3.1 4 11.8 odd 10
121.2.c.b.9.1 4 11.7 odd 10
121.2.c.b.27.1 4 11.2 odd 10
121.2.c.b.81.1 4 11.10 odd 2
121.2.c.d.3.1 4 11.3 even 5 inner
121.2.c.d.9.1 4 11.4 even 5 inner
121.2.c.d.27.1 4 11.9 even 5 inner
121.2.c.d.81.1 4 1.1 even 1 trivial
1089.2.a.c.1.1 1 33.17 even 10
1089.2.a.i.1.1 1 33.5 odd 10
1936.2.a.a.1.1 1 44.27 odd 10
1936.2.a.b.1.1 1 44.39 even 10
3025.2.a.b.1.1 1 55.39 odd 10
3025.2.a.e.1.1 1 55.49 even 10
5929.2.a.a.1.1 1 77.27 odd 10
5929.2.a.g.1.1 1 77.6 even 10
7744.2.a.c.1.1 1 88.61 odd 10
7744.2.a.f.1.1 1 88.5 even 10
7744.2.a.be.1.1 1 88.27 odd 10
7744.2.a.bf.1.1 1 88.83 even 10