Properties

Label 490.2.i.c.79.3
Level $490$
Weight $2$
Character 490.79
Analytic conductor $3.913$
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] = [490,2,Mod(79,490)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(490, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("490.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.i (of order \(6\), degree \(2\), 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: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.3
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 490.79
Dual form 490.2.i.c.459.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-2.12132 + 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.81431 - 1.30701i) q^{5} -2.44949 q^{6} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-2.12132 + 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.81431 - 1.30701i) q^{5} -2.44949 q^{6} +1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(-0.917738 - 2.03906i) q^{10} +(-2.44949 - 4.24264i) q^{11} +(-2.12132 - 1.22474i) q^{12} +0.449490i q^{13} +(5.44949 + 0.550510i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(3.22474 - 5.58542i) q^{19} +(0.224745 - 2.22474i) q^{20} -4.89898i q^{22} +(-5.97469 - 3.44949i) q^{23} +(-1.22474 - 2.12132i) q^{24} +(1.58346 + 4.74264i) q^{25} +(-0.224745 + 0.389270i) q^{26} +2.89898 q^{29} +(4.44414 + 3.20150i) q^{30} +(0.449490 + 0.778539i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(10.3923 + 6.00000i) q^{33} +2.00000 q^{34} +3.00000 q^{36} +(-1.73205 - 1.00000i) q^{37} +(5.58542 - 3.22474i) q^{38} +(-0.550510 - 0.953512i) q^{39} +(1.30701 - 1.81431i) q^{40} -10.8990 q^{41} -8.89898i q^{43} +(2.44949 - 4.24264i) q^{44} +(-6.11717 + 2.75321i) q^{45} +(-3.44949 - 5.97469i) q^{46} +(0.778539 + 0.449490i) q^{47} -2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} +(-2.44949 + 4.24264i) q^{51} +(-0.389270 + 0.224745i) q^{52} +(0.953512 - 0.550510i) q^{53} +(-1.10102 + 10.8990i) q^{55} +15.7980i q^{57} +(2.51059 + 1.44949i) q^{58} +(-3.22474 - 5.58542i) q^{59} +(2.24799 + 4.99465i) q^{60} +(-4.22474 + 7.31747i) q^{61} +0.898979i q^{62} -1.00000 q^{64} +(0.587486 - 0.815515i) q^{65} +(6.00000 + 10.3923i) q^{66} +(-6.92820 + 4.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} +16.8990 q^{69} -10.8990 q^{71} +(2.59808 + 1.50000i) q^{72} +(5.97469 - 3.44949i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-9.16756 - 8.12132i) q^{75} +6.44949 q^{76} -1.10102i q^{78} +(-1.44949 + 2.51059i) q^{79} +(2.03906 - 0.917738i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-9.43879 - 5.44949i) q^{82} -2.44949i q^{83} +(-4.44949 - 0.449490i) q^{85} +(4.44949 - 7.70674i) q^{86} +(-6.14966 + 3.55051i) q^{87} +(4.24264 - 2.44949i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(-6.67423 - 0.674235i) q^{90} -6.89898i q^{92} +(-1.90702 - 1.10102i) q^{93} +(0.449490 + 0.778539i) q^{94} +(-13.1509 + 5.91894i) q^{95} +(1.22474 - 2.12132i) q^{96} -3.79796i q^{97} -14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 4 q^{5} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 4 q^{5} + 12 q^{9} - 4 q^{10} + 24 q^{15} - 4 q^{16} + 16 q^{19} - 8 q^{20} + 8 q^{26} - 16 q^{29} - 12 q^{30} - 16 q^{31} + 16 q^{34} + 24 q^{36} - 24 q^{39} + 4 q^{40} - 48 q^{41} + 12 q^{45} - 8 q^{46} - 8 q^{50} - 48 q^{55} - 16 q^{59} + 12 q^{60} - 24 q^{61} - 8 q^{64} + 4 q^{65} + 48 q^{66} + 96 q^{69} - 48 q^{71} - 8 q^{74} + 32 q^{76} + 8 q^{79} - 4 q^{80} + 36 q^{81} - 16 q^{85} + 16 q^{86} - 40 q^{89} - 24 q^{90} - 16 q^{94} + 4 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −2.12132 + 1.22474i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.81431 1.30701i −0.811386 0.584511i
\(6\) −2.44949 −1.00000
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −0.917738 2.03906i −0.290214 0.644807i
\(11\) −2.44949 4.24264i −0.738549 1.27920i −0.953149 0.302502i \(-0.902178\pi\)
0.214600 0.976702i \(-0.431155\pi\)
\(12\) −2.12132 1.22474i −0.612372 0.353553i
\(13\) 0.449490i 0.124666i 0.998055 + 0.0623330i \(0.0198541\pi\)
−0.998055 + 0.0623330i \(0.980146\pi\)
\(14\) 0 0
\(15\) 5.44949 + 0.550510i 1.40705 + 0.142141i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.73205 1.00000i 0.420084 0.242536i −0.275029 0.961436i \(-0.588688\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 2.59808 1.50000i 0.612372 0.353553i
\(19\) 3.22474 5.58542i 0.739807 1.28138i −0.212775 0.977101i \(-0.568250\pi\)
0.952582 0.304282i \(-0.0984166\pi\)
\(20\) 0.224745 2.22474i 0.0502545 0.497468i
\(21\) 0 0
\(22\) 4.89898i 1.04447i
\(23\) −5.97469 3.44949i −1.24581 0.719268i −0.275538 0.961290i \(-0.588856\pi\)
−0.970271 + 0.242022i \(0.922189\pi\)
\(24\) −1.22474 2.12132i −0.250000 0.433013i
\(25\) 1.58346 + 4.74264i 0.316693 + 0.948528i
\(26\) −0.224745 + 0.389270i −0.0440761 + 0.0763420i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.89898 0.538327 0.269163 0.963095i \(-0.413253\pi\)
0.269163 + 0.963095i \(0.413253\pi\)
\(30\) 4.44414 + 3.20150i 0.811386 + 0.584511i
\(31\) 0.449490 + 0.778539i 0.0807307 + 0.139830i 0.903564 0.428453i \(-0.140941\pi\)
−0.822833 + 0.568283i \(0.807608\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 10.3923 + 6.00000i 1.80907 + 1.04447i
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) −1.73205 1.00000i −0.284747 0.164399i 0.350823 0.936442i \(-0.385902\pi\)
−0.635571 + 0.772043i \(0.719235\pi\)
\(38\) 5.58542 3.22474i 0.906075 0.523123i
\(39\) −0.550510 0.953512i −0.0881522 0.152684i
\(40\) 1.30701 1.81431i 0.206656 0.286868i
\(41\) −10.8990 −1.70213 −0.851067 0.525057i \(-0.824044\pi\)
−0.851067 + 0.525057i \(0.824044\pi\)
\(42\) 0 0
\(43\) 8.89898i 1.35708i −0.734563 0.678541i \(-0.762613\pi\)
0.734563 0.678541i \(-0.237387\pi\)
\(44\) 2.44949 4.24264i 0.369274 0.639602i
\(45\) −6.11717 + 2.75321i −0.911894 + 0.410425i
\(46\) −3.44949 5.97469i −0.508600 0.880920i
\(47\) 0.778539 + 0.449490i 0.113562 + 0.0655648i 0.555705 0.831380i \(-0.312448\pi\)
−0.442143 + 0.896944i \(0.645782\pi\)
\(48\) 2.44949i 0.353553i
\(49\) 0 0
\(50\) −1.00000 + 4.89898i −0.141421 + 0.692820i
\(51\) −2.44949 + 4.24264i −0.342997 + 0.594089i
\(52\) −0.389270 + 0.224745i −0.0539820 + 0.0311665i
\(53\) 0.953512 0.550510i 0.130975 0.0756184i −0.433081 0.901355i \(-0.642574\pi\)
0.564056 + 0.825737i \(0.309240\pi\)
\(54\) 0 0
\(55\) −1.10102 + 10.8990i −0.148462 + 1.46962i
\(56\) 0 0
\(57\) 15.7980i 2.09249i
\(58\) 2.51059 + 1.44949i 0.329657 + 0.190327i
\(59\) −3.22474 5.58542i −0.419826 0.727160i 0.576096 0.817382i \(-0.304576\pi\)
−0.995922 + 0.0902223i \(0.971242\pi\)
\(60\) 2.24799 + 4.99465i 0.290214 + 0.644807i
\(61\) −4.22474 + 7.31747i −0.540923 + 0.936906i 0.457928 + 0.888989i \(0.348592\pi\)
−0.998851 + 0.0479172i \(0.984742\pi\)
\(62\) 0.898979i 0.114171i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.587486 0.815515i 0.0728687 0.101152i
\(66\) 6.00000 + 10.3923i 0.738549 + 1.27920i
\(67\) −6.92820 + 4.00000i −0.846415 + 0.488678i −0.859440 0.511237i \(-0.829187\pi\)
0.0130248 + 0.999915i \(0.495854\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) 16.8990 2.03440
\(70\) 0 0
\(71\) −10.8990 −1.29347 −0.646735 0.762714i \(-0.723866\pi\)
−0.646735 + 0.762714i \(0.723866\pi\)
\(72\) 2.59808 + 1.50000i 0.306186 + 0.176777i
\(73\) 5.97469 3.44949i 0.699285 0.403732i −0.107796 0.994173i \(-0.534379\pi\)
0.807081 + 0.590441i \(0.201046\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) −9.16756 8.12132i −1.05858 0.937769i
\(76\) 6.44949 0.739807
\(77\) 0 0
\(78\) 1.10102i 0.124666i
\(79\) −1.44949 + 2.51059i −0.163080 + 0.282463i −0.935972 0.352075i \(-0.885476\pi\)
0.772892 + 0.634538i \(0.218810\pi\)
\(80\) 2.03906 0.917738i 0.227974 0.102606i
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) −9.43879 5.44949i −1.04234 0.601795i
\(83\) 2.44949i 0.268866i −0.990923 0.134433i \(-0.957079\pi\)
0.990923 0.134433i \(-0.0429214\pi\)
\(84\) 0 0
\(85\) −4.44949 0.449490i −0.482615 0.0487540i
\(86\) 4.44949 7.70674i 0.479801 0.831039i
\(87\) −6.14966 + 3.55051i −0.659313 + 0.380655i
\(88\) 4.24264 2.44949i 0.452267 0.261116i
\(89\) −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) −6.67423 0.674235i −0.703526 0.0710706i
\(91\) 0 0
\(92\) 6.89898i 0.719268i
\(93\) −1.90702 1.10102i −0.197749 0.114171i
\(94\) 0.449490 + 0.778539i 0.0463613 + 0.0803002i
\(95\) −13.1509 + 5.91894i −1.34925 + 0.607270i
\(96\) 1.22474 2.12132i 0.125000 0.216506i
\(97\) 3.79796i 0.385624i −0.981236 0.192812i \(-0.938239\pi\)
0.981236 0.192812i \(-0.0617608\pi\)
\(98\) 0 0
\(99\) −14.6969 −1.47710
\(100\) −3.31552 + 3.74264i −0.331552 + 0.374264i
\(101\) −4.22474 7.31747i −0.420378 0.728116i 0.575599 0.817732i \(-0.304769\pi\)
−0.995976 + 0.0896167i \(0.971436\pi\)
\(102\) −4.24264 + 2.44949i −0.420084 + 0.242536i
\(103\) 2.68556 + 1.55051i 0.264616 + 0.152776i 0.626439 0.779471i \(-0.284512\pi\)
−0.361822 + 0.932247i \(0.617845\pi\)
\(104\) −0.449490 −0.0440761
\(105\) 0 0
\(106\) 1.10102 0.106941
\(107\) 6.92820 + 4.00000i 0.669775 + 0.386695i 0.795991 0.605308i \(-0.206950\pi\)
−0.126217 + 0.992003i \(0.540283\pi\)
\(108\) 0 0
\(109\) −1.44949 2.51059i −0.138836 0.240471i 0.788220 0.615393i \(-0.211003\pi\)
−0.927056 + 0.374922i \(0.877669\pi\)
\(110\) −6.40300 + 8.88828i −0.610502 + 0.847465i
\(111\) 4.89898 0.464991
\(112\) 0 0
\(113\) 0.202041i 0.0190064i −0.999955 0.00950321i \(-0.996975\pi\)
0.999955 0.00950321i \(-0.00302501\pi\)
\(114\) −7.89898 + 13.6814i −0.739807 + 1.28138i
\(115\) 6.33145 + 14.0674i 0.590411 + 1.31179i
\(116\) 1.44949 + 2.51059i 0.134582 + 0.233102i
\(117\) 1.16781 + 0.674235i 0.107964 + 0.0623330i
\(118\) 6.44949i 0.593724i
\(119\) 0 0
\(120\) −0.550510 + 5.44949i −0.0502545 + 0.497468i
\(121\) −6.50000 + 11.2583i −0.590909 + 1.02348i
\(122\) −7.31747 + 4.22474i −0.662493 + 0.382490i
\(123\) 23.1202 13.3485i 2.08468 1.20359i
\(124\) −0.449490 + 0.778539i −0.0403654 + 0.0699149i
\(125\) 3.32577 10.6742i 0.297465 0.954733i
\(126\) 0 0
\(127\) 5.10102i 0.452642i −0.974053 0.226321i \(-0.927330\pi\)
0.974053 0.226321i \(-0.0726699\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 10.8990 + 18.8776i 0.959602 + 1.66208i
\(130\) 0.916536 0.412514i 0.0803855 0.0361798i
\(131\) 0.775255 1.34278i 0.0677344 0.117319i −0.830169 0.557511i \(-0.811756\pi\)
0.897904 + 0.440192i \(0.145090\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) 15.4135 8.89898i 1.31686 0.760291i 0.333640 0.942700i \(-0.391723\pi\)
0.983223 + 0.182409i \(0.0583896\pi\)
\(138\) 14.6349 + 8.44949i 1.24581 + 0.719268i
\(139\) −6.44949 −0.547039 −0.273519 0.961867i \(-0.588188\pi\)
−0.273519 + 0.961867i \(0.588188\pi\)
\(140\) 0 0
\(141\) −2.20204 −0.185445
\(142\) −9.43879 5.44949i −0.792086 0.457311i
\(143\) 1.90702 1.10102i 0.159473 0.0920720i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) −5.25966 3.78899i −0.436791 0.314658i
\(146\) 6.89898 0.570964
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) 7.89898 13.6814i 0.647110 1.12083i −0.336700 0.941612i \(-0.609311\pi\)
0.983810 0.179215i \(-0.0573557\pi\)
\(150\) −3.87868 11.6170i −0.316693 0.948528i
\(151\) 9.79796 + 16.9706i 0.797347 + 1.38104i 0.921338 + 0.388762i \(0.127097\pi\)
−0.123992 + 0.992283i \(0.539570\pi\)
\(152\) 5.58542 + 3.22474i 0.453038 + 0.261561i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0.202041 2.00000i 0.0162283 0.160644i
\(156\) 0.550510 0.953512i 0.0440761 0.0763420i
\(157\) 7.31747 4.22474i 0.583998 0.337171i −0.178723 0.983899i \(-0.557196\pi\)
0.762721 + 0.646728i \(0.223863\pi\)
\(158\) −2.51059 + 1.44949i −0.199732 + 0.115315i
\(159\) −1.34847 + 2.33562i −0.106941 + 0.185226i
\(160\) 2.22474 + 0.224745i 0.175882 + 0.0177676i
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) −14.6349 8.44949i −1.14630 0.661815i −0.198315 0.980138i \(-0.563547\pi\)
−0.947982 + 0.318323i \(0.896880\pi\)
\(164\) −5.44949 9.43879i −0.425534 0.737046i
\(165\) −11.0129 24.4687i −0.857349 1.90489i
\(166\) 1.22474 2.12132i 0.0950586 0.164646i
\(167\) 4.89898i 0.379094i 0.981872 + 0.189547i \(0.0607020\pi\)
−0.981872 + 0.189547i \(0.939298\pi\)
\(168\) 0 0
\(169\) 12.7980 0.984458
\(170\) −3.62863 2.61401i −0.278303 0.200486i
\(171\) −9.67423 16.7563i −0.739807 1.28138i
\(172\) 7.70674 4.44949i 0.587634 0.339270i
\(173\) 15.8028 + 9.12372i 1.20146 + 0.693664i 0.960880 0.276965i \(-0.0893286\pi\)
0.240581 + 0.970629i \(0.422662\pi\)
\(174\) −7.10102 −0.538327
\(175\) 0 0
\(176\) 4.89898 0.369274
\(177\) 13.6814 + 7.89898i 1.02836 + 0.593724i
\(178\) −8.66025 + 5.00000i −0.649113 + 0.374766i
\(179\) −2.89898 5.02118i −0.216680 0.375301i 0.737111 0.675772i \(-0.236189\pi\)
−0.953791 + 0.300471i \(0.902856\pi\)
\(180\) −5.44294 3.92102i −0.405693 0.292256i
\(181\) 14.2474 1.05900 0.529502 0.848309i \(-0.322379\pi\)
0.529502 + 0.848309i \(0.322379\pi\)
\(182\) 0 0
\(183\) 20.6969i 1.52996i
\(184\) 3.44949 5.97469i 0.254300 0.440460i
\(185\) 1.83548 + 4.07812i 0.134947 + 0.299829i
\(186\) −1.10102 1.90702i −0.0807307 0.139830i
\(187\) −8.48528 4.89898i −0.620505 0.358249i
\(188\) 0.898979i 0.0655648i
\(189\) 0 0
\(190\) −14.3485 1.44949i −1.04095 0.105157i
\(191\) 8.34847 14.4600i 0.604074 1.04629i −0.388123 0.921608i \(-0.626876\pi\)
0.992197 0.124679i \(-0.0397902\pi\)
\(192\) 2.12132 1.22474i 0.153093 0.0883883i
\(193\) −15.2385 + 8.79796i −1.09689 + 0.633291i −0.935403 0.353584i \(-0.884963\pi\)
−0.161489 + 0.986874i \(0.551630\pi\)
\(194\) 1.89898 3.28913i 0.136339 0.236146i
\(195\) −0.247449 + 2.44949i −0.0177202 + 0.175412i
\(196\) 0 0
\(197\) 9.10102i 0.648421i 0.945985 + 0.324210i \(0.105099\pi\)
−0.945985 + 0.324210i \(0.894901\pi\)
\(198\) −12.7279 7.34847i −0.904534 0.522233i
\(199\) 3.55051 + 6.14966i 0.251689 + 0.435938i 0.963991 0.265935i \(-0.0856807\pi\)
−0.712302 + 0.701873i \(0.752347\pi\)
\(200\) −4.74264 + 1.58346i −0.335355 + 0.111968i
\(201\) 9.79796 16.9706i 0.691095 1.19701i
\(202\) 8.44949i 0.594504i
\(203\) 0 0
\(204\) −4.89898 −0.342997
\(205\) 19.7742 + 14.2450i 1.38109 + 0.994917i
\(206\) 1.55051 + 2.68556i 0.108029 + 0.187112i
\(207\) −17.9241 + 10.3485i −1.24581 + 0.719268i
\(208\) −0.389270 0.224745i −0.0269910 0.0155833i
\(209\) −31.5959 −2.18554
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0.953512 + 0.550510i 0.0654875 + 0.0378092i
\(213\) 23.1202 13.3485i 1.58417 0.914622i
\(214\) 4.00000 + 6.92820i 0.273434 + 0.473602i
\(215\) −11.6310 + 16.1455i −0.793230 + 1.10112i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.89898i 0.196344i
\(219\) −8.44949 + 14.6349i −0.570964 + 0.988938i
\(220\) −9.98930 + 4.49598i −0.673479 + 0.303119i
\(221\) 0.449490 + 0.778539i 0.0302360 + 0.0523702i
\(222\) 4.24264 + 2.44949i 0.284747 + 0.164399i
\(223\) 4.00000i 0.267860i 0.990991 + 0.133930i \(0.0427597\pi\)
−0.990991 + 0.133930i \(0.957240\pi\)
\(224\) 0 0
\(225\) 14.6969 + 3.00000i 0.979796 + 0.200000i
\(226\) 0.101021 0.174973i 0.00671978 0.0116390i
\(227\) −6.36396 + 3.67423i −0.422391 + 0.243868i −0.696100 0.717945i \(-0.745083\pi\)
0.273709 + 0.961813i \(0.411750\pi\)
\(228\) −13.6814 + 7.89898i −0.906075 + 0.523123i
\(229\) 7.57321 13.1172i 0.500452 0.866808i −0.499548 0.866286i \(-0.666500\pi\)
1.00000 0.000522089i \(-0.000166186\pi\)
\(230\) −1.55051 + 15.3485i −0.102238 + 1.01205i
\(231\) 0 0
\(232\) 2.89898i 0.190327i
\(233\) 8.83523 + 5.10102i 0.578815 + 0.334179i 0.760662 0.649148i \(-0.224874\pi\)
−0.181847 + 0.983327i \(0.558208\pi\)
\(234\) 0.674235 + 1.16781i 0.0440761 + 0.0763420i
\(235\) −0.825027 1.83307i −0.0538188 0.119576i
\(236\) 3.22474 5.58542i 0.209913 0.363580i
\(237\) 7.10102i 0.461261i
\(238\) 0 0
\(239\) 25.7980 1.66873 0.834366 0.551211i \(-0.185834\pi\)
0.834366 + 0.551211i \(0.185834\pi\)
\(240\) −3.20150 + 4.44414i −0.206656 + 0.286868i
\(241\) −10.3485 17.9241i −0.666604 1.15459i −0.978848 0.204589i \(-0.934414\pi\)
0.312244 0.950002i \(-0.398919\pi\)
\(242\) −11.2583 + 6.50000i −0.723713 + 0.417836i
\(243\) −19.0919 11.0227i −1.22474 0.707107i
\(244\) −8.44949 −0.540923
\(245\) 0 0
\(246\) 26.6969 1.70213
\(247\) 2.51059 + 1.44949i 0.159745 + 0.0922288i
\(248\) −0.778539 + 0.449490i −0.0494373 + 0.0285426i
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 8.21731 7.58128i 0.519709 0.479482i
\(251\) −1.55051 −0.0978673 −0.0489337 0.998802i \(-0.515582\pi\)
−0.0489337 + 0.998802i \(0.515582\pi\)
\(252\) 0 0
\(253\) 33.7980i 2.12486i
\(254\) 2.55051 4.41761i 0.160033 0.277186i
\(255\) 9.98930 4.49598i 0.625554 0.281549i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −17.9241 10.3485i −1.11807 0.645520i −0.177165 0.984181i \(-0.556693\pi\)
−0.940908 + 0.338661i \(0.890026\pi\)
\(258\) 21.7980i 1.35708i
\(259\) 0 0
\(260\) 1.00000 + 0.101021i 0.0620174 + 0.00626503i
\(261\) 4.34847 7.53177i 0.269163 0.466205i
\(262\) 1.34278 0.775255i 0.0829573 0.0478954i
\(263\) 8.48528 4.89898i 0.523225 0.302084i −0.215028 0.976608i \(-0.568984\pi\)
0.738253 + 0.674524i \(0.235651\pi\)
\(264\) −6.00000 + 10.3923i −0.369274 + 0.639602i
\(265\) −2.44949 0.247449i −0.150471 0.0152007i
\(266\) 0 0
\(267\) 24.4949i 1.49906i
\(268\) −6.92820 4.00000i −0.423207 0.244339i
\(269\) −7.57321 13.1172i −0.461747 0.799769i 0.537301 0.843390i \(-0.319444\pi\)
−0.999048 + 0.0436212i \(0.986111\pi\)
\(270\) 0 0
\(271\) −6.00000 + 10.3923i −0.364474 + 0.631288i −0.988692 0.149963i \(-0.952085\pi\)
0.624218 + 0.781251i \(0.285418\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 17.7980 1.07521
\(275\) 16.2426 18.3351i 0.979468 1.10565i
\(276\) 8.44949 + 14.6349i 0.508600 + 0.880920i
\(277\) −4.41761 + 2.55051i −0.265429 + 0.153245i −0.626808 0.779173i \(-0.715639\pi\)
0.361380 + 0.932419i \(0.382306\pi\)
\(278\) −5.58542 3.22474i −0.334991 0.193407i
\(279\) 2.69694 0.161461
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −1.90702 1.10102i −0.113562 0.0655648i
\(283\) −24.4630 + 14.1237i −1.45417 + 0.839568i −0.998715 0.0506878i \(-0.983859\pi\)
−0.455460 + 0.890256i \(0.650525\pi\)
\(284\) −5.44949 9.43879i −0.323368 0.560089i
\(285\) 20.6480 28.6624i 1.22308 1.69782i
\(286\) 2.20204 0.130209
\(287\) 0 0
\(288\) 3.00000i 0.176777i
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) −2.66050 5.91119i −0.156230 0.347117i
\(291\) 4.65153 + 8.05669i 0.272678 + 0.472291i
\(292\) 5.97469 + 3.44949i 0.349642 + 0.201866i
\(293\) 6.24745i 0.364980i 0.983208 + 0.182490i \(0.0584157\pi\)
−0.983208 + 0.182490i \(0.941584\pi\)
\(294\) 0 0
\(295\) −1.44949 + 14.3485i −0.0843926 + 0.835400i
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 0 0
\(298\) 13.6814 7.89898i 0.792544 0.457576i
\(299\) 1.55051 2.68556i 0.0896683 0.155310i
\(300\) 2.44949 12.0000i 0.141421 0.692820i
\(301\) 0 0
\(302\) 19.5959i 1.12762i
\(303\) 17.9241 + 10.3485i 1.02971 + 0.594504i
\(304\) 3.22474 + 5.58542i 0.184952 + 0.320346i
\(305\) 17.2290 7.75442i 0.986530 0.444017i
\(306\) 3.00000 5.19615i 0.171499 0.297044i
\(307\) 4.24745i 0.242415i 0.992627 + 0.121207i \(0.0386766\pi\)
−0.992627 + 0.121207i \(0.961323\pi\)
\(308\) 0 0
\(309\) −7.59592 −0.432117
\(310\) 1.17497 1.63103i 0.0667340 0.0926363i
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) 0.953512 0.550510i 0.0539820 0.0311665i
\(313\) 15.2385 + 8.79796i 0.861332 + 0.497290i 0.864458 0.502705i \(-0.167662\pi\)
−0.00312637 + 0.999995i \(0.500995\pi\)
\(314\) 8.44949 0.476832
\(315\) 0 0
\(316\) −2.89898 −0.163080
\(317\) −22.9453 13.2474i −1.28873 0.744051i −0.310305 0.950637i \(-0.600431\pi\)
−0.978428 + 0.206586i \(0.933765\pi\)
\(318\) −2.33562 + 1.34847i −0.130975 + 0.0756184i
\(319\) −7.10102 12.2993i −0.397581 0.688630i
\(320\) 1.81431 + 1.30701i 0.101423 + 0.0730639i
\(321\) −19.5959 −1.09374
\(322\) 0 0
\(323\) 12.8990i 0.717718i
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) −2.13177 + 0.711751i −0.118249 + 0.0394808i
\(326\) −8.44949 14.6349i −0.467974 0.810555i
\(327\) 6.14966 + 3.55051i 0.340077 + 0.196344i
\(328\) 10.8990i 0.601795i
\(329\) 0 0
\(330\) 2.69694 26.6969i 0.148462 1.46962i
\(331\) −5.34847 + 9.26382i −0.293978 + 0.509186i −0.974747 0.223313i \(-0.928313\pi\)
0.680768 + 0.732499i \(0.261646\pi\)
\(332\) 2.12132 1.22474i 0.116423 0.0672166i
\(333\) −5.19615 + 3.00000i −0.284747 + 0.164399i
\(334\) −2.44949 + 4.24264i −0.134030 + 0.232147i
\(335\) 17.7980 + 1.79796i 0.972406 + 0.0982330i
\(336\) 0 0
\(337\) 29.5959i 1.61219i −0.591785 0.806096i \(-0.701576\pi\)
0.591785 0.806096i \(-0.298424\pi\)
\(338\) 11.0834 + 6.39898i 0.602855 + 0.348059i
\(339\) 0.247449 + 0.428594i 0.0134396 + 0.0232780i
\(340\) −1.83548 4.07812i −0.0995426 0.221167i
\(341\) 2.20204 3.81405i 0.119247 0.206542i
\(342\) 19.3485i 1.04625i
\(343\) 0 0
\(344\) 8.89898 0.479801
\(345\) −30.6600 22.0871i −1.65068 1.18913i
\(346\) 9.12372 + 15.8028i 0.490494 + 0.849561i
\(347\) 16.5420 9.55051i 0.888019 0.512698i 0.0147253 0.999892i \(-0.495313\pi\)
0.873294 + 0.487193i \(0.161979\pi\)
\(348\) −6.14966 3.55051i −0.329657 0.190327i
\(349\) 3.55051 0.190054 0.0950272 0.995475i \(-0.469706\pi\)
0.0950272 + 0.995475i \(0.469706\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.24264 + 2.44949i 0.226134 + 0.130558i
\(353\) −11.3458 + 6.55051i −0.603877 + 0.348648i −0.770565 0.637361i \(-0.780026\pi\)
0.166688 + 0.986010i \(0.446693\pi\)
\(354\) 7.89898 + 13.6814i 0.419826 + 0.727160i
\(355\) 19.7742 + 14.2450i 1.04950 + 0.756048i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 5.79796i 0.306432i
\(359\) 5.79796 10.0424i 0.306005 0.530015i −0.671480 0.741023i \(-0.734341\pi\)
0.977484 + 0.211007i \(0.0676744\pi\)
\(360\) −2.75321 6.11717i −0.145107 0.322403i
\(361\) −11.2980 19.5686i −0.594629 1.02993i
\(362\) 12.3387 + 7.12372i 0.648505 + 0.374415i
\(363\) 31.8434i 1.67134i
\(364\) 0 0
\(365\) −15.3485 1.55051i −0.803376 0.0811574i
\(366\) 10.3485 17.9241i 0.540923 0.936906i
\(367\) 27.7128 16.0000i 1.44660 0.835193i 0.448320 0.893873i \(-0.352022\pi\)
0.998277 + 0.0586798i \(0.0186891\pi\)
\(368\) 5.97469 3.44949i 0.311452 0.179817i
\(369\) −16.3485 + 28.3164i −0.851067 + 1.47409i
\(370\) −0.449490 + 4.44949i −0.0233679 + 0.231318i
\(371\) 0 0
\(372\) 2.20204i 0.114171i
\(373\) 21.3882 + 12.3485i 1.10744 + 0.639380i 0.938165 0.346190i \(-0.112525\pi\)
0.169273 + 0.985569i \(0.445858\pi\)
\(374\) −4.89898 8.48528i −0.253320 0.438763i
\(375\) 6.01820 + 26.7167i 0.310779 + 1.37964i
\(376\) −0.449490 + 0.778539i −0.0231807 + 0.0401501i
\(377\) 1.30306i 0.0671111i
\(378\) 0 0
\(379\) −1.30306 −0.0669338 −0.0334669 0.999440i \(-0.510655\pi\)
−0.0334669 + 0.999440i \(0.510655\pi\)
\(380\) −11.7014 8.42953i −0.600269 0.432426i
\(381\) 6.24745 + 10.8209i 0.320066 + 0.554371i
\(382\) 14.4600 8.34847i 0.739837 0.427145i
\(383\) −14.6349 8.44949i −0.747811 0.431749i 0.0770916 0.997024i \(-0.475437\pi\)
−0.824902 + 0.565275i \(0.808770\pi\)
\(384\) 2.44949 0.125000
\(385\) 0 0
\(386\) −17.5959 −0.895609
\(387\) −23.1202 13.3485i −1.17527 0.678541i
\(388\) 3.28913 1.89898i 0.166980 0.0964061i
\(389\) 11.4495 + 19.8311i 0.580512 + 1.00548i 0.995419 + 0.0956125i \(0.0304810\pi\)
−0.414906 + 0.909864i \(0.636186\pi\)
\(390\) −1.43904 + 1.99760i −0.0728687 + 0.101152i
\(391\) −13.7980 −0.697793
\(392\) 0 0
\(393\) 3.79796i 0.191582i
\(394\) −4.55051 + 7.88171i −0.229251 + 0.397075i
\(395\) 5.91119 2.66050i 0.297424 0.133864i
\(396\) −7.34847 12.7279i −0.369274 0.639602i
\(397\) 15.0242 + 8.67423i 0.754044 + 0.435347i 0.827153 0.561977i \(-0.189959\pi\)
−0.0731094 + 0.997324i \(0.523292\pi\)
\(398\) 7.10102i 0.355942i
\(399\) 0 0
\(400\) −4.89898 1.00000i −0.244949 0.0500000i
\(401\) −14.6969 + 25.4558i −0.733930 + 1.27120i 0.221261 + 0.975215i \(0.428983\pi\)
−0.955191 + 0.295990i \(0.904351\pi\)
\(402\) 16.9706 9.79796i 0.846415 0.488678i
\(403\) −0.349945 + 0.202041i −0.0174320 + 0.0100644i
\(404\) 4.22474 7.31747i 0.210189 0.364058i
\(405\) 2.02270 20.0227i 0.100509 0.994936i
\(406\) 0 0
\(407\) 9.79796i 0.485667i
\(408\) −4.24264 2.44949i −0.210042 0.121268i
\(409\) −7.24745 12.5529i −0.358363 0.620703i 0.629324 0.777143i \(-0.283332\pi\)
−0.987688 + 0.156439i \(0.949998\pi\)
\(410\) 10.0024 + 22.2237i 0.493984 + 1.09755i
\(411\) −21.7980 + 37.7552i −1.07521 + 1.86233i
\(412\) 3.10102i 0.152776i
\(413\) 0 0
\(414\) −20.6969 −1.01720
\(415\) −3.20150 + 4.44414i −0.157155 + 0.218154i
\(416\) −0.224745 0.389270i −0.0110190 0.0190855i
\(417\) 13.6814 7.89898i 0.669983 0.386815i
\(418\) −27.3629 15.7980i −1.33836 0.772703i
\(419\) 6.44949 0.315078 0.157539 0.987513i \(-0.449644\pi\)
0.157539 + 0.987513i \(0.449644\pi\)
\(420\) 0 0
\(421\) −23.7980 −1.15984 −0.579921 0.814673i \(-0.696917\pi\)
−0.579921 + 0.814673i \(0.696917\pi\)
\(422\) 10.3923 + 6.00000i 0.505889 + 0.292075i
\(423\) 2.33562 1.34847i 0.113562 0.0655648i
\(424\) 0.550510 + 0.953512i 0.0267351 + 0.0463066i
\(425\) 7.48528 + 6.63103i 0.363089 + 0.321652i
\(426\) 26.6969 1.29347
\(427\) 0 0
\(428\) 8.00000i 0.386695i
\(429\) −2.69694 + 4.67123i −0.130209 + 0.225529i
\(430\) −18.1455 + 8.16693i −0.875055 + 0.393844i
\(431\) −8.89898 15.4135i −0.428649 0.742441i 0.568105 0.822956i \(-0.307677\pi\)
−0.996753 + 0.0805149i \(0.974344\pi\)
\(432\) 0 0
\(433\) 19.7980i 0.951429i 0.879600 + 0.475715i \(0.157810\pi\)
−0.879600 + 0.475715i \(0.842190\pi\)
\(434\) 0 0
\(435\) 15.7980 + 1.59592i 0.757454 + 0.0765184i
\(436\) 1.44949 2.51059i 0.0694180 0.120235i
\(437\) −38.5337 + 22.2474i −1.84332 + 1.06424i
\(438\) −14.6349 + 8.44949i −0.699285 + 0.403732i
\(439\) 18.6969 32.3840i 0.892356 1.54561i 0.0553132 0.998469i \(-0.482384\pi\)
0.837043 0.547137i \(-0.184282\pi\)
\(440\) −10.8990 1.10102i −0.519588 0.0524891i
\(441\) 0 0
\(442\) 0.898979i 0.0427601i
\(443\) −8.48528 4.89898i −0.403148 0.232758i 0.284693 0.958619i \(-0.408108\pi\)
−0.687841 + 0.725861i \(0.741442\pi\)
\(444\) 2.44949 + 4.24264i 0.116248 + 0.201347i
\(445\) 20.3906 9.17738i 0.966606 0.435049i
\(446\) −2.00000 + 3.46410i −0.0947027 + 0.164030i
\(447\) 38.6969i 1.83030i
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 11.2279 + 9.94655i 0.529289 + 0.468885i
\(451\) 26.6969 + 46.2405i 1.25711 + 2.17738i
\(452\) 0.174973 0.101021i 0.00823002 0.00475161i
\(453\) −41.5692 24.0000i −1.95309 1.12762i
\(454\) −7.34847 −0.344881
\(455\) 0 0
\(456\) −15.7980 −0.739807
\(457\) 8.31031 + 4.79796i 0.388740 + 0.224439i 0.681614 0.731712i \(-0.261278\pi\)
−0.292874 + 0.956151i \(0.594612\pi\)
\(458\) 13.1172 7.57321i 0.612926 0.353873i
\(459\) 0 0
\(460\) −9.01702 + 12.5169i −0.420421 + 0.583604i
\(461\) 2.65153 0.123494 0.0617470 0.998092i \(-0.480333\pi\)
0.0617470 + 0.998092i \(0.480333\pi\)
\(462\) 0 0
\(463\) 35.5959i 1.65428i 0.561994 + 0.827141i \(0.310034\pi\)
−0.561994 + 0.827141i \(0.689966\pi\)
\(464\) −1.44949 + 2.51059i −0.0672909 + 0.116551i
\(465\) 2.02090 + 4.49009i 0.0937168 + 0.208223i
\(466\) 5.10102 + 8.83523i 0.236300 + 0.409284i
\(467\) −4.80688 2.77526i −0.222436 0.128423i 0.384642 0.923066i \(-0.374325\pi\)
−0.607078 + 0.794642i \(0.707658\pi\)
\(468\) 1.34847i 0.0623330i
\(469\) 0 0
\(470\) 0.202041 2.00000i 0.00931946 0.0922531i
\(471\) −10.3485 + 17.9241i −0.476832 + 0.825898i
\(472\) 5.58542 3.22474i 0.257090 0.148431i
\(473\) −37.7552 + 21.7980i −1.73598 + 1.00227i
\(474\) 3.55051 6.14966i 0.163080 0.282463i
\(475\) 31.5959 + 6.44949i 1.44972 + 0.295923i
\(476\) 0 0
\(477\) 3.30306i 0.151237i
\(478\) 22.3417 + 12.8990i 1.02189 + 0.589986i
\(479\) 19.3485 + 33.5125i 0.884054 + 1.53123i 0.846794 + 0.531921i \(0.178530\pi\)
0.0372602 + 0.999306i \(0.488137\pi\)
\(480\) −4.99465 + 2.24799i −0.227974 + 0.102606i
\(481\) 0.449490 0.778539i 0.0204950 0.0354983i
\(482\) 20.6969i 0.942720i
\(483\) 0 0
\(484\) −13.0000 −0.590909
\(485\) −4.96396 + 6.89069i −0.225402 + 0.312890i
\(486\) −11.0227 19.0919i −0.500000 0.866025i
\(487\) −31.7805 + 18.3485i −1.44011 + 0.831449i −0.997856 0.0654410i \(-0.979155\pi\)
−0.442255 + 0.896890i \(0.645821\pi\)
\(488\) −7.31747 4.22474i −0.331246 0.191245i
\(489\) 41.3939 1.87190
\(490\) 0 0
\(491\) −19.5959 −0.884351 −0.442176 0.896928i \(-0.645793\pi\)
−0.442176 + 0.896928i \(0.645793\pi\)
\(492\) 23.1202 + 13.3485i 1.04234 + 0.601795i
\(493\) 5.02118 2.89898i 0.226143 0.130563i
\(494\) 1.44949 + 2.51059i 0.0652156 + 0.112957i
\(495\) 26.6648 + 19.2090i 1.19850 + 0.863381i
\(496\) −0.898979 −0.0403654
\(497\) 0 0
\(498\) 6.00000i 0.268866i
\(499\) 12.8990 22.3417i 0.577438 1.00015i −0.418334 0.908293i \(-0.637386\pi\)
0.995772 0.0918583i \(-0.0292807\pi\)
\(500\) 10.9070 2.45692i 0.487778 0.109877i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) −1.34278 0.775255i −0.0599313 0.0346013i
\(503\) 4.00000i 0.178351i 0.996016 + 0.0891756i \(0.0284232\pi\)
−0.996016 + 0.0891756i \(0.971577\pi\)
\(504\) 0 0
\(505\) −1.89898 + 18.7980i −0.0845035 + 0.836498i
\(506\) −16.8990 + 29.2699i −0.751251 + 1.30121i
\(507\) −27.1486 + 15.6742i −1.20571 + 0.696117i
\(508\) 4.41761 2.55051i 0.196000 0.113161i
\(509\) −18.2247 + 31.5662i −0.807798 + 1.39915i 0.106588 + 0.994303i \(0.466007\pi\)
−0.914386 + 0.404843i \(0.867326\pi\)
\(510\) 10.8990 + 1.10102i 0.482615 + 0.0487540i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −10.3485 17.9241i −0.456451 0.790597i
\(515\) −2.84592 6.32316i −0.125406 0.278632i
\(516\) −10.8990 + 18.8776i −0.479801 + 0.831039i
\(517\) 4.40408i 0.193691i
\(518\) 0 0
\(519\) −44.6969 −1.96198
\(520\) 0.815515 + 0.587486i 0.0357627 + 0.0257630i
\(521\) −1.65153 2.86054i −0.0723549 0.125322i 0.827578 0.561351i \(-0.189718\pi\)
−0.899933 + 0.436028i \(0.856385\pi\)
\(522\) 7.53177 4.34847i 0.329657 0.190327i
\(523\) 0.992836 + 0.573214i 0.0434137 + 0.0250649i 0.521550 0.853221i \(-0.325354\pi\)
−0.478136 + 0.878286i \(0.658687\pi\)
\(524\) 1.55051 0.0677344
\(525\) 0 0
\(526\) 9.79796 0.427211
\(527\) 1.55708 + 0.898979i 0.0678274 + 0.0391602i
\(528\) −10.3923 + 6.00000i −0.452267 + 0.261116i
\(529\) 12.2980 + 21.3007i 0.534694 + 0.926117i
\(530\) −1.99760 1.43904i −0.0867700 0.0625080i
\(531\) −19.3485 −0.839652
\(532\) 0 0
\(533\) 4.89898i 0.212198i
\(534\) 12.2474 21.2132i 0.529999 0.917985i
\(535\) −7.34190 16.3125i −0.317418 0.705249i
\(536\) −4.00000 6.92820i −0.172774 0.299253i
\(537\) 12.2993 + 7.10102i 0.530755 + 0.306432i
\(538\) 15.1464i 0.653009i
\(539\) 0 0
\(540\) 0 0
\(541\) 14.7980 25.6308i 0.636214 1.10195i −0.350043 0.936734i \(-0.613833\pi\)
0.986257 0.165221i \(-0.0528338\pi\)
\(542\) −10.3923 + 6.00000i −0.446388 + 0.257722i
\(543\) −30.2234 + 17.4495i −1.29701 + 0.748829i
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) −0.651531 + 6.44949i −0.0279085 + 0.276266i
\(546\) 0 0
\(547\) 10.6969i 0.457368i 0.973501 + 0.228684i \(0.0734423\pi\)
−0.973501 + 0.228684i \(0.926558\pi\)
\(548\) 15.4135 + 8.89898i 0.658431 + 0.380146i
\(549\) 12.6742 + 21.9524i 0.540923 + 0.936906i
\(550\) 23.2341 7.75736i 0.990705 0.330775i
\(551\) 9.34847 16.1920i 0.398258 0.689803i
\(552\) 16.8990i 0.719268i
\(553\) 0 0
\(554\) −5.10102 −0.216722
\(555\) −8.88828 6.40300i −0.377287 0.271792i
\(556\) −3.22474 5.58542i −0.136760 0.236875i
\(557\) −14.4600 + 8.34847i −0.612689 + 0.353736i −0.774017 0.633165i \(-0.781756\pi\)
0.161328 + 0.986901i \(0.448422\pi\)
\(558\) 2.33562 + 1.34847i 0.0988746 + 0.0570853i
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) −15.5885 9.00000i −0.657559 0.379642i
\(563\) −12.1637 + 7.02270i −0.512638 + 0.295972i −0.733917 0.679239i \(-0.762310\pi\)
0.221279 + 0.975210i \(0.428977\pi\)
\(564\) −1.10102 1.90702i −0.0463613 0.0803002i
\(565\) −0.264069 + 0.366566i −0.0111095 + 0.0154215i
\(566\) −28.2474 −1.18733
\(567\) 0 0
\(568\) 10.8990i 0.457311i
\(569\) 7.10102 12.2993i 0.297690 0.515615i −0.677917 0.735139i \(-0.737117\pi\)
0.975607 + 0.219524i \(0.0704504\pi\)
\(570\) 32.2130 14.4984i 1.34925 0.607270i
\(571\) 10.4495 + 18.0990i 0.437298 + 0.757422i 0.997480 0.0709477i \(-0.0226023\pi\)
−0.560183 + 0.828369i \(0.689269\pi\)
\(572\) 1.90702 + 1.10102i 0.0797367 + 0.0460360i
\(573\) 40.8990i 1.70858i
\(574\) 0 0
\(575\) 6.89898 33.7980i 0.287707 1.40947i
\(576\) −1.50000 + 2.59808i −0.0625000 + 0.108253i
\(577\) 40.2658 23.2474i 1.67629 0.967804i 0.712290 0.701885i \(-0.247658\pi\)
0.963995 0.265919i \(-0.0856753\pi\)
\(578\) −11.2583 + 6.50000i −0.468285 + 0.270364i
\(579\) 21.5505 37.3266i 0.895609 1.55124i
\(580\) 0.651531 6.44949i 0.0270533 0.267800i
\(581\) 0 0
\(582\) 9.30306i 0.385624i
\(583\) −4.67123 2.69694i −0.193463 0.111696i
\(584\) 3.44949 + 5.97469i 0.142741 + 0.247234i
\(585\) −1.23754 2.74961i −0.0511660 0.113682i
\(586\) −3.12372 + 5.41045i −0.129040 + 0.223504i
\(587\) 33.1464i 1.36810i −0.729435 0.684050i \(-0.760217\pi\)
0.729435 0.684050i \(-0.239783\pi\)
\(588\) 0 0
\(589\) 5.79796 0.238901
\(590\) −8.42953 + 11.7014i −0.347038 + 0.481739i
\(591\) −11.1464 19.3062i −0.458503 0.794150i
\(592\) 1.73205 1.00000i 0.0711868 0.0410997i
\(593\) −0.953512 0.550510i −0.0391560 0.0226067i 0.480294 0.877107i \(-0.340530\pi\)
−0.519450 + 0.854501i \(0.673863\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.7980 0.647110
\(597\) −15.0635 8.69694i −0.616510 0.355942i
\(598\) 2.68556 1.55051i 0.109821 0.0634051i
\(599\) −11.4495 19.8311i −0.467813 0.810277i 0.531510 0.847052i \(-0.321625\pi\)
−0.999324 + 0.0367753i \(0.988291\pi\)
\(600\) 8.12132 9.16756i 0.331552 0.374264i
\(601\) 19.3939 0.791093 0.395546 0.918446i \(-0.370555\pi\)
0.395546 + 0.918446i \(0.370555\pi\)
\(602\) 0 0
\(603\) 24.0000i 0.977356i
\(604\) −9.79796 + 16.9706i −0.398673 + 0.690522i
\(605\) 26.5078 11.9306i 1.07769 0.485047i
\(606\) 10.3485 + 17.9241i 0.420378 + 0.728116i
\(607\) 21.9917 + 12.6969i 0.892617 + 0.515353i 0.874798 0.484488i \(-0.160994\pi\)
0.0178196 + 0.999841i \(0.494328\pi\)
\(608\) 6.44949i 0.261561i
\(609\) 0 0
\(610\) 18.7980 + 1.89898i 0.761107 + 0.0768874i
\(611\) −0.202041 + 0.349945i −0.00817371 + 0.0141573i
\(612\) 5.19615 3.00000i 0.210042 0.121268i
\(613\) 7.10318 4.10102i 0.286895 0.165639i −0.349646 0.936882i \(-0.613698\pi\)
0.636541 + 0.771243i \(0.280365\pi\)
\(614\) −2.12372 + 3.67840i −0.0857065 + 0.148448i
\(615\) −59.3939 6.00000i −2.39499 0.241943i
\(616\) 0 0
\(617\) 9.59592i 0.386317i −0.981168 0.193159i \(-0.938127\pi\)
0.981168 0.193159i \(-0.0618732\pi\)
\(618\) −6.57826 3.79796i −0.264616 0.152776i
\(619\) −23.2247 40.2264i −0.933481 1.61684i −0.777320 0.629106i \(-0.783421\pi\)
−0.156161 0.987732i \(-0.549912\pi\)
\(620\) 1.83307 0.825027i 0.0736179 0.0331339i
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 1.10102 0.0440761
\(625\) −19.9853 + 15.0196i −0.799411 + 0.600784i
\(626\) 8.79796 + 15.2385i 0.351637 + 0.609053i
\(627\) 67.0251 38.6969i 2.67672 1.54541i
\(628\) 7.31747 + 4.22474i 0.291999 + 0.168586i
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 6.49490 0.258558 0.129279 0.991608i \(-0.458734\pi\)
0.129279 + 0.991608i \(0.458734\pi\)
\(632\) −2.51059 1.44949i −0.0998659 0.0576576i
\(633\) −25.4558 + 14.6969i −1.01178 + 0.584151i
\(634\) −13.2474 22.9453i −0.526123 0.911272i
\(635\) −6.66707 + 9.25485i −0.264575 + 0.367267i
\(636\) −2.69694 −0.106941
\(637\) 0 0
\(638\) 14.2020i 0.562264i
\(639\) −16.3485 + 28.3164i −0.646735 + 1.12018i
\(640\) 0.917738 + 2.03906i 0.0362768 + 0.0806008i
\(641\) −3.10102 5.37113i −0.122483 0.212147i 0.798263 0.602309i \(-0.205752\pi\)
−0.920746 + 0.390162i \(0.872419\pi\)
\(642\) −16.9706 9.79796i −0.669775 0.386695i
\(643\) 9.14643i 0.360700i 0.983603 + 0.180350i \(0.0577230\pi\)
−0.983603 + 0.180350i \(0.942277\pi\)
\(644\) 0 0
\(645\) 4.89898 48.4949i 0.192897 1.90948i
\(646\) 6.44949 11.1708i 0.253752 0.439511i
\(647\) 19.3062 11.1464i 0.759004 0.438211i −0.0699339 0.997552i \(-0.522279\pi\)
0.828938 + 0.559340i \(0.188945\pi\)
\(648\) −7.79423 + 4.50000i −0.306186 + 0.176777i
\(649\) −15.7980 + 27.3629i −0.620124 + 1.07409i
\(650\) −2.20204 0.449490i −0.0863712 0.0176304i
\(651\) 0 0
\(652\) 16.8990i 0.661815i
\(653\) −34.4660 19.8990i −1.34876 0.778707i −0.360687 0.932687i \(-0.617458\pi\)
−0.988074 + 0.153980i \(0.950791\pi\)
\(654\) 3.55051 + 6.14966i 0.138836 + 0.240471i
\(655\) −3.16158 + 1.42296i −0.123533 + 0.0555997i
\(656\) 5.44949 9.43879i 0.212767 0.368523i
\(657\) 20.6969i 0.807464i
\(658\) 0 0
\(659\) −7.10102 −0.276616 −0.138308 0.990389i \(-0.544166\pi\)
−0.138308 + 0.990389i \(0.544166\pi\)
\(660\) 15.6841 21.7718i 0.610502 0.847465i
\(661\) −6.47219 11.2102i −0.251739 0.436025i 0.712266 0.701910i \(-0.247669\pi\)
−0.964005 + 0.265885i \(0.914336\pi\)
\(662\) −9.26382 + 5.34847i −0.360049 + 0.207874i
\(663\) −1.90702 1.10102i −0.0740627 0.0427601i
\(664\) 2.44949 0.0950586
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) −17.3205 10.0000i −0.670653 0.387202i
\(668\) −4.24264 + 2.44949i −0.164153 + 0.0947736i
\(669\) −4.89898 8.48528i −0.189405 0.328060i
\(670\) 14.5145 + 10.4561i 0.560744 + 0.403953i
\(671\) 41.3939 1.59799
\(672\) 0 0
\(673\) 1.79796i 0.0693062i −0.999399 0.0346531i \(-0.988967\pi\)
0.999399 0.0346531i \(-0.0110326\pi\)
\(674\) 14.7980 25.6308i 0.569996 0.987262i
\(675\) 0 0
\(676\) 6.39898 + 11.0834i 0.246115 + 0.426283i
\(677\) 27.3235 + 15.7753i 1.05013 + 0.606292i 0.922685 0.385554i \(-0.125989\pi\)
0.127444 + 0.991846i \(0.459323\pi\)
\(678\) 0.494897i 0.0190064i
\(679\) 0 0
\(680\) 0.449490 4.44949i 0.0172371 0.170630i
\(681\) 9.00000 15.5885i 0.344881 0.597351i
\(682\) 3.81405 2.20204i 0.146047 0.0843205i
\(683\) 30.8270 17.7980i 1.17956 0.681020i 0.223648 0.974670i \(-0.428203\pi\)
0.955913 + 0.293650i \(0.0948700\pi\)
\(684\) 9.67423 16.7563i 0.369904 0.640692i
\(685\) −39.5959 4.00000i −1.51288 0.152832i
\(686\) 0 0
\(687\) 37.1010i 1.41549i
\(688\) 7.70674 + 4.44949i 0.293817 + 0.169635i
\(689\) 0.247449 + 0.428594i 0.00942705 + 0.0163281i
\(690\) −15.5088 34.4580i −0.590411 1.31179i
\(691\) 6.57321 11.3851i 0.250057 0.433111i −0.713484 0.700671i \(-0.752884\pi\)
0.963541 + 0.267560i \(0.0862174\pi\)
\(692\) 18.2474i 0.693664i
\(693\) 0 0
\(694\) 19.1010 0.725065
\(695\) 11.7014 + 8.42953i 0.443859 + 0.319750i
\(696\) −3.55051 6.14966i −0.134582 0.233102i
\(697\) −18.8776 + 10.8990i −0.715040 + 0.412828i
\(698\) 3.07483 + 1.77526i 0.116384 + 0.0671944i
\(699\) −24.9898 −0.945201
\(700\) 0 0
\(701\) 40.6969 1.53710 0.768551 0.639788i \(-0.220978\pi\)
0.768551 + 0.639788i \(0.220978\pi\)
\(702\) 0 0
\(703\) −11.1708 + 6.44949i −0.421316 + 0.243247i
\(704\) 2.44949 + 4.24264i 0.0923186 + 0.159901i
\(705\) 3.99519 + 2.87808i 0.150468 + 0.108395i
\(706\) −13.1010 −0.493063
\(707\) 0 0
\(708\) 15.7980i 0.593724i
\(709\) 20.1464 34.8946i 0.756615 1.31050i −0.187952 0.982178i \(-0.560185\pi\)
0.944567 0.328317i \(-0.106482\pi\)
\(710\) 10.0024 + 22.2237i 0.375384 + 0.834039i
\(711\) 4.34847 + 7.53177i 0.163080 + 0.282463i
\(712\) −8.66025 5.00000i −0.324557 0.187383i
\(713\) 6.20204i 0.232268i
\(714\) 0 0
\(715\) −4.89898 0.494897i −0.183211 0.0185081i
\(716\) 2.89898 5.02118i 0.108340 0.187650i
\(717\) −54.7257 + 31.5959i −2.04377 + 1.17997i
\(718\) 10.0424 5.79796i 0.374778 0.216378i
\(719\) 22.2474 38.5337i 0.829690 1.43706i −0.0685918 0.997645i \(-0.521851\pi\)
0.898282 0.439420i \(-0.144816\pi\)
\(720\) 0.674235 6.67423i 0.0251272 0.248734i
\(721\) 0 0
\(722\) 22.5959i 0.840933i
\(723\) 43.9048 + 25.3485i 1.63284 + 0.942720i
\(724\) 7.12372 + 12.3387i 0.264751 + 0.458562i
\(725\) 4.59043 + 13.7488i 0.170484 + 0.510618i
\(726\) 15.9217 27.5772i 0.590909 1.02348i
\(727\) 6.69694i 0.248376i −0.992259 0.124188i \(-0.960367\pi\)
0.992259 0.124188i \(-0.0396325\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) −12.5169 9.01702i −0.463272 0.333735i
\(731\) −8.89898 15.4135i −0.329141 0.570088i
\(732\) 17.9241 10.3485i 0.662493 0.382490i
\(733\) −37.7945 21.8207i −1.39597 0.805965i −0.402004 0.915638i \(-0.631686\pi\)
−0.993968 + 0.109673i \(0.965020\pi\)
\(734\) 32.0000 1.18114
\(735\) 0 0
\(736\) 6.89898 0.254300
\(737\) 33.9411 + 19.5959i 1.25024 + 0.721825i
\(738\) −28.3164 + 16.3485i −1.04234 + 0.601795i
\(739\) −22.2474 38.5337i −0.818386 1.41749i −0.906871 0.421408i \(-0.861536\pi\)
0.0884855 0.996077i \(-0.471797\pi\)
\(740\) −2.61401 + 3.62863i −0.0960931 + 0.133391i
\(741\) −7.10102 −0.260863
\(742\) 0 0
\(743\) 15.3031i 0.561415i 0.959793 + 0.280707i \(0.0905691\pi\)
−0.959793 + 0.280707i \(0.909431\pi\)
\(744\) 1.10102 1.90702i 0.0403654 0.0699149i
\(745\) −32.2130 + 14.4984i −1.18019 + 0.531180i
\(746\) 12.3485 + 21.3882i 0.452110 + 0.783077i
\(747\) −6.36396 3.67423i −0.232845 0.134433i
\(748\) 9.79796i 0.358249i
\(749\) 0 0
\(750\) −8.14643 + 26.1464i −0.297465 + 0.954733i
\(751\) 11.1010 19.2275i 0.405082 0.701623i −0.589249 0.807951i \(-0.700576\pi\)
0.994331 + 0.106329i \(0.0339096\pi\)
\(752\) −0.778539 + 0.449490i −0.0283904 + 0.0163912i
\(753\) 3.28913 1.89898i 0.119863 0.0692027i
\(754\) −0.651531 + 1.12848i −0.0237274 + 0.0410970i
\(755\) 4.40408 43.5959i 0.160281 1.58662i
\(756\) 0 0
\(757\) 32.2020i 1.17040i −0.810888 0.585202i \(-0.801015\pi\)
0.810888 0.585202i \(-0.198985\pi\)
\(758\) −1.12848 0.651531i −0.0409884 0.0236647i
\(759\) −41.3939 71.6963i −1.50250 2.60241i
\(760\) −5.91894 13.1509i −0.214703 0.477033i
\(761\) 15.4495 26.7593i 0.560044 0.970024i −0.437448 0.899244i \(-0.644118\pi\)
0.997492 0.0707804i \(-0.0225489\pi\)
\(762\) 12.4949i 0.452642i
\(763\) 0 0
\(764\) 16.6969 0.604074
\(765\) −7.84204 + 10.8859i −0.283530 + 0.393580i
\(766\) −8.44949 14.6349i −0.305292 0.528782i
\(767\) 2.51059 1.44949i 0.0906521 0.0523380i
\(768\) 2.12132 + 1.22474i 0.0765466 + 0.0441942i
\(769\) 11.3031 0.407599 0.203799 0.979013i \(-0.434671\pi\)
0.203799 + 0.979013i \(0.434671\pi\)
\(770\) 0 0
\(771\) 50.6969 1.82581
\(772\) −15.2385 8.79796i −0.548446 0.316645i
\(773\) 11.5601 6.67423i 0.415788 0.240056i −0.277485 0.960730i \(-0.589501\pi\)
0.693274 + 0.720674i \(0.256168\pi\)
\(774\) −13.3485 23.1202i −0.479801 0.831039i
\(775\) −2.98058 + 3.36456i −0.107066 + 0.120858i
\(776\) 3.79796 0.136339
\(777\) 0 0
\(778\) 22.8990i 0.820968i
\(779\) −35.1464 + 60.8754i −1.25925 + 2.18109i
\(780\) −2.24504 + 1.01045i −0.0803855 + 0.0361798i
\(781\) 26.6969 + 46.2405i 0.955292 + 1.65461i
\(782\) −11.9494 6.89898i −0.427309 0.246707i
\(783\) 0 0
\(784\) 0 0
\(785\) −18.7980 1.89898i −0.670928 0.0677775i
\(786\) −1.89898 + 3.28913i −0.0677344 + 0.117319i
\(787\) 39.4479 22.7753i 1.40617 0.811850i 0.411150 0.911568i \(-0.365127\pi\)
0.995016 + 0.0997176i \(0.0317939\pi\)
\(788\) −7.88171 + 4.55051i −0.280774 + 0.162105i
\(789\) −12.0000 + 20.7846i −0.427211 + 0.739952i
\(790\) 6.44949 + 0.651531i 0.229463 + 0.0231804i
\(791\) 0 0
\(792\) 14.6969i 0.522233i
\(793\) −3.28913 1.89898i −0.116800 0.0674347i
\(794\) 8.67423 + 15.0242i 0.307837 + 0.533189i
\(795\) 5.49921 2.47508i 0.195037 0.0877821i
\(796\) −3.55051 + 6.14966i −0.125844 + 0.217969i
\(797\) 52.9444i 1.87539i 0.347464 + 0.937693i \(0.387043\pi\)
−0.347464 + 0.937693i \(0.612957\pi\)
\(798\) 0 0
\(799\) 1.79796 0.0636072
\(800\) −3.74264 3.31552i −0.132322 0.117221i
\(801\) 15.0000 + 25.9808i 0.529999 + 0.917985i
\(802\) −25.4558 + 14.6969i −0.898877 + 0.518967i
\(803\) −29.2699 16.8990i −1.03291 0.596352i
\(804\) 19.5959 0.691095
\(805\) 0 0
\(806\) −0.404082 −0.0142332
\(807\) 32.1304 + 18.5505i 1.13104 + 0.653009i
\(808\) 7.31747 4.22474i 0.257428 0.148626i
\(809\) 4.20204 + 7.27815i 0.147736 + 0.255886i 0.930390 0.366570i \(-0.119468\pi\)
−0.782654 + 0.622456i \(0.786135\pi\)
\(810\) 11.7631 16.3288i 0.413312 0.573736i
\(811\) −38.9444 −1.36752 −0.683761 0.729706i \(-0.739657\pi\)
−0.683761 + 0.729706i \(0.739657\pi\)
\(812\) 0 0
\(813\) 29.3939i 1.03089i
\(814\) −4.89898 + 8.48528i −0.171709 + 0.297409i
\(815\) 15.5088 + 34.4580i 0.543251 + 1.20701i
\(816\) −2.44949 4.24264i −0.0857493 0.148522i
\(817\) −49.7046 28.6969i −1.73894 1.00398i
\(818\) 14.4949i 0.506802i
\(819\) 0 0
\(820\) −2.44949 + 24.2474i −0.0855399 + 0.846758i
\(821\) −13.8990 + 24.0737i −0.485078 + 0.840179i −0.999853 0.0171459i \(-0.994542\pi\)
0.514775 + 0.857325i \(0.327875\pi\)
\(822\) −37.7552 + 21.7980i −1.31686 + 0.760291i
\(823\) −33.9411 + 19.5959i −1.18311 + 0.683071i −0.956733 0.290968i \(-0.906023\pi\)
−0.226381 + 0.974039i \(0.572689\pi\)
\(824\) −1.55051 + 2.68556i −0.0540146 + 0.0935560i
\(825\) −12.0000 + 58.7878i −0.417786 + 2.04673i
\(826\) 0 0
\(827\) 23.5959i 0.820510i 0.911971 + 0.410255i \(0.134560\pi\)
−0.911971 + 0.410255i \(0.865440\pi\)
\(828\) −17.9241 10.3485i −0.622905 0.359634i
\(829\) 19.8207 + 34.3304i 0.688400 + 1.19234i 0.972355 + 0.233506i \(0.0750200\pi\)
−0.283955 + 0.958838i \(0.591647\pi\)
\(830\) −4.99465 + 2.24799i −0.173367 + 0.0780288i
\(831\) 6.24745 10.8209i 0.216722 0.375373i
\(832\) 0.449490i 0.0155833i
\(833\) 0 0
\(834\) 15.7980 0.547039
\(835\) 6.40300 8.88828i 0.221585 0.307592i
\(836\) −15.7980 27.3629i −0.546384 0.946365i
\(837\) 0 0
\(838\) 5.58542 + 3.22474i 0.192945 + 0.111397i
\(839\) −27.1010 −0.935631 −0.467816 0.883826i \(-0.654959\pi\)
−0.467816 + 0.883826i \(0.654959\pi\)
\(840\) 0 0
\(841\) −20.5959 −0.710204
\(842\) −20.6096 11.8990i −0.710255 0.410066i
\(843\) 38.1838 22.0454i 1.31512 0.759284i
\(844\) 6.00000 + 10.3923i 0.206529 + 0.357718i
\(845\) −23.2195 16.7270i −0.798775 0.575427i
\(846\) 2.69694 0.0927227
\(847\) 0 0
\(848\) 1.10102i 0.0378092i
\(849\) 34.5959 59.9219i 1.18733 2.05651i
\(850\) 3.16693 + 9.48528i 0.108625 + 0.325342i
\(851\) 6.89898 + 11.9494i 0.236494 + 0.409620i
\(852\) 23.1202 + 13.3485i 0.792086 + 0.457311i
\(853\) 29.8434i 1.02182i −0.859635 0.510909i \(-0.829309\pi\)
0.859635 0.510909i \(-0.170691\pi\)
\(854\) 0 0
\(855\) −4.34847 + 43.0454i −0.148715 + 1.47212i
\(856\) −4.00000 + 6.92820i −0.136717 + 0.236801i
\(857\) 21.8168 12.5959i 0.745247 0.430268i −0.0787272 0.996896i \(-0.525086\pi\)
0.823974 + 0.566628i \(0.191752\pi\)
\(858\) −4.67123 + 2.69694i −0.159473 + 0.0920720i
\(859\) −14.8207 + 25.6701i −0.505674 + 0.875854i 0.494304 + 0.869289i \(0.335423\pi\)
−0.999978 + 0.00656478i \(0.997910\pi\)
\(860\) −19.7980 2.00000i −0.675105 0.0681994i
\(861\) 0 0
\(862\) 17.7980i 0.606201i
\(863\) 11.5994 + 6.69694i 0.394849 + 0.227966i 0.684259 0.729239i \(-0.260126\pi\)
−0.289410 + 0.957205i \(0.593459\pi\)
\(864\) 0 0
\(865\) −16.7464 37.2076i −0.569394 1.26510i
\(866\) −9.89898 + 17.1455i −0.336381 + 0.582629i
\(867\) 31.8434i 1.08146i
\(868\) 0 0
\(869\) 14.2020 0.481771
\(870\) 12.8835 + 9.28108i 0.436791 + 0.314658i
\(871\) −1.79796 3.11416i −0.0609215 0.105519i
\(872\) 2.51059 1.44949i 0.0850193 0.0490859i
\(873\) −9.86739 5.69694i −0.333960 0.192812i
\(874\) −44.4949 −1.50506
\(875\) 0 0
\(876\) −16.8990 −0.570964
\(877\) −16.7956 9.69694i −0.567147 0.327442i 0.188862 0.982004i \(-0.439520\pi\)
−0.756009 + 0.654561i \(0.772853\pi\)
\(878\) 32.3840 18.6969i 1.09291 0.630991i
\(879\) −7.65153 13.2528i −0.258080 0.447007i
\(880\) −8.88828 6.40300i −0.299624 0.215845i
\(881\) 27.7980 0.936537 0.468269 0.883586i \(-0.344878\pi\)
0.468269 + 0.883586i \(0.344878\pi\)
\(882\) 0 0
\(883\) 41.7980i 1.40661i −0.710887 0.703307i \(-0.751706\pi\)
0.710887 0.703307i \(-0.248294\pi\)
\(884\) −0.449490 + 0.778539i −0.0151180 + 0.0261851i
\(885\) −14.4984 32.2130i −0.487358 1.08283i
\(886\) −4.89898 8.48528i −0.164584 0.285069i
\(887\) 23.1202 + 13.3485i 0.776301 + 0.448198i 0.835118 0.550071i \(-0.185399\pi\)
−0.0588166 + 0.998269i \(0.518733\pi\)
\(888\) 4.89898i 0.164399i
\(889\) 0 0
\(890\) 22.2474 + 2.24745i 0.745736 + 0.0753347i
\(891\) 22.0454 38.1838i 0.738549 1.27920i
\(892\) −3.46410 + 2.00000i −0.115987 + 0.0669650i
\(893\) 5.02118 2.89898i 0.168027 0.0970106i
\(894\) −19.3485 + 33.5125i −0.647110 + 1.12083i
\(895\) −1.30306 + 12.8990i −0.0435565 + 0.431165i
\(896\) 0 0
\(897\) 7.59592i 0.253620i
\(898\) 8.66025 + 5.00000i 0.288996 + 0.166852i
\(899\) 1.30306 + 2.25697i 0.0434595 + 0.0752741i
\(900\) 4.75039 + 14.2279i 0.158346 + 0.474264i
\(901\) 1.10102 1.90702i 0.0366803 0.0635322i
\(902\) 53.3939i 1.77782i
\(903\) 0 0
\(904\) 0.202041 0.00671978
\(905\) −25.8493 18.6215i −0.859261 0.619000i
\(906\) −24.0000 41.5692i −0.797347 1.38104i
\(907\) −19.2275 + 11.1010i −0.638440 + 0.368603i −0.784013 0.620744i \(-0.786831\pi\)
0.145574 + 0.989347i \(0.453497\pi\)
\(908\) −6.36396 3.67423i −0.211195 0.121934i
\(909\) −25.3485 −0.840756
\(910\) 0 0
\(911\) 3.59592 0.119138 0.0595690 0.998224i \(-0.481027\pi\)
0.0595690 + 0.998224i \(0.481027\pi\)
\(912\) −13.6814 7.89898i −0.453038 0.261561i
\(913\) −10.3923 + 6.00000i −0.343935 + 0.198571i
\(914\) 4.79796 + 8.31031i 0.158702 + 0.274881i
\(915\) −27.0510 + 37.5507i −0.894280 + 1.24139i
\(916\) 15.1464 0.500452
\(917\) 0 0
\(918\) 0 0
\(919\) −8.55051 + 14.8099i −0.282055 + 0.488534i −0.971891 0.235432i \(-0.924350\pi\)
0.689836 + 0.723966i \(0.257683\pi\)
\(920\) −14.0674 + 6.33145i −0.463789 + 0.208742i
\(921\) −5.20204 9.01020i −0.171413 0.296896i
\(922\) 2.29629 + 1.32577i 0.0756244 + 0.0436618i
\(923\) 4.89898i 0.161252i
\(924\) 0 0
\(925\) 2.00000 9.79796i 0.0657596 0.322155i
\(926\) −17.7980 + 30.8270i −0.584877 + 1.01304i
\(927\) 8.05669 4.65153i 0.264616 0.152776i
\(928\) −2.51059 + 1.44949i −0.0824142 + 0.0475818i
\(929\) 20.1464 34.8946i 0.660983 1.14486i −0.319375 0.947628i \(-0.603473\pi\)
0.980358 0.197227i \(-0.0631938\pi\)
\(930\) −0.494897 + 4.89898i −0.0162283 + 0.160644i
\(931\) 0 0
\(932\) 10.2020i 0.334179i
\(933\) 25.4558 + 14.6969i 0.833387 + 0.481156i
\(934\) −2.77526 4.80688i −0.0908091 0.157286i
\(935\) 8.99196 + 19.9786i 0.294068 + 0.653370i
\(936\) −0.674235 + 1.16781i −0.0220380 + 0.0381710i
\(937\) 50.8990i 1.66280i −0.555677 0.831399i \(-0.687541\pi\)
0.555677 0.831399i \(-0.312459\pi\)
\(938\) 0 0
\(939\) −43.1010 −1.40655
\(940\) 1.17497 1.63103i 0.0383234 0.0531983i
\(941\) 12.2247 + 21.1739i 0.398515 + 0.690249i 0.993543 0.113456i \(-0.0361922\pi\)
−0.595028 + 0.803705i \(0.702859\pi\)
\(942\) −17.9241 + 10.3485i −0.583998 + 0.337171i
\(943\) 65.1180 + 37.5959i 2.12054 + 1.22429i
\(944\) 6.44949 0.209913
\(945\) 0 0
\(946\) −43.5959 −1.41743
\(947\) 38.1838 + 22.0454i 1.24081 + 0.716379i 0.969258 0.246046i \(-0.0791313\pi\)
0.271547 + 0.962425i \(0.412465\pi\)
\(948\) 6.14966 3.55051i 0.199732 0.115315i
\(949\) 1.55051 + 2.68556i 0.0503317 + 0.0871770i
\(950\) 24.1381 + 21.3834i 0.783144 + 0.693768i
\(951\) 64.8990 2.10449
\(952\) 0 0
\(953\) 21.7980i 0.706105i −0.935603 0.353053i \(-0.885144\pi\)
0.935603 0.353053i \(-0.114856\pi\)
\(954\) 1.65153 2.86054i 0.0534703 0.0926132i
\(955\) −34.0460 + 15.3234i −1.10170 + 0.495854i
\(956\) 12.8990 + 22.3417i 0.417183 + 0.722582i
\(957\) 30.1271 + 17.3939i 0.973870 + 0.562264i
\(958\) 38.6969i 1.25024i
\(959\) 0 0
\(960\) −5.44949 0.550510i −0.175882 0.0177676i
\(961\) 15.0959 26.1469i 0.486965 0.843448i
\(962\) 0.778539 0.449490i 0.0251011 0.0144921i
\(963\) 20.7846 12.0000i 0.669775 0.386695i
\(964\) 10.3485 17.9241i 0.333302 0.577296i
\(965\) 39.1464 + 3.95459i 1.26017 + 0.127303i
\(966\) 0 0
\(967\) 32.2929i 1.03847i 0.854632 + 0.519234i \(0.173783\pi\)
−0.854632 + 0.519234i \(0.826217\pi\)
\(968\) −11.2583 6.50000i −0.361856 0.208918i
\(969\) 15.7980 + 27.3629i 0.507504 + 0.879022i
\(970\) −7.74426 + 3.48553i −0.248653 + 0.111914i
\(971\) 7.22474 12.5136i 0.231853 0.401581i −0.726500 0.687166i \(-0.758854\pi\)
0.958353 + 0.285585i \(0.0921878\pi\)
\(972\) 22.0454i 0.707107i
\(973\) 0 0
\(974\) −36.6969 −1.17585
\(975\) 3.65045 4.12072i 0.116908 0.131969i
\(976\) −4.22474 7.31747i −0.135231 0.234227i
\(977\) 25.4558 14.6969i 0.814405 0.470197i −0.0340785 0.999419i \(-0.510850\pi\)
0.848483 + 0.529222i \(0.177516\pi\)
\(978\) 35.8481 + 20.6969i 1.14630 + 0.661815i
\(979\) 48.9898 1.56572
\(980\) 0 0
\(981\) −8.69694 −0.277672
\(982\) −16.9706 9.79796i −0.541552 0.312665i
\(983\) 36.9766 21.3485i 1.17937 0.680910i 0.223502 0.974703i \(-0.428251\pi\)
0.955869 + 0.293793i \(0.0949176\pi\)
\(984\) 13.3485 + 23.1202i 0.425534 + 0.737046i
\(985\) 11.8951 16.5121i 0.379009 0.526119i
\(986\) 5.79796 0.184645
\(987\) 0 0
\(988\) 2.89898i 0.0922288i
\(989\) −30.6969 + 53.1687i −0.976106 + 1.69066i
\(990\) 13.4879 + 29.9679i 0.428675 + 0.952443i
\(991\) −30.3485 52.5651i −0.964051 1.66979i −0.712144 0.702034i \(-0.752276\pi\)
−0.251907 0.967751i \(-0.581058\pi\)
\(992\) −0.778539 0.449490i −0.0247186 0.0142713i
\(993\) 26.2020i 0.831497i
\(994\) 0 0
\(995\) 1.59592 15.7980i 0.0505940 0.500829i
\(996\) −3.00000 + 5.19615i −0.0950586 + 0.164646i
\(997\) 36.9373 21.3258i 1.16982 0.675394i 0.216180 0.976354i \(-0.430640\pi\)
0.953637 + 0.300960i \(0.0973070\pi\)
\(998\) 22.3417 12.8990i 0.707214 0.408310i
\(999\) 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 490.2.i.c.79.3 8
5.4 even 2 inner 490.2.i.c.79.2 8
7.2 even 3 70.2.c.a.29.1 4
7.3 odd 6 490.2.i.f.459.1 8
7.4 even 3 inner 490.2.i.c.459.2 8
7.5 odd 6 490.2.c.e.99.2 4
7.6 odd 2 490.2.i.f.79.4 8
21.2 odd 6 630.2.g.g.379.4 4
28.23 odd 6 560.2.g.e.449.3 4
35.2 odd 12 350.2.a.h.1.1 2
35.4 even 6 inner 490.2.i.c.459.3 8
35.9 even 6 70.2.c.a.29.4 yes 4
35.12 even 12 2450.2.a.bq.1.2 2
35.19 odd 6 490.2.c.e.99.3 4
35.23 odd 12 350.2.a.g.1.2 2
35.24 odd 6 490.2.i.f.459.4 8
35.33 even 12 2450.2.a.bl.1.1 2
35.34 odd 2 490.2.i.f.79.1 8
56.37 even 6 2240.2.g.j.449.4 4
56.51 odd 6 2240.2.g.i.449.2 4
84.23 even 6 5040.2.t.t.1009.3 4
105.2 even 12 3150.2.a.bs.1.1 2
105.23 even 12 3150.2.a.bt.1.1 2
105.44 odd 6 630.2.g.g.379.2 4
140.23 even 12 2800.2.a.bm.1.1 2
140.79 odd 6 560.2.g.e.449.1 4
140.107 even 12 2800.2.a.bl.1.2 2
280.149 even 6 2240.2.g.j.449.2 4
280.219 odd 6 2240.2.g.i.449.4 4
420.359 even 6 5040.2.t.t.1009.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.c.a.29.1 4 7.2 even 3
70.2.c.a.29.4 yes 4 35.9 even 6
350.2.a.g.1.2 2 35.23 odd 12
350.2.a.h.1.1 2 35.2 odd 12
490.2.c.e.99.2 4 7.5 odd 6
490.2.c.e.99.3 4 35.19 odd 6
490.2.i.c.79.2 8 5.4 even 2 inner
490.2.i.c.79.3 8 1.1 even 1 trivial
490.2.i.c.459.2 8 7.4 even 3 inner
490.2.i.c.459.3 8 35.4 even 6 inner
490.2.i.f.79.1 8 35.34 odd 2
490.2.i.f.79.4 8 7.6 odd 2
490.2.i.f.459.1 8 7.3 odd 6
490.2.i.f.459.4 8 35.24 odd 6
560.2.g.e.449.1 4 140.79 odd 6
560.2.g.e.449.3 4 28.23 odd 6
630.2.g.g.379.2 4 105.44 odd 6
630.2.g.g.379.4 4 21.2 odd 6
2240.2.g.i.449.2 4 56.51 odd 6
2240.2.g.i.449.4 4 280.219 odd 6
2240.2.g.j.449.2 4 280.149 even 6
2240.2.g.j.449.4 4 56.37 even 6
2450.2.a.bl.1.1 2 35.33 even 12
2450.2.a.bq.1.2 2 35.12 even 12
2800.2.a.bl.1.2 2 140.107 even 12
2800.2.a.bm.1.1 2 140.23 even 12
3150.2.a.bs.1.1 2 105.2 even 12
3150.2.a.bt.1.1 2 105.23 even 12
5040.2.t.t.1009.3 4 84.23 even 6
5040.2.t.t.1009.4 4 420.359 even 6