Properties

Label 363.3.h.f.323.1
Level $363$
Weight $3$
Character 363.323
Analytic conductor $9.891$
Analytic rank $0$
Dimension $8$
CM discriminant -11
Inner twists $16$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,3,Mod(245,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.245");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 363.h (of order \(10\), 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: \(9.89103359628\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.228765625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label 323.1
Root \(1.42264 + 0.987975i\) of defining polynomial
Character \(\chi\) \(=\) 363.323
Dual form 363.3.h.f.245.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.804606 - 2.89009i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-5.84839 - 8.04962i) q^{5} +(-7.70522 + 4.65077i) q^{9} +O(q^{10})\) \(q+(-0.804606 - 2.89009i) q^{3} +(1.23607 + 3.80423i) q^{4} +(-5.84839 - 8.04962i) q^{5} +(-7.70522 + 4.65077i) q^{9} +(10.0000 - 6.63325i) q^{12} +(-18.5585 + 23.3791i) q^{15} +(-12.9443 + 9.40456i) q^{16} +(23.3936 - 32.1985i) q^{20} +29.8496i q^{23} +(-22.8673 + 70.3782i) q^{25} +(19.6408 + 18.5267i) q^{27} +(-29.9336 - 21.7481i) q^{31} +(-27.2167 - 23.5637i) q^{36} +(7.72542 + 23.7764i) q^{37} +(82.5000 + 34.8246i) q^{45} +(-75.7031 - 24.5974i) q^{47} +(37.5951 + 29.8431i) q^{48} +(39.6418 - 28.8015i) q^{49} +(-46.7871 + 64.3969i) q^{53} +(-47.3145 + 15.3734i) q^{59} +(-111.879 - 41.7023i) q^{60} +(-51.7771 - 37.6183i) q^{64} -35.0000 q^{67} +(86.2680 - 24.0172i) q^{69} +(29.2419 + 40.2481i) q^{71} +(221.798 + 9.46166i) q^{75} +(151.406 + 49.1949i) q^{80} +(37.7407 - 71.6703i) q^{81} -149.248i q^{89} +(-113.555 + 36.8962i) q^{92} +(-38.7690 + 104.009i) q^{93} +(-76.8566 - 55.8396i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 5 q^{3} - 8 q^{4} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 5 q^{3} - 8 q^{4} - 7 q^{9} + 80 q^{12} - 33 q^{15} - 32 q^{16} + 148 q^{25} + 10 q^{27} - 74 q^{31} - 28 q^{36} - 50 q^{37} + 660 q^{45} - 80 q^{48} + 98 q^{49} - 132 q^{60} - 128 q^{64} - 280 q^{67} - 99 q^{69} + 370 q^{75} + 113 q^{81} - 185 q^{93} - 190 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{5}\right)\)

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 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(3\) −0.804606 2.89009i −0.268202 0.963363i
\(4\) 1.23607 + 3.80423i 0.309017 + 0.951057i
\(5\) −5.84839 8.04962i −1.16968 1.60992i −0.665741 0.746183i \(-0.731884\pi\)
−0.503937 0.863740i \(-0.668116\pi\)
\(6\) 0 0
\(7\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(8\) 0 0
\(9\) −7.70522 + 4.65077i −0.856135 + 0.516752i
\(10\) 0 0
\(11\) 0 0
\(12\) 10.0000 6.63325i 0.833333 0.552771i
\(13\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(14\) 0 0
\(15\) −18.5585 + 23.3791i −1.23723 + 1.55861i
\(16\) −12.9443 + 9.40456i −0.809017 + 0.587785i
\(17\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) 0 0
\(19\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(20\) 23.3936 32.1985i 1.16968 1.60992i
\(21\) 0 0
\(22\) 0 0
\(23\) 29.8496i 1.29781i 0.760870 + 0.648905i \(0.224773\pi\)
−0.760870 + 0.648905i \(0.775227\pi\)
\(24\) 0 0
\(25\) −22.8673 + 70.3782i −0.914690 + 2.81513i
\(26\) 0 0
\(27\) 19.6408 + 18.5267i 0.727437 + 0.686175i
\(28\) 0 0
\(29\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(30\) 0 0
\(31\) −29.9336 21.7481i −0.965601 0.701550i −0.0111562 0.999938i \(-0.503551\pi\)
−0.954445 + 0.298388i \(0.903551\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −27.2167 23.5637i −0.756021 0.654548i
\(37\) 7.72542 + 23.7764i 0.208795 + 0.642606i 0.999536 + 0.0304547i \(0.00969555\pi\)
−0.790741 + 0.612151i \(0.790304\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 82.5000 + 34.8246i 1.83333 + 0.773879i
\(46\) 0 0
\(47\) −75.7031 24.5974i −1.61071 0.523350i −0.640982 0.767556i \(-0.721473\pi\)
−0.969723 + 0.244206i \(0.921473\pi\)
\(48\) 37.5951 + 29.8431i 0.783230 + 0.621732i
\(49\) 39.6418 28.8015i 0.809017 0.587785i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −46.7871 + 64.3969i −0.882776 + 1.21504i 0.0928686 + 0.995678i \(0.470396\pi\)
−0.975644 + 0.219358i \(0.929604\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −47.3145 + 15.3734i −0.801940 + 0.260566i −0.681180 0.732116i \(-0.738533\pi\)
−0.120760 + 0.992682i \(0.538533\pi\)
\(60\) −111.879 41.7023i −1.86465 0.695039i
\(61\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −51.7771 37.6183i −0.809017 0.587785i
\(65\) 0 0
\(66\) 0 0
\(67\) −35.0000 −0.522388 −0.261194 0.965286i \(-0.584116\pi\)
−0.261194 + 0.965286i \(0.584116\pi\)
\(68\) 0 0
\(69\) 86.2680 24.0172i 1.25026 0.348075i
\(70\) 0 0
\(71\) 29.2419 + 40.2481i 0.411858 + 0.566874i 0.963670 0.267094i \(-0.0860634\pi\)
−0.551812 + 0.833968i \(0.686063\pi\)
\(72\) 0 0
\(73\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(74\) 0 0
\(75\) 221.798 + 9.46166i 2.95731 + 0.126155i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(80\) 151.406 + 49.1949i 1.89258 + 0.614936i
\(81\) 37.7407 71.6703i 0.465935 0.884819i
\(82\) 0 0
\(83\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 149.248i 1.67695i −0.544944 0.838473i \(-0.683449\pi\)
0.544944 0.838473i \(-0.316551\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −113.555 + 36.8962i −1.23429 + 0.401045i
\(93\) −38.7690 + 104.009i −0.416871 + 1.11838i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −76.8566 55.8396i −0.792336 0.575666i 0.116320 0.993212i \(-0.462890\pi\)
−0.908656 + 0.417546i \(0.862890\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −296.000 −2.96000
\(101\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(102\) 0 0
\(103\) −58.7132 180.701i −0.570031 1.75438i −0.652507 0.757783i \(-0.726283\pi\)
0.0824753 0.996593i \(-0.473717\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) −46.2025 + 97.6183i −0.427801 + 0.903873i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 62.5000 41.4578i 0.563063 0.373494i
\(112\) 0 0
\(113\) −66.2402 21.5228i −0.586197 0.190467i 0.000877893 1.00000i \(-0.499721\pi\)
−0.587075 + 0.809533i \(0.699721\pi\)
\(114\) 0 0
\(115\) 240.278 174.572i 2.08937 1.51802i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 45.7345 140.756i 0.368827 1.13513i
\(125\) 463.682 150.659i 3.70945 1.20527i
\(126\) 0 0
\(127\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 34.2660 266.452i 0.253822 1.97372i
\(136\) 0 0
\(137\) −40.9387 56.3473i −0.298823 0.411294i 0.633032 0.774126i \(-0.281810\pi\)
−0.931855 + 0.362831i \(0.881810\pi\)
\(138\) 0 0
\(139\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(140\) 0 0
\(141\) −10.1775 + 238.580i −0.0721812 + 1.69206i
\(142\) 0 0
\(143\) 0 0
\(144\) 56.0000 132.665i 0.388889 0.921285i
\(145\) 0 0
\(146\) 0 0
\(147\) −115.135 91.3945i −0.783230 0.621732i
\(148\) −80.9017 + 58.7785i −0.546633 + 0.397152i
\(149\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0 0
\(151\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 368.145i 2.37513i
\(156\) 0 0
\(157\) −66.4387 + 204.477i −0.423176 + 1.30240i 0.481554 + 0.876417i \(0.340073\pi\)
−0.904730 + 0.425986i \(0.859927\pi\)
\(158\) 0 0
\(159\) 223.758 + 83.4047i 1.40728 + 0.524558i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 56.6312 + 41.1450i 0.347431 + 0.252423i 0.747790 0.663935i \(-0.231115\pi\)
−0.400360 + 0.916358i \(0.631115\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(168\) 0 0
\(169\) −52.2239 160.729i −0.309017 0.951057i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 82.5000 + 124.373i 0.466102 + 0.702675i
\(178\) 0 0
\(179\) 331.201 + 107.614i 1.85029 + 0.601194i 0.996787 + 0.0801009i \(0.0255242\pi\)
0.853500 + 0.521094i \(0.174476\pi\)
\(180\) −30.5049 + 356.894i −0.169472 + 1.98275i
\(181\) −212.771 + 154.588i −1.17553 + 0.854075i −0.991661 0.128875i \(-0.958863\pi\)
−0.183872 + 0.982950i \(0.558863\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 146.210 201.240i 0.790323 1.08779i
\(186\) 0 0
\(187\) 0 0
\(188\) 318.396i 1.69360i
\(189\) 0 0
\(190\) 0 0
\(191\) −331.201 + 107.614i −1.73404 + 0.563423i −0.994023 0.109168i \(-0.965181\pi\)
−0.740015 + 0.672591i \(0.765181\pi\)
\(192\) −67.0599 + 179.908i −0.349270 + 0.937022i
\(193\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 158.567 + 115.206i 0.809017 + 0.587785i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.0100503 −0.00502513 0.999987i \(-0.501600\pi\)
−0.00502513 + 0.999987i \(0.501600\pi\)
\(200\) 0 0
\(201\) 28.1612 + 101.153i 0.140106 + 0.503249i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −138.824 229.998i −0.670645 1.11110i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(212\) −302.813 98.3898i −1.42836 0.464103i
\(213\) 92.7923 116.896i 0.435644 0.548806i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −137.513 + 423.220i −0.616648 + 1.89785i −0.244672 + 0.969606i \(0.578680\pi\)
−0.371976 + 0.928242i \(0.621320\pi\)
\(224\) 0 0
\(225\) −151.115 648.629i −0.671623 2.88280i
\(226\) 0 0
\(227\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) 0 0
\(229\) −350.304 254.511i −1.52971 1.11140i −0.956398 0.292067i \(-0.905657\pi\)
−0.573316 0.819335i \(-0.694343\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(234\) 0 0
\(235\) 244.741 + 753.237i 1.04145 + 3.20526i
\(236\) −116.968 160.992i −0.495626 0.682171i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(240\) 20.3551 477.160i 0.0848129 1.98817i
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) −237.500 51.4077i −0.977366 0.211554i
\(244\) 0 0
\(245\) −463.682 150.659i −1.89258 0.614936i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −263.178 + 362.233i −1.04852 + 1.44316i −0.158428 + 0.987371i \(0.550642\pi\)
−0.890088 + 0.455788i \(0.849358\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 79.1084 243.470i 0.309017 0.951057i
\(257\) −454.219 + 147.585i −1.76739 + 0.574259i −0.997922 0.0644282i \(-0.979478\pi\)
−0.769466 + 0.638688i \(0.779478\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 792.000 2.98868
\(266\) 0 0
\(267\) −431.340 + 120.086i −1.61551 + 0.449760i
\(268\) −43.2624 133.148i −0.161427 0.496821i
\(269\) 233.936 + 321.985i 0.869649 + 1.19697i 0.979182 + 0.202986i \(0.0650646\pi\)
−0.109533 + 0.993983i \(0.534935\pi\)
\(270\) 0 0
\(271\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 198.000 + 298.496i 0.717391 + 1.08151i
\(277\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(278\) 0 0
\(279\) 331.790 + 28.3592i 1.18921 + 0.101646i
\(280\) 0 0
\(281\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(284\) −116.968 + 160.992i −0.411858 + 0.566874i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 89.3059 274.855i 0.309017 0.951057i
\(290\) 0 0
\(291\) −99.5420 + 267.051i −0.342069 + 0.917702i
\(292\) 0 0
\(293\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(294\) 0 0
\(295\) 400.463 + 290.954i 1.35750 + 0.986284i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 238.163 + 855.466i 0.793878 + 2.85155i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) −475.000 + 315.079i −1.53722 + 1.01967i
\(310\) 0 0
\(311\) 378.516 + 122.987i 1.21709 + 0.395457i 0.846022 0.533148i \(-0.178991\pi\)
0.371070 + 0.928605i \(0.378991\pi\)
\(312\) 0 0
\(313\) −214.390 + 155.763i −0.684950 + 0.497646i −0.874996 0.484130i \(-0.839136\pi\)
0.190046 + 0.981775i \(0.439136\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 368.449 507.126i 1.16230 1.59977i 0.459924 0.887958i \(-0.347877\pi\)
0.702374 0.711808i \(-0.252123\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 636.792i 1.98997i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 319.300 + 54.9849i 0.985495 + 0.169707i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 563.000 1.70091 0.850453 0.526051i \(-0.176328\pi\)
0.850453 + 0.526051i \(0.176328\pi\)
\(332\) 0 0
\(333\) −170.105 147.273i −0.510825 0.442262i
\(334\) 0 0
\(335\) 204.694 + 281.737i 0.611026 + 0.841005i
\(336\) 0 0
\(337\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(338\) 0 0
\(339\) −8.90535 + 208.758i −0.0262695 + 0.615804i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −697.858 553.963i −2.02278 1.60569i
\(346\) 0 0
\(347\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 328.346i 0.930158i −0.885269 0.465079i \(-0.846026\pi\)
0.885269 0.465079i \(-0.153974\pi\)
\(354\) 0 0
\(355\) 152.963 470.773i 0.430883 1.32612i
\(356\) 567.774 184.481i 1.59487 0.518205i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(360\) 0 0
\(361\) 292.055 + 212.190i 0.809017 + 0.587785i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 196.226 + 603.921i 0.534675 + 1.64556i 0.744350 + 0.667790i \(0.232759\pi\)
−0.209675 + 0.977771i \(0.567241\pi\)
\(368\) −280.723 386.382i −0.762833 1.04995i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −443.597 18.9233i −1.19246 0.0508691i
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) −808.500 1218.86i −2.15600 3.25029i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 107.599 78.1754i 0.283903 0.206268i −0.436715 0.899600i \(-0.643858\pi\)
0.720618 + 0.693332i \(0.243858\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −76.0291 + 104.645i −0.198509 + 0.273225i −0.896654 0.442732i \(-0.854009\pi\)
0.698145 + 0.715957i \(0.254009\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 117.426 361.401i 0.302646 0.931447i
\(389\) 520.459 169.107i 1.33794 0.434723i 0.449322 0.893370i \(-0.351666\pi\)
0.888619 + 0.458646i \(0.151666\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −790.000 −1.98992 −0.994962 0.100251i \(-0.968036\pi\)
−0.994962 + 0.100251i \(0.968036\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −365.876 1126.05i −0.914690 2.81513i
\(401\) −467.871 643.969i −1.16676 1.60591i −0.682238 0.731130i \(-0.738993\pi\)
−0.484523 0.874778i \(-0.661007\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −797.641 + 115.357i −1.96948 + 0.284833i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(410\) 0 0
\(411\) −129.909 + 163.654i −0.316081 + 0.398185i
\(412\) 614.853 446.717i 1.49236 1.08426i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 795.990i 1.89974i −0.312649 0.949869i \(-0.601216\pi\)
0.312649 0.949869i \(-0.398784\pi\)
\(420\) 0 0
\(421\) 229.291 705.684i 0.544633 1.67621i −0.177227 0.984170i \(-0.556713\pi\)
0.721860 0.692039i \(-0.243287\pi\)
\(422\) 0 0
\(423\) 697.706 162.549i 1.64942 0.384277i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(432\) −428.471 55.1018i −0.991832 0.127551i
\(433\) −7.72542 23.7764i −0.0178416 0.0549109i 0.941739 0.336344i \(-0.109190\pi\)
−0.959581 + 0.281433i \(0.909190\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −171.500 + 406.287i −0.388889 + 0.921285i
\(442\) 0 0
\(443\) 728.643 + 236.750i 1.64479 + 0.534425i 0.977602 0.210462i \(-0.0674970\pi\)
0.667190 + 0.744888i \(0.267497\pi\)
\(444\) 234.969 + 186.519i 0.529210 + 0.420089i
\(445\) −1201.39 + 872.861i −2.69975 + 1.96149i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 380.145 523.225i 0.846649 1.16531i −0.137942 0.990440i \(-0.544049\pi\)
0.984591 0.174872i \(-0.0559511\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 278.596i 0.616364i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 961.112 + 698.289i 2.08937 + 1.51802i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 35.0000 0.0755940 0.0377970 0.999285i \(-0.487966\pi\)
0.0377970 + 0.999285i \(0.487966\pi\)
\(464\) 0 0
\(465\) 1063.97 296.212i 2.28811 0.637015i
\(466\) 0 0
\(467\) −76.0291 104.645i −0.162803 0.224079i 0.719820 0.694161i \(-0.244224\pi\)
−0.882623 + 0.470082i \(0.844224\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 644.414 + 27.4899i 1.36818 + 0.0583651i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 61.0098 713.788i 0.127903 1.49641i
\(478\) 0 0
\(479\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 945.238i 1.94894i
\(486\) 0 0
\(487\) −270.390 + 832.174i −0.555215 + 1.70878i 0.140159 + 0.990129i \(0.455239\pi\)
−0.695374 + 0.718648i \(0.744761\pi\)
\(488\) 0 0
\(489\) 73.3468 196.775i 0.149993 0.402402i
\(490\) 0 0
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 592.000 1.19355
\(497\) 0 0
\(498\) 0 0
\(499\) −186.028 572.536i −0.372802 1.14737i −0.944950 0.327216i \(-0.893890\pi\)
0.572147 0.820151i \(-0.306110\pi\)
\(500\) 1146.28 + 1577.73i 2.29257 + 3.15545i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −422.500 + 280.255i −0.833333 + 0.552771i
\(508\) 0 0
\(509\) 141.943 + 46.1202i 0.278867 + 0.0906094i 0.445111 0.895475i \(-0.353164\pi\)
−0.166244 + 0.986085i \(0.553164\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1111.19 + 1529.43i −2.15766 + 2.96976i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −615.088 + 199.854i −1.18059 + 0.383597i −0.832586 0.553895i \(-0.813141\pi\)
−0.348005 + 0.937493i \(0.613141\pi\)
\(522\) 0 0
\(523\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −362.000 −0.684310
\(530\) 0 0
\(531\) 293.070 338.504i 0.551921 0.637484i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 44.5268 1043.79i 0.0829176 1.94374i
\(538\) 0 0
\(539\) 0 0
\(540\) 1056.00 198.997i 1.95556 0.368514i
\(541\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(542\) 0 0
\(543\) 617.969 + 490.546i 1.13806 + 0.903400i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(548\) 163.755 225.389i 0.298823 0.411294i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −699.244 260.640i −1.25990 0.469621i
\(556\) 0 0
\(557\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(564\) −920.192 + 256.183i −1.63155 + 0.454226i
\(565\) 214.149 + 659.082i 0.379024 + 1.16652i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 577.500 + 870.614i 1.00785 + 1.51940i
\(574\) 0 0
\(575\) −2100.76 682.579i −3.65350 1.18709i
\(576\) 573.907 + 49.0537i 0.996367 + 0.0851627i
\(577\) 853.513 620.113i 1.47923 1.07472i 0.501420 0.865204i \(-0.332811\pi\)
0.977805 0.209516i \(-0.0671888\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 302.813 98.3898i 0.515865 0.167615i −0.0395031 0.999219i \(-0.512577\pi\)
0.555368 + 0.831605i \(0.312577\pi\)
\(588\) 205.371 550.969i 0.349270 0.937022i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −323.607 235.114i −0.546633 0.397152i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.60921 + 5.78018i 0.00269550 + 0.00968204i
\(598\) 0 0
\(599\) −701.807 965.954i −1.17163 1.61261i −0.651995 0.758223i \(-0.726068\pi\)
−0.519635 0.854388i \(-0.673932\pi\)
\(600\) 0 0
\(601\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(602\) 0 0
\(603\) 269.683 162.777i 0.447235 0.269945i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1114.39i 1.80614i −0.429498 0.903068i \(-0.641309\pi\)
0.429498 0.903068i \(-0.358691\pi\)
\(618\) 0 0
\(619\) −382.254 + 1176.46i −0.617535 + 1.90058i −0.270549 + 0.962706i \(0.587205\pi\)
−0.346986 + 0.937870i \(0.612795\pi\)
\(620\) −1400.51 + 455.053i −2.25888 + 0.733956i
\(621\) −553.016 + 586.270i −0.890524 + 0.944074i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −2427.86 1763.94i −3.88458 2.82231i
\(626\) 0 0
\(627\) 0 0
\(628\) −860.000 −1.36943
\(629\) 0 0
\(630\) 0 0
\(631\) 374.838 + 1153.63i 0.594037 + 1.82826i 0.559460 + 0.828857i \(0.311008\pi\)
0.0345772 + 0.999402i \(0.488992\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −40.7102 + 954.320i −0.0640097 + 1.50050i
\(637\) 0 0
\(638\) 0 0
\(639\) −412.500 174.123i −0.645540 0.272493i
\(640\) 0 0
\(641\) 993.604 + 322.841i 1.55008 + 0.503653i 0.954137 0.299371i \(-0.0967768\pi\)
0.595947 + 0.803024i \(0.296777\pi\)
\(642\) 0 0
\(643\) −319.562 + 232.175i −0.496986 + 0.361081i −0.807864 0.589368i \(-0.799377\pi\)
0.310879 + 0.950450i \(0.399377\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 684.262 941.805i 1.05759 1.45565i 0.175554 0.984470i \(-0.443828\pi\)
0.882037 0.471180i \(-0.156172\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −86.5248 + 266.296i −0.132707 + 0.408429i
\(653\) 160.869 52.2696i 0.246354 0.0800453i −0.183237 0.983069i \(-0.558658\pi\)
0.429591 + 0.903023i \(0.358658\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 1153.00 1.74433 0.872163 0.489215i \(-0.162717\pi\)
0.872163 + 0.489215i \(0.162717\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1333.79 + 56.8978i 1.99370 + 0.0850490i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(674\) 0 0
\(675\) −1753.01 + 958.628i −2.59705 + 1.42019i
\(676\) 546.895 397.343i 0.809017 0.587785i
\(677\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1114.39i 1.63160i 0.578331 + 0.815802i \(0.303704\pi\)
−0.578331 + 0.815802i \(0.696296\pi\)
\(684\) 0 0
\(685\) −214.149 + 659.082i −0.312626 + 0.962164i
\(686\) 0 0
\(687\) −453.702 + 1217.19i −0.660411 + 1.77175i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 884.256 + 642.449i 1.27968 + 0.929738i 0.999543 0.0302230i \(-0.00962175\pi\)
0.280132 + 0.959961i \(0.409622\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 1980.00 1313.38i 2.80851 1.86296i
\(706\) 0 0
\(707\) 0 0
\(708\) −371.169 + 467.583i −0.524250 + 0.660427i
\(709\) −855.131 + 621.289i −1.20611 + 0.876289i −0.994872 0.101146i \(-0.967749\pi\)
−0.211237 + 0.977435i \(0.567749\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 649.171 893.508i 0.910479 1.25317i
\(714\) 0 0
\(715\) 0 0
\(716\) 1392.98i 1.94551i
\(717\) 0 0
\(718\) 0 0
\(719\) −804.346 + 261.348i −1.11870 + 0.363488i −0.809272 0.587435i \(-0.800138\pi\)
−0.309429 + 0.950922i \(0.600138\pi\)
\(720\) −1395.41 + 325.098i −1.93807 + 0.451525i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −851.086 618.350i −1.17553 0.854075i
\(725\) 0 0
\(726\) 0 0
\(727\) −1355.00 −1.86382 −0.931912 0.362685i \(-0.881860\pi\)
−0.931912 + 0.362685i \(0.881860\pi\)
\(728\) 0 0
\(729\) 42.5213 + 727.759i 0.0583282 + 0.998297i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(734\) 0 0
\(735\) −62.3375 + 1461.30i −0.0848129 + 1.98817i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(740\) 946.289 + 307.468i 1.27877 + 0.415497i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 300.674 925.378i 0.400364 1.23219i −0.524340 0.851509i \(-0.675688\pi\)
0.924705 0.380686i \(-0.124312\pi\)
\(752\) 1211.25 393.559i 1.61071 0.523350i
\(753\) 1258.64 + 469.151i 1.67150 + 0.623043i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −56.6312 41.1450i −0.0748100 0.0543527i 0.549752 0.835328i \(-0.314722\pi\)
−0.624562 + 0.780975i \(0.714722\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −818.775 1126.95i −1.07169 1.47506i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −767.302 32.7322i −0.999091 0.0426201i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 792.000 + 1193.98i 1.02724 + 1.54862i
\(772\) 0 0
\(773\) −681.328 221.377i −0.881408 0.286387i −0.166866 0.985980i \(-0.553365\pi\)
−0.714542 + 0.699593i \(0.753365\pi\)
\(774\) 0 0
\(775\) 2215.09 1609.36i 2.85818 2.07659i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −242.269 + 745.628i −0.309017 + 0.951057i
\(785\) 2034.52 661.056i 2.59175 0.842110i
\(786\) 0 0
\(787\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −637.248 2288.95i −0.801570 2.87918i
\(796\) −2.47214 7.60845i −0.00310570 0.00955836i
\(797\) 99.4226 + 136.843i 0.124746 + 0.171698i 0.866822 0.498617i \(-0.166159\pi\)
−0.742076 + 0.670316i \(0.766159\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 694.118 + 1149.99i 0.866564 + 1.43569i
\(802\) 0 0
\(803\) 0 0
\(804\) −350.000 + 232.164i −0.435323 + 0.288761i
\(805\) 0 0
\(806\) 0 0
\(807\) 742.338 935.165i 0.919874 1.15882i
\(808\) 0 0
\(809\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(810\) 0 0
\(811\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 696.491i 0.854590i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(822\) 0 0
\(823\) −610.808 443.778i −0.742172 0.539220i 0.151218 0.988500i \(-0.451680\pi\)
−0.893391 + 0.449281i \(0.851680\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(828\) 703.368 812.409i 0.849479 0.981171i
\(829\) −252.467 777.013i −0.304544 0.937290i −0.979847 0.199749i \(-0.935987\pi\)
0.675303 0.737540i \(-0.264013\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −185.000 981.721i −0.221027 1.17290i
\(838\) 0 0
\(839\) −1561.38 507.322i −1.86100 0.604675i −0.994402 0.105665i \(-0.966303\pi\)
−0.866596 0.499010i \(-0.833697\pi\)
\(840\) 0 0
\(841\) −680.383 + 494.327i −0.809017 + 0.587785i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −988.378 + 1360.39i −1.16968 + 1.60992i
\(846\) 0 0
\(847\) 0 0
\(848\) 1273.58i 1.50187i
\(849\) 0 0
\(850\) 0 0
\(851\) −709.717 + 230.601i −0.833980 + 0.270977i
\(852\) 559.395 + 208.512i 0.656567 + 0.244732i
\(853\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −757.000 −0.881257 −0.440629 0.897689i \(-0.645244\pi\)
−0.440629 + 0.897689i \(0.645244\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 982.529 + 1352.34i 1.13850 + 1.56702i 0.770803 + 0.637073i \(0.219855\pi\)
0.367701 + 0.929944i \(0.380145\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −866.212 36.9516i −0.999091 0.0426201i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 851.894 + 72.8141i 0.975823 + 0.0834068i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 945.238i 1.07291i 0.843927 + 0.536457i \(0.180238\pi\)
−0.843927 + 0.536457i \(0.819762\pi\)
\(882\) 0 0
\(883\) −423.353 + 1302.95i −0.479449 + 1.47559i 0.360414 + 0.932793i \(0.382636\pi\)
−0.839863 + 0.542799i \(0.817364\pi\)
\(884\) 0 0
\(885\) 518.666 1391.48i 0.586064 1.57229i
\(886\) 0 0
\(887\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −1780.00 −1.99552
\(893\) 0 0
\(894\) 0 0
\(895\) −1070.74 3295.41i −1.19636 3.68202i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 2280.74 1376.63i 2.53416 1.52959i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2488.74 + 808.641i 2.74999 + 0.893526i
\(906\) 0 0
\(907\) 1415.78 1028.62i 1.56095 1.13410i 0.625721 0.780047i \(-0.284805\pi\)
0.935227 0.354048i \(-0.115195\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −233.936 + 321.985i −0.256790 + 0.353441i −0.917875 0.396870i \(-0.870096\pi\)
0.661085 + 0.750311i \(0.270096\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 535.217 1647.23i 0.584299 1.79829i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1850.00 −2.00000
\(926\) 0 0
\(927\) 1292.80 + 1119.28i 1.39460 + 1.20742i
\(928\) 0 0
\(929\) 935.742 + 1287.94i 1.00726 + 1.38637i 0.920765 + 0.390119i \(0.127566\pi\)
0.0864930 + 0.996252i \(0.472434\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 50.8877 1192.90i 0.0545420 1.27856i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(938\) 0 0
\(939\) 622.668 + 494.277i 0.663118 + 0.526386i
\(940\) −2562.97 + 1862.10i −2.72656 + 1.98096i
\(941\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 467.871 643.969i 0.495626 0.682171i
\(945\) 0 0
\(946\) 0 0
\(947\) 1323.33i 1.39740i −0.715417 0.698698i \(-0.753763\pi\)
0.715417 0.698698i \(-0.246237\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −1762.09 656.812i −1.85289 0.690654i
\(952\) 0 0
\(953\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(954\) 0 0
\(955\) 2803.24 + 2036.68i 2.93533 + 2.13264i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1840.38 512.367i 1.91707 0.533715i
\(961\) 126.079 + 388.031i 0.131196 + 0.403778i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1845.26 + 599.563i 1.90037 + 0.617469i 0.963395 + 0.268087i \(0.0863915\pi\)
0.936980 + 0.349382i \(0.113609\pi\)
\(972\) −97.9997 967.047i −0.100823 0.994904i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −894.804 + 1231.59i −0.915869 + 1.26058i 0.0492540 + 0.998786i \(0.484316\pi\)
−0.965123 + 0.261799i \(0.915684\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1950.18i 1.98997i
\(981\) 0 0
\(982\) 0 0
\(983\) −1769.56 + 574.965i −1.80016 + 0.584909i −0.999892 0.0147282i \(-0.995312\pi\)
−0.800272 + 0.599637i \(0.795312\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1582.00 1.59637 0.798184 0.602414i \(-0.205794\pi\)
0.798184 + 0.602414i \(0.205794\pi\)
\(992\) 0 0
\(993\) −452.993 1627.12i −0.456187 1.63859i
\(994\) 0 0
\(995\) 11.6968 + 16.0992i 0.0117556 + 0.0161801i
\(996\) 0 0
\(997\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(998\) 0 0
\(999\) −288.766 + 610.114i −0.289055 + 0.610725i
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 363.3.h.f.323.1 8
3.2 odd 2 inner 363.3.h.f.323.2 8
11.2 odd 10 inner 363.3.h.f.269.1 8
11.3 even 5 inner 363.3.h.f.245.2 8
11.4 even 5 inner 363.3.h.f.251.2 8
11.5 even 5 363.3.b.c.122.1 2
11.6 odd 10 363.3.b.c.122.1 2
11.7 odd 10 inner 363.3.h.f.251.2 8
11.8 odd 10 inner 363.3.h.f.245.2 8
11.9 even 5 inner 363.3.h.f.269.1 8
11.10 odd 2 CM 363.3.h.f.323.1 8
33.2 even 10 inner 363.3.h.f.269.2 8
33.5 odd 10 363.3.b.c.122.2 yes 2
33.8 even 10 inner 363.3.h.f.245.1 8
33.14 odd 10 inner 363.3.h.f.245.1 8
33.17 even 10 363.3.b.c.122.2 yes 2
33.20 odd 10 inner 363.3.h.f.269.2 8
33.26 odd 10 inner 363.3.h.f.251.1 8
33.29 even 10 inner 363.3.h.f.251.1 8
33.32 even 2 inner 363.3.h.f.323.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.3.b.c.122.1 2 11.5 even 5
363.3.b.c.122.1 2 11.6 odd 10
363.3.b.c.122.2 yes 2 33.5 odd 10
363.3.b.c.122.2 yes 2 33.17 even 10
363.3.h.f.245.1 8 33.8 even 10 inner
363.3.h.f.245.1 8 33.14 odd 10 inner
363.3.h.f.245.2 8 11.3 even 5 inner
363.3.h.f.245.2 8 11.8 odd 10 inner
363.3.h.f.251.1 8 33.26 odd 10 inner
363.3.h.f.251.1 8 33.29 even 10 inner
363.3.h.f.251.2 8 11.4 even 5 inner
363.3.h.f.251.2 8 11.7 odd 10 inner
363.3.h.f.269.1 8 11.2 odd 10 inner
363.3.h.f.269.1 8 11.9 even 5 inner
363.3.h.f.269.2 8 33.2 even 10 inner
363.3.h.f.269.2 8 33.20 odd 10 inner
363.3.h.f.323.1 8 1.1 even 1 trivial
363.3.h.f.323.1 8 11.10 odd 2 CM
363.3.h.f.323.2 8 3.2 odd 2 inner
363.3.h.f.323.2 8 33.32 even 2 inner