Properties

Label 2520.2.bi.s.1801.3
Level $2520$
Weight $2$
Character 2520.1801
Analytic conductor $20.122$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2520,2,Mod(361,2520)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2520.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bi (of order \(3\), degree \(2\), 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: \(20.1223013094\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1801.3
Root \(2.03852i\) of defining polynomial
Character \(\chi\) \(=\) 2520.1801
Dual form 2520.2.bi.s.361.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(0.194868 - 2.63857i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(0.194868 - 2.63857i) q^{7} +(-1.26541 - 2.19175i) q^{11} +5.45654 q^{13} +(3.25817 + 5.64332i) q^{17} +(-0.0406394 + 0.0703895i) q^{19} +(-1.23551 + 2.13996i) q^{23} +(-0.500000 - 0.866025i) q^{25} +8.37709 q^{29} +(-0.852597 - 1.47674i) q^{31} +(-2.18763 - 1.48804i) q^{35} +(1.18763 - 2.05704i) q^{37} -3.75135 q^{41} +9.44207 q^{43} +(0.962862 - 1.66773i) q^{47} +(-6.92405 - 1.02834i) q^{49} +(-2.49368 - 4.31918i) q^{53} -2.53082 q^{55} +(-1.65773 - 2.87127i) q^{59} +(-0.150904 + 0.261373i) q^{61} +(2.72827 - 4.72550i) q^{65} +(-1.58460 - 2.74461i) q^{67} +0.684541 q^{71} +(-7.64159 - 13.2356i) q^{73} +(-6.02967 + 2.91176i) q^{77} +(7.29931 - 12.6428i) q^{79} -12.0753 q^{83} +6.51634 q^{85} +(-1.79881 + 3.11563i) q^{89} +(1.06330 - 14.3974i) q^{91} +(0.0406394 + 0.0703895i) q^{95} +9.20088 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 5 q^{5} - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 5 q^{5} - q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{17} + q^{19} - 8 q^{23} - 5 q^{25} + 7 q^{31} + q^{35} - 11 q^{37} - 20 q^{41} + 6 q^{43} - 23 q^{49} + 14 q^{53} + 4 q^{55} - 4 q^{59} - 6 q^{61} + 3 q^{65} - 7 q^{67} + 32 q^{71} + 3 q^{73} - 8 q^{77} - 19 q^{79} - 28 q^{83} - 4 q^{85} + 18 q^{89} - 21 q^{91} - q^{95} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 0.194868 2.63857i 0.0736531 0.997284i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.26541 2.19175i −0.381535 0.660838i 0.609747 0.792596i \(-0.291271\pi\)
−0.991282 + 0.131758i \(0.957938\pi\)
\(12\) 0 0
\(13\) 5.45654 1.51337 0.756686 0.653779i \(-0.226817\pi\)
0.756686 + 0.653779i \(0.226817\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.25817 + 5.64332i 0.790223 + 1.36871i 0.925829 + 0.377943i \(0.123368\pi\)
−0.135606 + 0.990763i \(0.543298\pi\)
\(18\) 0 0
\(19\) −0.0406394 + 0.0703895i −0.00932331 + 0.0161484i −0.870649 0.491904i \(-0.836301\pi\)
0.861326 + 0.508052i \(0.169634\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.23551 + 2.13996i −0.257621 + 0.446213i −0.965604 0.260017i \(-0.916272\pi\)
0.707983 + 0.706229i \(0.249605\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.37709 1.55559 0.777793 0.628520i \(-0.216339\pi\)
0.777793 + 0.628520i \(0.216339\pi\)
\(30\) 0 0
\(31\) −0.852597 1.47674i −0.153131 0.265231i 0.779246 0.626718i \(-0.215602\pi\)
−0.932377 + 0.361488i \(0.882269\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.18763 1.48804i −0.369777 0.251525i
\(36\) 0 0
\(37\) 1.18763 2.05704i 0.195245 0.338175i −0.751736 0.659465i \(-0.770783\pi\)
0.946981 + 0.321290i \(0.104116\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.75135 −0.585862 −0.292931 0.956134i \(-0.594631\pi\)
−0.292931 + 0.956134i \(0.594631\pi\)
\(42\) 0 0
\(43\) 9.44207 1.43990 0.719951 0.694025i \(-0.244164\pi\)
0.719951 + 0.694025i \(0.244164\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.962862 1.66773i 0.140448 0.243263i −0.787218 0.616675i \(-0.788479\pi\)
0.927665 + 0.373413i \(0.121812\pi\)
\(48\) 0 0
\(49\) −6.92405 1.02834i −0.989150 0.146906i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.49368 4.31918i −0.342533 0.593285i 0.642369 0.766395i \(-0.277952\pi\)
−0.984902 + 0.173111i \(0.944618\pi\)
\(54\) 0 0
\(55\) −2.53082 −0.341255
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.65773 2.87127i −0.215818 0.373808i 0.737707 0.675121i \(-0.235908\pi\)
−0.953525 + 0.301313i \(0.902575\pi\)
\(60\) 0 0
\(61\) −0.150904 + 0.261373i −0.0193213 + 0.0334654i −0.875524 0.483174i \(-0.839484\pi\)
0.856203 + 0.516639i \(0.172817\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.72827 4.72550i 0.338400 0.586126i
\(66\) 0 0
\(67\) −1.58460 2.74461i −0.193590 0.335308i 0.752847 0.658195i \(-0.228680\pi\)
−0.946437 + 0.322887i \(0.895347\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.684541 0.0812401 0.0406200 0.999175i \(-0.487067\pi\)
0.0406200 + 0.999175i \(0.487067\pi\)
\(72\) 0 0
\(73\) −7.64159 13.2356i −0.894380 1.54911i −0.834570 0.550902i \(-0.814284\pi\)
−0.0598097 0.998210i \(-0.519049\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.02967 + 2.91176i −0.687144 + 0.331826i
\(78\) 0 0
\(79\) 7.29931 12.6428i 0.821237 1.42242i −0.0835245 0.996506i \(-0.526618\pi\)
0.904762 0.425919i \(-0.140049\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −12.0753 −1.32543 −0.662717 0.748870i \(-0.730597\pi\)
−0.662717 + 0.748870i \(0.730597\pi\)
\(84\) 0 0
\(85\) 6.51634 0.706797
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.79881 + 3.11563i −0.190674 + 0.330256i −0.945474 0.325699i \(-0.894401\pi\)
0.754800 + 0.655955i \(0.227734\pi\)
\(90\) 0 0
\(91\) 1.06330 14.3974i 0.111464 1.50926i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.0406394 + 0.0703895i 0.00416951 + 0.00722181i
\(96\) 0 0
\(97\) 9.20088 0.934208 0.467104 0.884202i \(-0.345297\pi\)
0.467104 + 0.884202i \(0.345297\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.42273 + 11.1245i 0.639085 + 1.10693i 0.985634 + 0.168896i \(0.0540202\pi\)
−0.346549 + 0.938032i \(0.612646\pi\)
\(102\) 0 0
\(103\) 4.63975 8.03629i 0.457169 0.791839i −0.541641 0.840610i \(-0.682197\pi\)
0.998810 + 0.0487704i \(0.0155303\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.25817 3.91127i 0.218306 0.378116i −0.735984 0.676998i \(-0.763280\pi\)
0.954290 + 0.298882i \(0.0966137\pi\)
\(108\) 0 0
\(109\) −3.84277 6.65588i −0.368071 0.637518i 0.621193 0.783658i \(-0.286648\pi\)
−0.989264 + 0.146140i \(0.953315\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.77947 −0.261471 −0.130735 0.991417i \(-0.541734\pi\)
−0.130735 + 0.991417i \(0.541734\pi\)
\(114\) 0 0
\(115\) 1.23551 + 2.13996i 0.115212 + 0.199552i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 15.5252 7.49720i 1.42319 0.687267i
\(120\) 0 0
\(121\) 2.29748 3.97936i 0.208862 0.361760i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −3.76765 −0.334325 −0.167162 0.985929i \(-0.553460\pi\)
−0.167162 + 0.985929i \(0.553460\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.92314 + 5.06302i −0.255396 + 0.442358i −0.965003 0.262239i \(-0.915539\pi\)
0.709607 + 0.704597i \(0.248872\pi\)
\(132\) 0 0
\(133\) 0.177808 + 0.120946i 0.0154179 + 0.0104874i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.57363 + 16.5820i 0.817930 + 1.41670i 0.907204 + 0.420690i \(0.138212\pi\)
−0.0892740 + 0.996007i \(0.528455\pi\)
\(138\) 0 0
\(139\) 12.1266 1.02857 0.514283 0.857621i \(-0.328058\pi\)
0.514283 + 0.857621i \(0.328058\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −6.90475 11.9594i −0.577404 1.00009i
\(144\) 0 0
\(145\) 4.18855 7.25477i 0.347840 0.602476i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.90425 + 6.76235i −0.319848 + 0.553994i −0.980456 0.196738i \(-0.936965\pi\)
0.660608 + 0.750731i \(0.270299\pi\)
\(150\) 0 0
\(151\) −0.928544 1.60829i −0.0755638 0.130880i 0.825767 0.564011i \(-0.190742\pi\)
−0.901331 + 0.433130i \(0.857409\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.70519 −0.136965
\(156\) 0 0
\(157\) 0.158141 + 0.273908i 0.0126210 + 0.0218603i 0.872267 0.489030i \(-0.162649\pi\)
−0.859646 + 0.510890i \(0.829316\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.40567 + 3.67698i 0.426026 + 0.289786i
\(162\) 0 0
\(163\) −11.5976 + 20.0877i −0.908396 + 1.57339i −0.0921029 + 0.995749i \(0.529359\pi\)
−0.816293 + 0.577638i \(0.803974\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.471014 0.0364482 0.0182241 0.999834i \(-0.494199\pi\)
0.0182241 + 0.999834i \(0.494199\pi\)
\(168\) 0 0
\(169\) 16.7738 1.29029
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.88341 + 4.99422i −0.219222 + 0.379703i −0.954570 0.297986i \(-0.903685\pi\)
0.735348 + 0.677689i \(0.237019\pi\)
\(174\) 0 0
\(175\) −2.38250 + 1.15052i −0.180100 + 0.0869713i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −7.29840 12.6412i −0.545508 0.944848i −0.998575 0.0533709i \(-0.983003\pi\)
0.453067 0.891477i \(-0.350330\pi\)
\(180\) 0 0
\(181\) 13.5333 1.00592 0.502962 0.864308i \(-0.332243\pi\)
0.502962 + 0.864308i \(0.332243\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.18763 2.05704i −0.0873163 0.151236i
\(186\) 0 0
\(187\) 8.24583 14.2822i 0.602995 1.04442i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.12661 + 8.87954i −0.370948 + 0.642501i −0.989712 0.143076i \(-0.954301\pi\)
0.618763 + 0.785577i \(0.287634\pi\)
\(192\) 0 0
\(193\) −7.02949 12.1754i −0.505994 0.876407i −0.999976 0.00693486i \(-0.997793\pi\)
0.493982 0.869472i \(-0.335541\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.19423 −0.655062 −0.327531 0.944840i \(-0.606217\pi\)
−0.327531 + 0.944840i \(0.606217\pi\)
\(198\) 0 0
\(199\) 9.05698 + 15.6872i 0.642032 + 1.11203i 0.984978 + 0.172678i \(0.0552419\pi\)
−0.342946 + 0.939355i \(0.611425\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.63242 22.1035i 0.114574 1.55136i
\(204\) 0 0
\(205\) −1.87567 + 3.24876i −0.131003 + 0.226903i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.205702 0.0142287
\(210\) 0 0
\(211\) −14.6566 −1.00900 −0.504501 0.863411i \(-0.668324\pi\)
−0.504501 + 0.863411i \(0.668324\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.72103 8.17707i 0.321972 0.557671i
\(216\) 0 0
\(217\) −4.06262 + 1.96186i −0.275789 + 0.133180i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17.7783 + 30.7930i 1.19590 + 2.07136i
\(222\) 0 0
\(223\) 1.86639 0.124983 0.0624914 0.998046i \(-0.480095\pi\)
0.0624914 + 0.998046i \(0.480095\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −13.2455 22.9419i −0.879137 1.52271i −0.852290 0.523070i \(-0.824787\pi\)
−0.0268466 0.999640i \(-0.508547\pi\)
\(228\) 0 0
\(229\) 5.44839 9.43688i 0.360040 0.623607i −0.627927 0.778272i \(-0.716097\pi\)
0.987967 + 0.154665i \(0.0494298\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.29398 5.70535i 0.215796 0.373770i −0.737723 0.675104i \(-0.764099\pi\)
0.953519 + 0.301334i \(0.0974321\pi\)
\(234\) 0 0
\(235\) −0.962862 1.66773i −0.0628102 0.108790i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.12327 −0.525450 −0.262725 0.964871i \(-0.584621\pi\)
−0.262725 + 0.964871i \(0.584621\pi\)
\(240\) 0 0
\(241\) 13.3951 + 23.2010i 0.862855 + 1.49451i 0.869162 + 0.494528i \(0.164659\pi\)
−0.00630723 + 0.999980i \(0.502008\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.35260 + 5.48223i −0.278077 + 0.350247i
\(246\) 0 0
\(247\) −0.221750 + 0.384083i −0.0141096 + 0.0244386i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.2561 0.962954 0.481477 0.876459i \(-0.340101\pi\)
0.481477 + 0.876459i \(0.340101\pi\)
\(252\) 0 0
\(253\) 6.25368 0.393166
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.1063 26.1648i 0.942304 1.63212i 0.181242 0.983439i \(-0.441988\pi\)
0.761062 0.648679i \(-0.224678\pi\)
\(258\) 0 0
\(259\) −5.19619 3.53449i −0.322876 0.219623i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −14.4557 25.0380i −0.891378 1.54391i −0.838225 0.545325i \(-0.816406\pi\)
−0.0531531 0.998586i \(-0.516927\pi\)
\(264\) 0 0
\(265\) −4.98736 −0.306371
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.08046 + 12.2637i 0.431703 + 0.747732i 0.997020 0.0771421i \(-0.0245795\pi\)
−0.565317 + 0.824874i \(0.691246\pi\)
\(270\) 0 0
\(271\) 6.76300 11.7139i 0.410823 0.711566i −0.584157 0.811641i \(-0.698575\pi\)
0.994980 + 0.100074i \(0.0319081\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.26541 + 2.19175i −0.0763070 + 0.132168i
\(276\) 0 0
\(277\) −10.0177 17.3511i −0.601903 1.04253i −0.992533 0.121979i \(-0.961076\pi\)
0.390629 0.920548i \(-0.372257\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 18.1557 1.08308 0.541540 0.840675i \(-0.317841\pi\)
0.541540 + 0.840675i \(0.317841\pi\)
\(282\) 0 0
\(283\) −6.62711 11.4785i −0.393941 0.682326i 0.599025 0.800731i \(-0.295555\pi\)
−0.992965 + 0.118405i \(0.962222\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.731016 + 9.89817i −0.0431505 + 0.584271i
\(288\) 0 0
\(289\) −12.7314 + 22.0514i −0.748904 + 1.29714i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.46102 0.435878 0.217939 0.975962i \(-0.430067\pi\)
0.217939 + 0.975962i \(0.430067\pi\)
\(294\) 0 0
\(295\) −3.31546 −0.193033
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.74159 + 11.6768i −0.389876 + 0.675286i
\(300\) 0 0
\(301\) 1.83995 24.9135i 0.106053 1.43599i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.150904 + 0.261373i 0.00864073 + 0.0149662i
\(306\) 0 0
\(307\) 32.9561 1.88090 0.940451 0.339928i \(-0.110403\pi\)
0.940451 + 0.339928i \(0.110403\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 15.5638 + 26.9573i 0.882543 + 1.52861i 0.848505 + 0.529188i \(0.177503\pi\)
0.0340379 + 0.999421i \(0.489163\pi\)
\(312\) 0 0
\(313\) 2.87659 4.98240i 0.162594 0.281622i −0.773204 0.634157i \(-0.781347\pi\)
0.935798 + 0.352536i \(0.114680\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.5395 + 28.6473i −0.928951 + 1.60899i −0.143872 + 0.989596i \(0.545955\pi\)
−0.785080 + 0.619395i \(0.787378\pi\)
\(318\) 0 0
\(319\) −10.6004 18.3605i −0.593511 1.02799i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.529640 −0.0294700
\(324\) 0 0
\(325\) −2.72827 4.72550i −0.151337 0.262124i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −4.21277 2.86556i −0.232258 0.157983i
\(330\) 0 0
\(331\) −12.6547 + 21.9186i −0.695567 + 1.20476i 0.274422 + 0.961609i \(0.411513\pi\)
−0.969989 + 0.243148i \(0.921820\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.16921 −0.173152
\(336\) 0 0
\(337\) −28.6450 −1.56039 −0.780195 0.625536i \(-0.784880\pi\)
−0.780195 + 0.625536i \(0.784880\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.15777 + 3.73736i −0.116850 + 0.202390i
\(342\) 0 0
\(343\) −4.06262 + 18.0692i −0.219361 + 0.975644i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 17.9602 + 31.1080i 0.964156 + 1.66997i 0.711865 + 0.702316i \(0.247851\pi\)
0.252291 + 0.967651i \(0.418816\pi\)
\(348\) 0 0
\(349\) −10.8841 −0.582614 −0.291307 0.956630i \(-0.594090\pi\)
−0.291307 + 0.956630i \(0.594090\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −13.8026 23.9069i −0.734640 1.27243i −0.954881 0.296989i \(-0.904018\pi\)
0.220241 0.975446i \(-0.429316\pi\)
\(354\) 0 0
\(355\) 0.342271 0.592830i 0.0181658 0.0314641i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.45167 + 7.71053i −0.234950 + 0.406946i −0.959258 0.282531i \(-0.908826\pi\)
0.724308 + 0.689477i \(0.242159\pi\)
\(360\) 0 0
\(361\) 9.49670 + 16.4488i 0.499826 + 0.865724i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −15.2832 −0.799958
\(366\) 0 0
\(367\) 16.4788 + 28.5421i 0.860186 + 1.48989i 0.871749 + 0.489953i \(0.162986\pi\)
−0.0115631 + 0.999933i \(0.503681\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −11.8824 + 5.73806i −0.616902 + 0.297905i
\(372\) 0 0
\(373\) −8.17339 + 14.1567i −0.423202 + 0.733008i −0.996251 0.0865138i \(-0.972427\pi\)
0.573048 + 0.819521i \(0.305761\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 45.7099 2.35418
\(378\) 0 0
\(379\) −27.1083 −1.39246 −0.696231 0.717818i \(-0.745141\pi\)
−0.696231 + 0.717818i \(0.745141\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.3853 21.4519i 0.632858 1.09614i −0.354106 0.935205i \(-0.615215\pi\)
0.986965 0.160938i \(-0.0514518\pi\)
\(384\) 0 0
\(385\) −0.493174 + 6.67772i −0.0251345 + 0.340328i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.04046 + 6.99829i 0.204860 + 0.354827i 0.950088 0.311982i \(-0.100993\pi\)
−0.745228 + 0.666809i \(0.767660\pi\)
\(390\) 0 0
\(391\) −16.1020 −0.814312
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.29931 12.6428i −0.367268 0.636127i
\(396\) 0 0
\(397\) −13.9374 + 24.1403i −0.699498 + 1.21157i 0.269143 + 0.963100i \(0.413260\pi\)
−0.968641 + 0.248466i \(0.920074\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.05722 13.9555i 0.402358 0.696905i −0.591652 0.806194i \(-0.701524\pi\)
0.994010 + 0.109289i \(0.0348573\pi\)
\(402\) 0 0
\(403\) −4.65223 8.05790i −0.231744 0.401393i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6.01135 −0.297972
\(408\) 0 0
\(409\) −6.06048 10.4971i −0.299672 0.519046i 0.676389 0.736544i \(-0.263544\pi\)
−0.976061 + 0.217498i \(0.930210\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7.89908 + 3.81451i −0.388688 + 0.187700i
\(414\) 0 0
\(415\) −6.03764 + 10.4575i −0.296376 + 0.513339i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −29.7920 −1.45544 −0.727718 0.685876i \(-0.759419\pi\)
−0.727718 + 0.685876i \(0.759419\pi\)
\(420\) 0 0
\(421\) 6.96233 0.339323 0.169662 0.985502i \(-0.445733\pi\)
0.169662 + 0.985502i \(0.445733\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.25817 5.64332i 0.158045 0.273741i
\(426\) 0 0
\(427\) 0.660244 + 0.449103i 0.0319515 + 0.0217336i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.8326 23.9588i −0.666294 1.15406i −0.978933 0.204183i \(-0.934546\pi\)
0.312639 0.949872i \(-0.398787\pi\)
\(432\) 0 0
\(433\) 5.80177 0.278815 0.139408 0.990235i \(-0.455480\pi\)
0.139408 + 0.990235i \(0.455480\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.100420 0.173933i −0.00480376 0.00832036i
\(438\) 0 0
\(439\) −8.43224 + 14.6051i −0.402449 + 0.697062i −0.994021 0.109190i \(-0.965174\pi\)
0.591572 + 0.806252i \(0.298508\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.8173 29.1285i 0.799015 1.38394i −0.121243 0.992623i \(-0.538688\pi\)
0.920258 0.391312i \(-0.127979\pi\)
\(444\) 0 0
\(445\) 1.79881 + 3.11563i 0.0852718 + 0.147695i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8.87896 0.419024 0.209512 0.977806i \(-0.432812\pi\)
0.209512 + 0.977806i \(0.432812\pi\)
\(450\) 0 0
\(451\) 4.74698 + 8.22202i 0.223527 + 0.387160i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −11.9369 8.11957i −0.559610 0.380651i
\(456\) 0 0
\(457\) −15.8641 + 27.4774i −0.742092 + 1.28534i 0.209449 + 0.977819i \(0.432833\pi\)
−0.951541 + 0.307521i \(0.900500\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −19.0714 −0.888242 −0.444121 0.895967i \(-0.646484\pi\)
−0.444121 + 0.895967i \(0.646484\pi\)
\(462\) 0 0
\(463\) 21.5938 1.00355 0.501775 0.864998i \(-0.332681\pi\)
0.501775 + 0.864998i \(0.332681\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −14.4369 + 25.0054i −0.668060 + 1.15711i 0.310386 + 0.950611i \(0.399542\pi\)
−0.978446 + 0.206503i \(0.933792\pi\)
\(468\) 0 0
\(469\) −7.55063 + 3.64624i −0.348656 + 0.168368i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −11.9481 20.6947i −0.549373 0.951542i
\(474\) 0 0
\(475\) 0.0812787 0.00372932
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.97105 + 12.0742i 0.318515 + 0.551685i 0.980179 0.198116i \(-0.0634824\pi\)
−0.661663 + 0.749801i \(0.730149\pi\)
\(480\) 0 0
\(481\) 6.48035 11.2243i 0.295479 0.511784i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.60044 7.96820i 0.208895 0.361817i
\(486\) 0 0
\(487\) −7.55831 13.0914i −0.342500 0.593227i 0.642397 0.766372i \(-0.277940\pi\)
−0.984896 + 0.173146i \(0.944607\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 31.5713 1.42479 0.712396 0.701777i \(-0.247610\pi\)
0.712396 + 0.701777i \(0.247610\pi\)
\(492\) 0 0
\(493\) 27.2940 + 47.2746i 1.22926 + 2.12914i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.133395 1.80621i 0.00598358 0.0810194i
\(498\) 0 0
\(499\) −15.4432 + 26.7484i −0.691333 + 1.19742i 0.280068 + 0.959980i \(0.409643\pi\)
−0.971401 + 0.237444i \(0.923690\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −38.4451 −1.71418 −0.857091 0.515165i \(-0.827731\pi\)
−0.857091 + 0.515165i \(0.827731\pi\)
\(504\) 0 0
\(505\) 12.8455 0.571615
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11.1421 + 19.2987i −0.493864 + 0.855398i −0.999975 0.00707034i \(-0.997749\pi\)
0.506111 + 0.862469i \(0.331083\pi\)
\(510\) 0 0
\(511\) −36.4121 + 17.5836i −1.61078 + 0.777854i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.63975 8.03629i −0.204452 0.354121i
\(516\) 0 0
\(517\) −4.87365 −0.214343
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.98111 + 12.0916i 0.305848 + 0.529744i 0.977450 0.211168i \(-0.0677267\pi\)
−0.671602 + 0.740912i \(0.734393\pi\)
\(522\) 0 0
\(523\) 2.42987 4.20866i 0.106251 0.184032i −0.807998 0.589186i \(-0.799449\pi\)
0.914249 + 0.405154i \(0.132782\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.55582 9.62295i 0.242015 0.419182i
\(528\) 0 0
\(529\) 8.44704 + 14.6307i 0.367263 + 0.636118i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −20.4694 −0.886627
\(534\) 0 0
\(535\) −2.25817 3.91127i −0.0976293 0.169099i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.50788 + 16.4771i 0.280314 + 0.709718i
\(540\) 0 0
\(541\) −11.0587 + 19.1541i −0.475449 + 0.823501i −0.999605 0.0281212i \(-0.991048\pi\)
0.524156 + 0.851622i \(0.324381\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.68555 −0.329213
\(546\) 0 0
\(547\) 37.0636 1.58473 0.792364 0.610049i \(-0.208850\pi\)
0.792364 + 0.610049i \(0.208850\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.340440 + 0.589659i −0.0145032 + 0.0251203i
\(552\) 0 0
\(553\) −31.9364 21.7234i −1.35807 0.923772i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.4331 + 28.4629i 0.696291 + 1.20601i 0.969744 + 0.244126i \(0.0785009\pi\)
−0.273453 + 0.961885i \(0.588166\pi\)
\(558\) 0 0
\(559\) 51.5210 2.17911
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.83446 + 10.1056i 0.245893 + 0.425899i 0.962382 0.271699i \(-0.0875855\pi\)
−0.716489 + 0.697598i \(0.754252\pi\)
\(564\) 0 0
\(565\) −1.38974 + 2.40709i −0.0584666 + 0.101267i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.88932 5.00446i 0.121127 0.209798i −0.799086 0.601217i \(-0.794683\pi\)
0.920212 + 0.391420i \(0.128016\pi\)
\(570\) 0 0
\(571\) −11.7522 20.3554i −0.491814 0.851847i 0.508142 0.861274i \(-0.330333\pi\)
−0.999956 + 0.00942676i \(0.996999\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.47101 0.103048
\(576\) 0 0
\(577\) −3.48220 6.03135i −0.144966 0.251088i 0.784394 0.620263i \(-0.212974\pi\)
−0.929360 + 0.369174i \(0.879641\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.35308 + 31.8614i −0.0976223 + 1.32183i
\(582\) 0 0
\(583\) −6.31104 + 10.9310i −0.261377 + 0.452718i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.95568 0.410915 0.205457 0.978666i \(-0.434132\pi\)
0.205457 + 0.978666i \(0.434132\pi\)
\(588\) 0 0
\(589\) 0.138596 0.00571075
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 17.8531 30.9225i 0.733141 1.26984i −0.222394 0.974957i \(-0.571387\pi\)
0.955534 0.294880i \(-0.0952796\pi\)
\(594\) 0 0
\(595\) 1.26982 17.1938i 0.0520577 0.704877i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.76582 15.1828i −0.358162 0.620354i 0.629492 0.777007i \(-0.283263\pi\)
−0.987654 + 0.156653i \(0.949930\pi\)
\(600\) 0 0
\(601\) 24.9334 1.01705 0.508527 0.861046i \(-0.330190\pi\)
0.508527 + 0.861046i \(0.330190\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.29748 3.97936i −0.0934060 0.161784i
\(606\) 0 0
\(607\) −10.7969 + 18.7008i −0.438233 + 0.759042i −0.997553 0.0699099i \(-0.977729\pi\)
0.559320 + 0.828952i \(0.311062\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.25389 9.10001i 0.212550 0.368147i
\(612\) 0 0
\(613\) 8.54423 + 14.7990i 0.345098 + 0.597728i 0.985372 0.170419i \(-0.0545122\pi\)
−0.640273 + 0.768147i \(0.721179\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −29.7252 −1.19669 −0.598345 0.801239i \(-0.704175\pi\)
−0.598345 + 0.801239i \(0.704175\pi\)
\(618\) 0 0
\(619\) 7.12909 + 12.3479i 0.286542 + 0.496306i 0.972982 0.230881i \(-0.0741608\pi\)
−0.686440 + 0.727187i \(0.740827\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.87027 + 5.35342i 0.315316 + 0.214480i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 15.4780 0.617149
\(630\) 0 0
\(631\) −6.15725 −0.245116 −0.122558 0.992461i \(-0.539110\pi\)
−0.122558 + 0.992461i \(0.539110\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.88383 + 3.26288i −0.0747573 + 0.129483i
\(636\) 0 0
\(637\) −37.7814 5.61119i −1.49695 0.222323i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 14.2435 + 24.6704i 0.562583 + 0.974422i 0.997270 + 0.0738407i \(0.0235256\pi\)
−0.434687 + 0.900582i \(0.643141\pi\)
\(642\) 0 0
\(643\) 3.88877 0.153358 0.0766790 0.997056i \(-0.475568\pi\)
0.0766790 + 0.997056i \(0.475568\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.7725 + 18.6585i 0.423511 + 0.733542i 0.996280 0.0861744i \(-0.0274642\pi\)
−0.572769 + 0.819717i \(0.694131\pi\)
\(648\) 0 0
\(649\) −4.19541 + 7.26666i −0.164684 + 0.285241i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.20738 3.82330i 0.0863815 0.149617i −0.819598 0.572940i \(-0.805803\pi\)
0.905979 + 0.423322i \(0.139136\pi\)
\(654\) 0 0
\(655\) 2.92314 + 5.06302i 0.114216 + 0.197829i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 41.7579 1.62666 0.813329 0.581804i \(-0.197653\pi\)
0.813329 + 0.581804i \(0.197653\pi\)
\(660\) 0 0
\(661\) 5.13758 + 8.89855i 0.199829 + 0.346113i 0.948473 0.316859i \(-0.102628\pi\)
−0.748644 + 0.662972i \(0.769295\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.193646 0.0935130i 0.00750929 0.00362628i
\(666\) 0 0
\(667\) −10.3500 + 17.9267i −0.400752 + 0.694123i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.763820 0.0294870
\(672\) 0 0
\(673\) −23.0484 −0.888450 −0.444225 0.895915i \(-0.646521\pi\)
−0.444225 + 0.895915i \(0.646521\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.64407 + 2.84760i −0.0631866 + 0.109442i −0.895888 0.444280i \(-0.853460\pi\)
0.832702 + 0.553722i \(0.186793\pi\)
\(678\) 0 0
\(679\) 1.79296 24.2771i 0.0688073 0.931671i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −20.2241 35.0291i −0.773852 1.34035i −0.935438 0.353492i \(-0.884994\pi\)
0.161586 0.986859i \(-0.448339\pi\)
\(684\) 0 0
\(685\) 19.1473 0.731579
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −13.6069 23.5678i −0.518380 0.897860i
\(690\) 0 0
\(691\) −17.2144 + 29.8162i −0.654866 + 1.13426i 0.327061 + 0.945003i \(0.393942\pi\)
−0.981927 + 0.189259i \(0.939392\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.06330 10.5019i 0.229994 0.398362i
\(696\) 0 0
\(697\) −12.2225 21.1700i −0.462961 0.801872i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −15.1396 −0.571815 −0.285907 0.958257i \(-0.592295\pi\)
−0.285907 + 0.958257i \(0.592295\pi\)
\(702\) 0 0
\(703\) 0.0965291 + 0.167193i 0.00364067 + 0.00630582i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 30.6043 14.7790i 1.15099 0.555821i
\(708\) 0 0
\(709\) −19.0851 + 33.0564i −0.716756 + 1.24146i 0.245522 + 0.969391i \(0.421041\pi\)
−0.962278 + 0.272067i \(0.912293\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.21356 0.157799
\(714\) 0 0
\(715\) −13.8095 −0.516446
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −7.29398 + 12.6335i −0.272020 + 0.471152i −0.969379 0.245570i \(-0.921025\pi\)
0.697359 + 0.716722i \(0.254358\pi\)
\(720\) 0 0
\(721\) −20.3001 13.8083i −0.756017 0.514248i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.18855 7.25477i −0.155559 0.269436i
\(726\) 0 0
\(727\) 3.76798 0.139747 0.0698734 0.997556i \(-0.477740\pi\)
0.0698734 + 0.997556i \(0.477740\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 30.7639 + 53.2846i 1.13784 + 1.97080i
\(732\) 0 0
\(733\) −12.5404 + 21.7207i −0.463191 + 0.802271i −0.999118 0.0419938i \(-0.986629\pi\)
0.535927 + 0.844265i \(0.319962\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.01034 + 6.94611i −0.147723 + 0.255863i
\(738\) 0 0
\(739\) 8.32715 + 14.4230i 0.306319 + 0.530560i 0.977554 0.210684i \(-0.0675692\pi\)
−0.671235 + 0.741245i \(0.734236\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −11.8561 −0.434959 −0.217479 0.976065i \(-0.569783\pi\)
−0.217479 + 0.976065i \(0.569783\pi\)
\(744\) 0 0
\(745\) 3.90425 + 6.76235i 0.143041 + 0.247753i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9.88009 6.72051i −0.361011 0.245562i
\(750\) 0 0
\(751\) −20.0690 + 34.7605i −0.732327 + 1.26843i 0.223559 + 0.974690i \(0.428232\pi\)
−0.955886 + 0.293737i \(0.905101\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.85709 −0.0675864
\(756\) 0 0
\(757\) −0.732857 −0.0266361 −0.0133181 0.999911i \(-0.504239\pi\)
−0.0133181 + 0.999911i \(0.504239\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.02042 + 10.4277i −0.218240 + 0.378003i −0.954270 0.298946i \(-0.903365\pi\)
0.736030 + 0.676949i \(0.236698\pi\)
\(762\) 0 0
\(763\) −18.3108 + 8.84239i −0.662896 + 0.320116i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.04547 15.6672i −0.326613 0.565710i
\(768\) 0 0
\(769\) 20.3382 0.733413 0.366706 0.930337i \(-0.380485\pi\)
0.366706 + 0.930337i \(0.380485\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −23.4299 40.5818i −0.842716 1.45963i −0.887590 0.460634i \(-0.847622\pi\)
0.0448742 0.998993i \(-0.485711\pi\)
\(774\) 0 0
\(775\) −0.852597 + 1.47674i −0.0306262 + 0.0530461i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.152452 0.264055i 0.00546217 0.00946076i
\(780\) 0 0
\(781\) −0.866224 1.50034i −0.0309959 0.0536865i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.316282 0.0112886
\(786\) 0 0
\(787\) −10.2234 17.7074i −0.364424 0.631200i 0.624260 0.781217i \(-0.285401\pi\)
−0.988684 + 0.150016i \(0.952067\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −0.541629 + 7.33382i −0.0192581 + 0.260760i
\(792\) 0 0
\(793\) −0.823413 + 1.42619i −0.0292403 + 0.0506456i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.73313 0.309344 0.154672 0.987966i \(-0.450568\pi\)
0.154672 + 0.987966i \(0.450568\pi\)
\(798\) 0 0
\(799\) 12.5487 0.443940
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −19.3394 + 33.4969i −0.682474 + 1.18208i
\(804\) 0 0
\(805\) 5.88719 2.84296i 0.207496 0.100201i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0.922130 + 1.59718i 0.0324204 + 0.0561537i 0.881780 0.471660i \(-0.156345\pi\)
−0.849360 + 0.527814i \(0.823012\pi\)
\(810\) 0 0
\(811\) −35.0744 −1.23163 −0.615814 0.787891i \(-0.711173\pi\)
−0.615814 + 0.787891i \(0.711173\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 11.5976 + 20.0877i 0.406247 + 0.703640i
\(816\) 0 0
\(817\) −0.383720 + 0.664622i −0.0134247 + 0.0232522i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.73800 3.01031i 0.0606566 0.105060i −0.834102 0.551610i \(-0.814014\pi\)
0.894759 + 0.446549i \(0.147347\pi\)
\(822\) 0 0
\(823\) −25.4674 44.1108i −0.887737 1.53761i −0.842544 0.538627i \(-0.818943\pi\)
−0.0451923 0.998978i \(-0.514390\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14.1506 0.492063 0.246032 0.969262i \(-0.420873\pi\)
0.246032 + 0.969262i \(0.420873\pi\)
\(828\) 0 0
\(829\) −14.9756 25.9384i −0.520123 0.900879i −0.999726 0.0233937i \(-0.992553\pi\)
0.479604 0.877485i \(-0.340780\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −16.7565 42.4252i −0.580578 1.46994i
\(834\) 0 0
\(835\) 0.235507 0.407910i 0.00815006 0.0141163i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 48.6753 1.68046 0.840229 0.542232i \(-0.182421\pi\)
0.840229 + 0.542232i \(0.182421\pi\)
\(840\) 0 0
\(841\) 41.1757 1.41985
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.38691 14.5266i 0.288519 0.499729i
\(846\) 0 0
\(847\) −10.0521 6.83751i −0.345394 0.234940i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.93465 + 5.08297i 0.100599 + 0.174242i
\(852\) 0 0
\(853\) 7.93054 0.271537 0.135768 0.990741i \(-0.456650\pi\)
0.135768 + 0.990741i \(0.456650\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −16.0956 27.8784i −0.549816 0.952309i −0.998287 0.0585114i \(-0.981365\pi\)
0.448471 0.893797i \(-0.351969\pi\)
\(858\) 0 0
\(859\) 8.43224 14.6051i 0.287704 0.498319i −0.685557 0.728019i \(-0.740441\pi\)
0.973261 + 0.229700i \(0.0737746\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −23.4596 + 40.6331i −0.798573 + 1.38317i 0.121973 + 0.992533i \(0.461078\pi\)
−0.920546 + 0.390635i \(0.872255\pi\)
\(864\) 0 0
\(865\) 2.88341 + 4.99422i 0.0980390 + 0.169809i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −36.9465 −1.25332
\(870\) 0 0
\(871\) −8.64645 14.9761i −0.292974 0.507446i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.194868 + 2.63857i −0.00658773 + 0.0891998i
\(876\) 0 0
\(877\) 1.48380 2.57002i 0.0501044 0.0867834i −0.839885 0.542764i \(-0.817378\pi\)
0.889990 + 0.455980i \(0.150711\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 26.6911 0.899247 0.449623 0.893218i \(-0.351558\pi\)
0.449623 + 0.893218i \(0.351558\pi\)
\(882\) 0 0
\(883\) 2.25049 0.0757349 0.0378674 0.999283i \(-0.487944\pi\)
0.0378674 + 0.999283i \(0.487944\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −17.9899 + 31.1594i −0.604041 + 1.04623i 0.388162 + 0.921591i \(0.373110\pi\)
−0.992202 + 0.124638i \(0.960223\pi\)
\(888\) 0 0
\(889\) −0.734193 + 9.94119i −0.0246241 + 0.333417i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0.0782602 + 0.135551i 0.00261888 + 0.00453603i
\(894\) 0 0
\(895\) −14.5968 −0.487917
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −7.14229 12.3708i −0.238209 0.412589i
\(900\) 0 0
\(901\) 16.2497 28.1452i 0.541355 0.937654i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6.76667 11.7202i 0.224932 0.389593i
\(906\) 0 0
\(907\) 29.8575 + 51.7147i 0.991401 + 1.71716i 0.609025 + 0.793151i \(0.291561\pi\)
0.382376 + 0.924007i \(0.375106\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 53.5567 1.77441 0.887206 0.461373i \(-0.152643\pi\)
0.887206 + 0.461373i \(0.152643\pi\)
\(912\) 0 0
\(913\) 15.2802 + 26.4660i 0.505700 + 0.875897i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 12.7895 + 8.69951i 0.422346 + 0.287283i
\(918\) 0 0
\(919\) 0.381583 0.660921i 0.0125873 0.0218018i −0.859663 0.510861i \(-0.829327\pi\)
0.872250 + 0.489059i \(0.162660\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 3.73523 0.122946
\(924\) 0 0
\(925\) −2.37526 −0.0780981
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 27.8829 48.2945i 0.914807 1.58449i 0.107623 0.994192i \(-0.465676\pi\)
0.807184 0.590300i \(-0.200991\pi\)
\(930\) 0 0
\(931\) 0.353774 0.445589i 0.0115945 0.0146036i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −8.24583 14.2822i −0.269668 0.467078i
\(936\) 0 0
\(937\) 25.7785 0.842146 0.421073 0.907027i \(-0.361654\pi\)
0.421073 + 0.907027i \(0.361654\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 8.52595 + 14.7674i 0.277938 + 0.481403i 0.970872 0.239598i \(-0.0770157\pi\)
−0.692934 + 0.721001i \(0.743682\pi\)
\(942\) 0 0
\(943\) 4.63481 8.02773i 0.150930 0.261419i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15.6489 + 27.1047i −0.508521 + 0.880785i 0.491430 + 0.870917i \(0.336474\pi\)
−0.999951 + 0.00986776i \(0.996859\pi\)
\(948\) 0 0
\(949\) −41.6966 72.2207i −1.35353 2.34438i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −10.3637 −0.335713 −0.167857 0.985811i \(-0.553685\pi\)
−0.167857 + 0.985811i \(0.553685\pi\)
\(954\) 0 0
\(955\) 5.12661 + 8.87954i 0.165893 + 0.287335i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 45.6183 22.0293i 1.47309 0.711365i
\(960\) 0 0
\(961\) 14.0462 24.3287i 0.453102 0.784795i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −14.0590 −0.452575
\(966\) 0 0
\(967\) 43.1057 1.38618 0.693092 0.720849i \(-0.256248\pi\)
0.693092 + 0.720849i \(0.256248\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −18.2096 + 31.5400i −0.584375 + 1.01217i 0.410578 + 0.911826i \(0.365327\pi\)
−0.994953 + 0.100342i \(0.968006\pi\)
\(972\) 0 0
\(973\) 2.36308 31.9968i 0.0757570 1.02577i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −24.6092 42.6243i −0.787317 1.36367i −0.927605 0.373562i \(-0.878136\pi\)
0.140289 0.990111i \(-0.455197\pi\)
\(978\) 0 0
\(979\) 9.10492 0.290994
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −19.3368 33.4924i −0.616749 1.06824i −0.990075 0.140540i \(-0.955116\pi\)
0.373326 0.927700i \(-0.378217\pi\)
\(984\) 0 0
\(985\) −4.59712 + 7.96244i −0.146476 + 0.253704i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −11.6657 + 20.2057i −0.370949 + 0.642502i
\(990\) 0 0
\(991\) −4.33663 7.51127i −0.137758 0.238603i 0.788890 0.614535i \(-0.210656\pi\)
−0.926648 + 0.375931i \(0.877323\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 18.1140 0.574251
\(996\) 0 0
\(997\) 6.25185 + 10.8285i 0.197998 + 0.342943i 0.947879 0.318630i \(-0.103223\pi\)
−0.749881 + 0.661573i \(0.769889\pi\)
\(998\) 0 0
\(999\) 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 2520.2.bi.s.1801.3 yes 10
3.2 odd 2 2520.2.bi.r.1801.3 yes 10
7.4 even 3 inner 2520.2.bi.s.361.3 yes 10
21.11 odd 6 2520.2.bi.r.361.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2520.2.bi.r.361.3 10 21.11 odd 6
2520.2.bi.r.1801.3 yes 10 3.2 odd 2
2520.2.bi.s.361.3 yes 10 7.4 even 3 inner
2520.2.bi.s.1801.3 yes 10 1.1 even 1 trivial