Properties

Label 804.2.s.b.161.2
Level $804$
Weight $2$
Character 804.161
Analytic conductor $6.420$
Analytic rank $0$
Dimension $200$
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] = [804,2,Mod(5,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.s (of order \(22\), degree \(10\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 161.2
Character \(\chi\) \(=\) 804.161
Dual form 804.2.s.b.5.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.58909 - 0.689041i) q^{3} +(3.06595 + 0.900243i) q^{5} +(0.591666 - 0.512682i) q^{7} +(2.05045 + 2.18990i) q^{9} +O(q^{10})\) \(q+(-1.58909 - 0.689041i) q^{3} +(3.06595 + 0.900243i) q^{5} +(0.591666 - 0.512682i) q^{7} +(2.05045 + 2.18990i) q^{9} +(4.86665 + 1.42898i) q^{11} +(-2.95958 + 4.60520i) q^{13} +(-4.25177 - 3.54313i) q^{15} +(-4.50325 + 0.647469i) q^{17} +(1.29471 - 1.49418i) q^{19} +(-1.29347 + 0.407017i) q^{21} +(-2.56007 - 1.16914i) q^{23} +(4.38332 + 2.81699i) q^{25} +(-1.74942 - 4.89280i) q^{27} +4.91969i q^{29} +(3.39701 + 5.28586i) q^{31} +(-6.74894 - 5.62410i) q^{33} +(2.27555 - 1.03921i) q^{35} +3.77494 q^{37} +(7.87622 - 5.27882i) q^{39} +(0.190364 + 1.32401i) q^{41} +(8.46946 - 1.21772i) q^{43} +(4.31511 + 8.56002i) q^{45} +(1.21808 + 0.556280i) q^{47} +(-0.908978 + 6.32208i) q^{49} +(7.60222 + 2.07403i) q^{51} +(1.69585 - 11.7949i) q^{53} +(13.6344 + 8.76233i) q^{55} +(-3.08697 + 1.48228i) q^{57} +(-4.76970 - 7.42180i) q^{59} +(3.83621 + 13.0649i) q^{61} +(2.33590 + 0.244466i) q^{63} +(-13.2197 + 11.4549i) q^{65} +(1.21150 - 8.09520i) q^{67} +(3.26261 + 3.62188i) q^{69} +(-4.49276 - 0.645961i) q^{71} +(2.01307 - 0.591090i) q^{73} +(-5.02449 - 7.49675i) q^{75} +(3.61204 - 1.64956i) q^{77} +(2.99859 - 4.66590i) q^{79} +(-0.591350 + 8.98055i) q^{81} +(-1.16155 + 3.95589i) q^{83} +(-14.3896 - 2.06891i) q^{85} +(3.38987 - 7.81785i) q^{87} +(14.3613 - 6.55861i) q^{89} +(0.609916 + 4.24206i) q^{91} +(-1.75601 - 10.7404i) q^{93} +(5.31463 - 3.41551i) q^{95} -3.09130i q^{97} +(6.84947 + 13.5875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200 q - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{17}{22}\right)\) \(1\)

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 0
\(3\) −1.58909 0.689041i −0.917464 0.397818i
\(4\) 0 0
\(5\) 3.06595 + 0.900243i 1.37113 + 0.402601i 0.882674 0.469986i \(-0.155741\pi\)
0.488459 + 0.872587i \(0.337559\pi\)
\(6\) 0 0
\(7\) 0.591666 0.512682i 0.223629 0.193775i −0.535839 0.844320i \(-0.680005\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(8\) 0 0
\(9\) 2.05045 + 2.18990i 0.683482 + 0.729968i
\(10\) 0 0
\(11\) 4.86665 + 1.42898i 1.46735 + 0.430852i 0.915236 0.402917i \(-0.132004\pi\)
0.552112 + 0.833770i \(0.313822\pi\)
\(12\) 0 0
\(13\) −2.95958 + 4.60520i −0.820840 + 1.27725i 0.137179 + 0.990546i \(0.456196\pi\)
−0.958019 + 0.286705i \(0.907440\pi\)
\(14\) 0 0
\(15\) −4.25177 3.54313i −1.09780 0.914833i
\(16\) 0 0
\(17\) −4.50325 + 0.647469i −1.09220 + 0.157034i −0.664794 0.747027i \(-0.731481\pi\)
−0.427403 + 0.904061i \(0.640572\pi\)
\(18\) 0 0
\(19\) 1.29471 1.49418i 0.297027 0.342787i −0.587545 0.809192i \(-0.699905\pi\)
0.884572 + 0.466404i \(0.154451\pi\)
\(20\) 0 0
\(21\) −1.29347 + 0.407017i −0.282259 + 0.0888185i
\(22\) 0 0
\(23\) −2.56007 1.16914i −0.533812 0.243784i 0.130224 0.991485i \(-0.458430\pi\)
−0.664036 + 0.747701i \(0.731158\pi\)
\(24\) 0 0
\(25\) 4.38332 + 2.81699i 0.876664 + 0.563398i
\(26\) 0 0
\(27\) −1.74942 4.89280i −0.336676 0.941621i
\(28\) 0 0
\(29\) 4.91969i 0.913564i 0.889579 + 0.456782i \(0.150998\pi\)
−0.889579 + 0.456782i \(0.849002\pi\)
\(30\) 0 0
\(31\) 3.39701 + 5.28586i 0.610122 + 0.949368i 0.999599 + 0.0283318i \(0.00901950\pi\)
−0.389477 + 0.921036i \(0.627344\pi\)
\(32\) 0 0
\(33\) −6.74894 5.62410i −1.17484 0.979030i
\(34\) 0 0
\(35\) 2.27555 1.03921i 0.384639 0.175659i
\(36\) 0 0
\(37\) 3.77494 0.620596 0.310298 0.950639i \(-0.399571\pi\)
0.310298 + 0.950639i \(0.399571\pi\)
\(38\) 0 0
\(39\) 7.87622 5.27882i 1.26121 0.845288i
\(40\) 0 0
\(41\) 0.190364 + 1.32401i 0.0297299 + 0.206776i 0.999272 0.0381483i \(-0.0121459\pi\)
−0.969542 + 0.244924i \(0.921237\pi\)
\(42\) 0 0
\(43\) 8.46946 1.21772i 1.29158 0.185701i 0.537937 0.842985i \(-0.319204\pi\)
0.753643 + 0.657284i \(0.228295\pi\)
\(44\) 0 0
\(45\) 4.31511 + 8.56002i 0.643258 + 1.27605i
\(46\) 0 0
\(47\) 1.21808 + 0.556280i 0.177676 + 0.0811417i 0.502267 0.864713i \(-0.332499\pi\)
−0.324591 + 0.945854i \(0.605227\pi\)
\(48\) 0 0
\(49\) −0.908978 + 6.32208i −0.129854 + 0.903154i
\(50\) 0 0
\(51\) 7.60222 + 2.07403i 1.06452 + 0.290422i
\(52\) 0 0
\(53\) 1.69585 11.7949i 0.232943 1.62016i −0.452316 0.891858i \(-0.649402\pi\)
0.685259 0.728299i \(-0.259689\pi\)
\(54\) 0 0
\(55\) 13.6344 + 8.76233i 1.83847 + 1.18151i
\(56\) 0 0
\(57\) −3.08697 + 1.48228i −0.408879 + 0.196333i
\(58\) 0 0
\(59\) −4.76970 7.42180i −0.620963 0.966237i −0.999179 0.0405193i \(-0.987099\pi\)
0.378216 0.925717i \(-0.376538\pi\)
\(60\) 0 0
\(61\) 3.83621 + 13.0649i 0.491176 + 1.67279i 0.715766 + 0.698340i \(0.246078\pi\)
−0.224590 + 0.974453i \(0.572104\pi\)
\(62\) 0 0
\(63\) 2.33590 + 0.244466i 0.294296 + 0.0307998i
\(64\) 0 0
\(65\) −13.2197 + 11.4549i −1.63970 + 1.42081i
\(66\) 0 0
\(67\) 1.21150 8.09520i 0.148008 0.988986i
\(68\) 0 0
\(69\) 3.26261 + 3.62188i 0.392772 + 0.436023i
\(70\) 0 0
\(71\) −4.49276 0.645961i −0.533192 0.0766614i −0.129540 0.991574i \(-0.541350\pi\)
−0.403652 + 0.914913i \(0.632259\pi\)
\(72\) 0 0
\(73\) 2.01307 0.591090i 0.235612 0.0691818i −0.161795 0.986824i \(-0.551728\pi\)
0.397407 + 0.917643i \(0.369910\pi\)
\(74\) 0 0
\(75\) −5.02449 7.49675i −0.580178 0.865650i
\(76\) 0 0
\(77\) 3.61204 1.64956i 0.411630 0.187985i
\(78\) 0 0
\(79\) 2.99859 4.66590i 0.337368 0.524955i −0.630574 0.776129i \(-0.717180\pi\)
0.967942 + 0.251175i \(0.0808168\pi\)
\(80\) 0 0
\(81\) −0.591350 + 8.98055i −0.0657056 + 0.997839i
\(82\) 0 0
\(83\) −1.16155 + 3.95589i −0.127497 + 0.434215i −0.998356 0.0573178i \(-0.981745\pi\)
0.870859 + 0.491533i \(0.163563\pi\)
\(84\) 0 0
\(85\) −14.3896 2.06891i −1.56077 0.224405i
\(86\) 0 0
\(87\) 3.38987 7.81785i 0.363432 0.838162i
\(88\) 0 0
\(89\) 14.3613 6.55861i 1.52230 0.695211i 0.533685 0.845683i \(-0.320807\pi\)
0.988614 + 0.150472i \(0.0480795\pi\)
\(90\) 0 0
\(91\) 0.609916 + 4.24206i 0.0639366 + 0.444689i
\(92\) 0 0
\(93\) −1.75601 10.7404i −0.182089 1.11373i
\(94\) 0 0
\(95\) 5.31463 3.41551i 0.545270 0.350424i
\(96\) 0 0
\(97\) 3.09130i 0.313874i −0.987609 0.156937i \(-0.949838\pi\)
0.987609 0.156937i \(-0.0501619\pi\)
\(98\) 0 0
\(99\) 6.84947 + 13.5875i 0.688398 + 1.36560i
\(100\) 0 0
\(101\) −2.16124 + 2.49420i −0.215051 + 0.248182i −0.853018 0.521882i \(-0.825230\pi\)
0.637967 + 0.770064i \(0.279776\pi\)
\(102\) 0 0
\(103\) −4.11999 + 2.64776i −0.405955 + 0.260891i −0.727645 0.685954i \(-0.759385\pi\)
0.321691 + 0.946845i \(0.395749\pi\)
\(104\) 0 0
\(105\) −4.33213 + 0.0834544i −0.422773 + 0.00814432i
\(106\) 0 0
\(107\) 3.05837 + 10.4159i 0.295664 + 1.00694i 0.964622 + 0.263638i \(0.0849225\pi\)
−0.668958 + 0.743300i \(0.733259\pi\)
\(108\) 0 0
\(109\) 3.72176 5.79117i 0.356480 0.554693i −0.615981 0.787761i \(-0.711240\pi\)
0.972460 + 0.233068i \(0.0748765\pi\)
\(110\) 0 0
\(111\) −5.99873 2.60109i −0.569375 0.246884i
\(112\) 0 0
\(113\) 13.7712 4.04358i 1.29548 0.380388i 0.439896 0.898049i \(-0.355015\pi\)
0.855586 + 0.517661i \(0.173197\pi\)
\(114\) 0 0
\(115\) −6.79652 5.88922i −0.633779 0.549173i
\(116\) 0 0
\(117\) −16.1534 + 2.96151i −1.49338 + 0.273792i
\(118\) 0 0
\(119\) −2.33247 + 2.69182i −0.213817 + 0.246758i
\(120\) 0 0
\(121\) 12.3885 + 7.96159i 1.12622 + 0.723781i
\(122\) 0 0
\(123\) 0.609792 2.23515i 0.0549831 0.201537i
\(124\) 0 0
\(125\) 0.440399 + 0.508248i 0.0393905 + 0.0454590i
\(126\) 0 0
\(127\) −9.03409 10.4259i −0.801646 0.925149i 0.196824 0.980439i \(-0.436937\pi\)
−0.998470 + 0.0552898i \(0.982392\pi\)
\(128\) 0 0
\(129\) −14.2978 3.90072i −1.25885 0.343440i
\(130\) 0 0
\(131\) −14.8926 6.80123i −1.30117 0.594226i −0.360253 0.932854i \(-0.617310\pi\)
−0.940920 + 0.338628i \(0.890037\pi\)
\(132\) 0 0
\(133\) 1.54783i 0.134214i
\(134\) 0 0
\(135\) −0.958911 16.5760i −0.0825299 1.42663i
\(136\) 0 0
\(137\) 6.25736 13.7017i 0.534603 1.17062i −0.429006 0.903301i \(-0.641136\pi\)
0.963609 0.267315i \(-0.0861365\pi\)
\(138\) 0 0
\(139\) −1.64168 + 5.59103i −0.139245 + 0.474225i −0.999356 0.0358817i \(-0.988576\pi\)
0.860111 + 0.510107i \(0.170394\pi\)
\(140\) 0 0
\(141\) −1.55235 1.72329i −0.130731 0.145127i
\(142\) 0 0
\(143\) −20.9839 + 18.1827i −1.75477 + 1.52051i
\(144\) 0 0
\(145\) −4.42892 + 15.0835i −0.367801 + 1.25262i
\(146\) 0 0
\(147\) 5.80062 9.42006i 0.478427 0.776953i
\(148\) 0 0
\(149\) −15.6118 13.5277i −1.27897 1.10823i −0.988479 0.151358i \(-0.951635\pi\)
−0.290492 0.956877i \(-0.593819\pi\)
\(150\) 0 0
\(151\) −0.471751 3.28110i −0.0383906 0.267012i 0.961581 0.274521i \(-0.0885191\pi\)
−0.999972 + 0.00750825i \(0.997610\pi\)
\(152\) 0 0
\(153\) −10.6516 8.53407i −0.861127 0.689939i
\(154\) 0 0
\(155\) 5.65651 + 19.2643i 0.454342 + 1.54735i
\(156\) 0 0
\(157\) −8.02015 + 17.5617i −0.640077 + 1.40157i 0.259899 + 0.965636i \(0.416311\pi\)
−0.899977 + 0.435938i \(0.856417\pi\)
\(158\) 0 0
\(159\) −10.8221 + 17.5747i −0.858245 + 1.39377i
\(160\) 0 0
\(161\) −2.11411 + 0.620757i −0.166615 + 0.0489225i
\(162\) 0 0
\(163\) −18.4910 −1.44833 −0.724165 0.689627i \(-0.757775\pi\)
−0.724165 + 0.689627i \(0.757775\pi\)
\(164\) 0 0
\(165\) −15.6288 23.3189i −1.21670 1.81537i
\(166\) 0 0
\(167\) −4.74561 4.11209i −0.367226 0.318203i 0.451627 0.892207i \(-0.350844\pi\)
−0.818853 + 0.574004i \(0.805389\pi\)
\(168\) 0 0
\(169\) −7.04833 15.4337i −0.542179 1.18721i
\(170\) 0 0
\(171\) 5.92683 0.228435i 0.453236 0.0174688i
\(172\) 0 0
\(173\) −11.1237 17.3088i −0.845718 1.31596i −0.947042 0.321109i \(-0.895944\pi\)
0.101325 0.994853i \(-0.467692\pi\)
\(174\) 0 0
\(175\) 4.03768 0.580531i 0.305220 0.0438840i
\(176\) 0 0
\(177\) 2.46558 + 15.0805i 0.185325 + 1.13352i
\(178\) 0 0
\(179\) −9.19948 20.1440i −0.687601 1.50564i −0.854384 0.519643i \(-0.826065\pi\)
0.166782 0.985994i \(-0.446662\pi\)
\(180\) 0 0
\(181\) 0.297134 0.650633i 0.0220858 0.0483612i −0.898268 0.439449i \(-0.855174\pi\)
0.920353 + 0.391088i \(0.127901\pi\)
\(182\) 0 0
\(183\) 2.90617 23.4047i 0.214830 1.73013i
\(184\) 0 0
\(185\) 11.5738 + 3.39836i 0.850919 + 0.249853i
\(186\) 0 0
\(187\) −22.8409 3.28403i −1.67029 0.240152i
\(188\) 0 0
\(189\) −3.54352 1.99801i −0.257753 0.145334i
\(190\) 0 0
\(191\) 7.89553 + 17.2888i 0.571300 + 1.25097i 0.946102 + 0.323868i \(0.104984\pi\)
−0.374802 + 0.927105i \(0.622289\pi\)
\(192\) 0 0
\(193\) 0.0158178 0.0101655i 0.00113859 0.000731725i −0.540071 0.841619i \(-0.681603\pi\)
0.541210 + 0.840887i \(0.317966\pi\)
\(194\) 0 0
\(195\) 28.9003 9.09407i 2.06959 0.651240i
\(196\) 0 0
\(197\) −1.71963 + 11.9603i −0.122518 + 0.852135i 0.832168 + 0.554523i \(0.187099\pi\)
−0.954687 + 0.297612i \(0.903810\pi\)
\(198\) 0 0
\(199\) 5.58649 + 6.44716i 0.396016 + 0.457027i 0.918382 0.395694i \(-0.129496\pi\)
−0.522366 + 0.852721i \(0.674951\pi\)
\(200\) 0 0
\(201\) −7.50311 + 12.0293i −0.529228 + 0.848479i
\(202\) 0 0
\(203\) 2.52223 + 2.91081i 0.177026 + 0.204299i
\(204\) 0 0
\(205\) −0.608287 + 4.23073i −0.0424846 + 0.295487i
\(206\) 0 0
\(207\) −2.68897 8.00357i −0.186896 0.556287i
\(208\) 0 0
\(209\) 8.43604 5.42151i 0.583533 0.375014i
\(210\) 0 0
\(211\) 0.888906 + 1.94643i 0.0611948 + 0.133998i 0.937759 0.347288i \(-0.112897\pi\)
−0.876564 + 0.481286i \(0.840170\pi\)
\(212\) 0 0
\(213\) 6.69432 + 4.12219i 0.458687 + 0.282448i
\(214\) 0 0
\(215\) 27.0631 + 3.89109i 1.84569 + 0.265370i
\(216\) 0 0
\(217\) 4.71986 + 1.38588i 0.320405 + 0.0940794i
\(218\) 0 0
\(219\) −3.60624 0.447788i −0.243687 0.0302587i
\(220\) 0 0
\(221\) 10.3460 22.6546i 0.695947 1.52391i
\(222\) 0 0
\(223\) −0.873755 1.91326i −0.0585110 0.128121i 0.878118 0.478444i \(-0.158799\pi\)
−0.936629 + 0.350323i \(0.886072\pi\)
\(224\) 0 0
\(225\) 2.81882 + 15.3751i 0.187922 + 1.02501i
\(226\) 0 0
\(227\) 12.1107 1.74126i 0.803815 0.115571i 0.271853 0.962339i \(-0.412364\pi\)
0.531963 + 0.846768i \(0.321455\pi\)
\(228\) 0 0
\(229\) −2.95346 4.59567i −0.195170 0.303691i 0.729851 0.683606i \(-0.239589\pi\)
−0.925021 + 0.379916i \(0.875953\pi\)
\(230\) 0 0
\(231\) −6.87649 + 0.132469i −0.452440 + 0.00871583i
\(232\) 0 0
\(233\) 11.4074 + 24.9786i 0.747320 + 1.63640i 0.771123 + 0.636687i \(0.219696\pi\)
−0.0238023 + 0.999717i \(0.507577\pi\)
\(234\) 0 0
\(235\) 3.23379 + 2.80209i 0.210949 + 0.182788i
\(236\) 0 0
\(237\) −7.98004 + 5.34840i −0.518359 + 0.347416i
\(238\) 0 0
\(239\) −19.7308 −1.27628 −0.638139 0.769921i \(-0.720295\pi\)
−0.638139 + 0.769921i \(0.720295\pi\)
\(240\) 0 0
\(241\) 24.5144 7.19807i 1.57911 0.463668i 0.629473 0.777023i \(-0.283271\pi\)
0.949636 + 0.313354i \(0.101453\pi\)
\(242\) 0 0
\(243\) 7.12768 13.8635i 0.457241 0.889343i
\(244\) 0 0
\(245\) −8.47828 + 18.5648i −0.541658 + 1.18606i
\(246\) 0 0
\(247\) 3.04917 + 10.3845i 0.194014 + 0.660752i
\(248\) 0 0
\(249\) 4.57159 5.48593i 0.289713 0.347656i
\(250\) 0 0
\(251\) −1.52185 10.5847i −0.0960585 0.668102i −0.979778 0.200086i \(-0.935878\pi\)
0.883720 0.468016i \(-0.155031\pi\)
\(252\) 0 0
\(253\) −10.7883 9.34809i −0.678253 0.587710i
\(254\) 0 0
\(255\) 21.4409 + 13.2027i 1.34268 + 0.826786i
\(256\) 0 0
\(257\) −1.85895 + 6.33100i −0.115958 + 0.394917i −0.996934 0.0782437i \(-0.975069\pi\)
0.880976 + 0.473161i \(0.156887\pi\)
\(258\) 0 0
\(259\) 2.23350 1.93534i 0.138783 0.120256i
\(260\) 0 0
\(261\) −10.7736 + 10.0876i −0.666872 + 0.624404i
\(262\) 0 0
\(263\) 5.30404 18.0639i 0.327061 1.11387i −0.617784 0.786348i \(-0.711969\pi\)
0.944845 0.327519i \(-0.106213\pi\)
\(264\) 0 0
\(265\) 15.8177 34.6359i 0.971673 2.12767i
\(266\) 0 0
\(267\) −27.3407 + 0.526693i −1.67322 + 0.0322331i
\(268\) 0 0
\(269\) 6.99643i 0.426580i −0.976989 0.213290i \(-0.931582\pi\)
0.976989 0.213290i \(-0.0684179\pi\)
\(270\) 0 0
\(271\) 19.7238 + 9.00755i 1.19813 + 0.547170i 0.911671 0.410921i \(-0.134793\pi\)
0.286464 + 0.958091i \(0.407520\pi\)
\(272\) 0 0
\(273\) 1.95374 7.16129i 0.118246 0.433421i
\(274\) 0 0
\(275\) 17.3067 + 19.9729i 1.04363 + 1.20441i
\(276\) 0 0
\(277\) 2.37514 + 2.74106i 0.142708 + 0.164694i 0.822604 0.568615i \(-0.192520\pi\)
−0.679896 + 0.733309i \(0.737975\pi\)
\(278\) 0 0
\(279\) −4.61012 + 18.2775i −0.276001 + 1.09424i
\(280\) 0 0
\(281\) −3.31710 2.13177i −0.197882 0.127171i 0.437948 0.899000i \(-0.355705\pi\)
−0.635829 + 0.771830i \(0.719342\pi\)
\(282\) 0 0
\(283\) −7.98123 + 9.21083i −0.474435 + 0.547527i −0.941640 0.336622i \(-0.890716\pi\)
0.467205 + 0.884149i \(0.345261\pi\)
\(284\) 0 0
\(285\) −10.7989 + 1.76557i −0.639671 + 0.104583i
\(286\) 0 0
\(287\) 0.791429 + 0.685777i 0.0467166 + 0.0404802i
\(288\) 0 0
\(289\) 3.54863 1.04197i 0.208743 0.0612924i
\(290\) 0 0
\(291\) −2.13003 + 4.91237i −0.124865 + 0.287968i
\(292\) 0 0
\(293\) 0.657398 1.02293i 0.0384056 0.0597603i −0.821520 0.570180i \(-0.806874\pi\)
0.859926 + 0.510420i \(0.170510\pi\)
\(294\) 0 0
\(295\) −7.94223 27.0487i −0.462414 1.57484i
\(296\) 0 0
\(297\) −1.52210 26.3114i −0.0883213 1.52674i
\(298\) 0 0
\(299\) 12.9609 8.32945i 0.749547 0.481704i
\(300\) 0 0
\(301\) 4.38678 5.06262i 0.252850 0.291805i
\(302\) 0 0
\(303\) 5.15301 2.47434i 0.296033 0.142147i
\(304\) 0 0
\(305\) 43.5099i 2.49137i
\(306\) 0 0
\(307\) 12.7095 8.16791i 0.725370 0.466167i −0.125131 0.992140i \(-0.539935\pi\)
0.850501 + 0.525973i \(0.176299\pi\)
\(308\) 0 0
\(309\) 8.37147 1.36870i 0.476236 0.0778624i
\(310\) 0 0
\(311\) −1.95696 13.6110i −0.110969 0.771807i −0.966981 0.254850i \(-0.917974\pi\)
0.856011 0.516957i \(-0.172935\pi\)
\(312\) 0 0
\(313\) −8.14747 + 3.72083i −0.460522 + 0.210314i −0.632146 0.774849i \(-0.717826\pi\)
0.171624 + 0.985163i \(0.445099\pi\)
\(314\) 0 0
\(315\) 6.94167 + 2.85240i 0.391119 + 0.160714i
\(316\) 0 0
\(317\) −19.4743 2.79998i −1.09379 0.157263i −0.428273 0.903649i \(-0.640878\pi\)
−0.665513 + 0.746387i \(0.731787\pi\)
\(318\) 0 0
\(319\) −7.03012 + 23.9424i −0.393611 + 1.34052i
\(320\) 0 0
\(321\) 2.31691 18.6591i 0.129317 1.04145i
\(322\) 0 0
\(323\) −4.86297 + 7.56692i −0.270583 + 0.421035i
\(324\) 0 0
\(325\) −25.9456 + 11.8489i −1.43920 + 0.657261i
\(326\) 0 0
\(327\) −9.90457 + 6.63827i −0.547724 + 0.367097i
\(328\) 0 0
\(329\) 1.00589 0.295357i 0.0554567 0.0162835i
\(330\) 0 0
\(331\) 25.6433 + 3.68695i 1.40948 + 0.202653i 0.804673 0.593718i \(-0.202340\pi\)
0.604809 + 0.796371i \(0.293249\pi\)
\(332\) 0 0
\(333\) 7.74030 + 8.26675i 0.424166 + 0.453015i
\(334\) 0 0
\(335\) 11.0020 23.7288i 0.601105 1.29644i
\(336\) 0 0
\(337\) 11.4752 9.94335i 0.625096 0.541649i −0.283687 0.958917i \(-0.591558\pi\)
0.908784 + 0.417268i \(0.137012\pi\)
\(338\) 0 0
\(339\) −24.6699 3.06327i −1.33988 0.166374i
\(340\) 0 0
\(341\) 8.97870 + 30.5786i 0.486224 + 1.65593i
\(342\) 0 0
\(343\) 5.66622 + 8.81682i 0.305947 + 0.476063i
\(344\) 0 0
\(345\) 6.74241 + 14.0416i 0.362999 + 0.755975i
\(346\) 0 0
\(347\) −27.2097 17.4866i −1.46069 0.938731i −0.998654 0.0518726i \(-0.983481\pi\)
−0.462041 0.886859i \(-0.652883\pi\)
\(348\) 0 0
\(349\) 2.47093 17.1857i 0.132266 0.919931i −0.810325 0.585981i \(-0.800709\pi\)
0.942591 0.333950i \(-0.108382\pi\)
\(350\) 0 0
\(351\) 27.7099 + 6.42423i 1.47904 + 0.342900i
\(352\) 0 0
\(353\) −3.94534 + 27.4404i −0.209989 + 1.46051i 0.563194 + 0.826325i \(0.309572\pi\)
−0.773183 + 0.634183i \(0.781337\pi\)
\(354\) 0 0
\(355\) −13.1930 6.02505i −0.700213 0.319777i
\(356\) 0 0
\(357\) 5.56129 2.67038i 0.294335 0.141332i
\(358\) 0 0
\(359\) −1.35152 + 0.194319i −0.0713305 + 0.0102558i −0.177888 0.984051i \(-0.556926\pi\)
0.106557 + 0.994307i \(0.466017\pi\)
\(360\) 0 0
\(361\) 2.14770 + 14.9376i 0.113037 + 0.786187i
\(362\) 0 0
\(363\) −14.2006 21.1879i −0.745338 1.11208i
\(364\) 0 0
\(365\) 6.70408 0.350908
\(366\) 0 0
\(367\) −28.9579 + 13.2246i −1.51159 + 0.690320i −0.986953 0.161007i \(-0.948526\pi\)
−0.524636 + 0.851327i \(0.675798\pi\)
\(368\) 0 0
\(369\) −2.50913 + 3.13170i −0.130620 + 0.163030i
\(370\) 0 0
\(371\) −5.04366 7.84809i −0.261854 0.407452i
\(372\) 0 0
\(373\) 8.07461i 0.418088i 0.977906 + 0.209044i \(0.0670351\pi\)
−0.977906 + 0.209044i \(0.932965\pi\)
\(374\) 0 0
\(375\) −0.349632 1.11111i −0.0180549 0.0573773i
\(376\) 0 0
\(377\) −22.6561 14.5602i −1.16685 0.749889i
\(378\) 0 0
\(379\) −23.4477 10.7082i −1.20443 0.550044i −0.290875 0.956761i \(-0.593946\pi\)
−0.913554 + 0.406717i \(0.866674\pi\)
\(380\) 0 0
\(381\) 7.17216 + 22.7926i 0.367441 + 1.16770i
\(382\) 0 0
\(383\) 11.4000 13.1564i 0.582515 0.672259i −0.385628 0.922654i \(-0.626015\pi\)
0.968144 + 0.250396i \(0.0805607\pi\)
\(384\) 0 0
\(385\) 12.5593 1.80576i 0.640082 0.0920299i
\(386\) 0 0
\(387\) 20.0329 + 16.0504i 1.01833 + 0.815888i
\(388\) 0 0
\(389\) 11.8584 18.4520i 0.601245 0.935555i −0.398586 0.917131i \(-0.630499\pi\)
0.999830 0.0184238i \(-0.00586481\pi\)
\(390\) 0 0
\(391\) 12.2856 + 3.60738i 0.621310 + 0.182433i
\(392\) 0 0
\(393\) 18.9794 + 21.0694i 0.957387 + 1.06281i
\(394\) 0 0
\(395\) 13.3940 11.6059i 0.673923 0.583958i
\(396\) 0 0
\(397\) 21.6056 + 6.34398i 1.08436 + 0.318395i 0.774620 0.632427i \(-0.217941\pi\)
0.309736 + 0.950823i \(0.399759\pi\)
\(398\) 0 0
\(399\) −1.06652 + 2.45964i −0.0533926 + 0.123136i
\(400\) 0 0
\(401\) −23.7844 −1.18774 −0.593868 0.804563i \(-0.702400\pi\)
−0.593868 + 0.804563i \(0.702400\pi\)
\(402\) 0 0
\(403\) −34.3962 −1.71339
\(404\) 0 0
\(405\) −9.89773 + 27.0015i −0.491822 + 1.34172i
\(406\) 0 0
\(407\) 18.3713 + 5.39430i 0.910631 + 0.267385i
\(408\) 0 0
\(409\) −17.0685 + 14.7899i −0.843983 + 0.731316i −0.965257 0.261303i \(-0.915848\pi\)
0.121273 + 0.992619i \(0.461302\pi\)
\(410\) 0 0
\(411\) −19.3846 + 17.4617i −0.956171 + 0.861325i
\(412\) 0 0
\(413\) −6.62709 1.94589i −0.326098 0.0957510i
\(414\) 0 0
\(415\) −7.12252 + 11.0829i −0.349631 + 0.544036i
\(416\) 0 0
\(417\) 6.46123 7.75350i 0.316408 0.379691i
\(418\) 0 0
\(419\) 3.62622 0.521372i 0.177153 0.0254707i −0.0531675 0.998586i \(-0.516932\pi\)
0.230320 + 0.973115i \(0.426023\pi\)
\(420\) 0 0
\(421\) 5.73664 6.62044i 0.279587 0.322660i −0.598536 0.801096i \(-0.704251\pi\)
0.878123 + 0.478436i \(0.158796\pi\)
\(422\) 0 0
\(423\) 1.27941 + 3.80810i 0.0622072 + 0.185156i
\(424\) 0 0
\(425\) −21.5631 9.84753i −1.04596 0.477675i
\(426\) 0 0
\(427\) 8.96791 + 5.76332i 0.433987 + 0.278907i
\(428\) 0 0
\(429\) 45.8741 14.4352i 2.21482 0.696939i
\(430\) 0 0
\(431\) 18.3086i 0.881892i 0.897534 + 0.440946i \(0.145357\pi\)
−0.897534 + 0.440946i \(0.854643\pi\)
\(432\) 0 0
\(433\) −21.6063 33.6201i −1.03833 1.61568i −0.753909 0.656979i \(-0.771834\pi\)
−0.284424 0.958698i \(-0.591802\pi\)
\(434\) 0 0
\(435\) 17.4311 20.9174i 0.835758 1.00291i
\(436\) 0 0
\(437\) −5.06146 + 2.31149i −0.242122 + 0.110574i
\(438\) 0 0
\(439\) 31.7813 1.51684 0.758418 0.651768i \(-0.225972\pi\)
0.758418 + 0.651768i \(0.225972\pi\)
\(440\) 0 0
\(441\) −15.7085 + 10.9725i −0.748026 + 0.522500i
\(442\) 0 0
\(443\) −0.346201 2.40788i −0.0164485 0.114402i 0.979943 0.199278i \(-0.0638597\pi\)
−0.996392 + 0.0848761i \(0.972951\pi\)
\(444\) 0 0
\(445\) 49.9354 7.17963i 2.36717 0.340347i
\(446\) 0 0
\(447\) 15.4875 + 32.2540i 0.732535 + 1.52556i
\(448\) 0 0
\(449\) −37.8266 17.2748i −1.78515 0.815250i −0.972646 0.232294i \(-0.925377\pi\)
−0.812504 0.582956i \(-0.801896\pi\)
\(450\) 0 0
\(451\) −0.965547 + 6.71553i −0.0454658 + 0.316222i
\(452\) 0 0
\(453\) −1.51116 + 5.53904i −0.0710003 + 0.260247i
\(454\) 0 0
\(455\) −1.94892 + 13.5550i −0.0913665 + 0.635468i
\(456\) 0 0
\(457\) 6.94117 + 4.46082i 0.324694 + 0.208668i 0.692825 0.721106i \(-0.256366\pi\)
−0.368131 + 0.929774i \(0.620002\pi\)
\(458\) 0 0
\(459\) 11.0460 + 20.9008i 0.515583 + 0.975566i
\(460\) 0 0
\(461\) −17.1945 26.7552i −0.800828 1.24611i −0.965665 0.259791i \(-0.916346\pi\)
0.164837 0.986321i \(-0.447290\pi\)
\(462\) 0 0
\(463\) −1.35839 4.62626i −0.0631298 0.215000i 0.921887 0.387459i \(-0.126647\pi\)
−0.985017 + 0.172458i \(0.944829\pi\)
\(464\) 0 0
\(465\) 4.28516 34.5104i 0.198720 1.60038i
\(466\) 0 0
\(467\) 1.76214 1.52691i 0.0815423 0.0706568i −0.613136 0.789977i \(-0.710092\pi\)
0.694678 + 0.719321i \(0.255547\pi\)
\(468\) 0 0
\(469\) −3.43346 5.41077i −0.158542 0.249846i
\(470\) 0 0
\(471\) 24.8455 22.3810i 1.14482 1.03126i
\(472\) 0 0
\(473\) 42.9579 + 6.17642i 1.97521 + 0.283992i
\(474\) 0 0
\(475\) 9.88421 2.90226i 0.453518 0.133165i
\(476\) 0 0
\(477\) 29.3070 20.4711i 1.34187 0.937306i
\(478\) 0 0
\(479\) −5.85237 + 2.67269i −0.267402 + 0.122118i −0.544604 0.838693i \(-0.683320\pi\)
0.277202 + 0.960812i \(0.410593\pi\)
\(480\) 0 0
\(481\) −11.1722 + 17.3843i −0.509410 + 0.792657i
\(482\) 0 0
\(483\) 3.78724 + 0.470263i 0.172325 + 0.0213977i
\(484\) 0 0
\(485\) 2.78292 9.47776i 0.126366 0.430363i
\(486\) 0 0
\(487\) −14.0502 2.02011i −0.636675 0.0915400i −0.183583 0.983004i \(-0.558770\pi\)
−0.453091 + 0.891464i \(0.649679\pi\)
\(488\) 0 0
\(489\) 29.3840 + 12.7411i 1.32879 + 0.576172i
\(490\) 0 0
\(491\) 16.6419 7.60010i 0.751038 0.342988i −0.00284517 0.999996i \(-0.500906\pi\)
0.753883 + 0.657008i \(0.228178\pi\)
\(492\) 0 0
\(493\) −3.18535 22.1546i −0.143461 0.997792i
\(494\) 0 0
\(495\) 8.76804 + 47.8248i 0.394094 + 2.14956i
\(496\) 0 0
\(497\) −2.98938 + 1.92116i −0.134092 + 0.0861758i
\(498\) 0 0
\(499\) 39.6955i 1.77702i −0.458862 0.888508i \(-0.651743\pi\)
0.458862 0.888508i \(-0.348257\pi\)
\(500\) 0 0
\(501\) 4.70782 + 9.80442i 0.210330 + 0.438029i
\(502\) 0 0
\(503\) −0.907942 + 1.04782i −0.0404831 + 0.0467200i −0.775630 0.631188i \(-0.782568\pi\)
0.735147 + 0.677908i \(0.237113\pi\)
\(504\) 0 0
\(505\) −8.87162 + 5.70144i −0.394782 + 0.253711i
\(506\) 0 0
\(507\) 0.566020 + 29.3822i 0.0251378 + 1.30491i
\(508\) 0 0
\(509\) 6.46433 + 22.0155i 0.286526 + 0.975819i 0.969442 + 0.245322i \(0.0788936\pi\)
−0.682915 + 0.730498i \(0.739288\pi\)
\(510\) 0 0
\(511\) 0.888023 1.38179i 0.0392838 0.0611268i
\(512\) 0 0
\(513\) −9.57570 3.72083i −0.422777 0.164278i
\(514\) 0 0
\(515\) −15.0153 + 4.40889i −0.661653 + 0.194279i
\(516\) 0 0
\(517\) 5.13307 + 4.44783i 0.225752 + 0.195615i
\(518\) 0 0
\(519\) 5.75012 + 35.1700i 0.252402 + 1.54379i
\(520\) 0 0
\(521\) 24.3956 28.1540i 1.06879 1.23345i 0.0975814 0.995228i \(-0.468889\pi\)
0.971210 0.238224i \(-0.0765652\pi\)
\(522\) 0 0
\(523\) −13.5444 8.70448i −0.592257 0.380621i 0.209909 0.977721i \(-0.432683\pi\)
−0.802167 + 0.597100i \(0.796319\pi\)
\(524\) 0 0
\(525\) −6.81627 1.85961i −0.297486 0.0811600i
\(526\) 0 0
\(527\) −18.7200 21.6041i −0.815457 0.941087i
\(528\) 0 0
\(529\) −9.87474 11.3961i −0.429336 0.495481i
\(530\) 0 0
\(531\) 6.47302 25.6632i 0.280905 1.11369i
\(532\) 0 0
\(533\) −6.66074 3.04186i −0.288509 0.131757i
\(534\) 0 0
\(535\) 34.6877i 1.49968i
\(536\) 0 0
\(537\) 0.738769 + 38.3496i 0.0318803 + 1.65491i
\(538\) 0 0
\(539\) −13.4578 + 29.4684i −0.579667 + 1.26929i
\(540\) 0 0
\(541\) −4.89120 + 16.6579i −0.210289 + 0.716179i 0.785023 + 0.619466i \(0.212651\pi\)
−0.995312 + 0.0967127i \(0.969167\pi\)
\(542\) 0 0
\(543\) −0.920488 + 0.829181i −0.0395019 + 0.0355835i
\(544\) 0 0
\(545\) 16.6242 14.4049i 0.712101 0.617039i
\(546\) 0 0
\(547\) 9.47920 32.2832i 0.405301 1.38033i −0.463907 0.885884i \(-0.653553\pi\)
0.869209 0.494446i \(-0.164629\pi\)
\(548\) 0 0
\(549\) −20.7450 + 35.1899i −0.885375 + 1.50187i
\(550\) 0 0
\(551\) 7.35088 + 6.36957i 0.313158 + 0.271353i
\(552\) 0 0
\(553\) −0.617956 4.29798i −0.0262781 0.182769i
\(554\) 0 0
\(555\) −16.0502 13.3751i −0.681292 0.567742i
\(556\) 0 0
\(557\) 11.2361 + 38.2666i 0.476088 + 1.62141i 0.751256 + 0.660011i \(0.229448\pi\)
−0.275168 + 0.961396i \(0.588733\pi\)
\(558\) 0 0
\(559\) −19.4582 + 42.6075i −0.822993 + 1.80210i
\(560\) 0 0
\(561\) 34.0336 + 20.9570i 1.43690 + 0.884804i
\(562\) 0 0
\(563\) −28.2902 + 8.30676i −1.19229 + 0.350088i −0.816901 0.576778i \(-0.804310\pi\)
−0.375391 + 0.926867i \(0.622491\pi\)
\(564\) 0 0
\(565\) 45.8618 1.92942
\(566\) 0 0
\(567\) 4.25428 + 5.61666i 0.178663 + 0.235878i
\(568\) 0 0
\(569\) −4.57891 3.96765i −0.191958 0.166332i 0.553579 0.832796i \(-0.313262\pi\)
−0.745537 + 0.666464i \(0.767807\pi\)
\(570\) 0 0
\(571\) −4.09520 8.96724i −0.171379 0.375267i 0.804380 0.594115i \(-0.202498\pi\)
−0.975759 + 0.218848i \(0.929770\pi\)
\(572\) 0 0
\(573\) −0.634055 32.9139i −0.0264880 1.37500i
\(574\) 0 0
\(575\) −7.92814 12.3364i −0.330626 0.514464i
\(576\) 0 0
\(577\) 17.6365 2.53574i 0.734217 0.105564i 0.234943 0.972009i \(-0.424510\pi\)
0.499273 + 0.866445i \(0.333600\pi\)
\(578\) 0 0
\(579\) −0.0321403 + 0.00525479i −0.00133571 + 0.000218382i
\(580\) 0 0
\(581\) 1.34086 + 2.93607i 0.0556282 + 0.121809i
\(582\) 0 0
\(583\) 25.1078 54.9784i 1.03986 2.27697i
\(584\) 0 0
\(585\) −52.1915 5.46215i −2.15785 0.225832i
\(586\) 0 0
\(587\) 31.0273 + 9.11042i 1.28063 + 0.376027i 0.850135 0.526565i \(-0.176520\pi\)
0.430497 + 0.902592i \(0.358338\pi\)
\(588\) 0 0
\(589\) 12.2962 + 1.76792i 0.506654 + 0.0728459i
\(590\) 0 0
\(591\) 10.9738 17.8211i 0.451401 0.733063i
\(592\) 0 0
\(593\) −0.791302 1.73271i −0.0324949 0.0711538i 0.892689 0.450674i \(-0.148816\pi\)
−0.925183 + 0.379520i \(0.876089\pi\)
\(594\) 0 0
\(595\) −9.57452 + 6.15317i −0.392517 + 0.252255i
\(596\) 0 0
\(597\) −4.43511 14.0945i −0.181517 0.576848i
\(598\) 0 0
\(599\) −1.67155 + 11.6259i −0.0682976 + 0.475021i 0.926755 + 0.375667i \(0.122586\pi\)
−0.995052 + 0.0993532i \(0.968323\pi\)
\(600\) 0 0
\(601\) 2.88118 + 3.32506i 0.117526 + 0.135632i 0.811464 0.584403i \(-0.198671\pi\)
−0.693938 + 0.720035i \(0.744126\pi\)
\(602\) 0 0
\(603\) 20.2118 13.9457i 0.823088 0.567913i
\(604\) 0 0
\(605\) 30.8150 + 35.5624i 1.25281 + 1.44582i
\(606\) 0 0
\(607\) −4.10078 + 28.5216i −0.166446 + 1.15766i 0.719713 + 0.694272i \(0.244274\pi\)
−0.886158 + 0.463383i \(0.846635\pi\)
\(608\) 0 0
\(609\) −2.00240 6.36348i −0.0811413 0.257861i
\(610\) 0 0
\(611\) −6.16679 + 3.96316i −0.249482 + 0.160332i
\(612\) 0 0
\(613\) −2.51281 5.50228i −0.101491 0.222235i 0.852074 0.523421i \(-0.175345\pi\)
−0.953565 + 0.301186i \(0.902617\pi\)
\(614\) 0 0
\(615\) 3.88177 6.30389i 0.156528 0.254197i
\(616\) 0 0
\(617\) −14.1110 2.02885i −0.568087 0.0816785i −0.147714 0.989030i \(-0.547192\pi\)
−0.420373 + 0.907352i \(0.638101\pi\)
\(618\) 0 0
\(619\) −29.7888 8.74678i −1.19731 0.351563i −0.378488 0.925606i \(-0.623556\pi\)
−0.818825 + 0.574044i \(0.805374\pi\)
\(620\) 0 0
\(621\) −1.24176 + 14.5712i −0.0498302 + 0.584724i
\(622\) 0 0
\(623\) 5.13464 11.2433i 0.205715 0.450453i
\(624\) 0 0
\(625\) −9.92983 21.7433i −0.397193 0.869732i
\(626\) 0 0
\(627\) −17.1413 + 2.80252i −0.684558 + 0.111922i
\(628\) 0 0
\(629\) −16.9995 + 2.44416i −0.677813 + 0.0974549i
\(630\) 0 0
\(631\) 7.97701 + 12.4125i 0.317560 + 0.494132i 0.962935 0.269733i \(-0.0869354\pi\)
−0.645375 + 0.763865i \(0.723299\pi\)
\(632\) 0 0
\(633\) −0.0713841 3.70556i −0.00283726 0.147283i
\(634\) 0 0
\(635\) −18.3122 40.0981i −0.726697 1.59125i
\(636\) 0 0
\(637\) −26.4242 22.8967i −1.04697 0.907201i
\(638\) 0 0
\(639\) −7.79756 11.1632i −0.308467 0.441610i
\(640\) 0 0
\(641\) −22.0231 −0.869862 −0.434931 0.900464i \(-0.643227\pi\)
−0.434931 + 0.900464i \(0.643227\pi\)
\(642\) 0 0
\(643\) −0.988101 + 0.290133i −0.0389669 + 0.0114417i −0.301158 0.953574i \(-0.597373\pi\)
0.262191 + 0.965016i \(0.415555\pi\)
\(644\) 0 0
\(645\) −40.3248 24.8309i −1.58779 0.977717i
\(646\) 0 0
\(647\) 18.3102 40.0937i 0.719847 1.57625i −0.0942711 0.995547i \(-0.530052\pi\)
0.814118 0.580699i \(-0.197221\pi\)
\(648\) 0 0
\(649\) −12.6069 42.9351i −0.494863 1.68535i
\(650\) 0 0
\(651\) −6.54538 5.45447i −0.256534 0.213777i
\(652\) 0 0
\(653\) −3.35191 23.3131i −0.131171 0.912311i −0.944032 0.329854i \(-0.893000\pi\)
0.812861 0.582457i \(-0.197909\pi\)
\(654\) 0 0
\(655\) −39.5372 34.2592i −1.54485 1.33862i
\(656\) 0 0
\(657\) 5.42211 + 3.19642i 0.211537 + 0.124704i
\(658\) 0 0
\(659\) 2.20150 7.49761i 0.0857582 0.292066i −0.905436 0.424483i \(-0.860456\pi\)
0.991194 + 0.132418i \(0.0422740\pi\)
\(660\) 0 0
\(661\) −37.9559 + 32.8889i −1.47631 + 1.27923i −0.597678 + 0.801736i \(0.703910\pi\)
−0.878634 + 0.477496i \(0.841545\pi\)
\(662\) 0 0
\(663\) −32.0507 + 28.8714i −1.24475 + 1.12127i
\(664\) 0 0
\(665\) 1.39342 4.74555i 0.0540345 0.184025i
\(666\) 0 0
\(667\) 5.75183 12.5948i 0.222712 0.487671i
\(668\) 0 0
\(669\) 0.0701674 + 3.64240i 0.00271283 + 0.140823i
\(670\) 0 0
\(671\) 69.0642i 2.66620i
\(672\) 0 0
\(673\) 44.5977 + 20.3671i 1.71911 + 0.785093i 0.995487 + 0.0949009i \(0.0302534\pi\)
0.723626 + 0.690192i \(0.242474\pi\)
\(674\) 0 0
\(675\) 6.11471 26.3748i 0.235355 1.01517i
\(676\) 0 0
\(677\) −11.8582 13.6851i −0.455746 0.525959i 0.480646 0.876915i \(-0.340402\pi\)
−0.936392 + 0.350955i \(0.885857\pi\)
\(678\) 0 0
\(679\) −1.58485 1.82902i −0.0608210 0.0701912i
\(680\) 0 0
\(681\) −20.4448 5.57775i −0.783448 0.213740i
\(682\) 0 0
\(683\) 3.07753 + 1.97781i 0.117759 + 0.0756788i 0.598194 0.801351i \(-0.295885\pi\)
−0.480436 + 0.877030i \(0.659521\pi\)
\(684\) 0 0
\(685\) 31.5196 36.3756i 1.20430 1.38984i
\(686\) 0 0
\(687\) 1.52672 + 9.33801i 0.0582480 + 0.356267i
\(688\) 0 0
\(689\) 49.2989 + 42.7178i 1.87814 + 1.62742i
\(690\) 0 0
\(691\) −22.9206 + 6.73010i −0.871942 + 0.256025i −0.686941 0.726713i \(-0.741047\pi\)
−0.185001 + 0.982738i \(0.559229\pi\)
\(692\) 0 0
\(693\) 11.0187 + 4.52768i 0.418565 + 0.171992i
\(694\) 0 0
\(695\) −10.0666 + 15.6639i −0.381847 + 0.594166i
\(696\) 0 0
\(697\) −1.71451 5.83910i −0.0649419 0.221172i
\(698\) 0 0
\(699\) −0.916074 47.5535i −0.0346491 1.79864i
\(700\) 0 0
\(701\) 7.15827 4.60034i 0.270364 0.173752i −0.398433 0.917197i \(-0.630446\pi\)
0.668797 + 0.743445i \(0.266810\pi\)
\(702\) 0 0
\(703\) 4.88745 5.64042i 0.184334 0.212732i
\(704\) 0 0
\(705\) −3.20804 6.68101i −0.120822 0.251621i
\(706\) 0 0
\(707\) 2.58376i 0.0971722i
\(708\) 0 0
\(709\) 3.78525 2.43263i 0.142158 0.0913595i −0.467629 0.883925i \(-0.654891\pi\)
0.609787 + 0.792566i \(0.291255\pi\)
\(710\) 0 0
\(711\) 16.3663 3.00055i 0.613785 0.112529i
\(712\) 0 0
\(713\) −2.51666 17.5038i −0.0942497 0.655521i
\(714\) 0 0
\(715\) −80.7045 + 36.8565i −3.01818 + 1.37835i
\(716\) 0 0
\(717\) 31.3541 + 13.5953i 1.17094 + 0.507726i
\(718\) 0 0
\(719\) 43.8824 + 6.30933i 1.63654 + 0.235298i 0.898344 0.439292i \(-0.144771\pi\)
0.738192 + 0.674591i \(0.235680\pi\)
\(720\) 0 0
\(721\) −1.08020 + 3.67883i −0.0402288 + 0.137007i
\(722\) 0 0
\(723\) −43.9154 5.45299i −1.63323 0.202799i
\(724\) 0 0
\(725\) −13.8587 + 21.5646i −0.514700 + 0.800888i
\(726\) 0 0
\(727\) 10.1784 4.64832i 0.377496 0.172397i −0.217626 0.976032i \(-0.569831\pi\)
0.595122 + 0.803636i \(0.297104\pi\)
\(728\) 0 0
\(729\) −20.8791 + 17.1191i −0.773299 + 0.634042i
\(730\) 0 0
\(731\) −37.3516 + 10.9674i −1.38150 + 0.405645i
\(732\) 0 0
\(733\) 0.719942 + 0.103512i 0.0265917 + 0.00382330i 0.155598 0.987820i \(-0.450270\pi\)
−0.129006 + 0.991644i \(0.541179\pi\)
\(734\) 0 0
\(735\) 26.2647 23.6594i 0.968789 0.872691i
\(736\) 0 0
\(737\) 17.4638 37.6653i 0.643286 1.38742i
\(738\) 0 0
\(739\) −3.91386 + 3.39138i −0.143974 + 0.124754i −0.723870 0.689936i \(-0.757639\pi\)
0.579896 + 0.814690i \(0.303093\pi\)
\(740\) 0 0
\(741\) 2.30994 18.6030i 0.0848578 0.683399i
\(742\) 0 0
\(743\) 9.27006 + 31.5709i 0.340085 + 1.15822i 0.935063 + 0.354482i \(0.115343\pi\)
−0.594977 + 0.803742i \(0.702839\pi\)
\(744\) 0 0
\(745\) −35.6868 55.5297i −1.30746 2.03445i
\(746\) 0 0
\(747\) −11.0447 + 5.56764i −0.404105 + 0.203709i
\(748\) 0 0
\(749\) 7.14955 + 4.59474i 0.261239 + 0.167888i
\(750\) 0 0
\(751\) −4.72629 + 32.8721i −0.172465 + 1.19952i 0.701190 + 0.712974i \(0.252652\pi\)
−0.873655 + 0.486546i \(0.838257\pi\)
\(752\) 0 0
\(753\) −4.87494 + 17.8687i −0.177653 + 0.651173i
\(754\) 0 0
\(755\) 1.50742 10.4844i 0.0548608 0.381565i
\(756\) 0 0
\(757\) 36.8168 + 16.8137i 1.33813 + 0.611103i 0.950504 0.310713i \(-0.100568\pi\)
0.387626 + 0.921817i \(0.373295\pi\)
\(758\) 0 0
\(759\) 10.7024 + 22.2886i 0.388471 + 0.809024i
\(760\) 0 0
\(761\) 38.6217 5.55295i 1.40003 0.201294i 0.599401 0.800449i \(-0.295406\pi\)
0.800633 + 0.599155i \(0.204497\pi\)
\(762\) 0 0
\(763\) −0.766987 5.33451i −0.0277668 0.193122i
\(764\) 0 0
\(765\) −24.9743 35.7540i −0.902949 1.29269i
\(766\) 0 0
\(767\) 48.2952 1.74384
\(768\) 0 0
\(769\) 4.79533 2.18995i 0.172924 0.0789717i −0.327072 0.944999i \(-0.606062\pi\)
0.499996 + 0.866028i \(0.333335\pi\)
\(770\) 0 0
\(771\) 7.31636 8.77966i 0.263492 0.316192i
\(772\) 0 0
\(773\) −9.21678 14.3416i −0.331505 0.515831i 0.634989 0.772521i \(-0.281005\pi\)
−0.966494 + 0.256690i \(0.917368\pi\)
\(774\) 0 0
\(775\) 32.7390i 1.17602i
\(776\) 0 0
\(777\) −4.88278 + 1.53647i −0.175169 + 0.0551204i
\(778\) 0 0
\(779\) 2.22477 + 1.42978i 0.0797108 + 0.0512270i
\(780\) 0 0
\(781\) −20.9416 9.56370i −0.749349 0.342216i
\(782\) 0 0
\(783\) 24.0711 8.60660i 0.860230 0.307575i
\(784\) 0 0
\(785\) −40.3991 + 46.6231i −1.44191 + 1.66405i
\(786\) 0 0
\(787\) −52.9999 + 7.62023i −1.88924 + 0.271632i −0.987136 0.159884i \(-0.948888\pi\)
−0.902106 + 0.431516i \(0.857979\pi\)
\(788\) 0 0
\(789\) −20.8754 + 25.0505i −0.743183 + 0.891823i
\(790\) 0 0
\(791\) 6.07486 9.45267i 0.215997 0.336098i
\(792\) 0 0
\(793\) −71.5202 21.0002i −2.53976 0.745739i
\(794\) 0 0
\(795\) −49.0014 + 44.1407i −1.73790 + 1.56551i
\(796\) 0 0
\(797\) −6.18085 + 5.35574i −0.218937 + 0.189710i −0.757423 0.652924i \(-0.773542\pi\)
0.538486 + 0.842634i \(0.318996\pi\)
\(798\) 0 0
\(799\) −5.84550 1.71639i −0.206799 0.0607216i
\(800\) 0 0
\(801\) 43.8099 + 18.0019i 1.54795 + 0.636065i
\(802\) 0 0
\(803\) 10.6415 0.375532
\(804\) 0 0
\(805\) −7.04057 −0.248147
\(806\) 0 0
\(807\) −4.82083 + 11.1180i −0.169701 + 0.391372i
\(808\) 0 0
\(809\) 13.7255 + 4.03018i 0.482564 + 0.141693i 0.513961 0.857814i \(-0.328178\pi\)
−0.0313975 + 0.999507i \(0.509996\pi\)
\(810\) 0 0
\(811\) −30.0175 + 26.0103i −1.05406 + 0.913345i −0.996382 0.0849906i \(-0.972914\pi\)
−0.0576744 + 0.998335i \(0.518369\pi\)
\(812\) 0 0
\(813\) −25.1364 27.9043i −0.881572 0.978648i
\(814\) 0 0
\(815\) −56.6925 16.6464i −1.98585 0.583099i
\(816\) 0 0
\(817\) 9.14600 14.2315i 0.319978 0.497896i
\(818\) 0 0
\(819\) −8.03910 + 10.0338i −0.280909 + 0.350608i
\(820\) 0 0
\(821\) 34.5249 4.96393i 1.20493 0.173242i 0.489547 0.871977i \(-0.337162\pi\)
0.715381 + 0.698735i \(0.246253\pi\)
\(822\) 0 0
\(823\) −3.85918 + 4.45373i −0.134522 + 0.155247i −0.819014 0.573774i \(-0.805479\pi\)
0.684491 + 0.729021i \(0.260024\pi\)
\(824\) 0 0
\(825\) −13.7397 43.6639i −0.478356 1.52018i
\(826\) 0 0
\(827\) 33.6965 + 15.3887i 1.17174 + 0.535117i 0.903648 0.428276i \(-0.140879\pi\)
0.268095 + 0.963393i \(0.413606\pi\)
\(828\) 0 0
\(829\) 26.0769 + 16.7586i 0.905687 + 0.582050i 0.908472 0.417946i \(-0.137250\pi\)
−0.00278462 + 0.999996i \(0.500886\pi\)
\(830\) 0 0
\(831\) −1.88562 5.99237i −0.0654115 0.207873i
\(832\) 0 0
\(833\) 29.0584i 1.00681i
\(834\) 0 0
\(835\) −10.8479 16.8796i −0.375407 0.584144i
\(836\) 0 0
\(837\) 19.9199 25.8681i 0.688531 0.894133i
\(838\) 0 0
\(839\) −12.4517 + 5.68652i −0.429882 + 0.196320i −0.618592 0.785712i \(-0.712297\pi\)
0.188710 + 0.982033i \(0.439569\pi\)
\(840\) 0 0
\(841\) 4.79665 0.165402
\(842\) 0 0
\(843\) 3.80231 + 5.67321i 0.130959 + 0.195396i
\(844\) 0 0
\(845\) −7.71572 53.6640i −0.265429 1.84610i
\(846\) 0 0
\(847\) 11.4116 1.64074i 0.392107 0.0563765i
\(848\) 0 0
\(849\) 19.0296 9.13749i 0.653093 0.313598i
\(850\) 0 0
\(851\) −9.66411 4.41345i −0.331281 0.151291i
\(852\) 0 0
\(853\) 4.30316 29.9291i 0.147337 1.02475i −0.773218 0.634140i \(-0.781354\pi\)
0.920555 0.390613i \(-0.127737\pi\)
\(854\) 0 0
\(855\) 18.3770 + 4.63522i 0.628480 + 0.158521i
\(856\) 0 0
\(857\) −1.43579 + 9.98613i −0.0490456 + 0.341120i 0.950493 + 0.310746i \(0.100579\pi\)
−0.999539 + 0.0303737i \(0.990330\pi\)
\(858\) 0 0
\(859\) −25.4650 16.3654i −0.868855 0.558379i 0.0285476 0.999592i \(-0.490912\pi\)
−0.897402 + 0.441213i \(0.854548\pi\)
\(860\) 0 0
\(861\) −0.785127 1.63509i −0.0267571 0.0557238i
\(862\) 0 0
\(863\) 5.05620 + 7.86760i 0.172115 + 0.267816i 0.916585 0.399840i \(-0.130934\pi\)
−0.744470 + 0.667656i \(0.767298\pi\)
\(864\) 0 0
\(865\) −18.5225 63.0818i −0.629784 2.14485i
\(866\) 0 0
\(867\) −6.35706 0.789358i −0.215897 0.0268080i
\(868\) 0 0
\(869\) 21.2605 18.4224i 0.721214 0.624936i
\(870\) 0 0
\(871\) 33.6945 + 29.5376i 1.14169 + 1.00084i
\(872\) 0 0
\(873\) 6.76965 6.33854i 0.229118 0.214527i
\(874\) 0 0
\(875\) 0.521138 + 0.0749284i 0.0176177 + 0.00253304i
\(876\) 0 0
\(877\) 41.1969 12.0965i 1.39112 0.408469i 0.501494 0.865161i \(-0.332784\pi\)
0.889625 + 0.456691i \(0.150966\pi\)
\(878\) 0 0
\(879\) −1.74951 + 1.17256i −0.0590095 + 0.0395495i
\(880\) 0 0
\(881\) 9.51440 4.34508i 0.320548 0.146389i −0.248642 0.968596i \(-0.579984\pi\)
0.569190 + 0.822206i \(0.307257\pi\)
\(882\) 0 0
\(883\) 25.8555 40.2319i 0.870106 1.35391i −0.0643854 0.997925i \(-0.520509\pi\)
0.934491 0.355986i \(-0.115855\pi\)
\(884\) 0 0
\(885\) −6.01674 + 48.4555i −0.202250 + 1.62882i
\(886\) 0 0
\(887\) −15.8490 + 53.9766i −0.532156 + 1.81236i 0.0493046 + 0.998784i \(0.484299\pi\)
−0.581461 + 0.813574i \(0.697519\pi\)
\(888\) 0 0
\(889\) −10.6903 1.53704i −0.358542 0.0515506i
\(890\) 0 0
\(891\) −15.7109 + 42.8601i −0.526334 + 1.43587i
\(892\) 0 0
\(893\) 2.40824 1.09981i 0.0805888 0.0368037i
\(894\) 0 0
\(895\) −10.0706 70.0423i −0.336622 2.34126i
\(896\) 0 0
\(897\) −26.3354 + 4.30571i −0.879313 + 0.143763i
\(898\) 0 0
\(899\) −26.0048 + 16.7123i −0.867308 + 0.557385i
\(900\) 0 0
\(901\) 54.2134i 1.80611i
\(902\) 0 0
\(903\) −10.4594 + 5.02231i −0.348066 + 0.167132i
\(904\) 0 0
\(905\) 1.49673 1.72731i 0.0497529 0.0574179i
\(906\) 0 0
\(907\) 10.8640 6.98187i 0.360733 0.231829i −0.347702 0.937605i \(-0.613038\pi\)
0.708435 + 0.705776i \(0.249401\pi\)
\(908\) 0 0
\(909\) −9.89355 + 0.381321i −0.328148 + 0.0126476i
\(910\) 0 0
\(911\) −11.1851 38.0930i −0.370580 1.26208i −0.908074 0.418810i \(-0.862447\pi\)
0.537494 0.843267i \(-0.319371\pi\)
\(912\) 0 0
\(913\) −11.3057 + 17.5921i −0.374166 + 0.582213i
\(914\) 0 0
\(915\) 29.9801 69.1414i 0.991112 2.28574i
\(916\) 0 0
\(917\) −12.2983 + 3.61111i −0.406126 + 0.119249i
\(918\) 0 0
\(919\) 3.39100 + 2.93832i 0.111859 + 0.0969263i 0.708994 0.705214i \(-0.249149\pi\)
−0.597136 + 0.802140i \(0.703695\pi\)
\(920\) 0 0
\(921\) −25.8247 + 4.22221i −0.850951 + 0.139126i
\(922\) 0 0
\(923\) 16.2714 18.7783i 0.535581 0.618094i
\(924\) 0 0
\(925\) 16.5468 + 10.6340i 0.544054 + 0.349642i
\(926\) 0 0
\(927\) −14.2461 3.59330i −0.467905 0.118019i
\(928\) 0 0
\(929\) −4.69962 5.42365i −0.154190 0.177944i 0.673399 0.739279i \(-0.264834\pi\)
−0.827589 + 0.561335i \(0.810288\pi\)
\(930\) 0 0
\(931\) 8.26943 + 9.54343i 0.271020 + 0.312773i
\(932\) 0 0
\(933\) −6.26871 + 22.9775i −0.205229 + 0.752251i
\(934\) 0 0
\(935\) −67.0726 30.6310i −2.19351 1.00174i
\(936\) 0 0
\(937\) 43.5815i 1.42374i 0.702309 + 0.711872i \(0.252153\pi\)
−0.702309 + 0.711872i \(0.747847\pi\)
\(938\) 0 0
\(939\) 15.5109 0.298803i 0.506179 0.00975107i
\(940\) 0 0
\(941\) −18.3337 + 40.1452i −0.597662 + 1.30870i 0.333038 + 0.942913i \(0.391926\pi\)
−0.930700 + 0.365783i \(0.880801\pi\)
\(942\) 0 0
\(943\) 1.06062 3.61213i 0.0345384 0.117627i
\(944\) 0 0
\(945\) −9.06555 9.31583i −0.294902 0.303044i
\(946\) 0 0
\(947\) −25.1500 + 21.7926i −0.817265 + 0.708164i −0.959512 0.281667i \(-0.909113\pi\)
0.142247 + 0.989831i \(0.454567\pi\)
\(948\) 0 0
\(949\) −3.23575 + 11.0199i −0.105037 + 0.357723i
\(950\) 0 0
\(951\) 29.0172 + 17.8680i 0.940947 + 0.579410i
\(952\) 0 0
\(953\) −1.80134 1.56087i −0.0583511 0.0505615i 0.625197 0.780467i \(-0.285019\pi\)
−0.683548 + 0.729905i \(0.739564\pi\)
\(954\) 0 0
\(955\) 8.64315 + 60.1144i 0.279686 + 1.94526i
\(956\) 0 0
\(957\) 27.6688 33.2027i 0.894406 1.07329i
\(958\) 0 0
\(959\) −3.32235 11.3149i −0.107284 0.365376i
\(960\) 0 0
\(961\) −3.52272 + 7.71368i −0.113636 + 0.248828i
\(962\) 0 0
\(963\) −16.5387 + 28.0547i −0.532952 + 0.904049i
\(964\) 0 0
\(965\) 0.0576478 0.0169269i 0.00185575 0.000544897i
\(966\) 0 0
\(967\) −26.8692 −0.864054 −0.432027 0.901861i \(-0.642201\pi\)
−0.432027 + 0.901861i \(0.642201\pi\)
\(968\) 0 0
\(969\) 12.9416 8.67378i 0.415745 0.278642i
\(970\) 0 0
\(971\) −0.810892 0.702642i −0.0260228 0.0225489i 0.641752 0.766912i \(-0.278208\pi\)
−0.667775 + 0.744363i \(0.732753\pi\)
\(972\) 0 0
\(973\) 1.89510 + 4.14968i 0.0607540 + 0.133033i
\(974\) 0 0
\(975\) 49.3944 0.951537i 1.58189 0.0304736i
\(976\) 0 0
\(977\) 8.18397 + 12.7345i 0.261828 + 0.407413i 0.947132 0.320845i \(-0.103967\pi\)
−0.685303 + 0.728258i \(0.740330\pi\)
\(978\) 0 0
\(979\) 79.2637 11.3964i 2.53328 0.364230i
\(980\) 0 0
\(981\) 20.3133 3.72418i 0.648555 0.118904i
\(982\) 0 0
\(983\) −18.0171 39.4519i −0.574656 1.25832i −0.944281 0.329140i \(-0.893241\pi\)
0.369625 0.929181i \(-0.379486\pi\)
\(984\) 0 0
\(985\) −16.0394 + 35.1215i −0.511059 + 1.11906i
\(986\) 0 0
\(987\) −1.80197 0.223751i −0.0573574 0.00712208i
\(988\) 0 0
\(989\) −23.1061 6.78456i −0.734731 0.215737i
\(990\) 0 0
\(991\) 26.2272 + 3.77091i 0.833136 + 0.119787i 0.545666 0.838003i \(-0.316277\pi\)
0.287470 + 0.957790i \(0.407186\pi\)
\(992\) 0 0
\(993\) −38.2092 23.5282i −1.21253 0.746644i
\(994\) 0 0
\(995\) 11.3239 + 24.7958i 0.358991 + 0.786081i
\(996\) 0 0
\(997\) 8.95887 5.75751i 0.283730 0.182342i −0.391033 0.920377i \(-0.627882\pi\)
0.674763 + 0.738034i \(0.264246\pi\)
\(998\) 0 0
\(999\) −6.60395 18.4700i −0.208940 0.584366i
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 804.2.s.b.161.2 yes 200
3.2 odd 2 inner 804.2.s.b.161.4 yes 200
67.5 odd 22 inner 804.2.s.b.5.4 yes 200
201.5 even 22 inner 804.2.s.b.5.2 200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.s.b.5.2 200 201.5 even 22 inner
804.2.s.b.5.4 yes 200 67.5 odd 22 inner
804.2.s.b.161.2 yes 200 1.1 even 1 trivial
804.2.s.b.161.4 yes 200 3.2 odd 2 inner