Properties

Label 1078.2.i.d.901.12
Level $1078$
Weight $2$
Character 1078.901
Analytic conductor $8.608$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1078,2,Mod(901,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1078.901");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.12
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.d.1011.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.662827 - 0.382683i) q^{3} +(0.500000 + 0.866025i) q^{4} +(3.37695 + 1.94969i) q^{5} +0.765367 q^{6} +1.00000i q^{8} +(-1.20711 + 2.09077i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.662827 - 0.382683i) q^{3} +(0.500000 + 0.866025i) q^{4} +(3.37695 + 1.94969i) q^{5} +0.765367 q^{6} +1.00000i q^{8} +(-1.20711 + 2.09077i) q^{9} +(1.94969 + 3.37695i) q^{10} +(2.75881 - 1.84092i) q^{11} +(0.662827 + 0.382683i) q^{12} +1.81903 q^{13} +2.98445 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.03803 - 5.26202i) q^{17} +(-2.09077 + 1.20711i) q^{18} +(-3.41476 + 5.91454i) q^{19} +3.89937i q^{20} +(3.30966 - 0.214882i) q^{22} +(2.18834 - 3.79031i) q^{23} +(0.382683 + 0.662827i) q^{24} +(5.10255 + 8.83788i) q^{25} +(1.57532 + 0.909513i) q^{26} +4.14386i q^{27} -9.36112i q^{29} +(2.58461 + 1.49222i) q^{30} +(-6.82704 + 3.94159i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.12412 - 2.27596i) q^{33} -6.07606i q^{34} -2.41421 q^{36} +(2.30389 - 3.99045i) q^{37} +(-5.91454 + 3.41476i) q^{38} +(1.20570 - 0.696111i) q^{39} +(-1.94969 + 3.37695i) q^{40} -3.58235 q^{41} +3.25819i q^{43} +(2.97369 + 1.46874i) q^{44} +(-8.15269 + 4.70696i) q^{45} +(3.79031 - 2.18834i) q^{46} +(0.176542 + 0.101927i) q^{47} +0.765367i q^{48} +10.2051i q^{50} +(-4.02738 - 2.32521i) q^{51} +(0.909513 + 1.57532i) q^{52} +(-2.49222 - 4.31666i) q^{53} +(-2.07193 + 3.58869i) q^{54} +(12.9056 - 0.837904i) q^{55} +5.22709i q^{57} +(4.68056 - 8.10697i) q^{58} +(-4.50118 + 2.59876i) q^{59} +(1.49222 + 2.58461i) q^{60} +(4.49186 - 7.78013i) q^{61} -7.88318 q^{62} -1.00000 q^{64} +(6.14277 + 3.54653i) q^{65} +(2.11150 - 1.40898i) q^{66} +(4.01676 + 6.95724i) q^{67} +(3.03803 - 5.26202i) q^{68} -3.34976i q^{69} +8.86195 q^{71} +(-2.09077 - 1.20711i) q^{72} +(0.0278530 + 0.0482428i) q^{73} +(3.99045 - 2.30389i) q^{74} +(6.76422 + 3.90532i) q^{75} -6.82952 q^{76} +1.39222 q^{78} +(-7.34847 - 4.24264i) q^{79} +(-3.37695 + 1.94969i) q^{80} +(-2.03553 - 3.52565i) q^{81} +(-3.10240 - 1.79117i) q^{82} +10.4676 q^{83} -23.6928i q^{85} +(-1.62910 + 2.82168i) q^{86} +(-3.58235 - 6.20481i) q^{87} +(1.84092 + 2.75881i) q^{88} +(-1.46160 - 0.843855i) q^{89} -9.41392 q^{90} +4.37667 q^{92} +(-3.01676 + 5.22519i) q^{93} +(0.101927 + 0.176542i) q^{94} +(-23.0630 + 13.3154i) q^{95} +(-0.382683 + 0.662827i) q^{96} -9.23880i q^{97} +(0.518771 + 7.99022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.662827 0.382683i 0.382683 0.220942i −0.296302 0.955094i \(-0.595753\pi\)
0.678985 + 0.734152i \(0.262420\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 3.37695 + 1.94969i 1.51022 + 0.871926i 0.999929 + 0.0119244i \(0.00379573\pi\)
0.510291 + 0.860002i \(0.329538\pi\)
\(6\) 0.765367 0.312460
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.20711 + 2.09077i −0.402369 + 0.696923i
\(10\) 1.94969 + 3.37695i 0.616545 + 1.06789i
\(11\) 2.75881 1.84092i 0.831811 0.555059i
\(12\) 0.662827 + 0.382683i 0.191342 + 0.110471i
\(13\) 1.81903 0.504507 0.252254 0.967661i \(-0.418828\pi\)
0.252254 + 0.967661i \(0.418828\pi\)
\(14\) 0 0
\(15\) 2.98445 0.770582
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.03803 5.26202i −0.736830 1.27623i −0.953916 0.300075i \(-0.902988\pi\)
0.217085 0.976153i \(-0.430345\pi\)
\(18\) −2.09077 + 1.20711i −0.492799 + 0.284518i
\(19\) −3.41476 + 5.91454i −0.783400 + 1.35689i 0.146550 + 0.989203i \(0.453183\pi\)
−0.929950 + 0.367685i \(0.880150\pi\)
\(20\) 3.89937i 0.871926i
\(21\) 0 0
\(22\) 3.30966 0.214882i 0.705621 0.0458130i
\(23\) 2.18834 3.79031i 0.456300 0.790334i −0.542462 0.840080i \(-0.682508\pi\)
0.998762 + 0.0497460i \(0.0158412\pi\)
\(24\) 0.382683 + 0.662827i 0.0781149 + 0.135299i
\(25\) 5.10255 + 8.83788i 1.02051 + 1.76758i
\(26\) 1.57532 + 0.909513i 0.308946 + 0.178370i
\(27\) 4.14386i 0.797486i
\(28\) 0 0
\(29\) 9.36112i 1.73832i −0.494534 0.869158i \(-0.664661\pi\)
0.494534 0.869158i \(-0.335339\pi\)
\(30\) 2.58461 + 1.49222i 0.471883 + 0.272442i
\(31\) −6.82704 + 3.94159i −1.22617 + 0.707931i −0.966227 0.257693i \(-0.917038\pi\)
−0.259945 + 0.965623i \(0.583704\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 1.12412 2.27596i 0.195684 0.396194i
\(34\) 6.07606i 1.04204i
\(35\) 0 0
\(36\) −2.41421 −0.402369
\(37\) 2.30389 3.99045i 0.378757 0.656026i −0.612125 0.790761i \(-0.709685\pi\)
0.990882 + 0.134735i \(0.0430183\pi\)
\(38\) −5.91454 + 3.41476i −0.959465 + 0.553947i
\(39\) 1.20570 0.696111i 0.193067 0.111467i
\(40\) −1.94969 + 3.37695i −0.308272 + 0.533943i
\(41\) −3.58235 −0.559469 −0.279734 0.960077i \(-0.590246\pi\)
−0.279734 + 0.960077i \(0.590246\pi\)
\(42\) 0 0
\(43\) 3.25819i 0.496869i 0.968649 + 0.248435i \(0.0799161\pi\)
−0.968649 + 0.248435i \(0.920084\pi\)
\(44\) 2.97369 + 1.46874i 0.448300 + 0.221420i
\(45\) −8.15269 + 4.70696i −1.21533 + 0.701672i
\(46\) 3.79031 2.18834i 0.558851 0.322653i
\(47\) 0.176542 + 0.101927i 0.0257513 + 0.0148675i 0.512820 0.858496i \(-0.328601\pi\)
−0.487069 + 0.873363i \(0.661934\pi\)
\(48\) 0.765367i 0.110471i
\(49\) 0 0
\(50\) 10.2051i 1.44322i
\(51\) −4.02738 2.32521i −0.563945 0.325594i
\(52\) 0.909513 + 1.57532i 0.126127 + 0.218458i
\(53\) −2.49222 4.31666i −0.342333 0.592939i 0.642532 0.766259i \(-0.277884\pi\)
−0.984866 + 0.173320i \(0.944551\pi\)
\(54\) −2.07193 + 3.58869i −0.281954 + 0.488359i
\(55\) 12.9056 0.837904i 1.74019 0.112983i
\(56\) 0 0
\(57\) 5.22709i 0.692345i
\(58\) 4.68056 8.10697i 0.614588 1.06450i
\(59\) −4.50118 + 2.59876i −0.586004 + 0.338330i −0.763516 0.645789i \(-0.776529\pi\)
0.177512 + 0.984119i \(0.443195\pi\)
\(60\) 1.49222 + 2.58461i 0.192645 + 0.333672i
\(61\) 4.49186 7.78013i 0.575124 0.996143i −0.420905 0.907105i \(-0.638287\pi\)
0.996028 0.0890385i \(-0.0283794\pi\)
\(62\) −7.88318 −1.00117
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 6.14277 + 3.54653i 0.761917 + 0.439893i
\(66\) 2.11150 1.40898i 0.259907 0.173433i
\(67\) 4.01676 + 6.95724i 0.490726 + 0.849962i 0.999943 0.0106761i \(-0.00339837\pi\)
−0.509217 + 0.860638i \(0.670065\pi\)
\(68\) 3.03803 5.26202i 0.368415 0.638114i
\(69\) 3.34976i 0.403264i
\(70\) 0 0
\(71\) 8.86195 1.05172 0.525860 0.850571i \(-0.323744\pi\)
0.525860 + 0.850571i \(0.323744\pi\)
\(72\) −2.09077 1.20711i −0.246400 0.142259i
\(73\) 0.0278530 + 0.0482428i 0.00325995 + 0.00564639i 0.867651 0.497174i \(-0.165629\pi\)
−0.864391 + 0.502821i \(0.832296\pi\)
\(74\) 3.99045 2.30389i 0.463881 0.267822i
\(75\) 6.76422 + 3.90532i 0.781064 + 0.450948i
\(76\) −6.82952 −0.783400
\(77\) 0 0
\(78\) 1.39222 0.157638
\(79\) −7.34847 4.24264i −0.826767 0.477334i 0.0259772 0.999663i \(-0.491730\pi\)
−0.852745 + 0.522328i \(0.825064\pi\)
\(80\) −3.37695 + 1.94969i −0.377555 + 0.217982i
\(81\) −2.03553 3.52565i −0.226170 0.391739i
\(82\) −3.10240 1.79117i −0.342603 0.197802i
\(83\) 10.4676 1.14897 0.574483 0.818517i \(-0.305203\pi\)
0.574483 + 0.818517i \(0.305203\pi\)
\(84\) 0 0
\(85\) 23.6928i 2.56985i
\(86\) −1.62910 + 2.82168i −0.175670 + 0.304269i
\(87\) −3.58235 6.20481i −0.384068 0.665225i
\(88\) 1.84092 + 2.75881i 0.196243 + 0.294090i
\(89\) −1.46160 0.843855i −0.154929 0.0894484i 0.420531 0.907278i \(-0.361844\pi\)
−0.575460 + 0.817830i \(0.695177\pi\)
\(90\) −9.41392 −0.992314
\(91\) 0 0
\(92\) 4.37667 0.456300
\(93\) −3.01676 + 5.22519i −0.312824 + 0.541827i
\(94\) 0.101927 + 0.176542i 0.0105129 + 0.0182090i
\(95\) −23.0630 + 13.3154i −2.36621 + 1.36613i
\(96\) −0.382683 + 0.662827i −0.0390575 + 0.0676495i
\(97\) 9.23880i 0.938058i −0.883183 0.469029i \(-0.844604\pi\)
0.883183 0.469029i \(-0.155396\pi\)
\(98\) 0 0
\(99\) 0.518771 + 7.99022i 0.0521384 + 0.803047i
\(100\) −5.10255 + 8.83788i −0.510255 + 0.883788i
\(101\) 2.67283 + 4.62948i 0.265957 + 0.460651i 0.967814 0.251667i \(-0.0809788\pi\)
−0.701857 + 0.712318i \(0.747645\pi\)
\(102\) −2.32521 4.02738i −0.230230 0.398770i
\(103\) 3.67639 + 2.12256i 0.362246 + 0.209143i 0.670065 0.742302i \(-0.266266\pi\)
−0.307820 + 0.951445i \(0.599599\pi\)
\(104\) 1.81903i 0.178370i
\(105\) 0 0
\(106\) 4.98445i 0.484133i
\(107\) −6.26883 3.61931i −0.606031 0.349892i 0.165379 0.986230i \(-0.447115\pi\)
−0.771411 + 0.636338i \(0.780448\pi\)
\(108\) −3.58869 + 2.07193i −0.345322 + 0.199372i
\(109\) −5.19615 + 3.00000i −0.497701 + 0.287348i −0.727764 0.685828i \(-0.759440\pi\)
0.230063 + 0.973176i \(0.426107\pi\)
\(110\) 11.5955 + 5.72714i 1.10559 + 0.546062i
\(111\) 3.52664i 0.334734i
\(112\) 0 0
\(113\) 16.8400 1.58417 0.792085 0.610411i \(-0.208996\pi\)
0.792085 + 0.610411i \(0.208996\pi\)
\(114\) −2.61355 + 4.52679i −0.244781 + 0.423973i
\(115\) 14.7798 8.53314i 1.37823 0.795719i
\(116\) 8.10697 4.68056i 0.752713 0.434579i
\(117\) −2.19576 + 3.80317i −0.202998 + 0.351603i
\(118\) −5.19752 −0.478470
\(119\) 0 0
\(120\) 2.98445i 0.272442i
\(121\) 4.22202 10.1575i 0.383820 0.923408i
\(122\) 7.78013 4.49186i 0.704380 0.406674i
\(123\) −2.37448 + 1.37090i −0.214099 + 0.123610i
\(124\) −6.82704 3.94159i −0.613086 0.353965i
\(125\) 20.2966i 1.81538i
\(126\) 0 0
\(127\) 17.3300i 1.53779i 0.639375 + 0.768895i \(0.279193\pi\)
−0.639375 + 0.768895i \(0.720807\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 1.24686 + 2.15962i 0.109780 + 0.190144i
\(130\) 3.54653 + 6.14277i 0.311051 + 0.538757i
\(131\) −3.17776 + 5.50404i −0.277642 + 0.480890i −0.970798 0.239897i \(-0.922886\pi\)
0.693156 + 0.720788i \(0.256220\pi\)
\(132\) 2.53310 0.164463i 0.220478 0.0143147i
\(133\) 0 0
\(134\) 8.03353i 0.693991i
\(135\) −8.07922 + 13.9936i −0.695349 + 1.20438i
\(136\) 5.26202 3.03803i 0.451215 0.260509i
\(137\) −0.674793 1.16878i −0.0576515 0.0998553i 0.835759 0.549096i \(-0.185028\pi\)
−0.893411 + 0.449241i \(0.851695\pi\)
\(138\) 1.67488 2.90098i 0.142575 0.246948i
\(139\) −11.8957 −1.00898 −0.504491 0.863417i \(-0.668320\pi\)
−0.504491 + 0.863417i \(0.668320\pi\)
\(140\) 0 0
\(141\) 0.156023 0.0131395
\(142\) 7.67468 + 4.43098i 0.644045 + 0.371839i
\(143\) 5.01834 3.34868i 0.419655 0.280031i
\(144\) −1.20711 2.09077i −0.100592 0.174231i
\(145\) 18.2512 31.6121i 1.51568 2.62524i
\(146\) 0.0557060i 0.00461026i
\(147\) 0 0
\(148\) 4.60778 0.378757
\(149\) −5.69557 3.28834i −0.466599 0.269391i 0.248216 0.968705i \(-0.420156\pi\)
−0.714815 + 0.699314i \(0.753489\pi\)
\(150\) 3.90532 + 6.76422i 0.318868 + 0.552296i
\(151\) 7.48149 4.31944i 0.608835 0.351511i −0.163674 0.986514i \(-0.552335\pi\)
0.772509 + 0.635003i \(0.219001\pi\)
\(152\) −5.91454 3.41476i −0.479733 0.276974i
\(153\) 14.6689 1.18591
\(154\) 0 0
\(155\) −30.7395 −2.46905
\(156\) 1.20570 + 0.696111i 0.0965333 + 0.0557335i
\(157\) −2.12168 + 1.22495i −0.169329 + 0.0977619i −0.582269 0.812996i \(-0.697835\pi\)
0.412941 + 0.910758i \(0.364502\pi\)
\(158\) −4.24264 7.34847i −0.337526 0.584613i
\(159\) −3.30383 1.90747i −0.262011 0.151272i
\(160\) −3.89937 −0.308272
\(161\) 0 0
\(162\) 4.07107i 0.319853i
\(163\) −1.14503 + 1.98325i −0.0896854 + 0.155340i −0.907378 0.420315i \(-0.861920\pi\)
0.817693 + 0.575655i \(0.195253\pi\)
\(164\) −1.79117 3.10240i −0.139867 0.242257i
\(165\) 8.23352 5.49414i 0.640978 0.427718i
\(166\) 9.06519 + 5.23379i 0.703595 + 0.406221i
\(167\) −8.51406 −0.658838 −0.329419 0.944184i \(-0.606853\pi\)
−0.329419 + 0.944184i \(0.606853\pi\)
\(168\) 0 0
\(169\) −9.69114 −0.745473
\(170\) 11.8464 20.5186i 0.908578 1.57370i
\(171\) −8.24396 14.2790i −0.630432 1.09194i
\(172\) −2.82168 + 1.62910i −0.215151 + 0.124217i
\(173\) −11.9961 + 20.7778i −0.912044 + 1.57971i −0.100872 + 0.994899i \(0.532163\pi\)
−0.811172 + 0.584807i \(0.801170\pi\)
\(174\) 7.16469i 0.543154i
\(175\) 0 0
\(176\) 0.214882 + 3.30966i 0.0161973 + 0.249475i
\(177\) −1.98900 + 3.44506i −0.149503 + 0.258946i
\(178\) −0.843855 1.46160i −0.0632496 0.109552i
\(179\) −10.0792 17.4577i −0.753357 1.30485i −0.946187 0.323620i \(-0.895100\pi\)
0.192831 0.981232i \(-0.438233\pi\)
\(180\) −8.15269 4.70696i −0.607666 0.350836i
\(181\) 11.1135i 0.826062i −0.910717 0.413031i \(-0.864470\pi\)
0.910717 0.413031i \(-0.135530\pi\)
\(182\) 0 0
\(183\) 6.87584i 0.508277i
\(184\) 3.79031 + 2.18834i 0.279425 + 0.161326i
\(185\) 15.5603 8.98372i 1.14401 0.660496i
\(186\) −5.22519 + 3.01676i −0.383129 + 0.221200i
\(187\) −18.0683 8.92412i −1.32128 0.652596i
\(188\) 0.203854i 0.0148675i
\(189\) 0 0
\(190\) −26.6308 −1.93200
\(191\) 12.2542 21.2249i 0.886681 1.53578i 0.0429063 0.999079i \(-0.486338\pi\)
0.843775 0.536698i \(-0.180328\pi\)
\(192\) −0.662827 + 0.382683i −0.0478354 + 0.0276178i
\(193\) 10.9286 6.30966i 0.786661 0.454179i −0.0521247 0.998641i \(-0.516599\pi\)
0.838786 + 0.544462i \(0.183266\pi\)
\(194\) 4.61940 8.00103i 0.331653 0.574441i
\(195\) 5.42879 0.388764
\(196\) 0 0
\(197\) 17.2697i 1.23042i −0.788364 0.615209i \(-0.789072\pi\)
0.788364 0.615209i \(-0.210928\pi\)
\(198\) −3.54584 + 7.17912i −0.251992 + 0.510198i
\(199\) −7.95279 + 4.59154i −0.563758 + 0.325486i −0.754653 0.656125i \(-0.772195\pi\)
0.190894 + 0.981611i \(0.438861\pi\)
\(200\) −8.83788 + 5.10255i −0.624932 + 0.360805i
\(201\) 5.32484 + 3.07430i 0.375585 + 0.216844i
\(202\) 5.34567i 0.376120i
\(203\) 0 0
\(204\) 4.65041i 0.325594i
\(205\) −12.0974 6.98445i −0.844921 0.487815i
\(206\) 2.12256 + 3.67639i 0.147886 + 0.256146i
\(207\) 5.28311 + 9.15062i 0.367202 + 0.636012i
\(208\) −0.909513 + 1.57532i −0.0630634 + 0.109229i
\(209\) 1.46754 + 22.6034i 0.101512 + 1.56351i
\(210\) 0 0
\(211\) 2.12250i 0.146119i −0.997328 0.0730593i \(-0.976724\pi\)
0.997328 0.0730593i \(-0.0232762\pi\)
\(212\) 2.49222 4.31666i 0.171167 0.296469i
\(213\) 5.87394 3.39132i 0.402476 0.232370i
\(214\) −3.61931 6.26883i −0.247411 0.428529i
\(215\) −6.35245 + 11.0028i −0.433233 + 0.750382i
\(216\) −4.14386 −0.281954
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) 0.0369234 + 0.0213178i 0.00249505 + 0.00144052i
\(220\) 7.17844 + 10.7576i 0.483970 + 0.725278i
\(221\) −5.52625 9.57175i −0.371736 0.643866i
\(222\) 1.76332 3.05416i 0.118346 0.204982i
\(223\) 5.77586i 0.386780i 0.981122 + 0.193390i \(0.0619483\pi\)
−0.981122 + 0.193390i \(0.938052\pi\)
\(224\) 0 0
\(225\) −24.6373 −1.64249
\(226\) 14.5838 + 8.41998i 0.970102 + 0.560089i
\(227\) 0.605269 + 1.04836i 0.0401731 + 0.0695819i 0.885413 0.464805i \(-0.153876\pi\)
−0.845240 + 0.534387i \(0.820542\pi\)
\(228\) −4.52679 + 2.61355i −0.299794 + 0.173086i
\(229\) −16.8020 9.70062i −1.11031 0.641035i −0.171397 0.985202i \(-0.554828\pi\)
−0.938909 + 0.344167i \(0.888161\pi\)
\(230\) 17.0663 1.12532
\(231\) 0 0
\(232\) 9.36112 0.614588
\(233\) −17.0714 9.85619i −1.11839 0.645700i −0.177397 0.984139i \(-0.556768\pi\)
−0.940988 + 0.338439i \(0.890101\pi\)
\(234\) −3.80317 + 2.19576i −0.248621 + 0.143541i
\(235\) 0.397450 + 0.688404i 0.0259268 + 0.0449065i
\(236\) −4.50118 2.59876i −0.293002 0.169165i
\(237\) −6.49435 −0.421854
\(238\) 0 0
\(239\) 11.6292i 0.752229i 0.926573 + 0.376115i \(0.122740\pi\)
−0.926573 + 0.376115i \(0.877260\pi\)
\(240\) −1.49222 + 2.58461i −0.0963227 + 0.166836i
\(241\) 13.6869 + 23.7064i 0.881651 + 1.52706i 0.849505 + 0.527581i \(0.176901\pi\)
0.0321456 + 0.999483i \(0.489766\pi\)
\(242\) 8.73512 6.68563i 0.561515 0.429769i
\(243\) −13.4645 7.77372i −0.863747 0.498684i
\(244\) 8.98372 0.575124
\(245\) 0 0
\(246\) −2.74181 −0.174811
\(247\) −6.21154 + 10.7587i −0.395231 + 0.684560i
\(248\) −3.94159 6.82704i −0.250291 0.433517i
\(249\) 6.93819 4.00577i 0.439690 0.253855i
\(250\) −10.1483 + 17.5774i −0.641835 + 1.11169i
\(251\) 13.5021i 0.852243i −0.904666 0.426122i \(-0.859880\pi\)
0.904666 0.426122i \(-0.140120\pi\)
\(252\) 0 0
\(253\) −0.940467 14.4853i −0.0591267 0.910682i
\(254\) −8.66501 + 15.0082i −0.543691 + 0.941701i
\(255\) −9.06684 15.7042i −0.567788 0.983437i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.43041 1.40320i −0.151605 0.0875289i 0.422279 0.906466i \(-0.361230\pi\)
−0.573883 + 0.818937i \(0.694564\pi\)
\(258\) 2.49371i 0.155252i
\(259\) 0 0
\(260\) 7.09306i 0.439893i
\(261\) 19.5720 + 11.2999i 1.21147 + 0.699445i
\(262\) −5.50404 + 3.17776i −0.340041 + 0.196323i
\(263\) 7.34847 4.24264i 0.453126 0.261612i −0.256023 0.966671i \(-0.582412\pi\)
0.709150 + 0.705058i \(0.249079\pi\)
\(264\) 2.27596 + 1.12412i 0.140076 + 0.0691849i
\(265\) 19.4362i 1.19396i
\(266\) 0 0
\(267\) −1.29172 −0.0790518
\(268\) −4.01676 + 6.95724i −0.245363 + 0.424981i
\(269\) 18.1498 10.4788i 1.10662 0.638905i 0.168665 0.985673i \(-0.446054\pi\)
0.937951 + 0.346768i \(0.112721\pi\)
\(270\) −13.9936 + 8.07922i −0.851625 + 0.491686i
\(271\) 7.30660 12.6554i 0.443844 0.768761i −0.554127 0.832432i \(-0.686948\pi\)
0.997971 + 0.0636717i \(0.0202810\pi\)
\(272\) 6.07606 0.368415
\(273\) 0 0
\(274\) 1.34959i 0.0815315i
\(275\) 30.3468 + 14.9886i 1.82998 + 0.903846i
\(276\) 2.90098 1.67488i 0.174618 0.100816i
\(277\) −9.63380 + 5.56208i −0.578839 + 0.334193i −0.760672 0.649136i \(-0.775130\pi\)
0.181833 + 0.983329i \(0.441797\pi\)
\(278\) −10.3020 5.94786i −0.617873 0.356729i
\(279\) 19.0317i 1.13940i
\(280\) 0 0
\(281\) 7.28929i 0.434843i 0.976078 + 0.217421i \(0.0697646\pi\)
−0.976078 + 0.217421i \(0.930235\pi\)
\(282\) 0.135120 + 0.0780114i 0.00804626 + 0.00464551i
\(283\) −8.00696 13.8685i −0.475965 0.824395i 0.523656 0.851930i \(-0.324568\pi\)
−0.999621 + 0.0275349i \(0.991234\pi\)
\(284\) 4.43098 + 7.67468i 0.262930 + 0.455408i
\(285\) −10.1912 + 17.6516i −0.603674 + 1.04559i
\(286\) 6.02035 0.390876i 0.355991 0.0231130i
\(287\) 0 0
\(288\) 2.41421i 0.142259i
\(289\) −9.95924 + 17.2499i −0.585838 + 1.01470i
\(290\) 31.6121 18.2512i 1.85633 1.07175i
\(291\) −3.53553 6.12372i −0.207257 0.358979i
\(292\) −0.0278530 + 0.0482428i −0.00162997 + 0.00282320i
\(293\) −14.2550 −0.832783 −0.416392 0.909185i \(-0.636705\pi\)
−0.416392 + 0.909185i \(0.636705\pi\)
\(294\) 0 0
\(295\) −20.2671 −1.17999
\(296\) 3.99045 + 2.30389i 0.231940 + 0.133911i
\(297\) 7.62852 + 11.4321i 0.442652 + 0.663358i
\(298\) −3.28834 5.69557i −0.190488 0.329935i
\(299\) 3.98064 6.89467i 0.230206 0.398729i
\(300\) 7.81064i 0.450948i
\(301\) 0 0
\(302\) 8.63888 0.497112
\(303\) 3.54325 + 2.04570i 0.203555 + 0.117522i
\(304\) −3.41476 5.91454i −0.195850 0.339222i
\(305\) 30.3376 17.5154i 1.73713 1.00293i
\(306\) 12.7036 + 7.33445i 0.726219 + 0.419283i
\(307\) 6.75074 0.385285 0.192643 0.981269i \(-0.438294\pi\)
0.192643 + 0.981269i \(0.438294\pi\)
\(308\) 0 0
\(309\) 3.24908 0.184834
\(310\) −26.6212 15.3697i −1.51198 0.872942i
\(311\) 15.4763 8.93526i 0.877581 0.506672i 0.00772127 0.999970i \(-0.497542\pi\)
0.869860 + 0.493298i \(0.164209\pi\)
\(312\) 0.696111 + 1.20570i 0.0394095 + 0.0682593i
\(313\) 13.0188 + 7.51640i 0.735865 + 0.424852i 0.820564 0.571554i \(-0.193659\pi\)
−0.0846986 + 0.996407i \(0.526993\pi\)
\(314\) −2.44991 −0.138256
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) −4.86597 + 8.42810i −0.273300 + 0.473370i −0.969705 0.244280i \(-0.921449\pi\)
0.696405 + 0.717649i \(0.254782\pi\)
\(318\) −1.90747 3.30383i −0.106965 0.185270i
\(319\) −17.2331 25.8255i −0.964868 1.44595i
\(320\) −3.37695 1.94969i −0.188778 0.108991i
\(321\) −5.54020 −0.309224
\(322\) 0 0
\(323\) 41.4966 2.30893
\(324\) 2.03553 3.52565i 0.113085 0.195869i
\(325\) 9.28167 + 16.0763i 0.514854 + 0.891754i
\(326\) −1.98325 + 1.14503i −0.109842 + 0.0634172i
\(327\) −2.29610 + 3.97696i −0.126975 + 0.219927i
\(328\) 3.58235i 0.197802i
\(329\) 0 0
\(330\) 9.87750 0.641304i 0.543739 0.0353026i
\(331\) −9.12993 + 15.8135i −0.501826 + 0.869188i 0.498172 + 0.867078i \(0.334005\pi\)
−0.999998 + 0.00210996i \(0.999328\pi\)
\(332\) 5.23379 + 9.06519i 0.287241 + 0.497517i
\(333\) 5.56208 + 9.63380i 0.304800 + 0.527929i
\(334\) −7.37339 4.25703i −0.403454 0.232934i
\(335\) 31.3257i 1.71151i
\(336\) 0 0
\(337\) 29.6928i 1.61747i 0.588173 + 0.808735i \(0.299847\pi\)
−0.588173 + 0.808735i \(0.700153\pi\)
\(338\) −8.39278 4.84557i −0.456507 0.263564i
\(339\) 11.1620 6.44437i 0.606236 0.350010i
\(340\) 20.5186 11.8464i 1.11278 0.642461i
\(341\) −11.5783 + 23.4421i −0.627000 + 1.26946i
\(342\) 16.4879i 0.891565i
\(343\) 0 0
\(344\) −3.25819 −0.175670
\(345\) 6.53098 11.3120i 0.351616 0.609017i
\(346\) −20.7778 + 11.9961i −1.11702 + 0.644913i
\(347\) −16.6981 + 9.64063i −0.896399 + 0.517536i −0.876030 0.482256i \(-0.839817\pi\)
−0.0203688 + 0.999793i \(0.506484\pi\)
\(348\) 3.58235 6.20481i 0.192034 0.332613i
\(349\) 23.9921 1.28427 0.642135 0.766592i \(-0.278049\pi\)
0.642135 + 0.766592i \(0.278049\pi\)
\(350\) 0 0
\(351\) 7.53779i 0.402337i
\(352\) −1.46874 + 2.97369i −0.0782838 + 0.158498i
\(353\) −13.9844 + 8.07391i −0.744316 + 0.429731i −0.823636 0.567118i \(-0.808058\pi\)
0.0793204 + 0.996849i \(0.474725\pi\)
\(354\) −3.44506 + 1.98900i −0.183103 + 0.105714i
\(355\) 29.9264 + 17.2780i 1.58833 + 0.917022i
\(356\) 1.68771i 0.0894484i
\(357\) 0 0
\(358\) 20.1584i 1.06541i
\(359\) 15.7145 + 9.07278i 0.829381 + 0.478843i 0.853641 0.520862i \(-0.174390\pi\)
−0.0242599 + 0.999706i \(0.507723\pi\)
\(360\) −4.70696 8.15269i −0.248078 0.429685i
\(361\) −13.8212 23.9390i −0.727431 1.25995i
\(362\) 5.55676 9.62460i 0.292057 0.505858i
\(363\) −1.08864 8.34836i −0.0571385 0.438175i
\(364\) 0 0
\(365\) 0.217218i 0.0113697i
\(366\) 3.43792 5.95465i 0.179703 0.311255i
\(367\) −4.25692 + 2.45773i −0.222209 + 0.128293i −0.606973 0.794723i \(-0.707616\pi\)
0.384763 + 0.923015i \(0.374283\pi\)
\(368\) 2.18834 + 3.79031i 0.114075 + 0.197584i
\(369\) 4.32427 7.48986i 0.225113 0.389907i
\(370\) 17.9674 0.934083
\(371\) 0 0
\(372\) −6.03353 −0.312824
\(373\) −1.96420 1.13403i −0.101702 0.0587179i 0.448286 0.893890i \(-0.352035\pi\)
−0.549989 + 0.835172i \(0.685368\pi\)
\(374\) −11.1855 16.7627i −0.578391 0.866777i
\(375\) 7.76718 + 13.4531i 0.401095 + 0.694718i
\(376\) −0.101927 + 0.176542i −0.00525647 + 0.00910448i
\(377\) 17.0281i 0.876993i
\(378\) 0 0
\(379\) 14.7984 0.760143 0.380072 0.924957i \(-0.375899\pi\)
0.380072 + 0.924957i \(0.375899\pi\)
\(380\) −23.0630 13.3154i −1.18311 0.683067i
\(381\) 6.63191 + 11.4868i 0.339763 + 0.588487i
\(382\) 21.2249 12.2542i 1.08596 0.626978i
\(383\) −6.29627 3.63515i −0.321724 0.185748i 0.330437 0.943828i \(-0.392804\pi\)
−0.652161 + 0.758081i \(0.726137\pi\)
\(384\) −0.765367 −0.0390575
\(385\) 0 0
\(386\) 12.6193 0.642306
\(387\) −6.81213 3.93298i −0.346280 0.199925i
\(388\) 8.00103 4.61940i 0.406191 0.234514i
\(389\) 17.5968 + 30.4786i 0.892194 + 1.54533i 0.837239 + 0.546837i \(0.184168\pi\)
0.0549549 + 0.998489i \(0.482498\pi\)
\(390\) 4.70147 + 2.71440i 0.238068 + 0.137449i
\(391\) −26.5929 −1.34486
\(392\) 0 0
\(393\) 4.86431i 0.245372i
\(394\) 8.63486 14.9560i 0.435018 0.753473i
\(395\) −16.5436 28.6544i −0.832401 1.44176i
\(396\) −6.66035 + 4.44438i −0.334695 + 0.223338i
\(397\) −16.3081 9.41550i −0.818481 0.472550i 0.0314111 0.999507i \(-0.490000\pi\)
−0.849893 + 0.526956i \(0.823333\pi\)
\(398\) −9.18309 −0.460307
\(399\) 0 0
\(400\) −10.2051 −0.510255
\(401\) 3.55347 6.15480i 0.177452 0.307356i −0.763555 0.645743i \(-0.776548\pi\)
0.941007 + 0.338387i \(0.109881\pi\)
\(402\) 3.07430 + 5.32484i 0.153332 + 0.265579i
\(403\) −12.4186 + 7.16986i −0.618612 + 0.357156i
\(404\) −2.67283 + 4.62948i −0.132978 + 0.230325i
\(405\) 15.8746i 0.788816i
\(406\) 0 0
\(407\) −0.990128 15.2502i −0.0490788 0.755922i
\(408\) 2.32521 4.02738i 0.115115 0.199385i
\(409\) 4.85705 + 8.41267i 0.240166 + 0.415980i 0.960761 0.277376i \(-0.0894648\pi\)
−0.720595 + 0.693356i \(0.756131\pi\)
\(410\) −6.98445 12.0974i −0.344937 0.597449i
\(411\) −0.894543 0.516465i −0.0441245 0.0254753i
\(412\) 4.24513i 0.209143i
\(413\) 0 0
\(414\) 10.5662i 0.519301i
\(415\) 35.3485 + 20.4085i 1.73519 + 1.00181i
\(416\) −1.57532 + 0.909513i −0.0772366 + 0.0445925i
\(417\) −7.88481 + 4.55230i −0.386121 + 0.222927i
\(418\) −10.0308 + 20.3089i −0.490621 + 0.993339i
\(419\) 23.0474i 1.12594i 0.826478 + 0.562970i \(0.190341\pi\)
−0.826478 + 0.562970i \(0.809659\pi\)
\(420\) 0 0
\(421\) −1.67074 −0.0814270 −0.0407135 0.999171i \(-0.512963\pi\)
−0.0407135 + 0.999171i \(0.512963\pi\)
\(422\) 1.06125 1.83814i 0.0516608 0.0894790i
\(423\) −0.426211 + 0.246073i −0.0207231 + 0.0119645i
\(424\) 4.31666 2.49222i 0.209636 0.121033i
\(425\) 31.0034 53.6994i 1.50389 2.60481i
\(426\) 6.78265 0.328620
\(427\) 0 0
\(428\) 7.23863i 0.349892i
\(429\) 2.04481 4.14003i 0.0987242 0.199883i
\(430\) −11.0028 + 6.35245i −0.530600 + 0.306342i
\(431\) −33.6434 + 19.4240i −1.62055 + 0.935623i −0.633772 + 0.773520i \(0.718494\pi\)
−0.986774 + 0.162103i \(0.948172\pi\)
\(432\) −3.58869 2.07193i −0.172661 0.0996858i
\(433\) 31.8479i 1.53051i 0.643726 + 0.765256i \(0.277388\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(434\) 0 0
\(435\) 27.9378i 1.33951i
\(436\) −5.19615 3.00000i −0.248851 0.143674i
\(437\) 14.9453 + 25.8860i 0.714930 + 1.23830i
\(438\) 0.0213178 + 0.0369234i 0.00101860 + 0.00176427i
\(439\) −6.02035 + 10.4276i −0.287336 + 0.497680i −0.973173 0.230075i \(-0.926103\pi\)
0.685837 + 0.727755i \(0.259436\pi\)
\(440\) 0.837904 + 12.9056i 0.0399455 + 0.615249i
\(441\) 0 0
\(442\) 11.0525i 0.525714i
\(443\) 15.2762 26.4591i 0.725793 1.25711i −0.232854 0.972512i \(-0.574807\pi\)
0.958647 0.284598i \(-0.0918601\pi\)
\(444\) 3.05416 1.76332i 0.144944 0.0836835i
\(445\) −3.29050 5.69932i −0.155985 0.270174i
\(446\) −2.88793 + 5.00204i −0.136748 + 0.236854i
\(447\) −5.03357 −0.238080
\(448\) 0 0
\(449\) 15.7378 0.742712 0.371356 0.928490i \(-0.378893\pi\)
0.371356 + 0.928490i \(0.378893\pi\)
\(450\) −21.3365 12.3186i −1.00581 0.580706i
\(451\) −9.88300 + 6.59482i −0.465372 + 0.310538i
\(452\) 8.41998 + 14.5838i 0.396043 + 0.685966i
\(453\) 3.30596 5.72608i 0.155327 0.269035i
\(454\) 1.21054i 0.0568134i
\(455\) 0 0
\(456\) −5.22709 −0.244781
\(457\) −14.8669 8.58340i −0.695443 0.401514i 0.110205 0.993909i \(-0.464849\pi\)
−0.805648 + 0.592395i \(0.798183\pi\)
\(458\) −9.70062 16.8020i −0.453280 0.785105i
\(459\) 21.8051 12.5892i 1.01777 0.587612i
\(460\) 14.7798 + 8.53314i 0.689113 + 0.397860i
\(461\) −0.312096 −0.0145357 −0.00726787 0.999974i \(-0.502313\pi\)
−0.00726787 + 0.999974i \(0.502313\pi\)
\(462\) 0 0
\(463\) −31.9402 −1.48439 −0.742194 0.670185i \(-0.766215\pi\)
−0.742194 + 0.670185i \(0.766215\pi\)
\(464\) 8.10697 + 4.68056i 0.376357 + 0.217290i
\(465\) −20.3749 + 11.7635i −0.944866 + 0.545518i
\(466\) −9.85619 17.0714i −0.456579 0.790818i
\(467\) −16.3264 9.42604i −0.755495 0.436185i 0.0721810 0.997392i \(-0.477004\pi\)
−0.827676 + 0.561206i \(0.810337\pi\)
\(468\) −4.39152 −0.202998
\(469\) 0 0
\(470\) 0.794901i 0.0366660i
\(471\) −0.937539 + 1.62386i −0.0431995 + 0.0748237i
\(472\) −2.59876 4.50118i −0.119618 0.207184i
\(473\) 5.99807 + 8.98872i 0.275792 + 0.413302i
\(474\) −5.62427 3.24718i −0.258331 0.149148i
\(475\) −69.6960 −3.19787
\(476\) 0 0
\(477\) 12.0335 0.550977
\(478\) −5.81459 + 10.0712i −0.265953 + 0.460645i
\(479\) 14.5270 + 25.1615i 0.663755 + 1.14966i 0.979621 + 0.200854i \(0.0643717\pi\)
−0.315866 + 0.948804i \(0.602295\pi\)
\(480\) −2.58461 + 1.49222i −0.117971 + 0.0681104i
\(481\) 4.19083 7.25874i 0.191086 0.330970i
\(482\) 27.3738i 1.24684i
\(483\) 0 0
\(484\) 10.9077 1.42237i 0.495802 0.0646532i
\(485\) 18.0127 31.1990i 0.817917 1.41667i
\(486\) −7.77372 13.4645i −0.352623 0.610761i
\(487\) 16.5674 + 28.6956i 0.750742 + 1.30032i 0.947463 + 0.319864i \(0.103637\pi\)
−0.196721 + 0.980459i \(0.563029\pi\)
\(488\) 7.78013 + 4.49186i 0.352190 + 0.203337i
\(489\) 1.75273i 0.0792613i
\(490\) 0 0
\(491\) 42.4151i 1.91416i 0.289817 + 0.957082i \(0.406406\pi\)
−0.289817 + 0.957082i \(0.593594\pi\)
\(492\) −2.37448 1.37090i −0.107050 0.0618052i
\(493\) −49.2584 + 28.4394i −2.21849 + 1.28084i
\(494\) −10.7587 + 6.21154i −0.484057 + 0.279470i
\(495\) −13.8265 + 27.9940i −0.621457 + 1.25824i
\(496\) 7.88318i 0.353965i
\(497\) 0 0
\(498\) 8.01154 0.359005
\(499\) −7.72103 + 13.3732i −0.345641 + 0.598667i −0.985470 0.169850i \(-0.945672\pi\)
0.639829 + 0.768517i \(0.279005\pi\)
\(500\) −17.5774 + 10.1483i −0.786085 + 0.453846i
\(501\) −5.64335 + 3.25819i −0.252126 + 0.145565i
\(502\) 6.75103 11.6931i 0.301313 0.521890i
\(503\) 39.5816 1.76486 0.882429 0.470446i \(-0.155907\pi\)
0.882429 + 0.470446i \(0.155907\pi\)
\(504\) 0 0
\(505\) 20.8447i 0.927579i
\(506\) 6.42817 13.0149i 0.285767 0.578581i
\(507\) −6.42355 + 3.70864i −0.285280 + 0.164706i
\(508\) −15.0082 + 8.66501i −0.665883 + 0.384448i
\(509\) −4.57165 2.63944i −0.202635 0.116991i 0.395249 0.918574i \(-0.370658\pi\)
−0.597884 + 0.801583i \(0.703992\pi\)
\(510\) 18.1337i 0.802973i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −24.5090 14.1503i −1.08210 0.624751i
\(514\) −1.40320 2.43041i −0.0618923 0.107201i
\(515\) 8.27667 + 14.3356i 0.364714 + 0.631703i
\(516\) −1.24686 + 2.15962i −0.0548898 + 0.0950719i
\(517\) 0.674685 0.0438044i 0.0296726 0.00192652i
\(518\) 0 0
\(519\) 18.3628i 0.806037i
\(520\) −3.54653 + 6.14277i −0.155526 + 0.269378i
\(521\) −23.6500 + 13.6543i −1.03613 + 0.598207i −0.918733 0.394878i \(-0.870787\pi\)
−0.117392 + 0.993086i \(0.537453\pi\)
\(522\) 11.2999 + 19.5720i 0.494582 + 0.856641i
\(523\) 4.32645 7.49363i 0.189182 0.327673i −0.755796 0.654808i \(-0.772750\pi\)
0.944978 + 0.327134i \(0.106083\pi\)
\(524\) −6.35552 −0.277642
\(525\) 0 0
\(526\) 8.48528 0.369976
\(527\) 41.4815 + 23.9493i 1.80696 + 1.04325i
\(528\) 1.40898 + 2.11150i 0.0613180 + 0.0918912i
\(529\) 1.92237 + 3.32964i 0.0835813 + 0.144767i
\(530\) 9.71811 16.8323i 0.422128 0.731147i
\(531\) 12.5479i 0.544533i
\(532\) 0 0
\(533\) −6.51638 −0.282256
\(534\) −1.11866 0.645859i −0.0484092 0.0279490i
\(535\) −14.1130 24.4445i −0.610160 1.05683i
\(536\) −6.95724 + 4.01676i −0.300507 + 0.173498i
\(537\) −13.3616 7.71430i −0.576594 0.332897i
\(538\) 20.9576 0.903548
\(539\) 0 0
\(540\) −16.1584 −0.695349
\(541\) −0.447200 0.258191i −0.0192266 0.0111005i 0.490356 0.871522i \(-0.336867\pi\)
−0.509583 + 0.860422i \(0.670200\pi\)
\(542\) 12.6554 7.30660i 0.543596 0.313845i
\(543\) −4.25296 7.36635i −0.182512 0.316120i
\(544\) 5.26202 + 3.03803i 0.225607 + 0.130254i
\(545\) −23.3962 −1.00218
\(546\) 0 0
\(547\) 28.0407i 1.19894i 0.800399 + 0.599468i \(0.204621\pi\)
−0.800399 + 0.599468i \(0.795379\pi\)
\(548\) 0.674793 1.16878i 0.0288257 0.0499277i
\(549\) 10.8443 + 18.7829i 0.462824 + 0.801634i
\(550\) 18.7868 + 28.1539i 0.801071 + 1.20049i
\(551\) 55.3667 + 31.9660i 2.35870 + 1.36180i
\(552\) 3.34976 0.142575
\(553\) 0 0
\(554\) −11.1242 −0.472620
\(555\) 6.87584 11.9093i 0.291863 0.505522i
\(556\) −5.94786 10.3020i −0.252246 0.436902i
\(557\) 24.8942 14.3727i 1.05480 0.608989i 0.130811 0.991407i \(-0.458242\pi\)
0.923989 + 0.382418i \(0.124909\pi\)
\(558\) 9.51584 16.4819i 0.402838 0.697735i
\(559\) 5.92673i 0.250674i
\(560\) 0 0
\(561\) −15.3913 + 0.999289i −0.649820 + 0.0421900i
\(562\) −3.64465 + 6.31271i −0.153740 + 0.266286i
\(563\) −3.37537 5.84631i −0.142255 0.246393i 0.786090 0.618111i \(-0.212102\pi\)
−0.928345 + 0.371719i \(0.878769\pi\)
\(564\) 0.0780114 + 0.135120i 0.00328487 + 0.00568956i
\(565\) 56.8678 + 32.8326i 2.39245 + 1.38128i
\(566\) 16.0139i 0.673115i
\(567\) 0 0
\(568\) 8.86195i 0.371839i
\(569\) −8.41827 4.86029i −0.352912 0.203754i 0.313055 0.949735i \(-0.398648\pi\)
−0.665967 + 0.745981i \(0.731981\pi\)
\(570\) −17.6516 + 10.1912i −0.739346 + 0.426862i
\(571\) 17.6516 10.1912i 0.738698 0.426487i −0.0828978 0.996558i \(-0.526418\pi\)
0.821596 + 0.570071i \(0.193084\pi\)
\(572\) 5.40922 + 2.67167i 0.226171 + 0.111708i
\(573\) 18.7579i 0.783622i
\(574\) 0 0
\(575\) 44.6644 1.86263
\(576\) 1.20711 2.09077i 0.0502961 0.0871154i
\(577\) 10.5781 6.10726i 0.440371 0.254248i −0.263384 0.964691i \(-0.584839\pi\)
0.703755 + 0.710443i \(0.251505\pi\)
\(578\) −17.2499 + 9.95924i −0.717502 + 0.414250i
\(579\) 4.82920 8.36442i 0.200695 0.347614i
\(580\) 36.5025 1.51568
\(581\) 0 0
\(582\) 7.07107i 0.293105i
\(583\) −14.8222 7.32084i −0.613873 0.303198i
\(584\) −0.0482428 + 0.0278530i −0.00199630 + 0.00115257i
\(585\) −14.8300 + 8.56208i −0.613143 + 0.353998i
\(586\) −12.3451 7.12748i −0.509973 0.294433i
\(587\) 22.5689i 0.931519i 0.884911 + 0.465759i \(0.154219\pi\)
−0.884911 + 0.465759i \(0.845781\pi\)
\(588\) 0 0
\(589\) 53.8384i 2.21837i
\(590\) −17.5518 10.1335i −0.722596 0.417191i
\(591\) −6.60884 11.4468i −0.271851 0.470860i
\(592\) 2.30389 + 3.99045i 0.0946892 + 0.164007i
\(593\) 18.3348 31.7568i 0.752920 1.30410i −0.193481 0.981104i \(-0.561978\pi\)
0.946402 0.322992i \(-0.104689\pi\)
\(594\) 0.890440 + 13.7148i 0.0365352 + 0.562723i
\(595\) 0 0
\(596\) 6.57668i 0.269391i
\(597\) −3.51422 + 6.08680i −0.143827 + 0.249116i
\(598\) 6.89467 3.98064i 0.281944 0.162780i
\(599\) −3.17279 5.49543i −0.129637 0.224537i 0.793899 0.608049i \(-0.208048\pi\)
−0.923536 + 0.383512i \(0.874714\pi\)
\(600\) −3.90532 + 6.76422i −0.159434 + 0.276148i
\(601\) 1.60141 0.0653230 0.0326615 0.999466i \(-0.489602\pi\)
0.0326615 + 0.999466i \(0.489602\pi\)
\(602\) 0 0
\(603\) −19.3946 −0.789811
\(604\) 7.48149 + 4.31944i 0.304417 + 0.175755i
\(605\) 34.0615 26.0698i 1.38480 1.05989i
\(606\) 2.04570 + 3.54325i 0.0831008 + 0.143935i
\(607\) 8.37216 14.5010i 0.339815 0.588578i −0.644582 0.764535i \(-0.722969\pi\)
0.984398 + 0.175957i \(0.0563021\pi\)
\(608\) 6.82952i 0.276974i
\(609\) 0 0
\(610\) 35.0309 1.41836
\(611\) 0.321135 + 0.185407i 0.0129917 + 0.00750078i
\(612\) 7.33445 + 12.7036i 0.296478 + 0.513514i
\(613\) −1.57905 + 0.911666i −0.0637773 + 0.0368219i −0.531550 0.847027i \(-0.678390\pi\)
0.467772 + 0.883849i \(0.345057\pi\)
\(614\) 5.84631 + 3.37537i 0.235938 + 0.136219i
\(615\) −10.6913 −0.431116
\(616\) 0 0
\(617\) 46.7616 1.88255 0.941276 0.337638i \(-0.109628\pi\)
0.941276 + 0.337638i \(0.109628\pi\)
\(618\) 2.81379 + 1.62454i 0.113187 + 0.0653486i
\(619\) −35.0519 + 20.2372i −1.40885 + 0.813402i −0.995278 0.0970680i \(-0.969054\pi\)
−0.413576 + 0.910470i \(0.635720\pi\)
\(620\) −15.3697 26.6212i −0.617263 1.06913i
\(621\) 15.7065 + 9.06816i 0.630281 + 0.363893i
\(622\) 17.8705 0.716542
\(623\) 0 0
\(624\) 1.39222i 0.0557335i
\(625\) −14.0593 + 24.3514i −0.562371 + 0.974055i
\(626\) 7.51640 + 13.0188i 0.300416 + 0.520335i
\(627\) 9.62266 + 14.4205i 0.384292 + 0.575900i
\(628\) −2.12168 1.22495i −0.0846643 0.0488810i
\(629\) −27.9971 −1.11632
\(630\) 0 0
\(631\) 12.6619 0.504064 0.252032 0.967719i \(-0.418901\pi\)
0.252032 + 0.967719i \(0.418901\pi\)
\(632\) 4.24264 7.34847i 0.168763 0.292306i
\(633\) −0.812244 1.40685i −0.0322838 0.0559172i
\(634\) −8.42810 + 4.86597i −0.334723 + 0.193252i
\(635\) −33.7881 + 58.5227i −1.34084 + 2.32240i
\(636\) 3.81493i 0.151272i
\(637\) 0 0
\(638\) −2.01154 30.9821i −0.0796374 1.22659i
\(639\) −10.6973 + 18.5283i −0.423180 + 0.732969i
\(640\) −1.94969 3.37695i −0.0770681 0.133486i
\(641\) 0.653476 + 1.13185i 0.0258107 + 0.0447055i 0.878642 0.477481i \(-0.158450\pi\)
−0.852832 + 0.522186i \(0.825117\pi\)
\(642\) −4.79796 2.77010i −0.189360 0.109327i
\(643\) 39.1745i 1.54489i −0.635081 0.772446i \(-0.719033\pi\)
0.635081 0.772446i \(-0.280967\pi\)
\(644\) 0 0
\(645\) 9.72391i 0.382878i
\(646\) 35.9371 + 20.7483i 1.41393 + 0.816330i
\(647\) 14.3245 8.27023i 0.563153 0.325136i −0.191257 0.981540i \(-0.561256\pi\)
0.754410 + 0.656404i \(0.227923\pi\)
\(648\) 3.52565 2.03553i 0.138501 0.0799633i
\(649\) −7.63378 + 15.4558i −0.299652 + 0.606693i
\(650\) 18.5633i 0.728114i
\(651\) 0 0
\(652\) −2.29005 −0.0896854
\(653\) −17.3853 + 30.1122i −0.680339 + 1.17838i 0.294539 + 0.955639i \(0.404834\pi\)
−0.974878 + 0.222741i \(0.928499\pi\)
\(654\) −3.97696 + 2.29610i −0.155512 + 0.0897846i
\(655\) −21.4623 + 12.3913i −0.838602 + 0.484167i
\(656\) 1.79117 3.10240i 0.0699336 0.121128i
\(657\) −0.134486 −0.00524680
\(658\) 0 0
\(659\) 22.4888i 0.876039i −0.898966 0.438019i \(-0.855680\pi\)
0.898966 0.438019i \(-0.144320\pi\)
\(660\) 8.87482 + 4.38337i 0.345452 + 0.170622i
\(661\) 22.7587 13.1398i 0.885212 0.511077i 0.0128383 0.999918i \(-0.495913\pi\)
0.872373 + 0.488840i \(0.162580\pi\)
\(662\) −15.8135 + 9.12993i −0.614609 + 0.354845i
\(663\) −7.32590 4.22961i −0.284514 0.164265i
\(664\) 10.4676i 0.406221i
\(665\) 0 0
\(666\) 11.1242i 0.431052i
\(667\) −35.4815 20.4853i −1.37385 0.793193i
\(668\) −4.25703 7.37339i −0.164709 0.285285i
\(669\) 2.21033 + 3.82840i 0.0854562 + 0.148014i
\(670\) −15.6629 + 27.1289i −0.605109 + 1.04808i
\(671\) −1.93044 29.7330i −0.0745237 1.14783i
\(672\) 0 0
\(673\) 3.77457i 0.145499i 0.997350 + 0.0727495i \(0.0231774\pi\)
−0.997350 + 0.0727495i \(0.976823\pi\)
\(674\) −14.8464 + 25.7147i −0.571862 + 0.990494i
\(675\) −36.6229 + 21.1442i −1.40962 + 0.813843i
\(676\) −4.84557 8.39278i −0.186368 0.322799i
\(677\) −15.7129 + 27.2155i −0.603896 + 1.04598i 0.388329 + 0.921521i \(0.373052\pi\)
−0.992225 + 0.124457i \(0.960281\pi\)
\(678\) 12.8887 0.494989
\(679\) 0 0
\(680\) 23.6928 0.908578
\(681\) 0.802378 + 0.463253i 0.0307472 + 0.0177519i
\(682\) −21.7482 + 14.5123i −0.832780 + 0.555705i
\(683\) 9.95029 + 17.2344i 0.380737 + 0.659456i 0.991168 0.132614i \(-0.0423369\pi\)
−0.610431 + 0.792070i \(0.709004\pi\)
\(684\) 8.24396 14.2790i 0.315216 0.545970i
\(685\) 5.26254i 0.201071i
\(686\) 0 0
\(687\) −14.8491 −0.566527
\(688\) −2.82168 1.62910i −0.107575 0.0621087i
\(689\) −4.53342 7.85212i −0.172710 0.299142i
\(690\) 11.3120 6.53098i 0.430640 0.248630i
\(691\) 24.7690 + 14.3004i 0.942255 + 0.544011i 0.890667 0.454657i \(-0.150238\pi\)
0.0515887 + 0.998668i \(0.483572\pi\)
\(692\) −23.9921 −0.912044
\(693\) 0 0
\(694\) −19.2813 −0.731907
\(695\) −40.1713 23.1929i −1.52379 0.879758i
\(696\) 6.20481 3.58235i 0.235193 0.135788i
\(697\) 10.8833 + 18.8504i 0.412233 + 0.714009i
\(698\) 20.7778 + 11.9961i 0.786451 + 0.454058i
\(699\) −15.0872 −0.570650
\(700\) 0 0
\(701\) 21.2928i 0.804218i 0.915592 + 0.402109i \(0.131723\pi\)
−0.915592 + 0.402109i \(0.868277\pi\)
\(702\) −3.76889 + 6.52792i −0.142248 + 0.246380i
\(703\) 15.7345 + 27.2529i 0.593436 + 1.02786i
\(704\) −2.75881 + 1.84092i −0.103976 + 0.0693823i
\(705\) 0.526882 + 0.304195i 0.0198435 + 0.0114567i
\(706\) −16.1478 −0.607731
\(707\) 0 0
\(708\) −3.97801 −0.149503
\(709\) 8.43913 14.6170i 0.316938 0.548953i −0.662909 0.748700i \(-0.730679\pi\)
0.979848 + 0.199746i \(0.0640118\pi\)
\(710\) 17.2780 + 29.9264i 0.648433 + 1.12312i
\(711\) 17.7408 10.2426i 0.665331 0.384129i
\(712\) 0.843855 1.46160i 0.0316248 0.0547758i
\(713\) 34.5021i 1.29211i
\(714\) 0 0
\(715\) 23.4756 1.52417i 0.877937 0.0570007i
\(716\) 10.0792 17.4577i 0.376678 0.652426i
\(717\) 4.45030 + 7.70814i 0.166199 + 0.287866i
\(718\) 9.07278 + 15.7145i 0.338593 + 0.586461i
\(719\) −31.3046 18.0737i −1.16746 0.674036i −0.214383 0.976750i \(-0.568774\pi\)
−0.953081 + 0.302714i \(0.902107\pi\)
\(720\) 9.41392i 0.350836i
\(721\) 0 0
\(722\) 27.6424i 1.02874i
\(723\) 18.1441 + 10.4755i 0.674786 + 0.389588i
\(724\) 9.62460 5.55676i 0.357695 0.206515i
\(725\) 82.7324 47.7656i 3.07261 1.77397i
\(726\) 3.23139 7.77421i 0.119928 0.288528i
\(727\) 8.74172i 0.324212i 0.986773 + 0.162106i \(0.0518287\pi\)
−0.986773 + 0.162106i \(0.948171\pi\)
\(728\) 0 0
\(729\) 0.313708 0.0116188
\(730\) −0.108609 + 0.188117i −0.00401981 + 0.00696251i
\(731\) 17.1447 9.89848i 0.634118 0.366108i
\(732\) 5.95465 3.43792i 0.220090 0.127069i
\(733\) 6.73225 11.6606i 0.248661 0.430694i −0.714493 0.699642i \(-0.753343\pi\)
0.963155 + 0.268948i \(0.0866760\pi\)
\(734\) −4.91547 −0.181433
\(735\) 0 0
\(736\) 4.37667i 0.161326i
\(737\) 23.8892 + 11.7991i 0.879970 + 0.434626i
\(738\) 7.48986 4.32427i 0.275706 0.159179i
\(739\) −32.3387 + 18.6708i −1.18960 + 0.686816i −0.958216 0.286047i \(-0.907659\pi\)
−0.231384 + 0.972862i \(0.574325\pi\)
\(740\) 15.5603 + 8.98372i 0.572006 + 0.330248i
\(741\) 9.50821i 0.349293i
\(742\) 0 0
\(743\) 17.5472i 0.643746i 0.946783 + 0.321873i \(0.104312\pi\)
−0.946783 + 0.321873i \(0.895688\pi\)
\(744\) −5.22519 3.01676i −0.191565 0.110600i
\(745\) −12.8225 22.2091i −0.469778 0.813680i
\(746\) −1.13403 1.96420i −0.0415198 0.0719145i
\(747\) −12.6355 + 21.8853i −0.462308 + 0.800741i
\(748\) −1.30563 20.1097i −0.0477387 0.735282i
\(749\) 0 0
\(750\) 15.5344i 0.567235i
\(751\) 17.3623 30.0724i 0.633561 1.09736i −0.353258 0.935526i \(-0.614926\pi\)
0.986818 0.161833i \(-0.0517406\pi\)
\(752\) −0.176542 + 0.101927i −0.00643784 + 0.00371689i
\(753\) −5.16702 8.94954i −0.188297 0.326139i
\(754\) 8.51406 14.7468i 0.310064 0.537046i
\(755\) 33.6862 1.22597
\(756\) 0 0
\(757\) 28.0627 1.01996 0.509978 0.860187i \(-0.329653\pi\)
0.509978 + 0.860187i \(0.329653\pi\)
\(758\) 12.8158 + 7.39920i 0.465491 + 0.268751i
\(759\) −6.16664 9.24134i −0.223835 0.335439i
\(760\) −13.3154 23.0630i −0.483001 0.836583i
\(761\) 3.79149 6.56706i 0.137442 0.238056i −0.789086 0.614283i \(-0.789445\pi\)
0.926527 + 0.376227i \(0.122779\pi\)
\(762\) 13.2638i 0.480498i
\(763\) 0 0
\(764\) 24.5084 0.886681
\(765\) 49.5362 + 28.5997i 1.79099 + 1.03403i
\(766\) −3.63515 6.29627i −0.131343 0.227494i
\(767\) −8.18777 + 4.72721i −0.295643 + 0.170690i
\(768\) −0.662827 0.382683i −0.0239177 0.0138089i
\(769\) 1.95786 0.0706022 0.0353011 0.999377i \(-0.488761\pi\)
0.0353011 + 0.999377i \(0.488761\pi\)
\(770\) 0 0
\(771\) −2.14792 −0.0773554
\(772\) 10.9286 + 6.30966i 0.393331 + 0.227090i
\(773\) −8.18023 + 4.72286i −0.294223 + 0.169869i −0.639845 0.768504i \(-0.721001\pi\)
0.345622 + 0.938374i \(0.387668\pi\)
\(774\) −3.93298 6.81213i −0.141368 0.244857i
\(775\) −69.6706 40.2243i −2.50264 1.44490i
\(776\) 9.23880 0.331653
\(777\) 0 0
\(778\) 35.1936i 1.26175i
\(779\) 12.2329 21.1879i 0.438288 0.759136i
\(780\) 2.71440 + 4.70147i 0.0971910 + 0.168340i
\(781\) 24.4484 16.3142i 0.874833 0.583767i
\(782\) −23.0301 13.2965i −0.823556 0.475480i
\(783\) 38.7912 1.38628
\(784\) 0 0
\(785\) −9.55310 −0.340965
\(786\) −2.43215 + 4.21261i −0.0867520 + 0.150259i
\(787\) −10.0436 17.3960i −0.358016 0.620101i 0.629614 0.776908i \(-0.283213\pi\)
−0.987629 + 0.156807i \(0.949880\pi\)
\(788\) 14.9560 8.63486i 0.532786 0.307604i
\(789\) 3.24718 5.62427i 0.115603 0.200229i
\(790\) 33.0873i 1.17719i
\(791\) 0 0
\(792\) −7.99022 + 0.518771i −0.283920 + 0.0184337i
\(793\) 8.17081 14.1523i 0.290154 0.502561i
\(794\) −9.41550 16.3081i −0.334144 0.578754i
\(795\) −7.43792 12.8829i −0.263796 0.456908i
\(796\) −7.95279 4.59154i −0.281879 0.162743i
\(797\) 36.2219i 1.28304i 0.767105 + 0.641522i \(0.221697\pi\)
−0.767105 + 0.641522i \(0.778303\pi\)
\(798\) 0 0
\(799\) 1.23863i 0.0438194i
\(800\) −8.83788 5.10255i −0.312466 0.180402i
\(801\) 3.52861 2.03725i 0.124677 0.0719826i
\(802\) 6.15480 3.55347i 0.217333 0.125477i
\(803\) 0.165652 + 0.0818173i 0.00584574 + 0.00288727i
\(804\) 6.14859i 0.216844i
\(805\) 0 0
\(806\) −14.3397 −0.505095
\(807\) 8.02014 13.8913i 0.282322 0.488997i
\(808\) −4.62948 + 2.67283i −0.162865 + 0.0940299i
\(809\) −0.169942 + 0.0981160i −0.00597484 + 0.00344958i −0.502984 0.864295i \(-0.667765\pi\)
0.497010 + 0.867745i \(0.334431\pi\)
\(810\) 7.93730 13.7478i 0.278888 0.483049i
\(811\) −13.1515 −0.461811 −0.230905 0.972976i \(-0.574169\pi\)
−0.230905 + 0.972976i \(0.574169\pi\)
\(812\) 0 0
\(813\) 11.1845i 0.392256i
\(814\) 6.76760 13.7021i 0.237204 0.480258i
\(815\) −7.73341 + 4.46489i −0.270890 + 0.156398i
\(816\) 4.02738 2.32521i 0.140986 0.0813985i
\(817\) −19.2707 11.1259i −0.674196 0.389248i
\(818\) 9.71411i 0.339646i
\(819\) 0 0
\(820\) 13.9689i 0.487815i
\(821\) 16.2662 + 9.39127i 0.567693 + 0.327758i 0.756227 0.654309i \(-0.227040\pi\)
−0.188535 + 0.982067i \(0.560374\pi\)
\(822\) −0.516465 0.894543i −0.0180138 0.0312008i
\(823\) −18.1347 31.4103i −0.632137 1.09489i −0.987114 0.160019i \(-0.948844\pi\)
0.354977 0.934875i \(-0.384489\pi\)
\(824\) −2.12256 + 3.67639i −0.0739431 + 0.128073i
\(825\) 25.8506 1.67837i 0.900001 0.0584332i
\(826\) 0 0
\(827\) 26.5489i 0.923196i 0.887089 + 0.461598i \(0.152724\pi\)
−0.887089 + 0.461598i \(0.847276\pi\)
\(828\) −5.28311 + 9.15062i −0.183601 + 0.318006i
\(829\) −7.93057 + 4.57871i −0.275440 + 0.159025i −0.631357 0.775492i \(-0.717502\pi\)
0.355917 + 0.934517i \(0.384168\pi\)
\(830\) 20.4085 + 35.3485i 0.708389 + 1.22697i
\(831\) −4.25703 + 7.37339i −0.147675 + 0.255780i
\(832\) −1.81903 −0.0630634
\(833\) 0 0
\(834\) −9.10459 −0.315266
\(835\) −28.7516 16.5997i −0.994990 0.574458i
\(836\) −18.8413 + 12.5726i −0.651641 + 0.434833i
\(837\) −16.3334 28.2903i −0.564565 0.977855i
\(838\) −11.5237 + 19.9596i −0.398080 + 0.689494i
\(839\) 42.3516i 1.46214i 0.682302 + 0.731070i \(0.260979\pi\)
−0.682302 + 0.731070i \(0.739021\pi\)
\(840\) 0 0
\(841\) −58.6306 −2.02175
\(842\) −1.44690 0.835371i −0.0498636 0.0287888i
\(843\) 2.78949 + 4.83154i 0.0960752 + 0.166407i
\(844\) 1.83814 1.06125i 0.0632712 0.0365297i
\(845\) −32.7266 18.8947i −1.12583 0.649997i
\(846\) −0.492146 −0.0169203
\(847\) 0 0
\(848\) 4.98445 0.171167
\(849\) −10.6145 6.12826i −0.364287 0.210321i
\(850\) 53.6994 31.0034i 1.84188 1.06341i
\(851\) −10.0834 17.4649i −0.345653 0.598689i
\(852\) 5.87394 + 3.39132i 0.201238 + 0.116185i
\(853\) 56.4552 1.93299 0.966495 0.256686i \(-0.0826307\pi\)
0.966495 + 0.256686i \(0.0826307\pi\)
\(854\) 0 0
\(855\) 64.2926i 2.19876i
\(856\) 3.61931 6.26883i 0.123706 0.214264i
\(857\) −18.0227 31.2163i −0.615644 1.06633i −0.990271 0.139151i \(-0.955563\pi\)
0.374627 0.927176i \(-0.377771\pi\)
\(858\) 3.84087 2.56297i 0.131125 0.0874984i
\(859\) 0.0732103 + 0.0422680i 0.00249790 + 0.00144217i 0.501248 0.865303i \(-0.332874\pi\)
−0.498751 + 0.866746i \(0.666208\pi\)
\(860\) −12.7049 −0.433233
\(861\) 0 0
\(862\) −38.8481 −1.32317
\(863\) −22.8620 + 39.5981i −0.778230 + 1.34793i 0.154731 + 0.987957i \(0.450549\pi\)
−0.932961 + 0.359977i \(0.882784\pi\)
\(864\) −2.07193 3.58869i −0.0704885 0.122090i
\(865\) −81.0204 + 46.7771i −2.75477 + 1.59047i
\(866\) −15.9239 + 27.5811i −0.541118 + 0.937244i
\(867\) 15.2449i 0.517745i
\(868\) 0 0
\(869\) −28.0834 + 1.82333i −0.952663 + 0.0618523i
\(870\) 13.9689 24.1948i 0.473590 0.820282i
\(871\) 7.30660 + 12.6554i 0.247575 + 0.428812i
\(872\) −3.00000 5.19615i −0.101593 0.175964i
\(873\) 19.3162 + 11.1522i 0.653754 + 0.377445i
\(874\) 29.8906i 1.01106i
\(875\) 0 0
\(876\) 0.0426355i 0.00144052i
\(877\) 40.0453 + 23.1201i 1.35223 + 0.780712i 0.988562 0.150816i \(-0.0481900\pi\)
0.363671 + 0.931528i \(0.381523\pi\)
\(878\) −10.4276 + 6.02035i −0.351913 + 0.203177i
\(879\) −9.44857 + 5.45513i −0.318692 + 0.183997i
\(880\) −5.72714 + 11.5955i −0.193062 + 0.390885i
\(881\) 37.2892i 1.25630i −0.778091 0.628152i \(-0.783812\pi\)
0.778091 0.628152i \(-0.216188\pi\)
\(882\) 0 0
\(883\) −24.3548 −0.819603 −0.409801 0.912175i \(-0.634402\pi\)
−0.409801 + 0.912175i \(0.634402\pi\)
\(884\) 5.52625 9.57175i 0.185868 0.321933i
\(885\) −13.4336 + 7.75587i −0.451564 + 0.260711i
\(886\) 26.4591 15.2762i 0.888911 0.513213i
\(887\) 5.74396 9.94883i 0.192863 0.334049i −0.753335 0.657637i \(-0.771556\pi\)
0.946198 + 0.323588i \(0.104889\pi\)
\(888\) 3.52664 0.118346
\(889\) 0 0
\(890\) 6.58101i 0.220596i
\(891\) −12.1061 5.97932i −0.405569 0.200315i
\(892\) −5.00204 + 2.88793i −0.167481 + 0.0966951i
\(893\) −1.20570 + 0.696111i −0.0403472 + 0.0232945i
\(894\) −4.35920 2.51679i −0.145793 0.0841739i
\(895\) 78.6053i 2.62748i
\(896\) 0 0
\(897\) 6.09330i 0.203449i
\(898\) 13.6293 + 7.86890i 0.454817 + 0.262588i
\(899\) 36.8977 + 63.9087i 1.23061 + 2.13148i
\(900\) −12.3186 21.3365i −0.410621 0.711217i
\(901\) −15.1429 + 26.2283i −0.504483 + 0.873791i
\(902\) −11.8563 + 0.769781i −0.394773 + 0.0256309i
\(903\) 0 0
\(904\) 16.8400i 0.560089i
\(905\) 21.6679 37.5299i 0.720265 1.24754i
\(906\) 5.72608 3.30596i 0.190236 0.109833i
\(907\) 11.6507 + 20.1796i 0.386854 + 0.670051i 0.992025 0.126045i \(-0.0402283\pi\)
−0.605170 + 0.796096i \(0.706895\pi\)
\(908\) −0.605269 + 1.04836i −0.0200866 + 0.0347910i
\(909\) −12.9056 −0.428051
\(910\) 0 0
\(911\) −32.6447 −1.08157 −0.540784 0.841161i \(-0.681872\pi\)
−0.540784 + 0.841161i \(0.681872\pi\)
\(912\) −4.52679 2.61355i −0.149897 0.0865431i
\(913\) 28.8780 19.2700i 0.955722 0.637743i
\(914\) −8.58340 14.8669i −0.283914 0.491753i
\(915\) 13.4057 23.2194i 0.443180 0.767610i
\(916\) 19.4012i 0.641035i
\(917\) 0 0
\(918\) 25.1783 0.831009
\(919\) −33.0701 19.0931i −1.09088 0.629822i −0.157072 0.987587i \(-0.550205\pi\)
−0.933812 + 0.357765i \(0.883539\pi\)
\(920\) 8.53314 + 14.7798i 0.281329 + 0.487276i
\(921\) 4.47458 2.58340i 0.147442 0.0851258i
\(922\) −0.270283 0.156048i −0.00890129 0.00513916i
\(923\) 16.1201 0.530600
\(924\) 0 0
\(925\) 47.0228 1.54610
\(926\) −27.6610 15.9701i −0.908998 0.524810i
\(927\) −8.87559 + 5.12433i −0.291513 + 0.168305i
\(928\) 4.68056 + 8.10697i 0.153647 + 0.266124i
\(929\) 7.05212 + 4.07155i 0.231373 + 0.133583i 0.611205 0.791472i \(-0.290685\pi\)
−0.379832 + 0.925055i \(0.624018\pi\)
\(930\) −23.5270 −0.771479
\(931\) 0 0
\(932\) 19.7124i 0.645700i
\(933\) 6.83875 11.8451i 0.223891 0.387790i
\(934\) −9.42604 16.3264i −0.308429 0.534216i
\(935\) −43.6166 65.3638i −1.42642 2.13763i
\(936\) −3.80317 2.19576i −0.124310 0.0717706i
\(937\) −29.3997 −0.960445 −0.480222 0.877147i \(-0.659444\pi\)
−0.480222 + 0.877147i \(0.659444\pi\)
\(938\) 0 0
\(939\) 11.5056 0.375471
\(940\) −0.397450 + 0.688404i −0.0129634 + 0.0224533i
\(941\) 12.5519 + 21.7406i 0.409181 + 0.708722i 0.994798 0.101866i \(-0.0324811\pi\)
−0.585617 + 0.810588i \(0.699148\pi\)
\(942\) −1.62386 + 0.937539i −0.0529084 + 0.0305467i
\(943\) −7.83938 + 13.5782i −0.255285 + 0.442167i
\(944\) 5.19752i 0.169165i
\(945\) 0 0
\(946\) 0.700126 + 10.7835i 0.0227631 + 0.350602i
\(947\) −29.0590 + 50.3316i −0.944290 + 1.63556i −0.187124 + 0.982336i \(0.559917\pi\)
−0.757166 + 0.653222i \(0.773417\pi\)
\(948\) −3.24718 5.62427i −0.105463 0.182668i
\(949\) 0.0506653 + 0.0877549i 0.00164467 + 0.00284864i
\(950\) −60.3585 34.8480i −1.95829 1.13062i
\(951\) 7.44850i 0.241534i
\(952\) 0 0
\(953\) 56.3237i 1.82450i −0.409632 0.912251i \(-0.634343\pi\)
0.409632 0.912251i \(-0.365657\pi\)
\(954\) 10.4213 + 6.01676i 0.337403 + 0.194800i
\(955\) 82.7636 47.7836i 2.67817 1.54624i
\(956\) −10.0712 + 5.81459i −0.325725 + 0.188057i
\(957\) −21.3056 10.5230i −0.688711 0.340161i
\(958\) 29.0540i 0.938692i
\(959\) 0 0
\(960\) −2.98445 −0.0963227
\(961\) 15.5723 26.9720i 0.502332 0.870064i
\(962\) 7.25874 4.19083i 0.234031 0.135118i
\(963\) 15.1343 8.73779i 0.487696 0.281571i
\(964\) −13.6869 + 23.7064i −0.440825 + 0.763532i
\(965\) 49.2074 1.58404
\(966\) 0 0
\(967\) 28.3825i 0.912721i 0.889795 + 0.456360i \(0.150847\pi\)
−0.889795 + 0.456360i \(0.849153\pi\)
\(968\) 10.1575 + 4.22202i 0.326474 + 0.135701i
\(969\) 27.5051 15.8801i 0.883590 0.510141i
\(970\) 31.1990 18.0127i 1.00174 0.578354i
\(971\) 38.2269 + 22.0703i 1.22676 + 0.708270i 0.966351 0.257229i \(-0.0828094\pi\)
0.260409 + 0.965499i \(0.416143\pi\)
\(972\) 15.5474i 0.498684i
\(973\) 0 0
\(974\) 33.1349i 1.06171i
\(975\) 12.3043 + 7.10388i 0.394053 + 0.227506i
\(976\) 4.49186 + 7.78013i 0.143781 + 0.249036i
\(977\) 4.83203 + 8.36932i 0.154590 + 0.267758i 0.932910 0.360110i \(-0.117261\pi\)
−0.778319 + 0.627868i \(0.783928\pi\)
\(978\) −0.876366 + 1.51791i −0.0280231 + 0.0485374i
\(979\) −5.58574 + 0.362658i −0.178521 + 0.0115906i
\(980\) 0 0
\(981\) 14.4853i 0.462479i
\(982\) −21.2075 + 36.7325i −0.676759 + 1.17218i
\(983\) 23.1226 13.3498i 0.737497 0.425794i −0.0836616 0.996494i \(-0.526661\pi\)
0.821159 + 0.570700i \(0.193328\pi\)
\(984\) −1.37090 2.37448i −0.0437028 0.0756955i
\(985\) 33.6705 58.3191i 1.07283 1.85820i
\(986\) −56.8787 −1.81139
\(987\) 0 0
\(988\) −12.4231 −0.395231
\(989\) 12.3496 + 7.13002i 0.392693 + 0.226721i
\(990\) −25.9712 + 17.3303i −0.825418 + 0.550792i
\(991\) 18.2219 + 31.5612i 0.578837 + 1.00257i 0.995613 + 0.0935654i \(0.0298264\pi\)
−0.416777 + 0.909009i \(0.636840\pi\)
\(992\) 3.94159 6.82704i 0.125146 0.216759i
\(993\) 13.9755i 0.443499i
\(994\) 0 0
\(995\) −35.8083 −1.13520
\(996\) 6.93819 + 4.00577i 0.219845 + 0.126928i
\(997\) −14.5129 25.1370i −0.459627 0.796097i 0.539314 0.842104i \(-0.318683\pi\)
−0.998941 + 0.0460077i \(0.985350\pi\)
\(998\) −13.3732 + 7.72103i −0.423322 + 0.244405i
\(999\) 16.5359 + 9.54699i 0.523172 + 0.302053i
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 1078.2.i.d.901.12 32
7.2 even 3 1078.2.c.c.1077.5 yes 16
7.3 odd 6 inner 1078.2.i.d.1011.2 32
7.4 even 3 inner 1078.2.i.d.1011.1 32
7.5 odd 6 1078.2.c.c.1077.4 16
7.6 odd 2 inner 1078.2.i.d.901.11 32
11.10 odd 2 inner 1078.2.i.d.901.2 32
77.10 even 6 inner 1078.2.i.d.1011.12 32
77.32 odd 6 inner 1078.2.i.d.1011.11 32
77.54 even 6 1078.2.c.c.1077.12 yes 16
77.65 odd 6 1078.2.c.c.1077.13 yes 16
77.76 even 2 inner 1078.2.i.d.901.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1078.2.c.c.1077.4 16 7.5 odd 6
1078.2.c.c.1077.5 yes 16 7.2 even 3
1078.2.c.c.1077.12 yes 16 77.54 even 6
1078.2.c.c.1077.13 yes 16 77.65 odd 6
1078.2.i.d.901.1 32 77.76 even 2 inner
1078.2.i.d.901.2 32 11.10 odd 2 inner
1078.2.i.d.901.11 32 7.6 odd 2 inner
1078.2.i.d.901.12 32 1.1 even 1 trivial
1078.2.i.d.1011.1 32 7.4 even 3 inner
1078.2.i.d.1011.2 32 7.3 odd 6 inner
1078.2.i.d.1011.11 32 77.32 odd 6 inner
1078.2.i.d.1011.12 32 77.10 even 6 inner