Properties

Label 460.2.m.b.81.5
Level $460$
Weight $2$
Character 460.81
Analytic conductor $3.673$
Analytic rank $0$
Dimension $50$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(41,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(5\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 81.5
Character \(\chi\) \(=\) 460.81
Dual form 460.2.m.b.301.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.476853 - 3.31659i) q^{3} +(0.959493 - 0.281733i) q^{5} +(-0.777545 - 0.897335i) q^{7} +(-7.89387 - 2.31785i) q^{9} +O(q^{10})\) \(q+(0.476853 - 3.31659i) q^{3} +(0.959493 - 0.281733i) q^{5} +(-0.777545 - 0.897335i) q^{7} +(-7.89387 - 2.31785i) q^{9} +(3.68169 + 2.36608i) q^{11} +(2.32853 - 2.68726i) q^{13} +(-0.476853 - 3.31659i) q^{15} +(-3.09760 - 6.78281i) q^{17} +(-0.281041 + 0.615394i) q^{19} +(-3.34686 + 2.15090i) q^{21} +(-4.27638 + 2.17085i) q^{23} +(0.841254 - 0.540641i) q^{25} +(-7.27578 + 15.9317i) q^{27} +(2.30938 + 5.05684i) q^{29} +(1.06154 + 7.38314i) q^{31} +(9.60293 - 11.0824i) q^{33} +(-0.998858 - 0.641927i) q^{35} +(3.12643 + 0.918002i) q^{37} +(-7.80217 - 9.00418i) q^{39} +(-2.80653 + 0.824072i) q^{41} +(0.0371236 - 0.258201i) q^{43} -8.22713 q^{45} +8.95202 q^{47} +(0.795570 - 5.53331i) q^{49} +(-23.9729 + 7.03907i) q^{51} +(0.214590 + 0.247650i) q^{53} +(4.19916 + 1.23298i) q^{55} +(1.90699 + 1.22555i) q^{57} +(3.67676 - 4.24321i) q^{59} +(-1.80806 - 12.5753i) q^{61} +(4.05795 + 8.88568i) q^{63} +(1.47711 - 3.23443i) q^{65} +(5.13686 - 3.30126i) q^{67} +(5.16060 + 15.2182i) q^{69} +(8.11603 - 5.21585i) q^{71} +(1.66263 - 3.64065i) q^{73} +(-1.39193 - 3.04790i) q^{75} +(-0.739515 - 5.14344i) q^{77} +(-2.08434 + 2.40546i) q^{79} +(28.6062 + 18.3841i) q^{81} +(11.7857 + 3.46059i) q^{83} +(-4.88307 - 5.63536i) q^{85} +(17.8727 - 5.24789i) q^{87} +(-1.31347 + 9.13536i) q^{89} -4.22191 q^{91} +24.9930 q^{93} +(-0.0962803 + 0.669644i) q^{95} +(-6.30749 + 1.85205i) q^{97} +(-23.5786 - 27.2111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.476853 3.31659i 0.275311 1.91483i −0.113545 0.993533i \(-0.536220\pi\)
0.388856 0.921299i \(-0.372870\pi\)
\(4\) 0 0
\(5\) 0.959493 0.281733i 0.429098 0.125995i
\(6\) 0 0
\(7\) −0.777545 0.897335i −0.293884 0.339161i 0.589536 0.807742i \(-0.299311\pi\)
−0.883420 + 0.468582i \(0.844765\pi\)
\(8\) 0 0
\(9\) −7.89387 2.31785i −2.63129 0.772617i
\(10\) 0 0
\(11\) 3.68169 + 2.36608i 1.11007 + 0.713400i 0.961309 0.275473i \(-0.0888345\pi\)
0.148763 + 0.988873i \(0.452471\pi\)
\(12\) 0 0
\(13\) 2.32853 2.68726i 0.645817 0.745312i −0.334575 0.942369i \(-0.608593\pi\)
0.980392 + 0.197057i \(0.0631383\pi\)
\(14\) 0 0
\(15\) −0.476853 3.31659i −0.123123 0.856339i
\(16\) 0 0
\(17\) −3.09760 6.78281i −0.751279 1.64507i −0.764053 0.645154i \(-0.776793\pi\)
0.0127732 0.999918i \(-0.495934\pi\)
\(18\) 0 0
\(19\) −0.281041 + 0.615394i −0.0644752 + 0.141181i −0.939126 0.343572i \(-0.888363\pi\)
0.874651 + 0.484753i \(0.161090\pi\)
\(20\) 0 0
\(21\) −3.34686 + 2.15090i −0.730345 + 0.469364i
\(22\) 0 0
\(23\) −4.27638 + 2.17085i −0.891687 + 0.452653i
\(24\) 0 0
\(25\) 0.841254 0.540641i 0.168251 0.108128i
\(26\) 0 0
\(27\) −7.27578 + 15.9317i −1.40023 + 3.06607i
\(28\) 0 0
\(29\) 2.30938 + 5.05684i 0.428841 + 0.939032i 0.993513 + 0.113716i \(0.0362755\pi\)
−0.564672 + 0.825316i \(0.690997\pi\)
\(30\) 0 0
\(31\) 1.06154 + 7.38314i 0.190657 + 1.32605i 0.830273 + 0.557357i \(0.188184\pi\)
−0.639616 + 0.768695i \(0.720907\pi\)
\(32\) 0 0
\(33\) 9.60293 11.0824i 1.67166 1.92919i
\(34\) 0 0
\(35\) −0.998858 0.641927i −0.168838 0.108505i
\(36\) 0 0
\(37\) 3.12643 + 0.918002i 0.513982 + 0.150919i 0.528430 0.848977i \(-0.322781\pi\)
−0.0144482 + 0.999896i \(0.504599\pi\)
\(38\) 0 0
\(39\) −7.80217 9.00418i −1.24935 1.44182i
\(40\) 0 0
\(41\) −2.80653 + 0.824072i −0.438307 + 0.128699i −0.493439 0.869781i \(-0.664260\pi\)
0.0551318 + 0.998479i \(0.482442\pi\)
\(42\) 0 0
\(43\) 0.0371236 0.258201i 0.00566130 0.0393752i −0.986795 0.161974i \(-0.948214\pi\)
0.992456 + 0.122599i \(0.0391229\pi\)
\(44\) 0 0
\(45\) −8.22713 −1.22643
\(46\) 0 0
\(47\) 8.95202 1.30579 0.652893 0.757450i \(-0.273555\pi\)
0.652893 + 0.757450i \(0.273555\pi\)
\(48\) 0 0
\(49\) 0.795570 5.53331i 0.113653 0.790473i
\(50\) 0 0
\(51\) −23.9729 + 7.03907i −3.35687 + 0.985667i
\(52\) 0 0
\(53\) 0.214590 + 0.247650i 0.0294762 + 0.0340174i 0.770296 0.637686i \(-0.220108\pi\)
−0.740820 + 0.671704i \(0.765563\pi\)
\(54\) 0 0
\(55\) 4.19916 + 1.23298i 0.566214 + 0.166256i
\(56\) 0 0
\(57\) 1.90699 + 1.22555i 0.252587 + 0.162328i
\(58\) 0 0
\(59\) 3.67676 4.24321i 0.478673 0.552419i −0.464130 0.885767i \(-0.653633\pi\)
0.942804 + 0.333348i \(0.108179\pi\)
\(60\) 0 0
\(61\) −1.80806 12.5753i −0.231498 1.61010i −0.691630 0.722252i \(-0.743107\pi\)
0.460132 0.887850i \(-0.347802\pi\)
\(62\) 0 0
\(63\) 4.05795 + 8.88568i 0.511254 + 1.11949i
\(64\) 0 0
\(65\) 1.47711 3.23443i 0.183214 0.401182i
\(66\) 0 0
\(67\) 5.13686 3.30126i 0.627567 0.403313i −0.187841 0.982199i \(-0.560149\pi\)
0.815408 + 0.578887i \(0.196513\pi\)
\(68\) 0 0
\(69\) 5.16060 + 15.2182i 0.621263 + 1.83205i
\(70\) 0 0
\(71\) 8.11603 5.21585i 0.963195 0.619008i 0.0383145 0.999266i \(-0.487801\pi\)
0.924880 + 0.380258i \(0.124165\pi\)
\(72\) 0 0
\(73\) 1.66263 3.64065i 0.194596 0.426106i −0.787032 0.616913i \(-0.788383\pi\)
0.981628 + 0.190807i \(0.0611105\pi\)
\(74\) 0 0
\(75\) −1.39193 3.04790i −0.160726 0.351941i
\(76\) 0 0
\(77\) −0.739515 5.14344i −0.0842756 0.586150i
\(78\) 0 0
\(79\) −2.08434 + 2.40546i −0.234507 + 0.270635i −0.860790 0.508960i \(-0.830030\pi\)
0.626283 + 0.779596i \(0.284575\pi\)
\(80\) 0 0
\(81\) 28.6062 + 18.3841i 3.17847 + 2.04268i
\(82\) 0 0
\(83\) 11.7857 + 3.46059i 1.29365 + 0.379850i 0.854915 0.518767i \(-0.173609\pi\)
0.438734 + 0.898617i \(0.355427\pi\)
\(84\) 0 0
\(85\) −4.88307 5.63536i −0.529643 0.611241i
\(86\) 0 0
\(87\) 17.8727 5.24789i 1.91615 0.562633i
\(88\) 0 0
\(89\) −1.31347 + 9.13536i −0.139227 + 0.968347i 0.793707 + 0.608300i \(0.208148\pi\)
−0.932934 + 0.360047i \(0.882761\pi\)
\(90\) 0 0
\(91\) −4.22191 −0.442576
\(92\) 0 0
\(93\) 24.9930 2.59166
\(94\) 0 0
\(95\) −0.0962803 + 0.669644i −0.00987815 + 0.0687041i
\(96\) 0 0
\(97\) −6.30749 + 1.85205i −0.640428 + 0.188047i −0.585794 0.810460i \(-0.699217\pi\)
−0.0546339 + 0.998506i \(0.517399\pi\)
\(98\) 0 0
\(99\) −23.5786 27.2111i −2.36974 2.73482i
\(100\) 0 0
\(101\) 15.6564 + 4.59713i 1.55787 + 0.457432i 0.943441 0.331541i \(-0.107569\pi\)
0.614428 + 0.788973i \(0.289387\pi\)
\(102\) 0 0
\(103\) −5.25957 3.38012i −0.518240 0.333053i 0.255235 0.966879i \(-0.417847\pi\)
−0.773476 + 0.633826i \(0.781483\pi\)
\(104\) 0 0
\(105\) −2.60531 + 3.00669i −0.254253 + 0.293423i
\(106\) 0 0
\(107\) 0.909396 + 6.32499i 0.0879146 + 0.611460i 0.985380 + 0.170374i \(0.0544975\pi\)
−0.897465 + 0.441086i \(0.854593\pi\)
\(108\) 0 0
\(109\) −4.10505 8.98881i −0.393193 0.860972i −0.997915 0.0645360i \(-0.979443\pi\)
0.604723 0.796436i \(-0.293284\pi\)
\(110\) 0 0
\(111\) 4.53548 9.93131i 0.430489 0.942639i
\(112\) 0 0
\(113\) −15.1488 + 9.73552i −1.42508 + 0.915841i −0.425133 + 0.905131i \(0.639773\pi\)
−0.999943 + 0.0107101i \(0.996591\pi\)
\(114\) 0 0
\(115\) −3.49156 + 3.28771i −0.325589 + 0.306580i
\(116\) 0 0
\(117\) −24.6098 + 15.8157i −2.27517 + 1.46216i
\(118\) 0 0
\(119\) −3.67792 + 8.05353i −0.337155 + 0.738266i
\(120\) 0 0
\(121\) 3.38695 + 7.41639i 0.307905 + 0.674218i
\(122\) 0 0
\(123\) 1.39480 + 9.70107i 0.125765 + 0.874716i
\(124\) 0 0
\(125\) 0.654861 0.755750i 0.0585725 0.0675963i
\(126\) 0 0
\(127\) 0.995004 + 0.639450i 0.0882923 + 0.0567420i 0.584042 0.811723i \(-0.301470\pi\)
−0.495750 + 0.868465i \(0.665107\pi\)
\(128\) 0 0
\(129\) −0.838642 0.246247i −0.0738383 0.0216809i
\(130\) 0 0
\(131\) 4.93750 + 5.69817i 0.431391 + 0.497852i 0.929273 0.369393i \(-0.120434\pi\)
−0.497882 + 0.867245i \(0.665889\pi\)
\(132\) 0 0
\(133\) 0.770736 0.226309i 0.0668313 0.0196234i
\(134\) 0 0
\(135\) −2.49257 + 17.3362i −0.214526 + 1.49206i
\(136\) 0 0
\(137\) 6.34946 0.542471 0.271235 0.962513i \(-0.412568\pi\)
0.271235 + 0.962513i \(0.412568\pi\)
\(138\) 0 0
\(139\) −5.49299 −0.465909 −0.232955 0.972488i \(-0.574839\pi\)
−0.232955 + 0.972488i \(0.574839\pi\)
\(140\) 0 0
\(141\) 4.26880 29.6901i 0.359497 2.50036i
\(142\) 0 0
\(143\) 14.9312 4.38419i 1.24861 0.366625i
\(144\) 0 0
\(145\) 3.64051 + 4.20138i 0.302328 + 0.348905i
\(146\) 0 0
\(147\) −17.9723 5.27715i −1.48233 0.435252i
\(148\) 0 0
\(149\) −2.03314 1.30662i −0.166561 0.107042i 0.454705 0.890642i \(-0.349745\pi\)
−0.621266 + 0.783600i \(0.713381\pi\)
\(150\) 0 0
\(151\) 3.78272 4.36549i 0.307833 0.355258i −0.580662 0.814145i \(-0.697206\pi\)
0.888495 + 0.458887i \(0.151752\pi\)
\(152\) 0 0
\(153\) 8.73056 + 60.7224i 0.705824 + 4.90911i
\(154\) 0 0
\(155\) 3.09861 + 6.78500i 0.248886 + 0.544985i
\(156\) 0 0
\(157\) 5.52527 12.0987i 0.440964 0.965578i −0.550456 0.834864i \(-0.685546\pi\)
0.991420 0.130713i \(-0.0417267\pi\)
\(158\) 0 0
\(159\) 0.923682 0.593614i 0.0732527 0.0470767i
\(160\) 0 0
\(161\) 5.27306 + 2.14941i 0.415575 + 0.169397i
\(162\) 0 0
\(163\) −18.0420 + 11.5949i −1.41316 + 0.908181i −0.999997 0.00247816i \(-0.999211\pi\)
−0.413160 + 0.910659i \(0.635575\pi\)
\(164\) 0 0
\(165\) 6.09168 13.3389i 0.474237 1.03843i
\(166\) 0 0
\(167\) 4.56587 + 9.99786i 0.353317 + 0.773657i 0.999941 + 0.0108482i \(0.00345315\pi\)
−0.646624 + 0.762809i \(0.723820\pi\)
\(168\) 0 0
\(169\) 0.0507481 + 0.352961i 0.00390370 + 0.0271508i
\(170\) 0 0
\(171\) 3.64489 4.20643i 0.278732 0.321674i
\(172\) 0 0
\(173\) 9.61592 + 6.17977i 0.731084 + 0.469839i 0.852477 0.522765i \(-0.175100\pi\)
−0.121392 + 0.992605i \(0.538736\pi\)
\(174\) 0 0
\(175\) −1.13925 0.334514i −0.0861191 0.0252868i
\(176\) 0 0
\(177\) −12.3197 14.2177i −0.926004 1.06867i
\(178\) 0 0
\(179\) −23.2970 + 6.84061i −1.74130 + 0.511291i −0.989049 0.147588i \(-0.952849\pi\)
−0.752249 + 0.658879i \(0.771031\pi\)
\(180\) 0 0
\(181\) 0.378349 2.63147i 0.0281225 0.195596i −0.970917 0.239416i \(-0.923044\pi\)
0.999039 + 0.0438205i \(0.0139530\pi\)
\(182\) 0 0
\(183\) −42.5692 −3.14681
\(184\) 0 0
\(185\) 3.25842 0.239564
\(186\) 0 0
\(187\) 4.64424 32.3014i 0.339620 2.36211i
\(188\) 0 0
\(189\) 19.9534 5.85883i 1.45139 0.426167i
\(190\) 0 0
\(191\) −7.14252 8.24291i −0.516815 0.596436i 0.436016 0.899939i \(-0.356389\pi\)
−0.952830 + 0.303503i \(0.901844\pi\)
\(192\) 0 0
\(193\) 5.85222 + 1.71837i 0.421252 + 0.123691i 0.485487 0.874244i \(-0.338642\pi\)
−0.0642346 + 0.997935i \(0.520461\pi\)
\(194\) 0 0
\(195\) −10.0229 6.44133i −0.717755 0.461273i
\(196\) 0 0
\(197\) 1.33340 1.53883i 0.0950009 0.109637i −0.706258 0.707954i \(-0.749618\pi\)
0.801259 + 0.598317i \(0.204164\pi\)
\(198\) 0 0
\(199\) 0.564255 + 3.92448i 0.0399990 + 0.278199i 0.999998 0.00180308i \(-0.000573939\pi\)
−0.959999 + 0.280002i \(0.909665\pi\)
\(200\) 0 0
\(201\) −8.49938 18.6110i −0.599500 1.31272i
\(202\) 0 0
\(203\) 2.74203 6.00421i 0.192453 0.421413i
\(204\) 0 0
\(205\) −2.46068 + 1.58138i −0.171861 + 0.110449i
\(206\) 0 0
\(207\) 38.7889 7.22439i 2.69601 0.502130i
\(208\) 0 0
\(209\) −2.49078 + 1.60072i −0.172291 + 0.110724i
\(210\) 0 0
\(211\) −3.01935 + 6.61145i −0.207861 + 0.455151i −0.984634 0.174628i \(-0.944128\pi\)
0.776774 + 0.629780i \(0.216855\pi\)
\(212\) 0 0
\(213\) −13.4287 29.4047i −0.920117 2.01478i
\(214\) 0 0
\(215\) −0.0371236 0.258201i −0.00253181 0.0176091i
\(216\) 0 0
\(217\) 5.79976 6.69328i 0.393713 0.454369i
\(218\) 0 0
\(219\) −11.2817 7.25030i −0.762346 0.489930i
\(220\) 0 0
\(221\) −25.4400 7.46987i −1.71128 0.502478i
\(222\) 0 0
\(223\) 1.01476 + 1.17109i 0.0679531 + 0.0784221i 0.788708 0.614768i \(-0.210750\pi\)
−0.720755 + 0.693190i \(0.756205\pi\)
\(224\) 0 0
\(225\) −7.89387 + 2.31785i −0.526258 + 0.154523i
\(226\) 0 0
\(227\) −2.06611 + 14.3701i −0.137133 + 0.953778i 0.798800 + 0.601597i \(0.205469\pi\)
−0.935932 + 0.352180i \(0.885440\pi\)
\(228\) 0 0
\(229\) 0.521668 0.0344728 0.0172364 0.999851i \(-0.494513\pi\)
0.0172364 + 0.999851i \(0.494513\pi\)
\(230\) 0 0
\(231\) −17.4113 −1.14558
\(232\) 0 0
\(233\) −2.46616 + 17.1525i −0.161563 + 1.12370i 0.734124 + 0.679015i \(0.237593\pi\)
−0.895688 + 0.444683i \(0.853316\pi\)
\(234\) 0 0
\(235\) 8.58940 2.52207i 0.560310 0.164522i
\(236\) 0 0
\(237\) 6.98399 + 8.05995i 0.453659 + 0.523550i
\(238\) 0 0
\(239\) 22.5875 + 6.63229i 1.46106 + 0.429007i 0.913183 0.407549i \(-0.133617\pi\)
0.547881 + 0.836556i \(0.315435\pi\)
\(240\) 0 0
\(241\) 19.8246 + 12.7405i 1.27701 + 0.820686i 0.990516 0.137395i \(-0.0438730\pi\)
0.286496 + 0.958081i \(0.407509\pi\)
\(242\) 0 0
\(243\) 40.2047 46.3987i 2.57913 2.97648i
\(244\) 0 0
\(245\) −0.795570 5.53331i −0.0508271 0.353510i
\(246\) 0 0
\(247\) 0.999313 + 2.18819i 0.0635848 + 0.139231i
\(248\) 0 0
\(249\) 17.0974 37.4381i 1.08350 2.37254i
\(250\) 0 0
\(251\) −19.1642 + 12.3161i −1.20963 + 0.777384i −0.980597 0.196034i \(-0.937194\pi\)
−0.229036 + 0.973418i \(0.573557\pi\)
\(252\) 0 0
\(253\) −20.8807 2.12586i −1.31276 0.133652i
\(254\) 0 0
\(255\) −21.0187 + 13.5079i −1.31624 + 0.845896i
\(256\) 0 0
\(257\) 3.34037 7.31440i 0.208367 0.456259i −0.776377 0.630268i \(-0.782945\pi\)
0.984744 + 0.174009i \(0.0556722\pi\)
\(258\) 0 0
\(259\) −1.60718 3.51924i −0.0998655 0.218675i
\(260\) 0 0
\(261\) −6.50897 45.2709i −0.402895 2.80220i
\(262\) 0 0
\(263\) −7.36274 + 8.49705i −0.454006 + 0.523951i −0.935894 0.352282i \(-0.885406\pi\)
0.481888 + 0.876233i \(0.339951\pi\)
\(264\) 0 0
\(265\) 0.275669 + 0.177162i 0.0169342 + 0.0108830i
\(266\) 0 0
\(267\) 29.6719 + 8.71245i 1.81589 + 0.533193i
\(268\) 0 0
\(269\) 8.27290 + 9.54744i 0.504408 + 0.582117i 0.949658 0.313289i \(-0.101431\pi\)
−0.445250 + 0.895406i \(0.646885\pi\)
\(270\) 0 0
\(271\) 13.6644 4.01223i 0.830053 0.243726i 0.161013 0.986952i \(-0.448524\pi\)
0.669040 + 0.743227i \(0.266706\pi\)
\(272\) 0 0
\(273\) −2.01323 + 14.0023i −0.121846 + 0.847459i
\(274\) 0 0
\(275\) 4.37643 0.263909
\(276\) 0 0
\(277\) −27.3997 −1.64629 −0.823143 0.567834i \(-0.807781\pi\)
−0.823143 + 0.567834i \(0.807781\pi\)
\(278\) 0 0
\(279\) 8.73339 60.7421i 0.522854 3.63653i
\(280\) 0 0
\(281\) −19.0616 + 5.59698i −1.13712 + 0.333888i −0.795502 0.605952i \(-0.792793\pi\)
−0.341616 + 0.939839i \(0.610974\pi\)
\(282\) 0 0
\(283\) 11.0549 + 12.7581i 0.657147 + 0.758389i 0.982308 0.187270i \(-0.0599639\pi\)
−0.325161 + 0.945659i \(0.605418\pi\)
\(284\) 0 0
\(285\) 2.17502 + 0.638644i 0.128837 + 0.0378300i
\(286\) 0 0
\(287\) 2.92168 + 1.87765i 0.172461 + 0.110834i
\(288\) 0 0
\(289\) −25.2787 + 29.1732i −1.48698 + 1.71607i
\(290\) 0 0
\(291\) 3.13472 + 21.8025i 0.183761 + 1.27808i
\(292\) 0 0
\(293\) 4.96974 + 10.8822i 0.290336 + 0.635746i 0.997451 0.0713517i \(-0.0227313\pi\)
−0.707116 + 0.707098i \(0.750004\pi\)
\(294\) 0 0
\(295\) 2.33238 5.10719i 0.135796 0.297352i
\(296\) 0 0
\(297\) −64.4829 + 41.4407i −3.74168 + 2.40463i
\(298\) 0 0
\(299\) −4.12402 + 16.5466i −0.238498 + 0.956916i
\(300\) 0 0
\(301\) −0.260558 + 0.167450i −0.0150183 + 0.00965167i
\(302\) 0 0
\(303\) 22.7126 49.7336i 1.30480 2.85712i
\(304\) 0 0
\(305\) −5.27769 11.5565i −0.302200 0.661725i
\(306\) 0 0
\(307\) −1.68761 11.7376i −0.0963169 0.669899i −0.979585 0.201030i \(-0.935571\pi\)
0.883268 0.468868i \(-0.155338\pi\)
\(308\) 0 0
\(309\) −13.7185 + 15.8320i −0.780418 + 0.900650i
\(310\) 0 0
\(311\) −3.30266 2.12249i −0.187277 0.120356i 0.443643 0.896204i \(-0.353686\pi\)
−0.630920 + 0.775848i \(0.717322\pi\)
\(312\) 0 0
\(313\) −29.3419 8.61555i −1.65850 0.486979i −0.687525 0.726161i \(-0.741303\pi\)
−0.970975 + 0.239182i \(0.923121\pi\)
\(314\) 0 0
\(315\) 6.39696 + 7.38249i 0.360428 + 0.415956i
\(316\) 0 0
\(317\) 1.35653 0.398314i 0.0761905 0.0223715i −0.243415 0.969922i \(-0.578268\pi\)
0.319606 + 0.947551i \(0.396450\pi\)
\(318\) 0 0
\(319\) −3.46246 + 24.0819i −0.193860 + 1.34833i
\(320\) 0 0
\(321\) 21.4110 1.19505
\(322\) 0 0
\(323\) 5.04465 0.280692
\(324\) 0 0
\(325\) 0.506037 3.51956i 0.0280699 0.195230i
\(326\) 0 0
\(327\) −31.7697 + 9.32842i −1.75687 + 0.515863i
\(328\) 0 0
\(329\) −6.96060 8.03296i −0.383750 0.442871i
\(330\) 0 0
\(331\) −22.3304 6.55681i −1.22739 0.360395i −0.397127 0.917764i \(-0.629993\pi\)
−0.830265 + 0.557369i \(0.811811\pi\)
\(332\) 0 0
\(333\) −22.5518 14.4932i −1.23583 0.794221i
\(334\) 0 0
\(335\) 3.99871 4.61475i 0.218473 0.252131i
\(336\) 0 0
\(337\) −3.08117 21.4300i −0.167842 1.16737i −0.883334 0.468744i \(-0.844707\pi\)
0.715492 0.698621i \(-0.246203\pi\)
\(338\) 0 0
\(339\) 25.0650 + 54.8846i 1.36134 + 2.98092i
\(340\) 0 0
\(341\) −13.5609 + 29.6941i −0.734361 + 1.60803i
\(342\) 0 0
\(343\) −12.5758 + 8.08199i −0.679031 + 0.436387i
\(344\) 0 0
\(345\) 9.23901 + 13.1478i 0.497411 + 0.707854i
\(346\) 0 0
\(347\) 19.5292 12.5506i 1.04838 0.673753i 0.101335 0.994852i \(-0.467689\pi\)
0.947046 + 0.321099i \(0.104052\pi\)
\(348\) 0 0
\(349\) −1.14484 + 2.50684i −0.0612816 + 0.134188i −0.937795 0.347189i \(-0.887136\pi\)
0.876513 + 0.481377i \(0.159863\pi\)
\(350\) 0 0
\(351\) 25.8709 + 56.6494i 1.38089 + 3.02372i
\(352\) 0 0
\(353\) −4.83108 33.6009i −0.257132 1.78839i −0.553016 0.833171i \(-0.686523\pi\)
0.295884 0.955224i \(-0.404386\pi\)
\(354\) 0 0
\(355\) 6.31779 7.29112i 0.335314 0.386973i
\(356\) 0 0
\(357\) 24.9564 + 16.0385i 1.32083 + 0.848847i
\(358\) 0 0
\(359\) 21.6373 + 6.35329i 1.14197 + 0.335314i 0.797403 0.603447i \(-0.206206\pi\)
0.344571 + 0.938760i \(0.388025\pi\)
\(360\) 0 0
\(361\) 12.1426 + 14.0133i 0.639086 + 0.737544i
\(362\) 0 0
\(363\) 26.2122 7.69659i 1.37578 0.403966i
\(364\) 0 0
\(365\) 0.569591 3.96159i 0.0298138 0.207359i
\(366\) 0 0
\(367\) −32.4307 −1.69287 −0.846436 0.532491i \(-0.821256\pi\)
−0.846436 + 0.532491i \(0.821256\pi\)
\(368\) 0 0
\(369\) 24.0645 1.25275
\(370\) 0 0
\(371\) 0.0553717 0.385119i 0.00287476 0.0199944i
\(372\) 0 0
\(373\) 1.39550 0.409756i 0.0722563 0.0212164i −0.245405 0.969421i \(-0.578921\pi\)
0.317661 + 0.948204i \(0.397103\pi\)
\(374\) 0 0
\(375\) −2.19424 2.53228i −0.113310 0.130767i
\(376\) 0 0
\(377\) 18.9665 + 5.56907i 0.976825 + 0.286822i
\(378\) 0 0
\(379\) −4.26694 2.74219i −0.219178 0.140857i 0.426445 0.904514i \(-0.359766\pi\)
−0.645623 + 0.763656i \(0.723402\pi\)
\(380\) 0 0
\(381\) 2.59526 2.99509i 0.132959 0.153443i
\(382\) 0 0
\(383\) 3.54973 + 24.6889i 0.181383 + 1.26155i 0.853497 + 0.521098i \(0.174477\pi\)
−0.672114 + 0.740448i \(0.734613\pi\)
\(384\) 0 0
\(385\) −2.15864 4.72675i −0.110014 0.240898i
\(386\) 0 0
\(387\) −0.891519 + 1.95216i −0.0453185 + 0.0992336i
\(388\) 0 0
\(389\) −2.45119 + 1.57528i −0.124280 + 0.0798700i −0.601304 0.799020i \(-0.705352\pi\)
0.477024 + 0.878890i \(0.341716\pi\)
\(390\) 0 0
\(391\) 27.9710 + 22.2814i 1.41455 + 1.12682i
\(392\) 0 0
\(393\) 21.2529 13.6584i 1.07207 0.688977i
\(394\) 0 0
\(395\) −1.32222 + 2.89525i −0.0665279 + 0.145676i
\(396\) 0 0
\(397\) −1.09815 2.40462i −0.0551147 0.120684i 0.880071 0.474842i \(-0.157495\pi\)
−0.935186 + 0.354158i \(0.884768\pi\)
\(398\) 0 0
\(399\) −0.383044 2.66413i −0.0191762 0.133373i
\(400\) 0 0
\(401\) 10.2048 11.7770i 0.509603 0.588113i −0.441394 0.897313i \(-0.645516\pi\)
0.950997 + 0.309200i \(0.100061\pi\)
\(402\) 0 0
\(403\) 22.3122 + 14.3392i 1.11145 + 0.714287i
\(404\) 0 0
\(405\) 32.6268 + 9.58011i 1.62124 + 0.476039i
\(406\) 0 0
\(407\) 9.33848 + 10.7772i 0.462891 + 0.534205i
\(408\) 0 0
\(409\) −33.8135 + 9.92854i −1.67197 + 0.490935i −0.974256 0.225443i \(-0.927617\pi\)
−0.697713 + 0.716377i \(0.745799\pi\)
\(410\) 0 0
\(411\) 3.02776 21.0585i 0.149348 1.03874i
\(412\) 0 0
\(413\) −6.66642 −0.328033
\(414\) 0 0
\(415\) 12.2833 0.602962
\(416\) 0 0
\(417\) −2.61935 + 18.2180i −0.128270 + 0.892137i
\(418\) 0 0
\(419\) −3.71855 + 1.09187i −0.181663 + 0.0533411i −0.371299 0.928513i \(-0.621087\pi\)
0.189636 + 0.981855i \(0.439269\pi\)
\(420\) 0 0
\(421\) 5.68207 + 6.55746i 0.276927 + 0.319591i 0.877126 0.480259i \(-0.159457\pi\)
−0.600199 + 0.799851i \(0.704912\pi\)
\(422\) 0 0
\(423\) −70.6661 20.7494i −3.43590 1.00887i
\(424\) 0 0
\(425\) −6.27293 4.03137i −0.304282 0.195550i
\(426\) 0 0
\(427\) −9.87841 + 11.4003i −0.478050 + 0.551699i
\(428\) 0 0
\(429\) −7.42057 51.6112i −0.358268 2.49181i
\(430\) 0 0
\(431\) −8.80923 19.2895i −0.424326 0.929144i −0.994214 0.107421i \(-0.965741\pi\)
0.569888 0.821722i \(-0.306987\pi\)
\(432\) 0 0
\(433\) 9.62728 21.0808i 0.462658 1.01308i −0.524216 0.851585i \(-0.675642\pi\)
0.986874 0.161493i \(-0.0516311\pi\)
\(434\) 0 0
\(435\) 15.6702 10.0706i 0.751329 0.482850i
\(436\) 0 0
\(437\) −0.134088 3.24175i −0.00641432 0.155074i
\(438\) 0 0
\(439\) 17.1215 11.0033i 0.817162 0.525158i −0.0640124 0.997949i \(-0.520390\pi\)
0.881175 + 0.472791i \(0.156753\pi\)
\(440\) 0 0
\(441\) −19.1055 + 41.8353i −0.909787 + 1.99216i
\(442\) 0 0
\(443\) −12.9777 28.4171i −0.616587 1.35014i −0.917976 0.396636i \(-0.870177\pi\)
0.301389 0.953501i \(-0.402550\pi\)
\(444\) 0 0
\(445\) 1.31347 + 9.13536i 0.0622643 + 0.433058i
\(446\) 0 0
\(447\) −5.30301 + 6.12000i −0.250824 + 0.289466i
\(448\) 0 0
\(449\) −1.40518 0.903054i −0.0663145 0.0426177i 0.507063 0.861909i \(-0.330731\pi\)
−0.573378 + 0.819291i \(0.694367\pi\)
\(450\) 0 0
\(451\) −12.2826 3.60650i −0.578365 0.169823i
\(452\) 0 0
\(453\) −12.6747 14.6274i −0.595510 0.687255i
\(454\) 0 0
\(455\) −4.05089 + 1.18945i −0.189909 + 0.0557622i
\(456\) 0 0
\(457\) 2.47906 17.2422i 0.115966 0.806558i −0.845960 0.533246i \(-0.820972\pi\)
0.961925 0.273312i \(-0.0881191\pi\)
\(458\) 0 0
\(459\) 130.599 6.09586
\(460\) 0 0
\(461\) −9.03588 −0.420843 −0.210421 0.977611i \(-0.567484\pi\)
−0.210421 + 0.977611i \(0.567484\pi\)
\(462\) 0 0
\(463\) −4.57891 + 31.8470i −0.212800 + 1.48006i 0.550946 + 0.834541i \(0.314267\pi\)
−0.763746 + 0.645517i \(0.776642\pi\)
\(464\) 0 0
\(465\) 23.9806 7.04135i 1.11207 0.326535i
\(466\) 0 0
\(467\) −1.47939 1.70731i −0.0684580 0.0790048i 0.720487 0.693468i \(-0.243918\pi\)
−0.788946 + 0.614463i \(0.789373\pi\)
\(468\) 0 0
\(469\) −6.95647 2.04260i −0.321220 0.0943187i
\(470\) 0 0
\(471\) −37.4915 24.0943i −1.72752 1.11021i
\(472\) 0 0
\(473\) 0.747601 0.862777i 0.0343747 0.0396705i
\(474\) 0 0
\(475\) 0.0962803 + 0.669644i 0.00441764 + 0.0307254i
\(476\) 0 0
\(477\) −1.11993 2.45231i −0.0512782 0.112284i
\(478\) 0 0
\(479\) −12.7690 + 27.9603i −0.583433 + 1.27754i 0.355898 + 0.934525i \(0.384175\pi\)
−0.939330 + 0.343014i \(0.888552\pi\)
\(480\) 0 0
\(481\) 9.74688 6.26394i 0.444419 0.285611i
\(482\) 0 0
\(483\) 9.64318 16.4636i 0.438780 0.749119i
\(484\) 0 0
\(485\) −5.53021 + 3.55405i −0.251114 + 0.161381i
\(486\) 0 0
\(487\) 12.2074 26.7304i 0.553168 1.21127i −0.402118 0.915588i \(-0.631726\pi\)
0.955287 0.295682i \(-0.0955468\pi\)
\(488\) 0 0
\(489\) 29.8520 + 65.3668i 1.34995 + 2.95599i
\(490\) 0 0
\(491\) 1.12311 + 7.81139i 0.0506852 + 0.352523i 0.999344 + 0.0362213i \(0.0115321\pi\)
−0.948659 + 0.316302i \(0.897559\pi\)
\(492\) 0 0
\(493\) 27.1460 31.3282i 1.22260 1.41095i
\(494\) 0 0
\(495\) −30.2897 19.4660i −1.36142 0.874933i
\(496\) 0 0
\(497\) −10.9909 3.22723i −0.493011 0.144761i
\(498\) 0 0
\(499\) −9.86873 11.3891i −0.441785 0.509847i 0.490565 0.871405i \(-0.336790\pi\)
−0.932350 + 0.361558i \(0.882245\pi\)
\(500\) 0 0
\(501\) 35.3360 10.3756i 1.57870 0.463547i
\(502\) 0 0
\(503\) −1.60842 + 11.1868i −0.0717160 + 0.498796i 0.922029 + 0.387121i \(0.126531\pi\)
−0.993745 + 0.111675i \(0.964379\pi\)
\(504\) 0 0
\(505\) 16.3174 0.726113
\(506\) 0 0
\(507\) 1.19482 0.0530640
\(508\) 0 0
\(509\) −2.46057 + 17.1136i −0.109063 + 0.758548i 0.859743 + 0.510727i \(0.170624\pi\)
−0.968806 + 0.247821i \(0.920285\pi\)
\(510\) 0 0
\(511\) −4.55965 + 1.33883i −0.201707 + 0.0592265i
\(512\) 0 0
\(513\) −7.75950 8.95494i −0.342590 0.395370i
\(514\) 0 0
\(515\) −5.99881 1.76141i −0.264339 0.0776169i
\(516\) 0 0
\(517\) 32.9586 + 21.1812i 1.44952 + 0.931547i
\(518\) 0 0
\(519\) 25.0811 28.9452i 1.10094 1.27055i
\(520\) 0 0
\(521\) −0.00980726 0.0682110i −0.000429664 0.00298838i 0.989605 0.143809i \(-0.0459351\pi\)
−0.990035 + 0.140820i \(0.955026\pi\)
\(522\) 0 0
\(523\) −3.18939 6.98379i −0.139462 0.305380i 0.826994 0.562211i \(-0.190049\pi\)
−0.966456 + 0.256831i \(0.917322\pi\)
\(524\) 0 0
\(525\) −1.65270 + 3.61890i −0.0721296 + 0.157942i
\(526\) 0 0
\(527\) 46.7902 30.0702i 2.03821 1.30988i
\(528\) 0 0
\(529\) 13.5748 18.5667i 0.590211 0.807249i
\(530\) 0 0
\(531\) −38.8590 + 24.9732i −1.68634 + 1.08374i
\(532\) 0 0
\(533\) −4.32059 + 9.46076i −0.187145 + 0.409791i
\(534\) 0 0
\(535\) 2.65451 + 5.81257i 0.114765 + 0.251300i
\(536\) 0 0
\(537\) 11.5782 + 80.5284i 0.499638 + 3.47506i
\(538\) 0 0
\(539\) 16.0213 18.4896i 0.690086 0.796402i
\(540\) 0 0
\(541\) 36.9179 + 23.7257i 1.58723 + 1.02005i 0.972967 + 0.230944i \(0.0741814\pi\)
0.614259 + 0.789104i \(0.289455\pi\)
\(542\) 0 0
\(543\) −8.54709 2.50965i −0.366791 0.107700i
\(544\) 0 0
\(545\) −6.47121 7.46818i −0.277196 0.319902i
\(546\) 0 0
\(547\) −2.55632 + 0.750602i −0.109300 + 0.0320934i −0.335925 0.941889i \(-0.609049\pi\)
0.226625 + 0.973982i \(0.427231\pi\)
\(548\) 0 0
\(549\) −14.8751 + 103.459i −0.634854 + 4.41551i
\(550\) 0 0
\(551\) −3.76098 −0.160223
\(552\) 0 0
\(553\) 3.77917 0.160707
\(554\) 0 0
\(555\) 1.55379 10.8068i 0.0659545 0.458724i
\(556\) 0 0
\(557\) −20.7800 + 6.10156i −0.880477 + 0.258531i −0.690565 0.723270i \(-0.742638\pi\)
−0.189911 + 0.981801i \(0.560820\pi\)
\(558\) 0 0
\(559\) −0.607409 0.700988i −0.0256907 0.0296486i
\(560\) 0 0
\(561\) −104.916 30.8060i −4.42954 1.30063i
\(562\) 0 0
\(563\) 14.1247 + 9.07737i 0.595283 + 0.382565i 0.803313 0.595557i \(-0.203069\pi\)
−0.208030 + 0.978123i \(0.566705\pi\)
\(564\) 0 0
\(565\) −11.7923 + 13.6091i −0.496107 + 0.572538i
\(566\) 0 0
\(567\) −5.74593 39.9638i −0.241306 1.67832i
\(568\) 0 0
\(569\) 0.748818 + 1.63968i 0.0313921 + 0.0687391i 0.924679 0.380749i \(-0.124334\pi\)
−0.893286 + 0.449488i \(0.851606\pi\)
\(570\) 0 0
\(571\) −19.7417 + 43.2282i −0.826163 + 1.80904i −0.316802 + 0.948492i \(0.602609\pi\)
−0.509361 + 0.860553i \(0.670118\pi\)
\(572\) 0 0
\(573\) −30.7442 + 19.7581i −1.28436 + 0.825407i
\(574\) 0 0
\(575\) −2.42387 + 4.13822i −0.101082 + 0.172576i
\(576\) 0 0
\(577\) 10.1894 6.54836i 0.424192 0.272612i −0.311080 0.950384i \(-0.600691\pi\)
0.735272 + 0.677772i \(0.237054\pi\)
\(578\) 0 0
\(579\) 8.48976 18.5900i 0.352823 0.772574i
\(580\) 0 0
\(581\) −6.05860 13.2665i −0.251353 0.550387i
\(582\) 0 0
\(583\) 0.204095 + 1.41951i 0.00845274 + 0.0587901i
\(584\) 0 0
\(585\) −19.1571 + 22.1085i −0.792048 + 0.914072i
\(586\) 0 0
\(587\) −5.91913 3.80399i −0.244309 0.157008i 0.412757 0.910841i \(-0.364566\pi\)
−0.657065 + 0.753834i \(0.728202\pi\)
\(588\) 0 0
\(589\) −4.84187 1.42170i −0.199506 0.0585802i
\(590\) 0 0
\(591\) −4.46782 5.15613i −0.183781 0.212095i
\(592\) 0 0
\(593\) −11.8213 + 3.47104i −0.485442 + 0.142539i −0.515290 0.857016i \(-0.672316\pi\)
0.0298482 + 0.999554i \(0.490498\pi\)
\(594\) 0 0
\(595\) −1.26000 + 8.76349i −0.0516550 + 0.359268i
\(596\) 0 0
\(597\) 13.2849 0.543716
\(598\) 0 0
\(599\) −2.69791 −0.110234 −0.0551168 0.998480i \(-0.517553\pi\)
−0.0551168 + 0.998480i \(0.517553\pi\)
\(600\) 0 0
\(601\) −0.396108 + 2.75499i −0.0161576 + 0.112378i −0.996304 0.0858962i \(-0.972625\pi\)
0.980147 + 0.198275i \(0.0635338\pi\)
\(602\) 0 0
\(603\) −48.2015 + 14.1532i −1.96292 + 0.576365i
\(604\) 0 0
\(605\) 5.33920 + 6.16176i 0.217069 + 0.250511i
\(606\) 0 0
\(607\) −22.1795 6.51248i −0.900237 0.264333i −0.201311 0.979527i \(-0.564520\pi\)
−0.698926 + 0.715194i \(0.746338\pi\)
\(608\) 0 0
\(609\) −18.6059 11.9573i −0.753950 0.484535i
\(610\) 0 0
\(611\) 20.8450 24.0564i 0.843299 0.973218i
\(612\) 0 0
\(613\) −3.06633 21.3268i −0.123848 0.861382i −0.953132 0.302555i \(-0.902160\pi\)
0.829284 0.558828i \(-0.188749\pi\)
\(614\) 0 0
\(615\) 4.07141 + 8.91515i 0.164175 + 0.359493i
\(616\) 0 0
\(617\) −7.69786 + 16.8560i −0.309904 + 0.678596i −0.998935 0.0461363i \(-0.985309\pi\)
0.689031 + 0.724732i \(0.258036\pi\)
\(618\) 0 0
\(619\) −3.16537 + 2.03426i −0.127227 + 0.0817638i −0.602706 0.797963i \(-0.705911\pi\)
0.475479 + 0.879727i \(0.342275\pi\)
\(620\) 0 0
\(621\) −3.47138 83.9248i −0.139302 3.36779i
\(622\) 0 0
\(623\) 9.21876 5.92454i 0.369342 0.237362i
\(624\) 0 0
\(625\) 0.415415 0.909632i 0.0166166 0.0363853i
\(626\) 0 0
\(627\) 4.12121 + 9.02418i 0.164585 + 0.360391i
\(628\) 0 0
\(629\) −3.45781 24.0496i −0.137872 0.958919i
\(630\) 0 0
\(631\) 2.47004 2.85057i 0.0983306 0.113480i −0.704451 0.709752i \(-0.748807\pi\)
0.802782 + 0.596273i \(0.203352\pi\)
\(632\) 0 0
\(633\) 20.4877 + 13.1666i 0.814312 + 0.523326i
\(634\) 0 0
\(635\) 1.13485 + 0.333223i 0.0450353 + 0.0132236i
\(636\) 0 0
\(637\) −13.0170 15.0224i −0.515751 0.595208i
\(638\) 0 0
\(639\) −76.1564 + 22.3615i −3.01270 + 0.884609i
\(640\) 0 0
\(641\) 0.122868 0.854564i 0.00485298 0.0337532i −0.987251 0.159171i \(-0.949118\pi\)
0.992104 + 0.125418i \(0.0400270\pi\)
\(642\) 0 0
\(643\) −2.16664 −0.0854438 −0.0427219 0.999087i \(-0.513603\pi\)
−0.0427219 + 0.999087i \(0.513603\pi\)
\(644\) 0 0
\(645\) −0.874047 −0.0344156
\(646\) 0 0
\(647\) 0.813619 5.65884i 0.0319867 0.222472i −0.967558 0.252649i \(-0.918698\pi\)
0.999545 + 0.0301773i \(0.00960719\pi\)
\(648\) 0 0
\(649\) 23.5765 6.92267i 0.925457 0.271739i
\(650\) 0 0
\(651\) −19.4332 22.4271i −0.761647 0.878988i
\(652\) 0 0
\(653\) −37.6057 11.0420i −1.47163 0.432108i −0.554999 0.831851i \(-0.687281\pi\)
−0.916627 + 0.399743i \(0.869099\pi\)
\(654\) 0 0
\(655\) 6.34285 + 4.07630i 0.247836 + 0.159274i
\(656\) 0 0
\(657\) −21.5631 + 24.8851i −0.841255 + 0.970860i
\(658\) 0 0
\(659\) −6.29604 43.7899i −0.245259 1.70581i −0.624921 0.780688i \(-0.714869\pi\)
0.379662 0.925125i \(-0.376040\pi\)
\(660\) 0 0
\(661\) 10.1453 + 22.2152i 0.394608 + 0.864070i 0.997789 + 0.0664660i \(0.0211724\pi\)
−0.603181 + 0.797604i \(0.706100\pi\)
\(662\) 0 0
\(663\) −36.9056 + 80.8120i −1.43330 + 3.13848i
\(664\) 0 0
\(665\) 0.675757 0.434283i 0.0262048 0.0168408i
\(666\) 0 0
\(667\) −20.8534 16.6117i −0.807448 0.643206i
\(668\) 0 0
\(669\) 4.36792 2.80709i 0.168873 0.108528i
\(670\) 0 0
\(671\) 23.0975 50.5764i 0.891668 1.95248i
\(672\) 0 0
\(673\) 14.7475 + 32.2925i 0.568475 + 1.24479i 0.947605 + 0.319443i \(0.103496\pi\)
−0.379131 + 0.925343i \(0.623777\pi\)
\(674\) 0 0
\(675\) 2.49257 + 17.3362i 0.0959391 + 0.667271i
\(676\) 0 0
\(677\) 22.1260 25.5348i 0.850372 0.981381i −0.149601 0.988746i \(-0.547799\pi\)
0.999973 + 0.00736535i \(0.00234448\pi\)
\(678\) 0 0
\(679\) 6.56626 + 4.21988i 0.251990 + 0.161944i
\(680\) 0 0
\(681\) 46.6745 + 13.7049i 1.78857 + 0.525171i
\(682\) 0 0
\(683\) 12.1459 + 14.0171i 0.464748 + 0.536348i 0.938943 0.344072i \(-0.111806\pi\)
−0.474195 + 0.880420i \(0.657261\pi\)
\(684\) 0 0
\(685\) 6.09226 1.78885i 0.232773 0.0683484i
\(686\) 0 0
\(687\) 0.248759 1.73016i 0.00949074 0.0660096i
\(688\) 0 0
\(689\) 1.16518 0.0443898
\(690\) 0 0
\(691\) 9.80554 0.373020 0.186510 0.982453i \(-0.440282\pi\)
0.186510 + 0.982453i \(0.440282\pi\)
\(692\) 0 0
\(693\) −6.08409 + 42.3158i −0.231115 + 1.60744i
\(694\) 0 0
\(695\) −5.27048 + 1.54755i −0.199921 + 0.0587020i
\(696\) 0 0
\(697\) 14.2831 + 16.4835i 0.541009 + 0.624358i
\(698\) 0 0
\(699\) 55.7118 + 16.3585i 2.10721 + 0.618734i
\(700\) 0 0
\(701\) −16.9752 10.9093i −0.641146 0.412039i 0.179276 0.983799i \(-0.442625\pi\)
−0.820421 + 0.571760i \(0.806261\pi\)
\(702\) 0 0
\(703\) −1.44359 + 1.66599i −0.0544459 + 0.0628339i
\(704\) 0 0
\(705\) −4.26880 29.6901i −0.160772 1.11819i
\(706\) 0 0
\(707\) −8.04838 17.6235i −0.302691 0.662800i
\(708\) 0 0
\(709\) 12.1400 26.5830i 0.455928 0.998344i −0.532468 0.846450i \(-0.678736\pi\)
0.988397 0.151894i \(-0.0485372\pi\)
\(710\) 0 0
\(711\) 22.0290 14.1572i 0.826153 0.530936i
\(712\) 0 0
\(713\) −20.5672 29.2687i −0.770248 1.09612i
\(714\) 0 0
\(715\) 13.0912 8.41320i 0.489583 0.314636i
\(716\) 0 0
\(717\) 32.7675 71.7508i 1.22372 2.67958i
\(718\) 0 0
\(719\) 8.17751 + 17.9062i 0.304970 + 0.667790i 0.998620 0.0525218i \(-0.0167259\pi\)
−0.693650 + 0.720312i \(0.743999\pi\)
\(720\) 0 0
\(721\) 1.05645 + 7.34779i 0.0393443 + 0.273646i
\(722\) 0 0
\(723\) 51.7083 59.6745i 1.92305 2.21932i
\(724\) 0 0
\(725\) 4.67671 + 3.00554i 0.173689 + 0.111623i
\(726\) 0 0
\(727\) −34.1831 10.0371i −1.26778 0.372255i −0.422397 0.906411i \(-0.638811\pi\)
−0.845386 + 0.534156i \(0.820629\pi\)
\(728\) 0 0
\(729\) −67.9094 78.3716i −2.51516 2.90265i
\(730\) 0 0
\(731\) −1.86632 + 0.548001i −0.0690283 + 0.0202685i
\(732\) 0 0
\(733\) 3.64460 25.3488i 0.134616 0.936278i −0.804811 0.593531i \(-0.797734\pi\)
0.939428 0.342747i \(-0.111357\pi\)
\(734\) 0 0
\(735\) −18.7311 −0.690906
\(736\) 0 0
\(737\) 26.7234 0.984368
\(738\) 0 0
\(739\) −0.972178 + 6.76165i −0.0357622 + 0.248731i −0.999859 0.0168214i \(-0.994645\pi\)
0.964096 + 0.265553i \(0.0855544\pi\)
\(740\) 0 0
\(741\) 7.73385 2.27086i 0.284110 0.0834222i
\(742\) 0 0
\(743\) 20.2001 + 23.3122i 0.741071 + 0.855242i 0.993671 0.112329i \(-0.0358311\pi\)
−0.252600 + 0.967571i \(0.581286\pi\)
\(744\) 0 0
\(745\) −2.31890 0.680889i −0.0849577 0.0249458i
\(746\) 0 0
\(747\) −85.0137 54.6350i −3.11049 1.99899i
\(748\) 0 0
\(749\) 4.96854 5.73400i 0.181546 0.209516i
\(750\) 0 0
\(751\) 0.0565450 + 0.393279i 0.00206335 + 0.0143509i 0.990827 0.135136i \(-0.0431470\pi\)
−0.988764 + 0.149487i \(0.952238\pi\)
\(752\) 0 0
\(753\) 31.7088 + 69.4326i 1.15553 + 2.53027i
\(754\) 0 0
\(755\) 2.39959 5.25437i 0.0873300 0.191226i
\(756\) 0 0
\(757\) 0.137639 0.0884549i 0.00500256 0.00321495i −0.538137 0.842857i \(-0.680872\pi\)
0.543140 + 0.839642i \(0.317235\pi\)
\(758\) 0 0
\(759\) −17.0076 + 68.2389i −0.617338 + 2.47692i
\(760\) 0 0
\(761\) 43.3049 27.8303i 1.56980 1.00885i 0.590354 0.807145i \(-0.298988\pi\)
0.979446 0.201705i \(-0.0646481\pi\)
\(762\) 0 0
\(763\) −4.87411 + 10.6728i −0.176455 + 0.386382i
\(764\) 0 0
\(765\) 25.4844 + 55.8030i 0.921390 + 2.01756i
\(766\) 0 0
\(767\) −2.84118 19.7608i −0.102589 0.713522i
\(768\) 0 0
\(769\) −27.8730 + 32.1671i −1.00513 + 1.15998i −0.0180314 + 0.999837i \(0.505740\pi\)
−0.987094 + 0.160140i \(0.948806\pi\)
\(770\) 0 0
\(771\) −22.6660 14.5665i −0.816294 0.524600i
\(772\) 0 0
\(773\) −21.1356 6.20598i −0.760195 0.223214i −0.121414 0.992602i \(-0.538743\pi\)
−0.638781 + 0.769388i \(0.720561\pi\)
\(774\) 0 0
\(775\) 4.88465 + 5.63718i 0.175462 + 0.202494i
\(776\) 0 0
\(777\) −12.4383 + 3.65220i −0.446220 + 0.131022i
\(778\) 0 0
\(779\) 0.281622 1.95872i 0.0100901 0.0701785i
\(780\) 0 0
\(781\) 42.2218 1.51082
\(782\) 0 0
\(783\) −97.3668 −3.47961
\(784\) 0 0
\(785\) 1.89287 13.1652i 0.0675595 0.469887i
\(786\) 0 0
\(787\) −15.5638 + 4.56993i −0.554788 + 0.162900i −0.547096 0.837070i \(-0.684267\pi\)
−0.00769220 + 0.999970i \(0.502449\pi\)
\(788\) 0 0
\(789\) 24.6703 + 28.4710i 0.878285 + 1.01359i
\(790\) 0 0
\(791\) 20.5149 + 6.02371i 0.729425 + 0.214178i
\(792\) 0 0
\(793\) −38.0032 24.4232i −1.34953 0.867293i
\(794\) 0 0
\(795\) 0.719026 0.829800i 0.0255012 0.0294300i
\(796\) 0 0
\(797\) 6.10124 + 42.4350i 0.216117 + 1.50313i 0.752185 + 0.658951i \(0.229000\pi\)
−0.536069 + 0.844174i \(0.680091\pi\)
\(798\) 0 0
\(799\) −27.7298 60.7198i −0.981010 2.14811i
\(800\) 0 0
\(801\) 31.5427 69.0690i 1.11451 2.44043i
\(802\) 0 0
\(803\) 14.7353 9.46983i 0.519999 0.334183i
\(804\) 0 0
\(805\) 5.66502 + 0.576755i 0.199666 + 0.0203279i
\(806\) 0 0
\(807\) 35.6098 22.8851i 1.25353 0.805592i
\(808\) 0 0
\(809\) 13.3581 29.2501i 0.469645 1.02838i −0.515537 0.856867i \(-0.672408\pi\)
0.985182 0.171512i \(-0.0548651\pi\)
\(810\) 0 0
\(811\) −19.3621 42.3970i −0.679895 1.48876i −0.862755 0.505623i \(-0.831263\pi\)
0.182860 0.983139i \(-0.441464\pi\)
\(812\) 0 0
\(813\) −6.79099 47.2324i −0.238170 1.65651i
\(814\) 0 0
\(815\) −14.0445 + 16.2082i −0.491957 + 0.567749i
\(816\) 0 0
\(817\) 0.148462 + 0.0954106i 0.00519402 + 0.00333799i
\(818\) 0 0
\(819\) 33.3272 + 9.78575i 1.16455 + 0.341942i
\(820\) 0 0
\(821\) −30.3782 35.0583i −1.06021 1.22354i −0.973829 0.227281i \(-0.927017\pi\)
−0.0863770 0.996263i \(-0.527529\pi\)
\(822\) 0 0
\(823\) 29.1969 8.57297i 1.01774 0.298835i 0.270023 0.962854i \(-0.412969\pi\)
0.747716 + 0.664019i \(0.231151\pi\)
\(824\) 0 0
\(825\) 2.08692 14.5148i 0.0726571 0.505341i
\(826\) 0 0
\(827\) −15.9583 −0.554923 −0.277462 0.960737i \(-0.589493\pi\)
−0.277462 + 0.960737i \(0.589493\pi\)
\(828\) 0 0
\(829\) 44.9909 1.56260 0.781300 0.624156i \(-0.214557\pi\)
0.781300 + 0.624156i \(0.214557\pi\)
\(830\) 0 0
\(831\) −13.0656 + 90.8733i −0.453241 + 3.15236i
\(832\) 0 0
\(833\) −39.9958 + 11.7438i −1.38577 + 0.406899i
\(834\) 0 0
\(835\) 7.19764 + 8.30652i 0.249085 + 0.287459i
\(836\) 0 0
\(837\) −125.350 36.8060i −4.33272 1.27220i
\(838\) 0 0
\(839\) 2.11516 + 1.35933i 0.0730235 + 0.0469294i 0.576643 0.816996i \(-0.304362\pi\)
−0.503620 + 0.863926i \(0.667999\pi\)
\(840\) 0 0
\(841\) −1.24744 + 1.43962i −0.0430150 + 0.0496420i
\(842\) 0 0
\(843\) 9.47330 + 65.8883i 0.326278 + 2.26931i
\(844\) 0 0
\(845\) 0.148133 + 0.324366i 0.00509593 + 0.0111585i
\(846\) 0 0
\(847\) 4.02148 8.80581i 0.138180 0.302571i
\(848\) 0 0
\(849\) 47.5848 30.5809i 1.63311 1.04953i
\(850\) 0 0
\(851\) −15.3626 + 2.86127i −0.526624 + 0.0980832i
\(852\) 0 0
\(853\) −11.5136 + 7.39936i −0.394219 + 0.253349i −0.722701 0.691161i \(-0.757099\pi\)
0.328482 + 0.944510i \(0.393463\pi\)
\(854\) 0 0
\(855\) 2.31216 5.06292i 0.0790742 0.173148i
\(856\) 0 0
\(857\) 8.75381 + 19.1682i 0.299024 + 0.654772i 0.998187 0.0601908i \(-0.0191709\pi\)
−0.699163 + 0.714963i \(0.746444\pi\)
\(858\) 0 0
\(859\) −1.53104 10.6486i −0.0522386 0.363327i −0.999127 0.0417662i \(-0.986702\pi\)
0.946889 0.321561i \(-0.104208\pi\)
\(860\) 0 0
\(861\) 7.62058 8.79462i 0.259709 0.299720i
\(862\) 0 0
\(863\) 17.2661 + 11.0963i 0.587746 + 0.377721i 0.800454 0.599394i \(-0.204592\pi\)
−0.212708 + 0.977116i \(0.568228\pi\)
\(864\) 0 0
\(865\) 10.9674 + 3.22033i 0.372904 + 0.109495i
\(866\) 0 0
\(867\) 84.7011 + 97.7502i 2.87660 + 3.31977i
\(868\) 0 0
\(869\) −13.3654 + 3.92444i −0.453391 + 0.133128i
\(870\) 0 0
\(871\) 3.08996 21.4911i 0.104699 0.728200i
\(872\) 0 0
\(873\) 54.0832 1.83044
\(874\) 0 0
\(875\) −1.18734 −0.0401396
\(876\) 0 0
\(877\) −6.95382 + 48.3649i −0.234814 + 1.63317i 0.442003 + 0.897014i \(0.354268\pi\)
−0.676817 + 0.736152i \(0.736641\pi\)
\(878\) 0 0
\(879\) 38.4617 11.2934i 1.29728 0.380916i
\(880\) 0 0
\(881\) 18.1383 + 20.9327i 0.611094 + 0.705239i 0.973990 0.226590i \(-0.0727577\pi\)
−0.362897 + 0.931829i \(0.618212\pi\)
\(882\) 0 0
\(883\) 30.9319 + 9.08244i 1.04094 + 0.305648i 0.757153 0.653238i \(-0.226590\pi\)
0.283790 + 0.958886i \(0.408408\pi\)
\(884\) 0 0
\(885\) −15.8262 10.1709i −0.531993 0.341891i
\(886\) 0 0
\(887\) −12.1370 + 14.0068i −0.407519 + 0.470302i −0.921994 0.387203i \(-0.873441\pi\)
0.514475 + 0.857505i \(0.327987\pi\)
\(888\) 0 0
\(889\) −0.199859 1.39005i −0.00670307 0.0466209i
\(890\) 0 0
\(891\) 61.8210 + 135.369i 2.07108 + 4.53503i
\(892\) 0 0
\(893\) −2.51588 + 5.50901i −0.0841908 + 0.184352i
\(894\) 0 0
\(895\) −20.4261 + 13.1270i −0.682768 + 0.438788i
\(896\) 0 0
\(897\) 52.9117 + 21.5680i 1.76667 + 0.720134i
\(898\) 0 0
\(899\) −34.8839 + 22.4185i −1.16344 + 0.747699i
\(900\) 0 0
\(901\) 1.01505 2.22265i 0.0338162 0.0740471i
\(902\) 0 0
\(903\) 0.431115 + 0.944011i 0.0143466 + 0.0314147i
\(904\) 0 0
\(905\) −0.378349 2.63147i −0.0125767 0.0874732i
\(906\) 0 0
\(907\) 3.12306 3.60420i 0.103699 0.119675i −0.701527 0.712643i \(-0.747498\pi\)
0.805227 + 0.592967i \(0.202044\pi\)
\(908\) 0 0
\(909\) −112.934 72.5783i −3.74579 2.40727i
\(910\) 0 0
\(911\) −18.3651 5.39248i −0.608463 0.178661i −0.0370361 0.999314i \(-0.511792\pi\)
−0.571427 + 0.820653i \(0.693610\pi\)
\(912\) 0 0
\(913\) 35.2033 + 40.6268i 1.16506 + 1.34455i
\(914\) 0 0
\(915\) −40.8449 + 11.9931i −1.35029 + 0.396481i
\(916\) 0 0
\(917\) 1.27404 8.86117i 0.0420727 0.292622i
\(918\) 0 0
\(919\) 28.9673 0.955543 0.477771 0.878484i \(-0.341445\pi\)
0.477771 + 0.878484i \(0.341445\pi\)
\(920\) 0 0
\(921\) −39.7334 −1.30926
\(922\) 0 0
\(923\) 4.88201 33.9551i 0.160693 1.11765i
\(924\) 0 0
\(925\) 3.12643 0.918002i 0.102796 0.0301837i
\(926\) 0 0
\(927\) 33.6837 + 38.8731i 1.10632 + 1.27676i
\(928\) 0 0
\(929\) 17.1365 + 5.03174i 0.562231 + 0.165086i 0.550485 0.834845i \(-0.314443\pi\)
0.0117461 + 0.999931i \(0.496261\pi\)
\(930\) 0 0
\(931\) 3.18158 + 2.04468i 0.104272 + 0.0670116i
\(932\) 0 0
\(933\) −8.61432 + 9.94145i −0.282020 + 0.325469i
\(934\) 0 0
\(935\) −4.64424 32.3014i −0.151883 1.05637i
\(936\) 0 0
\(937\) −0.446757 0.978262i −0.0145949 0.0319584i 0.902194 0.431330i \(-0.141956\pi\)
−0.916789 + 0.399372i \(0.869228\pi\)
\(938\) 0 0
\(939\) −42.5659 + 93.2064i −1.38909 + 3.04168i
\(940\) 0 0
\(941\) −42.5753 + 27.3615i −1.38791 + 0.891958i −0.999563 0.0295535i \(-0.990591\pi\)
−0.388351 + 0.921512i \(0.626955\pi\)
\(942\) 0 0
\(943\) 10.2129 9.61660i 0.332577 0.313160i
\(944\) 0 0
\(945\) 17.4945 11.2430i 0.569096 0.365735i
\(946\) 0 0
\(947\) 15.7035 34.3859i 0.510295 1.11739i −0.462689 0.886521i \(-0.653115\pi\)
0.972984 0.230870i \(-0.0741574\pi\)
\(948\) 0 0
\(949\) −5.91190 12.9453i −0.191908 0.420221i
\(950\) 0 0
\(951\) −0.674175 4.68899i −0.0218616 0.152051i
\(952\) 0 0
\(953\) 11.9783 13.8237i 0.388016 0.447794i −0.527814 0.849360i \(-0.676988\pi\)
0.915830 + 0.401565i \(0.131534\pi\)
\(954\) 0 0
\(955\) −9.17549 5.89673i −0.296912 0.190814i
\(956\) 0 0
\(957\) 78.2186 + 22.9671i 2.52845 + 0.742420i
\(958\) 0 0
\(959\) −4.93699 5.69759i −0.159424 0.183985i
\(960\) 0 0
\(961\) −23.6396 + 6.94122i −0.762569 + 0.223910i
\(962\) 0 0
\(963\) 7.48172 52.0365i 0.241095 1.67685i
\(964\) 0 0
\(965\) 6.09929 0.196343
\(966\) 0 0
\(967\) 31.1178 1.00068 0.500341 0.865828i \(-0.333208\pi\)
0.500341 + 0.865828i \(0.333208\pi\)
\(968\) 0 0
\(969\) 2.40556 16.7310i 0.0772776 0.537478i
\(970\) 0 0
\(971\) −7.51133 + 2.20552i −0.241050 + 0.0707787i −0.400026 0.916504i \(-0.630999\pi\)
0.158976 + 0.987282i \(0.449181\pi\)
\(972\) 0 0
\(973\) 4.27105 + 4.92905i 0.136923 + 0.158018i
\(974\) 0 0
\(975\) −11.4316 3.35663i −0.366105 0.107498i
\(976\) 0 0
\(977\) −23.7949 15.2921i −0.761267 0.489237i 0.101502 0.994835i \(-0.467635\pi\)
−0.862769 + 0.505599i \(0.831272\pi\)
\(978\) 0 0
\(979\) −26.4508 + 30.5258i −0.845370 + 0.975609i
\(980\) 0 0
\(981\) 11.5700 + 80.4714i 0.369403 + 2.56926i
\(982\) 0 0
\(983\) −21.7860 47.7048i −0.694867 1.52155i −0.846086 0.533046i \(-0.821047\pi\)
0.151219 0.988500i \(-0.451680\pi\)
\(984\) 0 0
\(985\) 0.845852 1.85216i 0.0269511 0.0590146i
\(986\) 0 0
\(987\) −29.9612 + 19.2549i −0.953675 + 0.612889i
\(988\) 0 0
\(989\) 0.401759 + 1.18475i 0.0127752 + 0.0376730i
\(990\) 0 0
\(991\) 2.16409 1.39078i 0.0687447 0.0441796i −0.505817 0.862641i \(-0.668809\pi\)
0.574562 + 0.818461i \(0.305173\pi\)
\(992\) 0 0
\(993\) −32.3946 + 70.9342i −1.02801 + 2.25103i
\(994\) 0 0
\(995\) 1.64705 + 3.60654i 0.0522151 + 0.114335i
\(996\) 0 0
\(997\) −7.32465 50.9441i −0.231974 1.61342i −0.689545 0.724242i \(-0.742190\pi\)
0.457571 0.889173i \(-0.348719\pi\)
\(998\) 0 0
\(999\) −37.3726 + 43.1303i −1.18242 + 1.36458i
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 460.2.m.b.81.5 50
23.2 even 11 inner 460.2.m.b.301.5 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.m.b.81.5 50 1.1 even 1 trivial
460.2.m.b.301.5 yes 50 23.2 even 11 inner