Properties

Label 552.2.q.d.73.1
Level $552$
Weight $2$
Character 552.73
Analytic conductor $4.408$
Analytic rank $0$
Dimension $30$
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] = [552,2,Mod(25,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.q (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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 73.1
Character \(\chi\) \(=\) 552.73
Dual form 552.2.q.d.121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.959493 - 0.281733i) q^{3} +(-0.776140 - 0.498795i) q^{5} +(0.172807 + 1.20190i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\) \(q+(0.959493 - 0.281733i) q^{3} +(-0.776140 - 0.498795i) q^{5} +(0.172807 + 1.20190i) q^{7} +(0.841254 - 0.540641i) q^{9} +(1.08362 - 2.37279i) q^{11} +(0.851334 - 5.92116i) q^{13} +(-0.885227 - 0.259926i) q^{15} +(4.79395 + 5.53252i) q^{17} +(3.56144 - 4.11012i) q^{19} +(0.504420 + 1.10453i) q^{21} +(1.91294 + 4.39780i) q^{23} +(-1.72348 - 3.77389i) q^{25} +(0.654861 - 0.755750i) q^{27} +(-0.971937 - 1.12167i) q^{29} +(7.26162 + 2.13220i) q^{31} +(0.371231 - 2.58197i) q^{33} +(0.465378 - 1.01903i) q^{35} +(-6.92154 + 4.44820i) q^{37} +(-0.851334 - 5.92116i) q^{39} +(-7.88024 - 5.06433i) q^{41} +(7.55679 - 2.21887i) q^{43} -0.922599 q^{45} -10.1065 q^{47} +(5.30176 - 1.55674i) q^{49} +(6.15846 + 3.95780i) q^{51} +(-0.545566 - 3.79450i) q^{53} +(-2.02457 + 1.30111i) q^{55} +(2.25922 - 4.94701i) q^{57} +(-1.81494 + 12.6232i) q^{59} +(-5.38054 - 1.57987i) q^{61} +(0.795169 + 0.917673i) q^{63} +(-3.61420 + 4.17100i) q^{65} +(4.19459 + 9.18487i) q^{67} +(3.07446 + 3.68072i) q^{69} +(2.76110 + 6.04596i) q^{71} +(-6.43786 + 7.42969i) q^{73} +(-2.71689 - 3.13546i) q^{75} +(3.03910 + 0.892362i) q^{77} +(1.74805 - 12.1579i) q^{79} +(0.415415 - 0.909632i) q^{81} +(4.39148 - 2.82223i) q^{83} +(-0.961187 - 6.68521i) q^{85} +(-1.24858 - 0.802413i) q^{87} +(-3.57797 + 1.05059i) q^{89} +7.26374 q^{91} +7.56818 q^{93} +(-4.81428 + 1.41360i) q^{95} +(-7.58479 - 4.87445i) q^{97} +(-0.371231 - 2.58197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(e\left(\frac{2}{11}\right)\) \(1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.959493 0.281733i 0.553964 0.162658i
\(4\) 0 0
\(5\) −0.776140 0.498795i −0.347100 0.223068i 0.355461 0.934691i \(-0.384324\pi\)
−0.702561 + 0.711623i \(0.747960\pi\)
\(6\) 0 0
\(7\) 0.172807 + 1.20190i 0.0653148 + 0.454274i 0.996066 + 0.0886199i \(0.0282457\pi\)
−0.930751 + 0.365654i \(0.880845\pi\)
\(8\) 0 0
\(9\) 0.841254 0.540641i 0.280418 0.180214i
\(10\) 0 0
\(11\) 1.08362 2.37279i 0.326723 0.715423i −0.672984 0.739657i \(-0.734988\pi\)
0.999706 + 0.0242343i \(0.00771479\pi\)
\(12\) 0 0
\(13\) 0.851334 5.92116i 0.236118 1.64223i −0.434674 0.900588i \(-0.643136\pi\)
0.670791 0.741646i \(-0.265955\pi\)
\(14\) 0 0
\(15\) −0.885227 0.259926i −0.228565 0.0671126i
\(16\) 0 0
\(17\) 4.79395 + 5.53252i 1.16270 + 1.34183i 0.929244 + 0.369467i \(0.120460\pi\)
0.233461 + 0.972366i \(0.424995\pi\)
\(18\) 0 0
\(19\) 3.56144 4.11012i 0.817051 0.942927i −0.182135 0.983273i \(-0.558301\pi\)
0.999186 + 0.0403469i \(0.0128463\pi\)
\(20\) 0 0
\(21\) 0.504420 + 1.10453i 0.110074 + 0.241027i
\(22\) 0 0
\(23\) 1.91294 + 4.39780i 0.398876 + 0.917005i
\(24\) 0 0
\(25\) −1.72348 3.77389i −0.344696 0.754778i
\(26\) 0 0
\(27\) 0.654861 0.755750i 0.126028 0.145444i
\(28\) 0 0
\(29\) −0.971937 1.12167i −0.180484 0.208290i 0.658297 0.752758i \(-0.271277\pi\)
−0.838781 + 0.544468i \(0.816732\pi\)
\(30\) 0 0
\(31\) 7.26162 + 2.13220i 1.30423 + 0.382955i 0.858776 0.512352i \(-0.171226\pi\)
0.445450 + 0.895307i \(0.353044\pi\)
\(32\) 0 0
\(33\) 0.371231 2.58197i 0.0646230 0.449463i
\(34\) 0 0
\(35\) 0.465378 1.01903i 0.0786632 0.172248i
\(36\) 0 0
\(37\) −6.92154 + 4.44820i −1.13789 + 0.731280i −0.967193 0.254043i \(-0.918239\pi\)
−0.170701 + 0.985323i \(0.554603\pi\)
\(38\) 0 0
\(39\) −0.851334 5.92116i −0.136323 0.948144i
\(40\) 0 0
\(41\) −7.88024 5.06433i −1.23069 0.790915i −0.246689 0.969095i \(-0.579343\pi\)
−0.983998 + 0.178180i \(0.942979\pi\)
\(42\) 0 0
\(43\) 7.55679 2.21887i 1.15240 0.338375i 0.350925 0.936404i \(-0.385867\pi\)
0.801475 + 0.598029i \(0.204049\pi\)
\(44\) 0 0
\(45\) −0.922599 −0.137533
\(46\) 0 0
\(47\) −10.1065 −1.47419 −0.737094 0.675791i \(-0.763802\pi\)
−0.737094 + 0.675791i \(0.763802\pi\)
\(48\) 0 0
\(49\) 5.30176 1.55674i 0.757394 0.222391i
\(50\) 0 0
\(51\) 6.15846 + 3.95780i 0.862356 + 0.554203i
\(52\) 0 0
\(53\) −0.545566 3.79450i −0.0749393 0.521214i −0.992368 0.123313i \(-0.960648\pi\)
0.917428 0.397901i \(-0.130261\pi\)
\(54\) 0 0
\(55\) −2.02457 + 1.30111i −0.272993 + 0.175442i
\(56\) 0 0
\(57\) 2.25922 4.94701i 0.299241 0.655247i
\(58\) 0 0
\(59\) −1.81494 + 12.6232i −0.236285 + 1.64340i 0.433724 + 0.901046i \(0.357199\pi\)
−0.670009 + 0.742353i \(0.733710\pi\)
\(60\) 0 0
\(61\) −5.38054 1.57987i −0.688908 0.202282i −0.0815018 0.996673i \(-0.525972\pi\)
−0.607406 + 0.794392i \(0.707790\pi\)
\(62\) 0 0
\(63\) 0.795169 + 0.917673i 0.100182 + 0.115616i
\(64\) 0 0
\(65\) −3.61420 + 4.17100i −0.448286 + 0.517349i
\(66\) 0 0
\(67\) 4.19459 + 9.18487i 0.512451 + 1.12211i 0.972219 + 0.234072i \(0.0752051\pi\)
−0.459769 + 0.888039i \(0.652068\pi\)
\(68\) 0 0
\(69\) 3.07446 + 3.68072i 0.370121 + 0.443107i
\(70\) 0 0
\(71\) 2.76110 + 6.04596i 0.327682 + 0.717524i 0.999736 0.0229787i \(-0.00731498\pi\)
−0.672054 + 0.740502i \(0.734588\pi\)
\(72\) 0 0
\(73\) −6.43786 + 7.42969i −0.753495 + 0.869579i −0.994902 0.100845i \(-0.967845\pi\)
0.241408 + 0.970424i \(0.422391\pi\)
\(74\) 0 0
\(75\) −2.71689 3.13546i −0.313720 0.362052i
\(76\) 0 0
\(77\) 3.03910 + 0.892362i 0.346338 + 0.101694i
\(78\) 0 0
\(79\) 1.74805 12.1579i 0.196671 1.36787i −0.617190 0.786814i \(-0.711729\pi\)
0.813860 0.581060i \(-0.197362\pi\)
\(80\) 0 0
\(81\) 0.415415 0.909632i 0.0461572 0.101070i
\(82\) 0 0
\(83\) 4.39148 2.82223i 0.482027 0.309780i −0.276965 0.960880i \(-0.589329\pi\)
0.758992 + 0.651100i \(0.225692\pi\)
\(84\) 0 0
\(85\) −0.961187 6.68521i −0.104255 0.725112i
\(86\) 0 0
\(87\) −1.24858 0.802413i −0.133862 0.0860277i
\(88\) 0 0
\(89\) −3.57797 + 1.05059i −0.379264 + 0.111362i −0.465807 0.884886i \(-0.654236\pi\)
0.0865433 + 0.996248i \(0.472418\pi\)
\(90\) 0 0
\(91\) 7.26374 0.761447
\(92\) 0 0
\(93\) 7.56818 0.784784
\(94\) 0 0
\(95\) −4.81428 + 1.41360i −0.493935 + 0.145032i
\(96\) 0 0
\(97\) −7.58479 4.87445i −0.770118 0.494925i 0.0956225 0.995418i \(-0.469516\pi\)
−0.865741 + 0.500493i \(0.833152\pi\)
\(98\) 0 0
\(99\) −0.371231 2.58197i −0.0373101 0.259497i
\(100\) 0 0
\(101\) −10.7948 + 6.93742i −1.07413 + 0.690299i −0.953193 0.302362i \(-0.902225\pi\)
−0.120933 + 0.992661i \(0.538588\pi\)
\(102\) 0 0
\(103\) −2.70610 + 5.92552i −0.266639 + 0.583859i −0.994834 0.101511i \(-0.967632\pi\)
0.728195 + 0.685370i \(0.240360\pi\)
\(104\) 0 0
\(105\) 0.159431 1.10887i 0.0155589 0.108214i
\(106\) 0 0
\(107\) 0.439592 + 0.129076i 0.0424969 + 0.0124782i 0.302912 0.953019i \(-0.402041\pi\)
−0.260415 + 0.965497i \(0.583859\pi\)
\(108\) 0 0
\(109\) −6.01515 6.94185i −0.576147 0.664909i 0.390625 0.920550i \(-0.372259\pi\)
−0.966772 + 0.255641i \(0.917713\pi\)
\(110\) 0 0
\(111\) −5.38796 + 6.21804i −0.511403 + 0.590190i
\(112\) 0 0
\(113\) 0.354339 + 0.775894i 0.0333334 + 0.0729900i 0.925566 0.378586i \(-0.123589\pi\)
−0.892233 + 0.451576i \(0.850862\pi\)
\(114\) 0 0
\(115\) 0.708891 4.36747i 0.0661044 0.407269i
\(116\) 0 0
\(117\) −2.48503 5.44146i −0.229741 0.503063i
\(118\) 0 0
\(119\) −5.82109 + 6.71789i −0.533618 + 0.615828i
\(120\) 0 0
\(121\) 2.74756 + 3.17085i 0.249778 + 0.288259i
\(122\) 0 0
\(123\) −8.98782 2.63906i −0.810405 0.237956i
\(124\) 0 0
\(125\) −1.20123 + 8.35477i −0.107442 + 0.747273i
\(126\) 0 0
\(127\) −5.55691 + 12.1679i −0.493096 + 1.07973i 0.485556 + 0.874206i \(0.338617\pi\)
−0.978652 + 0.205525i \(0.934110\pi\)
\(128\) 0 0
\(129\) 6.62556 4.25799i 0.583348 0.374895i
\(130\) 0 0
\(131\) 0.635443 + 4.41961i 0.0555189 + 0.386143i 0.998568 + 0.0534901i \(0.0170346\pi\)
−0.943049 + 0.332653i \(0.892056\pi\)
\(132\) 0 0
\(133\) 5.55538 + 3.57023i 0.481713 + 0.309578i
\(134\) 0 0
\(135\) −0.885227 + 0.259926i −0.0761882 + 0.0223709i
\(136\) 0 0
\(137\) 19.5982 1.67439 0.837193 0.546907i \(-0.184195\pi\)
0.837193 + 0.546907i \(0.184195\pi\)
\(138\) 0 0
\(139\) 0.590626 0.0500962 0.0250481 0.999686i \(-0.492026\pi\)
0.0250481 + 0.999686i \(0.492026\pi\)
\(140\) 0 0
\(141\) −9.69713 + 2.84734i −0.816646 + 0.239789i
\(142\) 0 0
\(143\) −13.1271 8.43631i −1.09775 0.705479i
\(144\) 0 0
\(145\) 0.194873 + 1.35537i 0.0161833 + 0.112558i
\(146\) 0 0
\(147\) 4.64842 2.98736i 0.383395 0.246393i
\(148\) 0 0
\(149\) −7.36229 + 16.1212i −0.603142 + 1.32070i 0.324025 + 0.946049i \(0.394964\pi\)
−0.927167 + 0.374648i \(0.877763\pi\)
\(150\) 0 0
\(151\) −2.06189 + 14.3408i −0.167794 + 1.16703i 0.715637 + 0.698473i \(0.246137\pi\)
−0.883431 + 0.468562i \(0.844772\pi\)
\(152\) 0 0
\(153\) 7.02404 + 2.06244i 0.567860 + 0.166739i
\(154\) 0 0
\(155\) −4.57250 5.27694i −0.367272 0.423854i
\(156\) 0 0
\(157\) −0.237882 + 0.274530i −0.0189850 + 0.0219099i −0.765163 0.643837i \(-0.777341\pi\)
0.746178 + 0.665747i \(0.231887\pi\)
\(158\) 0 0
\(159\) −1.59250 3.48709i −0.126293 0.276544i
\(160\) 0 0
\(161\) −4.95513 + 3.05913i −0.390519 + 0.241093i
\(162\) 0 0
\(163\) −4.77773 10.4618i −0.374221 0.819429i −0.999246 0.0388246i \(-0.987639\pi\)
0.625025 0.780604i \(-0.285089\pi\)
\(164\) 0 0
\(165\) −1.57600 + 1.81880i −0.122691 + 0.141593i
\(166\) 0 0
\(167\) −3.08530 3.56063i −0.238748 0.275530i 0.623713 0.781653i \(-0.285623\pi\)
−0.862461 + 0.506124i \(0.831078\pi\)
\(168\) 0 0
\(169\) −21.8619 6.41925i −1.68169 0.493788i
\(170\) 0 0
\(171\) 0.773975 5.38311i 0.0591873 0.411657i
\(172\) 0 0
\(173\) −3.22786 + 7.06803i −0.245410 + 0.537372i −0.991749 0.128193i \(-0.959082\pi\)
0.746339 + 0.665565i \(0.231810\pi\)
\(174\) 0 0
\(175\) 4.23800 2.72360i 0.320363 0.205885i
\(176\) 0 0
\(177\) 1.81494 + 12.6232i 0.136419 + 0.948816i
\(178\) 0 0
\(179\) −12.4407 7.99518i −0.929865 0.597588i −0.0143609 0.999897i \(-0.504571\pi\)
−0.915504 + 0.402309i \(0.868208\pi\)
\(180\) 0 0
\(181\) 18.1390 5.32611i 1.34826 0.395886i 0.473654 0.880711i \(-0.342935\pi\)
0.874611 + 0.484825i \(0.161117\pi\)
\(182\) 0 0
\(183\) −5.60769 −0.414533
\(184\) 0 0
\(185\) 7.59082 0.558088
\(186\) 0 0
\(187\) 18.3223 5.37992i 1.33986 0.393419i
\(188\) 0 0
\(189\) 1.02150 + 0.656476i 0.0743030 + 0.0477516i
\(190\) 0 0
\(191\) 0.0524728 + 0.364957i 0.00379680 + 0.0264073i 0.991632 0.129099i \(-0.0412083\pi\)
−0.987835 + 0.155506i \(0.950299\pi\)
\(192\) 0 0
\(193\) −16.7208 + 10.7458i −1.20359 + 0.773499i −0.979573 0.201087i \(-0.935553\pi\)
−0.224014 + 0.974586i \(0.571916\pi\)
\(194\) 0 0
\(195\) −2.29269 + 5.02029i −0.164183 + 0.359510i
\(196\) 0 0
\(197\) −0.527469 + 3.66863i −0.0375806 + 0.261379i −0.999946 0.0103794i \(-0.996696\pi\)
0.962366 + 0.271758i \(0.0876052\pi\)
\(198\) 0 0
\(199\) −6.97900 2.04922i −0.494728 0.145265i 0.0248450 0.999691i \(-0.492091\pi\)
−0.519573 + 0.854426i \(0.673909\pi\)
\(200\) 0 0
\(201\) 6.61236 + 7.63107i 0.466400 + 0.538254i
\(202\) 0 0
\(203\) 1.18018 1.36200i 0.0828324 0.0955937i
\(204\) 0 0
\(205\) 3.59011 + 7.86125i 0.250744 + 0.549053i
\(206\) 0 0
\(207\) 3.98690 + 2.66545i 0.277109 + 0.185262i
\(208\) 0 0
\(209\) −5.89322 12.9043i −0.407642 0.892612i
\(210\) 0 0
\(211\) −0.678026 + 0.782483i −0.0466772 + 0.0538684i −0.778608 0.627511i \(-0.784074\pi\)
0.731931 + 0.681379i \(0.238619\pi\)
\(212\) 0 0
\(213\) 4.35260 + 5.02317i 0.298235 + 0.344182i
\(214\) 0 0
\(215\) −6.97188 2.04713i −0.475479 0.139613i
\(216\) 0 0
\(217\) −1.30783 + 9.09618i −0.0887815 + 0.617489i
\(218\) 0 0
\(219\) −4.08390 + 8.94249i −0.275964 + 0.604277i
\(220\) 0 0
\(221\) 36.8402 23.6757i 2.47814 1.59260i
\(222\) 0 0
\(223\) 0.0839960 + 0.584205i 0.00562479 + 0.0391213i 0.992441 0.122726i \(-0.0391638\pi\)
−0.986816 + 0.161848i \(0.948255\pi\)
\(224\) 0 0
\(225\) −3.49020 2.24302i −0.232680 0.149534i
\(226\) 0 0
\(227\) 17.7311 5.20632i 1.17685 0.345556i 0.365894 0.930657i \(-0.380763\pi\)
0.810960 + 0.585101i \(0.198945\pi\)
\(228\) 0 0
\(229\) 0.328364 0.0216989 0.0108494 0.999941i \(-0.496546\pi\)
0.0108494 + 0.999941i \(0.496546\pi\)
\(230\) 0 0
\(231\) 3.16741 0.208400
\(232\) 0 0
\(233\) 17.8023 5.22723i 1.16627 0.342448i 0.359403 0.933182i \(-0.382980\pi\)
0.806866 + 0.590735i \(0.201162\pi\)
\(234\) 0 0
\(235\) 7.84407 + 5.04108i 0.511691 + 0.328844i
\(236\) 0 0
\(237\) −1.74805 12.1579i −0.113548 0.789743i
\(238\) 0 0
\(239\) −4.08514 + 2.62536i −0.264246 + 0.169820i −0.666054 0.745903i \(-0.732018\pi\)
0.401809 + 0.915724i \(0.368382\pi\)
\(240\) 0 0
\(241\) 11.1472 24.4089i 0.718053 1.57232i −0.0985599 0.995131i \(-0.531424\pi\)
0.816613 0.577186i \(-0.195849\pi\)
\(242\) 0 0
\(243\) 0.142315 0.989821i 0.00912950 0.0634971i
\(244\) 0 0
\(245\) −4.89140 1.43624i −0.312500 0.0917582i
\(246\) 0 0
\(247\) −21.3047 24.5869i −1.35559 1.56443i
\(248\) 0 0
\(249\) 3.41848 3.94513i 0.216637 0.250013i
\(250\) 0 0
\(251\) −0.513571 1.12456i −0.0324163 0.0709818i 0.892731 0.450590i \(-0.148786\pi\)
−0.925148 + 0.379608i \(0.876059\pi\)
\(252\) 0 0
\(253\) 12.5080 + 0.226526i 0.786368 + 0.0142416i
\(254\) 0 0
\(255\) −2.80569 6.14361i −0.175699 0.384728i
\(256\) 0 0
\(257\) −0.0850846 + 0.0981929i −0.00530743 + 0.00612510i −0.758397 0.651793i \(-0.774017\pi\)
0.753090 + 0.657918i \(0.228563\pi\)
\(258\) 0 0
\(259\) −6.54237 7.55029i −0.406523 0.469152i
\(260\) 0 0
\(261\) −1.42407 0.418144i −0.0881476 0.0258825i
\(262\) 0 0
\(263\) 0.0268550 0.186781i 0.00165595 0.0115174i −0.988977 0.148071i \(-0.952694\pi\)
0.990633 + 0.136554i \(0.0436026\pi\)
\(264\) 0 0
\(265\) −1.46924 + 3.21718i −0.0902546 + 0.197630i
\(266\) 0 0
\(267\) −3.13705 + 2.01606i −0.191985 + 0.123381i
\(268\) 0 0
\(269\) −3.05392 21.2405i −0.186201 1.29506i −0.841735 0.539891i \(-0.818466\pi\)
0.655534 0.755165i \(-0.272443\pi\)
\(270\) 0 0
\(271\) 2.96855 + 1.90777i 0.180327 + 0.115889i 0.627690 0.778463i \(-0.284001\pi\)
−0.447363 + 0.894352i \(0.647637\pi\)
\(272\) 0 0
\(273\) 6.96950 2.04643i 0.421814 0.123856i
\(274\) 0 0
\(275\) −10.8222 −0.652606
\(276\) 0 0
\(277\) 18.6506 1.12061 0.560303 0.828288i \(-0.310685\pi\)
0.560303 + 0.828288i \(0.310685\pi\)
\(278\) 0 0
\(279\) 7.26162 2.13220i 0.434742 0.127652i
\(280\) 0 0
\(281\) 22.8746 + 14.7006i 1.36458 + 0.876964i 0.998560 0.0536420i \(-0.0170830\pi\)
0.366022 + 0.930606i \(0.380719\pi\)
\(282\) 0 0
\(283\) 0.528675 + 3.67701i 0.0314264 + 0.218576i 0.999483 0.0321569i \(-0.0102376\pi\)
−0.968056 + 0.250733i \(0.919329\pi\)
\(284\) 0 0
\(285\) −4.22101 + 2.71268i −0.250031 + 0.160685i
\(286\) 0 0
\(287\) 4.72504 10.3464i 0.278910 0.610728i
\(288\) 0 0
\(289\) −5.20741 + 36.2183i −0.306318 + 2.13049i
\(290\) 0 0
\(291\) −8.65084 2.54012i −0.507121 0.148904i
\(292\) 0 0
\(293\) 11.0833 + 12.7908i 0.647494 + 0.747248i 0.980681 0.195613i \(-0.0626696\pi\)
−0.333187 + 0.942861i \(0.608124\pi\)
\(294\) 0 0
\(295\) 7.70502 8.89207i 0.448604 0.517716i
\(296\) 0 0
\(297\) −1.08362 2.37279i −0.0628778 0.137683i
\(298\) 0 0
\(299\) 27.6686 7.58283i 1.60012 0.438526i
\(300\) 0 0
\(301\) 3.97272 + 8.69904i 0.228984 + 0.501404i
\(302\) 0 0
\(303\) −8.40307 + 9.69766i −0.482744 + 0.557116i
\(304\) 0 0
\(305\) 3.38802 + 3.90998i 0.193998 + 0.223885i
\(306\) 0 0
\(307\) 27.5809 + 8.09848i 1.57412 + 0.462204i 0.948198 0.317679i \(-0.102903\pi\)
0.625925 + 0.779883i \(0.284721\pi\)
\(308\) 0 0
\(309\) −0.927067 + 6.44789i −0.0527390 + 0.366808i
\(310\) 0 0
\(311\) 10.7308 23.4972i 0.608488 1.33240i −0.315115 0.949053i \(-0.602043\pi\)
0.923603 0.383350i \(-0.125230\pi\)
\(312\) 0 0
\(313\) 9.80550 6.30161i 0.554240 0.356188i −0.233346 0.972394i \(-0.574967\pi\)
0.787585 + 0.616206i \(0.211331\pi\)
\(314\) 0 0
\(315\) −0.159431 1.10887i −0.00898293 0.0624777i
\(316\) 0 0
\(317\) −13.0585 8.39220i −0.733440 0.471353i 0.119849 0.992792i \(-0.461759\pi\)
−0.853288 + 0.521439i \(0.825395\pi\)
\(318\) 0 0
\(319\) −3.71471 + 1.09074i −0.207984 + 0.0610695i
\(320\) 0 0
\(321\) 0.458150 0.0255714
\(322\) 0 0
\(323\) 39.8127 2.21524
\(324\) 0 0
\(325\) −23.8131 + 6.99215i −1.32091 + 0.387855i
\(326\) 0 0
\(327\) −7.72724 4.96599i −0.427317 0.274620i
\(328\) 0 0
\(329\) −1.74647 12.1470i −0.0962862 0.669685i
\(330\) 0 0
\(331\) −26.4789 + 17.0169i −1.45541 + 0.935335i −0.456450 + 0.889749i \(0.650879\pi\)
−0.998960 + 0.0455860i \(0.985484\pi\)
\(332\) 0 0
\(333\) −3.41789 + 7.48413i −0.187299 + 0.410128i
\(334\) 0 0
\(335\) 1.32578 9.22098i 0.0724349 0.503796i
\(336\) 0 0
\(337\) −18.1231 5.32144i −0.987231 0.289877i −0.252025 0.967721i \(-0.581096\pi\)
−0.735206 + 0.677844i \(0.762915\pi\)
\(338\) 0 0
\(339\) 0.558581 + 0.644636i 0.0303379 + 0.0350118i
\(340\) 0 0
\(341\) 12.9281 14.9198i 0.700095 0.807953i
\(342\) 0 0
\(343\) 6.31816 + 13.8348i 0.341148 + 0.747011i
\(344\) 0 0
\(345\) −0.550283 4.39028i −0.0296263 0.236365i
\(346\) 0 0
\(347\) −8.48901 18.5883i −0.455714 0.997874i −0.988444 0.151589i \(-0.951561\pi\)
0.532730 0.846285i \(-0.321166\pi\)
\(348\) 0 0
\(349\) 21.6680 25.0062i 1.15986 1.33855i 0.228896 0.973451i \(-0.426489\pi\)
0.930967 0.365102i \(-0.118966\pi\)
\(350\) 0 0
\(351\) −3.91741 4.52093i −0.209096 0.241309i
\(352\) 0 0
\(353\) −4.81493 1.41379i −0.256273 0.0752485i 0.151073 0.988523i \(-0.451727\pi\)
−0.407345 + 0.913274i \(0.633545\pi\)
\(354\) 0 0
\(355\) 0.872695 6.06973i 0.0463179 0.322148i
\(356\) 0 0
\(357\) −3.69264 + 8.08576i −0.195435 + 0.427944i
\(358\) 0 0
\(359\) −25.5448 + 16.4167i −1.34820 + 0.866438i −0.997543 0.0700638i \(-0.977680\pi\)
−0.350662 + 0.936502i \(0.614043\pi\)
\(360\) 0 0
\(361\) −1.50526 10.4693i −0.0792241 0.551016i
\(362\) 0 0
\(363\) 3.52960 + 2.26833i 0.185256 + 0.119057i
\(364\) 0 0
\(365\) 8.70257 2.55530i 0.455513 0.133751i
\(366\) 0 0
\(367\) 9.52268 0.497080 0.248540 0.968622i \(-0.420049\pi\)
0.248540 + 0.968622i \(0.420049\pi\)
\(368\) 0 0
\(369\) −9.36726 −0.487640
\(370\) 0 0
\(371\) 4.46632 1.31143i 0.231880 0.0680860i
\(372\) 0 0
\(373\) 4.07637 + 2.61972i 0.211067 + 0.135644i 0.641903 0.766786i \(-0.278145\pi\)
−0.430837 + 0.902430i \(0.641781\pi\)
\(374\) 0 0
\(375\) 1.20123 + 8.35477i 0.0620315 + 0.431438i
\(376\) 0 0
\(377\) −7.46906 + 4.80007i −0.384676 + 0.247216i
\(378\) 0 0
\(379\) −11.9353 + 26.1348i −0.613077 + 1.34245i 0.307372 + 0.951590i \(0.400551\pi\)
−0.920449 + 0.390863i \(0.872177\pi\)
\(380\) 0 0
\(381\) −1.90371 + 13.2406i −0.0975302 + 0.678337i
\(382\) 0 0
\(383\) −23.4241 6.87794i −1.19692 0.351446i −0.378243 0.925706i \(-0.623472\pi\)
−0.818673 + 0.574260i \(0.805290\pi\)
\(384\) 0 0
\(385\) −1.91366 2.20849i −0.0975294 0.112555i
\(386\) 0 0
\(387\) 5.15756 5.95214i 0.262174 0.302564i
\(388\) 0 0
\(389\) 0.102888 + 0.225294i 0.00521664 + 0.0114229i 0.912222 0.409695i \(-0.134365\pi\)
−0.907006 + 0.421118i \(0.861638\pi\)
\(390\) 0 0
\(391\) −15.1604 + 31.6662i −0.766693 + 1.60143i
\(392\) 0 0
\(393\) 1.85485 + 4.06155i 0.0935648 + 0.204878i
\(394\) 0 0
\(395\) −7.42104 + 8.56434i −0.373393 + 0.430919i
\(396\) 0 0
\(397\) 2.55739 + 2.95139i 0.128352 + 0.148126i 0.816288 0.577646i \(-0.196028\pi\)
−0.687936 + 0.725772i \(0.741483\pi\)
\(398\) 0 0
\(399\) 6.33620 + 1.86048i 0.317207 + 0.0931403i
\(400\) 0 0
\(401\) −0.491431 + 3.41798i −0.0245409 + 0.170686i −0.998406 0.0564420i \(-0.982024\pi\)
0.973865 + 0.227128i \(0.0729335\pi\)
\(402\) 0 0
\(403\) 18.8072 41.1820i 0.936852 2.05142i
\(404\) 0 0
\(405\) −0.776140 + 0.498795i −0.0385667 + 0.0247853i
\(406\) 0 0
\(407\) 3.05435 + 21.2435i 0.151399 + 1.05300i
\(408\) 0 0
\(409\) −18.6949 12.0145i −0.924403 0.594078i −0.0104711 0.999945i \(-0.503333\pi\)
−0.913932 + 0.405867i \(0.866969\pi\)
\(410\) 0 0
\(411\) 18.8043 5.52145i 0.927549 0.272353i
\(412\) 0 0
\(413\) −15.4854 −0.761986
\(414\) 0 0
\(415\) −4.81611 −0.236414
\(416\) 0 0
\(417\) 0.566701 0.166398i 0.0277515 0.00814857i
\(418\) 0 0
\(419\) −1.04864 0.673918i −0.0512292 0.0329230i 0.514776 0.857325i \(-0.327875\pi\)
−0.566005 + 0.824402i \(0.691512\pi\)
\(420\) 0 0
\(421\) −3.44772 23.9794i −0.168031 1.16868i −0.882947 0.469473i \(-0.844444\pi\)
0.714915 0.699211i \(-0.246465\pi\)
\(422\) 0 0
\(423\) −8.50214 + 5.46400i −0.413388 + 0.265669i
\(424\) 0 0
\(425\) 12.6168 27.6270i 0.612007 1.34011i
\(426\) 0 0
\(427\) 0.969047 6.73987i 0.0468954 0.326165i
\(428\) 0 0
\(429\) −14.9722 4.39623i −0.722864 0.212252i
\(430\) 0 0
\(431\) 17.8204 + 20.5658i 0.858378 + 0.990622i 1.00000 0.000700669i \(0.000223030\pi\)
−0.141621 + 0.989921i \(0.545232\pi\)
\(432\) 0 0
\(433\) −23.8363 + 27.5086i −1.14550 + 1.32198i −0.206349 + 0.978479i \(0.566158\pi\)
−0.939153 + 0.343500i \(0.888387\pi\)
\(434\) 0 0
\(435\) 0.568832 + 1.24557i 0.0272734 + 0.0597205i
\(436\) 0 0
\(437\) 24.8883 + 7.80009i 1.19057 + 0.373129i
\(438\) 0 0
\(439\) −2.41170 5.28088i −0.115104 0.252043i 0.843308 0.537430i \(-0.180605\pi\)
−0.958412 + 0.285388i \(0.907878\pi\)
\(440\) 0 0
\(441\) 3.61849 4.17596i 0.172309 0.198855i
\(442\) 0 0
\(443\) −14.3787 16.5939i −0.683153 0.788401i 0.303220 0.952920i \(-0.401938\pi\)
−0.986374 + 0.164519i \(0.947393\pi\)
\(444\) 0 0
\(445\) 3.30103 + 0.969270i 0.156484 + 0.0459478i
\(446\) 0 0
\(447\) −2.52221 + 17.5423i −0.119296 + 0.829724i
\(448\) 0 0
\(449\) 0.558752 1.22350i 0.0263691 0.0577403i −0.895989 0.444076i \(-0.853532\pi\)
0.922358 + 0.386336i \(0.126259\pi\)
\(450\) 0 0
\(451\) −20.5557 + 13.2104i −0.967932 + 0.622052i
\(452\) 0 0
\(453\) 2.06189 + 14.3408i 0.0968761 + 0.673788i
\(454\) 0 0
\(455\) −5.63767 3.62311i −0.264298 0.169854i
\(456\) 0 0
\(457\) −15.4742 + 4.54364i −0.723854 + 0.212543i −0.622848 0.782343i \(-0.714024\pi\)
−0.101006 + 0.994886i \(0.532206\pi\)
\(458\) 0 0
\(459\) 7.32057 0.341695
\(460\) 0 0
\(461\) −22.4689 −1.04648 −0.523240 0.852185i \(-0.675277\pi\)
−0.523240 + 0.852185i \(0.675277\pi\)
\(462\) 0 0
\(463\) 24.4326 7.17405i 1.13548 0.333406i 0.340620 0.940201i \(-0.389363\pi\)
0.794859 + 0.606795i \(0.207545\pi\)
\(464\) 0 0
\(465\) −5.87397 3.77497i −0.272399 0.175060i
\(466\) 0 0
\(467\) 1.78966 + 12.4474i 0.0828155 + 0.575995i 0.988405 + 0.151840i \(0.0485198\pi\)
−0.905590 + 0.424155i \(0.860571\pi\)
\(468\) 0 0
\(469\) −10.3144 + 6.62867i −0.476275 + 0.306084i
\(470\) 0 0
\(471\) −0.150902 + 0.330429i −0.00695319 + 0.0152254i
\(472\) 0 0
\(473\) 2.92374 20.3351i 0.134434 0.935008i
\(474\) 0 0
\(475\) −21.6492 6.35678i −0.993334 0.291669i
\(476\) 0 0
\(477\) −2.51042 2.89718i −0.114944 0.132653i
\(478\) 0 0
\(479\) 16.8571 19.4541i 0.770221 0.888883i −0.226142 0.974094i \(-0.572611\pi\)
0.996363 + 0.0852117i \(0.0271567\pi\)
\(480\) 0 0
\(481\) 20.4460 + 44.7704i 0.932256 + 2.04136i
\(482\) 0 0
\(483\) −3.89256 + 4.33123i −0.177118 + 0.197078i
\(484\) 0 0
\(485\) 3.45550 + 7.56650i 0.156906 + 0.343577i
\(486\) 0 0
\(487\) −11.9101 + 13.7450i −0.539697 + 0.622844i −0.958451 0.285256i \(-0.907921\pi\)
0.418754 + 0.908100i \(0.362467\pi\)
\(488\) 0 0
\(489\) −7.53162 8.69195i −0.340592 0.393064i
\(490\) 0 0
\(491\) −6.90525 2.02757i −0.311630 0.0915027i 0.122178 0.992508i \(-0.461012\pi\)
−0.433808 + 0.901005i \(0.642830\pi\)
\(492\) 0 0
\(493\) 1.54627 10.7545i 0.0696403 0.484359i
\(494\) 0 0
\(495\) −0.999744 + 2.18913i −0.0449351 + 0.0983942i
\(496\) 0 0
\(497\) −6.78948 + 4.36334i −0.304550 + 0.195722i
\(498\) 0 0
\(499\) 1.61778 + 11.2519i 0.0724217 + 0.503704i 0.993455 + 0.114221i \(0.0364372\pi\)
−0.921034 + 0.389483i \(0.872654\pi\)
\(500\) 0 0
\(501\) −3.96347 2.54717i −0.177075 0.113799i
\(502\) 0 0
\(503\) 38.2992 11.2456i 1.70767 0.501419i 0.725315 0.688417i \(-0.241694\pi\)
0.982360 + 0.186999i \(0.0598761\pi\)
\(504\) 0 0
\(505\) 11.8386 0.526813
\(506\) 0 0
\(507\) −22.7849 −1.01191
\(508\) 0 0
\(509\) −13.9259 + 4.08902i −0.617255 + 0.181243i −0.575388 0.817881i \(-0.695149\pi\)
−0.0418674 + 0.999123i \(0.513331\pi\)
\(510\) 0 0
\(511\) −10.0422 6.45374i −0.444242 0.285497i
\(512\) 0 0
\(513\) −0.773975 5.38311i −0.0341718 0.237670i
\(514\) 0 0
\(515\) 5.05593 3.24925i 0.222791 0.143179i
\(516\) 0 0
\(517\) −10.9516 + 23.9806i −0.481651 + 1.05467i
\(518\) 0 0
\(519\) −1.10582 + 7.69112i −0.0485399 + 0.337603i
\(520\) 0 0
\(521\) −22.7207 6.67139i −0.995411 0.292279i −0.256839 0.966454i \(-0.582681\pi\)
−0.738571 + 0.674175i \(0.764499\pi\)
\(522\) 0 0
\(523\) 16.0912 + 18.5703i 0.703620 + 0.812021i 0.989237 0.146323i \(-0.0467438\pi\)
−0.285617 + 0.958344i \(0.592198\pi\)
\(524\) 0 0
\(525\) 3.29900 3.80725i 0.143980 0.166162i
\(526\) 0 0
\(527\) 23.0154 + 50.3967i 1.00257 + 2.19532i
\(528\) 0 0
\(529\) −15.6813 + 16.8255i −0.681796 + 0.731542i
\(530\) 0 0
\(531\) 5.29778 + 11.6005i 0.229904 + 0.503420i
\(532\) 0 0
\(533\) −36.6954 + 42.3487i −1.58945 + 1.83433i
\(534\) 0 0
\(535\) −0.276802 0.319447i −0.0119672 0.0138109i
\(536\) 0 0
\(537\) −14.1893 4.16636i −0.612314 0.179792i
\(538\) 0 0
\(539\) 2.05127 14.2669i 0.0883543 0.614517i
\(540\) 0 0
\(541\) 9.70107 21.2424i 0.417082 0.913282i −0.578167 0.815918i \(-0.696232\pi\)
0.995249 0.0973633i \(-0.0310409\pi\)
\(542\) 0 0
\(543\) 15.9038 10.2207i 0.682495 0.438613i
\(544\) 0 0
\(545\) 1.20604 + 8.38817i 0.0516609 + 0.359310i
\(546\) 0 0
\(547\) −20.6404 13.2648i −0.882519 0.567160i 0.0190391 0.999819i \(-0.493939\pi\)
−0.901558 + 0.432658i \(0.857576\pi\)
\(548\) 0 0
\(549\) −5.38054 + 1.57987i −0.229636 + 0.0674272i
\(550\) 0 0
\(551\) −8.07172 −0.343867
\(552\) 0 0
\(553\) 14.9147 0.634236
\(554\) 0 0
\(555\) 7.28334 2.13858i 0.309160 0.0907777i
\(556\) 0 0
\(557\) −1.35322 0.869662i −0.0573378 0.0368488i 0.511658 0.859189i \(-0.329032\pi\)
−0.568996 + 0.822341i \(0.692668\pi\)
\(558\) 0 0
\(559\) −6.70495 46.6339i −0.283589 1.97241i
\(560\) 0 0
\(561\) 16.0644 10.3240i 0.678241 0.435879i
\(562\) 0 0
\(563\) −1.66197 + 3.63920i −0.0700435 + 0.153374i −0.941415 0.337249i \(-0.890504\pi\)
0.871372 + 0.490623i \(0.163231\pi\)
\(564\) 0 0
\(565\) 0.111995 0.778945i 0.00471168 0.0327705i
\(566\) 0 0
\(567\) 1.16507 + 0.342095i 0.0489283 + 0.0143667i
\(568\) 0 0
\(569\) −20.4197 23.5656i −0.856039 0.987921i 0.143960 0.989584i \(-0.454016\pi\)
−0.999999 + 0.00166215i \(0.999471\pi\)
\(570\) 0 0
\(571\) −2.05210 + 2.36825i −0.0858777 + 0.0991082i −0.797062 0.603897i \(-0.793614\pi\)
0.711184 + 0.703006i \(0.248159\pi\)
\(572\) 0 0
\(573\) 0.153167 + 0.335390i 0.00639866 + 0.0140111i
\(574\) 0 0
\(575\) 13.2999 14.7987i 0.554645 0.617150i
\(576\) 0 0
\(577\) −0.484755 1.06147i −0.0201806 0.0441894i 0.899273 0.437387i \(-0.144096\pi\)
−0.919454 + 0.393198i \(0.871369\pi\)
\(578\) 0 0
\(579\) −13.0160 + 15.0213i −0.540928 + 0.624264i
\(580\) 0 0
\(581\) 4.15091 + 4.79040i 0.172209 + 0.198739i
\(582\) 0 0
\(583\) −9.59473 2.81727i −0.397373 0.116679i
\(584\) 0 0
\(585\) −0.785440 + 5.46285i −0.0324739 + 0.225861i
\(586\) 0 0
\(587\) −5.12710 + 11.2268i −0.211618 + 0.463379i −0.985440 0.170024i \(-0.945615\pi\)
0.773822 + 0.633403i \(0.218343\pi\)
\(588\) 0 0
\(589\) 34.6254 22.2524i 1.42672 0.916895i
\(590\) 0 0
\(591\) 0.527469 + 3.66863i 0.0216972 + 0.150907i
\(592\) 0 0
\(593\) 6.59087 + 4.23569i 0.270655 + 0.173939i 0.668927 0.743328i \(-0.266754\pi\)
−0.398273 + 0.917267i \(0.630390\pi\)
\(594\) 0 0
\(595\) 7.86883 2.31050i 0.322590 0.0947211i
\(596\) 0 0
\(597\) −7.27363 −0.297690
\(598\) 0 0
\(599\) −24.6991 −1.00918 −0.504590 0.863359i \(-0.668356\pi\)
−0.504590 + 0.863359i \(0.668356\pi\)
\(600\) 0 0
\(601\) −13.1925 + 3.87365i −0.538131 + 0.158010i −0.539494 0.841989i \(-0.681384\pi\)
0.00136264 + 0.999999i \(0.499566\pi\)
\(602\) 0 0
\(603\) 8.49443 + 5.45904i 0.345920 + 0.222309i
\(604\) 0 0
\(605\) −0.550886 3.83149i −0.0223967 0.155772i
\(606\) 0 0
\(607\) −8.35547 + 5.36973i −0.339138 + 0.217951i −0.699113 0.715011i \(-0.746422\pi\)
0.359975 + 0.932962i \(0.382785\pi\)
\(608\) 0 0
\(609\) 0.748655 1.63933i 0.0303370 0.0664288i
\(610\) 0 0
\(611\) −8.60402 + 59.8423i −0.348082 + 2.42096i
\(612\) 0 0
\(613\) 16.1328 + 4.73701i 0.651596 + 0.191326i 0.590792 0.806824i \(-0.298815\pi\)
0.0608039 + 0.998150i \(0.480634\pi\)
\(614\) 0 0
\(615\) 5.65946 + 6.53136i 0.228211 + 0.263370i
\(616\) 0 0
\(617\) 10.7749 12.4350i 0.433783 0.500612i −0.496203 0.868206i \(-0.665273\pi\)
0.929986 + 0.367594i \(0.119818\pi\)
\(618\) 0 0
\(619\) 3.43906 + 7.53049i 0.138227 + 0.302676i 0.966068 0.258287i \(-0.0831581\pi\)
−0.827841 + 0.560963i \(0.810431\pi\)
\(620\) 0 0
\(621\) 4.57635 + 1.43424i 0.183642 + 0.0575542i
\(622\) 0 0
\(623\) −1.88099 4.11880i −0.0753604 0.165016i
\(624\) 0 0
\(625\) −8.48483 + 9.79201i −0.339393 + 0.391681i
\(626\) 0 0
\(627\) −9.29008 10.7213i −0.371010 0.428168i
\(628\) 0 0
\(629\) −57.7913 16.9691i −2.30429 0.676600i
\(630\) 0 0
\(631\) −4.21752 + 29.3335i −0.167897 + 1.16775i 0.715325 + 0.698792i \(0.246279\pi\)
−0.883222 + 0.468955i \(0.844631\pi\)
\(632\) 0 0
\(633\) −0.430110 + 0.941809i −0.0170953 + 0.0374336i
\(634\) 0 0
\(635\) 10.3822 6.67226i 0.412007 0.264781i
\(636\) 0 0
\(637\) −4.70412 32.7179i −0.186384 1.29633i
\(638\) 0 0
\(639\) 5.59148 + 3.59342i 0.221195 + 0.142154i
\(640\) 0 0
\(641\) 2.23010 0.654815i 0.0880835 0.0258637i −0.237394 0.971413i \(-0.576293\pi\)
0.325477 + 0.945550i \(0.394475\pi\)
\(642\) 0 0
\(643\) 5.66168 0.223275 0.111637 0.993749i \(-0.464390\pi\)
0.111637 + 0.993749i \(0.464390\pi\)
\(644\) 0 0
\(645\) −7.26622 −0.286107
\(646\) 0 0
\(647\) 39.7534 11.6726i 1.56287 0.458899i 0.617952 0.786216i \(-0.287963\pi\)
0.944915 + 0.327317i \(0.106145\pi\)
\(648\) 0 0
\(649\) 27.9855 + 17.9852i 1.09853 + 0.705979i
\(650\) 0 0
\(651\) 1.30783 + 9.09618i 0.0512580 + 0.356507i
\(652\) 0 0
\(653\) 2.41563 1.55243i 0.0945311 0.0607514i −0.492521 0.870300i \(-0.663925\pi\)
0.587052 + 0.809549i \(0.300288\pi\)
\(654\) 0 0
\(655\) 1.71128 3.74719i 0.0668653 0.146415i
\(656\) 0 0
\(657\) −1.39908 + 9.73082i −0.0545833 + 0.379635i
\(658\) 0 0
\(659\) −24.3652 7.15427i −0.949134 0.278691i −0.229708 0.973260i \(-0.573777\pi\)
−0.719426 + 0.694569i \(0.755595\pi\)
\(660\) 0 0
\(661\) −8.91404 10.2874i −0.346716 0.400132i 0.555429 0.831564i \(-0.312554\pi\)
−0.902145 + 0.431432i \(0.858008\pi\)
\(662\) 0 0
\(663\) 28.6777 33.0958i 1.11375 1.28533i
\(664\) 0 0
\(665\) −2.53094 5.54199i −0.0981457 0.214909i
\(666\) 0 0
\(667\) 3.07365 6.42008i 0.119012 0.248587i
\(668\) 0 0
\(669\) 0.245183 + 0.536876i 0.00947933 + 0.0207568i
\(670\) 0 0
\(671\) −9.57914 + 11.0549i −0.369799 + 0.426771i
\(672\) 0 0
\(673\) 20.9153 + 24.1376i 0.806227 + 0.930436i 0.998706 0.0508652i \(-0.0161979\pi\)
−0.192478 + 0.981301i \(0.561652\pi\)
\(674\) 0 0
\(675\) −3.98076 1.16886i −0.153219 0.0449893i
\(676\) 0 0
\(677\) −0.0795608 + 0.553358i −0.00305777 + 0.0212673i −0.991293 0.131673i \(-0.957965\pi\)
0.988235 + 0.152940i \(0.0488742\pi\)
\(678\) 0 0
\(679\) 4.54788 9.95846i 0.174532 0.382171i
\(680\) 0 0
\(681\) 15.5461 9.99085i 0.595727 0.382850i
\(682\) 0 0
\(683\) −0.697683 4.85249i −0.0266961 0.185675i 0.972110 0.234525i \(-0.0753535\pi\)
−0.998806 + 0.0488497i \(0.984444\pi\)
\(684\) 0 0
\(685\) −15.2109 9.77547i −0.581180 0.373502i
\(686\) 0 0
\(687\) 0.315063 0.0925108i 0.0120204 0.00352951i
\(688\) 0 0
\(689\) −22.9323 −0.873650
\(690\) 0 0
\(691\) −3.82259 −0.145418 −0.0727091 0.997353i \(-0.523164\pi\)
−0.0727091 + 0.997353i \(0.523164\pi\)
\(692\) 0 0
\(693\) 3.03910 0.892362i 0.115446 0.0338980i
\(694\) 0 0
\(695\) −0.458408 0.294601i −0.0173884 0.0111748i
\(696\) 0 0
\(697\) −9.75906 67.8757i −0.369651 2.57098i
\(698\) 0 0
\(699\) 15.6085 10.0310i 0.590369 0.379407i
\(700\) 0 0
\(701\) −8.61440 + 18.8629i −0.325361 + 0.712442i −0.999662 0.0260154i \(-0.991718\pi\)
0.674300 + 0.738457i \(0.264445\pi\)
\(702\) 0 0
\(703\) −6.36799 + 44.2904i −0.240173 + 1.67044i
\(704\) 0 0
\(705\) 8.94656 + 2.62695i 0.336947 + 0.0989366i
\(706\) 0 0
\(707\) −10.2035 11.7754i −0.383741 0.442861i
\(708\) 0 0
\(709\) −13.8730 + 16.0103i −0.521012 + 0.601280i −0.953884 0.300175i \(-0.902955\pi\)
0.432872 + 0.901455i \(0.357500\pi\)
\(710\) 0 0
\(711\) −5.10253 11.1730i −0.191360 0.419019i
\(712\) 0 0
\(713\) 4.51404 + 36.0139i 0.169052 + 1.34873i
\(714\) 0 0
\(715\) 5.98051 + 13.0955i 0.223659 + 0.489744i
\(716\) 0 0
\(717\) −3.18001 + 3.66993i −0.118760 + 0.137056i
\(718\) 0 0
\(719\) −18.3299 21.1538i −0.683589 0.788904i 0.302849 0.953039i \(-0.402062\pi\)
−0.986438 + 0.164135i \(0.947517\pi\)
\(720\) 0 0
\(721\) −7.58950 2.22848i −0.282648 0.0829928i
\(722\) 0 0
\(723\) 3.81885 26.5607i 0.142025 0.987803i
\(724\) 0 0
\(725\) −2.55797 + 5.60117i −0.0950005 + 0.208022i
\(726\) 0 0
\(727\) 10.1968 6.55311i 0.378180 0.243041i −0.337717 0.941248i \(-0.609655\pi\)
0.715896 + 0.698206i \(0.246018\pi\)
\(728\) 0 0
\(729\) −0.142315 0.989821i −0.00527092 0.0366601i
\(730\) 0 0
\(731\) 48.5029 + 31.1709i 1.79394 + 1.15290i
\(732\) 0 0
\(733\) 32.0885 9.42203i 1.18522 0.348011i 0.371033 0.928620i \(-0.379004\pi\)
0.814182 + 0.580609i \(0.197186\pi\)
\(734\) 0 0
\(735\) −5.09790 −0.188039
\(736\) 0 0
\(737\) 26.3391 0.970213
\(738\) 0 0
\(739\) −18.0190 + 5.29085i −0.662839 + 0.194627i −0.595812 0.803124i \(-0.703170\pi\)
−0.0670274 + 0.997751i \(0.521351\pi\)
\(740\) 0 0
\(741\) −27.3687 17.5888i −1.00541 0.646140i
\(742\) 0 0
\(743\) 0.518529 + 3.60645i 0.0190230 + 0.132308i 0.997120 0.0758428i \(-0.0241647\pi\)
−0.978097 + 0.208151i \(0.933256\pi\)
\(744\) 0 0
\(745\) 13.7553 8.84000i 0.503956 0.323873i
\(746\) 0 0
\(747\) 2.16853 4.74842i 0.0793424 0.173736i
\(748\) 0 0
\(749\) −0.0791714 + 0.550649i −0.00289286 + 0.0201203i
\(750\) 0 0
\(751\) 14.6666 + 4.30650i 0.535192 + 0.157146i 0.538150 0.842849i \(-0.319123\pi\)
−0.00295814 + 0.999996i \(0.500942\pi\)
\(752\) 0 0
\(753\) −0.809594 0.934321i −0.0295032 0.0340486i
\(754\) 0 0
\(755\) 8.75341 10.1020i 0.318569 0.367648i
\(756\) 0 0
\(757\) 9.93935 + 21.7642i 0.361252 + 0.791032i 0.999770 + 0.0214250i \(0.00682032\pi\)
−0.638518 + 0.769607i \(0.720452\pi\)
\(758\) 0 0
\(759\) 12.0651 3.30655i 0.437936 0.120020i
\(760\) 0 0
\(761\) −10.8888 23.8433i −0.394720 0.864317i −0.997778 0.0666199i \(-0.978779\pi\)
0.603058 0.797697i \(-0.293949\pi\)
\(762\) 0 0
\(763\) 7.30393 8.42919i 0.264420 0.305157i
\(764\) 0 0
\(765\) −4.42290 5.10430i −0.159910 0.184546i
\(766\) 0 0
\(767\) 73.1987 + 21.4931i 2.64305 + 0.776070i
\(768\) 0 0
\(769\) −3.09981 + 21.5597i −0.111782 + 0.777461i 0.854403 + 0.519611i \(0.173923\pi\)
−0.966185 + 0.257850i \(0.916986\pi\)
\(770\) 0 0
\(771\) −0.0539740 + 0.118186i −0.00194382 + 0.00425638i
\(772\) 0 0
\(773\) −3.38153 + 2.17318i −0.121625 + 0.0781638i −0.600039 0.799971i \(-0.704848\pi\)
0.478414 + 0.878135i \(0.341212\pi\)
\(774\) 0 0
\(775\) −4.46854 31.0794i −0.160515 1.11640i
\(776\) 0 0
\(777\) −8.40452 5.40126i −0.301510 0.193769i
\(778\) 0 0
\(779\) −48.8800 + 14.3525i −1.75131 + 0.514231i
\(780\) 0 0
\(781\) 17.3378 0.620394
\(782\) 0 0
\(783\) −1.48419 −0.0530406
\(784\) 0 0
\(785\) 0.321564 0.0944196i 0.0114771 0.00336998i
\(786\) 0 0
\(787\) −20.4488 13.1417i −0.728921 0.468449i 0.122809 0.992430i \(-0.460810\pi\)
−0.851730 + 0.523981i \(0.824446\pi\)
\(788\) 0 0
\(789\) −0.0268550 0.186781i −0.000956065 0.00664957i
\(790\) 0 0
\(791\) −0.871313 + 0.559959i −0.0309803 + 0.0199098i
\(792\) 0 0
\(793\) −13.9353 + 30.5140i −0.494857 + 1.08359i
\(794\) 0 0
\(795\) −0.503339 + 3.50080i −0.0178516 + 0.124161i
\(796\) 0 0
\(797\) 14.3220 + 4.20532i 0.507311 + 0.148960i 0.525365 0.850877i \(-0.323929\pi\)
−0.0180536 + 0.999837i \(0.505747\pi\)
\(798\) 0 0
\(799\) −48.4502 55.9145i −1.71404 1.97811i
\(800\) 0 0
\(801\) −2.44199 + 2.81821i −0.0862835 + 0.0995765i
\(802\) 0 0
\(803\) 10.6529 + 23.3266i 0.375933 + 0.823179i
\(804\) 0 0
\(805\) 5.37175 + 0.0972853i 0.189329 + 0.00342886i
\(806\) 0 0
\(807\) −8.91436 19.5197i −0.313800 0.687127i
\(808\) 0 0
\(809\) 20.2201 23.3352i 0.710901 0.820423i −0.279281 0.960209i \(-0.590096\pi\)
0.990182 + 0.139786i \(0.0446416\pi\)
\(810\) 0 0
\(811\) 5.84825 + 6.74925i 0.205360 + 0.236998i 0.849082 0.528262i \(-0.177156\pi\)
−0.643722 + 0.765260i \(0.722611\pi\)
\(812\) 0 0
\(813\) 3.38578 + 0.994156i 0.118745 + 0.0348666i
\(814\) 0 0
\(815\) −1.51009 + 10.5029i −0.0528961 + 0.367901i
\(816\) 0 0
\(817\) 17.7932 38.9617i 0.622506 1.36310i
\(818\) 0 0
\(819\) 6.11064 3.92707i 0.213523 0.137223i
\(820\) 0 0
\(821\) 2.47290 + 17.1994i 0.0863047 + 0.600263i 0.986374 + 0.164517i \(0.0526064\pi\)
−0.900070 + 0.435746i \(0.856485\pi\)
\(822\) 0 0
\(823\) 17.6060 + 11.3147i 0.613707 + 0.394405i 0.810245 0.586091i \(-0.199334\pi\)
−0.196539 + 0.980496i \(0.562970\pi\)
\(824\) 0 0
\(825\) −10.3839 + 3.04898i −0.361520 + 0.106152i
\(826\) 0 0
\(827\) −17.6637 −0.614226 −0.307113 0.951673i \(-0.599363\pi\)
−0.307113 + 0.951673i \(0.599363\pi\)
\(828\) 0 0
\(829\) 32.0581 1.11343 0.556713 0.830705i \(-0.312062\pi\)
0.556713 + 0.830705i \(0.312062\pi\)
\(830\) 0 0
\(831\) 17.8951 5.25448i 0.620775 0.182276i
\(832\) 0 0
\(833\) 34.0291 + 21.8691i 1.17904 + 0.757721i
\(834\) 0 0
\(835\) 0.618603 + 4.30248i 0.0214076 + 0.148893i
\(836\) 0 0
\(837\) 6.36676 4.09167i 0.220067 0.141429i
\(838\) 0 0
\(839\) 9.20564 20.1575i 0.317814 0.695916i −0.681543 0.731778i \(-0.738691\pi\)
0.999357 + 0.0358627i \(0.0114179\pi\)
\(840\) 0 0
\(841\) 3.81364 26.5244i 0.131505 0.914635i
\(842\) 0 0
\(843\) 26.0896 + 7.66061i 0.898575 + 0.263845i
\(844\) 0 0
\(845\) 13.7660 + 15.8868i 0.473566 + 0.546524i
\(846\) 0 0
\(847\) −3.33624 + 3.85023i −0.114635 + 0.132295i
\(848\) 0 0
\(849\) 1.54319 + 3.37912i 0.0529623 + 0.115971i
\(850\) 0 0
\(851\) −32.8028 21.9304i −1.12447 0.751764i
\(852\) 0 0
\(853\) −19.5118 42.7250i −0.668073 1.46288i −0.874804 0.484478i \(-0.839010\pi\)
0.206731 0.978398i \(-0.433718\pi\)
\(854\) 0 0
\(855\) −3.28578 + 3.79199i −0.112371 + 0.129683i
\(856\) 0 0
\(857\) 6.20842 + 7.16489i 0.212075 + 0.244748i 0.851814 0.523845i \(-0.175503\pi\)
−0.639738 + 0.768593i \(0.720957\pi\)
\(858\) 0 0
\(859\) −30.2143 8.87171i −1.03090 0.302699i −0.277822 0.960633i \(-0.589613\pi\)
−0.753076 + 0.657934i \(0.771431\pi\)
\(860\) 0 0
\(861\) 1.61873 11.2585i 0.0551660 0.383688i
\(862\) 0 0
\(863\) −14.4440 + 31.6278i −0.491678 + 1.07662i 0.487407 + 0.873175i \(0.337943\pi\)
−0.979085 + 0.203450i \(0.934785\pi\)
\(864\) 0 0
\(865\) 6.03077 3.87574i 0.205052 0.131779i
\(866\) 0 0
\(867\) 5.20741 + 36.2183i 0.176853 + 1.23004i
\(868\) 0 0
\(869\) −26.9540 17.3223i −0.914353 0.587619i
\(870\) 0 0
\(871\) 57.9561 17.0174i 1.96377 0.576614i
\(872\) 0 0
\(873\) −9.01605 −0.305147
\(874\) 0 0
\(875\) −10.2492 −0.346485
\(876\) 0 0
\(877\) 22.3108 6.55106i 0.753384 0.221213i 0.117579 0.993064i \(-0.462487\pi\)
0.635805 + 0.771850i \(0.280668\pi\)
\(878\) 0 0
\(879\) 14.2379 + 9.15017i 0.480234 + 0.308628i
\(880\) 0 0
\(881\) −7.44501 51.7812i −0.250829 1.74455i −0.593262 0.805010i \(-0.702160\pi\)
0.342433 0.939542i \(-0.388749\pi\)
\(882\) 0 0
\(883\) 1.81544 1.16672i 0.0610946 0.0392631i −0.509737 0.860330i \(-0.670257\pi\)
0.570832 + 0.821067i \(0.306621\pi\)
\(884\) 0 0
\(885\) 4.88773 10.7026i 0.164299 0.359765i
\(886\) 0 0
\(887\) 1.82373 12.6844i 0.0612350 0.425899i −0.936026 0.351932i \(-0.885525\pi\)
0.997261 0.0739672i \(-0.0235660\pi\)
\(888\) 0 0
\(889\) −15.5849 4.57613i −0.522700 0.153479i
\(890\) 0 0
\(891\) −1.70822 1.97139i −0.0572274 0.0660439i
\(892\) 0 0
\(893\) −35.9938 + 41.5390i −1.20449 + 1.39005i
\(894\) 0 0
\(895\) 5.66780 + 12.4108i 0.189454 + 0.414846i
\(896\) 0 0
\(897\) 24.4115 15.0708i 0.815077 0.503200i
\(898\) 0 0
\(899\) −4.66620 10.2175i −0.155626 0.340774i
\(900\) 0 0
\(901\) 18.3777 21.2090i 0.612250 0.706574i
\(902\) 0 0
\(903\) 6.26260 + 7.22743i 0.208406 + 0.240514i
\(904\) 0 0
\(905\) −16.7351 4.91386i −0.556292 0.163342i
\(906\) 0 0
\(907\) −1.27805 + 8.88901i −0.0424368 + 0.295155i 0.957540 + 0.288302i \(0.0930905\pi\)
−0.999977 + 0.00685318i \(0.997819\pi\)
\(908\) 0 0
\(909\) −5.33054 + 11.6723i −0.176803 + 0.387144i
\(910\) 0 0
\(911\) 15.0425 9.66724i 0.498381 0.320290i −0.267187 0.963645i \(-0.586094\pi\)
0.765568 + 0.643355i \(0.222458\pi\)
\(912\) 0 0
\(913\) −1.93788 13.4783i −0.0641345 0.446066i
\(914\) 0 0
\(915\) 4.35235 + 2.79709i 0.143884 + 0.0924688i
\(916\) 0 0
\(917\) −5.20210 + 1.52747i −0.171788 + 0.0504416i
\(918\) 0 0
\(919\) 52.1924 1.72167 0.860835 0.508885i \(-0.169942\pi\)
0.860835 + 0.508885i \(0.169942\pi\)
\(920\) 0 0
\(921\) 28.7453 0.947189
\(922\) 0 0
\(923\) 38.1497 11.2018i 1.25571 0.368711i
\(924\) 0 0
\(925\) 28.7161 + 18.4547i 0.944181 + 0.606788i
\(926\) 0 0
\(927\) 0.927067 + 6.44789i 0.0304489 + 0.211777i
\(928\) 0 0
\(929\) −22.6910 + 14.5826i −0.744467 + 0.478440i −0.857070 0.515200i \(-0.827718\pi\)
0.112603 + 0.993640i \(0.464081\pi\)
\(930\) 0 0
\(931\) 12.4835 27.3351i 0.409131 0.895871i
\(932\) 0 0
\(933\) 3.67621 25.5686i 0.120354 0.837078i
\(934\) 0 0
\(935\) −16.9041 4.96351i −0.552825 0.162324i
\(936\) 0 0
\(937\) 25.9973 + 30.0025i 0.849296 + 0.980140i 0.999964 0.00844436i \(-0.00268796\pi\)
−0.150668 + 0.988584i \(0.548143\pi\)
\(938\) 0 0
\(939\) 7.63294 8.80888i 0.249092 0.287467i
\(940\) 0 0
\(941\) −16.0338 35.1090i −0.522686 1.14452i −0.968413 0.249353i \(-0.919782\pi\)
0.445727 0.895169i \(-0.352945\pi\)
\(942\) 0 0
\(943\) 7.19746 44.3435i 0.234382 1.44402i
\(944\) 0 0
\(945\) −0.465378 1.01903i −0.0151387 0.0331492i
\(946\) 0 0
\(947\) −23.9757 + 27.6694i −0.779106 + 0.899136i −0.997044 0.0768267i \(-0.975521\pi\)
0.217939 + 0.975962i \(0.430067\pi\)
\(948\) 0 0
\(949\) 38.5116 + 44.4447i 1.25014 + 1.44274i
\(950\) 0 0
\(951\) −14.8939 4.37325i −0.482968 0.141812i
\(952\) 0 0
\(953\) −6.45166 + 44.8723i −0.208990 + 1.45356i 0.567472 + 0.823393i \(0.307921\pi\)
−0.776462 + 0.630164i \(0.782988\pi\)
\(954\) 0 0
\(955\) 0.141312 0.309430i 0.00457275 0.0100129i
\(956\) 0 0
\(957\) −3.25694 + 2.09311i −0.105282 + 0.0676606i
\(958\) 0 0
\(959\) 3.38670 + 23.5550i 0.109362 + 0.760631i
\(960\) 0 0
\(961\) 22.1060 + 14.2066i 0.713096 + 0.458279i
\(962\) 0 0
\(963\) 0.439592 0.129076i 0.0141656 0.00415941i
\(964\) 0 0
\(965\) 18.3376 0.590308
\(966\) 0 0
\(967\) 8.82892 0.283919 0.141959 0.989872i \(-0.454660\pi\)
0.141959 + 0.989872i \(0.454660\pi\)
\(968\) 0 0
\(969\) 38.2000 11.2165i 1.22716 0.360327i
\(970\) 0 0
\(971\) −6.37284 4.09558i −0.204514 0.131433i 0.434375 0.900732i \(-0.356969\pi\)
−0.638889 + 0.769299i \(0.720606\pi\)
\(972\) 0 0
\(973\) 0.102064 + 0.709871i 0.00327202 + 0.0227574i
\(974\) 0 0
\(975\) −20.8786 + 13.4178i −0.668649 + 0.429715i
\(976\) 0 0
\(977\) −8.42213 + 18.4419i −0.269448 + 0.590008i −0.995191 0.0979579i \(-0.968769\pi\)
0.725743 + 0.687966i \(0.241496\pi\)
\(978\) 0 0
\(979\) −1.38433 + 9.62821i −0.0442433 + 0.307719i
\(980\) 0 0
\(981\) −8.81331 2.58782i −0.281387 0.0826228i
\(982\) 0 0
\(983\) −13.7231 15.8373i −0.437698 0.505131i 0.493449 0.869775i \(-0.335736\pi\)
−0.931147 + 0.364644i \(0.881191\pi\)
\(984\) 0 0
\(985\) 2.23928 2.58427i 0.0713495 0.0823417i
\(986\) 0 0
\(987\) −5.09793 11.1629i −0.162269 0.355319i
\(988\) 0 0
\(989\) 24.2139 + 28.9887i 0.769956 + 0.921786i
\(990\) 0 0
\(991\) −11.5706 25.3360i −0.367551 0.804825i −0.999554 0.0298588i \(-0.990494\pi\)
0.632003 0.774966i \(-0.282233\pi\)
\(992\) 0 0
\(993\) −20.6121 + 23.7876i −0.654104 + 0.754876i
\(994\) 0 0
\(995\) 4.39454 + 5.07156i 0.139316 + 0.160779i
\(996\) 0 0
\(997\) 37.6349 + 11.0506i 1.19191 + 0.349976i 0.816754 0.576987i \(-0.195772\pi\)
0.375154 + 0.926962i \(0.377590\pi\)
\(998\) 0 0
\(999\) −1.17092 + 8.14390i −0.0370461 + 0.257662i
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 552.2.q.d.73.1 30
23.6 even 11 inner 552.2.q.d.121.1 yes 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.q.d.73.1 30 1.1 even 1 trivial
552.2.q.d.121.1 yes 30 23.6 even 11 inner