Properties

Label 525.2.bf.f.107.6
Level $525$
Weight $2$
Character 525.107
Analytic conductor $4.192$
Analytic rank $0$
Dimension $48$
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] = [525,2,Mod(32,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.32");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bf (of order \(12\), degree \(4\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 107.6
Character \(\chi\) \(=\) 525.107
Dual form 525.2.bf.f.368.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0799329 - 0.298314i) q^{2} +(-0.540759 - 1.64547i) q^{3} +(1.64945 - 0.952310i) q^{4} +(-0.447643 + 0.292843i) q^{6} +(2.46856 - 0.951942i) q^{7} +(-0.852694 - 0.852694i) q^{8} +(-2.41516 + 1.77961i) q^{9} +O(q^{10})\) \(q+(-0.0799329 - 0.298314i) q^{2} +(-0.540759 - 1.64547i) q^{3} +(1.64945 - 0.952310i) q^{4} +(-0.447643 + 0.292843i) q^{6} +(2.46856 - 0.951942i) q^{7} +(-0.852694 - 0.852694i) q^{8} +(-2.41516 + 1.77961i) q^{9} +(0.660315 - 0.381233i) q^{11} +(-2.45895 - 2.19915i) q^{12} +(2.27077 - 2.27077i) q^{13} +(-0.481297 - 0.660315i) q^{14} +(1.71841 - 2.97637i) q^{16} +(4.69471 + 1.25794i) q^{17} +(0.723932 + 0.578226i) q^{18} +(-1.41761 - 0.818455i) q^{19} +(-2.90129 - 3.54718i) q^{21} +(-0.166508 - 0.166508i) q^{22} +(-7.39003 + 1.98015i) q^{23} +(-0.941983 + 1.86419i) q^{24} +(-0.858909 - 0.495891i) q^{26} +(4.23432 + 3.01174i) q^{27} +(3.16523 - 3.92102i) q^{28} -4.94251 q^{29} +(2.96413 + 5.13403i) q^{31} +(-3.35485 - 0.898930i) q^{32} +(-0.984380 - 0.880375i) q^{33} -1.50105i q^{34} +(-2.28894 + 5.23535i) q^{36} +(-3.41587 + 0.915280i) q^{37} +(-0.130843 + 0.488313i) q^{38} +(-4.96442 - 2.50855i) q^{39} -4.35963i q^{41} +(-0.826265 + 1.14903i) q^{42} +(-2.69037 + 2.69037i) q^{43} +(0.726104 - 1.25765i) q^{44} +(1.18141 + 2.04627i) q^{46} +(-1.10971 - 4.14148i) q^{47} +(-5.82678 - 1.21809i) q^{48} +(5.18761 - 4.69986i) q^{49} +(-0.468795 - 8.40527i) q^{51} +(1.58304 - 5.90798i) q^{52} +(1.79889 - 6.71354i) q^{53} +(0.559982 - 1.50389i) q^{54} +(-2.91664 - 1.29321i) q^{56} +(-0.580162 + 2.77522i) q^{57} +(0.395069 + 1.47442i) q^{58} +(3.84501 + 6.65975i) q^{59} +(-2.19699 + 3.80529i) q^{61} +(1.29462 - 1.29462i) q^{62} +(-4.26789 + 6.69217i) q^{63} -5.80098i q^{64} +(-0.183944 + 0.364025i) q^{66} +(-0.0126297 + 0.0471345i) q^{67} +(8.94164 - 2.39591i) q^{68} +(7.25451 + 11.0893i) q^{69} +12.4172i q^{71} +(3.57685 + 0.541931i) q^{72} +(1.34043 + 0.359168i) q^{73} +(0.546081 + 0.945840i) q^{74} -3.11769 q^{76} +(1.26712 - 1.56968i) q^{77} +(-0.351513 + 1.68147i) q^{78} +(3.66808 + 2.11777i) q^{79} +(2.66599 - 8.59607i) q^{81} +(-1.30054 + 0.348478i) q^{82} +(5.05351 + 5.05351i) q^{83} +(-8.16355 - 3.08797i) q^{84} +(1.01762 + 0.587525i) q^{86} +(2.67271 + 8.13276i) q^{87} +(-0.888122 - 0.237971i) q^{88} +(-0.453600 + 0.785658i) q^{89} +(3.44389 - 7.76716i) q^{91} +(-10.3038 + 10.3038i) q^{92} +(6.84502 - 7.65367i) q^{93} +(-1.14676 + 0.662081i) q^{94} +(0.335002 + 6.00642i) q^{96} +(-3.73061 - 3.73061i) q^{97} +(-1.81669 - 1.17186i) q^{98} +(-0.916321 + 2.09584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 2 q^{3} - 24 q^{6} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 2 q^{3} - 24 q^{6} + 12 q^{7} + 10 q^{12} + 16 q^{13} - 8 q^{16} - 14 q^{18} - 28 q^{21} + 8 q^{22} - 40 q^{27} + 60 q^{28} - 24 q^{31} + 4 q^{33} + 8 q^{36} - 4 q^{37} - 14 q^{42} - 16 q^{43} - 32 q^{46} - 44 q^{48} + 8 q^{51} - 36 q^{52} + 88 q^{57} - 56 q^{58} - 8 q^{61} - 44 q^{63} + 76 q^{66} - 12 q^{67} + 34 q^{72} - 52 q^{73} + 64 q^{76} + 120 q^{78} + 20 q^{81} - 104 q^{82} + 46 q^{87} + 72 q^{91} + 44 q^{93} + 12 q^{96} + 120 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0799329 0.298314i −0.0565211 0.210940i 0.931890 0.362741i \(-0.118159\pi\)
−0.988411 + 0.151802i \(0.951492\pi\)
\(3\) −0.540759 1.64547i −0.312207 0.950014i
\(4\) 1.64945 0.952310i 0.824725 0.476155i
\(5\) 0 0
\(6\) −0.447643 + 0.292843i −0.182749 + 0.119553i
\(7\) 2.46856 0.951942i 0.933029 0.359800i
\(8\) −0.852694 0.852694i −0.301473 0.301473i
\(9\) −2.41516 + 1.77961i −0.805053 + 0.593203i
\(10\) 0 0
\(11\) 0.660315 0.381233i 0.199092 0.114946i −0.397140 0.917758i \(-0.629997\pi\)
0.596232 + 0.802812i \(0.296664\pi\)
\(12\) −2.45895 2.19915i −0.709839 0.634841i
\(13\) 2.27077 2.27077i 0.629797 0.629797i −0.318220 0.948017i \(-0.603085\pi\)
0.948017 + 0.318220i \(0.103085\pi\)
\(14\) −0.481297 0.660315i −0.128632 0.176477i
\(15\) 0 0
\(16\) 1.71841 2.97637i 0.429602 0.744092i
\(17\) 4.69471 + 1.25794i 1.13864 + 0.305096i 0.778402 0.627766i \(-0.216030\pi\)
0.360233 + 0.932862i \(0.382697\pi\)
\(18\) 0.723932 + 0.578226i 0.170632 + 0.136289i
\(19\) −1.41761 0.818455i −0.325221 0.187767i 0.328496 0.944505i \(-0.393458\pi\)
−0.653717 + 0.756739i \(0.726791\pi\)
\(20\) 0 0
\(21\) −2.90129 3.54718i −0.633114 0.774059i
\(22\) −0.166508 0.166508i −0.0354996 0.0354996i
\(23\) −7.39003 + 1.98015i −1.54093 + 0.412890i −0.926566 0.376133i \(-0.877253\pi\)
−0.614363 + 0.789024i \(0.710587\pi\)
\(24\) −0.941983 + 1.86419i −0.192281 + 0.380525i
\(25\) 0 0
\(26\) −0.858909 0.495891i −0.168446 0.0972523i
\(27\) 4.23432 + 3.01174i 0.814894 + 0.579610i
\(28\) 3.16523 3.92102i 0.598172 0.741003i
\(29\) −4.94251 −0.917801 −0.458900 0.888488i \(-0.651757\pi\)
−0.458900 + 0.888488i \(0.651757\pi\)
\(30\) 0 0
\(31\) 2.96413 + 5.13403i 0.532374 + 0.922099i 0.999286 + 0.0377949i \(0.0120334\pi\)
−0.466911 + 0.884304i \(0.654633\pi\)
\(32\) −3.35485 0.898930i −0.593060 0.158910i
\(33\) −0.984380 0.880375i −0.171358 0.153254i
\(34\) 1.50105i 0.257428i
\(35\) 0 0
\(36\) −2.28894 + 5.23535i −0.381491 + 0.872559i
\(37\) −3.41587 + 0.915280i −0.561566 + 0.150471i −0.528426 0.848980i \(-0.677217\pi\)
−0.0331401 + 0.999451i \(0.510551\pi\)
\(38\) −0.130843 + 0.488313i −0.0212255 + 0.0792148i
\(39\) −4.96442 2.50855i −0.794943 0.401689i
\(40\) 0 0
\(41\) 4.35963i 0.680860i −0.940270 0.340430i \(-0.889427\pi\)
0.940270 0.340430i \(-0.110573\pi\)
\(42\) −0.826265 + 1.14903i −0.127495 + 0.177299i
\(43\) −2.69037 + 2.69037i −0.410277 + 0.410277i −0.881835 0.471558i \(-0.843692\pi\)
0.471558 + 0.881835i \(0.343692\pi\)
\(44\) 0.726104 1.25765i 0.109464 0.189598i
\(45\) 0 0
\(46\) 1.18141 + 2.04627i 0.174190 + 0.301706i
\(47\) −1.10971 4.14148i −0.161867 0.604097i −0.998419 0.0562089i \(-0.982099\pi\)
0.836552 0.547888i \(-0.184568\pi\)
\(48\) −5.82678 1.21809i −0.841023 0.175817i
\(49\) 5.18761 4.69986i 0.741088 0.671408i
\(50\) 0 0
\(51\) −0.468795 8.40527i −0.0656444 1.17697i
\(52\) 1.58304 5.90798i 0.219528 0.819290i
\(53\) 1.79889 6.71354i 0.247096 0.922176i −0.725222 0.688515i \(-0.758263\pi\)
0.972318 0.233661i \(-0.0750705\pi\)
\(54\) 0.559982 1.50389i 0.0762039 0.204654i
\(55\) 0 0
\(56\) −2.91664 1.29321i −0.389753 0.172813i
\(57\) −0.580162 + 2.77522i −0.0768444 + 0.367587i
\(58\) 0.395069 + 1.47442i 0.0518751 + 0.193601i
\(59\) 3.84501 + 6.65975i 0.500577 + 0.867026i 1.00000 0.000666931i \(0.000212291\pi\)
−0.499422 + 0.866359i \(0.666454\pi\)
\(60\) 0 0
\(61\) −2.19699 + 3.80529i −0.281295 + 0.487218i −0.971704 0.236202i \(-0.924097\pi\)
0.690409 + 0.723420i \(0.257431\pi\)
\(62\) 1.29462 1.29462i 0.164417 0.164417i
\(63\) −4.26789 + 6.69217i −0.537704 + 0.843134i
\(64\) 5.80098i 0.725122i
\(65\) 0 0
\(66\) −0.183944 + 0.364025i −0.0226419 + 0.0448084i
\(67\) −0.0126297 + 0.0471345i −0.00154296 + 0.00575840i −0.966693 0.255939i \(-0.917615\pi\)
0.965150 + 0.261697i \(0.0842821\pi\)
\(68\) 8.94164 2.39591i 1.08433 0.290546i
\(69\) 7.25451 + 11.0893i 0.873341 + 1.33500i
\(70\) 0 0
\(71\) 12.4172i 1.47365i 0.676082 + 0.736826i \(0.263676\pi\)
−0.676082 + 0.736826i \(0.736324\pi\)
\(72\) 3.57685 + 0.541931i 0.421536 + 0.0638672i
\(73\) 1.34043 + 0.359168i 0.156886 + 0.0420374i 0.336407 0.941717i \(-0.390788\pi\)
−0.179521 + 0.983754i \(0.557455\pi\)
\(74\) 0.546081 + 0.945840i 0.0634806 + 0.109952i
\(75\) 0 0
\(76\) −3.11769 −0.357624
\(77\) 1.26712 1.56968i 0.144401 0.178882i
\(78\) −0.351513 + 1.68147i −0.0398010 + 0.190389i
\(79\) 3.66808 + 2.11777i 0.412692 + 0.238268i 0.691946 0.721950i \(-0.256754\pi\)
−0.279254 + 0.960217i \(0.590087\pi\)
\(80\) 0 0
\(81\) 2.66599 8.59607i 0.296221 0.955119i
\(82\) −1.30054 + 0.348478i −0.143620 + 0.0384830i
\(83\) 5.05351 + 5.05351i 0.554695 + 0.554695i 0.927792 0.373097i \(-0.121704\pi\)
−0.373097 + 0.927792i \(0.621704\pi\)
\(84\) −8.16355 3.08797i −0.890716 0.336925i
\(85\) 0 0
\(86\) 1.01762 + 0.587525i 0.109733 + 0.0633544i
\(87\) 2.67271 + 8.13276i 0.286544 + 0.871924i
\(88\) −0.888122 0.237971i −0.0946741 0.0253678i
\(89\) −0.453600 + 0.785658i −0.0480815 + 0.0832796i −0.889065 0.457782i \(-0.848644\pi\)
0.840983 + 0.541061i \(0.181977\pi\)
\(90\) 0 0
\(91\) 3.44389 7.76716i 0.361018 0.814220i
\(92\) −10.3038 + 10.3038i −1.07424 + 1.07424i
\(93\) 6.84502 7.65367i 0.709796 0.793649i
\(94\) −1.14676 + 0.662081i −0.118279 + 0.0682884i
\(95\) 0 0
\(96\) 0.335002 + 6.00642i 0.0341910 + 0.613028i
\(97\) −3.73061 3.73061i −0.378786 0.378786i 0.491878 0.870664i \(-0.336311\pi\)
−0.870664 + 0.491878i \(0.836311\pi\)
\(98\) −1.81669 1.17186i −0.183514 0.118376i
\(99\) −0.916321 + 2.09584i −0.0920937 + 0.210640i
\(100\) 0 0
\(101\) 16.4444 9.49420i 1.63628 0.944708i 0.654185 0.756335i \(-0.273012\pi\)
0.982098 0.188373i \(-0.0603214\pi\)
\(102\) −2.46993 + 0.811705i −0.244560 + 0.0803708i
\(103\) 3.26921 + 12.2009i 0.322125 + 1.20219i 0.917171 + 0.398494i \(0.130467\pi\)
−0.595046 + 0.803692i \(0.702866\pi\)
\(104\) −3.87254 −0.379733
\(105\) 0 0
\(106\) −2.14653 −0.208490
\(107\) 0.564395 + 2.10635i 0.0545621 + 0.203629i 0.987826 0.155563i \(-0.0497191\pi\)
−0.933264 + 0.359192i \(0.883052\pi\)
\(108\) 9.85240 + 0.935331i 0.948047 + 0.0900023i
\(109\) −2.04357 + 1.17986i −0.195739 + 0.113010i −0.594666 0.803973i \(-0.702716\pi\)
0.398928 + 0.916982i \(0.369382\pi\)
\(110\) 0 0
\(111\) 3.35323 + 5.12578i 0.318275 + 0.486517i
\(112\) 1.40867 8.98318i 0.133107 0.848831i
\(113\) 11.9386 + 11.9386i 1.12309 + 1.12309i 0.991274 + 0.131814i \(0.0420801\pi\)
0.131814 + 0.991274i \(0.457920\pi\)
\(114\) 0.874260 0.0487609i 0.0818819 0.00456688i
\(115\) 0 0
\(116\) −8.15242 + 4.70680i −0.756933 + 0.437015i
\(117\) −1.44319 + 9.52533i −0.133423 + 0.880617i
\(118\) 1.67935 1.67935i 0.154597 0.154597i
\(119\) 12.7867 1.36378i 1.17215 0.125017i
\(120\) 0 0
\(121\) −5.20932 + 9.02281i −0.473575 + 0.820256i
\(122\) 1.31078 + 0.351223i 0.118673 + 0.0317983i
\(123\) −7.17366 + 2.35751i −0.646827 + 0.212570i
\(124\) 9.77837 + 5.64555i 0.878124 + 0.506985i
\(125\) 0 0
\(126\) 2.33751 + 0.738246i 0.208242 + 0.0657682i
\(127\) −4.46126 4.46126i −0.395873 0.395873i 0.480901 0.876775i \(-0.340309\pi\)
−0.876775 + 0.480901i \(0.840309\pi\)
\(128\) −8.44022 + 2.26155i −0.746017 + 0.199895i
\(129\) 5.88177 + 2.97209i 0.517861 + 0.261678i
\(130\) 0 0
\(131\) 1.86149 + 1.07473i 0.162639 + 0.0938999i 0.579111 0.815249i \(-0.303400\pi\)
−0.416471 + 0.909149i \(0.636733\pi\)
\(132\) −2.46207 0.514699i −0.214296 0.0447988i
\(133\) −4.27857 0.670931i −0.370999 0.0581771i
\(134\) 0.0150704 0.00130188
\(135\) 0 0
\(136\) −2.93051 5.07580i −0.251289 0.435246i
\(137\) 8.51678 + 2.28207i 0.727638 + 0.194970i 0.603577 0.797305i \(-0.293742\pi\)
0.124061 + 0.992275i \(0.460408\pi\)
\(138\) 2.72822 3.05052i 0.232241 0.259678i
\(139\) 10.3626i 0.878941i −0.898257 0.439471i \(-0.855166\pi\)
0.898257 0.439471i \(-0.144834\pi\)
\(140\) 0 0
\(141\) −6.21461 + 4.06553i −0.523364 + 0.342380i
\(142\) 3.70423 0.992544i 0.310852 0.0832925i
\(143\) 0.633730 2.36511i 0.0529951 0.197780i
\(144\) 1.14654 + 10.2465i 0.0955452 + 0.853875i
\(145\) 0 0
\(146\) 0.428578i 0.0354694i
\(147\) −10.5387 5.99459i −0.869220 0.494425i
\(148\) −4.76267 + 4.76267i −0.391489 + 0.391489i
\(149\) 8.72716 15.1159i 0.714957 1.23834i −0.248019 0.968755i \(-0.579780\pi\)
0.962976 0.269586i \(-0.0868870\pi\)
\(150\) 0 0
\(151\) 7.60786 + 13.1772i 0.619119 + 1.07235i 0.989647 + 0.143524i \(0.0458434\pi\)
−0.370528 + 0.928821i \(0.620823\pi\)
\(152\) 0.510892 + 1.90668i 0.0414388 + 0.154652i
\(153\) −13.5771 + 5.31661i −1.09765 + 0.429823i
\(154\) −0.569541 0.252530i −0.0458949 0.0203494i
\(155\) 0 0
\(156\) −10.5775 + 0.589947i −0.846875 + 0.0472336i
\(157\) −2.36469 + 8.82516i −0.188723 + 0.704324i 0.805080 + 0.593167i \(0.202122\pi\)
−0.993803 + 0.111158i \(0.964544\pi\)
\(158\) 0.338559 1.26352i 0.0269343 0.100520i
\(159\) −12.0197 + 0.670387i −0.953225 + 0.0531652i
\(160\) 0 0
\(161\) −16.3578 + 11.9230i −1.28917 + 0.939665i
\(162\) −2.77743 0.108192i −0.218215 0.00850040i
\(163\) −0.700710 2.61508i −0.0548838 0.204829i 0.933039 0.359775i \(-0.117146\pi\)
−0.987923 + 0.154946i \(0.950480\pi\)
\(164\) −4.15172 7.19099i −0.324195 0.561522i
\(165\) 0 0
\(166\) 1.10359 1.91147i 0.0856551 0.148359i
\(167\) −3.85551 + 3.85551i −0.298348 + 0.298348i −0.840367 0.542018i \(-0.817660\pi\)
0.542018 + 0.840367i \(0.317660\pi\)
\(168\) −0.550747 + 5.49857i −0.0424911 + 0.424224i
\(169\) 2.68725i 0.206712i
\(170\) 0 0
\(171\) 4.88027 0.546083i 0.373204 0.0417600i
\(172\) −1.87556 + 6.99969i −0.143010 + 0.533721i
\(173\) −1.27815 + 0.342481i −0.0971763 + 0.0260383i −0.307080 0.951684i \(-0.599352\pi\)
0.209903 + 0.977722i \(0.432685\pi\)
\(174\) 2.21248 1.44738i 0.167727 0.109726i
\(175\) 0 0
\(176\) 2.62045i 0.197524i
\(177\) 8.87921 9.92818i 0.667403 0.746247i
\(178\) 0.270630 + 0.0725151i 0.0202846 + 0.00543524i
\(179\) 0.120836 + 0.209294i 0.00903168 + 0.0156433i 0.870506 0.492158i \(-0.163792\pi\)
−0.861474 + 0.507801i \(0.830458\pi\)
\(180\) 0 0
\(181\) 18.6864 1.38895 0.694475 0.719517i \(-0.255637\pi\)
0.694475 + 0.719517i \(0.255637\pi\)
\(182\) −2.59233 0.406508i −0.192156 0.0301324i
\(183\) 7.44955 + 1.55734i 0.550686 + 0.115122i
\(184\) 7.98990 + 4.61297i 0.589023 + 0.340073i
\(185\) 0 0
\(186\) −2.83034 1.43018i −0.207530 0.104866i
\(187\) 3.57956 0.959140i 0.261763 0.0701393i
\(188\) −5.77437 5.77437i −0.421140 0.421140i
\(189\) 13.3197 + 3.40385i 0.968864 + 0.247594i
\(190\) 0 0
\(191\) −12.3330 7.12049i −0.892388 0.515220i −0.0176651 0.999844i \(-0.505623\pi\)
−0.874723 + 0.484624i \(0.838957\pi\)
\(192\) −9.54535 + 3.13693i −0.688876 + 0.226388i
\(193\) 6.58385 + 1.76414i 0.473916 + 0.126985i 0.487868 0.872917i \(-0.337775\pi\)
−0.0139523 + 0.999903i \(0.504441\pi\)
\(194\) −0.814694 + 1.41109i −0.0584916 + 0.101310i
\(195\) 0 0
\(196\) 4.08099 12.6924i 0.291499 0.906599i
\(197\) 7.65626 7.65626i 0.545486 0.545486i −0.379646 0.925132i \(-0.623954\pi\)
0.925132 + 0.379646i \(0.123954\pi\)
\(198\) 0.698462 + 0.105824i 0.0496375 + 0.00752061i
\(199\) −14.1855 + 8.19000i −1.00558 + 0.580573i −0.909895 0.414838i \(-0.863838\pi\)
−0.0956874 + 0.995411i \(0.530505\pi\)
\(200\) 0 0
\(201\) 0.0843881 0.00470666i 0.00595228 0.000331982i
\(202\) −4.14670 4.14670i −0.291761 0.291761i
\(203\) −12.2009 + 4.70498i −0.856335 + 0.330225i
\(204\) −8.77767 13.4176i −0.614560 0.939421i
\(205\) 0 0
\(206\) 3.37836 1.95050i 0.235382 0.135898i
\(207\) 14.3242 17.9337i 0.995601 1.24648i
\(208\) −2.85654 10.6607i −0.198065 0.739189i
\(209\) −1.24809 −0.0863321
\(210\) 0 0
\(211\) −25.5028 −1.75568 −0.877842 0.478950i \(-0.841018\pi\)
−0.877842 + 0.478950i \(0.841018\pi\)
\(212\) −3.42620 12.7867i −0.235312 0.878197i
\(213\) 20.4322 6.71472i 1.39999 0.460085i
\(214\) 0.583239 0.336733i 0.0398694 0.0230186i
\(215\) 0 0
\(216\) −1.04248 6.17867i −0.0709320 0.420405i
\(217\) 12.2044 + 9.85200i 0.828492 + 0.668797i
\(218\) 0.515316 + 0.515316i 0.0349016 + 0.0349016i
\(219\) −0.133850 2.39987i −0.00904475 0.162168i
\(220\) 0 0
\(221\) 13.5171 7.80410i 0.909258 0.524960i
\(222\) 1.26106 1.41003i 0.0846365 0.0946352i
\(223\) 15.4546 15.4546i 1.03491 1.03491i 0.0355465 0.999368i \(-0.488683\pi\)
0.999368 0.0355465i \(-0.0113172\pi\)
\(224\) −9.13740 + 0.974557i −0.610518 + 0.0651154i
\(225\) 0 0
\(226\) 2.60716 4.51573i 0.173426 0.300382i
\(227\) −12.4101 3.32527i −0.823686 0.220706i −0.177728 0.984080i \(-0.556875\pi\)
−0.645957 + 0.763374i \(0.723542\pi\)
\(228\) 1.68592 + 5.13008i 0.111653 + 0.339748i
\(229\) −13.2508 7.65038i −0.875641 0.505551i −0.00642204 0.999979i \(-0.502044\pi\)
−0.869219 + 0.494428i \(0.835378\pi\)
\(230\) 0 0
\(231\) −3.26807 1.23619i −0.215023 0.0813353i
\(232\) 4.21445 + 4.21445i 0.276692 + 0.276692i
\(233\) 6.62761 1.77586i 0.434189 0.116341i −0.0351029 0.999384i \(-0.511176\pi\)
0.469292 + 0.883043i \(0.344509\pi\)
\(234\) 2.95690 0.330865i 0.193298 0.0216293i
\(235\) 0 0
\(236\) 12.6843 + 7.32328i 0.825677 + 0.476705i
\(237\) 1.50118 7.18093i 0.0975122 0.466452i
\(238\) −1.42891 3.70543i −0.0926225 0.240188i
\(239\) −18.7082 −1.21013 −0.605067 0.796174i \(-0.706854\pi\)
−0.605067 + 0.796174i \(0.706854\pi\)
\(240\) 0 0
\(241\) 0.986063 + 1.70791i 0.0635179 + 0.110016i 0.896036 0.443982i \(-0.146435\pi\)
−0.832518 + 0.553998i \(0.813101\pi\)
\(242\) 3.10802 + 0.832793i 0.199791 + 0.0535339i
\(243\) −15.5863 + 0.261589i −0.999859 + 0.0167810i
\(244\) 8.36885i 0.535761i
\(245\) 0 0
\(246\) 1.27669 + 1.95156i 0.0813987 + 0.124427i
\(247\) −5.07757 + 1.36053i −0.323078 + 0.0865685i
\(248\) 1.85026 6.90525i 0.117491 0.438484i
\(249\) 5.58268 11.0481i 0.353788 0.700148i
\(250\) 0 0
\(251\) 17.9016i 1.12994i −0.825112 0.564970i \(-0.808888\pi\)
0.825112 0.564970i \(-0.191112\pi\)
\(252\) −0.666655 + 15.1027i −0.0419953 + 0.951383i
\(253\) −4.12485 + 4.12485i −0.259327 + 0.259327i
\(254\) −0.974254 + 1.68746i −0.0611301 + 0.105881i
\(255\) 0 0
\(256\) −4.45168 7.71053i −0.278230 0.481908i
\(257\) 5.10358 + 19.0468i 0.318353 + 1.18811i 0.920827 + 0.389971i \(0.127515\pi\)
−0.602475 + 0.798138i \(0.705819\pi\)
\(258\) 0.416467 1.99218i 0.0259281 0.124028i
\(259\) −7.56100 + 5.51114i −0.469818 + 0.342445i
\(260\) 0 0
\(261\) 11.9369 8.79573i 0.738879 0.544442i
\(262\) 0.171813 0.641215i 0.0106147 0.0396144i
\(263\) 1.43607 5.35948i 0.0885517 0.330480i −0.907411 0.420244i \(-0.861945\pi\)
0.995963 + 0.0897640i \(0.0286113\pi\)
\(264\) 0.0886842 + 1.59006i 0.00545813 + 0.0978617i
\(265\) 0 0
\(266\) 0.141851 + 1.32999i 0.00869744 + 0.0815467i
\(267\) 1.53807 + 0.321534i 0.0941281 + 0.0196776i
\(268\) 0.0240547 + 0.0897733i 0.00146937 + 0.00548378i
\(269\) 5.02321 + 8.70045i 0.306270 + 0.530476i 0.977543 0.210734i \(-0.0675855\pi\)
−0.671273 + 0.741210i \(0.734252\pi\)
\(270\) 0 0
\(271\) 2.82028 4.88486i 0.171320 0.296734i −0.767562 0.640975i \(-0.778530\pi\)
0.938881 + 0.344241i \(0.111864\pi\)
\(272\) 11.8115 11.8115i 0.716180 0.716180i
\(273\) −14.6430 1.46667i −0.886233 0.0887667i
\(274\) 2.72309i 0.164508i
\(275\) 0 0
\(276\) 22.5264 + 11.3827i 1.35593 + 0.685158i
\(277\) −2.91038 + 10.8617i −0.174868 + 0.652615i 0.821707 + 0.569911i \(0.193022\pi\)
−0.996574 + 0.0827040i \(0.973644\pi\)
\(278\) −3.09130 + 0.828310i −0.185404 + 0.0496787i
\(279\) −16.2954 7.12451i −0.975581 0.426533i
\(280\) 0 0
\(281\) 1.92831i 0.115033i 0.998345 + 0.0575167i \(0.0183183\pi\)
−0.998345 + 0.0575167i \(0.981682\pi\)
\(282\) 1.70956 + 1.52893i 0.101803 + 0.0910466i
\(283\) −25.4667 6.82379i −1.51384 0.405632i −0.596132 0.802887i \(-0.703296\pi\)
−0.917709 + 0.397254i \(0.869963\pi\)
\(284\) 11.8250 + 20.4816i 0.701687 + 1.21536i
\(285\) 0 0
\(286\) −0.756201 −0.0447151
\(287\) −4.15012 10.7620i −0.244974 0.635263i
\(288\) 9.70225 3.79926i 0.571710 0.223874i
\(289\) 5.73548 + 3.31138i 0.337381 + 0.194787i
\(290\) 0 0
\(291\) −4.12126 + 8.15598i −0.241592 + 0.478112i
\(292\) 2.55301 0.684078i 0.149404 0.0400326i
\(293\) −7.83332 7.83332i −0.457627 0.457627i 0.440249 0.897876i \(-0.354890\pi\)
−0.897876 + 0.440249i \(0.854890\pi\)
\(294\) −0.945876 + 3.62301i −0.0551646 + 0.211298i
\(295\) 0 0
\(296\) 3.69315 + 2.13224i 0.214660 + 0.123934i
\(297\) 3.94416 + 0.374436i 0.228863 + 0.0217270i
\(298\) −5.20686 1.39517i −0.301625 0.0808203i
\(299\) −12.2846 + 21.2775i −0.710435 + 1.23051i
\(300\) 0 0
\(301\) −4.08027 + 9.20242i −0.235183 + 0.530418i
\(302\) 3.32282 3.32282i 0.191207 0.191207i
\(303\) −24.5149 21.9248i −1.40835 1.25955i
\(304\) −4.87205 + 2.81288i −0.279431 + 0.161330i
\(305\) 0 0
\(306\) 2.67128 + 3.62527i 0.152707 + 0.207243i
\(307\) 17.0769 + 17.0769i 0.974628 + 0.974628i 0.999686 0.0250576i \(-0.00797691\pi\)
−0.0250576 + 0.999686i \(0.507977\pi\)
\(308\) 0.595226 3.79579i 0.0339161 0.216285i
\(309\) 18.3083 11.9771i 1.04152 0.681354i
\(310\) 0 0
\(311\) −20.4797 + 11.8240i −1.16130 + 0.670475i −0.951615 0.307294i \(-0.900576\pi\)
−0.209683 + 0.977769i \(0.567243\pi\)
\(312\) 2.09411 + 6.37215i 0.118556 + 0.360752i
\(313\) 3.20409 + 11.9578i 0.181106 + 0.675895i 0.995431 + 0.0954864i \(0.0304406\pi\)
−0.814325 + 0.580409i \(0.802893\pi\)
\(314\) 2.82168 0.159237
\(315\) 0 0
\(316\) 8.06709 0.453809
\(317\) −1.13684 4.24276i −0.0638515 0.238297i 0.926623 0.375991i \(-0.122698\pi\)
−0.990475 + 0.137694i \(0.956031\pi\)
\(318\) 1.16076 + 3.53206i 0.0650920 + 0.198068i
\(319\) −3.26361 + 1.88425i −0.182727 + 0.105498i
\(320\) 0 0
\(321\) 3.16074 2.06772i 0.176415 0.115409i
\(322\) 4.86432 + 3.92671i 0.271078 + 0.218827i
\(323\) −5.62568 5.62568i −0.313021 0.313021i
\(324\) −3.78871 16.7176i −0.210484 0.928758i
\(325\) 0 0
\(326\) −0.724106 + 0.418063i −0.0401045 + 0.0231543i
\(327\) 3.04650 + 2.72462i 0.168472 + 0.150672i
\(328\) −3.71743 + 3.71743i −0.205261 + 0.205261i
\(329\) −6.68183 9.16713i −0.368381 0.505400i
\(330\) 0 0
\(331\) 3.10933 5.38552i 0.170904 0.296015i −0.767832 0.640651i \(-0.778664\pi\)
0.938736 + 0.344636i \(0.111998\pi\)
\(332\) 13.1480 + 3.52300i 0.721591 + 0.193350i
\(333\) 6.62103 8.28946i 0.362830 0.454259i
\(334\) 1.45833 + 0.841970i 0.0797965 + 0.0460705i
\(335\) 0 0
\(336\) −15.5433 + 2.53981i −0.847958 + 0.138558i
\(337\) −15.0501 15.0501i −0.819833 0.819833i 0.166250 0.986084i \(-0.446834\pi\)
−0.986084 + 0.166250i \(0.946834\pi\)
\(338\) 0.801644 0.214800i 0.0436037 0.0116836i
\(339\) 13.1887 26.1005i 0.716313 1.41759i
\(340\) 0 0
\(341\) 3.91452 + 2.26005i 0.211983 + 0.122389i
\(342\) −0.552999 1.41220i −0.0299027 0.0763632i
\(343\) 8.33197 16.5402i 0.449884 0.893087i
\(344\) 4.58812 0.247375
\(345\) 0 0
\(346\) 0.204333 + 0.353916i 0.0109850 + 0.0190266i
\(347\) −18.6057 4.98539i −0.998808 0.267630i −0.277862 0.960621i \(-0.589626\pi\)
−0.720946 + 0.692991i \(0.756292\pi\)
\(348\) 12.1534 + 10.8693i 0.651491 + 0.582657i
\(349\) 9.24369i 0.494803i −0.968913 0.247402i \(-0.920423\pi\)
0.968913 0.247402i \(-0.0795767\pi\)
\(350\) 0 0
\(351\) 16.4541 2.77618i 0.878254 0.148182i
\(352\) −2.55796 + 0.685404i −0.136340 + 0.0365321i
\(353\) 3.05649 11.4070i 0.162681 0.607132i −0.835644 0.549271i \(-0.814905\pi\)
0.998325 0.0578609i \(-0.0184280\pi\)
\(354\) −3.67145 1.85520i −0.195135 0.0986029i
\(355\) 0 0
\(356\) 1.72787i 0.0915769i
\(357\) −9.15857 20.3027i −0.484723 1.07453i
\(358\) 0.0527764 0.0527764i 0.00278932 0.00278932i
\(359\) −6.98129 + 12.0920i −0.368459 + 0.638189i −0.989325 0.145728i \(-0.953448\pi\)
0.620866 + 0.783917i \(0.286781\pi\)
\(360\) 0 0
\(361\) −8.16026 14.1340i −0.429487 0.743894i
\(362\) −1.49366 5.57441i −0.0785050 0.292985i
\(363\) 17.6638 + 3.69263i 0.927108 + 0.193813i
\(364\) −1.71622 16.0912i −0.0899544 0.843408i
\(365\) 0 0
\(366\) −0.130889 2.34678i −0.00684170 0.122668i
\(367\) 3.90370 14.5688i 0.203771 0.760485i −0.786049 0.618164i \(-0.787877\pi\)
0.989821 0.142321i \(-0.0454565\pi\)
\(368\) −6.80542 + 25.3982i −0.354757 + 1.32397i
\(369\) 7.75844 + 10.5292i 0.403888 + 0.548129i
\(370\) 0 0
\(371\) −1.95023 18.2852i −0.101251 0.949323i
\(372\) 4.00185 19.1429i 0.207486 0.992515i
\(373\) 9.01635 + 33.6495i 0.466849 + 1.74230i 0.650686 + 0.759347i \(0.274481\pi\)
−0.183837 + 0.982957i \(0.558852\pi\)
\(374\) −0.572249 0.991165i −0.0295903 0.0512519i
\(375\) 0 0
\(376\) −2.58517 + 4.47765i −0.133320 + 0.230917i
\(377\) −11.2233 + 11.2233i −0.578028 + 0.578028i
\(378\) −0.0492653 4.24552i −0.00253393 0.218366i
\(379\) 19.0602i 0.979056i 0.871988 + 0.489528i \(0.162831\pi\)
−0.871988 + 0.489528i \(0.837169\pi\)
\(380\) 0 0
\(381\) −4.92842 + 9.75335i −0.252491 + 0.499680i
\(382\) −1.13832 + 4.24828i −0.0582417 + 0.217361i
\(383\) −9.81007 + 2.62860i −0.501271 + 0.134315i −0.500590 0.865685i \(-0.666884\pi\)
−0.000681261 1.00000i \(0.500217\pi\)
\(384\) 8.28544 + 12.6652i 0.422815 + 0.646318i
\(385\) 0 0
\(386\) 2.10507i 0.107145i
\(387\) 1.70987 11.2855i 0.0869174 0.573672i
\(388\) −9.70615 2.60076i −0.492755 0.132033i
\(389\) −18.6290 32.2664i −0.944528 1.63597i −0.756693 0.653770i \(-0.773186\pi\)
−0.187835 0.982201i \(-0.560147\pi\)
\(390\) 0 0
\(391\) −37.1850 −1.88053
\(392\) −8.43099 0.415908i −0.425829 0.0210065i
\(393\) 0.761825 3.64421i 0.0384290 0.183826i
\(394\) −2.89595 1.67198i −0.145896 0.0842331i
\(395\) 0 0
\(396\) 0.484465 + 4.32960i 0.0243453 + 0.217571i
\(397\) −8.58658 + 2.30077i −0.430948 + 0.115472i −0.467771 0.883850i \(-0.654943\pi\)
0.0368231 + 0.999322i \(0.488276\pi\)
\(398\) 3.57708 + 3.57708i 0.179303 + 0.179303i
\(399\) 1.20968 + 7.40309i 0.0605597 + 0.370618i
\(400\) 0 0
\(401\) −4.02832 2.32575i −0.201165 0.116142i 0.396034 0.918236i \(-0.370386\pi\)
−0.597199 + 0.802093i \(0.703720\pi\)
\(402\) −0.00814945 0.0247979i −0.000406458 0.00123681i
\(403\) 18.3890 + 4.92733i 0.916023 + 0.245448i
\(404\) 18.0828 31.3204i 0.899655 1.55825i
\(405\) 0 0
\(406\) 2.37881 + 3.26361i 0.118059 + 0.161970i
\(407\) −1.90662 + 1.90662i −0.0945074 + 0.0945074i
\(408\) −6.76738 + 7.56686i −0.335035 + 0.374615i
\(409\) −23.0006 + 13.2794i −1.13731 + 0.656626i −0.945763 0.324858i \(-0.894683\pi\)
−0.191546 + 0.981484i \(0.561350\pi\)
\(410\) 0 0
\(411\) −0.850451 15.2482i −0.0419497 0.752137i
\(412\) 17.0114 + 17.0114i 0.838091 + 0.838091i
\(413\) 15.8313 + 12.7798i 0.779009 + 0.628853i
\(414\) −6.49486 2.83961i −0.319205 0.139559i
\(415\) 0 0
\(416\) −9.65934 + 5.57682i −0.473588 + 0.273426i
\(417\) −17.0513 + 5.60365i −0.835007 + 0.274412i
\(418\) 0.0997634 + 0.372322i 0.00487959 + 0.0182109i
\(419\) 25.8278 1.26177 0.630885 0.775876i \(-0.282692\pi\)
0.630885 + 0.775876i \(0.282692\pi\)
\(420\) 0 0
\(421\) 0.432430 0.0210753 0.0105377 0.999944i \(-0.496646\pi\)
0.0105377 + 0.999944i \(0.496646\pi\)
\(422\) 2.03851 + 7.60783i 0.0992332 + 0.370343i
\(423\) 10.0503 + 8.02749i 0.488664 + 0.390310i
\(424\) −7.25850 + 4.19070i −0.352504 + 0.203518i
\(425\) 0 0
\(426\) −3.63630 5.55847i −0.176179 0.269309i
\(427\) −1.80099 + 11.4850i −0.0871558 + 0.555799i
\(428\) 2.93684 + 2.93684i 0.141957 + 0.141957i
\(429\) −4.23442 + 0.236170i −0.204440 + 0.0114024i
\(430\) 0 0
\(431\) 14.1264 8.15586i 0.680443 0.392854i −0.119579 0.992825i \(-0.538154\pi\)
0.800022 + 0.599971i \(0.204821\pi\)
\(432\) 16.2403 7.42749i 0.781363 0.357355i
\(433\) 0.514238 0.514238i 0.0247127 0.0247127i −0.694642 0.719355i \(-0.744437\pi\)
0.719355 + 0.694642i \(0.244437\pi\)
\(434\) 1.96345 4.42825i 0.0942486 0.212563i
\(435\) 0 0
\(436\) −2.24718 + 3.89223i −0.107620 + 0.186404i
\(437\) 12.0968 + 3.24133i 0.578669 + 0.155054i
\(438\) −0.705214 + 0.231758i −0.0336964 + 0.0110738i
\(439\) 13.2487 + 7.64917i 0.632328 + 0.365075i 0.781653 0.623713i \(-0.214377\pi\)
−0.149325 + 0.988788i \(0.547710\pi\)
\(440\) 0 0
\(441\) −4.16501 + 20.5828i −0.198334 + 0.980135i
\(442\) −3.40853 3.40853i −0.162127 0.162127i
\(443\) 8.81439 2.36181i 0.418784 0.112213i −0.0432723 0.999063i \(-0.513778\pi\)
0.462057 + 0.886850i \(0.347112\pi\)
\(444\) 10.4123 + 5.26139i 0.494146 + 0.249695i
\(445\) 0 0
\(446\) −5.84564 3.37498i −0.276799 0.159810i
\(447\) −29.5921 6.18625i −1.39966 0.292600i
\(448\) −5.52219 14.3201i −0.260899 0.676560i
\(449\) 9.40891 0.444034 0.222017 0.975043i \(-0.428736\pi\)
0.222017 + 0.975043i \(0.428736\pi\)
\(450\) 0 0
\(451\) −1.66204 2.87873i −0.0782622 0.135554i
\(452\) 31.0613 + 8.32286i 1.46100 + 0.391474i
\(453\) 17.5687 19.6442i 0.825450 0.922966i
\(454\) 3.96789i 0.186222i
\(455\) 0 0
\(456\) 2.86111 1.87171i 0.133984 0.0876509i
\(457\) −33.3520 + 8.93665i −1.56014 + 0.418039i −0.932708 0.360631i \(-0.882561\pi\)
−0.627434 + 0.778670i \(0.715895\pi\)
\(458\) −1.22303 + 4.56443i −0.0571486 + 0.213282i
\(459\) 16.0903 + 19.4658i 0.751031 + 0.908585i
\(460\) 0 0
\(461\) 36.9326i 1.72012i 0.510192 + 0.860061i \(0.329574\pi\)
−0.510192 + 0.860061i \(0.670426\pi\)
\(462\) −0.107546 + 1.07372i −0.00500349 + 0.0499541i
\(463\) −26.3687 + 26.3687i −1.22546 + 1.22546i −0.259794 + 0.965664i \(0.583655\pi\)
−0.965664 + 0.259794i \(0.916345\pi\)
\(464\) −8.49325 + 14.7107i −0.394289 + 0.682929i
\(465\) 0 0
\(466\) −1.05953 1.83516i −0.0490817 0.0850120i
\(467\) −2.63979 9.85183i −0.122155 0.455888i 0.877567 0.479453i \(-0.159165\pi\)
−0.999722 + 0.0235650i \(0.992498\pi\)
\(468\) 6.69060 + 17.0859i 0.309273 + 0.789797i
\(469\) 0.0136922 + 0.128377i 0.000632247 + 0.00592791i
\(470\) 0 0
\(471\) 15.8003 0.881244i 0.728039 0.0406056i
\(472\) 2.40011 8.95734i 0.110474 0.412295i
\(473\) −0.750833 + 2.80215i −0.0345233 + 0.128843i
\(474\) −2.26216 + 0.126170i −0.103905 + 0.00579517i
\(475\) 0 0
\(476\) 19.7923 14.4264i 0.907177 0.661232i
\(477\) 7.60287 + 19.4156i 0.348112 + 0.888979i
\(478\) 1.49540 + 5.58092i 0.0683981 + 0.255265i
\(479\) 6.85350 + 11.8706i 0.313144 + 0.542382i 0.979041 0.203662i \(-0.0652843\pi\)
−0.665897 + 0.746044i \(0.731951\pi\)
\(480\) 0 0
\(481\) −5.67825 + 9.83503i −0.258906 + 0.448439i
\(482\) 0.430674 0.430674i 0.0196167 0.0196167i
\(483\) 28.4646 + 20.4688i 1.29518 + 0.931362i
\(484\) 19.8436i 0.901980i
\(485\) 0 0
\(486\) 1.32389 + 4.62869i 0.0600529 + 0.209961i
\(487\) 5.91662 22.0811i 0.268108 1.00059i −0.692213 0.721693i \(-0.743364\pi\)
0.960321 0.278898i \(-0.0899692\pi\)
\(488\) 5.11811 1.37139i 0.231686 0.0620800i
\(489\) −3.92413 + 2.56713i −0.177455 + 0.116090i
\(490\) 0 0
\(491\) 23.7476i 1.07172i 0.844308 + 0.535858i \(0.180012\pi\)
−0.844308 + 0.535858i \(0.819988\pi\)
\(492\) −9.58750 + 10.7201i −0.432238 + 0.483301i
\(493\) −23.2037 6.21740i −1.04504 0.280018i
\(494\) 0.811730 + 1.40596i 0.0365215 + 0.0632570i
\(495\) 0 0
\(496\) 20.3744 0.914836
\(497\) 11.8205 + 30.6527i 0.530220 + 1.37496i
\(498\) −3.74205 0.782280i −0.167685 0.0350548i
\(499\) −2.80187 1.61766i −0.125429 0.0724165i 0.435973 0.899960i \(-0.356404\pi\)
−0.561402 + 0.827543i \(0.689738\pi\)
\(500\) 0 0
\(501\) 8.42904 + 4.25924i 0.376582 + 0.190289i
\(502\) −5.34029 + 1.43093i −0.238349 + 0.0638654i
\(503\) 2.62851 + 2.62851i 0.117199 + 0.117199i 0.763274 0.646075i \(-0.223591\pi\)
−0.646075 + 0.763274i \(0.723591\pi\)
\(504\) 9.34558 2.06716i 0.416285 0.0920788i
\(505\) 0 0
\(506\) 1.56021 + 0.900788i 0.0693598 + 0.0400449i
\(507\) 4.42180 1.45316i 0.196379 0.0645369i
\(508\) −11.6071 3.11012i −0.514983 0.137989i
\(509\) 6.91189 11.9717i 0.306364 0.530638i −0.671200 0.741276i \(-0.734221\pi\)
0.977564 + 0.210638i \(0.0675541\pi\)
\(510\) 0 0
\(511\) 3.65085 0.389385i 0.161504 0.0172254i
\(512\) −14.3017 + 14.3017i −0.632050 + 0.632050i
\(513\) −3.53762 7.73506i −0.156190 0.341511i
\(514\) 5.27399 3.04494i 0.232626 0.134306i
\(515\) 0 0
\(516\) 12.5320 0.698960i 0.551691 0.0307700i
\(517\) −2.31162 2.31162i −0.101665 0.101665i
\(518\) 2.24842 + 1.81503i 0.0987899 + 0.0797478i
\(519\) 1.25472 + 1.91797i 0.0550759 + 0.0841895i
\(520\) 0 0
\(521\) 9.49156 5.47996i 0.415833 0.240081i −0.277460 0.960737i \(-0.589493\pi\)
0.693293 + 0.720656i \(0.256159\pi\)
\(522\) −3.57804 2.85789i −0.156607 0.125086i
\(523\) −3.54814 13.2418i −0.155149 0.579026i −0.999093 0.0425929i \(-0.986438\pi\)
0.843943 0.536433i \(-0.180229\pi\)
\(524\) 4.09392 0.178844
\(525\) 0 0
\(526\) −1.71360 −0.0747163
\(527\) 7.45743 + 27.8315i 0.324851 + 1.21236i
\(528\) −4.31189 + 1.41703i −0.187651 + 0.0616685i
\(529\) 30.7730 17.7668i 1.33796 0.772469i
\(530\) 0 0
\(531\) −21.1381 9.24175i −0.917313 0.401058i
\(532\) −7.69622 + 2.96786i −0.333674 + 0.128673i
\(533\) −9.89970 9.89970i −0.428804 0.428804i
\(534\) −0.0270240 0.484527i −0.00116944 0.0209676i
\(535\) 0 0
\(536\) 0.0509605 0.0294221i 0.00220116 0.00127084i
\(537\) 0.279044 0.312009i 0.0120416 0.0134642i
\(538\) 2.19394 2.19394i 0.0945876 0.0945876i
\(539\) 1.63372 5.08108i 0.0703692 0.218857i
\(540\) 0 0
\(541\) −3.53276 + 6.11892i −0.151885 + 0.263073i −0.931920 0.362663i \(-0.881868\pi\)
0.780035 + 0.625735i \(0.215201\pi\)
\(542\) −1.68265 0.450866i −0.0722762 0.0193663i
\(543\) −10.1048 30.7480i −0.433640 1.31952i
\(544\) −14.6193 8.44044i −0.626796 0.361881i
\(545\) 0 0
\(546\) 0.732928 + 4.48543i 0.0313664 + 0.191959i
\(547\) 19.7665 + 19.7665i 0.845154 + 0.845154i 0.989524 0.144370i \(-0.0461154\pi\)
−0.144370 + 0.989524i \(0.546115\pi\)
\(548\) 16.2212 4.34647i 0.692937 0.185672i
\(549\) −1.46586 13.1002i −0.0625612 0.559101i
\(550\) 0 0
\(551\) 7.00653 + 4.04522i 0.298488 + 0.172332i
\(552\) 3.26991 15.6417i 0.139176 0.665753i
\(553\) 11.0709 + 1.73605i 0.470782 + 0.0738242i
\(554\) 3.47282 0.147546
\(555\) 0 0
\(556\) −9.86837 17.0925i −0.418512 0.724884i
\(557\) −42.2902 11.3316i −1.79189 0.480137i −0.799228 0.601028i \(-0.794758\pi\)
−0.992666 + 0.120891i \(0.961425\pi\)
\(558\) −0.822798 + 5.43063i −0.0348318 + 0.229897i
\(559\) 12.2184i 0.516783i
\(560\) 0 0
\(561\) −3.51392 5.37140i −0.148358 0.226781i
\(562\) 0.575242 0.154136i 0.0242651 0.00650182i
\(563\) −2.87110 + 10.7151i −0.121002 + 0.451587i −0.999666 0.0258549i \(-0.991769\pi\)
0.878663 + 0.477442i \(0.158436\pi\)
\(564\) −6.37903 + 12.6241i −0.268606 + 0.531571i
\(565\) 0 0
\(566\) 8.14252i 0.342256i
\(567\) −1.60179 23.7578i −0.0672689 0.997735i
\(568\) 10.5881 10.5881i 0.444266 0.444266i
\(569\) −6.90318 + 11.9567i −0.289396 + 0.501249i −0.973666 0.227980i \(-0.926788\pi\)
0.684269 + 0.729229i \(0.260121\pi\)
\(570\) 0 0
\(571\) 6.56260 + 11.3668i 0.274636 + 0.475684i 0.970043 0.242932i \(-0.0781092\pi\)
−0.695407 + 0.718616i \(0.744776\pi\)
\(572\) −1.20701 4.50464i −0.0504678 0.188348i
\(573\) −5.04736 + 24.1442i −0.210857 + 1.00864i
\(574\) −2.87873 + 2.09828i −0.120156 + 0.0875804i
\(575\) 0 0
\(576\) 10.3235 + 14.0103i 0.430144 + 0.583762i
\(577\) 3.94772 14.7331i 0.164346 0.613347i −0.833777 0.552101i \(-0.813826\pi\)
0.998123 0.0612453i \(-0.0195072\pi\)
\(578\) 0.529377 1.97566i 0.0220192 0.0821767i
\(579\) −0.657437 11.7875i −0.0273221 0.489873i
\(580\) 0 0
\(581\) 17.2856 + 7.66426i 0.717126 + 0.317967i
\(582\) 2.76247 + 0.577496i 0.114508 + 0.0239380i
\(583\) −1.37159 5.11885i −0.0568055 0.212001i
\(584\) −0.836718 1.44924i −0.0346236 0.0599699i
\(585\) 0 0
\(586\) −1.71065 + 2.96293i −0.0706662 + 0.122397i
\(587\) 5.54217 5.54217i 0.228750 0.228750i −0.583421 0.812170i \(-0.698286\pi\)
0.812170 + 0.583421i \(0.198286\pi\)
\(588\) −23.0918 + 0.148375i −0.952290 + 0.00611888i
\(589\) 9.70404i 0.399848i
\(590\) 0 0
\(591\) −16.7384 8.45798i −0.688524 0.347915i
\(592\) −3.14565 + 11.7397i −0.129285 + 0.482499i
\(593\) 8.37814 2.24492i 0.344049 0.0921877i −0.0826570 0.996578i \(-0.526341\pi\)
0.426706 + 0.904390i \(0.359674\pi\)
\(594\) −0.203568 1.20653i −0.00835252 0.0495043i
\(595\) 0 0
\(596\) 33.2438i 1.36172i
\(597\) 21.1473 + 18.9130i 0.865503 + 0.774058i
\(598\) 7.32931 + 1.96388i 0.299718 + 0.0803091i
\(599\) −7.93869 13.7502i −0.324366 0.561819i 0.657018 0.753875i \(-0.271818\pi\)
−0.981384 + 0.192056i \(0.938484\pi\)
\(600\) 0 0
\(601\) 41.5249 1.69384 0.846919 0.531722i \(-0.178455\pi\)
0.846919 + 0.531722i \(0.178455\pi\)
\(602\) 3.07135 + 0.481625i 0.125179 + 0.0196296i
\(603\) −0.0533783 0.136313i −0.00217373 0.00555110i
\(604\) 25.0976 + 14.4901i 1.02120 + 0.589593i
\(605\) 0 0
\(606\) −4.58092 + 9.06565i −0.186087 + 0.368267i
\(607\) −14.7681 + 3.95710i −0.599418 + 0.160614i −0.545754 0.837945i \(-0.683757\pi\)
−0.0536641 + 0.998559i \(0.517090\pi\)
\(608\) 4.02013 + 4.02013i 0.163038 + 0.163038i
\(609\) 14.3397 + 17.5320i 0.581072 + 0.710432i
\(610\) 0 0
\(611\) −11.9242 6.88444i −0.482402 0.278515i
\(612\) −17.3317 + 21.6991i −0.700593 + 0.877135i
\(613\) 29.7879 + 7.98165i 1.20312 + 0.322376i 0.804060 0.594548i \(-0.202669\pi\)
0.399063 + 0.916924i \(0.369336\pi\)
\(614\) 3.72926 6.45927i 0.150501 0.260675i
\(615\) 0 0
\(616\) −2.41892 + 0.257992i −0.0974611 + 0.0103948i
\(617\) 13.2098 13.2098i 0.531808 0.531808i −0.389302 0.921110i \(-0.627284\pi\)
0.921110 + 0.389302i \(0.127284\pi\)
\(618\) −5.03637 4.50426i −0.202593 0.181188i
\(619\) −14.7495 + 8.51561i −0.592831 + 0.342271i −0.766216 0.642583i \(-0.777863\pi\)
0.173385 + 0.984854i \(0.444529\pi\)
\(620\) 0 0
\(621\) −37.2554 13.8723i −1.49501 0.556675i
\(622\) 5.16425 + 5.16425i 0.207068 + 0.207068i
\(623\) −0.371840 + 2.37125i −0.0148974 + 0.0950020i
\(624\) −15.9973 + 10.4652i −0.640403 + 0.418945i
\(625\) 0 0
\(626\) 3.31107 1.91165i 0.132337 0.0764047i
\(627\) 0.674915 + 2.05370i 0.0269535 + 0.0820167i
\(628\) 4.50384 + 16.8086i 0.179723 + 0.670735i
\(629\) −17.1879 −0.685327
\(630\) 0 0
\(631\) 6.51082 0.259191 0.129596 0.991567i \(-0.458632\pi\)
0.129596 + 0.991567i \(0.458632\pi\)
\(632\) −1.32194 4.93356i −0.0525841 0.196247i
\(633\) 13.7909 + 41.9641i 0.548138 + 1.66792i
\(634\) −1.17480 + 0.678272i −0.0466573 + 0.0269376i
\(635\) 0 0
\(636\) −19.1875 + 12.5523i −0.760834 + 0.497730i
\(637\) 1.10758 22.4521i 0.0438840 0.889586i
\(638\) 0.822967 + 0.822967i 0.0325816 + 0.0325816i
\(639\) −22.0978 29.9896i −0.874174 1.18637i
\(640\) 0 0
\(641\) −36.6801 + 21.1773i −1.44878 + 0.836451i −0.998409 0.0563924i \(-0.982040\pi\)
−0.450367 + 0.892843i \(0.648707\pi\)
\(642\) −0.869478 0.777613i −0.0343155 0.0306899i
\(643\) −11.2098 + 11.2098i −0.442072 + 0.442072i −0.892708 0.450636i \(-0.851197\pi\)
0.450636 + 0.892708i \(0.351197\pi\)
\(644\) −15.6269 + 35.2441i −0.615787 + 1.38881i
\(645\) 0 0
\(646\) −1.22854 + 2.12790i −0.0483363 + 0.0837209i
\(647\) −22.9610 6.15237i −0.902689 0.241875i −0.222518 0.974929i \(-0.571428\pi\)
−0.680171 + 0.733054i \(0.738094\pi\)
\(648\) −9.60309 + 5.05655i −0.377245 + 0.198640i
\(649\) 5.07783 + 2.93169i 0.199322 + 0.115079i
\(650\) 0 0
\(651\) 9.61153 25.4096i 0.376705 0.995882i
\(652\) −3.64616 3.64616i −0.142794 0.142794i
\(653\) 21.0505 5.64046i 0.823769 0.220728i 0.177775 0.984071i \(-0.443110\pi\)
0.645994 + 0.763343i \(0.276443\pi\)
\(654\) 0.569277 1.12660i 0.0222605 0.0440535i
\(655\) 0 0
\(656\) −12.9759 7.49163i −0.506623 0.292499i
\(657\) −3.87653 + 1.51800i −0.151238 + 0.0592227i
\(658\) −2.20058 + 2.72604i −0.0857876 + 0.106272i
\(659\) 42.6184 1.66018 0.830088 0.557632i \(-0.188290\pi\)
0.830088 + 0.557632i \(0.188290\pi\)
\(660\) 0 0
\(661\) −22.7467 39.3985i −0.884744 1.53242i −0.846006 0.533173i \(-0.821000\pi\)
−0.0387381 0.999249i \(-0.512334\pi\)
\(662\) −1.85511 0.497076i −0.0721010 0.0193194i
\(663\) −20.1509 18.0219i −0.782597 0.699911i
\(664\) 8.61819i 0.334451i
\(665\) 0 0
\(666\) −3.00210 1.31254i −0.116329 0.0508601i
\(667\) 36.5253 9.78693i 1.41427 0.378951i
\(668\) −2.68783 + 10.0311i −0.103995 + 0.388115i
\(669\) −33.7873 17.0729i −1.30629 0.660075i
\(670\) 0 0
\(671\) 3.35026i 0.129335i
\(672\) 6.54474 + 14.5083i 0.252469 + 0.559671i
\(673\) 32.1249 32.1249i 1.23832 1.23832i 0.277636 0.960686i \(-0.410449\pi\)
0.960686 0.277636i \(-0.0895508\pi\)
\(674\) −3.28666 + 5.69266i −0.126597 + 0.219273i
\(675\) 0 0
\(676\) 2.55910 + 4.43248i 0.0984268 + 0.170480i
\(677\) −11.0202 41.1280i −0.423542 1.58068i −0.767087 0.641543i \(-0.778295\pi\)
0.343545 0.939136i \(-0.388372\pi\)
\(678\) −8.84036 1.84809i −0.339512 0.0709753i
\(679\) −12.7606 5.65793i −0.489706 0.217131i
\(680\) 0 0
\(681\) 1.23922 + 22.2186i 0.0474870 + 0.851419i
\(682\) 0.361305 1.34841i 0.0138351 0.0516332i
\(683\) −0.603360 + 2.25177i −0.0230869 + 0.0861617i −0.976508 0.215481i \(-0.930868\pi\)
0.953421 + 0.301642i \(0.0975348\pi\)
\(684\) 7.52972 5.54827i 0.287906 0.212143i
\(685\) 0 0
\(686\) −5.60017 1.16343i −0.213815 0.0444201i
\(687\) −5.42298 + 25.9409i −0.206899 + 0.989708i
\(688\) 3.38438 + 12.6307i 0.129028 + 0.481540i
\(689\) −11.1600 19.3297i −0.425163 0.736404i
\(690\) 0 0
\(691\) 8.27824 14.3383i 0.314919 0.545456i −0.664501 0.747287i \(-0.731356\pi\)
0.979420 + 0.201831i \(0.0646893\pi\)
\(692\) −1.78210 + 1.78210i −0.0677454 + 0.0677454i
\(693\) −0.266878 + 6.04600i −0.0101379 + 0.229669i
\(694\) 5.94884i 0.225815i
\(695\) 0 0
\(696\) 4.65576 9.21376i 0.176476 0.349247i
\(697\) 5.48418 20.4672i 0.207728 0.775252i
\(698\) −2.75752 + 0.738875i −0.104374 + 0.0279668i
\(699\) −6.50607 9.94523i −0.246082 0.376163i
\(700\) 0 0
\(701\) 26.5973i 1.00457i −0.864703 0.502284i \(-0.832493\pi\)
0.864703 0.502284i \(-0.167507\pi\)
\(702\) −2.14340 4.68657i −0.0808973 0.176883i
\(703\) 5.59148 + 1.49823i 0.210886 + 0.0565069i
\(704\) −2.21152 3.83047i −0.0833500 0.144366i
\(705\) 0 0
\(706\) −3.64717 −0.137263
\(707\) 31.5562 39.0912i 1.18679 1.47017i
\(708\) 5.19111 24.8318i 0.195094 0.933235i
\(709\) −13.7850 7.95880i −0.517708 0.298899i 0.218288 0.975884i \(-0.429953\pi\)
−0.735997 + 0.676985i \(0.763286\pi\)
\(710\) 0 0
\(711\) −12.6278 + 1.41300i −0.473580 + 0.0529917i
\(712\) 1.05671 0.283144i 0.0396018 0.0106113i
\(713\) −32.0712 32.0712i −1.20108 1.20108i
\(714\) −5.32449 + 4.35498i −0.199264 + 0.162981i
\(715\) 0 0
\(716\) 0.398625 + 0.230146i 0.0148973 + 0.00860096i
\(717\) 10.1166 + 30.7839i 0.377813 + 1.14964i
\(718\) 4.16523 + 1.11607i 0.155445 + 0.0416514i
\(719\) −10.6906 + 18.5167i −0.398694 + 0.690558i −0.993565 0.113263i \(-0.963870\pi\)
0.594871 + 0.803821i \(0.297203\pi\)
\(720\) 0 0
\(721\) 19.6848 + 27.0065i 0.733099 + 1.00577i
\(722\) −3.56409 + 3.56409i −0.132642 + 0.132642i
\(723\) 2.27710 2.54611i 0.0846862 0.0946907i
\(724\) 30.8223 17.7952i 1.14550 0.661355i
\(725\) 0 0
\(726\) −0.310355 5.56451i −0.0115183 0.206518i
\(727\) −7.43836 7.43836i −0.275873 0.275873i 0.555586 0.831459i \(-0.312494\pi\)
−0.831459 + 0.555586i \(0.812494\pi\)
\(728\) −9.55960 + 3.68643i −0.354302 + 0.136628i
\(729\) 8.85885 + 25.5053i 0.328106 + 0.944641i
\(730\) 0 0
\(731\) −16.0148 + 9.24617i −0.592330 + 0.341982i
\(732\) 13.7707 4.52553i 0.508980 0.167268i
\(733\) −9.45077 35.2708i −0.349072 1.30276i −0.887782 0.460264i \(-0.847755\pi\)
0.538710 0.842491i \(-0.318912\pi\)
\(734\) −4.65810 −0.171934
\(735\) 0 0
\(736\) 26.5725 0.979475
\(737\) 0.00962968 + 0.0359385i 0.000354714 + 0.00132381i
\(738\) 2.52085 3.15608i 0.0927939 0.116177i
\(739\) 33.2198 19.1794i 1.22201 0.705527i 0.256663 0.966501i \(-0.417377\pi\)
0.965346 + 0.260974i \(0.0840437\pi\)
\(740\) 0 0
\(741\) 4.98446 + 7.61928i 0.183109 + 0.279901i
\(742\) −5.29885 + 2.04337i −0.194527 + 0.0750146i
\(743\) −30.8182 30.8182i −1.13061 1.13061i −0.990076 0.140534i \(-0.955118\pi\)
−0.140534 0.990076i \(-0.544882\pi\)
\(744\) −12.3630 + 0.689531i −0.453248 + 0.0252794i
\(745\) 0 0
\(746\) 9.31740 5.37940i 0.341134 0.196954i
\(747\) −21.1983 3.21177i −0.775605 0.117512i
\(748\) 4.99090 4.99090i 0.182485 0.182485i
\(749\) 3.39837 + 4.66239i 0.124174 + 0.170360i
\(750\) 0 0
\(751\) −19.9356 + 34.5294i −0.727459 + 1.26000i 0.230495 + 0.973074i \(0.425966\pi\)
−0.957954 + 0.286923i \(0.907368\pi\)
\(752\) −14.2335 3.81385i −0.519042 0.139077i
\(753\) −29.4566 + 9.68045i −1.07346 + 0.352775i
\(754\) 4.24517 + 2.45095i 0.154600 + 0.0892583i
\(755\) 0 0
\(756\) 25.2116 7.06998i 0.916939 0.257133i
\(757\) −0.798673 0.798673i −0.0290283 0.0290283i 0.692444 0.721472i \(-0.256534\pi\)
−0.721472 + 0.692444i \(0.756534\pi\)
\(758\) 5.68591 1.52354i 0.206522 0.0553373i
\(759\) 9.01787 + 4.55678i 0.327328 + 0.165401i
\(760\) 0 0
\(761\) −37.3941 21.5895i −1.35554 0.782619i −0.366518 0.930411i \(-0.619450\pi\)
−0.989019 + 0.147791i \(0.952784\pi\)
\(762\) 3.30350 + 0.690601i 0.119673 + 0.0250178i
\(763\) −3.92153 + 4.85791i −0.141969 + 0.175868i
\(764\) −27.1236 −0.981299
\(765\) 0 0
\(766\) 1.56829 + 2.71637i 0.0566648 + 0.0981463i
\(767\) 23.8538 + 6.39162i 0.861312 + 0.230788i
\(768\) −10.2802 + 11.4946i −0.370954 + 0.414777i
\(769\) 44.1875i 1.59344i −0.604348 0.796720i \(-0.706566\pi\)
0.604348 0.796720i \(-0.293434\pi\)
\(770\) 0 0
\(771\) 28.5812 18.6975i 1.02933 0.673376i
\(772\) 12.5397 3.36001i 0.451315 0.120929i
\(773\) −5.66214 + 21.1314i −0.203653 + 0.760043i 0.786203 + 0.617968i \(0.212044\pi\)
−0.989856 + 0.142075i \(0.954623\pi\)
\(774\) −3.50328 + 0.392003i −0.125923 + 0.0140903i
\(775\) 0 0
\(776\) 6.36214i 0.228388i
\(777\) 13.1571 + 9.46122i 0.472008 + 0.339420i
\(778\) −8.13643 + 8.13643i −0.291705 + 0.291705i
\(779\) −3.56817 + 6.18024i −0.127843 + 0.221430i
\(780\) 0 0
\(781\) 4.73385 + 8.19927i 0.169391 + 0.293393i
\(782\) 2.97231 + 11.0928i 0.106289 + 0.396678i
\(783\) −20.9281 14.8856i −0.747911 0.531966i
\(784\) −5.07407 23.5165i −0.181217 0.839876i
\(785\) 0 0
\(786\) −1.14801 + 0.0640291i −0.0409482 + 0.00228384i
\(787\) −0.0780372 + 0.291239i −0.00278173 + 0.0103815i −0.967303 0.253625i \(-0.918377\pi\)
0.964521 + 0.264006i \(0.0850439\pi\)
\(788\) 5.33748 19.9197i 0.190140 0.709612i
\(789\) −9.59544 + 0.535176i −0.341607 + 0.0190528i
\(790\) 0 0
\(791\) 40.8360 + 18.1063i 1.45196 + 0.643787i
\(792\) 2.56845 1.00577i 0.0912659 0.0357385i
\(793\) 3.65209 + 13.6298i 0.129689 + 0.484007i
\(794\) 1.37270 + 2.37759i 0.0487153 + 0.0843774i
\(795\) 0 0
\(796\) −15.5988 + 27.0180i −0.552886 + 0.957626i
\(797\) −8.45240 + 8.45240i −0.299399 + 0.299399i −0.840779 0.541379i \(-0.817902\pi\)
0.541379 + 0.840779i \(0.317902\pi\)
\(798\) 2.11175 0.952614i 0.0747551 0.0337222i
\(799\) 20.8390i 0.737231i
\(800\) 0 0
\(801\) −0.302647 2.70472i −0.0106935 0.0955665i
\(802\) −0.371808 + 1.38761i −0.0131290 + 0.0489981i
\(803\) 1.02203 0.273853i 0.0360668 0.00966407i
\(804\) 0.134712 0.0881271i 0.00475092 0.00310800i
\(805\) 0 0
\(806\) 5.87955i 0.207098i
\(807\) 11.6000 12.9704i 0.408340 0.456579i
\(808\) −22.1177 5.92642i −0.778098 0.208491i
\(809\) 18.5676 + 32.1600i 0.652801 + 1.13068i 0.982440 + 0.186577i \(0.0597394\pi\)
−0.329640 + 0.944107i \(0.606927\pi\)
\(810\) 0 0
\(811\) 23.5491 0.826921 0.413461 0.910522i \(-0.364320\pi\)
0.413461 + 0.910522i \(0.364320\pi\)
\(812\) −15.6442 + 19.3797i −0.549003 + 0.680093i
\(813\) −9.56300 1.99915i −0.335389 0.0701134i
\(814\) 0.721171 + 0.416368i 0.0252770 + 0.0145937i
\(815\) 0 0
\(816\) −25.8228 13.0484i −0.903977 0.456784i
\(817\) 6.01583 1.61194i 0.210467 0.0563945i
\(818\) 5.79994 + 5.79994i 0.202790 + 0.202790i
\(819\) 5.50496 + 24.8877i 0.192359 + 0.869647i
\(820\) 0 0
\(821\) 35.4996 + 20.4957i 1.23895 + 0.715306i 0.968879 0.247536i \(-0.0796208\pi\)
0.270067 + 0.962842i \(0.412954\pi\)
\(822\) −4.48076 + 1.47253i −0.156285 + 0.0513605i
\(823\) −24.8888 6.66893i −0.867568 0.232464i −0.202532 0.979276i \(-0.564917\pi\)
−0.665036 + 0.746812i \(0.731584\pi\)
\(824\) 7.61596 13.1912i 0.265315 0.459538i
\(825\) 0 0
\(826\) 2.54694 5.74423i 0.0886195 0.199867i
\(827\) 19.5668 19.5668i 0.680404 0.680404i −0.279687 0.960091i \(-0.590231\pi\)
0.960091 + 0.279687i \(0.0902308\pi\)
\(828\) 6.54857 43.2219i 0.227579 1.50206i
\(829\) 21.9279 12.6601i 0.761588 0.439703i −0.0682778 0.997666i \(-0.521750\pi\)
0.829866 + 0.557963i \(0.188417\pi\)
\(830\) 0 0
\(831\) 19.4464 1.08460i 0.674588 0.0376245i
\(832\) −13.1727 13.1727i −0.456680 0.456680i
\(833\) 30.2665 15.5388i 1.04867 0.538386i
\(834\) 3.03461 + 4.63873i 0.105080 + 0.160626i
\(835\) 0 0
\(836\) −2.05866 + 1.18857i −0.0712002 + 0.0411075i
\(837\) −2.91129 + 30.6663i −0.100629 + 1.05998i
\(838\) −2.06449 7.70479i −0.0713167 0.266157i
\(839\) −50.7484 −1.75203 −0.876014 0.482286i \(-0.839807\pi\)
−0.876014 + 0.482286i \(0.839807\pi\)
\(840\) 0 0
\(841\) −4.57160 −0.157641
\(842\) −0.0345654 0.129000i −0.00119120 0.00444563i
\(843\) 3.17299 1.04275i 0.109283 0.0359143i
\(844\) −42.0656 + 24.2866i −1.44796 + 0.835978i
\(845\) 0 0
\(846\) 1.59136 3.63981i 0.0547120 0.125139i
\(847\) −4.27036 + 27.2324i −0.146731 + 0.935715i
\(848\) −16.8908 16.8908i −0.580031 0.580031i
\(849\) 2.54300 + 45.5948i 0.0872757 + 1.56481i
\(850\) 0 0
\(851\) 23.4310 13.5279i 0.803204 0.463730i
\(852\) 27.3074 30.5334i 0.935535 1.04606i
\(853\) 18.8448 18.8448i 0.645233 0.645233i −0.306604 0.951837i \(-0.599193\pi\)
0.951837 + 0.306604i \(0.0991928\pi\)
\(854\) 3.57009 0.380772i 0.122166 0.0130297i
\(855\) 0 0
\(856\) 1.31482 2.27733i 0.0449395 0.0778375i
\(857\) 12.0212 + 3.22108i 0.410637 + 0.110030i 0.458223 0.888837i \(-0.348486\pi\)
−0.0475860 + 0.998867i \(0.515153\pi\)
\(858\) 0.408922 + 1.24431i 0.0139604 + 0.0424800i
\(859\) 3.33705 + 1.92665i 0.113859 + 0.0657364i 0.555848 0.831284i \(-0.312394\pi\)
−0.441989 + 0.897020i \(0.645727\pi\)
\(860\) 0 0
\(861\) −15.4644 + 12.6486i −0.527026 + 0.431062i
\(862\) −3.56217 3.56217i −0.121328 0.121328i
\(863\) −48.2127 + 12.9186i −1.64118 + 0.439753i −0.957125 0.289676i \(-0.906452\pi\)
−0.684056 + 0.729429i \(0.739786\pi\)
\(864\) −11.4982 13.9103i −0.391175 0.473238i
\(865\) 0 0
\(866\) −0.194509 0.112300i −0.00660967 0.00381610i
\(867\) 2.34727 11.2282i 0.0797176 0.381331i
\(868\) 29.5128 + 4.62795i 1.00173 + 0.157083i
\(869\) 3.22945 0.109552
\(870\) 0 0
\(871\) 0.0783524 + 0.135710i 0.00265487 + 0.00459837i
\(872\) 2.74860 + 0.736484i 0.0930793 + 0.0249405i
\(873\) 15.6491 + 2.37100i 0.529640 + 0.0802461i
\(874\) 3.86774i 0.130828i
\(875\) 0 0
\(876\) −2.50620 3.83099i −0.0846765 0.129437i
\(877\) −43.6713 + 11.7017i −1.47467 + 0.395138i −0.904531 0.426408i \(-0.859779\pi\)
−0.570143 + 0.821546i \(0.693112\pi\)
\(878\) 1.22284 4.56370i 0.0412689 0.154018i
\(879\) −8.65357 + 17.1254i −0.291878 + 0.577627i
\(880\) 0 0
\(881\) 25.2055i 0.849195i −0.905382 0.424597i \(-0.860416\pi\)
0.905382 0.424597i \(-0.139584\pi\)
\(882\) 6.47306 0.402765i 0.217959 0.0135618i
\(883\) 14.2942 14.2942i 0.481039 0.481039i −0.424424 0.905463i \(-0.639524\pi\)
0.905463 + 0.424424i \(0.139524\pi\)
\(884\) 14.8638 25.7449i 0.499925 0.865895i
\(885\) 0 0
\(886\) −1.40912 2.44067i −0.0473403 0.0819958i
\(887\) 10.0709 + 37.5853i 0.338149 + 1.26199i 0.900415 + 0.435033i \(0.143263\pi\)
−0.562266 + 0.826957i \(0.690070\pi\)
\(888\) 1.51144 7.23000i 0.0507206 0.242623i
\(889\) −15.2598 6.76605i −0.511796 0.226926i
\(890\) 0 0
\(891\) −1.51671 6.69248i −0.0508118 0.224207i
\(892\) 10.7740 40.2091i 0.360740 1.34630i
\(893\) −1.81649 + 6.77923i −0.0607865 + 0.226858i
\(894\) 0.519936 + 9.32220i 0.0173893 + 0.311781i
\(895\) 0 0
\(896\) −18.6823 + 13.6174i −0.624133 + 0.454924i
\(897\) 41.6545 + 8.70792i 1.39080 + 0.290749i
\(898\) −0.752081 2.80681i −0.0250973 0.0936643i
\(899\) −14.6503 25.3750i −0.488613 0.846303i
\(900\) 0 0
\(901\) 16.8905 29.2553i 0.562705 0.974634i
\(902\) −0.725914 + 0.725914i −0.0241703 + 0.0241703i
\(903\) 17.3488 + 1.73768i 0.577331 + 0.0578265i
\(904\) 20.3599i 0.677161i
\(905\) 0 0
\(906\) −7.26446 3.67077i −0.241345 0.121953i
\(907\) −0.623721 + 2.32776i −0.0207103 + 0.0772920i −0.975508 0.219966i \(-0.929405\pi\)
0.954797 + 0.297258i \(0.0960721\pi\)
\(908\) −23.6365 + 6.33337i −0.784404 + 0.210180i
\(909\) −22.8200 + 52.1946i −0.756891 + 1.73119i
\(910\) 0 0
\(911\) 19.3662i 0.641631i −0.947142 0.320815i \(-0.896043\pi\)
0.947142 0.320815i \(-0.103957\pi\)
\(912\) 7.26312 + 6.49574i 0.240506 + 0.215095i
\(913\) 5.26347 + 1.41034i 0.174196 + 0.0466755i
\(914\) 5.33185 + 9.23503i 0.176362 + 0.305468i
\(915\) 0 0
\(916\) −29.1421 −0.962883
\(917\) 5.61830 + 0.881015i 0.185533 + 0.0290937i
\(918\) 4.52077 6.35591i 0.149208 0.209776i
\(919\) 29.5591 + 17.0659i 0.975063 + 0.562953i 0.900776 0.434284i \(-0.142998\pi\)
0.0742872 + 0.997237i \(0.476332\pi\)
\(920\) 0 0
\(921\) 18.8650 37.3340i 0.621625 1.23020i
\(922\) 11.0175 2.95213i 0.362842 0.0972231i
\(923\) 28.1966 + 28.1966i 0.928102 + 0.928102i
\(924\) −6.56775 + 1.07318i −0.216063 + 0.0353051i
\(925\) 0 0
\(926\) 9.97388 + 5.75842i 0.327762 + 0.189233i
\(927\) −29.6084 23.6491i −0.972467 0.776738i
\(928\) 16.5814 + 4.44297i 0.544311 + 0.145848i
\(929\) −9.86232 + 17.0820i −0.323572 + 0.560443i −0.981222 0.192880i \(-0.938217\pi\)
0.657650 + 0.753323i \(0.271550\pi\)
\(930\) 0 0
\(931\) −11.2006 + 2.41672i −0.367085 + 0.0792047i
\(932\) 9.24073 9.24073i 0.302690 0.302690i
\(933\) 30.5306 + 27.3049i 0.999527 + 0.893922i
\(934\) −2.72793 + 1.57497i −0.0892606 + 0.0515346i
\(935\) 0 0
\(936\) 9.35279 6.89159i 0.305706 0.225259i
\(937\) 17.3041 + 17.3041i 0.565300 + 0.565300i 0.930808 0.365508i \(-0.119105\pi\)
−0.365508 + 0.930808i \(0.619105\pi\)
\(938\) 0.0372022 0.0143461i 0.00121470 0.000468418i
\(939\) 17.9436 11.7385i 0.585568 0.383072i
\(940\) 0 0
\(941\) −3.89269 + 2.24744i −0.126898 + 0.0732646i −0.562105 0.827066i \(-0.690008\pi\)
0.435207 + 0.900330i \(0.356675\pi\)
\(942\) −1.52585 4.64300i −0.0497149 0.151277i
\(943\) 8.63274 + 32.2178i 0.281121 + 1.04916i
\(944\) 26.4292 0.860196
\(945\) 0 0
\(946\) 0.895935 0.0291294
\(947\) −3.88234 14.4891i −0.126159 0.470832i 0.873719 0.486431i \(-0.161701\pi\)
−0.999878 + 0.0155984i \(0.995035\pi\)
\(948\) −4.36235 13.2742i −0.141683 0.431125i
\(949\) 3.85939 2.22822i 0.125281 0.0723311i
\(950\) 0 0
\(951\) −6.36658 + 4.16495i −0.206451 + 0.135058i
\(952\) −12.0660 9.74025i −0.391062 0.315683i
\(953\) 21.6181 + 21.6181i 0.700277 + 0.700277i 0.964470 0.264193i \(-0.0851054\pi\)
−0.264193 + 0.964470i \(0.585105\pi\)
\(954\) 5.18422 3.81999i 0.167845 0.123677i
\(955\) 0 0
\(956\) −30.8583 + 17.8160i −0.998028 + 0.576212i
\(957\) 4.86531 + 4.35126i 0.157273 + 0.140656i
\(958\) 2.99334 2.99334i 0.0967106 0.0967106i
\(959\) 23.1966 2.47406i 0.749058 0.0798915i
\(960\) 0 0
\(961\) −2.07218 + 3.58912i −0.0668444 + 0.115778i
\(962\) 3.38780 + 0.907759i 0.109227 + 0.0292673i
\(963\) −5.11158 4.08277i −0.164718 0.131565i
\(964\) 3.25292 + 1.87807i 0.104769 + 0.0604887i
\(965\) 0 0
\(966\) 3.83086 10.1275i 0.123256 0.325847i
\(967\) −16.1911 16.1911i −0.520672 0.520672i 0.397102 0.917774i \(-0.370016\pi\)
−0.917774 + 0.397102i \(0.870016\pi\)
\(968\) 12.1357 3.25174i 0.390055 0.104515i
\(969\) −6.21477 + 12.2990i −0.199647 + 0.395102i
\(970\) 0 0
\(971\) −15.8437 9.14738i −0.508450 0.293553i 0.223747 0.974647i \(-0.428171\pi\)
−0.732196 + 0.681094i \(0.761505\pi\)
\(972\) −25.4596 + 15.2744i −0.816618 + 0.489928i
\(973\) −9.86456 25.5807i −0.316243 0.820078i
\(974\) −7.06004 −0.226218
\(975\) 0 0
\(976\) 7.55064 + 13.0781i 0.241690 + 0.418619i
\(977\) −14.3951 3.85716i −0.460540 0.123401i 0.0210868 0.999778i \(-0.493287\pi\)
−0.481627 + 0.876376i \(0.659954\pi\)
\(978\) 1.07948 + 0.965425i 0.0345179 + 0.0308709i
\(979\) 0.691709i 0.0221071i
\(980\) 0 0
\(981\) 2.83587 6.48630i 0.0905423 0.207092i
\(982\) 7.08425 1.89822i 0.226067 0.0605746i
\(983\) −3.04352 + 11.3586i −0.0970733 + 0.362283i −0.997326 0.0730860i \(-0.976715\pi\)
0.900252 + 0.435368i \(0.143382\pi\)
\(984\) 8.12717 + 4.10670i 0.259085 + 0.130917i
\(985\) 0 0
\(986\) 7.41895i 0.236267i
\(987\) −11.4710 + 15.9520i −0.365126 + 0.507757i
\(988\) −7.07955 + 7.07955i −0.225230 + 0.225230i
\(989\) 14.5546 25.2092i 0.462808 0.801607i
\(990\) 0 0
\(991\) −5.02003 8.69495i −0.159467 0.276204i 0.775210 0.631704i \(-0.217644\pi\)
−0.934676 + 0.355499i \(0.884311\pi\)
\(992\) −5.32910 19.8885i −0.169199 0.631459i
\(993\) −10.5431 2.20405i −0.334576 0.0699434i
\(994\) 8.19927 5.97636i 0.260065 0.189559i
\(995\) 0 0
\(996\) −1.31291 23.5398i −0.0416010 0.745887i
\(997\) 3.64290 13.5955i 0.115372 0.430574i −0.883943 0.467596i \(-0.845120\pi\)
0.999314 + 0.0370216i \(0.0117870\pi\)
\(998\) −0.258609 + 0.965142i −0.00818612 + 0.0305510i
\(999\) −17.2205 6.41213i −0.544831 0.202871i
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 525.2.bf.f.107.6 48
3.2 odd 2 inner 525.2.bf.f.107.7 48
5.2 odd 4 105.2.x.a.23.7 yes 48
5.3 odd 4 inner 525.2.bf.f.443.6 48
5.4 even 2 105.2.x.a.2.7 yes 48
7.4 even 3 inner 525.2.bf.f.32.7 48
15.2 even 4 105.2.x.a.23.6 yes 48
15.8 even 4 inner 525.2.bf.f.443.7 48
15.14 odd 2 105.2.x.a.2.6 48
21.11 odd 6 inner 525.2.bf.f.32.6 48
35.2 odd 12 735.2.j.g.638.6 24
35.4 even 6 105.2.x.a.32.6 yes 48
35.9 even 6 735.2.j.g.197.7 24
35.12 even 12 735.2.j.e.638.6 24
35.17 even 12 735.2.y.i.263.6 48
35.18 odd 12 inner 525.2.bf.f.368.7 48
35.19 odd 6 735.2.j.e.197.7 24
35.24 odd 6 735.2.y.i.557.6 48
35.27 even 4 735.2.y.i.128.7 48
35.32 odd 12 105.2.x.a.53.6 yes 48
35.34 odd 2 735.2.y.i.422.7 48
105.2 even 12 735.2.j.g.638.7 24
105.17 odd 12 735.2.y.i.263.7 48
105.32 even 12 105.2.x.a.53.7 yes 48
105.44 odd 6 735.2.j.g.197.6 24
105.47 odd 12 735.2.j.e.638.7 24
105.53 even 12 inner 525.2.bf.f.368.6 48
105.59 even 6 735.2.y.i.557.7 48
105.62 odd 4 735.2.y.i.128.6 48
105.74 odd 6 105.2.x.a.32.7 yes 48
105.89 even 6 735.2.j.e.197.6 24
105.104 even 2 735.2.y.i.422.6 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.x.a.2.6 48 15.14 odd 2
105.2.x.a.2.7 yes 48 5.4 even 2
105.2.x.a.23.6 yes 48 15.2 even 4
105.2.x.a.23.7 yes 48 5.2 odd 4
105.2.x.a.32.6 yes 48 35.4 even 6
105.2.x.a.32.7 yes 48 105.74 odd 6
105.2.x.a.53.6 yes 48 35.32 odd 12
105.2.x.a.53.7 yes 48 105.32 even 12
525.2.bf.f.32.6 48 21.11 odd 6 inner
525.2.bf.f.32.7 48 7.4 even 3 inner
525.2.bf.f.107.6 48 1.1 even 1 trivial
525.2.bf.f.107.7 48 3.2 odd 2 inner
525.2.bf.f.368.6 48 105.53 even 12 inner
525.2.bf.f.368.7 48 35.18 odd 12 inner
525.2.bf.f.443.6 48 5.3 odd 4 inner
525.2.bf.f.443.7 48 15.8 even 4 inner
735.2.j.e.197.6 24 105.89 even 6
735.2.j.e.197.7 24 35.19 odd 6
735.2.j.e.638.6 24 35.12 even 12
735.2.j.e.638.7 24 105.47 odd 12
735.2.j.g.197.6 24 105.44 odd 6
735.2.j.g.197.7 24 35.9 even 6
735.2.j.g.638.6 24 35.2 odd 12
735.2.j.g.638.7 24 105.2 even 12
735.2.y.i.128.6 48 105.62 odd 4
735.2.y.i.128.7 48 35.27 even 4
735.2.y.i.263.6 48 35.17 even 12
735.2.y.i.263.7 48 105.17 odd 12
735.2.y.i.422.6 48 105.104 even 2
735.2.y.i.422.7 48 35.34 odd 2
735.2.y.i.557.6 48 35.24 odd 6
735.2.y.i.557.7 48 105.59 even 6