Properties

Label 441.2.o.e.146.8
Level $441$
Weight $2$
Character 441.146
Analytic conductor $3.521$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(146,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.146");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.o (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 146.8
Character \(\chi\) \(=\) 441.146
Dual form 441.2.o.e.293.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.02035 - 0.589100i) q^{2} +(1.61957 - 0.613991i) q^{3} +(-0.305921 - 0.529871i) q^{4} +(-2.16601 - 3.75164i) q^{5} +(-2.01424 - 0.327604i) q^{6} +3.07728i q^{8} +(2.24603 - 1.98880i) q^{9} +O(q^{10})\) \(q+(-1.02035 - 0.589100i) q^{2} +(1.61957 - 0.613991i) q^{3} +(-0.305921 - 0.529871i) q^{4} +(-2.16601 - 3.75164i) q^{5} +(-2.01424 - 0.327604i) q^{6} +3.07728i q^{8} +(2.24603 - 1.98880i) q^{9} +5.10399i q^{10} +(-1.87238 - 1.08102i) q^{11} +(-0.820798 - 0.670332i) q^{12} +(2.25256 - 1.30052i) q^{13} +(-5.81148 - 4.74614i) q^{15} +(1.20098 - 2.08016i) q^{16} -1.17115 q^{17} +(-3.46335 + 0.706143i) q^{18} +2.41658i q^{19} +(-1.32526 + 2.29541i) q^{20} +(1.27366 + 2.20604i) q^{22} +(-3.16186 + 1.82550i) q^{23} +(1.88942 + 4.98387i) q^{24} +(-6.88321 + 11.9221i) q^{25} -3.06454 q^{26} +(2.41650 - 4.60006i) q^{27} +(0.589262 + 0.340210i) q^{29} +(3.13380 + 8.26629i) q^{30} +(5.67723 - 3.27775i) q^{31} +(2.87915 - 1.66228i) q^{32} +(-3.69620 - 0.601166i) q^{33} +(1.19499 + 0.689926i) q^{34} +(-1.74092 - 0.581689i) q^{36} -5.10692 q^{37} +(1.42361 - 2.46576i) q^{38} +(2.84968 - 3.48933i) q^{39} +(11.5448 - 6.66541i) q^{40} +(-3.68473 - 6.38214i) q^{41} +(-2.12577 + 3.68194i) q^{43} +1.32283i q^{44} +(-12.3262 - 4.11853i) q^{45} +4.30162 q^{46} +(3.57157 - 6.18614i) q^{47} +(0.667877 - 4.10636i) q^{48} +(14.0466 - 8.10980i) q^{50} +(-1.89677 + 0.719077i) q^{51} +(-1.37821 - 0.795711i) q^{52} -3.23289i q^{53} +(-5.17558 + 3.27011i) q^{54} +9.36601i q^{55} +(1.48376 + 3.91383i) q^{57} +(-0.400836 - 0.694269i) q^{58} +(2.91810 + 5.05430i) q^{59} +(-0.736989 + 4.53129i) q^{60} +(6.21638 + 3.58903i) q^{61} -7.72370 q^{62} -8.72092 q^{64} +(-9.75814 - 5.63387i) q^{65} +(3.41727 + 2.79083i) q^{66} +(-3.32682 - 5.76221i) q^{67} +(0.358281 + 0.620560i) q^{68} +(-4.00003 + 4.89789i) q^{69} -1.95976i q^{71} +(6.12010 + 6.91166i) q^{72} -11.9069i q^{73} +(5.21085 + 3.00849i) q^{74} +(-3.82782 + 23.5349i) q^{75} +(1.28048 - 0.739283i) q^{76} +(-4.96324 + 1.88160i) q^{78} +(4.87702 - 8.44725i) q^{79} -10.4054 q^{80} +(1.08931 - 8.93383i) q^{81} +8.68270i q^{82} +(0.796736 - 1.37999i) q^{83} +(2.53673 + 4.39374i) q^{85} +(4.33806 - 2.50458i) q^{86} +(1.16324 + 0.189194i) q^{87} +(3.32660 - 5.76184i) q^{88} -6.09921 q^{89} +(10.1508 + 11.4637i) q^{90} +(1.93456 + 1.11692i) q^{92} +(7.18218 - 8.79432i) q^{93} +(-7.28851 + 4.20802i) q^{94} +(9.06614 - 5.23434i) q^{95} +(3.64237 - 4.45995i) q^{96} +(-2.36387 - 1.36478i) q^{97} +(-6.35537 + 1.29580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02035 0.589100i −0.721498 0.416557i 0.0938059 0.995591i \(-0.470097\pi\)
−0.815304 + 0.579034i \(0.803430\pi\)
\(3\) 1.61957 0.613991i 0.935061 0.354488i
\(4\) −0.305921 0.529871i −0.152961 0.264936i
\(5\) −2.16601 3.75164i −0.968670 1.67778i −0.699415 0.714716i \(-0.746556\pi\)
−0.269254 0.963069i \(-0.586777\pi\)
\(6\) −2.01424 0.327604i −0.822308 0.133744i
\(7\) 0 0
\(8\) 3.07728i 1.08798i
\(9\) 2.24603 1.98880i 0.748677 0.662935i
\(10\) 5.10399i 1.61402i
\(11\) −1.87238 1.08102i −0.564545 0.325940i 0.190423 0.981702i \(-0.439014\pi\)
−0.754968 + 0.655762i \(0.772347\pi\)
\(12\) −0.820798 0.670332i −0.236944 0.193508i
\(13\) 2.25256 1.30052i 0.624748 0.360698i −0.153967 0.988076i \(-0.549205\pi\)
0.778715 + 0.627378i \(0.215872\pi\)
\(14\) 0 0
\(15\) −5.81148 4.74614i −1.50052 1.22545i
\(16\) 1.20098 2.08016i 0.300245 0.520040i
\(17\) −1.17115 −0.284046 −0.142023 0.989863i \(-0.545361\pi\)
−0.142023 + 0.989863i \(0.545361\pi\)
\(18\) −3.46335 + 0.706143i −0.816319 + 0.166440i
\(19\) 2.41658i 0.554402i 0.960812 + 0.277201i \(0.0894067\pi\)
−0.960812 + 0.277201i \(0.910593\pi\)
\(20\) −1.32526 + 2.29541i −0.296337 + 0.513270i
\(21\) 0 0
\(22\) 1.27366 + 2.20604i 0.271545 + 0.470330i
\(23\) −3.16186 + 1.82550i −0.659294 + 0.380644i −0.792008 0.610511i \(-0.790964\pi\)
0.132714 + 0.991154i \(0.457631\pi\)
\(24\) 1.88942 + 4.98387i 0.385676 + 1.01733i
\(25\) −6.88321 + 11.9221i −1.37664 + 2.38441i
\(26\) −3.06454 −0.601006
\(27\) 2.41650 4.60006i 0.465056 0.885281i
\(28\) 0 0
\(29\) 0.589262 + 0.340210i 0.109423 + 0.0631755i 0.553713 0.832708i \(-0.313211\pi\)
−0.444290 + 0.895883i \(0.646544\pi\)
\(30\) 3.13380 + 8.26629i 0.572152 + 1.50921i
\(31\) 5.67723 3.27775i 1.01966 0.588702i 0.105655 0.994403i \(-0.466306\pi\)
0.914006 + 0.405701i \(0.132973\pi\)
\(32\) 2.87915 1.66228i 0.508967 0.293852i
\(33\) −3.69620 0.601166i −0.643425 0.104650i
\(34\) 1.19499 + 0.689926i 0.204939 + 0.118321i
\(35\) 0 0
\(36\) −1.74092 0.581689i −0.290153 0.0969482i
\(37\) −5.10692 −0.839572 −0.419786 0.907623i \(-0.637895\pi\)
−0.419786 + 0.907623i \(0.637895\pi\)
\(38\) 1.42361 2.46576i 0.230940 0.399999i
\(39\) 2.84968 3.48933i 0.456314 0.558740i
\(40\) 11.5448 6.66541i 1.82540 1.05389i
\(41\) −3.68473 6.38214i −0.575458 0.996723i −0.995992 0.0894458i \(-0.971490\pi\)
0.420534 0.907277i \(-0.361843\pi\)
\(42\) 0 0
\(43\) −2.12577 + 3.68194i −0.324176 + 0.561490i −0.981345 0.192253i \(-0.938420\pi\)
0.657169 + 0.753743i \(0.271754\pi\)
\(44\) 1.32283i 0.199424i
\(45\) −12.3262 4.11853i −1.83748 0.613954i
\(46\) 4.30162 0.634239
\(47\) 3.57157 6.18614i 0.520967 0.902341i −0.478736 0.877959i \(-0.658905\pi\)
0.999703 0.0243819i \(-0.00776176\pi\)
\(48\) 0.667877 4.10636i 0.0963998 0.592703i
\(49\) 0 0
\(50\) 14.0466 8.10980i 1.98649 1.14690i
\(51\) −1.89677 + 0.719077i −0.265600 + 0.100691i
\(52\) −1.37821 0.795711i −0.191124 0.110345i
\(53\) 3.23289i 0.444071i −0.975039 0.222036i \(-0.928730\pi\)
0.975039 0.222036i \(-0.0712702\pi\)
\(54\) −5.17558 + 3.27011i −0.704307 + 0.445006i
\(55\) 9.36601i 1.26291i
\(56\) 0 0
\(57\) 1.48376 + 3.91383i 0.196528 + 0.518399i
\(58\) −0.400836 0.694269i −0.0526324 0.0911619i
\(59\) 2.91810 + 5.05430i 0.379905 + 0.658014i 0.991048 0.133506i \(-0.0426234\pi\)
−0.611143 + 0.791520i \(0.709290\pi\)
\(60\) −0.736989 + 4.53129i −0.0951448 + 0.584986i
\(61\) 6.21638 + 3.58903i 0.795925 + 0.459528i 0.842044 0.539408i \(-0.181352\pi\)
−0.0461190 + 0.998936i \(0.514685\pi\)
\(62\) −7.72370 −0.980911
\(63\) 0 0
\(64\) −8.72092 −1.09012
\(65\) −9.75814 5.63387i −1.21035 0.698795i
\(66\) 3.41727 + 2.79083i 0.420637 + 0.343528i
\(67\) −3.32682 5.76221i −0.406435 0.703966i 0.588052 0.808823i \(-0.299895\pi\)
−0.994487 + 0.104857i \(0.966562\pi\)
\(68\) 0.358281 + 0.620560i 0.0434479 + 0.0752540i
\(69\) −4.00003 + 4.89789i −0.481547 + 0.589637i
\(70\) 0 0
\(71\) 1.95976i 0.232580i −0.993215 0.116290i \(-0.962900\pi\)
0.993215 0.116290i \(-0.0371003\pi\)
\(72\) 6.12010 + 6.91166i 0.721261 + 0.814546i
\(73\) 11.9069i 1.39360i −0.717266 0.696799i \(-0.754607\pi\)
0.717266 0.696799i \(-0.245393\pi\)
\(74\) 5.21085 + 3.00849i 0.605749 + 0.349729i
\(75\) −3.82782 + 23.5349i −0.441998 + 2.71757i
\(76\) 1.28048 0.739283i 0.146881 0.0848016i
\(77\) 0 0
\(78\) −4.96324 + 1.88160i −0.561977 + 0.213049i
\(79\) 4.87702 8.44725i 0.548708 0.950390i −0.449656 0.893202i \(-0.648453\pi\)
0.998363 0.0571879i \(-0.0182134\pi\)
\(80\) −10.4054 −1.16335
\(81\) 1.08931 8.93383i 0.121034 0.992648i
\(82\) 8.68270i 0.958844i
\(83\) 0.796736 1.37999i 0.0874531 0.151473i −0.818981 0.573821i \(-0.805461\pi\)
0.906434 + 0.422348i \(0.138794\pi\)
\(84\) 0 0
\(85\) 2.53673 + 4.39374i 0.275147 + 0.476568i
\(86\) 4.33806 2.50458i 0.467785 0.270076i
\(87\) 1.16324 + 0.189194i 0.124712 + 0.0202838i
\(88\) 3.32660 5.76184i 0.354617 0.614214i
\(89\) −6.09921 −0.646515 −0.323258 0.946311i \(-0.604778\pi\)
−0.323258 + 0.946311i \(0.604778\pi\)
\(90\) 10.1508 + 11.4637i 1.06999 + 1.20838i
\(91\) 0 0
\(92\) 1.93456 + 1.11692i 0.201692 + 0.116447i
\(93\) 7.18218 8.79432i 0.744757 0.911929i
\(94\) −7.28851 + 4.20802i −0.751753 + 0.434025i
\(95\) 9.06614 5.23434i 0.930166 0.537032i
\(96\) 3.64237 4.45995i 0.371748 0.455192i
\(97\) −2.36387 1.36478i −0.240014 0.138572i 0.375169 0.926956i \(-0.377585\pi\)
−0.615183 + 0.788384i \(0.710918\pi\)
\(98\) 0 0
\(99\) −6.35537 + 1.29580i −0.638738 + 0.130233i
\(100\) 8.42288 0.842288
\(101\) 7.99849 13.8538i 0.795880 1.37850i −0.126400 0.991979i \(-0.540342\pi\)
0.922279 0.386524i \(-0.126324\pi\)
\(102\) 2.35898 + 0.383675i 0.233574 + 0.0379895i
\(103\) −2.61251 + 1.50834i −0.257419 + 0.148621i −0.623156 0.782097i \(-0.714150\pi\)
0.365738 + 0.930718i \(0.380817\pi\)
\(104\) 4.00205 + 6.93175i 0.392433 + 0.679714i
\(105\) 0 0
\(106\) −1.90450 + 3.29868i −0.184981 + 0.320397i
\(107\) 11.8484i 1.14543i 0.819754 + 0.572716i \(0.194110\pi\)
−0.819754 + 0.572716i \(0.805890\pi\)
\(108\) −3.17670 + 0.126820i −0.305678 + 0.0122033i
\(109\) 7.16157 0.685954 0.342977 0.939344i \(-0.388565\pi\)
0.342977 + 0.939344i \(0.388565\pi\)
\(110\) 5.51752 9.55662i 0.526075 0.911188i
\(111\) −8.27102 + 3.13560i −0.785051 + 0.297618i
\(112\) 0 0
\(113\) 2.46102 1.42087i 0.231514 0.133664i −0.379756 0.925086i \(-0.623992\pi\)
0.611270 + 0.791422i \(0.290659\pi\)
\(114\) 0.791682 4.86756i 0.0741478 0.455889i
\(115\) 13.6973 + 7.90812i 1.27728 + 0.737436i
\(116\) 0.416310i 0.0386535i
\(117\) 2.47285 7.40090i 0.228615 0.684214i
\(118\) 6.87623i 0.633008i
\(119\) 0 0
\(120\) 14.6052 17.8835i 1.33327 1.63254i
\(121\) −3.16279 5.47811i −0.287526 0.498010i
\(122\) −4.22859 7.32414i −0.382839 0.663096i
\(123\) −9.88626 8.07395i −0.891414 0.728003i
\(124\) −3.47357 2.00547i −0.311936 0.180096i
\(125\) 37.9763 3.39670
\(126\) 0 0
\(127\) 18.5344 1.64466 0.822332 0.569009i \(-0.192673\pi\)
0.822332 + 0.569009i \(0.192673\pi\)
\(128\) 3.14011 + 1.81294i 0.277549 + 0.160243i
\(129\) −1.18216 + 7.26836i −0.104083 + 0.639944i
\(130\) 6.63783 + 11.4971i 0.582176 + 1.00836i
\(131\) 3.35221 + 5.80619i 0.292884 + 0.507289i 0.974490 0.224429i \(-0.0720518\pi\)
−0.681607 + 0.731719i \(0.738718\pi\)
\(132\) 0.812205 + 2.14242i 0.0706933 + 0.186474i
\(133\) 0 0
\(134\) 7.83931i 0.677214i
\(135\) −22.4919 + 0.897922i −1.93580 + 0.0772808i
\(136\) 3.60396i 0.309037i
\(137\) 11.8181 + 6.82316i 1.00969 + 0.582942i 0.911099 0.412187i \(-0.135235\pi\)
0.0985856 + 0.995129i \(0.468568\pi\)
\(138\) 6.96678 2.64115i 0.593052 0.224830i
\(139\) 7.74126 4.46942i 0.656605 0.379091i −0.134377 0.990930i \(-0.542903\pi\)
0.790982 + 0.611839i \(0.209570\pi\)
\(140\) 0 0
\(141\) 1.98618 12.2118i 0.167267 1.02842i
\(142\) −1.15449 + 1.99964i −0.0968830 + 0.167806i
\(143\) −5.62354 −0.470264
\(144\) −1.43959 7.06062i −0.119966 0.588385i
\(145\) 2.94760i 0.244785i
\(146\) −7.01436 + 12.1492i −0.580513 + 1.00548i
\(147\) 0 0
\(148\) 1.56231 + 2.70601i 0.128421 + 0.222432i
\(149\) −3.29003 + 1.89950i −0.269530 + 0.155613i −0.628674 0.777669i \(-0.716402\pi\)
0.359144 + 0.933282i \(0.383069\pi\)
\(150\) 17.7701 21.7589i 1.45092 1.77661i
\(151\) 1.91083 3.30965i 0.155501 0.269336i −0.777740 0.628586i \(-0.783634\pi\)
0.933241 + 0.359250i \(0.116967\pi\)
\(152\) −7.43648 −0.603178
\(153\) −2.63044 + 2.32919i −0.212659 + 0.188304i
\(154\) 0 0
\(155\) −24.5939 14.1993i −1.97543 1.14051i
\(156\) −2.72067 0.442503i −0.217828 0.0354286i
\(157\) −18.6081 + 10.7434i −1.48509 + 0.857417i −0.999856 0.0169675i \(-0.994599\pi\)
−0.485234 + 0.874384i \(0.661265\pi\)
\(158\) −9.95256 + 5.74611i −0.791783 + 0.457136i
\(159\) −1.98496 5.23590i −0.157418 0.415234i
\(160\) −12.4725 7.20102i −0.986041 0.569291i
\(161\) 0 0
\(162\) −6.37441 + 8.47394i −0.500821 + 0.665776i
\(163\) 12.5175 0.980447 0.490223 0.871597i \(-0.336915\pi\)
0.490223 + 0.871597i \(0.336915\pi\)
\(164\) −2.25448 + 3.90487i −0.176045 + 0.304919i
\(165\) 5.75064 + 15.1689i 0.447687 + 1.18090i
\(166\) −1.62590 + 0.938715i −0.126194 + 0.0728584i
\(167\) −7.70819 13.3510i −0.596477 1.03313i −0.993337 0.115250i \(-0.963233\pi\)
0.396859 0.917880i \(-0.370100\pi\)
\(168\) 0 0
\(169\) −3.11731 + 5.39935i −0.239793 + 0.415334i
\(170\) 5.97755i 0.458457i
\(171\) 4.80611 + 5.42771i 0.367532 + 0.415068i
\(172\) 2.60127 0.198345
\(173\) −4.30737 + 7.46059i −0.327483 + 0.567218i −0.982012 0.188820i \(-0.939534\pi\)
0.654528 + 0.756037i \(0.272867\pi\)
\(174\) −1.07546 0.878309i −0.0815302 0.0665844i
\(175\) 0 0
\(176\) −4.49739 + 2.59657i −0.339004 + 0.195724i
\(177\) 7.82938 + 6.39413i 0.588492 + 0.480612i
\(178\) 6.22334 + 3.59305i 0.466459 + 0.269310i
\(179\) 19.1384i 1.43047i 0.698882 + 0.715237i \(0.253681\pi\)
−0.698882 + 0.715237i \(0.746319\pi\)
\(180\) 1.58856 + 7.79125i 0.118404 + 0.580725i
\(181\) 7.69817i 0.572200i −0.958200 0.286100i \(-0.907641\pi\)
0.958200 0.286100i \(-0.0923590\pi\)
\(182\) 0 0
\(183\) 12.2715 + 1.99589i 0.907135 + 0.147541i
\(184\) −5.61758 9.72993i −0.414133 0.717300i
\(185\) 11.0616 + 19.1593i 0.813268 + 1.40862i
\(186\) −12.5091 + 4.74228i −0.917211 + 0.347721i
\(187\) 2.19285 + 1.26604i 0.160357 + 0.0925820i
\(188\) −4.37047 −0.318750
\(189\) 0 0
\(190\) −12.3342 −0.894817
\(191\) 16.1203 + 9.30704i 1.16642 + 0.673433i 0.952834 0.303491i \(-0.0981521\pi\)
0.213587 + 0.976924i \(0.431485\pi\)
\(192\) −14.1242 + 5.35456i −1.01932 + 0.386432i
\(193\) −9.05721 15.6875i −0.651952 1.12921i −0.982649 0.185477i \(-0.940617\pi\)
0.330696 0.943737i \(-0.392716\pi\)
\(194\) 1.60799 + 2.78511i 0.115447 + 0.199959i
\(195\) −19.2632 3.13305i −1.37946 0.224362i
\(196\) 0 0
\(197\) 16.5945i 1.18231i 0.806559 + 0.591154i \(0.201328\pi\)
−0.806559 + 0.591154i \(0.798672\pi\)
\(198\) 7.24807 + 2.42178i 0.515098 + 0.172108i
\(199\) 2.71887i 0.192735i −0.995346 0.0963677i \(-0.969278\pi\)
0.995346 0.0963677i \(-0.0307225\pi\)
\(200\) −36.6875 21.1815i −2.59420 1.49776i
\(201\) −8.92596 7.28969i −0.629589 0.514175i
\(202\) −16.3225 + 9.42383i −1.14845 + 0.663058i
\(203\) 0 0
\(204\) 0.961279 + 0.785061i 0.0673030 + 0.0549653i
\(205\) −15.9623 + 27.6476i −1.11486 + 1.93099i
\(206\) 3.55425 0.247636
\(207\) −3.47108 + 10.3885i −0.241256 + 0.722048i
\(208\) 6.24759i 0.433192i
\(209\) 2.61237 4.52476i 0.180702 0.312984i
\(210\) 0 0
\(211\) −13.9445 24.1526i −0.959979 1.66273i −0.722539 0.691330i \(-0.757025\pi\)
−0.237440 0.971402i \(-0.576308\pi\)
\(212\) −1.71301 + 0.989010i −0.117650 + 0.0679255i
\(213\) −1.20327 3.17397i −0.0824469 0.217477i
\(214\) 6.97992 12.0896i 0.477138 0.826427i
\(215\) 18.4177 1.25608
\(216\) 14.1556 + 7.43624i 0.963169 + 0.505972i
\(217\) 0 0
\(218\) −7.30732 4.21888i −0.494914 0.285739i
\(219\) −7.31073 19.2841i −0.494013 1.30310i
\(220\) 4.96278 2.86526i 0.334590 0.193176i
\(221\) −2.63809 + 1.52310i −0.177457 + 0.102455i
\(222\) 10.2865 + 1.67305i 0.690387 + 0.112288i
\(223\) 6.64349 + 3.83562i 0.444881 + 0.256852i 0.705666 0.708545i \(-0.250648\pi\)
−0.260785 + 0.965397i \(0.583981\pi\)
\(224\) 0 0
\(225\) 8.25076 + 40.4667i 0.550051 + 2.69778i
\(226\) −3.34815 −0.222715
\(227\) 1.16439 2.01677i 0.0772829 0.133858i −0.824794 0.565434i \(-0.808709\pi\)
0.902077 + 0.431576i \(0.142042\pi\)
\(228\) 1.61991 1.98352i 0.107281 0.131362i
\(229\) −10.3653 + 5.98443i −0.684961 + 0.395463i −0.801722 0.597698i \(-0.796082\pi\)
0.116760 + 0.993160i \(0.462749\pi\)
\(230\) −9.31735 16.1381i −0.614368 1.06412i
\(231\) 0 0
\(232\) −1.04692 + 1.81332i −0.0687337 + 0.119050i
\(233\) 2.52779i 0.165601i 0.996566 + 0.0828007i \(0.0263865\pi\)
−0.996566 + 0.0828007i \(0.973614\pi\)
\(234\) −6.88305 + 6.09477i −0.449959 + 0.398428i
\(235\) −30.9442 −2.01858
\(236\) 1.78542 3.09244i 0.116221 0.201301i
\(237\) 2.71216 16.6754i 0.176174 1.08318i
\(238\) 0 0
\(239\) 17.4587 10.0798i 1.12931 0.652006i 0.185546 0.982636i \(-0.440595\pi\)
0.943761 + 0.330630i \(0.107261\pi\)
\(240\) −16.8522 + 6.38879i −1.08781 + 0.412395i
\(241\) −18.1254 10.4647i −1.16756 0.674091i −0.214455 0.976734i \(-0.568798\pi\)
−0.953104 + 0.302643i \(0.902131\pi\)
\(242\) 7.45280i 0.479084i
\(243\) −3.72107 15.1378i −0.238707 0.971092i
\(244\) 4.39184i 0.281159i
\(245\) 0 0
\(246\) 5.33110 + 14.0623i 0.339899 + 0.896578i
\(247\) 3.14280 + 5.44349i 0.199972 + 0.346361i
\(248\) 10.0865 + 17.4704i 0.640496 + 1.10937i
\(249\) 0.443072 2.72418i 0.0280786 0.172638i
\(250\) −38.7492 22.3718i −2.45071 1.41492i
\(251\) −25.5747 −1.61426 −0.807130 0.590374i \(-0.798980\pi\)
−0.807130 + 0.590374i \(0.798980\pi\)
\(252\) 0 0
\(253\) 7.89363 0.496268
\(254\) −18.9116 10.9186i −1.18662 0.685096i
\(255\) 6.80613 + 5.55846i 0.426217 + 0.348084i
\(256\) 6.58491 + 11.4054i 0.411557 + 0.712837i
\(257\) 5.93725 + 10.2836i 0.370355 + 0.641474i 0.989620 0.143708i \(-0.0459026\pi\)
−0.619265 + 0.785182i \(0.712569\pi\)
\(258\) 5.48801 6.71988i 0.341669 0.418361i
\(259\) 0 0
\(260\) 6.89408i 0.427553i
\(261\) 2.00011 0.407803i 0.123804 0.0252424i
\(262\) 7.89915i 0.488011i
\(263\) 19.3705 + 11.1836i 1.19444 + 0.689608i 0.959309 0.282357i \(-0.0911162\pi\)
0.235127 + 0.971965i \(0.424450\pi\)
\(264\) 1.84995 11.3742i 0.113857 0.700034i
\(265\) −12.1286 + 7.00247i −0.745056 + 0.430158i
\(266\) 0 0
\(267\) −9.87812 + 3.74486i −0.604531 + 0.229182i
\(268\) −2.03549 + 3.52557i −0.124337 + 0.215358i
\(269\) 4.22669 0.257706 0.128853 0.991664i \(-0.458870\pi\)
0.128853 + 0.991664i \(0.458870\pi\)
\(270\) 23.4786 + 12.3338i 1.42887 + 0.750612i
\(271\) 22.3943i 1.36036i −0.733046 0.680179i \(-0.761902\pi\)
0.733046 0.680179i \(-0.238098\pi\)
\(272\) −1.40653 + 2.43619i −0.0852836 + 0.147715i
\(273\) 0 0
\(274\) −8.03905 13.9240i −0.485657 0.841183i
\(275\) 25.7760 14.8818i 1.55435 0.897405i
\(276\) 3.81894 + 0.621130i 0.229873 + 0.0373877i
\(277\) −5.69230 + 9.85935i −0.342017 + 0.592391i −0.984807 0.173651i \(-0.944443\pi\)
0.642790 + 0.766042i \(0.277777\pi\)
\(278\) −10.5317 −0.631652
\(279\) 6.23243 18.6528i 0.373126 1.11672i
\(280\) 0 0
\(281\) −0.702700 0.405704i −0.0419196 0.0242023i 0.478894 0.877873i \(-0.341038\pi\)
−0.520813 + 0.853671i \(0.674371\pi\)
\(282\) −9.22059 + 11.2903i −0.549078 + 0.672326i
\(283\) 15.8740 9.16486i 0.943611 0.544794i 0.0525206 0.998620i \(-0.483274\pi\)
0.891090 + 0.453826i \(0.149941\pi\)
\(284\) −1.03842 + 0.599532i −0.0616188 + 0.0355757i
\(285\) 11.4694 14.0439i 0.679391 0.831890i
\(286\) 5.73799 + 3.31283i 0.339294 + 0.195892i
\(287\) 0 0
\(288\) 3.16071 9.45959i 0.186247 0.557412i
\(289\) −15.6284 −0.919318
\(290\) −1.73643 + 3.00759i −0.101967 + 0.176612i
\(291\) −4.66642 0.758967i −0.273550 0.0444914i
\(292\) −6.30913 + 3.64258i −0.369214 + 0.213166i
\(293\) 6.23639 + 10.8017i 0.364334 + 0.631044i 0.988669 0.150112i \(-0.0479634\pi\)
−0.624335 + 0.781156i \(0.714630\pi\)
\(294\) 0 0
\(295\) 12.6413 21.8954i 0.736004 1.27480i
\(296\) 15.7154i 0.913438i
\(297\) −9.49737 + 6.00078i −0.551093 + 0.348200i
\(298\) 4.47599 0.259287
\(299\) −4.74819 + 8.22411i −0.274595 + 0.475613i
\(300\) 13.6415 5.17157i 0.787590 0.298581i
\(301\) 0 0
\(302\) −3.89943 + 2.25134i −0.224387 + 0.129550i
\(303\) 4.44804 27.3482i 0.255533 1.57111i
\(304\) 5.02688 + 2.90227i 0.288311 + 0.166457i
\(305\) 31.0955i 1.78052i
\(306\) 4.05611 0.827001i 0.231872 0.0472765i
\(307\) 21.3241i 1.21703i 0.793543 + 0.608514i \(0.208234\pi\)
−0.793543 + 0.608514i \(0.791766\pi\)
\(308\) 0 0
\(309\) −3.30505 + 4.04692i −0.188018 + 0.230221i
\(310\) 16.7296 + 28.9765i 0.950178 + 1.64576i
\(311\) −3.92094 6.79126i −0.222336 0.385097i 0.733181 0.680034i \(-0.238035\pi\)
−0.955517 + 0.294936i \(0.904702\pi\)
\(312\) 10.7376 + 8.76925i 0.607899 + 0.496461i
\(313\) 8.57593 + 4.95131i 0.484740 + 0.279865i 0.722390 0.691486i \(-0.243044\pi\)
−0.237650 + 0.971351i \(0.576377\pi\)
\(314\) 25.3158 1.42865
\(315\) 0 0
\(316\) −5.96794 −0.335723
\(317\) 20.8358 + 12.0296i 1.17025 + 0.675647i 0.953740 0.300632i \(-0.0971977\pi\)
0.216515 + 0.976279i \(0.430531\pi\)
\(318\) −1.05911 + 6.51180i −0.0593919 + 0.365164i
\(319\) −0.735549 1.27401i −0.0411828 0.0713308i
\(320\) 18.8896 + 32.7178i 1.05596 + 1.82898i
\(321\) 7.27483 + 19.1894i 0.406042 + 1.07105i
\(322\) 0 0
\(323\) 2.83018i 0.157476i
\(324\) −5.06703 + 2.15586i −0.281501 + 0.119770i
\(325\) 35.8069i 1.98621i
\(326\) −12.7723 7.37407i −0.707390 0.408412i
\(327\) 11.5987 4.39713i 0.641408 0.243162i
\(328\) 19.6396 11.3389i 1.08442 0.626088i
\(329\) 0 0
\(330\) 3.06835 18.8654i 0.168907 1.03850i
\(331\) 4.53686 7.85807i 0.249368 0.431918i −0.713982 0.700164i \(-0.753110\pi\)
0.963351 + 0.268245i \(0.0864437\pi\)
\(332\) −0.974954 −0.0535075
\(333\) −11.4703 + 10.1567i −0.628568 + 0.556581i
\(334\) 18.1636i 0.993867i
\(335\) −14.4118 + 24.9620i −0.787403 + 1.36382i
\(336\) 0 0
\(337\) 4.02012 + 6.96304i 0.218990 + 0.379301i 0.954499 0.298213i \(-0.0963906\pi\)
−0.735510 + 0.677514i \(0.763057\pi\)
\(338\) 6.36152 3.67282i 0.346021 0.199775i
\(339\) 3.11340 3.81225i 0.169097 0.207053i
\(340\) 1.55208 2.68828i 0.0841733 0.145792i
\(341\) −14.1733 −0.767525
\(342\) −1.70645 8.36946i −0.0922743 0.452568i
\(343\) 0 0
\(344\) −11.3303 6.54157i −0.610891 0.352698i
\(345\) 27.0392 + 4.39778i 1.45574 + 0.236769i
\(346\) 8.79007 5.07495i 0.472557 0.272831i
\(347\) −30.6345 + 17.6868i −1.64454 + 0.949478i −0.665356 + 0.746526i \(0.731720\pi\)
−0.979189 + 0.202952i \(0.934946\pi\)
\(348\) −0.255611 0.674245i −0.0137022 0.0361433i
\(349\) 21.1868 + 12.2322i 1.13411 + 0.654776i 0.944964 0.327174i \(-0.106096\pi\)
0.189141 + 0.981950i \(0.439430\pi\)
\(350\) 0 0
\(351\) −0.539130 13.5046i −0.0287766 0.720823i
\(352\) −7.18783 −0.383112
\(353\) −0.485949 + 0.841688i −0.0258644 + 0.0447985i −0.878668 0.477433i \(-0.841567\pi\)
0.852803 + 0.522232i \(0.174900\pi\)
\(354\) −4.22194 11.1365i −0.224394 0.591901i
\(355\) −7.35231 + 4.24486i −0.390220 + 0.225294i
\(356\) 1.86588 + 3.23180i 0.0988914 + 0.171285i
\(357\) 0 0
\(358\) 11.2745 19.5279i 0.595874 1.03208i
\(359\) 15.9210i 0.840276i −0.907460 0.420138i \(-0.861982\pi\)
0.907460 0.420138i \(-0.138018\pi\)
\(360\) 12.6738 37.9311i 0.667970 1.99915i
\(361\) 13.1601 0.692639
\(362\) −4.53499 + 7.85484i −0.238354 + 0.412841i
\(363\) −8.48588 6.93028i −0.445393 0.363745i
\(364\) 0 0
\(365\) −44.6704 + 25.7905i −2.33816 + 1.34994i
\(366\) −11.3455 9.26566i −0.593037 0.484324i
\(367\) −21.3983 12.3543i −1.11698 0.644891i −0.176355 0.984327i \(-0.556431\pi\)
−0.940629 + 0.339435i \(0.889764\pi\)
\(368\) 8.76958i 0.457146i
\(369\) −20.9688 7.00627i −1.09159 0.364732i
\(370\) 26.0657i 1.35509i
\(371\) 0 0
\(372\) −6.85704 1.11526i −0.355521 0.0578235i
\(373\) 4.71810 + 8.17200i 0.244294 + 0.423130i 0.961933 0.273286i \(-0.0881104\pi\)
−0.717639 + 0.696416i \(0.754777\pi\)
\(374\) −1.49165 2.58361i −0.0771314 0.133595i
\(375\) 61.5054 23.3171i 3.17612 1.20409i
\(376\) 19.0364 + 10.9907i 0.981730 + 0.566802i
\(377\) 1.76980 0.0911492
\(378\) 0 0
\(379\) 20.8031 1.06858 0.534292 0.845300i \(-0.320578\pi\)
0.534292 + 0.845300i \(0.320578\pi\)
\(380\) −5.54705 3.20259i −0.284558 0.164289i
\(381\) 30.0178 11.3800i 1.53786 0.583013i
\(382\) −10.9656 18.9929i −0.561047 0.971761i
\(383\) −3.23008 5.59467i −0.165050 0.285874i 0.771623 0.636080i \(-0.219445\pi\)
−0.936673 + 0.350205i \(0.886112\pi\)
\(384\) 6.19876 + 1.00819i 0.316329 + 0.0514492i
\(385\) 0 0
\(386\) 21.3424i 1.08630i
\(387\) 2.54811 + 12.4975i 0.129528 + 0.635283i
\(388\) 1.67006i 0.0847845i
\(389\) −0.0445846 0.0257409i −0.00226053 0.00130512i 0.498869 0.866677i \(-0.333749\pi\)
−0.501130 + 0.865372i \(0.667082\pi\)
\(390\) 17.8095 + 14.5447i 0.901820 + 0.736502i
\(391\) 3.70303 2.13794i 0.187270 0.108120i
\(392\) 0 0
\(393\) 8.99409 + 7.34533i 0.453692 + 0.370523i
\(394\) 9.77582 16.9322i 0.492499 0.853033i
\(395\) −42.2547 −2.12607
\(396\) 2.63085 + 2.97111i 0.132205 + 0.149304i
\(397\) 12.7131i 0.638052i 0.947746 + 0.319026i \(0.103356\pi\)
−0.947746 + 0.319026i \(0.896644\pi\)
\(398\) −1.60169 + 2.77420i −0.0802853 + 0.139058i
\(399\) 0 0
\(400\) 16.5332 + 28.6364i 0.826660 + 1.43182i
\(401\) −2.19725 + 1.26858i −0.109725 + 0.0633500i −0.553858 0.832611i \(-0.686845\pi\)
0.444133 + 0.895961i \(0.353512\pi\)
\(402\) 4.81327 + 12.6963i 0.240064 + 0.633236i
\(403\) 8.52554 14.7667i 0.424687 0.735580i
\(404\) −9.78764 −0.486953
\(405\) −35.8760 + 15.2641i −1.78269 + 0.758478i
\(406\) 0 0
\(407\) 9.56210 + 5.52068i 0.473976 + 0.273650i
\(408\) −2.21280 5.83687i −0.109550 0.288968i
\(409\) −0.0495655 + 0.0286167i −0.00245086 + 0.00141500i −0.501225 0.865317i \(-0.667117\pi\)
0.498774 + 0.866732i \(0.333784\pi\)
\(410\) 32.5744 18.8068i 1.60873 0.928803i
\(411\) 23.3296 + 3.79443i 1.15076 + 0.187165i
\(412\) 1.59845 + 0.922864i 0.0787499 + 0.0454663i
\(413\) 0 0
\(414\) 9.66157 8.55508i 0.474840 0.420459i
\(415\) −6.90295 −0.338853
\(416\) 4.32364 7.48876i 0.211984 0.367167i
\(417\) 9.79335 11.9916i 0.479583 0.587232i
\(418\) −5.33108 + 3.07790i −0.260752 + 0.150545i
\(419\) 3.08007 + 5.33484i 0.150471 + 0.260624i 0.931401 0.363995i \(-0.118588\pi\)
−0.780930 + 0.624619i \(0.785254\pi\)
\(420\) 0 0
\(421\) 15.0693 26.1007i 0.734431 1.27207i −0.220542 0.975378i \(-0.570783\pi\)
0.954973 0.296694i \(-0.0958842\pi\)
\(422\) 32.8588i 1.59954i
\(423\) −4.28117 20.9974i −0.208157 1.02093i
\(424\) 9.94849 0.483141
\(425\) 8.06128 13.9626i 0.391030 0.677283i
\(426\) −0.642025 + 3.94741i −0.0311062 + 0.191253i
\(427\) 0 0
\(428\) 6.27815 3.62469i 0.303466 0.175206i
\(429\) −9.10773 + 3.45280i −0.439725 + 0.166703i
\(430\) −18.7926 10.8499i −0.906258 0.523228i
\(431\) 8.07140i 0.388785i −0.980924 0.194393i \(-0.937726\pi\)
0.980924 0.194393i \(-0.0622736\pi\)
\(432\) −6.66668 10.5513i −0.320751 0.507650i
\(433\) 28.4938i 1.36933i 0.728860 + 0.684663i \(0.240051\pi\)
−0.728860 + 0.684663i \(0.759949\pi\)
\(434\) 0 0
\(435\) −1.80980 4.77385i −0.0867731 0.228889i
\(436\) −2.19088 3.79471i −0.104924 0.181734i
\(437\) −4.41147 7.64090i −0.211029 0.365514i
\(438\) −3.90076 + 23.9833i −0.186385 + 1.14597i
\(439\) 1.77067 + 1.02230i 0.0845096 + 0.0487916i 0.541659 0.840598i \(-0.317796\pi\)
−0.457150 + 0.889390i \(0.651130\pi\)
\(440\) −28.8218 −1.37402
\(441\) 0 0
\(442\) 3.58904 0.170713
\(443\) −21.1324 12.2008i −1.00403 0.579677i −0.0945924 0.995516i \(-0.530155\pi\)
−0.909438 + 0.415839i \(0.863488\pi\)
\(444\) 4.19175 + 3.42333i 0.198931 + 0.162464i
\(445\) 13.2110 + 22.8821i 0.626260 + 1.08471i
\(446\) −4.51913 7.82737i −0.213987 0.370637i
\(447\) −4.16217 + 5.09643i −0.196864 + 0.241053i
\(448\) 0 0
\(449\) 0.293539i 0.0138529i −0.999976 0.00692647i \(-0.997795\pi\)
0.999976 0.00692647i \(-0.00220478\pi\)
\(450\) 15.4203 46.1508i 0.726918 2.17557i
\(451\) 15.9331i 0.750259i
\(452\) −1.50576 0.869351i −0.0708250 0.0408908i
\(453\) 1.06263 6.53345i 0.0499267 0.306968i
\(454\) −2.37616 + 1.37188i −0.111519 + 0.0643855i
\(455\) 0 0
\(456\) −12.0439 + 4.56593i −0.564008 + 0.213819i
\(457\) −8.27470 + 14.3322i −0.387074 + 0.670432i −0.992055 0.125808i \(-0.959848\pi\)
0.604981 + 0.796240i \(0.293181\pi\)
\(458\) 14.1017 0.658931
\(459\) −2.83009 + 5.38737i −0.132097 + 0.251461i
\(460\) 9.67705i 0.451195i
\(461\) 10.0560 17.4175i 0.468354 0.811213i −0.530992 0.847377i \(-0.678180\pi\)
0.999346 + 0.0361638i \(0.0115138\pi\)
\(462\) 0 0
\(463\) 9.34602 + 16.1878i 0.434346 + 0.752310i 0.997242 0.0742181i \(-0.0236461\pi\)
−0.562896 + 0.826528i \(0.690313\pi\)
\(464\) 1.41538 0.817173i 0.0657076 0.0379363i
\(465\) −48.5498 7.89636i −2.25144 0.366185i
\(466\) 1.48912 2.57924i 0.0689824 0.119481i
\(467\) 29.3605 1.35864 0.679322 0.733841i \(-0.262274\pi\)
0.679322 + 0.733841i \(0.262274\pi\)
\(468\) −4.67802 + 0.953804i −0.216242 + 0.0440896i
\(469\) 0 0
\(470\) 31.5740 + 18.2293i 1.45640 + 0.840853i
\(471\) −23.5409 + 28.8249i −1.08471 + 1.32818i
\(472\) −15.5535 + 8.97981i −0.715907 + 0.413329i
\(473\) 7.96050 4.59599i 0.366024 0.211324i
\(474\) −12.5908 + 15.4170i −0.578316 + 0.708127i
\(475\) −28.8106 16.6338i −1.32192 0.763212i
\(476\) 0 0
\(477\) −6.42958 7.26117i −0.294390 0.332466i
\(478\) −23.7520 −1.08639
\(479\) 10.9660 18.9938i 0.501051 0.867847i −0.498948 0.866632i \(-0.666280\pi\)
0.999999 0.00121455i \(-0.000386605\pi\)
\(480\) −24.6215 4.00456i −1.12381 0.182782i
\(481\) −11.5036 + 6.64163i −0.524521 + 0.302832i
\(482\) 12.3295 + 21.3554i 0.561594 + 0.972710i
\(483\) 0 0
\(484\) −1.93513 + 3.35174i −0.0879604 + 0.152352i
\(485\) 11.8245i 0.536923i
\(486\) −5.12089 + 17.6380i −0.232288 + 0.800075i
\(487\) 1.07779 0.0488394 0.0244197 0.999702i \(-0.492226\pi\)
0.0244197 + 0.999702i \(0.492226\pi\)
\(488\) −11.0444 + 19.1295i −0.499957 + 0.865952i
\(489\) 20.2730 7.68563i 0.916777 0.347556i
\(490\) 0 0
\(491\) 16.3708 9.45168i 0.738804 0.426549i −0.0828305 0.996564i \(-0.526396\pi\)
0.821634 + 0.570015i \(0.193063\pi\)
\(492\) −1.25374 + 7.70844i −0.0565228 + 0.347523i
\(493\) −0.690115 0.398438i −0.0310812 0.0179448i
\(494\) 7.40570i 0.333198i
\(495\) 18.6272 + 21.0363i 0.837229 + 0.945513i
\(496\) 15.7461i 0.707020i
\(497\) 0 0
\(498\) −2.05690 + 2.51860i −0.0921721 + 0.112861i
\(499\) 8.34290 + 14.4503i 0.373479 + 0.646885i 0.990098 0.140377i \(-0.0448314\pi\)
−0.616619 + 0.787262i \(0.711498\pi\)
\(500\) −11.6178 20.1225i −0.519562 0.899908i
\(501\) −20.6813 16.8901i −0.923974 0.754595i
\(502\) 26.0952 + 15.0661i 1.16468 + 0.672431i
\(503\) 21.2386 0.946981 0.473491 0.880799i \(-0.342994\pi\)
0.473491 + 0.880799i \(0.342994\pi\)
\(504\) 0 0
\(505\) −69.2993 −3.08378
\(506\) −8.05428 4.65014i −0.358056 0.206724i
\(507\) −1.73357 + 10.6586i −0.0769905 + 0.473367i
\(508\) −5.67007 9.82085i −0.251569 0.435730i
\(509\) −5.72252 9.91170i −0.253646 0.439328i 0.710881 0.703313i \(-0.248297\pi\)
−0.964527 + 0.263984i \(0.914963\pi\)
\(510\) −3.67016 9.68108i −0.162517 0.428685i
\(511\) 0 0
\(512\) 22.7685i 1.00623i
\(513\) 11.1164 + 5.83967i 0.490801 + 0.257828i
\(514\) 13.9905i 0.617096i
\(515\) 11.3175 + 6.53414i 0.498707 + 0.287929i
\(516\) 4.21295 1.59716i 0.185465 0.0703108i
\(517\) −13.3747 + 7.72188i −0.588218 + 0.339608i
\(518\) 0 0
\(519\) −2.39537 + 14.7276i −0.105145 + 0.646472i
\(520\) 17.3370 30.0285i 0.760276 1.31684i
\(521\) 20.7998 0.911254 0.455627 0.890171i \(-0.349415\pi\)
0.455627 + 0.890171i \(0.349415\pi\)
\(522\) −2.28106 0.762164i −0.0998391 0.0333590i
\(523\) 14.9338i 0.653009i −0.945196 0.326505i \(-0.894129\pi\)
0.945196 0.326505i \(-0.105871\pi\)
\(524\) 2.05102 3.55248i 0.0895994 0.155191i
\(525\) 0 0
\(526\) −13.1765 22.8223i −0.574522 0.995101i
\(527\) −6.64890 + 3.83875i −0.289631 + 0.167218i
\(528\) −5.68959 + 6.96669i −0.247607 + 0.303186i
\(529\) −4.83508 + 8.37460i −0.210221 + 0.364113i
\(530\) 16.5006 0.716742
\(531\) 16.6062 + 5.54858i 0.720647 + 0.240788i
\(532\) 0 0
\(533\) −16.6002 9.58410i −0.719033 0.415134i
\(534\) 12.2853 + 1.99813i 0.531635 + 0.0864675i
\(535\) 44.4511 25.6639i 1.92179 1.10955i
\(536\) 17.7319 10.2375i 0.765902 0.442194i
\(537\) 11.7508 + 30.9961i 0.507085 + 1.33758i
\(538\) −4.31272 2.48995i −0.185934 0.107349i
\(539\) 0 0
\(540\) 7.35654 + 11.6431i 0.316575 + 0.501041i
\(541\) 31.1677 1.34000 0.670002 0.742360i \(-0.266293\pi\)
0.670002 + 0.742360i \(0.266293\pi\)
\(542\) −13.1925 + 22.8501i −0.566667 + 0.981496i
\(543\) −4.72660 12.4677i −0.202838 0.535042i
\(544\) −3.37192 + 1.94678i −0.144570 + 0.0834675i
\(545\) −15.5120 26.8676i −0.664462 1.15088i
\(546\) 0 0
\(547\) −15.7410 + 27.2642i −0.673035 + 1.16573i 0.304004 + 0.952671i \(0.401677\pi\)
−0.977039 + 0.213061i \(0.931657\pi\)
\(548\) 8.34940i 0.356669i
\(549\) 21.1000 4.30209i 0.900528 0.183609i
\(550\) −35.0674 −1.49528
\(551\) −0.822146 + 1.42400i −0.0350246 + 0.0606644i
\(552\) −15.0722 12.3092i −0.641514 0.523914i
\(553\) 0 0
\(554\) 11.6163 6.70667i 0.493529 0.284939i
\(555\) 29.6788 + 24.2382i 1.25979 + 1.02885i
\(556\) −4.73643 2.73458i −0.200870 0.115972i
\(557\) 27.2389i 1.15415i 0.816692 + 0.577074i \(0.195806\pi\)
−0.816692 + 0.577074i \(0.804194\pi\)
\(558\) −17.3477 + 15.3609i −0.734385 + 0.650280i
\(559\) 11.0584i 0.467720i
\(560\) 0 0
\(561\) 4.32881 + 0.704057i 0.182762 + 0.0297253i
\(562\) 0.478001 + 0.827922i 0.0201633 + 0.0349238i
\(563\) 14.1871 + 24.5728i 0.597916 + 1.03562i 0.993128 + 0.117031i \(0.0373377\pi\)
−0.395212 + 0.918590i \(0.629329\pi\)
\(564\) −7.07830 + 2.68343i −0.298050 + 0.112993i
\(565\) −10.6612 6.15525i −0.448521 0.258953i
\(566\) −21.5961 −0.907751
\(567\) 0 0
\(568\) 6.03071 0.253043
\(569\) 29.4616 + 17.0097i 1.23509 + 0.713082i 0.968087 0.250613i \(-0.0806321\pi\)
0.267007 + 0.963695i \(0.413965\pi\)
\(570\) −19.9761 + 7.57309i −0.836708 + 0.317202i
\(571\) 22.3455 + 38.7035i 0.935130 + 1.61969i 0.774402 + 0.632693i \(0.218051\pi\)
0.160727 + 0.986999i \(0.448616\pi\)
\(572\) 1.72036 + 2.97975i 0.0719319 + 0.124590i
\(573\) 31.8224 + 5.17573i 1.32940 + 0.216219i
\(574\) 0 0
\(575\) 50.2613i 2.09604i
\(576\) −19.5875 + 17.3442i −0.816144 + 0.722675i
\(577\) 7.34738i 0.305875i 0.988236 + 0.152938i \(0.0488734\pi\)
−0.988236 + 0.152938i \(0.951127\pi\)
\(578\) 15.9465 + 9.20670i 0.663286 + 0.382948i
\(579\) −24.3008 19.8461i −1.00991 0.824775i
\(580\) −1.56185 + 0.901733i −0.0648522 + 0.0374424i
\(581\) 0 0
\(582\) 4.31428 + 3.52340i 0.178833 + 0.146050i
\(583\) −3.49482 + 6.05320i −0.144741 + 0.250698i
\(584\) 36.6408 1.51621
\(585\) −33.1217 + 6.75320i −1.36942 + 0.279211i
\(586\) 14.6954i 0.607063i
\(587\) 13.1328 22.7466i 0.542048 0.938855i −0.456738 0.889601i \(-0.650982\pi\)
0.998786 0.0492535i \(-0.0156842\pi\)
\(588\) 0 0
\(589\) 7.92095 + 13.7195i 0.326377 + 0.565302i
\(590\) −25.7971 + 14.8940i −1.06205 + 0.613175i
\(591\) 10.1889 + 26.8760i 0.419114 + 1.10553i
\(592\) −6.13331 + 10.6232i −0.252078 + 0.436611i
\(593\) 9.12418 0.374685 0.187343 0.982295i \(-0.440013\pi\)
0.187343 + 0.982295i \(0.440013\pi\)
\(594\) 13.2257 0.527997i 0.542658 0.0216640i
\(595\) 0 0
\(596\) 2.01298 + 1.16220i 0.0824550 + 0.0476054i
\(597\) −1.66936 4.40340i −0.0683223 0.180219i
\(598\) 9.68966 5.59433i 0.396240 0.228769i
\(599\) −20.0987 + 11.6040i −0.821210 + 0.474126i −0.850834 0.525435i \(-0.823903\pi\)
0.0296234 + 0.999561i \(0.490569\pi\)
\(600\) −72.4233 11.7792i −2.95667 0.480886i
\(601\) 19.0021 + 10.9709i 0.775111 + 0.447510i 0.834695 0.550713i \(-0.185644\pi\)
−0.0595840 + 0.998223i \(0.518977\pi\)
\(602\) 0 0
\(603\) −18.9320 6.32572i −0.770973 0.257603i
\(604\) −2.33825 −0.0951421
\(605\) −13.7013 + 23.7313i −0.557036 + 0.964815i
\(606\) −20.6494 + 25.2845i −0.838825 + 1.02711i
\(607\) 38.6289 22.3024i 1.56790 0.905226i 0.571484 0.820613i \(-0.306368\pi\)
0.996414 0.0846136i \(-0.0269656\pi\)
\(608\) 4.01703 + 6.95770i 0.162912 + 0.282172i
\(609\) 0 0
\(610\) −18.3184 + 31.7283i −0.741689 + 1.28464i
\(611\) 18.5795i 0.751647i
\(612\) 2.03888 + 0.681247i 0.0824169 + 0.0275378i
\(613\) 11.6560 0.470780 0.235390 0.971901i \(-0.424363\pi\)
0.235390 + 0.971901i \(0.424363\pi\)
\(614\) 12.5620 21.7580i 0.506961 0.878083i
\(615\) −8.87681 + 54.5780i −0.357947 + 2.20080i
\(616\) 0 0
\(617\) 36.6143 21.1393i 1.47403 0.851034i 0.474462 0.880276i \(-0.342643\pi\)
0.999572 + 0.0292416i \(0.00930923\pi\)
\(618\) 5.75636 2.18227i 0.231555 0.0877839i
\(619\) 30.0633 + 17.3571i 1.20835 + 0.697640i 0.962398 0.271643i \(-0.0875670\pi\)
0.245949 + 0.969283i \(0.420900\pi\)
\(620\) 17.3755i 0.697815i
\(621\) 0.756764 + 18.9561i 0.0303679 + 0.760681i
\(622\) 9.23930i 0.370462i
\(623\) 0 0
\(624\) −3.83596 10.1184i −0.153561 0.405061i
\(625\) −47.8410 82.8631i −1.91364 3.31452i
\(626\) −5.83364 10.1042i −0.233159 0.403844i
\(627\) 1.45277 8.93215i 0.0580179 0.356716i
\(628\) 11.3852 + 6.57327i 0.454321 + 0.262302i
\(629\) 5.98098 0.238477
\(630\) 0 0
\(631\) −12.8860 −0.512982 −0.256491 0.966547i \(-0.582566\pi\)
−0.256491 + 0.966547i \(0.582566\pi\)
\(632\) 25.9945 + 15.0079i 1.03401 + 0.596984i
\(633\) −37.4136 30.5551i −1.48706 1.21446i
\(634\) −14.1732 24.5488i −0.562891 0.974956i
\(635\) −40.1457 69.5345i −1.59314 2.75939i
\(636\) −2.16711 + 2.65355i −0.0859315 + 0.105220i
\(637\) 0 0
\(638\) 1.73325i 0.0686200i
\(639\) −3.89758 4.40168i −0.154186 0.174128i
\(640\) 15.7074i 0.620890i
\(641\) −16.5666 9.56474i −0.654342 0.377785i 0.135776 0.990740i \(-0.456647\pi\)
−0.790118 + 0.612955i \(0.789981\pi\)
\(642\) 3.88160 23.8656i 0.153195 0.941899i
\(643\) 9.77521 5.64372i 0.385497 0.222567i −0.294710 0.955587i \(-0.595223\pi\)
0.680207 + 0.733020i \(0.261890\pi\)
\(644\) 0 0
\(645\) 29.8289 11.3083i 1.17451 0.445265i
\(646\) −1.66726 + 2.88778i −0.0655976 + 0.113618i
\(647\) 5.08677 0.199982 0.0999909 0.994988i \(-0.468119\pi\)
0.0999909 + 0.994988i \(0.468119\pi\)
\(648\) 27.4919 + 3.35211i 1.07998 + 0.131683i
\(649\) 12.6181i 0.495305i
\(650\) 21.0939 36.5356i 0.827369 1.43305i
\(651\) 0 0
\(652\) −3.82937 6.63267i −0.149970 0.259755i
\(653\) −32.9044 + 18.9974i −1.28765 + 0.743424i −0.978234 0.207503i \(-0.933466\pi\)
−0.309414 + 0.950927i \(0.600133\pi\)
\(654\) −14.4251 2.34616i −0.564066 0.0917421i
\(655\) 14.5218 25.1526i 0.567415 0.982792i
\(656\) −17.7012 −0.691115
\(657\) −23.6805 26.7433i −0.923865 1.04335i
\(658\) 0 0
\(659\) 9.97949 + 5.76166i 0.388746 + 0.224442i 0.681617 0.731710i \(-0.261277\pi\)
−0.292871 + 0.956152i \(0.594611\pi\)
\(660\) 6.27834 7.68760i 0.244384 0.299239i
\(661\) −38.0928 + 21.9929i −1.48164 + 0.855424i −0.999783 0.0208274i \(-0.993370\pi\)
−0.481854 + 0.876251i \(0.660037\pi\)
\(662\) −9.25838 + 5.34533i −0.359837 + 0.207752i
\(663\) −3.33741 + 4.08654i −0.129614 + 0.158708i
\(664\) 4.24660 + 2.45178i 0.164800 + 0.0951473i
\(665\) 0 0
\(666\) 17.6870 3.60621i 0.685358 0.139738i
\(667\) −2.48422 −0.0961894
\(668\) −4.71620 + 8.16869i −0.182475 + 0.316056i
\(669\) 13.1147 + 2.13303i 0.507042 + 0.0824675i
\(670\) 29.4103 16.9800i 1.13622 0.655996i
\(671\) −7.75962 13.4401i −0.299557 0.518848i
\(672\) 0 0
\(673\) −21.9316 + 37.9866i −0.845400 + 1.46428i 0.0398735 + 0.999205i \(0.487305\pi\)
−0.885273 + 0.465071i \(0.846029\pi\)
\(674\) 9.47301i 0.364887i
\(675\) 38.2089 + 60.4728i 1.47066 + 2.32760i
\(676\) 3.81461 0.146716
\(677\) 0.738999 1.27998i 0.0284020 0.0491938i −0.851475 0.524395i \(-0.824291\pi\)
0.879877 + 0.475201i \(0.157625\pi\)
\(678\) −5.42257 + 2.05573i −0.208252 + 0.0789499i
\(679\) 0 0
\(680\) −13.5208 + 7.80621i −0.518497 + 0.299355i
\(681\) 0.647526 3.98123i 0.0248132 0.152561i
\(682\) 14.4617 + 8.34948i 0.553768 + 0.319718i
\(683\) 10.3259i 0.395111i −0.980292 0.197555i \(-0.936700\pi\)
0.980292 0.197555i \(-0.0633002\pi\)
\(684\) 1.40570 4.20707i 0.0537483 0.160861i
\(685\) 59.1162i 2.25871i
\(686\) 0 0
\(687\) −13.1130 + 16.0565i −0.500294 + 0.612592i
\(688\) 5.10601 + 8.84388i 0.194665 + 0.337170i
\(689\) −4.20442 7.28228i −0.160176 0.277433i
\(690\) −24.9988 20.4161i −0.951688 0.777228i
\(691\) 6.58166 + 3.79992i 0.250378 + 0.144556i 0.619937 0.784651i \(-0.287158\pi\)
−0.369559 + 0.929207i \(0.620491\pi\)
\(692\) 5.27087 0.200368
\(693\) 0 0
\(694\) 41.6773 1.58205
\(695\) −33.5353 19.3616i −1.27207 0.734428i
\(696\) −0.582203 + 3.57960i −0.0220683 + 0.135685i
\(697\) 4.31538 + 7.47446i 0.163457 + 0.283115i
\(698\) −14.4120 24.9624i −0.545503 0.944839i
\(699\) 1.55204 + 4.09395i 0.0587036 + 0.154847i
\(700\) 0 0
\(701\) 6.35907i 0.240179i 0.992763 + 0.120089i \(0.0383181\pi\)
−0.992763 + 0.120089i \(0.961682\pi\)
\(702\) −7.40547 + 14.0971i −0.279501 + 0.532059i
\(703\) 12.3413i 0.465460i
\(704\) 16.3289 + 9.42749i 0.615419 + 0.355312i
\(705\) −50.1164 + 18.9995i −1.88749 + 0.715561i
\(706\) 0.991677 0.572545i 0.0373223 0.0215480i
\(707\) 0 0
\(708\) 0.992890 6.10466i 0.0373151 0.229427i
\(709\) 23.8048 41.2311i 0.894007 1.54847i 0.0589776 0.998259i \(-0.481216\pi\)
0.835029 0.550206i \(-0.185451\pi\)
\(710\) 10.0026 0.375390
\(711\) −5.84599 28.6722i −0.219242 1.07529i
\(712\) 18.7690i 0.703396i
\(713\) −11.9671 + 20.7276i −0.448171 + 0.776255i
\(714\) 0 0
\(715\) 12.1806 + 21.0975i 0.455530 + 0.789002i
\(716\) 10.1409 5.85486i 0.378983 0.218806i
\(717\) 22.0867 27.0444i 0.824843 1.00999i
\(718\) −9.37904 + 16.2450i −0.350023 + 0.606257i
\(719\) −14.1470 −0.527594 −0.263797 0.964578i \(-0.584975\pi\)
−0.263797 + 0.964578i \(0.584975\pi\)
\(720\) −23.3708 + 20.6942i −0.870977 + 0.771228i
\(721\) 0 0
\(722\) −13.4280 7.75264i −0.499737 0.288524i
\(723\) −35.7806 5.81952i −1.33070 0.216430i
\(724\) −4.07904 + 2.35503i −0.151596 + 0.0875241i
\(725\) −8.11202 + 4.68348i −0.301273 + 0.173940i
\(726\) 4.57595 + 12.0704i 0.169829 + 0.447973i
\(727\) −40.1828 23.1996i −1.49030 0.860424i −0.490360 0.871520i \(-0.663135\pi\)
−0.999938 + 0.0110955i \(0.996468\pi\)
\(728\) 0 0
\(729\) −15.3210 22.2321i −0.567446 0.823411i
\(730\) 60.7728 2.24930
\(731\) 2.48960 4.31211i 0.0920811 0.159489i
\(732\) −2.69655 7.11290i −0.0996673 0.262900i
\(733\) −22.8893 + 13.2151i −0.845436 + 0.488112i −0.859108 0.511794i \(-0.828981\pi\)
0.0136726 + 0.999907i \(0.495648\pi\)
\(734\) 14.5559 + 25.2115i 0.537268 + 0.930575i
\(735\) 0 0
\(736\) −6.06899 + 10.5118i −0.223706 + 0.387470i
\(737\) 14.3854i 0.529894i
\(738\) 17.2682 + 19.5016i 0.635651 + 0.717865i
\(739\) −46.2670 −1.70196 −0.850979 0.525200i \(-0.823991\pi\)
−0.850979 + 0.525200i \(0.823991\pi\)
\(740\) 6.76798 11.7225i 0.248796 0.430927i
\(741\) 8.43225 + 6.88648i 0.309766 + 0.252981i
\(742\) 0 0
\(743\) −36.5640 + 21.1102i −1.34140 + 0.774458i −0.987013 0.160640i \(-0.948644\pi\)
−0.354388 + 0.935098i \(0.615311\pi\)
\(744\) 27.0626 + 22.1015i 0.992161 + 0.810282i
\(745\) 14.2525 + 8.22868i 0.522171 + 0.301476i
\(746\) 11.1177i 0.407050i
\(747\) −0.955031 4.68404i −0.0349428 0.171380i
\(748\) 1.54923i 0.0566456i
\(749\) 0 0
\(750\) −76.4932 12.4412i −2.79314 0.454288i
\(751\) 8.02320 + 13.8966i 0.292771 + 0.507094i 0.974464 0.224544i \(-0.0720894\pi\)
−0.681693 + 0.731638i \(0.738756\pi\)
\(752\) −8.57877 14.8589i −0.312836 0.541847i
\(753\) −41.4201 + 15.7026i −1.50943 + 0.572235i
\(754\) −1.80582 1.04259i −0.0657639 0.0379688i
\(755\) −16.5555 −0.602516
\(756\) 0 0
\(757\) 25.0149 0.909183 0.454591 0.890700i \(-0.349785\pi\)
0.454591 + 0.890700i \(0.349785\pi\)
\(758\) −21.2265 12.2551i −0.770981 0.445126i
\(759\) 12.7843 4.84661i 0.464041 0.175921i
\(760\) 16.1075 + 27.8990i 0.584281 + 1.01200i
\(761\) −3.00365 5.20247i −0.108882 0.188589i 0.806436 0.591322i \(-0.201394\pi\)
−0.915318 + 0.402733i \(0.868060\pi\)
\(762\) −37.3327 6.07196i −1.35242 0.219964i
\(763\) 0 0
\(764\) 11.3889i 0.412035i
\(765\) 14.4359 + 4.82343i 0.521930 + 0.174391i
\(766\) 7.61138i 0.275010i
\(767\) 13.1464 + 7.59008i 0.474689 + 0.274062i
\(768\) 17.6675 + 14.4288i 0.637523 + 0.520654i
\(769\) −28.9946 + 16.7400i −1.04557 + 0.603661i −0.921406 0.388600i \(-0.872959\pi\)
−0.124166 + 0.992262i \(0.539625\pi\)
\(770\) 0 0
\(771\) 15.9298 + 13.0096i 0.573699 + 0.468531i
\(772\) −5.54159 + 9.59831i −0.199446 + 0.345451i
\(773\) −36.2016 −1.30208 −0.651040 0.759043i \(-0.725667\pi\)
−0.651040 + 0.759043i \(0.725667\pi\)
\(774\) 4.76230 14.2529i 0.171177 0.512311i
\(775\) 90.2458i 3.24172i
\(776\) 4.19980 7.27427i 0.150764 0.261131i
\(777\) 0 0
\(778\) 0.0303280 + 0.0525296i 0.00108731 + 0.00188328i
\(779\) 15.4230 8.90445i 0.552585 0.319035i
\(780\) 4.23290 + 11.1655i 0.151562 + 0.399788i
\(781\) −2.11854 + 3.66942i −0.0758073 + 0.131302i
\(782\) −5.03785 −0.180153
\(783\) 2.98894 1.88852i 0.106816 0.0674901i
\(784\) 0 0
\(785\) 80.6108 + 46.5407i 2.87712 + 1.66111i
\(786\) −4.85000 12.7932i −0.172994 0.456320i
\(787\) −14.1930 + 8.19433i −0.505926 + 0.292096i −0.731157 0.682209i \(-0.761019\pi\)
0.225232 + 0.974305i \(0.427686\pi\)
\(788\) 8.79294 5.07661i 0.313236 0.180847i
\(789\) 38.2385 + 6.21929i 1.36133 + 0.221412i
\(790\) 43.1147 + 24.8923i 1.53395 + 0.885628i
\(791\) 0 0
\(792\) −3.98753 19.5572i −0.141691 0.694935i
\(793\) 18.6703 0.663004
\(794\) 7.48929 12.9718i 0.265785 0.460353i
\(795\) −15.3438 + 18.7879i −0.544187 + 0.666337i
\(796\) −1.44065 + 0.831760i −0.0510625 + 0.0294809i
\(797\) 23.3328 + 40.4137i 0.826492 + 1.43153i 0.900774 + 0.434288i \(0.143000\pi\)
−0.0742821 + 0.997237i \(0.523667\pi\)
\(798\) 0 0
\(799\) −4.18285 + 7.24491i −0.147979 + 0.256306i
\(800\) 45.7672i 1.61811i
\(801\) −13.6990 + 12.1301i −0.484031 + 0.428598i
\(802\) 2.98929 0.105555
\(803\) −12.8716 + 22.2943i −0.454229 + 0.786748i
\(804\) −1.13195 + 6.95968i −0.0399209 + 0.245449i
\(805\) 0 0
\(806\) −17.3981 + 10.0448i −0.612822 + 0.353813i
\(807\) 6.84544 2.59515i 0.240971 0.0913536i
\(808\) 42.6319 + 24.6136i 1.49979 + 0.865902i
\(809\) 29.8980i 1.05116i −0.850744 0.525580i \(-0.823849\pi\)
0.850744 0.525580i \(-0.176151\pi\)
\(810\) 45.5982 + 5.55983i 1.60216 + 0.195352i
\(811\) 25.3404i 0.889821i −0.895575 0.444911i \(-0.853235\pi\)
0.895575 0.444911i \(-0.146765\pi\)
\(812\) 0 0
\(813\) −13.7499 36.2693i −0.482230 1.27202i
\(814\) −6.50447 11.2661i −0.227982 0.394876i
\(815\) −27.1131 46.9612i −0.949729 1.64498i
\(816\) −0.782186 + 4.80918i −0.0273820 + 0.168355i
\(817\) −8.89769 5.13709i −0.311291 0.179724i
\(818\) 0.0674323 0.00235772
\(819\) 0 0
\(820\) 19.5329 0.682117
\(821\) 9.23012 + 5.32901i 0.322133 + 0.185984i 0.652343 0.757924i \(-0.273786\pi\)
−0.330210 + 0.943908i \(0.607119\pi\)
\(822\) −21.5691 17.6151i −0.752308 0.614397i
\(823\) −8.55239 14.8132i −0.298118 0.516355i 0.677588 0.735442i \(-0.263025\pi\)
−0.975705 + 0.219087i \(0.929692\pi\)
\(824\) −4.64156 8.03943i −0.161697 0.280067i
\(825\) 32.6088 39.9283i 1.13529 1.39013i
\(826\) 0 0
\(827\) 18.3221i 0.637121i −0.947903 0.318560i \(-0.896801\pi\)
0.947903 0.318560i \(-0.103199\pi\)
\(828\) 6.56643 1.33883i 0.228199 0.0465276i
\(829\) 7.73341i 0.268592i 0.990941 + 0.134296i \(0.0428774\pi\)
−0.990941 + 0.134296i \(0.957123\pi\)
\(830\) 7.04344 + 4.06653i 0.244481 + 0.141151i
\(831\) −3.16554 + 19.4629i −0.109811 + 0.675162i
\(832\) −19.6444 + 11.3417i −0.681047 + 0.393203i
\(833\) 0 0
\(834\) −17.0569 + 6.46639i −0.590633 + 0.223913i
\(835\) −33.3920 + 57.8367i −1.15558 + 2.00152i
\(836\) −3.19672 −0.110561
\(837\) −1.35879 34.0363i −0.0469668 1.17647i
\(838\) 7.25788i 0.250719i
\(839\) 9.73588 16.8630i 0.336120 0.582177i −0.647579 0.761998i \(-0.724219\pi\)
0.983699 + 0.179821i \(0.0575519\pi\)
\(840\) 0 0
\(841\) −14.2685 24.7138i −0.492018 0.852200i
\(842\) −30.7519 + 17.7546i −1.05978 + 0.611865i
\(843\) −1.38717 0.225616i −0.0477768 0.00777063i
\(844\) −8.53184 + 14.7776i −0.293678 + 0.508665i
\(845\) 27.0085 0.929122
\(846\) −8.00128 + 23.9468i −0.275090 + 0.823307i
\(847\) 0 0
\(848\) −6.72493 3.88264i −0.230935 0.133330i
\(849\) 20.0820 24.5896i 0.689211 0.843914i
\(850\) −16.4507 + 9.49781i −0.564254 + 0.325772i
\(851\) 16.1474 9.32269i 0.553525 0.319578i
\(852\) −1.31369 + 1.60856i −0.0450062 + 0.0551085i
\(853\) 0.812274 + 0.468967i 0.0278117 + 0.0160571i 0.513841 0.857885i \(-0.328222\pi\)
−0.486030 + 0.873942i \(0.661555\pi\)
\(854\) 0 0
\(855\) 9.95275 29.7873i 0.340377 1.01870i
\(856\) −36.4609 −1.24621
\(857\) 9.00087 15.5900i 0.307464 0.532543i −0.670343 0.742051i \(-0.733853\pi\)
0.977807 + 0.209509i \(0.0671864\pi\)
\(858\) 11.3271 + 1.84230i 0.386702 + 0.0628950i
\(859\) 23.1160 13.3460i 0.788709 0.455361i −0.0507989 0.998709i \(-0.516177\pi\)
0.839508 + 0.543348i \(0.182843\pi\)
\(860\) −5.63438 9.75903i −0.192131 0.332780i
\(861\) 0 0
\(862\) −4.75486 + 8.23566i −0.161951 + 0.280508i
\(863\) 27.7596i 0.944946i −0.881345 0.472473i \(-0.843361\pi\)
0.881345 0.472473i \(-0.156639\pi\)
\(864\) −0.689099 17.2611i −0.0234436 0.587236i
\(865\) 37.3193 1.26889
\(866\) 16.7857 29.0737i 0.570402 0.987966i
\(867\) −25.3113 + 9.59569i −0.859618 + 0.325887i
\(868\) 0 0
\(869\) −18.2633 + 10.5443i −0.619540 + 0.357692i
\(870\) −0.965646 + 5.93716i −0.0327385 + 0.201289i
\(871\) −14.9877 8.65316i −0.507839 0.293201i
\(872\) 22.0381i 0.746305i
\(873\) −8.02360 + 1.63593i −0.271558 + 0.0553680i
\(874\) 10.3952i 0.351623i
\(875\) 0 0
\(876\) −7.98158 + 9.77316i −0.269673 + 0.330205i
\(877\) −6.90978 11.9681i −0.233327 0.404134i 0.725458 0.688266i \(-0.241628\pi\)
−0.958785 + 0.284132i \(0.908295\pi\)
\(878\) −1.20447 2.08621i −0.0406490 0.0704061i
\(879\) 16.7325 + 13.6651i 0.564372 + 0.460913i
\(880\) 19.4828 + 11.2484i 0.656765 + 0.379184i
\(881\) −43.9006 −1.47905 −0.739525 0.673129i \(-0.764950\pi\)
−0.739525 + 0.673129i \(0.764950\pi\)
\(882\) 0 0
\(883\) 7.96743 0.268125 0.134063 0.990973i \(-0.457198\pi\)
0.134063 + 0.990973i \(0.457198\pi\)
\(884\) 1.61410 + 0.931899i 0.0542880 + 0.0313432i
\(885\) 7.02994 43.2228i 0.236309 1.45292i
\(886\) 14.3750 + 24.8982i 0.482937 + 0.836472i
\(887\) 10.6080 + 18.3736i 0.356181 + 0.616924i 0.987319 0.158747i \(-0.0507453\pi\)
−0.631138 + 0.775670i \(0.717412\pi\)
\(888\) −9.64910 25.4522i −0.323803 0.854120i
\(889\) 0 0
\(890\) 31.1303i 1.04349i
\(891\) −11.6973 + 15.5500i −0.391873 + 0.520944i
\(892\) 4.69359i 0.157153i
\(893\) 14.9493 + 8.63098i 0.500259 + 0.288825i
\(894\) 7.24919 2.74822i 0.242449 0.0919141i
\(895\) 71.8005 41.4541i 2.40003 1.38566i
\(896\) 0 0
\(897\) −2.64052 + 16.2349i −0.0881643 + 0.542067i
\(898\) −0.172924 + 0.299513i −0.00577054 + 0.00999487i
\(899\) 4.46050 0.148766
\(900\) 18.9180 16.7515i 0.630602 0.558382i
\(901\) 3.78621i 0.126137i
\(902\) 9.38618 16.2573i 0.312526 0.541310i
\(903\) 0 0
\(904\) 4.37242 + 7.57325i 0.145424 + 0.251883i
\(905\) −28.8808 + 16.6743i −0.960029 + 0.554273i
\(906\) −4.93311 + 6.04042i −0.163892 + 0.200680i
\(907\) −1.88344 + 3.26221i −0.0625385 + 0.108320i −0.895599 0.444861i \(-0.853253\pi\)
0.833061 + 0.553181i \(0.186586\pi\)
\(908\) −1.42484 −0.0472850
\(909\) −9.58763 47.0235i −0.318002 1.55967i
\(910\) 0 0
\(911\) 40.0013 + 23.0947i 1.32530 + 0.765163i 0.984569 0.174998i \(-0.0559917\pi\)
0.340732 + 0.940160i \(0.389325\pi\)
\(912\) 9.92336 + 1.61398i 0.328595 + 0.0534442i
\(913\) −2.98359 + 1.72258i −0.0987423 + 0.0570089i
\(914\) 16.8862 9.74926i 0.558546 0.322477i
\(915\) −19.0923 50.3614i −0.631173 1.66490i
\(916\) 6.34196 + 3.66153i 0.209544 + 0.120980i
\(917\) 0 0
\(918\) 6.06139 3.82980i 0.200056 0.126402i
\(919\) 1.21522 0.0400864 0.0200432 0.999799i \(-0.493620\pi\)
0.0200432 + 0.999799i \(0.493620\pi\)
\(920\) −24.3355 + 42.1503i −0.802316 + 1.38965i
\(921\) 13.0928 + 34.5359i 0.431421 + 1.13800i
\(922\) −20.5213 + 11.8480i −0.675833 + 0.390192i
\(923\) −2.54870 4.41447i −0.0838914 0.145304i
\(924\) 0 0
\(925\) 35.1520 60.8850i 1.15579 2.00189i
\(926\) 22.0230i 0.723720i
\(927\) −2.86800 + 8.58355i −0.0941976 + 0.281921i
\(928\) 2.26210 0.0742570
\(929\) −9.44516 + 16.3595i −0.309886 + 0.536737i −0.978337 0.207018i \(-0.933624\pi\)
0.668452 + 0.743756i \(0.266957\pi\)
\(930\) 44.8862 + 36.6578i 1.47188 + 1.20206i
\(931\) 0 0
\(932\) 1.33941 0.773306i 0.0438737 0.0253305i
\(933\) −10.5200 8.59152i −0.344410 0.281274i
\(934\) −29.9581 17.2963i −0.980258 0.565952i
\(935\) 10.9690i 0.358725i
\(936\) 22.7746 + 7.60963i 0.744412 + 0.248729i
\(937\) 27.0448i 0.883516i 0.897134 + 0.441758i \(0.145645\pi\)
−0.897134 + 0.441758i \(0.854355\pi\)
\(938\) 0 0
\(939\) 16.9294 + 2.75347i 0.552470 + 0.0898562i
\(940\) 9.46650 + 16.3965i 0.308763 + 0.534793i
\(941\) −8.16024 14.1339i −0.266016 0.460754i 0.701813 0.712361i \(-0.252374\pi\)
−0.967829 + 0.251607i \(0.919041\pi\)
\(942\) 41.0007 15.5437i 1.33588 0.506440i
\(943\) 23.3012 + 13.4530i 0.758793 + 0.438089i
\(944\) 14.0184 0.456259
\(945\) 0 0
\(946\) −10.8300 −0.352114
\(947\) −24.8567 14.3510i −0.807734 0.466345i 0.0384343 0.999261i \(-0.487763\pi\)
−0.846168 + 0.532916i \(0.821096\pi\)
\(948\) −9.66551 + 3.66426i −0.313921 + 0.119010i
\(949\) −15.4851 26.8210i −0.502668 0.870647i
\(950\) 19.5980 + 33.9447i 0.635842 + 1.10131i
\(951\) 41.1311 + 6.68975i 1.33377 + 0.216930i
\(952\) 0 0
\(953\) 34.5757i 1.12002i −0.828486 0.560009i \(-0.810798\pi\)
0.828486 0.560009i \(-0.189202\pi\)
\(954\) 2.28288 + 11.1966i 0.0739110 + 0.362504i
\(955\) 80.6366i 2.60934i
\(956\) −10.6820 6.16723i −0.345479 0.199462i
\(957\) −1.97350 1.61173i −0.0637943 0.0520998i
\(958\) −22.3785 + 12.9202i −0.723015 + 0.417433i
\(959\) 0 0
\(960\) 50.6815 + 41.3907i 1.63574 + 1.33588i
\(961\) 5.98731 10.3703i 0.193139 0.334527i
\(962\) 15.6503 0.504587
\(963\) 23.5642 + 26.6120i 0.759347 + 0.857559i
\(964\) 12.8055i 0.412437i
\(965\) −39.2360 + 67.9588i −1.26305 + 2.18767i
\(966\) 0 0
\(967\) −5.25000 9.09327i −0.168829 0.292420i 0.769180 0.639033i \(-0.220665\pi\)
−0.938008 + 0.346613i \(0.887332\pi\)
\(968\) 16.8577 9.73277i 0.541826 0.312823i
\(969\) −1.73771 4.58369i −0.0558232 0.147249i
\(970\) 6.96583 12.0652i 0.223659 0.387389i
\(971\) −22.8312 −0.732689 −0.366345 0.930479i \(-0.619391\pi\)
−0.366345 + 0.930479i \(0.619391\pi\)
\(972\) −6.88274 + 6.60267i −0.220764 + 0.211781i
\(973\) 0 0
\(974\) −1.09973 0.634927i −0.0352375 0.0203444i
\(975\) 21.9851 + 57.9919i 0.704087 + 1.85723i
\(976\) 14.9315 8.62071i 0.477946 0.275942i
\(977\) −8.88551 + 5.13005i −0.284273 + 0.164125i −0.635356 0.772219i \(-0.719147\pi\)
0.351083 + 0.936344i \(0.385813\pi\)
\(978\) −25.2132 4.10079i −0.806230 0.131129i
\(979\) 11.4201 + 6.59337i 0.364987 + 0.210725i
\(980\) 0 0
\(981\) 16.0851 14.2430i 0.513558 0.454743i
\(982\) −22.2720 −0.710727
\(983\) −16.9599 + 29.3754i −0.540937 + 0.936930i 0.457913 + 0.888997i \(0.348597\pi\)
−0.998851 + 0.0479337i \(0.984736\pi\)
\(984\) 24.8458 30.4228i 0.792054 0.969842i
\(985\) 62.2566 35.9438i 1.98366 1.14527i
\(986\) 0.469440 + 0.813095i 0.0149500 + 0.0258942i
\(987\) 0 0
\(988\) 1.92290 3.33056i 0.0611756 0.105959i
\(989\) 15.5224i 0.493583i
\(990\) −6.61374 32.4377i −0.210199 1.03094i
\(991\) 22.8556 0.726031 0.363015 0.931783i \(-0.381747\pi\)
0.363015 + 0.931783i \(0.381747\pi\)
\(992\) 10.8971 18.8743i 0.345982 0.599259i
\(993\) 2.52299 15.5123i 0.0800647 0.492268i
\(994\) 0 0
\(995\) −10.2002 + 5.88910i −0.323369 + 0.186697i
\(996\) −1.57901 + 0.598612i −0.0500328 + 0.0189678i
\(997\) −5.65867 3.26704i −0.179212 0.103468i 0.407710 0.913111i \(-0.366327\pi\)
−0.586922 + 0.809643i \(0.699661\pi\)
\(998\) 19.6592i 0.622302i
\(999\) −12.3409 + 23.4921i −0.390448 + 0.743257i
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 441.2.o.e.146.8 yes 48
3.2 odd 2 1323.2.o.e.440.18 48
7.2 even 3 441.2.i.d.227.17 48
7.3 odd 6 441.2.s.d.362.18 48
7.4 even 3 441.2.s.d.362.17 48
7.5 odd 6 441.2.i.d.227.18 48
7.6 odd 2 inner 441.2.o.e.146.7 48
9.4 even 3 1323.2.o.e.881.17 48
9.5 odd 6 inner 441.2.o.e.293.7 yes 48
21.2 odd 6 1323.2.i.d.521.1 48
21.5 even 6 1323.2.i.d.521.20 48
21.11 odd 6 1323.2.s.d.656.7 48
21.17 even 6 1323.2.s.d.656.8 48
21.20 even 2 1323.2.o.e.440.17 48
63.4 even 3 1323.2.i.d.1097.20 48
63.5 even 6 441.2.s.d.374.17 48
63.13 odd 6 1323.2.o.e.881.18 48
63.23 odd 6 441.2.s.d.374.18 48
63.31 odd 6 1323.2.i.d.1097.1 48
63.32 odd 6 441.2.i.d.68.8 48
63.40 odd 6 1323.2.s.d.962.7 48
63.41 even 6 inner 441.2.o.e.293.8 yes 48
63.58 even 3 1323.2.s.d.962.8 48
63.59 even 6 441.2.i.d.68.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.i.d.68.7 48 63.59 even 6
441.2.i.d.68.8 48 63.32 odd 6
441.2.i.d.227.17 48 7.2 even 3
441.2.i.d.227.18 48 7.5 odd 6
441.2.o.e.146.7 48 7.6 odd 2 inner
441.2.o.e.146.8 yes 48 1.1 even 1 trivial
441.2.o.e.293.7 yes 48 9.5 odd 6 inner
441.2.o.e.293.8 yes 48 63.41 even 6 inner
441.2.s.d.362.17 48 7.4 even 3
441.2.s.d.362.18 48 7.3 odd 6
441.2.s.d.374.17 48 63.5 even 6
441.2.s.d.374.18 48 63.23 odd 6
1323.2.i.d.521.1 48 21.2 odd 6
1323.2.i.d.521.20 48 21.5 even 6
1323.2.i.d.1097.1 48 63.31 odd 6
1323.2.i.d.1097.20 48 63.4 even 3
1323.2.o.e.440.17 48 21.20 even 2
1323.2.o.e.440.18 48 3.2 odd 2
1323.2.o.e.881.17 48 9.4 even 3
1323.2.o.e.881.18 48 63.13 odd 6
1323.2.s.d.656.7 48 21.11 odd 6
1323.2.s.d.656.8 48 21.17 even 6
1323.2.s.d.962.7 48 63.40 odd 6
1323.2.s.d.962.8 48 63.58 even 3