Properties

Label 585.2.bt.b.571.39
Level $585$
Weight $2$
Character 585.571
Analytic conductor $4.671$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [585,2,Mod(376,585)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("585.376");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bt (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: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(54\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 571.39
Character \(\chi\) \(=\) 585.571
Dual form 585.2.bt.b.376.39

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.16682 - 0.673666i) q^{2} +(0.619932 + 1.61731i) q^{3} +(-0.0923480 + 0.159951i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.81288 + 1.46949i) q^{6} +(4.07352 - 2.35185i) q^{7} +2.94351i q^{8} +(-2.23137 + 2.00524i) q^{9} +O(q^{10})\) \(q+(1.16682 - 0.673666i) q^{2} +(0.619932 + 1.61731i) q^{3} +(-0.0923480 + 0.159951i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.81288 + 1.46949i) q^{6} +(4.07352 - 2.35185i) q^{7} +2.94351i q^{8} +(-2.23137 + 2.00524i) q^{9} -1.34733 q^{10} +(1.11056 - 0.641180i) q^{11} +(-0.315940 - 0.0501961i) q^{12} +(2.91362 - 2.12387i) q^{13} +(3.16872 - 5.48839i) q^{14} +(0.271777 - 1.71060i) q^{15} +(1.79825 + 3.11466i) q^{16} -0.689981 q^{17} +(-1.25275 + 3.84296i) q^{18} +6.46642i q^{19} +(0.159951 - 0.0923480i) q^{20} +(6.32897 + 5.13015i) q^{21} +(0.863882 - 1.49629i) q^{22} +(-2.10450 + 3.64510i) q^{23} +(-4.76056 + 1.82478i) q^{24} +(0.500000 + 0.866025i) q^{25} +(1.96891 - 4.44099i) q^{26} +(-4.62639 - 2.36569i) q^{27} +0.868754i q^{28} +(2.78420 + 4.82237i) q^{29} +(-0.835255 - 2.17905i) q^{30} +(0.646732 + 0.373391i) q^{31} +(-0.901834 - 0.520674i) q^{32} +(1.72545 + 1.39862i) q^{33} +(-0.805086 + 0.464817i) q^{34} -4.70370 q^{35} +(-0.114679 - 0.542091i) q^{36} -8.06746i q^{37} +(4.35621 + 7.54517i) q^{38} +(5.24119 + 3.39557i) q^{39} +(1.47176 - 2.54916i) q^{40} +(-6.39700 - 3.69331i) q^{41} +(10.8408 + 1.72237i) q^{42} +(-5.42456 - 9.39562i) q^{43} +0.236847i q^{44} +(2.93504 - 0.620907i) q^{45} +5.67092i q^{46} +(6.50187 - 3.75385i) q^{47} +(-3.92257 + 4.83920i) q^{48} +(7.56239 - 13.0984i) q^{49} +(1.16682 + 0.673666i) q^{50} +(-0.427741 - 1.11591i) q^{51} +(0.0706481 + 0.662173i) q^{52} -5.44121 q^{53} +(-6.99187 + 0.356295i) q^{54} -1.28236 q^{55} +(6.92270 + 11.9905i) q^{56} +(-10.4582 + 4.00874i) q^{57} +(6.49733 + 3.75124i) q^{58} +(-0.357947 - 0.206661i) q^{59} +(0.248514 + 0.201441i) q^{60} +(-2.91595 - 5.05058i) q^{61} +1.00616 q^{62} +(-4.37350 + 13.4162i) q^{63} -8.59603 q^{64} +(-3.58520 + 0.382510i) q^{65} +(2.95551 + 0.469566i) q^{66} +(9.45733 + 5.46019i) q^{67} +(0.0637184 - 0.110363i) q^{68} +(-7.19989 - 1.14391i) q^{69} +(-5.48839 + 3.16872i) q^{70} +5.80266i q^{71} +(-5.90245 - 6.56806i) q^{72} -9.51919i q^{73} +(-5.43478 - 9.41331i) q^{74} +(-1.09066 + 1.34553i) q^{75} +(-1.03431 - 0.597161i) q^{76} +(3.01592 - 5.22372i) q^{77} +(8.40303 + 0.431220i) q^{78} +(-2.41946 - 4.19062i) q^{79} -3.59650i q^{80} +(0.958005 - 8.94887i) q^{81} -9.95222 q^{82} +(2.46941 - 1.42572i) q^{83} +(-1.40504 + 0.538569i) q^{84} +(0.597541 + 0.344990i) q^{85} +(-12.6590 - 7.30869i) q^{86} +(-6.07324 + 7.49245i) q^{87} +(1.88732 + 3.26893i) q^{88} -10.7367i q^{89} +(3.00639 - 2.70173i) q^{90} +(6.87370 - 15.5040i) q^{91} +(-0.388693 - 0.673235i) q^{92} +(-0.202958 + 1.27744i) q^{93} +(5.05769 - 8.76017i) q^{94} +(3.23321 - 5.60008i) q^{95} +(0.283014 - 1.78133i) q^{96} +(1.55060 - 0.895240i) q^{97} -20.3781i q^{98} +(-1.19234 + 3.65764i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16682 0.673666i 0.825069 0.476354i −0.0270923 0.999633i \(-0.508625\pi\)
0.852161 + 0.523279i \(0.175291\pi\)
\(3\) 0.619932 + 1.61731i 0.357918 + 0.933753i
\(4\) −0.0923480 + 0.159951i −0.0461740 + 0.0799757i
\(5\) −0.866025 0.500000i −0.387298 0.223607i
\(6\) 1.81288 + 1.46949i 0.740104 + 0.599915i
\(7\) 4.07352 2.35185i 1.53965 0.888916i 0.540788 0.841159i \(-0.318126\pi\)
0.998859 0.0477566i \(-0.0152072\pi\)
\(8\) 2.94351i 1.04069i
\(9\) −2.23137 + 2.00524i −0.743789 + 0.668414i
\(10\) −1.34733 −0.426064
\(11\) 1.11056 0.641180i 0.334845 0.193323i −0.323145 0.946349i \(-0.604740\pi\)
0.657990 + 0.753027i \(0.271407\pi\)
\(12\) −0.315940 0.0501961i −0.0912041 0.0144904i
\(13\) 2.91362 2.12387i 0.808094 0.589054i
\(14\) 3.16872 5.48839i 0.846877 1.46683i
\(15\) 0.271777 1.71060i 0.0701724 0.441674i
\(16\) 1.79825 + 3.11466i 0.449562 + 0.778664i
\(17\) −0.689981 −0.167345 −0.0836725 0.996493i \(-0.526665\pi\)
−0.0836725 + 0.996493i \(0.526665\pi\)
\(18\) −1.25275 + 3.84296i −0.295276 + 0.905795i
\(19\) 6.46642i 1.48350i 0.670678 + 0.741749i \(0.266003\pi\)
−0.670678 + 0.741749i \(0.733997\pi\)
\(20\) 0.159951 0.0923480i 0.0357662 0.0206496i
\(21\) 6.32897 + 5.13015i 1.38110 + 1.11949i
\(22\) 0.863882 1.49629i 0.184180 0.319010i
\(23\) −2.10450 + 3.64510i −0.438818 + 0.760056i −0.997599 0.0692600i \(-0.977936\pi\)
0.558780 + 0.829316i \(0.311270\pi\)
\(24\) −4.76056 + 1.82478i −0.971746 + 0.372481i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 1.96891 4.44099i 0.386135 0.870949i
\(27\) −4.62639 2.36569i −0.890349 0.455278i
\(28\) 0.868754i 0.164179i
\(29\) 2.78420 + 4.82237i 0.517012 + 0.895492i 0.999805 + 0.0197568i \(0.00628921\pi\)
−0.482792 + 0.875735i \(0.660377\pi\)
\(30\) −0.835255 2.17905i −0.152496 0.397838i
\(31\) 0.646732 + 0.373391i 0.116157 + 0.0670630i 0.556953 0.830544i \(-0.311970\pi\)
−0.440796 + 0.897607i \(0.645304\pi\)
\(32\) −0.901834 0.520674i −0.159423 0.0920431i
\(33\) 1.72545 + 1.39862i 0.300363 + 0.243469i
\(34\) −0.805086 + 0.464817i −0.138071 + 0.0797154i
\(35\) −4.70370 −0.795070
\(36\) −0.114679 0.542091i −0.0191132 0.0903484i
\(37\) 8.06746i 1.32628i −0.748494 0.663141i \(-0.769223\pi\)
0.748494 0.663141i \(-0.230777\pi\)
\(38\) 4.35621 + 7.54517i 0.706670 + 1.22399i
\(39\) 5.24119 + 3.39557i 0.839262 + 0.543727i
\(40\) 1.47176 2.54916i 0.232705 0.403057i
\(41\) −6.39700 3.69331i −0.999043 0.576798i −0.0910779 0.995844i \(-0.529031\pi\)
−0.907965 + 0.419046i \(0.862365\pi\)
\(42\) 10.8408 + 1.72237i 1.67277 + 0.265767i
\(43\) −5.42456 9.39562i −0.827238 1.43282i −0.900197 0.435483i \(-0.856578\pi\)
0.0729590 0.997335i \(-0.476756\pi\)
\(44\) 0.236847i 0.0357060i
\(45\) 2.93504 0.620907i 0.437530 0.0925594i
\(46\) 5.67092i 0.836131i
\(47\) 6.50187 3.75385i 0.948394 0.547556i 0.0558127 0.998441i \(-0.482225\pi\)
0.892582 + 0.450885i \(0.148892\pi\)
\(48\) −3.92257 + 4.83920i −0.566174 + 0.698478i
\(49\) 7.56239 13.0984i 1.08034 1.87121i
\(50\) 1.16682 + 0.673666i 0.165014 + 0.0952708i
\(51\) −0.427741 1.11591i −0.0598958 0.156259i
\(52\) 0.0706481 + 0.662173i 0.00979712 + 0.0918269i
\(53\) −5.44121 −0.747407 −0.373704 0.927548i \(-0.621912\pi\)
−0.373704 + 0.927548i \(0.621912\pi\)
\(54\) −6.99187 + 0.356295i −0.951473 + 0.0484856i
\(55\) −1.28236 −0.172913
\(56\) 6.92270 + 11.9905i 0.925084 + 1.60229i
\(57\) −10.4582 + 4.00874i −1.38522 + 0.530971i
\(58\) 6.49733 + 3.75124i 0.853142 + 0.492562i
\(59\) −0.357947 0.206661i −0.0466007 0.0269050i 0.476519 0.879164i \(-0.341898\pi\)
−0.523119 + 0.852259i \(0.675232\pi\)
\(60\) 0.248514 + 0.201441i 0.0320830 + 0.0260059i
\(61\) −2.91595 5.05058i −0.373350 0.646661i 0.616729 0.787176i \(-0.288457\pi\)
−0.990079 + 0.140515i \(0.955124\pi\)
\(62\) 1.00616 0.127783
\(63\) −4.37350 + 13.4162i −0.551009 + 1.69029i
\(64\) −8.59603 −1.07450
\(65\) −3.58520 + 0.382510i −0.444690 + 0.0474445i
\(66\) 2.95551 + 0.469566i 0.363798 + 0.0577996i
\(67\) 9.45733 + 5.46019i 1.15540 + 0.667068i 0.950196 0.311652i \(-0.100882\pi\)
0.205200 + 0.978720i \(0.434216\pi\)
\(68\) 0.0637184 0.110363i 0.00772699 0.0133835i
\(69\) −7.19989 1.14391i −0.866765 0.137710i
\(70\) −5.48839 + 3.16872i −0.655988 + 0.378735i
\(71\) 5.80266i 0.688649i 0.938851 + 0.344325i \(0.111892\pi\)
−0.938851 + 0.344325i \(0.888108\pi\)
\(72\) −5.90245 6.56806i −0.695611 0.774053i
\(73\) 9.51919i 1.11414i −0.830467 0.557068i \(-0.811926\pi\)
0.830467 0.557068i \(-0.188074\pi\)
\(74\) −5.43478 9.41331i −0.631780 1.09427i
\(75\) −1.09066 + 1.34553i −0.125939 + 0.155369i
\(76\) −1.03431 0.597161i −0.118644 0.0684990i
\(77\) 3.01592 5.22372i 0.343695 0.595298i
\(78\) 8.40303 + 0.431220i 0.951456 + 0.0488261i
\(79\) −2.41946 4.19062i −0.272210 0.471482i 0.697217 0.716860i \(-0.254421\pi\)
−0.969427 + 0.245378i \(0.921088\pi\)
\(80\) 3.59650i 0.402100i
\(81\) 0.958005 8.94887i 0.106445 0.994319i
\(82\) −9.95222 −1.09904
\(83\) 2.46941 1.42572i 0.271053 0.156493i −0.358313 0.933602i \(-0.616648\pi\)
0.629366 + 0.777109i \(0.283315\pi\)
\(84\) −1.40504 + 0.538569i −0.153303 + 0.0587627i
\(85\) 0.597541 + 0.344990i 0.0648124 + 0.0374195i
\(86\) −12.6590 7.30869i −1.36506 0.788116i
\(87\) −6.07324 + 7.49245i −0.651120 + 0.803274i
\(88\) 1.88732 + 3.26893i 0.201189 + 0.348469i
\(89\) 10.7367i 1.13809i −0.822306 0.569045i \(-0.807313\pi\)
0.822306 0.569045i \(-0.192687\pi\)
\(90\) 3.00639 2.70173i 0.316902 0.284787i
\(91\) 6.87370 15.5040i 0.720559 1.62526i
\(92\) −0.388693 0.673235i −0.0405240 0.0701896i
\(93\) −0.202958 + 1.27744i −0.0210458 + 0.132465i
\(94\) 5.05769 8.76017i 0.521661 0.903543i
\(95\) 3.23321 5.60008i 0.331720 0.574556i
\(96\) 0.283014 1.78133i 0.0288850 0.181806i
\(97\) 1.55060 0.895240i 0.157440 0.0908979i −0.419210 0.907889i \(-0.637693\pi\)
0.576650 + 0.816991i \(0.304360\pi\)
\(98\) 20.3781i 2.05850i
\(99\) −1.19234 + 3.65764i −0.119834 + 0.367607i
\(100\) −0.184696 −0.0184696
\(101\) −1.85667 3.21584i −0.184745 0.319988i 0.758746 0.651387i \(-0.225813\pi\)
−0.943491 + 0.331399i \(0.892479\pi\)
\(102\) −1.25085 1.01392i −0.123853 0.100393i
\(103\) −5.29740 + 9.17537i −0.521969 + 0.904076i 0.477705 + 0.878520i \(0.341469\pi\)
−0.999673 + 0.0255558i \(0.991864\pi\)
\(104\) 6.25162 + 8.57628i 0.613022 + 0.840974i
\(105\) −2.91598 7.60733i −0.284570 0.742399i
\(106\) −6.34893 + 3.66556i −0.616663 + 0.356030i
\(107\) −14.5036 −1.40211 −0.701056 0.713106i \(-0.747288\pi\)
−0.701056 + 0.713106i \(0.747288\pi\)
\(108\) 0.805634 0.521531i 0.0775222 0.0501843i
\(109\) 4.43511i 0.424806i 0.977182 + 0.212403i \(0.0681290\pi\)
−0.977182 + 0.212403i \(0.931871\pi\)
\(110\) −1.49629 + 0.863882i −0.142665 + 0.0823679i
\(111\) 13.0476 5.00128i 1.23842 0.474701i
\(112\) 14.6504 + 8.45842i 1.38433 + 0.799245i
\(113\) 3.57608 6.19396i 0.336409 0.582678i −0.647345 0.762197i \(-0.724121\pi\)
0.983755 + 0.179519i \(0.0574540\pi\)
\(114\) −9.50231 + 11.7228i −0.889973 + 1.09794i
\(115\) 3.64510 2.10450i 0.339907 0.196246i
\(116\) −1.02846 −0.0954901
\(117\) −2.24250 + 10.5816i −0.207319 + 0.978273i
\(118\) −0.556882 −0.0512651
\(119\) −2.81065 + 1.62273i −0.257652 + 0.148756i
\(120\) 5.03516 + 0.799978i 0.459645 + 0.0730276i
\(121\) −4.67778 + 8.10215i −0.425253 + 0.736559i
\(122\) −6.80481 3.92876i −0.616078 0.355693i
\(123\) 2.00751 12.6355i 0.181011 1.13931i
\(124\) −0.119449 + 0.0689638i −0.0107268 + 0.00619313i
\(125\) 1.00000i 0.0894427i
\(126\) 3.93496 + 18.6007i 0.350554 + 1.65708i
\(127\) 10.7582 0.954634 0.477317 0.878731i \(-0.341609\pi\)
0.477317 + 0.878731i \(0.341609\pi\)
\(128\) −8.22639 + 4.74951i −0.727117 + 0.419801i
\(129\) 11.8327 14.5978i 1.04181 1.28527i
\(130\) −3.92562 + 2.86155i −0.344299 + 0.250975i
\(131\) −8.92688 + 15.4618i −0.779945 + 1.35090i 0.152028 + 0.988376i \(0.451420\pi\)
−0.931973 + 0.362528i \(0.881914\pi\)
\(132\) −0.383054 + 0.146829i −0.0333406 + 0.0127798i
\(133\) 15.2080 + 26.3411i 1.31870 + 2.28406i
\(134\) 14.7134 1.27104
\(135\) 2.82373 + 4.36195i 0.243028 + 0.375417i
\(136\) 2.03097i 0.174154i
\(137\) −3.72175 + 2.14875i −0.317970 + 0.183580i −0.650488 0.759517i \(-0.725435\pi\)
0.332517 + 0.943097i \(0.392102\pi\)
\(138\) −9.17162 + 3.51559i −0.780740 + 0.299267i
\(139\) 0.0771951 0.133706i 0.00654761 0.0113408i −0.862733 0.505660i \(-0.831249\pi\)
0.869281 + 0.494319i \(0.164582\pi\)
\(140\) 0.434377 0.752363i 0.0367116 0.0635863i
\(141\) 10.1019 + 8.18838i 0.850729 + 0.689586i
\(142\) 3.90906 + 6.77068i 0.328041 + 0.568183i
\(143\) 1.87396 4.22683i 0.156708 0.353465i
\(144\) −10.2582 3.34402i −0.854849 0.278668i
\(145\) 5.56839i 0.462430i
\(146\) −6.41276 11.1072i −0.530723 0.919240i
\(147\) 25.8724 + 4.11056i 2.13392 + 0.339034i
\(148\) 1.29040 + 0.745014i 0.106070 + 0.0612398i
\(149\) −8.04826 4.64667i −0.659339 0.380670i 0.132686 0.991158i \(-0.457640\pi\)
−0.792025 + 0.610488i \(0.790973\pi\)
\(150\) −0.366173 + 2.30474i −0.0298979 + 0.188181i
\(151\) 6.14219 3.54620i 0.499845 0.288585i −0.228805 0.973472i \(-0.573482\pi\)
0.728649 + 0.684887i \(0.240148\pi\)
\(152\) −19.0340 −1.54386
\(153\) 1.53960 1.38358i 0.124469 0.111856i
\(154\) 8.12688i 0.654883i
\(155\) −0.373391 0.646732i −0.0299915 0.0519468i
\(156\) −1.02714 + 0.524762i −0.0822370 + 0.0420146i
\(157\) −6.72039 + 11.6401i −0.536345 + 0.928978i 0.462751 + 0.886488i \(0.346862\pi\)
−0.999097 + 0.0424895i \(0.986471\pi\)
\(158\) −5.64616 3.25981i −0.449184 0.259337i
\(159\) −3.37318 8.80011i −0.267511 0.697894i
\(160\) 0.520674 + 0.901834i 0.0411629 + 0.0712963i
\(161\) 19.7979i 1.56029i
\(162\) −4.91073 11.0871i −0.385823 0.871087i
\(163\) 4.64686i 0.363970i −0.983301 0.181985i \(-0.941748\pi\)
0.983301 0.181985i \(-0.0582523\pi\)
\(164\) 1.18150 0.682139i 0.0922596 0.0532661i
\(165\) −0.794976 2.07397i −0.0618888 0.161458i
\(166\) 1.92091 3.32712i 0.149092 0.258234i
\(167\) −10.9080 6.29773i −0.844086 0.487333i 0.0145650 0.999894i \(-0.495364\pi\)
−0.858651 + 0.512561i \(0.828697\pi\)
\(168\) −15.1007 + 18.6294i −1.16504 + 1.43729i
\(169\) 3.97839 12.3763i 0.306030 0.952022i
\(170\) 0.929633 0.0712996
\(171\) −12.9667 14.4290i −0.991591 1.10341i
\(172\) 2.00379 0.152788
\(173\) 10.8444 + 18.7831i 0.824485 + 1.42805i 0.902313 + 0.431082i \(0.141868\pi\)
−0.0778279 + 0.996967i \(0.524798\pi\)
\(174\) −2.03900 + 12.8337i −0.154576 + 0.972920i
\(175\) 4.07352 + 2.35185i 0.307929 + 0.177783i
\(176\) 3.99411 + 2.30600i 0.301067 + 0.173821i
\(177\) 0.112331 0.707026i 0.00844333 0.0531434i
\(178\) −7.23297 12.5279i −0.542134 0.939004i
\(179\) −15.5830 −1.16473 −0.582364 0.812928i \(-0.697872\pi\)
−0.582364 + 0.812928i \(0.697872\pi\)
\(180\) −0.171730 + 0.526804i −0.0128000 + 0.0392656i
\(181\) −23.6483 −1.75776 −0.878882 0.477040i \(-0.841710\pi\)
−0.878882 + 0.477040i \(0.841710\pi\)
\(182\) −2.42414 22.7210i −0.179689 1.68419i
\(183\) 6.36065 7.84701i 0.470193 0.580068i
\(184\) −10.7294 6.19462i −0.790981 0.456673i
\(185\) −4.03373 + 6.98663i −0.296566 + 0.513667i
\(186\) 0.623753 + 1.62728i 0.0457358 + 0.119318i
\(187\) −0.766262 + 0.442402i −0.0560346 + 0.0323516i
\(188\) 1.38664i 0.101131i
\(189\) −24.4095 + 1.24387i −1.77553 + 0.0904781i
\(190\) 8.71241i 0.632065i
\(191\) −0.337619 0.584773i −0.0244292 0.0423127i 0.853552 0.521007i \(-0.174444\pi\)
−0.877982 + 0.478694i \(0.841110\pi\)
\(192\) −5.32896 13.9024i −0.384584 1.00332i
\(193\) 12.7236 + 7.34599i 0.915867 + 0.528776i 0.882314 0.470661i \(-0.155985\pi\)
0.0335526 + 0.999437i \(0.489318\pi\)
\(194\) 1.20619 2.08918i 0.0865991 0.149994i
\(195\) −2.84122 5.56125i −0.203464 0.398249i
\(196\) 1.39674 + 2.41923i 0.0997674 + 0.172802i
\(197\) 2.61631i 0.186404i −0.995647 0.0932021i \(-0.970290\pi\)
0.995647 0.0932021i \(-0.0297103\pi\)
\(198\) 1.07278 + 5.07106i 0.0762392 + 0.360385i
\(199\) 25.9577 1.84009 0.920045 0.391813i \(-0.128152\pi\)
0.920045 + 0.391813i \(0.128152\pi\)
\(200\) −2.54916 + 1.47176i −0.180253 + 0.104069i
\(201\) −2.96790 + 18.6804i −0.209340 + 1.31761i
\(202\) −4.33280 2.50154i −0.304855 0.176008i
\(203\) 22.6830 + 13.0960i 1.59203 + 0.919161i
\(204\) 0.217993 + 0.0346343i 0.0152625 + 0.00242489i
\(205\) 3.69331 + 6.39700i 0.257952 + 0.446786i
\(206\) 14.2747i 0.994567i
\(207\) −2.61340 12.3536i −0.181644 0.858634i
\(208\) 11.8545 + 5.25570i 0.821963 + 0.364417i
\(209\) 4.14613 + 7.18132i 0.286794 + 0.496742i
\(210\) −8.52723 6.91202i −0.588435 0.476975i
\(211\) −5.16589 + 8.94758i −0.355634 + 0.615977i −0.987226 0.159324i \(-0.949069\pi\)
0.631592 + 0.775301i \(0.282402\pi\)
\(212\) 0.502485 0.870329i 0.0345108 0.0597744i
\(213\) −9.38469 + 3.59726i −0.643028 + 0.246480i
\(214\) −16.9231 + 9.77056i −1.15684 + 0.667902i
\(215\) 10.8491i 0.739904i
\(216\) 6.96345 13.6178i 0.473802 0.926576i
\(217\) 3.51264 0.238453
\(218\) 2.98778 + 5.17499i 0.202358 + 0.350494i
\(219\) 15.3955 5.90125i 1.04033 0.398770i
\(220\) 0.118423 0.205115i 0.00798410 0.0138289i
\(221\) −2.01034 + 1.46543i −0.135230 + 0.0985753i
\(222\) 11.8550 14.6253i 0.795657 0.981587i
\(223\) −15.3886 + 8.88463i −1.03050 + 0.594959i −0.917128 0.398594i \(-0.869498\pi\)
−0.113371 + 0.993553i \(0.536165\pi\)
\(224\) −4.89819 −0.327274
\(225\) −2.85227 0.929800i −0.190152 0.0619867i
\(226\) 9.63634i 0.641000i
\(227\) 24.6734 14.2452i 1.63763 0.945485i 0.655981 0.754777i \(-0.272255\pi\)
0.981647 0.190707i \(-0.0610782\pi\)
\(228\) 0.324589 2.04300i 0.0214964 0.135301i
\(229\) 5.24154 + 3.02620i 0.346371 + 0.199977i 0.663086 0.748544i \(-0.269247\pi\)
−0.316715 + 0.948521i \(0.602580\pi\)
\(230\) 2.83546 4.91116i 0.186965 0.323832i
\(231\) 10.3180 + 1.63931i 0.678876 + 0.107859i
\(232\) −14.1947 + 8.19531i −0.931928 + 0.538049i
\(233\) 8.75020 0.573244 0.286622 0.958044i \(-0.407468\pi\)
0.286622 + 0.958044i \(0.407468\pi\)
\(234\) 4.51189 + 13.8576i 0.294952 + 0.905900i
\(235\) −7.50771 −0.489749
\(236\) 0.0661114 0.0381694i 0.00430349 0.00248462i
\(237\) 5.27763 6.51091i 0.342819 0.422929i
\(238\) −2.18636 + 3.78688i −0.141721 + 0.245467i
\(239\) −24.3851 14.0788i −1.57734 0.910679i −0.995229 0.0975716i \(-0.968892\pi\)
−0.582114 0.813107i \(-0.697774\pi\)
\(240\) 5.81664 2.22958i 0.375462 0.143919i
\(241\) 2.53789 1.46525i 0.163480 0.0943852i −0.416028 0.909352i \(-0.636578\pi\)
0.579508 + 0.814967i \(0.303245\pi\)
\(242\) 12.6050i 0.810283i
\(243\) 15.0670 3.99830i 0.966547 0.256491i
\(244\) 1.07713 0.0689562
\(245\) −13.0984 + 7.56239i −0.836829 + 0.483143i
\(246\) −6.16970 16.0958i −0.393366 1.02623i
\(247\) 13.7338 + 18.8407i 0.873861 + 1.19880i
\(248\) −1.09908 + 1.90366i −0.0697917 + 0.120883i
\(249\) 3.83669 + 3.10995i 0.243140 + 0.197085i
\(250\) −0.673666 1.16682i −0.0426064 0.0737964i
\(251\) 14.7686 0.932185 0.466093 0.884736i \(-0.345661\pi\)
0.466093 + 0.884736i \(0.345661\pi\)
\(252\) −1.74206 1.93851i −0.109740 0.122115i
\(253\) 5.39745i 0.339335i
\(254\) 12.5529 7.24742i 0.787639 0.454744i
\(255\) −0.187521 + 1.18028i −0.0117430 + 0.0739119i
\(256\) 2.19687 3.80509i 0.137304 0.237818i
\(257\) −8.52231 + 14.7611i −0.531607 + 0.920771i 0.467712 + 0.883881i \(0.345078\pi\)
−0.999319 + 0.0368900i \(0.988255\pi\)
\(258\) 3.97266 25.0044i 0.247327 1.55671i
\(259\) −18.9735 32.8630i −1.17895 2.04201i
\(260\) 0.269903 0.608783i 0.0167387 0.0377551i
\(261\) −15.8826 5.17749i −0.983108 0.320479i
\(262\) 24.0549i 1.48612i
\(263\) −6.10773 10.5789i −0.376619 0.652323i 0.613949 0.789346i \(-0.289580\pi\)
−0.990568 + 0.137023i \(0.956247\pi\)
\(264\) −4.11686 + 5.07889i −0.253375 + 0.312584i
\(265\) 4.71222 + 2.72060i 0.289470 + 0.167125i
\(266\) 35.4902 + 20.4903i 2.17604 + 1.25634i
\(267\) 17.3646 6.65604i 1.06270 0.407343i
\(268\) −1.74673 + 1.00848i −0.106699 + 0.0616024i
\(269\) 14.2974 0.871727 0.435863 0.900013i \(-0.356443\pi\)
0.435863 + 0.900013i \(0.356443\pi\)
\(270\) 6.23329 + 3.18738i 0.379346 + 0.193977i
\(271\) 3.84476i 0.233553i −0.993158 0.116776i \(-0.962744\pi\)
0.993158 0.116776i \(-0.0372561\pi\)
\(272\) −1.24076 2.14905i −0.0752319 0.130306i
\(273\) 29.3360 + 1.50544i 1.77549 + 0.0911135i
\(274\) −2.89508 + 5.01443i −0.174898 + 0.302933i
\(275\) 1.11056 + 0.641180i 0.0669690 + 0.0386646i
\(276\) 0.847865 1.04600i 0.0510355 0.0629615i
\(277\) 13.5454 + 23.4614i 0.813865 + 1.40966i 0.910140 + 0.414301i \(0.135974\pi\)
−0.0962743 + 0.995355i \(0.530693\pi\)
\(278\) 0.208015i 0.0124759i
\(279\) −2.19184 + 0.463682i −0.131222 + 0.0277599i
\(280\) 13.8454i 0.827420i
\(281\) −7.02708 + 4.05709i −0.419201 + 0.242026i −0.694735 0.719266i \(-0.744478\pi\)
0.275535 + 0.961291i \(0.411145\pi\)
\(282\) 17.3033 + 2.74912i 1.03040 + 0.163708i
\(283\) 12.1427 21.0317i 0.721807 1.25021i −0.238468 0.971150i \(-0.576645\pi\)
0.960275 0.279056i \(-0.0900215\pi\)
\(284\) −0.928144 0.535864i −0.0550752 0.0317977i
\(285\) 11.0614 + 1.75742i 0.655222 + 0.104101i
\(286\) −0.660887 6.19438i −0.0390791 0.366282i
\(287\) −34.7444 −2.05090
\(288\) 3.05640 0.646581i 0.180100 0.0381001i
\(289\) −16.5239 −0.971996
\(290\) −3.75124 6.49733i −0.220280 0.381537i
\(291\) 2.40915 + 1.95281i 0.141227 + 0.114476i
\(292\) 1.52261 + 0.879078i 0.0891039 + 0.0514442i
\(293\) 22.8249 + 13.1779i 1.33344 + 0.769864i 0.985826 0.167773i \(-0.0536575\pi\)
0.347617 + 0.937637i \(0.386991\pi\)
\(294\) 32.9577 12.6330i 1.92213 0.736774i
\(295\) 0.206661 + 0.357947i 0.0120323 + 0.0208405i
\(296\) 23.7467 1.38025
\(297\) −6.65470 + 0.339113i −0.386145 + 0.0196773i
\(298\) −12.5212 −0.725334
\(299\) 1.60998 + 15.0901i 0.0931077 + 0.872684i
\(300\) −0.114499 0.298710i −0.00661060 0.0172460i
\(301\) −44.1941 25.5155i −2.54731 1.47069i
\(302\) 4.77791 8.27557i 0.274938 0.476206i
\(303\) 4.04999 4.99640i 0.232666 0.287036i
\(304\) −20.1407 + 11.6282i −1.15515 + 0.666924i
\(305\) 5.83191i 0.333934i
\(306\) 0.864373 2.65157i 0.0494129 0.151580i
\(307\) 17.8331i 1.01779i 0.860828 + 0.508896i \(0.169946\pi\)
−0.860828 + 0.508896i \(0.830054\pi\)
\(308\) 0.557028 + 0.964800i 0.0317396 + 0.0549746i
\(309\) −18.1234 2.87942i −1.03101 0.163805i
\(310\) −0.871363 0.503082i −0.0494901 0.0285731i
\(311\) 12.4668 21.5932i 0.706929 1.22444i −0.259062 0.965861i \(-0.583413\pi\)
0.965991 0.258576i \(-0.0832533\pi\)
\(312\) −9.99490 + 15.4275i −0.565850 + 0.873411i
\(313\) 0.556344 + 0.963617i 0.0314464 + 0.0544668i 0.881320 0.472519i \(-0.156655\pi\)
−0.849874 + 0.526986i \(0.823322\pi\)
\(314\) 18.1092i 1.02196i
\(315\) 10.4957 9.43206i 0.591365 0.531436i
\(316\) 0.893728 0.0502761
\(317\) −23.8124 + 13.7481i −1.33744 + 0.772169i −0.986427 0.164203i \(-0.947495\pi\)
−0.351010 + 0.936372i \(0.614162\pi\)
\(318\) −9.86424 7.99578i −0.553159 0.448381i
\(319\) 6.18401 + 3.57034i 0.346238 + 0.199901i
\(320\) 7.44438 + 4.29802i 0.416154 + 0.240266i
\(321\) −8.99123 23.4567i −0.501841 1.30923i
\(322\) 13.3371 + 23.1006i 0.743250 + 1.28735i
\(323\) 4.46170i 0.248256i
\(324\) 1.34291 + 0.979644i 0.0746064 + 0.0544247i
\(325\) 3.29613 + 1.46134i 0.182837 + 0.0810605i
\(326\) −3.13043 5.42207i −0.173379 0.300301i
\(327\) −7.17293 + 2.74947i −0.396664 + 0.152046i
\(328\) 10.8713 18.8296i 0.600267 1.03969i
\(329\) 17.6570 30.5828i 0.973462 1.68609i
\(330\) −2.32476 1.88441i −0.127974 0.103733i
\(331\) 10.6947 6.17460i 0.587835 0.339387i −0.176406 0.984317i \(-0.556447\pi\)
0.764241 + 0.644931i \(0.223114\pi\)
\(332\) 0.526648i 0.0289036i
\(333\) 16.1772 + 18.0015i 0.886506 + 0.986475i
\(334\) −16.9703 −0.928572
\(335\) −5.46019 9.45733i −0.298322 0.516709i
\(336\) −4.59760 + 28.9379i −0.250820 + 1.57869i
\(337\) −0.663331 + 1.14892i −0.0361339 + 0.0625858i −0.883527 0.468381i \(-0.844838\pi\)
0.847393 + 0.530966i \(0.178171\pi\)
\(338\) −3.69540 17.1211i −0.201003 0.931262i
\(339\) 12.2345 + 1.94379i 0.664485 + 0.105572i
\(340\) −0.110363 + 0.0637184i −0.00598530 + 0.00345561i
\(341\) 0.957643 0.0518593
\(342\) −24.8502 8.10080i −1.34374 0.438041i
\(343\) 38.2165i 2.06350i
\(344\) 27.6561 15.9673i 1.49112 0.860897i
\(345\) 5.66334 + 4.59060i 0.304904 + 0.247150i
\(346\) 25.3070 + 14.6110i 1.36051 + 0.785493i
\(347\) 12.6904 21.9804i 0.681256 1.17997i −0.293342 0.956008i \(-0.594767\pi\)
0.974598 0.223963i \(-0.0718993\pi\)
\(348\) −0.637576 1.66334i −0.0341776 0.0891642i
\(349\) 11.4337 6.60123i 0.612030 0.353355i −0.161730 0.986835i \(-0.551707\pi\)
0.773759 + 0.633480i \(0.218374\pi\)
\(350\) 6.33744 0.338751
\(351\) −18.5040 + 2.93309i −0.987669 + 0.156557i
\(352\) −1.33538 −0.0711761
\(353\) −8.09353 + 4.67280i −0.430775 + 0.248708i −0.699677 0.714460i \(-0.746673\pi\)
0.268902 + 0.963168i \(0.413339\pi\)
\(354\) −0.345229 0.900649i −0.0183487 0.0478689i
\(355\) 2.90133 5.02525i 0.153987 0.266713i
\(356\) 1.71736 + 0.991515i 0.0910196 + 0.0525502i
\(357\) −4.36687 3.53971i −0.231119 0.187341i
\(358\) −18.1826 + 10.4977i −0.960981 + 0.554823i
\(359\) 29.6022i 1.56234i −0.624315 0.781172i \(-0.714622\pi\)
0.624315 0.781172i \(-0.285378\pi\)
\(360\) 1.82765 + 8.63933i 0.0963254 + 0.455333i
\(361\) −22.8145 −1.20077
\(362\) −27.5934 + 15.9311i −1.45028 + 0.837318i
\(363\) −16.0036 2.54262i −0.839970 0.133453i
\(364\) 1.84512 + 2.53122i 0.0967104 + 0.132672i
\(365\) −4.75959 + 8.24386i −0.249129 + 0.431503i
\(366\) 2.13549 13.4410i 0.111624 0.702574i
\(367\) 9.36803 + 16.2259i 0.489007 + 0.846985i 0.999920 0.0126473i \(-0.00402586\pi\)
−0.510913 + 0.859633i \(0.670693\pi\)
\(368\) −15.1376 −0.789104
\(369\) 21.6800 4.58640i 1.12862 0.238758i
\(370\) 10.8696i 0.565081i
\(371\) −22.1649 + 12.7969i −1.15074 + 0.664382i
\(372\) −0.185586 0.150433i −0.00962218 0.00779957i
\(373\) 7.12935 12.3484i 0.369144 0.639375i −0.620288 0.784374i \(-0.712984\pi\)
0.989432 + 0.144998i \(0.0463177\pi\)
\(374\) −0.596062 + 1.03241i −0.0308216 + 0.0533846i
\(375\) 1.61731 0.619932i 0.0835174 0.0320132i
\(376\) 11.0495 + 19.1383i 0.569835 + 0.986983i
\(377\) 18.3542 + 8.13731i 0.945287 + 0.419093i
\(378\) −27.6436 + 17.8952i −1.42183 + 0.920430i
\(379\) 2.12905i 0.109362i −0.998504 0.0546811i \(-0.982586\pi\)
0.998504 0.0546811i \(-0.0174142\pi\)
\(380\) 0.597161 + 1.03431i 0.0306337 + 0.0530591i
\(381\) 6.66934 + 17.3993i 0.341681 + 0.891392i
\(382\) −0.787883 0.454885i −0.0403116 0.0232739i
\(383\) 10.5441 + 6.08761i 0.538776 + 0.311063i 0.744583 0.667530i \(-0.232648\pi\)
−0.205807 + 0.978593i \(0.565982\pi\)
\(384\) −12.7812 10.3602i −0.652239 0.528693i
\(385\) −5.22372 + 3.01592i −0.266225 + 0.153705i
\(386\) 19.7950 1.00754
\(387\) 30.9447 + 10.0875i 1.57301 + 0.512777i
\(388\) 0.330695i 0.0167885i
\(389\) 12.7383 + 22.0634i 0.645858 + 1.11866i 0.984103 + 0.177600i \(0.0568333\pi\)
−0.338245 + 0.941058i \(0.609833\pi\)
\(390\) −7.06163 4.57496i −0.357579 0.231662i
\(391\) 1.45206 2.51505i 0.0734340 0.127191i
\(392\) 38.5554 + 22.2600i 1.94734 + 1.12430i
\(393\) −30.5406 4.85223i −1.54057 0.244763i
\(394\) −1.76252 3.05277i −0.0887943 0.153796i
\(395\) 4.83891i 0.243472i
\(396\) −0.474935 0.528492i −0.0238664 0.0265577i
\(397\) 18.5900i 0.933004i 0.884520 + 0.466502i \(0.154486\pi\)
−0.884520 + 0.466502i \(0.845514\pi\)
\(398\) 30.2880 17.4868i 1.51820 0.876534i
\(399\) −33.1737 + 40.9258i −1.66076 + 2.04885i
\(400\) −1.79825 + 3.11466i −0.0899124 + 0.155733i
\(401\) −3.02411 1.74597i −0.151017 0.0871897i 0.422587 0.906322i \(-0.361122\pi\)
−0.573604 + 0.819132i \(0.694455\pi\)
\(402\) 9.12130 + 23.7961i 0.454929 + 1.18684i
\(403\) 2.67737 0.285652i 0.133369 0.0142293i
\(404\) 0.685837 0.0341217
\(405\) −5.30409 + 7.27094i −0.263562 + 0.361296i
\(406\) 35.2894 1.75138
\(407\) −5.17269 8.95937i −0.256401 0.444099i
\(408\) 3.28470 1.25906i 0.162617 0.0623328i
\(409\) −6.29168 3.63250i −0.311103 0.179616i 0.336317 0.941749i \(-0.390819\pi\)
−0.647420 + 0.762133i \(0.724152\pi\)
\(410\) 8.61888 + 4.97611i 0.425656 + 0.245753i
\(411\) −5.78242 4.68713i −0.285226 0.231199i
\(412\) −0.978409 1.69465i −0.0482028 0.0834896i
\(413\) −1.94414 −0.0956649
\(414\) −11.3716 12.6539i −0.558882 0.621906i
\(415\) −2.85143 −0.139971
\(416\) −3.73345 + 0.398326i −0.183047 + 0.0195295i
\(417\) 0.264099 + 0.0419597i 0.0129330 + 0.00205477i
\(418\) 9.67562 + 5.58622i 0.473250 + 0.273231i
\(419\) −8.78209 + 15.2110i −0.429033 + 0.743107i −0.996788 0.0800910i \(-0.974479\pi\)
0.567755 + 0.823198i \(0.307812\pi\)
\(420\) 1.48609 + 0.236107i 0.0725136 + 0.0115209i
\(421\) −13.8198 + 7.97886i −0.673536 + 0.388866i −0.797415 0.603431i \(-0.793800\pi\)
0.123879 + 0.992297i \(0.460466\pi\)
\(422\) 13.9203i 0.677631i
\(423\) −6.98067 + 21.4140i −0.339412 + 1.04119i
\(424\) 16.0163i 0.777818i
\(425\) −0.344990 0.597541i −0.0167345 0.0289850i
\(426\) −8.52693 + 10.5195i −0.413131 + 0.509672i
\(427\) −23.7564 13.7158i −1.14965 0.663753i
\(428\) 1.33938 2.31987i 0.0647412 0.112135i
\(429\) 7.99781 + 0.410425i 0.386138 + 0.0198155i
\(430\) 7.30869 + 12.6590i 0.352456 + 0.610472i
\(431\) 2.36438i 0.113888i −0.998377 0.0569440i \(-0.981864\pi\)
0.998377 0.0569440i \(-0.0181356\pi\)
\(432\) −0.951075 18.6637i −0.0457586 0.897959i
\(433\) −15.9227 −0.765194 −0.382597 0.923915i \(-0.624970\pi\)
−0.382597 + 0.923915i \(0.624970\pi\)
\(434\) 4.09863 2.36634i 0.196741 0.113588i
\(435\) 9.00580 3.45203i 0.431795 0.165512i
\(436\) −0.709402 0.409573i −0.0339742 0.0196150i
\(437\) −23.5707 13.6086i −1.12754 0.650986i
\(438\) 13.9883 17.2571i 0.668387 0.824577i
\(439\) 12.2763 + 21.2632i 0.585916 + 1.01484i 0.994761 + 0.102233i \(0.0325986\pi\)
−0.408844 + 0.912604i \(0.634068\pi\)
\(440\) 3.77464i 0.179949i
\(441\) 9.39108 + 44.3919i 0.447195 + 2.11390i
\(442\) −1.35851 + 3.06420i −0.0646177 + 0.145749i
\(443\) 10.9342 + 18.9386i 0.519501 + 0.899802i 0.999743 + 0.0226659i \(0.00721539\pi\)
−0.480242 + 0.877136i \(0.659451\pi\)
\(444\) −0.404955 + 2.54884i −0.0192183 + 0.120962i
\(445\) −5.36836 + 9.29828i −0.254485 + 0.440781i
\(446\) −11.9705 + 20.7336i −0.566822 + 0.981764i
\(447\) 2.52571 15.8971i 0.119462 0.751909i
\(448\) −35.0161 + 20.2166i −1.65436 + 0.955143i
\(449\) 13.2031i 0.623092i 0.950231 + 0.311546i \(0.100847\pi\)
−0.950231 + 0.311546i \(0.899153\pi\)
\(450\) −3.95448 + 0.836568i −0.186416 + 0.0394362i
\(451\) −9.47229 −0.446033
\(452\) 0.660488 + 1.14400i 0.0310667 + 0.0538092i
\(453\) 9.54304 + 7.73541i 0.448371 + 0.363441i
\(454\) 19.1930 33.2432i 0.900771 1.56018i
\(455\) −13.7048 + 9.99002i −0.642491 + 0.468339i
\(456\) −11.7998 30.7838i −0.552575 1.44158i
\(457\) −14.3166 + 8.26571i −0.669704 + 0.386654i −0.795964 0.605344i \(-0.793036\pi\)
0.126261 + 0.991997i \(0.459702\pi\)
\(458\) 8.15460 0.381039
\(459\) 3.19212 + 1.63228i 0.148995 + 0.0761885i
\(460\) 0.777385i 0.0362458i
\(461\) 30.1732 17.4205i 1.40531 0.811354i 0.410375 0.911917i \(-0.365398\pi\)
0.994931 + 0.100563i \(0.0320645\pi\)
\(462\) 13.1437 5.03812i 0.611499 0.234394i
\(463\) −28.0327 16.1847i −1.30279 0.752167i −0.321910 0.946770i \(-0.604325\pi\)
−0.980882 + 0.194603i \(0.937658\pi\)
\(464\) −10.0134 + 17.3436i −0.464858 + 0.805158i
\(465\) 0.814488 1.00482i 0.0377710 0.0465973i
\(466\) 10.2099 5.89471i 0.472966 0.273067i
\(467\) 8.15829 0.377521 0.188760 0.982023i \(-0.439553\pi\)
0.188760 + 0.982023i \(0.439553\pi\)
\(468\) −1.48546 1.33588i −0.0686654 0.0617513i
\(469\) 51.3662 2.37187
\(470\) −8.76017 + 5.05769i −0.404077 + 0.233294i
\(471\) −22.9917 3.65289i −1.05940 0.168316i
\(472\) 0.608309 1.05362i 0.0279997 0.0484969i
\(473\) −12.0486 6.95624i −0.553993 0.319848i
\(474\) 1.77188 11.1524i 0.0813852 0.512249i
\(475\) −5.60008 + 3.23321i −0.256949 + 0.148350i
\(476\) 0.599424i 0.0274746i
\(477\) 12.1413 10.9109i 0.555914 0.499578i
\(478\) −37.9375 −1.73522
\(479\) 15.9891 9.23132i 0.730561 0.421790i −0.0880661 0.996115i \(-0.528069\pi\)
0.818628 + 0.574325i \(0.194735\pi\)
\(480\) −1.13576 + 1.40117i −0.0518401 + 0.0639542i
\(481\) −17.1342 23.5055i −0.781252 1.07176i
\(482\) 1.97418 3.41938i 0.0899215 0.155749i
\(483\) −32.0192 + 12.2733i −1.45693 + 0.558456i
\(484\) −0.863967 1.49643i −0.0392712 0.0680197i
\(485\) −1.79048 −0.0813015
\(486\) 14.8870 14.8154i 0.675287 0.672041i
\(487\) 36.5271i 1.65520i −0.561317 0.827601i \(-0.689705\pi\)
0.561317 0.827601i \(-0.310295\pi\)
\(488\) 14.8664 8.58314i 0.672972 0.388541i
\(489\) 7.51540 2.88074i 0.339858 0.130272i
\(490\) −10.1891 + 17.6480i −0.460295 + 0.797254i
\(491\) −12.3472 + 21.3859i −0.557220 + 0.965133i 0.440508 + 0.897749i \(0.354798\pi\)
−0.997727 + 0.0673836i \(0.978535\pi\)
\(492\) 1.83568 + 1.48797i 0.0827588 + 0.0670828i
\(493\) −1.92104 3.32734i −0.0865194 0.149856i
\(494\) 28.7173 + 12.7318i 1.29205 + 0.572830i
\(495\) 2.86141 2.57144i 0.128611 0.115578i
\(496\) 2.68580i 0.120596i
\(497\) 13.6470 + 23.6373i 0.612151 + 1.06028i
\(498\) 6.57181 + 1.04412i 0.294490 + 0.0467881i
\(499\) −6.04869 3.49221i −0.270776 0.156333i 0.358464 0.933544i \(-0.383301\pi\)
−0.629240 + 0.777211i \(0.716634\pi\)
\(500\) 0.159951 + 0.0923480i 0.00715325 + 0.00412993i
\(501\) 3.42315 21.5458i 0.152935 0.962593i
\(502\) 17.2323 9.94910i 0.769117 0.444050i
\(503\) 10.0965 0.450179 0.225089 0.974338i \(-0.427733\pi\)
0.225089 + 0.974338i \(0.427733\pi\)
\(504\) −39.4909 12.8734i −1.75906 0.573429i
\(505\) 3.71333i 0.165241i
\(506\) 3.63608 + 6.29787i 0.161643 + 0.279974i
\(507\) 22.4826 1.23817i 0.998487 0.0549892i
\(508\) −0.993496 + 1.72079i −0.0440793 + 0.0763475i
\(509\) 25.1392 + 14.5141i 1.11427 + 0.643326i 0.939933 0.341359i \(-0.110887\pi\)
0.174341 + 0.984685i \(0.444221\pi\)
\(510\) 0.576310 + 1.50350i 0.0255194 + 0.0665762i
\(511\) −22.3877 38.7766i −0.990374 1.71538i
\(512\) 24.9179i 1.10122i
\(513\) 15.2976 29.9162i 0.675404 1.32083i
\(514\) 22.9648i 1.01293i
\(515\) 9.17537 5.29740i 0.404315 0.233431i
\(516\) 1.24221 + 3.24074i 0.0546854 + 0.142666i
\(517\) 4.81379 8.33773i 0.211710 0.366693i
\(518\) −44.2774 25.5636i −1.94544 1.12320i
\(519\) −23.6552 + 29.1830i −1.03835 + 1.28099i
\(520\) −1.12592 10.5531i −0.0493750 0.462784i
\(521\) 11.5657 0.506701 0.253350 0.967375i \(-0.418467\pi\)
0.253350 + 0.967375i \(0.418467\pi\)
\(522\) −22.0201 + 4.65834i −0.963793 + 0.203890i
\(523\) 6.17284 0.269919 0.134960 0.990851i \(-0.456910\pi\)
0.134960 + 0.990851i \(0.456910\pi\)
\(524\) −1.64876 2.85573i −0.0720264 0.124753i
\(525\) −1.27836 + 8.04613i −0.0557920 + 0.351162i
\(526\) −14.2533 8.22914i −0.621473 0.358808i
\(527\) −0.446233 0.257633i −0.0194382 0.0112227i
\(528\) −1.25343 + 7.88926i −0.0545487 + 0.343336i
\(529\) 2.64217 + 4.57637i 0.114877 + 0.198973i
\(530\) 7.33111 0.318443
\(531\) 1.21312 0.256634i 0.0526448 0.0111370i
\(532\) −5.61773 −0.243559
\(533\) −26.4825 + 2.82545i −1.14709 + 0.122384i
\(534\) 15.7775 19.4644i 0.682758 0.842306i
\(535\) 12.5605 + 7.25178i 0.543036 + 0.313522i
\(536\) −16.0721 + 27.8377i −0.694210 + 1.20241i
\(537\) −9.66040 25.2025i −0.416877 1.08757i
\(538\) 16.6825 9.63166i 0.719235 0.415250i
\(539\) 19.3954i 0.835419i
\(540\) −0.958465 + 0.0488419i −0.0412458 + 0.00210182i
\(541\) 10.6019i 0.455811i 0.973683 + 0.227905i \(0.0731877\pi\)
−0.973683 + 0.227905i \(0.926812\pi\)
\(542\) −2.59009 4.48616i −0.111254 0.192697i
\(543\) −14.6603 38.2466i −0.629135 1.64132i
\(544\) 0.622248 + 0.359255i 0.0266787 + 0.0154029i
\(545\) 2.21755 3.84091i 0.0949895 0.164527i
\(546\) 35.2441 18.0061i 1.50831 0.770589i
\(547\) −13.0254 22.5607i −0.556926 0.964624i −0.997751 0.0670308i \(-0.978647\pi\)
0.440825 0.897593i \(-0.354686\pi\)
\(548\) 0.793732i 0.0339065i
\(549\) 16.6342 + 5.42251i 0.709931 + 0.231427i
\(550\) 1.72776 0.0736721
\(551\) −31.1835 + 18.0038i −1.32846 + 0.766987i
\(552\) 3.36710 21.1930i 0.143313 0.902033i
\(553\) −19.7114 11.3804i −0.838215 0.483944i
\(554\) 31.6102 + 18.2502i 1.34299 + 0.775376i
\(555\) −13.8002 2.19255i −0.585784 0.0930685i
\(556\) 0.0142576 + 0.0246949i 0.000604658 + 0.00104730i
\(557\) 33.4373i 1.41678i 0.705819 + 0.708392i \(0.250579\pi\)
−0.705819 + 0.708392i \(0.749421\pi\)
\(558\) −2.24512 + 2.01760i −0.0950435 + 0.0854119i
\(559\) −35.7601 15.8542i −1.51249 0.670563i
\(560\) −8.45842 14.6504i −0.357433 0.619093i
\(561\) −1.19053 0.965023i −0.0502642 0.0407433i
\(562\) −5.46625 + 9.46782i −0.230580 + 0.399376i
\(563\) −6.04230 + 10.4656i −0.254653 + 0.441071i −0.964801 0.262981i \(-0.915294\pi\)
0.710148 + 0.704052i \(0.248628\pi\)
\(564\) −2.24263 + 0.859625i −0.0944317 + 0.0361967i
\(565\) −6.19396 + 3.57608i −0.260582 + 0.150447i
\(566\) 32.7204i 1.37534i
\(567\) −17.1439 38.7065i −0.719978 1.62552i
\(568\) −17.0802 −0.716669
\(569\) −2.87574 4.98094i −0.120557 0.208812i 0.799430 0.600759i \(-0.205135\pi\)
−0.919988 + 0.391947i \(0.871802\pi\)
\(570\) 14.0906 5.40111i 0.590192 0.226227i
\(571\) 3.34805 5.79900i 0.140112 0.242681i −0.787427 0.616408i \(-0.788587\pi\)
0.927539 + 0.373728i \(0.121921\pi\)
\(572\) 0.503030 + 0.690082i 0.0210328 + 0.0288538i
\(573\) 0.736457 0.908553i 0.0307659 0.0379553i
\(574\) −40.5406 + 23.4061i −1.69213 + 0.976953i
\(575\) −4.20900 −0.175527
\(576\) 19.1809 17.2371i 0.799205 0.718214i
\(577\) 21.0568i 0.876607i −0.898827 0.438304i \(-0.855579\pi\)
0.898827 0.438304i \(-0.144421\pi\)
\(578\) −19.2805 + 11.1316i −0.801964 + 0.463014i
\(579\) −3.99294 + 25.1320i −0.165941 + 1.04445i
\(580\) 0.890673 + 0.514230i 0.0369832 + 0.0213522i
\(581\) 6.70614 11.6154i 0.278217 0.481887i
\(582\) 4.12659 + 0.655627i 0.171053 + 0.0271766i
\(583\) −6.04276 + 3.48879i −0.250266 + 0.144491i
\(584\) 28.0198 1.15947
\(585\) 7.23288 8.04272i 0.299043 0.332526i
\(586\) 35.5101 1.46691
\(587\) 13.1797 7.60928i 0.543983 0.314069i −0.202709 0.979239i \(-0.564974\pi\)
0.746692 + 0.665170i \(0.231641\pi\)
\(588\) −3.04675 + 3.75872i −0.125646 + 0.155007i
\(589\) −2.41450 + 4.18204i −0.0994878 + 0.172318i
\(590\) 0.482274 + 0.278441i 0.0198549 + 0.0114632i
\(591\) 4.23137 1.62193i 0.174055 0.0667174i
\(592\) 25.1274 14.5073i 1.03273 0.596246i
\(593\) 31.4829i 1.29285i 0.762979 + 0.646423i \(0.223736\pi\)
−0.762979 + 0.646423i \(0.776264\pi\)
\(594\) −7.53641 + 4.87873i −0.309223 + 0.200177i
\(595\) 3.24546 0.133051
\(596\) 1.48648 0.858221i 0.0608887 0.0351541i
\(597\) 16.0920 + 41.9815i 0.658601 + 1.71819i
\(598\) 12.0443 + 16.5229i 0.492527 + 0.675672i
\(599\) −3.53079 + 6.11551i −0.144264 + 0.249873i −0.929098 0.369833i \(-0.879415\pi\)
0.784834 + 0.619706i \(0.212748\pi\)
\(600\) −3.96059 3.21038i −0.161690 0.131063i
\(601\) −0.0378043 0.0654790i −0.00154207 0.00267094i 0.865253 0.501335i \(-0.167158\pi\)
−0.866795 + 0.498664i \(0.833824\pi\)
\(602\) −68.7557 −2.80227
\(603\) −32.0518 + 6.78054i −1.30525 + 0.276125i
\(604\) 1.30994i 0.0533006i
\(605\) 8.10215 4.67778i 0.329399 0.190179i
\(606\) 1.35972 8.55826i 0.0552350 0.347656i
\(607\) −22.5595 + 39.0742i −0.915663 + 1.58597i −0.109735 + 0.993961i \(0.535000\pi\)
−0.805928 + 0.592014i \(0.798333\pi\)
\(608\) 3.36690 5.83164i 0.136546 0.236504i
\(609\) −7.11839 + 44.8040i −0.288452 + 1.81555i
\(610\) 3.92876 + 6.80481i 0.159071 + 0.275519i
\(611\) 10.9713 24.7464i 0.443851 1.00113i
\(612\) 0.0791264 + 0.374032i 0.00319849 + 0.0151194i
\(613\) 18.2482i 0.737039i 0.929620 + 0.368519i \(0.120135\pi\)
−0.929620 + 0.368519i \(0.879865\pi\)
\(614\) 12.0136 + 20.8081i 0.484829 + 0.839748i
\(615\) −8.05631 + 9.93892i −0.324862 + 0.400776i
\(616\) 15.3761 + 8.87738i 0.619520 + 0.357680i
\(617\) 6.90824 + 3.98847i 0.278115 + 0.160570i 0.632570 0.774503i \(-0.282000\pi\)
−0.354455 + 0.935073i \(0.615333\pi\)
\(618\) −23.0866 + 8.84936i −0.928680 + 0.355974i
\(619\) 3.59308 2.07447i 0.144418 0.0833799i −0.426050 0.904700i \(-0.640095\pi\)
0.570468 + 0.821320i \(0.306762\pi\)
\(620\) 0.137928 0.00553931
\(621\) 18.3594 11.8851i 0.736738 0.476931i
\(622\) 33.5939i 1.34699i
\(623\) −25.2512 43.7363i −1.01167 1.75226i
\(624\) −1.15108 + 22.4306i −0.0460799 + 0.897942i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 1.29831 + 0.749581i 0.0518910 + 0.0299593i
\(627\) −9.04407 + 11.1575i −0.361186 + 0.445588i
\(628\) −1.24123 2.14987i −0.0495304 0.0857892i
\(629\) 5.56640i 0.221947i
\(630\) 5.89256 18.0761i 0.234765 0.720170i
\(631\) 47.5878i 1.89444i 0.320586 + 0.947219i \(0.396120\pi\)
−0.320586 + 0.947219i \(0.603880\pi\)
\(632\) 12.3351 7.12170i 0.490666 0.283286i
\(633\) −17.6735 2.80794i −0.702458 0.111605i
\(634\) −18.5232 + 32.0832i −0.735652 + 1.27419i
\(635\) −9.31686 5.37909i −0.369728 0.213463i
\(636\) 1.71910 + 0.273127i 0.0681666 + 0.0108302i
\(637\) −5.78538 54.2254i −0.229225 2.14849i
\(638\) 9.62087 0.380894
\(639\) −11.6357 12.9479i −0.460303 0.512210i
\(640\) 9.49901 0.375482
\(641\) −22.3444 38.7016i −0.882549 1.52862i −0.848497 0.529200i \(-0.822492\pi\)
−0.0340518 0.999420i \(-0.510841\pi\)
\(642\) −26.2932 21.3128i −1.03771 0.841148i
\(643\) 40.3294 + 23.2842i 1.59043 + 0.918238i 0.993232 + 0.116148i \(0.0370546\pi\)
0.597203 + 0.802090i \(0.296279\pi\)
\(644\) −3.16670 1.82829i −0.124785 0.0720448i
\(645\) −17.5464 + 6.72572i −0.690888 + 0.264825i
\(646\) −3.00570 5.20602i −0.118258 0.204828i
\(647\) 9.01192 0.354295 0.177148 0.984184i \(-0.443313\pi\)
0.177148 + 0.984184i \(0.443313\pi\)
\(648\) 26.3411 + 2.81990i 1.03478 + 0.110776i
\(649\) −0.530027 −0.0208054
\(650\) 4.83046 0.515368i 0.189466 0.0202144i
\(651\) 2.17760 + 5.68102i 0.0853468 + 0.222657i
\(652\) 0.743272 + 0.429128i 0.0291088 + 0.0168060i
\(653\) −1.39222 + 2.41140i −0.0544820 + 0.0943655i −0.891980 0.452075i \(-0.850684\pi\)
0.837498 + 0.546440i \(0.184017\pi\)
\(654\) −6.51732 + 8.04030i −0.254848 + 0.314401i
\(655\) 15.4618 8.92688i 0.604143 0.348802i
\(656\) 26.5659i 1.03722i
\(657\) 19.0883 + 21.2408i 0.744705 + 0.828683i
\(658\) 47.5797i 1.85485i
\(659\) 24.3369 + 42.1528i 0.948033 + 1.64204i 0.749562 + 0.661934i \(0.230264\pi\)
0.198471 + 0.980107i \(0.436402\pi\)
\(660\) 0.405149 + 0.0643694i 0.0157704 + 0.00250557i
\(661\) −17.4542 10.0772i −0.678889 0.391957i 0.120547 0.992708i \(-0.461535\pi\)
−0.799436 + 0.600751i \(0.794868\pi\)
\(662\) 8.31923 14.4093i 0.323336 0.560035i
\(663\) −3.61632 2.34288i −0.140446 0.0909899i
\(664\) 4.19661 + 7.26874i 0.162860 + 0.282082i
\(665\) 30.4161i 1.17948i
\(666\) 31.0030 + 10.1065i 1.20134 + 0.391619i
\(667\) −23.4374 −0.907498
\(668\) 2.01466 1.16317i 0.0779497 0.0450043i
\(669\) −23.9091 19.3803i −0.924379 0.749285i
\(670\) −12.7422 7.35669i −0.492273 0.284214i
\(671\) −6.47666 3.73930i −0.250029 0.144354i
\(672\) −3.03655 7.92188i −0.117137 0.305593i
\(673\) −6.19480 10.7297i −0.238792 0.413600i 0.721576 0.692335i \(-0.243418\pi\)
−0.960368 + 0.278735i \(0.910085\pi\)
\(674\) 1.78745i 0.0688502i
\(675\) −0.264445 5.18942i −0.0101785 0.199741i
\(676\) 1.61221 + 1.77927i 0.0620080 + 0.0684336i
\(677\) −23.2146 40.2088i −0.892208 1.54535i −0.837223 0.546862i \(-0.815822\pi\)
−0.0549850 0.998487i \(-0.517511\pi\)
\(678\) 15.5849 5.97388i 0.598536 0.229425i
\(679\) 4.21094 7.29356i 0.161601 0.279901i
\(680\) −1.01548 + 1.75887i −0.0389420 + 0.0674495i
\(681\) 38.3346 + 31.0734i 1.46899 + 1.19073i
\(682\) 1.11740 0.645131i 0.0427875 0.0247034i
\(683\) 19.0750i 0.729884i 0.931030 + 0.364942i \(0.118911\pi\)
−0.931030 + 0.364942i \(0.881089\pi\)
\(684\) 3.50538 0.741563i 0.134032 0.0283544i
\(685\) 4.29750 0.164199
\(686\) −25.7452 44.5920i −0.982956 1.70253i
\(687\) −1.64490 + 10.3532i −0.0627570 + 0.395000i
\(688\) 19.5094 33.7913i 0.743789 1.28828i
\(689\) −15.8536 + 11.5564i −0.603975 + 0.440263i
\(690\) 9.70065 + 1.54122i 0.369297 + 0.0586734i
\(691\) −14.9252 + 8.61704i −0.567779 + 0.327808i −0.756262 0.654269i \(-0.772976\pi\)
0.188483 + 0.982077i \(0.439643\pi\)
\(692\) −4.00584 −0.152279
\(693\) 3.74521 + 17.7037i 0.142269 + 0.672507i
\(694\) 34.1964i 1.29808i
\(695\) −0.133706 + 0.0771951i −0.00507175 + 0.00292818i
\(696\) −22.0541 17.8767i −0.835958 0.677613i
\(697\) 4.41380 + 2.54831i 0.167185 + 0.0965242i
\(698\) 8.89404 15.4049i 0.336645 0.583085i
\(699\) 5.42453 + 14.1518i 0.205175 + 0.535269i
\(700\) −0.752363 + 0.434377i −0.0284367 + 0.0164179i
\(701\) −37.1790 −1.40423 −0.702116 0.712063i \(-0.747761\pi\)
−0.702116 + 0.712063i \(0.747761\pi\)
\(702\) −19.6150 + 15.8879i −0.740319 + 0.599650i
\(703\) 52.1676 1.96754
\(704\) −9.54637 + 5.51160i −0.359792 + 0.207726i
\(705\) −4.65427 12.1423i −0.175290 0.457304i
\(706\) −6.29581 + 10.9047i −0.236946 + 0.410403i
\(707\) −15.1263 8.73319i −0.568884 0.328446i
\(708\) 0.102716 + 0.0832600i 0.00386032 + 0.00312910i
\(709\) 4.67297 2.69794i 0.175497 0.101323i −0.409678 0.912230i \(-0.634359\pi\)
0.585175 + 0.810907i \(0.301026\pi\)
\(710\) 7.81811i 0.293409i
\(711\) 13.8019 + 4.49922i 0.517612 + 0.168734i
\(712\) 31.6037 1.18440
\(713\) −2.72209 + 1.57160i −0.101943 + 0.0588570i
\(714\) −7.47995 1.18840i −0.279930 0.0444748i
\(715\) −3.73631 + 2.72356i −0.139730 + 0.101855i
\(716\) 1.43906 2.49252i 0.0537801 0.0931499i
\(717\) 7.65255 48.1661i 0.285790 1.79880i
\(718\) −19.9420 34.5406i −0.744229 1.28904i
\(719\) −13.0486 −0.486630 −0.243315 0.969947i \(-0.578235\pi\)
−0.243315 + 0.969947i \(0.578235\pi\)
\(720\) 7.21185 + 8.02510i 0.268770 + 0.299078i
\(721\) 49.8348i 1.85594i
\(722\) −26.6206 + 15.3694i −0.990715 + 0.571989i
\(723\) 3.94308 + 3.19619i 0.146645 + 0.118868i
\(724\) 2.18387 3.78258i 0.0811630 0.140578i
\(725\) −2.78420 + 4.82237i −0.103402 + 0.179098i
\(726\) −20.3862 + 7.81427i −0.756604 + 0.290015i
\(727\) 13.1337 + 22.7482i 0.487102 + 0.843685i 0.999890 0.0148298i \(-0.00472065\pi\)
−0.512788 + 0.858515i \(0.671387\pi\)
\(728\) 45.6362 + 20.2328i 1.69139 + 0.749878i
\(729\) 15.8070 + 21.8892i 0.585444 + 0.810713i
\(730\) 12.8255i 0.474693i
\(731\) 3.74284 + 6.48280i 0.138434 + 0.239775i
\(732\) 0.667748 + 1.74205i 0.0246807 + 0.0643880i
\(733\) 0.173348 + 0.100083i 0.00640277 + 0.00369664i 0.503198 0.864171i \(-0.332157\pi\)
−0.496795 + 0.867868i \(0.665490\pi\)
\(734\) 21.8617 + 12.6218i 0.806929 + 0.465881i
\(735\) −20.3509 16.4960i −0.750653 0.608466i
\(736\) 3.79582 2.19152i 0.139916 0.0807804i
\(737\) 14.0038 0.515838
\(738\) 22.2071 19.9566i 0.817453 0.734613i
\(739\) 18.4711i 0.679469i 0.940521 + 0.339734i \(0.110337\pi\)
−0.940521 + 0.339734i \(0.889663\pi\)
\(740\) −0.745014 1.29040i −0.0273873 0.0474361i
\(741\) −21.9572 + 33.8917i −0.806617 + 1.24504i
\(742\) −17.2417 + 29.8635i −0.632962 + 1.09632i
\(743\) −39.2169 22.6419i −1.43873 0.830651i −0.440969 0.897523i \(-0.645365\pi\)
−0.997762 + 0.0668712i \(0.978698\pi\)
\(744\) −3.76017 0.597409i −0.137854 0.0219021i
\(745\) 4.64667 + 8.04826i 0.170241 + 0.294865i
\(746\) 19.2112i 0.703372i
\(747\) −2.65126 + 8.13306i −0.0970045 + 0.297573i
\(748\) 0.163420i 0.00597521i
\(749\) −59.0806 + 34.1102i −2.15876 + 1.24636i
\(750\) 1.46949 1.81288i 0.0536580 0.0661969i
\(751\) 1.17321 2.03207i 0.0428112 0.0741511i −0.843826 0.536617i \(-0.819702\pi\)
0.886637 + 0.462466i \(0.153035\pi\)
\(752\) 23.3839 + 13.5007i 0.852724 + 0.492320i
\(753\) 9.15553 + 23.8854i 0.333646 + 0.870431i
\(754\) 26.8979 2.86977i 0.979564 0.104511i
\(755\) −7.09239 −0.258119
\(756\) 2.05521 4.01920i 0.0747471 0.146177i
\(757\) 16.5812 0.602655 0.301328 0.953521i \(-0.402570\pi\)
0.301328 + 0.953521i \(0.402570\pi\)
\(758\) −1.43427 2.48423i −0.0520951 0.0902313i
\(759\) −8.72933 + 3.34605i −0.316855 + 0.121454i
\(760\) 16.4839 + 9.51699i 0.597934 + 0.345217i
\(761\) −33.9243 19.5862i −1.22976 0.709999i −0.262776 0.964857i \(-0.584638\pi\)
−0.966979 + 0.254857i \(0.917972\pi\)
\(762\) 19.5033 + 15.8090i 0.706528 + 0.572699i
\(763\) 10.4307 + 18.0665i 0.377617 + 0.654051i
\(764\) 0.124714 0.00451198
\(765\) −2.02512 + 0.428414i −0.0732185 + 0.0154893i
\(766\) 16.4041 0.592703
\(767\) −1.48184 + 0.158100i −0.0535062 + 0.00570865i
\(768\) 7.51591 + 1.19412i 0.271207 + 0.0430889i
\(769\) 11.5984 + 6.69637i 0.418251 + 0.241477i 0.694329 0.719658i \(-0.255701\pi\)
−0.276078 + 0.961135i \(0.589035\pi\)
\(770\) −4.06344 + 7.03808i −0.146436 + 0.253635i
\(771\) −29.1565 4.63233i −1.05004 0.166829i
\(772\) −2.35000 + 1.35677i −0.0845785 + 0.0488314i
\(773\) 1.74544i 0.0627792i 0.999507 + 0.0313896i \(0.00999327\pi\)
−0.999507 + 0.0313896i \(0.990007\pi\)
\(774\) 42.9026 9.07603i 1.54210 0.326231i
\(775\) 0.746782i 0.0268252i
\(776\) 2.63515 + 4.56421i 0.0945964 + 0.163846i
\(777\) 41.3873 51.0587i 1.48476 1.83172i
\(778\) 29.7267 + 17.1627i 1.06575 + 0.615313i
\(779\) 23.8825 41.3656i 0.855678 1.48208i
\(780\) 1.15191 + 0.0591129i 0.0412450 + 0.00211658i
\(781\) 3.72055 + 6.44418i 0.133132 + 0.230591i
\(782\) 3.91283i 0.139922i
\(783\) −1.47253 28.8967i −0.0526240 1.03268i
\(784\) 54.3962 1.94272
\(785\) 11.6401 6.72039i 0.415451 0.239861i
\(786\) −38.9042 + 14.9124i −1.38767 + 0.531909i
\(787\) −6.26287 3.61587i −0.223247 0.128892i 0.384206 0.923248i \(-0.374475\pi\)
−0.607453 + 0.794356i \(0.707809\pi\)
\(788\) 0.418482 + 0.241611i 0.0149078 + 0.00860702i
\(789\) 13.3230 16.4363i 0.474310 0.585147i
\(790\) 3.25981 + 5.64616i 0.115979 + 0.200881i
\(791\) 33.6416i 1.19616i
\(792\) −10.7663 3.50966i −0.382564 0.124710i
\(793\) −19.2227 8.52239i −0.682620 0.302639i
\(794\) 12.5234 + 21.6912i 0.444440 + 0.769792i
\(795\) −1.47879 + 9.30771i −0.0524474 + 0.330110i
\(796\) −2.39714 + 4.15196i −0.0849643 + 0.147162i
\(797\) −0.166846 + 0.288986i −0.00590999 + 0.0102364i −0.868965 0.494873i \(-0.835215\pi\)
0.863055 + 0.505109i \(0.168548\pi\)
\(798\) −11.1376 + 70.1012i −0.394265 + 2.48155i
\(799\) −4.48616 + 2.59009i −0.158709 + 0.0916307i
\(800\) 1.04135i 0.0368172i
\(801\) 21.5297 + 23.9576i 0.760716 + 0.846500i
\(802\) −4.70481 −0.166133
\(803\) −6.10351 10.5716i −0.215388 0.373063i
\(804\) −2.71387 2.19981i −0.0957108 0.0775814i
\(805\) 9.89893 17.1454i 0.348891 0.604298i
\(806\) 2.93158 2.13696i 0.103261 0.0752710i
\(807\) 8.86341 + 23.1233i 0.312007 + 0.813977i
\(808\) 9.46586 5.46511i 0.333008 0.192262i
\(809\) −21.5481 −0.757589 −0.378795 0.925481i \(-0.623661\pi\)
−0.378795 + 0.925481i \(0.623661\pi\)
\(810\) −1.29075 + 12.0571i −0.0453524 + 0.423643i
\(811\) 38.3145i 1.34540i 0.739913 + 0.672702i \(0.234867\pi\)
−0.739913 + 0.672702i \(0.765133\pi\)
\(812\) −4.18946 + 2.41878i −0.147021 + 0.0848826i
\(813\) 6.21816 2.38349i 0.218081 0.0835927i
\(814\) −12.0712 6.96933i −0.423097 0.244275i
\(815\) −2.32343 + 4.02430i −0.0813862 + 0.140965i
\(816\) 2.70650 3.33895i 0.0947463 0.116887i
\(817\) 60.7560 35.0775i 2.12558 1.22721i
\(818\) −9.78837 −0.342242
\(819\) 15.7516 + 48.3786i 0.550404 + 1.69048i
\(820\) −1.36428 −0.0476427
\(821\) 2.80704 1.62065i 0.0979665 0.0565610i −0.450216 0.892920i \(-0.648653\pi\)
0.548183 + 0.836359i \(0.315320\pi\)
\(822\) −9.90463 1.57363i −0.345464 0.0548867i
\(823\) −10.2808 + 17.8069i −0.358367 + 0.620711i −0.987688 0.156435i \(-0.950000\pi\)
0.629321 + 0.777146i \(0.283333\pi\)
\(824\) −27.0078 15.5930i −0.940862 0.543207i
\(825\) −0.348515 + 2.19360i −0.0121337 + 0.0763713i
\(826\) −2.26847 + 1.30970i −0.0789302 + 0.0455704i
\(827\) 15.8002i 0.549426i −0.961526 0.274713i \(-0.911417\pi\)
0.961526 0.274713i \(-0.0885828\pi\)
\(828\) 2.21732 + 0.722813i 0.0770571 + 0.0251195i
\(829\) −36.2323 −1.25840 −0.629201 0.777243i \(-0.716618\pi\)
−0.629201 + 0.777243i \(0.716618\pi\)
\(830\) −3.32712 + 1.92091i −0.115486 + 0.0666758i
\(831\) −29.5470 + 36.4516i −1.02497 + 1.26449i
\(832\) −25.0456 + 18.2568i −0.868300 + 0.632941i
\(833\) −5.21791 + 9.03768i −0.180790 + 0.313137i
\(834\) 0.336424 0.128955i 0.0116494 0.00446535i
\(835\) 6.29773 + 10.9080i 0.217942 + 0.377487i
\(836\) −1.53155 −0.0529697
\(837\) −2.10871 3.25742i −0.0728876 0.112593i
\(838\) 23.6648i 0.817486i
\(839\) 38.1830 22.0450i 1.31822 0.761077i 0.334781 0.942296i \(-0.391338\pi\)
0.983443 + 0.181219i \(0.0580043\pi\)
\(840\) 22.3923 8.58321i 0.772606 0.296149i
\(841\) −1.00350 + 1.73812i −0.0346035 + 0.0599350i
\(842\) −10.7502 + 18.6199i −0.370476 + 0.641683i
\(843\) −10.9179 8.84984i −0.376032 0.304805i
\(844\) −0.954119 1.65258i −0.0328421 0.0568842i
\(845\) −9.63353 + 8.72898i −0.331404 + 0.300286i
\(846\) 6.28071 + 29.6891i 0.215935 + 1.02073i
\(847\) 44.0057i 1.51205i
\(848\) −9.78464 16.9475i −0.336006 0.581979i
\(849\) 41.5424 + 6.60019i 1.42573 + 0.226518i
\(850\) −0.805086 0.464817i −0.0276142 0.0159431i
\(851\) 29.4067 + 16.9780i 1.00805 + 0.581997i
\(852\) 0.291271 1.83329i 0.00997877 0.0628076i
\(853\) −24.3692 + 14.0696i −0.834386 + 0.481733i −0.855352 0.518047i \(-0.826659\pi\)
0.0209659 + 0.999780i \(0.493326\pi\)
\(854\) −36.9594 −1.26472
\(855\) 4.01504 + 18.9792i 0.137312 + 0.649075i
\(856\) 42.6914i 1.45916i
\(857\) 22.0174 + 38.1353i 0.752100 + 1.30268i 0.946803 + 0.321813i \(0.104292\pi\)
−0.194703 + 0.980862i \(0.562374\pi\)
\(858\) 9.60852 4.90896i 0.328029 0.167589i
\(859\) 1.83197 3.17306i 0.0625060 0.108263i −0.833079 0.553154i \(-0.813424\pi\)
0.895585 + 0.444891i \(0.146757\pi\)
\(860\) −1.73533 1.00189i −0.0591744 0.0341643i
\(861\) −21.5392 56.1924i −0.734053 1.91503i
\(862\) −1.59280 2.75881i −0.0542510 0.0939654i
\(863\) 27.1013i 0.922539i −0.887260 0.461269i \(-0.847394\pi\)
0.887260 0.461269i \(-0.152606\pi\)
\(864\) 2.94048 + 4.54231i 0.100037 + 0.154532i
\(865\) 21.6888i 0.737441i
\(866\) −18.5789 + 10.7266i −0.631338 + 0.364503i
\(867\) −10.2437 26.7243i −0.347895 0.907604i
\(868\) −0.324385 + 0.561851i −0.0110103 + 0.0190705i
\(869\) −5.37388 3.10261i −0.182296 0.105249i
\(870\) 8.18267 10.0948i 0.277419 0.342246i
\(871\) 39.1518 4.17715i 1.32661 0.141537i
\(872\) −13.0548 −0.442091
\(873\) −1.66479 + 5.10694i −0.0563446 + 0.172844i
\(874\) −36.6705 −1.24040
\(875\) −2.35185 4.07352i −0.0795070 0.137710i
\(876\) −0.477826 + 3.00749i −0.0161442 + 0.101614i
\(877\) −21.1948 12.2368i −0.715697 0.413208i 0.0974701 0.995238i \(-0.468925\pi\)
−0.813167 + 0.582031i \(0.802258\pi\)
\(878\) 28.6486 + 16.5403i 0.966843 + 0.558207i
\(879\) −7.16291 + 45.0843i −0.241599 + 1.52065i
\(880\) −2.30600 3.99411i −0.0777352 0.134641i
\(881\) 39.3187 1.32468 0.662341 0.749203i \(-0.269563\pi\)
0.662341 + 0.749203i \(0.269563\pi\)
\(882\) 40.8630 + 45.4711i 1.37593 + 1.53109i
\(883\) −19.4346 −0.654027 −0.327014 0.945020i \(-0.606042\pi\)
−0.327014 + 0.945020i \(0.606042\pi\)
\(884\) −0.0487458 0.456887i −0.00163950 0.0153668i
\(885\) −0.450795 + 0.556137i −0.0151533 + 0.0186943i
\(886\) 25.5166 + 14.7320i 0.857248 + 0.494932i
\(887\) 18.3946 31.8604i 0.617631 1.06977i −0.372285 0.928118i \(-0.621426\pi\)
0.989917 0.141650i \(-0.0452409\pi\)
\(888\) 14.7213 + 38.4057i 0.494015 + 1.28881i
\(889\) 43.8237 25.3016i 1.46980 0.848589i
\(890\) 14.4659i 0.484899i
\(891\) −4.67391 10.5525i −0.156582 0.353521i
\(892\) 3.28191i 0.109887i
\(893\) 24.2740 + 42.0438i 0.812298 + 1.40694i
\(894\) −7.76230 20.2506i −0.259610 0.677283i
\(895\) 13.4953 + 7.79150i 0.451097 + 0.260441i
\(896\) −22.3403 + 38.6945i −0.746335 + 1.29269i
\(897\) −23.4073 + 11.9587i −0.781546 + 0.399289i
\(898\) 8.89447 + 15.4057i 0.296812 + 0.514094i
\(899\) 4.15838i 0.138690i
\(900\) 0.412125 0.370360i 0.0137375 0.0123453i
\(901\) 3.75433 0.125075
\(902\) −11.0525 + 6.38116i −0.368008 + 0.212469i
\(903\) 13.8690 87.2934i 0.461533 2.90494i
\(904\) 18.2320 + 10.5262i 0.606387 + 0.350097i
\(905\) 20.4800 + 11.8241i 0.680779 + 0.393048i
\(906\) 16.3461 + 2.59705i 0.543064 + 0.0862811i
\(907\) 7.55603 + 13.0874i 0.250894 + 0.434561i 0.963772 0.266727i \(-0.0859421\pi\)
−0.712878 + 0.701288i \(0.752609\pi\)
\(908\) 5.26205i 0.174627i
\(909\) 10.5914 + 3.45265i 0.351296 + 0.114517i
\(910\) −9.26115 + 20.8891i −0.307004 + 0.692466i
\(911\) 1.15976 + 2.00877i 0.0384247 + 0.0665535i 0.884598 0.466354i \(-0.154433\pi\)
−0.846174 + 0.532907i \(0.821099\pi\)
\(912\) −31.2923 25.3649i −1.03619 0.839917i
\(913\) 1.82828 3.16667i 0.0605072 0.104802i
\(914\) −11.1367 + 19.2893i −0.368368 + 0.638032i
\(915\) −9.43199 + 3.61539i −0.311812 + 0.119521i
\(916\) −0.968091 + 0.558928i −0.0319866 + 0.0184675i
\(917\) 83.9787i 2.77322i
\(918\) 4.82426 0.245837i 0.159224 0.00811382i
\(919\) −2.41646 −0.0797116 −0.0398558 0.999205i \(-0.512690\pi\)
−0.0398558 + 0.999205i \(0.512690\pi\)
\(920\) 6.19462 + 10.7294i 0.204230 + 0.353738i
\(921\) −28.8417 + 11.0553i −0.950366 + 0.364286i
\(922\) 23.4712 40.6533i 0.772983 1.33885i
\(923\) 12.3241 + 16.9068i 0.405652 + 0.556493i
\(924\) −1.21506 + 1.49900i −0.0399725 + 0.0493133i
\(925\) 6.98663 4.03373i 0.229719 0.132628i
\(926\) −43.6124 −1.43319
\(927\) −6.57839 31.0962i −0.216063 1.02133i
\(928\) 5.79864i 0.190350i
\(929\) −14.6055 + 8.43250i −0.479191 + 0.276661i −0.720079 0.693892i \(-0.755895\pi\)
0.240888 + 0.970553i \(0.422561\pi\)
\(930\) 0.273452 1.72114i 0.00896684 0.0564384i
\(931\) 84.7000 + 48.9016i 2.77593 + 1.60268i
\(932\) −0.808063 + 1.39961i −0.0264690 + 0.0458456i
\(933\) 42.6514 + 6.77639i 1.39634 + 0.221849i
\(934\) 9.51929 5.49596i 0.311481 0.179833i
\(935\) 0.884803 0.0289362
\(936\) −31.1472 6.60082i −1.01808 0.215755i
\(937\) 7.73841 0.252803 0.126401 0.991979i \(-0.459657\pi\)
0.126401 + 0.991979i \(0.459657\pi\)
\(938\) 59.9353 34.6036i 1.95696 1.12985i
\(939\) −1.21357 + 1.49716i −0.0396033 + 0.0488579i
\(940\) 0.693322 1.20087i 0.0226137 0.0391680i
\(941\) 50.6505 + 29.2431i 1.65116 + 0.953298i 0.976596 + 0.215082i \(0.0690018\pi\)
0.674564 + 0.738216i \(0.264332\pi\)
\(942\) −29.2881 + 11.2265i −0.954259 + 0.365778i
\(943\) 26.9249 15.5451i 0.876797 0.506219i
\(944\) 1.48651i 0.0483818i
\(945\) 21.7612 + 11.1275i 0.707890 + 0.361978i
\(946\) −18.7447 −0.609443
\(947\) 4.70833 2.71836i 0.153000 0.0883347i −0.421545 0.906807i \(-0.638512\pi\)
0.574546 + 0.818473i \(0.305179\pi\)
\(948\) 0.554051 + 1.44543i 0.0179947 + 0.0469455i
\(949\) −20.2175 27.7353i −0.656287 0.900327i
\(950\) −4.35621 + 7.54517i −0.141334 + 0.244798i
\(951\) −36.9969 29.9891i −1.19971 0.972462i
\(952\) −4.77653 8.27319i −0.154808 0.268136i
\(953\) −4.08765 −0.132412 −0.0662059 0.997806i \(-0.521089\pi\)
−0.0662059 + 0.997806i \(0.521089\pi\)
\(954\) 6.81647 20.9104i 0.220691 0.676998i
\(955\) 0.675237i 0.0218502i
\(956\) 4.50383 2.60029i 0.145664 0.0840994i
\(957\) −1.94067 + 12.2148i −0.0627330 + 0.394849i
\(958\) 12.4377 21.5427i 0.401842 0.696011i
\(959\) −10.1071 + 17.5060i −0.326375 + 0.565297i
\(960\) −2.33620 + 14.7043i −0.0754006 + 0.474580i
\(961\) −15.2212 26.3638i −0.491005 0.850446i
\(962\) −35.8275 15.8841i −1.15512 0.512124i
\(963\) 32.3628 29.0832i 1.04288 0.937192i
\(964\) 0.541253i 0.0174326i
\(965\) −7.34599 12.7236i −0.236476 0.409588i
\(966\) −29.0927 + 35.8911i −0.936041 + 1.15478i
\(967\) −22.6264 13.0634i −0.727616 0.420089i 0.0899337 0.995948i \(-0.471334\pi\)
−0.817549 + 0.575859i \(0.804668\pi\)
\(968\) −23.8488 13.7691i −0.766528 0.442555i
\(969\) 7.21595 2.76595i 0.231810 0.0888553i
\(970\) −2.08918 + 1.20619i −0.0670794 + 0.0387283i
\(971\) 17.6665 0.566945 0.283473 0.958980i \(-0.408513\pi\)
0.283473 + 0.958980i \(0.408513\pi\)
\(972\) −0.751870 + 2.77922i −0.0241162 + 0.0891435i
\(973\) 0.726205i 0.0232811i
\(974\) −24.6071 42.6207i −0.788462 1.36566i
\(975\) −0.320055 + 6.23679i −0.0102500 + 0.199737i
\(976\) 10.4872 18.1644i 0.335688 0.581428i
\(977\) −4.95084 2.85837i −0.158391 0.0914473i 0.418709 0.908120i \(-0.362483\pi\)
−0.577101 + 0.816673i \(0.695816\pi\)
\(978\) 6.82850 8.42419i 0.218351 0.269376i
\(979\) −6.88417 11.9237i −0.220019 0.381084i
\(980\) 2.79349i 0.0892347i
\(981\) −8.89346 9.89635i −0.283946 0.315966i
\(982\) 33.2715i 1.06173i
\(983\) 23.1189 13.3477i 0.737380 0.425726i −0.0837361 0.996488i \(-0.526685\pi\)
0.821116 + 0.570762i \(0.193352\pi\)
\(984\) 37.1928 + 5.90913i 1.18566 + 0.188376i
\(985\) −1.30815 + 2.26579i −0.0416812 + 0.0721940i
\(986\) −4.48304 2.58828i −0.142769 0.0824277i
\(987\) 60.4080 + 9.59752i 1.92281 + 0.305492i
\(988\) −4.28189 + 0.456840i −0.136225 + 0.0145340i
\(989\) 45.6639 1.45203
\(990\) 1.60647 4.92806i 0.0510571 0.156624i
\(991\) 16.9888 0.539668 0.269834 0.962907i \(-0.413031\pi\)
0.269834 + 0.962907i \(0.413031\pi\)
\(992\) −0.388830 0.673474i −0.0123454 0.0213828i
\(993\) 16.6162 + 13.4688i 0.527300 + 0.427420i
\(994\) 31.8473 + 18.3870i 1.01013 + 0.583201i
\(995\) −22.4800 12.9788i −0.712664 0.411457i
\(996\) −0.851752 + 0.326486i −0.0269888 + 0.0103451i
\(997\) −6.32338 10.9524i −0.200263 0.346867i 0.748350 0.663304i \(-0.230846\pi\)
−0.948613 + 0.316438i \(0.897513\pi\)
\(998\) −9.41034 −0.297879
\(999\) −19.0851 + 37.3232i −0.603827 + 1.18085i
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 585.2.bt.b.571.39 yes 108
9.7 even 3 inner 585.2.bt.b.376.16 108
13.12 even 2 inner 585.2.bt.b.571.16 yes 108
117.25 even 6 inner 585.2.bt.b.376.39 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.bt.b.376.16 108 9.7 even 3 inner
585.2.bt.b.376.39 yes 108 117.25 even 6 inner
585.2.bt.b.571.16 yes 108 13.12 even 2 inner
585.2.bt.b.571.39 yes 108 1.1 even 1 trivial