Properties

Label 1755.2.i.f.586.6
Level $1755$
Weight $2$
Character 1755.586
Analytic conductor $14.014$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1755,2,Mod(586,1755)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1755, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1755.586");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.i (of order \(3\), degree \(2\), not 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: \(14.0137455547\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + 326 x^{7} + 551 x^{6} + 859 x^{5} + 1118 x^{4} + 1215 x^{3} + 1103 x^{2} + \cdots + 268 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 585)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 586.6
Root \(-0.317019 - 1.12493i\) of defining polynomial
Character \(\chi\) \(=\) 1755.586
Dual form 1755.2.i.f.1171.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.817019 - 1.41512i) q^{2} +(-0.335039 - 0.580304i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.06506 + 1.84473i) q^{7} +2.17314 q^{8} +O(q^{10})\) \(q+(0.817019 - 1.41512i) q^{2} +(-0.335039 - 0.580304i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.06506 + 1.84473i) q^{7} +2.17314 q^{8} -1.63404 q^{10} +(-0.0263229 + 0.0455925i) q^{11} +(0.500000 + 0.866025i) q^{13} +(1.74034 + 3.01437i) q^{14} +(2.44558 - 4.23586i) q^{16} +2.48047 q^{17} +2.13105 q^{19} +(-0.335039 + 0.580304i) q^{20} +(0.0430125 + 0.0744999i) q^{22} +(2.46542 + 4.27023i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.63404 q^{26} +1.42734 q^{28} +(-1.24347 + 2.15375i) q^{29} +(4.08030 + 7.06728i) q^{31} +(-1.82302 - 3.15756i) q^{32} +(2.02659 - 3.51016i) q^{34} +2.13012 q^{35} -1.11963 q^{37} +(1.74110 - 3.01568i) q^{38} +(-1.08657 - 1.88200i) q^{40} +(-2.73708 - 4.74077i) q^{41} +(4.73861 - 8.20752i) q^{43} +0.0352767 q^{44} +8.05716 q^{46} +(4.88280 - 8.45726i) q^{47} +(1.23130 + 2.13268i) q^{49} +(0.817019 + 1.41512i) q^{50} +(0.335039 - 0.580304i) q^{52} +3.64091 q^{53} +0.0526457 q^{55} +(-2.31452 + 4.00887i) q^{56} +(2.03187 + 3.51931i) q^{58} +(3.74544 + 6.48728i) q^{59} +(2.89202 - 5.00912i) q^{61} +13.3347 q^{62} +3.82454 q^{64} +(0.500000 - 0.866025i) q^{65} +(3.11795 + 5.40045i) q^{67} +(-0.831054 - 1.43943i) q^{68} +(1.74034 - 3.01437i) q^{70} -2.50050 q^{71} -1.10245 q^{73} +(-0.914759 + 1.58441i) q^{74} +(-0.713983 - 1.23666i) q^{76} +(-0.0560707 - 0.0971174i) q^{77} +(7.80779 - 13.5235i) q^{79} -4.89115 q^{80} -8.94500 q^{82} +(0.244576 - 0.423618i) q^{83} +(-1.24024 - 2.14815i) q^{85} +(-7.74307 - 13.4114i) q^{86} +(-0.0572033 + 0.0990790i) q^{88} +4.64901 q^{89} -2.13012 q^{91} +(1.65202 - 2.86138i) q^{92} +(-7.97868 - 13.8195i) q^{94} +(-1.06552 - 1.84554i) q^{95} +(-3.67049 + 6.35747i) q^{97} +4.02399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.817019 1.41512i 0.577719 1.00064i −0.418021 0.908437i \(-0.637276\pi\)
0.995740 0.0922020i \(-0.0293905\pi\)
\(3\) 0 0
\(4\) −0.335039 0.580304i −0.167519 0.290152i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −1.06506 + 1.84473i −0.402554 + 0.697244i −0.994033 0.109076i \(-0.965211\pi\)
0.591479 + 0.806320i \(0.298544\pi\)
\(8\) 2.17314 0.768322
\(9\) 0 0
\(10\) −1.63404 −0.516728
\(11\) −0.0263229 + 0.0455925i −0.00793664 + 0.0137467i −0.869966 0.493111i \(-0.835860\pi\)
0.862030 + 0.506858i \(0.169193\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i
\(14\) 1.74034 + 3.01437i 0.465127 + 0.805623i
\(15\) 0 0
\(16\) 2.44558 4.23586i 0.611394 1.05897i
\(17\) 2.48047 0.601603 0.300801 0.953687i \(-0.402746\pi\)
0.300801 + 0.953687i \(0.402746\pi\)
\(18\) 0 0
\(19\) 2.13105 0.488895 0.244448 0.969662i \(-0.421393\pi\)
0.244448 + 0.969662i \(0.421393\pi\)
\(20\) −0.335039 + 0.580304i −0.0749170 + 0.129760i
\(21\) 0 0
\(22\) 0.0430125 + 0.0744999i 0.00917030 + 0.0158834i
\(23\) 2.46542 + 4.27023i 0.514075 + 0.890404i 0.999867 + 0.0163291i \(0.00519795\pi\)
−0.485792 + 0.874074i \(0.661469\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.63404 0.320461
\(27\) 0 0
\(28\) 1.42734 0.269743
\(29\) −1.24347 + 2.15375i −0.230906 + 0.399941i −0.958075 0.286517i \(-0.907502\pi\)
0.727169 + 0.686459i \(0.240836\pi\)
\(30\) 0 0
\(31\) 4.08030 + 7.06728i 0.732843 + 1.26932i 0.955663 + 0.294462i \(0.0951404\pi\)
−0.222820 + 0.974860i \(0.571526\pi\)
\(32\) −1.82302 3.15756i −0.322267 0.558183i
\(33\) 0 0
\(34\) 2.02659 3.51016i 0.347558 0.601987i
\(35\) 2.13012 0.360055
\(36\) 0 0
\(37\) −1.11963 −0.184066 −0.0920331 0.995756i \(-0.529337\pi\)
−0.0920331 + 0.995756i \(0.529337\pi\)
\(38\) 1.74110 3.01568i 0.282444 0.489208i
\(39\) 0 0
\(40\) −1.08657 1.88200i −0.171802 0.297570i
\(41\) −2.73708 4.74077i −0.427461 0.740384i 0.569186 0.822209i \(-0.307258\pi\)
−0.996647 + 0.0818250i \(0.973925\pi\)
\(42\) 0 0
\(43\) 4.73861 8.20752i 0.722632 1.25163i −0.237310 0.971434i \(-0.576266\pi\)
0.959941 0.280201i \(-0.0904010\pi\)
\(44\) 0.0352767 0.00531816
\(45\) 0 0
\(46\) 8.05716 1.18796
\(47\) 4.88280 8.45726i 0.712230 1.23362i −0.251789 0.967782i \(-0.581019\pi\)
0.964018 0.265836i \(-0.0856479\pi\)
\(48\) 0 0
\(49\) 1.23130 + 2.13268i 0.175900 + 0.304668i
\(50\) 0.817019 + 1.41512i 0.115544 + 0.200128i
\(51\) 0 0
\(52\) 0.335039 0.580304i 0.0464615 0.0804737i
\(53\) 3.64091 0.500118 0.250059 0.968231i \(-0.419550\pi\)
0.250059 + 0.968231i \(0.419550\pi\)
\(54\) 0 0
\(55\) 0.0526457 0.00709875
\(56\) −2.31452 + 4.00887i −0.309291 + 0.535708i
\(57\) 0 0
\(58\) 2.03187 + 3.51931i 0.266798 + 0.462108i
\(59\) 3.74544 + 6.48728i 0.487614 + 0.844572i 0.999899 0.0142434i \(-0.00453397\pi\)
−0.512284 + 0.858816i \(0.671201\pi\)
\(60\) 0 0
\(61\) 2.89202 5.00912i 0.370285 0.641352i −0.619324 0.785135i \(-0.712593\pi\)
0.989609 + 0.143783i \(0.0459267\pi\)
\(62\) 13.3347 1.69351
\(63\) 0 0
\(64\) 3.82454 0.478067
\(65\) 0.500000 0.866025i 0.0620174 0.107417i
\(66\) 0 0
\(67\) 3.11795 + 5.40045i 0.380919 + 0.659770i 0.991194 0.132419i \(-0.0422745\pi\)
−0.610275 + 0.792189i \(0.708941\pi\)
\(68\) −0.831054 1.43943i −0.100780 0.174556i
\(69\) 0 0
\(70\) 1.74034 3.01437i 0.208011 0.360286i
\(71\) −2.50050 −0.296755 −0.148377 0.988931i \(-0.547405\pi\)
−0.148377 + 0.988931i \(0.547405\pi\)
\(72\) 0 0
\(73\) −1.10245 −0.129032 −0.0645159 0.997917i \(-0.520550\pi\)
−0.0645159 + 0.997917i \(0.520550\pi\)
\(74\) −0.914759 + 1.58441i −0.106339 + 0.184184i
\(75\) 0 0
\(76\) −0.713983 1.23666i −0.0818995 0.141854i
\(77\) −0.0560707 0.0971174i −0.00638985 0.0110676i
\(78\) 0 0
\(79\) 7.80779 13.5235i 0.878445 1.52151i 0.0253969 0.999677i \(-0.491915\pi\)
0.853048 0.521833i \(-0.174752\pi\)
\(80\) −4.89115 −0.546847
\(81\) 0 0
\(82\) −8.94500 −0.987810
\(83\) 0.244576 0.423618i 0.0268457 0.0464981i −0.852290 0.523069i \(-0.824787\pi\)
0.879136 + 0.476571i \(0.158120\pi\)
\(84\) 0 0
\(85\) −1.24024 2.14815i −0.134522 0.233000i
\(86\) −7.74307 13.4114i −0.834957 1.44619i
\(87\) 0 0
\(88\) −0.0572033 + 0.0990790i −0.00609789 + 0.0105619i
\(89\) 4.64901 0.492794 0.246397 0.969169i \(-0.420753\pi\)
0.246397 + 0.969169i \(0.420753\pi\)
\(90\) 0 0
\(91\) −2.13012 −0.223297
\(92\) 1.65202 2.86138i 0.172235 0.298320i
\(93\) 0 0
\(94\) −7.97868 13.8195i −0.822938 1.42537i
\(95\) −1.06552 1.84554i −0.109320 0.189348i
\(96\) 0 0
\(97\) −3.67049 + 6.35747i −0.372682 + 0.645503i −0.989977 0.141228i \(-0.954895\pi\)
0.617296 + 0.786731i \(0.288228\pi\)
\(98\) 4.02399 0.406484
\(99\) 0 0
\(100\) 0.670078 0.0670078
\(101\) 0.276429 0.478790i 0.0275058 0.0476414i −0.851945 0.523632i \(-0.824577\pi\)
0.879451 + 0.475990i \(0.157910\pi\)
\(102\) 0 0
\(103\) 3.91898 + 6.78787i 0.386148 + 0.668828i 0.991928 0.126804i \(-0.0404720\pi\)
−0.605780 + 0.795633i \(0.707139\pi\)
\(104\) 1.08657 + 1.88200i 0.106547 + 0.184545i
\(105\) 0 0
\(106\) 2.97469 5.15232i 0.288928 0.500437i
\(107\) −19.4173 −1.87714 −0.938572 0.345084i \(-0.887851\pi\)
−0.938572 + 0.345084i \(0.887851\pi\)
\(108\) 0 0
\(109\) −2.13502 −0.204498 −0.102249 0.994759i \(-0.532604\pi\)
−0.102249 + 0.994759i \(0.532604\pi\)
\(110\) 0.0430125 0.0744999i 0.00410108 0.00710328i
\(111\) 0 0
\(112\) 5.20936 + 9.02288i 0.492238 + 0.852582i
\(113\) −3.11765 5.39992i −0.293283 0.507982i 0.681301 0.732004i \(-0.261415\pi\)
−0.974584 + 0.224022i \(0.928081\pi\)
\(114\) 0 0
\(115\) 2.46542 4.27023i 0.229901 0.398201i
\(116\) 1.66644 0.154725
\(117\) 0 0
\(118\) 12.2404 1.12682
\(119\) −2.64185 + 4.57581i −0.242178 + 0.419464i
\(120\) 0 0
\(121\) 5.49861 + 9.52388i 0.499874 + 0.865807i
\(122\) −4.72567 8.18509i −0.427842 0.741043i
\(123\) 0 0
\(124\) 2.73412 4.73563i 0.245531 0.425272i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −10.6036 −0.940918 −0.470459 0.882422i \(-0.655912\pi\)
−0.470459 + 0.882422i \(0.655912\pi\)
\(128\) 6.77076 11.7273i 0.598456 1.03656i
\(129\) 0 0
\(130\) −0.817019 1.41512i −0.0716573 0.124114i
\(131\) −8.09616 14.0230i −0.707365 1.22519i −0.965831 0.259171i \(-0.916551\pi\)
0.258467 0.966020i \(-0.416783\pi\)
\(132\) 0 0
\(133\) −2.26969 + 3.93121i −0.196807 + 0.340880i
\(134\) 10.1897 0.880256
\(135\) 0 0
\(136\) 5.39042 0.462224
\(137\) −10.3843 + 17.9861i −0.887189 + 1.53666i −0.0440058 + 0.999031i \(0.514012\pi\)
−0.843184 + 0.537626i \(0.819321\pi\)
\(138\) 0 0
\(139\) 1.25038 + 2.16571i 0.106055 + 0.183693i 0.914169 0.405333i \(-0.132845\pi\)
−0.808113 + 0.589027i \(0.799511\pi\)
\(140\) −0.713672 1.23612i −0.0603163 0.104471i
\(141\) 0 0
\(142\) −2.04295 + 3.53850i −0.171441 + 0.296944i
\(143\) −0.0526457 −0.00440245
\(144\) 0 0
\(145\) 2.48694 0.206529
\(146\) −0.900721 + 1.56009i −0.0745442 + 0.129114i
\(147\) 0 0
\(148\) 0.375120 + 0.649727i 0.0308347 + 0.0534072i
\(149\) −0.945127 1.63701i −0.0774279 0.134109i 0.824712 0.565553i \(-0.191337\pi\)
−0.902139 + 0.431444i \(0.858004\pi\)
\(150\) 0 0
\(151\) 2.44343 4.23214i 0.198843 0.344406i −0.749310 0.662219i \(-0.769615\pi\)
0.948154 + 0.317812i \(0.102948\pi\)
\(152\) 4.63107 0.375629
\(153\) 0 0
\(154\) −0.183243 −0.0147662
\(155\) 4.08030 7.06728i 0.327737 0.567658i
\(156\) 0 0
\(157\) 8.99989 + 15.5883i 0.718269 + 1.24408i 0.961685 + 0.274157i \(0.0883987\pi\)
−0.243416 + 0.969922i \(0.578268\pi\)
\(158\) −12.7582 22.0979i −1.01499 1.75801i
\(159\) 0 0
\(160\) −1.82302 + 3.15756i −0.144122 + 0.249627i
\(161\) −10.5032 −0.827772
\(162\) 0 0
\(163\) 9.41748 0.737634 0.368817 0.929502i \(-0.379763\pi\)
0.368817 + 0.929502i \(0.379763\pi\)
\(164\) −1.83406 + 3.17668i −0.143216 + 0.248057i
\(165\) 0 0
\(166\) −0.399646 0.692207i −0.0310185 0.0537257i
\(167\) −7.74523 13.4151i −0.599344 1.03809i −0.992918 0.118801i \(-0.962095\pi\)
0.393574 0.919293i \(-0.371238\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) −4.05318 −0.310865
\(171\) 0 0
\(172\) −6.35048 −0.484219
\(173\) −4.83831 + 8.38021i −0.367850 + 0.637135i −0.989229 0.146375i \(-0.953239\pi\)
0.621379 + 0.783510i \(0.286573\pi\)
\(174\) 0 0
\(175\) −1.06506 1.84473i −0.0805108 0.139449i
\(176\) 0.128749 + 0.223000i 0.00970482 + 0.0168092i
\(177\) 0 0
\(178\) 3.79832 6.57889i 0.284696 0.493109i
\(179\) 3.31630 0.247872 0.123936 0.992290i \(-0.460448\pi\)
0.123936 + 0.992290i \(0.460448\pi\)
\(180\) 0 0
\(181\) −22.6189 −1.68125 −0.840623 0.541621i \(-0.817811\pi\)
−0.840623 + 0.541621i \(0.817811\pi\)
\(182\) −1.74034 + 3.01437i −0.129003 + 0.223440i
\(183\) 0 0
\(184\) 5.35770 + 9.27981i 0.394975 + 0.684117i
\(185\) 0.559815 + 0.969629i 0.0411585 + 0.0712885i
\(186\) 0 0
\(187\) −0.0652931 + 0.113091i −0.00477470 + 0.00827003i
\(188\) −6.54371 −0.477249
\(189\) 0 0
\(190\) −3.48221 −0.252626
\(191\) 2.94105 5.09405i 0.212807 0.368593i −0.739785 0.672843i \(-0.765073\pi\)
0.952592 + 0.304251i \(0.0984061\pi\)
\(192\) 0 0
\(193\) 0.229769 + 0.397972i 0.0165392 + 0.0286467i 0.874177 0.485608i \(-0.161402\pi\)
−0.857637 + 0.514255i \(0.828069\pi\)
\(194\) 5.99771 + 10.3883i 0.430611 + 0.745840i
\(195\) 0 0
\(196\) 0.825068 1.42906i 0.0589335 0.102076i
\(197\) 2.31119 0.164665 0.0823326 0.996605i \(-0.473763\pi\)
0.0823326 + 0.996605i \(0.473763\pi\)
\(198\) 0 0
\(199\) 24.3734 1.72779 0.863893 0.503675i \(-0.168019\pi\)
0.863893 + 0.503675i \(0.168019\pi\)
\(200\) −1.08657 + 1.88200i −0.0768322 + 0.133077i
\(201\) 0 0
\(202\) −0.451696 0.782360i −0.0317812 0.0550467i
\(203\) −2.64873 4.58774i −0.185904 0.321996i
\(204\) 0 0
\(205\) −2.73708 + 4.74077i −0.191166 + 0.331110i
\(206\) 12.8075 0.892341
\(207\) 0 0
\(208\) 4.89115 0.339140
\(209\) −0.0560952 + 0.0971597i −0.00388019 + 0.00672068i
\(210\) 0 0
\(211\) −13.6969 23.7237i −0.942934 1.63321i −0.759836 0.650114i \(-0.774721\pi\)
−0.183097 0.983095i \(-0.558612\pi\)
\(212\) −1.21985 2.11284i −0.0837794 0.145110i
\(213\) 0 0
\(214\) −15.8643 + 27.4778i −1.08446 + 1.87834i
\(215\) −9.47722 −0.646341
\(216\) 0 0
\(217\) −17.3830 −1.18004
\(218\) −1.74435 + 3.02131i −0.118142 + 0.204629i
\(219\) 0 0
\(220\) −0.0176384 0.0305505i −0.00118918 0.00205972i
\(221\) 1.24024 + 2.14815i 0.0834273 + 0.144500i
\(222\) 0 0
\(223\) −12.6679 + 21.9415i −0.848307 + 1.46931i 0.0344101 + 0.999408i \(0.489045\pi\)
−0.882718 + 0.469904i \(0.844289\pi\)
\(224\) 7.76649 0.518920
\(225\) 0 0
\(226\) −10.1887 −0.677742
\(227\) −10.6209 + 18.3959i −0.704931 + 1.22098i 0.261785 + 0.965126i \(0.415689\pi\)
−0.966716 + 0.255850i \(0.917645\pi\)
\(228\) 0 0
\(229\) −6.11686 10.5947i −0.404214 0.700119i 0.590016 0.807392i \(-0.299121\pi\)
−0.994230 + 0.107273i \(0.965788\pi\)
\(230\) −4.02858 6.97771i −0.265637 0.460096i
\(231\) 0 0
\(232\) −2.70223 + 4.68040i −0.177410 + 0.307284i
\(233\) −11.4048 −0.747154 −0.373577 0.927599i \(-0.621869\pi\)
−0.373577 + 0.927599i \(0.621869\pi\)
\(234\) 0 0
\(235\) −9.76560 −0.637038
\(236\) 2.50973 4.34698i 0.163370 0.282965i
\(237\) 0 0
\(238\) 4.31687 + 7.47705i 0.279821 + 0.484665i
\(239\) 7.42854 + 12.8666i 0.480512 + 0.832272i 0.999750 0.0223581i \(-0.00711739\pi\)
−0.519238 + 0.854630i \(0.673784\pi\)
\(240\) 0 0
\(241\) 9.29538 16.1001i 0.598768 1.03710i −0.394235 0.919010i \(-0.628990\pi\)
0.993003 0.118087i \(-0.0376763\pi\)
\(242\) 17.9699 1.15515
\(243\) 0 0
\(244\) −3.87575 −0.248120
\(245\) 1.23130 2.13268i 0.0786650 0.136252i
\(246\) 0 0
\(247\) 1.06552 + 1.84554i 0.0677976 + 0.117429i
\(248\) 8.86707 + 15.3582i 0.563059 + 0.975247i
\(249\) 0 0
\(250\) 0.817019 1.41512i 0.0516728 0.0894999i
\(251\) −30.0723 −1.89815 −0.949073 0.315058i \(-0.897976\pi\)
−0.949073 + 0.315058i \(0.897976\pi\)
\(252\) 0 0
\(253\) −0.259587 −0.0163201
\(254\) −8.66334 + 15.0054i −0.543587 + 0.941520i
\(255\) 0 0
\(256\) −7.23913 12.5385i −0.452446 0.783659i
\(257\) 1.52032 + 2.63327i 0.0948348 + 0.164259i 0.909540 0.415617i \(-0.136434\pi\)
−0.814705 + 0.579876i \(0.803101\pi\)
\(258\) 0 0
\(259\) 1.19247 2.06542i 0.0740966 0.128339i
\(260\) −0.670078 −0.0415565
\(261\) 0 0
\(262\) −26.4588 −1.63463
\(263\) −2.40051 + 4.15780i −0.148022 + 0.256381i −0.930496 0.366301i \(-0.880624\pi\)
0.782474 + 0.622683i \(0.213957\pi\)
\(264\) 0 0
\(265\) −1.82046 3.15312i −0.111830 0.193695i
\(266\) 3.70875 + 6.42375i 0.227398 + 0.393865i
\(267\) 0 0
\(268\) 2.08927 3.61872i 0.127623 0.221049i
\(269\) 16.8723 1.02873 0.514363 0.857573i \(-0.328029\pi\)
0.514363 + 0.857573i \(0.328029\pi\)
\(270\) 0 0
\(271\) −2.34099 −0.142205 −0.0711026 0.997469i \(-0.522652\pi\)
−0.0711026 + 0.997469i \(0.522652\pi\)
\(272\) 6.06618 10.5069i 0.367816 0.637076i
\(273\) 0 0
\(274\) 16.9683 + 29.3900i 1.02509 + 1.77551i
\(275\) −0.0263229 0.0455925i −0.00158733 0.00274933i
\(276\) 0 0
\(277\) 1.88617 3.26693i 0.113329 0.196291i −0.803782 0.594924i \(-0.797182\pi\)
0.917110 + 0.398633i \(0.130515\pi\)
\(278\) 4.08632 0.245081
\(279\) 0 0
\(280\) 4.62905 0.276638
\(281\) 5.47798 9.48813i 0.326789 0.566015i −0.655084 0.755556i \(-0.727367\pi\)
0.981873 + 0.189541i \(0.0607001\pi\)
\(282\) 0 0
\(283\) −8.78483 15.2158i −0.522204 0.904484i −0.999666 0.0258318i \(-0.991777\pi\)
0.477462 0.878652i \(-0.341557\pi\)
\(284\) 0.837764 + 1.45105i 0.0497122 + 0.0861040i
\(285\) 0 0
\(286\) −0.0430125 + 0.0744999i −0.00254338 + 0.00440527i
\(287\) 11.6606 0.688305
\(288\) 0 0
\(289\) −10.8473 −0.638074
\(290\) 2.03187 3.51931i 0.119316 0.206661i
\(291\) 0 0
\(292\) 0.369363 + 0.639756i 0.0216153 + 0.0374389i
\(293\) 12.2723 + 21.2562i 0.716953 + 1.24180i 0.962202 + 0.272338i \(0.0877969\pi\)
−0.245249 + 0.969460i \(0.578870\pi\)
\(294\) 0 0
\(295\) 3.74544 6.48728i 0.218068 0.377704i
\(296\) −2.43312 −0.141422
\(297\) 0 0
\(298\) −3.08875 −0.178926
\(299\) −2.46542 + 4.27023i −0.142579 + 0.246954i
\(300\) 0 0
\(301\) 10.0938 + 17.4830i 0.581797 + 1.00770i
\(302\) −3.99265 6.91547i −0.229751 0.397941i
\(303\) 0 0
\(304\) 5.21163 9.02681i 0.298908 0.517723i
\(305\) −5.78404 −0.331193
\(306\) 0 0
\(307\) −11.0689 −0.631735 −0.315868 0.948803i \(-0.602296\pi\)
−0.315868 + 0.948803i \(0.602296\pi\)
\(308\) −0.0375718 + 0.0650762i −0.00214085 + 0.00370806i
\(309\) 0 0
\(310\) −6.66736 11.5482i −0.378680 0.655894i
\(311\) 7.39666 + 12.8114i 0.419426 + 0.726468i 0.995882 0.0906608i \(-0.0288979\pi\)
−0.576456 + 0.817129i \(0.695565\pi\)
\(312\) 0 0
\(313\) −13.5262 + 23.4281i −0.764548 + 1.32424i 0.175937 + 0.984401i \(0.443704\pi\)
−0.940485 + 0.339834i \(0.889629\pi\)
\(314\) 29.4123 1.65983
\(315\) 0 0
\(316\) −10.4636 −0.588626
\(317\) 0.288999 0.500561i 0.0162318 0.0281143i −0.857795 0.513991i \(-0.828166\pi\)
0.874027 + 0.485877i \(0.161500\pi\)
\(318\) 0 0
\(319\) −0.0654632 0.113386i −0.00366524 0.00634838i
\(320\) −1.91227 3.31215i −0.106899 0.185155i
\(321\) 0 0
\(322\) −8.58135 + 14.8633i −0.478220 + 0.828301i
\(323\) 5.28600 0.294121
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 7.69425 13.3268i 0.426145 0.738105i
\(327\) 0 0
\(328\) −5.94808 10.3024i −0.328428 0.568853i
\(329\) 10.4009 + 18.0149i 0.573422 + 0.993196i
\(330\) 0 0
\(331\) 12.0570 20.8833i 0.662712 1.14785i −0.317188 0.948363i \(-0.602739\pi\)
0.979900 0.199489i \(-0.0639281\pi\)
\(332\) −0.327770 −0.0179887
\(333\) 0 0
\(334\) −25.3120 −1.38501
\(335\) 3.11795 5.40045i 0.170352 0.295058i
\(336\) 0 0
\(337\) −3.06746 5.31299i −0.167095 0.289417i 0.770302 0.637679i \(-0.220105\pi\)
−0.937397 + 0.348262i \(0.886772\pi\)
\(338\) 0.817019 + 1.41512i 0.0444400 + 0.0769723i
\(339\) 0 0
\(340\) −0.831054 + 1.43943i −0.0450702 + 0.0780640i
\(341\) −0.429620 −0.0232652
\(342\) 0 0
\(343\) −20.1564 −1.08835
\(344\) 10.2977 17.8361i 0.555214 0.961658i
\(345\) 0 0
\(346\) 7.90599 + 13.6936i 0.425028 + 0.736171i
\(347\) −1.86200 3.22507i −0.0999572 0.173131i 0.811710 0.584061i \(-0.198537\pi\)
−0.911667 + 0.410930i \(0.865204\pi\)
\(348\) 0 0
\(349\) 1.67433 2.90002i 0.0896246 0.155234i −0.817728 0.575605i \(-0.804767\pi\)
0.907352 + 0.420371i \(0.138100\pi\)
\(350\) −3.48069 −0.186051
\(351\) 0 0
\(352\) 0.191948 0.0102309
\(353\) −17.7813 + 30.7981i −0.946403 + 1.63922i −0.193486 + 0.981103i \(0.561979\pi\)
−0.752917 + 0.658115i \(0.771354\pi\)
\(354\) 0 0
\(355\) 1.25025 + 2.16550i 0.0663563 + 0.114933i
\(356\) −1.55760 2.69784i −0.0825525 0.142985i
\(357\) 0 0
\(358\) 2.70948 4.69296i 0.143200 0.248030i
\(359\) −9.06902 −0.478645 −0.239322 0.970940i \(-0.576925\pi\)
−0.239322 + 0.970940i \(0.576925\pi\)
\(360\) 0 0
\(361\) −14.4586 −0.760981
\(362\) −18.4800 + 32.0083i −0.971289 + 1.68232i
\(363\) 0 0
\(364\) 0.713672 + 1.23612i 0.0374066 + 0.0647901i
\(365\) 0.551224 + 0.954749i 0.0288524 + 0.0499738i
\(366\) 0 0
\(367\) 12.3093 21.3203i 0.642541 1.11291i −0.342323 0.939582i \(-0.611214\pi\)
0.984864 0.173331i \(-0.0554529\pi\)
\(368\) 24.1174 1.25721
\(369\) 0 0
\(370\) 1.82952 0.0951121
\(371\) −3.87778 + 6.71652i −0.201324 + 0.348704i
\(372\) 0 0
\(373\) −13.4879 23.3617i −0.698376 1.20962i −0.969029 0.246946i \(-0.920573\pi\)
0.270653 0.962677i \(-0.412760\pi\)
\(374\) 0.106691 + 0.184795i 0.00551688 + 0.00955551i
\(375\) 0 0
\(376\) 10.6110 18.3788i 0.547222 0.947816i
\(377\) −2.48694 −0.128084
\(378\) 0 0
\(379\) 14.2429 0.731611 0.365805 0.930691i \(-0.380794\pi\)
0.365805 + 0.930691i \(0.380794\pi\)
\(380\) −0.713983 + 1.23666i −0.0366266 + 0.0634391i
\(381\) 0 0
\(382\) −4.80579 8.32387i −0.245886 0.425886i
\(383\) 12.9868 + 22.4938i 0.663595 + 1.14938i 0.979664 + 0.200644i \(0.0643033\pi\)
−0.316070 + 0.948736i \(0.602363\pi\)
\(384\) 0 0
\(385\) −0.0560707 + 0.0971174i −0.00285763 + 0.00494956i
\(386\) 0.750903 0.0382200
\(387\) 0 0
\(388\) 4.91902 0.249726
\(389\) 12.8953 22.3354i 0.653819 1.13245i −0.328370 0.944549i \(-0.606499\pi\)
0.982189 0.187898i \(-0.0601675\pi\)
\(390\) 0 0
\(391\) 6.11539 + 10.5922i 0.309269 + 0.535669i
\(392\) 2.67580 + 4.63461i 0.135148 + 0.234083i
\(393\) 0 0
\(394\) 1.88828 3.27060i 0.0951303 0.164771i
\(395\) −15.6156 −0.785705
\(396\) 0 0
\(397\) −19.2890 −0.968086 −0.484043 0.875044i \(-0.660832\pi\)
−0.484043 + 0.875044i \(0.660832\pi\)
\(398\) 19.9135 34.4913i 0.998176 1.72889i
\(399\) 0 0
\(400\) 2.44558 + 4.23586i 0.122279 + 0.211793i
\(401\) −8.23155 14.2575i −0.411064 0.711983i 0.583943 0.811795i \(-0.301509\pi\)
−0.995006 + 0.0998116i \(0.968176\pi\)
\(402\) 0 0
\(403\) −4.08030 + 7.06728i −0.203254 + 0.352046i
\(404\) −0.370458 −0.0184310
\(405\) 0 0
\(406\) −8.65625 −0.429602
\(407\) 0.0294719 0.0510468i 0.00146087 0.00253030i
\(408\) 0 0
\(409\) 9.87631 + 17.1063i 0.488352 + 0.845850i 0.999910 0.0133982i \(-0.00426491\pi\)
−0.511558 + 0.859249i \(0.670932\pi\)
\(410\) 4.47250 + 7.74660i 0.220881 + 0.382577i
\(411\) 0 0
\(412\) 2.62602 4.54840i 0.129375 0.224084i
\(413\) −15.9564 −0.785164
\(414\) 0 0
\(415\) −0.489152 −0.0240115
\(416\) 1.82302 3.15756i 0.0893809 0.154812i
\(417\) 0 0
\(418\) 0.0916617 + 0.158763i 0.00448332 + 0.00776533i
\(419\) −8.72915 15.1193i −0.426447 0.738628i 0.570107 0.821570i \(-0.306902\pi\)
−0.996554 + 0.0829423i \(0.973568\pi\)
\(420\) 0 0
\(421\) 3.70798 6.42241i 0.180716 0.313009i −0.761409 0.648272i \(-0.775492\pi\)
0.942125 + 0.335263i \(0.108825\pi\)
\(422\) −44.7625 −2.17900
\(423\) 0 0
\(424\) 7.91222 0.384251
\(425\) −1.24024 + 2.14815i −0.0601603 + 0.104201i
\(426\) 0 0
\(427\) 6.16034 + 10.6700i 0.298120 + 0.516358i
\(428\) 6.50556 + 11.2680i 0.314458 + 0.544657i
\(429\) 0 0
\(430\) −7.74307 + 13.4114i −0.373404 + 0.646755i
\(431\) −33.6097 −1.61892 −0.809461 0.587174i \(-0.800240\pi\)
−0.809461 + 0.587174i \(0.800240\pi\)
\(432\) 0 0
\(433\) 30.2826 1.45529 0.727644 0.685955i \(-0.240615\pi\)
0.727644 + 0.685955i \(0.240615\pi\)
\(434\) −14.2022 + 24.5990i −0.681730 + 1.18079i
\(435\) 0 0
\(436\) 0.715315 + 1.23896i 0.0342574 + 0.0593355i
\(437\) 5.25391 + 9.10005i 0.251329 + 0.435314i
\(438\) 0 0
\(439\) 14.3685 24.8870i 0.685772 1.18779i −0.287422 0.957804i \(-0.592798\pi\)
0.973194 0.229987i \(-0.0738685\pi\)
\(440\) 0.114407 0.00545412
\(441\) 0 0
\(442\) 4.05318 0.192790
\(443\) −11.2109 + 19.4179i −0.532646 + 0.922570i 0.466627 + 0.884454i \(0.345469\pi\)
−0.999273 + 0.0381159i \(0.987864\pi\)
\(444\) 0 0
\(445\) −2.32450 4.02616i −0.110192 0.190858i
\(446\) 20.6999 + 35.8532i 0.980167 + 1.69770i
\(447\) 0 0
\(448\) −4.07336 + 7.05526i −0.192448 + 0.333330i
\(449\) −16.0149 −0.755791 −0.377895 0.925848i \(-0.623352\pi\)
−0.377895 + 0.925848i \(0.623352\pi\)
\(450\) 0 0
\(451\) 0.288192 0.0135704
\(452\) −2.08907 + 3.61837i −0.0982614 + 0.170194i
\(453\) 0 0
\(454\) 17.3549 + 30.0595i 0.814505 + 1.41076i
\(455\) 1.06506 + 1.84473i 0.0499307 + 0.0864825i
\(456\) 0 0
\(457\) −0.532780 + 0.922803i −0.0249224 + 0.0431669i −0.878218 0.478261i \(-0.841267\pi\)
0.853295 + 0.521428i \(0.174601\pi\)
\(458\) −19.9904 −0.934089
\(459\) 0 0
\(460\) −3.30404 −0.154052
\(461\) 12.3193 21.3377i 0.573769 0.993798i −0.422405 0.906407i \(-0.638814\pi\)
0.996174 0.0873903i \(-0.0278527\pi\)
\(462\) 0 0
\(463\) −3.56164 6.16895i −0.165524 0.286695i 0.771318 0.636451i \(-0.219598\pi\)
−0.936841 + 0.349755i \(0.886265\pi\)
\(464\) 6.08199 + 10.5343i 0.282349 + 0.489043i
\(465\) 0 0
\(466\) −9.31794 + 16.1391i −0.431645 + 0.747631i
\(467\) −20.4662 −0.947063 −0.473531 0.880777i \(-0.657021\pi\)
−0.473531 + 0.880777i \(0.657021\pi\)
\(468\) 0 0
\(469\) −13.2832 −0.613361
\(470\) −7.97868 + 13.8195i −0.368029 + 0.637445i
\(471\) 0 0
\(472\) 8.13936 + 14.0978i 0.374645 + 0.648903i
\(473\) 0.249468 + 0.432090i 0.0114705 + 0.0198675i
\(474\) 0 0
\(475\) −1.06552 + 1.84554i −0.0488895 + 0.0846792i
\(476\) 3.54048 0.162278
\(477\) 0 0
\(478\) 24.2770 1.11041
\(479\) −7.23493 + 12.5313i −0.330573 + 0.572568i −0.982624 0.185606i \(-0.940575\pi\)
0.652052 + 0.758175i \(0.273908\pi\)
\(480\) 0 0
\(481\) −0.559815 0.969629i −0.0255254 0.0442113i
\(482\) −15.1890 26.3081i −0.691840 1.19830i
\(483\) 0 0
\(484\) 3.68450 6.38174i 0.167477 0.290079i
\(485\) 7.34097 0.333336
\(486\) 0 0
\(487\) 29.8595 1.35306 0.676531 0.736414i \(-0.263483\pi\)
0.676531 + 0.736414i \(0.263483\pi\)
\(488\) 6.28477 10.8855i 0.284498 0.492765i
\(489\) 0 0
\(490\) −2.01199 3.48488i −0.0908926 0.157431i
\(491\) 11.0235 + 19.0932i 0.497483 + 0.861665i 0.999996 0.00290444i \(-0.000924514\pi\)
−0.502513 + 0.864570i \(0.667591\pi\)
\(492\) 0 0
\(493\) −3.08439 + 5.34231i −0.138914 + 0.240606i
\(494\) 3.48221 0.156672
\(495\) 0 0
\(496\) 39.9147 1.79222
\(497\) 2.66318 4.61276i 0.119460 0.206910i
\(498\) 0 0
\(499\) −10.5861 18.3357i −0.473901 0.820820i 0.525653 0.850699i \(-0.323821\pi\)
−0.999554 + 0.0298789i \(0.990488\pi\)
\(500\) −0.335039 0.580304i −0.0149834 0.0259520i
\(501\) 0 0
\(502\) −24.5696 + 42.5558i −1.09660 + 1.89936i
\(503\) 40.3143 1.79752 0.898762 0.438436i \(-0.144467\pi\)
0.898762 + 0.438436i \(0.144467\pi\)
\(504\) 0 0
\(505\) −0.552859 −0.0246019
\(506\) −0.212088 + 0.367346i −0.00942844 + 0.0163305i
\(507\) 0 0
\(508\) 3.55262 + 6.15332i 0.157622 + 0.273009i
\(509\) 9.50834 + 16.4689i 0.421450 + 0.729973i 0.996082 0.0884396i \(-0.0281880\pi\)
−0.574632 + 0.818412i \(0.694855\pi\)
\(510\) 0 0
\(511\) 1.17417 2.03373i 0.0519423 0.0899667i
\(512\) 3.42501 0.151366
\(513\) 0 0
\(514\) 4.96851 0.219152
\(515\) 3.91898 6.78787i 0.172691 0.299109i
\(516\) 0 0
\(517\) 0.257059 + 0.445238i 0.0113054 + 0.0195816i
\(518\) −1.94854 3.37498i −0.0856141 0.148288i
\(519\) 0 0
\(520\) 1.08657 1.88200i 0.0476493 0.0825310i
\(521\) 33.4407 1.46507 0.732533 0.680732i \(-0.238338\pi\)
0.732533 + 0.680732i \(0.238338\pi\)
\(522\) 0 0
\(523\) −6.40250 −0.279962 −0.139981 0.990154i \(-0.544704\pi\)
−0.139981 + 0.990154i \(0.544704\pi\)
\(524\) −5.42505 + 9.39647i −0.236995 + 0.410487i
\(525\) 0 0
\(526\) 3.92252 + 6.79401i 0.171030 + 0.296233i
\(527\) 10.1211 + 17.5302i 0.440880 + 0.763627i
\(528\) 0 0
\(529\) −0.656552 + 1.13718i −0.0285457 + 0.0494426i
\(530\) −5.94939 −0.258425
\(531\) 0 0
\(532\) 3.04173 0.131876
\(533\) 2.73708 4.74077i 0.118556 0.205346i
\(534\) 0 0
\(535\) 9.70866 + 16.8159i 0.419742 + 0.727015i
\(536\) 6.77576 + 11.7360i 0.292668 + 0.506916i
\(537\) 0 0
\(538\) 13.7850 23.8764i 0.594315 1.02938i
\(539\) −0.129646 −0.00558423
\(540\) 0 0
\(541\) −17.4745 −0.751286 −0.375643 0.926764i \(-0.622578\pi\)
−0.375643 + 0.926764i \(0.622578\pi\)
\(542\) −1.91264 + 3.31278i −0.0821547 + 0.142296i
\(543\) 0 0
\(544\) −4.52195 7.83224i −0.193877 0.335805i
\(545\) 1.06751 + 1.84898i 0.0457271 + 0.0792017i
\(546\) 0 0
\(547\) 5.03733 8.72491i 0.215381 0.373050i −0.738010 0.674790i \(-0.764234\pi\)
0.953390 + 0.301740i \(0.0975675\pi\)
\(548\) 13.9166 0.594486
\(549\) 0 0
\(550\) −0.0860250 −0.00366812
\(551\) −2.64989 + 4.58974i −0.112889 + 0.195529i
\(552\) 0 0
\(553\) 16.6315 + 28.8066i 0.707243 + 1.22498i
\(554\) −3.08206 5.33829i −0.130944 0.226802i
\(555\) 0 0
\(556\) 0.837849 1.45120i 0.0355327 0.0615444i
\(557\) −21.2315 −0.899607 −0.449804 0.893127i \(-0.648506\pi\)
−0.449804 + 0.893127i \(0.648506\pi\)
\(558\) 0 0
\(559\) 9.47722 0.400844
\(560\) 5.20936 9.02288i 0.220136 0.381286i
\(561\) 0 0
\(562\) −8.95122 15.5040i −0.377584 0.653995i
\(563\) 6.17245 + 10.6910i 0.260138 + 0.450572i 0.966278 0.257500i \(-0.0828986\pi\)
−0.706140 + 0.708072i \(0.749565\pi\)
\(564\) 0 0
\(565\) −3.11765 + 5.39992i −0.131160 + 0.227176i
\(566\) −28.7095 −1.20675
\(567\) 0 0
\(568\) −5.43394 −0.228003
\(569\) 3.87874 6.71817i 0.162605 0.281640i −0.773197 0.634166i \(-0.781344\pi\)
0.935802 + 0.352526i \(0.114677\pi\)
\(570\) 0 0
\(571\) 5.10696 + 8.84552i 0.213720 + 0.370173i 0.952876 0.303361i \(-0.0981087\pi\)
−0.739156 + 0.673534i \(0.764775\pi\)
\(572\) 0.0176384 + 0.0305505i 0.000737497 + 0.00127738i
\(573\) 0 0
\(574\) 9.52694 16.5011i 0.397647 0.688745i
\(575\) −4.93083 −0.205630
\(576\) 0 0
\(577\) −44.5539 −1.85480 −0.927402 0.374065i \(-0.877964\pi\)
−0.927402 + 0.374065i \(0.877964\pi\)
\(578\) −8.86242 + 15.3502i −0.368628 + 0.638482i
\(579\) 0 0
\(580\) −0.833220 1.44318i −0.0345976 0.0599248i
\(581\) 0.520975 + 0.902355i 0.0216137 + 0.0374360i
\(582\) 0 0
\(583\) −0.0958392 + 0.165998i −0.00396925 + 0.00687495i
\(584\) −2.39578 −0.0991380
\(585\) 0 0
\(586\) 40.1066 1.65679
\(587\) 10.4535 18.1059i 0.431461 0.747312i −0.565539 0.824722i \(-0.691332\pi\)
0.996999 + 0.0774099i \(0.0246650\pi\)
\(588\) 0 0
\(589\) 8.69530 + 15.0607i 0.358284 + 0.620565i
\(590\) −6.12018 10.6005i −0.251964 0.436414i
\(591\) 0 0
\(592\) −2.73814 + 4.74260i −0.112537 + 0.194920i
\(593\) 7.48843 0.307513 0.153756 0.988109i \(-0.450863\pi\)
0.153756 + 0.988109i \(0.450863\pi\)
\(594\) 0 0
\(595\) 5.28369 0.216610
\(596\) −0.633309 + 1.09692i −0.0259413 + 0.0449317i
\(597\) 0 0
\(598\) 4.02858 + 6.97771i 0.164741 + 0.285340i
\(599\) −13.9657 24.1893i −0.570623 0.988349i −0.996502 0.0835684i \(-0.973368\pi\)
0.425879 0.904780i \(-0.359965\pi\)
\(600\) 0 0
\(601\) −16.3890 + 28.3866i −0.668521 + 1.15791i 0.309796 + 0.950803i \(0.399739\pi\)
−0.978318 + 0.207110i \(0.933594\pi\)
\(602\) 32.9873 1.34446
\(603\) 0 0
\(604\) −3.27457 −0.133240
\(605\) 5.49861 9.52388i 0.223550 0.387201i
\(606\) 0 0
\(607\) −19.5852 33.9226i −0.794940 1.37688i −0.922878 0.385093i \(-0.874169\pi\)
0.127938 0.991782i \(-0.459164\pi\)
\(608\) −3.88494 6.72891i −0.157555 0.272893i
\(609\) 0 0
\(610\) −4.72567 + 8.18509i −0.191337 + 0.331405i
\(611\) 9.76560 0.395074
\(612\) 0 0
\(613\) −10.2019 −0.412051 −0.206026 0.978547i \(-0.566053\pi\)
−0.206026 + 0.978547i \(0.566053\pi\)
\(614\) −9.04350 + 15.6638i −0.364966 + 0.632139i
\(615\) 0 0
\(616\) −0.121850 0.211050i −0.00490946 0.00850344i
\(617\) −4.84474 8.39133i −0.195042 0.337822i 0.751872 0.659309i \(-0.229151\pi\)
−0.946914 + 0.321486i \(0.895818\pi\)
\(618\) 0 0
\(619\) 9.93748 17.2122i 0.399421 0.691818i −0.594233 0.804293i \(-0.702544\pi\)
0.993655 + 0.112475i \(0.0358778\pi\)
\(620\) −5.46823 −0.219610
\(621\) 0 0
\(622\) 24.1728 0.969243
\(623\) −4.95146 + 8.57618i −0.198376 + 0.343598i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 22.1024 + 38.2824i 0.883388 + 1.53007i
\(627\) 0 0
\(628\) 6.03062 10.4453i 0.240648 0.416815i
\(629\) −2.77721 −0.110735
\(630\) 0 0
\(631\) −38.9270 −1.54966 −0.774830 0.632170i \(-0.782165\pi\)
−0.774830 + 0.632170i \(0.782165\pi\)
\(632\) 16.9674 29.3885i 0.674928 1.16901i
\(633\) 0 0
\(634\) −0.472235 0.817935i −0.0187548 0.0324843i
\(635\) 5.30180 + 9.18299i 0.210396 + 0.364416i
\(636\) 0 0
\(637\) −1.23130 + 2.13268i −0.0487860 + 0.0844998i
\(638\) −0.213939 −0.00846991
\(639\) 0 0
\(640\) −13.5415 −0.535275
\(641\) −3.94706 + 6.83651i −0.155899 + 0.270026i −0.933386 0.358874i \(-0.883161\pi\)
0.777487 + 0.628899i \(0.216494\pi\)
\(642\) 0 0
\(643\) −17.8875 30.9821i −0.705415 1.22182i −0.966541 0.256511i \(-0.917427\pi\)
0.261126 0.965305i \(-0.415906\pi\)
\(644\) 3.51900 + 6.09508i 0.138668 + 0.240180i
\(645\) 0 0
\(646\) 4.31876 7.48031i 0.169919 0.294309i
\(647\) 1.47889 0.0581412 0.0290706 0.999577i \(-0.490745\pi\)
0.0290706 + 0.999577i \(0.490745\pi\)
\(648\) 0 0
\(649\) −0.394362 −0.0154801
\(650\) −0.817019 + 1.41512i −0.0320461 + 0.0555055i
\(651\) 0 0
\(652\) −3.15522 5.46500i −0.123568 0.214026i
\(653\) −3.47523 6.01927i −0.135996 0.235552i 0.789981 0.613131i \(-0.210090\pi\)
−0.925978 + 0.377579i \(0.876757\pi\)
\(654\) 0 0
\(655\) −8.09616 + 14.0230i −0.316343 + 0.547922i
\(656\) −26.7750 −1.04539
\(657\) 0 0
\(658\) 33.9910 1.32511
\(659\) 15.4773 26.8075i 0.602910 1.04427i −0.389469 0.921040i \(-0.627341\pi\)
0.992378 0.123230i \(-0.0393254\pi\)
\(660\) 0 0
\(661\) −1.78839 3.09758i −0.0695603 0.120482i 0.829147 0.559030i \(-0.188826\pi\)
−0.898708 + 0.438548i \(0.855493\pi\)
\(662\) −19.7016 34.1241i −0.765724 1.32627i
\(663\) 0 0
\(664\) 0.531498 0.920582i 0.0206261 0.0357255i
\(665\) 4.53938 0.176029
\(666\) 0 0
\(667\) −12.2627 −0.474812
\(668\) −5.18991 + 8.98918i −0.200804 + 0.347802i
\(669\) 0 0
\(670\) −5.09485 8.82454i −0.196831 0.340922i
\(671\) 0.152252 + 0.263709i 0.00587764 + 0.0101804i
\(672\) 0 0
\(673\) 14.0497 24.3347i 0.541575 0.938035i −0.457239 0.889344i \(-0.651162\pi\)
0.998814 0.0486913i \(-0.0155051\pi\)
\(674\) −10.0247 −0.386136
\(675\) 0 0
\(676\) 0.670078 0.0257722
\(677\) 22.1467 38.3592i 0.851167 1.47426i −0.0289890 0.999580i \(-0.509229\pi\)
0.880156 0.474685i \(-0.157438\pi\)
\(678\) 0 0
\(679\) −7.81856 13.5422i −0.300049 0.519700i
\(680\) −2.69521 4.66824i −0.103357 0.179019i
\(681\) 0 0
\(682\) −0.351008 + 0.607963i −0.0134408 + 0.0232801i
\(683\) 1.69041 0.0646816 0.0323408 0.999477i \(-0.489704\pi\)
0.0323408 + 0.999477i \(0.489704\pi\)
\(684\) 0 0
\(685\) 20.7686 0.793526
\(686\) −16.4682 + 28.5237i −0.628759 + 1.08904i
\(687\) 0 0
\(688\) −23.1773 40.1442i −0.883625 1.53048i
\(689\) 1.82046 + 3.15312i 0.0693538 + 0.120124i
\(690\) 0 0
\(691\) 5.40719 9.36552i 0.205699 0.356281i −0.744656 0.667448i \(-0.767387\pi\)
0.950355 + 0.311167i \(0.100720\pi\)
\(692\) 6.48409 0.246488
\(693\) 0 0
\(694\) −6.08514 −0.230989
\(695\) 1.25038 2.16571i 0.0474294 0.0821502i
\(696\) 0 0
\(697\) −6.78926 11.7593i −0.257162 0.445417i
\(698\) −2.73591 4.73874i −0.103556 0.179364i
\(699\) 0 0
\(700\) −0.713672 + 1.23612i −0.0269743 + 0.0467208i
\(701\) 32.1755 1.21525 0.607626 0.794224i \(-0.292122\pi\)
0.607626 + 0.794224i \(0.292122\pi\)
\(702\) 0 0
\(703\) −2.38598 −0.0899891
\(704\) −0.100673 + 0.174370i −0.00379425 + 0.00657183i
\(705\) 0 0
\(706\) 29.0553 + 50.3253i 1.09351 + 1.89402i
\(707\) 0.588827 + 1.01988i 0.0221451 + 0.0383565i
\(708\) 0 0
\(709\) −15.9560 + 27.6366i −0.599240 + 1.03791i 0.393694 + 0.919242i \(0.371197\pi\)
−0.992934 + 0.118672i \(0.962136\pi\)
\(710\) 4.08591 0.153341
\(711\) 0 0
\(712\) 10.1030 0.378624
\(713\) −20.1193 + 34.8476i −0.753472 + 1.30505i
\(714\) 0 0
\(715\) 0.0263229 + 0.0455925i 0.000984419 + 0.00170506i
\(716\) −1.11109 1.92446i −0.0415234 0.0719206i
\(717\) 0 0
\(718\) −7.40956 + 12.8337i −0.276522 + 0.478951i
\(719\) −20.6891 −0.771572 −0.385786 0.922588i \(-0.626070\pi\)
−0.385786 + 0.922588i \(0.626070\pi\)
\(720\) 0 0
\(721\) −16.6958 −0.621782
\(722\) −11.8130 + 20.4607i −0.439634 + 0.761468i
\(723\) 0 0
\(724\) 7.57820 + 13.1258i 0.281641 + 0.487817i
\(725\) −1.24347 2.15375i −0.0461812 0.0799882i
\(726\) 0 0
\(727\) 12.3396 21.3728i 0.457649 0.792672i −0.541187 0.840902i \(-0.682025\pi\)
0.998836 + 0.0482305i \(0.0153582\pi\)
\(728\) −4.62905 −0.171564
\(729\) 0 0
\(730\) 1.80144 0.0666744
\(731\) 11.7540 20.3585i 0.434737 0.752987i
\(732\) 0 0
\(733\) 10.8729 + 18.8325i 0.401602 + 0.695594i 0.993919 0.110110i \(-0.0351203\pi\)
−0.592318 + 0.805704i \(0.701787\pi\)
\(734\) −20.1139 34.8382i −0.742416 1.28590i
\(735\) 0 0
\(736\) 8.98900 15.5694i 0.331339 0.573896i
\(737\) −0.328294 −0.0120929
\(738\) 0 0
\(739\) 43.0460 1.58347 0.791736 0.610864i \(-0.209178\pi\)
0.791736 + 0.610864i \(0.209178\pi\)
\(740\) 0.375120 0.649727i 0.0137897 0.0238844i
\(741\) 0 0
\(742\) 6.33644 + 10.9750i 0.232618 + 0.402906i
\(743\) 3.94908 + 6.84001i 0.144878 + 0.250936i 0.929327 0.369257i \(-0.120388\pi\)
−0.784450 + 0.620193i \(0.787054\pi\)
\(744\) 0 0
\(745\) −0.945127 + 1.63701i −0.0346268 + 0.0599754i
\(746\) −44.0794 −1.61386
\(747\) 0 0
\(748\) 0.0875029 0.00319942
\(749\) 20.6806 35.8198i 0.755652 1.30883i
\(750\) 0 0
\(751\) −19.3225 33.4676i −0.705089 1.22125i −0.966660 0.256065i \(-0.917574\pi\)
0.261571 0.965184i \(-0.415759\pi\)
\(752\) −23.8825 41.3657i −0.870906 1.50845i
\(753\) 0 0
\(754\) −2.03187 + 3.51931i −0.0739964 + 0.128166i
\(755\) −4.88685 −0.177851
\(756\) 0 0
\(757\) −15.3437 −0.557678 −0.278839 0.960338i \(-0.589950\pi\)
−0.278839 + 0.960338i \(0.589950\pi\)
\(758\) 11.6367 20.1554i 0.422666 0.732078i
\(759\) 0 0
\(760\) −2.31553 4.01062i −0.0839932 0.145481i
\(761\) 24.3585 + 42.1902i 0.882995 + 1.52939i 0.847994 + 0.530005i \(0.177810\pi\)
0.0350009 + 0.999387i \(0.488857\pi\)
\(762\) 0 0
\(763\) 2.27392 3.93855i 0.0823215 0.142585i
\(764\) −3.94147 −0.142597
\(765\) 0 0
\(766\) 42.4418 1.53349
\(767\) −3.74544 + 6.48728i −0.135240 + 0.234242i
\(768\) 0 0
\(769\) −3.18555 5.51753i −0.114874 0.198967i 0.802856 0.596174i \(-0.203313\pi\)
−0.917729 + 0.397206i \(0.869980\pi\)
\(770\) 0.0916217 + 0.158693i 0.00330182 + 0.00571891i
\(771\) 0 0
\(772\) 0.153963 0.266672i 0.00554126 0.00959775i
\(773\) −29.8732 −1.07446 −0.537232 0.843435i \(-0.680530\pi\)
−0.537232 + 0.843435i \(0.680530\pi\)
\(774\) 0 0
\(775\) −8.16059 −0.293137
\(776\) −7.97649 + 13.8157i −0.286339 + 0.495954i
\(777\) 0 0
\(778\) −21.0714 36.4968i −0.755448 1.30847i
\(779\) −5.83285 10.1028i −0.208984 0.361970i
\(780\) 0 0
\(781\) 0.0658203 0.114004i 0.00235523 0.00407938i
\(782\) 19.9856 0.714682
\(783\) 0 0
\(784\) 12.0450 0.430178
\(785\) 8.99989 15.5883i 0.321220 0.556369i
\(786\) 0 0
\(787\) 11.8278 + 20.4864i 0.421616 + 0.730261i 0.996098 0.0882568i \(-0.0281296\pi\)
−0.574482 + 0.818518i \(0.694796\pi\)
\(788\) −0.774338 1.34119i −0.0275846 0.0477780i
\(789\) 0 0
\(790\) −12.7582 + 22.0979i −0.453917 + 0.786207i
\(791\) 13.2819 0.472250
\(792\) 0 0
\(793\) 5.78404 0.205397
\(794\) −15.7594 + 27.2962i −0.559282 + 0.968705i
\(795\) 0 0
\(796\) −8.16605 14.1440i −0.289438 0.501321i
\(797\) −15.0003 25.9813i −0.531339 0.920305i −0.999331 0.0365729i \(-0.988356\pi\)
0.467992 0.883732i \(-0.344977\pi\)
\(798\) 0 0
\(799\) 12.1116 20.9780i 0.428479 0.742148i
\(800\) 3.64604 0.128907
\(801\) 0 0
\(802\) −26.9013 −0.949918
\(803\) 0.0290196 0.0502634i 0.00102408 0.00177376i
\(804\) 0 0
\(805\) 5.25162 + 9.09608i 0.185095 + 0.320595i
\(806\) 6.66736 + 11.5482i 0.234848 + 0.406768i
\(807\) 0 0
\(808\) 0.600720 1.04048i 0.0211333 0.0366039i
\(809\) −37.0787 −1.30362 −0.651808 0.758384i \(-0.725989\pi\)
−0.651808 + 0.758384i \(0.725989\pi\)
\(810\) 0 0
\(811\) −42.7582 −1.50144 −0.750722 0.660618i \(-0.770294\pi\)
−0.750722 + 0.660618i \(0.770294\pi\)
\(812\) −1.77486 + 3.07414i −0.0622852 + 0.107881i
\(813\) 0 0
\(814\) −0.0481581 0.0834124i −0.00168794 0.00292360i
\(815\) −4.70874 8.15577i −0.164940 0.285684i
\(816\) 0 0
\(817\) 10.0982 17.4906i 0.353291 0.611918i
\(818\) 32.2765 1.12852
\(819\) 0 0
\(820\) 3.66812 0.128096
\(821\) 14.2835 24.7397i 0.498496 0.863421i −0.501502 0.865156i \(-0.667219\pi\)
0.999998 + 0.00173559i \(0.000552457\pi\)
\(822\) 0 0
\(823\) −16.0021 27.7164i −0.557797 0.966133i −0.997680 0.0680777i \(-0.978313\pi\)
0.439883 0.898055i \(-0.355020\pi\)
\(824\) 8.51649 + 14.7510i 0.296686 + 0.513875i
\(825\) 0 0
\(826\) −13.0367 + 22.5802i −0.453605 + 0.785666i
\(827\) −31.4986 −1.09531 −0.547657 0.836703i \(-0.684480\pi\)
−0.547657 + 0.836703i \(0.684480\pi\)
\(828\) 0 0
\(829\) 32.3851 1.12478 0.562390 0.826872i \(-0.309882\pi\)
0.562390 + 0.826872i \(0.309882\pi\)
\(830\) −0.399646 + 0.692207i −0.0138719 + 0.0240269i
\(831\) 0 0
\(832\) 1.91227 + 3.31215i 0.0662960 + 0.114828i
\(833\) 3.05421 + 5.29005i 0.105822 + 0.183289i
\(834\) 0 0
\(835\) −7.74523 + 13.4151i −0.268035 + 0.464250i
\(836\) 0.0751763 0.00260003
\(837\) 0 0
\(838\) −28.5275 −0.985467
\(839\) 23.0381 39.9032i 0.795365 1.37761i −0.127242 0.991872i \(-0.540612\pi\)
0.922607 0.385741i \(-0.126054\pi\)
\(840\) 0 0
\(841\) 11.4076 + 19.7585i 0.393365 + 0.681328i
\(842\) −6.05898 10.4945i −0.208806 0.361663i
\(843\) 0 0
\(844\) −9.17799 + 15.8967i −0.315919 + 0.547189i
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −23.4254 −0.804905
\(848\) 8.90413 15.4224i 0.305769 0.529607i
\(849\) 0 0
\(850\) 2.02659 + 3.51016i 0.0695115 + 0.120397i
\(851\) −2.76036 4.78108i −0.0946238 0.163893i
\(852\) 0 0
\(853\) −24.3786 + 42.2250i −0.834709 + 1.44576i 0.0595585 + 0.998225i \(0.481031\pi\)
−0.894267 + 0.447533i \(0.852303\pi\)
\(854\) 20.1324 0.688918
\(855\) 0 0
\(856\) −42.1966 −1.44225
\(857\) 15.9740 27.6677i 0.545660 0.945111i −0.452905 0.891559i \(-0.649612\pi\)
0.998565 0.0535519i \(-0.0170542\pi\)
\(858\) 0 0
\(859\) 3.66749 + 6.35229i 0.125133 + 0.216737i 0.921785 0.387701i \(-0.126731\pi\)
−0.796652 + 0.604439i \(0.793397\pi\)
\(860\) 3.17524 + 5.49967i 0.108275 + 0.187537i
\(861\) 0 0
\(862\) −27.4597 + 47.5617i −0.935282 + 1.61996i
\(863\) −28.4742 −0.969273 −0.484637 0.874716i \(-0.661048\pi\)
−0.484637 + 0.874716i \(0.661048\pi\)
\(864\) 0 0
\(865\) 9.67663 0.329015
\(866\) 24.7414 42.8534i 0.840748 1.45622i
\(867\) 0 0
\(868\) 5.82399 + 10.0874i 0.197679 + 0.342390i
\(869\) 0.411046 + 0.711953i 0.0139438 + 0.0241514i
\(870\) 0 0
\(871\) −3.11795 + 5.40045i −0.105648 + 0.182987i
\(872\) −4.63970 −0.157120
\(873\) 0 0
\(874\) 17.1702 0.580790
\(875\) −1.06506 + 1.84473i −0.0360055 + 0.0623634i
\(876\) 0 0
\(877\) −22.9264 39.7098i −0.774171 1.34090i −0.935259 0.353963i \(-0.884834\pi\)
0.161089 0.986940i \(-0.448499\pi\)
\(878\) −23.4787 40.6663i −0.792367 1.37242i
\(879\) 0 0
\(880\) 0.128749 0.223000i 0.00434013 0.00751732i
\(881\) 37.4454 1.26157 0.630784 0.775959i \(-0.282733\pi\)
0.630784 + 0.775959i \(0.282733\pi\)
\(882\) 0 0
\(883\) 50.8068 1.70978 0.854892 0.518805i \(-0.173623\pi\)
0.854892 + 0.518805i \(0.173623\pi\)
\(884\) 0.831054 1.43943i 0.0279514 0.0484132i
\(885\) 0 0
\(886\) 18.3190 + 31.7295i 0.615440 + 1.06597i
\(887\) −22.6484 39.2282i −0.760459 1.31715i −0.942614 0.333884i \(-0.891641\pi\)
0.182155 0.983270i \(-0.441693\pi\)
\(888\) 0 0
\(889\) 11.2935 19.5608i 0.378770 0.656050i
\(890\) −7.59665 −0.254640
\(891\) 0 0
\(892\) 16.9770 0.568432
\(893\) 10.4055 18.0228i 0.348206 0.603110i
\(894\) 0 0
\(895\) −1.65815 2.87200i −0.0554258 0.0960004i
\(896\) 14.4225 + 24.9805i 0.481822 + 0.834540i
\(897\) 0 0
\(898\) −13.0845 + 22.6630i −0.436635 + 0.756274i
\(899\) −20.2949 −0.676872
\(900\) 0 0
\(901\) 9.03118 0.300872
\(902\) 0.235458 0.407825i 0.00783989 0.0135791i
\(903\) 0 0
\(904\) −6.77509 11.7348i −0.225336 0.390294i
\(905\) 11.3094 + 19.5885i 0.375938 + 0.651144i
\(906\) 0 0
\(907\) −7.18452 + 12.4439i −0.238558 + 0.413195i −0.960301 0.278967i \(-0.910008\pi\)
0.721743 + 0.692161i \(0.243341\pi\)
\(908\) 14.2336 0.472359
\(909\) 0 0
\(910\) 3.48069 0.115384
\(911\) 26.9532 46.6843i 0.892998 1.54672i 0.0567359 0.998389i \(-0.481931\pi\)
0.836262 0.548329i \(-0.184736\pi\)
\(912\) 0 0
\(913\) 0.0128759 + 0.0223017i 0.000426129 + 0.000738077i
\(914\) 0.870583 + 1.50789i 0.0287963 + 0.0498767i
\(915\) 0 0
\(916\) −4.09877 + 7.09929i −0.135427 + 0.234567i
\(917\) 34.4915 1.13901
\(918\) 0 0
\(919\) −15.6573 −0.516487 −0.258244 0.966080i \(-0.583144\pi\)
−0.258244 + 0.966080i \(0.583144\pi\)
\(920\) 5.35770 9.27981i 0.176638 0.305946i
\(921\) 0 0
\(922\) −20.1303 34.8667i −0.662955 1.14827i
\(923\) −1.25025 2.16550i −0.0411525 0.0712781i
\(924\) 0 0
\(925\) 0.559815 0.969629i 0.0184066 0.0318812i
\(926\) −11.6397 −0.382505
\(927\) 0 0
\(928\) 9.06746 0.297654
\(929\) −11.5720 + 20.0432i −0.379664 + 0.657597i −0.991013 0.133764i \(-0.957294\pi\)
0.611350 + 0.791361i \(0.290627\pi\)
\(930\) 0 0
\(931\) 2.62396 + 4.54483i 0.0859969 + 0.148951i
\(932\) 3.82105 + 6.61826i 0.125163 + 0.216788i
\(933\) 0 0
\(934\) −16.7213 + 28.9621i −0.547137 + 0.947668i
\(935\) 0.130586 0.00427062
\(936\) 0 0
\(937\) 14.6354 0.478118 0.239059 0.971005i \(-0.423161\pi\)
0.239059 + 0.971005i \(0.423161\pi\)
\(938\) −10.8526 + 18.7973i −0.354351 + 0.613754i
\(939\) 0 0
\(940\) 3.27186 + 5.66702i 0.106716 + 0.184838i
\(941\) −11.0197 19.0866i −0.359231 0.622206i 0.628602 0.777727i \(-0.283628\pi\)
−0.987833 + 0.155521i \(0.950294\pi\)
\(942\) 0 0
\(943\) 13.4961 23.3759i 0.439494 0.761225i
\(944\) 36.6390 1.19250
\(945\) 0 0
\(946\) 0.815279 0.0265070
\(947\) −25.1953 + 43.6396i −0.818737 + 1.41809i 0.0878754 + 0.996131i \(0.471992\pi\)
−0.906613 + 0.421963i \(0.861341\pi\)
\(948\) 0 0
\(949\) −0.551224 0.954749i −0.0178935 0.0309925i
\(950\) 1.74110 + 3.01568i 0.0564889 + 0.0978416i
\(951\) 0 0
\(952\) −5.74111 + 9.94389i −0.186070 + 0.322283i
\(953\) 7.28058 0.235841 0.117921 0.993023i \(-0.462377\pi\)
0.117921 + 0.993023i \(0.462377\pi\)
\(954\) 0 0
\(955\) −5.88211 −0.190340
\(956\) 4.97770 8.62163i 0.160990 0.278843i
\(957\) 0 0
\(958\) 11.8222 + 20.4766i 0.381956 + 0.661568i
\(959\) −22.1197 38.3125i −0.714283 1.23718i
\(960\) 0 0
\(961\) −17.7977 + 30.8264i −0.574118 + 0.994401i
\(962\) −1.82952 −0.0589861
\(963\) 0 0
\(964\) −12.4573 −0.401221
\(965\) 0.229769 0.397972i 0.00739654 0.0128112i
\(966\) 0 0
\(967\) −0.821636 1.42312i −0.0264220 0.0457643i 0.852512 0.522708i \(-0.175078\pi\)
−0.878934 + 0.476943i \(0.841745\pi\)
\(968\) 11.9493 + 20.6967i 0.384064 + 0.665219i
\(969\) 0 0
\(970\) 5.99771 10.3883i 0.192575 0.333550i
\(971\) −59.5135 −1.90988 −0.954939 0.296803i \(-0.904080\pi\)
−0.954939 + 0.296803i \(0.904080\pi\)
\(972\) 0 0
\(973\) −5.32689 −0.170772
\(974\) 24.3957 42.2547i 0.781690 1.35393i
\(975\) 0 0
\(976\) −14.1453 24.5004i −0.452780 0.784238i
\(977\) −7.66363 13.2738i −0.245181 0.424666i 0.717001 0.697072i \(-0.245514\pi\)
−0.962183 + 0.272405i \(0.912181\pi\)
\(978\) 0 0
\(979\) −0.122375 + 0.211960i −0.00391112 + 0.00677427i
\(980\) −1.65014 −0.0527117
\(981\) 0 0
\(982\) 36.0255 1.14962
\(983\) −1.63477 + 2.83150i −0.0521411 + 0.0903110i −0.890918 0.454164i \(-0.849938\pi\)
0.838777 + 0.544475i \(0.183271\pi\)
\(984\) 0 0
\(985\) −1.15559 2.00155i −0.0368203 0.0637746i
\(986\) 5.04000 + 8.72954i 0.160506 + 0.278005i
\(987\) 0 0
\(988\) 0.713983 1.23666i 0.0227148 0.0393432i
\(989\) 46.7306 1.48595
\(990\) 0 0
\(991\) −39.2309 −1.24621 −0.623106 0.782138i \(-0.714129\pi\)
−0.623106 + 0.782138i \(0.714129\pi\)
\(992\) 14.8769 25.7676i 0.472343 0.818122i
\(993\) 0 0
\(994\) −4.35173 7.53742i −0.138028 0.239072i
\(995\) −12.1867 21.1080i −0.386345 0.669169i
\(996\) 0 0
\(997\) 16.4127 28.4276i 0.519795 0.900312i −0.479940 0.877301i \(-0.659342\pi\)
0.999735 0.0230105i \(-0.00732513\pi\)
\(998\) −34.5963 −1.09513
\(999\) 0 0
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 1755.2.i.f.586.6 16
3.2 odd 2 585.2.i.e.196.3 16
9.2 odd 6 5265.2.a.bf.1.6 8
9.4 even 3 inner 1755.2.i.f.1171.6 16
9.5 odd 6 585.2.i.e.391.3 yes 16
9.7 even 3 5265.2.a.ba.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.i.e.196.3 16 3.2 odd 2
585.2.i.e.391.3 yes 16 9.5 odd 6
1755.2.i.f.586.6 16 1.1 even 1 trivial
1755.2.i.f.1171.6 16 9.4 even 3 inner
5265.2.a.ba.1.3 8 9.7 even 3
5265.2.a.bf.1.6 8 9.2 odd 6