Properties

Label 693.2.m.k.190.5
Level $693$
Weight $2$
Character 693.190
Analytic conductor $5.534$
Analytic rank $0$
Dimension $32$
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] = [693,2,Mod(64,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.m (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 190.5
Character \(\chi\) \(=\) 693.190
Dual form 693.2.m.k.631.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.614338 - 0.446343i) q^{2} +(-0.439845 + 1.35370i) q^{4} +(-2.31804 - 1.68415i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.803314 + 2.47235i) q^{8} +O(q^{10})\) \(q+(0.614338 - 0.446343i) q^{2} +(-0.439845 + 1.35370i) q^{4} +(-2.31804 - 1.68415i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.803314 + 2.47235i) q^{8} -2.17577 q^{10} +(-3.15889 + 1.01064i) q^{11} +(5.63576 - 4.09462i) q^{13} +(-0.234656 - 0.722197i) q^{14} +(-0.706036 - 0.512965i) q^{16} +(-5.38702 - 3.91390i) q^{17} +(-1.77718 - 5.46959i) q^{19} +(3.29942 - 2.39717i) q^{20} +(-1.48953 + 2.03082i) q^{22} -0.724581 q^{23} +(0.991838 + 3.05256i) q^{25} +(1.63466 - 5.03096i) q^{26} +(1.15153 + 0.836634i) q^{28} +(2.33846 - 7.19703i) q^{29} +(-2.28117 + 1.65737i) q^{31} -5.86186 q^{32} -5.05639 q^{34} +(-2.31804 + 1.68415i) q^{35} +(-0.532161 + 1.63782i) q^{37} +(-3.53310 - 2.56694i) q^{38} +(2.30170 - 7.08389i) q^{40} +(0.346364 + 1.06600i) q^{41} -11.7092 q^{43} +(0.0213116 - 4.72073i) q^{44} +(-0.445138 + 0.323411i) q^{46} +(1.60366 + 4.93556i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(1.97181 + 1.43261i) q^{50} +(3.06404 + 9.43015i) q^{52} +(5.06259 - 3.67819i) q^{53} +(9.02450 + 2.97735i) q^{55} +2.59958 q^{56} +(-1.77574 - 5.46516i) q^{58} +(1.23059 - 3.78737i) q^{59} +(4.83043 + 3.50951i) q^{61} +(-0.661656 + 2.03637i) q^{62} +(-2.18909 + 1.59047i) q^{64} -19.9599 q^{65} +10.3611 q^{67} +(7.66771 - 5.57092i) q^{68} +(-0.672349 + 2.06928i) q^{70} +(0.805120 + 0.584954i) q^{71} +(1.09294 - 3.36374i) q^{73} +(0.404104 + 1.24370i) q^{74} +8.18588 q^{76} +(-0.0149727 + 3.31659i) q^{77} +(0.541875 - 0.393695i) q^{79} +(0.772706 + 2.37814i) q^{80} +(0.688585 + 0.500286i) q^{82} +(-10.8603 - 7.89044i) q^{83} +(5.89571 + 18.1451i) q^{85} +(-7.19343 + 5.22633i) q^{86} +(-5.03624 - 6.99801i) q^{88} +16.6006 q^{89} +(-2.15267 - 6.62524i) q^{91} +(0.318703 - 0.980868i) q^{92} +(3.18814 + 2.31632i) q^{94} +(-5.09205 + 15.6717i) q^{95} +(-8.18083 + 5.94372i) q^{97} -0.759363 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.614338 0.446343i 0.434402 0.315612i −0.349004 0.937121i \(-0.613480\pi\)
0.783407 + 0.621509i \(0.213480\pi\)
\(3\) 0 0
\(4\) −0.439845 + 1.35370i −0.219922 + 0.676851i
\(5\) −2.31804 1.68415i −1.03666 0.753175i −0.0670269 0.997751i \(-0.521351\pi\)
−0.969630 + 0.244576i \(0.921351\pi\)
\(6\) 0 0
\(7\) 0.309017 0.951057i 0.116797 0.359466i
\(8\) 0.803314 + 2.47235i 0.284014 + 0.874107i
\(9\) 0 0
\(10\) −2.17577 −0.688038
\(11\) −3.15889 + 1.01064i −0.952442 + 0.304720i
\(12\) 0 0
\(13\) 5.63576 4.09462i 1.56308 1.13564i 0.629652 0.776877i \(-0.283197\pi\)
0.933427 0.358767i \(-0.116803\pi\)
\(14\) −0.234656 0.722197i −0.0627145 0.193015i
\(15\) 0 0
\(16\) −0.706036 0.512965i −0.176509 0.128241i
\(17\) −5.38702 3.91390i −1.30654 0.949260i −0.306548 0.951855i \(-0.599174\pi\)
−0.999997 + 0.00259534i \(0.999174\pi\)
\(18\) 0 0
\(19\) −1.77718 5.46959i −0.407712 1.25481i −0.918609 0.395167i \(-0.870687\pi\)
0.510897 0.859642i \(-0.329313\pi\)
\(20\) 3.29942 2.39717i 0.737772 0.536023i
\(21\) 0 0
\(22\) −1.48953 + 2.03082i −0.317570 + 0.432973i
\(23\) −0.724581 −0.151086 −0.0755428 0.997143i \(-0.524069\pi\)
−0.0755428 + 0.997143i \(0.524069\pi\)
\(24\) 0 0
\(25\) 0.991838 + 3.05256i 0.198368 + 0.610513i
\(26\) 1.63466 5.03096i 0.320583 0.986653i
\(27\) 0 0
\(28\) 1.15153 + 0.836634i 0.217618 + 0.158109i
\(29\) 2.33846 7.19703i 0.434240 1.33645i −0.459623 0.888114i \(-0.652015\pi\)
0.893863 0.448340i \(-0.147985\pi\)
\(30\) 0 0
\(31\) −2.28117 + 1.65737i −0.409710 + 0.297672i −0.773484 0.633815i \(-0.781488\pi\)
0.363774 + 0.931487i \(0.381488\pi\)
\(32\) −5.86186 −1.03624
\(33\) 0 0
\(34\) −5.05639 −0.867164
\(35\) −2.31804 + 1.68415i −0.391820 + 0.284674i
\(36\) 0 0
\(37\) −0.532161 + 1.63782i −0.0874868 + 0.269257i −0.985223 0.171277i \(-0.945211\pi\)
0.897736 + 0.440534i \(0.145211\pi\)
\(38\) −3.53310 2.56694i −0.573144 0.416413i
\(39\) 0 0
\(40\) 2.30170 7.08389i 0.363930 1.12006i
\(41\) 0.346364 + 1.06600i 0.0540929 + 0.166481i 0.974453 0.224591i \(-0.0721045\pi\)
−0.920360 + 0.391072i \(0.872104\pi\)
\(42\) 0 0
\(43\) −11.7092 −1.78564 −0.892821 0.450411i \(-0.851277\pi\)
−0.892821 + 0.450411i \(0.851277\pi\)
\(44\) 0.0213116 4.72073i 0.00321285 0.711676i
\(45\) 0 0
\(46\) −0.445138 + 0.323411i −0.0656320 + 0.0476844i
\(47\) 1.60366 + 4.93556i 0.233918 + 0.719926i 0.997263 + 0.0739350i \(0.0235557\pi\)
−0.763345 + 0.645991i \(0.776444\pi\)
\(48\) 0 0
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) 1.97181 + 1.43261i 0.278856 + 0.202601i
\(51\) 0 0
\(52\) 3.06404 + 9.43015i 0.424906 + 1.30773i
\(53\) 5.06259 3.67819i 0.695401 0.505238i −0.183030 0.983107i \(-0.558591\pi\)
0.878431 + 0.477869i \(0.158591\pi\)
\(54\) 0 0
\(55\) 9.02450 + 2.97735i 1.21686 + 0.401465i
\(56\) 2.59958 0.347383
\(57\) 0 0
\(58\) −1.77574 5.46516i −0.233166 0.717611i
\(59\) 1.23059 3.78737i 0.160209 0.493074i −0.838442 0.544991i \(-0.816533\pi\)
0.998651 + 0.0519172i \(0.0165332\pi\)
\(60\) 0 0
\(61\) 4.83043 + 3.50951i 0.618473 + 0.449347i 0.852388 0.522910i \(-0.175154\pi\)
−0.233915 + 0.972257i \(0.575154\pi\)
\(62\) −0.661656 + 2.03637i −0.0840303 + 0.258619i
\(63\) 0 0
\(64\) −2.18909 + 1.59047i −0.273636 + 0.198808i
\(65\) −19.9599 −2.47572
\(66\) 0 0
\(67\) 10.3611 1.26581 0.632906 0.774229i \(-0.281862\pi\)
0.632906 + 0.774229i \(0.281862\pi\)
\(68\) 7.66771 5.57092i 0.929846 0.675573i
\(69\) 0 0
\(70\) −0.672349 + 2.06928i −0.0803610 + 0.247326i
\(71\) 0.805120 + 0.584954i 0.0955502 + 0.0694213i 0.634535 0.772894i \(-0.281192\pi\)
−0.538984 + 0.842316i \(0.681192\pi\)
\(72\) 0 0
\(73\) 1.09294 3.36374i 0.127919 0.393696i −0.866502 0.499173i \(-0.833637\pi\)
0.994422 + 0.105478i \(0.0336372\pi\)
\(74\) 0.404104 + 1.24370i 0.0469761 + 0.144578i
\(75\) 0 0
\(76\) 8.18588 0.938984
\(77\) −0.0149727 + 3.31659i −0.00170629 + 0.377961i
\(78\) 0 0
\(79\) 0.541875 0.393695i 0.0609657 0.0442942i −0.556885 0.830590i \(-0.688004\pi\)
0.617851 + 0.786295i \(0.288004\pi\)
\(80\) 0.772706 + 2.37814i 0.0863912 + 0.265885i
\(81\) 0 0
\(82\) 0.688585 + 0.500286i 0.0760415 + 0.0552474i
\(83\) −10.8603 7.89044i −1.19207 0.866089i −0.198587 0.980083i \(-0.563635\pi\)
−0.993481 + 0.113994i \(0.963635\pi\)
\(84\) 0 0
\(85\) 5.89571 + 18.1451i 0.639479 + 1.96811i
\(86\) −7.19343 + 5.22633i −0.775688 + 0.563570i
\(87\) 0 0
\(88\) −5.03624 6.99801i −0.536865 0.745991i
\(89\) 16.6006 1.75966 0.879828 0.475292i \(-0.157657\pi\)
0.879828 + 0.475292i \(0.157657\pi\)
\(90\) 0 0
\(91\) −2.15267 6.62524i −0.225661 0.694514i
\(92\) 0.318703 0.980868i 0.0332271 0.102263i
\(93\) 0 0
\(94\) 3.18814 + 2.31632i 0.328832 + 0.238910i
\(95\) −5.09205 + 15.6717i −0.522434 + 1.60789i
\(96\) 0 0
\(97\) −8.18083 + 5.94372i −0.830638 + 0.603493i −0.919740 0.392529i \(-0.871600\pi\)
0.0891021 + 0.996022i \(0.471600\pi\)
\(98\) −0.759363 −0.0767073
\(99\) 0 0
\(100\) −4.56852 −0.456852
\(101\) −5.19674 + 3.77565i −0.517095 + 0.375692i −0.815508 0.578745i \(-0.803543\pi\)
0.298413 + 0.954437i \(0.403543\pi\)
\(102\) 0 0
\(103\) −2.76813 + 8.51944i −0.272752 + 0.839446i 0.717053 + 0.697019i \(0.245491\pi\)
−0.989805 + 0.142427i \(0.954509\pi\)
\(104\) 14.6506 + 10.6443i 1.43661 + 1.04376i
\(105\) 0 0
\(106\) 1.46841 4.51930i 0.142625 0.438953i
\(107\) 1.39951 + 4.30724i 0.135296 + 0.416397i 0.995636 0.0933231i \(-0.0297489\pi\)
−0.860340 + 0.509720i \(0.829749\pi\)
\(108\) 0 0
\(109\) −1.02744 −0.0984106 −0.0492053 0.998789i \(-0.515669\pi\)
−0.0492053 + 0.998789i \(0.515669\pi\)
\(110\) 6.87301 2.19892i 0.655316 0.209659i
\(111\) 0 0
\(112\) −0.706036 + 0.512965i −0.0667142 + 0.0484707i
\(113\) 4.09077 + 12.5901i 0.384827 + 1.18438i 0.936605 + 0.350386i \(0.113950\pi\)
−0.551778 + 0.833991i \(0.686050\pi\)
\(114\) 0 0
\(115\) 1.67961 + 1.22030i 0.156624 + 0.113794i
\(116\) 8.71408 + 6.33115i 0.809082 + 0.587832i
\(117\) 0 0
\(118\) −0.934466 2.87599i −0.0860245 0.264756i
\(119\) −5.38702 + 3.91390i −0.493827 + 0.358787i
\(120\) 0 0
\(121\) 8.95720 6.38503i 0.814291 0.580457i
\(122\) 4.53396 0.410486
\(123\) 0 0
\(124\) −1.24022 3.81701i −0.111375 0.342778i
\(125\) −1.58519 + 4.87871i −0.141784 + 0.436365i
\(126\) 0 0
\(127\) −13.1816 9.57702i −1.16968 0.849823i −0.178711 0.983902i \(-0.557193\pi\)
−0.990971 + 0.134078i \(0.957193\pi\)
\(128\) 2.98788 9.19576i 0.264094 0.812798i
\(129\) 0 0
\(130\) −12.2621 + 8.90894i −1.07546 + 0.781365i
\(131\) 6.19831 0.541549 0.270774 0.962643i \(-0.412720\pi\)
0.270774 + 0.962643i \(0.412720\pi\)
\(132\) 0 0
\(133\) −5.75106 −0.498680
\(134\) 6.36522 4.62460i 0.549871 0.399505i
\(135\) 0 0
\(136\) 5.34905 16.4627i 0.458677 1.41166i
\(137\) −12.9520 9.41016i −1.10656 0.803964i −0.124443 0.992227i \(-0.539714\pi\)
−0.982119 + 0.188262i \(0.939714\pi\)
\(138\) 0 0
\(139\) 1.42581 4.38819i 0.120935 0.372201i −0.872203 0.489144i \(-0.837309\pi\)
0.993139 + 0.116943i \(0.0373094\pi\)
\(140\) −1.26026 3.87870i −0.106512 0.327810i
\(141\) 0 0
\(142\) 0.755706 0.0634174
\(143\) −13.6646 + 18.6302i −1.14269 + 1.55794i
\(144\) 0 0
\(145\) −17.5415 + 12.7447i −1.45674 + 1.05839i
\(146\) −0.829942 2.55430i −0.0686865 0.211395i
\(147\) 0 0
\(148\) −1.98306 1.44078i −0.163006 0.118431i
\(149\) 5.83982 + 4.24287i 0.478416 + 0.347590i 0.800712 0.599049i \(-0.204455\pi\)
−0.322296 + 0.946639i \(0.604455\pi\)
\(150\) 0 0
\(151\) 0.193552 + 0.595693i 0.0157511 + 0.0484768i 0.958623 0.284678i \(-0.0918867\pi\)
−0.942872 + 0.333155i \(0.891887\pi\)
\(152\) 12.0951 8.78759i 0.981041 0.712768i
\(153\) 0 0
\(154\) 1.47114 + 2.04419i 0.118548 + 0.164726i
\(155\) 8.07909 0.648928
\(156\) 0 0
\(157\) −1.89969 5.84664i −0.151612 0.466613i 0.846190 0.532881i \(-0.178891\pi\)
−0.997802 + 0.0662683i \(0.978891\pi\)
\(158\) 0.157171 0.483724i 0.0125039 0.0384830i
\(159\) 0 0
\(160\) 13.5880 + 9.87226i 1.07423 + 0.780471i
\(161\) −0.223908 + 0.689118i −0.0176464 + 0.0543101i
\(162\) 0 0
\(163\) −17.5084 + 12.7206i −1.37136 + 0.996352i −0.373732 + 0.927537i \(0.621922\pi\)
−0.997629 + 0.0688158i \(0.978078\pi\)
\(164\) −1.59539 −0.124579
\(165\) 0 0
\(166\) −10.1937 −0.791186
\(167\) 19.4121 14.1037i 1.50216 1.09138i 0.532644 0.846339i \(-0.321198\pi\)
0.969513 0.245042i \(-0.0788017\pi\)
\(168\) 0 0
\(169\) 10.9787 33.7889i 0.844514 2.59915i
\(170\) 11.7209 + 8.51573i 0.898951 + 0.653126i
\(171\) 0 0
\(172\) 5.15025 15.8508i 0.392703 1.20861i
\(173\) −3.34074 10.2817i −0.253992 0.781707i −0.994027 0.109138i \(-0.965191\pi\)
0.740035 0.672569i \(-0.234809\pi\)
\(174\) 0 0
\(175\) 3.20966 0.242627
\(176\) 2.74872 + 0.906852i 0.207192 + 0.0683565i
\(177\) 0 0
\(178\) 10.1984 7.40954i 0.764399 0.555368i
\(179\) 1.83197 + 5.63824i 0.136928 + 0.421422i 0.995885 0.0906265i \(-0.0288869\pi\)
−0.858957 + 0.512048i \(0.828887\pi\)
\(180\) 0 0
\(181\) 3.92063 + 2.84851i 0.291418 + 0.211728i 0.723882 0.689923i \(-0.242356\pi\)
−0.432464 + 0.901651i \(0.642356\pi\)
\(182\) −4.27959 3.10931i −0.317224 0.230477i
\(183\) 0 0
\(184\) −0.582066 1.79142i −0.0429105 0.132065i
\(185\) 3.99191 2.90029i 0.293491 0.213234i
\(186\) 0 0
\(187\) 20.9726 + 6.91923i 1.53367 + 0.505984i
\(188\) −7.38665 −0.538727
\(189\) 0 0
\(190\) 3.86672 + 11.9005i 0.280521 + 0.863356i
\(191\) −4.84920 + 14.9243i −0.350876 + 1.07988i 0.607487 + 0.794330i \(0.292178\pi\)
−0.958362 + 0.285555i \(0.907822\pi\)
\(192\) 0 0
\(193\) 18.4090 + 13.3749i 1.32511 + 0.962749i 0.999853 + 0.0171238i \(0.00545094\pi\)
0.325257 + 0.945626i \(0.394549\pi\)
\(194\) −2.37286 + 7.30291i −0.170361 + 0.524318i
\(195\) 0 0
\(196\) 1.15153 0.836634i 0.0822520 0.0597596i
\(197\) 15.3025 1.09026 0.545129 0.838352i \(-0.316481\pi\)
0.545129 + 0.838352i \(0.316481\pi\)
\(198\) 0 0
\(199\) −0.547814 −0.0388335 −0.0194168 0.999811i \(-0.506181\pi\)
−0.0194168 + 0.999811i \(0.506181\pi\)
\(200\) −6.75024 + 4.90434i −0.477314 + 0.346789i
\(201\) 0 0
\(202\) −1.50732 + 4.63905i −0.106055 + 0.326403i
\(203\) −6.12216 4.44801i −0.429691 0.312189i
\(204\) 0 0
\(205\) 0.992419 3.05435i 0.0693135 0.213325i
\(206\) 2.10202 + 6.46935i 0.146455 + 0.450741i
\(207\) 0 0
\(208\) −6.07945 −0.421534
\(209\) 11.1417 + 15.4817i 0.770688 + 1.07089i
\(210\) 0 0
\(211\) 11.2232 8.15412i 0.772636 0.561353i −0.130124 0.991498i \(-0.541538\pi\)
0.902760 + 0.430145i \(0.141538\pi\)
\(212\) 2.75242 + 8.47108i 0.189037 + 0.581796i
\(213\) 0 0
\(214\) 2.78228 + 2.02144i 0.190193 + 0.138183i
\(215\) 27.1424 + 19.7201i 1.85110 + 1.34490i
\(216\) 0 0
\(217\) 0.871329 + 2.68168i 0.0591497 + 0.182044i
\(218\) −0.631193 + 0.458589i −0.0427498 + 0.0310595i
\(219\) 0 0
\(220\) −7.99982 + 10.9069i −0.539348 + 0.735345i
\(221\) −46.3859 −3.12025
\(222\) 0 0
\(223\) −2.34908 7.22973i −0.157306 0.484138i 0.841081 0.540909i \(-0.181920\pi\)
−0.998387 + 0.0567705i \(0.981920\pi\)
\(224\) −1.81142 + 5.57496i −0.121030 + 0.372493i
\(225\) 0 0
\(226\) 8.13261 + 5.90869i 0.540973 + 0.393040i
\(227\) −0.0912083 + 0.280710i −0.00605371 + 0.0186314i −0.954038 0.299686i \(-0.903118\pi\)
0.947984 + 0.318318i \(0.103118\pi\)
\(228\) 0 0
\(229\) −5.75269 + 4.17958i −0.380149 + 0.276194i −0.761407 0.648275i \(-0.775491\pi\)
0.381258 + 0.924469i \(0.375491\pi\)
\(230\) 1.57652 0.103953
\(231\) 0 0
\(232\) 19.6721 1.29153
\(233\) −8.29543 + 6.02698i −0.543452 + 0.394841i −0.825365 0.564599i \(-0.809031\pi\)
0.281914 + 0.959440i \(0.409031\pi\)
\(234\) 0 0
\(235\) 4.59489 14.1416i 0.299738 0.922498i
\(236\) 4.58570 + 3.33171i 0.298504 + 0.216876i
\(237\) 0 0
\(238\) −1.56251 + 4.80891i −0.101283 + 0.311716i
\(239\) −6.11983 18.8349i −0.395859 1.21833i −0.928291 0.371856i \(-0.878722\pi\)
0.532432 0.846473i \(-0.321278\pi\)
\(240\) 0 0
\(241\) −20.0305 −1.29028 −0.645138 0.764066i \(-0.723200\pi\)
−0.645138 + 0.764066i \(0.723200\pi\)
\(242\) 2.65284 7.92054i 0.170531 0.509152i
\(243\) 0 0
\(244\) −6.87548 + 4.99533i −0.440157 + 0.319793i
\(245\) 0.885411 + 2.72501i 0.0565668 + 0.174095i
\(246\) 0 0
\(247\) −32.4116 23.5484i −2.06230 1.49835i
\(248\) −5.93008 4.30846i −0.376561 0.273587i
\(249\) 0 0
\(250\) 1.20374 + 3.70472i 0.0761309 + 0.234307i
\(251\) 2.17876 1.58296i 0.137522 0.0999155i −0.516897 0.856047i \(-0.672913\pi\)
0.654419 + 0.756132i \(0.272913\pi\)
\(252\) 0 0
\(253\) 2.28887 0.732293i 0.143900 0.0460389i
\(254\) −12.3726 −0.776327
\(255\) 0 0
\(256\) −3.94121 12.1298i −0.246325 0.758111i
\(257\) 7.83640 24.1179i 0.488821 1.50444i −0.337549 0.941308i \(-0.609598\pi\)
0.826370 0.563128i \(-0.190402\pi\)
\(258\) 0 0
\(259\) 1.39322 + 1.01223i 0.0865702 + 0.0628970i
\(260\) 8.77924 27.0197i 0.544465 1.67569i
\(261\) 0 0
\(262\) 3.80786 2.76657i 0.235250 0.170919i
\(263\) −9.04980 −0.558034 −0.279017 0.960286i \(-0.590009\pi\)
−0.279017 + 0.960286i \(0.590009\pi\)
\(264\) 0 0
\(265\) −17.9299 −1.10142
\(266\) −3.53310 + 2.56694i −0.216628 + 0.157389i
\(267\) 0 0
\(268\) −4.55728 + 14.0259i −0.278380 + 0.856766i
\(269\) −2.21095 1.60635i −0.134804 0.0979410i 0.518340 0.855175i \(-0.326550\pi\)
−0.653144 + 0.757234i \(0.726550\pi\)
\(270\) 0 0
\(271\) 5.54748 17.0734i 0.336986 1.03714i −0.628750 0.777608i \(-0.716433\pi\)
0.965736 0.259528i \(-0.0835669\pi\)
\(272\) 1.79574 + 5.52671i 0.108883 + 0.335106i
\(273\) 0 0
\(274\) −12.1570 −0.734434
\(275\) −6.21816 8.64033i −0.374969 0.521031i
\(276\) 0 0
\(277\) 9.02080 6.55399i 0.542007 0.393791i −0.282823 0.959172i \(-0.591271\pi\)
0.824830 + 0.565381i \(0.191271\pi\)
\(278\) −1.08271 3.33223i −0.0649364 0.199854i
\(279\) 0 0
\(280\) −6.02592 4.37809i −0.360118 0.261641i
\(281\) −3.20564 2.32904i −0.191233 0.138939i 0.488049 0.872816i \(-0.337709\pi\)
−0.679282 + 0.733877i \(0.737709\pi\)
\(282\) 0 0
\(283\) 1.77657 + 5.46773i 0.105606 + 0.325023i 0.989872 0.141961i \(-0.0453407\pi\)
−0.884266 + 0.466984i \(0.845341\pi\)
\(284\) −1.14598 + 0.832605i −0.0680015 + 0.0494060i
\(285\) 0 0
\(286\) −0.0792034 + 17.5443i −0.00468340 + 1.03742i
\(287\) 1.12086 0.0661621
\(288\) 0 0
\(289\) 8.44809 + 26.0005i 0.496946 + 1.52944i
\(290\) −5.08793 + 15.6590i −0.298774 + 0.919531i
\(291\) 0 0
\(292\) 4.07277 + 2.95904i 0.238341 + 0.173165i
\(293\) 7.18272 22.1061i 0.419619 1.29145i −0.488434 0.872601i \(-0.662432\pi\)
0.908053 0.418854i \(-0.137568\pi\)
\(294\) 0 0
\(295\) −9.23106 + 6.70676i −0.537453 + 0.390482i
\(296\) −4.47676 −0.260206
\(297\) 0 0
\(298\) 5.48140 0.317529
\(299\) −4.08357 + 2.96689i −0.236159 + 0.171579i
\(300\) 0 0
\(301\) −3.61835 + 11.1362i −0.208558 + 0.641877i
\(302\) 0.384790 + 0.279566i 0.0221422 + 0.0160872i
\(303\) 0 0
\(304\) −1.55096 + 4.77336i −0.0889535 + 0.273771i
\(305\) −5.28656 16.2704i −0.302707 0.931638i
\(306\) 0 0
\(307\) 3.87940 0.221409 0.110705 0.993853i \(-0.464689\pi\)
0.110705 + 0.993853i \(0.464689\pi\)
\(308\) −4.48309 1.47905i −0.255448 0.0842769i
\(309\) 0 0
\(310\) 4.96329 3.60604i 0.281896 0.204809i
\(311\) 1.15776 + 3.56321i 0.0656504 + 0.202051i 0.978501 0.206243i \(-0.0661238\pi\)
−0.912850 + 0.408294i \(0.866124\pi\)
\(312\) 0 0
\(313\) −14.6142 10.6178i −0.826044 0.600156i 0.0923934 0.995723i \(-0.470548\pi\)
−0.918437 + 0.395567i \(0.870548\pi\)
\(314\) −3.77666 2.74390i −0.213129 0.154847i
\(315\) 0 0
\(316\) 0.294606 + 0.906703i 0.0165729 + 0.0510060i
\(317\) −5.99841 + 4.35810i −0.336904 + 0.244775i −0.743354 0.668898i \(-0.766766\pi\)
0.406450 + 0.913673i \(0.366766\pi\)
\(318\) 0 0
\(319\) −0.113304 + 25.0980i −0.00634382 + 1.40522i
\(320\) 7.75298 0.433405
\(321\) 0 0
\(322\) 0.170027 + 0.523291i 0.00947526 + 0.0291619i
\(323\) −11.8337 + 36.4205i −0.658446 + 2.02649i
\(324\) 0 0
\(325\) 18.0889 + 13.1423i 1.00339 + 0.729005i
\(326\) −5.07832 + 15.6295i −0.281262 + 0.865636i
\(327\) 0 0
\(328\) −2.35728 + 1.71266i −0.130159 + 0.0945660i
\(329\) 5.18956 0.286110
\(330\) 0 0
\(331\) 14.5172 0.797937 0.398968 0.916965i \(-0.369368\pi\)
0.398968 + 0.916965i \(0.369368\pi\)
\(332\) 15.4581 11.2310i 0.848376 0.616381i
\(333\) 0 0
\(334\) 5.63051 17.3289i 0.308088 0.948197i
\(335\) −24.0174 17.4497i −1.31221 0.953378i
\(336\) 0 0
\(337\) 3.26146 10.0378i 0.177663 0.546791i −0.822082 0.569369i \(-0.807187\pi\)
0.999745 + 0.0225781i \(0.00718744\pi\)
\(338\) −8.33681 25.6581i −0.453463 1.39561i
\(339\) 0 0
\(340\) −27.1563 −1.47276
\(341\) 5.53096 7.54089i 0.299518 0.408362i
\(342\) 0 0
\(343\) −0.809017 + 0.587785i −0.0436828 + 0.0317374i
\(344\) −9.40620 28.9493i −0.507148 1.56084i
\(345\) 0 0
\(346\) −6.64153 4.82535i −0.357051 0.259413i
\(347\) 18.2109 + 13.2310i 0.977615 + 0.710279i 0.957174 0.289512i \(-0.0934931\pi\)
0.0204406 + 0.999791i \(0.493493\pi\)
\(348\) 0 0
\(349\) −6.40301 19.7064i −0.342745 1.05486i −0.962780 0.270287i \(-0.912881\pi\)
0.620034 0.784575i \(-0.287119\pi\)
\(350\) 1.97181 1.43261i 0.105398 0.0765760i
\(351\) 0 0
\(352\) 18.5170 5.92425i 0.986959 0.315764i
\(353\) 6.01460 0.320125 0.160062 0.987107i \(-0.448830\pi\)
0.160062 + 0.987107i \(0.448830\pi\)
\(354\) 0 0
\(355\) −0.881146 2.71189i −0.0467664 0.143932i
\(356\) −7.30167 + 22.4722i −0.386988 + 1.19103i
\(357\) 0 0
\(358\) 3.64204 + 2.64609i 0.192488 + 0.139850i
\(359\) −5.70755 + 17.5660i −0.301233 + 0.927100i 0.679823 + 0.733376i \(0.262056\pi\)
−0.981056 + 0.193724i \(0.937944\pi\)
\(360\) 0 0
\(361\) −11.3867 + 8.27292i −0.599300 + 0.435417i
\(362\) 3.68000 0.193417
\(363\) 0 0
\(364\) 9.91544 0.519710
\(365\) −8.19852 + 5.95658i −0.429130 + 0.311781i
\(366\) 0 0
\(367\) −1.24531 + 3.83267i −0.0650046 + 0.200063i −0.978284 0.207271i \(-0.933542\pi\)
0.913279 + 0.407335i \(0.133542\pi\)
\(368\) 0.511581 + 0.371685i 0.0266680 + 0.0193754i
\(369\) 0 0
\(370\) 1.15786 3.56352i 0.0601942 0.185259i
\(371\) −1.93374 5.95144i −0.100395 0.308983i
\(372\) 0 0
\(373\) 5.06561 0.262287 0.131144 0.991363i \(-0.458135\pi\)
0.131144 + 0.991363i \(0.458135\pi\)
\(374\) 15.9726 5.11021i 0.825923 0.264242i
\(375\) 0 0
\(376\) −10.9142 + 7.92962i −0.562856 + 0.408939i
\(377\) −16.2901 50.1358i −0.838984 2.58213i
\(378\) 0 0
\(379\) −1.77707 1.29111i −0.0912817 0.0663201i 0.541208 0.840889i \(-0.317967\pi\)
−0.632490 + 0.774569i \(0.717967\pi\)
\(380\) −18.9752 13.7863i −0.973405 0.707220i
\(381\) 0 0
\(382\) 3.68230 + 11.3330i 0.188403 + 0.579845i
\(383\) 19.8093 14.3923i 1.01221 0.735413i 0.0475374 0.998869i \(-0.484863\pi\)
0.964671 + 0.263457i \(0.0848627\pi\)
\(384\) 0 0
\(385\) 5.62035 7.66276i 0.286440 0.390530i
\(386\) 17.2792 0.879487
\(387\) 0 0
\(388\) −4.44774 13.6887i −0.225800 0.694940i
\(389\) 10.6057 32.6410i 0.537730 1.65496i −0.199944 0.979807i \(-0.564076\pi\)
0.737675 0.675156i \(-0.235924\pi\)
\(390\) 0 0
\(391\) 3.90333 + 2.83594i 0.197400 + 0.143420i
\(392\) 0.803314 2.47235i 0.0405735 0.124872i
\(393\) 0 0
\(394\) 9.40090 6.83016i 0.473611 0.344098i
\(395\) −1.91913 −0.0965618
\(396\) 0 0
\(397\) 8.46742 0.424968 0.212484 0.977165i \(-0.431845\pi\)
0.212484 + 0.977165i \(0.431845\pi\)
\(398\) −0.336543 + 0.244513i −0.0168694 + 0.0122563i
\(399\) 0 0
\(400\) 0.865586 2.66400i 0.0432793 0.133200i
\(401\) −23.3870 16.9917i −1.16789 0.848523i −0.177137 0.984186i \(-0.556684\pi\)
−0.990755 + 0.135663i \(0.956684\pi\)
\(402\) 0 0
\(403\) −6.06984 + 18.6811i −0.302360 + 0.930570i
\(404\) −2.82535 8.69554i −0.140567 0.432619i
\(405\) 0 0
\(406\) −5.74641 −0.285189
\(407\) 0.0257846 5.71153i 0.00127809 0.283110i
\(408\) 0 0
\(409\) 1.29084 0.937848i 0.0638278 0.0463736i −0.555414 0.831574i \(-0.687440\pi\)
0.619242 + 0.785200i \(0.287440\pi\)
\(410\) −0.753606 2.31936i −0.0372180 0.114545i
\(411\) 0 0
\(412\) −10.3152 7.49446i −0.508196 0.369226i
\(413\) −3.22173 2.34072i −0.158531 0.115179i
\(414\) 0 0
\(415\) 11.8858 + 36.5807i 0.583450 + 1.79567i
\(416\) −33.0361 + 24.0021i −1.61973 + 1.17680i
\(417\) 0 0
\(418\) 13.7549 + 4.53800i 0.672776 + 0.221961i
\(419\) −0.224640 −0.0109744 −0.00548719 0.999985i \(-0.501747\pi\)
−0.00548719 + 0.999985i \(0.501747\pi\)
\(420\) 0 0
\(421\) 3.56288 + 10.9654i 0.173644 + 0.534422i 0.999569 0.0293585i \(-0.00934643\pi\)
−0.825925 + 0.563780i \(0.809346\pi\)
\(422\) 3.25530 10.0188i 0.158465 0.487706i
\(423\) 0 0
\(424\) 13.1606 + 9.56175i 0.639136 + 0.464359i
\(425\) 6.60438 20.3262i 0.320359 0.985964i
\(426\) 0 0
\(427\) 4.83043 3.50951i 0.233761 0.169837i
\(428\) −6.44630 −0.311593
\(429\) 0 0
\(430\) 25.4766 1.22859
\(431\) −22.5643 + 16.3940i −1.08689 + 0.789669i −0.978871 0.204480i \(-0.934450\pi\)
−0.108016 + 0.994149i \(0.534450\pi\)
\(432\) 0 0
\(433\) 8.02421 24.6960i 0.385619 1.18681i −0.550412 0.834893i \(-0.685529\pi\)
0.936030 0.351919i \(-0.114471\pi\)
\(434\) 1.73224 + 1.25854i 0.0831500 + 0.0604120i
\(435\) 0 0
\(436\) 0.451912 1.39084i 0.0216427 0.0666093i
\(437\) 1.28771 + 3.96316i 0.0615995 + 0.189584i
\(438\) 0 0
\(439\) 23.5551 1.12422 0.562112 0.827061i \(-0.309989\pi\)
0.562112 + 0.827061i \(0.309989\pi\)
\(440\) −0.111523 + 24.7034i −0.00531666 + 1.17769i
\(441\) 0 0
\(442\) −28.4966 + 20.7040i −1.35545 + 0.984789i
\(443\) 7.67635 + 23.6254i 0.364714 + 1.12248i 0.950160 + 0.311764i \(0.100920\pi\)
−0.585445 + 0.810712i \(0.699080\pi\)
\(444\) 0 0
\(445\) −38.4807 27.9579i −1.82416 1.32533i
\(446\) −4.67007 3.39300i −0.221134 0.160663i
\(447\) 0 0
\(448\) 0.836158 + 2.57343i 0.0395048 + 0.121583i
\(449\) 14.8961 10.8227i 0.702993 0.510754i −0.177913 0.984046i \(-0.556935\pi\)
0.880906 + 0.473292i \(0.156935\pi\)
\(450\) 0 0
\(451\) −2.17147 3.01732i −0.102251 0.142080i
\(452\) −18.8426 −0.886279
\(453\) 0 0
\(454\) 0.0692602 + 0.213161i 0.00325054 + 0.0100041i
\(455\) −6.16794 + 18.9830i −0.289157 + 0.889935i
\(456\) 0 0
\(457\) −3.73256 2.71186i −0.174602 0.126856i 0.497052 0.867721i \(-0.334416\pi\)
−0.671654 + 0.740865i \(0.734416\pi\)
\(458\) −1.66857 + 5.13534i −0.0779673 + 0.239959i
\(459\) 0 0
\(460\) −2.39070 + 1.73694i −0.111467 + 0.0809853i
\(461\) 33.5148 1.56094 0.780470 0.625193i \(-0.214980\pi\)
0.780470 + 0.625193i \(0.214980\pi\)
\(462\) 0 0
\(463\) −16.5338 −0.768392 −0.384196 0.923252i \(-0.625521\pi\)
−0.384196 + 0.923252i \(0.625521\pi\)
\(464\) −5.34286 + 3.88182i −0.248036 + 0.180209i
\(465\) 0 0
\(466\) −2.40610 + 7.40521i −0.111460 + 0.343040i
\(467\) 15.7310 + 11.4292i 0.727944 + 0.528882i 0.888912 0.458077i \(-0.151462\pi\)
−0.160969 + 0.986960i \(0.551462\pi\)
\(468\) 0 0
\(469\) 3.20176 9.85400i 0.147844 0.455016i
\(470\) −3.48919 10.7386i −0.160944 0.495336i
\(471\) 0 0
\(472\) 10.3522 0.476501
\(473\) 36.9882 11.8339i 1.70072 0.544122i
\(474\) 0 0
\(475\) 14.9336 10.8499i 0.685200 0.497827i
\(476\) −2.92880 9.01393i −0.134242 0.413153i
\(477\) 0 0
\(478\) −12.1665 8.83945i −0.556481 0.404307i
\(479\) −31.7747 23.0857i −1.45182 1.05481i −0.985401 0.170250i \(-0.945543\pi\)
−0.466423 0.884562i \(-0.654457\pi\)
\(480\) 0 0
\(481\) 3.70713 + 11.4094i 0.169031 + 0.520223i
\(482\) −12.3055 + 8.94045i −0.560499 + 0.407227i
\(483\) 0 0
\(484\) 4.70365 + 14.9338i 0.213802 + 0.678809i
\(485\) 28.9736 1.31562
\(486\) 0 0
\(487\) −5.28443 16.2638i −0.239461 0.736984i −0.996498 0.0836126i \(-0.973354\pi\)
0.757038 0.653371i \(-0.226646\pi\)
\(488\) −4.79638 + 14.7617i −0.217122 + 0.668233i
\(489\) 0 0
\(490\) 1.76023 + 1.27888i 0.0795191 + 0.0577740i
\(491\) −10.7494 + 33.0833i −0.485115 + 1.49303i 0.346700 + 0.937976i \(0.387302\pi\)
−0.831815 + 0.555053i \(0.812698\pi\)
\(492\) 0 0
\(493\) −40.7657 + 29.6180i −1.83600 + 1.33393i
\(494\) −30.4224 −1.36877
\(495\) 0 0
\(496\) 2.46076 0.110491
\(497\) 0.805120 0.584954i 0.0361146 0.0262388i
\(498\) 0 0
\(499\) 4.83850 14.8914i 0.216601 0.666629i −0.782435 0.622732i \(-0.786023\pi\)
0.999036 0.0438968i \(-0.0139773\pi\)
\(500\) −5.90709 4.29175i −0.264173 0.191933i
\(501\) 0 0
\(502\) 0.631951 1.94494i 0.0282053 0.0868071i
\(503\) 6.76687 + 20.8263i 0.301720 + 0.928598i 0.980881 + 0.194609i \(0.0623438\pi\)
−0.679161 + 0.733989i \(0.737656\pi\)
\(504\) 0 0
\(505\) 18.4050 0.819012
\(506\) 1.07929 1.47150i 0.0479802 0.0654160i
\(507\) 0 0
\(508\) 18.7623 13.6316i 0.832443 0.604805i
\(509\) 8.29518 + 25.5299i 0.367677 + 1.13159i 0.948287 + 0.317413i \(0.102814\pi\)
−0.580610 + 0.814182i \(0.697186\pi\)
\(510\) 0 0
\(511\) −2.86136 2.07890i −0.126579 0.0919653i
\(512\) 7.80948 + 5.67392i 0.345134 + 0.250754i
\(513\) 0 0
\(514\) −5.95067 18.3143i −0.262473 0.807809i
\(515\) 20.7647 15.0864i 0.915000 0.664787i
\(516\) 0 0
\(517\) −10.0539 13.9702i −0.442170 0.614408i
\(518\) 1.30771 0.0574574
\(519\) 0 0
\(520\) −16.0340 49.3477i −0.703139 2.16404i
\(521\) 4.93408 15.1855i 0.216166 0.665291i −0.782903 0.622144i \(-0.786262\pi\)
0.999069 0.0431466i \(-0.0137383\pi\)
\(522\) 0 0
\(523\) −10.7132 7.78356i −0.468453 0.340351i 0.328385 0.944544i \(-0.393496\pi\)
−0.796838 + 0.604193i \(0.793496\pi\)
\(524\) −2.72629 + 8.39067i −0.119099 + 0.366548i
\(525\) 0 0
\(526\) −5.55963 + 4.03931i −0.242411 + 0.176122i
\(527\) 18.7755 0.817873
\(528\) 0 0
\(529\) −22.4750 −0.977173
\(530\) −11.0150 + 8.00288i −0.478462 + 0.347623i
\(531\) 0 0
\(532\) 2.52957 7.78523i 0.109671 0.337533i
\(533\) 6.31688 + 4.58948i 0.273615 + 0.198793i
\(534\) 0 0
\(535\) 4.00994 12.3413i 0.173365 0.533562i
\(536\) 8.32323 + 25.6163i 0.359509 + 1.10645i
\(537\) 0 0
\(538\) −2.07526 −0.0894706
\(539\) 3.14964 + 1.03912i 0.135665 + 0.0447582i
\(540\) 0 0
\(541\) 20.7068 15.0444i 0.890256 0.646809i −0.0456887 0.998956i \(-0.514548\pi\)
0.935945 + 0.352147i \(0.114548\pi\)
\(542\) −4.21256 12.9649i −0.180945 0.556891i
\(543\) 0 0
\(544\) 31.5780 + 22.9427i 1.35389 + 0.983662i
\(545\) 2.38163 + 1.73036i 0.102018 + 0.0741204i
\(546\) 0 0
\(547\) 9.31845 + 28.6792i 0.398428 + 1.22624i 0.926259 + 0.376887i \(0.123005\pi\)
−0.527831 + 0.849349i \(0.676995\pi\)
\(548\) 18.4354 13.3941i 0.787522 0.572168i
\(549\) 0 0
\(550\) −7.67660 2.53265i −0.327331 0.107993i
\(551\) −43.5206 −1.85404
\(552\) 0 0
\(553\) −0.206978 0.637012i −0.00880159 0.0270885i
\(554\) 2.61649 8.05273i 0.111164 0.342128i
\(555\) 0 0
\(556\) 5.31316 + 3.86024i 0.225328 + 0.163711i
\(557\) −0.226688 + 0.697675i −0.00960509 + 0.0295614i −0.955744 0.294199i \(-0.904947\pi\)
0.946139 + 0.323760i \(0.104947\pi\)
\(558\) 0 0
\(559\) −65.9905 + 47.9449i −2.79110 + 2.02785i
\(560\) 2.50053 0.105667
\(561\) 0 0
\(562\) −3.00890 −0.126923
\(563\) 16.9114 12.2868i 0.712730 0.517828i −0.171324 0.985215i \(-0.554804\pi\)
0.884053 + 0.467387i \(0.154804\pi\)
\(564\) 0 0
\(565\) 11.7211 36.0738i 0.493109 1.51763i
\(566\) 3.53190 + 2.56607i 0.148457 + 0.107860i
\(567\) 0 0
\(568\) −0.799445 + 2.46044i −0.0335440 + 0.103238i
\(569\) 8.73053 + 26.8698i 0.366003 + 1.12644i 0.949351 + 0.314218i \(0.101742\pi\)
−0.583348 + 0.812222i \(0.698258\pi\)
\(570\) 0 0
\(571\) 38.7512 1.62169 0.810843 0.585264i \(-0.199009\pi\)
0.810843 + 0.585264i \(0.199009\pi\)
\(572\) −19.2095 26.6922i −0.803189 1.11606i
\(573\) 0 0
\(574\) 0.688585 0.500286i 0.0287410 0.0208815i
\(575\) −0.718667 2.21183i −0.0299705 0.0922397i
\(576\) 0 0
\(577\) −10.2889 7.47535i −0.428334 0.311203i 0.352648 0.935756i \(-0.385281\pi\)
−0.780982 + 0.624553i \(0.785281\pi\)
\(578\) 16.7951 + 12.2024i 0.698585 + 0.507552i
\(579\) 0 0
\(580\) −9.53693 29.3517i −0.396000 1.21876i
\(581\) −10.8603 + 7.89044i −0.450560 + 0.327351i
\(582\) 0 0
\(583\) −12.2748 + 16.7355i −0.508372 + 0.693113i
\(584\) 9.19430 0.380463
\(585\) 0 0
\(586\) −5.45430 16.7866i −0.225315 0.693448i
\(587\) 2.40107 7.38974i 0.0991029 0.305007i −0.889198 0.457522i \(-0.848737\pi\)
0.988301 + 0.152515i \(0.0487371\pi\)
\(588\) 0 0
\(589\) 13.1192 + 9.53162i 0.540565 + 0.392744i
\(590\) −2.67748 + 8.24043i −0.110230 + 0.339253i
\(591\) 0 0
\(592\) 1.21587 0.883383i 0.0499720 0.0363068i
\(593\) −25.2949 −1.03874 −0.519368 0.854551i \(-0.673832\pi\)
−0.519368 + 0.854551i \(0.673832\pi\)
\(594\) 0 0
\(595\) 19.0789 0.782159
\(596\) −8.31220 + 6.03917i −0.340481 + 0.247374i
\(597\) 0 0
\(598\) −1.18444 + 3.64534i −0.0484355 + 0.149069i
\(599\) 9.64302 + 7.00606i 0.394003 + 0.286260i 0.767094 0.641535i \(-0.221702\pi\)
−0.373091 + 0.927795i \(0.621702\pi\)
\(600\) 0 0
\(601\) 6.49264 19.9823i 0.264840 0.815095i −0.726890 0.686754i \(-0.759035\pi\)
0.991730 0.128341i \(-0.0409650\pi\)
\(602\) 2.74765 + 8.45638i 0.111986 + 0.344657i
\(603\) 0 0
\(604\) −0.891525 −0.0362756
\(605\) −31.5165 0.284566i −1.28133 0.0115693i
\(606\) 0 0
\(607\) −20.8578 + 15.1541i −0.846593 + 0.615086i −0.924204 0.381898i \(-0.875271\pi\)
0.0776118 + 0.996984i \(0.475271\pi\)
\(608\) 10.4176 + 32.0620i 0.422488 + 1.30028i
\(609\) 0 0
\(610\) −10.5099 7.63588i −0.425533 0.309168i
\(611\) 29.2471 + 21.2493i 1.18321 + 0.859654i
\(612\) 0 0
\(613\) −9.86298 30.3551i −0.398362 1.22603i −0.926312 0.376757i \(-0.877039\pi\)
0.527950 0.849275i \(-0.322961\pi\)
\(614\) 2.38326 1.73154i 0.0961807 0.0698794i
\(615\) 0 0
\(616\) −8.21179 + 2.62725i −0.330863 + 0.105855i
\(617\) 13.9772 0.562701 0.281350 0.959605i \(-0.409218\pi\)
0.281350 + 0.959605i \(0.409218\pi\)
\(618\) 0 0
\(619\) 6.94500 + 21.3745i 0.279143 + 0.859114i 0.988093 + 0.153856i \(0.0491691\pi\)
−0.708950 + 0.705259i \(0.750831\pi\)
\(620\) −3.55354 + 10.9367i −0.142714 + 0.439228i
\(621\) 0 0
\(622\) 2.30167 + 1.67226i 0.0922884 + 0.0670515i
\(623\) 5.12986 15.7881i 0.205523 0.632536i
\(624\) 0 0
\(625\) 24.8744 18.0723i 0.994974 0.722891i
\(626\) −13.7173 −0.548252
\(627\) 0 0
\(628\) 8.75018 0.349170
\(629\) 9.27704 6.74016i 0.369900 0.268748i
\(630\) 0 0
\(631\) −12.6815 + 39.0297i −0.504843 + 1.55375i 0.296190 + 0.955129i \(0.404284\pi\)
−0.801034 + 0.598619i \(0.795716\pi\)
\(632\) 1.40865 + 1.02344i 0.0560330 + 0.0407103i
\(633\) 0 0
\(634\) −1.73984 + 5.35469i −0.0690980 + 0.212662i
\(635\) 14.4264 + 44.3998i 0.572493 + 1.76195i
\(636\) 0 0
\(637\) −6.96619 −0.276010
\(638\) 11.1327 + 15.4692i 0.440747 + 0.612432i
\(639\) 0 0
\(640\) −22.4131 + 16.2840i −0.885954 + 0.643683i
\(641\) 4.27426 + 13.1548i 0.168823 + 0.519584i 0.999298 0.0374724i \(-0.0119306\pi\)
−0.830475 + 0.557057i \(0.811931\pi\)
\(642\) 0 0
\(643\) 27.1122 + 19.6982i 1.06920 + 0.776820i 0.975768 0.218806i \(-0.0702160\pi\)
0.0934326 + 0.995626i \(0.470216\pi\)
\(644\) −0.834376 0.606210i −0.0328790 0.0238880i
\(645\) 0 0
\(646\) 8.98610 + 27.6564i 0.353553 + 1.08813i
\(647\) 6.94635 5.04682i 0.273089 0.198411i −0.442808 0.896616i \(-0.646018\pi\)
0.715897 + 0.698205i \(0.246018\pi\)
\(648\) 0 0
\(649\) −0.0596253 + 13.2076i −0.00234050 + 0.518443i
\(650\) 16.9787 0.665957
\(651\) 0 0
\(652\) −9.51892 29.2962i −0.372789 1.14733i
\(653\) 14.6622 45.1255i 0.573775 1.76590i −0.0665369 0.997784i \(-0.521195\pi\)
0.640312 0.768115i \(-0.278805\pi\)
\(654\) 0 0
\(655\) −14.3679 10.4389i −0.561400 0.407881i
\(656\) 0.302275 0.930306i 0.0118018 0.0363224i
\(657\) 0 0
\(658\) 3.18814 2.31632i 0.124287 0.0902996i
\(659\) 47.4501 1.84839 0.924197 0.381916i \(-0.124736\pi\)
0.924197 + 0.381916i \(0.124736\pi\)
\(660\) 0 0
\(661\) −24.3627 −0.947599 −0.473800 0.880633i \(-0.657118\pi\)
−0.473800 + 0.880633i \(0.657118\pi\)
\(662\) 8.91846 6.47964i 0.346626 0.251838i
\(663\) 0 0
\(664\) 10.7837 33.1888i 0.418489 1.28798i
\(665\) 13.3312 + 9.68566i 0.516961 + 0.375594i
\(666\) 0 0
\(667\) −1.69440 + 5.21483i −0.0656075 + 0.201919i
\(668\) 10.5540 + 32.4817i 0.408345 + 1.25676i
\(669\) 0 0
\(670\) −22.5433 −0.870926
\(671\) −18.8057 6.20433i −0.725985 0.239516i
\(672\) 0 0
\(673\) −25.8454 + 18.7778i −0.996268 + 0.723831i −0.961285 0.275557i \(-0.911138\pi\)
−0.0349835 + 0.999388i \(0.511138\pi\)
\(674\) −2.47664 7.62230i −0.0953965 0.293600i
\(675\) 0 0
\(676\) 40.9112 + 29.7237i 1.57351 + 1.14322i
\(677\) −0.820859 0.596389i −0.0315482 0.0229211i 0.571899 0.820324i \(-0.306207\pi\)
−0.603448 + 0.797403i \(0.706207\pi\)
\(678\) 0 0
\(679\) 3.12480 + 9.61714i 0.119919 + 0.369072i
\(680\) −40.1249 + 29.1525i −1.53872 + 1.11795i
\(681\) 0 0
\(682\) 0.0320589 7.10136i 0.00122760 0.271925i
\(683\) −0.904878 −0.0346242 −0.0173121 0.999850i \(-0.505511\pi\)
−0.0173121 + 0.999850i \(0.505511\pi\)
\(684\) 0 0
\(685\) 14.1750 + 43.6262i 0.541599 + 1.66687i
\(686\) −0.234656 + 0.722197i −0.00895921 + 0.0275736i
\(687\) 0 0
\(688\) 8.26715 + 6.00644i 0.315182 + 0.228993i
\(689\) 13.4708 41.4588i 0.513196 1.57945i
\(690\) 0 0
\(691\) 17.3563 12.6101i 0.660263 0.479709i −0.206489 0.978449i \(-0.566204\pi\)
0.866752 + 0.498740i \(0.166204\pi\)
\(692\) 15.3878 0.584958
\(693\) 0 0
\(694\) 17.0932 0.648851
\(695\) −10.6954 + 7.77069i −0.405701 + 0.294759i
\(696\) 0 0
\(697\) 2.30634 7.09819i 0.0873589 0.268863i
\(698\) −12.7294 9.24848i −0.481816 0.350060i
\(699\) 0 0
\(700\) −1.41175 + 4.34492i −0.0533591 + 0.164223i
\(701\) 5.89450 + 18.1414i 0.222632 + 0.685192i 0.998523 + 0.0543248i \(0.0173006\pi\)
−0.775891 + 0.630867i \(0.782699\pi\)
\(702\) 0 0
\(703\) 9.90396 0.373535
\(704\) 5.30771 7.23651i 0.200042 0.272736i
\(705\) 0 0
\(706\) 3.69500 2.68457i 0.139063 0.101035i
\(707\) 1.98498 + 6.10914i 0.0746528 + 0.229758i
\(708\) 0 0
\(709\) 7.86023 + 5.71079i 0.295197 + 0.214473i 0.725519 0.688202i \(-0.241600\pi\)
−0.430322 + 0.902676i \(0.641600\pi\)
\(710\) −1.75175 1.27272i −0.0657421 0.0477644i
\(711\) 0 0
\(712\) 13.3355 + 41.0424i 0.499768 + 1.53813i
\(713\) 1.65289 1.20090i 0.0619013 0.0449739i
\(714\) 0 0
\(715\) 63.0511 20.1723i 2.35798 0.754401i
\(716\) −8.43828 −0.315353
\(717\) 0 0
\(718\) 4.33410 + 13.3390i 0.161747 + 0.497807i
\(719\) 3.77630 11.6223i 0.140832 0.433437i −0.855619 0.517606i \(-0.826823\pi\)
0.996452 + 0.0841686i \(0.0268234\pi\)
\(720\) 0 0
\(721\) 7.24707 + 5.26530i 0.269895 + 0.196090i
\(722\) −3.30272 + 10.1647i −0.122915 + 0.378292i
\(723\) 0 0
\(724\) −5.58050 + 4.05447i −0.207398 + 0.150683i
\(725\) 24.2888 0.902062
\(726\) 0 0
\(727\) 0.0225849 0.000837628 0.000418814 1.00000i \(-0.499867\pi\)
0.000418814 1.00000i \(0.499867\pi\)
\(728\) 14.6506 10.6443i 0.542988 0.394504i
\(729\) 0 0
\(730\) −2.37799 + 7.31870i −0.0880134 + 0.270877i
\(731\) 63.0779 + 45.8288i 2.33302 + 1.69504i
\(732\) 0 0
\(733\) 1.63230 5.02369i 0.0602902 0.185554i −0.916375 0.400320i \(-0.868899\pi\)
0.976666 + 0.214766i \(0.0688989\pi\)
\(734\) 0.945642 + 2.91039i 0.0349043 + 0.107424i
\(735\) 0 0
\(736\) 4.24740 0.156561
\(737\) −32.7296 + 10.4714i −1.20561 + 0.385718i
\(738\) 0 0
\(739\) 29.1919 21.2091i 1.07384 0.780191i 0.0972419 0.995261i \(-0.468998\pi\)
0.976599 + 0.215070i \(0.0689979\pi\)
\(740\) 2.17031 + 6.67954i 0.0797823 + 0.245545i
\(741\) 0 0
\(742\) −3.84435 2.79308i −0.141130 0.102537i
\(743\) −27.6724 20.1052i −1.01520 0.737587i −0.0499072 0.998754i \(-0.515893\pi\)
−0.965294 + 0.261167i \(0.915893\pi\)
\(744\) 0 0
\(745\) −6.39126 19.6703i −0.234158 0.720663i
\(746\) 3.11200 2.26100i 0.113938 0.0827810i
\(747\) 0 0
\(748\) −18.5913 + 25.3472i −0.679764 + 0.926787i
\(749\) 4.52891 0.165483
\(750\) 0 0
\(751\) 2.26664 + 6.97600i 0.0827108 + 0.254558i 0.983857 0.178958i \(-0.0572727\pi\)
−0.901146 + 0.433516i \(0.857273\pi\)
\(752\) 1.39953 4.30731i 0.0510356 0.157071i
\(753\) 0 0
\(754\) −32.3854 23.5294i −1.17941 0.856889i
\(755\) 0.554576 1.70681i 0.0201831 0.0621172i
\(756\) 0 0
\(757\) 28.2299 20.5102i 1.02603 0.745457i 0.0585230 0.998286i \(-0.481361\pi\)
0.967511 + 0.252829i \(0.0813609\pi\)
\(758\) −1.66800 −0.0605844
\(759\) 0 0
\(760\) −42.8365 −1.55384
\(761\) 1.85160 1.34527i 0.0671205 0.0487659i −0.553719 0.832704i \(-0.686792\pi\)
0.620840 + 0.783938i \(0.286792\pi\)
\(762\) 0 0
\(763\) −0.317495 + 0.977150i −0.0114941 + 0.0353752i
\(764\) −18.0702 13.1287i −0.653756 0.474981i
\(765\) 0 0
\(766\) 5.74571 17.6835i 0.207601 0.638930i
\(767\) −8.57253 26.3835i −0.309536 0.952654i
\(768\) 0 0
\(769\) −9.59977 −0.346176 −0.173088 0.984906i \(-0.555375\pi\)
−0.173088 + 0.984906i \(0.555375\pi\)
\(770\) 0.0325770 7.21612i 0.00117399 0.260051i
\(771\) 0 0
\(772\) −26.2028 + 19.0375i −0.943060 + 0.685173i
\(773\) −4.25705 13.1019i −0.153116 0.471241i 0.844850 0.535004i \(-0.179690\pi\)
−0.997965 + 0.0637628i \(0.979690\pi\)
\(774\) 0 0
\(775\) −7.32177 5.31958i −0.263006 0.191085i
\(776\) −21.2667 15.4512i −0.763431 0.554665i
\(777\) 0 0
\(778\) −8.05358 24.7864i −0.288735 0.888634i
\(779\) 5.21502 3.78893i 0.186847 0.135753i
\(780\) 0 0
\(781\) −3.13447 1.03412i −0.112160 0.0370036i
\(782\) 3.66377 0.131016
\(783\) 0 0
\(784\) 0.269682 + 0.829996i 0.00963150 + 0.0296427i
\(785\) −5.44308 + 16.7521i −0.194272 + 0.597908i
\(786\) 0 0
\(787\) 1.81440 + 1.31824i 0.0646763 + 0.0469901i 0.619654 0.784875i \(-0.287273\pi\)
−0.554977 + 0.831865i \(0.687273\pi\)
\(788\) −6.73072 + 20.7150i −0.239772 + 0.737942i
\(789\) 0 0
\(790\) −1.17899 + 0.856589i −0.0419467 + 0.0304761i
\(791\) 13.2380 0.470689
\(792\) 0 0
\(793\) 41.5933 1.47702
\(794\) 5.20186 3.77937i 0.184607 0.134125i
\(795\) 0 0
\(796\) 0.240953 0.741578i 0.00854036 0.0262845i
\(797\) −14.7167 10.6923i −0.521293 0.378741i 0.295798 0.955251i \(-0.404414\pi\)
−0.817091 + 0.576509i \(0.804414\pi\)
\(798\) 0 0
\(799\) 10.6783 32.8646i 0.377773 1.16266i
\(800\) −5.81402 17.8937i −0.205557 0.632638i
\(801\) 0 0
\(802\) −21.9516 −0.775139
\(803\) −0.0529560 + 11.7303i −0.00186878 + 0.413952i
\(804\) 0 0
\(805\) 1.67961 1.22030i 0.0591983 0.0430101i
\(806\) 4.60922 + 14.1857i 0.162353 + 0.499670i
\(807\) 0 0
\(808\) −13.5093 9.81511i −0.475257 0.345294i
\(809\) 25.2420 + 18.3394i 0.887463 + 0.644780i 0.935215 0.354079i \(-0.115206\pi\)
−0.0477521 + 0.998859i \(0.515206\pi\)
\(810\) 0 0
\(811\) −7.78729 23.9668i −0.273449 0.841589i −0.989626 0.143670i \(-0.954110\pi\)
0.716177 0.697919i \(-0.245890\pi\)
\(812\) 8.71408 6.33115i 0.305804 0.222180i
\(813\) 0 0
\(814\) −2.53346 3.52032i −0.0887977 0.123387i
\(815\) 62.0084 2.17206
\(816\) 0 0
\(817\) 20.8094 + 64.0447i 0.728028 + 2.24064i
\(818\) 0.374409 1.15231i 0.0130909 0.0402896i
\(819\) 0 0
\(820\) 3.69817 + 2.68688i 0.129146 + 0.0938299i
\(821\) −3.67308 + 11.3046i −0.128191 + 0.394532i −0.994469 0.105030i \(-0.966506\pi\)
0.866278 + 0.499563i \(0.166506\pi\)
\(822\) 0 0
\(823\) −6.17171 + 4.48401i −0.215132 + 0.156303i −0.690133 0.723683i \(-0.742448\pi\)
0.475000 + 0.879986i \(0.342448\pi\)
\(824\) −23.2867 −0.811231
\(825\) 0 0
\(826\) −3.02399 −0.105218
\(827\) 9.22846 6.70487i 0.320905 0.233151i −0.415657 0.909522i \(-0.636448\pi\)
0.736562 + 0.676370i \(0.236448\pi\)
\(828\) 0 0
\(829\) −13.7968 + 42.4622i −0.479183 + 1.47477i 0.361050 + 0.932546i \(0.382418\pi\)
−0.840233 + 0.542226i \(0.817582\pi\)
\(830\) 23.6294 + 17.1678i 0.820188 + 0.595902i
\(831\) 0 0
\(832\) −5.82484 + 17.9270i −0.201940 + 0.621507i
\(833\) 2.05766 + 6.33282i 0.0712936 + 0.219419i
\(834\) 0 0
\(835\) −68.7509 −2.37922
\(836\) −25.8583 + 8.27300i −0.894328 + 0.286128i
\(837\) 0 0
\(838\) −0.138005 + 0.100266i −0.00476730 + 0.00346364i
\(839\) 3.11638 + 9.59122i 0.107589 + 0.331126i 0.990329 0.138736i \(-0.0443039\pi\)
−0.882740 + 0.469861i \(0.844304\pi\)
\(840\) 0 0
\(841\) −22.8673 16.6141i −0.788529 0.572900i
\(842\) 7.08315 + 5.14621i 0.244101 + 0.177350i
\(843\) 0 0
\(844\) 6.10180 + 18.7794i 0.210033 + 0.646414i
\(845\) −82.3546 + 59.8341i −2.83308 + 2.05836i
\(846\) 0 0
\(847\) −3.30459 10.4919i −0.113547 0.360505i
\(848\) −5.46116 −0.187537
\(849\) 0 0
\(850\) −5.01512 15.4350i −0.172017 0.529415i
\(851\) 0.385594 1.18674i 0.0132180 0.0406808i
\(852\) 0 0
\(853\) 15.3816 + 11.1754i 0.526654 + 0.382637i 0.819105 0.573644i \(-0.194471\pi\)
−0.292450 + 0.956281i \(0.594471\pi\)
\(854\) 1.40107 4.31205i 0.0479437 0.147555i
\(855\) 0 0
\(856\) −9.52476 + 6.92014i −0.325550 + 0.236526i
\(857\) −29.8781 −1.02062 −0.510308 0.859992i \(-0.670469\pi\)
−0.510308 + 0.859992i \(0.670469\pi\)
\(858\) 0 0
\(859\) −16.6976 −0.569714 −0.284857 0.958570i \(-0.591946\pi\)
−0.284857 + 0.958570i \(0.591946\pi\)
\(860\) −38.6337 + 28.0690i −1.31740 + 0.957145i
\(861\) 0 0
\(862\) −6.54481 + 20.1429i −0.222917 + 0.686068i
\(863\) −13.5768 9.86413i −0.462160 0.335779i 0.332218 0.943203i \(-0.392203\pi\)
−0.794378 + 0.607424i \(0.792203\pi\)
\(864\) 0 0
\(865\) −9.57206 + 29.4598i −0.325460 + 1.00166i
\(866\) −6.09329 18.7532i −0.207058 0.637260i
\(867\) 0 0
\(868\) −4.01344 −0.136225
\(869\) −1.31384 + 1.79128i −0.0445690 + 0.0607651i
\(870\) 0 0
\(871\) 58.3928 42.4248i 1.97856 1.43751i
\(872\) −0.825354 2.54018i −0.0279500 0.0860213i
\(873\) 0 0
\(874\) 2.56002 + 1.85996i 0.0865938 + 0.0629141i
\(875\) 4.15008 + 3.01521i 0.140298 + 0.101933i
\(876\) 0 0
\(877\) 1.71138 + 5.26709i 0.0577893 + 0.177857i 0.975784 0.218735i \(-0.0701929\pi\)
−0.917995 + 0.396592i \(0.870193\pi\)
\(878\) 14.4708 10.5136i 0.488365 0.354818i
\(879\) 0 0
\(880\) −4.84435 6.73137i −0.163303 0.226915i
\(881\) −6.77615 −0.228294 −0.114147 0.993464i \(-0.536414\pi\)
−0.114147 + 0.993464i \(0.536414\pi\)
\(882\) 0 0
\(883\) −7.40416 22.7877i −0.249170 0.766866i −0.994923 0.100643i \(-0.967910\pi\)
0.745753 0.666223i \(-0.232090\pi\)
\(884\) 20.4026 62.7927i 0.686213 2.11195i
\(885\) 0 0
\(886\) 15.2609 + 11.0877i 0.512699 + 0.372498i
\(887\) −8.55610 + 26.3330i −0.287286 + 0.884175i 0.698418 + 0.715690i \(0.253887\pi\)
−0.985704 + 0.168485i \(0.946113\pi\)
\(888\) 0 0
\(889\) −13.1816 + 9.57702i −0.442098 + 0.321203i
\(890\) −36.1189 −1.21071
\(891\) 0 0
\(892\) 10.8201 0.362285
\(893\) 24.1455 17.5427i 0.807999 0.587045i
\(894\) 0 0
\(895\) 5.24906 16.1550i 0.175457 0.540001i
\(896\) −7.82238 5.68329i −0.261327 0.189865i
\(897\) 0 0
\(898\) 4.32064 13.2976i 0.144182 0.443746i
\(899\) 6.59370 + 20.2933i 0.219912 + 0.676820i
\(900\) 0 0
\(901\) −41.6684 −1.38817
\(902\) −2.68078 0.884436i −0.0892601 0.0294485i
\(903\) 0 0
\(904\) −27.8409 + 20.2276i −0.925975 + 0.672760i
\(905\) −4.29085 13.2059i −0.142633 0.438978i
\(906\) 0 0
\(907\) −12.1001 8.79121i −0.401776 0.291907i 0.368488 0.929633i \(-0.379876\pi\)
−0.770264 + 0.637725i \(0.779876\pi\)
\(908\) −0.339881 0.246938i −0.0112793 0.00819492i
\(909\) 0 0
\(910\) 4.68371 + 14.4150i 0.155263 + 0.477851i
\(911\) −20.3804 + 14.8073i −0.675234 + 0.490586i −0.871773 0.489910i \(-0.837030\pi\)
0.196539 + 0.980496i \(0.437030\pi\)
\(912\) 0 0
\(913\) 42.2808 + 13.9492i 1.39929 + 0.461651i
\(914\) −3.50347 −0.115884
\(915\) 0 0
\(916\) −3.12761 9.62580i −0.103339 0.318045i
\(917\) 1.91538 5.89494i 0.0632515 0.194668i
\(918\) 0 0
\(919\) −21.6652 15.7407i −0.714668 0.519237i 0.170008 0.985443i \(-0.445621\pi\)
−0.884676 + 0.466206i \(0.845621\pi\)
\(920\) −1.66777 + 5.13286i −0.0549846 + 0.169225i
\(921\) 0 0
\(922\) 20.5894 14.9591i 0.678076 0.492651i
\(923\) 6.93263 0.228190
\(924\) 0 0
\(925\) −5.52738 −0.181739
\(926\) −10.1574 + 7.37975i −0.333791 + 0.242514i
\(927\) 0 0
\(928\) −13.7077 + 42.1880i −0.449978 + 1.38489i
\(929\) 4.57116 + 3.32114i 0.149975 + 0.108963i 0.660242 0.751053i \(-0.270454\pi\)
−0.510267 + 0.860016i \(0.670454\pi\)
\(930\) 0 0
\(931\) −1.77718 + 5.46959i −0.0582446 + 0.179258i
\(932\) −4.51004 13.8805i −0.147731 0.454670i
\(933\) 0 0
\(934\) 14.7655 0.483142
\(935\) −36.9621 51.3600i −1.20879 1.67965i
\(936\) 0 0
\(937\) 36.6328 26.6153i 1.19674 0.869484i 0.202782 0.979224i \(-0.435002\pi\)
0.993960 + 0.109740i \(0.0350018\pi\)
\(938\) −2.43130 7.48277i −0.0793847 0.244321i
\(939\) 0 0
\(940\) 17.1225 + 12.4402i 0.558475 + 0.405756i
\(941\) −26.4448 19.2133i −0.862076 0.626335i 0.0663733 0.997795i \(-0.478857\pi\)
−0.928449 + 0.371460i \(0.878857\pi\)
\(942\) 0 0
\(943\) −0.250969 0.772402i −0.00817267 0.0251529i
\(944\) −2.81163 + 2.04277i −0.0915108 + 0.0664865i
\(945\) 0 0
\(946\) 17.4413 23.7794i 0.567066 0.773135i
\(947\) 39.8004 1.29334 0.646669 0.762771i \(-0.276162\pi\)
0.646669 + 0.762771i \(0.276162\pi\)
\(948\) 0 0
\(949\) −7.61365 23.4324i −0.247150 0.760648i
\(950\) 4.33150 13.3310i 0.140533 0.432515i
\(951\) 0 0
\(952\) −14.0040 10.1745i −0.453872 0.329757i
\(953\) 3.86809 11.9048i 0.125300 0.385633i −0.868656 0.495416i \(-0.835016\pi\)
0.993956 + 0.109783i \(0.0350156\pi\)
\(954\) 0 0
\(955\) 36.3754 26.4283i 1.17708 0.855199i
\(956\) 28.1886 0.911686
\(957\) 0 0
\(958\) −29.8245 −0.963587
\(959\) −12.9520 + 9.41016i −0.418241 + 0.303870i
\(960\) 0 0
\(961\) −7.12266 + 21.9213i −0.229763 + 0.707138i
\(962\) 7.36993 + 5.35457i 0.237616 + 0.172638i
\(963\) 0 0
\(964\) 8.81030 27.1153i 0.283761 0.873325i
\(965\) −20.1474 62.0072i −0.648566 1.99608i
\(966\) 0 0
\(967\) 12.7139 0.408850 0.204425 0.978882i \(-0.434468\pi\)
0.204425 + 0.978882i \(0.434468\pi\)
\(968\) 22.9814 + 17.0161i 0.738652 + 0.546919i
\(969\) 0 0
\(970\) 17.7996 12.9321i 0.571510 0.415226i
\(971\) −6.98768 21.5059i −0.224245 0.690156i −0.998367 0.0571199i \(-0.981808\pi\)
0.774122 0.633037i \(-0.218192\pi\)
\(972\) 0 0
\(973\) −3.73281 2.71205i −0.119669 0.0869443i
\(974\) −10.5057 7.63281i −0.336623 0.244571i
\(975\) 0 0
\(976\) −1.61020 4.95569i −0.0515413 0.158628i
\(977\) 14.5376 10.5622i 0.465098 0.337913i −0.330430 0.943831i \(-0.607194\pi\)
0.795528 + 0.605917i \(0.207194\pi\)
\(978\) 0 0
\(979\) −52.4394 + 16.7772i −1.67597 + 0.536203i
\(980\) −4.07830 −0.130277
\(981\) 0 0
\(982\) 8.16272 + 25.1223i 0.260483 + 0.801683i
\(983\) 14.8966 45.8471i 0.475129 1.46230i −0.370655 0.928771i \(-0.620867\pi\)
0.845784 0.533526i \(-0.179133\pi\)
\(984\) 0 0
\(985\) −35.4717 25.7717i −1.13022 0.821155i
\(986\) −11.8241 + 36.3910i −0.376558 + 1.15892i
\(987\) 0 0
\(988\) 46.1337 33.5181i 1.46771 1.06635i
\(989\) 8.48430 0.269785
\(990\) 0 0
\(991\) −6.62493 −0.210448 −0.105224 0.994449i \(-0.533556\pi\)
−0.105224 + 0.994449i \(0.533556\pi\)
\(992\) 13.3719 9.71526i 0.424558 0.308460i
\(993\) 0 0
\(994\) 0.233526 0.718719i 0.00740699 0.0227964i
\(995\) 1.26985 + 0.922602i 0.0402571 + 0.0292485i
\(996\) 0 0
\(997\) −8.69144 + 26.7495i −0.275261 + 0.847165i 0.713890 + 0.700258i \(0.246932\pi\)
−0.989150 + 0.146907i \(0.953068\pi\)
\(998\) −3.67418 11.3080i −0.116304 0.357947i
\(999\) 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 693.2.m.k.190.5 yes 32
3.2 odd 2 inner 693.2.m.k.190.4 32
11.2 odd 10 7623.2.a.db.1.10 16
11.4 even 5 inner 693.2.m.k.631.5 yes 32
11.9 even 5 7623.2.a.dc.1.7 16
33.2 even 10 7623.2.a.db.1.7 16
33.20 odd 10 7623.2.a.dc.1.10 16
33.26 odd 10 inner 693.2.m.k.631.4 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
693.2.m.k.190.4 32 3.2 odd 2 inner
693.2.m.k.190.5 yes 32 1.1 even 1 trivial
693.2.m.k.631.4 yes 32 33.26 odd 10 inner
693.2.m.k.631.5 yes 32 11.4 even 5 inner
7623.2.a.db.1.7 16 33.2 even 10
7623.2.a.db.1.10 16 11.2 odd 10
7623.2.a.dc.1.7 16 11.9 even 5
7623.2.a.dc.1.10 16 33.20 odd 10