Properties

Label 555.2.bb.a.454.5
Level $555$
Weight $2$
Character 555.454
Analytic conductor $4.432$
Analytic rank $0$
Dimension $72$
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] = [555,2,Mod(454,555)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(555, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("555.454");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 555.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.43169731218\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 454.5
Character \(\chi\) \(=\) 555.454
Dual form 555.2.bb.a.544.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96173 - 1.13261i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.56559 + 2.71168i) q^{4} +(0.414545 + 2.19731i) q^{5} +2.26521 q^{6} +(1.72326 - 0.994927i) q^{7} -2.56237i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.96173 - 1.13261i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.56559 + 2.71168i) q^{4} +(0.414545 + 2.19731i) q^{5} +2.26521 q^{6} +(1.72326 - 0.994927i) q^{7} -2.56237i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.67546 - 4.78004i) q^{10} -0.139104 q^{11} +(-2.71168 - 1.56559i) q^{12} +(1.16325 - 0.671601i) q^{13} -4.50744 q^{14} +(-1.45766 - 1.69565i) q^{15} +(0.229029 - 0.396689i) q^{16} +(1.17935 + 0.680898i) q^{17} +(-1.96173 + 1.13261i) q^{18} +(-0.744884 - 1.29018i) q^{19} +(-5.30939 + 4.56420i) q^{20} +(-0.994927 + 1.72326i) q^{21} +(0.272885 + 0.157550i) q^{22} +5.72279i q^{23} +(1.28118 + 2.21908i) q^{24} +(-4.65631 + 1.82176i) q^{25} -3.04264 q^{26} +1.00000i q^{27} +(5.39585 + 3.11530i) q^{28} -3.64762 q^{29} +(0.939032 + 4.97736i) q^{30} +7.21023 q^{31} +(-5.33674 + 3.08117i) q^{32} +(0.120468 - 0.0695522i) q^{33} +(-1.54238 - 2.67148i) q^{34} +(2.90053 + 3.37410i) q^{35} +3.13118 q^{36} +(4.12279 + 4.47243i) q^{37} +3.37464i q^{38} +(-0.671601 + 1.16325i) q^{39} +(5.63031 - 1.06222i) q^{40} +(1.54324 + 2.67297i) q^{41} +(3.90356 - 2.25372i) q^{42} +2.43821i q^{43} +(-0.217781 - 0.377207i) q^{44} +(2.11020 + 0.739647i) q^{45} +(6.48167 - 11.2266i) q^{46} -4.92965i q^{47} +0.458057i q^{48} +(-1.52024 + 2.63314i) q^{49} +(11.1978 + 1.69995i) q^{50} -1.36180 q^{51} +(3.64234 + 2.10291i) q^{52} +(7.32836 + 4.23103i) q^{53} +(1.13261 - 1.96173i) q^{54} +(-0.0576650 - 0.305655i) q^{55} +(-2.54937 - 4.41564i) q^{56} +(1.29018 + 0.744884i) q^{57} +(7.15566 + 4.13132i) q^{58} +(2.53188 - 4.38534i) q^{59} +(2.31597 - 6.60741i) q^{60} +(-0.665693 - 1.15301i) q^{61} +(-14.1445 - 8.16635i) q^{62} -1.98985i q^{63} +13.0429 q^{64} +(1.95793 + 2.27760i) q^{65} -0.315101 q^{66} +(5.66355 - 3.26985i) q^{67} +4.26403i q^{68} +(-2.86140 - 4.95608i) q^{69} +(-1.86854 - 9.90422i) q^{70} +(3.69038 + 6.39193i) q^{71} +(-2.21908 - 1.28118i) q^{72} +7.96602i q^{73} +(-3.02231 - 13.4432i) q^{74} +(3.12160 - 3.90585i) q^{75} +(2.33237 - 4.03978i) q^{76} +(-0.239713 + 0.138399i) q^{77} +(2.63500 - 1.52132i) q^{78} +(3.57273 + 6.18814i) q^{79} +(0.966590 + 0.338800i) q^{80} +(-0.500000 - 0.866025i) q^{81} -6.99152i q^{82} +(-5.18475 - 2.99342i) q^{83} -6.23060 q^{84} +(-1.00725 + 2.87365i) q^{85} +(2.76153 - 4.78310i) q^{86} +(3.15893 - 1.82381i) q^{87} +0.356437i q^{88} +(-7.58937 + 13.1452i) q^{89} +(-3.30191 - 3.84101i) q^{90} +(1.33639 - 2.31469i) q^{91} +(-15.5184 + 8.95956i) q^{92} +(-6.24424 + 3.60512i) q^{93} +(-5.58335 + 9.67065i) q^{94} +(2.52612 - 2.17157i) q^{95} +(3.08117 - 5.33674i) q^{96} +10.2833i q^{97} +(5.96461 - 3.44367i) q^{98} +(-0.0695522 + 0.120468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/555\mathbb{Z}\right)^\times\).

\(n\) \(76\) \(112\) \(371\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96173 1.13261i −1.38715 0.800873i −0.394160 0.919042i \(-0.628964\pi\)
−0.992994 + 0.118169i \(0.962298\pi\)
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 1.56559 + 2.71168i 0.782796 + 1.35584i
\(5\) 0.414545 + 2.19731i 0.185390 + 0.982665i
\(6\) 2.26521 0.924769
\(7\) 1.72326 0.994927i 0.651332 0.376047i −0.137634 0.990483i \(-0.543950\pi\)
0.788967 + 0.614436i \(0.210616\pi\)
\(8\) 2.56237i 0.905935i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.67546 4.78004i 0.529826 1.51158i
\(11\) −0.139104 −0.0419415 −0.0209708 0.999780i \(-0.506676\pi\)
−0.0209708 + 0.999780i \(0.506676\pi\)
\(12\) −2.71168 1.56559i −0.782796 0.451947i
\(13\) 1.16325 0.671601i 0.322627 0.186269i −0.329936 0.944003i \(-0.607027\pi\)
0.652563 + 0.757735i \(0.273694\pi\)
\(14\) −4.50744 −1.20466
\(15\) −1.45766 1.69565i −0.376366 0.437815i
\(16\) 0.229029 0.396689i 0.0572572 0.0991723i
\(17\) 1.17935 + 0.680898i 0.286034 + 0.165142i 0.636152 0.771564i \(-0.280525\pi\)
−0.350118 + 0.936706i \(0.613858\pi\)
\(18\) −1.96173 + 1.13261i −0.462384 + 0.266958i
\(19\) −0.744884 1.29018i −0.170888 0.295987i 0.767843 0.640639i \(-0.221330\pi\)
−0.938731 + 0.344652i \(0.887997\pi\)
\(20\) −5.30939 + 4.56420i −1.18722 + 1.02059i
\(21\) −0.994927 + 1.72326i −0.217111 + 0.376047i
\(22\) 0.272885 + 0.157550i 0.0581793 + 0.0335899i
\(23\) 5.72279i 1.19328i 0.802507 + 0.596642i \(0.203499\pi\)
−0.802507 + 0.596642i \(0.796501\pi\)
\(24\) 1.28118 + 2.21908i 0.261521 + 0.452967i
\(25\) −4.65631 + 1.82176i −0.931261 + 0.364353i
\(26\) −3.04264 −0.596710
\(27\) 1.00000i 0.192450i
\(28\) 5.39585 + 3.11530i 1.01972 + 0.588736i
\(29\) −3.64762 −0.677347 −0.338673 0.940904i \(-0.609978\pi\)
−0.338673 + 0.940904i \(0.609978\pi\)
\(30\) 0.939032 + 4.97736i 0.171443 + 0.908738i
\(31\) 7.21023 1.29500 0.647498 0.762067i \(-0.275815\pi\)
0.647498 + 0.762067i \(0.275815\pi\)
\(32\) −5.33674 + 3.08117i −0.943411 + 0.544679i
\(33\) 0.120468 0.0695522i 0.0209708 0.0121075i
\(34\) −1.54238 2.67148i −0.264515 0.458154i
\(35\) 2.90053 + 3.37410i 0.490279 + 0.570326i
\(36\) 3.13118 0.521864
\(37\) 4.12279 + 4.47243i 0.677782 + 0.735263i
\(38\) 3.37464i 0.547439i
\(39\) −0.671601 + 1.16325i −0.107542 + 0.186269i
\(40\) 5.63031 1.06222i 0.890230 0.167951i
\(41\) 1.54324 + 2.67297i 0.241013 + 0.417447i 0.961003 0.276537i \(-0.0891869\pi\)
−0.719990 + 0.693985i \(0.755854\pi\)
\(42\) 3.90356 2.25372i 0.602332 0.347756i
\(43\) 2.43821i 0.371823i 0.982567 + 0.185911i \(0.0595237\pi\)
−0.982567 + 0.185911i \(0.940476\pi\)
\(44\) −0.217781 0.377207i −0.0328317 0.0568661i
\(45\) 2.11020 + 0.739647i 0.314569 + 0.110260i
\(46\) 6.48167 11.2266i 0.955670 1.65527i
\(47\) 4.92965i 0.719064i −0.933133 0.359532i \(-0.882936\pi\)
0.933133 0.359532i \(-0.117064\pi\)
\(48\) 0.458057i 0.0661149i
\(49\) −1.52024 + 2.63314i −0.217177 + 0.376162i
\(50\) 11.1978 + 1.69995i 1.58360 + 0.240409i
\(51\) −1.36180 −0.190689
\(52\) 3.64234 + 2.10291i 0.505102 + 0.291621i
\(53\) 7.32836 + 4.23103i 1.00663 + 0.581177i 0.910203 0.414163i \(-0.135926\pi\)
0.0964253 + 0.995340i \(0.469259\pi\)
\(54\) 1.13261 1.96173i 0.154128 0.266958i
\(55\) −0.0576650 0.305655i −0.00777554 0.0412145i
\(56\) −2.54937 4.41564i −0.340674 0.590064i
\(57\) 1.29018 + 0.744884i 0.170888 + 0.0986623i
\(58\) 7.15566 + 4.13132i 0.939584 + 0.542469i
\(59\) 2.53188 4.38534i 0.329623 0.570923i −0.652814 0.757518i \(-0.726412\pi\)
0.982437 + 0.186595i \(0.0597451\pi\)
\(60\) 2.31597 6.60741i 0.298990 0.853013i
\(61\) −0.665693 1.15301i −0.0852333 0.147628i 0.820257 0.571995i \(-0.193830\pi\)
−0.905491 + 0.424366i \(0.860497\pi\)
\(62\) −14.1445 8.16635i −1.79636 1.03713i
\(63\) 1.98985i 0.250698i
\(64\) 13.0429 1.63036
\(65\) 1.95793 + 2.27760i 0.242851 + 0.282502i
\(66\) −0.315101 −0.0387862
\(67\) 5.66355 3.26985i 0.691913 0.399476i −0.112415 0.993661i \(-0.535859\pi\)
0.804328 + 0.594185i \(0.202525\pi\)
\(68\) 4.26403i 0.517090i
\(69\) −2.86140 4.95608i −0.344472 0.596642i
\(70\) −1.86854 9.90422i −0.223333 1.18378i
\(71\) 3.69038 + 6.39193i 0.437968 + 0.758582i 0.997533 0.0702042i \(-0.0223651\pi\)
−0.559565 + 0.828786i \(0.689032\pi\)
\(72\) −2.21908 1.28118i −0.261521 0.150989i
\(73\) 7.96602i 0.932352i 0.884692 + 0.466176i \(0.154369\pi\)
−0.884692 + 0.466176i \(0.845631\pi\)
\(74\) −3.02231 13.4432i −0.351336 1.56274i
\(75\) 3.12160 3.90585i 0.360451 0.451008i
\(76\) 2.33237 4.03978i 0.267541 0.463394i
\(77\) −0.239713 + 0.138399i −0.0273179 + 0.0157720i
\(78\) 2.63500 1.52132i 0.298355 0.172255i
\(79\) 3.57273 + 6.18814i 0.401963 + 0.696221i 0.993963 0.109718i \(-0.0349947\pi\)
−0.592000 + 0.805938i \(0.701661\pi\)
\(80\) 0.966590 + 0.338800i 0.108068 + 0.0378790i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 6.99152i 0.772084i
\(83\) −5.18475 2.99342i −0.569100 0.328570i 0.187690 0.982228i \(-0.439900\pi\)
−0.756790 + 0.653658i \(0.773233\pi\)
\(84\) −6.23060 −0.679814
\(85\) −1.00725 + 2.87365i −0.109251 + 0.311691i
\(86\) 2.76153 4.78310i 0.297783 0.515775i
\(87\) 3.15893 1.82381i 0.338673 0.195533i
\(88\) 0.356437i 0.0379963i
\(89\) −7.58937 + 13.1452i −0.804472 + 1.39339i 0.112175 + 0.993688i \(0.464218\pi\)
−0.916647 + 0.399698i \(0.869115\pi\)
\(90\) −3.30191 3.84101i −0.348052 0.404878i
\(91\) 1.33639 2.31469i 0.140091 0.242646i
\(92\) −15.5184 + 8.95956i −1.61791 + 0.934098i
\(93\) −6.24424 + 3.60512i −0.647498 + 0.373833i
\(94\) −5.58335 + 9.67065i −0.575879 + 0.997452i
\(95\) 2.52612 2.17157i 0.259175 0.222799i
\(96\) 3.08117 5.33674i 0.314470 0.544679i
\(97\) 10.2833i 1.04411i 0.852912 + 0.522055i \(0.174835\pi\)
−0.852912 + 0.522055i \(0.825165\pi\)
\(98\) 5.96461 3.44367i 0.602517 0.347863i
\(99\) −0.0695522 + 0.120468i −0.00699026 + 0.0121075i
\(100\) −12.2299 9.77429i −1.22299 0.977429i
\(101\) −4.47080 −0.444862 −0.222431 0.974948i \(-0.571399\pi\)
−0.222431 + 0.974948i \(0.571399\pi\)
\(102\) 2.67148 + 1.54238i 0.264515 + 0.152718i
\(103\) 17.0377i 1.67878i 0.543531 + 0.839389i \(0.317087\pi\)
−0.543531 + 0.839389i \(0.682913\pi\)
\(104\) −1.72089 2.98067i −0.168747 0.292279i
\(105\) −4.19898 1.47179i −0.409778 0.143632i
\(106\) −9.58418 16.6003i −0.930898 1.61236i
\(107\) 7.81698 4.51314i 0.755696 0.436301i −0.0720523 0.997401i \(-0.522955\pi\)
0.827748 + 0.561100i \(0.189622\pi\)
\(108\) −2.71168 + 1.56559i −0.260932 + 0.150649i
\(109\) −2.31790 + 4.01473i −0.222015 + 0.384541i −0.955420 0.295251i \(-0.904597\pi\)
0.733405 + 0.679792i \(0.237930\pi\)
\(110\) −0.233063 + 0.664924i −0.0222217 + 0.0633980i
\(111\) −5.80665 1.81184i −0.551143 0.171972i
\(112\) 0.911467i 0.0861255i
\(113\) 3.79159 + 2.18907i 0.356683 + 0.205931i 0.667625 0.744498i \(-0.267311\pi\)
−0.310942 + 0.950429i \(0.600644\pi\)
\(114\) −1.68732 2.92252i −0.158032 0.273719i
\(115\) −12.5747 + 2.37235i −1.17260 + 0.221223i
\(116\) −5.71069 9.89120i −0.530224 0.918375i
\(117\) 1.34320i 0.124179i
\(118\) −9.93373 + 5.73524i −0.914474 + 0.527972i
\(119\) 2.70977 0.248404
\(120\) −4.34488 + 3.73506i −0.396632 + 0.340963i
\(121\) −10.9806 −0.998241
\(122\) 3.01587i 0.273044i
\(123\) −2.67297 1.54324i −0.241013 0.139149i
\(124\) 11.2883 + 19.5519i 1.01372 + 1.75581i
\(125\) −5.93322 9.47612i −0.530683 0.847570i
\(126\) −2.25372 + 3.90356i −0.200777 + 0.347756i
\(127\) −4.66716 2.69459i −0.414144 0.239106i 0.278425 0.960458i \(-0.410188\pi\)
−0.692569 + 0.721352i \(0.743521\pi\)
\(128\) −14.9131 8.61011i −1.31815 0.761033i
\(129\) −1.21910 2.11155i −0.107336 0.185911i
\(130\) −1.26131 6.68560i −0.110624 0.586366i
\(131\) −0.931640 + 1.61365i −0.0813978 + 0.140985i −0.903851 0.427848i \(-0.859272\pi\)
0.822453 + 0.568833i \(0.192605\pi\)
\(132\) 0.377207 + 0.217781i 0.0328317 + 0.0189554i
\(133\) −2.56726 1.48221i −0.222610 0.128524i
\(134\) −14.8138 −1.27972
\(135\) −2.19731 + 0.414545i −0.189114 + 0.0356783i
\(136\) 1.74471 3.02193i 0.149608 0.259128i
\(137\) 12.0562i 1.03003i −0.857181 0.515016i \(-0.827786\pi\)
0.857181 0.515016i \(-0.172214\pi\)
\(138\) 12.9633i 1.10351i
\(139\) −0.0613544 + 0.106269i −0.00520402 + 0.00901362i −0.868616 0.495486i \(-0.834990\pi\)
0.863412 + 0.504500i \(0.168323\pi\)
\(140\) −4.60844 + 13.1478i −0.389484 + 1.11119i
\(141\) 2.46483 + 4.26921i 0.207576 + 0.359532i
\(142\) 16.7190i 1.40303i
\(143\) −0.161813 + 0.0934226i −0.0135315 + 0.00781239i
\(144\) −0.229029 0.396689i −0.0190857 0.0330574i
\(145\) −1.51210 8.01494i −0.125573 0.665605i
\(146\) 9.02236 15.6272i 0.746696 1.29332i
\(147\) 3.04048i 0.250775i
\(148\) −5.67321 + 18.1817i −0.466335 + 1.49453i
\(149\) 21.3770 1.75127 0.875634 0.482975i \(-0.160444\pi\)
0.875634 + 0.482975i \(0.160444\pi\)
\(150\) −10.5475 + 4.12668i −0.861201 + 0.336942i
\(151\) −3.88553 6.72993i −0.316200 0.547674i 0.663492 0.748183i \(-0.269074\pi\)
−0.979692 + 0.200509i \(0.935740\pi\)
\(152\) −3.30591 + 1.90867i −0.268145 + 0.154813i
\(153\) 1.17935 0.680898i 0.0953447 0.0550473i
\(154\) 0.627004 0.0505254
\(155\) 2.98896 + 15.8431i 0.240079 + 1.27255i
\(156\) −4.20581 −0.336734
\(157\) 9.27102 + 5.35263i 0.739908 + 0.427186i 0.822036 0.569436i \(-0.192838\pi\)
−0.0821279 + 0.996622i \(0.526172\pi\)
\(158\) 16.1860i 1.28769i
\(159\) −8.46206 −0.671085
\(160\) −8.98259 10.4492i −0.710136 0.826079i
\(161\) 5.69376 + 9.86188i 0.448731 + 0.777225i
\(162\) 2.26521i 0.177972i
\(163\) −12.1261 7.00099i −0.949787 0.548360i −0.0567722 0.998387i \(-0.518081\pi\)
−0.893015 + 0.450027i \(0.851414\pi\)
\(164\) −4.83216 + 8.36955i −0.377328 + 0.653552i
\(165\) 0.202767 + 0.235872i 0.0157854 + 0.0183626i
\(166\) 6.78072 + 11.7446i 0.526286 + 0.911555i
\(167\) 6.07830 3.50931i 0.470353 0.271558i −0.246035 0.969261i \(-0.579128\pi\)
0.716387 + 0.697703i \(0.245794\pi\)
\(168\) 4.41564 + 2.54937i 0.340674 + 0.196688i
\(169\) −5.59790 + 9.69585i −0.430608 + 0.745835i
\(170\) 5.23066 4.49652i 0.401174 0.344867i
\(171\) −1.48977 −0.113925
\(172\) −6.61164 + 3.81723i −0.504133 + 0.291061i
\(173\) −19.4871 11.2509i −1.48157 0.855387i −0.481793 0.876285i \(-0.660014\pi\)
−0.999782 + 0.0208979i \(0.993347\pi\)
\(174\) −8.26264 −0.626389
\(175\) −6.21152 + 7.77206i −0.469547 + 0.587513i
\(176\) −0.0318589 + 0.0551812i −0.00240145 + 0.00415944i
\(177\) 5.06376i 0.380615i
\(178\) 29.7766 17.1915i 2.23185 1.28856i
\(179\) 14.8705 1.11148 0.555738 0.831358i \(-0.312436\pi\)
0.555738 + 0.831358i \(0.312436\pi\)
\(180\) 1.29802 + 6.88017i 0.0967484 + 0.512817i
\(181\) −10.8613 18.8122i −0.807310 1.39830i −0.914720 0.404088i \(-0.867589\pi\)
0.107410 0.994215i \(-0.465744\pi\)
\(182\) −5.24326 + 3.02720i −0.388657 + 0.224391i
\(183\) 1.15301 + 0.665693i 0.0852333 + 0.0492095i
\(184\) 14.6639 1.08104
\(185\) −8.11821 + 10.9131i −0.596863 + 0.802343i
\(186\) 16.3327 1.19757
\(187\) −0.164053 0.0947158i −0.0119967 0.00692631i
\(188\) 13.3677 7.71783i 0.974937 0.562880i
\(189\) 0.994927 + 1.72326i 0.0723703 + 0.125349i
\(190\) −7.41511 + 1.39894i −0.537949 + 0.101490i
\(191\) 8.91725 0.645230 0.322615 0.946530i \(-0.395438\pi\)
0.322615 + 0.946530i \(0.395438\pi\)
\(192\) −11.2955 + 6.52144i −0.815180 + 0.470644i
\(193\) 10.5019i 0.755947i −0.925816 0.377973i \(-0.876621\pi\)
0.925816 0.377973i \(-0.123379\pi\)
\(194\) 11.6469 20.1731i 0.836200 1.44834i
\(195\) −2.83442 0.993495i −0.202977 0.0711456i
\(196\) −9.52031 −0.680022
\(197\) −13.6453 7.87814i −0.972190 0.561294i −0.0722866 0.997384i \(-0.523030\pi\)
−0.899903 + 0.436090i \(0.856363\pi\)
\(198\) 0.272885 0.157550i 0.0193931 0.0111966i
\(199\) 27.6222 1.95809 0.979043 0.203654i \(-0.0652817\pi\)
0.979043 + 0.203654i \(0.0652817\pi\)
\(200\) 4.66803 + 11.9312i 0.330080 + 0.843662i
\(201\) −3.26985 + 5.66355i −0.230638 + 0.399476i
\(202\) 8.77051 + 5.06366i 0.617091 + 0.356278i
\(203\) −6.28582 + 3.62912i −0.441178 + 0.254714i
\(204\) −2.13202 3.69276i −0.149271 0.258545i
\(205\) −5.23358 + 4.49903i −0.365529 + 0.314226i
\(206\) 19.2970 33.4234i 1.34449 2.32872i
\(207\) 4.95608 + 2.86140i 0.344472 + 0.198881i
\(208\) 0.615263i 0.0426608i
\(209\) 0.103617 + 0.179469i 0.00716731 + 0.0124141i
\(210\) 6.57031 + 7.64304i 0.453394 + 0.527420i
\(211\) −19.3433 −1.33165 −0.665824 0.746109i \(-0.731920\pi\)
−0.665824 + 0.746109i \(0.731920\pi\)
\(212\) 26.4963i 1.81977i
\(213\) −6.39193 3.69038i −0.437968 0.252861i
\(214\) −20.4464 −1.39769
\(215\) −5.35748 + 1.01075i −0.365377 + 0.0689323i
\(216\) 2.56237 0.174347
\(217\) 12.4251 7.17365i 0.843473 0.486979i
\(218\) 9.09421 5.25054i 0.615937 0.355612i
\(219\) −3.98301 6.89878i −0.269147 0.466176i
\(220\) 0.738559 0.634900i 0.0497937 0.0428049i
\(221\) 1.82917 0.123043
\(222\) 9.33899 + 10.1310i 0.626792 + 0.679948i
\(223\) 5.21380i 0.349142i −0.984645 0.174571i \(-0.944146\pi\)
0.984645 0.174571i \(-0.0558539\pi\)
\(224\) −6.13107 + 10.6193i −0.409650 + 0.709534i
\(225\) −0.750459 + 4.94336i −0.0500306 + 0.329557i
\(226\) −4.95872 8.58875i −0.329849 0.571315i
\(227\) 13.7651 7.94726i 0.913619 0.527478i 0.0320249 0.999487i \(-0.489804\pi\)
0.881594 + 0.472009i \(0.156471\pi\)
\(228\) 4.66473i 0.308930i
\(229\) 8.81122 + 15.2615i 0.582261 + 1.00851i 0.995211 + 0.0977525i \(0.0311653\pi\)
−0.412949 + 0.910754i \(0.635501\pi\)
\(230\) 27.3552 + 9.58829i 1.80375 + 0.632233i
\(231\) 0.138399 0.239713i 0.00910596 0.0157720i
\(232\) 9.34656i 0.613632i
\(233\) 22.9559i 1.50389i −0.659225 0.751946i \(-0.729115\pi\)
0.659225 0.751946i \(-0.270885\pi\)
\(234\) −1.52132 + 2.63500i −0.0994517 + 0.172255i
\(235\) 10.8320 2.04356i 0.706599 0.133307i
\(236\) 15.8556 1.03211
\(237\) −6.18814 3.57273i −0.401963 0.232074i
\(238\) −5.31584 3.06910i −0.344575 0.198940i
\(239\) −0.483112 + 0.836775i −0.0312499 + 0.0541265i −0.881227 0.472693i \(-0.843282\pi\)
0.849977 + 0.526819i \(0.176615\pi\)
\(240\) −1.00649 + 0.189885i −0.0649688 + 0.0122570i
\(241\) 0.272240 + 0.471533i 0.0175365 + 0.0303741i 0.874660 0.484736i \(-0.161084\pi\)
−0.857124 + 0.515110i \(0.827751\pi\)
\(242\) 21.5411 + 12.4367i 1.38471 + 0.799464i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 2.08441 3.61030i 0.133441 0.231126i
\(245\) −6.41601 2.24888i −0.409904 0.143676i
\(246\) 3.49576 + 6.05484i 0.222882 + 0.386042i
\(247\) −1.73297 1.00053i −0.110266 0.0636622i
\(248\) 18.4753i 1.17318i
\(249\) 5.98684 0.379400
\(250\) 0.906665 + 25.3096i 0.0573425 + 1.60072i
\(251\) 9.15687 0.577976 0.288988 0.957333i \(-0.406681\pi\)
0.288988 + 0.957333i \(0.406681\pi\)
\(252\) 5.39585 3.11530i 0.339907 0.196245i
\(253\) 0.796065i 0.0500482i
\(254\) 6.10381 + 10.5721i 0.382987 + 0.663353i
\(255\) −0.564525 2.99228i −0.0353519 0.187384i
\(256\) 6.46083 + 11.1905i 0.403802 + 0.699405i
\(257\) 14.1361 + 8.16146i 0.881783 + 0.509098i 0.871246 0.490847i \(-0.163312\pi\)
0.0105373 + 0.999944i \(0.496646\pi\)
\(258\) 5.52305i 0.343850i
\(259\) 11.5544 + 3.60530i 0.717955 + 0.224022i
\(260\) −3.11081 + 8.87508i −0.192925 + 0.550409i
\(261\) −1.82381 + 3.15893i −0.112891 + 0.195533i
\(262\) 3.65526 2.11036i 0.225822 0.130379i
\(263\) 15.0422 8.68461i 0.927541 0.535516i 0.0415080 0.999138i \(-0.486784\pi\)
0.886033 + 0.463622i \(0.153450\pi\)
\(264\) −0.178218 0.308683i −0.0109686 0.0189981i
\(265\) −6.25894 + 17.8566i −0.384483 + 1.09692i
\(266\) 3.35752 + 5.81539i 0.205863 + 0.356564i
\(267\) 15.1787i 0.928924i
\(268\) 17.7336 + 10.2385i 1.08325 + 0.625416i
\(269\) −20.7235 −1.26353 −0.631767 0.775158i \(-0.717670\pi\)
−0.631767 + 0.775158i \(0.717670\pi\)
\(270\) 4.78004 + 1.67546i 0.290904 + 0.101965i
\(271\) 10.7704 18.6549i 0.654257 1.13321i −0.327823 0.944739i \(-0.606315\pi\)
0.982080 0.188467i \(-0.0603517\pi\)
\(272\) 0.540209 0.311890i 0.0327550 0.0189111i
\(273\) 2.67277i 0.161764i
\(274\) −13.6549 + 23.6510i −0.824925 + 1.42881i
\(275\) 0.647712 0.253415i 0.0390585 0.0152815i
\(276\) 8.95956 15.5184i 0.539302 0.934098i
\(277\) 9.66521 5.58021i 0.580726 0.335282i −0.180696 0.983539i \(-0.557835\pi\)
0.761422 + 0.648257i \(0.224502\pi\)
\(278\) 0.240722 0.138981i 0.0144375 0.00833551i
\(279\) 3.60512 6.24424i 0.215833 0.373833i
\(280\) 8.64568 7.43223i 0.516678 0.444160i
\(281\) −14.1081 + 24.4360i −0.841619 + 1.45773i 0.0469055 + 0.998899i \(0.485064\pi\)
−0.888525 + 0.458828i \(0.848269\pi\)
\(282\) 11.1667i 0.664968i
\(283\) 21.9041 12.6463i 1.30206 0.751745i 0.321304 0.946976i \(-0.395879\pi\)
0.980757 + 0.195231i \(0.0625457\pi\)
\(284\) −11.5553 + 20.0143i −0.685679 + 1.18763i
\(285\) −1.10190 + 3.14370i −0.0652710 + 0.186217i
\(286\) 0.423244 0.0250269
\(287\) 5.31881 + 3.07082i 0.313960 + 0.181265i
\(288\) 6.16234i 0.363119i
\(289\) −7.57276 13.1164i −0.445456 0.771553i
\(290\) −6.11143 + 17.4358i −0.358876 + 1.02386i
\(291\) −5.14165 8.90560i −0.301409 0.522055i
\(292\) −21.6013 + 12.4715i −1.26412 + 0.729842i
\(293\) −7.98837 + 4.61209i −0.466685 + 0.269441i −0.714851 0.699277i \(-0.753506\pi\)
0.248166 + 0.968718i \(0.420172\pi\)
\(294\) −3.44367 + 5.96461i −0.200839 + 0.347863i
\(295\) 10.6855 + 3.74539i 0.622135 + 0.218065i
\(296\) 11.4600 10.5641i 0.666100 0.614026i
\(297\) 0.139104i 0.00807165i
\(298\) −41.9358 24.2117i −2.42928 1.40254i
\(299\) 3.84343 + 6.65702i 0.222271 + 0.384985i
\(300\) 15.4786 + 2.34983i 0.893656 + 0.135667i
\(301\) 2.42584 + 4.20167i 0.139823 + 0.242180i
\(302\) 17.6031i 1.01294i
\(303\) 3.87183 2.23540i 0.222431 0.128420i
\(304\) −0.682399 −0.0391382
\(305\) 2.25757 1.94071i 0.129268 0.111125i
\(306\) −3.08475 −0.176344
\(307\) 6.43870i 0.367476i −0.982975 0.183738i \(-0.941180\pi\)
0.982975 0.183738i \(-0.0588198\pi\)
\(308\) −0.750587 0.433351i −0.0427686 0.0246925i
\(309\) −8.51887 14.7551i −0.484621 0.839389i
\(310\) 12.0804 34.4652i 0.686122 1.95749i
\(311\) 0.829152 1.43613i 0.0470169 0.0814356i −0.841559 0.540165i \(-0.818362\pi\)
0.888576 + 0.458729i \(0.151695\pi\)
\(312\) 2.98067 + 1.72089i 0.168747 + 0.0974262i
\(313\) −6.97020 4.02425i −0.393979 0.227464i 0.289904 0.957056i \(-0.406377\pi\)
−0.683883 + 0.729592i \(0.739710\pi\)
\(314\) −12.1248 21.0008i −0.684244 1.18514i
\(315\) 4.37232 0.824883i 0.246352 0.0464769i
\(316\) −11.1869 + 19.3762i −0.629310 + 1.09000i
\(317\) 7.55926 + 4.36434i 0.424570 + 0.245126i 0.697031 0.717041i \(-0.254504\pi\)
−0.272461 + 0.962167i \(0.587837\pi\)
\(318\) 16.6003 + 9.58418i 0.930898 + 0.537454i
\(319\) 0.507400 0.0284090
\(320\) 5.40686 + 28.6592i 0.302253 + 1.60210i
\(321\) −4.51314 + 7.81698i −0.251899 + 0.436301i
\(322\) 25.7951i 1.43751i
\(323\) 2.02876i 0.112883i
\(324\) 1.56559 2.71168i 0.0869773 0.150649i
\(325\) −4.19294 + 5.24634i −0.232582 + 0.291015i
\(326\) 15.8587 + 27.4681i 0.878333 + 1.52132i
\(327\) 4.63581i 0.256361i
\(328\) 6.84913 3.95435i 0.378180 0.218342i
\(329\) −4.90464 8.49509i −0.270402 0.468350i
\(330\) −0.130623 0.692373i −0.00719058 0.0381139i
\(331\) 0.388850 0.673509i 0.0213732 0.0370194i −0.855141 0.518395i \(-0.826530\pi\)
0.876514 + 0.481376i \(0.159863\pi\)
\(332\) 18.7459i 1.02881i
\(333\) 5.93463 1.33423i 0.325216 0.0731152i
\(334\) −15.8986 −0.869935
\(335\) 9.53266 + 11.0891i 0.520825 + 0.605860i
\(336\) 0.455733 + 0.789353i 0.0248623 + 0.0430628i
\(337\) −18.4108 + 10.6295i −1.00290 + 0.579026i −0.909106 0.416565i \(-0.863234\pi\)
−0.0937967 + 0.995591i \(0.529900\pi\)
\(338\) 21.9632 12.6804i 1.19464 0.689725i
\(339\) −4.37815 −0.237788
\(340\) −9.36938 + 1.76763i −0.508126 + 0.0958633i
\(341\) −1.00297 −0.0543141
\(342\) 2.92252 + 1.68732i 0.158032 + 0.0912398i
\(343\) 19.9791i 1.07877i
\(344\) 6.24758 0.336847
\(345\) 9.70385 8.34188i 0.522438 0.449112i
\(346\) 25.4856 + 44.1423i 1.37011 + 2.37311i
\(347\) 31.7474i 1.70429i −0.523307 0.852144i \(-0.675302\pi\)
0.523307 0.852144i \(-0.324698\pi\)
\(348\) 9.89120 + 5.71069i 0.530224 + 0.306125i
\(349\) 13.3130 23.0587i 0.712626 1.23430i −0.251242 0.967924i \(-0.580839\pi\)
0.963868 0.266380i \(-0.0858277\pi\)
\(350\) 20.9880 8.21149i 1.12186 0.438922i
\(351\) 0.671601 + 1.16325i 0.0358474 + 0.0620895i
\(352\) 0.742364 0.428604i 0.0395681 0.0228447i
\(353\) −15.2388 8.79810i −0.811078 0.468276i 0.0362524 0.999343i \(-0.488458\pi\)
−0.847330 + 0.531067i \(0.821791\pi\)
\(354\) 5.73524 9.93373i 0.304825 0.527972i
\(355\) −12.5152 + 10.7586i −0.664237 + 0.571009i
\(356\) −47.5274 −2.51895
\(357\) −2.34673 + 1.35489i −0.124202 + 0.0717082i
\(358\) −29.1720 16.8425i −1.54179 0.890151i
\(359\) −14.0849 −0.743375 −0.371688 0.928358i \(-0.621221\pi\)
−0.371688 + 0.928358i \(0.621221\pi\)
\(360\) 1.89525 5.40710i 0.0998883 0.284979i
\(361\) 8.39030 14.5324i 0.441595 0.764864i
\(362\) 49.2061i 2.58621i
\(363\) 9.50952 5.49032i 0.499120 0.288167i
\(364\) 8.36895 0.438652
\(365\) −17.5038 + 3.30227i −0.916190 + 0.172849i
\(366\) −1.50794 2.61182i −0.0788211 0.136522i
\(367\) −24.0112 + 13.8628i −1.25337 + 0.723635i −0.971778 0.235899i \(-0.924197\pi\)
−0.281594 + 0.959534i \(0.590863\pi\)
\(368\) 2.27017 + 1.31068i 0.118341 + 0.0683241i
\(369\) 3.08648 0.160676
\(370\) 28.2859 12.2137i 1.47052 0.634962i
\(371\) 16.8383 0.874199
\(372\) −19.5519 11.2883i −1.01372 0.585270i
\(373\) −5.02514 + 2.90126i −0.260192 + 0.150222i −0.624422 0.781087i \(-0.714665\pi\)
0.364230 + 0.931309i \(0.381332\pi\)
\(374\) 0.214551 + 0.371614i 0.0110942 + 0.0192157i
\(375\) 9.87638 + 5.23995i 0.510014 + 0.270590i
\(376\) −12.6316 −0.651425
\(377\) −4.24309 + 2.44975i −0.218530 + 0.126168i
\(378\) 4.50744i 0.231838i
\(379\) 9.64665 16.7085i 0.495515 0.858257i −0.504472 0.863428i \(-0.668313\pi\)
0.999987 + 0.00517107i \(0.00164601\pi\)
\(380\) 9.84350 + 3.45025i 0.504961 + 0.176994i
\(381\) 5.38918 0.276096
\(382\) −17.4932 10.0997i −0.895032 0.516747i
\(383\) −11.1439 + 6.43392i −0.569425 + 0.328758i −0.756920 0.653508i \(-0.773297\pi\)
0.187494 + 0.982266i \(0.439963\pi\)
\(384\) 17.2202 0.878765
\(385\) −0.403476 0.469351i −0.0205630 0.0239204i
\(386\) −11.8946 + 20.6020i −0.605418 + 1.04861i
\(387\) 2.11155 + 1.21910i 0.107336 + 0.0619705i
\(388\) −27.8851 + 16.0994i −1.41565 + 0.817326i
\(389\) −13.2314 22.9174i −0.670857 1.16196i −0.977662 0.210185i \(-0.932593\pi\)
0.306805 0.951772i \(-0.400740\pi\)
\(390\) 4.43513 + 5.15925i 0.224581 + 0.261249i
\(391\) −3.89664 + 6.74917i −0.197061 + 0.341320i
\(392\) 6.74707 + 3.89542i 0.340778 + 0.196749i
\(393\) 1.86328i 0.0939901i
\(394\) 17.8456 + 30.9096i 0.899051 + 1.55720i
\(395\) −12.1162 + 10.4156i −0.609632 + 0.524068i
\(396\) −0.435561 −0.0218878
\(397\) 9.66789i 0.485217i −0.970124 0.242609i \(-0.921997\pi\)
0.970124 0.242609i \(-0.0780031\pi\)
\(398\) −54.1873 31.2851i −2.71617 1.56818i
\(399\) 2.96442 0.148407
\(400\) −0.343753 + 2.26434i −0.0171877 + 0.113217i
\(401\) −31.0922 −1.55267 −0.776336 0.630319i \(-0.782924\pi\)
−0.776336 + 0.630319i \(0.782924\pi\)
\(402\) 12.8291 7.40691i 0.639859 0.369423i
\(403\) 8.38728 4.84240i 0.417800 0.241217i
\(404\) −6.99945 12.1234i −0.348236 0.603162i
\(405\) 1.69565 1.45766i 0.0842575 0.0724317i
\(406\) 16.4414 0.815975
\(407\) −0.573498 0.622134i −0.0284272 0.0308380i
\(408\) 3.48942i 0.172752i
\(409\) −6.25333 + 10.8311i −0.309207 + 0.535563i −0.978189 0.207716i \(-0.933397\pi\)
0.668982 + 0.743279i \(0.266730\pi\)
\(410\) 15.3625 2.89830i 0.758700 0.143137i
\(411\) 6.02811 + 10.4410i 0.297345 + 0.515016i
\(412\) −46.2010 + 26.6741i −2.27616 + 1.31414i
\(413\) 10.0761i 0.495814i
\(414\) −6.48167 11.2266i −0.318557 0.551756i
\(415\) 4.42814 12.6334i 0.217369 0.620149i
\(416\) −4.13863 + 7.16832i −0.202913 + 0.351456i
\(417\) 0.122709i 0.00600908i
\(418\) 0.469427i 0.0229604i
\(419\) 16.2092 28.0752i 0.791872 1.37156i −0.132934 0.991125i \(-0.542440\pi\)
0.924807 0.380438i \(-0.124227\pi\)
\(420\) −2.58286 13.6905i −0.126031 0.668029i
\(421\) 37.4186 1.82367 0.911835 0.410558i \(-0.134666\pi\)
0.911835 + 0.410558i \(0.134666\pi\)
\(422\) 37.9463 + 21.9083i 1.84720 + 1.06648i
\(423\) −4.26921 2.46483i −0.207576 0.119844i
\(424\) 10.8415 18.7780i 0.526508 0.911939i
\(425\) −6.73184 1.02197i −0.326542 0.0495729i
\(426\) 8.35949 + 14.4791i 0.405019 + 0.701513i
\(427\) −2.29433 1.32463i −0.111030 0.0641034i
\(428\) 24.4764 + 14.1315i 1.18311 + 0.683070i
\(429\) 0.0934226 0.161813i 0.00451049 0.00781239i
\(430\) 11.6547 + 4.08510i 0.562040 + 0.197001i
\(431\) −10.0691 17.4401i −0.485010 0.840062i 0.514842 0.857285i \(-0.327851\pi\)
−0.999852 + 0.0172235i \(0.994517\pi\)
\(432\) 0.396689 + 0.229029i 0.0190857 + 0.0110191i
\(433\) 25.4748i 1.22424i 0.790765 + 0.612120i \(0.209683\pi\)
−0.790765 + 0.612120i \(0.790317\pi\)
\(434\) −32.4997 −1.56003
\(435\) 5.31699 + 6.18509i 0.254930 + 0.296553i
\(436\) −14.5156 −0.695170
\(437\) 7.38341 4.26281i 0.353196 0.203918i
\(438\) 18.0447i 0.862210i
\(439\) 17.9509 + 31.0919i 0.856749 + 1.48393i 0.875013 + 0.484100i \(0.160853\pi\)
−0.0182633 + 0.999833i \(0.505814\pi\)
\(440\) −0.783200 + 0.147759i −0.0373376 + 0.00704413i
\(441\) 1.52024 + 2.63314i 0.0723925 + 0.125387i
\(442\) −3.58833 2.07172i −0.170680 0.0985419i
\(443\) 1.13498i 0.0539245i 0.999636 + 0.0269622i \(0.00858339\pi\)
−0.999636 + 0.0269622i \(0.991417\pi\)
\(444\) −4.17771 18.5824i −0.198265 0.881882i
\(445\) −32.0301 11.2269i −1.51837 0.532206i
\(446\) −5.90518 + 10.2281i −0.279618 + 0.484313i
\(447\) −18.5130 + 10.6885i −0.875634 + 0.505548i
\(448\) 22.4763 12.9767i 1.06191 0.613092i
\(449\) 11.7119 + 20.2856i 0.552718 + 0.957336i 0.998077 + 0.0619838i \(0.0197427\pi\)
−0.445359 + 0.895352i \(0.646924\pi\)
\(450\) 7.07108 8.84757i 0.333334 0.417078i
\(451\) −0.214671 0.371821i −0.0101085 0.0175084i
\(452\) 13.7088i 0.644807i
\(453\) 6.72993 + 3.88553i 0.316200 + 0.182558i
\(454\) −36.0044 −1.68977
\(455\) 5.64008 + 1.97691i 0.264411 + 0.0926789i
\(456\) 1.90867 3.30591i 0.0893815 0.154813i
\(457\) 5.77512 3.33427i 0.270149 0.155970i −0.358806 0.933412i \(-0.616816\pi\)
0.628955 + 0.777442i \(0.283483\pi\)
\(458\) 39.9185i 1.86527i
\(459\) −0.680898 + 1.17935i −0.0317816 + 0.0550473i
\(460\) −26.1200 30.3845i −1.21785 1.41669i
\(461\) 6.31363 10.9355i 0.294055 0.509318i −0.680710 0.732553i \(-0.738328\pi\)
0.974765 + 0.223235i \(0.0716618\pi\)
\(462\) −0.543002 + 0.313502i −0.0252627 + 0.0145854i
\(463\) −17.0860 + 9.86458i −0.794052 + 0.458446i −0.841387 0.540433i \(-0.818260\pi\)
0.0473353 + 0.998879i \(0.484927\pi\)
\(464\) −0.835410 + 1.44697i −0.0387829 + 0.0671740i
\(465\) −10.5101 12.2260i −0.487392 0.566969i
\(466\) −26.0000 + 45.0333i −1.20443 + 2.08613i
\(467\) 4.79533i 0.221902i 0.993826 + 0.110951i \(0.0353896\pi\)
−0.993826 + 0.110951i \(0.964610\pi\)
\(468\) 3.64234 2.10291i 0.168367 0.0972069i
\(469\) 6.50653 11.2696i 0.300443 0.520383i
\(470\) −23.5639 8.25942i −1.08692 0.380979i
\(471\) −10.7053 −0.493272
\(472\) −11.2369 6.48761i −0.517219 0.298617i
\(473\) 0.339165i 0.0155948i
\(474\) 8.09298 + 14.0175i 0.371723 + 0.643843i
\(475\) 5.81880 + 4.65045i 0.266985 + 0.213377i
\(476\) 4.24240 + 7.34805i 0.194450 + 0.336797i
\(477\) 7.32836 4.23103i 0.335543 0.193726i
\(478\) 1.89547 1.09435i 0.0866969 0.0500545i
\(479\) 9.44020 16.3509i 0.431334 0.747092i −0.565655 0.824642i \(-0.691377\pi\)
0.996988 + 0.0775503i \(0.0247099\pi\)
\(480\) 13.0037 + 4.55795i 0.593536 + 0.208041i
\(481\) 7.79951 + 2.43367i 0.355627 + 0.110966i
\(482\) 1.23336i 0.0561781i
\(483\) −9.86188 5.69376i −0.448731 0.259075i
\(484\) −17.1912 29.7761i −0.781419 1.35346i
\(485\) −22.5956 + 4.26289i −1.02601 + 0.193568i
\(486\) −1.13261 1.96173i −0.0513760 0.0889859i
\(487\) 0.945335i 0.0428372i −0.999771 0.0214186i \(-0.993182\pi\)
0.999771 0.0214186i \(-0.00681827\pi\)
\(488\) −2.95445 + 1.70575i −0.133742 + 0.0772158i
\(489\) 14.0020 0.633191
\(490\) 10.0394 + 11.6785i 0.453534 + 0.527582i
\(491\) −34.5732 −1.56027 −0.780133 0.625613i \(-0.784849\pi\)
−0.780133 + 0.625613i \(0.784849\pi\)
\(492\) 9.66432i 0.435701i
\(493\) −4.30182 2.48366i −0.193744 0.111858i
\(494\) 2.26641 + 3.92554i 0.101971 + 0.176618i
\(495\) −0.293537 0.102888i −0.0131935 0.00462447i
\(496\) 1.65135 2.86022i 0.0741478 0.128428i
\(497\) 12.7190 + 7.34332i 0.570525 + 0.329393i
\(498\) −11.7446 6.78072i −0.526286 0.303852i
\(499\) 1.74047 + 3.01458i 0.0779142 + 0.134951i 0.902350 0.431004i \(-0.141841\pi\)
−0.824436 + 0.565956i \(0.808507\pi\)
\(500\) 16.4073 30.9248i 0.733755 1.38300i
\(501\) −3.50931 + 6.07830i −0.156784 + 0.271558i
\(502\) −17.9633 10.3711i −0.801742 0.462886i
\(503\) 6.13867 + 3.54416i 0.273710 + 0.158026i 0.630572 0.776131i \(-0.282820\pi\)
−0.356863 + 0.934157i \(0.616154\pi\)
\(504\) −5.09874 −0.227116
\(505\) −1.85335 9.82372i −0.0824729 0.437150i
\(506\) −0.901628 + 1.56167i −0.0400823 + 0.0694245i
\(507\) 11.1958i 0.497223i
\(508\) 16.8745i 0.748685i
\(509\) 7.83602 13.5724i 0.347326 0.601585i −0.638448 0.769665i \(-0.720423\pi\)
0.985773 + 0.168080i \(0.0537566\pi\)
\(510\) −2.28163 + 6.50943i −0.101032 + 0.288243i
\(511\) 7.92561 + 13.7276i 0.350608 + 0.607271i
\(512\) 5.17013i 0.228489i
\(513\) 1.29018 0.744884i 0.0569627 0.0328874i
\(514\) −18.4874 32.0212i −0.815446 1.41239i
\(515\) −37.4371 + 7.06290i −1.64968 + 0.311229i
\(516\) 3.81723 6.61164i 0.168044 0.291061i
\(517\) 0.685736i 0.0301586i
\(518\) −18.5832 20.1592i −0.816500 0.885744i
\(519\) 22.5017 0.987716
\(520\) 5.83606 5.01694i 0.255928 0.220007i
\(521\) 3.04069 + 5.26664i 0.133215 + 0.230736i 0.924914 0.380176i \(-0.124137\pi\)
−0.791699 + 0.610911i \(0.790803\pi\)
\(522\) 7.15566 4.13132i 0.313195 0.180823i
\(523\) −31.0251 + 17.9124i −1.35663 + 0.783253i −0.989169 0.146784i \(-0.953108\pi\)
−0.367466 + 0.930037i \(0.619775\pi\)
\(524\) −5.83427 −0.254871
\(525\) 1.49330 9.83656i 0.0651731 0.429303i
\(526\) −39.3450 −1.71552
\(527\) 8.50338 + 4.90943i 0.370413 + 0.213858i
\(528\) 0.0637177i 0.00277296i
\(529\) −9.75035 −0.423928
\(530\) 32.5028 27.9409i 1.41183 1.21368i
\(531\) −2.53188 4.38534i −0.109874 0.190308i
\(532\) 9.28214i 0.402432i
\(533\) 3.59033 + 2.07288i 0.155515 + 0.0897864i
\(534\) −17.1915 + 29.7766i −0.743950 + 1.28856i
\(535\) 13.1572 + 15.3054i 0.568837 + 0.661710i
\(536\) −8.37857 14.5121i −0.361899 0.626828i
\(537\) −12.8783 + 7.43527i −0.555738 + 0.320855i
\(538\) 40.6539 + 23.4716i 1.75272 + 1.01193i
\(539\) 0.211472 0.366281i 0.00910875 0.0157768i
\(540\) −4.56420 5.30939i −0.196412 0.228480i
\(541\) −35.3488 −1.51976 −0.759882 0.650061i \(-0.774743\pi\)
−0.759882 + 0.650061i \(0.774743\pi\)
\(542\) −42.2573 + 24.3973i −1.81511 + 1.04795i
\(543\) 18.8122 + 10.8613i 0.807310 + 0.466101i
\(544\) −8.39184 −0.359797
\(545\) −9.78246 3.42886i −0.419035 0.146876i
\(546\) 3.02720 5.24326i 0.129552 0.224391i
\(547\) 9.47749i 0.405228i 0.979259 + 0.202614i \(0.0649437\pi\)
−0.979259 + 0.202614i \(0.935056\pi\)
\(548\) 32.6926 18.8751i 1.39656 0.806305i
\(549\) −1.33139 −0.0568222
\(550\) −1.55766 0.236470i −0.0664187 0.0100831i
\(551\) 2.71706 + 4.70608i 0.115750 + 0.200486i
\(552\) −12.6993 + 7.33195i −0.540519 + 0.312069i
\(553\) 12.3135 + 7.10920i 0.523623 + 0.302314i
\(554\) −25.2807 −1.07407
\(555\) 1.57405 13.5101i 0.0668147 0.573471i
\(556\) −0.384224 −0.0162947
\(557\) 29.9805 + 17.3093i 1.27032 + 0.733417i 0.975047 0.221997i \(-0.0712575\pi\)
0.295269 + 0.955414i \(0.404591\pi\)
\(558\) −14.1445 + 8.16635i −0.598786 + 0.345709i
\(559\) 1.63750 + 2.83623i 0.0692589 + 0.119960i
\(560\) 2.00277 0.377844i 0.0846325 0.0159668i
\(561\) 0.189432 0.00799781
\(562\) 55.3526 31.9579i 2.33491 1.34806i
\(563\) 9.69540i 0.408613i −0.978907 0.204306i \(-0.934506\pi\)
0.978907 0.204306i \(-0.0654938\pi\)
\(564\) −7.71783 + 13.3677i −0.324979 + 0.562880i
\(565\) −3.23828 + 9.23875i −0.136236 + 0.388677i
\(566\) −57.2931 −2.40821
\(567\) −1.72326 0.994927i −0.0723703 0.0417830i
\(568\) 16.3785 9.45612i 0.687226 0.396770i
\(569\) 23.2169 0.973304 0.486652 0.873596i \(-0.338218\pi\)
0.486652 + 0.873596i \(0.338218\pi\)
\(570\) 5.72221 4.91907i 0.239677 0.206037i
\(571\) 18.3832 31.8406i 0.769313 1.33249i −0.168623 0.985681i \(-0.553932\pi\)
0.937936 0.346808i \(-0.112735\pi\)
\(572\) −0.506665 0.292523i −0.0211847 0.0122310i
\(573\) −7.72257 + 4.45863i −0.322615 + 0.186262i
\(574\) −6.95605 12.0482i −0.290340 0.502884i
\(575\) −10.4256 26.6471i −0.434776 1.11126i
\(576\) 6.52144 11.2955i 0.271727 0.470644i
\(577\) 12.7911 + 7.38496i 0.532502 + 0.307440i 0.742035 0.670362i \(-0.233861\pi\)
−0.209533 + 0.977802i \(0.567194\pi\)
\(578\) 34.3078i 1.42702i
\(579\) 5.25097 + 9.09495i 0.218223 + 0.377973i
\(580\) 19.3667 16.6485i 0.804157 0.691290i
\(581\) −11.9129 −0.494231
\(582\) 23.2938i 0.965561i
\(583\) −1.01941 0.588555i −0.0422195 0.0243754i
\(584\) 20.4119 0.844650
\(585\) 2.95143 0.556817i 0.122026 0.0230216i
\(586\) 20.8947 0.863152
\(587\) 0.112600 0.0650099i 0.00464752 0.00268325i −0.497674 0.867364i \(-0.665813\pi\)
0.502322 + 0.864681i \(0.332479\pi\)
\(588\) 8.24483 4.76016i 0.340011 0.196306i
\(589\) −5.37078 9.30247i −0.221299 0.383302i
\(590\) −16.7201 19.4499i −0.688354 0.800741i
\(591\) 15.7563 0.648126
\(592\) 2.71840 0.611152i 0.111726 0.0251182i
\(593\) 25.0529i 1.02880i 0.857551 + 0.514399i \(0.171985\pi\)
−0.857551 + 0.514399i \(0.828015\pi\)
\(594\) −0.157550 + 0.272885i −0.00646437 + 0.0111966i
\(595\) 1.12332 + 5.95420i 0.0460517 + 0.244098i
\(596\) 33.4676 + 57.9676i 1.37089 + 2.37444i
\(597\) −23.9215 + 13.8111i −0.979043 + 0.565251i
\(598\) 17.4124i 0.712045i
\(599\) −8.03951 13.9248i −0.328485 0.568953i 0.653726 0.756731i \(-0.273205\pi\)
−0.982212 + 0.187778i \(0.939872\pi\)
\(600\) −10.0082 7.99869i −0.408584 0.326545i
\(601\) 8.45821 14.6500i 0.345017 0.597588i −0.640339 0.768092i \(-0.721206\pi\)
0.985357 + 0.170504i \(0.0545397\pi\)
\(602\) 10.9901i 0.447921i
\(603\) 6.53970i 0.266317i
\(604\) 12.1663 21.0726i 0.495040 0.857434i
\(605\) −4.55197 24.1278i −0.185064 0.980936i
\(606\) −10.1273 −0.411394
\(607\) −1.22625 0.707974i −0.0497718 0.0287358i 0.474908 0.880036i \(-0.342481\pi\)
−0.524679 + 0.851300i \(0.675815\pi\)
\(608\) 7.95050 + 4.59022i 0.322435 + 0.186158i
\(609\) 3.62912 6.28582i 0.147059 0.254714i
\(610\) −6.62679 + 1.25021i −0.268311 + 0.0506197i
\(611\) −3.31076 5.73441i −0.133939 0.231989i
\(612\) 3.69276 + 2.13202i 0.149271 + 0.0861816i
\(613\) 16.9668 + 9.79576i 0.685281 + 0.395647i 0.801842 0.597536i \(-0.203854\pi\)
−0.116561 + 0.993184i \(0.537187\pi\)
\(614\) −7.29251 + 12.6310i −0.294302 + 0.509745i
\(615\) 2.28290 6.51307i 0.0920555 0.262632i
\(616\) 0.354628 + 0.614234i 0.0142884 + 0.0247482i
\(617\) −8.13849 4.69876i −0.327643 0.189165i 0.327151 0.944972i \(-0.393911\pi\)
−0.654794 + 0.755807i \(0.727245\pi\)
\(618\) 38.5941i 1.55248i
\(619\) 38.5635 1.55000 0.775000 0.631961i \(-0.217750\pi\)
0.775000 + 0.631961i \(0.217750\pi\)
\(620\) −38.2819 + 32.9089i −1.53744 + 1.32165i
\(621\) −5.72279 −0.229648
\(622\) −3.25315 + 1.87820i −0.130439 + 0.0753091i
\(623\) 30.2035i 1.21008i
\(624\) 0.307632 + 0.532834i 0.0123151 + 0.0213304i
\(625\) 18.3624 16.9654i 0.734494 0.678615i
\(626\) 9.11578 + 15.7890i 0.364340 + 0.631055i
\(627\) −0.179469 0.103617i −0.00716731 0.00413805i
\(628\) 33.5201i 1.33760i
\(629\) 1.81694 + 8.08175i 0.0724463 + 0.322241i
\(630\) −9.51157 3.33391i −0.378950 0.132826i
\(631\) 10.4190 18.0463i 0.414776 0.718413i −0.580629 0.814168i \(-0.697193\pi\)
0.995405 + 0.0957554i \(0.0305267\pi\)
\(632\) 15.8563 9.15465i 0.630730 0.364152i
\(633\) 16.7518 9.67165i 0.665824 0.384413i
\(634\) −9.88615 17.1233i −0.392629 0.680054i
\(635\) 3.98609 11.3722i 0.158183 0.451293i
\(636\) −13.2481 22.9464i −0.525323 0.909886i
\(637\) 4.08398i 0.161813i
\(638\) −0.995383 0.574684i −0.0394076 0.0227520i
\(639\) 7.38076 0.291978
\(640\) 12.7369 36.3380i 0.503469 1.43639i
\(641\) 15.3203 26.5356i 0.605116 1.04809i −0.386917 0.922114i \(-0.626460\pi\)
0.992033 0.125977i \(-0.0402066\pi\)
\(642\) 17.7071 10.2232i 0.698844 0.403478i
\(643\) 34.8708i 1.37517i 0.726104 + 0.687585i \(0.241329\pi\)
−0.726104 + 0.687585i \(0.758671\pi\)
\(644\) −17.8282 + 30.8793i −0.702530 + 1.21682i
\(645\) 4.13434 3.55407i 0.162790 0.139941i
\(646\) −2.29778 + 3.97988i −0.0904051 + 0.156586i
\(647\) 22.9615 13.2569i 0.902711 0.521181i 0.0246324 0.999697i \(-0.492158\pi\)
0.878079 + 0.478516i \(0.158825\pi\)
\(648\) −2.21908 + 1.28118i −0.0871736 + 0.0503297i
\(649\) −0.352195 + 0.610020i −0.0138249 + 0.0239454i
\(650\) 14.1674 5.54296i 0.555693 0.217413i
\(651\) −7.17365 + 12.4251i −0.281158 + 0.486979i
\(652\) 43.8428i 1.71702i
\(653\) 11.2002 6.46642i 0.438296 0.253051i −0.264578 0.964364i \(-0.585233\pi\)
0.702875 + 0.711314i \(0.251899\pi\)
\(654\) −5.25054 + 9.09421i −0.205312 + 0.355612i
\(655\) −3.93189 1.37817i −0.153631 0.0538495i
\(656\) 1.41378 0.0551989
\(657\) 6.89878 + 3.98301i 0.269147 + 0.155392i
\(658\) 22.2201i 0.866230i
\(659\) 21.9111 + 37.9512i 0.853536 + 1.47837i 0.877996 + 0.478668i \(0.158880\pi\)
−0.0244598 + 0.999701i \(0.507787\pi\)
\(660\) −0.322161 + 0.919119i −0.0125401 + 0.0357767i
\(661\) 1.61157 + 2.79132i 0.0626829 + 0.108570i 0.895664 0.444732i \(-0.146701\pi\)
−0.832981 + 0.553302i \(0.813368\pi\)
\(662\) −1.52564 + 0.880829i −0.0592957 + 0.0342344i
\(663\) −1.58410 + 0.914583i −0.0615215 + 0.0355195i
\(664\) −7.67024 + 13.2853i −0.297663 + 0.515568i
\(665\) 2.19262 6.25550i 0.0850262 0.242578i
\(666\) −13.1533 4.10420i −0.509680 0.159035i
\(667\) 20.8746i 0.808267i
\(668\) 19.0323 + 10.9883i 0.736381 + 0.425150i
\(669\) 2.60690 + 4.51528i 0.100789 + 0.174571i
\(670\) −6.14099 32.5505i −0.237247 1.25753i
\(671\) 0.0926008 + 0.160389i 0.00357482 + 0.00619176i
\(672\) 12.2621i 0.473023i
\(673\) 39.3576 22.7231i 1.51712 0.875912i 0.517326 0.855788i \(-0.326927\pi\)
0.999797 0.0201237i \(-0.00640599\pi\)
\(674\) 48.1562 1.85491
\(675\) −1.82176 4.65631i −0.0701197 0.179221i
\(676\) −35.0561 −1.34831
\(677\) 31.8762i 1.22510i 0.790431 + 0.612551i \(0.209857\pi\)
−0.790431 + 0.612551i \(0.790143\pi\)
\(678\) 8.58875 + 4.95872i 0.329849 + 0.190438i
\(679\) 10.2311 + 17.7208i 0.392635 + 0.680063i
\(680\) 7.36336 + 2.58094i 0.282372 + 0.0989745i
\(681\) −7.94726 + 13.7651i −0.304540 + 0.527478i
\(682\) 1.96757 + 1.13597i 0.0753420 + 0.0434987i
\(683\) −26.1641 15.1059i −1.00114 0.578009i −0.0925558 0.995708i \(-0.529504\pi\)
−0.908586 + 0.417698i \(0.862837\pi\)
\(684\) −2.33237 4.03978i −0.0891803 0.154465i
\(685\) 26.4912 4.99784i 1.01218 0.190958i
\(686\) 22.6284 39.1936i 0.863958 1.49642i
\(687\) −15.2615 8.81122i −0.582261 0.336169i
\(688\) 0.967210 + 0.558419i 0.0368745 + 0.0212895i
\(689\) 11.3663 0.433020
\(690\) −28.4844 + 5.37388i −1.08438 + 0.204580i
\(691\) 12.6294 21.8748i 0.480445 0.832156i −0.519303 0.854590i \(-0.673808\pi\)
0.999748 + 0.0224344i \(0.00714170\pi\)
\(692\) 70.4570i 2.67837i
\(693\) 0.276797i 0.0105147i
\(694\) −35.9572 + 62.2798i −1.36492 + 2.36411i
\(695\) −0.258940 0.0907612i −0.00982214 0.00344277i
\(696\) −4.67328 8.09436i −0.177140 0.306816i
\(697\) 4.20315i 0.159206i
\(698\) −52.2329 + 30.1567i −1.97704 + 1.14145i
\(699\) 11.4780 + 19.8804i 0.434136 + 0.751946i
\(700\) −30.8001 4.67581i −1.16413 0.176729i
\(701\) −3.14432 + 5.44612i −0.118759 + 0.205697i −0.919276 0.393613i \(-0.871225\pi\)
0.800517 + 0.599310i \(0.204558\pi\)
\(702\) 3.04264i 0.114837i
\(703\) 2.69922 8.65056i 0.101803 0.326262i
\(704\) −1.81432 −0.0683798
\(705\) −8.35897 + 7.18576i −0.314817 + 0.270631i
\(706\) 19.9296 + 34.5190i 0.750059 + 1.29914i
\(707\) −7.70437 + 4.44812i −0.289753 + 0.167289i
\(708\) −13.7313 + 7.92778i −0.516054 + 0.297944i
\(709\) −21.6686 −0.813782 −0.406891 0.913477i \(-0.633387\pi\)
−0.406891 + 0.913477i \(0.633387\pi\)
\(710\) 36.7367 6.93077i 1.37870 0.260107i
\(711\) 7.14545 0.267975
\(712\) 33.6828 + 19.4468i 1.26232 + 0.728799i
\(713\) 41.2627i 1.54530i
\(714\) 6.13821 0.229717
\(715\) −0.272357 0.316824i −0.0101856 0.0118486i
\(716\) 23.2812 + 40.3242i 0.870059 + 1.50699i
\(717\) 0.966225i 0.0360843i
\(718\) 27.6309 + 15.9527i 1.03118 + 0.595349i
\(719\) 21.1134 36.5696i 0.787399 1.36381i −0.140157 0.990129i \(-0.544761\pi\)
0.927556 0.373685i \(-0.121906\pi\)
\(720\) 0.776705 0.667691i 0.0289461 0.0248834i
\(721\) 16.9513 + 29.3605i 0.631299 + 1.09344i
\(722\) −32.9190 + 19.0058i −1.22512 + 0.707323i
\(723\) −0.471533 0.272240i −0.0175365 0.0101247i
\(724\) 34.0086 58.9046i 1.26392 2.18917i
\(725\) 16.9844 6.64511i 0.630787 0.246793i
\(726\) −24.8735 −0.923142
\(727\) −25.9086 + 14.9583i −0.960896 + 0.554774i −0.896449 0.443148i \(-0.853862\pi\)
−0.0644473 + 0.997921i \(0.520528\pi\)
\(728\) −5.93109 3.42432i −0.219821 0.126914i
\(729\) −1.00000 −0.0370370
\(730\) 38.0779 + 13.3467i 1.40933 + 0.493984i
\(731\) −1.66017 + 2.87550i −0.0614035 + 0.106354i
\(732\) 4.16882i 0.154084i
\(733\) 26.9123 15.5378i 0.994029 0.573903i 0.0875528 0.996160i \(-0.472095\pi\)
0.906476 + 0.422257i \(0.138762\pi\)
\(734\) 62.8046 2.31816
\(735\) 6.68087 1.26042i 0.246428 0.0464912i
\(736\) −17.6329 30.5410i −0.649957 1.12576i
\(737\) −0.787824 + 0.454851i −0.0290199 + 0.0167546i
\(738\) −6.05484 3.49576i −0.222882 0.128681i
\(739\) −35.9209 −1.32137 −0.660686 0.750663i \(-0.729734\pi\)
−0.660686 + 0.750663i \(0.729734\pi\)
\(740\) −42.3026 4.92864i −1.55507 0.181180i
\(741\) 2.00106 0.0735107
\(742\) −33.0321 19.0711i −1.21265 0.700123i
\(743\) 40.0021 23.0952i 1.46753 0.847281i 0.468194 0.883626i \(-0.344905\pi\)
0.999339 + 0.0363450i \(0.0115715\pi\)
\(744\) 9.23764 + 16.0001i 0.338668 + 0.586591i
\(745\) 8.86171 + 46.9717i 0.324668 + 1.72091i
\(746\) 13.1440 0.481234
\(747\) −5.18475 + 2.99342i −0.189700 + 0.109523i
\(748\) 0.593145i 0.0216875i
\(749\) 8.98048 15.5546i 0.328140 0.568354i
\(750\) −13.4400 21.4654i −0.490759 0.783806i
\(751\) −47.4564 −1.73171 −0.865854 0.500296i \(-0.833225\pi\)
−0.865854 + 0.500296i \(0.833225\pi\)
\(752\) −1.95554 1.12903i −0.0713112 0.0411716i
\(753\) −7.93008 + 4.57843i −0.288988 + 0.166847i
\(754\) 11.0984 0.404180
\(755\) 13.1770 11.3275i 0.479560 0.412252i
\(756\) −3.11530 + 5.39585i −0.113302 + 0.196245i
\(757\) −13.4300 7.75380i −0.488121 0.281817i 0.235674 0.971832i \(-0.424270\pi\)
−0.723795 + 0.690016i \(0.757604\pi\)
\(758\) −37.8483 + 21.8517i −1.37471 + 0.793689i
\(759\) 0.398033 + 0.689413i 0.0144477 + 0.0250241i
\(760\) −5.56437 6.47286i −0.201841 0.234795i
\(761\) −8.91886 + 15.4479i −0.323308 + 0.559986i −0.981169 0.193154i \(-0.938128\pi\)
0.657860 + 0.753140i \(0.271462\pi\)
\(762\) −10.5721 6.10381i −0.382987 0.221118i
\(763\) 9.22458i 0.333952i
\(764\) 13.9608 + 24.1808i 0.505083 + 0.874830i
\(765\) 1.98503 + 2.30913i 0.0717690 + 0.0834867i
\(766\) 29.1484 1.05317
\(767\) 6.80165i 0.245593i
\(768\) −11.1905 6.46083i −0.403802 0.233135i
\(769\) −21.2282 −0.765510 −0.382755 0.923850i \(-0.625025\pi\)
−0.382755 + 0.923850i \(0.625025\pi\)
\(770\) 0.259921 + 1.37772i 0.00936692 + 0.0496496i
\(771\) −16.3229 −0.587856
\(772\) 28.4780 16.4418i 1.02494 0.591752i
\(773\) −33.6932 + 19.4528i −1.21186 + 0.699668i −0.963164 0.268913i \(-0.913336\pi\)
−0.248697 + 0.968581i \(0.580002\pi\)
\(774\) −2.76153 4.78310i −0.0992610 0.171925i
\(775\) −33.5730 + 13.1353i −1.20598 + 0.471835i
\(776\) 26.3496 0.945896
\(777\) −11.8090 + 2.65492i −0.423647 + 0.0952446i
\(778\) 59.9437i 2.14908i
\(779\) 2.29907 3.98210i 0.0823726 0.142673i
\(780\) −1.74350 9.24145i −0.0624272 0.330897i
\(781\) −0.513348 0.889145i −0.0183690 0.0318161i
\(782\) 15.2883 8.82670i 0.546708 0.315642i
\(783\) 3.64762i 0.130355i
\(784\) 0.696358 + 1.20613i 0.0248699 + 0.0430760i
\(785\) −7.91810 + 22.5902i −0.282609 + 0.806278i
\(786\) −2.11036 + 3.65526i −0.0752741 + 0.130379i
\(787\) 0.610223i 0.0217521i 0.999941 + 0.0108760i \(0.00346202\pi\)
−0.999941 + 0.0108760i \(0.996538\pi\)
\(788\) 49.3358i 1.75751i
\(789\) −8.68461 + 15.0422i −0.309180 + 0.535516i
\(790\) 35.5655 6.70981i 1.26536 0.238724i
\(791\) 8.71187 0.309759
\(792\) 0.308683 + 0.178218i 0.0109686 + 0.00633271i
\(793\) −1.54873 0.894161i −0.0549971 0.0317526i
\(794\) −10.9499 + 18.9658i −0.388598 + 0.673071i
\(795\) −3.50790 18.5937i −0.124413 0.659452i
\(796\) 43.2451 + 74.9027i 1.53278 + 2.65486i
\(797\) −22.9411 13.2450i −0.812615 0.469163i 0.0352485 0.999379i \(-0.488778\pi\)
−0.847863 + 0.530215i \(0.822111\pi\)
\(798\) −5.81539 3.35752i −0.205863 0.118855i
\(799\) 3.35659 5.81378i 0.118748 0.205677i
\(800\) 19.2363 24.0691i 0.680107 0.850972i
\(801\) 7.58937 + 13.1452i 0.268157 + 0.464462i
\(802\) 60.9946 + 35.2152i 2.15379 + 1.24349i
\(803\) 1.10811i 0.0391043i
\(804\) −20.4770 −0.722169
\(805\) −19.3092 + 16.5991i −0.680561 + 0.585042i
\(806\) −21.9381 −0.772737
\(807\) 17.9471 10.3618i 0.631767 0.364751i
\(808\) 11.4559i 0.403015i
\(809\) 2.54245 + 4.40365i 0.0893876 + 0.154824i 0.907252 0.420587i \(-0.138176\pi\)
−0.817865 + 0.575410i \(0.804842\pi\)
\(810\) −4.97736 + 0.939032i −0.174887 + 0.0329942i
\(811\) 15.8725 + 27.4920i 0.557358 + 0.965373i 0.997716 + 0.0675505i \(0.0215184\pi\)
−0.440357 + 0.897823i \(0.645148\pi\)
\(812\) −19.6820 11.3634i −0.690704 0.398778i
\(813\) 21.5408i 0.755471i
\(814\) 0.420416 + 1.87001i 0.0147356 + 0.0655437i
\(815\) 10.3565 29.5469i 0.362773 1.03498i
\(816\) −0.311890 + 0.540209i −0.0109183 + 0.0189111i
\(817\) 3.14571 1.81618i 0.110055 0.0635401i
\(818\) 24.5347 14.1651i 0.857836 0.495272i
\(819\) −1.33639 2.31469i −0.0466972 0.0808818i
\(820\) −20.3936 7.14818i −0.712176 0.249625i
\(821\) −2.62563 4.54772i −0.0916350 0.158716i 0.816564 0.577255i \(-0.195876\pi\)
−0.908199 + 0.418538i \(0.862543\pi\)
\(822\) 27.3099i 0.952541i
\(823\) −31.9125 18.4247i −1.11240 0.642244i −0.172949 0.984931i \(-0.555330\pi\)
−0.939450 + 0.342687i \(0.888663\pi\)
\(824\) 43.6570 1.52086
\(825\) −0.434228 + 0.543320i −0.0151179 + 0.0189160i
\(826\) −11.4123 + 19.7667i −0.397084 + 0.687770i
\(827\) −26.0304 + 15.0286i −0.905165 + 0.522597i −0.878872 0.477057i \(-0.841703\pi\)
−0.0262926 + 0.999654i \(0.508370\pi\)
\(828\) 17.9191i 0.622732i
\(829\) 11.2631 19.5082i 0.391182 0.677548i −0.601423 0.798930i \(-0.705400\pi\)
0.992606 + 0.121383i \(0.0387329\pi\)
\(830\) −22.9955 + 19.7680i −0.798184 + 0.686156i
\(831\) −5.58021 + 9.66521i −0.193575 + 0.335282i
\(832\) 15.1721 8.75961i 0.525998 0.303685i
\(833\) −3.58579 + 2.07026i −0.124240 + 0.0717302i
\(834\) −0.138981 + 0.240722i −0.00481251 + 0.00833551i
\(835\) 10.2307 + 11.9011i 0.354050 + 0.411855i
\(836\) −0.324442 + 0.561951i −0.0112211 + 0.0194355i
\(837\) 7.21023i 0.249222i
\(838\) −63.5962 + 36.7173i −2.19690 + 1.26838i
\(839\) −14.5451 + 25.1929i −0.502153 + 0.869755i 0.497844 + 0.867267i \(0.334125\pi\)
−0.999997 + 0.00248802i \(0.999208\pi\)
\(840\) −3.77127 + 10.7593i −0.130121 + 0.371232i
\(841\) −15.6948 −0.541201
\(842\) −73.4052 42.3805i −2.52971 1.46053i
\(843\) 28.2162i 0.971818i
\(844\) −30.2837 52.4529i −1.04241 1.80550i
\(845\) −23.6253 8.28094i −0.812736 0.284873i
\(846\) 5.58335 + 9.67065i 0.191960 + 0.332484i
\(847\) −18.9226 + 10.9249i −0.650187 + 0.375385i
\(848\) 3.35681 1.93805i 0.115273 0.0665531i
\(849\) −12.6463 + 21.9041i −0.434020 + 0.751745i
\(850\) 12.0486 + 9.62936i 0.413263 + 0.330284i
\(851\) −25.5948 + 23.5939i −0.877377 + 0.808787i
\(852\) 23.1105i 0.791753i
\(853\) −1.34282 0.775276i −0.0459772 0.0265449i 0.476835 0.878993i \(-0.341784\pi\)
−0.522812 + 0.852448i \(0.675117\pi\)
\(854\) 3.00057 + 5.19714i 0.102677 + 0.177843i
\(855\) −0.617575 3.27347i −0.0211206 0.111950i
\(856\) −11.5643 20.0300i −0.395260 0.684611i
\(857\) 29.4919i 1.00743i −0.863871 0.503713i \(-0.831967\pi\)
0.863871 0.503713i \(-0.168033\pi\)
\(858\) −0.366540 + 0.211622i −0.0125135 + 0.00722465i
\(859\) −34.7843 −1.18683 −0.593413 0.804898i \(-0.702220\pi\)
−0.593413 + 0.804898i \(0.702220\pi\)
\(860\) −11.1285 12.9454i −0.379477 0.441434i
\(861\) −6.14163 −0.209306
\(862\) 45.6171i 1.55373i
\(863\) 5.54212 + 3.19974i 0.188656 + 0.108920i 0.591353 0.806413i \(-0.298594\pi\)
−0.402697 + 0.915333i \(0.631927\pi\)
\(864\) −3.08117 5.33674i −0.104823 0.181560i
\(865\) 16.6433 47.4830i 0.565890 1.61447i
\(866\) 28.8529 49.9747i 0.980461 1.69821i
\(867\) 13.1164 + 7.57276i 0.445456 + 0.257184i
\(868\) 38.9054 + 22.4620i 1.32053 + 0.762411i
\(869\) −0.496982 0.860798i −0.0168590 0.0292006i
\(870\) −3.42523 18.1555i −0.116126 0.615531i
\(871\) 4.39207 7.60729i 0.148820 0.257763i
\(872\) 10.2872 + 5.93933i 0.348369 + 0.201131i
\(873\) 8.90560 + 5.14165i 0.301409 + 0.174018i
\(874\) −19.3124 −0.653250
\(875\) −19.6525 10.4267i −0.664377 0.352488i
\(876\) 12.4715 21.6013i 0.421374 0.729842i
\(877\) 13.1412i 0.443748i 0.975075 + 0.221874i \(0.0712174\pi\)
−0.975075 + 0.221874i \(0.928783\pi\)
\(878\) 81.3251i 2.74459i
\(879\) 4.61209 7.98837i 0.155562 0.269441i
\(880\) −0.134457 0.0471286i −0.00453254 0.00158870i
\(881\) 7.80597 + 13.5203i 0.262990 + 0.455511i 0.967035 0.254644i \(-0.0819582\pi\)
−0.704045 + 0.710155i \(0.748625\pi\)
\(882\) 6.88734i 0.231909i
\(883\) −19.8501 + 11.4605i −0.668009 + 0.385675i −0.795322 0.606188i \(-0.792698\pi\)
0.127313 + 0.991863i \(0.459365\pi\)
\(884\) 2.86373 + 4.96012i 0.0963176 + 0.166827i
\(885\) −11.1266 + 2.09916i −0.374017 + 0.0705623i
\(886\) 1.28548 2.22652i 0.0431867 0.0748015i
\(887\) 36.4877i 1.22514i −0.790417 0.612569i \(-0.790136\pi\)
0.790417 0.612569i \(-0.209864\pi\)
\(888\) −4.64261 + 14.8788i −0.155796 + 0.499300i
\(889\) −10.7237 −0.359660
\(890\) 50.1188 + 58.3017i 1.67999 + 1.95428i
\(891\) 0.0695522 + 0.120468i 0.00233009 + 0.00403583i
\(892\) 14.1382 8.16269i 0.473381 0.273307i
\(893\) −6.36012 + 3.67202i −0.212833 + 0.122879i
\(894\) 48.4233 1.61952
\(895\) 6.16450 + 32.6751i 0.206057 + 1.09221i
\(896\) −34.2657 −1.14474
\(897\) −6.65702 3.84343i −0.222271 0.128328i
\(898\) 53.0598i 1.77063i
\(899\) −26.3002 −0.877161
\(900\) −14.5797 + 5.70428i −0.485992 + 0.190143i
\(901\) 5.76180 + 9.97973i 0.191953 + 0.332473i
\(902\) 0.972551i 0.0323824i
\(903\) −4.20167 2.42584i −0.139823 0.0807267i
\(904\) 5.60922 9.71545i 0.186560 0.323131i
\(905\) 36.8338 31.6640i 1.22440 1.05255i
\(906\) −8.80154 15.2447i −0.292412 0.506472i
\(907\) 13.8965 8.02316i 0.461426 0.266405i −0.251217 0.967931i \(-0.580831\pi\)
0.712644 + 0.701526i \(0.247498\pi\)
\(908\) 43.1009 + 24.8843i 1.43035 + 0.825815i
\(909\) −2.23540 + 3.87183i −0.0741436 + 0.128420i
\(910\) −8.82525 10.2661i −0.292554 0.340319i
\(911\) −12.1034 −0.401002 −0.200501 0.979693i \(-0.564257\pi\)
−0.200501 + 0.979693i \(0.564257\pi\)
\(912\) 0.590975 0.341199i 0.0195691 0.0112982i
\(913\) 0.721221 + 0.416397i 0.0238689 + 0.0137807i
\(914\) −15.1056 −0.499650
\(915\) −0.984755 + 2.80949i −0.0325550 + 0.0928787i
\(916\) −27.5895 + 47.7865i −0.911584 + 1.57891i
\(917\) 3.70766i 0.122438i
\(918\) 2.67148 1.54238i 0.0881718 0.0509060i
\(919\) 8.10690 0.267422 0.133711 0.991020i \(-0.457311\pi\)
0.133711 + 0.991020i \(0.457311\pi\)
\(920\) 6.07885 + 32.2211i 0.200414 + 1.06230i
\(921\) 3.21935 + 5.57608i 0.106081 + 0.183738i
\(922\) −24.7713 + 14.3017i −0.815799 + 0.471002i
\(923\) 8.58565 + 4.95693i 0.282600 + 0.163159i
\(924\) 0.866703 0.0285124
\(925\) −27.3447 13.3142i −0.899087 0.437769i
\(926\) 44.6907 1.46863
\(927\) 14.7551 + 8.51887i 0.484621 + 0.279796i
\(928\) 19.4664 11.2389i 0.639016 0.368936i
\(929\) 11.4317 + 19.8003i 0.375063 + 0.649628i 0.990336 0.138686i \(-0.0442878\pi\)
−0.615274 + 0.788314i \(0.710954\pi\)
\(930\) 6.77064 + 35.8879i 0.222018 + 1.17681i
\(931\) 4.52961 0.148452
\(932\) 62.2492 35.9396i 2.03904 1.17724i
\(933\) 1.65830i 0.0542904i
\(934\) 5.43122 9.40716i 0.177715 0.307812i
\(935\) 0.140112 0.399738i 0.00458217 0.0130728i
\(936\) −3.44178 −0.112498
\(937\) 36.1461 + 20.8689i 1.18084 + 0.681758i 0.956209 0.292685i \(-0.0945489\pi\)
0.224631 + 0.974444i \(0.427882\pi\)
\(938\) −25.5281 + 14.7387i −0.833522 + 0.481234i
\(939\) 8.04850 0.262653
\(940\) 22.4999 + 26.1735i 0.733866 + 0.853684i
\(941\) −13.0833 + 22.6609i −0.426502 + 0.738724i −0.996559 0.0828812i \(-0.973588\pi\)
0.570057 + 0.821605i \(0.306921\pi\)
\(942\) 21.0008 + 12.1248i 0.684244 + 0.395048i
\(943\) −15.2968 + 8.83163i −0.498133 + 0.287597i
\(944\) −1.15975 2.00874i −0.0377465 0.0653789i
\(945\) −3.37410 + 2.90053i −0.109759 + 0.0943542i
\(946\) −0.384140 + 0.665350i −0.0124895 + 0.0216324i
\(947\) −37.1492 21.4481i −1.20719 0.696969i −0.245042 0.969512i \(-0.578802\pi\)
−0.962143 + 0.272544i \(0.912135\pi\)
\(948\) 22.3737i 0.726665i
\(949\) 5.34999 + 9.26645i 0.173668 + 0.300802i
\(950\) −6.14779 15.7133i −0.199461 0.509808i
\(951\) −8.72868 −0.283047
\(952\) 6.94344i 0.225038i
\(953\) −28.0503 16.1949i −0.908640 0.524604i −0.0286466 0.999590i \(-0.509120\pi\)
−0.879993 + 0.474986i \(0.842453\pi\)
\(954\) −19.1684 −0.620599
\(955\) 3.69660 + 19.5939i 0.119619 + 0.634045i
\(956\) −3.02543 −0.0978493
\(957\) −0.439422 + 0.253700i −0.0142045 + 0.00820096i
\(958\) −37.0383 + 21.3840i −1.19665 + 0.690887i
\(959\) −11.9950 20.7760i −0.387340 0.670893i
\(960\) −19.0121 22.1162i −0.613612 0.713796i
\(961\) 20.9874 0.677014
\(962\) −12.5442 13.6080i −0.404440 0.438739i
\(963\) 9.02627i 0.290868i
\(964\) −0.852433 + 1.47646i −0.0274550 + 0.0475535i
\(965\) 23.0760 4.35353i 0.742842 0.140145i
\(966\) 12.8976 + 22.3392i 0.414972 + 0.718753i
\(967\) −14.8606 + 8.57978i −0.477885 + 0.275907i −0.719535 0.694456i \(-0.755645\pi\)
0.241649 + 0.970364i \(0.422312\pi\)
\(968\) 28.1365i 0.904341i
\(969\) 1.01438 + 1.75696i 0.0325865 + 0.0564416i
\(970\) 49.1546 + 17.2292i 1.57826 + 0.553197i
\(971\) 15.7970 27.3612i 0.506949 0.878061i −0.493019 0.870019i \(-0.664107\pi\)
0.999968 0.00804267i \(-0.00256009\pi\)
\(972\) 3.13118i 0.100433i
\(973\) 0.244173i 0.00782782i
\(974\) −1.07069 + 1.85449i −0.0343072 + 0.0594218i
\(975\) 1.00802 6.63993i 0.0322824 0.212648i
\(976\) −0.609851 −0.0195209
\(977\) 25.9721 + 14.9950i 0.830922 + 0.479733i 0.854168 0.519997i \(-0.174067\pi\)
−0.0232466 + 0.999730i \(0.507400\pi\)
\(978\) −27.4681 15.8587i −0.878333 0.507106i
\(979\) 1.05571 1.82855i 0.0337408 0.0584408i
\(980\) −3.94660 20.9190i −0.126069 0.668234i
\(981\) 2.31790 + 4.01473i 0.0740050 + 0.128180i
\(982\) 67.8233 + 39.1578i 2.16433 + 1.24958i
\(983\) 44.3450 + 25.6026i 1.41439 + 0.816596i 0.995798 0.0915810i \(-0.0291920\pi\)
0.418587 + 0.908177i \(0.362525\pi\)
\(984\) −3.95435 + 6.84913i −0.126060 + 0.218342i
\(985\) 11.6541 33.2488i 0.371330 1.05940i
\(986\) 5.62601 + 9.74454i 0.179169 + 0.310329i
\(987\) 8.49509 + 4.90464i 0.270402 + 0.156117i
\(988\) 6.26568i 0.199338i
\(989\) −13.9533 −0.443690
\(990\) 0.459309 + 0.534301i 0.0145978 + 0.0169812i
\(991\) −16.7140 −0.530939 −0.265469 0.964119i \(-0.585527\pi\)
−0.265469 + 0.964119i \(0.585527\pi\)
\(992\) −38.4791 + 22.2159i −1.22171 + 0.705357i
\(993\) 0.777701i 0.0246796i
\(994\) −16.6342 28.8112i −0.527604 0.913837i
\(995\) 11.4506 + 60.6944i 0.363010 + 1.92414i
\(996\) 9.37294 + 16.2344i 0.296993 + 0.514407i
\(997\) −30.7507 17.7539i −0.973886 0.562273i −0.0734671 0.997298i \(-0.523406\pi\)
−0.900419 + 0.435024i \(0.856740\pi\)
\(998\) 7.88507i 0.249598i
\(999\) −4.47243 + 4.12279i −0.141501 + 0.130439i
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 555.2.bb.a.454.5 72
5.4 even 2 inner 555.2.bb.a.454.32 yes 72
37.26 even 3 inner 555.2.bb.a.544.32 yes 72
185.174 even 6 inner 555.2.bb.a.544.5 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
555.2.bb.a.454.5 72 1.1 even 1 trivial
555.2.bb.a.454.32 yes 72 5.4 even 2 inner
555.2.bb.a.544.5 yes 72 185.174 even 6 inner
555.2.bb.a.544.32 yes 72 37.26 even 3 inner