Properties

Label 675.2.r.a.46.12
Level $675$
Weight $2$
Character 675.46
Analytic conductor $5.390$
Analytic rank $0$
Dimension $224$
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] = [675,2,Mod(46,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.r (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 46.12
Character \(\chi\) \(=\) 675.46
Dual form 675.2.r.a.631.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.510289 - 0.566733i) q^{2} +(0.148265 - 1.41065i) q^{4} +(0.965605 + 2.01683i) q^{5} +(-0.476660 + 0.825599i) q^{7} +(-2.10906 + 1.53232i) q^{8} +O(q^{10})\) \(q+(-0.510289 - 0.566733i) q^{2} +(0.148265 - 1.41065i) q^{4} +(0.965605 + 2.01683i) q^{5} +(-0.476660 + 0.825599i) q^{7} +(-2.10906 + 1.53232i) q^{8} +(0.650268 - 1.57641i) q^{10} +(-1.93658 - 2.15079i) q^{11} +(1.30724 - 1.45184i) q^{13} +(0.711129 - 0.151155i) q^{14} +(-0.830202 - 0.176465i) q^{16} +(5.51944 - 4.01011i) q^{17} +(3.77403 - 2.74200i) q^{19} +(2.98821 - 1.06310i) q^{20} +(-0.230709 + 2.19505i) q^{22} +(8.61700 - 1.83160i) q^{23} +(-3.13521 + 3.89492i) q^{25} -1.48988 q^{26} +(1.09396 + 0.794807i) q^{28} +(-0.852862 + 0.379719i) q^{29} +(-2.42766 - 1.08086i) q^{31} +(2.93057 + 5.07590i) q^{32} +(-5.08917 - 1.08174i) q^{34} +(-2.12536 - 0.164140i) q^{35} +(0.799338 + 2.46011i) q^{37} +(-3.47983 - 0.739660i) q^{38} +(-5.12694 - 2.77400i) q^{40} +(3.62683 - 4.02800i) q^{41} +(4.43871 - 7.68807i) q^{43} +(-3.32113 + 2.41294i) q^{44} +(-5.43519 - 3.94889i) q^{46} +(3.66588 - 1.63216i) q^{47} +(3.04559 + 5.27512i) q^{49} +(3.80725 - 0.210706i) q^{50} +(-1.85422 - 2.05932i) q^{52} +(-4.30252 - 3.12596i) q^{53} +(2.46781 - 5.98256i) q^{55} +(-0.259779 - 2.47163i) q^{56} +(0.650405 + 0.289579i) q^{58} +(-3.21068 + 3.56582i) q^{59} +(-7.51779 - 8.34935i) q^{61} +(0.626247 + 1.92739i) q^{62} +(0.856686 - 2.63661i) q^{64} +(4.19039 + 1.23458i) q^{65} +(3.38246 + 1.50597i) q^{67} +(-4.83851 - 8.38055i) q^{68} +(0.991523 + 1.28827i) q^{70} +(0.125408 + 0.0911140i) q^{71} +(-3.09917 + 9.53828i) q^{73} +(0.986332 - 1.70838i) q^{74} +(-3.30843 - 5.73038i) q^{76} +(2.69878 - 0.573643i) q^{77} +(3.86470 - 1.72068i) q^{79} +(-0.445747 - 1.84477i) q^{80} -4.13353 q^{82} +(-0.344989 - 3.28235i) q^{83} +(13.4173 + 7.25960i) q^{85} +(-6.62211 + 1.40757i) q^{86} +(7.38004 + 1.56868i) q^{88} +(-5.32122 + 16.3770i) q^{89} +(0.575527 + 1.77129i) q^{91} +(-1.30614 - 12.4271i) q^{92} +(-2.79565 - 1.24471i) q^{94} +(9.17437 + 4.96390i) q^{95} +(-1.77459 + 0.790097i) q^{97} +(1.43545 - 4.41787i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.510289 0.566733i −0.360829 0.400741i 0.535208 0.844720i \(-0.320233\pi\)
−0.896037 + 0.443979i \(0.853566\pi\)
\(3\) 0 0
\(4\) 0.148265 1.41065i 0.0741326 0.705324i
\(5\) 0.965605 + 2.01683i 0.431832 + 0.901954i
\(6\) 0 0
\(7\) −0.476660 + 0.825599i −0.180161 + 0.312047i −0.941935 0.335795i \(-0.890995\pi\)
0.761775 + 0.647842i \(0.224328\pi\)
\(8\) −2.10906 + 1.53232i −0.745664 + 0.541757i
\(9\) 0 0
\(10\) 0.650268 1.57641i 0.205633 0.498504i
\(11\) −1.93658 2.15079i −0.583900 0.648487i 0.376728 0.926324i \(-0.377049\pi\)
−0.960628 + 0.277837i \(0.910382\pi\)
\(12\) 0 0
\(13\) 1.30724 1.45184i 0.362564 0.402668i −0.534070 0.845440i \(-0.679338\pi\)
0.896634 + 0.442772i \(0.146005\pi\)
\(14\) 0.711129 0.151155i 0.190057 0.0403979i
\(15\) 0 0
\(16\) −0.830202 0.176465i −0.207551 0.0441162i
\(17\) 5.51944 4.01011i 1.33866 0.972594i 0.339168 0.940726i \(-0.389854\pi\)
0.999492 0.0318678i \(-0.0101456\pi\)
\(18\) 0 0
\(19\) 3.77403 2.74200i 0.865823 0.629057i −0.0636402 0.997973i \(-0.520271\pi\)
0.929463 + 0.368916i \(0.120271\pi\)
\(20\) 2.98821 1.06310i 0.668183 0.237717i
\(21\) 0 0
\(22\) −0.230709 + 2.19505i −0.0491872 + 0.467985i
\(23\) 8.61700 1.83160i 1.79677 0.381915i 0.816149 0.577841i \(-0.196105\pi\)
0.980619 + 0.195926i \(0.0627713\pi\)
\(24\) 0 0
\(25\) −3.13521 + 3.89492i −0.627043 + 0.778985i
\(26\) −1.48988 −0.292189
\(27\) 0 0
\(28\) 1.09396 + 0.794807i 0.206739 + 0.150204i
\(29\) −0.852862 + 0.379719i −0.158372 + 0.0705120i −0.484392 0.874851i \(-0.660959\pi\)
0.326020 + 0.945363i \(0.394292\pi\)
\(30\) 0 0
\(31\) −2.42766 1.08086i −0.436021 0.194129i 0.176975 0.984215i \(-0.443369\pi\)
−0.612995 + 0.790086i \(0.710036\pi\)
\(32\) 2.93057 + 5.07590i 0.518057 + 0.897300i
\(33\) 0 0
\(34\) −5.08917 1.08174i −0.872785 0.185516i
\(35\) −2.12536 0.164140i −0.359251 0.0277447i
\(36\) 0 0
\(37\) 0.799338 + 2.46011i 0.131410 + 0.404439i 0.995014 0.0997312i \(-0.0317983\pi\)
−0.863604 + 0.504171i \(0.831798\pi\)
\(38\) −3.47983 0.739660i −0.564502 0.119989i
\(39\) 0 0
\(40\) −5.12694 2.77400i −0.810641 0.438607i
\(41\) 3.62683 4.02800i 0.566415 0.629068i −0.390092 0.920776i \(-0.627557\pi\)
0.956507 + 0.291708i \(0.0942236\pi\)
\(42\) 0 0
\(43\) 4.43871 7.68807i 0.676897 1.17242i −0.299014 0.954249i \(-0.596658\pi\)
0.975911 0.218171i \(-0.0700090\pi\)
\(44\) −3.32113 + 2.41294i −0.500679 + 0.363765i
\(45\) 0 0
\(46\) −5.43519 3.94889i −0.801374 0.582233i
\(47\) 3.66588 1.63216i 0.534724 0.238074i −0.121566 0.992583i \(-0.538792\pi\)
0.656290 + 0.754509i \(0.272125\pi\)
\(48\) 0 0
\(49\) 3.04559 + 5.27512i 0.435084 + 0.753588i
\(50\) 3.80725 0.210706i 0.538426 0.0297983i
\(51\) 0 0
\(52\) −1.85422 2.05932i −0.257134 0.285576i
\(53\) −4.30252 3.12596i −0.590996 0.429384i 0.251675 0.967812i \(-0.419018\pi\)
−0.842672 + 0.538428i \(0.819018\pi\)
\(54\) 0 0
\(55\) 2.46781 5.98256i 0.332759 0.806688i
\(56\) −0.259779 2.47163i −0.0347144 0.330285i
\(57\) 0 0
\(58\) 0.650405 + 0.289579i 0.0854024 + 0.0380236i
\(59\) −3.21068 + 3.56582i −0.417995 + 0.464231i −0.914963 0.403539i \(-0.867780\pi\)
0.496968 + 0.867769i \(0.334447\pi\)
\(60\) 0 0
\(61\) −7.51779 8.34935i −0.962554 1.06902i −0.997572 0.0696383i \(-0.977815\pi\)
0.0350179 0.999387i \(-0.488851\pi\)
\(62\) 0.626247 + 1.92739i 0.0795334 + 0.244779i
\(63\) 0 0
\(64\) 0.856686 2.63661i 0.107086 0.329576i
\(65\) 4.19039 + 1.23458i 0.519754 + 0.153131i
\(66\) 0 0
\(67\) 3.38246 + 1.50597i 0.413234 + 0.183983i 0.602814 0.797882i \(-0.294046\pi\)
−0.189580 + 0.981865i \(0.560713\pi\)
\(68\) −4.83851 8.38055i −0.586756 1.01629i
\(69\) 0 0
\(70\) 0.991523 + 1.28827i 0.118510 + 0.153978i
\(71\) 0.125408 + 0.0911140i 0.0148832 + 0.0108132i 0.595202 0.803576i \(-0.297072\pi\)
−0.580319 + 0.814389i \(0.697072\pi\)
\(72\) 0 0
\(73\) −3.09917 + 9.53828i −0.362731 + 1.11637i 0.588659 + 0.808381i \(0.299656\pi\)
−0.951390 + 0.307989i \(0.900344\pi\)
\(74\) 0.986332 1.70838i 0.114659 0.198595i
\(75\) 0 0
\(76\) −3.30843 5.73038i −0.379503 0.657319i
\(77\) 2.69878 0.573643i 0.307554 0.0653726i
\(78\) 0 0
\(79\) 3.86470 1.72068i 0.434813 0.193591i −0.177644 0.984095i \(-0.556848\pi\)
0.612458 + 0.790503i \(0.290181\pi\)
\(80\) −0.445747 1.84477i −0.0498361 0.206252i
\(81\) 0 0
\(82\) −4.13353 −0.456472
\(83\) −0.344989 3.28235i −0.0378675 0.360285i −0.997005 0.0773432i \(-0.975356\pi\)
0.959137 0.282942i \(-0.0913104\pi\)
\(84\) 0 0
\(85\) 13.4173 + 7.25960i 1.45531 + 0.787414i
\(86\) −6.62211 + 1.40757i −0.714080 + 0.151782i
\(87\) 0 0
\(88\) 7.38004 + 1.56868i 0.786715 + 0.167221i
\(89\) −5.32122 + 16.3770i −0.564048 + 1.73596i 0.106716 + 0.994290i \(0.465966\pi\)
−0.670764 + 0.741671i \(0.734034\pi\)
\(90\) 0 0
\(91\) 0.575527 + 1.77129i 0.0603317 + 0.185682i
\(92\) −1.30614 12.4271i −0.136175 1.29562i
\(93\) 0 0
\(94\) −2.79565 1.24471i −0.288350 0.128382i
\(95\) 9.17437 + 4.96390i 0.941270 + 0.509286i
\(96\) 0 0
\(97\) −1.77459 + 0.790097i −0.180182 + 0.0802222i −0.494845 0.868981i \(-0.664775\pi\)
0.314663 + 0.949203i \(0.398108\pi\)
\(98\) 1.43545 4.41787i 0.145003 0.446272i
\(99\) 0 0
\(100\) 5.02952 + 5.00017i 0.502952 + 0.500017i
\(101\) −3.61804 + 6.26663i −0.360009 + 0.623553i −0.987962 0.154698i \(-0.950560\pi\)
0.627953 + 0.778251i \(0.283893\pi\)
\(102\) 0 0
\(103\) 1.85476 17.6469i 0.182755 1.73880i −0.391552 0.920156i \(-0.628062\pi\)
0.574307 0.818640i \(-0.305272\pi\)
\(104\) −0.532366 + 5.06512i −0.0522027 + 0.496676i
\(105\) 0 0
\(106\) 0.423940 + 4.03352i 0.0411767 + 0.391770i
\(107\) −1.19151 −0.115188 −0.0575940 0.998340i \(-0.518343\pi\)
−0.0575940 + 0.998340i \(0.518343\pi\)
\(108\) 0 0
\(109\) 0.597453 + 1.83877i 0.0572256 + 0.176122i 0.975584 0.219628i \(-0.0704845\pi\)
−0.918358 + 0.395751i \(0.870484\pi\)
\(110\) −4.64981 + 1.65425i −0.443342 + 0.157726i
\(111\) 0 0
\(112\) 0.541413 0.601300i 0.0511588 0.0568176i
\(113\) −5.37736 + 5.97216i −0.505859 + 0.561814i −0.940938 0.338579i \(-0.890054\pi\)
0.435079 + 0.900392i \(0.356721\pi\)
\(114\) 0 0
\(115\) 12.0146 + 15.6104i 1.12037 + 1.45568i
\(116\) 0.409200 + 1.25939i 0.0379932 + 0.116931i
\(117\) 0 0
\(118\) 3.65924 0.336861
\(119\) 0.679846 + 6.46830i 0.0623214 + 0.592948i
\(120\) 0 0
\(121\) 0.274260 2.60941i 0.0249327 0.237219i
\(122\) −0.895610 + 8.52116i −0.0810847 + 0.771470i
\(123\) 0 0
\(124\) −1.88466 + 3.26432i −0.169247 + 0.293145i
\(125\) −10.8828 2.56224i −0.973385 0.229174i
\(126\) 0 0
\(127\) −4.50280 + 13.8582i −0.399559 + 1.22972i 0.525794 + 0.850612i \(0.323768\pi\)
−0.925354 + 0.379105i \(0.876232\pi\)
\(128\) 8.77743 3.90796i 0.775822 0.345418i
\(129\) 0 0
\(130\) −1.43863 3.00483i −0.126176 0.263541i
\(131\) −12.3994 5.52056i −1.08334 0.482334i −0.214144 0.976802i \(-0.568696\pi\)
−0.869195 + 0.494469i \(0.835363\pi\)
\(132\) 0 0
\(133\) 0.464859 + 4.42284i 0.0403084 + 0.383509i
\(134\) −0.872550 2.68543i −0.0753768 0.231986i
\(135\) 0 0
\(136\) −5.49604 + 16.9151i −0.471282 + 1.45046i
\(137\) −8.55444 1.81830i −0.730855 0.155348i −0.172570 0.984997i \(-0.555207\pi\)
−0.558285 + 0.829649i \(0.688541\pi\)
\(138\) 0 0
\(139\) −18.5125 + 3.93495i −1.57021 + 0.333758i −0.909115 0.416545i \(-0.863241\pi\)
−0.661094 + 0.750303i \(0.729908\pi\)
\(140\) −0.546660 + 2.97380i −0.0462012 + 0.251332i
\(141\) 0 0
\(142\) −0.0123568 0.117567i −0.00103696 0.00986602i
\(143\) −5.65417 −0.472825
\(144\) 0 0
\(145\) −1.58936 1.35342i −0.131989 0.112395i
\(146\) 6.98713 3.11087i 0.578259 0.257458i
\(147\) 0 0
\(148\) 3.58886 0.762836i 0.295003 0.0627048i
\(149\) −3.03989 5.26524i −0.249037 0.431345i 0.714222 0.699919i \(-0.246781\pi\)
−0.963259 + 0.268574i \(0.913447\pi\)
\(150\) 0 0
\(151\) 4.71367 8.16432i 0.383593 0.664403i −0.607980 0.793952i \(-0.708020\pi\)
0.991573 + 0.129550i \(0.0413532\pi\)
\(152\) −3.75804 + 11.5660i −0.304817 + 0.938130i
\(153\) 0 0
\(154\) −1.70226 1.23676i −0.137172 0.0996612i
\(155\) −0.164240 5.93987i −0.0131921 0.477102i
\(156\) 0 0
\(157\) 10.2999 + 17.8399i 0.822020 + 1.42378i 0.904175 + 0.427162i \(0.140486\pi\)
−0.0821548 + 0.996620i \(0.526180\pi\)
\(158\) −2.94728 1.31221i −0.234473 0.104394i
\(159\) 0 0
\(160\) −7.40745 + 10.8118i −0.585611 + 0.854746i
\(161\) −2.59521 + 7.98723i −0.204531 + 0.629482i
\(162\) 0 0
\(163\) −3.22118 9.91378i −0.252302 0.776507i −0.994349 0.106159i \(-0.966145\pi\)
0.742047 0.670348i \(-0.233855\pi\)
\(164\) −5.14436 5.71339i −0.401707 0.446141i
\(165\) 0 0
\(166\) −1.68418 + 1.87047i −0.130717 + 0.145176i
\(167\) 14.1271 + 6.28980i 1.09319 + 0.486719i 0.872495 0.488624i \(-0.162501\pi\)
0.220695 + 0.975343i \(0.429168\pi\)
\(168\) 0 0
\(169\) 0.959914 + 9.13298i 0.0738396 + 0.702537i
\(170\) −2.73245 11.3085i −0.209569 0.867324i
\(171\) 0 0
\(172\) −10.1871 7.40133i −0.776756 0.564346i
\(173\) 9.95195 + 11.0528i 0.756633 + 0.840326i 0.991282 0.131754i \(-0.0420610\pi\)
−0.234650 + 0.972080i \(0.575394\pi\)
\(174\) 0 0
\(175\) −1.72121 4.44498i −0.130112 0.336009i
\(176\) 1.22821 + 2.12733i 0.0925800 + 0.160353i
\(177\) 0 0
\(178\) 11.9968 5.34130i 0.899195 0.400347i
\(179\) 21.5801 + 15.6788i 1.61297 + 1.17189i 0.852954 + 0.521987i \(0.174809\pi\)
0.760016 + 0.649904i \(0.225191\pi\)
\(180\) 0 0
\(181\) 16.0289 11.6457i 1.19142 0.865617i 0.198007 0.980201i \(-0.436553\pi\)
0.993414 + 0.114583i \(0.0365533\pi\)
\(182\) 0.710164 1.23004i 0.0526409 0.0911767i
\(183\) 0 0
\(184\) −15.3671 + 17.0669i −1.13288 + 1.25819i
\(185\) −4.18978 + 3.98762i −0.308039 + 0.293176i
\(186\) 0 0
\(187\) −19.3137 4.10525i −1.41236 0.300206i
\(188\) −1.75888 5.41326i −0.128279 0.394803i
\(189\) 0 0
\(190\) −1.86837 7.73244i −0.135546 0.560970i
\(191\) −11.7458 2.49665i −0.849896 0.180651i −0.237682 0.971343i \(-0.576388\pi\)
−0.612214 + 0.790692i \(0.709721\pi\)
\(192\) 0 0
\(193\) 12.6897 + 21.9792i 0.913424 + 1.58210i 0.809192 + 0.587544i \(0.199905\pi\)
0.104232 + 0.994553i \(0.466762\pi\)
\(194\) 1.35333 + 0.602539i 0.0971631 + 0.0432598i
\(195\) 0 0
\(196\) 7.89289 3.51414i 0.563778 0.251010i
\(197\) 1.37622 + 0.999883i 0.0980516 + 0.0712387i 0.635731 0.771911i \(-0.280699\pi\)
−0.537679 + 0.843150i \(0.680699\pi\)
\(198\) 0 0
\(199\) −6.51877 −0.462104 −0.231052 0.972941i \(-0.574217\pi\)
−0.231052 + 0.972941i \(0.574217\pi\)
\(200\) 0.644079 13.0188i 0.0455433 0.920565i
\(201\) 0 0
\(202\) 5.39776 1.14733i 0.379785 0.0807258i
\(203\) 0.0930297 0.885119i 0.00652941 0.0621231i
\(204\) 0 0
\(205\) 11.6259 + 3.42524i 0.811986 + 0.239229i
\(206\) −10.9475 + 7.95384i −0.762750 + 0.554170i
\(207\) 0 0
\(208\) −1.34147 + 0.974638i −0.0930145 + 0.0675790i
\(209\) −13.2062 2.80705i −0.913489 0.194168i
\(210\) 0 0
\(211\) −7.80500 + 1.65900i −0.537318 + 0.114210i −0.468575 0.883424i \(-0.655232\pi\)
−0.0687434 + 0.997634i \(0.521899\pi\)
\(212\) −5.04755 + 5.60587i −0.346667 + 0.385013i
\(213\) 0 0
\(214\) 0.608017 + 0.675271i 0.0415632 + 0.0461606i
\(215\) 19.7916 + 1.52849i 1.34977 + 0.104242i
\(216\) 0 0
\(217\) 2.04953 1.48907i 0.139131 0.101085i
\(218\) 0.737219 1.27690i 0.0499307 0.0864826i
\(219\) 0 0
\(220\) −8.07340 4.36821i −0.544308 0.294505i
\(221\) 1.39321 13.2555i 0.0937175 0.891662i
\(222\) 0 0
\(223\) −6.31480 7.01329i −0.422870 0.469645i 0.493634 0.869670i \(-0.335668\pi\)
−0.916504 + 0.400025i \(0.869002\pi\)
\(224\) −5.58754 −0.373333
\(225\) 0 0
\(226\) 6.12863 0.407670
\(227\) 15.7939 + 17.5409i 1.04828 + 1.16423i 0.986097 + 0.166169i \(0.0531397\pi\)
0.0621833 + 0.998065i \(0.480194\pi\)
\(228\) 0 0
\(229\) 1.64184 15.6210i 0.108496 1.03227i −0.795858 0.605484i \(-0.792980\pi\)
0.904354 0.426784i \(-0.140354\pi\)
\(230\) 2.71601 14.7749i 0.179088 0.974229i
\(231\) 0 0
\(232\) 1.21688 2.10770i 0.0798923 0.138378i
\(233\) 1.52687 1.10933i 0.100028 0.0726749i −0.536647 0.843807i \(-0.680309\pi\)
0.636675 + 0.771132i \(0.280309\pi\)
\(234\) 0 0
\(235\) 6.83157 + 5.81744i 0.445643 + 0.379488i
\(236\) 4.55409 + 5.05783i 0.296446 + 0.329237i
\(237\) 0 0
\(238\) 3.31888 3.68599i 0.215131 0.238927i
\(239\) −1.40198 + 0.298000i −0.0906865 + 0.0192760i −0.253031 0.967458i \(-0.581428\pi\)
0.162345 + 0.986734i \(0.448094\pi\)
\(240\) 0 0
\(241\) −10.7140 2.27733i −0.690150 0.146696i −0.150531 0.988605i \(-0.548098\pi\)
−0.539619 + 0.841910i \(0.681432\pi\)
\(242\) −1.61879 + 1.17612i −0.104060 + 0.0756039i
\(243\) 0 0
\(244\) −12.8926 + 9.36704i −0.825366 + 0.599663i
\(245\) −7.69818 + 11.2361i −0.491819 + 0.717849i
\(246\) 0 0
\(247\) 0.952637 9.06374i 0.0606149 0.576712i
\(248\) 6.77630 1.44035i 0.430296 0.0914621i
\(249\) 0 0
\(250\) 4.10125 + 7.47512i 0.259386 + 0.472768i
\(251\) −9.34568 −0.589894 −0.294947 0.955514i \(-0.595302\pi\)
−0.294947 + 0.955514i \(0.595302\pi\)
\(252\) 0 0
\(253\) −20.6269 14.9863i −1.29680 0.942180i
\(254\) 10.1516 4.51980i 0.636970 0.283597i
\(255\) 0 0
\(256\) −11.7590 5.23546i −0.734939 0.327216i
\(257\) 3.12162 + 5.40681i 0.194722 + 0.337268i 0.946809 0.321795i \(-0.104286\pi\)
−0.752088 + 0.659063i \(0.770953\pi\)
\(258\) 0 0
\(259\) −2.41208 0.512703i −0.149879 0.0318578i
\(260\) 2.36285 5.72813i 0.146538 0.355243i
\(261\) 0 0
\(262\) 3.19858 + 9.84422i 0.197609 + 0.608178i
\(263\) 1.82124 + 0.387117i 0.112303 + 0.0238707i 0.263720 0.964599i \(-0.415050\pi\)
−0.151418 + 0.988470i \(0.548384\pi\)
\(264\) 0 0
\(265\) 2.15001 11.6959i 0.132074 0.718473i
\(266\) 2.26936 2.52038i 0.139143 0.154534i
\(267\) 0 0
\(268\) 2.62589 4.54818i 0.160402 0.277824i
\(269\) −3.89397 + 2.82914i −0.237420 + 0.172496i −0.700133 0.714012i \(-0.746876\pi\)
0.462713 + 0.886508i \(0.346876\pi\)
\(270\) 0 0
\(271\) 18.4402 + 13.3976i 1.12016 + 0.813846i 0.984234 0.176873i \(-0.0565982\pi\)
0.135929 + 0.990719i \(0.456598\pi\)
\(272\) −5.28989 + 2.35521i −0.320747 + 0.142806i
\(273\) 0 0
\(274\) 3.33474 + 5.77595i 0.201459 + 0.348938i
\(275\) 14.4487 0.799641i 0.871292 0.0482202i
\(276\) 0 0
\(277\) 5.22689 + 5.80505i 0.314054 + 0.348792i 0.879419 0.476049i \(-0.157931\pi\)
−0.565365 + 0.824841i \(0.691265\pi\)
\(278\) 11.6768 + 8.48368i 0.700327 + 0.508817i
\(279\) 0 0
\(280\) 4.73402 2.91055i 0.282912 0.173938i
\(281\) −0.164928 1.56918i −0.00983878 0.0936097i 0.988501 0.151218i \(-0.0483194\pi\)
−0.998339 + 0.0576078i \(0.981653\pi\)
\(282\) 0 0
\(283\) −7.09288 3.15795i −0.421628 0.187721i 0.184945 0.982749i \(-0.440789\pi\)
−0.606573 + 0.795028i \(0.707456\pi\)
\(284\) 0.147123 0.163397i 0.00873017 0.00969584i
\(285\) 0 0
\(286\) 2.88526 + 3.20441i 0.170609 + 0.189481i
\(287\) 1.59675 + 4.91429i 0.0942532 + 0.290081i
\(288\) 0 0
\(289\) 9.12995 28.0991i 0.537056 1.65289i
\(290\) 0.0440023 + 1.59138i 0.00258391 + 0.0934488i
\(291\) 0 0
\(292\) 12.9957 + 5.78604i 0.760513 + 0.338602i
\(293\) −5.25540 9.10262i −0.307024 0.531781i 0.670686 0.741741i \(-0.266000\pi\)
−0.977710 + 0.209961i \(0.932666\pi\)
\(294\) 0 0
\(295\) −10.2919 3.03223i −0.599218 0.176543i
\(296\) −5.45552 3.96367i −0.317096 0.230383i
\(297\) 0 0
\(298\) −1.43276 + 4.40960i −0.0829978 + 0.255441i
\(299\) 8.60531 14.9048i 0.497658 0.861969i
\(300\) 0 0
\(301\) 4.23151 + 7.32919i 0.243900 + 0.422447i
\(302\) −7.03232 + 1.49477i −0.404665 + 0.0860141i
\(303\) 0 0
\(304\) −3.61708 + 1.61043i −0.207454 + 0.0923643i
\(305\) 9.58002 23.2243i 0.548550 1.32982i
\(306\) 0 0
\(307\) 3.00205 0.171336 0.0856680 0.996324i \(-0.472698\pi\)
0.0856680 + 0.996324i \(0.472698\pi\)
\(308\) −0.409074 3.89208i −0.0233091 0.221772i
\(309\) 0 0
\(310\) −3.28251 + 3.12413i −0.186434 + 0.177439i
\(311\) −13.7061 + 2.91331i −0.777199 + 0.165199i −0.579399 0.815044i \(-0.696713\pi\)
−0.197800 + 0.980242i \(0.563380\pi\)
\(312\) 0 0
\(313\) 5.43306 + 1.15483i 0.307095 + 0.0652751i 0.358882 0.933383i \(-0.383158\pi\)
−0.0517865 + 0.998658i \(0.516492\pi\)
\(314\) 4.85456 14.9408i 0.273959 0.843158i
\(315\) 0 0
\(316\) −1.85427 5.70685i −0.104311 0.321036i
\(317\) 0.475026 + 4.51957i 0.0266801 + 0.253844i 0.999730 + 0.0232485i \(0.00740090\pi\)
−0.973050 + 0.230596i \(0.925932\pi\)
\(318\) 0 0
\(319\) 2.46833 + 1.09897i 0.138200 + 0.0615305i
\(320\) 6.14481 0.818131i 0.343506 0.0457349i
\(321\) 0 0
\(322\) 5.85094 2.60501i 0.326060 0.145171i
\(323\) 9.83485 30.2685i 0.547226 1.68419i
\(324\) 0 0
\(325\) 1.55632 + 9.64343i 0.0863290 + 0.534921i
\(326\) −3.97473 + 6.88444i −0.220140 + 0.381294i
\(327\) 0 0
\(328\) −1.47700 + 14.0527i −0.0815538 + 0.775932i
\(329\) −0.399872 + 3.80453i −0.0220457 + 0.209751i
\(330\) 0 0
\(331\) −0.606412 5.76962i −0.0333314 0.317127i −0.998466 0.0553723i \(-0.982365\pi\)
0.965134 0.261755i \(-0.0843012\pi\)
\(332\) −4.68140 −0.256925
\(333\) 0 0
\(334\) −3.64427 11.2159i −0.199406 0.613708i
\(335\) 0.228836 + 8.27603i 0.0125027 + 0.452168i
\(336\) 0 0
\(337\) 3.28848 3.65223i 0.179135 0.198950i −0.646890 0.762584i \(-0.723931\pi\)
0.826025 + 0.563634i \(0.190597\pi\)
\(338\) 4.68613 5.20447i 0.254892 0.283086i
\(339\) 0 0
\(340\) 12.2301 17.8508i 0.663268 0.968093i
\(341\) 2.37664 + 7.31456i 0.128702 + 0.396106i
\(342\) 0 0
\(343\) −12.4801 −0.673861
\(344\) 2.41909 + 23.0161i 0.130428 + 1.24094i
\(345\) 0 0
\(346\) 1.18560 11.2802i 0.0637381 0.606427i
\(347\) 1.04204 9.91437i 0.0559398 0.532231i −0.930287 0.366833i \(-0.880442\pi\)
0.986227 0.165399i \(-0.0528911\pi\)
\(348\) 0 0
\(349\) 7.15701 12.3963i 0.383106 0.663559i −0.608398 0.793632i \(-0.708188\pi\)
0.991504 + 0.130073i \(0.0415210\pi\)
\(350\) −1.64080 + 3.24370i −0.0877046 + 0.173383i
\(351\) 0 0
\(352\) 5.24190 16.1329i 0.279394 0.859887i
\(353\) −23.1580 + 10.3106i −1.23257 + 0.548778i −0.916530 0.399966i \(-0.869022\pi\)
−0.316045 + 0.948744i \(0.602355\pi\)
\(354\) 0 0
\(355\) −0.0626673 + 0.340906i −0.00332604 + 0.0180934i
\(356\) 22.3133 + 9.93451i 1.18260 + 0.526528i
\(357\) 0 0
\(358\) −2.12635 20.2309i −0.112381 1.06923i
\(359\) −6.35182 19.5489i −0.335236 1.03175i −0.966606 0.256269i \(-0.917507\pi\)
0.631369 0.775482i \(-0.282493\pi\)
\(360\) 0 0
\(361\) 0.853463 2.62669i 0.0449191 0.138247i
\(362\) −14.7794 3.14145i −0.776787 0.165111i
\(363\) 0 0
\(364\) 2.58400 0.549246i 0.135438 0.0287883i
\(365\) −22.2297 + 2.95970i −1.16355 + 0.154918i
\(366\) 0 0
\(367\) −3.00921 28.6307i −0.157080 1.49451i −0.734803 0.678280i \(-0.762725\pi\)
0.577724 0.816233i \(-0.303941\pi\)
\(368\) −7.47706 −0.389769
\(369\) 0 0
\(370\) 4.39792 + 0.339648i 0.228637 + 0.0176575i
\(371\) 4.63163 2.06213i 0.240462 0.107061i
\(372\) 0 0
\(373\) −11.1760 + 2.37553i −0.578671 + 0.123000i −0.487943 0.872875i \(-0.662253\pi\)
−0.0907279 + 0.995876i \(0.528919\pi\)
\(374\) 7.52898 + 13.0406i 0.389314 + 0.674312i
\(375\) 0 0
\(376\) −5.23057 + 9.05960i −0.269746 + 0.467213i
\(377\) −0.563606 + 1.73460i −0.0290272 + 0.0893365i
\(378\) 0 0
\(379\) 2.90335 + 2.10941i 0.149135 + 0.108353i 0.659851 0.751397i \(-0.270620\pi\)
−0.510716 + 0.859750i \(0.670620\pi\)
\(380\) 8.36256 12.2058i 0.428990 0.626146i
\(381\) 0 0
\(382\) 4.57882 + 7.93074i 0.234273 + 0.405772i
\(383\) −4.67766 2.08263i −0.239017 0.106417i 0.283733 0.958903i \(-0.408427\pi\)
−0.522750 + 0.852486i \(0.675094\pi\)
\(384\) 0 0
\(385\) 3.76289 + 4.88906i 0.191775 + 0.249170i
\(386\) 5.98093 18.4074i 0.304421 0.936912i
\(387\) 0 0
\(388\) 0.851440 + 2.62046i 0.0432253 + 0.133034i
\(389\) −20.6772 22.9643i −1.04837 1.16434i −0.986079 0.166279i \(-0.946825\pi\)
−0.0622946 0.998058i \(-0.519842\pi\)
\(390\) 0 0
\(391\) 40.2161 44.6645i 2.03381 2.25878i
\(392\) −14.5065 6.45870i −0.732688 0.326214i
\(393\) 0 0
\(394\) −0.135603 1.29018i −0.00683159 0.0649983i
\(395\) 7.20209 + 6.13296i 0.362376 + 0.308583i
\(396\) 0 0
\(397\) −5.15821 3.74766i −0.258883 0.188090i 0.450771 0.892639i \(-0.351149\pi\)
−0.709654 + 0.704550i \(0.751149\pi\)
\(398\) 3.32646 + 3.69441i 0.166740 + 0.185184i
\(399\) 0 0
\(400\) 3.29018 2.68032i 0.164509 0.134016i
\(401\) −8.96136 15.5215i −0.447509 0.775108i 0.550714 0.834694i \(-0.314355\pi\)
−0.998223 + 0.0595856i \(0.981022\pi\)
\(402\) 0 0
\(403\) −4.74278 + 2.11162i −0.236255 + 0.105187i
\(404\) 8.30359 + 6.03291i 0.413119 + 0.300149i
\(405\) 0 0
\(406\) −0.549098 + 0.398943i −0.0272513 + 0.0197992i
\(407\) 3.74319 6.48340i 0.185543 0.321370i
\(408\) 0 0
\(409\) −25.7159 + 28.5604i −1.27157 + 1.41222i −0.404109 + 0.914711i \(0.632418\pi\)
−0.867459 + 0.497508i \(0.834248\pi\)
\(410\) −3.99136 8.33663i −0.197119 0.411717i
\(411\) 0 0
\(412\) −24.6185 5.23283i −1.21287 0.257803i
\(413\) −1.41354 4.35042i −0.0695556 0.214070i
\(414\) 0 0
\(415\) 6.28683 3.86524i 0.308608 0.189737i
\(416\) 11.2004 + 2.38071i 0.549142 + 0.116724i
\(417\) 0 0
\(418\) 5.14810 + 8.91677i 0.251802 + 0.436134i
\(419\) −4.82889 2.14996i −0.235907 0.105033i 0.285379 0.958415i \(-0.407881\pi\)
−0.521285 + 0.853382i \(0.674547\pi\)
\(420\) 0 0
\(421\) −24.7502 + 11.0195i −1.20625 + 0.537057i −0.908620 0.417625i \(-0.862863\pi\)
−0.297629 + 0.954681i \(0.596196\pi\)
\(422\) 4.92301 + 3.57678i 0.239649 + 0.174115i
\(423\) 0 0
\(424\) 13.8642 0.673306
\(425\) −1.68557 + 34.0703i −0.0817620 + 1.65265i
\(426\) 0 0
\(427\) 10.4766 2.22688i 0.507000 0.107766i
\(428\) −0.176660 + 1.68081i −0.00853919 + 0.0812449i
\(429\) 0 0
\(430\) −9.23317 11.9965i −0.445263 0.578523i
\(431\) 28.0178 20.3561i 1.34957 0.980518i 0.350535 0.936550i \(-0.386000\pi\)
0.999033 0.0439685i \(-0.0140001\pi\)
\(432\) 0 0
\(433\) −7.43160 + 5.39937i −0.357140 + 0.259477i −0.751858 0.659325i \(-0.770842\pi\)
0.394718 + 0.918802i \(0.370842\pi\)
\(434\) −1.88976 0.401680i −0.0907113 0.0192813i
\(435\) 0 0
\(436\) 2.68244 0.570170i 0.128466 0.0273062i
\(437\) 27.4986 30.5403i 1.31544 1.46094i
\(438\) 0 0
\(439\) 4.80344 + 5.33476i 0.229256 + 0.254614i 0.846787 0.531932i \(-0.178534\pi\)
−0.617531 + 0.786546i \(0.711867\pi\)
\(440\) 3.96245 + 16.3990i 0.188902 + 0.781792i
\(441\) 0 0
\(442\) −8.22328 + 5.97456i −0.391141 + 0.284181i
\(443\) −12.6804 + 21.9630i −0.602462 + 1.04349i 0.389985 + 0.920821i \(0.372480\pi\)
−0.992447 + 0.122673i \(0.960853\pi\)
\(444\) 0 0
\(445\) −38.1679 + 5.08173i −1.80933 + 0.240897i
\(446\) −0.752295 + 7.15761i −0.0356222 + 0.338923i
\(447\) 0 0
\(448\) 1.76843 + 1.96404i 0.0835506 + 0.0927924i
\(449\) 7.13943 0.336930 0.168465 0.985708i \(-0.446119\pi\)
0.168465 + 0.985708i \(0.446119\pi\)
\(450\) 0 0
\(451\) −15.6870 −0.738672
\(452\) 7.62735 + 8.47103i 0.358760 + 0.398444i
\(453\) 0 0
\(454\) 1.88157 17.9019i 0.0883062 0.840178i
\(455\) −3.01666 + 2.87111i −0.141423 + 0.134600i
\(456\) 0 0
\(457\) −17.8907 + 30.9875i −0.836890 + 1.44954i 0.0555925 + 0.998454i \(0.482295\pi\)
−0.892482 + 0.451082i \(0.851038\pi\)
\(458\) −9.69078 + 7.04076i −0.452820 + 0.328993i
\(459\) 0 0
\(460\) 23.8022 14.6340i 1.10978 0.682311i
\(461\) 10.1936 + 11.3211i 0.474763 + 0.527278i 0.932190 0.361969i \(-0.117895\pi\)
−0.457427 + 0.889247i \(0.651229\pi\)
\(462\) 0 0
\(463\) −16.6298 + 18.4693i −0.772852 + 0.858339i −0.993120 0.117100i \(-0.962640\pi\)
0.220268 + 0.975439i \(0.429307\pi\)
\(464\) 0.775055 0.164743i 0.0359810 0.00764800i
\(465\) 0 0
\(466\) −1.40784 0.299246i −0.0652170 0.0138623i
\(467\) 21.1648 15.3771i 0.979389 0.711568i 0.0218169 0.999762i \(-0.493055\pi\)
0.957572 + 0.288194i \(0.0930549\pi\)
\(468\) 0 0
\(469\) −2.85561 + 2.07472i −0.131860 + 0.0958018i
\(470\) −0.189137 6.84026i −0.00872422 0.315518i
\(471\) 0 0
\(472\) 1.30753 12.4403i 0.0601839 0.572612i
\(473\) −25.1313 + 5.34182i −1.15554 + 0.245617i
\(474\) 0 0
\(475\) −1.15254 + 23.2963i −0.0528823 + 1.06891i
\(476\) 9.22529 0.422841
\(477\) 0 0
\(478\) 0.884301 + 0.642482i 0.0404470 + 0.0293865i
\(479\) 8.78889 3.91307i 0.401575 0.178793i −0.196004 0.980603i \(-0.562796\pi\)
0.597578 + 0.801811i \(0.296130\pi\)
\(480\) 0 0
\(481\) 4.61661 + 2.05545i 0.210499 + 0.0937203i
\(482\) 4.17660 + 7.23408i 0.190239 + 0.329503i
\(483\) 0 0
\(484\) −3.64030 0.773769i −0.165468 0.0351713i
\(485\) −3.30704 2.81612i −0.150165 0.127873i
\(486\) 0 0
\(487\) 12.1864 + 37.5059i 0.552219 + 1.69956i 0.703177 + 0.711015i \(0.251764\pi\)
−0.150958 + 0.988540i \(0.548236\pi\)
\(488\) 28.6493 + 6.08960i 1.29689 + 0.275663i
\(489\) 0 0
\(490\) 10.2962 1.37085i 0.465134 0.0619287i
\(491\) −6.51647 + 7.23727i −0.294084 + 0.326614i −0.872021 0.489468i \(-0.837191\pi\)
0.577937 + 0.816081i \(0.303858\pi\)
\(492\) 0 0
\(493\) −3.18461 + 5.51590i −0.143427 + 0.248424i
\(494\) −5.62284 + 4.08523i −0.252984 + 0.183803i
\(495\) 0 0
\(496\) 1.82471 + 1.32573i 0.0819321 + 0.0595272i
\(497\) −0.135001 + 0.0601061i −0.00605560 + 0.00269613i
\(498\) 0 0
\(499\) −4.37718 7.58149i −0.195949 0.339394i 0.751262 0.660004i \(-0.229445\pi\)
−0.947211 + 0.320610i \(0.896112\pi\)
\(500\) −5.22796 + 14.9719i −0.233801 + 0.669563i
\(501\) 0 0
\(502\) 4.76899 + 5.29650i 0.212851 + 0.236395i
\(503\) 16.1674 + 11.7463i 0.720867 + 0.523741i 0.886661 0.462420i \(-0.153019\pi\)
−0.165794 + 0.986160i \(0.553019\pi\)
\(504\) 0 0
\(505\) −16.1323 1.24589i −0.717880 0.0554414i
\(506\) 2.03243 + 19.3373i 0.0903524 + 0.859646i
\(507\) 0 0
\(508\) 18.8814 + 8.40656i 0.837729 + 0.372981i
\(509\) 22.3109 24.7788i 0.988914 1.09830i −0.00624107 0.999981i \(-0.501987\pi\)
0.995155 0.0983195i \(-0.0313467\pi\)
\(510\) 0 0
\(511\) −6.39754 7.10519i −0.283011 0.314315i
\(512\) −2.90473 8.93985i −0.128372 0.395089i
\(513\) 0 0
\(514\) 1.47129 4.52816i 0.0648958 0.199729i
\(515\) 37.3817 13.2992i 1.64723 0.586031i
\(516\) 0 0
\(517\) −10.6097 4.72373i −0.466613 0.207750i
\(518\) 0.940290 + 1.62863i 0.0413140 + 0.0715579i
\(519\) 0 0
\(520\) −10.7295 + 3.81721i −0.470522 + 0.167396i
\(521\) 18.9750 + 13.7861i 0.831308 + 0.603981i 0.919929 0.392085i \(-0.128246\pi\)
−0.0886210 + 0.996065i \(0.528246\pi\)
\(522\) 0 0
\(523\) 6.59815 20.3070i 0.288517 0.887963i −0.696806 0.717260i \(-0.745396\pi\)
0.985322 0.170703i \(-0.0546040\pi\)
\(524\) −9.62597 + 16.6727i −0.420512 + 0.728349i
\(525\) 0 0
\(526\) −0.709968 1.22970i −0.0309561 0.0536175i
\(527\) −17.7337 + 3.76941i −0.772492 + 0.164198i
\(528\) 0 0
\(529\) 49.8863 22.2108i 2.16897 0.965688i
\(530\) −7.72558 + 4.74981i −0.335578 + 0.206318i
\(531\) 0 0
\(532\) 6.30799 0.273486
\(533\) −1.10687 10.5311i −0.0479437 0.456154i
\(534\) 0 0
\(535\) −1.15053 2.40308i −0.0497419 0.103894i
\(536\) −9.44143 + 2.00684i −0.407808 + 0.0866822i
\(537\) 0 0
\(538\) 3.59042 + 0.763167i 0.154794 + 0.0329025i
\(539\) 5.44763 16.7661i 0.234646 0.722167i
\(540\) 0 0
\(541\) 10.3808 + 31.9488i 0.446305 + 1.37358i 0.881047 + 0.473029i \(0.156840\pi\)
−0.434742 + 0.900555i \(0.643160\pi\)
\(542\) −1.81697 17.2873i −0.0780455 0.742554i
\(543\) 0 0
\(544\) 36.5300 + 16.2642i 1.56621 + 0.697322i
\(545\) −3.13158 + 2.98049i −0.134142 + 0.127670i
\(546\) 0 0
\(547\) 30.3937 13.5321i 1.29954 0.578593i 0.363864 0.931452i \(-0.381457\pi\)
0.935677 + 0.352859i \(0.114790\pi\)
\(548\) −3.83331 + 11.7977i −0.163751 + 0.503974i
\(549\) 0 0
\(550\) −7.82621 7.78053i −0.333711 0.331763i
\(551\) −2.17754 + 3.77161i −0.0927664 + 0.160676i
\(552\) 0 0
\(553\) −0.421560 + 4.01087i −0.0179265 + 0.170560i
\(554\) 0.622691 5.92451i 0.0264556 0.251708i
\(555\) 0 0
\(556\) 2.80608 + 26.6980i 0.119004 + 1.13225i
\(557\) −29.7702 −1.26140 −0.630702 0.776025i \(-0.717233\pi\)
−0.630702 + 0.776025i \(0.717233\pi\)
\(558\) 0 0
\(559\) −5.35937 16.4945i −0.226677 0.697641i
\(560\) 1.73551 + 0.511321i 0.0733388 + 0.0216072i
\(561\) 0 0
\(562\) −0.805148 + 0.894208i −0.0339631 + 0.0377199i
\(563\) −15.8795 + 17.6360i −0.669243 + 0.743270i −0.978168 0.207817i \(-0.933364\pi\)
0.308925 + 0.951086i \(0.400031\pi\)
\(564\) 0 0
\(565\) −17.2372 5.07848i −0.725176 0.213653i
\(566\) 1.82970 + 5.63124i 0.0769080 + 0.236699i
\(567\) 0 0
\(568\) −0.404108 −0.0169560
\(569\) 3.04989 + 29.0177i 0.127858 + 1.21649i 0.850767 + 0.525543i \(0.176138\pi\)
−0.722909 + 0.690943i \(0.757195\pi\)
\(570\) 0 0
\(571\) 0.278873 2.65330i 0.0116705 0.111037i −0.987136 0.159884i \(-0.948888\pi\)
0.998806 + 0.0488470i \(0.0155547\pi\)
\(572\) −0.838316 + 7.97605i −0.0350518 + 0.333495i
\(573\) 0 0
\(574\) 1.97029 3.41264i 0.0822382 0.142441i
\(575\) −19.8822 + 39.3050i −0.829145 + 1.63913i
\(576\) 0 0
\(577\) −10.1294 + 31.1750i −0.421692 + 1.29783i 0.484435 + 0.874827i \(0.339025\pi\)
−0.906127 + 0.423007i \(0.860975\pi\)
\(578\) −20.5836 + 9.16441i −0.856165 + 0.381189i
\(579\) 0 0
\(580\) −2.14485 + 2.04136i −0.0890599 + 0.0847627i
\(581\) 2.87435 + 1.27974i 0.119248 + 0.0530927i
\(582\) 0 0
\(583\) 1.60888 + 15.3075i 0.0666330 + 0.633971i
\(584\) −8.07935 24.8657i −0.334326 1.02895i
\(585\) 0 0
\(586\) −2.47698 + 7.62337i −0.102323 + 0.314919i
\(587\) −4.17376 0.887160i −0.172270 0.0366170i 0.120969 0.992656i \(-0.461400\pi\)
−0.293239 + 0.956039i \(0.594733\pi\)
\(588\) 0 0
\(589\) −12.1258 + 2.57742i −0.499635 + 0.106201i
\(590\) 3.53338 + 7.38008i 0.145467 + 0.303833i
\(591\) 0 0
\(592\) −0.229489 2.18344i −0.00943194 0.0897389i
\(593\) 7.81313 0.320847 0.160423 0.987048i \(-0.448714\pi\)
0.160423 + 0.987048i \(0.448714\pi\)
\(594\) 0 0
\(595\) −12.3890 + 7.61695i −0.507900 + 0.312265i
\(596\) −7.87811 + 3.50756i −0.322700 + 0.143675i
\(597\) 0 0
\(598\) −12.8383 + 2.72886i −0.524995 + 0.111591i
\(599\) −22.2102 38.4691i −0.907483 1.57181i −0.817550 0.575858i \(-0.804668\pi\)
−0.0899331 0.995948i \(-0.528665\pi\)
\(600\) 0 0
\(601\) −7.98356 + 13.8279i −0.325656 + 0.564053i −0.981645 0.190718i \(-0.938919\pi\)
0.655989 + 0.754771i \(0.272252\pi\)
\(602\) 1.99440 6.13814i 0.0812858 0.250172i
\(603\) 0 0
\(604\) −10.8181 7.85982i −0.440183 0.319811i
\(605\) 5.52757 1.96652i 0.224728 0.0799506i
\(606\) 0 0
\(607\) −5.79724 10.0411i −0.235303 0.407557i 0.724058 0.689739i \(-0.242275\pi\)
−0.959361 + 0.282183i \(0.908942\pi\)
\(608\) 24.9782 + 11.1210i 1.01300 + 0.451016i
\(609\) 0 0
\(610\) −18.0506 + 6.42178i −0.730845 + 0.260010i
\(611\) 2.42257 7.45589i 0.0980065 0.301633i
\(612\) 0 0
\(613\) 0.0509077 + 0.156678i 0.00205614 + 0.00632816i 0.952079 0.305851i \(-0.0989410\pi\)
−0.950023 + 0.312179i \(0.898941\pi\)
\(614\) −1.53191 1.70136i −0.0618229 0.0686613i
\(615\) 0 0
\(616\) −4.81287 + 5.34523i −0.193916 + 0.215365i
\(617\) −32.8935 14.6451i −1.32424 0.589591i −0.381888 0.924208i \(-0.624726\pi\)
−0.942354 + 0.334618i \(0.891393\pi\)
\(618\) 0 0
\(619\) 4.99377 + 47.5125i 0.200716 + 1.90969i 0.378469 + 0.925614i \(0.376451\pi\)
−0.177753 + 0.984075i \(0.556883\pi\)
\(620\) −8.40342 0.648990i −0.337489 0.0260641i
\(621\) 0 0
\(622\) 8.64512 + 6.28105i 0.346638 + 0.251847i
\(623\) −10.9844 12.1995i −0.440082 0.488761i
\(624\) 0 0
\(625\) −5.34086 24.4228i −0.213634 0.976914i
\(626\) −2.11795 3.66840i −0.0846503 0.146619i
\(627\) 0 0
\(628\) 26.6930 11.8845i 1.06517 0.474242i
\(629\) 14.2772 + 10.3730i 0.569269 + 0.413598i
\(630\) 0 0
\(631\) −12.6855 + 9.21654i −0.505001 + 0.366905i −0.810924 0.585152i \(-0.801035\pi\)
0.305923 + 0.952056i \(0.401035\pi\)
\(632\) −5.51425 + 9.55096i −0.219345 + 0.379917i
\(633\) 0 0
\(634\) 2.31899 2.57550i 0.0920989 0.102286i
\(635\) −32.2976 + 4.30015i −1.28169 + 0.170646i
\(636\) 0 0
\(637\) 11.6399 + 2.47415i 0.461191 + 0.0980293i
\(638\) −0.636737 1.95967i −0.0252087 0.0775843i
\(639\) 0 0
\(640\) 16.3572 + 13.9290i 0.646576 + 0.550594i
\(641\) −36.2559 7.70643i −1.43202 0.304386i −0.574361 0.818602i \(-0.694749\pi\)
−0.857660 + 0.514216i \(0.828083\pi\)
\(642\) 0 0
\(643\) 3.29095 + 5.70009i 0.129782 + 0.224790i 0.923592 0.383376i \(-0.125239\pi\)
−0.793810 + 0.608166i \(0.791905\pi\)
\(644\) 10.8824 + 4.84516i 0.428827 + 0.190926i
\(645\) 0 0
\(646\) −22.1728 + 9.87197i −0.872377 + 0.388407i
\(647\) −2.22736 1.61827i −0.0875666 0.0636209i 0.543141 0.839642i \(-0.317235\pi\)
−0.630707 + 0.776021i \(0.717235\pi\)
\(648\) 0 0
\(649\) 13.8871 0.545115
\(650\) 4.67108 5.80295i 0.183215 0.227611i
\(651\) 0 0
\(652\) −14.4624 + 3.07409i −0.566393 + 0.120391i
\(653\) 0.676372 6.43525i 0.0264685 0.251831i −0.973284 0.229603i \(-0.926257\pi\)
0.999753 0.0222280i \(-0.00707598\pi\)
\(654\) 0 0
\(655\) −0.838865 30.3381i −0.0327772 1.18541i
\(656\) −3.72180 + 2.70405i −0.145312 + 0.105575i
\(657\) 0 0
\(658\) 2.36020 1.71479i 0.0920103 0.0668494i
\(659\) 9.56798 + 2.03374i 0.372716 + 0.0792231i 0.390461 0.920619i \(-0.372316\pi\)
−0.0177456 + 0.999843i \(0.505649\pi\)
\(660\) 0 0
\(661\) 0.325445 0.0691755i 0.0126583 0.00269062i −0.201578 0.979472i \(-0.564607\pi\)
0.214237 + 0.976782i \(0.431274\pi\)
\(662\) −2.96039 + 3.28785i −0.115059 + 0.127786i
\(663\) 0 0
\(664\) 5.75722 + 6.39404i 0.223423 + 0.248137i
\(665\) −8.47125 + 5.20826i −0.328501 + 0.201967i
\(666\) 0 0
\(667\) −6.65361 + 4.83413i −0.257629 + 0.187178i
\(668\) 10.9673 18.9958i 0.424336 0.734971i
\(669\) 0 0
\(670\) 4.57353 4.35285i 0.176691 0.168165i
\(671\) −3.39890 + 32.3383i −0.131213 + 1.24841i
\(672\) 0 0
\(673\) −4.12557 4.58191i −0.159029 0.176620i 0.658365 0.752699i \(-0.271249\pi\)
−0.817394 + 0.576079i \(0.804582\pi\)
\(674\) −3.74792 −0.144364
\(675\) 0 0
\(676\) 13.0257 0.500990
\(677\) 9.77758 + 10.8591i 0.375783 + 0.417349i 0.901137 0.433535i \(-0.142734\pi\)
−0.525354 + 0.850884i \(0.676067\pi\)
\(678\) 0 0
\(679\) 0.193571 1.84170i 0.00742857 0.0706781i
\(680\) −39.4219 + 5.24869i −1.51176 + 0.201278i
\(681\) 0 0
\(682\) 2.93263 5.07946i 0.112296 0.194503i
\(683\) −16.7839 + 12.1942i −0.642217 + 0.466598i −0.860611 0.509263i \(-0.829918\pi\)
0.218394 + 0.975861i \(0.429918\pi\)
\(684\) 0 0
\(685\) −4.59300 19.0086i −0.175490 0.726282i
\(686\) 6.36845 + 7.07288i 0.243148 + 0.270044i
\(687\) 0 0
\(688\) −5.04170 + 5.59938i −0.192213 + 0.213474i
\(689\) −10.1628 + 2.16018i −0.387173 + 0.0822961i
\(690\) 0 0
\(691\) −25.5937 5.44011i −0.973630 0.206951i −0.306482 0.951876i \(-0.599152\pi\)
−0.667148 + 0.744925i \(0.732485\pi\)
\(692\) 17.0671 12.4000i 0.648793 0.471376i
\(693\) 0 0
\(694\) −6.15055 + 4.46863i −0.233472 + 0.169627i
\(695\) −25.8119 33.5370i −0.979101 1.27213i
\(696\) 0 0
\(697\) 3.86534 36.7762i 0.146410 1.39300i
\(698\) −10.6775 + 2.26958i −0.404151 + 0.0859049i
\(699\) 0 0
\(700\) −6.52551 + 1.76899i −0.246641 + 0.0668616i
\(701\) 24.6481 0.930945 0.465472 0.885062i \(-0.345884\pi\)
0.465472 + 0.885062i \(0.345884\pi\)
\(702\) 0 0
\(703\) 9.76234 + 7.09275i 0.368193 + 0.267508i
\(704\) −7.32982 + 3.26345i −0.276253 + 0.122996i
\(705\) 0 0
\(706\) 17.6606 + 7.86301i 0.664666 + 0.295928i
\(707\) −3.44915 5.97411i −0.129719 0.224679i
\(708\) 0 0
\(709\) 26.8700 + 5.71140i 1.00912 + 0.214496i 0.682678 0.730719i \(-0.260815\pi\)
0.326447 + 0.945216i \(0.394149\pi\)
\(710\) 0.225181 0.138445i 0.00845091 0.00519575i
\(711\) 0 0
\(712\) −13.8721 42.6938i −0.519878 1.60002i
\(713\) −22.8989 4.86730i −0.857569 0.182282i
\(714\) 0 0
\(715\) −5.45969 11.4035i −0.204181 0.426467i
\(716\) 25.3169 28.1173i 0.946137 1.05079i
\(717\) 0 0
\(718\) −7.83774 + 13.5754i −0.292502 + 0.506628i
\(719\) −29.6588 + 21.5483i −1.10609 + 0.803618i −0.982043 0.188659i \(-0.939586\pi\)
−0.124042 + 0.992277i \(0.539586\pi\)
\(720\) 0 0
\(721\) 13.6851 + 9.94284i 0.509661 + 0.370291i
\(722\) −1.92415 + 0.856685i −0.0716093 + 0.0318825i
\(723\) 0 0
\(724\) −14.0514 24.3378i −0.522218 0.904508i
\(725\) 1.19493 4.51233i 0.0443786 0.167584i
\(726\) 0 0
\(727\) 6.36275 + 7.06654i 0.235981 + 0.262084i 0.849491 0.527604i \(-0.176909\pi\)
−0.613509 + 0.789687i \(0.710243\pi\)
\(728\) −3.92800 2.85386i −0.145581 0.105771i
\(729\) 0 0
\(730\) 13.0209 + 11.0880i 0.481925 + 0.410385i
\(731\) −6.33080 60.2335i −0.234153 2.22782i
\(732\) 0 0
\(733\) 9.20387 + 4.09783i 0.339953 + 0.151357i 0.569611 0.821915i \(-0.307094\pi\)
−0.229658 + 0.973271i \(0.573761\pi\)
\(734\) −14.6904 + 16.3154i −0.542234 + 0.602211i
\(735\) 0 0
\(736\) 34.5497 + 38.3714i 1.27352 + 1.41439i
\(737\) −3.31138 10.1914i −0.121976 0.375404i
\(738\) 0 0
\(739\) −5.85917 + 18.0327i −0.215533 + 0.663342i 0.783582 + 0.621288i \(0.213390\pi\)
−0.999115 + 0.0420544i \(0.986610\pi\)
\(740\) 5.00394 + 6.50153i 0.183948 + 0.239001i
\(741\) 0 0
\(742\) −3.53215 1.57261i −0.129669 0.0577325i
\(743\) 10.9750 + 19.0092i 0.402633 + 0.697381i 0.994043 0.108990i \(-0.0347617\pi\)
−0.591410 + 0.806371i \(0.701428\pi\)
\(744\) 0 0
\(745\) 7.68376 11.2151i 0.281511 0.410888i
\(746\) 7.04928 + 5.12160i 0.258092 + 0.187515i
\(747\) 0 0
\(748\) −8.65462 + 26.6362i −0.316444 + 0.973915i
\(749\) 0.567947 0.983714i 0.0207523 0.0359441i
\(750\) 0 0
\(751\) −6.43136 11.1394i −0.234684 0.406484i 0.724497 0.689278i \(-0.242072\pi\)
−0.959181 + 0.282794i \(0.908739\pi\)
\(752\) −3.33144 + 0.708119i −0.121485 + 0.0258225i
\(753\) 0 0
\(754\) 1.27066 0.565734i 0.0462747 0.0206028i
\(755\) 21.0176 + 1.62317i 0.764908 + 0.0590733i
\(756\) 0 0
\(757\) −3.01935 −0.109740 −0.0548701 0.998494i \(-0.517474\pi\)
−0.0548701 + 0.998494i \(0.517474\pi\)
\(758\) −0.286076 2.72183i −0.0103907 0.0988613i
\(759\) 0 0
\(760\) −26.9555 + 3.58890i −0.977780 + 0.130183i
\(761\) 40.9454 8.70321i 1.48427 0.315491i 0.606696 0.794934i \(-0.292495\pi\)
0.877573 + 0.479443i \(0.159161\pi\)
\(762\) 0 0
\(763\) −1.80287 0.383212i −0.0652682 0.0138732i
\(764\) −5.26338 + 16.1990i −0.190422 + 0.586060i
\(765\) 0 0
\(766\) 1.20666 + 3.71373i 0.0435985 + 0.134183i
\(767\) 0.979864 + 9.32278i 0.0353808 + 0.336626i
\(768\) 0 0
\(769\) 42.9240 + 19.1110i 1.54788 + 0.689160i 0.990040 0.140789i \(-0.0449640\pi\)
0.557839 + 0.829949i \(0.311631\pi\)
\(770\) 0.850633 4.62739i 0.0306547 0.166760i
\(771\) 0 0
\(772\) 32.8864 14.6419i 1.18361 0.526975i
\(773\) −8.38597 + 25.8093i −0.301622 + 0.928298i 0.679294 + 0.733866i \(0.262286\pi\)
−0.980916 + 0.194431i \(0.937714\pi\)
\(774\) 0 0
\(775\) 11.8211 6.06681i 0.424627 0.217926i
\(776\) 2.53202 4.38559i 0.0908943 0.157434i
\(777\) 0 0
\(778\) −2.46331 + 23.4369i −0.0883141 + 0.840252i
\(779\) 2.64301 25.1465i 0.0946956 0.900968i
\(780\) 0 0
\(781\) −0.0468948 0.446175i −0.00167803 0.0159654i
\(782\) −45.8346 −1.63904
\(783\) 0 0
\(784\) −1.59758 4.91685i −0.0570565 0.175602i
\(785\) −26.0345 + 37.9994i −0.929211 + 1.35626i
\(786\) 0 0
\(787\) −5.95642 + 6.61528i −0.212323 + 0.235809i −0.839894 0.542751i \(-0.817383\pi\)
0.627570 + 0.778560i \(0.284049\pi\)
\(788\) 1.61453 1.79312i 0.0575152 0.0638771i
\(789\) 0 0
\(790\) −0.199395 7.21124i −0.00709414 0.256565i
\(791\) −2.36744 7.28623i −0.0841765 0.259069i
\(792\) 0 0
\(793\) −21.9495 −0.779449
\(794\) 0.508254 + 4.83572i 0.0180373 + 0.171613i
\(795\) 0 0
\(796\) −0.966507 + 9.19570i −0.0342569 + 0.325933i
\(797\) 3.95641 37.6427i 0.140143 1.33337i −0.667900 0.744251i \(-0.732807\pi\)
0.808043 0.589123i \(-0.200527\pi\)
\(798\) 0 0
\(799\) 13.6885 23.7091i 0.484264 0.838769i
\(800\) −28.9582 4.49968i −1.02383 0.159088i
\(801\) 0 0
\(802\) −4.22368 + 12.9992i −0.149143 + 0.459016i
\(803\) 26.5166 11.8059i 0.935750 0.416623i
\(804\) 0 0
\(805\) −18.6148 + 2.47841i −0.656087 + 0.0873525i
\(806\) 3.61691 + 1.61035i 0.127400 + 0.0567223i
\(807\) 0 0
\(808\) −1.97183 18.7607i −0.0693686 0.659998i
\(809\) −5.78411 17.8016i −0.203358 0.625873i −0.999777 0.0211267i \(-0.993275\pi\)
0.796418 0.604746i \(-0.206725\pi\)
\(810\) 0 0
\(811\) 13.0270 40.0931i 0.457441 1.40786i −0.410804 0.911723i \(-0.634752\pi\)
0.868245 0.496135i \(-0.165248\pi\)
\(812\) −1.23480 0.262464i −0.0433329 0.00921070i
\(813\) 0 0
\(814\) −5.58446 + 1.18701i −0.195735 + 0.0416048i
\(815\) 16.8840 16.0694i 0.591422 0.562886i
\(816\) 0 0
\(817\) −4.32882 41.1859i −0.151446 1.44091i
\(818\) 29.3086 1.02475
\(819\) 0 0
\(820\) 6.55552 15.8922i 0.228929 0.554979i
\(821\) 26.4525 11.7774i 0.923197 0.411034i 0.110603 0.993865i \(-0.464722\pi\)
0.812593 + 0.582831i \(0.198055\pi\)
\(822\) 0 0
\(823\) 11.9474 2.53950i 0.416461 0.0885215i 0.00508458 0.999987i \(-0.498382\pi\)
0.411376 + 0.911466i \(0.365048\pi\)
\(824\) 23.1288 + 40.0603i 0.805731 + 1.39557i
\(825\) 0 0
\(826\) −1.74422 + 3.02107i −0.0606890 + 0.105116i
\(827\) −5.83473 + 17.9575i −0.202894 + 0.624442i 0.796900 + 0.604112i \(0.206472\pi\)
−0.999793 + 0.0203307i \(0.993528\pi\)
\(828\) 0 0
\(829\) −10.2118 7.41933i −0.354672 0.257684i 0.396155 0.918184i \(-0.370344\pi\)
−0.750826 + 0.660500i \(0.770344\pi\)
\(830\) −5.39866 1.59057i −0.187390 0.0552093i
\(831\) 0 0
\(832\) −2.70804 4.69045i −0.0938842 0.162612i
\(833\) 37.9637 + 16.9025i 1.31537 + 0.585638i
\(834\) 0 0
\(835\) 0.955752 + 34.5655i 0.0330752 + 1.19619i
\(836\) −5.91778 + 18.2131i −0.204671 + 0.629912i
\(837\) 0 0
\(838\) 1.24568 + 3.83380i 0.0430312 + 0.132436i
\(839\) 29.4416 + 32.6982i 1.01644 + 1.12887i 0.991622 + 0.129177i \(0.0412335\pi\)
0.0248166 + 0.999692i \(0.492100\pi\)
\(840\) 0 0
\(841\) −18.8216 + 20.9035i −0.649021 + 0.720811i
\(842\) 18.8748 + 8.40362i 0.650470 + 0.289608i
\(843\) 0 0
\(844\) 1.18306 + 11.2561i 0.0407227 + 0.387450i
\(845\) −17.4928 + 10.7548i −0.601770 + 0.369977i
\(846\) 0 0
\(847\) 2.02360 + 1.47023i 0.0695317 + 0.0505177i
\(848\) 3.02034 + 3.35442i 0.103719 + 0.115191i
\(849\) 0 0
\(850\) 20.1689 16.4304i 0.691788 0.563560i
\(851\) 11.3938 + 19.7347i 0.390575 + 0.676496i
\(852\) 0 0
\(853\) −43.7951 + 19.4988i −1.49952 + 0.667627i −0.982143 0.188133i \(-0.939756\pi\)
−0.517372 + 0.855761i \(0.673090\pi\)
\(854\) −6.60816 4.80111i −0.226127 0.164291i
\(855\) 0 0
\(856\) 2.51297 1.82578i 0.0858916 0.0624039i
\(857\) 12.6888 21.9776i 0.433440 0.750741i −0.563727 0.825961i \(-0.690633\pi\)
0.997167 + 0.0752208i \(0.0239662\pi\)
\(858\) 0 0
\(859\) −5.62539 + 6.24763i −0.191936 + 0.213166i −0.831430 0.555630i \(-0.812477\pi\)
0.639494 + 0.768796i \(0.279144\pi\)
\(860\) 5.09056 27.6923i 0.173587 0.944301i
\(861\) 0 0
\(862\) −25.8336 5.49110i −0.879897 0.187028i
\(863\) 9.08240 + 27.9528i 0.309168 + 0.951523i 0.978089 + 0.208189i \(0.0667568\pi\)
−0.668920 + 0.743334i \(0.733243\pi\)
\(864\) 0 0
\(865\) −12.6819 + 30.7440i −0.431197 + 1.04533i
\(866\) 6.85227 + 1.45649i 0.232850 + 0.0494937i
\(867\) 0 0
\(868\) −1.79668 3.11194i −0.0609833 0.105626i
\(869\) −11.1851 4.97993i −0.379429 0.168933i
\(870\) 0 0
\(871\) 6.60812 2.94212i 0.223908 0.0996901i
\(872\) −4.07764 2.96258i −0.138086 0.100326i
\(873\) 0 0
\(874\) −31.3404 −1.06011
\(875\) 7.30277 7.76350i 0.246879 0.262454i
\(876\) 0 0
\(877\) 44.7629 9.51464i 1.51153 0.321287i 0.623779 0.781601i \(-0.285597\pi\)
0.887756 + 0.460314i \(0.152263\pi\)
\(878\) 0.572244 5.44454i 0.0193123 0.183744i
\(879\) 0 0
\(880\) −3.10449 + 4.53125i −0.104652 + 0.152748i
\(881\) −22.8783 + 16.6220i −0.770789 + 0.560011i −0.902200 0.431317i \(-0.858049\pi\)
0.131412 + 0.991328i \(0.458049\pi\)
\(882\) 0 0
\(883\) 9.86953 7.17063i 0.332136 0.241311i −0.409200 0.912445i \(-0.634192\pi\)
0.741336 + 0.671134i \(0.234192\pi\)
\(884\) −18.4923 3.93066i −0.621963 0.132202i
\(885\) 0 0
\(886\) 18.9178 4.02111i 0.635556 0.135092i
\(887\) −7.43378 + 8.25605i −0.249602 + 0.277211i −0.854906 0.518784i \(-0.826385\pi\)
0.605304 + 0.795995i \(0.293052\pi\)
\(888\) 0 0
\(889\) −9.29502 10.3232i −0.311745 0.346228i
\(890\) 22.3566 + 19.0378i 0.749396 + 0.638150i
\(891\) 0 0
\(892\) −10.8296 + 7.86813i −0.362600 + 0.263445i
\(893\) 9.35979 16.2116i 0.313214 0.542502i
\(894\) 0 0
\(895\) −10.7837 + 58.6629i −0.360461 + 1.96088i
\(896\) −0.957437 + 9.10941i −0.0319857 + 0.304324i
\(897\) 0 0
\(898\) −3.64317 4.04615i −0.121574 0.135022i
\(899\) 2.48088 0.0827421
\(900\) 0 0
\(901\) −36.2829 −1.20876
\(902\) 8.00490 + 8.89034i 0.266534 + 0.296016i
\(903\) 0 0
\(904\) 2.18989 20.8355i 0.0728348 0.692977i
\(905\) 38.9650 + 21.0825i 1.29524 + 0.700806i
\(906\) 0 0
\(907\) 20.6216 35.7176i 0.684728 1.18598i −0.288794 0.957391i \(-0.593254\pi\)
0.973522 0.228593i \(-0.0734125\pi\)
\(908\) 27.0858 19.6790i 0.898874 0.653070i
\(909\) 0 0
\(910\) 3.16652 + 0.244548i 0.104969 + 0.00810670i
\(911\) 8.06488 + 8.95695i 0.267201 + 0.296757i 0.861782 0.507279i \(-0.169349\pi\)
−0.594581 + 0.804036i \(0.702682\pi\)
\(912\) 0 0
\(913\) −6.39155 + 7.09853i −0.211529 + 0.234927i
\(914\) 26.6911 5.67336i 0.882862 0.187658i
\(915\) 0 0
\(916\) −21.7924 4.63211i −0.720040 0.153049i
\(917\) 10.4681 7.60549i 0.345686 0.251155i
\(918\) 0 0
\(919\) 31.2727 22.7209i 1.03159 0.749494i 0.0629636 0.998016i \(-0.479945\pi\)
0.968626 + 0.248522i \(0.0799448\pi\)
\(920\) −49.2597 14.5130i −1.62404 0.478479i
\(921\) 0 0
\(922\) 1.21439 11.5541i 0.0399937 0.380514i
\(923\) 0.296221 0.0629637i 0.00975024 0.00207248i
\(924\) 0 0
\(925\) −12.0880 4.59961i −0.397452 0.151234i
\(926\) 18.9531 0.622839
\(927\) 0 0
\(928\) −4.42678 3.21625i −0.145316 0.105578i
\(929\) 41.6150 18.5282i 1.36535 0.607891i 0.412391 0.911007i \(-0.364694\pi\)
0.952954 + 0.303116i \(0.0980269\pi\)
\(930\) 0 0
\(931\) 25.9585 + 11.5575i 0.850756 + 0.378781i
\(932\) −1.33850 2.31835i −0.0438440 0.0759401i
\(933\) 0 0
\(934\) −19.5149 4.14801i −0.638546 0.135727i
\(935\) −10.3698 42.9165i −0.339129 1.40352i
\(936\) 0 0
\(937\) −10.9573 33.7230i −0.357958 1.10168i −0.954274 0.298932i \(-0.903370\pi\)
0.596316 0.802750i \(-0.296630\pi\)
\(938\) 2.63300 + 0.559662i 0.0859705 + 0.0182736i
\(939\) 0 0
\(940\) 9.21925 8.77442i 0.300699 0.286190i
\(941\) −13.4712 + 14.9612i −0.439147 + 0.487723i −0.921568 0.388217i \(-0.873091\pi\)
0.482420 + 0.875940i \(0.339758\pi\)
\(942\) 0 0
\(943\) 23.8747 41.3521i 0.777466 1.34661i
\(944\) 3.29476 2.39378i 0.107235 0.0779109i
\(945\) 0 0
\(946\) 15.8516 + 11.5169i 0.515380 + 0.374446i
\(947\) 22.1124 9.84509i 0.718558 0.319923i −0.0146824 0.999892i \(-0.504674\pi\)
0.733240 + 0.679970i \(0.238007\pi\)
\(948\) 0 0
\(949\) 9.79667 + 16.9683i 0.318013 + 0.550815i
\(950\) 13.7909 11.2347i 0.447437 0.364501i
\(951\) 0 0
\(952\) −11.3453 12.6003i −0.367704 0.408377i
\(953\) 14.5798 + 10.5929i 0.472287 + 0.343137i 0.798332 0.602218i \(-0.205716\pi\)
−0.326045 + 0.945354i \(0.605716\pi\)
\(954\) 0 0
\(955\) −6.30648 26.1001i −0.204073 0.844578i
\(956\) 0.212509 + 2.02188i 0.00687302 + 0.0653924i
\(957\) 0 0
\(958\) −6.70254 2.98416i −0.216549 0.0964139i
\(959\) 5.57875 6.19583i 0.180147 0.200074i
\(960\) 0 0
\(961\) −16.0178 17.7895i −0.516703 0.573856i
\(962\) −1.19091 3.66526i −0.0383966 0.118173i
\(963\) 0 0
\(964\) −4.80103 + 14.7760i −0.154631 + 0.475904i
\(965\) −32.0751 + 46.8162i −1.03253 + 1.50707i
\(966\) 0 0
\(967\) −33.2214 14.7911i −1.06833 0.475651i −0.204204 0.978928i \(-0.565461\pi\)
−0.864125 + 0.503277i \(0.832127\pi\)
\(968\) 3.42002 + 5.92365i 0.109924 + 0.190393i
\(969\) 0 0
\(970\) 0.0915576 + 3.31124i 0.00293974 + 0.106318i
\(971\) −46.1160 33.5052i −1.47993 1.07523i −0.977578 0.210572i \(-0.932467\pi\)
−0.502354 0.864662i \(-0.667533\pi\)
\(972\) 0 0
\(973\) 5.57547 17.1595i 0.178741 0.550109i
\(974\) 15.0373 26.0453i 0.481825 0.834545i
\(975\) 0 0
\(976\) 4.76792 + 8.25828i 0.152617 + 0.264341i
\(977\) −15.1510 + 3.22044i −0.484722 + 0.103031i −0.443790 0.896131i \(-0.646366\pi\)
−0.0409326 + 0.999162i \(0.513033\pi\)
\(978\) 0 0
\(979\) 45.5284 20.2706i 1.45509 0.647850i
\(980\) 14.7088 + 12.5254i 0.469857 + 0.400108i
\(981\) 0 0
\(982\) 7.42689 0.237001
\(983\) −1.64381 15.6398i −0.0524293 0.498831i −0.988953 0.148228i \(-0.952643\pi\)
0.936524 0.350604i \(-0.114024\pi\)
\(984\) 0 0
\(985\) −0.687709 + 3.74109i −0.0219122 + 0.119201i
\(986\) 4.75111 1.00988i 0.151306 0.0321611i
\(987\) 0 0
\(988\) −12.6445 2.68767i −0.402275 0.0855063i
\(989\) 24.1669 74.3780i 0.768462 2.36508i
\(990\) 0 0
\(991\) 6.23054 + 19.1756i 0.197920 + 0.609134i 0.999930 + 0.0118242i \(0.00376384\pi\)
−0.802010 + 0.597310i \(0.796236\pi\)
\(992\) −1.62808 15.4901i −0.0516915 0.491811i
\(993\) 0 0
\(994\) 0.102953 + 0.0458378i 0.00326548 + 0.00145389i
\(995\) −6.29456 13.1473i −0.199551 0.416796i
\(996\) 0 0
\(997\) −37.2806 + 16.5984i −1.18069 + 0.525677i −0.900749 0.434341i \(-0.856981\pi\)
−0.279940 + 0.960017i \(0.590315\pi\)
\(998\) −2.06306 + 6.34944i −0.0653050 + 0.200988i
\(999\) 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 675.2.r.a.46.12 224
3.2 odd 2 225.2.q.a.196.17 yes 224
9.4 even 3 inner 675.2.r.a.496.17 224
9.5 odd 6 225.2.q.a.121.12 yes 224
25.6 even 5 inner 675.2.r.a.181.17 224
75.56 odd 10 225.2.q.a.106.12 yes 224
225.31 even 15 inner 675.2.r.a.631.12 224
225.131 odd 30 225.2.q.a.31.17 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.17 224 225.131 odd 30
225.2.q.a.106.12 yes 224 75.56 odd 10
225.2.q.a.121.12 yes 224 9.5 odd 6
225.2.q.a.196.17 yes 224 3.2 odd 2
675.2.r.a.46.12 224 1.1 even 1 trivial
675.2.r.a.181.17 224 25.6 even 5 inner
675.2.r.a.496.17 224 9.4 even 3 inner
675.2.r.a.631.12 224 225.31 even 15 inner