Properties

Label 819.2.fm.f.496.1
Level $819$
Weight $2$
Character 819.496
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [819,2,Mod(370,819)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(819, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("819.370");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 496.1
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.f.748.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.37607 - 0.636667i) q^{2} +(3.50833 + 2.02554i) q^{4} +(-0.498430 - 0.498430i) q^{5} +(-2.12397 + 1.57758i) q^{7} +(-3.56765 - 3.56765i) q^{8} +O(q^{10})\) \(q+(-2.37607 - 0.636667i) q^{2} +(3.50833 + 2.02554i) q^{4} +(-0.498430 - 0.498430i) q^{5} +(-2.12397 + 1.57758i) q^{7} +(-3.56765 - 3.56765i) q^{8} +(0.866973 + 1.50164i) q^{10} +(-0.184478 + 0.688480i) q^{11} +(3.17894 - 1.70127i) q^{13} +(6.05110 - 2.39618i) q^{14} +(2.15452 + 3.73174i) q^{16} +(-2.27300 + 3.93695i) q^{17} +(-3.25000 + 0.870835i) q^{19} +(-0.739070 - 2.75825i) q^{20} +(0.876665 - 1.51843i) q^{22} +(1.67026 - 0.964326i) q^{23} -4.50313i q^{25} +(-8.63655 + 2.01842i) q^{26} +(-10.6470 + 1.23248i) q^{28} +(-0.185925 - 0.322032i) q^{29} +(-3.53994 - 3.53994i) q^{31} +(-0.131724 - 0.491600i) q^{32} +(7.90735 - 7.90735i) q^{34} +(1.84496 + 0.272339i) q^{35} +(-0.545727 + 2.03668i) q^{37} +8.27667 q^{38} +3.55645i q^{40} +(3.11983 - 11.6434i) q^{41} +(6.38504 + 3.68640i) q^{43} +(-2.04175 + 2.04175i) q^{44} +(-4.58262 + 1.22791i) q^{46} +(-3.55898 + 3.55898i) q^{47} +(2.02250 - 6.70145i) q^{49} +(-2.86700 + 10.6998i) q^{50} +(14.5988 + 0.470438i) q^{52} +4.97712 q^{53} +(0.435109 - 0.251210i) q^{55} +(13.2058 + 1.94934i) q^{56} +(0.236745 + 0.883543i) q^{58} +(-1.03416 - 3.85953i) q^{59} +(-10.0720 - 5.81509i) q^{61} +(6.15739 + 10.6649i) q^{62} -7.36614i q^{64} +(-2.43245 - 0.736516i) q^{65} +(-12.5870 - 3.37267i) q^{67} +(-15.9489 + 9.20809i) q^{68} +(-4.21038 - 1.82173i) q^{70} +(-2.10681 - 7.86274i) q^{71} +(-0.608899 + 0.608899i) q^{73} +(2.59337 - 4.49186i) q^{74} +(-13.1660 - 3.52781i) q^{76} +(-0.694305 - 1.75334i) q^{77} +9.81537 q^{79} +(0.786133 - 2.93389i) q^{80} +(-14.8259 + 25.6792i) q^{82} +(-2.25452 - 2.25452i) q^{83} +(3.09523 - 0.829364i) q^{85} +(-12.8243 - 12.8243i) q^{86} +(3.11441 - 1.79810i) q^{88} +(-17.5524 - 4.70315i) q^{89} +(-4.06809 + 8.62848i) q^{91} +7.81311 q^{92} +(10.7223 - 6.19052i) q^{94} +(2.05395 + 1.18585i) q^{95} +(-8.73810 + 2.34137i) q^{97} +(-9.07221 + 14.6355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37607 0.636667i −1.68014 0.450192i −0.712322 0.701852i \(-0.752357\pi\)
−0.967816 + 0.251661i \(0.919023\pi\)
\(3\) 0 0
\(4\) 3.50833 + 2.02554i 1.75417 + 1.01277i
\(5\) −0.498430 0.498430i −0.222905 0.222905i 0.586816 0.809721i \(-0.300381\pi\)
−0.809721 + 0.586816i \(0.800381\pi\)
\(6\) 0 0
\(7\) −2.12397 + 1.57758i −0.802785 + 0.596268i
\(8\) −3.56765 3.56765i −1.26135 1.26135i
\(9\) 0 0
\(10\) 0.866973 + 1.50164i 0.274161 + 0.474861i
\(11\) −0.184478 + 0.688480i −0.0556221 + 0.207585i −0.988144 0.153528i \(-0.950936\pi\)
0.932522 + 0.361113i \(0.117603\pi\)
\(12\) 0 0
\(13\) 3.17894 1.70127i 0.881680 0.471848i
\(14\) 6.05110 2.39618i 1.61723 0.640405i
\(15\) 0 0
\(16\) 2.15452 + 3.73174i 0.538630 + 0.932934i
\(17\) −2.27300 + 3.93695i −0.551284 + 0.954852i 0.446898 + 0.894585i \(0.352529\pi\)
−0.998182 + 0.0602669i \(0.980805\pi\)
\(18\) 0 0
\(19\) −3.25000 + 0.870835i −0.745601 + 0.199783i −0.611566 0.791193i \(-0.709460\pi\)
−0.134035 + 0.990977i \(0.542793\pi\)
\(20\) −0.739070 2.75825i −0.165261 0.616763i
\(21\) 0 0
\(22\) 0.876665 1.51843i 0.186906 0.323730i
\(23\) 1.67026 0.964326i 0.348274 0.201076i −0.315651 0.948875i \(-0.602223\pi\)
0.663925 + 0.747799i \(0.268890\pi\)
\(24\) 0 0
\(25\) 4.50313i 0.900627i
\(26\) −8.63655 + 2.01842i −1.69377 + 0.395845i
\(27\) 0 0
\(28\) −10.6470 + 1.23248i −2.01210 + 0.232917i
\(29\) −0.185925 0.322032i −0.0345254 0.0597998i 0.848246 0.529602i \(-0.177659\pi\)
−0.882772 + 0.469802i \(0.844325\pi\)
\(30\) 0 0
\(31\) −3.53994 3.53994i −0.635792 0.635792i 0.313723 0.949515i \(-0.398424\pi\)
−0.949515 + 0.313723i \(0.898424\pi\)
\(32\) −0.131724 0.491600i −0.0232857 0.0869034i
\(33\) 0 0
\(34\) 7.90735 7.90735i 1.35610 1.35610i
\(35\) 1.84496 + 0.272339i 0.311856 + 0.0460337i
\(36\) 0 0
\(37\) −0.545727 + 2.03668i −0.0897169 + 0.334828i −0.996166 0.0874879i \(-0.972116\pi\)
0.906449 + 0.422316i \(0.138783\pi\)
\(38\) 8.27667 1.34265
\(39\) 0 0
\(40\) 3.55645i 0.562324i
\(41\) 3.11983 11.6434i 0.487236 1.81839i −0.0825406 0.996588i \(-0.526303\pi\)
0.569776 0.821800i \(-0.307030\pi\)
\(42\) 0 0
\(43\) 6.38504 + 3.68640i 0.973709 + 0.562171i 0.900365 0.435136i \(-0.143300\pi\)
0.0733440 + 0.997307i \(0.476633\pi\)
\(44\) −2.04175 + 2.04175i −0.307805 + 0.307805i
\(45\) 0 0
\(46\) −4.58262 + 1.22791i −0.675671 + 0.181045i
\(47\) −3.55898 + 3.55898i −0.519131 + 0.519131i −0.917308 0.398177i \(-0.869643\pi\)
0.398177 + 0.917308i \(0.369643\pi\)
\(48\) 0 0
\(49\) 2.02250 6.70145i 0.288929 0.957351i
\(50\) −2.86700 + 10.6998i −0.405455 + 1.51318i
\(51\) 0 0
\(52\) 14.5988 + 0.470438i 2.02449 + 0.0652380i
\(53\) 4.97712 0.683660 0.341830 0.939762i \(-0.388953\pi\)
0.341830 + 0.939762i \(0.388953\pi\)
\(54\) 0 0
\(55\) 0.435109 0.251210i 0.0586700 0.0338732i
\(56\) 13.2058 + 1.94934i 1.76470 + 0.260492i
\(57\) 0 0
\(58\) 0.236745 + 0.883543i 0.0310861 + 0.116015i
\(59\) −1.03416 3.85953i −0.134636 0.502467i −0.999999 0.00132252i \(-0.999579\pi\)
0.865363 0.501145i \(-0.167088\pi\)
\(60\) 0 0
\(61\) −10.0720 5.81509i −1.28959 0.744546i −0.311011 0.950406i \(-0.600667\pi\)
−0.978581 + 0.205860i \(0.934001\pi\)
\(62\) 6.15739 + 10.6649i 0.781990 + 1.35445i
\(63\) 0 0
\(64\) 7.36614i 0.920767i
\(65\) −2.43245 0.736516i −0.301708 0.0913536i
\(66\) 0 0
\(67\) −12.5870 3.37267i −1.53774 0.412037i −0.612207 0.790697i \(-0.709718\pi\)
−0.925536 + 0.378660i \(0.876385\pi\)
\(68\) −15.9489 + 9.20809i −1.93409 + 1.11665i
\(69\) 0 0
\(70\) −4.21038 1.82173i −0.503237 0.217738i
\(71\) −2.10681 7.86274i −0.250033 0.933135i −0.970787 0.239944i \(-0.922871\pi\)
0.720754 0.693191i \(-0.243796\pi\)
\(72\) 0 0
\(73\) −0.608899 + 0.608899i −0.0712663 + 0.0712663i −0.741842 0.670575i \(-0.766047\pi\)
0.670575 + 0.741842i \(0.266047\pi\)
\(74\) 2.59337 4.49186i 0.301474 0.522168i
\(75\) 0 0
\(76\) −13.1660 3.52781i −1.51024 0.404668i
\(77\) −0.694305 1.75334i −0.0791234 0.199812i
\(78\) 0 0
\(79\) 9.81537 1.10432 0.552158 0.833740i \(-0.313805\pi\)
0.552158 + 0.833740i \(0.313805\pi\)
\(80\) 0.786133 2.93389i 0.0878924 0.328019i
\(81\) 0 0
\(82\) −14.8259 + 25.6792i −1.63725 + 2.83579i
\(83\) −2.25452 2.25452i −0.247465 0.247465i 0.572464 0.819930i \(-0.305988\pi\)
−0.819930 + 0.572464i \(0.805988\pi\)
\(84\) 0 0
\(85\) 3.09523 0.829364i 0.335725 0.0899572i
\(86\) −12.8243 12.8243i −1.38288 1.38288i
\(87\) 0 0
\(88\) 3.11441 1.79810i 0.331997 0.191678i
\(89\) −17.5524 4.70315i −1.86055 0.498533i −0.860609 0.509266i \(-0.829917\pi\)
−0.999942 + 0.0107329i \(0.996584\pi\)
\(90\) 0 0
\(91\) −4.06809 + 8.62848i −0.426452 + 0.904510i
\(92\) 7.81311 0.814573
\(93\) 0 0
\(94\) 10.7223 6.19052i 1.10592 0.638503i
\(95\) 2.05395 + 1.18585i 0.210731 + 0.121665i
\(96\) 0 0
\(97\) −8.73810 + 2.34137i −0.887220 + 0.237730i −0.673520 0.739169i \(-0.735218\pi\)
−0.213700 + 0.976899i \(0.568552\pi\)
\(98\) −9.07221 + 14.6355i −0.916432 + 1.47841i
\(99\) 0 0
\(100\) 9.12126 15.7985i 0.912126 1.57985i
\(101\) −6.77353 11.7321i −0.673991 1.16739i −0.976763 0.214324i \(-0.931245\pi\)
0.302772 0.953063i \(-0.402088\pi\)
\(102\) 0 0
\(103\) −16.4565 −1.62151 −0.810756 0.585385i \(-0.800944\pi\)
−0.810756 + 0.585385i \(0.800944\pi\)
\(104\) −17.4109 5.27181i −1.70728 0.516943i
\(105\) 0 0
\(106\) −11.8260 3.16877i −1.14864 0.307778i
\(107\) −8.35835 14.4771i −0.808033 1.39955i −0.914225 0.405208i \(-0.867199\pi\)
0.106192 0.994346i \(-0.466134\pi\)
\(108\) 0 0
\(109\) 1.77768 1.77768i 0.170271 0.170271i −0.616827 0.787099i \(-0.711582\pi\)
0.787099 + 0.616827i \(0.211582\pi\)
\(110\) −1.19379 + 0.319874i −0.113823 + 0.0304988i
\(111\) 0 0
\(112\) −10.4632 4.52718i −0.988683 0.427778i
\(113\) 2.96252 5.13124i 0.278691 0.482706i −0.692369 0.721544i \(-0.743433\pi\)
0.971060 + 0.238837i \(0.0767662\pi\)
\(114\) 0 0
\(115\) −1.31316 0.351860i −0.122453 0.0328111i
\(116\) 1.50639i 0.139865i
\(117\) 0 0
\(118\) 9.82893i 0.904826i
\(119\) −1.38306 11.9478i −0.126785 1.09525i
\(120\) 0 0
\(121\) 9.08631 + 5.24598i 0.826028 + 0.476907i
\(122\) 20.2296 + 20.2296i 1.83150 + 1.83150i
\(123\) 0 0
\(124\) −5.24901 19.5896i −0.471375 1.75919i
\(125\) −4.73665 + 4.73665i −0.423659 + 0.423659i
\(126\) 0 0
\(127\) −17.4169 + 10.0556i −1.54550 + 0.892293i −0.547019 + 0.837120i \(0.684238\pi\)
−0.998477 + 0.0551724i \(0.982429\pi\)
\(128\) −4.95322 + 18.4857i −0.437807 + 1.63392i
\(129\) 0 0
\(130\) 5.31076 + 3.29868i 0.465784 + 0.289313i
\(131\) 12.0796i 1.05540i 0.849430 + 0.527702i \(0.176946\pi\)
−0.849430 + 0.527702i \(0.823054\pi\)
\(132\) 0 0
\(133\) 5.52909 6.97675i 0.479433 0.604961i
\(134\) 27.7603 + 16.0274i 2.39813 + 1.38456i
\(135\) 0 0
\(136\) 22.1549 5.93640i 1.89977 0.509042i
\(137\) 13.9883 3.74816i 1.19510 0.320227i 0.394202 0.919024i \(-0.371021\pi\)
0.800901 + 0.598797i \(0.204354\pi\)
\(138\) 0 0
\(139\) 6.95647 + 4.01632i 0.590040 + 0.340660i 0.765113 0.643896i \(-0.222683\pi\)
−0.175073 + 0.984555i \(0.556016\pi\)
\(140\) 5.92111 + 4.69250i 0.500425 + 0.396588i
\(141\) 0 0
\(142\) 20.0238i 1.68036i
\(143\) 0.584848 + 2.50248i 0.0489074 + 0.209268i
\(144\) 0 0
\(145\) −0.0678396 + 0.253181i −0.00563378 + 0.0210255i
\(146\) 1.83446 1.05912i 0.151821 0.0876537i
\(147\) 0 0
\(148\) −6.03996 + 6.03996i −0.496481 + 0.496481i
\(149\) 2.13325 + 7.96140i 0.174763 + 0.652223i 0.996592 + 0.0824894i \(0.0262870\pi\)
−0.821829 + 0.569734i \(0.807046\pi\)
\(150\) 0 0
\(151\) −4.15300 4.15300i −0.337966 0.337966i 0.517635 0.855601i \(-0.326812\pi\)
−0.855601 + 0.517635i \(0.826812\pi\)
\(152\) 14.7017 + 8.48802i 1.19246 + 0.688469i
\(153\) 0 0
\(154\) 0.533427 + 4.60810i 0.0429848 + 0.371332i
\(155\) 3.52883i 0.283442i
\(156\) 0 0
\(157\) 14.6163i 1.16651i −0.812291 0.583253i \(-0.801780\pi\)
0.812291 0.583253i \(-0.198220\pi\)
\(158\) −23.3220 6.24912i −1.85540 0.497154i
\(159\) 0 0
\(160\) −0.179373 + 0.310684i −0.0141807 + 0.0245617i
\(161\) −2.02629 + 4.68317i −0.159694 + 0.369085i
\(162\) 0 0
\(163\) 7.35195 1.96995i 0.575849 0.154298i 0.0408715 0.999164i \(-0.486987\pi\)
0.534978 + 0.844866i \(0.320320\pi\)
\(164\) 34.5294 34.5294i 2.69630 2.69630i
\(165\) 0 0
\(166\) 3.92152 + 6.79228i 0.304369 + 0.527183i
\(167\) 7.60079 + 2.03663i 0.588167 + 0.157599i 0.540615 0.841270i \(-0.318191\pi\)
0.0475517 + 0.998869i \(0.484858\pi\)
\(168\) 0 0
\(169\) 7.21135 10.8165i 0.554719 0.832038i
\(170\) −7.88252 −0.604562
\(171\) 0 0
\(172\) 14.9339 + 25.8662i 1.13870 + 1.97228i
\(173\) 5.36019 9.28412i 0.407528 0.705859i −0.587084 0.809526i \(-0.699724\pi\)
0.994612 + 0.103667i \(0.0330577\pi\)
\(174\) 0 0
\(175\) 7.10404 + 9.56453i 0.537015 + 0.723010i
\(176\) −2.96669 + 0.794922i −0.223623 + 0.0599195i
\(177\) 0 0
\(178\) 38.7115 + 22.3501i 2.90155 + 1.67521i
\(179\) −8.63169 + 4.98351i −0.645163 + 0.372485i −0.786601 0.617462i \(-0.788161\pi\)
0.141438 + 0.989947i \(0.454828\pi\)
\(180\) 0 0
\(181\) 3.96508 0.294722 0.147361 0.989083i \(-0.452922\pi\)
0.147361 + 0.989083i \(0.452922\pi\)
\(182\) 15.1596 17.9119i 1.12370 1.32772i
\(183\) 0 0
\(184\) −9.39929 2.51853i −0.692925 0.185669i
\(185\) 1.28715 0.743136i 0.0946331 0.0546365i
\(186\) 0 0
\(187\) −2.29120 2.29120i −0.167549 0.167549i
\(188\) −19.6949 + 5.27724i −1.43640 + 0.384882i
\(189\) 0 0
\(190\) −4.12534 4.12534i −0.299284 0.299284i
\(191\) 9.17881 15.8982i 0.664155 1.15035i −0.315358 0.948973i \(-0.602125\pi\)
0.979514 0.201378i \(-0.0645420\pi\)
\(192\) 0 0
\(193\) 4.24786 15.8532i 0.305767 1.14114i −0.626515 0.779409i \(-0.715519\pi\)
0.932283 0.361731i \(-0.117814\pi\)
\(194\) 22.2531 1.59768
\(195\) 0 0
\(196\) 20.6696 19.4143i 1.47640 1.38673i
\(197\) −5.69553 1.52611i −0.405790 0.108731i 0.0501498 0.998742i \(-0.484030\pi\)
−0.455940 + 0.890011i \(0.650697\pi\)
\(198\) 0 0
\(199\) 9.61483 16.6534i 0.681578 1.18053i −0.292922 0.956136i \(-0.594628\pi\)
0.974499 0.224391i \(-0.0720391\pi\)
\(200\) −16.0656 + 16.0656i −1.13601 + 1.13601i
\(201\) 0 0
\(202\) 8.62496 + 32.1888i 0.606850 + 2.26480i
\(203\) 0.902929 + 0.390675i 0.0633732 + 0.0274200i
\(204\) 0 0
\(205\) −7.35842 + 4.24839i −0.513935 + 0.296720i
\(206\) 39.1020 + 10.4773i 2.72436 + 0.729991i
\(207\) 0 0
\(208\) 13.1978 + 8.19756i 0.915102 + 0.568398i
\(209\) 2.39821i 0.165888i
\(210\) 0 0
\(211\) −4.61920 8.00070i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980070 + 0.198650i \(0.936344\pi\)
\(212\) 17.4614 + 10.0813i 1.19925 + 0.692389i
\(213\) 0 0
\(214\) 10.6430 + 39.7201i 0.727539 + 2.71521i
\(215\) −1.34508 5.01991i −0.0917338 0.342355i
\(216\) 0 0
\(217\) 13.1033 + 1.93420i 0.889507 + 0.131302i
\(218\) −5.35570 + 3.09212i −0.362734 + 0.209425i
\(219\) 0 0
\(220\) 2.03534 0.137223
\(221\) −0.527913 + 16.3823i −0.0355112 + 1.10200i
\(222\) 0 0
\(223\) −0.482353 + 1.80016i −0.0323007 + 0.120548i −0.980194 0.198041i \(-0.936542\pi\)
0.947893 + 0.318589i \(0.103209\pi\)
\(224\) 1.05531 + 0.836340i 0.0705112 + 0.0558803i
\(225\) 0 0
\(226\) −10.3061 + 10.3061i −0.685549 + 0.685549i
\(227\) 5.38143 1.44195i 0.357178 0.0957056i −0.0757678 0.997125i \(-0.524141\pi\)
0.432946 + 0.901420i \(0.357474\pi\)
\(228\) 0 0
\(229\) −0.153144 + 0.153144i −0.0101200 + 0.0101200i −0.712149 0.702029i \(-0.752278\pi\)
0.702029 + 0.712149i \(0.252278\pi\)
\(230\) 2.89615 + 1.67209i 0.190966 + 0.110254i
\(231\) 0 0
\(232\) −0.485580 + 1.81221i −0.0318799 + 0.118977i
\(233\) 19.7822i 1.29598i 0.761650 + 0.647989i \(0.224390\pi\)
−0.761650 + 0.647989i \(0.775610\pi\)
\(234\) 0 0
\(235\) 3.54781 0.231434
\(236\) 4.18944 15.6352i 0.272710 1.01777i
\(237\) 0 0
\(238\) −4.32053 + 29.2694i −0.280058 + 1.89726i
\(239\) 0.636908 0.636908i 0.0411982 0.0411982i −0.686208 0.727406i \(-0.740726\pi\)
0.727406 + 0.686208i \(0.240726\pi\)
\(240\) 0 0
\(241\) 5.16499 + 19.2760i 0.332706 + 1.24168i 0.906335 + 0.422561i \(0.138869\pi\)
−0.573629 + 0.819116i \(0.694465\pi\)
\(242\) −18.2498 18.2498i −1.17314 1.17314i
\(243\) 0 0
\(244\) −23.5574 40.8025i −1.50811 2.61212i
\(245\) −4.34828 + 2.33213i −0.277802 + 0.148994i
\(246\) 0 0
\(247\) −8.85003 + 8.29746i −0.563114 + 0.527955i
\(248\) 25.2585i 1.60392i
\(249\) 0 0
\(250\) 14.2703 8.23896i 0.902533 0.521078i
\(251\) −14.0053 + 24.2580i −0.884010 + 1.53115i −0.0371651 + 0.999309i \(0.511833\pi\)
−0.846845 + 0.531840i \(0.821501\pi\)
\(252\) 0 0
\(253\) 0.355793 + 1.32784i 0.0223685 + 0.0834805i
\(254\) 47.7858 12.8042i 2.99835 0.803405i
\(255\) 0 0
\(256\) 16.1723 28.0113i 1.01077 1.75070i
\(257\) 4.51978 + 7.82849i 0.281936 + 0.488328i 0.971862 0.235553i \(-0.0756900\pi\)
−0.689925 + 0.723880i \(0.742357\pi\)
\(258\) 0 0
\(259\) −2.05391 5.18677i −0.127624 0.322290i
\(260\) −7.04199 7.51095i −0.436726 0.465809i
\(261\) 0 0
\(262\) 7.69071 28.7021i 0.475134 1.77322i
\(263\) 11.6573 + 20.1910i 0.718819 + 1.24503i 0.961468 + 0.274917i \(0.0886503\pi\)
−0.242649 + 0.970114i \(0.578016\pi\)
\(264\) 0 0
\(265\) −2.48075 2.48075i −0.152391 0.152391i
\(266\) −17.5794 + 13.0571i −1.07786 + 0.800581i
\(267\) 0 0
\(268\) −37.3278 37.3278i −2.28016 2.28016i
\(269\) −24.9574 14.4092i −1.52168 0.878543i −0.999672 0.0256040i \(-0.991849\pi\)
−0.522010 0.852939i \(-0.674818\pi\)
\(270\) 0 0
\(271\) 11.9008 + 3.18880i 0.722920 + 0.193706i 0.601474 0.798892i \(-0.294580\pi\)
0.121446 + 0.992598i \(0.461247\pi\)
\(272\) −19.5889 −1.18775
\(273\) 0 0
\(274\) −35.6236 −2.15210
\(275\) 3.10032 + 0.830728i 0.186956 + 0.0500948i
\(276\) 0 0
\(277\) −12.3959 7.15677i −0.744797 0.430009i 0.0790140 0.996874i \(-0.474823\pi\)
−0.823811 + 0.566865i \(0.808156\pi\)
\(278\) −13.9720 13.9720i −0.837987 0.837987i
\(279\) 0 0
\(280\) −5.61057 7.55379i −0.335296 0.451425i
\(281\) 10.7886 + 10.7886i 0.643591 + 0.643591i 0.951437 0.307845i \(-0.0996078\pi\)
−0.307845 + 0.951437i \(0.599608\pi\)
\(282\) 0 0
\(283\) 6.96923 + 12.0711i 0.414278 + 0.717550i 0.995352 0.0963004i \(-0.0307009\pi\)
−0.581075 + 0.813850i \(0.697368\pi\)
\(284\) 8.53485 31.8525i 0.506450 1.89010i
\(285\) 0 0
\(286\) 0.203609 6.31844i 0.0120396 0.373617i
\(287\) 11.7419 + 29.6519i 0.693101 + 1.75030i
\(288\) 0 0
\(289\) −1.83307 3.17497i −0.107828 0.186763i
\(290\) 0.322384 0.558385i 0.0189310 0.0327895i
\(291\) 0 0
\(292\) −3.36957 + 0.902873i −0.197189 + 0.0528367i
\(293\) −4.49081 16.7599i −0.262356 0.979126i −0.963849 0.266450i \(-0.914149\pi\)
0.701493 0.712677i \(-0.252517\pi\)
\(294\) 0 0
\(295\) −1.40825 + 2.43916i −0.0819915 + 0.142013i
\(296\) 9.21312 5.31920i 0.535502 0.309172i
\(297\) 0 0
\(298\) 20.2750i 1.17450i
\(299\) 3.66909 5.90711i 0.212189 0.341617i
\(300\) 0 0
\(301\) −19.3772 + 2.24308i −1.11688 + 0.129289i
\(302\) 7.22375 + 12.5119i 0.415680 + 0.719980i
\(303\) 0 0
\(304\) −10.2519 10.2519i −0.587988 0.587988i
\(305\) 2.12179 + 7.91863i 0.121493 + 0.453419i
\(306\) 0 0
\(307\) 14.5281 14.5281i 0.829164 0.829164i −0.158237 0.987401i \(-0.550581\pi\)
0.987401 + 0.158237i \(0.0505810\pi\)
\(308\) 1.11560 7.55763i 0.0635672 0.430636i
\(309\) 0 0
\(310\) 2.24669 8.38475i 0.127603 0.476222i
\(311\) 7.52888 0.426924 0.213462 0.976951i \(-0.431526\pi\)
0.213462 + 0.976951i \(0.431526\pi\)
\(312\) 0 0
\(313\) 7.90713i 0.446938i −0.974711 0.223469i \(-0.928262\pi\)
0.974711 0.223469i \(-0.0717381\pi\)
\(314\) −9.30570 + 34.7293i −0.525151 + 1.95989i
\(315\) 0 0
\(316\) 34.4356 + 19.8814i 1.93715 + 1.11842i
\(317\) −12.2598 + 12.2598i −0.688580 + 0.688580i −0.961918 0.273338i \(-0.911872\pi\)
0.273338 + 0.961918i \(0.411872\pi\)
\(318\) 0 0
\(319\) 0.256011 0.0685980i 0.0143339 0.00384075i
\(320\) −3.67151 + 3.67151i −0.205243 + 0.205243i
\(321\) 0 0
\(322\) 7.79623 9.83748i 0.434467 0.548221i
\(323\) 3.95882 14.7745i 0.220274 0.822075i
\(324\) 0 0
\(325\) −7.66105 14.3152i −0.424959 0.794065i
\(326\) −18.7230 −1.03697
\(327\) 0 0
\(328\) −52.6699 + 30.4090i −2.90821 + 1.67905i
\(329\) 1.94461 13.1737i 0.107210 0.726292i
\(330\) 0 0
\(331\) 1.27846 + 4.77126i 0.0702703 + 0.262252i 0.992119 0.125297i \(-0.0399884\pi\)
−0.921849 + 0.387549i \(0.873322\pi\)
\(332\) −3.34299 12.4762i −0.183470 0.684720i
\(333\) 0 0
\(334\) −16.7634 9.67835i −0.917252 0.529576i
\(335\) 4.59269 + 7.95477i 0.250925 + 0.434615i
\(336\) 0 0
\(337\) 7.35624i 0.400720i 0.979722 + 0.200360i \(0.0642112\pi\)
−0.979722 + 0.200360i \(0.935789\pi\)
\(338\) −24.0212 + 21.1095i −1.30658 + 1.14821i
\(339\) 0 0
\(340\) 12.5390 + 3.35982i 0.680023 + 0.182212i
\(341\) 3.09022 1.78414i 0.167345 0.0966165i
\(342\) 0 0
\(343\) 6.27632 + 17.4243i 0.338890 + 0.940826i
\(344\) −9.62778 35.9314i −0.519095 1.93729i
\(345\) 0 0
\(346\) −18.6471 + 18.6471i −1.00247 + 1.00247i
\(347\) −1.58494 + 2.74519i −0.0850839 + 0.147370i −0.905427 0.424502i \(-0.860449\pi\)
0.820343 + 0.571872i \(0.193782\pi\)
\(348\) 0 0
\(349\) 26.0697 + 6.98534i 1.39548 + 0.373917i 0.876718 0.481004i \(-0.159728\pi\)
0.518758 + 0.854921i \(0.326395\pi\)
\(350\) −10.7903 27.2489i −0.576766 1.45652i
\(351\) 0 0
\(352\) 0.362757 0.0193350
\(353\) −1.36374 + 5.08954i −0.0725845 + 0.270889i −0.992675 0.120817i \(-0.961448\pi\)
0.920090 + 0.391706i \(0.128115\pi\)
\(354\) 0 0
\(355\) −2.86893 + 4.96913i −0.152267 + 0.263734i
\(356\) −52.0533 52.0533i −2.75882 2.75882i
\(357\) 0 0
\(358\) 23.6824 6.34567i 1.25165 0.335379i
\(359\) −17.8470 17.8470i −0.941927 0.941927i 0.0564767 0.998404i \(-0.482013\pi\)
−0.998404 + 0.0564767i \(0.982013\pi\)
\(360\) 0 0
\(361\) −6.65034 + 3.83958i −0.350018 + 0.202083i
\(362\) −9.42133 2.52444i −0.495174 0.132682i
\(363\) 0 0
\(364\) −31.7495 + 22.0315i −1.66413 + 1.15476i
\(365\) 0.606988 0.0317712
\(366\) 0 0
\(367\) −28.6206 + 16.5241i −1.49398 + 0.862551i −0.999976 0.00690739i \(-0.997801\pi\)
−0.494006 + 0.869458i \(0.664468\pi\)
\(368\) 7.19723 + 4.15532i 0.375181 + 0.216611i
\(369\) 0 0
\(370\) −3.53149 + 0.946261i −0.183594 + 0.0491938i
\(371\) −10.5713 + 7.85179i −0.548832 + 0.407645i
\(372\) 0 0
\(373\) 13.8983 24.0726i 0.719627 1.24643i −0.241521 0.970396i \(-0.577646\pi\)
0.961148 0.276035i \(-0.0890204\pi\)
\(374\) 3.98532 + 6.90278i 0.206076 + 0.356934i
\(375\) 0 0
\(376\) 25.3944 1.30962
\(377\) −1.13891 0.707411i −0.0586567 0.0364335i
\(378\) 0 0
\(379\) 14.6943 + 3.93733i 0.754797 + 0.202247i 0.615645 0.788024i \(-0.288896\pi\)
0.139152 + 0.990271i \(0.455562\pi\)
\(380\) 4.80395 + 8.32069i 0.246438 + 0.426843i
\(381\) 0 0
\(382\) −31.9314 + 31.9314i −1.63375 + 1.63375i
\(383\) 8.30637 2.22568i 0.424436 0.113727i −0.0402774 0.999189i \(-0.512824\pi\)
0.464713 + 0.885461i \(0.346158\pi\)
\(384\) 0 0
\(385\) −0.527855 + 1.21998i −0.0269020 + 0.0621759i
\(386\) −20.1864 + 34.9639i −1.02746 + 1.77962i
\(387\) 0 0
\(388\) −35.3987 9.48505i −1.79710 0.481530i
\(389\) 11.3461i 0.575268i −0.957740 0.287634i \(-0.907131\pi\)
0.957740 0.287634i \(-0.0928686\pi\)
\(390\) 0 0
\(391\) 8.76766i 0.443400i
\(392\) −31.1240 + 16.6929i −1.57200 + 0.843116i
\(393\) 0 0
\(394\) 12.5614 + 7.25232i 0.632833 + 0.365366i
\(395\) −4.89228 4.89228i −0.246157 0.246157i
\(396\) 0 0
\(397\) 4.16966 + 15.5614i 0.209269 + 0.781003i 0.988106 + 0.153776i \(0.0491435\pi\)
−0.778836 + 0.627227i \(0.784190\pi\)
\(398\) −33.4482 + 33.4482i −1.67661 + 1.67661i
\(399\) 0 0
\(400\) 16.8045 9.70209i 0.840226 0.485105i
\(401\) 9.35796 34.9244i 0.467314 1.74404i −0.181787 0.983338i \(-0.558188\pi\)
0.649101 0.760702i \(-0.275145\pi\)
\(402\) 0 0
\(403\) −17.2757 5.23087i −0.860562 0.260568i
\(404\) 54.8801i 2.73039i
\(405\) 0 0
\(406\) −1.89670 1.50314i −0.0941314 0.0745994i
\(407\) −1.30154 0.751444i −0.0645149 0.0372477i
\(408\) 0 0
\(409\) −13.9857 + 3.74745i −0.691547 + 0.185300i −0.587441 0.809267i \(-0.699865\pi\)
−0.104106 + 0.994566i \(0.533198\pi\)
\(410\) 20.1890 5.40962i 0.997062 0.267162i
\(411\) 0 0
\(412\) −57.7350 33.3333i −2.84440 1.64221i
\(413\) 8.28522 + 6.56606i 0.407689 + 0.323095i
\(414\) 0 0
\(415\) 2.24744i 0.110322i
\(416\) −1.25509 1.33867i −0.0615357 0.0656337i
\(417\) 0 0
\(418\) −1.52686 + 5.69832i −0.0746812 + 0.278714i
\(419\) 19.0889 11.0210i 0.932553 0.538410i 0.0449347 0.998990i \(-0.485692\pi\)
0.887618 + 0.460580i \(0.152359\pi\)
\(420\) 0 0
\(421\) −7.69603 + 7.69603i −0.375082 + 0.375082i −0.869324 0.494243i \(-0.835445\pi\)
0.494243 + 0.869324i \(0.335445\pi\)
\(422\) 5.88179 + 21.9511i 0.286321 + 1.06856i
\(423\) 0 0
\(424\) −17.7566 17.7566i −0.862338 0.862338i
\(425\) 17.7286 + 10.2356i 0.859965 + 0.496501i
\(426\) 0 0
\(427\) 30.5665 3.53832i 1.47921 0.171232i
\(428\) 67.7206i 3.27340i
\(429\) 0 0
\(430\) 12.7840i 0.616502i
\(431\) 26.2932 + 7.04525i 1.26650 + 0.339358i 0.828689 0.559709i \(-0.189087\pi\)
0.437812 + 0.899067i \(0.355754\pi\)
\(432\) 0 0
\(433\) 6.55214 11.3486i 0.314876 0.545381i −0.664535 0.747257i \(-0.731371\pi\)
0.979411 + 0.201876i \(0.0647038\pi\)
\(434\) −29.9029 12.9382i −1.43538 0.621054i
\(435\) 0 0
\(436\) 9.83747 2.63594i 0.471129 0.126239i
\(437\) −4.58858 + 4.58858i −0.219502 + 0.219502i
\(438\) 0 0
\(439\) −19.9333 34.5255i −0.951364 1.64781i −0.742477 0.669872i \(-0.766349\pi\)
−0.208887 0.977940i \(-0.566984\pi\)
\(440\) −2.44854 0.656085i −0.116730 0.0312776i
\(441\) 0 0
\(442\) 11.6845 38.5896i 0.555773 1.83552i
\(443\) −23.0066 −1.09308 −0.546539 0.837433i \(-0.684055\pi\)
−0.546539 + 0.837433i \(0.684055\pi\)
\(444\) 0 0
\(445\) 6.40446 + 11.0928i 0.303600 + 0.525851i
\(446\) 2.29221 3.97023i 0.108539 0.187996i
\(447\) 0 0
\(448\) 11.6206 + 15.6455i 0.549024 + 0.739178i
\(449\) −15.6281 + 4.18754i −0.737536 + 0.197622i −0.607983 0.793950i \(-0.708021\pi\)
−0.129553 + 0.991572i \(0.541354\pi\)
\(450\) 0 0
\(451\) 7.44068 + 4.29588i 0.350368 + 0.202285i
\(452\) 20.7870 12.0014i 0.977739 0.564498i
\(453\) 0 0
\(454\) −13.7047 −0.643194
\(455\) 6.32836 2.27303i 0.296678 0.106561i
\(456\) 0 0
\(457\) 0.658952 + 0.176566i 0.0308245 + 0.00825939i 0.274198 0.961673i \(-0.411588\pi\)
−0.243374 + 0.969933i \(0.578254\pi\)
\(458\) 0.461383 0.266380i 0.0215590 0.0124471i
\(459\) 0 0
\(460\) −3.89429 3.89429i −0.181572 0.181572i
\(461\) 8.08252 2.16570i 0.376440 0.100867i −0.0656375 0.997844i \(-0.520908\pi\)
0.442078 + 0.896977i \(0.354241\pi\)
\(462\) 0 0
\(463\) 22.3879 + 22.3879i 1.04045 + 1.04045i 0.999146 + 0.0413082i \(0.0131525\pi\)
0.0413082 + 0.999146i \(0.486847\pi\)
\(464\) 0.801158 1.38765i 0.0371928 0.0644199i
\(465\) 0 0
\(466\) 12.5947 47.0041i 0.583438 2.17742i
\(467\) −13.5832 −0.628554 −0.314277 0.949331i \(-0.601762\pi\)
−0.314277 + 0.949331i \(0.601762\pi\)
\(468\) 0 0
\(469\) 32.0550 12.6935i 1.48016 0.586130i
\(470\) −8.42986 2.25877i −0.388840 0.104189i
\(471\) 0 0
\(472\) −10.0799 + 17.4589i −0.463966 + 0.803613i
\(473\) −3.71591 + 3.71591i −0.170858 + 0.170858i
\(474\) 0 0
\(475\) 3.92148 + 14.6352i 0.179930 + 0.671508i
\(476\) 19.3485 44.7183i 0.886836 2.04966i
\(477\) 0 0
\(478\) −1.91884 + 1.10784i −0.0877656 + 0.0506715i
\(479\) −4.03229 1.08045i −0.184240 0.0493669i 0.165519 0.986207i \(-0.447070\pi\)
−0.349759 + 0.936840i \(0.613737\pi\)
\(480\) 0 0
\(481\) 1.73011 + 7.40292i 0.0788863 + 0.337544i
\(482\) 49.0896i 2.23597i
\(483\) 0 0
\(484\) 21.2518 + 36.8093i 0.965993 + 1.67315i
\(485\) 5.52235 + 3.18833i 0.250757 + 0.144775i
\(486\) 0 0
\(487\) 4.28159 + 15.9791i 0.194018 + 0.724083i 0.992519 + 0.122090i \(0.0389598\pi\)
−0.798501 + 0.601993i \(0.794374\pi\)
\(488\) 15.1873 + 56.6797i 0.687496 + 2.56577i
\(489\) 0 0
\(490\) 11.8166 2.77291i 0.533821 0.125267i
\(491\) −27.7156 + 16.0016i −1.25079 + 0.722143i −0.971266 0.237996i \(-0.923510\pi\)
−0.279523 + 0.960139i \(0.590176\pi\)
\(492\) 0 0
\(493\) 1.69043 0.0761332
\(494\) 26.3111 14.0809i 1.18379 0.633528i
\(495\) 0 0
\(496\) 5.58326 20.8370i 0.250696 0.935609i
\(497\) 16.8789 + 13.3766i 0.757121 + 0.600021i
\(498\) 0 0
\(499\) −14.4246 + 14.4246i −0.645734 + 0.645734i −0.951959 0.306225i \(-0.900934\pi\)
0.306225 + 0.951959i \(0.400934\pi\)
\(500\) −26.2120 + 7.02348i −1.17224 + 0.314100i
\(501\) 0 0
\(502\) 48.7220 48.7220i 2.17457 2.17457i
\(503\) 23.6349 + 13.6456i 1.05383 + 0.608427i 0.923718 0.383072i \(-0.125134\pi\)
0.130109 + 0.991500i \(0.458467\pi\)
\(504\) 0 0
\(505\) −2.47150 + 9.22376i −0.109980 + 0.410452i
\(506\) 3.38157i 0.150329i
\(507\) 0 0
\(508\) −81.4721 −3.61474
\(509\) 8.17110 30.4949i 0.362177 1.35166i −0.509030 0.860749i \(-0.669996\pi\)
0.871207 0.490916i \(-0.163338\pi\)
\(510\) 0 0
\(511\) 0.332699 2.25387i 0.0147177 0.0997054i
\(512\) −29.1956 + 29.1956i −1.29027 + 1.29027i
\(513\) 0 0
\(514\) −5.75519 21.4787i −0.253851 0.947383i
\(515\) 8.20244 + 8.20244i 0.361443 + 0.361443i
\(516\) 0 0
\(517\) −1.79374 3.10684i −0.0788884 0.136639i
\(518\) 1.57800 + 13.6318i 0.0693332 + 0.598948i
\(519\) 0 0
\(520\) 6.05048 + 11.3057i 0.265331 + 0.495790i
\(521\) 13.1042i 0.574107i 0.957915 + 0.287054i \(0.0926758\pi\)
−0.957915 + 0.287054i \(0.907324\pi\)
\(522\) 0 0
\(523\) −7.44365 + 4.29760i −0.325488 + 0.187921i −0.653836 0.756636i \(-0.726841\pi\)
0.328348 + 0.944557i \(0.393508\pi\)
\(524\) −24.4678 + 42.3794i −1.06888 + 1.85135i
\(525\) 0 0
\(526\) −14.8436 55.3971i −0.647212 2.41543i
\(527\) 21.9829 5.89029i 0.957589 0.256585i
\(528\) 0 0
\(529\) −9.64015 + 16.6972i −0.419137 + 0.725966i
\(530\) 4.31503 + 7.47385i 0.187433 + 0.324643i
\(531\) 0 0
\(532\) 33.5295 13.2774i 1.45369 0.575647i
\(533\) −9.89076 42.3213i −0.428417 1.83314i
\(534\) 0 0
\(535\) −3.04977 + 11.3819i −0.131853 + 0.492082i
\(536\) 32.8734 + 56.9384i 1.41991 + 2.45936i
\(537\) 0 0
\(538\) 50.1269 + 50.1269i 2.16112 + 2.16112i
\(539\) 4.24071 + 2.62872i 0.182660 + 0.113227i
\(540\) 0 0
\(541\) 6.09190 + 6.09190i 0.261911 + 0.261911i 0.825830 0.563919i \(-0.190707\pi\)
−0.563919 + 0.825830i \(0.690707\pi\)
\(542\) −26.2469 15.1537i −1.12740 0.650905i
\(543\) 0 0
\(544\) 2.23482 + 0.598817i 0.0958169 + 0.0256741i
\(545\) −1.77210 −0.0759086
\(546\) 0 0
\(547\) 30.2438 1.29313 0.646566 0.762858i \(-0.276205\pi\)
0.646566 + 0.762858i \(0.276205\pi\)
\(548\) 56.6677 + 15.1841i 2.42072 + 0.648631i
\(549\) 0 0
\(550\) −6.83769 3.94774i −0.291560 0.168332i
\(551\) 0.884692 + 0.884692i 0.0376892 + 0.0376892i
\(552\) 0 0
\(553\) −20.8476 + 15.4845i −0.886528 + 0.658468i
\(554\) 24.8971 + 24.8971i 1.05778 + 1.05778i
\(555\) 0 0
\(556\) 16.2704 + 28.1812i 0.690019 + 1.19515i
\(557\) 11.7586 43.8837i 0.498228 1.85941i −0.0129131 0.999917i \(-0.504110\pi\)
0.511141 0.859497i \(-0.329223\pi\)
\(558\) 0 0
\(559\) 26.5692 + 0.856180i 1.12376 + 0.0362126i
\(560\) 2.95871 + 7.47168i 0.125028 + 0.315736i
\(561\) 0 0
\(562\) −18.7657 32.5031i −0.791583 1.37106i
\(563\) −12.5992 + 21.8224i −0.530992 + 0.919704i 0.468354 + 0.883541i \(0.344847\pi\)
−0.999346 + 0.0361636i \(0.988486\pi\)
\(564\) 0 0
\(565\) −4.03418 + 1.08095i −0.169719 + 0.0454761i
\(566\) −8.87415 33.1188i −0.373009 1.39209i
\(567\) 0 0
\(568\) −20.5351 + 35.5679i −0.861634 + 1.49239i
\(569\) −13.9572 + 8.05819i −0.585116 + 0.337817i −0.763164 0.646205i \(-0.776355\pi\)
0.178048 + 0.984022i \(0.443022\pi\)
\(570\) 0 0
\(571\) 13.5825i 0.568409i −0.958764 0.284204i \(-0.908271\pi\)
0.958764 0.284204i \(-0.0917294\pi\)
\(572\) −3.01703 + 9.96418i −0.126149 + 0.416623i
\(573\) 0 0
\(574\) −9.02115 77.9308i −0.376535 3.25277i
\(575\) −4.34249 7.52142i −0.181094 0.313665i
\(576\) 0 0
\(577\) −33.5657 33.5657i −1.39736 1.39736i −0.807528 0.589829i \(-0.799195\pi\)
−0.589829 0.807528i \(-0.700805\pi\)
\(578\) 2.33411 + 8.71103i 0.0970863 + 0.362331i
\(579\) 0 0
\(580\) −0.750831 + 0.750831i −0.0311766 + 0.0311766i
\(581\) 8.34520 + 1.23185i 0.346217 + 0.0511059i
\(582\) 0 0
\(583\) −0.918168 + 3.42665i −0.0380266 + 0.141917i
\(584\) 4.34468 0.179784
\(585\) 0 0
\(586\) 42.6820i 1.76318i
\(587\) −6.29368 + 23.4883i −0.259768 + 0.969467i 0.705607 + 0.708603i \(0.250674\pi\)
−0.965375 + 0.260864i \(0.915992\pi\)
\(588\) 0 0
\(589\) 14.5875 + 8.42210i 0.601067 + 0.347026i
\(590\) 4.89904 4.89904i 0.201690 0.201690i
\(591\) 0 0
\(592\) −8.77613 + 2.35156i −0.360697 + 0.0966484i
\(593\) −10.0628 + 10.0628i −0.413231 + 0.413231i −0.882863 0.469631i \(-0.844387\pi\)
0.469631 + 0.882863i \(0.344387\pi\)
\(594\) 0 0
\(595\) −5.26579 + 6.64451i −0.215876 + 0.272398i
\(596\) −8.64195 + 32.2522i −0.353988 + 1.32110i
\(597\) 0 0
\(598\) −12.4789 + 11.6997i −0.510299 + 0.478438i
\(599\) −15.7719 −0.644422 −0.322211 0.946668i \(-0.604426\pi\)
−0.322211 + 0.946668i \(0.604426\pi\)
\(600\) 0 0
\(601\) −18.2565 + 10.5404i −0.744698 + 0.429952i −0.823775 0.566917i \(-0.808136\pi\)
0.0790767 + 0.996869i \(0.474803\pi\)
\(602\) 47.4698 + 7.00712i 1.93472 + 0.285589i
\(603\) 0 0
\(604\) −6.15805 22.9821i −0.250567 0.935130i
\(605\) −1.91413 7.14365i −0.0778206 0.290431i
\(606\) 0 0
\(607\) 14.6360 + 8.45008i 0.594056 + 0.342978i 0.766700 0.642006i \(-0.221898\pi\)
−0.172644 + 0.984984i \(0.555231\pi\)
\(608\) 0.856205 + 1.48299i 0.0347237 + 0.0601432i
\(609\) 0 0
\(610\) 20.1661i 0.816502i
\(611\) −5.25901 + 17.3686i −0.212757 + 0.702658i
\(612\) 0 0
\(613\) 17.4644 + 4.67958i 0.705381 + 0.189006i 0.593640 0.804731i \(-0.297690\pi\)
0.111742 + 0.993737i \(0.464357\pi\)
\(614\) −43.7695 + 25.2703i −1.76639 + 1.01983i
\(615\) 0 0
\(616\) −3.77826 + 8.73233i −0.152230 + 0.351836i
\(617\) −5.54500 20.6942i −0.223233 0.833118i −0.983105 0.183045i \(-0.941405\pi\)
0.759871 0.650074i \(-0.225262\pi\)
\(618\) 0 0
\(619\) −19.4756 + 19.4756i −0.782790 + 0.782790i −0.980301 0.197511i \(-0.936714\pi\)
0.197511 + 0.980301i \(0.436714\pi\)
\(620\) −7.14777 + 12.3803i −0.287061 + 0.497205i
\(621\) 0 0
\(622\) −17.8892 4.79339i −0.717291 0.192197i
\(623\) 44.7004 17.7009i 1.79088 0.709172i
\(624\) 0 0
\(625\) −17.7939 −0.711756
\(626\) −5.03421 + 18.7879i −0.201208 + 0.750917i
\(627\) 0 0
\(628\) 29.6058 51.2787i 1.18140 2.04624i
\(629\) −6.77788 6.77788i −0.270252 0.270252i
\(630\) 0 0
\(631\) −20.8332 + 5.58224i −0.829356 + 0.222225i −0.648433 0.761272i \(-0.724575\pi\)
−0.180923 + 0.983497i \(0.557909\pi\)
\(632\) −35.0178 35.0178i −1.39293 1.39293i
\(633\) 0 0
\(634\) 36.9357 21.3248i 1.46690 0.846916i
\(635\) 13.6931 + 3.66906i 0.543395 + 0.145602i
\(636\) 0 0
\(637\) −4.97157 24.7444i −0.196981 0.980407i
\(638\) −0.651976 −0.0258120
\(639\) 0 0
\(640\) 11.6827 6.74499i 0.461798 0.266619i
\(641\) −25.3468 14.6340i −1.00114 0.578006i −0.0925521 0.995708i \(-0.529502\pi\)
−0.908584 + 0.417701i \(0.862836\pi\)
\(642\) 0 0
\(643\) −12.4873 + 3.34595i −0.492449 + 0.131951i −0.496494 0.868040i \(-0.665379\pi\)
0.00404423 + 0.999992i \(0.498713\pi\)
\(644\) −16.5948 + 12.3258i −0.653927 + 0.485704i
\(645\) 0 0
\(646\) −18.8129 + 32.5849i −0.740183 + 1.28203i
\(647\) −18.8428 32.6368i −0.740788 1.28308i −0.952137 0.305672i \(-0.901119\pi\)
0.211348 0.977411i \(-0.432215\pi\)
\(648\) 0 0
\(649\) 2.84798 0.111793
\(650\) 9.08921 + 38.8915i 0.356508 + 1.52545i
\(651\) 0 0
\(652\) 29.7833 + 7.98041i 1.16640 + 0.312537i
\(653\) 20.0158 + 34.6685i 0.783280 + 1.35668i 0.930021 + 0.367507i \(0.119788\pi\)
−0.146740 + 0.989175i \(0.546878\pi\)
\(654\) 0 0
\(655\) 6.02086 6.02086i 0.235255 0.235255i
\(656\) 50.1717 13.4435i 1.95888 0.524879i
\(657\) 0 0
\(658\) −13.0078 + 30.0637i −0.507097 + 1.17201i
\(659\) −15.0023 + 25.9848i −0.584407 + 1.01222i 0.410542 + 0.911842i \(0.365340\pi\)
−0.994949 + 0.100381i \(0.967994\pi\)
\(660\) 0 0
\(661\) 19.0751 + 5.11115i 0.741934 + 0.198801i 0.609937 0.792450i \(-0.291195\pi\)
0.131996 + 0.991250i \(0.457861\pi\)
\(662\) 12.1508i 0.472255i
\(663\) 0 0
\(664\) 16.0866i 0.624283i
\(665\) −6.23329 + 0.721556i −0.241717 + 0.0279807i
\(666\) 0 0
\(667\) −0.621087 0.358585i −0.0240486 0.0138845i
\(668\) 22.5408 + 22.5408i 0.872131 + 0.872131i
\(669\) 0 0
\(670\) −5.84803 21.8251i −0.225929 0.843178i
\(671\) 5.86164 5.86164i 0.226286 0.226286i
\(672\) 0 0
\(673\) −39.4906 + 22.7999i −1.52225 + 0.878872i −0.522597 + 0.852580i \(0.675037\pi\)
−0.999654 + 0.0262924i \(0.991630\pi\)
\(674\) 4.68348 17.4790i 0.180401 0.673265i
\(675\) 0 0
\(676\) 47.2090 23.3410i 1.81573 0.897730i
\(677\) 6.55217i 0.251821i 0.992042 + 0.125910i \(0.0401851\pi\)
−0.992042 + 0.125910i \(0.959815\pi\)
\(678\) 0 0
\(679\) 14.8658 18.7580i 0.570497 0.719867i
\(680\) −14.0016 8.08381i −0.536936 0.310000i
\(681\) 0 0
\(682\) −8.47849 + 2.27180i −0.324658 + 0.0869919i
\(683\) −42.6432 + 11.4262i −1.63170 + 0.437212i −0.954408 0.298504i \(-0.903512\pi\)
−0.677290 + 0.735716i \(0.736846\pi\)
\(684\) 0 0
\(685\) −8.84040 5.10401i −0.337774 0.195014i
\(686\) −3.81950 45.3975i −0.145829 1.73328i
\(687\) 0 0
\(688\) 31.7697i 1.21121i
\(689\) 15.8220 8.46743i 0.602769 0.322584i
\(690\) 0 0
\(691\) −8.50701 + 31.7486i −0.323622 + 1.20777i 0.592068 + 0.805888i \(0.298312\pi\)
−0.915690 + 0.401885i \(0.868355\pi\)
\(692\) 37.6106 21.7145i 1.42974 0.825462i
\(693\) 0 0
\(694\) 5.51370 5.51370i 0.209297 0.209297i
\(695\) −1.46546 5.46917i −0.0555881 0.207457i
\(696\) 0 0
\(697\) 38.7480 + 38.7480i 1.46769 + 1.46769i
\(698\) −57.4961 33.1954i −2.17626 1.25646i
\(699\) 0 0
\(700\) 5.55004 + 47.9450i 0.209772 + 1.81215i
\(701\) 8.83206i 0.333582i −0.985992 0.166791i \(-0.946659\pi\)
0.985992 0.166791i \(-0.0533406\pi\)
\(702\) 0 0
\(703\) 7.09444i 0.267572i
\(704\) 5.07144 + 1.35889i 0.191137 + 0.0512150i
\(705\) 0 0
\(706\) 6.48069 11.2249i 0.243904 0.422454i
\(707\) 32.8950 + 14.2329i 1.23715 + 0.535282i
\(708\) 0 0
\(709\) 28.7065 7.69188i 1.07809 0.288874i 0.324279 0.945961i \(-0.394878\pi\)
0.753815 + 0.657087i \(0.228212\pi\)
\(710\) 9.98046 9.98046i 0.374560 0.374560i
\(711\) 0 0
\(712\) 45.8416 + 79.4000i 1.71799 + 2.97564i
\(713\) −9.32628 2.49897i −0.349272 0.0935872i
\(714\) 0 0
\(715\) 0.955809 1.53882i 0.0357452 0.0575486i
\(716\) −40.3771 −1.50896
\(717\) 0 0
\(718\) 31.0431 + 53.7683i 1.15852 + 2.00662i
\(719\) −18.6597 + 32.3196i −0.695890 + 1.20532i 0.273990 + 0.961733i \(0.411657\pi\)
−0.969880 + 0.243584i \(0.921677\pi\)
\(720\) 0 0
\(721\) 34.9532 25.9615i 1.30173 0.966855i
\(722\) 18.2462 4.88907i 0.679055 0.181952i
\(723\) 0 0
\(724\) 13.9108 + 8.03142i 0.516992 + 0.298485i
\(725\) −1.45015 + 0.837245i −0.0538573 + 0.0310945i
\(726\) 0 0
\(727\) 9.88660 0.366674 0.183337 0.983050i \(-0.441310\pi\)
0.183337 + 0.983050i \(0.441310\pi\)
\(728\) 45.2969 16.2698i 1.67881 0.603001i
\(729\) 0 0
\(730\) −1.44225 0.386449i −0.0533800 0.0143031i
\(731\) −29.0264 + 16.7584i −1.07358 + 0.619832i
\(732\) 0 0
\(733\) −14.5543 14.5543i −0.537577 0.537577i 0.385240 0.922817i \(-0.374119\pi\)
−0.922817 + 0.385240i \(0.874119\pi\)
\(734\) 78.5250 21.0407i 2.89841 0.776626i
\(735\) 0 0
\(736\) −0.694076 0.694076i −0.0255840 0.0255840i
\(737\) 4.64403 8.04370i 0.171065 0.296293i
\(738\) 0 0
\(739\) 13.1964 49.2497i 0.485438 1.81168i −0.0926405 0.995700i \(-0.529531\pi\)
0.578079 0.815981i \(-0.303803\pi\)
\(740\) 6.02100 0.221336
\(741\) 0 0
\(742\) 30.1171 11.9261i 1.10563 0.437820i
\(743\) 13.4007 + 3.59070i 0.491623 + 0.131730i 0.496109 0.868260i \(-0.334761\pi\)
−0.00448658 + 0.999990i \(0.501428\pi\)
\(744\) 0 0
\(745\) 2.90493 5.03148i 0.106428 0.184339i
\(746\) −48.3496 + 48.3496i −1.77020 + 1.77020i
\(747\) 0 0
\(748\) −3.39737 12.6792i −0.124220 0.463597i
\(749\) 40.5916 + 17.5630i 1.48319 + 0.641737i
\(750\) 0 0
\(751\) −7.39608 + 4.27013i −0.269887 + 0.155819i −0.628836 0.777538i \(-0.716468\pi\)
0.358949 + 0.933357i \(0.383135\pi\)
\(752\) −20.9491 5.61329i −0.763935 0.204696i
\(753\) 0 0
\(754\) 2.25574 + 2.40597i 0.0821494 + 0.0876201i
\(755\) 4.13996i 0.150669i
\(756\) 0 0
\(757\) −5.08375 8.80531i −0.184772 0.320034i 0.758728 0.651408i \(-0.225821\pi\)
−0.943500 + 0.331374i \(0.892488\pi\)
\(758\) −32.4080 18.7108i −1.17711 0.679606i
\(759\) 0 0
\(760\) −3.09708 11.5585i −0.112343 0.419269i
\(761\) 0.975866 + 3.64198i 0.0353751 + 0.132022i 0.981355 0.192203i \(-0.0615632\pi\)
−0.945980 + 0.324225i \(0.894897\pi\)
\(762\) 0 0
\(763\) −0.971316 + 6.58019i −0.0351640 + 0.238219i
\(764\) 64.4046 37.1840i 2.33008 1.34527i
\(765\) 0 0
\(766\) −21.1536 −0.764309
\(767\) −9.85363 10.5098i −0.355794 0.379488i
\(768\) 0 0
\(769\) 1.12134 4.18491i 0.0404367 0.150912i −0.942756 0.333484i \(-0.891776\pi\)
0.983192 + 0.182572i \(0.0584424\pi\)
\(770\) 2.03094 2.56270i 0.0731901 0.0923531i
\(771\) 0 0
\(772\) 47.0142 47.0142i 1.69208 1.69208i
\(773\) 14.9644 4.00970i 0.538233 0.144219i 0.0205453 0.999789i \(-0.493460\pi\)
0.517687 + 0.855570i \(0.326793\pi\)
\(774\) 0 0
\(775\) −15.9408 + 15.9408i −0.572611 + 0.572611i
\(776\) 39.5277 + 22.8213i 1.41896 + 0.819237i
\(777\) 0 0
\(778\) −7.22366 + 26.9591i −0.258981 + 0.966529i
\(779\) 40.5578i 1.45313i
\(780\) 0 0
\(781\) 5.80200 0.207612
\(782\) 5.58208 20.8326i 0.199615 0.744973i
\(783\) 0 0
\(784\) 29.3656 6.89097i 1.04877 0.246106i
\(785\) −7.28519 + 7.28519i −0.260020 + 0.260020i
\(786\) 0 0
\(787\) −11.1122 41.4712i −0.396106 1.47829i −0.819888 0.572524i \(-0.805964\pi\)
0.423782 0.905764i \(-0.360702\pi\)
\(788\) −16.8906 16.8906i −0.601703 0.601703i
\(789\) 0 0
\(790\) 8.50966 + 14.7392i 0.302760 + 0.524396i
\(791\) 1.80261 + 15.5722i 0.0640936 + 0.553684i
\(792\) 0 0
\(793\) −41.9115 1.35058i −1.48832 0.0479604i
\(794\) 39.6297i 1.40640i
\(795\) 0 0
\(796\) 67.4641 38.9504i 2.39120 1.38056i
\(797\) 23.6527 40.9678i 0.837823 1.45115i −0.0538875 0.998547i \(-0.517161\pi\)
0.891711 0.452606i \(-0.149505\pi\)
\(798\) 0 0
\(799\) −5.92198 22.1011i −0.209505 0.781882i
\(800\) −2.21374 + 0.593170i −0.0782676 + 0.0209717i
\(801\) 0 0
\(802\) −44.4704 + 77.0250i −1.57030 + 2.71985i
\(803\) −0.306887 0.531543i −0.0108298 0.0187578i
\(804\) 0 0
\(805\) 3.34420 1.32427i 0.117867 0.0466744i
\(806\) 37.7179 + 23.4278i 1.32856 + 0.825208i
\(807\) 0 0
\(808\) −17.6904 + 66.0215i −0.622347 + 2.32263i
\(809\) −9.15672 15.8599i −0.321933 0.557604i 0.658954 0.752183i \(-0.270999\pi\)
−0.980887 + 0.194579i \(0.937666\pi\)
\(810\) 0 0
\(811\) 7.95198 + 7.95198i 0.279232 + 0.279232i 0.832802 0.553571i \(-0.186735\pi\)
−0.553571 + 0.832802i \(0.686735\pi\)
\(812\) 2.37645 + 3.19953i 0.0833970 + 0.112282i
\(813\) 0 0
\(814\) 2.61413 + 2.61413i 0.0916253 + 0.0916253i
\(815\) −4.64632 2.68255i −0.162753 0.0939658i
\(816\) 0 0
\(817\) −23.9616 6.42049i −0.838311 0.224625i
\(818\) 35.6169 1.24532
\(819\) 0 0
\(820\) −34.4210 −1.20204
\(821\) 35.4162 + 9.48973i 1.23603 + 0.331194i 0.816926 0.576743i \(-0.195677\pi\)
0.419107 + 0.907937i \(0.362343\pi\)
\(822\) 0 0
\(823\) −14.5778 8.41649i −0.508150 0.293380i 0.223923 0.974607i \(-0.428114\pi\)
−0.732073 + 0.681226i \(0.761447\pi\)
\(824\) 58.7112 + 58.7112i 2.04530 + 2.04530i
\(825\) 0 0
\(826\) −15.5059 20.8764i −0.539519 0.726381i
\(827\) 20.4920 + 20.4920i 0.712578 + 0.712578i 0.967074 0.254496i \(-0.0819096\pi\)
−0.254496 + 0.967074i \(0.581910\pi\)
\(828\) 0 0
\(829\) 2.04801 + 3.54725i 0.0711302 + 0.123201i 0.899397 0.437133i \(-0.144006\pi\)
−0.828267 + 0.560334i \(0.810673\pi\)
\(830\) 1.43087 5.34008i 0.0496662 0.185357i
\(831\) 0 0
\(832\) −12.5318 23.4165i −0.434462 0.811822i
\(833\) 21.7862 + 23.1949i 0.754846 + 0.803656i
\(834\) 0 0
\(835\) −2.77335 4.80358i −0.0959757 0.166235i
\(836\) 4.85766 8.41371i 0.168006 0.290994i
\(837\) 0 0
\(838\) −52.3733 + 14.0334i −1.80920 + 0.484775i
\(839\) 8.69536 + 32.4515i 0.300197 + 1.12035i 0.937001 + 0.349326i \(0.113589\pi\)
−0.636804 + 0.771026i \(0.719744\pi\)
\(840\) 0 0
\(841\) 14.4309 24.9950i 0.497616 0.861896i
\(842\) 23.1861 13.3865i 0.799047 0.461330i
\(843\) 0 0
\(844\) 37.4255i 1.28824i
\(845\) −8.98562 + 1.79691i −0.309115 + 0.0618156i
\(846\) 0 0
\(847\) −27.5750 + 3.19204i −0.947488 + 0.109680i
\(848\) 10.7233 + 18.5733i 0.368240 + 0.637810i
\(849\) 0 0
\(850\) −35.6079 35.6079i −1.22134 1.22134i
\(851\) 1.05252 + 3.92805i 0.0360798 + 0.134652i
\(852\) 0 0
\(853\) −6.65000 + 6.65000i −0.227692 + 0.227692i −0.811728 0.584036i \(-0.801473\pi\)
0.584036 + 0.811728i \(0.301473\pi\)
\(854\) −74.8809 11.0533i −2.56237 0.378237i
\(855\) 0 0
\(856\) −21.8295 + 81.4688i −0.746117 + 2.78455i
\(857\) −38.2819 −1.30768 −0.653842 0.756631i \(-0.726844\pi\)
−0.653842 + 0.756631i \(0.726844\pi\)
\(858\) 0 0
\(859\) 16.5870i 0.565942i −0.959128 0.282971i \(-0.908680\pi\)
0.959128 0.282971i \(-0.0913201\pi\)
\(860\) 5.44902 20.3360i 0.185810 0.693453i
\(861\) 0 0
\(862\) −57.9892 33.4801i −1.97512 1.14034i
\(863\) 11.6109 11.6109i 0.395240 0.395240i −0.481310 0.876550i \(-0.659839\pi\)
0.876550 + 0.481310i \(0.159839\pi\)
\(864\) 0 0
\(865\) −7.29917 + 1.95581i −0.248179 + 0.0664994i
\(866\) −22.7937 + 22.7937i −0.774560 + 0.774560i
\(867\) 0 0
\(868\) 42.0528 + 33.3269i 1.42736 + 1.13119i
\(869\) −1.81072 + 6.75769i −0.0614244 + 0.229239i
\(870\) 0 0
\(871\) −45.7511 + 10.6923i −1.55022 + 0.362296i
\(872\) −12.6843 −0.429545
\(873\) 0 0
\(874\) 13.8242 7.98141i 0.467611 0.269975i
\(875\) 2.58808 17.5329i 0.0874929 0.592721i
\(876\) 0 0
\(877\) −5.37931 20.0759i −0.181646 0.677914i −0.995324 0.0965967i \(-0.969204\pi\)
0.813677 0.581317i \(-0.197462\pi\)
\(878\) 25.3817 + 94.7260i 0.856592 + 3.19685i
\(879\) 0 0
\(880\) 1.87490 + 1.08247i 0.0632029 + 0.0364902i
\(881\) −6.22366 10.7797i −0.209680 0.363177i 0.741934 0.670473i \(-0.233909\pi\)
−0.951614 + 0.307297i \(0.900576\pi\)
\(882\) 0 0
\(883\) 28.9456i 0.974097i −0.873375 0.487049i \(-0.838073\pi\)
0.873375 0.487049i \(-0.161927\pi\)
\(884\) −35.0351 + 56.4054i −1.17836 + 1.89712i
\(885\) 0 0
\(886\) 54.6655 + 14.6476i 1.83652 + 0.492095i
\(887\) −6.26961 + 3.61976i −0.210513 + 0.121540i −0.601550 0.798835i \(-0.705450\pi\)
0.391037 + 0.920375i \(0.372117\pi\)
\(888\) 0 0
\(889\) 21.1294 48.8343i 0.708656 1.63785i
\(890\) −8.15502 30.4349i −0.273357 1.02018i
\(891\) 0 0
\(892\) −5.33855 + 5.33855i −0.178748 + 0.178748i
\(893\) 8.46740 14.6660i 0.283351 0.490778i
\(894\) 0 0
\(895\) 6.78623 + 1.81836i 0.226839 + 0.0607812i
\(896\) −18.6421 47.0771i −0.622788 1.57274i
\(897\) 0 0
\(898\) 39.7996 1.32813
\(899\) −0.481809 + 1.79814i −0.0160692 + 0.0599712i
\(900\) 0 0
\(901\) −11.3130 + 19.5947i −0.376891 + 0.652794i
\(902\) −14.9446 14.9446i −0.497600 0.497600i
\(903\) 0 0
\(904\) −28.8757 + 7.73722i −0.960391 + 0.257336i
\(905\) −1.97632 1.97632i −0.0656950 0.0656950i
\(906\) 0 0
\(907\) 0.515467 0.297605i 0.0171158 0.00988182i −0.491418 0.870924i \(-0.663521\pi\)
0.508533 + 0.861042i \(0.330188\pi\)
\(908\) 21.8006 + 5.84144i 0.723477 + 0.193855i
\(909\) 0 0
\(910\) −16.4838 + 1.37184i −0.546433 + 0.0454760i
\(911\) 23.8117 0.788915 0.394458 0.918914i \(-0.370932\pi\)
0.394458 + 0.918914i \(0.370932\pi\)
\(912\) 0 0
\(913\) 1.96810 1.13628i 0.0651345 0.0376054i
\(914\) −1.45331 0.839066i −0.0480711 0.0277538i
\(915\) 0 0
\(916\) −0.847479 + 0.227081i −0.0280015 + 0.00750297i
\(917\) −19.0566 25.6568i −0.629303 0.847263i
\(918\) 0 0
\(919\) −2.86358 + 4.95987i −0.0944609 + 0.163611i −0.909383 0.415959i \(-0.863446\pi\)
0.814923 + 0.579570i \(0.196779\pi\)
\(920\) 3.42958 + 5.94020i 0.113070 + 0.195843i
\(921\) 0 0
\(922\) −20.5835 −0.677881
\(923\) −20.0741 21.4109i −0.660747 0.704749i
\(924\) 0 0
\(925\) 9.17144 + 2.45748i 0.301555 + 0.0808015i
\(926\) −38.9417 67.4490i −1.27970 2.21651i
\(927\) 0 0
\(928\) −0.133820 + 0.133820i −0.00439286 + 0.00439286i
\(929\) −23.7758 + 6.37070i −0.780058 + 0.209016i −0.626810 0.779172i \(-0.715640\pi\)
−0.153247 + 0.988188i \(0.548973\pi\)
\(930\) 0 0
\(931\) −0.737273 + 23.5410i −0.0241631 + 0.771524i
\(932\) −40.0696 + 69.4026i −1.31252 + 2.27336i
\(933\) 0 0
\(934\) 32.2746 + 8.64795i 1.05606 + 0.282970i
\(935\) 2.28400i 0.0746949i
\(936\) 0 0
\(937\) 26.2867i 0.858749i 0.903127 + 0.429374i \(0.141266\pi\)
−0.903127 + 0.429374i \(0.858734\pi\)
\(938\) −84.2466 + 9.75225i −2.75075 + 0.318422i
\(939\) 0 0
\(940\) 12.4469 + 7.18622i 0.405973 + 0.234389i
\(941\) −2.11330 2.11330i −0.0688916 0.0688916i 0.671821 0.740713i \(-0.265512\pi\)
−0.740713 + 0.671821i \(0.765512\pi\)
\(942\) 0 0
\(943\) −6.01707 22.4560i −0.195943 0.731268i
\(944\) 12.1746 12.1746i 0.396250 0.396250i
\(945\) 0 0
\(946\) 11.1951 6.46348i 0.363983 0.210146i
\(947\) 0.631600 2.35716i 0.0205243 0.0765976i −0.954904 0.296914i \(-0.904042\pi\)
0.975428 + 0.220317i \(0.0707091\pi\)
\(948\) 0 0
\(949\) −0.899753 + 2.97156i −0.0292072 + 0.0964609i
\(950\) 37.2709i 1.20923i
\(951\) 0 0
\(952\) −37.6913 + 47.5599i −1.22158 + 1.54142i
\(953\) 11.0082 + 6.35559i 0.356591 + 0.205878i 0.667584 0.744534i \(-0.267328\pi\)
−0.310994 + 0.950412i \(0.600662\pi\)
\(954\) 0 0
\(955\) −12.4991 + 3.34913i −0.404462 + 0.108375i
\(956\) 3.52456 0.944404i 0.113993 0.0305442i
\(957\) 0 0
\(958\) 8.89312 + 5.13445i 0.287324 + 0.165886i
\(959\) −23.7978 + 30.0286i −0.768470 + 0.969675i
\(960\) 0 0
\(961\) 5.93766i 0.191537i
\(962\) 0.602320 18.6914i 0.0194196 0.602634i
\(963\) 0 0
\(964\) −20.9237 + 78.0885i −0.673908 + 2.51506i
\(965\) −10.0190 + 5.78446i −0.322523 + 0.186209i
\(966\) 0 0
\(967\) −12.3880 + 12.3880i −0.398371 + 0.398371i −0.877658 0.479287i \(-0.840895\pi\)
0.479287 + 0.877658i \(0.340895\pi\)
\(968\) −13.7009 51.1326i −0.440365 1.64346i
\(969\) 0 0
\(970\) −11.0916 11.0916i −0.356130 0.356130i
\(971\) 6.20175 + 3.58058i 0.199024 + 0.114906i 0.596200 0.802836i \(-0.296677\pi\)
−0.397176 + 0.917742i \(0.630010\pi\)
\(972\) 0 0
\(973\) −21.1114 + 2.44382i −0.676800 + 0.0783453i
\(974\) 40.6935i 1.30390i
\(975\) 0 0
\(976\) 50.1149i 1.60414i
\(977\) 3.17102 + 0.849671i 0.101450 + 0.0271834i 0.309187 0.951001i \(-0.399943\pi\)
−0.207737 + 0.978185i \(0.566610\pi\)
\(978\) 0 0
\(979\) 6.47605 11.2169i 0.206976 0.358492i
\(980\) −19.9790 0.625717i −0.638207 0.0199878i
\(981\) 0 0
\(982\) 76.0421 20.3754i 2.42660 0.650206i
\(983\) −10.1688 + 10.1688i −0.324335 + 0.324335i −0.850428 0.526092i \(-0.823657\pi\)
0.526092 + 0.850428i \(0.323657\pi\)
\(984\) 0 0
\(985\) 2.07817 + 3.59949i 0.0662159 + 0.114689i
\(986\) −4.01659 1.07624i −0.127914 0.0342745i
\(987\) 0 0
\(988\) −47.8557 + 11.1842i −1.52249 + 0.355816i
\(989\) 14.2196 0.452156
\(990\) 0 0
\(991\) −4.87954 8.45161i −0.155004 0.268474i 0.778057 0.628194i \(-0.216206\pi\)
−0.933060 + 0.359720i \(0.882872\pi\)
\(992\) −1.27394 + 2.20653i −0.0404476 + 0.0700574i
\(993\) 0 0
\(994\) −31.5891 42.5299i −1.00194 1.34897i
\(995\) −13.0929 + 3.50823i −0.415072 + 0.111218i
\(996\) 0 0
\(997\) −27.8354 16.0708i −0.881555 0.508966i −0.0103840 0.999946i \(-0.503305\pi\)
−0.871171 + 0.490980i \(0.836639\pi\)
\(998\) 43.4576 25.0903i 1.37563 0.794218i
\(999\) 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 819.2.fm.f.496.1 32
3.2 odd 2 273.2.by.c.223.8 yes 32
7.6 odd 2 819.2.fm.e.496.1 32
13.7 odd 12 819.2.fm.e.748.1 32
21.20 even 2 273.2.by.d.223.8 yes 32
39.20 even 12 273.2.by.d.202.8 yes 32
91.20 even 12 inner 819.2.fm.f.748.1 32
273.20 odd 12 273.2.by.c.202.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.by.c.202.8 32 273.20 odd 12
273.2.by.c.223.8 yes 32 3.2 odd 2
273.2.by.d.202.8 yes 32 39.20 even 12
273.2.by.d.223.8 yes 32 21.20 even 2
819.2.fm.e.496.1 32 7.6 odd 2
819.2.fm.e.748.1 32 13.7 odd 12
819.2.fm.f.496.1 32 1.1 even 1 trivial
819.2.fm.f.748.1 32 91.20 even 12 inner