Properties

Label 891.2.f.e.730.6
Level $891$
Weight $2$
Character 891.730
Analytic conductor $7.115$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(82,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.f (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 730.6
Character \(\chi\) \(=\) 891.730
Dual form 891.2.f.e.487.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.467460 + 0.339629i) q^{2} +(-0.514863 - 1.58459i) q^{4} +(2.43063 - 1.76596i) q^{5} +(-0.359795 - 1.10733i) q^{7} +(0.654602 - 2.01466i) q^{8} +1.73599 q^{10} +(-3.11301 - 1.14420i) q^{11} +(3.19252 + 2.31950i) q^{13} +(0.207894 - 0.639831i) q^{14} +(-1.70562 + 1.23921i) q^{16} +(-0.254185 + 0.184677i) q^{17} +(1.96794 - 6.05670i) q^{19} +(-4.04976 - 2.94232i) q^{20} +(-1.06660 - 1.59213i) q^{22} +0.0855002 q^{23} +(1.24428 - 3.82951i) q^{25} +(0.704604 + 2.16855i) q^{26} +(-1.56942 + 1.14025i) q^{28} +(2.37938 + 7.32296i) q^{29} +(-5.28194 - 3.83755i) q^{31} -5.45485 q^{32} -0.181543 q^{34} +(-2.83004 - 2.05614i) q^{35} +(-1.92922 - 5.93753i) q^{37} +(2.97697 - 2.16289i) q^{38} +(-1.96670 - 6.05289i) q^{40} +(-1.79510 + 5.52475i) q^{41} -6.78458 q^{43} +(-0.210303 + 5.52194i) q^{44} +(0.0399679 + 0.0290384i) q^{46} +(0.101276 - 0.311695i) q^{47} +(4.56638 - 3.31767i) q^{49} +(1.88227 - 1.36755i) q^{50} +(2.03174 - 6.25305i) q^{52} +(-1.96000 - 1.42402i) q^{53} +(-9.58718 + 2.71632i) q^{55} -2.46642 q^{56} +(-1.37483 + 4.23130i) q^{58} +(0.709513 + 2.18366i) q^{59} +(11.0732 - 8.04513i) q^{61} +(-1.16575 - 3.58780i) q^{62} +(0.861321 + 0.625787i) q^{64} +11.8560 q^{65} +11.6798 q^{67} +(0.423507 + 0.307696i) q^{68} +(-0.624602 - 1.92233i) q^{70} +(7.05272 - 5.12410i) q^{71} +(0.910538 + 2.80235i) q^{73} +(1.11473 - 3.43078i) q^{74} -10.6106 q^{76} +(-0.146963 + 3.85882i) q^{77} +(7.18989 + 5.22376i) q^{79} +(-1.95735 + 6.02412i) q^{80} +(-2.71551 + 1.97293i) q^{82} +(4.01093 - 2.91411i) q^{83} +(-0.291701 + 0.897762i) q^{85} +(-3.17152 - 2.30424i) q^{86} +(-4.34294 + 5.52265i) q^{88} -2.12862 q^{89} +(1.41981 - 4.36973i) q^{91} +(-0.0440209 - 0.135482i) q^{92} +(0.153203 - 0.111309i) q^{94} +(-5.91254 - 18.1969i) q^{95} +(0.0718724 + 0.0522184i) q^{97} +3.26138 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.467460 + 0.339629i 0.330544 + 0.240154i 0.740661 0.671878i \(-0.234512\pi\)
−0.410117 + 0.912033i \(0.634512\pi\)
\(3\) 0 0
\(4\) −0.514863 1.58459i −0.257432 0.792293i
\(5\) 2.43063 1.76596i 1.08701 0.789761i 0.108120 0.994138i \(-0.465517\pi\)
0.978892 + 0.204377i \(0.0655169\pi\)
\(6\) 0 0
\(7\) −0.359795 1.10733i −0.135990 0.418533i 0.859753 0.510710i \(-0.170617\pi\)
−0.995743 + 0.0921770i \(0.970617\pi\)
\(8\) 0.654602 2.01466i 0.231437 0.712289i
\(9\) 0 0
\(10\) 1.73599 0.548970
\(11\) −3.11301 1.14420i −0.938607 0.344988i
\(12\) 0 0
\(13\) 3.19252 + 2.31950i 0.885446 + 0.643314i 0.934687 0.355473i \(-0.115680\pi\)
−0.0492409 + 0.998787i \(0.515680\pi\)
\(14\) 0.207894 0.639831i 0.0555619 0.171002i
\(15\) 0 0
\(16\) −1.70562 + 1.23921i −0.426406 + 0.309802i
\(17\) −0.254185 + 0.184677i −0.0616490 + 0.0447906i −0.618183 0.786034i \(-0.712131\pi\)
0.556534 + 0.830825i \(0.312131\pi\)
\(18\) 0 0
\(19\) 1.96794 6.05670i 0.451477 1.38950i −0.423746 0.905781i \(-0.639285\pi\)
0.875222 0.483721i \(-0.160715\pi\)
\(20\) −4.04976 2.94232i −0.905554 0.657923i
\(21\) 0 0
\(22\) −1.06660 1.59213i −0.227401 0.339444i
\(23\) 0.0855002 0.0178280 0.00891401 0.999960i \(-0.497163\pi\)
0.00891401 + 0.999960i \(0.497163\pi\)
\(24\) 0 0
\(25\) 1.24428 3.82951i 0.248857 0.765902i
\(26\) 0.704604 + 2.16855i 0.138184 + 0.425287i
\(27\) 0 0
\(28\) −1.56942 + 1.14025i −0.296593 + 0.215487i
\(29\) 2.37938 + 7.32296i 0.441839 + 1.35984i 0.885914 + 0.463850i \(0.153532\pi\)
−0.444075 + 0.895990i \(0.646468\pi\)
\(30\) 0 0
\(31\) −5.28194 3.83755i −0.948664 0.689245i 0.00182628 0.999998i \(-0.499419\pi\)
−0.950491 + 0.310753i \(0.899419\pi\)
\(32\) −5.45485 −0.964291
\(33\) 0 0
\(34\) −0.181543 −0.0311344
\(35\) −2.83004 2.05614i −0.478363 0.347551i
\(36\) 0 0
\(37\) −1.92922 5.93753i −0.317162 0.976124i −0.974855 0.222838i \(-0.928468\pi\)
0.657694 0.753286i \(-0.271532\pi\)
\(38\) 2.97697 2.16289i 0.482928 0.350868i
\(39\) 0 0
\(40\) −1.96670 6.05289i −0.310963 0.957046i
\(41\) −1.79510 + 5.52475i −0.280348 + 0.862822i 0.707407 + 0.706807i \(0.249865\pi\)
−0.987755 + 0.156015i \(0.950135\pi\)
\(42\) 0 0
\(43\) −6.78458 −1.03464 −0.517320 0.855792i \(-0.673070\pi\)
−0.517320 + 0.855792i \(0.673070\pi\)
\(44\) −0.210303 + 5.52194i −0.0317043 + 0.832463i
\(45\) 0 0
\(46\) 0.0399679 + 0.0290384i 0.00589294 + 0.00428147i
\(47\) 0.101276 0.311695i 0.0147726 0.0454654i −0.943398 0.331661i \(-0.892391\pi\)
0.958171 + 0.286196i \(0.0923908\pi\)
\(48\) 0 0
\(49\) 4.56638 3.31767i 0.652340 0.473953i
\(50\) 1.88227 1.36755i 0.266193 0.193400i
\(51\) 0 0
\(52\) 2.03174 6.25305i 0.281752 0.867142i
\(53\) −1.96000 1.42402i −0.269227 0.195605i 0.444978 0.895541i \(-0.353211\pi\)
−0.714205 + 0.699937i \(0.753211\pi\)
\(54\) 0 0
\(55\) −9.58718 + 2.71632i −1.29274 + 0.366269i
\(56\) −2.46642 −0.329589
\(57\) 0 0
\(58\) −1.37483 + 4.23130i −0.180524 + 0.555596i
\(59\) 0.709513 + 2.18366i 0.0923707 + 0.284288i 0.986560 0.163402i \(-0.0522468\pi\)
−0.894189 + 0.447690i \(0.852247\pi\)
\(60\) 0 0
\(61\) 11.0732 8.04513i 1.41778 1.03007i 0.425641 0.904892i \(-0.360049\pi\)
0.992134 0.125182i \(-0.0399515\pi\)
\(62\) −1.16575 3.58780i −0.148050 0.455652i
\(63\) 0 0
\(64\) 0.861321 + 0.625787i 0.107665 + 0.0782233i
\(65\) 11.8560 1.47055
\(66\) 0 0
\(67\) 11.6798 1.42691 0.713456 0.700700i \(-0.247129\pi\)
0.713456 + 0.700700i \(0.247129\pi\)
\(68\) 0.423507 + 0.307696i 0.0513578 + 0.0373136i
\(69\) 0 0
\(70\) −0.624602 1.92233i −0.0746542 0.229762i
\(71\) 7.05272 5.12410i 0.837004 0.608119i −0.0845279 0.996421i \(-0.526938\pi\)
0.921532 + 0.388302i \(0.126938\pi\)
\(72\) 0 0
\(73\) 0.910538 + 2.80235i 0.106570 + 0.327990i 0.990096 0.140393i \(-0.0448367\pi\)
−0.883525 + 0.468383i \(0.844837\pi\)
\(74\) 1.11473 3.43078i 0.129584 0.398820i
\(75\) 0 0
\(76\) −10.6106 −1.21712
\(77\) −0.146963 + 3.85882i −0.0167480 + 0.439753i
\(78\) 0 0
\(79\) 7.18989 + 5.22376i 0.808926 + 0.587719i 0.913519 0.406796i \(-0.133354\pi\)
−0.104593 + 0.994515i \(0.533354\pi\)
\(80\) −1.95735 + 6.02412i −0.218839 + 0.673517i
\(81\) 0 0
\(82\) −2.71551 + 1.97293i −0.299878 + 0.217874i
\(83\) 4.01093 2.91411i 0.440257 0.319865i −0.345480 0.938426i \(-0.612284\pi\)
0.785737 + 0.618561i \(0.212284\pi\)
\(84\) 0 0
\(85\) −0.291701 + 0.897762i −0.0316394 + 0.0973760i
\(86\) −3.17152 2.30424i −0.341994 0.248473i
\(87\) 0 0
\(88\) −4.34294 + 5.52265i −0.462959 + 0.588717i
\(89\) −2.12862 −0.225634 −0.112817 0.993616i \(-0.535987\pi\)
−0.112817 + 0.993616i \(0.535987\pi\)
\(90\) 0 0
\(91\) 1.41981 4.36973i 0.148837 0.458072i
\(92\) −0.0440209 0.135482i −0.00458950 0.0141250i
\(93\) 0 0
\(94\) 0.153203 0.111309i 0.0158017 0.0114806i
\(95\) −5.91254 18.1969i −0.606613 1.86696i
\(96\) 0 0
\(97\) 0.0718724 + 0.0522184i 0.00729754 + 0.00530197i 0.591428 0.806358i \(-0.298564\pi\)
−0.584131 + 0.811660i \(0.698564\pi\)
\(98\) 3.26138 0.329449
\(99\) 0 0
\(100\) −6.70883 −0.670883
\(101\) −1.66373 1.20877i −0.165547 0.120277i 0.501927 0.864910i \(-0.332625\pi\)
−0.667474 + 0.744633i \(0.732625\pi\)
\(102\) 0 0
\(103\) −0.932216 2.86907i −0.0918540 0.282698i 0.894567 0.446934i \(-0.147484\pi\)
−0.986421 + 0.164236i \(0.947484\pi\)
\(104\) 6.76283 4.91348i 0.663150 0.481807i
\(105\) 0 0
\(106\) −0.432581 1.33135i −0.0420160 0.129312i
\(107\) −3.70600 + 11.4059i −0.358272 + 1.10265i 0.595815 + 0.803121i \(0.296829\pi\)
−0.954088 + 0.299527i \(0.903171\pi\)
\(108\) 0 0
\(109\) 5.20013 0.498082 0.249041 0.968493i \(-0.419885\pi\)
0.249041 + 0.968493i \(0.419885\pi\)
\(110\) −5.40417 1.98632i −0.515267 0.189388i
\(111\) 0 0
\(112\) 1.98589 + 1.44283i 0.187649 + 0.136335i
\(113\) −5.94164 + 18.2865i −0.558943 + 1.72025i 0.126355 + 0.991985i \(0.459672\pi\)
−0.685298 + 0.728263i \(0.740328\pi\)
\(114\) 0 0
\(115\) 0.207820 0.150990i 0.0193793 0.0140799i
\(116\) 10.3788 7.54065i 0.963649 0.700132i
\(117\) 0 0
\(118\) −0.409965 + 1.26174i −0.0377403 + 0.116153i
\(119\) 0.295953 + 0.215023i 0.0271300 + 0.0197111i
\(120\) 0 0
\(121\) 8.38163 + 7.12378i 0.761967 + 0.647616i
\(122\) 7.90863 0.716014
\(123\) 0 0
\(124\) −3.36146 + 10.3455i −0.301868 + 0.929054i
\(125\) 0.903736 + 2.78141i 0.0808326 + 0.248777i
\(126\) 0 0
\(127\) 10.6652 7.74873i 0.946384 0.687588i −0.00356461 0.999994i \(-0.501135\pi\)
0.949949 + 0.312405i \(0.101135\pi\)
\(128\) 3.56138 + 10.9608i 0.314785 + 0.968808i
\(129\) 0 0
\(130\) 5.54220 + 4.02664i 0.486083 + 0.353160i
\(131\) 17.9718 1.57020 0.785100 0.619369i \(-0.212611\pi\)
0.785100 + 0.619369i \(0.212611\pi\)
\(132\) 0 0
\(133\) −7.41484 −0.642949
\(134\) 5.45983 + 3.96680i 0.471657 + 0.342679i
\(135\) 0 0
\(136\) 0.205670 + 0.632986i 0.0176360 + 0.0542781i
\(137\) −13.2693 + 9.64070i −1.13367 + 0.823661i −0.986225 0.165409i \(-0.947105\pi\)
−0.147447 + 0.989070i \(0.547105\pi\)
\(138\) 0 0
\(139\) −3.67780 11.3191i −0.311947 0.960073i −0.976993 0.213271i \(-0.931588\pi\)
0.665046 0.746802i \(-0.268412\pi\)
\(140\) −1.80105 + 5.54307i −0.152217 + 0.468475i
\(141\) 0 0
\(142\) 5.03716 0.422709
\(143\) −7.28438 10.8735i −0.609150 0.909287i
\(144\) 0 0
\(145\) 18.7154 + 13.5976i 1.55423 + 1.12922i
\(146\) −0.526120 + 1.61923i −0.0435420 + 0.134008i
\(147\) 0 0
\(148\) −8.41525 + 6.11403i −0.691729 + 0.502571i
\(149\) −3.66623 + 2.66368i −0.300350 + 0.218217i −0.727745 0.685848i \(-0.759431\pi\)
0.427395 + 0.904065i \(0.359431\pi\)
\(150\) 0 0
\(151\) −0.905687 + 2.78742i −0.0737037 + 0.226837i −0.981121 0.193393i \(-0.938051\pi\)
0.907418 + 0.420230i \(0.138051\pi\)
\(152\) −10.9140 7.92945i −0.885239 0.643164i
\(153\) 0 0
\(154\) −1.37927 + 1.75393i −0.111144 + 0.141336i
\(155\) −19.6154 −1.57555
\(156\) 0 0
\(157\) −5.57888 + 17.1700i −0.445243 + 1.37032i 0.436974 + 0.899474i \(0.356050\pi\)
−0.882217 + 0.470843i \(0.843950\pi\)
\(158\) 1.58684 + 4.88380i 0.126242 + 0.388534i
\(159\) 0 0
\(160\) −13.2587 + 9.63304i −1.04820 + 0.761559i
\(161\) −0.0307625 0.0946773i −0.00242443 0.00746161i
\(162\) 0 0
\(163\) 4.71129 + 3.42295i 0.369017 + 0.268106i 0.756803 0.653643i \(-0.226760\pi\)
−0.387786 + 0.921749i \(0.626760\pi\)
\(164\) 9.67868 0.755778
\(165\) 0 0
\(166\) 2.86467 0.222341
\(167\) −4.06266 2.95170i −0.314378 0.228409i 0.419395 0.907804i \(-0.362242\pi\)
−0.733773 + 0.679395i \(0.762242\pi\)
\(168\) 0 0
\(169\) 0.794875 + 2.44637i 0.0611442 + 0.188182i
\(170\) −0.441265 + 0.320598i −0.0338435 + 0.0245887i
\(171\) 0 0
\(172\) 3.49313 + 10.7508i 0.266349 + 0.819738i
\(173\) 4.81753 14.8268i 0.366270 1.12726i −0.582912 0.812536i \(-0.698087\pi\)
0.949182 0.314728i \(-0.101913\pi\)
\(174\) 0 0
\(175\) −4.68824 −0.354397
\(176\) 6.72751 1.90610i 0.507105 0.143677i
\(177\) 0 0
\(178\) −0.995046 0.722943i −0.0745818 0.0541869i
\(179\) −2.17822 + 6.70387i −0.162808 + 0.501071i −0.998868 0.0475668i \(-0.984853\pi\)
0.836060 + 0.548638i \(0.184853\pi\)
\(180\) 0 0
\(181\) −2.02068 + 1.46811i −0.150196 + 0.109124i −0.660345 0.750962i \(-0.729590\pi\)
0.510149 + 0.860086i \(0.329590\pi\)
\(182\) 2.14779 1.56046i 0.159205 0.115669i
\(183\) 0 0
\(184\) 0.0559686 0.172254i 0.00412606 0.0126987i
\(185\) −15.1747 11.0250i −1.11566 0.810577i
\(186\) 0 0
\(187\) 1.00259 0.284062i 0.0733165 0.0207727i
\(188\) −0.546051 −0.0398249
\(189\) 0 0
\(190\) 3.41633 10.5144i 0.247847 0.762795i
\(191\) 3.65350 + 11.2443i 0.264358 + 0.813611i 0.991841 + 0.127484i \(0.0406902\pi\)
−0.727483 + 0.686126i \(0.759310\pi\)
\(192\) 0 0
\(193\) −5.45816 + 3.96559i −0.392887 + 0.285449i −0.766637 0.642080i \(-0.778072\pi\)
0.373751 + 0.927529i \(0.378072\pi\)
\(194\) 0.0158626 + 0.0488200i 0.00113887 + 0.00350507i
\(195\) 0 0
\(196\) −7.60820 5.52768i −0.543443 0.394834i
\(197\) 20.6474 1.47107 0.735534 0.677488i \(-0.236931\pi\)
0.735534 + 0.677488i \(0.236931\pi\)
\(198\) 0 0
\(199\) −13.2862 −0.941832 −0.470916 0.882178i \(-0.656077\pi\)
−0.470916 + 0.882178i \(0.656077\pi\)
\(200\) −6.90064 5.01361i −0.487949 0.354516i
\(201\) 0 0
\(202\) −0.367193 1.13010i −0.0258356 0.0795138i
\(203\) 7.25288 5.26953i 0.509053 0.369848i
\(204\) 0 0
\(205\) 5.39325 + 16.5987i 0.376681 + 1.15931i
\(206\) 0.538646 1.65778i 0.0375292 0.115503i
\(207\) 0 0
\(208\) −8.31958 −0.576859
\(209\) −13.0563 + 16.6028i −0.903120 + 1.14844i
\(210\) 0 0
\(211\) 6.75126 + 4.90508i 0.464776 + 0.337680i 0.795402 0.606082i \(-0.207260\pi\)
−0.330626 + 0.943762i \(0.607260\pi\)
\(212\) −1.24736 + 3.83897i −0.0856688 + 0.263661i
\(213\) 0 0
\(214\) −5.60618 + 4.07313i −0.383231 + 0.278433i
\(215\) −16.4908 + 11.9813i −1.12467 + 0.817117i
\(216\) 0 0
\(217\) −2.34904 + 7.22960i −0.159463 + 0.490778i
\(218\) 2.43085 + 1.76612i 0.164638 + 0.119616i
\(219\) 0 0
\(220\) 9.24034 + 13.7932i 0.622984 + 0.929936i
\(221\) −1.23985 −0.0834013
\(222\) 0 0
\(223\) −0.118556 + 0.364878i −0.00793910 + 0.0244340i −0.954948 0.296774i \(-0.904089\pi\)
0.947008 + 0.321209i \(0.104089\pi\)
\(224\) 1.96263 + 6.04035i 0.131134 + 0.403588i
\(225\) 0 0
\(226\) −8.98811 + 6.53024i −0.597880 + 0.434385i
\(227\) −5.56664 17.1324i −0.369471 1.13711i −0.947134 0.320839i \(-0.896035\pi\)
0.577663 0.816276i \(-0.303965\pi\)
\(228\) 0 0
\(229\) −10.8634 7.89270i −0.717872 0.521565i 0.167832 0.985816i \(-0.446324\pi\)
−0.885704 + 0.464251i \(0.846324\pi\)
\(230\) 0.148428 0.00978704
\(231\) 0 0
\(232\) 16.3108 1.07086
\(233\) −2.72611 1.98063i −0.178593 0.129756i 0.494897 0.868952i \(-0.335206\pi\)
−0.673490 + 0.739196i \(0.735206\pi\)
\(234\) 0 0
\(235\) −0.304276 0.936466i −0.0198488 0.0610883i
\(236\) 3.09489 2.24857i 0.201460 0.146369i
\(237\) 0 0
\(238\) 0.0653183 + 0.201029i 0.00423395 + 0.0130308i
\(239\) 7.16820 22.0615i 0.463673 1.42704i −0.396972 0.917831i \(-0.629939\pi\)
0.860644 0.509207i \(-0.170061\pi\)
\(240\) 0 0
\(241\) 15.1641 0.976807 0.488404 0.872618i \(-0.337579\pi\)
0.488404 + 0.872618i \(0.337579\pi\)
\(242\) 1.49863 + 6.17673i 0.0963358 + 0.397055i
\(243\) 0 0
\(244\) −18.4494 13.4043i −1.18110 0.858120i
\(245\) 5.24033 16.1281i 0.334792 1.03039i
\(246\) 0 0
\(247\) 20.3312 14.7715i 1.29364 0.939887i
\(248\) −11.1889 + 8.12923i −0.710497 + 0.516207i
\(249\) 0 0
\(250\) −0.522189 + 1.60713i −0.0330262 + 0.101644i
\(251\) −0.471095 0.342271i −0.0297353 0.0216039i 0.572818 0.819682i \(-0.305850\pi\)
−0.602554 + 0.798078i \(0.705850\pi\)
\(252\) 0 0
\(253\) −0.266163 0.0978289i −0.0167335 0.00615045i
\(254\) 7.61725 0.477949
\(255\) 0 0
\(256\) −1.39982 + 4.30820i −0.0874887 + 0.269263i
\(257\) 3.39036 + 10.4344i 0.211485 + 0.650883i 0.999385 + 0.0350793i \(0.0111684\pi\)
−0.787900 + 0.615803i \(0.788832\pi\)
\(258\) 0 0
\(259\) −5.88071 + 4.27258i −0.365409 + 0.265485i
\(260\) −6.10421 18.7868i −0.378567 1.16511i
\(261\) 0 0
\(262\) 8.40108 + 6.10374i 0.519020 + 0.377090i
\(263\) 14.3954 0.887656 0.443828 0.896112i \(-0.353620\pi\)
0.443828 + 0.896112i \(0.353620\pi\)
\(264\) 0 0
\(265\) −7.27881 −0.447134
\(266\) −3.46614 2.51830i −0.212523 0.154407i
\(267\) 0 0
\(268\) −6.01349 18.5076i −0.367333 1.13053i
\(269\) 0.395590 0.287413i 0.0241195 0.0175239i −0.575660 0.817689i \(-0.695255\pi\)
0.599780 + 0.800165i \(0.295255\pi\)
\(270\) 0 0
\(271\) 6.77950 + 20.8652i 0.411825 + 1.26747i 0.915060 + 0.403318i \(0.132143\pi\)
−0.503234 + 0.864150i \(0.667857\pi\)
\(272\) 0.204692 0.629977i 0.0124113 0.0381980i
\(273\) 0 0
\(274\) −9.47712 −0.572534
\(275\) −8.25517 + 10.4976i −0.497806 + 0.633029i
\(276\) 0 0
\(277\) −2.32149 1.68666i −0.139485 0.101342i 0.515855 0.856676i \(-0.327474\pi\)
−0.655340 + 0.755334i \(0.727474\pi\)
\(278\) 2.12508 6.54031i 0.127454 0.392262i
\(279\) 0 0
\(280\) −5.99497 + 4.35560i −0.358268 + 0.260297i
\(281\) 14.7064 10.6848i 0.877308 0.637402i −0.0552299 0.998474i \(-0.517589\pi\)
0.932538 + 0.361072i \(0.117589\pi\)
\(282\) 0 0
\(283\) −6.34632 + 19.5320i −0.377249 + 1.16105i 0.564699 + 0.825297i \(0.308992\pi\)
−0.941949 + 0.335757i \(0.891008\pi\)
\(284\) −11.7508 8.53744i −0.697280 0.506604i
\(285\) 0 0
\(286\) 0.287805 7.55691i 0.0170183 0.446849i
\(287\) 6.76362 0.399244
\(288\) 0 0
\(289\) −5.22278 + 16.0741i −0.307223 + 0.945534i
\(290\) 4.13058 + 12.7126i 0.242556 + 0.746511i
\(291\) 0 0
\(292\) 3.97176 2.88565i 0.232430 0.168870i
\(293\) −0.265775 0.817972i −0.0155268 0.0477864i 0.942993 0.332813i \(-0.107998\pi\)
−0.958520 + 0.285026i \(0.907998\pi\)
\(294\) 0 0
\(295\) 5.58081 + 4.05470i 0.324927 + 0.236074i
\(296\) −13.2250 −0.768685
\(297\) 0 0
\(298\) −2.61848 −0.151684
\(299\) 0.272961 + 0.198318i 0.0157857 + 0.0114690i
\(300\) 0 0
\(301\) 2.44106 + 7.51280i 0.140700 + 0.433031i
\(302\) −1.37006 + 0.995408i −0.0788382 + 0.0572793i
\(303\) 0 0
\(304\) 4.14894 + 12.7691i 0.237958 + 0.732360i
\(305\) 12.7075 39.1095i 0.727627 2.23941i
\(306\) 0 0
\(307\) 3.48920 0.199139 0.0995696 0.995031i \(-0.468253\pi\)
0.0995696 + 0.995031i \(0.468253\pi\)
\(308\) 6.19029 1.75389i 0.352725 0.0999370i
\(309\) 0 0
\(310\) −9.16942 6.66197i −0.520788 0.378375i
\(311\) −3.35138 + 10.3145i −0.190039 + 0.584881i −0.999999 0.00160485i \(-0.999489\pi\)
0.809959 + 0.586486i \(0.199489\pi\)
\(312\) 0 0
\(313\) 22.8799 16.6232i 1.29325 0.939598i 0.293381 0.955996i \(-0.405220\pi\)
0.999866 + 0.0163974i \(0.00521967\pi\)
\(314\) −8.43935 + 6.13155i −0.476260 + 0.346023i
\(315\) 0 0
\(316\) 4.57569 14.0825i 0.257403 0.792204i
\(317\) −0.900053 0.653927i −0.0505520 0.0367282i 0.562222 0.826986i \(-0.309947\pi\)
−0.612774 + 0.790258i \(0.709947\pi\)
\(318\) 0 0
\(319\) 0.971887 25.5189i 0.0544152 1.42878i
\(320\) 3.19867 0.178811
\(321\) 0 0
\(322\) 0.0177750 0.0547057i 0.000990559 0.00304863i
\(323\) 0.618308 + 1.90296i 0.0344036 + 0.105883i
\(324\) 0 0
\(325\) 12.8550 9.33967i 0.713065 0.518072i
\(326\) 1.03980 + 3.20018i 0.0575894 + 0.177242i
\(327\) 0 0
\(328\) 9.95541 + 7.23303i 0.549696 + 0.399377i
\(329\) −0.381589 −0.0210377
\(330\) 0 0
\(331\) −12.3783 −0.680373 −0.340187 0.940358i \(-0.610490\pi\)
−0.340187 + 0.940358i \(0.610490\pi\)
\(332\) −6.68275 4.85530i −0.366763 0.266469i
\(333\) 0 0
\(334\) −0.896648 2.75960i −0.0490624 0.150999i
\(335\) 28.3893 20.6260i 1.55107 1.12692i
\(336\) 0 0
\(337\) 4.16358 + 12.8142i 0.226804 + 0.698032i 0.998103 + 0.0615594i \(0.0196074\pi\)
−0.771299 + 0.636473i \(0.780393\pi\)
\(338\) −0.459288 + 1.41354i −0.0249820 + 0.0768866i
\(339\) 0 0
\(340\) 1.57277 0.0852953
\(341\) 12.0518 + 17.9899i 0.652642 + 0.974208i
\(342\) 0 0
\(343\) −11.9104 8.65342i −0.643102 0.467241i
\(344\) −4.44120 + 13.6686i −0.239453 + 0.736962i
\(345\) 0 0
\(346\) 7.28763 5.29478i 0.391786 0.284649i
\(347\) 7.87915 5.72454i 0.422975 0.307309i −0.355859 0.934540i \(-0.615812\pi\)
0.778834 + 0.627230i \(0.215812\pi\)
\(348\) 0 0
\(349\) −1.37210 + 4.22288i −0.0734466 + 0.226045i −0.981040 0.193804i \(-0.937917\pi\)
0.907594 + 0.419850i \(0.137917\pi\)
\(350\) −2.19156 1.59226i −0.117144 0.0851100i
\(351\) 0 0
\(352\) 16.9810 + 6.24142i 0.905090 + 0.332669i
\(353\) −32.5235 −1.73105 −0.865527 0.500863i \(-0.833016\pi\)
−0.865527 + 0.500863i \(0.833016\pi\)
\(354\) 0 0
\(355\) 8.09363 24.9096i 0.429565 1.32207i
\(356\) 1.09595 + 3.37299i 0.0580852 + 0.178768i
\(357\) 0 0
\(358\) −3.29506 + 2.39400i −0.174149 + 0.126527i
\(359\) 8.58143 + 26.4109i 0.452911 + 1.39392i 0.873571 + 0.486697i \(0.161799\pi\)
−0.420660 + 0.907218i \(0.638201\pi\)
\(360\) 0 0
\(361\) −17.4395 12.6705i −0.917868 0.666870i
\(362\) −1.44320 −0.0758529
\(363\) 0 0
\(364\) −7.65523 −0.401243
\(365\) 7.16201 + 5.20351i 0.374877 + 0.272364i
\(366\) 0 0
\(367\) 0.362229 + 1.11483i 0.0189082 + 0.0581934i 0.960065 0.279776i \(-0.0902601\pi\)
−0.941157 + 0.337969i \(0.890260\pi\)
\(368\) −0.145831 + 0.105952i −0.00760197 + 0.00552315i
\(369\) 0 0
\(370\) −3.34912 10.3075i −0.174112 0.535862i
\(371\) −0.871672 + 2.68273i −0.0452550 + 0.139280i
\(372\) 0 0
\(373\) 21.7668 1.12704 0.563520 0.826102i \(-0.309447\pi\)
0.563520 + 0.826102i \(0.309447\pi\)
\(374\) 0.565145 + 0.207721i 0.0292230 + 0.0107410i
\(375\) 0 0
\(376\) −0.561664 0.408072i −0.0289656 0.0210447i
\(377\) −9.38942 + 28.8977i −0.483580 + 1.48831i
\(378\) 0 0
\(379\) 13.1440 9.54967i 0.675161 0.490533i −0.196588 0.980486i \(-0.562986\pi\)
0.871749 + 0.489953i \(0.162986\pi\)
\(380\) −25.7904 + 18.7379i −1.32302 + 0.961232i
\(381\) 0 0
\(382\) −2.11104 + 6.49710i −0.108010 + 0.332421i
\(383\) 5.01052 + 3.64036i 0.256026 + 0.186014i 0.708393 0.705818i \(-0.249420\pi\)
−0.452367 + 0.891832i \(0.649420\pi\)
\(384\) 0 0
\(385\) 6.45730 + 9.63890i 0.329094 + 0.491244i
\(386\) −3.89830 −0.198418
\(387\) 0 0
\(388\) 0.0457401 0.140773i 0.00232210 0.00714669i
\(389\) 0.223485 + 0.687817i 0.0113312 + 0.0348737i 0.956562 0.291528i \(-0.0941637\pi\)
−0.945231 + 0.326402i \(0.894164\pi\)
\(390\) 0 0
\(391\) −0.0217329 + 0.0157899i −0.00109908 + 0.000798528i
\(392\) −3.69481 11.3714i −0.186616 0.574345i
\(393\) 0 0
\(394\) 9.65184 + 7.01247i 0.486253 + 0.353283i
\(395\) 26.7009 1.34347
\(396\) 0 0
\(397\) 4.08994 0.205268 0.102634 0.994719i \(-0.467273\pi\)
0.102634 + 0.994719i \(0.467273\pi\)
\(398\) −6.21075 4.51238i −0.311317 0.226185i
\(399\) 0 0
\(400\) 2.62328 + 8.07363i 0.131164 + 0.403681i
\(401\) −4.56793 + 3.31879i −0.228111 + 0.165733i −0.695970 0.718071i \(-0.745026\pi\)
0.467859 + 0.883803i \(0.345026\pi\)
\(402\) 0 0
\(403\) −7.96148 24.5029i −0.396590 1.22058i
\(404\) −1.05881 + 3.25868i −0.0526777 + 0.162125i
\(405\) 0 0
\(406\) 5.18012 0.257085
\(407\) −0.788016 + 20.6910i −0.0390605 + 1.02561i
\(408\) 0 0
\(409\) −7.64422 5.55385i −0.377982 0.274620i 0.382531 0.923943i \(-0.375053\pi\)
−0.760513 + 0.649323i \(0.775053\pi\)
\(410\) −3.11629 + 9.59094i −0.153902 + 0.473663i
\(411\) 0 0
\(412\) −4.06632 + 2.95436i −0.200333 + 0.145551i
\(413\) 2.16276 1.57134i 0.106422 0.0773204i
\(414\) 0 0
\(415\) 4.60290 14.1663i 0.225948 0.695395i
\(416\) −17.4147 12.6525i −0.853827 0.620342i
\(417\) 0 0
\(418\) −11.7421 + 3.32687i −0.574324 + 0.162723i
\(419\) −0.151564 −0.00740438 −0.00370219 0.999993i \(-0.501178\pi\)
−0.00370219 + 0.999993i \(0.501178\pi\)
\(420\) 0 0
\(421\) 5.24605 16.1457i 0.255677 0.786892i −0.738019 0.674780i \(-0.764239\pi\)
0.993696 0.112112i \(-0.0357615\pi\)
\(422\) 1.49003 + 4.58585i 0.0725337 + 0.223236i
\(423\) 0 0
\(424\) −4.15194 + 3.01656i −0.201636 + 0.146497i
\(425\) 0.390942 + 1.20320i 0.0189635 + 0.0583636i
\(426\) 0 0
\(427\) −12.8927 9.36711i −0.623923 0.453306i
\(428\) 19.9817 0.965852
\(429\) 0 0
\(430\) −11.7780 −0.567986
\(431\) −20.5242 14.9117i −0.988618 0.718273i −0.0289998 0.999579i \(-0.509232\pi\)
−0.959618 + 0.281307i \(0.909232\pi\)
\(432\) 0 0
\(433\) 5.10950 + 15.7254i 0.245547 + 0.755716i 0.995546 + 0.0942769i \(0.0300539\pi\)
−0.749999 + 0.661439i \(0.769946\pi\)
\(434\) −3.55347 + 2.58175i −0.170572 + 0.123928i
\(435\) 0 0
\(436\) −2.67736 8.24005i −0.128222 0.394627i
\(437\) 0.168259 0.517849i 0.00804893 0.0247721i
\(438\) 0 0
\(439\) −39.2413 −1.87289 −0.936443 0.350819i \(-0.885903\pi\)
−0.936443 + 0.350819i \(0.885903\pi\)
\(440\) −0.803326 + 21.0930i −0.0382971 + 1.00557i
\(441\) 0 0
\(442\) −0.579580 0.421089i −0.0275678 0.0200292i
\(443\) −9.94706 + 30.6139i −0.472599 + 1.45451i 0.376570 + 0.926388i \(0.377104\pi\)
−0.849169 + 0.528122i \(0.822896\pi\)
\(444\) 0 0
\(445\) −5.17390 + 3.75906i −0.245266 + 0.178197i
\(446\) −0.179344 + 0.130301i −0.00849216 + 0.00616992i
\(447\) 0 0
\(448\) 0.383056 1.17893i 0.0180977 0.0556990i
\(449\) −20.9085 15.1909i −0.986731 0.716902i −0.0275281 0.999621i \(-0.508764\pi\)
−0.959203 + 0.282719i \(0.908764\pi\)
\(450\) 0 0
\(451\) 11.9096 15.1447i 0.560799 0.713134i
\(452\) 32.0357 1.50683
\(453\) 0 0
\(454\) 3.21647 9.89928i 0.150957 0.464596i
\(455\) −4.26572 13.1285i −0.199980 0.615476i
\(456\) 0 0
\(457\) 10.2877 7.47444i 0.481238 0.349640i −0.320567 0.947226i \(-0.603873\pi\)
0.801805 + 0.597586i \(0.203873\pi\)
\(458\) −2.39760 7.37904i −0.112032 0.344800i
\(459\) 0 0
\(460\) −0.346255 0.251569i −0.0161442 0.0117295i
\(461\) 19.0217 0.885931 0.442965 0.896539i \(-0.353927\pi\)
0.442965 + 0.896539i \(0.353927\pi\)
\(462\) 0 0
\(463\) −22.8667 −1.06271 −0.531353 0.847150i \(-0.678316\pi\)
−0.531353 + 0.847150i \(0.678316\pi\)
\(464\) −13.1330 9.54168i −0.609684 0.442961i
\(465\) 0 0
\(466\) −0.601664 1.85173i −0.0278716 0.0857798i
\(467\) 12.8819 9.35921i 0.596101 0.433093i −0.248392 0.968660i \(-0.579902\pi\)
0.844493 + 0.535567i \(0.179902\pi\)
\(468\) 0 0
\(469\) −4.20232 12.9334i −0.194045 0.597210i
\(470\) 0.175814 0.541101i 0.00810971 0.0249591i
\(471\) 0 0
\(472\) 4.86377 0.223873
\(473\) 21.1205 + 7.76289i 0.971120 + 0.356938i
\(474\) 0 0
\(475\) −20.7455 15.0725i −0.951870 0.691574i
\(476\) 0.188347 0.579671i 0.00863285 0.0265692i
\(477\) 0 0
\(478\) 10.8436 7.87832i 0.495973 0.360346i
\(479\) −13.2598 + 9.63378i −0.605854 + 0.440179i −0.847952 0.530073i \(-0.822164\pi\)
0.242098 + 0.970252i \(0.422164\pi\)
\(480\) 0 0
\(481\) 7.61303 23.4305i 0.347124 1.06834i
\(482\) 7.08862 + 5.15018i 0.322878 + 0.234584i
\(483\) 0 0
\(484\) 6.97285 16.9492i 0.316948 0.770418i
\(485\) 0.266911 0.0121198
\(486\) 0 0
\(487\) 7.04142 21.6713i 0.319077 0.982019i −0.654966 0.755658i \(-0.727317\pi\)
0.974044 0.226361i \(-0.0726828\pi\)
\(488\) −8.95967 27.5750i −0.405585 1.24826i
\(489\) 0 0
\(490\) 7.92722 5.75946i 0.358115 0.260186i
\(491\) 13.4864 + 41.5070i 0.608634 + 1.87318i 0.469558 + 0.882901i \(0.344413\pi\)
0.139076 + 0.990282i \(0.455587\pi\)
\(492\) 0 0
\(493\) −1.95718 1.42198i −0.0881471 0.0640426i
\(494\) 14.5209 0.653324
\(495\) 0 0
\(496\) 13.7645 0.618045
\(497\) −8.21163 5.96610i −0.368342 0.267616i
\(498\) 0 0
\(499\) −6.21233 19.1196i −0.278102 0.855910i −0.988382 0.151991i \(-0.951432\pi\)
0.710280 0.703919i \(-0.248568\pi\)
\(500\) 3.94209 2.86410i 0.176296 0.128086i
\(501\) 0 0
\(502\) −0.103973 0.319996i −0.00464054 0.0142821i
\(503\) 3.27815 10.0891i 0.146165 0.449850i −0.850994 0.525176i \(-0.824000\pi\)
0.997159 + 0.0753254i \(0.0239995\pi\)
\(504\) 0 0
\(505\) −6.17856 −0.274942
\(506\) −0.0911948 0.136128i −0.00405410 0.00605162i
\(507\) 0 0
\(508\) −17.7697 12.9104i −0.788401 0.572807i
\(509\) 13.7415 42.2919i 0.609080 1.87456i 0.143240 0.989688i \(-0.454248\pi\)
0.465840 0.884869i \(-0.345752\pi\)
\(510\) 0 0
\(511\) 2.77553 2.01654i 0.122782 0.0892064i
\(512\) 16.5301 12.0098i 0.730534 0.530764i
\(513\) 0 0
\(514\) −1.95899 + 6.02915i −0.0864073 + 0.265934i
\(515\) −7.33253 5.32739i −0.323110 0.234753i
\(516\) 0 0
\(517\) −0.671913 + 0.854430i −0.0295507 + 0.0375778i
\(518\) −4.20009 −0.184541
\(519\) 0 0
\(520\) 7.76095 23.8858i 0.340340 1.04746i
\(521\) −5.23819 16.1215i −0.229489 0.706296i −0.997805 0.0662243i \(-0.978905\pi\)
0.768315 0.640071i \(-0.221095\pi\)
\(522\) 0 0
\(523\) −24.4438 + 17.7595i −1.06885 + 0.776567i −0.975706 0.219085i \(-0.929693\pi\)
−0.0931472 + 0.995652i \(0.529693\pi\)
\(524\) −9.25301 28.4778i −0.404219 1.24406i
\(525\) 0 0
\(526\) 6.72925 + 4.88909i 0.293409 + 0.213174i
\(527\) 2.05130 0.0893560
\(528\) 0 0
\(529\) −22.9927 −0.999682
\(530\) −3.40255 2.47210i −0.147797 0.107381i
\(531\) 0 0
\(532\) 3.81763 + 11.7495i 0.165515 + 0.509404i
\(533\) −18.5456 + 13.4741i −0.803298 + 0.583630i
\(534\) 0 0
\(535\) 11.1344 + 34.2682i 0.481382 + 1.48154i
\(536\) 7.64561 23.5308i 0.330240 1.01637i
\(537\) 0 0
\(538\) 0.282536 0.0121810
\(539\) −18.0112 + 5.10310i −0.775799 + 0.219806i
\(540\) 0 0
\(541\) −9.57164 6.95421i −0.411517 0.298985i 0.362699 0.931906i \(-0.381855\pi\)
−0.774216 + 0.632922i \(0.781855\pi\)
\(542\) −3.91728 + 12.0561i −0.168262 + 0.517856i
\(543\) 0 0
\(544\) 1.38654 1.00738i 0.0594476 0.0431912i
\(545\) 12.6396 9.18321i 0.541421 0.393365i
\(546\) 0 0
\(547\) 0.786698 2.42121i 0.0336368 0.103523i −0.932828 0.360321i \(-0.882667\pi\)
0.966465 + 0.256797i \(0.0826673\pi\)
\(548\) 22.1084 + 16.0627i 0.944424 + 0.686164i
\(549\) 0 0
\(550\) −7.42425 + 2.10350i −0.316571 + 0.0896937i
\(551\) 49.0355 2.08898
\(552\) 0 0
\(553\) 3.19757 9.84109i 0.135974 0.418486i
\(554\) −0.512364 1.57690i −0.0217683 0.0669959i
\(555\) 0 0
\(556\) −16.0425 + 11.6556i −0.680355 + 0.494307i
\(557\) −2.98987 9.20189i −0.126685 0.389896i 0.867519 0.497404i \(-0.165713\pi\)
−0.994204 + 0.107507i \(0.965713\pi\)
\(558\) 0 0
\(559\) −21.6599 15.7368i −0.916117 0.665598i
\(560\) 7.37496 0.311649
\(561\) 0 0
\(562\) 10.5035 0.443064
\(563\) −19.4061 14.0993i −0.817868 0.594216i 0.0982327 0.995163i \(-0.468681\pi\)
−0.916101 + 0.400947i \(0.868681\pi\)
\(564\) 0 0
\(565\) 17.8512 + 54.9404i 0.751007 + 2.31136i
\(566\) −9.60027 + 6.97501i −0.403530 + 0.293181i
\(567\) 0 0
\(568\) −5.70659 17.5631i −0.239443 0.736930i
\(569\) 11.6249 35.7779i 0.487343 1.49989i −0.341215 0.939985i \(-0.610838\pi\)
0.828558 0.559903i \(-0.189162\pi\)
\(570\) 0 0
\(571\) −14.7548 −0.617469 −0.308735 0.951148i \(-0.599905\pi\)
−0.308735 + 0.951148i \(0.599905\pi\)
\(572\) −13.4795 + 17.1411i −0.563608 + 0.716705i
\(573\) 0 0
\(574\) 3.16172 + 2.29712i 0.131968 + 0.0958801i
\(575\) 0.106386 0.327424i 0.00443662 0.0136545i
\(576\) 0 0
\(577\) 18.0466 13.1116i 0.751289 0.545843i −0.144937 0.989441i \(-0.546298\pi\)
0.896226 + 0.443598i \(0.146298\pi\)
\(578\) −7.90067 + 5.74017i −0.328625 + 0.238760i
\(579\) 0 0
\(580\) 11.9106 36.6571i 0.494562 1.52210i
\(581\) −4.67001 3.39296i −0.193745 0.140764i
\(582\) 0 0
\(583\) 4.47213 + 6.67562i 0.185217 + 0.276476i
\(584\) 6.24181 0.258288
\(585\) 0 0
\(586\) 0.153568 0.472634i 0.00634384 0.0195243i
\(587\) 0.772594 + 2.37780i 0.0318884 + 0.0981424i 0.965734 0.259534i \(-0.0835690\pi\)
−0.933846 + 0.357677i \(0.883569\pi\)
\(588\) 0 0
\(589\) −33.6374 + 24.4390i −1.38601 + 1.00699i
\(590\) 1.23171 + 3.79081i 0.0507087 + 0.156065i
\(591\) 0 0
\(592\) 10.6484 + 7.73648i 0.437645 + 0.317968i
\(593\) 10.8953 0.447417 0.223708 0.974656i \(-0.428184\pi\)
0.223708 + 0.974656i \(0.428184\pi\)
\(594\) 0 0
\(595\) 1.09907 0.0450577
\(596\) 6.10843 + 4.43804i 0.250211 + 0.181789i
\(597\) 0 0
\(598\) 0.0602437 + 0.185411i 0.00246355 + 0.00758203i
\(599\) −29.8026 + 21.6529i −1.21770 + 0.884713i −0.995907 0.0903802i \(-0.971192\pi\)
−0.221796 + 0.975093i \(0.571192\pi\)
\(600\) 0 0
\(601\) −4.77564 14.6979i −0.194802 0.599540i −0.999979 0.00650456i \(-0.997930\pi\)
0.805177 0.593035i \(-0.202070\pi\)
\(602\) −1.41047 + 4.34099i −0.0574866 + 0.176925i
\(603\) 0 0
\(604\) 4.88321 0.198695
\(605\) 32.9530 + 2.51367i 1.33973 + 0.102195i
\(606\) 0 0
\(607\) 20.6112 + 14.9749i 0.836585 + 0.607814i 0.921415 0.388581i \(-0.127035\pi\)
−0.0848299 + 0.996395i \(0.527035\pi\)
\(608\) −10.7348 + 33.0384i −0.435355 + 1.33988i
\(609\) 0 0
\(610\) 19.2230 13.9663i 0.778316 0.565479i
\(611\) 1.04630 0.760183i 0.0423289 0.0307537i
\(612\) 0 0
\(613\) −11.6728 + 35.9252i −0.471461 + 1.45101i 0.379211 + 0.925310i \(0.376195\pi\)
−0.850672 + 0.525697i \(0.823805\pi\)
\(614\) 1.63106 + 1.18503i 0.0658243 + 0.0478241i
\(615\) 0 0
\(616\) 7.67799 + 2.82207i 0.309355 + 0.113704i
\(617\) −41.8928 −1.68654 −0.843271 0.537489i \(-0.819373\pi\)
−0.843271 + 0.537489i \(0.819373\pi\)
\(618\) 0 0
\(619\) −1.85089 + 5.69646i −0.0743936 + 0.228960i −0.981338 0.192290i \(-0.938409\pi\)
0.906945 + 0.421250i \(0.138409\pi\)
\(620\) 10.0993 + 31.0823i 0.405596 + 1.24830i
\(621\) 0 0
\(622\) −5.06974 + 3.68338i −0.203278 + 0.147690i
\(623\) 0.765867 + 2.35710i 0.0306838 + 0.0944351i
\(624\) 0 0
\(625\) 23.3964 + 16.9985i 0.935856 + 0.679939i
\(626\) 16.3411 0.653123
\(627\) 0 0
\(628\) 30.0798 1.20031
\(629\) 1.58690 + 1.15295i 0.0632739 + 0.0459712i
\(630\) 0 0
\(631\) −6.64368 20.4471i −0.264481 0.813988i −0.991813 0.127702i \(-0.959240\pi\)
0.727332 0.686286i \(-0.240760\pi\)
\(632\) 15.2306 11.0657i 0.605841 0.440169i
\(633\) 0 0
\(634\) −0.198646 0.611369i −0.00788923 0.0242806i
\(635\) 12.2393 37.6686i 0.485701 1.49483i
\(636\) 0 0
\(637\) 22.2736 0.882512
\(638\) 9.12129 11.5990i 0.361115 0.459208i
\(639\) 0 0
\(640\) 28.0127 + 20.3525i 1.10730 + 0.804501i
\(641\) −3.96685 + 12.2087i −0.156681 + 0.482215i −0.998327 0.0578142i \(-0.981587\pi\)
0.841646 + 0.540029i \(0.181587\pi\)
\(642\) 0 0
\(643\) −22.9401 + 16.6670i −0.904671 + 0.657282i −0.939661 0.342106i \(-0.888860\pi\)
0.0349907 + 0.999388i \(0.488860\pi\)
\(644\) −0.134186 + 0.0974917i −0.00528766 + 0.00384171i
\(645\) 0 0
\(646\) −0.357266 + 1.09955i −0.0140564 + 0.0432613i
\(647\) −14.1536 10.2832i −0.556436 0.404274i 0.273717 0.961810i \(-0.411747\pi\)
−0.830153 + 0.557536i \(0.811747\pi\)
\(648\) 0 0
\(649\) 0.289810 7.60956i 0.0113760 0.298701i
\(650\) 9.18120 0.360116
\(651\) 0 0
\(652\) 2.99829 9.22780i 0.117422 0.361389i
\(653\) 9.05488 + 27.8681i 0.354345 + 1.09056i 0.956388 + 0.292098i \(0.0943534\pi\)
−0.602043 + 0.798463i \(0.705647\pi\)
\(654\) 0 0
\(655\) 43.6828 31.7374i 1.70683 1.24008i
\(656\) −3.78455 11.6477i −0.147762 0.454764i
\(657\) 0 0
\(658\) −0.178378 0.129599i −0.00695388 0.00505229i
\(659\) −27.5870 −1.07464 −0.537319 0.843379i \(-0.680563\pi\)
−0.537319 + 0.843379i \(0.680563\pi\)
\(660\) 0 0
\(661\) 29.7552 1.15734 0.578672 0.815560i \(-0.303571\pi\)
0.578672 + 0.815560i \(0.303571\pi\)
\(662\) −5.78636 4.20404i −0.224893 0.163395i
\(663\) 0 0
\(664\) −3.24537 9.98823i −0.125945 0.387619i
\(665\) −18.0228 + 13.0943i −0.698893 + 0.507775i
\(666\) 0 0
\(667\) 0.203437 + 0.626115i 0.00787711 + 0.0242433i
\(668\) −2.58550 + 7.95736i −0.100036 + 0.307880i
\(669\) 0 0
\(670\) 20.2760 0.783332
\(671\) −43.6761 + 12.3747i −1.68610 + 0.477720i
\(672\) 0 0
\(673\) −7.80999 5.67429i −0.301053 0.218728i 0.426995 0.904254i \(-0.359572\pi\)
−0.728048 + 0.685526i \(0.759572\pi\)
\(674\) −2.40577 + 7.40418i −0.0926666 + 0.285198i
\(675\) 0 0
\(676\) 3.46724 2.51910i 0.133355 0.0968883i
\(677\) −0.0793768 + 0.0576706i −0.00305070 + 0.00221646i −0.589310 0.807907i \(-0.700600\pi\)
0.586259 + 0.810124i \(0.300600\pi\)
\(678\) 0 0
\(679\) 0.0319639 0.0983747i 0.00122666 0.00377528i
\(680\) 1.61774 + 1.17535i 0.0620373 + 0.0450727i
\(681\) 0 0
\(682\) −0.476165 + 12.5027i −0.0182333 + 0.478753i
\(683\) −30.5246 −1.16799 −0.583996 0.811756i \(-0.698512\pi\)
−0.583996 + 0.811756i \(0.698512\pi\)
\(684\) 0 0
\(685\) −15.2277 + 46.8660i −0.581820 + 1.79066i
\(686\) −2.62868 8.09025i −0.100364 0.308887i
\(687\) 0 0
\(688\) 11.5719 8.40751i 0.441176 0.320533i
\(689\) −2.95431 9.09244i −0.112550 0.346395i
\(690\) 0 0
\(691\) −26.5371 19.2804i −1.00952 0.733459i −0.0454115 0.998968i \(-0.514460\pi\)
−0.964108 + 0.265509i \(0.914460\pi\)
\(692\) −25.9748 −0.987413
\(693\) 0 0
\(694\) 5.62741 0.213614
\(695\) −28.9284 21.0177i −1.09732 0.797248i
\(696\) 0 0
\(697\) −0.564004 1.73583i −0.0213632 0.0657491i
\(698\) −2.07561 + 1.50802i −0.0785631 + 0.0570794i
\(699\) 0 0
\(700\) 2.41380 + 7.42892i 0.0912331 + 0.280787i
\(701\) 2.70365 8.32098i 0.102115 0.314279i −0.886927 0.461909i \(-0.847165\pi\)
0.989043 + 0.147630i \(0.0471646\pi\)
\(702\) 0 0
\(703\) −39.7584 −1.49952
\(704\) −1.96528 2.93360i −0.0740692 0.110564i
\(705\) 0 0
\(706\) −15.2034 11.0460i −0.572189 0.415720i
\(707\) −0.739912 + 2.27721i −0.0278273 + 0.0856435i
\(708\) 0 0
\(709\) −21.6621 + 15.7385i −0.813539 + 0.591071i −0.914854 0.403784i \(-0.867695\pi\)
0.101316 + 0.994854i \(0.467695\pi\)
\(710\) 12.2435 8.89542i 0.459490 0.333839i
\(711\) 0 0
\(712\) −1.39340 + 4.28845i −0.0522199 + 0.160716i
\(713\) −0.451607 0.328111i −0.0169128 0.0122879i
\(714\) 0 0
\(715\) −36.9078 13.5656i −1.38027 0.507323i
\(716\) 11.7443 0.438907
\(717\) 0 0
\(718\) −4.95846 + 15.2606i −0.185048 + 0.569519i
\(719\) 4.63672 + 14.2703i 0.172920 + 0.532194i 0.999532 0.0305782i \(-0.00973486\pi\)
−0.826612 + 0.562772i \(0.809735\pi\)
\(720\) 0 0
\(721\) −2.84161 + 2.06455i −0.105827 + 0.0768879i
\(722\) −3.84897 11.8459i −0.143244 0.440860i
\(723\) 0 0
\(724\) 3.36672 + 2.44607i 0.125123 + 0.0909073i
\(725\) 31.0040 1.15146
\(726\) 0 0
\(727\) 27.5325 1.02112 0.510562 0.859841i \(-0.329437\pi\)
0.510562 + 0.859841i \(0.329437\pi\)
\(728\) −7.87410 5.72087i −0.291834 0.212029i
\(729\) 0 0
\(730\) 1.58069 + 4.86486i 0.0585039 + 0.180057i
\(731\) 1.72454 1.25295i 0.0637845 0.0463422i
\(732\) 0 0
\(733\) 14.7524 + 45.4031i 0.544891 + 1.67700i 0.721248 + 0.692677i \(0.243569\pi\)
−0.176357 + 0.984326i \(0.556431\pi\)
\(734\) −0.209300 + 0.644160i −0.00772541 + 0.0237764i
\(735\) 0 0
\(736\) −0.466391 −0.0171914
\(737\) −36.3593 13.3640i −1.33931 0.492267i
\(738\) 0 0
\(739\) −1.20421 0.874910i −0.0442976 0.0321841i 0.565416 0.824806i \(-0.308716\pi\)
−0.609714 + 0.792622i \(0.708716\pi\)
\(740\) −9.65725 + 29.7220i −0.355007 + 1.09260i
\(741\) 0 0
\(742\) −1.31861 + 0.958023i −0.0484076 + 0.0351701i
\(743\) −14.6919 + 10.6743i −0.538993 + 0.391601i −0.823711 0.567010i \(-0.808100\pi\)
0.284718 + 0.958611i \(0.408100\pi\)
\(744\) 0 0
\(745\) −4.20733 + 12.9488i −0.154145 + 0.474409i
\(746\) 10.1751 + 7.39264i 0.372537 + 0.270664i
\(747\) 0 0
\(748\) −0.966316 1.44243i −0.0353320 0.0527406i
\(749\) 13.9635 0.510216
\(750\) 0 0
\(751\) −1.35802 + 4.17956i −0.0495550 + 0.152514i −0.972772 0.231765i \(-0.925550\pi\)
0.923217 + 0.384279i \(0.125550\pi\)
\(752\) 0.213517 + 0.657136i 0.00778615 + 0.0239633i
\(753\) 0 0
\(754\) −14.2037 + 10.3196i −0.517267 + 0.375817i
\(755\) 2.72107 + 8.37459i 0.0990299 + 0.304783i
\(756\) 0 0
\(757\) 11.1369 + 8.09140i 0.404776 + 0.294087i 0.771483 0.636249i \(-0.219515\pi\)
−0.366708 + 0.930336i \(0.619515\pi\)
\(758\) 9.38763 0.340974
\(759\) 0 0
\(760\) −40.5309 −1.47021
\(761\) −25.1654 18.2837i −0.912244 0.662784i 0.0293374 0.999570i \(-0.490660\pi\)
−0.941581 + 0.336786i \(0.890660\pi\)
\(762\) 0 0
\(763\) −1.87098 5.75828i −0.0677340 0.208464i
\(764\) 15.9365 11.5786i 0.576564 0.418898i
\(765\) 0 0
\(766\) 1.10585 + 3.40344i 0.0399558 + 0.122971i
\(767\) −2.79986 + 8.61708i −0.101097 + 0.311145i
\(768\) 0 0
\(769\) 21.9353 0.791009 0.395504 0.918464i \(-0.370570\pi\)
0.395504 + 0.918464i \(0.370570\pi\)
\(770\) −0.255127 + 6.69888i −0.00919413 + 0.241411i
\(771\) 0 0
\(772\) 9.09402 + 6.60719i 0.327301 + 0.237798i
\(773\) 3.92965 12.0942i 0.141340 0.434999i −0.855182 0.518327i \(-0.826555\pi\)
0.996522 + 0.0833281i \(0.0265549\pi\)
\(774\) 0 0
\(775\) −21.2682 + 15.4522i −0.763976 + 0.555061i
\(776\) 0.152250 0.110616i 0.00546546 0.00397089i
\(777\) 0 0
\(778\) −0.129132 + 0.397429i −0.00462962 + 0.0142485i
\(779\) 29.9291 + 21.7448i 1.07232 + 0.779087i
\(780\) 0 0
\(781\) −27.8182 + 7.88168i −0.995412 + 0.282029i
\(782\) −0.0155220 −0.000555064
\(783\) 0 0
\(784\) −3.67724 + 11.3174i −0.131330 + 0.404193i
\(785\) 16.7613 + 51.5861i 0.598238 + 1.84119i
\(786\) 0 0
\(787\) 13.9650 10.1461i 0.497797 0.361671i −0.310378 0.950613i \(-0.600455\pi\)
0.808175 + 0.588942i \(0.200455\pi\)
\(788\) −10.6306 32.7176i −0.378700 1.16552i
\(789\) 0 0
\(790\) 12.4816 + 9.06842i 0.444076 + 0.322640i
\(791\) 22.3870 0.795991
\(792\) 0 0
\(793\) 54.0120 1.91802
\(794\) 1.91188 + 1.38906i 0.0678501 + 0.0492960i
\(795\) 0 0
\(796\) 6.84057 + 21.0531i 0.242457 + 0.746207i
\(797\) 28.4786 20.6909i 1.00876 0.732910i 0.0448149 0.998995i \(-0.485730\pi\)
0.963950 + 0.266085i \(0.0857302\pi\)
\(798\) 0 0
\(799\) 0.0318199 + 0.0979317i 0.00112571 + 0.00346457i
\(800\) −6.78739 + 20.8894i −0.239970 + 0.738553i
\(801\) 0 0
\(802\) −3.26248 −0.115202
\(803\) 0.371921 9.76556i 0.0131248 0.344619i
\(804\) 0 0
\(805\) −0.241968 0.175800i −0.00852827 0.00619615i
\(806\) 4.60024 14.1581i 0.162037 0.498697i
\(807\) 0 0
\(808\) −3.52434 + 2.56058i −0.123986 + 0.0900810i
\(809\) −15.4367 + 11.2154i −0.542725 + 0.394313i −0.825096 0.564992i \(-0.808879\pi\)
0.282371 + 0.959305i \(0.408879\pi\)
\(810\) 0 0
\(811\) −9.59769 + 29.5387i −0.337020 + 1.03724i 0.628698 + 0.777650i \(0.283588\pi\)
−0.965718 + 0.259593i \(0.916412\pi\)
\(812\) −12.0843 8.77973i −0.424075 0.308108i
\(813\) 0 0
\(814\) −7.39563 + 9.40457i −0.259217 + 0.329630i
\(815\) 17.4962 0.612865
\(816\) 0 0
\(817\) −13.3517 + 41.0922i −0.467115 + 1.43763i
\(818\) −1.68711 5.19240i −0.0589885 0.181548i
\(819\) 0 0
\(820\) 23.5253 17.0922i 0.821540 0.596884i
\(821\) −10.5092 32.3440i −0.366774 1.12881i −0.948863 0.315689i \(-0.897764\pi\)
0.582089 0.813125i \(-0.302236\pi\)
\(822\) 0 0
\(823\) −12.5851 9.14359i −0.438688 0.318726i 0.346425 0.938078i \(-0.387395\pi\)
−0.785113 + 0.619352i \(0.787395\pi\)
\(824\) −6.39042 −0.222621
\(825\) 0 0
\(826\) 1.54467 0.0537461
\(827\) 12.9667 + 9.42084i 0.450895 + 0.327595i 0.789949 0.613172i \(-0.210107\pi\)
−0.339054 + 0.940767i \(0.610107\pi\)
\(828\) 0 0
\(829\) 5.90205 + 18.1646i 0.204987 + 0.630884i 0.999714 + 0.0239173i \(0.00761382\pi\)
−0.794727 + 0.606967i \(0.792386\pi\)
\(830\) 6.96296 5.05888i 0.241688 0.175596i
\(831\) 0 0
\(832\) 1.29827 + 3.99567i 0.0450095 + 0.138525i
\(833\) −0.548012 + 1.68661i −0.0189875 + 0.0584375i
\(834\) 0 0
\(835\) −15.0874 −0.522122
\(836\) 33.0308 + 12.1406i 1.14240 + 0.419891i
\(837\) 0 0
\(838\) −0.0708501 0.0514756i −0.00244747 0.00177819i
\(839\) −0.459793 + 1.41510i −0.0158738 + 0.0488545i −0.958680 0.284488i \(-0.908176\pi\)
0.942806 + 0.333342i \(0.108176\pi\)
\(840\) 0 0
\(841\) −24.5029 + 17.8024i −0.844927 + 0.613875i
\(842\) 7.93586 5.76574i 0.273488 0.198700i
\(843\) 0 0
\(844\) 4.29654 13.2234i 0.147893 0.455168i
\(845\) 6.25224 + 4.54252i 0.215084 + 0.156267i
\(846\) 0 0
\(847\) 4.87274 11.8444i 0.167429 0.406977i
\(848\) 5.10768 0.175399
\(849\) 0 0
\(850\) −0.225891 + 0.695221i −0.00774800 + 0.0238459i
\(851\) −0.164949 0.507660i −0.00565437 0.0174024i
\(852\) 0 0
\(853\) −30.5825 + 22.2195i −1.04713 + 0.760781i −0.971664 0.236367i \(-0.924043\pi\)
−0.0754620 + 0.997149i \(0.524043\pi\)
\(854\) −2.84548 8.75750i −0.0973704 0.299675i
\(855\) 0 0
\(856\) 20.5530 + 14.9326i 0.702487 + 0.510387i
\(857\) −19.8270 −0.677276 −0.338638 0.940917i \(-0.609966\pi\)
−0.338638 + 0.940917i \(0.609966\pi\)
\(858\) 0 0
\(859\) −15.7153 −0.536199 −0.268099 0.963391i \(-0.586396\pi\)
−0.268099 + 0.963391i \(0.586396\pi\)
\(860\) 27.4759 + 19.9624i 0.936921 + 0.680713i
\(861\) 0 0
\(862\) −4.52979 13.9413i −0.154285 0.474842i
\(863\) 6.57548 4.77736i 0.223832 0.162623i −0.470218 0.882550i \(-0.655825\pi\)
0.694050 + 0.719927i \(0.255825\pi\)
\(864\) 0 0
\(865\) −14.4739 44.5462i −0.492128 1.51462i
\(866\) −2.95233 + 9.08634i −0.100324 + 0.308766i
\(867\) 0 0
\(868\) 12.6654 0.429891
\(869\) −16.4052 24.4882i −0.556508 0.830707i
\(870\) 0 0
\(871\) 37.2879 + 27.0913i 1.26345 + 0.917953i
\(872\) 3.40401 10.4765i 0.115274 0.354778i
\(873\) 0 0
\(874\) 0.254531 0.184928i 0.00860964 0.00625527i
\(875\) 2.75479 2.00148i 0.0931290 0.0676622i
\(876\) 0 0
\(877\) −0.782904 + 2.40953i −0.0264368 + 0.0813640i −0.963404 0.268052i \(-0.913620\pi\)
0.936968 + 0.349416i \(0.113620\pi\)
\(878\) −18.3437 13.3275i −0.619071 0.449782i
\(879\) 0 0
\(880\) 12.9860 16.5135i 0.437759 0.556671i
\(881\) 47.4109 1.59731 0.798657 0.601786i \(-0.205544\pi\)
0.798657 + 0.601786i \(0.205544\pi\)
\(882\) 0 0
\(883\) 8.19295 25.2153i 0.275715 0.848563i −0.713315 0.700844i \(-0.752807\pi\)
0.989029 0.147719i \(-0.0471930\pi\)
\(884\) 0.638353 + 1.96465i 0.0214701 + 0.0660783i
\(885\) 0 0
\(886\) −15.0472 + 10.9325i −0.505522 + 0.367283i
\(887\) 14.7801 + 45.4884i 0.496266 + 1.52735i 0.814974 + 0.579498i \(0.196751\pi\)
−0.318707 + 0.947853i \(0.603249\pi\)
\(888\) 0 0
\(889\) −12.4177 9.02200i −0.416477 0.302588i
\(890\) −3.69528 −0.123866
\(891\) 0 0
\(892\) 0.639221 0.0214027
\(893\) −1.68854 1.22680i −0.0565048 0.0410531i
\(894\) 0 0
\(895\) 6.54430 + 20.1413i 0.218752 + 0.673249i
\(896\) 10.8559 7.88728i 0.362671 0.263496i
\(897\) 0 0
\(898\) −4.61459 14.2023i −0.153991 0.473935i
\(899\) 15.5345 47.8104i 0.518106 1.59457i
\(900\) 0 0
\(901\) 0.761187 0.0253588
\(902\) 10.7108 3.03468i 0.356631 0.101044i
\(903\) 0 0
\(904\) 32.9516 + 23.9407i 1.09595 + 0.796257i
\(905\) −2.31891 + 7.13687i −0.0770832 + 0.237238i
\(906\) 0 0
\(907\) −38.3946 + 27.8953i −1.27487 + 0.926249i −0.999385 0.0350562i \(-0.988839\pi\)
−0.275487 + 0.961305i \(0.588839\pi\)
\(908\) −24.2817 + 17.6417i −0.805815 + 0.585459i
\(909\) 0 0
\(910\) 2.46479 7.58583i 0.0817068 0.251468i
\(911\) −23.0022 16.7120i −0.762095 0.553695i 0.137457 0.990508i \(-0.456107\pi\)
−0.899552 + 0.436813i \(0.856107\pi\)
\(912\) 0 0
\(913\) −15.8204 + 4.48236i −0.523578 + 0.148345i
\(914\) 7.34762 0.243038
\(915\) 0 0
\(916\) −6.91352 + 21.2776i −0.228429 + 0.703032i
\(917\) −6.46615 19.9008i −0.213531 0.657181i
\(918\) 0 0
\(919\) −31.0442 + 22.5550i −1.02406 + 0.744020i −0.967110 0.254358i \(-0.918136\pi\)
−0.0569449 + 0.998377i \(0.518136\pi\)
\(920\) −0.168154 0.517523i −0.00554386 0.0170622i
\(921\) 0 0
\(922\) 8.89190 + 6.46034i 0.292839 + 0.212760i
\(923\) 34.4013 1.13233
\(924\) 0 0
\(925\) −25.1383 −0.826543
\(926\) −10.6893 7.76621i −0.351271 0.255214i
\(927\) 0 0
\(928\) −12.9791 39.9457i −0.426061 1.31128i
\(929\) 10.8309 7.86907i 0.355349 0.258176i −0.395761 0.918354i \(-0.629519\pi\)
0.751109 + 0.660178i \(0.229519\pi\)
\(930\) 0 0
\(931\) −11.1078 34.1862i −0.364042 1.12041i
\(932\) −1.73491 + 5.33951i −0.0568289 + 0.174901i
\(933\) 0 0
\(934\) 9.20041 0.301047
\(935\) 1.93528 2.46098i 0.0632905 0.0804826i
\(936\) 0 0
\(937\) 19.9588 + 14.5010i 0.652027 + 0.473725i 0.863961 0.503559i \(-0.167976\pi\)
−0.211934 + 0.977284i \(0.567976\pi\)
\(938\) 2.42815 7.47309i 0.0792820 0.244005i
\(939\) 0 0
\(940\) −1.32725 + 0.964304i −0.0432901 + 0.0314521i
\(941\) 6.71670 4.87997i 0.218958 0.159082i −0.472899 0.881116i \(-0.656793\pi\)
0.691858 + 0.722034i \(0.256793\pi\)
\(942\) 0 0
\(943\) −0.153481 + 0.472367i −0.00499804 + 0.0153824i
\(944\) −3.91616 2.84526i −0.127460 0.0926053i
\(945\) 0 0
\(946\) 7.23646 + 10.8020i 0.235278 + 0.351202i
\(947\) −37.9496 −1.23320 −0.616598 0.787278i \(-0.711490\pi\)
−0.616598 + 0.787278i \(0.711490\pi\)
\(948\) 0 0
\(949\) −3.59314 + 11.0585i −0.116638 + 0.358975i
\(950\) −4.57863 14.0916i −0.148550 0.457191i
\(951\) 0 0
\(952\) 0.626929 0.455490i 0.0203189 0.0147625i
\(953\) 15.0400 + 46.2884i 0.487194 + 1.49943i 0.828778 + 0.559578i \(0.189037\pi\)
−0.341583 + 0.939852i \(0.610963\pi\)
\(954\) 0 0
\(955\) 28.7373 + 20.8789i 0.929918 + 0.675625i
\(956\) −38.6490 −1.25000
\(957\) 0 0
\(958\) −9.47032 −0.305972
\(959\) 15.4497 + 11.2249i 0.498897 + 0.362470i
\(960\) 0 0
\(961\) 3.59254 + 11.0567i 0.115888 + 0.356668i
\(962\) 11.5165 8.36721i 0.371306 0.269770i
\(963\) 0 0
\(964\) −7.80746 24.0289i −0.251461 0.773918i
\(965\) −6.26373 + 19.2778i −0.201636 + 0.620573i
\(966\) 0 0
\(967\) 10.9780 0.353029 0.176515 0.984298i \(-0.443518\pi\)
0.176515 + 0.984298i \(0.443518\pi\)
\(968\) 19.8386 12.2229i 0.637637 0.392858i
\(969\) 0 0
\(970\) 0.124770 + 0.0906508i 0.00400613 + 0.00291062i
\(971\) −4.03687 + 12.4242i −0.129549 + 0.398712i −0.994702 0.102796i \(-0.967221\pi\)
0.865153 + 0.501508i \(0.167221\pi\)
\(972\) 0 0
\(973\) −11.2108 + 8.14510i −0.359401 + 0.261120i
\(974\) 10.6518 7.73897i 0.341305 0.247973i
\(975\) 0 0
\(976\) −8.91708 + 27.4439i −0.285429 + 0.878459i
\(977\) −8.96092 6.51049i −0.286685 0.208289i 0.435143 0.900361i \(-0.356698\pi\)
−0.721828 + 0.692072i \(0.756698\pi\)
\(978\) 0 0
\(979\) 6.62642 + 2.43556i 0.211781 + 0.0778409i
\(980\) −28.2544 −0.902554
\(981\) 0 0
\(982\) −7.79262 + 23.9832i −0.248673 + 0.765336i
\(983\) 8.16778 + 25.1378i 0.260512 + 0.801772i 0.992693 + 0.120663i \(0.0385021\pi\)
−0.732182 + 0.681109i \(0.761498\pi\)
\(984\) 0 0
\(985\) 50.1863 36.4625i 1.59907 1.16179i
\(986\) −0.431959 1.32943i −0.0137564 0.0423378i
\(987\) 0 0
\(988\) −33.8745 24.6113i −1.07769 0.782989i
\(989\) −0.580083 −0.0184456
\(990\) 0 0
\(991\) −18.9911 −0.603272 −0.301636 0.953423i \(-0.597533\pi\)
−0.301636 + 0.953423i \(0.597533\pi\)
\(992\) 28.8122 + 20.9333i 0.914788 + 0.664633i
\(993\) 0 0
\(994\) −1.81234 5.57782i −0.0574841 0.176918i
\(995\) −32.2938 + 23.4628i −1.02378 + 0.743822i
\(996\) 0 0
\(997\) 6.83334 + 21.0309i 0.216414 + 0.666054i 0.999050 + 0.0435746i \(0.0138746\pi\)
−0.782636 + 0.622480i \(0.786125\pi\)
\(998\) 3.58956 11.0475i 0.113625 0.349703i
\(999\) 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 891.2.f.e.730.6 36
3.2 odd 2 891.2.f.f.730.4 36
9.2 odd 6 99.2.m.b.4.4 72
9.4 even 3 297.2.n.b.235.4 72
9.5 odd 6 99.2.m.b.70.6 yes 72
9.7 even 3 297.2.n.b.37.6 72
11.3 even 5 inner 891.2.f.e.487.6 36
11.5 even 5 9801.2.a.cp.1.8 18
11.6 odd 10 9801.2.a.cn.1.11 18
33.5 odd 10 9801.2.a.cm.1.11 18
33.14 odd 10 891.2.f.f.487.4 36
33.17 even 10 9801.2.a.co.1.8 18
99.5 odd 30 1089.2.e.p.727.8 36
99.14 odd 30 99.2.m.b.25.4 yes 72
99.25 even 15 297.2.n.b.91.4 72
99.38 odd 30 1089.2.e.p.364.8 36
99.47 odd 30 99.2.m.b.58.6 yes 72
99.50 even 30 1089.2.e.o.727.11 36
99.58 even 15 297.2.n.b.289.6 72
99.83 even 30 1089.2.e.o.364.11 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.4 72 9.2 odd 6
99.2.m.b.25.4 yes 72 99.14 odd 30
99.2.m.b.58.6 yes 72 99.47 odd 30
99.2.m.b.70.6 yes 72 9.5 odd 6
297.2.n.b.37.6 72 9.7 even 3
297.2.n.b.91.4 72 99.25 even 15
297.2.n.b.235.4 72 9.4 even 3
297.2.n.b.289.6 72 99.58 even 15
891.2.f.e.487.6 36 11.3 even 5 inner
891.2.f.e.730.6 36 1.1 even 1 trivial
891.2.f.f.487.4 36 33.14 odd 10
891.2.f.f.730.4 36 3.2 odd 2
1089.2.e.o.364.11 36 99.83 even 30
1089.2.e.o.727.11 36 99.50 even 30
1089.2.e.p.364.8 36 99.38 odd 30
1089.2.e.p.727.8 36 99.5 odd 30
9801.2.a.cm.1.11 18 33.5 odd 10
9801.2.a.cn.1.11 18 11.6 odd 10
9801.2.a.co.1.8 18 33.17 even 10
9801.2.a.cp.1.8 18 11.5 even 5