Properties

Label 95.2.i.b.49.3
Level $95$
Weight $2$
Character 95.49
Analytic conductor $0.759$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,2,Mod(49,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.i (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(-1.83525 - 1.05958i\) of defining polynomial
Character \(\chi\) \(=\) 95.49
Dual form 95.2.i.b.64.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.408663 - 0.235942i) q^{2} +(-0.900858 - 0.520111i) q^{3} +(-0.888663 - 1.53921i) q^{4} +(-2.19202 - 0.441641i) q^{5} +(0.245432 + 0.425100i) q^{6} -1.17540i q^{7} +1.78246i q^{8} +(-0.958970 - 1.66098i) q^{9} +O(q^{10})\) \(q+(-0.408663 - 0.235942i) q^{2} +(-0.900858 - 0.520111i) q^{3} +(-0.888663 - 1.53921i) q^{4} +(-2.19202 - 0.441641i) q^{5} +(0.245432 + 0.425100i) q^{6} -1.17540i q^{7} +1.78246i q^{8} +(-0.958970 - 1.66098i) q^{9} +(0.791597 + 0.697672i) q^{10} +0.713538 q^{11} +1.84881i q^{12} +(3.55344 - 2.05158i) q^{13} +(-0.277326 + 0.480342i) q^{14} +(1.74500 + 1.53795i) q^{15} +(-1.35677 + 2.34999i) q^{16} +(2.21038 + 1.27616i) q^{17} +0.905045i q^{18} +(-1.57031 - 4.06622i) q^{19} +(1.26819 + 3.76645i) q^{20} +(-0.611337 + 1.05887i) q^{21} +(-0.291597 - 0.168353i) q^{22} +(-0.525730 + 0.303530i) q^{23} +(0.927076 - 1.60574i) q^{24} +(4.60991 + 1.93617i) q^{25} -1.93621 q^{26} +5.11575i q^{27} +(-1.80918 + 1.04453i) q^{28} +(-0.429693 - 0.744250i) q^{29} +(-0.350250 - 1.04022i) q^{30} +2.50914 q^{31} +(4.19623 - 2.42270i) q^{32} +(-0.642796 - 0.371119i) q^{33} +(-0.602201 - 1.04304i) q^{34} +(-0.519104 + 2.57650i) q^{35} +(-1.70440 + 2.95211i) q^{36} -9.38171i q^{37} +(-0.317665 + 2.03222i) q^{38} -4.26819 q^{39} +(0.787207 - 3.90719i) q^{40} +(2.06117 - 3.57005i) q^{41} +(0.499662 - 0.288480i) q^{42} +(-8.76759 - 5.06197i) q^{43} +(-0.634095 - 1.09828i) q^{44} +(1.36852 + 4.06443i) q^{45} +0.286462 q^{46} +(-9.10919 + 5.25919i) q^{47} +(2.44451 - 1.41134i) q^{48} +5.61844 q^{49} +(-1.42708 - 1.87891i) q^{50} +(-1.32749 - 2.29928i) q^{51} +(-6.31561 - 3.64632i) q^{52} +(4.31330 - 2.49028i) q^{53} +(1.20702 - 2.09062i) q^{54} +(-1.56409 - 0.315128i) q^{55} +2.09510 q^{56} +(-0.700260 + 4.47982i) q^{57} +0.405530i q^{58} +(-3.12496 + 5.41259i) q^{59} +(0.816511 - 4.05263i) q^{60} +(2.27733 + 3.94444i) q^{61} +(-1.02539 - 0.592010i) q^{62} +(-1.95232 + 1.12717i) q^{63} +3.14061 q^{64} +(-8.69527 + 2.92776i) q^{65} +(0.175125 + 0.303325i) q^{66} +(4.48783 - 2.59105i) q^{67} -4.53632i q^{68} +0.631477 q^{69} +(0.820042 - 0.930441i) q^{70} +(6.58393 - 11.4037i) q^{71} +(2.96064 - 1.70932i) q^{72} +(10.7199 + 6.18914i) q^{73} +(-2.21354 + 3.83396i) q^{74} +(-3.14585 - 4.14188i) q^{75} +(-4.86329 + 6.03053i) q^{76} -0.838691i q^{77} +(1.74425 + 1.00704i) q^{78} +(-2.98173 + 5.16450i) q^{79} +(4.01192 - 4.55203i) q^{80} +(-0.216155 + 0.374392i) q^{81} +(-1.68465 + 0.972633i) q^{82} +13.8603i q^{83} +2.17309 q^{84} +(-4.28159 - 3.77357i) q^{85} +(2.38866 + 4.13729i) q^{86} +0.893952i q^{87} +1.27185i q^{88} +(7.98173 + 13.8248i) q^{89} +(0.399705 - 1.98388i) q^{90} +(-2.41142 - 4.17670i) q^{91} +(0.934393 + 0.539472i) q^{92} +(-2.26038 - 1.30503i) q^{93} +4.96345 q^{94} +(1.64634 + 9.60675i) q^{95} -5.04028 q^{96} +(14.4643 + 8.35099i) q^{97} +(-2.29605 - 1.32563i) q^{98} +(-0.684261 - 1.18518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 8 q^{9} + 6 q^{10} + 4 q^{11} + 22 q^{14} - 4 q^{15} - 14 q^{16} - 12 q^{19} - 40 q^{20} - 20 q^{21} + 2 q^{24} - 6 q^{25} - 44 q^{26} - 12 q^{29} + 12 q^{30} + 60 q^{31} + 10 q^{34} + 14 q^{36} + 4 q^{39} + 10 q^{40} - 12 q^{41} + 20 q^{44} + 60 q^{45} + 8 q^{46} - 4 q^{49} - 8 q^{50} - 40 q^{51} - 4 q^{54} - 18 q^{55} + 92 q^{56} + 20 q^{59} + 4 q^{60} + 2 q^{61} + 24 q^{64} - 40 q^{65} - 6 q^{66} - 36 q^{69} + 46 q^{70} + 2 q^{71} - 22 q^{74} - 56 q^{75} - 70 q^{76} + 24 q^{79} - 22 q^{80} - 14 q^{81} - 96 q^{84} + 2 q^{85} + 16 q^{86} + 36 q^{89} - 8 q^{90} + 24 q^{91} - 60 q^{94} + 46 q^{95} + 52 q^{96} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.408663 0.235942i −0.288969 0.166836i 0.348508 0.937306i \(-0.386688\pi\)
−0.637477 + 0.770470i \(0.720022\pi\)
\(3\) −0.900858 0.520111i −0.520111 0.300286i 0.216869 0.976201i \(-0.430415\pi\)
−0.736980 + 0.675915i \(0.763749\pi\)
\(4\) −0.888663 1.53921i −0.444331 0.769605i
\(5\) −2.19202 0.441641i −0.980301 0.197508i
\(6\) 0.245432 + 0.425100i 0.100197 + 0.173546i
\(7\) 1.17540i 0.444259i −0.975017 0.222129i \(-0.928699\pi\)
0.975017 0.222129i \(-0.0713007\pi\)
\(8\) 1.78246i 0.630194i
\(9\) −0.958970 1.66098i −0.319657 0.553661i
\(10\) 0.791597 + 0.697672i 0.250325 + 0.220623i
\(11\) 0.713538 0.215140 0.107570 0.994198i \(-0.465693\pi\)
0.107570 + 0.994198i \(0.465693\pi\)
\(12\) 1.84881i 0.533706i
\(13\) 3.55344 2.05158i 0.985546 0.569005i 0.0816060 0.996665i \(-0.473995\pi\)
0.903940 + 0.427659i \(0.140662\pi\)
\(14\) −0.277326 + 0.480342i −0.0741184 + 0.128377i
\(15\) 1.74500 + 1.53795i 0.450556 + 0.397097i
\(16\) −1.35677 + 2.34999i −0.339192 + 0.587498i
\(17\) 2.21038 + 1.27616i 0.536096 + 0.309515i 0.743495 0.668741i \(-0.233167\pi\)
−0.207399 + 0.978256i \(0.566500\pi\)
\(18\) 0.905045i 0.213321i
\(19\) −1.57031 4.06622i −0.360253 0.932855i
\(20\) 1.26819 + 3.76645i 0.283576 + 0.842203i
\(21\) −0.611337 + 1.05887i −0.133405 + 0.231064i
\(22\) −0.291597 0.168353i −0.0621686 0.0358931i
\(23\) −0.525730 + 0.303530i −0.109622 + 0.0632904i −0.553809 0.832644i \(-0.686826\pi\)
0.444186 + 0.895934i \(0.353493\pi\)
\(24\) 0.927076 1.60574i 0.189239 0.327771i
\(25\) 4.60991 + 1.93617i 0.921981 + 0.387234i
\(26\) −1.93621 −0.379722
\(27\) 5.11575i 0.984526i
\(28\) −1.80918 + 1.04453i −0.341904 + 0.197398i
\(29\) −0.429693 0.744250i −0.0797920 0.138204i 0.823368 0.567508i \(-0.192092\pi\)
−0.903160 + 0.429304i \(0.858759\pi\)
\(30\) −0.350250 1.04022i −0.0639466 0.189918i
\(31\) 2.50914 0.450654 0.225327 0.974283i \(-0.427655\pi\)
0.225327 + 0.974283i \(0.427655\pi\)
\(32\) 4.19623 2.42270i 0.741796 0.428276i
\(33\) −0.642796 0.371119i −0.111897 0.0646035i
\(34\) −0.602201 1.04304i −0.103277 0.178880i
\(35\) −0.519104 + 2.57650i −0.0877446 + 0.435507i
\(36\) −1.70440 + 2.95211i −0.284067 + 0.492018i
\(37\) 9.38171i 1.54234i −0.636627 0.771172i \(-0.719671\pi\)
0.636627 0.771172i \(-0.280329\pi\)
\(38\) −0.317665 + 2.03222i −0.0515320 + 0.329669i
\(39\) −4.26819 −0.683457
\(40\) 0.787207 3.90719i 0.124468 0.617780i
\(41\) 2.06117 3.57005i 0.321901 0.557548i −0.658979 0.752161i \(-0.729012\pi\)
0.980880 + 0.194612i \(0.0623449\pi\)
\(42\) 0.499662 0.288480i 0.0770996 0.0445134i
\(43\) −8.76759 5.06197i −1.33705 0.771944i −0.350677 0.936496i \(-0.614049\pi\)
−0.986368 + 0.164553i \(0.947382\pi\)
\(44\) −0.634095 1.09828i −0.0955934 0.165573i
\(45\) 1.36852 + 4.06443i 0.204007 + 0.605890i
\(46\) 0.286462 0.0422365
\(47\) −9.10919 + 5.25919i −1.32871 + 0.767132i −0.985100 0.171980i \(-0.944984\pi\)
−0.343611 + 0.939112i \(0.611650\pi\)
\(48\) 2.44451 1.41134i 0.352835 0.203709i
\(49\) 5.61844 0.802634
\(50\) −1.42708 1.87891i −0.201819 0.265718i
\(51\) −1.32749 2.29928i −0.185886 0.321964i
\(52\) −6.31561 3.64632i −0.875818 0.505654i
\(53\) 4.31330 2.49028i 0.592477 0.342067i −0.173599 0.984816i \(-0.555540\pi\)
0.766076 + 0.642750i \(0.222206\pi\)
\(54\) 1.20702 2.09062i 0.164254 0.284497i
\(55\) −1.56409 0.315128i −0.210902 0.0424918i
\(56\) 2.09510 0.279969
\(57\) −0.700260 + 4.47982i −0.0927517 + 0.593367i
\(58\) 0.405530i 0.0532488i
\(59\) −3.12496 + 5.41259i −0.406835 + 0.704659i −0.994533 0.104421i \(-0.966701\pi\)
0.587698 + 0.809080i \(0.300034\pi\)
\(60\) 0.816511 4.05263i 0.105411 0.523193i
\(61\) 2.27733 + 3.94444i 0.291582 + 0.505034i 0.974184 0.225756i \(-0.0724852\pi\)
−0.682602 + 0.730790i \(0.739152\pi\)
\(62\) −1.02539 0.592010i −0.130225 0.0751854i
\(63\) −1.95232 + 1.12717i −0.245969 + 0.142010i
\(64\) 3.14061 0.392577
\(65\) −8.69527 + 2.92776i −1.07851 + 0.363144i
\(66\) 0.175125 + 0.303325i 0.0215564 + 0.0373368i
\(67\) 4.48783 2.59105i 0.548276 0.316547i −0.200151 0.979765i \(-0.564143\pi\)
0.748426 + 0.663218i \(0.230810\pi\)
\(68\) 4.53632i 0.550109i
\(69\) 0.631477 0.0760209
\(70\) 0.820042 0.930441i 0.0980138 0.111209i
\(71\) 6.58393 11.4037i 0.781368 1.35337i −0.149776 0.988720i \(-0.547855\pi\)
0.931145 0.364650i \(-0.118811\pi\)
\(72\) 2.96064 1.70932i 0.348914 0.201446i
\(73\) 10.7199 + 6.18914i 1.25467 + 0.724384i 0.972033 0.234842i \(-0.0754574\pi\)
0.282637 + 0.959227i \(0.408791\pi\)
\(74\) −2.21354 + 3.83396i −0.257319 + 0.445689i
\(75\) −3.14585 4.14188i −0.363251 0.478263i
\(76\) −4.86329 + 6.03053i −0.557857 + 0.691749i
\(77\) 0.838691i 0.0955777i
\(78\) 1.74425 + 1.00704i 0.197498 + 0.114025i
\(79\) −2.98173 + 5.16450i −0.335471 + 0.581052i −0.983575 0.180499i \(-0.942229\pi\)
0.648105 + 0.761551i \(0.275562\pi\)
\(80\) 4.01192 4.55203i 0.448546 0.508932i
\(81\) −0.216155 + 0.374392i −0.0240172 + 0.0415991i
\(82\) −1.68465 + 0.972633i −0.186038 + 0.107409i
\(83\) 13.8603i 1.52136i 0.649124 + 0.760682i \(0.275136\pi\)
−0.649124 + 0.760682i \(0.724864\pi\)
\(84\) 2.17309 0.237104
\(85\) −4.28159 3.77357i −0.464404 0.409301i
\(86\) 2.38866 + 4.13729i 0.257576 + 0.446135i
\(87\) 0.893952i 0.0958417i
\(88\) 1.27185i 0.135580i
\(89\) 7.98173 + 13.8248i 0.846061 + 1.46542i 0.884696 + 0.466168i \(0.154366\pi\)
−0.0386349 + 0.999253i \(0.512301\pi\)
\(90\) 0.399705 1.98388i 0.0421326 0.209119i
\(91\) −2.41142 4.17670i −0.252786 0.437837i
\(92\) 0.934393 + 0.539472i 0.0974172 + 0.0562439i
\(93\) −2.26038 1.30503i −0.234390 0.135325i
\(94\) 4.96345 0.511941
\(95\) 1.64634 + 9.60675i 0.168911 + 0.985631i
\(96\) −5.04028 −0.514421
\(97\) 14.4643 + 8.35099i 1.46863 + 0.847915i 0.999382 0.0351512i \(-0.0111913\pi\)
0.469249 + 0.883066i \(0.344525\pi\)
\(98\) −2.29605 1.32563i −0.231936 0.133908i
\(99\) −0.684261 1.18518i −0.0687708 0.119115i
\(100\) −1.11648 8.81621i −0.111648 0.881621i
\(101\) −7.01362 12.1479i −0.697881 1.20877i −0.969200 0.246276i \(-0.920793\pi\)
0.271318 0.962490i \(-0.412540\pi\)
\(102\) 1.25284i 0.124050i
\(103\) 3.55382i 0.350169i 0.984553 + 0.175084i \(0.0560198\pi\)
−0.984553 + 0.175084i \(0.943980\pi\)
\(104\) 3.65685 + 6.33385i 0.358584 + 0.621085i
\(105\) 1.80770 2.05107i 0.176414 0.200164i
\(106\) −2.35025 −0.228276
\(107\) 3.63127i 0.351048i −0.984475 0.175524i \(-0.943838\pi\)
0.984475 0.175524i \(-0.0561620\pi\)
\(108\) 7.87420 4.54617i 0.757696 0.437456i
\(109\) −3.11134 + 5.38899i −0.298012 + 0.516172i −0.975681 0.219195i \(-0.929657\pi\)
0.677669 + 0.735367i \(0.262990\pi\)
\(110\) 0.564834 + 0.497815i 0.0538548 + 0.0474648i
\(111\) −4.87953 + 8.45159i −0.463144 + 0.802189i
\(112\) 2.76218 + 1.59474i 0.261001 + 0.150689i
\(113\) 12.2707i 1.15433i −0.816626 0.577167i \(-0.804158\pi\)
0.816626 0.577167i \(-0.195842\pi\)
\(114\) 1.34315 1.66552i 0.125797 0.155990i
\(115\) 1.28646 0.433161i 0.119963 0.0403925i
\(116\) −0.763705 + 1.32278i −0.0709082 + 0.122817i
\(117\) −6.81528 3.93480i −0.630072 0.363773i
\(118\) 2.55411 1.47462i 0.235125 0.135750i
\(119\) 1.50000 2.59808i 0.137505 0.238165i
\(120\) −2.74133 + 3.11039i −0.250248 + 0.283938i
\(121\) −10.4909 −0.953715
\(122\) 2.14927i 0.194585i
\(123\) −3.71364 + 2.14407i −0.334848 + 0.193325i
\(124\) −2.22978 3.86209i −0.200240 0.346826i
\(125\) −9.24992 6.28005i −0.827338 0.561705i
\(126\) 1.06379 0.0947697
\(127\) −1.86879 + 1.07894i −0.165828 + 0.0957408i −0.580617 0.814177i \(-0.697189\pi\)
0.414789 + 0.909918i \(0.363855\pi\)
\(128\) −9.67592 5.58639i −0.855239 0.493772i
\(129\) 5.26557 + 9.12024i 0.463608 + 0.802992i
\(130\) 4.24422 + 0.855111i 0.372242 + 0.0749982i
\(131\) 8.77471 15.1982i 0.766650 1.32788i −0.172720 0.984971i \(-0.555256\pi\)
0.939370 0.342906i \(-0.111411\pi\)
\(132\) 1.31920i 0.114821i
\(133\) −4.77943 + 1.84574i −0.414429 + 0.160046i
\(134\) −2.44535 −0.211246
\(135\) 2.25932 11.2138i 0.194452 0.965132i
\(136\) −2.27471 + 3.93991i −0.195055 + 0.337845i
\(137\) −4.39469 + 2.53728i −0.375464 + 0.216774i −0.675843 0.737046i \(-0.736220\pi\)
0.300379 + 0.953820i \(0.402887\pi\)
\(138\) −0.258062 0.148992i −0.0219677 0.0126830i
\(139\) 2.99086 + 5.18033i 0.253682 + 0.439390i 0.964537 0.263949i \(-0.0850251\pi\)
−0.710855 + 0.703339i \(0.751692\pi\)
\(140\) 4.42708 1.49063i 0.374156 0.125981i
\(141\) 10.9414 0.921436
\(142\) −5.38122 + 3.10685i −0.451582 + 0.260721i
\(143\) 2.53551 1.46388i 0.212030 0.122416i
\(144\) 5.20440 0.433700
\(145\) 0.613205 + 1.82118i 0.0509239 + 0.151241i
\(146\) −2.92056 5.05855i −0.241707 0.418649i
\(147\) −5.06142 2.92221i −0.417459 0.241020i
\(148\) −14.4404 + 8.33718i −1.18699 + 0.685312i
\(149\) 4.80008 8.31399i 0.393238 0.681108i −0.599636 0.800273i \(-0.704688\pi\)
0.992875 + 0.119164i \(0.0380215\pi\)
\(150\) 0.308350 + 2.43487i 0.0251767 + 0.198806i
\(151\) 7.53638 0.613302 0.306651 0.951822i \(-0.400792\pi\)
0.306651 + 0.951822i \(0.400792\pi\)
\(152\) 7.24787 2.79901i 0.587880 0.227029i
\(153\) 4.89521i 0.395754i
\(154\) −0.197882 + 0.342742i −0.0159458 + 0.0276190i
\(155\) −5.50008 1.10814i −0.441777 0.0890077i
\(156\) 3.79298 + 6.56964i 0.303682 + 0.525992i
\(157\) −8.53560 4.92803i −0.681215 0.393300i 0.119098 0.992883i \(-0.462000\pi\)
−0.800313 + 0.599583i \(0.795333\pi\)
\(158\) 2.43705 1.40703i 0.193881 0.111937i
\(159\) −5.18089 −0.410872
\(160\) −10.2682 + 3.45737i −0.811772 + 0.273329i
\(161\) 0.356769 + 0.617942i 0.0281173 + 0.0487007i
\(162\) 0.176669 0.102000i 0.0138805 0.00801389i
\(163\) 0.0688234i 0.00539067i −0.999996 0.00269533i \(-0.999142\pi\)
0.999996 0.00269533i \(-0.000857952\pi\)
\(164\) −7.32674 −0.572122
\(165\) 1.24512 + 1.09738i 0.0969326 + 0.0854313i
\(166\) 3.27022 5.66419i 0.253819 0.439627i
\(167\) 14.4143 8.32212i 1.11542 0.643985i 0.175189 0.984535i \(-0.443946\pi\)
0.940227 + 0.340550i \(0.110613\pi\)
\(168\) −1.88739 1.08968i −0.145615 0.0840709i
\(169\) 1.91794 3.32197i 0.147534 0.255536i
\(170\) 0.859386 + 2.55233i 0.0659119 + 0.195755i
\(171\) −5.24805 + 6.50764i −0.401328 + 0.497651i
\(172\) 17.9935i 1.37200i
\(173\) −10.5097 6.06778i −0.799038 0.461325i 0.0440965 0.999027i \(-0.485959\pi\)
−0.843135 + 0.537702i \(0.819292\pi\)
\(174\) 0.210921 0.365325i 0.0159899 0.0276952i
\(175\) 2.27577 5.41848i 0.172032 0.409598i
\(176\) −0.968106 + 1.67681i −0.0729737 + 0.126394i
\(177\) 5.63029 3.25065i 0.423198 0.244334i
\(178\) 7.53290i 0.564614i
\(179\) −11.7538 −0.878522 −0.439261 0.898360i \(-0.644760\pi\)
−0.439261 + 0.898360i \(0.644760\pi\)
\(180\) 5.03986 5.71835i 0.375649 0.426221i
\(181\) 4.41794 + 7.65210i 0.328383 + 0.568776i 0.982191 0.187884i \(-0.0601631\pi\)
−0.653808 + 0.756660i \(0.726830\pi\)
\(182\) 2.27582i 0.168695i
\(183\) 4.73785i 0.350232i
\(184\) −0.541030 0.937092i −0.0398853 0.0690833i
\(185\) −4.14335 + 20.5649i −0.304625 + 1.51196i
\(186\) 0.615822 + 1.06663i 0.0451543 + 0.0782095i
\(187\) 1.57719 + 0.910591i 0.115336 + 0.0665890i
\(188\) 16.1900 + 9.34730i 1.18078 + 0.681722i
\(189\) 6.01304 0.437384
\(190\) 1.59384 4.31436i 0.115629 0.312997i
\(191\) 14.2447 1.03071 0.515355 0.856977i \(-0.327660\pi\)
0.515355 + 0.856977i \(0.327660\pi\)
\(192\) −2.82925 1.63347i −0.204183 0.117885i
\(193\) 16.8924 + 9.75283i 1.21594 + 0.702024i 0.964047 0.265731i \(-0.0856133\pi\)
0.251894 + 0.967755i \(0.418947\pi\)
\(194\) −3.94070 6.82549i −0.282926 0.490041i
\(195\) 9.35596 + 1.88501i 0.669994 + 0.134988i
\(196\) −4.99290 8.64795i −0.356636 0.617711i
\(197\) 4.33232i 0.308665i −0.988019 0.154332i \(-0.950677\pi\)
0.988019 0.154332i \(-0.0493226\pi\)
\(198\) 0.645784i 0.0458938i
\(199\) −6.31574 10.9392i −0.447711 0.775458i 0.550526 0.834818i \(-0.314427\pi\)
−0.998237 + 0.0593602i \(0.981094\pi\)
\(200\) −3.45115 + 8.21697i −0.244033 + 0.581027i
\(201\) −5.39053 −0.380219
\(202\) 6.61923i 0.465727i
\(203\) −0.874790 + 0.505060i −0.0613983 + 0.0354483i
\(204\) −2.35939 + 4.08658i −0.165190 + 0.286118i
\(205\) −6.09481 + 6.91533i −0.425680 + 0.482988i
\(206\) 0.838496 1.45232i 0.0584208 0.101188i
\(207\) 1.00832 + 0.582153i 0.0700830 + 0.0404624i
\(208\) 11.1341i 0.772009i
\(209\) −1.12047 2.90140i −0.0775048 0.200694i
\(210\) −1.22267 + 0.411683i −0.0843725 + 0.0284088i
\(211\) −11.1223 + 19.2645i −0.765694 + 1.32622i 0.174186 + 0.984713i \(0.444271\pi\)
−0.939879 + 0.341507i \(0.889063\pi\)
\(212\) −7.66614 4.42605i −0.526512 0.303982i
\(213\) −11.8624 + 6.84874i −0.812796 + 0.469268i
\(214\) −0.856769 + 1.48397i −0.0585675 + 0.101442i
\(215\) 16.9832 + 14.9681i 1.15824 + 1.02081i
\(216\) −9.11861 −0.620443
\(217\) 2.94923i 0.200207i
\(218\) 2.54298 1.46819i 0.172232 0.0994383i
\(219\) −6.43808 11.1511i −0.435045 0.753520i
\(220\) 0.904901 + 2.68750i 0.0610084 + 0.181191i
\(221\) 10.4726 0.704463
\(222\) 3.98817 2.30257i 0.267668 0.154538i
\(223\) 11.7974 + 6.81125i 0.790015 + 0.456115i 0.839968 0.542636i \(-0.182574\pi\)
−0.0499529 + 0.998752i \(0.515907\pi\)
\(224\) −2.84763 4.93224i −0.190265 0.329549i
\(225\) −1.20481 9.51371i −0.0803207 0.634248i
\(226\) −2.89518 + 5.01460i −0.192585 + 0.333566i
\(227\) 6.58913i 0.437336i 0.975799 + 0.218668i \(0.0701711\pi\)
−0.975799 + 0.218668i \(0.929829\pi\)
\(228\) 7.51768 2.90320i 0.497870 0.192269i
\(229\) 0.585962 0.0387215 0.0193607 0.999813i \(-0.493837\pi\)
0.0193607 + 0.999813i \(0.493837\pi\)
\(230\) −0.627931 0.126513i −0.0414045 0.00834204i
\(231\) −0.436212 + 0.755542i −0.0287007 + 0.0497110i
\(232\) 1.32660 0.765910i 0.0870953 0.0502845i
\(233\) 6.19855 + 3.57873i 0.406080 + 0.234451i 0.689104 0.724662i \(-0.258004\pi\)
−0.283024 + 0.959113i \(0.591338\pi\)
\(234\) 1.85677 + 3.21602i 0.121381 + 0.210238i
\(235\) 22.2902 7.50527i 1.45405 0.489590i
\(236\) 11.1081 0.723078
\(237\) 5.37223 3.10166i 0.348964 0.201474i
\(238\) −1.22599 + 0.707826i −0.0794691 + 0.0458815i
\(239\) −3.65498 −0.236421 −0.118211 0.992989i \(-0.537716\pi\)
−0.118211 + 0.992989i \(0.537716\pi\)
\(240\) −5.98173 + 2.01409i −0.386119 + 0.130009i
\(241\) −8.63148 14.9502i −0.556002 0.963024i −0.997825 0.0659218i \(-0.979001\pi\)
0.441822 0.897103i \(-0.354332\pi\)
\(242\) 4.28723 + 2.47523i 0.275594 + 0.159114i
\(243\) 13.6805 7.89847i 0.877608 0.506687i
\(244\) 4.04755 7.01056i 0.259118 0.448805i
\(245\) −12.3157 2.48133i −0.786823 0.158527i
\(246\) 2.02351 0.129014
\(247\) −13.9221 11.2274i −0.885845 0.714385i
\(248\) 4.47243i 0.284000i
\(249\) 7.20889 12.4862i 0.456845 0.791278i
\(250\) 2.29837 + 4.74887i 0.145362 + 0.300345i
\(251\) 9.70702 + 16.8130i 0.612702 + 1.06123i 0.990783 + 0.135458i \(0.0432506\pi\)
−0.378082 + 0.925772i \(0.623416\pi\)
\(252\) 3.46990 + 2.00335i 0.218583 + 0.126199i
\(253\) −0.375128 + 0.216580i −0.0235841 + 0.0136163i
\(254\) 1.01827 0.0638921
\(255\) 1.89443 + 5.62635i 0.118634 + 0.352336i
\(256\) −0.504485 0.873793i −0.0315303 0.0546121i
\(257\) −12.0316 + 6.94643i −0.750509 + 0.433306i −0.825878 0.563849i \(-0.809320\pi\)
0.0753689 + 0.997156i \(0.475987\pi\)
\(258\) 4.96948i 0.309386i
\(259\) −11.0272 −0.685199
\(260\) 12.2336 + 10.7820i 0.758695 + 0.668674i
\(261\) −0.824125 + 1.42743i −0.0510121 + 0.0883555i
\(262\) −7.17180 + 4.14064i −0.443076 + 0.255810i
\(263\) −12.9803 7.49417i −0.800399 0.462110i 0.0432118 0.999066i \(-0.486241\pi\)
−0.843611 + 0.536955i \(0.819574\pi\)
\(264\) 0.661504 1.14576i 0.0407127 0.0705165i
\(265\) −10.5547 + 3.55382i −0.648367 + 0.218310i
\(266\) 2.38866 + 0.373382i 0.146458 + 0.0228935i
\(267\) 16.6055i 1.01624i
\(268\) −7.97633 4.60514i −0.487232 0.281304i
\(269\) 9.68613 16.7769i 0.590574 1.02290i −0.403582 0.914944i \(-0.632235\pi\)
0.994155 0.107960i \(-0.0344318\pi\)
\(270\) −3.56911 + 4.04961i −0.217209 + 0.246451i
\(271\) −5.95897 + 10.3212i −0.361982 + 0.626971i −0.988287 0.152607i \(-0.951233\pi\)
0.626305 + 0.779578i \(0.284566\pi\)
\(272\) −5.99795 + 3.46292i −0.363679 + 0.209970i
\(273\) 5.01682i 0.303632i
\(274\) 2.39460 0.144663
\(275\) 3.28934 + 1.38153i 0.198355 + 0.0833095i
\(276\) −0.561171 0.971976i −0.0337785 0.0585061i
\(277\) 10.9824i 0.659866i 0.944004 + 0.329933i \(0.107026\pi\)
−0.944004 + 0.329933i \(0.892974\pi\)
\(278\) 2.82268i 0.169293i
\(279\) −2.40619 4.16764i −0.144055 0.249510i
\(280\) −4.59250 0.925281i −0.274454 0.0552961i
\(281\) −7.32488 12.6871i −0.436965 0.756846i 0.560488 0.828162i \(-0.310613\pi\)
−0.997454 + 0.0713160i \(0.977280\pi\)
\(282\) −4.47137 2.58155i −0.266266 0.153729i
\(283\) −16.3927 9.46435i −0.974447 0.562597i −0.0738576 0.997269i \(-0.523531\pi\)
−0.900589 + 0.434672i \(0.856864\pi\)
\(284\) −23.4036 −1.38875
\(285\) 3.51346 9.51059i 0.208119 0.563359i
\(286\) −1.38156 −0.0816934
\(287\) −4.19623 2.42270i −0.247696 0.143007i
\(288\) −8.04812 4.64658i −0.474240 0.273803i
\(289\) −5.24281 9.08082i −0.308401 0.534166i
\(290\) 0.179099 0.888931i 0.0105170 0.0521998i
\(291\) −8.68688 15.0461i −0.509234 0.882019i
\(292\) 22.0002i 1.28747i
\(293\) 5.59625i 0.326937i −0.986549 0.163468i \(-0.947732\pi\)
0.986549 0.163468i \(-0.0522681\pi\)
\(294\) 1.37894 + 2.38840i 0.0804216 + 0.139294i
\(295\) 9.24039 10.4844i 0.537996 0.610425i
\(296\) 16.7225 0.971976
\(297\) 3.65028i 0.211811i
\(298\) −3.92324 + 2.26508i −0.227267 + 0.131213i
\(299\) −1.24543 + 2.15715i −0.0720252 + 0.124751i
\(300\) −3.57962 + 8.52285i −0.206669 + 0.492067i
\(301\) −5.94983 + 10.3054i −0.342943 + 0.593994i
\(302\) −3.07984 1.77815i −0.177225 0.102321i
\(303\) 14.5914i 0.838256i
\(304\) 11.6861 + 1.82671i 0.670245 + 0.104769i
\(305\) −3.24992 9.65206i −0.186090 0.552675i
\(306\) −1.15498 + 2.00049i −0.0660261 + 0.114361i
\(307\) 17.8678 + 10.3160i 1.01977 + 0.588764i 0.914037 0.405631i \(-0.132948\pi\)
0.105732 + 0.994395i \(0.466282\pi\)
\(308\) −1.29092 + 0.745314i −0.0735571 + 0.0424682i
\(309\) 1.84838 3.20149i 0.105151 0.182127i
\(310\) 1.98622 + 1.75055i 0.112810 + 0.0994248i
\(311\) −24.6587 −1.39827 −0.699134 0.714991i \(-0.746431\pi\)
−0.699134 + 0.714991i \(0.746431\pi\)
\(312\) 7.60787i 0.430711i
\(313\) 3.02985 1.74928i 0.171257 0.0988753i −0.411921 0.911219i \(-0.635142\pi\)
0.583178 + 0.812344i \(0.301809\pi\)
\(314\) 2.32546 + 4.02781i 0.131233 + 0.227303i
\(315\) 4.77733 1.60856i 0.269172 0.0906320i
\(316\) 10.5990 0.596240
\(317\) −27.1680 + 15.6854i −1.52590 + 0.880982i −0.526377 + 0.850251i \(0.676450\pi\)
−0.999528 + 0.0307305i \(0.990217\pi\)
\(318\) 2.11724 + 1.22239i 0.118729 + 0.0685482i
\(319\) −0.306602 0.531051i −0.0171664 0.0297331i
\(320\) −6.88429 1.38702i −0.384843 0.0775370i
\(321\) −1.88866 + 3.27126i −0.105415 + 0.182584i
\(322\) 0.336707i 0.0187639i
\(323\) 1.71818 10.9919i 0.0956024 0.611603i
\(324\) 0.768356 0.0426865
\(325\) 20.3532 2.57752i 1.12899 0.142975i
\(326\) −0.0162383 + 0.0281256i −0.000899358 + 0.00155773i
\(327\) 5.60575 3.23648i 0.309999 0.178978i
\(328\) 6.36347 + 3.67395i 0.351364 + 0.202860i
\(329\) 6.18164 + 10.7069i 0.340805 + 0.590292i
\(330\) −0.249917 0.742237i −0.0137575 0.0408588i
\(331\) 35.7497 1.96498 0.982492 0.186305i \(-0.0596512\pi\)
0.982492 + 0.186305i \(0.0596512\pi\)
\(332\) 21.3339 12.3171i 1.17085 0.675990i
\(333\) −15.5829 + 8.99677i −0.853936 + 0.493020i
\(334\) −7.85415 −0.429760
\(335\) −10.9817 + 3.69762i −0.599996 + 0.202023i
\(336\) −1.65889 2.87328i −0.0904997 0.156750i
\(337\) 22.9403 + 13.2446i 1.24964 + 0.721480i 0.971038 0.238927i \(-0.0767956\pi\)
0.278602 + 0.960407i \(0.410129\pi\)
\(338\) −1.56758 + 0.905045i −0.0852653 + 0.0492279i
\(339\) −6.38214 + 11.0542i −0.346630 + 0.600382i
\(340\) −2.00342 + 9.94370i −0.108651 + 0.539273i
\(341\) 1.79036 0.0969536
\(342\) 3.68011 1.42120i 0.198998 0.0768496i
\(343\) 14.8317i 0.800836i
\(344\) 9.02276 15.6279i 0.486474 0.842599i
\(345\) −1.38421 0.278886i −0.0745234 0.0150147i
\(346\) 2.86329 + 4.95936i 0.153931 + 0.266617i
\(347\) 29.7392 + 17.1699i 1.59648 + 0.921729i 0.992158 + 0.124990i \(0.0398898\pi\)
0.604323 + 0.796739i \(0.293444\pi\)
\(348\) 1.37598 0.794422i 0.0737602 0.0425855i
\(349\) 21.4308 1.14717 0.573583 0.819148i \(-0.305553\pi\)
0.573583 + 0.819148i \(0.305553\pi\)
\(350\) −2.20847 + 1.67738i −0.118048 + 0.0896599i
\(351\) 10.4953 + 18.1785i 0.560200 + 0.970295i
\(352\) 2.99417 1.72869i 0.159590 0.0921393i
\(353\) 19.5659i 1.04139i 0.853744 + 0.520693i \(0.174326\pi\)
−0.853744 + 0.520693i \(0.825674\pi\)
\(354\) −3.06786 −0.163055
\(355\) −19.4684 + 22.0894i −1.03328 + 1.17238i
\(356\) 14.1861 24.5711i 0.751863 1.30227i
\(357\) −2.70257 + 1.56033i −0.143035 + 0.0825815i
\(358\) 4.80335 + 2.77322i 0.253865 + 0.146569i
\(359\) −8.23630 + 14.2657i −0.434695 + 0.752914i −0.997271 0.0738319i \(-0.976477\pi\)
0.562576 + 0.826746i \(0.309811\pi\)
\(360\) −7.24468 + 2.43934i −0.381828 + 0.128564i
\(361\) −14.0683 + 12.7704i −0.740435 + 0.672128i
\(362\) 4.16951i 0.219144i
\(363\) 9.45078 + 5.45641i 0.496037 + 0.286387i
\(364\) −4.28588 + 7.42336i −0.224641 + 0.389090i
\(365\) −20.7649 18.3011i −1.08688 0.957922i
\(366\) −1.11786 + 1.93618i −0.0584313 + 0.101206i
\(367\) −11.0286 + 6.36735i −0.575687 + 0.332373i −0.759418 0.650603i \(-0.774516\pi\)
0.183730 + 0.982977i \(0.441183\pi\)
\(368\) 1.64728i 0.0858705i
\(369\) −7.90640 −0.411591
\(370\) 6.54535 7.42653i 0.340277 0.386087i
\(371\) −2.92708 5.06984i −0.151966 0.263213i
\(372\) 4.63892i 0.240517i
\(373\) 19.3342i 1.00109i −0.865711 0.500544i \(-0.833133\pi\)
0.865711 0.500544i \(-0.166867\pi\)
\(374\) −0.429693 0.744250i −0.0222189 0.0384843i
\(375\) 5.06654 + 10.4684i 0.261635 + 0.540587i
\(376\) −9.37429 16.2368i −0.483442 0.837346i
\(377\) −3.05377 1.76310i −0.157277 0.0908041i
\(378\) −2.45731 1.41873i −0.126390 0.0729715i
\(379\) −9.85789 −0.506366 −0.253183 0.967418i \(-0.581477\pi\)
−0.253183 + 0.967418i \(0.581477\pi\)
\(380\) 13.3238 11.0712i 0.683494 0.567941i
\(381\) 2.24468 0.114999
\(382\) −5.82128 3.36092i −0.297843 0.171959i
\(383\) 17.6091 + 10.1666i 0.899784 + 0.519490i 0.877130 0.480253i \(-0.159455\pi\)
0.0226536 + 0.999743i \(0.492789\pi\)
\(384\) 5.81109 + 10.0651i 0.296546 + 0.513632i
\(385\) −0.370400 + 1.83843i −0.0188773 + 0.0936950i
\(386\) −4.60220 7.97125i −0.234246 0.405726i
\(387\) 19.4171i 0.987027i
\(388\) 29.6849i 1.50702i
\(389\) −0.502617 0.870559i −0.0254837 0.0441391i 0.853002 0.521907i \(-0.174779\pi\)
−0.878486 + 0.477768i \(0.841446\pi\)
\(390\) −3.37869 2.97780i −0.171086 0.150787i
\(391\) −1.54942 −0.0783574
\(392\) 10.0146i 0.505816i
\(393\) −15.8095 + 9.12764i −0.797486 + 0.460428i
\(394\) −1.02217 + 1.77046i −0.0514964 + 0.0891944i
\(395\) 8.81686 10.0038i 0.443625 0.503348i
\(396\) −1.21616 + 2.10644i −0.0611141 + 0.105853i
\(397\) −8.54093 4.93111i −0.428657 0.247485i 0.270117 0.962827i \(-0.412937\pi\)
−0.698774 + 0.715342i \(0.746271\pi\)
\(398\) 5.96059i 0.298777i
\(399\) 5.26557 + 0.823085i 0.263608 + 0.0412058i
\(400\) −10.8046 + 8.20631i −0.540228 + 0.410315i
\(401\) −14.9159 + 25.8351i −0.744865 + 1.29014i 0.205393 + 0.978680i \(0.434153\pi\)
−0.950258 + 0.311464i \(0.899181\pi\)
\(402\) 2.20291 + 1.27185i 0.109871 + 0.0634342i
\(403\) 8.91606 5.14769i 0.444140 0.256425i
\(404\) −12.4655 + 21.5909i −0.620181 + 1.07419i
\(405\) 0.639163 0.725211i 0.0317603 0.0360360i
\(406\) 0.476660 0.0236562
\(407\) 6.69420i 0.331819i
\(408\) 4.09838 2.36620i 0.202900 0.117144i
\(409\) 13.8221 + 23.9406i 0.683458 + 1.18378i 0.973919 + 0.226898i \(0.0728583\pi\)
−0.290460 + 0.956887i \(0.593808\pi\)
\(410\) 4.12234 1.38802i 0.203588 0.0685495i
\(411\) 5.27866 0.260377
\(412\) 5.47008 3.15815i 0.269491 0.155591i
\(413\) 6.36194 + 3.67307i 0.313051 + 0.180740i
\(414\) −0.274708 0.475809i −0.0135012 0.0233847i
\(415\) 6.12127 30.3820i 0.300481 1.49140i
\(416\) 9.94070 17.2178i 0.487383 0.844172i
\(417\) 6.22232i 0.304708i
\(418\) −0.226666 + 1.45006i −0.0110866 + 0.0709249i
\(419\) 11.2902 0.551562 0.275781 0.961220i \(-0.411064\pi\)
0.275781 + 0.961220i \(0.411064\pi\)
\(420\) −4.76346 0.959726i −0.232433 0.0468298i
\(421\) −2.27471 + 3.93991i −0.110863 + 0.192019i −0.916118 0.400908i \(-0.868695\pi\)
0.805256 + 0.592928i \(0.202028\pi\)
\(422\) 9.09059 5.24845i 0.442523 0.255491i
\(423\) 17.4709 + 10.0868i 0.849463 + 0.490438i
\(424\) 4.43883 + 7.68828i 0.215569 + 0.373376i
\(425\) 7.71877 + 10.1627i 0.374415 + 0.492962i
\(426\) 6.46362 0.313163
\(427\) 4.63629 2.67676i 0.224366 0.129538i
\(428\) −5.58929 + 3.22698i −0.270168 + 0.155982i
\(429\) −3.04551 −0.147039
\(430\) −3.40880 10.1239i −0.164387 0.488220i
\(431\) −16.4517 28.4952i −0.792451 1.37256i −0.924445 0.381314i \(-0.875472\pi\)
0.131995 0.991250i \(-0.457862\pi\)
\(432\) −12.0220 6.94089i −0.578407 0.333943i
\(433\) −19.3204 + 11.1547i −0.928481 + 0.536059i −0.886331 0.463052i \(-0.846754\pi\)
−0.0421503 + 0.999111i \(0.513421\pi\)
\(434\) −0.695848 + 1.20524i −0.0334018 + 0.0578536i
\(435\) 0.394806 1.95956i 0.0189295 0.0939537i
\(436\) 11.0597 0.529664
\(437\) 2.05978 + 1.66110i 0.0985325 + 0.0794611i
\(438\) 6.07605i 0.290325i
\(439\) 2.85287 4.94131i 0.136160 0.235836i −0.789880 0.613261i \(-0.789857\pi\)
0.926040 + 0.377425i \(0.123191\pi\)
\(440\) 0.561702 2.78793i 0.0267781 0.132909i
\(441\) −5.38791 9.33214i −0.256567 0.444388i
\(442\) −4.27976 2.47092i −0.203568 0.117530i
\(443\) −10.0265 + 5.78881i −0.476374 + 0.275034i −0.718904 0.695109i \(-0.755356\pi\)
0.242530 + 0.970144i \(0.422023\pi\)
\(444\) 17.3450 0.823158
\(445\) −11.3905 33.8292i −0.539963 1.60366i
\(446\) −3.21412 5.56702i −0.152193 0.263606i
\(447\) −8.64839 + 4.99315i −0.409055 + 0.236168i
\(448\) 3.69147i 0.174406i
\(449\) 25.4726 1.20213 0.601063 0.799202i \(-0.294744\pi\)
0.601063 + 0.799202i \(0.294744\pi\)
\(450\) −1.75232 + 4.17217i −0.0826052 + 0.196678i
\(451\) 1.47072 2.54737i 0.0692537 0.119951i
\(452\) −18.8872 + 10.9046i −0.888381 + 0.512907i
\(453\) −6.78921 3.91975i −0.318985 0.184166i
\(454\) 1.55465 2.69274i 0.0729634 0.126376i
\(455\) 3.44128 + 10.2204i 0.161330 + 0.479140i
\(456\) −7.98509 1.24818i −0.373936 0.0584516i
\(457\) 6.92830i 0.324092i −0.986783 0.162046i \(-0.948191\pi\)
0.986783 0.162046i \(-0.0518094\pi\)
\(458\) −0.239461 0.138253i −0.0111893 0.00646014i
\(459\) −6.52853 + 11.3077i −0.304726 + 0.527800i
\(460\) −1.80996 1.59520i −0.0843896 0.0743766i
\(461\) −16.2473 + 28.1411i −0.756712 + 1.31066i 0.187806 + 0.982206i \(0.439862\pi\)
−0.944519 + 0.328458i \(0.893471\pi\)
\(462\) 0.356528 0.205841i 0.0165872 0.00957661i
\(463\) 21.5062i 0.999477i −0.866176 0.499738i \(-0.833429\pi\)
0.866176 0.499738i \(-0.166571\pi\)
\(464\) 2.33198 0.108259
\(465\) 4.37844 + 3.85892i 0.203045 + 0.178953i
\(466\) −1.68875 2.92499i −0.0782296 0.135498i
\(467\) 16.9509i 0.784392i −0.919882 0.392196i \(-0.871715\pi\)
0.919882 0.392196i \(-0.128285\pi\)
\(468\) 13.9868i 0.646542i
\(469\) −3.04551 5.27499i −0.140629 0.243576i
\(470\) −10.8800 2.19206i −0.501857 0.101112i
\(471\) 5.12624 + 8.87891i 0.236205 + 0.409119i
\(472\) −9.64771 5.57011i −0.444072 0.256385i
\(473\) −6.25601 3.61191i −0.287652 0.166076i
\(474\) −2.92724 −0.134453
\(475\) 0.633930 21.7853i 0.0290867 0.999577i
\(476\) −5.33198 −0.244391
\(477\) −8.27265 4.77621i −0.378778 0.218688i
\(478\) 1.49366 + 0.862364i 0.0683183 + 0.0394436i
\(479\) 4.42894 + 7.67115i 0.202364 + 0.350504i 0.949290 0.314403i \(-0.101804\pi\)
−0.746926 + 0.664907i \(0.768471\pi\)
\(480\) 11.0484 + 2.22599i 0.504288 + 0.101602i
\(481\) −19.2473 33.3373i −0.877601 1.52005i
\(482\) 8.14611i 0.371045i
\(483\) 0.742237i 0.0337730i
\(484\) 9.32284 + 16.1476i 0.423765 + 0.733983i
\(485\) −28.0180 24.6936i −1.27223 1.12128i
\(486\) −7.45432 −0.338135
\(487\) 30.0628i 1.36227i −0.732156 0.681137i \(-0.761486\pi\)
0.732156 0.681137i \(-0.238514\pi\)
\(488\) −7.03081 + 4.05924i −0.318270 + 0.183753i
\(489\) −0.0357958 + 0.0620001i −0.00161874 + 0.00280374i
\(490\) 4.44754 + 3.91983i 0.200919 + 0.177080i
\(491\) −1.55017 + 2.68497i −0.0699580 + 0.121171i −0.898883 0.438190i \(-0.855620\pi\)
0.828925 + 0.559360i \(0.188953\pi\)
\(492\) 6.60036 + 3.81072i 0.297567 + 0.171800i
\(493\) 2.19343i 0.0987873i
\(494\) 3.04045 + 7.87306i 0.136796 + 0.354226i
\(495\) 0.976493 + 2.90013i 0.0438901 + 0.130351i
\(496\) −3.40432 + 5.89645i −0.152858 + 0.264759i
\(497\) −13.4039 7.73874i −0.601246 0.347130i
\(498\) −5.89202 + 3.40176i −0.264028 + 0.152436i
\(499\) 16.0696 27.8333i 0.719372 1.24599i −0.241877 0.970307i \(-0.577763\pi\)
0.961249 0.275682i \(-0.0889037\pi\)
\(500\) −1.44626 + 19.8184i −0.0646785 + 0.886306i
\(501\) −17.3137 −0.773519
\(502\) 9.16117i 0.408883i
\(503\) 7.29040 4.20911i 0.325063 0.187675i −0.328584 0.944475i \(-0.606571\pi\)
0.653647 + 0.756800i \(0.273238\pi\)
\(504\) −2.00914 3.47993i −0.0894940 0.155008i
\(505\) 10.0090 + 29.7261i 0.445393 + 1.32279i
\(506\) 0.204402 0.00908676
\(507\) −3.45558 + 1.99508i −0.153468 + 0.0886047i
\(508\) 3.32144 + 1.91764i 0.147365 + 0.0850813i
\(509\) 10.1725 + 17.6193i 0.450888 + 0.780962i 0.998441 0.0558093i \(-0.0177739\pi\)
−0.547553 + 0.836771i \(0.684441\pi\)
\(510\) 0.553307 2.74626i 0.0245009 0.121606i
\(511\) 7.27471 12.6002i 0.321814 0.557398i
\(512\) 22.8217i 1.00859i
\(513\) 20.8017 8.03329i 0.918419 0.354678i
\(514\) 6.55582 0.289165
\(515\) 1.56951 7.79006i 0.0691611 0.343271i
\(516\) 9.35864 16.2096i 0.411991 0.713589i
\(517\) −6.49975 + 3.75263i −0.285859 + 0.165041i
\(518\) 4.50643 + 2.60179i 0.198001 + 0.114316i
\(519\) 6.31184 + 10.9324i 0.277059 + 0.479880i
\(520\) −5.21861 15.4990i −0.228851 0.679674i
\(521\) 15.3502 0.672507 0.336253 0.941772i \(-0.390840\pi\)
0.336253 + 0.941772i \(0.390840\pi\)
\(522\) 0.673580 0.388891i 0.0294818 0.0170213i
\(523\) 11.4633 6.61835i 0.501256 0.289400i −0.227976 0.973667i \(-0.573211\pi\)
0.729232 + 0.684267i \(0.239878\pi\)
\(524\) −31.1910 −1.36259
\(525\) −4.86836 + 3.69762i −0.212472 + 0.161378i
\(526\) 3.53638 + 6.12519i 0.154193 + 0.267071i
\(527\) 5.54614 + 3.20207i 0.241594 + 0.139484i
\(528\) 1.74425 1.00704i 0.0759088 0.0438260i
\(529\) −11.3157 + 19.5994i −0.491989 + 0.852149i
\(530\) 5.15180 + 1.03797i 0.223780 + 0.0450864i
\(531\) 11.9870 0.520190
\(532\) 7.08827 + 5.71630i 0.307316 + 0.247833i
\(533\) 16.9146i 0.732653i
\(534\) −3.91794 + 6.78607i −0.169546 + 0.293662i
\(535\) −1.60372 + 7.95982i −0.0693348 + 0.344133i
\(536\) 4.61844 + 7.99937i 0.199486 + 0.345520i
\(537\) 10.5885 + 6.11329i 0.456928 + 0.263808i
\(538\) −7.91673 + 4.57073i −0.341315 + 0.197058i
\(539\) 4.00897 0.172679
\(540\) −19.2682 + 6.48773i −0.829171 + 0.279188i
\(541\) 13.8704 + 24.0242i 0.596335 + 1.03288i 0.993357 + 0.115073i \(0.0367102\pi\)
−0.397022 + 0.917809i \(0.629956\pi\)
\(542\) 4.87043 2.81194i 0.209203 0.120783i
\(543\) 9.19127i 0.394435i
\(544\) 12.3670 0.530232
\(545\) 9.20011 10.4387i 0.394090 0.447144i
\(546\) 1.18368 2.05019i 0.0506568 0.0877401i
\(547\) −14.7745 + 8.53008i −0.631714 + 0.364720i −0.781415 0.624011i \(-0.785502\pi\)
0.149702 + 0.988731i \(0.452169\pi\)
\(548\) 7.81080 + 4.50957i 0.333661 + 0.192639i
\(549\) 4.36777 7.56520i 0.186412 0.322875i
\(550\) −1.01827 1.34068i −0.0434193 0.0571666i
\(551\) −2.35153 + 2.91593i −0.100179 + 0.124223i
\(552\) 1.12558i 0.0479080i
\(553\) 6.07035 + 3.50472i 0.258137 + 0.149036i
\(554\) 2.59120 4.48808i 0.110089 0.190680i
\(555\) 14.4286 16.3711i 0.612459 0.694913i
\(556\) 5.31574 9.20713i 0.225438 0.390469i
\(557\) 22.9856 13.2708i 0.973932 0.562300i 0.0734992 0.997295i \(-0.476583\pi\)
0.900433 + 0.434995i \(0.143250\pi\)
\(558\) 2.27088i 0.0961340i
\(559\) −41.5401 −1.75696
\(560\) −5.35044 4.71560i −0.226098 0.199271i
\(561\) −0.947216 1.64063i −0.0399915 0.0692673i
\(562\) 6.91298i 0.291606i
\(563\) 35.5594i 1.49865i 0.662203 + 0.749325i \(0.269622\pi\)
−0.662203 + 0.749325i \(0.730378\pi\)
\(564\) −9.72326 16.8412i −0.409423 0.709141i
\(565\) −5.41926 + 26.8977i −0.227990 + 1.13160i
\(566\) 4.46607 + 7.73546i 0.187723 + 0.325146i
\(567\) 0.440059 + 0.254068i 0.0184808 + 0.0106699i
\(568\) 20.3266 + 11.7356i 0.852886 + 0.492414i
\(569\) 14.9713 0.627628 0.313814 0.949485i \(-0.398393\pi\)
0.313814 + 0.949485i \(0.398393\pi\)
\(570\) −3.67977 + 3.05766i −0.154129 + 0.128071i
\(571\) 5.92724 0.248047 0.124024 0.992279i \(-0.460420\pi\)
0.124024 + 0.992279i \(0.460420\pi\)
\(572\) −4.50643 2.60179i −0.188423 0.108786i
\(573\) −12.8324 7.40881i −0.536083 0.309508i
\(574\) 1.14323 + 1.98013i 0.0477175 + 0.0826492i
\(575\) −3.01125 + 0.381343i −0.125578 + 0.0159031i
\(576\) −3.01175 5.21651i −0.125490 0.217355i
\(577\) 14.5559i 0.605970i −0.952995 0.302985i \(-0.902017\pi\)
0.952995 0.302985i \(-0.0979832\pi\)
\(578\) 4.94800i 0.205810i
\(579\) −10.1451 17.5718i −0.421616 0.730260i
\(580\) 2.25825 2.56227i 0.0937686 0.106392i
\(581\) 16.2914 0.675880
\(582\) 8.19839i 0.339834i
\(583\) 3.07770 1.77691i 0.127465 0.0735922i
\(584\) −11.0319 + 19.1078i −0.456503 + 0.790686i
\(585\) 13.2015 + 11.6351i 0.545813 + 0.481051i
\(586\) −1.32039 + 2.28698i −0.0545448 + 0.0944744i
\(587\) −17.8262 10.2919i −0.735765 0.424794i 0.0847626 0.996401i \(-0.472987\pi\)
−0.820527 + 0.571607i \(0.806320\pi\)
\(588\) 10.3874i 0.428371i
\(589\) −3.94011 10.2027i −0.162350 0.420395i
\(590\) −6.24992 + 2.10439i −0.257305 + 0.0866364i
\(591\) −2.25328 + 3.90280i −0.0926877 + 0.160540i
\(592\) 22.0469 + 12.7288i 0.906124 + 0.523151i
\(593\) −12.4120 + 7.16609i −0.509701 + 0.294276i −0.732711 0.680540i \(-0.761745\pi\)
0.223010 + 0.974816i \(0.428412\pi\)
\(594\) 0.861254 1.49174i 0.0353377 0.0612066i
\(595\) −4.43545 + 5.03257i −0.181836 + 0.206315i
\(596\) −17.0626 −0.698912
\(597\) 13.1395i 0.537765i
\(598\) 1.01792 0.587699i 0.0416260 0.0240328i
\(599\) 1.25008 + 2.16521i 0.0510770 + 0.0884680i 0.890434 0.455113i \(-0.150401\pi\)
−0.839356 + 0.543581i \(0.817068\pi\)
\(600\) 7.38273 5.60734i 0.301399 0.228919i
\(601\) 14.5259 0.592524 0.296262 0.955107i \(-0.404260\pi\)
0.296262 + 0.955107i \(0.404260\pi\)
\(602\) 4.86296 2.80763i 0.198199 0.114430i
\(603\) −8.60739 4.96948i −0.350520 0.202373i
\(604\) −6.69730 11.6001i −0.272509 0.472000i
\(605\) 22.9962 + 4.63319i 0.934928 + 0.188366i
\(606\) 3.44273 5.96299i 0.139851 0.242230i
\(607\) 31.8704i 1.29358i 0.762669 + 0.646789i \(0.223889\pi\)
−0.762669 + 0.646789i \(0.776111\pi\)
\(608\) −16.4406 13.2584i −0.666754 0.537700i
\(609\) 1.05075 0.0425785
\(610\) −0.949204 + 4.71124i −0.0384321 + 0.190752i
\(611\) −21.5793 + 37.3764i −0.873004 + 1.51209i
\(612\) −7.53475 + 4.35019i −0.304574 + 0.175846i
\(613\) −17.3628 10.0244i −0.701277 0.404882i 0.106546 0.994308i \(-0.466021\pi\)
−0.807823 + 0.589425i \(0.799354\pi\)
\(614\) −4.86794 8.43152i −0.196454 0.340268i
\(615\) 9.08729 3.05976i 0.366435 0.123381i
\(616\) 1.49493 0.0602325
\(617\) 17.3914 10.0410i 0.700153 0.404234i −0.107251 0.994232i \(-0.534205\pi\)
0.807404 + 0.589998i \(0.200872\pi\)
\(618\) −1.51073 + 0.872222i −0.0607706 + 0.0350859i
\(619\) −5.62217 −0.225974 −0.112987 0.993596i \(-0.536042\pi\)
−0.112987 + 0.993596i \(0.536042\pi\)
\(620\) 3.18206 + 9.45053i 0.127795 + 0.379542i
\(621\) −1.55278 2.68950i −0.0623111 0.107926i
\(622\) 10.0771 + 5.81803i 0.404056 + 0.233282i
\(623\) 16.2496 9.38171i 0.651026 0.375870i
\(624\) 5.79095 10.0302i 0.231823 0.401530i
\(625\) 17.5025 + 17.8511i 0.700099 + 0.714046i
\(626\) −1.65092 −0.0659839
\(627\) −0.499662 + 3.19652i −0.0199546 + 0.127657i
\(628\) 17.5174i 0.699022i
\(629\) 11.9726 20.7371i 0.477378 0.826844i
\(630\) −2.33184 0.469812i −0.0929029 0.0187178i
\(631\) 2.42184 + 4.19475i 0.0964120 + 0.166990i 0.910197 0.414176i \(-0.135930\pi\)
−0.813785 + 0.581166i \(0.802597\pi\)
\(632\) −9.20551 5.31481i −0.366176 0.211412i
\(633\) 20.0393 11.5697i 0.796491 0.459854i
\(634\) 14.8034 0.587918
\(635\) 4.57292 1.53974i 0.181471 0.0611025i
\(636\) 4.60407 + 7.97448i 0.182563 + 0.316209i
\(637\) 19.9648 11.5267i 0.791033 0.456703i
\(638\) 0.289361i 0.0114559i
\(639\) −25.2552 −0.999078
\(640\) 18.7426 + 16.5188i 0.740868 + 0.652962i
\(641\) 12.6503 21.9110i 0.499658 0.865433i −0.500342 0.865828i \(-0.666792\pi\)
1.00000 0.000394734i \(0.000125648\pi\)
\(642\) 1.54365 0.891229i 0.0609232 0.0351740i
\(643\) −12.0773 6.97283i −0.476282 0.274981i 0.242584 0.970130i \(-0.422005\pi\)
−0.718866 + 0.695149i \(0.755338\pi\)
\(644\) 0.634095 1.09828i 0.0249868 0.0432785i
\(645\) −7.51437 22.3172i −0.295878 0.878740i
\(646\) −3.29560 + 4.08658i −0.129664 + 0.160784i
\(647\) 2.51360i 0.0988200i 0.998779 + 0.0494100i \(0.0157341\pi\)
−0.998779 + 0.0494100i \(0.984266\pi\)
\(648\) −0.667338 0.385288i −0.0262155 0.0151355i
\(649\) −2.22978 + 3.86209i −0.0875264 + 0.151600i
\(650\) −8.92576 3.74884i −0.350097 0.147042i
\(651\) −1.53393 + 2.65684i −0.0601194 + 0.104130i
\(652\) −0.105934 + 0.0611608i −0.00414868 + 0.00239524i
\(653\) 1.92873i 0.0754770i 0.999288 + 0.0377385i \(0.0120154\pi\)
−0.999288 + 0.0377385i \(0.987985\pi\)
\(654\) −3.05448 −0.119440
\(655\) −25.9465 + 29.4396i −1.01381 + 1.15030i
\(656\) 5.59306 + 9.68747i 0.218372 + 0.378232i
\(657\) 23.7408i 0.926217i
\(658\) 5.83404i 0.227434i
\(659\) 7.90042 + 13.6839i 0.307757 + 0.533050i 0.977871 0.209208i \(-0.0670884\pi\)
−0.670115 + 0.742258i \(0.733755\pi\)
\(660\) 0.582612 2.89171i 0.0226781 0.112560i
\(661\) −8.20178 14.2059i −0.319012 0.552546i 0.661270 0.750148i \(-0.270018\pi\)
−0.980282 + 0.197602i \(0.936685\pi\)
\(662\) −14.6096 8.43486i −0.567819 0.327830i
\(663\) −9.43432 5.44691i −0.366399 0.211540i
\(664\) −24.7054 −0.958755
\(665\) 11.2918 1.93510i 0.437875 0.0750400i
\(666\) 8.49086 0.329014
\(667\) 0.451805 + 0.260850i 0.0174940 + 0.0101001i
\(668\) −25.6190 14.7911i −0.991228 0.572286i
\(669\) −7.08521 12.2719i −0.273930 0.474461i
\(670\) 5.36025 + 1.07997i 0.207085 + 0.0417227i
\(671\) 1.62496 + 2.81451i 0.0627308 + 0.108653i
\(672\) 5.92434i 0.228536i
\(673\) 17.0878i 0.658686i 0.944210 + 0.329343i \(0.106827\pi\)
−0.944210 + 0.329343i \(0.893173\pi\)
\(674\) −6.24992 10.8252i −0.240738 0.416970i
\(675\) −9.90496 + 23.5831i −0.381242 + 0.907714i
\(676\) −6.81761 −0.262216
\(677\) 4.57680i 0.175901i 0.996125 + 0.0879504i \(0.0280317\pi\)
−0.996125 + 0.0879504i \(0.971968\pi\)
\(678\) 5.21630 3.01163i 0.200331 0.115661i
\(679\) 9.81574 17.0014i 0.376693 0.652452i
\(680\) 6.72623 7.63176i 0.257939 0.292665i
\(681\) 3.42708 5.93587i 0.131326 0.227463i
\(682\) −0.731656 0.422422i −0.0280166 0.0161754i
\(683\) 29.0692i 1.11230i −0.831082 0.556151i \(-0.812278\pi\)
0.831082 0.556151i \(-0.187722\pi\)
\(684\) 14.6804 + 2.29475i 0.561318 + 0.0877420i
\(685\) 10.7538 3.62089i 0.410882 0.138347i
\(686\) −3.49942 + 6.06117i −0.133608 + 0.231416i
\(687\) −0.527869 0.304765i −0.0201395 0.0116275i
\(688\) 23.7912 13.7359i 0.907031 0.523675i
\(689\) 10.2180 17.6981i 0.389276 0.674245i
\(690\) 0.499876 + 0.440564i 0.0190299 + 0.0167720i
\(691\) −6.07833 −0.231230 −0.115615 0.993294i \(-0.536884\pi\)
−0.115615 + 0.993294i \(0.536884\pi\)
\(692\) 21.5689i 0.819925i
\(693\) −1.39305 + 0.804279i −0.0529177 + 0.0305521i
\(694\) −8.10220 14.0334i −0.307555 0.532701i
\(695\) −4.26819 12.6763i −0.161902 0.480838i
\(696\) −1.59343 −0.0603989
\(697\) 9.11194 5.26078i 0.345139 0.199266i
\(698\) −8.75799 5.05643i −0.331495 0.191389i
\(699\) −3.72267 6.44786i −0.140804 0.243881i
\(700\) −10.3626 + 1.31231i −0.391668 + 0.0496006i
\(701\) −5.20569 + 9.01651i −0.196616 + 0.340549i −0.947429 0.319966i \(-0.896329\pi\)
0.750813 + 0.660515i \(0.229662\pi\)
\(702\) 9.90517i 0.373847i
\(703\) −38.1481 + 14.7322i −1.43878 + 0.555634i
\(704\) 2.24095 0.0844589
\(705\) −23.9839 4.83219i −0.903285 0.181991i
\(706\) 4.61640 7.99585i 0.173741 0.300928i
\(707\) −14.2787 + 8.24380i −0.537005 + 0.310040i
\(708\) −10.0069 5.77746i −0.376081 0.217130i
\(709\) −0.265572 0.459984i −0.00997377 0.0172751i 0.860995 0.508613i \(-0.169841\pi\)
−0.870969 + 0.491338i \(0.836508\pi\)
\(710\) 13.1679 4.43371i 0.494181 0.166394i
\(711\) 11.4375 0.428941
\(712\) −24.6421 + 14.2271i −0.923500 + 0.533183i
\(713\) −1.31913 + 0.761599i −0.0494017 + 0.0285221i
\(714\) 1.47259 0.0551103
\(715\) −6.20440 + 2.08907i −0.232031 + 0.0781266i
\(716\) 10.4452 + 18.0916i 0.390355 + 0.676114i
\(717\) 3.29262 + 1.90100i 0.122965 + 0.0709940i
\(718\) 6.73174 3.88657i 0.251226 0.145046i
\(719\) 11.2135 19.4224i 0.418194 0.724334i −0.577564 0.816346i \(-0.695996\pi\)
0.995758 + 0.0920118i \(0.0293298\pi\)
\(720\) −11.4082 2.29848i −0.425157 0.0856592i
\(721\) 4.17716 0.155566
\(722\) 8.76227 1.89951i 0.326098 0.0706924i
\(723\) 17.9573i 0.667839i
\(724\) 7.85212 13.6003i 0.291822 0.505450i
\(725\) −0.539849 4.26288i −0.0200495 0.158320i
\(726\) −2.57479 4.45967i −0.0955595 0.165514i
\(727\) −39.8141 22.9867i −1.47662 0.852529i −0.476972 0.878918i \(-0.658266\pi\)
−0.999652 + 0.0263888i \(0.991599\pi\)
\(728\) 7.44480 4.29826i 0.275923 0.159304i
\(729\) −15.1354 −0.560570
\(730\) 4.16786 + 12.3783i 0.154259 + 0.458141i
\(731\) −12.9198 22.3778i −0.477856 0.827671i
\(732\) −7.29254 + 4.21035i −0.269540 + 0.155619i
\(733\) 42.5178i 1.57043i 0.619223 + 0.785215i \(0.287448\pi\)
−0.619223 + 0.785215i \(0.712552\pi\)
\(734\) 6.00930 0.221807
\(735\) 9.80416 + 8.64087i 0.361632 + 0.318723i
\(736\) −1.47072 + 2.54737i −0.0542116 + 0.0938972i
\(737\) 3.20224 1.84881i 0.117956 0.0681019i
\(738\) 3.23106 + 1.86545i 0.118937 + 0.0686682i
\(739\) −1.70889 + 2.95988i −0.0628624 + 0.108881i −0.895744 0.444571i \(-0.853356\pi\)
0.832881 + 0.553452i \(0.186690\pi\)
\(740\) 35.3357 11.8978i 1.29897 0.437371i
\(741\) 6.70237 + 17.3554i 0.246218 + 0.637566i
\(742\) 2.76248i 0.101414i
\(743\) 8.41853 + 4.86044i 0.308846 + 0.178312i 0.646410 0.762990i \(-0.276270\pi\)
−0.337564 + 0.941303i \(0.609603\pi\)
\(744\) 2.32616 4.02903i 0.0852812 0.147711i
\(745\) −14.1937 + 16.1045i −0.520016 + 0.590024i
\(746\) −4.56175 + 7.90119i −0.167018 + 0.289283i
\(747\) 23.0217 13.2916i 0.842321 0.486314i
\(748\) 3.23683i 0.118350i
\(749\) −4.26819 −0.155956
\(750\) 0.399428 5.47347i 0.0145851 0.199863i
\(751\) 5.69265 + 9.85996i 0.207728 + 0.359795i 0.950998 0.309196i \(-0.100060\pi\)
−0.743271 + 0.668991i \(0.766727\pi\)
\(752\) 28.5420i 1.04082i
\(753\) 20.1949i 0.735943i
\(754\) 0.831977 + 1.44103i 0.0302988 + 0.0524791i
\(755\) −16.5199 3.32837i −0.601221 0.121132i
\(756\) −5.34356 9.25532i −0.194344 0.336613i
\(757\) 19.7317 + 11.3921i 0.717160 + 0.414053i 0.813707 0.581276i \(-0.197446\pi\)
−0.0965464 + 0.995328i \(0.530780\pi\)
\(758\) 4.02856 + 2.32589i 0.146324 + 0.0844801i
\(759\) 0.450583 0.0163551
\(760\) −17.1236 + 2.93453i −0.621139 + 0.106446i
\(761\) −36.7665 −1.33279 −0.666393 0.745601i \(-0.732163\pi\)
−0.666393 + 0.745601i \(0.732163\pi\)
\(762\) −0.917319 0.529615i −0.0332310 0.0191859i
\(763\) 6.33421 + 3.65706i 0.229314 + 0.132394i
\(764\) −12.6587 21.9255i −0.457976 0.793238i
\(765\) −2.16192 + 10.7304i −0.0781645 + 0.387958i
\(766\) −4.79747 8.30945i −0.173339 0.300233i
\(767\) 25.6444i 0.925965i
\(768\) 1.04955i 0.0378724i
\(769\) −10.4004 18.0140i −0.375049 0.649603i 0.615286 0.788304i \(-0.289041\pi\)
−0.990334 + 0.138701i \(0.955707\pi\)
\(770\) 0.585131 0.663905i 0.0210867 0.0239255i
\(771\) 14.4517 0.520464
\(772\) 34.6679i 1.24772i
\(773\) 18.1944 10.5046i 0.654409 0.377823i −0.135735 0.990745i \(-0.543339\pi\)
0.790143 + 0.612922i \(0.210006\pi\)
\(774\) 4.58131 7.93506i 0.164672 0.285220i
\(775\) 11.5669 + 4.85812i 0.415495 + 0.174509i
\(776\) −14.8853 + 25.7821i −0.534351 + 0.925523i
\(777\) 9.93398 + 5.73539i 0.356380 + 0.205756i
\(778\) 0.474354i 0.0170064i
\(779\) −17.7533 2.77509i −0.636077 0.0994280i
\(780\) −5.41287 16.0759i −0.193812 0.575610i
\(781\) 4.69788 8.13697i 0.168103 0.291164i
\(782\) 0.633190 + 0.365572i 0.0226428 + 0.0130728i
\(783\) 3.80740 2.19820i 0.136065 0.0785573i
\(784\) −7.62292 + 13.2033i −0.272247 + 0.471546i
\(785\) 16.5338 + 14.5720i 0.590116 + 0.520097i
\(786\) 8.61437 0.307264
\(787\) 18.0606i 0.643791i 0.946775 + 0.321896i \(0.104320\pi\)
−0.946775 + 0.321896i \(0.895680\pi\)
\(788\) −6.66834 + 3.84997i −0.237550 + 0.137149i
\(789\) 7.79560 + 13.5024i 0.277531 + 0.480697i
\(790\) −5.96345 + 2.00794i −0.212170 + 0.0714392i
\(791\) −14.4230 −0.512823
\(792\) 2.11253 1.21967i 0.0750653 0.0433390i
\(793\) 16.1847 + 9.34422i 0.574734 + 0.331823i
\(794\) 2.32691 + 4.03033i 0.0825789 + 0.143031i
\(795\) 11.3566 + 2.28809i 0.402778 + 0.0811504i
\(796\) −11.2251 + 19.4425i −0.397864 + 0.689121i
\(797\) 24.2571i 0.859229i −0.903012 0.429615i \(-0.858649\pi\)
0.903012 0.429615i \(-0.141351\pi\)
\(798\) −1.95765 1.57873i −0.0692999 0.0558866i
\(799\) −26.8463 −0.949756
\(800\) 24.0350 3.04378i 0.849765 0.107614i
\(801\) 15.3085 26.5150i 0.540898 0.936863i
\(802\) 12.1912 7.03857i 0.430485 0.248541i
\(803\) 7.64906 + 4.41619i 0.269930 + 0.155844i
\(804\) 4.79036 + 8.29715i 0.168943 + 0.292618i
\(805\) −0.509136 1.51211i −0.0179447 0.0532947i
\(806\) −4.85822 −0.171124
\(807\) −17.4517 + 10.0757i −0.614327 + 0.354682i
\(808\) 21.6532 12.5015i 0.761758 0.439801i
\(809\) 4.27192 0.150193 0.0750964 0.997176i \(-0.476074\pi\)
0.0750964 + 0.997176i \(0.476074\pi\)
\(810\) −0.432310 + 0.145562i −0.0151898 + 0.00511452i
\(811\) −5.09120 8.81821i −0.178776 0.309649i 0.762685 0.646770i \(-0.223880\pi\)
−0.941462 + 0.337120i \(0.890547\pi\)
\(812\) 1.55479 + 0.897657i 0.0545623 + 0.0315016i
\(813\) 10.7364 6.19865i 0.376541 0.217396i
\(814\) −1.57944 + 2.73568i −0.0553595 + 0.0958854i
\(815\) −0.0303952 + 0.150862i −0.00106470 + 0.00528448i
\(816\) 7.20440 0.252205
\(817\) −6.81528 + 43.5998i −0.238436 + 1.52536i
\(818\) 13.0448i 0.456102i
\(819\) −4.62496 + 8.01066i −0.161609 + 0.279915i
\(820\) 16.0604 + 3.23579i 0.560852 + 0.112999i
\(821\) 28.0108 + 48.5162i 0.977585 + 1.69323i 0.671127 + 0.741343i \(0.265811\pi\)
0.306458 + 0.951884i \(0.400856\pi\)
\(822\) −2.15719 1.24546i −0.0752408 0.0434403i
\(823\) −29.0479 + 16.7708i −1.01255 + 0.584593i −0.911936 0.410333i \(-0.865413\pi\)
−0.100610 + 0.994926i \(0.532079\pi\)
\(824\) −6.33455 −0.220674
\(825\) −2.24468 2.95539i −0.0781498 0.102893i
\(826\) −1.73326 3.00210i −0.0603079 0.104456i
\(827\) −0.0313960 + 0.0181265i −0.00109175 + 0.000630320i −0.500546 0.865710i \(-0.666867\pi\)
0.499454 + 0.866340i \(0.333534\pi\)
\(828\) 2.06935i 0.0719149i
\(829\) −39.5662 −1.37419 −0.687095 0.726567i \(-0.741115\pi\)
−0.687095 + 0.726567i \(0.741115\pi\)
\(830\) −9.66994 + 10.9718i −0.335648 + 0.380835i
\(831\) 5.71204 9.89354i 0.198148 0.343203i
\(832\) 11.1600 6.44321i 0.386902 0.223378i
\(833\) 12.4189 + 7.17005i 0.430289 + 0.248427i
\(834\) −1.46811 + 2.54283i −0.0508364 + 0.0880512i
\(835\) −35.2719 + 11.8763i −1.22064 + 0.410996i
\(836\) −3.47014 + 4.30301i −0.120017 + 0.148823i
\(837\) 12.8361i 0.443681i
\(838\) −4.61389 2.66383i −0.159384 0.0920205i
\(839\) 20.0811 34.7816i 0.693278 1.20079i −0.277480 0.960732i \(-0.589499\pi\)
0.970758 0.240061i \(-0.0771676\pi\)
\(840\) 3.65594 + 3.22216i 0.126142 + 0.111175i
\(841\) 14.1307 24.4751i 0.487266 0.843970i
\(842\) 1.85918 1.07340i 0.0640716 0.0369917i
\(843\) 15.2390i 0.524858i
\(844\) 39.5360 1.36089
\(845\) −5.67128 + 6.43478i −0.195098 + 0.221363i
\(846\) −4.75980 8.24422i −0.163645 0.283442i
\(847\) 12.3309i 0.423696i
\(848\) 13.5150i 0.464106i
\(849\) 9.84502 + 17.0521i 0.337880 + 0.585225i
\(850\) −0.756580 5.97429i −0.0259505 0.204917i
\(851\) 2.84763 + 4.93224i 0.0976156 + 0.169075i
\(852\) 21.0833 + 12.1724i 0.722302 + 0.417021i
\(853\) 14.2563 + 8.23086i 0.488126 + 0.281819i 0.723796 0.690014i \(-0.242395\pi\)
−0.235671 + 0.971833i \(0.575729\pi\)
\(854\) −2.52624 −0.0864463
\(855\) 14.3779 11.9471i 0.491713 0.408583i
\(856\) 6.47259 0.221229
\(857\) −4.85549 2.80332i −0.165860 0.0957595i 0.414772 0.909925i \(-0.363861\pi\)
−0.580632 + 0.814166i \(0.697195\pi\)
\(858\) 1.24459 + 0.718565i 0.0424896 + 0.0245314i
\(859\) 12.5149 + 21.6765i 0.427003 + 0.739591i 0.996605 0.0823296i \(-0.0262360\pi\)
−0.569602 + 0.821921i \(0.692903\pi\)
\(860\) 7.94669 39.4422i 0.270980 1.34497i
\(861\) 2.52014 + 4.36501i 0.0858862 + 0.148759i
\(862\) 15.5266i 0.528837i
\(863\) 42.4307i 1.44436i 0.691707 + 0.722178i \(0.256859\pi\)
−0.691707 + 0.722178i \(0.743141\pi\)
\(864\) 12.3939 + 21.4669i 0.421649 + 0.730317i
\(865\) 20.3577 + 17.9422i 0.692183 + 0.610054i
\(866\) 10.5274 0.357736
\(867\) 10.9074i 0.370434i
\(868\) −4.53949 + 2.62087i −0.154080 + 0.0889583i
\(869\) −2.12758 + 3.68507i −0.0721731 + 0.125007i
\(870\) −0.623685 + 0.707649i −0.0211449 + 0.0239916i
\(871\) 10.6315 18.4143i 0.360234 0.623943i
\(872\) −9.60566 5.54583i −0.325289 0.187806i
\(873\) 32.0334i 1.08417i
\(874\) −0.449833 1.16482i −0.0152158 0.0394005i
\(875\) −7.38156 + 10.8723i −0.249542 + 0.367552i
\(876\) −11.4426 + 19.8191i −0.386608 + 0.669625i
\(877\) −0.482588 0.278622i −0.0162958 0.00940841i 0.491830 0.870691i \(-0.336328\pi\)
−0.508126 + 0.861283i \(0.669662\pi\)
\(878\) −2.33172 + 1.34622i −0.0786919 + 0.0454328i
\(879\) −2.91067 + 5.04143i −0.0981745 + 0.170043i
\(880\) 2.86266 3.24804i 0.0965001 0.109492i
\(881\) 8.35432 0.281464 0.140732 0.990048i \(-0.455054\pi\)
0.140732 + 0.990048i \(0.455054\pi\)
\(882\) 5.08494i 0.171219i
\(883\) −16.8738 + 9.74209i −0.567848 + 0.327847i −0.756289 0.654237i \(-0.772990\pi\)
0.188441 + 0.982084i \(0.439657\pi\)
\(884\) −9.30660 16.1195i −0.313015 0.542158i
\(885\) −13.7773 + 4.63892i −0.463120 + 0.155936i
\(886\) 5.46329 0.183543
\(887\) 31.1226 17.9686i 1.04499 0.603328i 0.123751 0.992313i \(-0.460508\pi\)
0.921244 + 0.388985i \(0.127174\pi\)
\(888\) −15.0646 8.69755i −0.505535 0.291871i
\(889\) 1.26819 + 2.19657i 0.0425337 + 0.0736705i
\(890\) −3.32683 + 16.5123i −0.111516 + 0.553492i
\(891\) −0.154235 + 0.267143i −0.00516706 + 0.00894962i
\(892\) 24.2116i 0.810666i
\(893\) 35.6892 + 28.7814i 1.19429 + 0.963133i
\(894\) 4.71237 0.157605
\(895\) 25.7646 + 5.19097i 0.861216 + 0.173515i
\(896\) −6.56624 + 11.3731i −0.219363 + 0.379947i
\(897\) 2.24391 1.29552i 0.0749221 0.0432563i
\(898\) −10.4097 6.01005i −0.347377 0.200558i
\(899\) −1.07816 1.86743i −0.0359586 0.0622821i
\(900\) −13.5729 + 10.3089i −0.452431 + 0.343631i
\(901\) 12.7120 0.423499
\(902\) −1.20206 + 0.694011i −0.0400243 + 0.0231080i
\(903\) 10.7199 6.18914i 0.356736 0.205962i
\(904\) 21.8721 0.727455
\(905\) −6.30473 18.7247i −0.209576 0.622430i
\(906\) 1.84967 + 3.20372i 0.0614511 + 0.106436i
\(907\) −42.3922 24.4751i −1.40761 0.812683i −0.412452 0.910980i \(-0.635327\pi\)
−0.995157 + 0.0982962i \(0.968661\pi\)
\(908\) 10.1420 5.85551i 0.336576 0.194322i
\(909\) −13.4517 + 23.2990i −0.446165 + 0.772780i
\(910\) 1.00510 4.98864i 0.0333186 0.165372i
\(911\) −19.7811 −0.655376 −0.327688 0.944786i \(-0.606269\pi\)
−0.327688 + 0.944786i \(0.606269\pi\)
\(912\) −9.57745 7.72369i −0.317141 0.255757i
\(913\) 9.88984i 0.327306i
\(914\) −1.63468 + 2.83134i −0.0540703 + 0.0936525i
\(915\) −2.09243 + 10.3855i −0.0691735 + 0.343333i
\(916\) −0.520723 0.901919i −0.0172052 0.0298002i
\(917\) −17.8640 10.3138i −0.589921 0.340591i
\(918\) 5.33594 3.08071i 0.176112 0.101678i
\(919\) −26.0582 −0.859581 −0.429791 0.902929i \(-0.641413\pi\)
−0.429791 + 0.902929i \(0.641413\pi\)
\(920\) 0.772091 + 2.29307i 0.0254551 + 0.0756001i
\(921\) −10.7309 18.5865i −0.353595 0.612444i
\(922\) 13.2794 7.66684i 0.437332 0.252494i
\(923\) 54.0298i 1.77841i
\(924\) 1.55058 0.0510104
\(925\) 18.1646 43.2488i 0.597248 1.42201i
\(926\) −5.07421 + 8.78879i −0.166749 + 0.288817i
\(927\) 5.90285 3.40801i 0.193875 0.111934i
\(928\) −3.60618 2.08203i −0.118379 0.0683460i
\(929\) −3.98900 + 6.90914i −0.130875 + 0.226682i −0.924014 0.382359i \(-0.875112\pi\)
0.793139 + 0.609040i \(0.208445\pi\)
\(930\) −0.878825 2.61006i −0.0288178 0.0855872i
\(931\) −8.82267 22.8458i −0.289151 0.748741i
\(932\) 12.7211i 0.416695i
\(933\) 22.2140 + 12.8253i 0.727254 + 0.419880i
\(934\) −3.99942 + 6.92719i −0.130865 + 0.226665i
\(935\) −3.05508 2.69259i −0.0999117 0.0880570i
\(936\) 7.01362 12.1479i 0.229247 0.397068i
\(937\) −40.4037 + 23.3271i −1.31993 + 0.762063i −0.983717 0.179722i \(-0.942480\pi\)
−0.336215 + 0.941785i \(0.609147\pi\)
\(938\) 2.87426i 0.0938479i
\(939\) −3.63928 −0.118763
\(940\) −31.3606 27.6396i −1.02287 0.901505i
\(941\) 0.700500 + 1.21330i 0.0228356 + 0.0395525i 0.877217 0.480093i \(-0.159397\pi\)
−0.854382 + 0.519646i \(0.826064\pi\)
\(942\) 4.83798i 0.157630i
\(943\) 2.50251i 0.0814930i
\(944\) −8.47969 14.6873i −0.275990 0.478030i
\(945\) −13.1807 2.65560i −0.428768 0.0863868i
\(946\) 1.70440 + 2.95211i 0.0554149 + 0.0959814i
\(947\) 33.1255 + 19.1250i 1.07643 + 0.621480i 0.929932 0.367730i \(-0.119865\pi\)
0.146502 + 0.989210i \(0.453198\pi\)
\(948\) −9.54820 5.51265i −0.310111 0.179043i
\(949\) 50.7900 1.64871
\(950\) −5.39912 + 8.75327i −0.175171 + 0.283994i
\(951\) 32.6326 1.05819
\(952\) 4.63096 + 2.67369i 0.150090 + 0.0866547i
\(953\) −47.1455 27.2195i −1.52719 0.881726i −0.999478 0.0323042i \(-0.989715\pi\)
−0.527715 0.849421i \(-0.676951\pi\)
\(954\) 2.25382 + 3.90373i 0.0729701 + 0.126388i
\(955\) −31.2246 6.29103i −1.01041 0.203573i
\(956\) 3.24805 + 5.62579i 0.105049 + 0.181951i
\(957\) 0.637869i 0.0206194i
\(958\) 4.17989i 0.135046i
\(959\) 2.98231 + 5.16551i 0.0963038 + 0.166803i
\(960\) 5.48036 + 4.83010i 0.176878 + 0.155891i
\(961\) −24.7042 −0.796911
\(962\) 18.1650i 0.585662i
\(963\) −6.03148 + 3.48228i −0.194362 + 0.112215i
\(964\) −15.3409 + 26.5713i −0.494099 + 0.855804i
\(965\) −32.7212 28.8388i −1.05333 0.928353i
\(966\) −0.175125 + 0.303325i −0.00563455 + 0.00975933i
\(967\) 4.32077 + 2.49460i 0.138946 + 0.0802208i 0.567862 0.823124i \(-0.307771\pi\)
−0.428915 + 0.903345i \(0.641104\pi\)
\(968\) 18.6995i 0.601026i
\(969\) −7.26482 + 9.00846i −0.233380 + 0.289393i
\(970\) 5.62367 + 16.7020i 0.180565 + 0.536268i
\(971\) 7.27006 12.5921i 0.233307 0.404100i −0.725472 0.688252i \(-0.758379\pi\)
0.958779 + 0.284152i \(0.0917119\pi\)
\(972\) −24.3148 14.0381i −0.779897 0.450274i
\(973\) 6.08895 3.51546i 0.195203 0.112700i
\(974\) −7.09306 + 12.2855i −0.227276 + 0.393654i
\(975\) −19.6760 8.26395i −0.630135 0.264658i
\(976\) −12.3592 −0.395609
\(977\) 26.1353i 0.836141i −0.908415 0.418071i \(-0.862706\pi\)
0.908415 0.418071i \(-0.137294\pi\)
\(978\) 0.0292569 0.0168915i 0.000935531 0.000540129i
\(979\) 5.69527 + 9.86449i 0.182021 + 0.315270i
\(980\) 7.12524 + 21.1616i 0.227608 + 0.675981i
\(981\) 11.9347 0.381046
\(982\) 1.26699 0.731499i 0.0404314 0.0233431i
\(983\) −39.9376 23.0580i −1.27381 0.735436i −0.298109 0.954532i \(-0.596356\pi\)
−0.975703 + 0.219096i \(0.929689\pi\)
\(984\) −3.82172 6.61942i −0.121832 0.211019i
\(985\) −1.91333 + 9.49652i −0.0609637 + 0.302584i
\(986\) −0.517523 + 0.896376i −0.0164813 + 0.0285464i
\(987\) 12.8606i 0.409356i
\(988\) −4.90929 + 31.4065i −0.156185 + 0.999174i
\(989\) 6.14585 0.195427
\(990\) 0.285204 1.41557i 0.00906439 0.0449898i
\(991\) 15.6640 27.1308i 0.497582 0.861837i −0.502414 0.864627i \(-0.667555\pi\)
0.999996 + 0.00278993i \(0.000888065\pi\)
\(992\) 10.5289 6.07887i 0.334294 0.193004i
\(993\) −32.2055 18.5938i −1.02201 0.590057i
\(994\) 3.65178 + 6.32508i 0.115828 + 0.200619i
\(995\) 9.01304 + 26.7682i 0.285733 + 0.848609i
\(996\) −25.6251 −0.811962
\(997\) 18.7186 10.8072i 0.592826 0.342268i −0.173388 0.984854i \(-0.555472\pi\)
0.766214 + 0.642586i \(0.222138\pi\)
\(998\) −13.1341 + 7.58296i −0.415752 + 0.240035i
\(999\) 47.9944 1.51848
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 95.2.i.b.49.3 12
3.2 odd 2 855.2.be.d.334.4 12
5.2 odd 4 475.2.e.g.201.4 12
5.3 odd 4 475.2.e.g.201.3 12
5.4 even 2 inner 95.2.i.b.49.4 yes 12
15.14 odd 2 855.2.be.d.334.3 12
19.7 even 3 inner 95.2.i.b.64.4 yes 12
19.8 odd 6 1805.2.b.g.1084.3 6
19.11 even 3 1805.2.b.f.1084.4 6
57.26 odd 6 855.2.be.d.64.3 12
95.7 odd 12 475.2.e.g.26.4 12
95.8 even 12 9025.2.a.bt.1.3 6
95.27 even 12 9025.2.a.bt.1.4 6
95.49 even 6 1805.2.b.f.1084.3 6
95.64 even 6 inner 95.2.i.b.64.3 yes 12
95.68 odd 12 9025.2.a.bu.1.4 6
95.83 odd 12 475.2.e.g.26.3 12
95.84 odd 6 1805.2.b.g.1084.4 6
95.87 odd 12 9025.2.a.bu.1.3 6
285.254 odd 6 855.2.be.d.64.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.i.b.49.3 12 1.1 even 1 trivial
95.2.i.b.49.4 yes 12 5.4 even 2 inner
95.2.i.b.64.3 yes 12 95.64 even 6 inner
95.2.i.b.64.4 yes 12 19.7 even 3 inner
475.2.e.g.26.3 12 95.83 odd 12
475.2.e.g.26.4 12 95.7 odd 12
475.2.e.g.201.3 12 5.3 odd 4
475.2.e.g.201.4 12 5.2 odd 4
855.2.be.d.64.3 12 57.26 odd 6
855.2.be.d.64.4 12 285.254 odd 6
855.2.be.d.334.3 12 15.14 odd 2
855.2.be.d.334.4 12 3.2 odd 2
1805.2.b.f.1084.3 6 95.49 even 6
1805.2.b.f.1084.4 6 19.11 even 3
1805.2.b.g.1084.3 6 19.8 odd 6
1805.2.b.g.1084.4 6 95.84 odd 6
9025.2.a.bt.1.3 6 95.8 even 12
9025.2.a.bt.1.4 6 95.27 even 12
9025.2.a.bu.1.3 6 95.87 odd 12
9025.2.a.bu.1.4 6 95.68 odd 12