Properties

Label 418.2.j.c.111.2
Level $418$
Weight $2$
Character 418.111
Analytic conductor $3.338$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [418,2,Mod(23,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.j (of order \(9\), degree \(6\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 111.2
Character \(\chi\) \(=\) 418.111
Dual form 418.2.j.c.177.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766044 - 0.642788i) q^{2} +(-0.305857 + 0.111323i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.749682 - 4.25166i) q^{5} +(0.305857 + 0.111323i) q^{6} +(-1.19826 - 2.07545i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.21698 + 1.86027i) q^{9} +O(q^{10})\) \(q+(-0.766044 - 0.642788i) q^{2} +(-0.305857 + 0.111323i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.749682 - 4.25166i) q^{5} +(0.305857 + 0.111323i) q^{6} +(-1.19826 - 2.07545i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.21698 + 1.86027i) q^{9} +(-3.30720 + 2.77507i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.162743 - 0.281879i) q^{12} +(-4.65508 - 1.69431i) q^{13} +(-0.416153 + 2.36012i) q^{14} +(0.244011 + 1.38386i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.18738 + 2.67453i) q^{17} +2.89406 q^{18} +(4.07155 + 1.55643i) q^{19} +4.31725 q^{20} +(0.597543 + 0.501398i) q^{21} +(0.939693 - 0.342020i) q^{22} +(-0.236031 - 1.33860i) q^{23} +(-0.0565201 + 0.320541i) q^{24} +(-12.8161 - 4.66468i) q^{25} +(2.47692 + 4.29014i) q^{26} +(0.959217 - 1.66141i) q^{27} +(1.83585 - 1.54046i) q^{28} +(-6.91798 + 5.80487i) q^{29} +(0.702602 - 1.21694i) q^{30} +(-3.51083 - 6.08094i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0565201 - 0.320541i) q^{33} +(-0.722521 - 4.09762i) q^{34} +(-9.72243 + 3.53868i) q^{35} +(-2.21698 - 1.86027i) q^{36} +1.26563 q^{37} +(-2.11853 - 3.80944i) q^{38} +1.61240 q^{39} +(-3.30720 - 2.77507i) q^{40} +(-6.40580 + 2.33152i) q^{41} +(-0.135452 - 0.768186i) q^{42} +(1.05426 - 5.97903i) q^{43} +(-0.939693 - 0.342020i) q^{44} +(6.24718 + 10.8204i) q^{45} +(-0.679623 + 1.17714i) q^{46} +(7.85790 - 6.59356i) q^{47} +(0.249337 - 0.209219i) q^{48} +(0.628329 - 1.08830i) q^{49} +(6.81931 + 11.8114i) q^{50} +(-1.27262 - 0.463196i) q^{51} +(0.860224 - 4.87857i) q^{52} +(-0.959843 - 5.44354i) q^{53} +(-1.80274 + 0.656143i) q^{54} +(3.30720 + 2.77507i) q^{55} -2.39653 q^{56} +(-1.41858 - 0.0227896i) q^{57} +9.03078 q^{58} +(0.924752 + 0.775959i) q^{59} +(-1.32046 + 0.480608i) q^{60} +(-1.12343 - 6.37130i) q^{61} +(-1.21930 + 6.91499i) q^{62} +(6.51742 + 2.37215i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-10.6935 + 18.5216i) q^{65} +(-0.249337 + 0.209219i) q^{66} +(-9.06743 + 7.60848i) q^{67} +(-2.08042 + 3.60339i) q^{68} +(0.221208 + 0.383143i) q^{69} +(9.72243 + 3.53868i) q^{70} +(1.47522 - 8.36639i) q^{71} +(0.502548 + 2.85009i) q^{72} +(6.03518 - 2.19663i) q^{73} +(-0.969532 - 0.813534i) q^{74} +4.43918 q^{75} +(-0.825771 + 4.27997i) q^{76} +2.39653 q^{77} +(-1.23517 - 1.03643i) q^{78} +(9.95046 - 3.62167i) q^{79} +(0.749682 + 4.25166i) q^{80} +(1.39921 - 7.93534i) q^{81} +(6.40580 + 2.33152i) q^{82} +(1.87900 + 3.25453i) q^{83} +(-0.390018 + 0.675531i) q^{84} +(13.7607 - 11.5466i) q^{85} +(-4.65086 + 3.90254i) q^{86} +(1.46970 - 2.54559i) q^{87} +(0.500000 + 0.866025i) q^{88} +(10.1630 + 3.69904i) q^{89} +(2.16962 - 12.3045i) q^{90} +(2.06155 + 11.6916i) q^{91} +(1.27727 - 0.464890i) q^{92} +(1.75076 + 1.46906i) q^{93} -10.2578 q^{94} +(9.66979 - 16.1440i) q^{95} -0.325486 q^{96} +(-3.60440 - 3.02445i) q^{97} +(-1.18087 + 0.429802i) q^{98} +(-0.502548 - 2.85009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 12 q^{7} + 15 q^{8} - 15 q^{11} + 3 q^{12} - 3 q^{13} + 9 q^{14} + 27 q^{15} - 36 q^{18} - 9 q^{19} + 18 q^{20} - 27 q^{21} - 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{28} + 3 q^{29} + 9 q^{30} + 30 q^{31} - 9 q^{34} + 15 q^{35} + 18 q^{37} + 6 q^{38} - 6 q^{41} - 45 q^{42} + 39 q^{43} - 18 q^{45} + 21 q^{46} + 45 q^{47} - 33 q^{49} + 36 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} + 45 q^{54} - 24 q^{56} - 24 q^{57} - 30 q^{58} + 3 q^{59} - 9 q^{60} - 27 q^{61} + 15 q^{62} - 93 q^{63} - 15 q^{64} + 18 q^{65} - 9 q^{67} - 21 q^{68} + 48 q^{69} - 15 q^{70} + 39 q^{73} + 3 q^{74} - 42 q^{75} - 15 q^{76} + 24 q^{77} + 6 q^{78} + 21 q^{79} + 84 q^{81} + 6 q^{82} - 36 q^{83} - 27 q^{84} + 63 q^{85} + 6 q^{86} - 21 q^{87} + 15 q^{88} + 54 q^{89} + 12 q^{90} + 3 q^{91} - 3 q^{92} + 51 q^{93} - 78 q^{94} + 6 q^{95} + 6 q^{96} - 18 q^{97} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766044 0.642788i −0.541675 0.454519i
\(3\) −0.305857 + 0.111323i −0.176587 + 0.0642723i −0.428800 0.903399i \(-0.641064\pi\)
0.252214 + 0.967672i \(0.418841\pi\)
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) 0.749682 4.25166i 0.335268 1.90140i −0.0893029 0.996005i \(-0.528464\pi\)
0.424571 0.905395i \(-0.360425\pi\)
\(6\) 0.305857 + 0.111323i 0.124866 + 0.0454474i
\(7\) −1.19826 2.07545i −0.452901 0.784448i 0.545664 0.838004i \(-0.316278\pi\)
−0.998565 + 0.0535566i \(0.982944\pi\)
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) −2.21698 + 1.86027i −0.738993 + 0.620088i
\(10\) −3.30720 + 2.77507i −1.04583 + 0.877555i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) −0.162743 0.281879i −0.0469799 0.0813716i
\(13\) −4.65508 1.69431i −1.29109 0.469917i −0.397003 0.917817i \(-0.629950\pi\)
−0.894084 + 0.447900i \(0.852172\pi\)
\(14\) −0.416153 + 2.36012i −0.111221 + 0.630768i
\(15\) 0.244011 + 1.38386i 0.0630034 + 0.357310i
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 3.18738 + 2.67453i 0.773054 + 0.648670i 0.941489 0.337043i \(-0.109427\pi\)
−0.168435 + 0.985713i \(0.553871\pi\)
\(18\) 2.89406 0.682136
\(19\) 4.07155 + 1.55643i 0.934077 + 0.357070i
\(20\) 4.31725 0.965366
\(21\) 0.597543 + 0.501398i 0.130394 + 0.109414i
\(22\) 0.939693 0.342020i 0.200343 0.0729189i
\(23\) −0.236031 1.33860i −0.0492158 0.279117i 0.950261 0.311454i \(-0.100816\pi\)
−0.999477 + 0.0323375i \(0.989705\pi\)
\(24\) −0.0565201 + 0.320541i −0.0115371 + 0.0654302i
\(25\) −12.8161 4.66468i −2.56322 0.932936i
\(26\) 2.47692 + 4.29014i 0.485763 + 0.841367i
\(27\) 0.959217 1.66141i 0.184601 0.319739i
\(28\) 1.83585 1.54046i 0.346942 0.291119i
\(29\) −6.91798 + 5.80487i −1.28464 + 1.07794i −0.292049 + 0.956403i \(0.594337\pi\)
−0.992587 + 0.121535i \(0.961218\pi\)
\(30\) 0.702602 1.21694i 0.128277 0.222182i
\(31\) −3.51083 6.08094i −0.630564 1.09217i −0.987437 0.158016i \(-0.949490\pi\)
0.356873 0.934153i \(-0.383843\pi\)
\(32\) 0.939693 + 0.342020i 0.166116 + 0.0604612i
\(33\) 0.0565201 0.320541i 0.00983888 0.0557991i
\(34\) −0.722521 4.09762i −0.123911 0.702737i
\(35\) −9.72243 + 3.53868i −1.64339 + 0.598146i
\(36\) −2.21698 1.86027i −0.369496 0.310044i
\(37\) 1.26563 0.208069 0.104035 0.994574i \(-0.466825\pi\)
0.104035 + 0.994574i \(0.466825\pi\)
\(38\) −2.11853 3.80944i −0.343671 0.617973i
\(39\) 1.61240 0.258191
\(40\) −3.30720 2.77507i −0.522915 0.438778i
\(41\) −6.40580 + 2.33152i −1.00042 + 0.364123i −0.789746 0.613434i \(-0.789788\pi\)
−0.210673 + 0.977557i \(0.567565\pi\)
\(42\) −0.135452 0.768186i −0.0209007 0.118534i
\(43\) 1.05426 5.97903i 0.160774 0.911794i −0.792542 0.609818i \(-0.791243\pi\)
0.953315 0.301976i \(-0.0976463\pi\)
\(44\) −0.939693 0.342020i −0.141664 0.0515615i
\(45\) 6.24718 + 10.8204i 0.931275 + 1.61302i
\(46\) −0.679623 + 1.17714i −0.100205 + 0.173560i
\(47\) 7.85790 6.59356i 1.14619 0.961769i 0.146568 0.989201i \(-0.453177\pi\)
0.999624 + 0.0274312i \(0.00873272\pi\)
\(48\) 0.249337 0.209219i 0.0359887 0.0301981i
\(49\) 0.628329 1.08830i 0.0897613 0.155471i
\(50\) 6.81931 + 11.8114i 0.964396 + 1.67038i
\(51\) −1.27262 0.463196i −0.178203 0.0648604i
\(52\) 0.860224 4.87857i 0.119292 0.676536i
\(53\) −0.959843 5.44354i −0.131845 0.747728i −0.977005 0.213215i \(-0.931606\pi\)
0.845161 0.534512i \(-0.179505\pi\)
\(54\) −1.80274 + 0.656143i −0.245322 + 0.0892898i
\(55\) 3.30720 + 2.77507i 0.445943 + 0.374191i
\(56\) −2.39653 −0.320249
\(57\) −1.41858 0.0227896i −0.187895 0.00301856i
\(58\) 9.03078 1.18580
\(59\) 0.924752 + 0.775959i 0.120392 + 0.101021i 0.700996 0.713165i \(-0.252739\pi\)
−0.580604 + 0.814186i \(0.697183\pi\)
\(60\) −1.32046 + 0.480608i −0.170471 + 0.0620462i
\(61\) −1.12343 6.37130i −0.143841 0.815761i −0.968291 0.249826i \(-0.919627\pi\)
0.824450 0.565935i \(-0.191485\pi\)
\(62\) −1.21930 + 6.91499i −0.154851 + 0.878205i
\(63\) 6.51742 + 2.37215i 0.821117 + 0.298862i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −10.6935 + 18.5216i −1.32636 + 2.29732i
\(66\) −0.249337 + 0.209219i −0.0306913 + 0.0257530i
\(67\) −9.06743 + 7.60848i −1.10776 + 0.929524i −0.997923 0.0644255i \(-0.979479\pi\)
−0.109841 + 0.993949i \(0.535034\pi\)
\(68\) −2.08042 + 3.60339i −0.252288 + 0.436975i
\(69\) 0.221208 + 0.383143i 0.0266303 + 0.0461250i
\(70\) 9.72243 + 3.53868i 1.16205 + 0.422953i
\(71\) 1.47522 8.36639i 0.175076 0.992907i −0.762979 0.646423i \(-0.776264\pi\)
0.938056 0.346484i \(-0.112625\pi\)
\(72\) 0.502548 + 2.85009i 0.0592259 + 0.335887i
\(73\) 6.03518 2.19663i 0.706365 0.257096i 0.0362388 0.999343i \(-0.488462\pi\)
0.670126 + 0.742247i \(0.266240\pi\)
\(74\) −0.969532 0.813534i −0.112706 0.0945714i
\(75\) 4.43918 0.512593
\(76\) −0.825771 + 4.27997i −0.0947224 + 0.490946i
\(77\) 2.39653 0.273110
\(78\) −1.23517 1.03643i −0.139856 0.117353i
\(79\) 9.95046 3.62167i 1.11951 0.407470i 0.285039 0.958516i \(-0.407993\pi\)
0.834475 + 0.551046i \(0.185771\pi\)
\(80\) 0.749682 + 4.25166i 0.0838170 + 0.475350i
\(81\) 1.39921 7.93534i 0.155468 0.881704i
\(82\) 6.40580 + 2.33152i 0.707403 + 0.257474i
\(83\) 1.87900 + 3.25453i 0.206247 + 0.357231i 0.950529 0.310635i \(-0.100542\pi\)
−0.744282 + 0.667865i \(0.767208\pi\)
\(84\) −0.390018 + 0.675531i −0.0425545 + 0.0737065i
\(85\) 13.7607 11.5466i 1.49256 1.25241i
\(86\) −4.65086 + 3.90254i −0.501515 + 0.420821i
\(87\) 1.46970 2.54559i 0.157568 0.272916i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 10.1630 + 3.69904i 1.07728 + 0.392098i 0.818895 0.573944i \(-0.194587\pi\)
0.258386 + 0.966042i \(0.416810\pi\)
\(90\) 2.16962 12.3045i 0.228698 1.29701i
\(91\) 2.06155 + 11.6916i 0.216109 + 1.22562i
\(92\) 1.27727 0.464890i 0.133165 0.0484681i
\(93\) 1.75076 + 1.46906i 0.181545 + 0.152335i
\(94\) −10.2578 −1.05801
\(95\) 9.66979 16.1440i 0.992100 1.65634i
\(96\) −0.325486 −0.0332198
\(97\) −3.60440 3.02445i −0.365972 0.307087i 0.441194 0.897412i \(-0.354555\pi\)
−0.807166 + 0.590325i \(0.799000\pi\)
\(98\) −1.18087 + 0.429802i −0.119286 + 0.0434166i
\(99\) −0.502548 2.85009i −0.0505080 0.286445i
\(100\) 2.36832 13.4314i 0.236832 1.34314i
\(101\) −12.8296 4.66959i −1.27659 0.464642i −0.387289 0.921959i \(-0.626588\pi\)
−0.889304 + 0.457317i \(0.848811\pi\)
\(102\) 0.677147 + 1.17285i 0.0670476 + 0.116130i
\(103\) 6.16281 10.6743i 0.607240 1.05177i −0.384453 0.923145i \(-0.625610\pi\)
0.991693 0.128626i \(-0.0410567\pi\)
\(104\) −3.79486 + 3.18426i −0.372116 + 0.312243i
\(105\) 2.57974 2.16466i 0.251757 0.211249i
\(106\) −2.76376 + 4.78697i −0.268440 + 0.464951i
\(107\) 1.85606 + 3.21480i 0.179432 + 0.310786i 0.941686 0.336492i \(-0.109241\pi\)
−0.762254 + 0.647278i \(0.775907\pi\)
\(108\) 1.80274 + 0.656143i 0.173469 + 0.0631374i
\(109\) −1.98326 + 11.2476i −0.189962 + 1.07733i 0.729451 + 0.684033i \(0.239776\pi\)
−0.919413 + 0.393294i \(0.871335\pi\)
\(110\) −0.749682 4.25166i −0.0714794 0.405380i
\(111\) −0.387103 + 0.140894i −0.0367422 + 0.0133731i
\(112\) 1.83585 + 1.54046i 0.173471 + 0.145560i
\(113\) 11.2564 1.05891 0.529457 0.848337i \(-0.322396\pi\)
0.529457 + 0.848337i \(0.322396\pi\)
\(114\) 1.07205 + 0.929303i 0.100406 + 0.0870372i
\(115\) −5.86820 −0.547212
\(116\) −6.91798 5.80487i −0.642318 0.538969i
\(117\) 13.4721 4.90343i 1.24549 0.453323i
\(118\) −0.209624 1.18884i −0.0192975 0.109441i
\(119\) 1.73154 9.82006i 0.158730 0.900204i
\(120\) 1.32046 + 0.480608i 0.120541 + 0.0438733i
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −3.23479 + 5.60282i −0.292864 + 0.507256i
\(123\) 1.69971 1.42622i 0.153258 0.128598i
\(124\) 5.37891 4.51344i 0.483040 0.405319i
\(125\) −18.6475 + 32.2985i −1.66789 + 2.88886i
\(126\) −3.46784 6.00648i −0.308940 0.535100i
\(127\) −8.32800 3.03114i −0.738990 0.268971i −0.0550250 0.998485i \(-0.517524\pi\)
−0.683965 + 0.729514i \(0.739746\pi\)
\(128\) −0.173648 + 0.984808i −0.0153485 + 0.0870455i
\(129\) 0.343149 + 1.94609i 0.0302126 + 0.171344i
\(130\) 20.0971 7.31476i 1.76263 0.641547i
\(131\) 11.4389 + 9.59841i 0.999425 + 0.838617i 0.986905 0.161305i \(-0.0515702\pi\)
0.0125201 + 0.999922i \(0.496015\pi\)
\(132\) 0.325486 0.0283299
\(133\) −1.64848 10.3153i −0.142942 0.894452i
\(134\) 11.8367 1.02253
\(135\) −6.34465 5.32380i −0.546061 0.458199i
\(136\) 3.90991 1.42309i 0.335272 0.122029i
\(137\) −1.70297 9.65802i −0.145494 0.825140i −0.966969 0.254895i \(-0.917959\pi\)
0.821474 0.570246i \(-0.193152\pi\)
\(138\) 0.0768247 0.435695i 0.00653975 0.0370888i
\(139\) −1.93580 0.704572i −0.164192 0.0597610i 0.258616 0.965980i \(-0.416733\pi\)
−0.422808 + 0.906219i \(0.638956\pi\)
\(140\) −5.17320 8.96024i −0.437215 0.757279i
\(141\) −1.66938 + 2.89145i −0.140587 + 0.243504i
\(142\) −6.50789 + 5.46077i −0.546130 + 0.458258i
\(143\) 3.79486 3.18426i 0.317342 0.266281i
\(144\) 1.44703 2.50633i 0.120586 0.208861i
\(145\) 19.4941 + 33.7647i 1.61889 + 2.80400i
\(146\) −6.03518 2.19663i −0.499475 0.181794i
\(147\) −0.0710264 + 0.402811i −0.00585816 + 0.0332233i
\(148\) 0.219775 + 1.24641i 0.0180654 + 0.102454i
\(149\) −2.11161 + 0.768565i −0.172990 + 0.0629633i −0.427063 0.904222i \(-0.640452\pi\)
0.254073 + 0.967185i \(0.418230\pi\)
\(150\) −3.40061 2.85345i −0.277659 0.232983i
\(151\) 0.400935 0.0326276 0.0163138 0.999867i \(-0.494807\pi\)
0.0163138 + 0.999867i \(0.494807\pi\)
\(152\) 3.38369 2.74785i 0.274453 0.222880i
\(153\) −12.0417 −0.973514
\(154\) −1.83585 1.54046i −0.147937 0.124134i
\(155\) −28.4861 + 10.3681i −2.28806 + 0.832785i
\(156\) 0.279991 + 1.58791i 0.0224172 + 0.127134i
\(157\) 1.41427 8.02072i 0.112871 0.640123i −0.874911 0.484283i \(-0.839080\pi\)
0.987782 0.155840i \(-0.0498084\pi\)
\(158\) −9.95046 3.62167i −0.791616 0.288125i
\(159\) 0.899565 + 1.55809i 0.0713401 + 0.123565i
\(160\) 2.15862 3.73885i 0.170654 0.295582i
\(161\) −2.49537 + 2.09386i −0.196662 + 0.165019i
\(162\) −6.17260 + 5.17942i −0.484965 + 0.406934i
\(163\) 9.74378 16.8767i 0.763192 1.32189i −0.178005 0.984030i \(-0.556964\pi\)
0.941197 0.337858i \(-0.109702\pi\)
\(164\) −3.40846 5.90362i −0.266156 0.460995i
\(165\) −1.32046 0.480608i −0.102798 0.0374153i
\(166\) 0.652571 3.70091i 0.0506493 0.287246i
\(167\) 2.02397 + 11.4785i 0.156620 + 0.888234i 0.957290 + 0.289129i \(0.0933658\pi\)
−0.800670 + 0.599105i \(0.795523\pi\)
\(168\) 0.732995 0.266788i 0.0565518 0.0205832i
\(169\) 8.84050 + 7.41806i 0.680039 + 0.570620i
\(170\) −17.9634 −1.37773
\(171\) −11.9219 + 4.12358i −0.911691 + 0.315338i
\(172\) 6.07127 0.462930
\(173\) 8.06249 + 6.76523i 0.612980 + 0.514351i 0.895588 0.444884i \(-0.146755\pi\)
−0.282608 + 0.959235i \(0.591200\pi\)
\(174\) −2.76213 + 1.00533i −0.209396 + 0.0762140i
\(175\) 5.67575 + 32.1888i 0.429046 + 2.43324i
\(176\) 0.173648 0.984808i 0.0130892 0.0742327i
\(177\) −0.369224 0.134387i −0.0277526 0.0101011i
\(178\) −5.40764 9.36631i −0.405320 0.702034i
\(179\) 6.11737 10.5956i 0.457234 0.791952i −0.541580 0.840649i \(-0.682174\pi\)
0.998814 + 0.0486972i \(0.0155069\pi\)
\(180\) −9.57124 + 8.03122i −0.713398 + 0.598612i
\(181\) 12.4649 10.4593i 0.926511 0.777435i −0.0486768 0.998815i \(-0.515500\pi\)
0.975188 + 0.221380i \(0.0710560\pi\)
\(182\) 5.93600 10.2814i 0.440005 0.762112i
\(183\) 1.05288 + 1.82364i 0.0778311 + 0.134807i
\(184\) −1.27727 0.464890i −0.0941618 0.0342721i
\(185\) 0.948823 5.38104i 0.0697589 0.395622i
\(186\) −0.396865 2.25073i −0.0290996 0.165032i
\(187\) −3.90991 + 1.42309i −0.285921 + 0.104067i
\(188\) 7.85790 + 6.59356i 0.573096 + 0.480885i
\(189\) −4.59758 −0.334425
\(190\) −17.7847 + 6.15140i −1.29023 + 0.446270i
\(191\) −25.6348 −1.85487 −0.927436 0.373981i \(-0.877992\pi\)
−0.927436 + 0.373981i \(0.877992\pi\)
\(192\) 0.249337 + 0.209219i 0.0179943 + 0.0150990i
\(193\) −13.8360 + 5.03591i −0.995940 + 0.362492i −0.788017 0.615653i \(-0.788892\pi\)
−0.207922 + 0.978145i \(0.566670\pi\)
\(194\) 0.817052 + 4.63373i 0.0586609 + 0.332683i
\(195\) 1.20879 6.85539i 0.0865633 0.490925i
\(196\) 1.18087 + 0.429802i 0.0843480 + 0.0307002i
\(197\) −0.199622 0.345756i −0.0142225 0.0246341i 0.858827 0.512266i \(-0.171194\pi\)
−0.873049 + 0.487632i \(0.837861\pi\)
\(198\) −1.44703 + 2.50633i −0.102836 + 0.178117i
\(199\) −2.06268 + 1.73080i −0.146220 + 0.122693i −0.712963 0.701201i \(-0.752647\pi\)
0.566744 + 0.823894i \(0.308203\pi\)
\(200\) −10.4478 + 8.76673i −0.738770 + 0.619902i
\(201\) 1.92634 3.33652i 0.135874 0.235340i
\(202\) 6.82649 + 11.8238i 0.480310 + 0.831921i
\(203\) 20.3373 + 7.40217i 1.42740 + 0.519531i
\(204\) 0.235171 1.33372i 0.0164652 0.0933791i
\(205\) 5.11052 + 28.9832i 0.356934 + 2.02427i
\(206\) −11.5823 + 4.21561i −0.806977 + 0.293716i
\(207\) 3.01342 + 2.52856i 0.209447 + 0.175747i
\(208\) 4.95383 0.343486
\(209\) −3.38369 + 2.74785i −0.234054 + 0.190073i
\(210\) −3.36761 −0.232387
\(211\) −5.27588 4.42699i −0.363207 0.304767i 0.442861 0.896590i \(-0.353964\pi\)
−0.806067 + 0.591824i \(0.798408\pi\)
\(212\) 5.19417 1.89052i 0.356737 0.129842i
\(213\) 0.480164 + 2.72314i 0.0329003 + 0.186587i
\(214\) 0.644604 3.65573i 0.0440642 0.249901i
\(215\) −24.6304 8.96475i −1.67978 0.611391i
\(216\) −0.959217 1.66141i −0.0652665 0.113045i
\(217\) −8.41380 + 14.5731i −0.571166 + 0.989289i
\(218\) 8.74910 7.34137i 0.592564 0.497220i
\(219\) −1.60137 + 1.34371i −0.108210 + 0.0907993i
\(220\) −2.15862 + 3.73885i −0.145534 + 0.252073i
\(221\) −10.3060 17.8506i −0.693259 1.20076i
\(222\) 0.387103 + 0.140894i 0.0259807 + 0.00945619i
\(223\) −2.42581 + 13.7574i −0.162444 + 0.921266i 0.789217 + 0.614115i \(0.210487\pi\)
−0.951661 + 0.307151i \(0.900624\pi\)
\(224\) −0.416153 2.36012i −0.0278054 0.157692i
\(225\) 37.0906 13.4999i 2.47270 0.899991i
\(226\) −8.62290 7.23548i −0.573587 0.481297i
\(227\) 1.24242 0.0824622 0.0412311 0.999150i \(-0.486872\pi\)
0.0412311 + 0.999150i \(0.486872\pi\)
\(228\) −0.223890 1.40098i −0.0148275 0.0927825i
\(229\) 2.33480 0.154288 0.0771440 0.997020i \(-0.475420\pi\)
0.0771440 + 0.997020i \(0.475420\pi\)
\(230\) 4.49530 + 3.77201i 0.296411 + 0.248719i
\(231\) −0.732995 + 0.266788i −0.0482275 + 0.0175534i
\(232\) 1.56818 + 8.89358i 0.102956 + 0.583892i
\(233\) −1.43152 + 8.11854i −0.0937818 + 0.531863i 0.901332 + 0.433129i \(0.142590\pi\)
−0.995114 + 0.0987343i \(0.968521\pi\)
\(234\) −13.4721 4.90343i −0.880697 0.320548i
\(235\) −22.1426 38.3522i −1.44443 2.50182i
\(236\) −0.603589 + 1.04545i −0.0392903 + 0.0680528i
\(237\) −2.64024 + 2.21543i −0.171502 + 0.143907i
\(238\) −7.63865 + 6.40959i −0.495140 + 0.415472i
\(239\) 13.4212 23.2462i 0.868147 1.50367i 0.00425815 0.999991i \(-0.498645\pi\)
0.863888 0.503683i \(-0.168022\pi\)
\(240\) −0.702602 1.21694i −0.0453528 0.0785533i
\(241\) −9.08552 3.30686i −0.585250 0.213014i 0.0323890 0.999475i \(-0.489688\pi\)
−0.617639 + 0.786462i \(0.711911\pi\)
\(242\) −0.173648 + 0.984808i −0.0111625 + 0.0633058i
\(243\) 1.45482 + 8.25071i 0.0933269 + 0.529283i
\(244\) 6.07942 2.21273i 0.389195 0.141655i
\(245\) −4.15602 3.48732i −0.265519 0.222797i
\(246\) −2.21881 −0.141466
\(247\) −16.3163 14.1438i −1.03818 0.899948i
\(248\) −7.02166 −0.445876
\(249\) −0.937009 0.786244i −0.0593805 0.0498262i
\(250\) 35.0459 12.7557i 2.21650 0.806739i
\(251\) 1.20130 + 6.81292i 0.0758255 + 0.430028i 0.998962 + 0.0455550i \(0.0145056\pi\)
−0.923136 + 0.384473i \(0.874383\pi\)
\(252\) −1.20437 + 6.83032i −0.0758682 + 0.430270i
\(253\) 1.27727 + 0.464890i 0.0803015 + 0.0292274i
\(254\) 4.43124 + 7.67513i 0.278040 + 0.481580i
\(255\) −2.92341 + 5.06350i −0.183071 + 0.317089i
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −2.36199 + 1.98195i −0.147337 + 0.123630i −0.713477 0.700679i \(-0.752881\pi\)
0.566140 + 0.824309i \(0.308436\pi\)
\(258\) 0.988057 1.71137i 0.0615138 0.106545i
\(259\) −1.51656 2.62676i −0.0942347 0.163219i
\(260\) −20.0971 7.31476i −1.24637 0.453642i
\(261\) 4.53840 25.7386i 0.280920 1.59318i
\(262\) −2.59300 14.7056i −0.160196 0.908516i
\(263\) 24.6400 8.96824i 1.51937 0.553005i 0.558378 0.829586i \(-0.311424\pi\)
0.960991 + 0.276581i \(0.0892015\pi\)
\(264\) −0.249337 0.209219i −0.0153456 0.0128765i
\(265\) −23.8636 −1.46593
\(266\) −5.36775 + 8.96162i −0.329118 + 0.549472i
\(267\) −3.52022 −0.215434
\(268\) −9.06743 7.60848i −0.553882 0.464762i
\(269\) −21.8767 + 7.96246i −1.33385 + 0.485480i −0.907869 0.419254i \(-0.862292\pi\)
−0.425976 + 0.904734i \(0.640069\pi\)
\(270\) 1.43822 + 8.15653i 0.0875270 + 0.496391i
\(271\) 3.17445 18.0032i 0.192834 1.09362i −0.722635 0.691230i \(-0.757069\pi\)
0.915469 0.402388i \(-0.131820\pi\)
\(272\) −3.90991 1.42309i −0.237073 0.0862875i
\(273\) −1.93209 3.34647i −0.116935 0.202538i
\(274\) −4.90351 + 8.49312i −0.296232 + 0.513088i
\(275\) 10.4478 8.76673i 0.630025 0.528654i
\(276\) −0.338910 + 0.284379i −0.0204000 + 0.0171176i
\(277\) 0.760611 1.31742i 0.0457007 0.0791559i −0.842270 0.539056i \(-0.818781\pi\)
0.887971 + 0.459900i \(0.152115\pi\)
\(278\) 1.03002 + 1.78404i 0.0617762 + 0.107000i
\(279\) 19.0956 + 6.95023i 1.14322 + 0.416099i
\(280\) −1.79663 + 10.1892i −0.107369 + 0.608922i
\(281\) 2.63818 + 14.9619i 0.157381 + 0.892551i 0.956577 + 0.291480i \(0.0941478\pi\)
−0.799196 + 0.601070i \(0.794741\pi\)
\(282\) 3.13741 1.14192i 0.186830 0.0680005i
\(283\) −8.21685 6.89476i −0.488441 0.409851i 0.365026 0.930997i \(-0.381060\pi\)
−0.853467 + 0.521146i \(0.825505\pi\)
\(284\) 8.49545 0.504112
\(285\) −1.16038 + 6.01423i −0.0687348 + 0.356252i
\(286\) −4.95383 −0.292926
\(287\) 12.5148 + 10.5012i 0.738726 + 0.619864i
\(288\) −2.71953 + 0.989826i −0.160250 + 0.0583261i
\(289\) 0.0542736 + 0.307801i 0.00319257 + 0.0181059i
\(290\) 6.77021 38.3958i 0.397561 2.25468i
\(291\) 1.43912 + 0.523798i 0.0843629 + 0.0307056i
\(292\) 3.21125 + 5.56205i 0.187924 + 0.325495i
\(293\) −4.81403 + 8.33814i −0.281238 + 0.487119i −0.971690 0.236259i \(-0.924079\pi\)
0.690452 + 0.723379i \(0.257412\pi\)
\(294\) 0.313331 0.262916i 0.0182739 0.0153336i
\(295\) 3.99238 3.35001i 0.232446 0.195045i
\(296\) 0.632817 1.09607i 0.0367818 0.0637079i
\(297\) 0.959217 + 1.66141i 0.0556594 + 0.0964050i
\(298\) 2.11161 + 0.768565i 0.122323 + 0.0445218i
\(299\) −1.16926 + 6.63118i −0.0676198 + 0.383491i
\(300\) 0.770856 + 4.37174i 0.0445054 + 0.252403i
\(301\) −13.6725 + 4.97638i −0.788069 + 0.286834i
\(302\) −0.307134 0.257716i −0.0176736 0.0148299i
\(303\) 4.44385 0.255293
\(304\) −4.35834 0.0700172i −0.249968 0.00401576i
\(305\) −27.9308 −1.59931
\(306\) 9.22448 + 7.74026i 0.527328 + 0.442481i
\(307\) 25.5630 9.30417i 1.45896 0.531017i 0.513879 0.857863i \(-0.328208\pi\)
0.945078 + 0.326846i \(0.105986\pi\)
\(308\) 0.416153 + 2.36012i 0.0237125 + 0.134480i
\(309\) −0.696646 + 3.95087i −0.0396308 + 0.224757i
\(310\) 28.4861 + 10.3681i 1.61790 + 0.588868i
\(311\) 10.2539 + 17.7603i 0.581446 + 1.00709i 0.995308 + 0.0967543i \(0.0308461\pi\)
−0.413862 + 0.910339i \(0.635821\pi\)
\(312\) 0.806202 1.39638i 0.0456422 0.0790546i
\(313\) 6.86998 5.76460i 0.388314 0.325834i −0.427642 0.903948i \(-0.640656\pi\)
0.815956 + 0.578114i \(0.196211\pi\)
\(314\) −6.23901 + 5.23515i −0.352088 + 0.295437i
\(315\) 14.9715 25.9315i 0.843551 1.46107i
\(316\) 5.29453 + 9.17039i 0.297840 + 0.515875i
\(317\) 6.61359 + 2.40715i 0.371456 + 0.135199i 0.521001 0.853556i \(-0.325559\pi\)
−0.149545 + 0.988755i \(0.547781\pi\)
\(318\) 0.312416 1.77180i 0.0175194 0.0993574i
\(319\) −1.56818 8.89358i −0.0878011 0.497945i
\(320\) −4.05688 + 1.47659i −0.226787 + 0.0825436i
\(321\) −0.925570 0.776645i −0.0516603 0.0433481i
\(322\) 3.25747 0.181532
\(323\) 8.81486 + 15.8504i 0.490472 + 0.881942i
\(324\) 8.05775 0.447653
\(325\) 51.7566 + 43.4289i 2.87094 + 2.40900i
\(326\) −18.3123 + 6.66514i −1.01423 + 0.369148i
\(327\) −0.645524 3.66095i −0.0356976 0.202451i
\(328\) −1.18374 + 6.71335i −0.0653614 + 0.370683i
\(329\) −23.1005 8.40788i −1.27357 0.463541i
\(330\) 0.702602 + 1.21694i 0.0386770 + 0.0669905i
\(331\) −1.86555 + 3.23123i −0.102540 + 0.177605i −0.912730 0.408562i \(-0.866030\pi\)
0.810190 + 0.586167i \(0.199364\pi\)
\(332\) −2.87880 + 2.41560i −0.157995 + 0.132573i
\(333\) −2.80588 + 2.35442i −0.153761 + 0.129021i
\(334\) 5.82780 10.0940i 0.318883 0.552321i
\(335\) 25.5510 + 44.2556i 1.39600 + 2.41794i
\(336\) −0.732995 0.266788i −0.0399881 0.0145545i
\(337\) 1.73311 9.82895i 0.0944085 0.535417i −0.900519 0.434818i \(-0.856813\pi\)
0.994927 0.100599i \(-0.0320760\pi\)
\(338\) −2.00398 11.3651i −0.109002 0.618182i
\(339\) −3.44285 + 1.25309i −0.186990 + 0.0680588i
\(340\) 13.7607 + 11.5466i 0.746280 + 0.626203i
\(341\) 7.02166 0.380244
\(342\) 11.7833 + 4.50441i 0.637168 + 0.243571i
\(343\) −19.7873 −1.06841
\(344\) −4.65086 3.90254i −0.250758 0.210411i
\(345\) 1.79483 0.653265i 0.0966304 0.0351706i
\(346\) −1.82762 10.3649i −0.0982533 0.557222i
\(347\) −0.617210 + 3.50037i −0.0331336 + 0.187910i −0.996882 0.0789012i \(-0.974859\pi\)
0.963749 + 0.266811i \(0.0859699\pi\)
\(348\) 2.76213 + 1.00533i 0.148066 + 0.0538915i
\(349\) −10.5104 18.2046i −0.562611 0.974471i −0.997268 0.0738749i \(-0.976463\pi\)
0.434656 0.900596i \(-0.356870\pi\)
\(350\) 16.3427 28.3063i 0.873552 1.51304i
\(351\) −7.28018 + 6.10880i −0.388587 + 0.326064i
\(352\) −0.766044 + 0.642788i −0.0408303 + 0.0342607i
\(353\) 4.97463 8.61632i 0.264773 0.458600i −0.702731 0.711456i \(-0.748036\pi\)
0.967504 + 0.252855i \(0.0813696\pi\)
\(354\) 0.196460 + 0.340279i 0.0104417 + 0.0180856i
\(355\) −34.4651 12.5443i −1.82922 0.665780i
\(356\) −1.87805 + 10.6510i −0.0995367 + 0.564500i
\(357\) 0.563593 + 3.19630i 0.0298285 + 0.169166i
\(358\) −11.4969 + 4.18453i −0.607630 + 0.221159i
\(359\) 19.6616 + 16.4981i 1.03770 + 0.870735i 0.991747 0.128208i \(-0.0409227\pi\)
0.0459544 + 0.998944i \(0.485367\pi\)
\(360\) 12.4944 0.658511
\(361\) 14.1550 + 12.6742i 0.745002 + 0.667063i
\(362\) −16.2718 −0.855227
\(363\) 0.249337 + 0.209219i 0.0130868 + 0.0109811i
\(364\) −11.1560 + 4.06046i −0.584735 + 0.212826i
\(365\) −4.81484 27.3063i −0.252020 1.42928i
\(366\) 0.365661 2.07377i 0.0191134 0.108398i
\(367\) 10.4115 + 3.78949i 0.543477 + 0.197810i 0.599146 0.800640i \(-0.295507\pi\)
−0.0556688 + 0.998449i \(0.517729\pi\)
\(368\) 0.679623 + 1.17714i 0.0354278 + 0.0613627i
\(369\) 9.86427 17.0854i 0.513514 0.889432i
\(370\) −4.18571 + 3.51223i −0.217605 + 0.182592i
\(371\) −10.1477 + 8.51490i −0.526841 + 0.442072i
\(372\) −1.14273 + 1.97926i −0.0592477 + 0.102620i
\(373\) −4.24572 7.35380i −0.219835 0.380765i 0.734922 0.678151i \(-0.237219\pi\)
−0.954757 + 0.297386i \(0.903885\pi\)
\(374\) 3.90991 + 1.42309i 0.202176 + 0.0735862i
\(375\) 2.10792 11.9546i 0.108852 0.617333i
\(376\) −1.78124 10.1019i −0.0918605 0.520967i
\(377\) 42.0390 15.3009i 2.16512 0.788039i
\(378\) 3.52195 + 2.95527i 0.181150 + 0.152003i
\(379\) −24.9177 −1.27994 −0.639969 0.768401i \(-0.721053\pi\)
−0.639969 + 0.768401i \(0.721053\pi\)
\(380\) 17.5779 + 6.71951i 0.901726 + 0.344703i
\(381\) 2.88461 0.147783
\(382\) 19.6374 + 16.4778i 1.00474 + 0.843076i
\(383\) −1.63704 + 0.595834i −0.0836488 + 0.0304457i −0.383506 0.923539i \(-0.625283\pi\)
0.299857 + 0.953984i \(0.403061\pi\)
\(384\) −0.0565201 0.320541i −0.00288428 0.0163576i
\(385\) 1.79663 10.1892i 0.0915649 0.519290i
\(386\) 13.8360 + 5.03591i 0.704236 + 0.256321i
\(387\) 8.78531 + 15.2166i 0.446582 + 0.773503i
\(388\) 2.35261 4.07484i 0.119436 0.206868i
\(389\) −24.9075 + 20.8999i −1.26286 + 1.05967i −0.267489 + 0.963561i \(0.586194\pi\)
−0.995371 + 0.0961051i \(0.969362\pi\)
\(390\) −5.33255 + 4.47454i −0.270024 + 0.226577i
\(391\) 2.82780 4.89789i 0.143008 0.247697i
\(392\) −0.628329 1.08830i −0.0317354 0.0549674i
\(393\) −4.56720 1.66233i −0.230385 0.0838532i
\(394\) −0.0693281 + 0.393179i −0.00349270 + 0.0198081i
\(395\) −7.93842 45.0210i −0.399425 2.26525i
\(396\) 2.71953 0.989826i 0.136661 0.0497406i
\(397\) −9.72266 8.15828i −0.487966 0.409452i 0.365331 0.930878i \(-0.380956\pi\)
−0.853297 + 0.521426i \(0.825400\pi\)
\(398\) 2.69264 0.134970
\(399\) 1.65253 + 2.97150i 0.0827301 + 0.148761i
\(400\) 13.6386 0.681931
\(401\) −15.0467 12.6257i −0.751399 0.630498i 0.184474 0.982837i \(-0.440942\pi\)
−0.935872 + 0.352339i \(0.885386\pi\)
\(402\) −3.62034 + 1.31769i −0.180566 + 0.0657206i
\(403\) 6.04020 + 34.2557i 0.300884 + 1.70640i
\(404\) 2.37081 13.4456i 0.117952 0.668941i
\(405\) −32.6894 11.8980i −1.62435 0.591214i
\(406\) −10.8213 18.7430i −0.537050 0.930198i
\(407\) −0.632817 + 1.09607i −0.0313676 + 0.0543302i
\(408\) −1.03745 + 0.870524i −0.0513614 + 0.0430973i
\(409\) −3.28189 + 2.75383i −0.162279 + 0.136168i −0.720311 0.693651i \(-0.756001\pi\)
0.558032 + 0.829819i \(0.311557\pi\)
\(410\) 14.7151 25.4874i 0.726729 1.25873i
\(411\) 1.59602 + 2.76439i 0.0787260 + 0.136357i
\(412\) 11.5823 + 4.21561i 0.570619 + 0.207688i
\(413\) 0.502370 2.84908i 0.0247200 0.140194i
\(414\) −0.683086 3.87398i −0.0335719 0.190396i
\(415\) 15.2458 5.54901i 0.748386 0.272390i
\(416\) −3.79486 3.18426i −0.186058 0.156121i
\(417\) 0.670512 0.0328351
\(418\) 4.35834 + 0.0700172i 0.213173 + 0.00342465i
\(419\) 15.3658 0.750668 0.375334 0.926890i \(-0.377528\pi\)
0.375334 + 0.926890i \(0.377528\pi\)
\(420\) 2.57974 + 2.16466i 0.125878 + 0.105624i
\(421\) −17.2959 + 6.29518i −0.842949 + 0.306809i −0.727162 0.686466i \(-0.759161\pi\)
−0.115787 + 0.993274i \(0.536939\pi\)
\(422\) 1.19595 + 6.78254i 0.0582177 + 0.330169i
\(423\) −5.15501 + 29.2355i −0.250645 + 1.42148i
\(424\) −5.19417 1.89052i −0.252251 0.0918118i
\(425\) −28.3740 49.1452i −1.37634 2.38389i
\(426\) 1.38258 2.39469i 0.0669860 0.116023i
\(427\) −11.8772 + 9.96612i −0.574776 + 0.482294i
\(428\) −2.84365 + 2.38611i −0.137453 + 0.115337i
\(429\) −0.806202 + 1.39638i −0.0389238 + 0.0674180i
\(430\) 13.1056 + 22.6995i 0.632007 + 1.09467i
\(431\) 20.5138 + 7.46641i 0.988115 + 0.359644i 0.784990 0.619508i \(-0.212668\pi\)
0.203125 + 0.979153i \(0.434890\pi\)
\(432\) −0.333133 + 1.88929i −0.0160279 + 0.0908985i
\(433\) −1.60034 9.07598i −0.0769075 0.436164i −0.998811 0.0487450i \(-0.984478\pi\)
0.921904 0.387419i \(-0.126633\pi\)
\(434\) 15.8128 5.75538i 0.759038 0.276267i
\(435\) −9.72117 8.15703i −0.466095 0.391100i
\(436\) −11.4211 −0.546974
\(437\) 1.12243 5.81753i 0.0536929 0.278290i
\(438\) 2.09044 0.0998850
\(439\) 4.13458 + 3.46932i 0.197333 + 0.165582i 0.736100 0.676873i \(-0.236665\pi\)
−0.538767 + 0.842455i \(0.681110\pi\)
\(440\) 4.05688 1.47659i 0.193404 0.0703934i
\(441\) 0.631531 + 3.58159i 0.0300729 + 0.170552i
\(442\) −3.57925 + 20.2989i −0.170248 + 0.965522i
\(443\) 21.9117 + 7.97520i 1.04106 + 0.378913i 0.805280 0.592894i \(-0.202015\pi\)
0.235775 + 0.971808i \(0.424237\pi\)
\(444\) −0.205973 0.356756i −0.00977506 0.0169309i
\(445\) 23.3461 40.4367i 1.10671 1.91688i
\(446\) 10.7014 8.97953i 0.506725 0.425193i
\(447\) 0.560293 0.470142i 0.0265010 0.0222369i
\(448\) −1.19826 + 2.07545i −0.0566126 + 0.0980559i
\(449\) 11.0017 + 19.0555i 0.519201 + 0.899283i 0.999751 + 0.0223152i \(0.00710374\pi\)
−0.480550 + 0.876967i \(0.659563\pi\)
\(450\) −37.0906 13.4999i −1.74847 0.636390i
\(451\) 1.18374 6.71335i 0.0557404 0.316119i
\(452\) 1.95465 + 11.0854i 0.0919392 + 0.521413i
\(453\) −0.122629 + 0.0446332i −0.00576160 + 0.00209705i
\(454\) −0.951748 0.798611i −0.0446677 0.0374807i
\(455\) 51.2543 2.40284
\(456\) −0.729026 + 1.21713i −0.0341398 + 0.0569973i
\(457\) 9.65301 0.451549 0.225774 0.974180i \(-0.427509\pi\)
0.225774 + 0.974180i \(0.427509\pi\)
\(458\) −1.78856 1.50078i −0.0835740 0.0701269i
\(459\) 7.50090 2.73010i 0.350112 0.127430i
\(460\) −1.01900 5.77905i −0.0475112 0.269450i
\(461\) 2.72935 15.4789i 0.127119 0.720926i −0.852908 0.522061i \(-0.825163\pi\)
0.980027 0.198865i \(-0.0637255\pi\)
\(462\) 0.732995 + 0.266788i 0.0341020 + 0.0124121i
\(463\) 10.5481 + 18.2698i 0.490211 + 0.849070i 0.999937 0.0112669i \(-0.00358644\pi\)
−0.509726 + 0.860337i \(0.670253\pi\)
\(464\) 4.51539 7.82089i 0.209622 0.363075i
\(465\) 7.55846 6.34230i 0.350515 0.294117i
\(466\) 6.31510 5.29900i 0.292541 0.245471i
\(467\) 2.72113 4.71313i 0.125919 0.218098i −0.796173 0.605069i \(-0.793145\pi\)
0.922092 + 0.386972i \(0.126479\pi\)
\(468\) 7.16834 + 12.4159i 0.331357 + 0.573927i
\(469\) 26.6562 + 9.70207i 1.23087 + 0.448000i
\(470\) −7.69005 + 43.6125i −0.354716 + 2.01169i
\(471\) 0.460325 + 2.61063i 0.0212107 + 0.120292i
\(472\) 1.13438 0.412879i 0.0522139 0.0190043i
\(473\) 4.65086 + 3.90254i 0.213847 + 0.179439i
\(474\) 3.44659 0.158307
\(475\) −44.9212 38.9399i −2.06112 1.78669i
\(476\) 9.97155 0.457045
\(477\) 12.2544 + 10.2826i 0.561089 + 0.470810i
\(478\) −25.2236 + 9.18066i −1.15370 + 0.419913i
\(479\) 5.47927 + 31.0745i 0.250354 + 1.41983i 0.807722 + 0.589563i \(0.200700\pi\)
−0.557368 + 0.830266i \(0.688189\pi\)
\(480\) −0.244011 + 1.38386i −0.0111375 + 0.0631641i
\(481\) −5.89163 2.14438i −0.268635 0.0977752i
\(482\) 4.83430 + 8.37326i 0.220197 + 0.381392i
\(483\) 0.530131 0.918213i 0.0241218 0.0417802i
\(484\) 0.766044 0.642788i 0.0348202 0.0292176i
\(485\) −15.5611 + 13.0573i −0.706593 + 0.592902i
\(486\) 4.18900 7.25555i 0.190017 0.329119i
\(487\) −0.328430 0.568857i −0.0148826 0.0257774i 0.858488 0.512833i \(-0.171404\pi\)
−0.873371 + 0.487056i \(0.838071\pi\)
\(488\) −6.07942 2.21273i −0.275202 0.100165i
\(489\) −1.10144 + 6.24657i −0.0498088 + 0.282480i
\(490\) 0.942094 + 5.34288i 0.0425595 + 0.241367i
\(491\) −22.0056 + 8.00940i −0.993101 + 0.361459i −0.786920 0.617055i \(-0.788326\pi\)
−0.206181 + 0.978514i \(0.566103\pi\)
\(492\) 1.69971 + 1.42622i 0.0766288 + 0.0642992i
\(493\) −37.5756 −1.69232
\(494\) 3.40756 + 21.3227i 0.153313 + 0.959353i
\(495\) −12.4944 −0.561580
\(496\) 5.37891 + 4.51344i 0.241520 + 0.202659i
\(497\) −19.1317 + 6.96339i −0.858176 + 0.312351i
\(498\) 0.212403 + 1.20460i 0.00951799 + 0.0539792i
\(499\) −0.0345393 + 0.195882i −0.00154619 + 0.00876889i −0.985571 0.169262i \(-0.945862\pi\)
0.984025 + 0.178031i \(0.0569727\pi\)
\(500\) −35.0459 12.7557i −1.56730 0.570450i
\(501\) −1.89687 3.28547i −0.0847458 0.146784i
\(502\) 3.45901 5.99118i 0.154383 0.267400i
\(503\) −8.73114 + 7.32630i −0.389302 + 0.326663i −0.816341 0.577570i \(-0.804001\pi\)
0.427039 + 0.904233i \(0.359557\pi\)
\(504\) 5.31305 4.45818i 0.236662 0.198583i
\(505\) −29.4716 + 51.0463i −1.31147 + 2.27153i
\(506\) −0.679623 1.17714i −0.0302129 0.0523303i
\(507\) −3.52973 1.28472i −0.156761 0.0570563i
\(508\) 1.53895 8.72783i 0.0682800 0.387235i
\(509\) 6.05044 + 34.3137i 0.268181 + 1.52093i 0.759821 + 0.650132i \(0.225286\pi\)
−0.491640 + 0.870798i \(0.663603\pi\)
\(510\) 5.49422 1.99973i 0.243288 0.0885496i
\(511\) −11.7907 9.89360i −0.521591 0.437667i
\(512\) −1.00000 −0.0441942
\(513\) 6.49138 5.27157i 0.286601 0.232745i
\(514\) 3.08336 0.136001
\(515\) −40.7633 34.2045i −1.79625 1.50723i
\(516\) −1.85694 + 0.675871i −0.0817472 + 0.0297536i
\(517\) 1.78124 + 10.1019i 0.0783389 + 0.444282i
\(518\) −0.526697 + 2.98705i −0.0231417 + 0.131243i
\(519\) −3.21909 1.17165i −0.141303 0.0514299i
\(520\) 10.6935 + 18.5216i 0.468939 + 0.812226i
\(521\) 3.69593 6.40154i 0.161922 0.280457i −0.773636 0.633630i \(-0.781564\pi\)
0.935558 + 0.353173i \(0.114897\pi\)
\(522\) −20.0210 + 16.7996i −0.876297 + 0.735301i
\(523\) −2.05890 + 1.72763i −0.0900296 + 0.0755438i −0.686692 0.726949i \(-0.740938\pi\)
0.596662 + 0.802493i \(0.296493\pi\)
\(524\) −7.46624 + 12.9319i −0.326164 + 0.564933i
\(525\) −5.31931 9.21332i −0.232154 0.402102i
\(526\) −24.6400 8.96824i −1.07436 0.391034i
\(527\) 5.07330 28.7721i 0.220997 1.25333i
\(528\) 0.0565201 + 0.320541i 0.00245972 + 0.0139498i
\(529\) 19.8768 7.23456i 0.864209 0.314546i
\(530\) 18.2806 + 15.3393i 0.794059 + 0.666295i
\(531\) −3.49365 −0.151611
\(532\) 9.87236 3.41468i 0.428021 0.148045i
\(533\) 33.7698 1.46273
\(534\) 2.69665 + 2.26276i 0.116695 + 0.0979191i
\(535\) 15.0597 5.48127i 0.651086 0.236976i
\(536\) 2.05542 + 11.6569i 0.0887806 + 0.503500i
\(537\) −0.691509 + 3.92174i −0.0298408 + 0.169236i
\(538\) 21.8767 + 7.96246i 0.943171 + 0.343286i
\(539\) 0.628329 + 1.08830i 0.0270641 + 0.0468763i
\(540\) 4.14118 7.17273i 0.178208 0.308665i
\(541\) −31.3470 + 26.3033i −1.34771 + 1.13087i −0.368143 + 0.929769i \(0.620006\pi\)
−0.979571 + 0.201098i \(0.935549\pi\)
\(542\) −14.0040 + 11.7508i −0.601524 + 0.504738i
\(543\) −2.64813 + 4.58669i −0.113642 + 0.196834i
\(544\) 2.08042 + 3.60339i 0.0891972 + 0.154494i
\(545\) 46.3343 + 16.8643i 1.98474 + 0.722387i
\(546\) −0.671006 + 3.80546i −0.0287164 + 0.162859i
\(547\) −1.84775 10.4791i −0.0790040 0.448054i −0.998490 0.0549315i \(-0.982506\pi\)
0.919486 0.393122i \(-0.128605\pi\)
\(548\) 9.21558 3.35420i 0.393670 0.143284i
\(549\) 14.3429 + 12.0351i 0.612141 + 0.513647i
\(550\) −13.6386 −0.581553
\(551\) −37.2018 + 12.8675i −1.58485 + 0.548172i
\(552\) 0.442416 0.0188305
\(553\) −19.4399 16.3120i −0.826668 0.693657i
\(554\) −1.42948 + 0.520289i −0.0607328 + 0.0221049i
\(555\) 0.308829 + 1.75146i 0.0131091 + 0.0743452i
\(556\) 0.357721 2.02873i 0.0151707 0.0860375i
\(557\) 11.1012 + 4.04051i 0.470374 + 0.171202i 0.566322 0.824184i \(-0.308366\pi\)
−0.0959479 + 0.995386i \(0.530588\pi\)
\(558\) −10.1606 17.5986i −0.430131 0.745008i
\(559\) −15.0380 + 26.0466i −0.636041 + 1.10165i
\(560\) 7.92580 6.65054i 0.334926 0.281036i
\(561\) 1.03745 0.870524i 0.0438012 0.0367535i
\(562\) 7.59634 13.1573i 0.320432 0.555005i
\(563\) −9.17750 15.8959i −0.386785 0.669932i 0.605230 0.796051i \(-0.293081\pi\)
−0.992015 + 0.126119i \(0.959748\pi\)
\(564\) −3.13741 1.14192i −0.132109 0.0480836i
\(565\) 8.43872 47.8584i 0.355020 2.01342i
\(566\) 1.86261 + 10.5634i 0.0782913 + 0.444012i
\(567\) −18.1460 + 6.60462i −0.762062 + 0.277368i
\(568\) −6.50789 5.46077i −0.273065 0.229129i
\(569\) 35.7955 1.50063 0.750313 0.661083i \(-0.229903\pi\)
0.750313 + 0.661083i \(0.229903\pi\)
\(570\) 4.75477 3.86129i 0.199155 0.161732i
\(571\) −31.3480 −1.31187 −0.655937 0.754815i \(-0.727726\pi\)
−0.655937 + 0.754815i \(0.727726\pi\)
\(572\) 3.79486 + 3.18426i 0.158671 + 0.133141i
\(573\) 7.84060 2.85374i 0.327546 0.119217i
\(574\) −2.83688 16.0887i −0.118409 0.671530i
\(575\) −3.21913 + 18.2566i −0.134247 + 0.761353i
\(576\) 2.71953 + 0.989826i 0.113314 + 0.0412428i
\(577\) 14.1501 + 24.5088i 0.589078 + 1.02031i 0.994353 + 0.106119i \(0.0338424\pi\)
−0.405275 + 0.914195i \(0.632824\pi\)
\(578\) 0.156275 0.270676i 0.00650017 0.0112586i
\(579\) 3.67124 3.08053i 0.152571 0.128023i
\(580\) −29.8666 + 25.0611i −1.24014 + 1.04060i
\(581\) 4.50308 7.79956i 0.186819 0.323580i
\(582\) −0.765741 1.32630i −0.0317410 0.0549770i
\(583\) 5.19417 + 1.89052i 0.215120 + 0.0782974i
\(584\) 1.11526 6.32494i 0.0461497 0.261728i
\(585\) −10.7480 60.9547i −0.444373 2.52017i
\(586\) 9.04741 3.29299i 0.373745 0.136032i
\(587\) 2.37629 + 1.99394i 0.0980798 + 0.0822988i 0.690509 0.723324i \(-0.257387\pi\)
−0.592429 + 0.805623i \(0.701831\pi\)
\(588\) −0.409025 −0.0168679
\(589\) −4.82995 30.2232i −0.199015 1.24533i
\(590\) −5.21169 −0.214562
\(591\) 0.0995464 + 0.0835294i 0.00409479 + 0.00343594i
\(592\) −1.18931 + 0.432872i −0.0488802 + 0.0177909i
\(593\) −3.54385 20.0982i −0.145529 0.825334i −0.966941 0.254999i \(-0.917925\pi\)
0.821413 0.570334i \(-0.193186\pi\)
\(594\) 0.333133 1.88929i 0.0136686 0.0775185i
\(595\) −40.4534 14.7238i −1.65843 0.603619i
\(596\) −1.12357 1.94607i −0.0460231 0.0797143i
\(597\) 0.438208 0.758999i 0.0179347 0.0310638i
\(598\) 5.15814 4.32820i 0.210932 0.176993i
\(599\) 25.7287 21.5889i 1.05125 0.882100i 0.0580222 0.998315i \(-0.481521\pi\)
0.993224 + 0.116215i \(0.0370761\pi\)
\(600\) 2.21959 3.84444i 0.0906144 0.156949i
\(601\) −6.08201 10.5343i −0.248090 0.429705i 0.714906 0.699221i \(-0.246470\pi\)
−0.962996 + 0.269516i \(0.913136\pi\)
\(602\) 13.6725 + 4.97638i 0.557249 + 0.202822i
\(603\) 5.94851 33.7357i 0.242242 1.37382i
\(604\) 0.0696216 + 0.394844i 0.00283286 + 0.0160660i
\(605\) −4.05688 + 1.47659i −0.164936 + 0.0600317i
\(606\) −3.40419 2.85645i −0.138286 0.116036i
\(607\) −7.97995 −0.323896 −0.161948 0.986799i \(-0.551778\pi\)
−0.161948 + 0.986799i \(0.551778\pi\)
\(608\) 3.29367 + 2.85512i 0.133576 + 0.115790i
\(609\) −7.04434 −0.285451
\(610\) 21.3962 + 17.9536i 0.866308 + 0.726919i
\(611\) −47.7507 + 17.3798i −1.93179 + 0.703112i
\(612\) −2.09102 11.8588i −0.0845245 0.479362i
\(613\) 0.199063 1.12894i 0.00804009 0.0455976i −0.980524 0.196400i \(-0.937075\pi\)
0.988564 + 0.150803i \(0.0481859\pi\)
\(614\) −25.5630 9.30417i −1.03164 0.375486i
\(615\) −4.78958 8.29579i −0.193134 0.334519i
\(616\) 1.19826 2.07545i 0.0482794 0.0836224i
\(617\) 34.4432 28.9013i 1.38663 1.16352i 0.419947 0.907549i \(-0.362049\pi\)
0.966684 0.255973i \(-0.0823958\pi\)
\(618\) 3.07323 2.57875i 0.123624 0.103733i
\(619\) 5.90044 10.2199i 0.237159 0.410771i −0.722739 0.691121i \(-0.757117\pi\)
0.959898 + 0.280350i \(0.0904505\pi\)
\(620\) −15.1571 26.2529i −0.608725 1.05434i
\(621\) −2.45037 0.891860i −0.0983298 0.0357891i
\(622\) 3.56115 20.1963i 0.142789 0.809796i
\(623\) −4.50081 25.5253i −0.180321 1.02265i
\(624\) −1.51516 + 0.551475i −0.0606551 + 0.0220767i
\(625\) 71.1033 + 59.6628i 2.84413 + 2.38651i
\(626\) −8.96812 −0.358438
\(627\) 0.729026 1.21713i 0.0291145 0.0486075i
\(628\) 8.14445 0.324999
\(629\) 4.03406 + 3.38498i 0.160849 + 0.134968i
\(630\) −28.1373 + 10.2411i −1.12102 + 0.408017i
\(631\) 7.69293 + 43.6288i 0.306251 + 1.73683i 0.617558 + 0.786525i \(0.288122\pi\)
−0.311308 + 0.950309i \(0.600767\pi\)
\(632\) 1.83877 10.4282i 0.0731424 0.414811i
\(633\) 2.10649 + 0.766700i 0.0837255 + 0.0304736i
\(634\) −3.51902 6.09511i −0.139758 0.242068i
\(635\) −19.1307 + 33.1354i −0.759180 + 1.31494i
\(636\) −1.37821 + 1.15646i −0.0546497 + 0.0458566i
\(637\) −4.76884 + 4.00153i −0.188948 + 0.158546i
\(638\) −4.51539 + 7.82089i −0.178766 + 0.309632i
\(639\) 12.2932 + 21.2924i 0.486310 + 0.842314i
\(640\) 4.05688 + 1.47659i 0.160362 + 0.0583672i
\(641\) 2.14040 12.1388i 0.0845408 0.479454i −0.912914 0.408152i \(-0.866173\pi\)
0.997455 0.0713025i \(-0.0227156\pi\)
\(642\) 0.209810 + 1.18989i 0.00828053 + 0.0469612i
\(643\) −32.3849 + 11.7871i −1.27713 + 0.464839i −0.889483 0.456968i \(-0.848936\pi\)
−0.387651 + 0.921806i \(0.626713\pi\)
\(644\) −2.49537 2.09386i −0.0983312 0.0825097i
\(645\) 8.53137 0.335923
\(646\) 3.43590 17.8082i 0.135184 0.700655i
\(647\) −10.5506 −0.414788 −0.207394 0.978258i \(-0.566498\pi\)
−0.207394 + 0.978258i \(0.566498\pi\)
\(648\) −6.17260 5.17942i −0.242482 0.203467i
\(649\) −1.13438 + 0.412879i −0.0445282 + 0.0162069i
\(650\) −11.7323 66.5370i −0.460177 2.60980i
\(651\) 0.951098 5.39394i 0.0372765 0.211405i
\(652\) 18.3123 + 6.66514i 0.717166 + 0.261027i
\(653\) −15.8936 27.5285i −0.621964 1.07727i −0.989120 0.147114i \(-0.953002\pi\)
0.367155 0.930160i \(-0.380332\pi\)
\(654\) −1.85871 + 3.21938i −0.0726814 + 0.125888i
\(655\) 49.3847 41.4387i 1.92962 1.61914i
\(656\) 5.22206 4.38183i 0.203887 0.171082i
\(657\) −9.29356 + 16.0969i −0.362576 + 0.628000i
\(658\) 12.2915 + 21.2895i 0.479172 + 0.829951i
\(659\) −3.30554 1.20312i −0.128766 0.0468669i 0.276834 0.960918i \(-0.410715\pi\)
−0.405599 + 0.914051i \(0.632937\pi\)
\(660\) 0.244011 1.38386i 0.00949812 0.0538665i
\(661\) 3.10356 + 17.6012i 0.120715 + 0.684607i 0.983761 + 0.179482i \(0.0574423\pi\)
−0.863047 + 0.505124i \(0.831447\pi\)
\(662\) 3.50609 1.27611i 0.136268 0.0495975i
\(663\) 5.13935 + 4.31243i 0.199596 + 0.167481i
\(664\) 3.75800 0.145839
\(665\) −45.0931 0.724425i −1.74863 0.0280920i
\(666\) 3.66282 0.141931
\(667\) 9.40324 + 7.89025i 0.364095 + 0.305512i
\(668\) −10.9527 + 3.98645i −0.423772 + 0.154240i
\(669\) −0.789567 4.47786i −0.0305264 0.173124i
\(670\) 8.87376 50.3256i 0.342823 1.94425i
\(671\) 6.07942 + 2.21273i 0.234693 + 0.0854214i
\(672\) 0.390018 + 0.675531i 0.0150453 + 0.0260592i
\(673\) −8.85580 + 15.3387i −0.341366 + 0.591263i −0.984687 0.174334i \(-0.944223\pi\)
0.643321 + 0.765597i \(0.277556\pi\)
\(674\) −7.64557 + 6.41539i −0.294496 + 0.247112i
\(675\) −20.0434 + 16.8184i −0.771471 + 0.647341i
\(676\) −5.77023 + 9.99433i −0.221932 + 0.384397i
\(677\) −13.3030 23.0415i −0.511276 0.885555i −0.999915 0.0130692i \(-0.995840\pi\)
0.488639 0.872486i \(-0.337493\pi\)
\(678\) 3.44285 + 1.25309i 0.132222 + 0.0481248i
\(679\) −1.95809 + 11.1049i −0.0751445 + 0.426166i
\(680\) −3.11930 17.6904i −0.119620 0.678398i
\(681\) −0.380002 + 0.138310i −0.0145617 + 0.00530003i
\(682\) −5.37891 4.51344i −0.205969 0.172828i
\(683\) 39.5428 1.51306 0.756531 0.653958i \(-0.226893\pi\)
0.756531 + 0.653958i \(0.226893\pi\)
\(684\) −6.13115 11.0247i −0.234431 0.421541i
\(685\) −42.3393 −1.61770
\(686\) 15.1580 + 12.7190i 0.578733 + 0.485615i
\(687\) −0.714115 + 0.259917i −0.0272452 + 0.00991644i
\(688\) 1.05426 + 5.97903i 0.0401935 + 0.227949i
\(689\) −4.75490 + 26.9664i −0.181147 + 1.02734i
\(690\) −1.79483 0.653265i −0.0683280 0.0248694i
\(691\) −6.21240 10.7602i −0.236331 0.409337i 0.723328 0.690505i \(-0.242612\pi\)
−0.959659 + 0.281168i \(0.909278\pi\)
\(692\) −5.26242 + 9.11477i −0.200047 + 0.346492i
\(693\) −5.31305 + 4.45818i −0.201826 + 0.169352i
\(694\) 2.72280 2.28470i 0.103356 0.0867262i
\(695\) −4.44683 + 7.70214i −0.168678 + 0.292159i
\(696\) −1.46970 2.54559i −0.0557087 0.0964904i
\(697\) −26.6535 9.70108i −1.00957 0.367455i
\(698\) −3.65024 + 20.7015i −0.138164 + 0.783565i
\(699\) −0.465939 2.64247i −0.0176234 0.0999475i
\(700\) −30.7142 + 11.1790i −1.16089 + 0.422528i
\(701\) −8.77645 7.36431i −0.331482 0.278146i 0.461822 0.886973i \(-0.347196\pi\)
−0.793303 + 0.608827i \(0.791641\pi\)
\(702\) 9.50360 0.358690
\(703\) 5.15309 + 1.96988i 0.194353 + 0.0742953i
\(704\) 1.00000 0.0376889
\(705\) 11.0419 + 9.26530i 0.415864 + 0.348951i
\(706\) −9.34925 + 3.40285i −0.351864 + 0.128068i
\(707\) 5.68172 + 32.2226i 0.213683 + 1.21186i
\(708\) 0.0682298 0.386951i 0.00256423 0.0145425i
\(709\) 44.6796 + 16.2620i 1.67798 + 0.610733i 0.993030 0.117861i \(-0.0376036\pi\)
0.684946 + 0.728594i \(0.259826\pi\)
\(710\) 18.3385 + 31.7632i 0.688231 + 1.19205i
\(711\) −15.3227 + 26.5397i −0.574645 + 0.995315i
\(712\) 8.28499 6.95193i 0.310493 0.260535i
\(713\) −7.31126 + 6.13487i −0.273809 + 0.229753i
\(714\) 1.62280 2.81077i 0.0607318 0.105191i
\(715\) −10.6935 18.5216i −0.399913 0.692669i
\(716\) 11.4969 + 4.18453i 0.429659 + 0.156383i
\(717\) −1.51714 + 8.60411i −0.0566585 + 0.321326i
\(718\) −4.45693 25.2765i −0.166331 0.943311i
\(719\) −32.1919 + 11.7169i −1.20055 + 0.436966i −0.863418 0.504490i \(-0.831681\pi\)
−0.337137 + 0.941456i \(0.609458\pi\)
\(720\) −9.57124 8.03122i −0.356699 0.299306i
\(721\) −29.5387 −1.10008
\(722\) −2.69657 18.8077i −0.100356 0.699949i
\(723\) 3.14700 0.117038
\(724\) 12.4649 + 10.4593i 0.463255 + 0.388718i
\(725\) 115.739 42.1257i 4.29846 1.56451i
\(726\) −0.0565201 0.320541i −0.00209766 0.0118964i
\(727\) −4.41280 + 25.0262i −0.163662 + 0.928171i 0.786772 + 0.617244i \(0.211751\pi\)
−0.950434 + 0.310928i \(0.899360\pi\)
\(728\) 11.1560 + 4.06046i 0.413470 + 0.150491i
\(729\) 10.7232 + 18.5731i 0.397154 + 0.687892i
\(730\) −13.8638 + 24.0128i −0.513121 + 0.888752i
\(731\) 19.3515 16.2378i 0.715740 0.600577i
\(732\) −1.61311 + 1.35356i −0.0596221 + 0.0500289i
\(733\) −16.6450 + 28.8299i −0.614796 + 1.06486i 0.375624 + 0.926772i \(0.377428\pi\)
−0.990420 + 0.138086i \(0.955905\pi\)
\(734\) −5.53986 9.59531i −0.204480 0.354170i
\(735\) 1.65937 + 0.603960i 0.0612067 + 0.0222774i
\(736\) 0.236031 1.33860i 0.00870020 0.0493413i
\(737\) −2.05542 11.6569i −0.0757124 0.429386i
\(738\) −18.5388 + 6.74756i −0.682422 + 0.248381i
\(739\) 36.6828 + 30.7805i 1.34940 + 1.13228i 0.979103 + 0.203364i \(0.0651873\pi\)
0.370293 + 0.928915i \(0.379257\pi\)
\(740\) 5.46406 0.200863
\(741\) 6.56498 + 2.50960i 0.241171 + 0.0921925i
\(742\) 13.2468 0.486307
\(743\) −31.3755 26.3272i −1.15106 0.965851i −0.151312 0.988486i \(-0.548350\pi\)
−0.999744 + 0.0226354i \(0.992794\pi\)
\(744\) 2.14763 0.781672i 0.0787358 0.0286575i
\(745\) 1.68464 + 9.55404i 0.0617203 + 0.350033i
\(746\) −1.47452 + 8.36243i −0.0539861 + 0.306170i
\(747\) −10.2200 3.71977i −0.373930 0.136099i
\(748\) −2.08042 3.60339i −0.0760676 0.131753i
\(749\) 4.44811 7.70434i 0.162530 0.281511i
\(750\) −9.29903 + 7.80281i −0.339553 + 0.284918i
\(751\) −28.1177 + 23.5936i −1.02603 + 0.860941i −0.990373 0.138423i \(-0.955797\pi\)
−0.0356564 + 0.999364i \(0.511352\pi\)
\(752\) −5.12888 + 8.88348i −0.187031 + 0.323947i
\(753\) −1.12586 1.95005i −0.0410286 0.0710637i
\(754\) −42.0390 15.3009i −1.53097 0.557228i
\(755\) 0.300574 1.70464i 0.0109390 0.0620381i
\(756\) −0.798362 4.52773i −0.0290361 0.164672i
\(757\) −3.13209 + 1.13999i −0.113838 + 0.0414336i −0.398311 0.917250i \(-0.630404\pi\)
0.284473 + 0.958684i \(0.408181\pi\)
\(758\) 19.0881 + 16.0168i 0.693311 + 0.581757i
\(759\) −0.442416 −0.0160587
\(760\) −9.14622 16.4463i −0.331768 0.596570i
\(761\) 29.2637 1.06081 0.530404 0.847745i \(-0.322040\pi\)
0.530404 + 0.847745i \(0.322040\pi\)
\(762\) −2.20974 1.85419i −0.0800505 0.0671703i
\(763\) 25.7204 9.36146i 0.931141 0.338908i
\(764\) −4.45144 25.2454i −0.161048 0.913346i
\(765\) −9.02745 + 51.1972i −0.326388 + 1.85104i
\(766\) 1.63704 + 0.595834i 0.0591486 + 0.0215283i
\(767\) −2.99008 5.17897i −0.107966 0.187002i
\(768\) −0.162743 + 0.281879i −0.00587249 + 0.0101714i
\(769\) 24.3465 20.4292i 0.877958 0.736694i −0.0878004 0.996138i \(-0.527984\pi\)
0.965758 + 0.259444i \(0.0835393\pi\)
\(770\) −7.92580 + 6.65054i −0.285626 + 0.239669i
\(771\) 0.501795 0.869135i 0.0180717 0.0313011i
\(772\) −7.36200 12.7514i −0.264964 0.458932i
\(773\) 33.3444 + 12.1364i 1.19931 + 0.436515i 0.862985 0.505230i \(-0.168592\pi\)
0.336329 + 0.941744i \(0.390814\pi\)
\(774\) 3.05110 17.3037i 0.109670 0.621968i
\(775\) 16.6296 + 94.3109i 0.597351 + 3.38775i
\(776\) −4.42146 + 1.60928i −0.158721 + 0.0577697i
\(777\) 0.756270 + 0.634586i 0.0271311 + 0.0227657i
\(778\) 32.5144 1.16570
\(779\) −29.7104 0.477301i −1.06449 0.0171011i
\(780\) 6.96115 0.249249
\(781\) 6.50789 + 5.46077i 0.232871 + 0.195402i
\(782\) −5.31452 + 1.93433i −0.190047 + 0.0691714i
\(783\) 3.00845 + 17.0618i 0.107513 + 0.609738i
\(784\) −0.218216 + 1.23757i −0.00779344 + 0.0441988i
\(785\) −33.0411 12.0260i −1.17929 0.429226i
\(786\) 2.43016 + 4.20916i 0.0866808 + 0.150136i
\(787\) 13.2859 23.0119i 0.473592 0.820285i −0.525951 0.850515i \(-0.676291\pi\)
0.999543 + 0.0302300i \(0.00962397\pi\)
\(788\) 0.305839 0.256629i 0.0108951 0.00914205i
\(789\) −6.53795 + 5.48600i −0.232757 + 0.195307i
\(790\) −22.8578 + 39.5908i −0.813243 + 1.40858i
\(791\) −13.4881 23.3621i −0.479583 0.830662i
\(792\) −2.71953 0.989826i −0.0966341 0.0351719i
\(793\) −5.56529 + 31.5623i −0.197629 + 1.12081i
\(794\) 2.20395 + 12.4992i 0.0782152 + 0.443580i
\(795\) 7.29886 2.65657i 0.258864 0.0942188i
\(796\) −2.06268 1.73080i −0.0731098 0.0613464i
\(797\) −21.9242 −0.776596 −0.388298 0.921534i \(-0.626937\pi\)
−0.388298 + 0.921534i \(0.626937\pi\)
\(798\) 0.644131 3.33853i 0.0228020 0.118183i
\(799\) 42.6808 1.50994
\(800\) −10.4478 8.76673i −0.369385 0.309951i
\(801\) −29.4124 + 10.7053i −1.03924 + 0.378251i
\(802\) 3.41082 + 19.3437i 0.120440 + 0.683051i
\(803\) −1.11526 + 6.32494i −0.0393566 + 0.223202i
\(804\) 3.62034 + 1.31769i 0.127679 + 0.0464715i
\(805\) 7.03165 + 12.1792i 0.247833 + 0.429260i
\(806\) 17.3921 30.1240i 0.612610 1.06107i
\(807\) 5.80473 4.87075i 0.204336 0.171459i
\(808\) −10.4588 + 8.77596i −0.367939 + 0.308737i
\(809\) 12.4138 21.5013i 0.436444 0.755944i −0.560968 0.827838i \(-0.689571\pi\)
0.997412 + 0.0718936i \(0.0229042\pi\)
\(810\) 17.3937 + 30.1267i 0.611151 + 1.05854i
\(811\) −6.67529 2.42961i −0.234401 0.0853151i 0.222149 0.975013i \(-0.428693\pi\)
−0.456550 + 0.889698i \(0.650915\pi\)
\(812\) −3.75818 + 21.3137i −0.131886 + 0.747965i
\(813\) 1.03324 + 5.85980i 0.0362373 + 0.205512i
\(814\) 1.18931 0.432872i 0.0416852 0.0151722i
\(815\) −64.4493 54.0794i −2.25756 1.89432i
\(816\) 1.35429 0.0474098
\(817\) 13.5985 22.7030i 0.475750 0.794279i
\(818\) 4.28420 0.149794
\(819\) −26.3199 22.0851i −0.919693 0.771714i
\(820\) −27.6554 + 10.0658i −0.965770 + 0.351511i
\(821\) −2.89647 16.4267i −0.101088 0.573296i −0.992711 0.120518i \(-0.961544\pi\)
0.891624 0.452777i \(-0.149567\pi\)
\(822\) 0.554293 3.14355i 0.0193332 0.109644i
\(823\) 26.3196 + 9.57956i 0.917445 + 0.333923i 0.757221 0.653158i \(-0.226556\pi\)
0.160223 + 0.987081i \(0.448779\pi\)
\(824\) −6.16281 10.6743i −0.214692 0.371857i
\(825\) −2.21959 + 3.84444i −0.0772762 + 0.133846i
\(826\) −2.21619 + 1.85961i −0.0771112 + 0.0647040i
\(827\) 17.0359 14.2948i 0.592397 0.497080i −0.296594 0.955004i \(-0.595851\pi\)
0.888992 + 0.457923i \(0.151407\pi\)
\(828\) −1.96687 + 3.40672i −0.0683534 + 0.118392i
\(829\) −16.4406 28.4759i −0.571005 0.989009i −0.996463 0.0840310i \(-0.973221\pi\)
0.425459 0.904978i \(-0.360113\pi\)
\(830\) −15.2458 5.54901i −0.529189 0.192609i
\(831\) −0.0859796 + 0.487615i −0.00298260 + 0.0169152i
\(832\) 0.860224 + 4.87857i 0.0298229 + 0.169134i
\(833\) 4.91342 1.78834i 0.170240 0.0619622i
\(834\) −0.513642 0.430997i −0.0177860 0.0149242i
\(835\) 50.3201 1.74140
\(836\) −3.29367 2.85512i −0.113914 0.0987464i
\(837\) −13.4706 −0.465612
\(838\) −11.7709 9.87694i −0.406618 0.341193i
\(839\) −27.5696 + 10.0345i −0.951807 + 0.346430i −0.770818 0.637055i \(-0.780152\pi\)
−0.180989 + 0.983485i \(0.557930\pi\)
\(840\) −0.584779 3.31645i −0.0201768 0.114428i
\(841\) 9.12608 51.7566i 0.314692 1.78471i
\(842\) 17.2959 + 6.29518i 0.596055 + 0.216946i
\(843\) −2.47251 4.28250i −0.0851576 0.147497i
\(844\) 3.44359 5.96447i 0.118533 0.205305i
\(845\) 38.1666 32.0256i 1.31297 1.10171i
\(846\) 22.7412 19.0821i 0.781859 0.656058i
\(847\) −1.19826 + 2.07545i −0.0411728 + 0.0713134i
\(848\) 2.76376 + 4.78697i 0.0949078 + 0.164385i
\(849\) 3.28073 + 1.19409i 0.112594 + 0.0409809i
\(850\) −9.85419 + 55.8859i −0.337996 + 1.91687i
\(851\) −0.298728 1.69417i −0.0102403 0.0580755i
\(852\) −2.59839 + 0.945738i −0.0890195 + 0.0324004i
\(853\) 3.24416 + 2.72217i 0.111078 + 0.0932055i 0.696635 0.717426i \(-0.254680\pi\)
−0.585557 + 0.810631i \(0.699124\pi\)
\(854\) 15.5045 0.530554
\(855\) 8.59442 + 53.7793i 0.293923 + 1.83921i
\(856\) 3.71213 0.126878
\(857\) −10.1686 8.53244i −0.347351 0.291462i 0.452374 0.891828i \(-0.350577\pi\)
−0.799725 + 0.600366i \(0.795022\pi\)
\(858\) 1.51516 0.551475i 0.0517269 0.0188270i
\(859\) −1.31621 7.46459i −0.0449084 0.254688i 0.954085 0.299534i \(-0.0968314\pi\)
−0.998994 + 0.0448461i \(0.985720\pi\)
\(860\) 4.55152 25.8130i 0.155206 0.880215i
\(861\) −4.99676 1.81867i −0.170289 0.0619802i
\(862\) −10.9152 18.9056i −0.371772 0.643928i
\(863\) −3.46486 + 6.00131i −0.117945 + 0.204287i −0.918953 0.394366i \(-0.870964\pi\)
0.801008 + 0.598654i \(0.204297\pi\)
\(864\) 1.46961 1.23315i 0.0499970 0.0419525i
\(865\) 34.8077 29.2072i 1.18350 0.993074i
\(866\) −4.60800 + 7.98128i −0.156586 + 0.271215i
\(867\) −0.0508653 0.0881012i −0.00172747 0.00299207i
\(868\) −15.8128 5.75538i −0.536721 0.195350i
\(869\) −1.83877 + 10.4282i −0.0623760 + 0.353752i
\(870\) 2.20361 + 12.4973i 0.0747094 + 0.423698i
\(871\) 55.1007 20.0550i 1.86702 0.679539i
\(872\) 8.74910 + 7.34137i 0.296282 + 0.248610i
\(873\) 13.6172 0.460871
\(874\) −4.59926 + 3.73500i −0.155572 + 0.126338i
\(875\) 89.3786 3.02155
\(876\) −1.60137 1.34371i −0.0541052 0.0453997i
\(877\) −12.1783 + 4.43255i −0.411233 + 0.149677i −0.539349 0.842083i \(-0.681329\pi\)
0.128115 + 0.991759i \(0.459107\pi\)
\(878\) −0.937232 5.31531i −0.0316301 0.179383i
\(879\) 0.544178 3.08619i 0.0183547 0.104095i
\(880\) −4.05688 1.47659i −0.136758 0.0497757i
\(881\) 20.9607 + 36.3050i 0.706184 + 1.22315i 0.966262 + 0.257560i \(0.0829184\pi\)
−0.260078 + 0.965588i \(0.583748\pi\)
\(882\) 1.81842 3.14960i 0.0612294 0.106052i
\(883\) −1.80390 + 1.51365i −0.0607062 + 0.0509385i −0.672636 0.739974i \(-0.734838\pi\)
0.611930 + 0.790912i \(0.290394\pi\)
\(884\) 15.7898 13.2492i 0.531067 0.445618i
\(885\) −0.848166 + 1.46907i −0.0285108 + 0.0493821i
\(886\) −11.6590 20.1939i −0.391691 0.678428i
\(887\) −24.0285 8.74566i −0.806798 0.293650i −0.0944974 0.995525i \(-0.530124\pi\)
−0.712300 + 0.701875i \(0.752347\pi\)
\(888\) −0.0715338 + 0.405688i −0.00240052 + 0.0136140i
\(889\) 3.68814 + 20.9165i 0.123696 + 0.701516i
\(890\) −43.8763 + 15.9697i −1.47074 + 0.535305i
\(891\) 6.17260 + 5.17942i 0.206790 + 0.173517i
\(892\) −13.9697 −0.467739
\(893\) 42.2563 14.6157i 1.41405 0.489096i
\(894\) −0.731411 −0.0244620
\(895\) −40.4628 33.9523i −1.35252 1.13490i
\(896\) 2.25200 0.819661i 0.0752340 0.0273829i
\(897\) −0.380577 2.15836i −0.0127071 0.0720655i
\(898\) 3.82084 21.6691i 0.127503 0.723106i
\(899\) 59.5869 + 21.6879i 1.98734 + 0.723331i
\(900\) 19.7355 + 34.1829i 0.657849 + 1.13943i
\(901\) 11.4995 19.9178i 0.383105 0.663558i
\(902\) −5.22206 + 4.38183i −0.173876 + 0.145899i
\(903\) 3.62784 3.04412i 0.120727 0.101302i
\(904\) 5.62820 9.74833i 0.187191 0.324225i
\(905\) −35.1247 60.8378i −1.16758 2.02232i
\(906\) 0.122629 + 0.0446332i 0.00407407 + 0.00148284i
\(907\) 4.58203 25.9860i 0.152144 0.862851i −0.809207 0.587524i \(-0.800103\pi\)
0.961351 0.275327i \(-0.0887861\pi\)
\(908\) 0.215744 + 1.22354i 0.00715970 + 0.0406047i
\(909\) 37.1296 13.5141i 1.23151 0.448233i
\(910\) −39.2631 32.9456i −1.30156 1.09214i
\(911\) 11.8984 0.394212 0.197106 0.980382i \(-0.436846\pi\)
0.197106 + 0.980382i \(0.436846\pi\)
\(912\) 1.34082 0.463767i 0.0443991 0.0153569i
\(913\) −3.75800 −0.124372
\(914\) −7.39463 6.20483i −0.244593 0.205238i
\(915\) 8.54283 3.10933i 0.282417 0.102791i
\(916\) 0.405434 + 2.29933i 0.0133959 + 0.0759720i
\(917\) 6.21419 35.2424i 0.205211 1.16381i
\(918\) −7.50090 2.73010i −0.247567 0.0901069i
\(919\) −6.59005 11.4143i −0.217386 0.376523i 0.736622 0.676304i \(-0.236420\pi\)
−0.954008 + 0.299781i \(0.903086\pi\)
\(920\) −2.93410 + 5.08201i −0.0967344 + 0.167549i
\(921\) −6.78285 + 5.69149i −0.223503 + 0.187541i
\(922\) −12.0405 + 10.1032i −0.396532 + 0.332730i
\(923\) −21.0425 + 36.4467i −0.692623 + 1.19966i
\(924\) −0.390018 0.675531i −0.0128307 0.0222234i
\(925\) −16.2205 5.90378i −0.533327 0.194115i
\(926\) 3.66331 20.7757i 0.120384 0.682731i
\(927\) 6.19422 + 35.1292i 0.203445 + 1.15379i
\(928\) −8.48616 + 3.08871i −0.278572 + 0.101392i
\(929\) −24.1767 20.2866i −0.793211 0.665583i 0.153327 0.988176i \(-0.451001\pi\)
−0.946538 + 0.322592i \(0.895446\pi\)
\(930\) −9.86687 −0.323547
\(931\) 4.25214 3.45311i 0.139358 0.113171i
\(932\) −8.24378 −0.270034
\(933\) −5.11336 4.29062i −0.167404 0.140468i
\(934\) −5.11404 + 1.86136i −0.167337 + 0.0609055i
\(935\) 3.11930 + 17.6904i 0.102012 + 0.578540i
\(936\) 2.48954 14.1189i 0.0813731 0.461490i
\(937\) 34.1649 + 12.4350i 1.11612 + 0.406235i 0.833235 0.552919i \(-0.186486\pi\)
0.282885 + 0.959154i \(0.408708\pi\)
\(938\) −14.1835 24.5665i −0.463107 0.802125i
\(939\) −1.45950 + 2.52793i −0.0476290 + 0.0824958i
\(940\) 33.9245 28.4660i 1.10649 0.928459i
\(941\) 2.04052 1.71220i 0.0665191 0.0558161i −0.608922 0.793230i \(-0.708398\pi\)
0.675441 + 0.737414i \(0.263953\pi\)
\(942\) 1.32545 2.29575i 0.0431856 0.0747997i
\(943\) 4.63293 + 8.02447i 0.150869 + 0.261313i
\(944\) −1.13438 0.412879i −0.0369208 0.0134381i
\(945\) −3.44672 + 19.5473i −0.112122 + 0.635875i
\(946\) −1.05426 5.97903i −0.0342771 0.194395i
\(947\) 25.1333 9.14777i 0.816723 0.297263i 0.100325 0.994955i \(-0.468012\pi\)
0.716398 + 0.697692i \(0.245790\pi\)
\(948\) −2.64024 2.21543i −0.0857511 0.0719537i
\(949\) −31.8160 −1.03279
\(950\) 9.38151 + 58.7045i 0.304376 + 1.90462i
\(951\) −2.29078 −0.0742837
\(952\) −7.63865 6.40959i −0.247570 0.207736i
\(953\) −37.7533 + 13.7411i −1.22295 + 0.445118i −0.871178 0.490968i \(-0.836643\pi\)
−0.351773 + 0.936085i \(0.614421\pi\)
\(954\) −2.77784 15.7539i −0.0899359 0.510052i
\(955\) −19.2180 + 108.991i −0.621879 + 3.52685i
\(956\) 25.2236 + 9.18066i 0.815791 + 0.296924i
\(957\) 1.46970 + 2.54559i 0.0475086 + 0.0822872i
\(958\) 15.7769 27.3264i 0.509729 0.882877i
\(959\) −18.0042 + 15.1073i −0.581385 + 0.487840i
\(960\) 1.07645 0.903248i 0.0347422 0.0291522i
\(961\) −9.15188 + 15.8515i −0.295222 + 0.511340i
\(962\) 3.13487 + 5.42975i 0.101072 + 0.175062i
\(963\) −10.0952 3.67436i −0.325314 0.118405i
\(964\) 1.67894 9.52172i 0.0540749 0.306674i
\(965\) 11.0383 + 62.6014i 0.355336 + 2.01521i
\(966\) −0.996320 + 0.362631i −0.0320561 + 0.0116675i
\(967\) 26.7890 + 22.4787i 0.861477 + 0.722865i 0.962286 0.272041i \(-0.0876986\pi\)
−0.100809 + 0.994906i \(0.532143\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −4.46060 3.86667i −0.143295 0.124215i
\(970\) 20.3136 0.652230
\(971\) 23.9166 + 20.0685i 0.767522 + 0.644027i 0.940073 0.340973i \(-0.110757\pi\)
−0.172551 + 0.985001i \(0.555201\pi\)
\(972\) −7.87274 + 2.86544i −0.252518 + 0.0919091i
\(973\) 0.857287 + 4.86192i 0.0274834 + 0.155866i
\(974\) −0.114062 + 0.646880i −0.00365480 + 0.0207274i
\(975\) −20.6647 7.52135i −0.661802 0.240876i
\(976\) 3.23479 + 5.60282i 0.103543 + 0.179342i
\(977\) −28.3259 + 49.0618i −0.906225 + 1.56963i −0.0869604 + 0.996212i \(0.527715\pi\)
−0.819264 + 0.573416i \(0.805618\pi\)
\(978\) 4.85897 4.07716i 0.155373 0.130373i
\(979\) −8.28499 + 6.95193i −0.264789 + 0.222185i
\(980\) 2.71265 4.69845i 0.0866525 0.150087i
\(981\) −16.5267 28.6251i −0.527658 0.913930i
\(982\) 22.0056 + 8.00940i 0.702228 + 0.255590i
\(983\) −1.15136 + 6.52969i −0.0367227 + 0.208265i −0.997648 0.0685424i \(-0.978165\pi\)
0.960926 + 0.276807i \(0.0892763\pi\)
\(984\) −0.385293 2.18510i −0.0122827 0.0696585i
\(985\) −1.61969 + 0.589519i −0.0516076 + 0.0187836i
\(986\) 28.7846 + 24.1531i 0.916687 + 0.769192i
\(987\) 8.00142 0.254688
\(988\) 11.0956 18.5245i 0.352999 0.589342i
\(989\) −8.25235 −0.262409
\(990\) 9.57124 + 8.03122i 0.304194 + 0.255249i
\(991\) 54.1005 19.6910i 1.71856 0.625504i 0.720846 0.693096i \(-0.243754\pi\)
0.997713 + 0.0675912i \(0.0215314\pi\)
\(992\) −1.21930 6.91499i −0.0387128 0.219551i
\(993\) 0.210882 1.19597i 0.00669215 0.0379531i
\(994\) 19.1317 + 6.96339i 0.606822 + 0.220865i
\(995\) 5.81239 + 10.0674i 0.184265 + 0.319157i
\(996\) 0.611589 1.05930i 0.0193789 0.0335653i
\(997\) 25.7992 21.6481i 0.817070 0.685603i −0.135214 0.990816i \(-0.543172\pi\)
0.952284 + 0.305213i \(0.0987278\pi\)
\(998\) 0.152369 0.127853i 0.00482316 0.00404711i
\(999\) 1.21402 2.10274i 0.0384098 0.0665278i
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 418.2.j.c.111.2 30
19.5 even 9 7942.2.a.bz.1.9 15
19.6 even 9 inner 418.2.j.c.177.2 yes 30
19.14 odd 18 7942.2.a.cb.1.7 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.j.c.111.2 30 1.1 even 1 trivial
418.2.j.c.177.2 yes 30 19.6 even 9 inner
7942.2.a.bz.1.9 15 19.5 even 9
7942.2.a.cb.1.7 15 19.14 odd 18