Properties

Label 28.3.c.a.15.4
Level $28$
Weight $3$
Character 28.15
Analytic conductor $0.763$
Analytic rank $0$
Dimension $6$
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] = [28,3,Mod(15,28)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("28.15");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 28.c (of order \(2\), degree \(1\), 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: \(0.762944740209\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.1539727.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 3x^{3} - 8x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 15.4
Root \(1.35935 - 0.390070i\) of defining polynomial
Character \(\chi\) \(=\) 28.15
Dual form 28.3.c.a.15.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.163664 + 1.99329i) q^{2} +1.56028i q^{3} +(-3.94643 - 0.652459i) q^{4} +3.43742 q^{5} +(-3.11009 - 0.255361i) q^{6} -2.64575i q^{7} +(1.94643 - 7.75960i) q^{8} +6.56553 q^{9} +O(q^{10})\) \(q+(-0.163664 + 1.99329i) q^{2} +1.56028i q^{3} +(-3.94643 - 0.652459i) q^{4} +3.43742 q^{5} +(-3.11009 - 0.255361i) q^{6} -2.64575i q^{7} +(1.94643 - 7.75960i) q^{8} +6.56553 q^{9} +(-0.562581 + 6.85178i) q^{10} -8.48389i q^{11} +(1.01802 - 6.15753i) q^{12} -18.5685 q^{13} +(5.27376 + 0.433013i) q^{14} +5.36333i q^{15} +(15.1486 + 5.14977i) q^{16} -8.87484 q^{17} +(-1.07454 + 13.0870i) q^{18} +30.3324i q^{19} +(-13.5655 - 2.24278i) q^{20} +4.12811 q^{21} +(16.9109 + 1.38850i) q^{22} -26.5293i q^{23} +(12.1071 + 3.03697i) q^{24} -13.1841 q^{25} +(3.03899 - 37.0124i) q^{26} +24.2866i q^{27} +(-1.72624 + 10.4413i) q^{28} +18.6245 q^{29} +(-10.6907 - 0.877783i) q^{30} -41.2544i q^{31} +(-12.7443 + 29.3527i) q^{32} +13.2372 q^{33} +(1.45249 - 17.6901i) q^{34} -9.09456i q^{35} +(-25.9104 - 4.28374i) q^{36} -3.49346 q^{37} +(-60.4613 - 4.96431i) q^{38} -28.9720i q^{39} +(6.69069 - 26.6730i) q^{40} +37.7556 q^{41} +(-0.675622 + 8.22853i) q^{42} +50.8159i q^{43} +(-5.53539 + 33.4811i) q^{44} +22.5685 q^{45} +(52.8807 + 4.34189i) q^{46} +51.9810i q^{47} +(-8.03507 + 23.6360i) q^{48} -7.00000 q^{49} +(2.15777 - 26.2799i) q^{50} -13.8472i q^{51} +(73.2792 + 12.1152i) q^{52} +15.3814 q^{53} +(-48.4102 - 3.97483i) q^{54} -29.1627i q^{55} +(-20.5300 - 5.14977i) q^{56} -47.3270 q^{57} +(-3.04816 + 37.1241i) q^{58} +38.3291i q^{59} +(3.49936 - 21.1660i) q^{60} -72.5744 q^{61} +(82.2320 + 6.75184i) q^{62} -17.3708i q^{63} +(-56.4228 - 30.2070i) q^{64} -63.8276 q^{65} +(-2.16645 + 26.3857i) q^{66} -32.0834i q^{67} +(35.0239 + 5.79047i) q^{68} +41.3932 q^{69} +(18.1281 + 1.48845i) q^{70} -50.6160i q^{71} +(12.7793 - 50.9459i) q^{72} -5.48756 q^{73} +(0.571752 - 6.96348i) q^{74} -20.5709i q^{75} +(19.7906 - 119.705i) q^{76} -22.4463 q^{77} +(57.7497 + 4.74166i) q^{78} +39.8894i q^{79} +(52.0721 + 17.7019i) q^{80} +21.1959 q^{81} +(-6.17922 + 75.2579i) q^{82} +4.28106i q^{83} +(-16.2913 - 2.69342i) q^{84} -30.5065 q^{85} +(-101.291 - 8.31672i) q^{86} +29.0594i q^{87} +(-65.8316 - 16.5133i) q^{88} +123.906 q^{89} +(-3.69364 + 44.9856i) q^{90} +49.1276i q^{91} +(-17.3093 + 104.696i) q^{92} +64.3683 q^{93} +(-103.613 - 8.50740i) q^{94} +104.265i q^{95} +(-45.7985 - 19.8846i) q^{96} -32.0177 q^{97} +(1.14565 - 13.9530i) q^{98} -55.7012i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9} - 28 q^{10} + 6 q^{12} + 12 q^{13} + 7 q^{14} + 17 q^{16} - 4 q^{17} + 43 q^{18} - 32 q^{20} + 52 q^{22} + 122 q^{24} - 30 q^{25} - 56 q^{26} - 35 q^{28} - 36 q^{29} - 64 q^{30} - 101 q^{32} + 80 q^{33} + 58 q^{34} - 131 q^{36} + 28 q^{37} - 190 q^{38} + 40 q^{40} - 20 q^{41} + 70 q^{42} + 164 q^{44} + 12 q^{45} + 120 q^{46} - 98 q^{48} - 42 q^{49} + 161 q^{50} + 292 q^{52} + 92 q^{53} - 44 q^{54} - 49 q^{56} + 160 q^{57} - 166 q^{58} - 176 q^{60} - 164 q^{61} + 148 q^{62} - 215 q^{64} - 136 q^{65} - 408 q^{66} + 62 q^{68} - 48 q^{69} + 84 q^{70} + 151 q^{72} - 132 q^{73} + 250 q^{74} - 78 q^{76} + 112 q^{77} + 248 q^{78} + 312 q^{80} - 218 q^{81} - 86 q^{82} - 98 q^{84} - 232 q^{85} - 164 q^{86} - 100 q^{88} + 348 q^{89} + 52 q^{90} - 104 q^{92} + 288 q^{93} - 276 q^{94} + 170 q^{96} + 252 q^{97} + 7 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.163664 + 1.99329i −0.0818318 + 0.996646i
\(3\) 1.56028i 0.520093i 0.965596 + 0.260046i \(0.0837379\pi\)
−0.965596 + 0.260046i \(0.916262\pi\)
\(4\) −3.94643 0.652459i −0.986607 0.163115i
\(5\) 3.43742 0.687484 0.343742 0.939064i \(-0.388305\pi\)
0.343742 + 0.939064i \(0.388305\pi\)
\(6\) −3.11009 0.255361i −0.518349 0.0425602i
\(7\) 2.64575i 0.377964i
\(8\) 1.94643 7.75960i 0.243304 0.969950i
\(9\) 6.56553 0.729503
\(10\) −0.562581 + 6.85178i −0.0562581 + 0.685178i
\(11\) 8.48389i 0.771263i −0.922653 0.385631i \(-0.873984\pi\)
0.922653 0.385631i \(-0.126016\pi\)
\(12\) 1.01802 6.15753i 0.0848348 0.513127i
\(13\) −18.5685 −1.42834 −0.714172 0.699970i \(-0.753197\pi\)
−0.714172 + 0.699970i \(0.753197\pi\)
\(14\) 5.27376 + 0.433013i 0.376697 + 0.0309295i
\(15\) 5.36333i 0.357556i
\(16\) 15.1486 + 5.14977i 0.946787 + 0.321860i
\(17\) −8.87484 −0.522049 −0.261025 0.965332i \(-0.584060\pi\)
−0.261025 + 0.965332i \(0.584060\pi\)
\(18\) −1.07454 + 13.0870i −0.0596966 + 0.727057i
\(19\) 30.3324i 1.59644i 0.602365 + 0.798221i \(0.294225\pi\)
−0.602365 + 0.798221i \(0.705775\pi\)
\(20\) −13.5655 2.24278i −0.678276 0.112139i
\(21\) 4.12811 0.196577
\(22\) 16.9109 + 1.38850i 0.768676 + 0.0631138i
\(23\) 26.5293i 1.15345i −0.816938 0.576725i \(-0.804330\pi\)
0.816938 0.576725i \(-0.195670\pi\)
\(24\) 12.1071 + 3.03697i 0.504464 + 0.126540i
\(25\) −13.1841 −0.527366
\(26\) 3.03899 37.0124i 0.116884 1.42355i
\(27\) 24.2866i 0.899503i
\(28\) −1.72624 + 10.4413i −0.0616516 + 0.372902i
\(29\) 18.6245 0.642225 0.321112 0.947041i \(-0.395943\pi\)
0.321112 + 0.947041i \(0.395943\pi\)
\(30\) −10.6907 0.877783i −0.356356 0.0292594i
\(31\) 41.2544i 1.33079i −0.746493 0.665393i \(-0.768264\pi\)
0.746493 0.665393i \(-0.231736\pi\)
\(32\) −12.7443 + 29.3527i −0.398258 + 0.917273i
\(33\) 13.2372 0.401128
\(34\) 1.45249 17.6901i 0.0427203 0.520298i
\(35\) 9.09456i 0.259844i
\(36\) −25.9104 4.28374i −0.719733 0.118993i
\(37\) −3.49346 −0.0944178 −0.0472089 0.998885i \(-0.515033\pi\)
−0.0472089 + 0.998885i \(0.515033\pi\)
\(38\) −60.4613 4.96431i −1.59109 0.130640i
\(39\) 28.9720i 0.742872i
\(40\) 6.69069 26.6730i 0.167267 0.666825i
\(41\) 37.7556 0.920868 0.460434 0.887694i \(-0.347694\pi\)
0.460434 + 0.887694i \(0.347694\pi\)
\(42\) −0.675622 + 8.22853i −0.0160862 + 0.195917i
\(43\) 50.8159i 1.18177i 0.806757 + 0.590883i \(0.201220\pi\)
−0.806757 + 0.590883i \(0.798780\pi\)
\(44\) −5.53539 + 33.4811i −0.125804 + 0.760933i
\(45\) 22.5685 0.501522
\(46\) 52.8807 + 4.34189i 1.14958 + 0.0943889i
\(47\) 51.9810i 1.10598i 0.833188 + 0.552990i \(0.186513\pi\)
−0.833188 + 0.552990i \(0.813487\pi\)
\(48\) −8.03507 + 23.6360i −0.167397 + 0.492417i
\(49\) −7.00000 −0.142857
\(50\) 2.15777 26.2799i 0.0431553 0.525597i
\(51\) 13.8472i 0.271514i
\(52\) 73.2792 + 12.1152i 1.40921 + 0.232984i
\(53\) 15.3814 0.290215 0.145107 0.989416i \(-0.453647\pi\)
0.145107 + 0.989416i \(0.453647\pi\)
\(54\) −48.4102 3.97483i −0.896486 0.0736079i
\(55\) 29.1627i 0.530231i
\(56\) −20.5300 5.14977i −0.366607 0.0919601i
\(57\) −47.3270 −0.830298
\(58\) −3.04816 + 37.1241i −0.0525544 + 0.640071i
\(59\) 38.3291i 0.649645i 0.945775 + 0.324823i \(0.105305\pi\)
−0.945775 + 0.324823i \(0.894695\pi\)
\(60\) 3.49936 21.1660i 0.0583226 0.352767i
\(61\) −72.5744 −1.18974 −0.594872 0.803820i \(-0.702797\pi\)
−0.594872 + 0.803820i \(0.702797\pi\)
\(62\) 82.2320 + 6.75184i 1.32632 + 0.108901i
\(63\) 17.3708i 0.275726i
\(64\) −56.4228 30.2070i −0.881607 0.471985i
\(65\) −63.8276 −0.981964
\(66\) −2.16645 + 26.3857i −0.0328251 + 0.399783i
\(67\) 32.0834i 0.478856i −0.970914 0.239428i \(-0.923040\pi\)
0.970914 0.239428i \(-0.0769599\pi\)
\(68\) 35.0239 + 5.79047i 0.515058 + 0.0851539i
\(69\) 41.3932 0.599901
\(70\) 18.1281 + 1.48845i 0.258973 + 0.0212635i
\(71\) 50.6160i 0.712902i −0.934314 0.356451i \(-0.883987\pi\)
0.934314 0.356451i \(-0.116013\pi\)
\(72\) 12.7793 50.9459i 0.177491 0.707582i
\(73\) −5.48756 −0.0751720 −0.0375860 0.999293i \(-0.511967\pi\)
−0.0375860 + 0.999293i \(0.511967\pi\)
\(74\) 0.571752 6.96348i 0.00772638 0.0941011i
\(75\) 20.5709i 0.274279i
\(76\) 19.7906 119.705i 0.260403 1.57506i
\(77\) −22.4463 −0.291510
\(78\) 57.7497 + 4.74166i 0.740380 + 0.0607906i
\(79\) 39.8894i 0.504929i 0.967606 + 0.252464i \(0.0812410\pi\)
−0.967606 + 0.252464i \(0.918759\pi\)
\(80\) 52.0721 + 17.7019i 0.650901 + 0.221274i
\(81\) 21.1959 0.261678
\(82\) −6.17922 + 75.2579i −0.0753563 + 0.917779i
\(83\) 4.28106i 0.0515791i 0.999667 + 0.0257895i \(0.00820997\pi\)
−0.999667 + 0.0257895i \(0.991790\pi\)
\(84\) −16.2913 2.69342i −0.193944 0.0320646i
\(85\) −30.5065 −0.358901
\(86\) −101.291 8.31672i −1.17780 0.0967060i
\(87\) 29.0594i 0.334017i
\(88\) −65.8316 16.5133i −0.748087 0.187651i
\(89\) 123.906 1.39220 0.696099 0.717946i \(-0.254917\pi\)
0.696099 + 0.717946i \(0.254917\pi\)
\(90\) −3.69364 + 44.9856i −0.0410404 + 0.499840i
\(91\) 49.1276i 0.539863i
\(92\) −17.3093 + 104.696i −0.188145 + 1.13800i
\(93\) 64.3683 0.692132
\(94\) −103.613 8.50740i −1.10227 0.0905043i
\(95\) 104.265i 1.09753i
\(96\) −45.7985 19.8846i −0.477067 0.207131i
\(97\) −32.0177 −0.330079 −0.165040 0.986287i \(-0.552775\pi\)
−0.165040 + 0.986287i \(0.552775\pi\)
\(98\) 1.14565 13.9530i 0.0116903 0.142378i
\(99\) 55.7012i 0.562639i
\(100\) 52.0303 + 8.60212i 0.520303 + 0.0860212i
\(101\) −0.718521 −0.00711407 −0.00355703 0.999994i \(-0.501132\pi\)
−0.00355703 + 0.999994i \(0.501132\pi\)
\(102\) 27.6016 + 2.26629i 0.270604 + 0.0222185i
\(103\) 116.453i 1.13062i −0.824880 0.565308i \(-0.808757\pi\)
0.824880 0.565308i \(-0.191243\pi\)
\(104\) −36.1422 + 144.084i −0.347521 + 1.38542i
\(105\) 14.1900 0.135143
\(106\) −2.51737 + 30.6596i −0.0237488 + 0.289241i
\(107\) 37.9431i 0.354608i 0.984156 + 0.177304i \(0.0567377\pi\)
−0.984156 + 0.177304i \(0.943262\pi\)
\(108\) 15.8460 95.8452i 0.146722 0.887456i
\(109\) 88.2300 0.809450 0.404725 0.914438i \(-0.367367\pi\)
0.404725 + 0.914438i \(0.367367\pi\)
\(110\) 58.1298 + 4.77287i 0.528452 + 0.0433898i
\(111\) 5.45077i 0.0491060i
\(112\) 13.6250 40.0794i 0.121652 0.357852i
\(113\) 125.115 1.10721 0.553605 0.832780i \(-0.313252\pi\)
0.553605 + 0.832780i \(0.313252\pi\)
\(114\) 7.74571 94.3366i 0.0679448 0.827514i
\(115\) 91.1925i 0.792978i
\(116\) −73.5003 12.1517i −0.633623 0.104756i
\(117\) −121.912 −1.04198
\(118\) −76.4011 6.27308i −0.647467 0.0531617i
\(119\) 23.4806i 0.197316i
\(120\) 41.6173 + 10.4393i 0.346811 + 0.0869945i
\(121\) 49.0236 0.405154
\(122\) 11.8778 144.662i 0.0973589 1.18575i
\(123\) 58.9092i 0.478937i
\(124\) −26.9168 + 162.807i −0.217071 + 1.31296i
\(125\) −131.255 −1.05004
\(126\) 34.6250 + 2.84296i 0.274802 + 0.0225632i
\(127\) 51.8936i 0.408611i 0.978907 + 0.204305i \(0.0654936\pi\)
−0.978907 + 0.204305i \(0.934506\pi\)
\(128\) 69.4458 107.523i 0.542545 0.840027i
\(129\) −79.2870 −0.614628
\(130\) 10.4463 127.227i 0.0803559 0.978670i
\(131\) 242.670i 1.85245i −0.376976 0.926223i \(-0.623036\pi\)
0.376976 0.926223i \(-0.376964\pi\)
\(132\) −52.2398 8.63675i −0.395756 0.0654300i
\(133\) 80.2520 0.603398
\(134\) 63.9515 + 5.25088i 0.477250 + 0.0391857i
\(135\) 83.4831i 0.618393i
\(136\) −17.2742 + 68.8652i −0.127016 + 0.506362i
\(137\) −270.560 −1.97489 −0.987444 0.157970i \(-0.949505\pi\)
−0.987444 + 0.157970i \(0.949505\pi\)
\(138\) −6.77456 + 82.5087i −0.0490910 + 0.597889i
\(139\) 15.6948i 0.112912i −0.998405 0.0564562i \(-0.982020\pi\)
0.998405 0.0564562i \(-0.0179801\pi\)
\(140\) −5.93383 + 35.8910i −0.0423845 + 0.256364i
\(141\) −81.1049 −0.575212
\(142\) 100.893 + 8.28400i 0.710511 + 0.0583381i
\(143\) 157.533i 1.10163i
\(144\) 99.4585 + 33.8109i 0.690684 + 0.234798i
\(145\) 64.0203 0.441519
\(146\) 0.898114 10.9383i 0.00615147 0.0749199i
\(147\) 10.9220i 0.0742990i
\(148\) 13.7867 + 2.27934i 0.0931532 + 0.0154009i
\(149\) 24.4627 0.164179 0.0820895 0.996625i \(-0.473841\pi\)
0.0820895 + 0.996625i \(0.473841\pi\)
\(150\) 41.0039 + 3.36672i 0.273359 + 0.0224448i
\(151\) 189.391i 1.25425i 0.778920 + 0.627124i \(0.215768\pi\)
−0.778920 + 0.627124i \(0.784232\pi\)
\(152\) 235.367 + 59.0398i 1.54847 + 0.388420i
\(153\) −58.2680 −0.380837
\(154\) 3.67364 44.7420i 0.0238548 0.290532i
\(155\) 141.809i 0.914894i
\(156\) −18.9030 + 114.336i −0.121173 + 0.732923i
\(157\) 101.743 0.648047 0.324024 0.946049i \(-0.394964\pi\)
0.324024 + 0.946049i \(0.394964\pi\)
\(158\) −79.5112 6.52844i −0.503235 0.0413192i
\(159\) 23.9992i 0.150939i
\(160\) −43.8074 + 100.898i −0.273796 + 0.630611i
\(161\) −70.1900 −0.435963
\(162\) −3.46901 + 42.2497i −0.0214136 + 0.260801i
\(163\) 68.5832i 0.420756i −0.977620 0.210378i \(-0.932531\pi\)
0.977620 0.210378i \(-0.0674695\pi\)
\(164\) −149.000 24.6340i −0.908535 0.150207i
\(165\) 45.5019 0.275769
\(166\) −8.53341 0.700654i −0.0514061 0.00422081i
\(167\) 55.7795i 0.334009i −0.985956 0.167004i \(-0.946591\pi\)
0.985956 0.167004i \(-0.0534094\pi\)
\(168\) 8.03507 32.0325i 0.0478278 0.190670i
\(169\) 175.788 1.04017
\(170\) 4.99281 60.8085i 0.0293695 0.357697i
\(171\) 199.148i 1.16461i
\(172\) 33.1553 200.541i 0.192763 1.16594i
\(173\) 19.2284 0.111147 0.0555734 0.998455i \(-0.482301\pi\)
0.0555734 + 0.998455i \(0.482301\pi\)
\(174\) −57.9240 4.75597i −0.332896 0.0273332i
\(175\) 34.8820i 0.199326i
\(176\) 43.6901 128.519i 0.248239 0.730222i
\(177\) −59.8041 −0.337876
\(178\) −20.2788 + 246.980i −0.113926 + 1.38753i
\(179\) 195.745i 1.09355i −0.837280 0.546774i \(-0.815856\pi\)
0.837280 0.546774i \(-0.184144\pi\)
\(180\) −89.0649 14.7250i −0.494805 0.0818056i
\(181\) 82.5482 0.456067 0.228034 0.973653i \(-0.426770\pi\)
0.228034 + 0.973653i \(0.426770\pi\)
\(182\) −97.9256 8.04040i −0.538053 0.0441780i
\(183\) 113.236i 0.618777i
\(184\) −205.857 51.6375i −1.11879 0.280638i
\(185\) −12.0085 −0.0649107
\(186\) −10.5348 + 128.305i −0.0566384 + 0.689811i
\(187\) 75.2932i 0.402637i
\(188\) 33.9155 205.139i 0.180402 1.09117i
\(189\) 64.2562 0.339980
\(190\) −207.831 17.0644i −1.09385 0.0898127i
\(191\) 159.670i 0.835968i 0.908454 + 0.417984i \(0.137263\pi\)
−0.908454 + 0.417984i \(0.862737\pi\)
\(192\) 47.1314 88.0354i 0.245476 0.458517i
\(193\) 106.455 0.551583 0.275791 0.961218i \(-0.411060\pi\)
0.275791 + 0.961218i \(0.411060\pi\)
\(194\) 5.24013 63.8206i 0.0270110 0.328972i
\(195\) 99.5889i 0.510712i
\(196\) 27.6250 + 4.56721i 0.140944 + 0.0233021i
\(197\) −177.868 −0.902881 −0.451441 0.892301i \(-0.649090\pi\)
−0.451441 + 0.892301i \(0.649090\pi\)
\(198\) 111.029 + 9.11627i 0.560752 + 0.0460418i
\(199\) 267.633i 1.34489i −0.740148 0.672444i \(-0.765244\pi\)
0.740148 0.672444i \(-0.234756\pi\)
\(200\) −25.6620 + 102.304i −0.128310 + 0.511519i
\(201\) 50.0590 0.249050
\(202\) 0.117596 1.43222i 0.000582157 0.00709021i
\(203\) 49.2758i 0.242738i
\(204\) −9.03475 + 54.6471i −0.0442880 + 0.267878i
\(205\) 129.782 0.633082
\(206\) 232.126 + 19.0592i 1.12682 + 0.0925204i
\(207\) 174.179i 0.841445i
\(208\) −281.286 95.6233i −1.35234 0.459727i
\(209\) 257.337 1.23128
\(210\) −2.32239 + 28.2849i −0.0110590 + 0.134690i
\(211\) 162.784i 0.771487i 0.922606 + 0.385744i \(0.126055\pi\)
−0.922606 + 0.385744i \(0.873945\pi\)
\(212\) −60.7015 10.0357i −0.286328 0.0473383i
\(213\) 78.9751 0.370775
\(214\) −75.6317 6.20991i −0.353419 0.0290183i
\(215\) 174.676i 0.812445i
\(216\) 188.454 + 47.2721i 0.872473 + 0.218852i
\(217\) −109.149 −0.502990
\(218\) −14.4401 + 175.868i −0.0662388 + 0.806735i
\(219\) 8.56212i 0.0390965i
\(220\) −19.0275 + 115.088i −0.0864885 + 0.523129i
\(221\) 164.792 0.745666
\(222\) 10.8650 + 0.892093i 0.0489413 + 0.00401844i
\(223\) 317.727i 1.42479i 0.701780 + 0.712393i \(0.252389\pi\)
−0.701780 + 0.712393i \(0.747611\pi\)
\(224\) 77.6601 + 33.7181i 0.346697 + 0.150527i
\(225\) −86.5609 −0.384715
\(226\) −20.4767 + 249.390i −0.0906050 + 1.10350i
\(227\) 116.168i 0.511754i −0.966709 0.255877i \(-0.917636\pi\)
0.966709 0.255877i \(-0.0823642\pi\)
\(228\) 186.773 + 30.8789i 0.819178 + 0.135434i
\(229\) −357.643 −1.56176 −0.780880 0.624681i \(-0.785229\pi\)
−0.780880 + 0.624681i \(0.785229\pi\)
\(230\) 181.773 + 14.9249i 0.790319 + 0.0648908i
\(231\) 35.0224i 0.151612i
\(232\) 36.2513 144.519i 0.156256 0.622926i
\(233\) −402.307 −1.72664 −0.863319 0.504658i \(-0.831618\pi\)
−0.863319 + 0.504658i \(0.831618\pi\)
\(234\) 19.9525 243.006i 0.0852673 1.03849i
\(235\) 178.681i 0.760343i
\(236\) 25.0082 151.263i 0.105967 0.640945i
\(237\) −62.2385 −0.262610
\(238\) −46.8037 3.84292i −0.196654 0.0161467i
\(239\) 241.476i 1.01036i 0.863014 + 0.505179i \(0.168574\pi\)
−0.863014 + 0.505179i \(0.831426\pi\)
\(240\) −27.6199 + 81.2470i −0.115083 + 0.338529i
\(241\) −116.678 −0.484143 −0.242071 0.970258i \(-0.577827\pi\)
−0.242071 + 0.970258i \(0.577827\pi\)
\(242\) −8.02338 + 97.7183i −0.0331545 + 0.403795i
\(243\) 251.651i 1.03560i
\(244\) 286.410 + 47.3518i 1.17381 + 0.194065i
\(245\) −24.0619 −0.0982120
\(246\) −117.423 9.64130i −0.477331 0.0391923i
\(247\) 563.226i 2.28027i
\(248\) −320.117 80.2986i −1.29080 0.323785i
\(249\) −6.67965 −0.0268259
\(250\) 21.4817 261.629i 0.0859266 1.04652i
\(251\) 7.21755i 0.0287552i −0.999897 0.0143776i \(-0.995423\pi\)
0.999897 0.0143776i \(-0.00457669\pi\)
\(252\) −11.3337 + 68.5525i −0.0449750 + 0.272034i
\(253\) −225.072 −0.889613
\(254\) −103.439 8.49309i −0.407240 0.0334374i
\(255\) 47.5987i 0.186662i
\(256\) 202.960 + 156.023i 0.792812 + 0.609466i
\(257\) 380.233 1.47951 0.739754 0.672878i \(-0.234942\pi\)
0.739754 + 0.672878i \(0.234942\pi\)
\(258\) 12.9764 158.042i 0.0502961 0.612567i
\(259\) 9.24282i 0.0356866i
\(260\) 251.891 + 41.6449i 0.968812 + 0.160173i
\(261\) 122.280 0.468505
\(262\) 483.713 + 39.7163i 1.84623 + 0.151589i
\(263\) 313.354i 1.19146i −0.803184 0.595731i \(-0.796863\pi\)
0.803184 0.595731i \(-0.203137\pi\)
\(264\) 25.7653 102.716i 0.0975960 0.389075i
\(265\) 52.8723 0.199518
\(266\) −13.1343 + 159.966i −0.0493772 + 0.601375i
\(267\) 193.327i 0.724072i
\(268\) −20.9331 + 126.615i −0.0781085 + 0.472443i
\(269\) −170.127 −0.632442 −0.316221 0.948686i \(-0.602414\pi\)
−0.316221 + 0.948686i \(0.602414\pi\)
\(270\) −166.406 13.6632i −0.616319 0.0506043i
\(271\) 50.3103i 0.185647i −0.995683 0.0928234i \(-0.970411\pi\)
0.995683 0.0928234i \(-0.0295892\pi\)
\(272\) −134.441 45.7033i −0.494270 0.168027i
\(273\) −76.6527 −0.280779
\(274\) 44.2808 539.304i 0.161609 1.96826i
\(275\) 111.853i 0.406738i
\(276\) −163.355 27.0074i −0.591867 0.0978527i
\(277\) 58.9777 0.212916 0.106458 0.994317i \(-0.466049\pi\)
0.106458 + 0.994317i \(0.466049\pi\)
\(278\) 31.2844 + 2.56867i 0.112534 + 0.00923983i
\(279\) 270.857i 0.970812i
\(280\) −70.5701 17.7019i −0.252036 0.0632211i
\(281\) 325.523 1.15844 0.579222 0.815170i \(-0.303356\pi\)
0.579222 + 0.815170i \(0.303356\pi\)
\(282\) 13.2739 161.666i 0.0470706 0.573283i
\(283\) 282.815i 0.999348i −0.866214 0.499674i \(-0.833453\pi\)
0.866214 0.499674i \(-0.166547\pi\)
\(284\) −33.0249 + 199.753i −0.116285 + 0.703354i
\(285\) −162.683 −0.570817
\(286\) −314.009 25.7824i −1.09793 0.0901483i
\(287\) 99.8919i 0.348055i
\(288\) −83.6728 + 192.716i −0.290531 + 0.669154i
\(289\) −210.237 −0.727464
\(290\) −10.4778 + 127.611i −0.0361303 + 0.440038i
\(291\) 49.9565i 0.171672i
\(292\) 21.6563 + 3.58041i 0.0741653 + 0.0122617i
\(293\) 47.5056 0.162135 0.0810676 0.996709i \(-0.474167\pi\)
0.0810676 + 0.996709i \(0.474167\pi\)
\(294\) 21.7706 + 1.78753i 0.0740498 + 0.00608002i
\(295\) 131.753i 0.446621i
\(296\) −6.79976 + 27.1078i −0.0229722 + 0.0915805i
\(297\) 206.045 0.693753
\(298\) −4.00365 + 48.7613i −0.0134351 + 0.163628i
\(299\) 492.610i 1.64752i
\(300\) −13.4217 + 81.1818i −0.0447390 + 0.270606i
\(301\) 134.446 0.446665
\(302\) −377.512 30.9965i −1.25004 0.102637i
\(303\) 1.12109i 0.00369998i
\(304\) −156.205 + 459.493i −0.513831 + 1.51149i
\(305\) −249.469 −0.817930
\(306\) 9.53636 116.145i 0.0311646 0.379559i
\(307\) 349.978i 1.13999i 0.821647 + 0.569997i \(0.193055\pi\)
−0.821647 + 0.569997i \(0.806945\pi\)
\(308\) 88.5826 + 14.6453i 0.287606 + 0.0475496i
\(309\) 181.700 0.588026
\(310\) 282.666 + 23.2089i 0.911825 + 0.0748674i
\(311\) 344.941i 1.10914i 0.832138 + 0.554568i \(0.187116\pi\)
−0.832138 + 0.554568i \(0.812884\pi\)
\(312\) −224.811 56.3919i −0.720549 0.180743i
\(313\) 281.520 0.899424 0.449712 0.893174i \(-0.351527\pi\)
0.449712 + 0.893174i \(0.351527\pi\)
\(314\) −16.6517 + 202.804i −0.0530309 + 0.645874i
\(315\) 59.7106i 0.189557i
\(316\) 26.0262 157.420i 0.0823613 0.498166i
\(317\) 525.202 1.65679 0.828394 0.560146i \(-0.189255\pi\)
0.828394 + 0.560146i \(0.189255\pi\)
\(318\) −47.8375 3.92780i −0.150432 0.0123516i
\(319\) 158.008i 0.495324i
\(320\) −193.949 103.834i −0.606090 0.324482i
\(321\) −59.2018 −0.184429
\(322\) 11.4876 139.909i 0.0356757 0.434501i
\(323\) 269.195i 0.833421i
\(324\) −83.6483 13.8295i −0.258174 0.0426836i
\(325\) 244.810 0.753260
\(326\) 136.706 + 11.2246i 0.419345 + 0.0344312i
\(327\) 137.663i 0.420989i
\(328\) 73.4885 292.968i 0.224050 0.893196i
\(329\) 137.529 0.418021
\(330\) −7.44701 + 90.6987i −0.0225667 + 0.274844i
\(331\) 177.187i 0.535309i −0.963515 0.267655i \(-0.913751\pi\)
0.963515 0.267655i \(-0.0862486\pi\)
\(332\) 2.79322 16.8949i 0.00841331 0.0508883i
\(333\) −22.9364 −0.0688781
\(334\) 111.185 + 9.12907i 0.332889 + 0.0273326i
\(335\) 110.284i 0.329206i
\(336\) 62.5351 + 21.2588i 0.186116 + 0.0632702i
\(337\) −111.377 −0.330495 −0.165247 0.986252i \(-0.552842\pi\)
−0.165247 + 0.986252i \(0.552842\pi\)
\(338\) −28.7702 + 350.398i −0.0851188 + 1.03668i
\(339\) 195.214i 0.575852i
\(340\) 120.392 + 19.9043i 0.354094 + 0.0585420i
\(341\) −349.997 −1.02639
\(342\) −396.961 32.5933i −1.16070 0.0953021i
\(343\) 18.5203i 0.0539949i
\(344\) 394.311 + 98.9095i 1.14625 + 0.287528i
\(345\) 142.286 0.412422
\(346\) −3.14699 + 38.3278i −0.00909534 + 0.110774i
\(347\) 52.1533i 0.150298i 0.997172 + 0.0751488i \(0.0239432\pi\)
−0.997172 + 0.0751488i \(0.976057\pi\)
\(348\) 18.9601 114.681i 0.0544830 0.329543i
\(349\) −419.921 −1.20321 −0.601606 0.798793i \(-0.705472\pi\)
−0.601606 + 0.798793i \(0.705472\pi\)
\(350\) −69.5300 5.70891i −0.198657 0.0163112i
\(351\) 450.965i 1.28480i
\(352\) 249.026 + 108.121i 0.707459 + 0.307162i
\(353\) −198.456 −0.562198 −0.281099 0.959679i \(-0.590699\pi\)
−0.281099 + 0.959679i \(0.590699\pi\)
\(354\) 9.78775 119.207i 0.0276490 0.336743i
\(355\) 173.989i 0.490108i
\(356\) −488.985 80.8433i −1.37355 0.227088i
\(357\) −36.6363 −0.102623
\(358\) 390.177 + 32.0363i 1.08988 + 0.0894870i
\(359\) 234.090i 0.652063i 0.945359 + 0.326031i \(0.105711\pi\)
−0.945359 + 0.326031i \(0.894289\pi\)
\(360\) 43.9279 175.122i 0.122022 0.486451i
\(361\) −559.054 −1.54863
\(362\) −13.5101 + 164.543i −0.0373208 + 0.454538i
\(363\) 76.4905i 0.210718i
\(364\) 32.0537 193.878i 0.0880597 0.532633i
\(365\) −18.8630 −0.0516796
\(366\) 225.713 + 18.5327i 0.616702 + 0.0506357i
\(367\) 369.480i 1.00676i −0.864066 0.503379i \(-0.832090\pi\)
0.864066 0.503379i \(-0.167910\pi\)
\(368\) 136.620 401.882i 0.371250 1.09207i
\(369\) 247.885 0.671776
\(370\) 1.96535 23.9364i 0.00531176 0.0646930i
\(371\) 40.6953i 0.109691i
\(372\) −254.025 41.9977i −0.682863 0.112897i
\(373\) −280.481 −0.751960 −0.375980 0.926628i \(-0.622694\pi\)
−0.375980 + 0.926628i \(0.622694\pi\)
\(374\) −150.081 12.3228i −0.401287 0.0329485i
\(375\) 204.794i 0.546118i
\(376\) 403.352 + 101.177i 1.07274 + 0.269089i
\(377\) −345.829 −0.917318
\(378\) −10.5164 + 128.081i −0.0278212 + 0.338840i
\(379\) 259.908i 0.685772i 0.939377 + 0.342886i \(0.111404\pi\)
−0.939377 + 0.342886i \(0.888596\pi\)
\(380\) 68.0288 411.475i 0.179023 1.08283i
\(381\) −80.9685 −0.212516
\(382\) −318.269 26.1322i −0.833164 0.0684088i
\(383\) 412.996i 1.07832i −0.842203 0.539160i \(-0.818742\pi\)
0.842203 0.539160i \(-0.181258\pi\)
\(384\) 167.767 + 108.355i 0.436892 + 0.282174i
\(385\) −77.1572 −0.200408
\(386\) −17.4229 + 212.197i −0.0451370 + 0.549733i
\(387\) 333.633i 0.862102i
\(388\) 126.356 + 20.8902i 0.325659 + 0.0538408i
\(389\) 348.842 0.896766 0.448383 0.893842i \(-0.352000\pi\)
0.448383 + 0.893842i \(0.352000\pi\)
\(390\) 198.510 + 16.2991i 0.509000 + 0.0417925i
\(391\) 235.444i 0.602158i
\(392\) −13.6250 + 54.3172i −0.0347577 + 0.138564i
\(393\) 378.634 0.963444
\(394\) 29.1105 354.542i 0.0738844 0.899853i
\(395\) 137.116i 0.347130i
\(396\) −36.3428 + 219.821i −0.0917747 + 0.555103i
\(397\) 33.6988 0.0848836 0.0424418 0.999099i \(-0.486486\pi\)
0.0424418 + 0.999099i \(0.486486\pi\)
\(398\) 533.470 + 43.8018i 1.34038 + 0.110055i
\(399\) 125.215i 0.313823i
\(400\) −199.721 67.8953i −0.499303 0.169738i
\(401\) 140.120 0.349426 0.174713 0.984619i \(-0.444100\pi\)
0.174713 + 0.984619i \(0.444100\pi\)
\(402\) −8.19284 + 99.7822i −0.0203802 + 0.248214i
\(403\) 766.031i 1.90082i
\(404\) 2.83559 + 0.468805i 0.00701879 + 0.00116041i
\(405\) 72.8593 0.179900
\(406\) 98.2211 + 8.06466i 0.241924 + 0.0198637i
\(407\) 29.6381i 0.0728209i
\(408\) −107.449 26.9526i −0.263355 0.0660604i
\(409\) −707.963 −1.73096 −0.865480 0.500943i \(-0.832987\pi\)
−0.865480 + 0.500943i \(0.832987\pi\)
\(410\) −21.2406 + 258.693i −0.0518062 + 0.630958i
\(411\) 422.148i 1.02713i
\(412\) −75.9811 + 459.575i −0.184420 + 1.11547i
\(413\) 101.409 0.245543
\(414\) 347.190 + 28.5068i 0.838623 + 0.0688570i
\(415\) 14.7158i 0.0354598i
\(416\) 236.642 545.036i 0.568850 1.31018i
\(417\) 24.4883 0.0587250
\(418\) −42.1167 + 512.947i −0.100758 + 1.22715i
\(419\) 596.341i 1.42325i −0.702560 0.711625i \(-0.747960\pi\)
0.702560 0.711625i \(-0.252040\pi\)
\(420\) −56.0000 9.25842i −0.133333 0.0220439i
\(421\) −162.813 −0.386728 −0.193364 0.981127i \(-0.561940\pi\)
−0.193364 + 0.981127i \(0.561940\pi\)
\(422\) −324.476 26.6418i −0.768900 0.0631322i
\(423\) 341.283i 0.806815i
\(424\) 29.9388 119.353i 0.0706103 0.281494i
\(425\) 117.007 0.275311
\(426\) −12.9254 + 157.420i −0.0303412 + 0.369532i
\(427\) 192.014i 0.449681i
\(428\) 24.7563 149.740i 0.0578419 0.349859i
\(429\) −245.795 −0.572950
\(430\) −348.180 28.5880i −0.809720 0.0664838i
\(431\) 386.832i 0.897522i 0.893652 + 0.448761i \(0.148135\pi\)
−0.893652 + 0.448761i \(0.851865\pi\)
\(432\) −125.070 + 367.907i −0.289514 + 0.851637i
\(433\) 574.844 1.32758 0.663792 0.747918i \(-0.268946\pi\)
0.663792 + 0.747918i \(0.268946\pi\)
\(434\) 17.8637 217.565i 0.0411606 0.501303i
\(435\) 99.8895i 0.229631i
\(436\) −348.194 57.5665i −0.798609 0.132033i
\(437\) 804.699 1.84142
\(438\) 17.0668 + 1.40131i 0.0389653 + 0.00319933i
\(439\) 295.206i 0.672450i −0.941782 0.336225i \(-0.890850\pi\)
0.941782 0.336225i \(-0.109150\pi\)
\(440\) −226.291 56.7631i −0.514297 0.129007i
\(441\) −45.9587 −0.104215
\(442\) −26.9705 + 328.479i −0.0610192 + 0.743165i
\(443\) 426.510i 0.962776i −0.876508 0.481388i \(-0.840133\pi\)
0.876508 0.481388i \(-0.159867\pi\)
\(444\) −3.55640 + 21.5111i −0.00800992 + 0.0484483i
\(445\) 425.916 0.957114
\(446\) −633.324 52.0004i −1.42001 0.116593i
\(447\) 38.1686i 0.0853884i
\(448\) −79.9203 + 149.281i −0.178393 + 0.333216i
\(449\) −458.779 −1.02178 −0.510889 0.859646i \(-0.670684\pi\)
−0.510889 + 0.859646i \(0.670684\pi\)
\(450\) 14.1669 172.541i 0.0314819 0.383425i
\(451\) 320.314i 0.710231i
\(452\) −493.756 81.6322i −1.09238 0.180602i
\(453\) −295.503 −0.652325
\(454\) 231.557 + 19.0125i 0.510038 + 0.0418778i
\(455\) 168.872i 0.371147i
\(456\) −92.1186 + 367.239i −0.202015 + 0.805348i
\(457\) 384.429 0.841202 0.420601 0.907246i \(-0.361819\pi\)
0.420601 + 0.907246i \(0.361819\pi\)
\(458\) 58.5332 712.887i 0.127802 1.55652i
\(459\) 215.539i 0.469585i
\(460\) −59.4994 + 359.885i −0.129346 + 0.782358i
\(461\) −48.0796 −0.104294 −0.0521471 0.998639i \(-0.516606\pi\)
−0.0521471 + 0.998639i \(0.516606\pi\)
\(462\) 69.8100 + 5.73190i 0.151104 + 0.0124067i
\(463\) 62.2803i 0.134515i 0.997736 + 0.0672573i \(0.0214249\pi\)
−0.997736 + 0.0672573i \(0.978575\pi\)
\(464\) 282.135 + 95.9119i 0.608050 + 0.206707i
\(465\) 221.261 0.475830
\(466\) 65.8430 801.915i 0.141294 1.72085i
\(467\) 358.971i 0.768674i −0.923193 0.384337i \(-0.874430\pi\)
0.923193 0.384337i \(-0.125570\pi\)
\(468\) 481.117 + 79.5425i 1.02803 + 0.169963i
\(469\) −84.8846 −0.180991
\(470\) −356.163 29.2435i −0.757793 0.0622202i
\(471\) 158.748i 0.337045i
\(472\) 297.418 + 74.6048i 0.630124 + 0.158061i
\(473\) 431.117 0.911452
\(474\) 10.1862 124.060i 0.0214898 0.261729i
\(475\) 399.907i 0.841909i
\(476\) 15.3201 92.6646i 0.0321852 0.194673i
\(477\) 100.987 0.211713
\(478\) −481.332 39.5208i −1.00697 0.0826795i
\(479\) 196.744i 0.410740i 0.978684 + 0.205370i \(0.0658398\pi\)
−0.978684 + 0.205370i \(0.934160\pi\)
\(480\) −157.429 68.3517i −0.327976 0.142399i
\(481\) 64.8682 0.134861
\(482\) 19.0960 232.574i 0.0396183 0.482519i
\(483\) 109.516i 0.226741i
\(484\) −193.468 31.9859i −0.399727 0.0660865i
\(485\) −110.058 −0.226924
\(486\) −501.613 41.1861i −1.03213 0.0847450i
\(487\) 490.201i 1.00657i 0.864120 + 0.503287i \(0.167876\pi\)
−0.864120 + 0.503287i \(0.832124\pi\)
\(488\) −141.261 + 563.148i −0.289469 + 1.15399i
\(489\) 107.009 0.218832
\(490\) 3.93806 47.9625i 0.00803687 0.0978826i
\(491\) 852.129i 1.73550i −0.497004 0.867748i \(-0.665567\pi\)
0.497004 0.867748i \(-0.334433\pi\)
\(492\) 38.4359 232.481i 0.0781217 0.472522i
\(493\) −165.290 −0.335273
\(494\) 1122.67 + 92.1797i 2.27262 + 0.186599i
\(495\) 191.469i 0.386805i
\(496\) 212.450 624.945i 0.428327 1.25997i
\(497\) −133.917 −0.269452
\(498\) 1.09322 13.3145i 0.00219521 0.0267359i
\(499\) 851.935i 1.70729i 0.520859 + 0.853643i \(0.325612\pi\)
−0.520859 + 0.853643i \(0.674388\pi\)
\(500\) 517.988 + 85.6385i 1.03598 + 0.171277i
\(501\) 87.0315 0.173716
\(502\) 14.3867 + 1.18125i 0.0286587 + 0.00235309i
\(503\) 483.294i 0.960823i 0.877043 + 0.480411i \(0.159513\pi\)
−0.877043 + 0.480411i \(0.840487\pi\)
\(504\) −134.790 33.8109i −0.267441 0.0670852i
\(505\) −2.46986 −0.00489081
\(506\) 36.8361 448.634i 0.0727986 0.886629i
\(507\) 274.279i 0.540984i
\(508\) 33.8584 204.794i 0.0666505 0.403138i
\(509\) −653.399 −1.28369 −0.641846 0.766833i \(-0.721831\pi\)
−0.641846 + 0.766833i \(0.721831\pi\)
\(510\) 94.8782 + 7.79018i 0.186036 + 0.0152749i
\(511\) 14.5187i 0.0284124i
\(512\) −344.217 + 379.023i −0.672300 + 0.740279i
\(513\) −736.670 −1.43600
\(514\) −62.2304 + 757.916i −0.121071 + 1.47455i
\(515\) 400.299i 0.777280i
\(516\) 312.900 + 51.7315i 0.606396 + 0.100255i
\(517\) 441.001 0.853001
\(518\) −18.4236 1.51271i −0.0355669 0.00292030i
\(519\) 30.0016i 0.0578066i
\(520\) −124.236 + 495.277i −0.238915 + 0.952456i
\(521\) −70.1290 −0.134605 −0.0673023 0.997733i \(-0.521439\pi\)
−0.0673023 + 0.997733i \(0.521439\pi\)
\(522\) −20.0128 + 243.739i −0.0383386 + 0.466934i
\(523\) 288.438i 0.551507i −0.961228 0.275753i \(-0.911073\pi\)
0.961228 0.275753i \(-0.0889273\pi\)
\(524\) −158.332 + 957.681i −0.302161 + 1.82764i
\(525\) −54.4256 −0.103668
\(526\) 624.607 + 51.2847i 1.18747 + 0.0974995i
\(527\) 366.126i 0.694736i
\(528\) 200.526 + 68.1687i 0.379783 + 0.129107i
\(529\) −174.806 −0.330446
\(530\) −8.65327 + 105.390i −0.0163269 + 0.198849i
\(531\) 251.651i 0.473918i
\(532\) −316.709 52.3611i −0.595317 0.0984232i
\(533\) −701.064 −1.31532
\(534\) −385.358 31.6407i −0.721644 0.0592522i
\(535\) 130.426i 0.243788i
\(536\) −248.954 62.4480i −0.464467 0.116507i
\(537\) 305.417 0.568746
\(538\) 27.8436 339.112i 0.0517539 0.630321i
\(539\) 59.3872i 0.110180i
\(540\) 54.4693 329.460i 0.100869 0.610111i
\(541\) −9.90711 −0.0183126 −0.00915630 0.999958i \(-0.502915\pi\)
−0.00915630 + 0.999958i \(0.502915\pi\)
\(542\) 100.283 + 8.23397i 0.185024 + 0.0151918i
\(543\) 128.798i 0.237197i
\(544\) 113.103 260.501i 0.207910 0.478862i
\(545\) 303.284 0.556484
\(546\) 12.5453 152.791i 0.0229767 0.279838i
\(547\) 265.156i 0.484746i −0.970183 0.242373i \(-0.922074\pi\)
0.970183 0.242373i \(-0.0779257\pi\)
\(548\) 1067.74 + 176.529i 1.94844 + 0.322133i
\(549\) −476.489 −0.867922
\(550\) −222.955 18.3063i −0.405374 0.0332841i
\(551\) 564.926i 1.02527i
\(552\) 80.5689 321.195i 0.145958 0.581874i
\(553\) 105.537 0.190845
\(554\) −9.65251 + 117.560i −0.0174233 + 0.212202i
\(555\) 18.7366i 0.0337596i
\(556\) −10.2402 + 61.9385i −0.0184177 + 0.111400i
\(557\) −718.935 −1.29073 −0.645363 0.763876i \(-0.723294\pi\)
−0.645363 + 0.763876i \(0.723294\pi\)
\(558\) 539.896 + 44.3294i 0.967556 + 0.0794434i
\(559\) 943.574i 1.68797i
\(560\) 46.8348 137.770i 0.0836336 0.246017i
\(561\) −117.478 −0.209409
\(562\) −53.2763 + 648.862i −0.0947976 + 1.15456i
\(563\) 283.534i 0.503613i 0.967778 + 0.251807i \(0.0810247\pi\)
−0.967778 + 0.251807i \(0.918975\pi\)
\(564\) 320.075 + 52.9176i 0.567508 + 0.0938256i
\(565\) 430.072 0.761189
\(566\) 563.734 + 46.2866i 0.995996 + 0.0817785i
\(567\) 56.0792i 0.0989051i
\(568\) −392.760 98.5205i −0.691479 0.173452i
\(569\) 31.4542 0.0552798 0.0276399 0.999618i \(-0.491201\pi\)
0.0276399 + 0.999618i \(0.491201\pi\)
\(570\) 26.6253 324.274i 0.0467110 0.568902i
\(571\) 580.635i 1.01687i −0.861099 0.508437i \(-0.830224\pi\)
0.861099 0.508437i \(-0.169776\pi\)
\(572\) 102.784 621.693i 0.179692 1.08688i
\(573\) −249.130 −0.434781
\(574\) 199.114 + 16.3487i 0.346888 + 0.0284820i
\(575\) 349.767i 0.608290i
\(576\) −370.446 198.325i −0.643135 0.344314i
\(577\) 909.096 1.57556 0.787778 0.615959i \(-0.211231\pi\)
0.787778 + 0.615959i \(0.211231\pi\)
\(578\) 34.4082 419.064i 0.0595297 0.725025i
\(579\) 166.100i 0.286874i
\(580\) −252.651 41.7706i −0.435606 0.0720183i
\(581\) 11.3266 0.0194951
\(582\) 99.5780 + 8.17607i 0.171096 + 0.0140482i
\(583\) 130.494i 0.223832i
\(584\) −10.6811 + 42.5813i −0.0182896 + 0.0729131i
\(585\) −419.062 −0.716346
\(586\) −7.77495 + 94.6926i −0.0132678 + 0.161591i
\(587\) 30.9295i 0.0526908i 0.999653 + 0.0263454i \(0.00838696\pi\)
−0.999653 + 0.0263454i \(0.991613\pi\)
\(588\) −7.12613 + 43.1027i −0.0121193 + 0.0733039i
\(589\) 1251.34 2.12452
\(590\) −262.622 21.5632i −0.445123 0.0365478i
\(591\) 277.523i 0.469582i
\(592\) −52.9210 17.9905i −0.0893935 0.0303893i
\(593\) −879.391 −1.48295 −0.741476 0.670979i \(-0.765874\pi\)
−0.741476 + 0.670979i \(0.765874\pi\)
\(594\) −33.7220 + 410.707i −0.0567711 + 0.691426i
\(595\) 80.7127i 0.135652i
\(596\) −96.5402 15.9609i −0.161980 0.0267800i
\(597\) 417.582 0.699467
\(598\) −981.915 80.6223i −1.64200 0.134820i
\(599\) 252.069i 0.420816i 0.977614 + 0.210408i \(0.0674793\pi\)
−0.977614 + 0.210408i \(0.932521\pi\)
\(600\) −159.622 40.0399i −0.266037 0.0667331i
\(601\) −475.958 −0.791943 −0.395972 0.918263i \(-0.629592\pi\)
−0.395972 + 0.918263i \(0.629592\pi\)
\(602\) −22.0040 + 267.991i −0.0365514 + 0.445167i
\(603\) 210.644i 0.349327i
\(604\) 123.570 747.420i 0.204586 1.23745i
\(605\) 168.515 0.278537
\(606\) 2.23467 + 0.183482i 0.00368757 + 0.000302776i
\(607\) 150.523i 0.247979i 0.992284 + 0.123989i \(0.0395689\pi\)
−0.992284 + 0.123989i \(0.960431\pi\)
\(608\) −890.339 386.564i −1.46437 0.635796i
\(609\) 76.8841 0.126246
\(610\) 40.8289 497.264i 0.0669327 0.815187i
\(611\) 965.208i 1.57972i
\(612\) 229.951 + 38.0175i 0.375736 + 0.0621201i
\(613\) 184.999 0.301794 0.150897 0.988550i \(-0.451784\pi\)
0.150897 + 0.988550i \(0.451784\pi\)
\(614\) −697.608 57.2787i −1.13617 0.0932877i
\(615\) 202.496i 0.329261i
\(616\) −43.6901 + 174.174i −0.0709254 + 0.282750i
\(617\) −40.0241 −0.0648689 −0.0324345 0.999474i \(-0.510326\pi\)
−0.0324345 + 0.999474i \(0.510326\pi\)
\(618\) −29.7377 + 362.181i −0.0481192 + 0.586053i
\(619\) 389.507i 0.629253i −0.949216 0.314626i \(-0.898121\pi\)
0.949216 0.314626i \(-0.101879\pi\)
\(620\) −92.5242 + 559.637i −0.149233 + 0.902641i
\(621\) 644.307 1.03753
\(622\) −687.569 56.4544i −1.10542 0.0907626i
\(623\) 327.823i 0.526201i
\(624\) 149.199 438.885i 0.239101 0.703342i
\(625\) −121.575 −0.194519
\(626\) −46.0745 + 561.151i −0.0736015 + 0.896407i
\(627\) 401.517i 0.640378i
\(628\) −401.523 66.3834i −0.639368 0.105706i
\(629\) 31.0039 0.0492907
\(630\) 119.021 + 9.77245i 0.188922 + 0.0155118i
\(631\) 615.708i 0.975765i 0.872909 + 0.487883i \(0.162231\pi\)
−0.872909 + 0.487883i \(0.837769\pi\)
\(632\) 309.526 + 77.6418i 0.489756 + 0.122851i
\(633\) −253.988 −0.401245
\(634\) −85.9565 + 1046.88i −0.135578 + 1.65123i
\(635\) 178.380i 0.280913i
\(636\) 15.6585 94.7113i 0.0246203 0.148917i
\(637\) 129.979 0.204049
\(638\) 314.957 + 25.8602i 0.493663 + 0.0405333i
\(639\) 332.321i 0.520064i
\(640\) 238.714 369.603i 0.372991 0.577505i
\(641\) 975.771 1.52226 0.761132 0.648597i \(-0.224644\pi\)
0.761132 + 0.648597i \(0.224644\pi\)
\(642\) 9.68919 118.007i 0.0150922 0.183811i
\(643\) 888.565i 1.38190i 0.722900 + 0.690952i \(0.242809\pi\)
−0.722900 + 0.690952i \(0.757191\pi\)
\(644\) 277.000 + 45.7961i 0.430124 + 0.0711120i
\(645\) −272.543 −0.422547
\(646\) 536.585 + 44.0575i 0.830626 + 0.0682004i
\(647\) 263.161i 0.406740i −0.979102 0.203370i \(-0.934811\pi\)
0.979102 0.203370i \(-0.0651894\pi\)
\(648\) 41.2564 164.472i 0.0636673 0.253815i
\(649\) 325.180 0.501047
\(650\) −40.0664 + 487.977i −0.0616407 + 0.750734i
\(651\) 170.303i 0.261601i
\(652\) −44.7478 + 270.659i −0.0686315 + 0.415121i
\(653\) 923.879 1.41482 0.707411 0.706803i \(-0.249863\pi\)
0.707411 + 0.706803i \(0.249863\pi\)
\(654\) −274.404 22.5305i −0.419577 0.0344503i
\(655\) 834.160i 1.27353i
\(656\) 571.944 + 194.432i 0.871866 + 0.296391i
\(657\) −36.0287 −0.0548383
\(658\) −22.5085 + 274.135i −0.0342074 + 0.416619i
\(659\) 1297.45i 1.96882i 0.175881 + 0.984411i \(0.443723\pi\)
−0.175881 + 0.984411i \(0.556277\pi\)
\(660\) −179.570 29.6881i −0.272076 0.0449820i
\(661\) −597.632 −0.904133 −0.452067 0.891984i \(-0.649313\pi\)
−0.452067 + 0.891984i \(0.649313\pi\)
\(662\) 353.186 + 28.9991i 0.533514 + 0.0438053i
\(663\) 257.122i 0.387816i
\(664\) 33.2193 + 8.33278i 0.0500291 + 0.0125494i
\(665\) 275.860 0.414827
\(666\) 3.75385 45.7189i 0.00563642 0.0686471i
\(667\) 494.096i 0.740774i
\(668\) −36.3938 + 220.130i −0.0544818 + 0.329535i
\(669\) −495.743 −0.741022
\(670\) 219.828 + 18.0495i 0.328102 + 0.0269395i
\(671\) 615.713i 0.917605i
\(672\) −52.6097 + 121.171i −0.0782883 + 0.180315i
\(673\) 478.696 0.711287 0.355643 0.934622i \(-0.384262\pi\)
0.355643 + 0.934622i \(0.384262\pi\)
\(674\) 18.2283 222.006i 0.0270450 0.329386i
\(675\) 320.198i 0.474367i
\(676\) −693.736 114.695i −1.02624 0.169667i
\(677\) 208.658 0.308210 0.154105 0.988054i \(-0.450751\pi\)
0.154105 + 0.988054i \(0.450751\pi\)
\(678\) −389.118 31.9494i −0.573920 0.0471230i
\(679\) 84.7109i 0.124758i
\(680\) −59.3788 + 236.719i −0.0873218 + 0.348116i
\(681\) 181.255 0.266160
\(682\) 57.2819 697.647i 0.0839910 1.02294i
\(683\) 12.4224i 0.0181880i 0.999959 + 0.00909400i \(0.00289475\pi\)
−0.999959 + 0.00909400i \(0.997105\pi\)
\(684\) 129.936 785.924i 0.189965 1.14901i
\(685\) −930.027 −1.35770
\(686\) −36.9163 3.03109i −0.0538138 0.00441850i
\(687\) 558.023i 0.812261i
\(688\) −261.690 + 769.790i −0.380363 + 1.11888i
\(689\) −285.609 −0.414527
\(690\) −23.2870 + 283.617i −0.0337493 + 0.411039i
\(691\) 914.850i 1.32395i 0.749526 + 0.661975i \(0.230282\pi\)
−0.749526 + 0.661975i \(0.769718\pi\)
\(692\) −75.8834 12.5457i −0.109658 0.0181297i
\(693\) −147.372 −0.212657
\(694\) −103.957 8.53560i −0.149794 0.0122991i
\(695\) 53.9497i 0.0776255i
\(696\) 225.490 + 56.5621i 0.323979 + 0.0812674i
\(697\) −335.075 −0.480738
\(698\) 68.7258 837.026i 0.0984611 1.19918i
\(699\) 627.711i 0.898012i
\(700\) 22.7591 137.659i 0.0325129 0.196656i
\(701\) 338.736 0.483218 0.241609 0.970374i \(-0.422325\pi\)
0.241609 + 0.970374i \(0.422325\pi\)
\(702\) 898.904 + 73.8065i 1.28049 + 0.105137i
\(703\) 105.965i 0.150732i
\(704\) −256.273 + 478.685i −0.364024 + 0.679951i
\(705\) −278.792 −0.395449
\(706\) 32.4800 395.581i 0.0460057 0.560313i
\(707\) 1.90103i 0.00268886i
\(708\) 236.012 + 39.0197i 0.333351 + 0.0551126i
\(709\) −665.756 −0.939006 −0.469503 0.882931i \(-0.655567\pi\)
−0.469503 + 0.882931i \(0.655567\pi\)
\(710\) 346.810 + 28.4756i 0.488465 + 0.0401065i
\(711\) 261.895i 0.368347i
\(712\) 241.173 961.458i 0.338727 1.35036i
\(713\) −1094.45 −1.53499
\(714\) 5.99603 73.0269i 0.00839780 0.102279i
\(715\) 541.507i 0.757352i
\(716\) −127.716 + 772.494i −0.178374 + 1.07890i
\(717\) −376.769 −0.525480
\(718\) −466.611 38.3121i −0.649876 0.0533595i
\(719\) 517.776i 0.720134i 0.932926 + 0.360067i \(0.117246\pi\)
−0.932926 + 0.360067i \(0.882754\pi\)
\(720\) 341.881 + 116.222i 0.474834 + 0.161420i
\(721\) −308.107 −0.427333
\(722\) 91.4969 1114.36i 0.126727 1.54343i
\(723\) 182.051i 0.251799i
\(724\) −325.771 53.8593i −0.449959 0.0743913i
\(725\) −245.548 −0.338687
\(726\) −152.468 12.5187i −0.210011 0.0172434i
\(727\) 428.891i 0.589946i −0.955506 0.294973i \(-0.904689\pi\)
0.955506 0.294973i \(-0.0953106\pi\)
\(728\) 381.210 + 95.6233i 0.523641 + 0.131351i
\(729\) −201.882 −0.276930
\(730\) 3.08719 37.5996i 0.00422903 0.0515062i
\(731\) 450.983i 0.616940i
\(732\) −73.8820 + 446.879i −0.100932 + 0.610490i
\(733\) 758.896 1.03533 0.517665 0.855584i \(-0.326802\pi\)
0.517665 + 0.855584i \(0.326802\pi\)
\(734\) 736.482 + 60.4705i 1.00338 + 0.0823849i
\(735\) 37.5433i 0.0510794i
\(736\) 778.709 + 338.097i 1.05803 + 0.459371i
\(737\) −272.192 −0.369324
\(738\) −40.5698 + 494.108i −0.0549727 + 0.669523i
\(739\) 1100.00i 1.48849i −0.667906 0.744246i \(-0.732809\pi\)
0.667906 0.744246i \(-0.267191\pi\)
\(740\) 47.3906 + 7.83504i 0.0640413 + 0.0105879i
\(741\) 878.790 1.18595
\(742\) 81.1176 + 6.66034i 0.109323 + 0.00897620i
\(743\) 1056.59i 1.42205i −0.703165 0.711027i \(-0.748231\pi\)
0.703165 0.711027i \(-0.251769\pi\)
\(744\) 125.288 499.472i 0.168398 0.671334i
\(745\) 84.0885 0.112870
\(746\) 45.9046 559.081i 0.0615343 0.749438i
\(747\) 28.1074i 0.0376271i
\(748\) 49.1257 297.139i 0.0656761 0.397245i
\(749\) 100.388 0.134029
\(750\) 408.215 + 33.5174i 0.544287 + 0.0446898i
\(751\) 42.1730i 0.0561557i −0.999606 0.0280779i \(-0.991061\pi\)
0.999606 0.0280779i \(-0.00893864\pi\)
\(752\) −267.690 + 787.439i −0.355971 + 1.04713i
\(753\) 11.2614 0.0149554
\(754\) 56.5996 689.338i 0.0750658 0.914242i
\(755\) 651.018i 0.862275i
\(756\) −253.583 41.9245i −0.335427 0.0554558i
\(757\) −931.250 −1.23018 −0.615092 0.788455i \(-0.710881\pi\)
−0.615092 + 0.788455i \(0.710881\pi\)
\(758\) −518.072 42.5374i −0.683472 0.0561180i
\(759\) 351.175i 0.462681i
\(760\) 809.056 + 202.945i 1.06455 + 0.267032i
\(761\) −423.281 −0.556217 −0.278108 0.960550i \(-0.589707\pi\)
−0.278108 + 0.960550i \(0.589707\pi\)
\(762\) 13.2516 161.394i 0.0173905 0.211803i
\(763\) 233.435i 0.305943i
\(764\) 104.178 630.126i 0.136359 0.824772i
\(765\) −200.292 −0.261819
\(766\) 823.223 + 67.5925i 1.07470 + 0.0882409i
\(767\) 711.713i 0.927917i
\(768\) −243.440 + 316.674i −0.316979 + 0.412336i
\(769\) 600.534 0.780928 0.390464 0.920618i \(-0.372315\pi\)
0.390464 + 0.920618i \(0.372315\pi\)
\(770\) 12.6278 153.797i 0.0163998 0.199736i
\(771\) 593.270i 0.769481i
\(772\) −420.119 69.4578i −0.544196 0.0899713i
\(773\) 120.049 0.155303 0.0776516 0.996981i \(-0.475258\pi\)
0.0776516 + 0.996981i \(0.475258\pi\)
\(774\) −665.029 54.6037i −0.859210 0.0705474i
\(775\) 543.903i 0.701811i
\(776\) −62.3201 + 248.445i −0.0803095 + 0.320160i
\(777\) −14.4214 −0.0185603
\(778\) −57.0928 + 695.344i −0.0733840 + 0.893758i
\(779\) 1145.22i 1.47011i
\(780\) −64.9777 + 393.021i −0.0833047 + 0.503873i
\(781\) −429.421 −0.549835
\(782\) −469.308 38.5336i −0.600138 0.0492757i
\(783\) 452.326i 0.577683i
\(784\) −106.040 36.0484i −0.135255 0.0459800i
\(785\) 349.735 0.445522
\(786\) −61.9685 + 754.727i −0.0788404 + 0.960213i
\(787\) 1277.61i 1.62339i 0.584081 + 0.811696i \(0.301455\pi\)
−0.584081 + 0.811696i \(0.698545\pi\)
\(788\) 701.942 + 116.051i 0.890789 + 0.147273i
\(789\) 488.920 0.619671
\(790\) −273.313 22.4410i −0.345966 0.0284063i
\(791\) 331.022i 0.418486i
\(792\) −432.219 108.418i −0.545732 0.136892i
\(793\) 1347.60 1.69936
\(794\) −5.51527 + 67.1715i −0.00694618 + 0.0845989i
\(795\) 82.4955i 0.103768i
\(796\) −174.619 + 1056.19i −0.219371 + 1.32688i
\(797\) 84.2194 0.105670 0.0528352 0.998603i \(-0.483174\pi\)
0.0528352 + 0.998603i \(0.483174\pi\)
\(798\) −249.591 20.4932i −0.312771 0.0256807i
\(799\) 461.323i 0.577376i
\(800\) 168.022 386.991i 0.210028 0.483739i
\(801\) 813.506 1.01561
\(802\) −22.9326 + 279.300i −0.0285942 + 0.348254i
\(803\) 46.5559i 0.0579774i
\(804\) −197.554 32.6614i −0.245714 0.0406237i
\(805\) −241.273 −0.299718
\(806\) −1526.92 125.371i −1.89445 0.155548i
\(807\) 265.445i 0.328928i
\(808\) −1.39855 + 5.57544i −0.00173088 + 0.00690029i
\(809\) 1224.02 1.51300 0.756501 0.653993i \(-0.226907\pi\)
0.756501 + 0.653993i \(0.226907\pi\)
\(810\) −11.9244 + 145.230i −0.0147215 + 0.179296i
\(811\) 346.748i 0.427556i 0.976882 + 0.213778i \(0.0685769\pi\)
−0.976882 + 0.213778i \(0.931423\pi\)
\(812\) −32.1505 + 194.464i −0.0395942 + 0.239487i
\(813\) 78.4981 0.0965536
\(814\) −59.0774 4.85068i −0.0725767 0.00595907i
\(815\) 235.749i 0.289263i
\(816\) 71.3100 209.766i 0.0873897 0.257066i
\(817\) −1541.37 −1.88662
\(818\) 115.868 1411.18i 0.141648 1.72515i
\(819\) 322.549i 0.393832i
\(820\) −512.174 84.6773i −0.624603 0.103265i
\(821\) −1288.46 −1.56938 −0.784690 0.619888i \(-0.787178\pi\)
−0.784690 + 0.619888i \(0.787178\pi\)
\(822\) 841.465 + 69.0904i 1.02368 + 0.0840515i
\(823\) 496.071i 0.602759i 0.953504 + 0.301379i \(0.0974471\pi\)
−0.953504 + 0.301379i \(0.902553\pi\)
\(824\) −903.633 226.668i −1.09664 0.275083i
\(825\) −174.522 −0.211541
\(826\) −16.5970 + 202.138i −0.0200932 + 0.244719i
\(827\) 2.15878i 0.00261037i 0.999999 + 0.00130519i \(0.000415453\pi\)
−0.999999 + 0.00130519i \(0.999585\pi\)
\(828\) −113.645 + 687.386i −0.137252 + 0.830176i
\(829\) 501.082 0.604442 0.302221 0.953238i \(-0.402272\pi\)
0.302221 + 0.953238i \(0.402272\pi\)
\(830\) −29.3329 2.40844i −0.0353408 0.00290174i
\(831\) 92.0217i 0.110736i
\(832\) 1047.69 + 560.898i 1.25924 + 0.674157i
\(833\) 62.1239 0.0745785
\(834\) −4.00785 + 48.8124i −0.00480557 + 0.0585280i
\(835\) 191.737i 0.229626i
\(836\) −1015.56 167.902i −1.21479 0.200839i
\(837\) 1001.93 1.19704
\(838\) 1188.68 + 97.5994i 1.41848 + 0.116467i
\(839\) 1576.56i 1.87909i −0.342424 0.939546i \(-0.611248\pi\)
0.342424 0.939546i \(-0.388752\pi\)
\(840\) 27.6199 110.109i 0.0328808 0.131082i
\(841\) −494.127 −0.587547
\(842\) 26.6465 324.533i 0.0316467 0.385431i
\(843\) 507.907i 0.602499i
\(844\) 106.210 642.415i 0.125841 0.761155i
\(845\) 604.258 0.715099
\(846\) −680.277 55.8556i −0.804109 0.0660232i
\(847\) 129.704i 0.153134i
\(848\) 233.006 + 79.2105i 0.274772 + 0.0934086i
\(849\) 441.271 0.519754
\(850\) −19.1498 + 233.230i −0.0225292 + 0.274388i
\(851\) 92.6791i 0.108906i
\(852\) −311.670 51.5280i −0.365809 0.0604789i
\(853\) 1502.12 1.76098 0.880490 0.474065i \(-0.157214\pi\)
0.880490 + 0.474065i \(0.157214\pi\)
\(854\) −382.740 31.4257i −0.448173 0.0367982i
\(855\) 684.556i 0.800650i
\(856\) 294.423 + 73.8535i 0.343953 + 0.0862775i
\(857\) −112.940 −0.131786 −0.0658929 0.997827i \(-0.520990\pi\)
−0.0658929 + 0.997827i \(0.520990\pi\)
\(858\) 40.2278 489.942i 0.0468855 0.571028i
\(859\) 7.56729i 0.00880941i −0.999990 0.00440471i \(-0.998598\pi\)
0.999990 0.00440471i \(-0.00140207\pi\)
\(860\) 113.969 689.345i 0.132522 0.801564i
\(861\) 155.859 0.181021
\(862\) −771.069 63.3104i −0.894512 0.0734459i
\(863\) 1013.78i 1.17472i −0.809327 0.587358i \(-0.800168\pi\)
0.809327 0.587358i \(-0.199832\pi\)
\(864\) −712.878 309.514i −0.825090 0.358234i
\(865\) 66.0960 0.0764116
\(866\) −94.0810 + 1145.83i −0.108639 + 1.32313i
\(867\) 328.029i 0.378349i
\(868\) 430.748 + 71.2151i 0.496253 + 0.0820450i
\(869\) 338.417 0.389433
\(870\) −199.109 16.3483i −0.228861 0.0187911i
\(871\) 595.739i 0.683972i
\(872\) 171.733 684.630i 0.196942 0.785126i
\(873\) −210.213 −0.240794
\(874\) −131.700 + 1604.00i −0.150686 + 1.83524i
\(875\) 347.268i 0.396878i
\(876\) −5.58643 + 33.7898i −0.00637721 + 0.0385728i
\(877\) −1231.12 −1.40378 −0.701890 0.712285i \(-0.747660\pi\)
−0.701890 + 0.712285i \(0.747660\pi\)
\(878\) 588.431 + 48.3144i 0.670195 + 0.0550278i
\(879\) 74.1220i 0.0843254i
\(880\) 150.181 441.774i 0.170660 0.502016i
\(881\) 1270.31 1.44189 0.720945 0.692992i \(-0.243708\pi\)
0.720945 + 0.692992i \(0.243708\pi\)
\(882\) 7.52177 91.6091i 0.00852808 0.103865i
\(883\) 1407.95i 1.59451i −0.603646 0.797253i \(-0.706286\pi\)
0.603646 0.797253i \(-0.293714\pi\)
\(884\) −650.341 107.520i −0.735680 0.121629i
\(885\) −205.572 −0.232284
\(886\) 850.159 + 69.8042i 0.959547 + 0.0787857i
\(887\) 1721.23i 1.94051i −0.242093 0.970253i \(-0.577834\pi\)
0.242093 0.970253i \(-0.422166\pi\)
\(888\) −42.2958 10.6095i −0.0476304 0.0119477i
\(889\) 137.298 0.154440
\(890\) −69.7069 + 848.974i −0.0783224 + 0.953904i
\(891\) 179.824i 0.201823i
\(892\) 207.304 1253.89i 0.232404 1.40570i
\(893\) −1576.71 −1.76563
\(894\) −76.0812 6.24681i −0.0851020 0.00698749i
\(895\) 672.858i 0.751796i
\(896\) −284.480 183.736i −0.317500 0.205063i
\(897\) −768.608 −0.856865
\(898\) 75.0854 914.480i 0.0836140 1.01835i
\(899\) 768.342i 0.854663i
\(900\) 341.606 + 56.4774i 0.379563 + 0.0627527i
\(901\) −136.507 −0.151506
\(902\) 638.480 + 52.4238i 0.707849 + 0.0581195i
\(903\) 209.774i 0.232308i
\(904\) 243.527 970.840i 0.269388 1.07394i
\(905\) 283.753 0.313539
\(906\) 48.3632 589.025i 0.0533810 0.650138i
\(907\) 1181.35i 1.30248i 0.758871 + 0.651241i \(0.225751\pi\)
−0.758871 + 0.651241i \(0.774249\pi\)
\(908\) −75.7950 + 458.449i −0.0834746 + 0.504900i
\(909\) −4.71747 −0.00518974
\(910\) −336.611 27.6382i −0.369903 0.0303717i
\(911\) 1286.03i 1.41166i 0.708379 + 0.705832i \(0.249427\pi\)
−0.708379 + 0.705832i \(0.750573\pi\)
\(912\) −716.938 243.723i −0.786116 0.267240i
\(913\) 36.3201 0.0397810
\(914\) −62.9171 + 766.280i −0.0688371 + 0.838381i
\(915\) 389.241i 0.425400i
\(916\) 1411.41 + 233.347i 1.54084 + 0.254746i
\(917\) −642.046 −0.700159
\(918\) 429.633 + 35.2760i 0.468010 + 0.0384270i
\(919\) 1618.74i 1.76142i 0.473659 + 0.880708i \(0.342933\pi\)
−0.473659 + 0.880708i \(0.657067\pi\)
\(920\) −707.617 177.500i −0.769149 0.192934i
\(921\) −546.063 −0.592902
\(922\) 7.86889 95.8368i 0.00853459 0.103944i
\(923\) 939.863i 1.01827i
\(924\) −22.8507 + 138.214i −0.0247302 + 0.149582i
\(925\) 46.0583 0.0497927
\(926\) −124.143 10.1930i −0.134064 0.0110076i
\(927\) 764.579i 0.824788i
\(928\) −237.356 + 546.681i −0.255771 + 0.589096i
\(929\) −551.019 −0.593131 −0.296566 0.955012i \(-0.595841\pi\)
−0.296566 + 0.955012i \(0.595841\pi\)
\(930\) −36.2124 + 441.038i −0.0389380 + 0.474234i
\(931\) 212.327i 0.228063i
\(932\) 1587.67 + 262.489i 1.70351 + 0.281640i
\(933\) −538.205 −0.576854
\(934\) 715.533 + 58.7504i 0.766096 + 0.0629020i
\(935\) 258.814i 0.276807i
\(936\) −237.293 + 945.988i −0.253518 + 1.01067i
\(937\) −1710.84 −1.82587 −0.912934 0.408108i \(-0.866189\pi\)
−0.912934 + 0.408108i \(0.866189\pi\)
\(938\) 13.8925 169.200i 0.0148108 0.180384i
\(939\) 439.249i 0.467784i
\(940\) 116.582 705.150i 0.124023 0.750160i
\(941\) 32.9788 0.0350466 0.0175233 0.999846i \(-0.494422\pi\)
0.0175233 + 0.999846i \(0.494422\pi\)
\(942\) −316.431 25.9813i −0.335914 0.0275810i
\(943\) 1001.63i 1.06217i
\(944\) −197.386 + 580.632i −0.209095 + 0.615076i
\(945\) 220.876 0.233731
\(946\) −70.5581 + 859.342i −0.0745858 + 0.908395i
\(947\) 1186.26i 1.25265i 0.779560 + 0.626327i \(0.215443\pi\)
−0.779560 + 0.626327i \(0.784557\pi\)
\(948\) 245.620 + 40.6081i 0.259093 + 0.0428355i
\(949\) 101.896 0.107372
\(950\) 797.131 + 65.4502i 0.839085 + 0.0688950i
\(951\) 819.461i 0.861684i
\(952\) 182.200 + 45.7033i 0.191387 + 0.0480077i
\(953\) 572.985 0.601244 0.300622 0.953743i \(-0.402806\pi\)
0.300622 + 0.953743i \(0.402806\pi\)
\(954\) −16.5279 + 201.296i −0.0173248 + 0.211003i
\(955\) 548.852i 0.574715i
\(956\) 157.553 952.966i 0.164804 0.996827i
\(957\) 246.537 0.257615
\(958\) −392.169 32.1999i −0.409362 0.0336116i
\(959\) 715.833i 0.746437i
\(960\) 162.010 302.614i 0.168761 0.315223i
\(961\) −740.921 −0.770990
\(962\) −10.6166 + 129.301i −0.0110359 + 0.134409i
\(963\) 249.117i 0.258688i
\(964\) 460.463 + 76.1278i 0.477658 + 0.0789708i
\(965\) 365.932 0.379204
\(966\) 218.298 + 17.9238i 0.225981 + 0.0185547i
\(967\) 717.087i 0.741558i −0.928721 0.370779i \(-0.879091\pi\)
0.928721 0.370779i \(-0.120909\pi\)
\(968\) 95.4209 380.404i 0.0985753 0.392979i
\(969\) 420.020 0.433457
\(970\) 18.0125 219.378i 0.0185696 0.226163i
\(971\) 675.604i 0.695782i −0.937535 0.347891i \(-0.886898\pi\)
0.937535 0.347891i \(-0.113102\pi\)
\(972\) 164.192 993.121i 0.168922 1.02173i
\(973\) −41.5246 −0.0426769
\(974\) −977.114 80.2281i −1.00320 0.0823697i
\(975\) 381.971i 0.391765i
\(976\) −1099.40 373.741i −1.12643 0.382931i
\(977\) 582.678 0.596395 0.298197 0.954504i \(-0.403615\pi\)
0.298197 + 0.954504i \(0.403615\pi\)
\(978\) −17.5135 + 213.300i −0.0179074 + 0.218098i
\(979\) 1051.20i 1.07375i
\(980\) 94.9587 + 15.6994i 0.0968966 + 0.0160198i
\(981\) 579.277 0.590496
\(982\) 1698.54 + 139.462i 1.72968 + 0.142019i
\(983\) 448.087i 0.455837i −0.973680 0.227918i \(-0.926808\pi\)
0.973680 0.227918i \(-0.0731919\pi\)
\(984\) 457.112 + 114.663i 0.464545 + 0.116527i
\(985\) −611.406 −0.620716
\(986\) 27.0519 329.470i 0.0274360 0.334149i
\(987\) 214.583i 0.217410i
\(988\) −367.482 + 2222.73i −0.371946 + 2.24973i
\(989\) 1348.11 1.36311
\(990\) 381.653 + 31.3364i 0.385508 + 0.0316530i
\(991\) 872.154i 0.880075i 0.897979 + 0.440037i \(0.145035\pi\)
−0.897979 + 0.440037i \(0.854965\pi\)
\(992\) 1210.93 + 525.756i 1.22069 + 0.529996i
\(993\) 276.462 0.278410
\(994\) 21.9174 266.937i 0.0220497 0.268548i
\(995\) 919.966i 0.924589i
\(996\) 26.3608 + 4.35820i 0.0264666 + 0.00437570i
\(997\) −1176.24 −1.17978 −0.589888 0.807485i \(-0.700828\pi\)
−0.589888 + 0.807485i \(0.700828\pi\)
\(998\) −1698.16 139.431i −1.70156 0.139710i
\(999\) 84.8441i 0.0849290i
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 28.3.c.a.15.4 yes 6
3.2 odd 2 252.3.g.a.127.3 6
4.3 odd 2 inner 28.3.c.a.15.3 6
7.2 even 3 196.3.g.k.67.6 12
7.3 odd 6 196.3.g.j.79.2 12
7.4 even 3 196.3.g.k.79.2 12
7.5 odd 6 196.3.g.j.67.6 12
7.6 odd 2 196.3.c.g.99.4 6
8.3 odd 2 448.3.d.d.127.4 6
8.5 even 2 448.3.d.d.127.3 6
12.11 even 2 252.3.g.a.127.4 6
16.3 odd 4 1792.3.g.g.127.7 12
16.5 even 4 1792.3.g.g.127.8 12
16.11 odd 4 1792.3.g.g.127.6 12
16.13 even 4 1792.3.g.g.127.5 12
28.3 even 6 196.3.g.j.79.6 12
28.11 odd 6 196.3.g.k.79.6 12
28.19 even 6 196.3.g.j.67.2 12
28.23 odd 6 196.3.g.k.67.2 12
28.27 even 2 196.3.c.g.99.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.3.c.a.15.3 6 4.3 odd 2 inner
28.3.c.a.15.4 yes 6 1.1 even 1 trivial
196.3.c.g.99.3 6 28.27 even 2
196.3.c.g.99.4 6 7.6 odd 2
196.3.g.j.67.2 12 28.19 even 6
196.3.g.j.67.6 12 7.5 odd 6
196.3.g.j.79.2 12 7.3 odd 6
196.3.g.j.79.6 12 28.3 even 6
196.3.g.k.67.2 12 28.23 odd 6
196.3.g.k.67.6 12 7.2 even 3
196.3.g.k.79.2 12 7.4 even 3
196.3.g.k.79.6 12 28.11 odd 6
252.3.g.a.127.3 6 3.2 odd 2
252.3.g.a.127.4 6 12.11 even 2
448.3.d.d.127.3 6 8.5 even 2
448.3.d.d.127.4 6 8.3 odd 2
1792.3.g.g.127.5 12 16.13 even 4
1792.3.g.g.127.6 12 16.11 odd 4
1792.3.g.g.127.7 12 16.3 odd 4
1792.3.g.g.127.8 12 16.5 even 4