Properties

Label 105.3.e.a.34.7
Level $105$
Weight $3$
Character 105.34
Analytic conductor $2.861$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(34,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.34");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.e (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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 72 x^{14} - 292 x^{13} + 1148 x^{12} - 2304 x^{11} + 4996 x^{10} - 4490 x^{9} + 9786 x^{8} - 5744 x^{7} + 8608 x^{6} + 4740 x^{5} + 22841 x^{4} + \cdots + 1849 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.7
Root \(1.36603 - 0.959486i\) of defining polynomial
Character \(\chi\) \(=\) 105.34
Dual form 105.3.e.a.34.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.702393i q^{2} -1.73205 q^{3} +3.50664 q^{4} +(-0.979490 + 4.90312i) q^{5} +1.21658i q^{6} +(3.48021 + 6.07356i) q^{7} -5.27261i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-0.702393i q^{2} -1.73205 q^{3} +3.50664 q^{4} +(-0.979490 + 4.90312i) q^{5} +1.21658i q^{6} +(3.48021 + 6.07356i) q^{7} -5.27261i q^{8} +3.00000 q^{9} +(3.44392 + 0.687987i) q^{10} +5.39422 q^{11} -6.07369 q^{12} +12.5287 q^{13} +(4.26603 - 2.44447i) q^{14} +(1.69653 - 8.49246i) q^{15} +10.3231 q^{16} -8.14665 q^{17} -2.10718i q^{18} +1.94137i q^{19} +(-3.43472 + 17.1935i) q^{20} +(-6.02789 - 10.5197i) q^{21} -3.78886i q^{22} +11.4362i q^{23} +9.13243i q^{24} +(-23.0812 - 9.60512i) q^{25} -8.80004i q^{26} -5.19615 q^{27} +(12.2038 + 21.2978i) q^{28} -44.2627 q^{29} +(-5.96504 - 1.19163i) q^{30} -50.4355i q^{31} -28.3413i q^{32} -9.34307 q^{33} +5.72215i q^{34} +(-33.1882 + 11.1149i) q^{35} +10.5199 q^{36} +41.7759i q^{37} +1.36360 q^{38} -21.7003 q^{39} +(25.8523 + 5.16447i) q^{40} -36.0308i q^{41} +(-7.38897 + 4.23395i) q^{42} +1.13722i q^{43} +18.9156 q^{44} +(-2.93847 + 14.7094i) q^{45} +8.03272 q^{46} +24.3975 q^{47} -17.8802 q^{48} +(-24.7763 + 42.2745i) q^{49} +(-6.74657 + 16.2121i) q^{50} +14.1104 q^{51} +43.9335 q^{52} -88.3754i q^{53} +3.64974i q^{54} +(-5.28359 + 26.4485i) q^{55} +(32.0235 - 18.3498i) q^{56} -3.36255i q^{57} +31.0898i q^{58} +46.9226i q^{59} +(5.94912 - 29.7800i) q^{60} -47.5558i q^{61} -35.4256 q^{62} +(10.4406 + 18.2207i) q^{63} +21.3858 q^{64} +(-12.2717 + 61.4295i) q^{65} +6.56250i q^{66} -104.927i q^{67} -28.5674 q^{68} -19.8081i q^{69} +(7.80701 + 23.3112i) q^{70} +52.7310 q^{71} -15.8178i q^{72} -74.2238 q^{73} +29.3431 q^{74} +(39.9778 + 16.6366i) q^{75} +6.80769i q^{76} +(18.7730 + 32.7621i) q^{77} +15.2421i q^{78} +76.3265 q^{79} +(-10.1114 + 50.6156i) q^{80} +9.00000 q^{81} -25.3078 q^{82} +140.936 q^{83} +(-21.1377 - 36.8889i) q^{84} +(7.97956 - 39.9440i) q^{85} +0.798775 q^{86} +76.6652 q^{87} -28.4416i q^{88} +33.4260i q^{89} +(10.3318 + 2.06396i) q^{90} +(43.6023 + 76.0936i) q^{91} +40.1028i q^{92} +87.3569i q^{93} -17.1366i q^{94} +(-9.51876 - 1.90155i) q^{95} +49.0886i q^{96} -120.963 q^{97} +(29.6933 + 17.4027i) q^{98} +16.1827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 32 q^{4} + 48 q^{9} - 56 q^{11} - 84 q^{14} + 24 q^{15} + 112 q^{16} - 12 q^{21} + 16 q^{25} - 32 q^{29} - 72 q^{30} - 4 q^{35} - 96 q^{36} + 72 q^{39} + 568 q^{44} - 96 q^{46} - 152 q^{49} - 96 q^{50} + 24 q^{51} + 444 q^{56} - 288 q^{60} - 992 q^{64} - 296 q^{65} + 504 q^{70} - 56 q^{71} - 48 q^{74} + 464 q^{79} + 144 q^{81} + 228 q^{84} + 608 q^{85} - 456 q^{86} - 88 q^{91} - 24 q^{95} - 168 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.702393i 0.351196i −0.984462 0.175598i \(-0.943814\pi\)
0.984462 0.175598i \(-0.0561860\pi\)
\(3\) −1.73205 −0.577350
\(4\) 3.50664 0.876661
\(5\) −0.979490 + 4.90312i −0.195898 + 0.980624i
\(6\) 1.21658i 0.202763i
\(7\) 3.48021 + 6.07356i 0.497172 + 0.867652i
\(8\) 5.27261i 0.659077i
\(9\) 3.00000 0.333333
\(10\) 3.44392 + 0.687987i 0.344392 + 0.0687987i
\(11\) 5.39422 0.490384 0.245192 0.969475i \(-0.421149\pi\)
0.245192 + 0.969475i \(0.421149\pi\)
\(12\) −6.07369 −0.506141
\(13\) 12.5287 0.963743 0.481871 0.876242i \(-0.339957\pi\)
0.481871 + 0.876242i \(0.339957\pi\)
\(14\) 4.26603 2.44447i 0.304716 0.174605i
\(15\) 1.69653 8.49246i 0.113102 0.566164i
\(16\) 10.3231 0.645196
\(17\) −8.14665 −0.479215 −0.239607 0.970870i \(-0.577019\pi\)
−0.239607 + 0.970870i \(0.577019\pi\)
\(18\) 2.10718i 0.117065i
\(19\) 1.94137i 0.102177i 0.998694 + 0.0510886i \(0.0162691\pi\)
−0.998694 + 0.0510886i \(0.983731\pi\)
\(20\) −3.43472 + 17.1935i −0.171736 + 0.859675i
\(21\) −6.02789 10.5197i −0.287043 0.500939i
\(22\) 3.78886i 0.172221i
\(23\) 11.4362i 0.497227i 0.968603 + 0.248613i \(0.0799749\pi\)
−0.968603 + 0.248613i \(0.920025\pi\)
\(24\) 9.13243i 0.380518i
\(25\) −23.0812 9.60512i −0.923248 0.384205i
\(26\) 8.80004i 0.338463i
\(27\) −5.19615 −0.192450
\(28\) 12.2038 + 21.2978i 0.435852 + 0.760637i
\(29\) −44.2627 −1.52630 −0.763150 0.646221i \(-0.776348\pi\)
−0.763150 + 0.646221i \(0.776348\pi\)
\(30\) −5.96504 1.19163i −0.198835 0.0397209i
\(31\) 50.4355i 1.62695i −0.581598 0.813476i \(-0.697572\pi\)
0.581598 0.813476i \(-0.302428\pi\)
\(32\) 28.3413i 0.885667i
\(33\) −9.34307 −0.283123
\(34\) 5.72215i 0.168298i
\(35\) −33.1882 + 11.1149i −0.948236 + 0.317568i
\(36\) 10.5199 0.292220
\(37\) 41.7759i 1.12908i 0.825406 + 0.564540i \(0.190946\pi\)
−0.825406 + 0.564540i \(0.809054\pi\)
\(38\) 1.36360 0.0358843
\(39\) −21.7003 −0.556417
\(40\) 25.8523 + 5.16447i 0.646307 + 0.129112i
\(41\) 36.0308i 0.878800i −0.898292 0.439400i \(-0.855191\pi\)
0.898292 0.439400i \(-0.144809\pi\)
\(42\) −7.38897 + 4.23395i −0.175928 + 0.100808i
\(43\) 1.13722i 0.0264470i 0.999913 + 0.0132235i \(0.00420929\pi\)
−0.999913 + 0.0132235i \(0.995791\pi\)
\(44\) 18.9156 0.429900
\(45\) −2.93847 + 14.7094i −0.0652994 + 0.326875i
\(46\) 8.03272 0.174624
\(47\) 24.3975 0.519096 0.259548 0.965730i \(-0.416426\pi\)
0.259548 + 0.965730i \(0.416426\pi\)
\(48\) −17.8802 −0.372504
\(49\) −24.7763 + 42.2745i −0.505639 + 0.862745i
\(50\) −6.74657 + 16.2121i −0.134931 + 0.324241i
\(51\) 14.1104 0.276675
\(52\) 43.9335 0.844876
\(53\) 88.3754i 1.66746i −0.552172 0.833730i \(-0.686201\pi\)
0.552172 0.833730i \(-0.313799\pi\)
\(54\) 3.64974i 0.0675878i
\(55\) −5.28359 + 26.4485i −0.0960652 + 0.480882i
\(56\) 32.0235 18.3498i 0.571849 0.327675i
\(57\) 3.36255i 0.0589921i
\(58\) 31.0898i 0.536031i
\(59\) 46.9226i 0.795298i 0.917538 + 0.397649i \(0.130174\pi\)
−0.917538 + 0.397649i \(0.869826\pi\)
\(60\) 5.94912 29.7800i 0.0991519 0.496334i
\(61\) 47.5558i 0.779604i −0.920899 0.389802i \(-0.872543\pi\)
0.920899 0.389802i \(-0.127457\pi\)
\(62\) −35.4256 −0.571380
\(63\) 10.4406 + 18.2207i 0.165724 + 0.289217i
\(64\) 21.3858 0.334153
\(65\) −12.2717 + 61.4295i −0.188795 + 0.945069i
\(66\) 6.56250i 0.0994319i
\(67\) 104.927i 1.56607i −0.621976 0.783037i \(-0.713670\pi\)
0.621976 0.783037i \(-0.286330\pi\)
\(68\) −28.5674 −0.420109
\(69\) 19.8081i 0.287074i
\(70\) 7.80701 + 23.3112i 0.111529 + 0.333017i
\(71\) 52.7310 0.742690 0.371345 0.928495i \(-0.378897\pi\)
0.371345 + 0.928495i \(0.378897\pi\)
\(72\) 15.8178i 0.219692i
\(73\) −74.2238 −1.01676 −0.508382 0.861131i \(-0.669756\pi\)
−0.508382 + 0.861131i \(0.669756\pi\)
\(74\) 29.3431 0.396529
\(75\) 39.9778 + 16.6366i 0.533037 + 0.221821i
\(76\) 6.80769i 0.0895748i
\(77\) 18.7730 + 32.7621i 0.243805 + 0.425482i
\(78\) 15.2421i 0.195412i
\(79\) 76.3265 0.966158 0.483079 0.875577i \(-0.339518\pi\)
0.483079 + 0.875577i \(0.339518\pi\)
\(80\) −10.1114 + 50.6156i −0.126393 + 0.632695i
\(81\) 9.00000 0.111111
\(82\) −25.3078 −0.308631
\(83\) 140.936 1.69802 0.849010 0.528377i \(-0.177199\pi\)
0.849010 + 0.528377i \(0.177199\pi\)
\(84\) −21.1377 36.8889i −0.251639 0.439154i
\(85\) 7.97956 39.9440i 0.0938772 0.469929i
\(86\) 0.798775 0.00928809
\(87\) 76.6652 0.881210
\(88\) 28.4416i 0.323201i
\(89\) 33.4260i 0.375574i 0.982210 + 0.187787i \(0.0601314\pi\)
−0.982210 + 0.187787i \(0.939869\pi\)
\(90\) 10.3318 + 2.06396i 0.114797 + 0.0229329i
\(91\) 43.6023 + 76.0936i 0.479146 + 0.836193i
\(92\) 40.1028i 0.435900i
\(93\) 87.3569i 0.939322i
\(94\) 17.1366i 0.182305i
\(95\) −9.51876 1.90155i −0.100198 0.0200163i
\(96\) 49.0886i 0.511340i
\(97\) −120.963 −1.24704 −0.623520 0.781807i \(-0.714298\pi\)
−0.623520 + 0.781807i \(0.714298\pi\)
\(98\) 29.6933 + 17.4027i 0.302993 + 0.177579i
\(99\) 16.1827 0.163461
\(100\) −80.9376 33.6817i −0.809376 0.336817i
\(101\) 47.0704i 0.466044i −0.972472 0.233022i \(-0.925139\pi\)
0.972472 0.233022i \(-0.0748613\pi\)
\(102\) 9.91105i 0.0971672i
\(103\) −146.806 −1.42530 −0.712648 0.701522i \(-0.752504\pi\)
−0.712648 + 0.701522i \(0.752504\pi\)
\(104\) 66.0587i 0.635180i
\(105\) 57.4837 19.2515i 0.547464 0.183348i
\(106\) −62.0742 −0.585606
\(107\) 111.640i 1.04337i 0.853139 + 0.521684i \(0.174696\pi\)
−0.853139 + 0.521684i \(0.825304\pi\)
\(108\) −18.2211 −0.168714
\(109\) −75.0358 −0.688402 −0.344201 0.938896i \(-0.611850\pi\)
−0.344201 + 0.938896i \(0.611850\pi\)
\(110\) 18.5773 + 3.71115i 0.168884 + 0.0337378i
\(111\) 72.3580i 0.651874i
\(112\) 35.9266 + 62.6982i 0.320774 + 0.559805i
\(113\) 168.123i 1.48781i −0.668285 0.743905i \(-0.732972\pi\)
0.668285 0.743905i \(-0.267028\pi\)
\(114\) −2.36183 −0.0207178
\(115\) −56.0732 11.2017i −0.487593 0.0974058i
\(116\) −155.214 −1.33805
\(117\) 37.5860 0.321248
\(118\) 32.9581 0.279306
\(119\) −28.3520 49.4792i −0.238252 0.415791i
\(120\) −44.7774 8.94513i −0.373145 0.0745427i
\(121\) −91.9024 −0.759524
\(122\) −33.4029 −0.273794
\(123\) 62.4072i 0.507375i
\(124\) 176.860i 1.42629i
\(125\) 69.7029 103.762i 0.557623 0.830094i
\(126\) 12.7981 7.33342i 0.101572 0.0582017i
\(127\) 109.069i 0.858812i −0.903111 0.429406i \(-0.858723\pi\)
0.903111 0.429406i \(-0.141277\pi\)
\(128\) 128.387i 1.00302i
\(129\) 1.96972i 0.0152692i
\(130\) 43.1476 + 8.61955i 0.331905 + 0.0663042i
\(131\) 185.046i 1.41257i 0.707929 + 0.706284i \(0.249630\pi\)
−0.707929 + 0.706284i \(0.750370\pi\)
\(132\) −32.7628 −0.248203
\(133\) −11.7910 + 6.75636i −0.0886543 + 0.0507997i
\(134\) −73.6999 −0.549999
\(135\) 5.08958 25.4774i 0.0377006 0.188721i
\(136\) 42.9541i 0.315839i
\(137\) 161.715i 1.18040i 0.807257 + 0.590200i \(0.200951\pi\)
−0.807257 + 0.590200i \(0.799049\pi\)
\(138\) −13.9131 −0.100819
\(139\) 233.420i 1.67928i 0.543143 + 0.839640i \(0.317234\pi\)
−0.543143 + 0.839640i \(0.682766\pi\)
\(140\) −116.379 + 38.9759i −0.831281 + 0.278399i
\(141\) −42.2577 −0.299700
\(142\) 37.0379i 0.260830i
\(143\) 67.5823 0.472604
\(144\) 30.9694 0.215065
\(145\) 43.3549 217.025i 0.298999 1.49673i
\(146\) 52.1343i 0.357084i
\(147\) 42.9139 73.2216i 0.291931 0.498106i
\(148\) 146.493i 0.989820i
\(149\) −18.6015 −0.124842 −0.0624210 0.998050i \(-0.519882\pi\)
−0.0624210 + 0.998050i \(0.519882\pi\)
\(150\) 11.6854 28.0801i 0.0779026 0.187201i
\(151\) 82.0432 0.543333 0.271666 0.962392i \(-0.412425\pi\)
0.271666 + 0.962392i \(0.412425\pi\)
\(152\) 10.2361 0.0673427
\(153\) −24.4399 −0.159738
\(154\) 23.0119 13.1860i 0.149428 0.0856235i
\(155\) 247.292 + 49.4011i 1.59543 + 0.318717i
\(156\) −76.0951 −0.487789
\(157\) 134.069 0.853940 0.426970 0.904266i \(-0.359581\pi\)
0.426970 + 0.904266i \(0.359581\pi\)
\(158\) 53.6112i 0.339311i
\(159\) 153.071i 0.962709i
\(160\) 138.961 + 27.7601i 0.868507 + 0.173500i
\(161\) −69.4586 + 39.8004i −0.431420 + 0.247207i
\(162\) 6.32154i 0.0390218i
\(163\) 10.1526i 0.0622859i 0.999515 + 0.0311429i \(0.00991471\pi\)
−0.999515 + 0.0311429i \(0.990085\pi\)
\(164\) 126.347i 0.770410i
\(165\) 9.15144 45.8102i 0.0554633 0.277638i
\(166\) 98.9921i 0.596338i
\(167\) −292.034 −1.74871 −0.874353 0.485290i \(-0.838714\pi\)
−0.874353 + 0.485290i \(0.838714\pi\)
\(168\) −55.4664 + 31.7828i −0.330157 + 0.189183i
\(169\) −12.0329 −0.0712003
\(170\) −28.0564 5.60479i −0.165038 0.0329693i
\(171\) 5.82410i 0.0340591i
\(172\) 3.98783i 0.0231850i
\(173\) 193.657 1.11941 0.559704 0.828693i \(-0.310915\pi\)
0.559704 + 0.828693i \(0.310915\pi\)
\(174\) 53.8491i 0.309478i
\(175\) −21.9900 173.613i −0.125657 0.992074i
\(176\) 55.6853 0.316394
\(177\) 81.2723i 0.459165i
\(178\) 23.4782 0.131900
\(179\) 203.588 1.13736 0.568682 0.822557i \(-0.307453\pi\)
0.568682 + 0.822557i \(0.307453\pi\)
\(180\) −10.3042 + 51.5805i −0.0572454 + 0.286558i
\(181\) 292.439i 1.61569i 0.589396 + 0.807844i \(0.299366\pi\)
−0.589396 + 0.807844i \(0.700634\pi\)
\(182\) 53.4476 30.6259i 0.293668 0.168274i
\(183\) 82.3691i 0.450105i
\(184\) 60.2988 0.327711
\(185\) −204.832 40.9191i −1.10720 0.221184i
\(186\) 61.3589 0.329886
\(187\) −43.9448 −0.234999
\(188\) 85.5534 0.455071
\(189\) −18.0837 31.5592i −0.0956809 0.166980i
\(190\) −1.33564 + 6.68591i −0.00702966 + 0.0351890i
\(191\) 81.7472 0.427996 0.213998 0.976834i \(-0.431351\pi\)
0.213998 + 0.976834i \(0.431351\pi\)
\(192\) −37.0412 −0.192923
\(193\) 270.371i 1.40089i 0.713709 + 0.700443i \(0.247014\pi\)
−0.713709 + 0.700443i \(0.752986\pi\)
\(194\) 84.9635i 0.437956i
\(195\) 21.2552 106.399i 0.109001 0.545636i
\(196\) −86.8818 + 148.242i −0.443274 + 0.756335i
\(197\) 40.8502i 0.207361i 0.994611 + 0.103681i \(0.0330620\pi\)
−0.994611 + 0.103681i \(0.966938\pi\)
\(198\) 11.3666i 0.0574070i
\(199\) 12.5172i 0.0629007i −0.999505 0.0314503i \(-0.989987\pi\)
0.999505 0.0314503i \(-0.0100126\pi\)
\(200\) −50.6441 + 121.698i −0.253220 + 0.608491i
\(201\) 181.739i 0.904173i
\(202\) −33.0619 −0.163673
\(203\) −154.043 268.832i −0.758834 1.32430i
\(204\) 49.4802 0.242550
\(205\) 176.663 + 35.2918i 0.861772 + 0.172155i
\(206\) 103.115i 0.500559i
\(207\) 34.3087i 0.165742i
\(208\) 129.335 0.621803
\(209\) 10.4722i 0.0501061i
\(210\) −13.5221 40.3762i −0.0643911 0.192267i
\(211\) 22.0149 0.104336 0.0521681 0.998638i \(-0.483387\pi\)
0.0521681 + 0.998638i \(0.483387\pi\)
\(212\) 309.901i 1.46180i
\(213\) −91.3327 −0.428792
\(214\) 78.4154 0.366427
\(215\) −5.57593 1.11390i −0.0259346 0.00518091i
\(216\) 27.3973i 0.126839i
\(217\) 306.323 175.526i 1.41163 0.808876i
\(218\) 52.7046i 0.241764i
\(219\) 128.559 0.587029
\(220\) −18.5277 + 92.7456i −0.0842167 + 0.421571i
\(221\) −102.067 −0.461840
\(222\) −50.8238 −0.228936
\(223\) 109.535 0.491190 0.245595 0.969373i \(-0.421017\pi\)
0.245595 + 0.969373i \(0.421017\pi\)
\(224\) 172.133 98.6337i 0.768451 0.440329i
\(225\) −69.2436 28.8154i −0.307749 0.128068i
\(226\) −118.088 −0.522513
\(227\) 369.492 1.62772 0.813859 0.581062i \(-0.197363\pi\)
0.813859 + 0.581062i \(0.197363\pi\)
\(228\) 11.7913i 0.0517161i
\(229\) 362.391i 1.58249i −0.611498 0.791246i \(-0.709433\pi\)
0.611498 0.791246i \(-0.290567\pi\)
\(230\) −7.86797 + 39.3854i −0.0342086 + 0.171241i
\(231\) −32.5158 56.7457i −0.140761 0.245652i
\(232\) 233.380i 1.00595i
\(233\) 28.1243i 0.120705i −0.998177 0.0603525i \(-0.980778\pi\)
0.998177 0.0603525i \(-0.0192225\pi\)
\(234\) 26.4001i 0.112821i
\(235\) −23.8971 + 119.624i −0.101690 + 0.509038i
\(236\) 164.541i 0.697207i
\(237\) −132.201 −0.557812
\(238\) −34.7538 + 19.9143i −0.146024 + 0.0836733i
\(239\) −223.554 −0.935372 −0.467686 0.883895i \(-0.654912\pi\)
−0.467686 + 0.883895i \(0.654912\pi\)
\(240\) 17.5135 87.6687i 0.0729728 0.365286i
\(241\) 139.669i 0.579538i −0.957097 0.289769i \(-0.906421\pi\)
0.957097 0.289769i \(-0.0935785\pi\)
\(242\) 64.5516i 0.266742i
\(243\) −15.5885 −0.0641500
\(244\) 166.761i 0.683448i
\(245\) −183.009 162.889i −0.746975 0.664852i
\(246\) 43.8343 0.178188
\(247\) 24.3227i 0.0984726i
\(248\) −265.927 −1.07229
\(249\) −244.108 −0.980352
\(250\) −72.8815 48.9588i −0.291526 0.195835i
\(251\) 332.508i 1.32473i −0.749180 0.662367i \(-0.769552\pi\)
0.749180 0.662367i \(-0.230448\pi\)
\(252\) 36.6115 + 63.8935i 0.145284 + 0.253546i
\(253\) 61.6895i 0.243832i
\(254\) −76.6094 −0.301612
\(255\) −13.8210 + 69.1850i −0.0542000 + 0.271314i
\(256\) −4.63472 −0.0181044
\(257\) −427.288 −1.66260 −0.831300 0.555824i \(-0.812403\pi\)
−0.831300 + 0.555824i \(0.812403\pi\)
\(258\) −1.38352 −0.00536248
\(259\) −253.729 + 145.389i −0.979648 + 0.561347i
\(260\) −43.0325 + 215.411i −0.165509 + 0.828506i
\(261\) −132.788 −0.508767
\(262\) 129.975 0.496089
\(263\) 175.650i 0.667872i 0.942596 + 0.333936i \(0.108377\pi\)
−0.942596 + 0.333936i \(0.891623\pi\)
\(264\) 49.2624i 0.186600i
\(265\) 433.315 + 86.5628i 1.63515 + 0.326652i
\(266\) 4.74562 + 8.28193i 0.0178407 + 0.0311351i
\(267\) 57.8956i 0.216837i
\(268\) 367.941i 1.37292i
\(269\) 283.803i 1.05503i 0.849546 + 0.527515i \(0.176876\pi\)
−0.849546 + 0.527515i \(0.823124\pi\)
\(270\) −17.8951 3.57488i −0.0662782 0.0132403i
\(271\) 230.603i 0.850934i −0.904974 0.425467i \(-0.860110\pi\)
0.904974 0.425467i \(-0.139890\pi\)
\(272\) −84.0989 −0.309187
\(273\) −75.5214 131.798i −0.276635 0.482776i
\(274\) 113.587 0.414552
\(275\) −124.505 51.8122i −0.452746 0.188408i
\(276\) 69.4600i 0.251667i
\(277\) 365.707i 1.32024i 0.751160 + 0.660121i \(0.229495\pi\)
−0.751160 + 0.660121i \(0.770505\pi\)
\(278\) 163.952 0.589757
\(279\) 151.307i 0.542318i
\(280\) 58.6045 + 174.989i 0.209302 + 0.624960i
\(281\) −308.169 −1.09669 −0.548343 0.836254i \(-0.684741\pi\)
−0.548343 + 0.836254i \(0.684741\pi\)
\(282\) 29.6815i 0.105254i
\(283\) −27.0678 −0.0956458 −0.0478229 0.998856i \(-0.515228\pi\)
−0.0478229 + 0.998856i \(0.515228\pi\)
\(284\) 184.909 0.651087
\(285\) 16.4870 + 3.29358i 0.0578491 + 0.0115564i
\(286\) 47.4694i 0.165977i
\(287\) 218.835 125.395i 0.762492 0.436915i
\(288\) 85.0240i 0.295222i
\(289\) −222.632 −0.770353
\(290\) −152.437 30.4522i −0.525645 0.105007i
\(291\) 209.514 0.719979
\(292\) −260.277 −0.891358
\(293\) −178.392 −0.608845 −0.304423 0.952537i \(-0.598464\pi\)
−0.304423 + 0.952537i \(0.598464\pi\)
\(294\) −51.4303 30.1424i −0.174933 0.102525i
\(295\) −230.067 45.9602i −0.779888 0.155797i
\(296\) 220.268 0.744150
\(297\) −28.0292 −0.0943744
\(298\) 13.0655i 0.0438441i
\(299\) 143.280i 0.479199i
\(300\) 140.188 + 58.3385i 0.467293 + 0.194462i
\(301\) −6.90698 + 3.95776i −0.0229468 + 0.0131487i
\(302\) 57.6266i 0.190816i
\(303\) 81.5283i 0.269070i
\(304\) 20.0410i 0.0659243i
\(305\) 233.172 + 46.5805i 0.764499 + 0.152723i
\(306\) 17.1664i 0.0560995i
\(307\) −385.291 −1.25502 −0.627510 0.778609i \(-0.715926\pi\)
−0.627510 + 0.778609i \(0.715926\pi\)
\(308\) 65.8303 + 114.885i 0.213735 + 0.373004i
\(309\) 254.275 0.822895
\(310\) 34.6990 173.696i 0.111932 0.560309i
\(311\) 118.862i 0.382192i −0.981571 0.191096i \(-0.938796\pi\)
0.981571 0.191096i \(-0.0612042\pi\)
\(312\) 114.417i 0.366721i
\(313\) 171.117 0.546701 0.273350 0.961915i \(-0.411868\pi\)
0.273350 + 0.961915i \(0.411868\pi\)
\(314\) 94.1688i 0.299901i
\(315\) −99.5647 + 33.3446i −0.316079 + 0.105856i
\(316\) 267.650 0.846993
\(317\) 149.801i 0.472557i 0.971685 + 0.236279i \(0.0759278\pi\)
−0.971685 + 0.236279i \(0.924072\pi\)
\(318\) 107.516 0.338100
\(319\) −238.763 −0.748473
\(320\) −20.9472 + 104.857i −0.0654599 + 0.327678i
\(321\) 193.367i 0.602389i
\(322\) 27.9555 + 48.7872i 0.0868184 + 0.151513i
\(323\) 15.8156i 0.0489648i
\(324\) 31.5598 0.0974068
\(325\) −289.176 120.339i −0.889773 0.370274i
\(326\) 7.13111 0.0218746
\(327\) 129.966 0.397449
\(328\) −189.976 −0.579196
\(329\) 84.9084 + 148.180i 0.258080 + 0.450395i
\(330\) −32.1768 6.42791i −0.0975053 0.0194785i
\(331\) 278.204 0.840497 0.420248 0.907409i \(-0.361943\pi\)
0.420248 + 0.907409i \(0.361943\pi\)
\(332\) 494.211 1.48859
\(333\) 125.328i 0.376360i
\(334\) 205.123i 0.614139i
\(335\) 514.469 + 102.775i 1.53573 + 0.306791i
\(336\) −62.2268 108.596i −0.185199 0.323204i
\(337\) 346.170i 1.02721i −0.858027 0.513605i \(-0.828310\pi\)
0.858027 0.513605i \(-0.171690\pi\)
\(338\) 8.45179i 0.0250053i
\(339\) 291.197i 0.858987i
\(340\) 27.9815 140.069i 0.0822985 0.411969i
\(341\) 272.061i 0.797832i
\(342\) 4.09081 0.0119614
\(343\) −342.984 3.35656i −0.999952 0.00978589i
\(344\) 5.99612 0.0174306
\(345\) 97.1216 + 19.4019i 0.281512 + 0.0562373i
\(346\) 136.024i 0.393132i
\(347\) 83.7750i 0.241426i −0.992687 0.120713i \(-0.961482\pi\)
0.992687 0.120713i \(-0.0385182\pi\)
\(348\) 268.838 0.772522
\(349\) 304.482i 0.872443i 0.899839 + 0.436221i \(0.143684\pi\)
−0.899839 + 0.436221i \(0.856316\pi\)
\(350\) −121.944 + 15.4456i −0.348413 + 0.0441304i
\(351\) −65.1008 −0.185472
\(352\) 152.880i 0.434317i
\(353\) 188.542 0.534113 0.267056 0.963681i \(-0.413949\pi\)
0.267056 + 0.963681i \(0.413949\pi\)
\(354\) −57.0851 −0.161257
\(355\) −51.6495 + 258.546i −0.145491 + 0.728300i
\(356\) 117.213i 0.329251i
\(357\) 49.1071 + 85.7005i 0.137555 + 0.240057i
\(358\) 142.999i 0.399438i
\(359\) −359.444 −1.00124 −0.500619 0.865668i \(-0.666894\pi\)
−0.500619 + 0.865668i \(0.666894\pi\)
\(360\) 77.5568 + 15.4934i 0.215436 + 0.0430373i
\(361\) 357.231 0.989560
\(362\) 205.407 0.567424
\(363\) 159.180 0.438511
\(364\) 152.898 + 266.833i 0.420049 + 0.733058i
\(365\) 72.7015 363.928i 0.199182 0.997064i
\(366\) 57.8555 0.158075
\(367\) −30.8366 −0.0840235 −0.0420117 0.999117i \(-0.513377\pi\)
−0.0420117 + 0.999117i \(0.513377\pi\)
\(368\) 118.058i 0.320809i
\(369\) 108.092i 0.292933i
\(370\) −28.7413 + 143.873i −0.0776792 + 0.388845i
\(371\) 536.754 307.565i 1.44677 0.829015i
\(372\) 306.330i 0.823467i
\(373\) 11.2949i 0.0302813i 0.999885 + 0.0151406i \(0.00481960\pi\)
−0.999885 + 0.0151406i \(0.995180\pi\)
\(374\) 30.8665i 0.0825308i
\(375\) −120.729 + 179.721i −0.321944 + 0.479255i
\(376\) 128.639i 0.342124i
\(377\) −554.552 −1.47096
\(378\) −22.1669 + 12.7018i −0.0586427 + 0.0336028i
\(379\) 292.999 0.773084 0.386542 0.922272i \(-0.373669\pi\)
0.386542 + 0.922272i \(0.373669\pi\)
\(380\) −33.3789 6.66806i −0.0878393 0.0175475i
\(381\) 188.913i 0.495836i
\(382\) 57.4186i 0.150311i
\(383\) −37.2078 −0.0971484 −0.0485742 0.998820i \(-0.515468\pi\)
−0.0485742 + 0.998820i \(0.515468\pi\)
\(384\) 222.372i 0.579094i
\(385\) −179.025 + 59.9561i −0.464999 + 0.155730i
\(386\) 189.907 0.491986
\(387\) 3.41166i 0.00881566i
\(388\) −424.174 −1.09323
\(389\) 164.681 0.423345 0.211672 0.977341i \(-0.432109\pi\)
0.211672 + 0.977341i \(0.432109\pi\)
\(390\) −74.7339 14.9295i −0.191625 0.0382808i
\(391\) 93.1669i 0.238278i
\(392\) 222.897 + 130.636i 0.568615 + 0.333255i
\(393\) 320.510i 0.815546i
\(394\) 28.6929 0.0728245
\(395\) −74.7610 + 374.238i −0.189268 + 0.947438i
\(396\) 56.7469 0.143300
\(397\) 149.521 0.376627 0.188314 0.982109i \(-0.439698\pi\)
0.188314 + 0.982109i \(0.439698\pi\)
\(398\) −8.79202 −0.0220905
\(399\) 20.4226 11.7024i 0.0511846 0.0293292i
\(400\) −238.270 99.1549i −0.595676 0.247887i
\(401\) 439.691 1.09649 0.548244 0.836319i \(-0.315297\pi\)
0.548244 + 0.836319i \(0.315297\pi\)
\(402\) 127.652 0.317542
\(403\) 631.889i 1.56796i
\(404\) 165.059i 0.408562i
\(405\) −8.81541 + 44.1281i −0.0217665 + 0.108958i
\(406\) −188.826 + 108.199i −0.465088 + 0.266500i
\(407\) 225.349i 0.553682i
\(408\) 74.3987i 0.182350i
\(409\) 252.435i 0.617200i −0.951192 0.308600i \(-0.900139\pi\)
0.951192 0.308600i \(-0.0998605\pi\)
\(410\) 24.7887 124.087i 0.0604603 0.302651i
\(411\) 280.098i 0.681505i
\(412\) −514.795 −1.24950
\(413\) −284.987 + 163.300i −0.690042 + 0.395400i
\(414\) 24.0982 0.0582081
\(415\) −138.045 + 691.024i −0.332639 + 1.66512i
\(416\) 355.079i 0.853555i
\(417\) 404.295i 0.969533i
\(418\) 7.35558 0.0175971
\(419\) 107.610i 0.256826i −0.991721 0.128413i \(-0.959012\pi\)
0.991721 0.128413i \(-0.0409884\pi\)
\(420\) 201.575 67.5083i 0.479940 0.160734i
\(421\) −202.537 −0.481085 −0.240543 0.970639i \(-0.577325\pi\)
−0.240543 + 0.970639i \(0.577325\pi\)
\(422\) 15.4631i 0.0366425i
\(423\) 73.1925 0.173032
\(424\) −465.969 −1.09898
\(425\) 188.034 + 78.2495i 0.442434 + 0.184117i
\(426\) 64.1514i 0.150590i
\(427\) 288.833 165.504i 0.676425 0.387598i
\(428\) 391.483i 0.914681i
\(429\) −117.056 −0.272858
\(430\) −0.782393 + 3.91649i −0.00181952 + 0.00910812i
\(431\) −797.330 −1.84995 −0.924977 0.380023i \(-0.875916\pi\)
−0.924977 + 0.380023i \(0.875916\pi\)
\(432\) −53.6406 −0.124168
\(433\) 707.252 1.63338 0.816689 0.577079i \(-0.195807\pi\)
0.816689 + 0.577079i \(0.195807\pi\)
\(434\) −123.288 215.159i −0.284074 0.495759i
\(435\) −75.0929 + 375.899i −0.172627 + 0.864136i
\(436\) −263.124 −0.603495
\(437\) −22.2019 −0.0508053
\(438\) 90.2992i 0.206163i
\(439\) 260.969i 0.594463i 0.954806 + 0.297231i \(0.0960632\pi\)
−0.954806 + 0.297231i \(0.903937\pi\)
\(440\) 139.453 + 27.8583i 0.316938 + 0.0633144i
\(441\) −74.3290 + 126.824i −0.168546 + 0.287582i
\(442\) 71.6908i 0.162196i
\(443\) 690.031i 1.55763i 0.627253 + 0.778816i \(0.284179\pi\)
−0.627253 + 0.778816i \(0.715821\pi\)
\(444\) 253.734i 0.571473i
\(445\) −163.892 32.7405i −0.368297 0.0735741i
\(446\) 76.9368i 0.172504i
\(447\) 32.2187 0.0720776
\(448\) 74.4269 + 129.888i 0.166131 + 0.289928i
\(449\) 118.832 0.264659 0.132329 0.991206i \(-0.457754\pi\)
0.132329 + 0.991206i \(0.457754\pi\)
\(450\) −20.2397 + 48.6362i −0.0449771 + 0.108080i
\(451\) 194.358i 0.430949i
\(452\) 589.546i 1.30430i
\(453\) −142.103 −0.313693
\(454\) 259.529i 0.571649i
\(455\) −415.804 + 139.254i −0.913855 + 0.306054i
\(456\) −17.7294 −0.0388803
\(457\) 363.943i 0.796375i 0.917304 + 0.398187i \(0.130361\pi\)
−0.917304 + 0.398187i \(0.869639\pi\)
\(458\) −254.541 −0.555766
\(459\) 42.3312 0.0922249
\(460\) −196.629 39.2803i −0.427454 0.0853919i
\(461\) 376.970i 0.817722i 0.912597 + 0.408861i \(0.134074\pi\)
−0.912597 + 0.408861i \(0.865926\pi\)
\(462\) −39.8578 + 22.8389i −0.0862722 + 0.0494348i
\(463\) 206.801i 0.446654i 0.974744 + 0.223327i \(0.0716918\pi\)
−0.974744 + 0.223327i \(0.928308\pi\)
\(464\) −456.930 −0.984762
\(465\) −428.322 85.5653i −0.921122 0.184011i
\(466\) −19.7543 −0.0423912
\(467\) −108.098 −0.231473 −0.115736 0.993280i \(-0.536923\pi\)
−0.115736 + 0.993280i \(0.536923\pi\)
\(468\) 131.801 0.281625
\(469\) 637.280 365.167i 1.35881 0.778608i
\(470\) 84.0230 + 16.7852i 0.178772 + 0.0357131i
\(471\) −232.214 −0.493022
\(472\) 247.405 0.524162
\(473\) 6.13442i 0.0129692i
\(474\) 92.8573i 0.195901i
\(475\) 18.6471 44.8091i 0.0392570 0.0943350i
\(476\) −99.4204 173.506i −0.208866 0.364508i
\(477\) 265.126i 0.555820i
\(478\) 157.023i 0.328499i
\(479\) 438.982i 0.916456i −0.888835 0.458228i \(-0.848484\pi\)
0.888835 0.458228i \(-0.151516\pi\)
\(480\) −240.688 48.0819i −0.501433 0.100171i
\(481\) 523.396i 1.08814i
\(482\) −98.1023 −0.203532
\(483\) 120.306 68.9363i 0.249080 0.142725i
\(484\) −322.269 −0.665845
\(485\) 118.482 593.096i 0.244293 1.22288i
\(486\) 10.9492i 0.0225293i
\(487\) 439.990i 0.903471i −0.892152 0.451735i \(-0.850805\pi\)
0.892152 0.451735i \(-0.149195\pi\)
\(488\) −250.744 −0.513819
\(489\) 17.5848i 0.0359608i
\(490\) −114.412 + 128.544i −0.233494 + 0.262335i
\(491\) 111.892 0.227886 0.113943 0.993487i \(-0.463652\pi\)
0.113943 + 0.993487i \(0.463652\pi\)
\(492\) 218.840i 0.444796i
\(493\) 360.593 0.731425
\(494\) 17.0841 0.0345832
\(495\) −15.8508 + 79.3456i −0.0320217 + 0.160294i
\(496\) 520.653i 1.04970i
\(497\) 183.515 + 320.265i 0.369245 + 0.644396i
\(498\) 171.459i 0.344296i
\(499\) 78.8110 0.157938 0.0789689 0.996877i \(-0.474837\pi\)
0.0789689 + 0.996877i \(0.474837\pi\)
\(500\) 244.423 363.856i 0.488846 0.727711i
\(501\) 505.818 1.00962
\(502\) −233.551 −0.465241
\(503\) 37.3888 0.0743316 0.0371658 0.999309i \(-0.488167\pi\)
0.0371658 + 0.999309i \(0.488167\pi\)
\(504\) 96.0706 55.0493i 0.190616 0.109225i
\(505\) 230.792 + 46.1050i 0.457014 + 0.0912970i
\(506\) 43.3303 0.0856329
\(507\) 20.8415 0.0411075
\(508\) 382.467i 0.752887i
\(509\) 114.044i 0.224055i −0.993705 0.112027i \(-0.964266\pi\)
0.993705 0.112027i \(-0.0357345\pi\)
\(510\) 48.5951 + 9.70778i 0.0952845 + 0.0190349i
\(511\) −258.314 450.803i −0.505507 0.882198i
\(512\) 510.291i 0.996662i
\(513\) 10.0876i 0.0196640i
\(514\) 300.124i 0.583899i
\(515\) 143.795 719.805i 0.279213 1.39768i
\(516\) 6.90712i 0.0133859i
\(517\) 131.606 0.254556
\(518\) 102.120 + 178.217i 0.197143 + 0.344049i
\(519\) −335.425 −0.646290
\(520\) 323.894 + 64.7039i 0.622873 + 0.124431i
\(521\) 921.332i 1.76839i 0.467116 + 0.884196i \(0.345293\pi\)
−0.467116 + 0.884196i \(0.654707\pi\)
\(522\) 93.2694i 0.178677i
\(523\) −21.3685 −0.0408575 −0.0204287 0.999791i \(-0.506503\pi\)
−0.0204287 + 0.999791i \(0.506503\pi\)
\(524\) 648.892i 1.23834i
\(525\) 38.0879 + 300.706i 0.0725483 + 0.572774i
\(526\) 123.376 0.234554
\(527\) 410.881i 0.779660i
\(528\) −96.4497 −0.182670
\(529\) 398.213 0.752765
\(530\) 60.8011 304.358i 0.114719 0.574260i
\(531\) 140.768i 0.265099i
\(532\) −41.3469 + 23.6922i −0.0777198 + 0.0445341i
\(533\) 451.417i 0.846937i
\(534\) −40.6655 −0.0761525
\(535\) −547.387 109.351i −1.02315 0.204394i
\(536\) −553.239 −1.03216
\(537\) −352.625 −0.656658
\(538\) 199.341 0.370523
\(539\) −133.649 + 228.038i −0.247957 + 0.423076i
\(540\) 17.8473 89.3401i 0.0330506 0.165445i
\(541\) −352.307 −0.651215 −0.325607 0.945505i \(-0.605569\pi\)
−0.325607 + 0.945505i \(0.605569\pi\)
\(542\) −161.974 −0.298845
\(543\) 506.520i 0.932818i
\(544\) 230.887i 0.424425i
\(545\) 73.4969 367.910i 0.134857 0.675064i
\(546\) −92.5739 + 53.0457i −0.169549 + 0.0971533i
\(547\) 424.917i 0.776814i 0.921488 + 0.388407i \(0.126974\pi\)
−0.921488 + 0.388407i \(0.873026\pi\)
\(548\) 567.077i 1.03481i
\(549\) 142.668i 0.259868i
\(550\) −36.3925 + 87.4515i −0.0661681 + 0.159003i
\(551\) 85.9302i 0.155953i
\(552\) −104.441 −0.189204
\(553\) 265.632 + 463.574i 0.480347 + 0.838289i
\(554\) 256.870 0.463664
\(555\) 354.780 + 70.8740i 0.639244 + 0.127701i
\(556\) 818.521i 1.47216i
\(557\) 130.707i 0.234662i −0.993093 0.117331i \(-0.962566\pi\)
0.993093 0.117331i \(-0.0374338\pi\)
\(558\) −106.277 −0.190460
\(559\) 14.2478i 0.0254881i
\(560\) −342.607 + 114.740i −0.611798 + 0.204894i
\(561\) 76.1147 0.135677
\(562\) 216.455i 0.385152i
\(563\) 30.8033 0.0547129 0.0273564 0.999626i \(-0.491291\pi\)
0.0273564 + 0.999626i \(0.491291\pi\)
\(564\) −148.183 −0.262735
\(565\) 824.325 + 164.674i 1.45898 + 0.291459i
\(566\) 19.0122i 0.0335905i
\(567\) 31.3219 + 54.6621i 0.0552414 + 0.0964058i
\(568\) 278.030i 0.489489i
\(569\) 636.391 1.11844 0.559219 0.829020i \(-0.311101\pi\)
0.559219 + 0.829020i \(0.311101\pi\)
\(570\) 2.31339 11.5803i 0.00405858 0.0203164i
\(571\) 565.901 0.991070 0.495535 0.868588i \(-0.334972\pi\)
0.495535 + 0.868588i \(0.334972\pi\)
\(572\) 236.987 0.414313
\(573\) −141.590 −0.247103
\(574\) −88.0762 153.708i −0.153443 0.267784i
\(575\) 109.846 263.962i 0.191037 0.459064i
\(576\) 64.1573 0.111384
\(577\) 775.389 1.34383 0.671914 0.740629i \(-0.265472\pi\)
0.671914 + 0.740629i \(0.265472\pi\)
\(578\) 156.375i 0.270545i
\(579\) 468.296i 0.808801i
\(580\) 152.030 761.031i 0.262121 1.31212i
\(581\) 490.485 + 855.981i 0.844208 + 1.47329i
\(582\) 147.161i 0.252854i
\(583\) 476.717i 0.817696i
\(584\) 391.354i 0.670126i
\(585\) −36.8151 + 184.289i −0.0629318 + 0.315023i
\(586\) 125.301i 0.213824i
\(587\) −386.248 −0.658003 −0.329001 0.944329i \(-0.606712\pi\)
−0.329001 + 0.944329i \(0.606712\pi\)
\(588\) 150.484 256.762i 0.255925 0.436670i
\(589\) 97.9140 0.166238
\(590\) −32.2821 + 161.597i −0.0547154 + 0.273894i
\(591\) 70.7546i 0.119720i
\(592\) 431.258i 0.728477i
\(593\) −918.373 −1.54869 −0.774345 0.632764i \(-0.781920\pi\)
−0.774345 + 0.632764i \(0.781920\pi\)
\(594\) 19.6875i 0.0331440i
\(595\) 270.373 90.5490i 0.454408 0.152183i
\(596\) −65.2287 −0.109444
\(597\) 21.6805i 0.0363157i
\(598\) 100.639 0.168293
\(599\) −52.1903 −0.0871291 −0.0435645 0.999051i \(-0.513871\pi\)
−0.0435645 + 0.999051i \(0.513871\pi\)
\(600\) 87.7181 210.787i 0.146197 0.351312i
\(601\) 474.802i 0.790020i 0.918677 + 0.395010i \(0.129259\pi\)
−0.918677 + 0.395010i \(0.870741\pi\)
\(602\) 2.77990 + 4.85141i 0.00461778 + 0.00805882i
\(603\) 314.781i 0.522024i
\(604\) 287.696 0.476318
\(605\) 90.0175 450.608i 0.148789 0.744807i
\(606\) 57.2649 0.0944965
\(607\) 187.465 0.308839 0.154420 0.988005i \(-0.450649\pi\)
0.154420 + 0.988005i \(0.450649\pi\)
\(608\) 55.0210 0.0904950
\(609\) 266.811 + 465.631i 0.438113 + 0.764583i
\(610\) 32.7178 163.778i 0.0536357 0.268489i
\(611\) 305.668 0.500275
\(612\) −85.7022 −0.140036
\(613\) 24.8739i 0.0405774i −0.999794 0.0202887i \(-0.993541\pi\)
0.999794 0.0202887i \(-0.00645854\pi\)
\(614\) 270.626i 0.440758i
\(615\) −305.990 61.1272i −0.497544 0.0993938i
\(616\) 172.742 98.9828i 0.280426 0.160686i
\(617\) 154.454i 0.250331i −0.992136 0.125165i \(-0.960054\pi\)
0.992136 0.125165i \(-0.0399461\pi\)
\(618\) 178.601i 0.288998i
\(619\) 305.924i 0.494223i −0.968987 0.247111i \(-0.920519\pi\)
0.968987 0.247111i \(-0.0794813\pi\)
\(620\) 867.164 + 173.232i 1.39865 + 0.279407i
\(621\) 59.4243i 0.0956914i
\(622\) −83.4877 −0.134225
\(623\) −203.015 + 116.330i −0.325867 + 0.186725i
\(624\) −224.015 −0.358998
\(625\) 440.483 + 443.395i 0.704773 + 0.709433i
\(626\) 120.192i 0.191999i
\(627\) 18.1383i 0.0289288i
\(628\) 470.131 0.748616
\(629\) 340.334i 0.541071i
\(630\) 23.4210 + 69.9335i 0.0371762 + 0.111006i
\(631\) −622.718 −0.986875 −0.493438 0.869781i \(-0.664260\pi\)
−0.493438 + 0.869781i \(0.664260\pi\)
\(632\) 402.440i 0.636772i
\(633\) −38.1310 −0.0602386
\(634\) 105.219 0.165960
\(635\) 534.779 + 106.832i 0.842172 + 0.168240i
\(636\) 536.764i 0.843969i
\(637\) −310.414 + 529.643i −0.487306 + 0.831464i
\(638\) 167.705i 0.262861i
\(639\) 158.193 0.247563
\(640\) 629.495 + 125.753i 0.983586 + 0.196490i
\(641\) −915.315 −1.42795 −0.713974 0.700172i \(-0.753107\pi\)
−0.713974 + 0.700172i \(0.753107\pi\)
\(642\) −135.820 −0.211557
\(643\) −232.129 −0.361009 −0.180505 0.983574i \(-0.557773\pi\)
−0.180505 + 0.983574i \(0.557773\pi\)
\(644\) −243.567 + 139.566i −0.378209 + 0.216717i
\(645\) 9.65779 + 1.92932i 0.0149733 + 0.00299120i
\(646\) −11.1088 −0.0171963
\(647\) −267.653 −0.413683 −0.206842 0.978374i \(-0.566318\pi\)
−0.206842 + 0.978374i \(0.566318\pi\)
\(648\) 47.4535i 0.0732307i
\(649\) 253.111i 0.390001i
\(650\) −84.5254 + 203.115i −0.130039 + 0.312485i
\(651\) −530.568 + 304.020i −0.815004 + 0.467005i
\(652\) 35.6016i 0.0546036i
\(653\) 157.117i 0.240608i −0.992737 0.120304i \(-0.961613\pi\)
0.992737 0.120304i \(-0.0383869\pi\)
\(654\) 91.2871i 0.139583i
\(655\) −907.305 181.251i −1.38520 0.276719i
\(656\) 371.951i 0.566998i
\(657\) −222.671 −0.338922
\(658\) 104.080 59.6390i 0.158177 0.0906368i
\(659\) 162.032 0.245876 0.122938 0.992414i \(-0.460768\pi\)
0.122938 + 0.992414i \(0.460768\pi\)
\(660\) 32.0909 160.640i 0.0486225 0.243394i
\(661\) 908.541i 1.37450i 0.726423 + 0.687248i \(0.241181\pi\)
−0.726423 + 0.687248i \(0.758819\pi\)
\(662\) 195.409i 0.295179i
\(663\) 176.784 0.266643
\(664\) 743.099i 1.11912i
\(665\) −21.5781 64.4306i −0.0324482 0.0968881i
\(666\) 88.0293 0.132176
\(667\) 506.198i 0.758917i
\(668\) −1024.06 −1.53302
\(669\) −189.721 −0.283589
\(670\) 72.1883 361.360i 0.107744 0.539343i
\(671\) 256.527i 0.382305i
\(672\) −298.143 + 170.839i −0.443665 + 0.254224i
\(673\) 44.7205i 0.0664495i −0.999448 0.0332247i \(-0.989422\pi\)
0.999448 0.0332247i \(-0.0105777\pi\)
\(674\) −243.147 −0.360753
\(675\) 119.933 + 49.9097i 0.177679 + 0.0739402i
\(676\) −42.1949 −0.0624185
\(677\) 315.654 0.466254 0.233127 0.972446i \(-0.425104\pi\)
0.233127 + 0.972446i \(0.425104\pi\)
\(678\) 204.534 0.301673
\(679\) −420.976 734.676i −0.619994 1.08200i
\(680\) −210.609 42.0731i −0.309720 0.0618723i
\(681\) −639.979 −0.939764
\(682\) −191.093 −0.280196
\(683\) 191.841i 0.280879i 0.990089 + 0.140440i \(0.0448516\pi\)
−0.990089 + 0.140440i \(0.955148\pi\)
\(684\) 20.4231i 0.0298583i
\(685\) −792.908 158.398i −1.15753 0.231238i
\(686\) −2.35762 + 240.909i −0.00343677 + 0.351180i
\(687\) 627.679i 0.913652i
\(688\) 11.7397i 0.0170635i
\(689\) 1107.22i 1.60700i
\(690\) 13.6277 68.2175i 0.0197503 0.0988659i
\(691\) 569.279i 0.823849i 0.911218 + 0.411924i \(0.135143\pi\)
−0.911218 + 0.411924i \(0.864857\pi\)
\(692\) 679.088 0.981341
\(693\) 56.3190 + 98.2864i 0.0812684 + 0.141827i
\(694\) −58.8429 −0.0847881
\(695\) −1144.49 228.633i −1.64674 0.328968i
\(696\) 404.226i 0.580785i
\(697\) 293.530i 0.421134i
\(698\) 213.866 0.306399
\(699\) 48.7127i 0.0696891i
\(700\) −77.1112 608.799i −0.110159 0.869712i
\(701\) −1169.70 −1.66862 −0.834308 0.551298i \(-0.814133\pi\)
−0.834308 + 0.551298i \(0.814133\pi\)
\(702\) 45.7263i 0.0651372i
\(703\) −81.1025 −0.115366
\(704\) 115.360 0.163863
\(705\) 41.3910 207.195i 0.0587107 0.293893i
\(706\) 132.430i 0.187578i
\(707\) 285.885 163.815i 0.404364 0.231704i
\(708\) 284.993i 0.402532i
\(709\) 174.767 0.246499 0.123249 0.992376i \(-0.460669\pi\)
0.123249 + 0.992376i \(0.460669\pi\)
\(710\) 181.601 + 36.2782i 0.255776 + 0.0510961i
\(711\) 228.979 0.322053
\(712\) 176.243 0.247532
\(713\) 576.792 0.808965
\(714\) 60.1954 34.4925i 0.0843073 0.0483088i
\(715\) −66.1963 + 331.364i −0.0925822 + 0.463447i
\(716\) 713.911 0.997083
\(717\) 387.207 0.540037
\(718\) 252.471i 0.351631i
\(719\) 1311.82i 1.82451i −0.409622 0.912255i \(-0.634339\pi\)
0.409622 0.912255i \(-0.365661\pi\)
\(720\) −30.3342 + 151.847i −0.0421309 + 0.210898i
\(721\) −510.914 891.633i −0.708618 1.23666i
\(722\) 250.917i 0.347530i
\(723\) 241.913i 0.334597i
\(724\) 1025.48i 1.41641i
\(725\) 1021.64 + 425.148i 1.40915 + 0.586412i
\(726\) 111.807i 0.154004i
\(727\) −422.239 −0.580796 −0.290398 0.956906i \(-0.593788\pi\)
−0.290398 + 0.956906i \(0.593788\pi\)
\(728\) 401.212 229.898i 0.551115 0.315794i
\(729\) 27.0000 0.0370370
\(730\) −255.621 51.0650i −0.350165 0.0699521i
\(731\) 9.26453i 0.0126738i
\(732\) 288.839i 0.394589i
\(733\) −952.458 −1.29940 −0.649699 0.760192i \(-0.725105\pi\)
−0.649699 + 0.760192i \(0.725105\pi\)
\(734\) 21.6594i 0.0295087i
\(735\) 316.981 + 282.132i 0.431266 + 0.383853i
\(736\) 324.118 0.440378
\(737\) 565.999i 0.767977i
\(738\) −75.9233 −0.102877
\(739\) −19.1678 −0.0259375 −0.0129687 0.999916i \(-0.504128\pi\)
−0.0129687 + 0.999916i \(0.504128\pi\)
\(740\) −718.275 143.489i −0.970641 0.193904i
\(741\) 42.1282i 0.0568532i
\(742\) −216.031 377.012i −0.291147 0.508102i
\(743\) 1326.11i 1.78480i 0.451246 + 0.892400i \(0.350980\pi\)
−0.451246 + 0.892400i \(0.649020\pi\)
\(744\) 460.599 0.619085
\(745\) 18.2199 91.2052i 0.0244563 0.122423i
\(746\) 7.93346 0.0106347
\(747\) 422.807 0.566006
\(748\) −154.099 −0.206015
\(749\) −678.055 + 388.532i −0.905281 + 0.518734i
\(750\) 126.235 + 84.7991i 0.168313 + 0.113065i
\(751\) −866.144 −1.15332 −0.576660 0.816984i \(-0.695644\pi\)
−0.576660 + 0.816984i \(0.695644\pi\)
\(752\) 251.859 0.334919
\(753\) 575.921i 0.764835i
\(754\) 389.513i 0.516596i
\(755\) −80.3605 + 402.268i −0.106438 + 0.532805i
\(756\) −63.4130 110.667i −0.0838797 0.146385i
\(757\) 1069.24i 1.41248i −0.707975 0.706238i \(-0.750391\pi\)
0.707975 0.706238i \(-0.249609\pi\)
\(758\) 205.800i 0.271504i
\(759\) 106.849i 0.140777i
\(760\) −10.0261 + 50.1888i −0.0131923 + 0.0660378i
\(761\) 371.263i 0.487863i 0.969793 + 0.243931i \(0.0784371\pi\)
−0.969793 + 0.243931i \(0.921563\pi\)
\(762\) 132.691 0.174136
\(763\) −261.140 455.735i −0.342255 0.597293i
\(764\) 286.658 0.375207
\(765\) 23.9387 119.832i 0.0312924 0.156643i
\(766\) 26.1345i 0.0341182i
\(767\) 587.877i 0.766462i
\(768\) 8.02757 0.0104526
\(769\) 388.419i 0.505096i −0.967584 0.252548i \(-0.918731\pi\)
0.967584 0.252548i \(-0.0812686\pi\)
\(770\) 42.1128 + 125.746i 0.0546919 + 0.163306i
\(771\) 740.085 0.959903
\(772\) 948.094i 1.22810i
\(773\) 732.499 0.947605 0.473803 0.880631i \(-0.342881\pi\)
0.473803 + 0.880631i \(0.342881\pi\)
\(774\) 2.39633 0.00309603
\(775\) −484.439 + 1164.11i −0.625083 + 1.50208i
\(776\) 637.791i 0.821895i
\(777\) 439.471 251.821i 0.565600 0.324094i
\(778\) 115.671i 0.148677i
\(779\) 69.9490 0.0897934
\(780\) 74.5344 373.104i 0.0955569 0.478338i
\(781\) 284.443 0.364203
\(782\) −65.4397 −0.0836825
\(783\) 229.996 0.293737
\(784\) −255.769 + 436.405i −0.326236 + 0.556639i
\(785\) −131.319 + 657.354i −0.167285 + 0.837394i
\(786\) −225.124 −0.286417
\(787\) −1123.40 −1.42745 −0.713725 0.700426i \(-0.752993\pi\)
−0.713725 + 0.700426i \(0.752993\pi\)
\(788\) 143.247i 0.181786i
\(789\) 304.235i 0.385596i
\(790\) 262.862 + 52.5116i 0.332737 + 0.0664704i
\(791\) 1021.10 585.101i 1.29090 0.739698i
\(792\) 85.3249i 0.107734i
\(793\) 595.811i 0.751337i
\(794\) 105.022i 0.132270i
\(795\) −750.524 149.931i −0.944056 0.188593i
\(796\) 43.8935i 0.0551426i
\(797\) 1107.27 1.38929 0.694646 0.719351i \(-0.255561\pi\)
0.694646 + 0.719351i \(0.255561\pi\)
\(798\) −8.21966 14.3447i −0.0103003 0.0179758i
\(799\) −198.758 −0.248758
\(800\) −272.222 + 654.152i −0.340278 + 0.817690i
\(801\) 100.278i 0.125191i
\(802\) 308.836i 0.385082i
\(803\) −400.380 −0.498605
\(804\) 637.293i 0.792653i
\(805\) −127.112 379.548i −0.157903 0.471488i
\(806\) −443.835 −0.550663
\(807\) 491.561i 0.609122i
\(808\) −248.184 −0.307158
\(809\) 358.280 0.442867 0.221434 0.975175i \(-0.428926\pi\)
0.221434 + 0.975175i \(0.428926\pi\)
\(810\) 30.9953 + 6.19188i 0.0382657 + 0.00764430i
\(811\) 272.867i 0.336458i −0.985748 0.168229i \(-0.946195\pi\)
0.985748 0.168229i \(-0.0538047\pi\)
\(812\) −540.175 942.699i −0.665240 1.16096i
\(813\) 399.416i 0.491287i
\(814\) 158.283 0.194451
\(815\) −49.7794 9.94437i −0.0610790 0.0122017i
\(816\) 145.664 0.178509
\(817\) −2.20776 −0.00270228
\(818\) −177.308 −0.216759
\(819\) 130.807 + 228.281i 0.159715 + 0.278731i
\(820\) 619.495 + 123.756i 0.755482 + 0.150922i
\(821\) 669.181 0.815080 0.407540 0.913187i \(-0.366387\pi\)
0.407540 + 0.913187i \(0.366387\pi\)
\(822\) −196.739 −0.239342
\(823\) 71.5057i 0.0868843i 0.999056 + 0.0434421i \(0.0138324\pi\)
−0.999056 + 0.0434421i \(0.986168\pi\)
\(824\) 774.049i 0.939380i
\(825\) 215.649 + 89.7413i 0.261393 + 0.108777i
\(826\) 114.701 + 200.173i 0.138863 + 0.242340i
\(827\) 1255.08i 1.51763i 0.651306 + 0.758815i \(0.274221\pi\)
−0.651306 + 0.758815i \(0.725779\pi\)
\(828\) 120.308i 0.145300i
\(829\) 398.796i 0.481057i −0.970642 0.240528i \(-0.922679\pi\)
0.970642 0.240528i \(-0.0773207\pi\)
\(830\) 485.370 + 96.9618i 0.584784 + 0.116821i
\(831\) 633.423i 0.762242i
\(832\) 267.935 0.322037
\(833\) 201.844 344.396i 0.242310 0.413440i
\(834\) −283.974 −0.340496
\(835\) 286.044 1431.88i 0.342568 1.71482i
\(836\) 36.7222i 0.0439261i
\(837\) 262.071i 0.313107i
\(838\) −75.5847 −0.0901965
\(839\) 72.2323i 0.0860934i 0.999073 + 0.0430467i \(0.0137064\pi\)
−0.999073 + 0.0430467i \(0.986294\pi\)
\(840\) −101.506 303.089i −0.120840 0.360821i
\(841\) 1118.19 1.32959
\(842\) 142.260i 0.168955i
\(843\) 533.764 0.633172
\(844\) 77.1986 0.0914675
\(845\) 11.7861 58.9985i 0.0139480 0.0698208i
\(846\) 51.4099i 0.0607682i
\(847\) −319.839 558.175i −0.377614 0.659002i
\(848\) 912.311i 1.07584i
\(849\) 46.8827 0.0552211
\(850\) 54.9619 132.074i 0.0646611 0.155381i
\(851\) −477.759 −0.561409
\(852\) −320.271 −0.375905
\(853\) −977.259 −1.14567 −0.572836 0.819670i \(-0.694157\pi\)
−0.572836 + 0.819670i \(0.694157\pi\)
\(854\) −116.249 202.874i −0.136123 0.237558i
\(855\) −28.5563 5.70465i −0.0333992 0.00667211i
\(856\) 588.637 0.687660
\(857\) −919.007 −1.07235 −0.536177 0.844106i \(-0.680132\pi\)
−0.536177 + 0.844106i \(0.680132\pi\)
\(858\) 82.2193i 0.0958267i
\(859\) 1258.07i 1.46457i 0.680996 + 0.732287i \(0.261547\pi\)
−0.680996 + 0.732287i \(0.738453\pi\)
\(860\) −19.5528 3.90604i −0.0227358 0.00454190i
\(861\) −379.034 + 217.190i −0.440225 + 0.252253i
\(862\) 560.039i 0.649697i
\(863\) 740.363i 0.857895i −0.903329 0.428947i \(-0.858885\pi\)
0.903329 0.428947i \(-0.141115\pi\)
\(864\) 147.266i 0.170447i
\(865\) −189.686 + 949.526i −0.219290 + 1.09772i
\(866\) 496.769i 0.573636i
\(867\) 385.610 0.444764
\(868\) 1074.17 615.508i 1.23752 0.709110i
\(869\) 411.722 0.473788
\(870\) 264.029 + 52.7447i 0.303481 + 0.0606261i
\(871\) 1314.59i 1.50929i
\(872\) 395.635i 0.453710i
\(873\) −362.889 −0.415680
\(874\) 15.5945i 0.0178426i
\(875\) 872.784 + 62.2323i 0.997468 + 0.0711226i
\(876\) 450.812 0.514626
\(877\) 1161.99i 1.32496i −0.749078 0.662482i \(-0.769503\pi\)
0.749078 0.662482i \(-0.230497\pi\)
\(878\) 183.303 0.208773
\(879\) 308.983 0.351517
\(880\) −54.5432 + 273.032i −0.0619809 + 0.310263i
\(881\) 434.212i 0.492863i 0.969160 + 0.246431i \(0.0792580\pi\)
−0.969160 + 0.246431i \(0.920742\pi\)
\(882\) 89.0799 + 52.2081i 0.100998 + 0.0591929i
\(883\) 1390.88i 1.57518i 0.616200 + 0.787589i \(0.288671\pi\)
−0.616200 + 0.787589i \(0.711329\pi\)
\(884\) −357.911 −0.404877
\(885\) 398.488 + 79.6054i 0.450269 + 0.0899496i
\(886\) 484.673 0.547034
\(887\) 505.489 0.569886 0.284943 0.958544i \(-0.408025\pi\)
0.284943 + 0.958544i \(0.408025\pi\)
\(888\) −381.516 −0.429635
\(889\) 662.438 379.583i 0.745150 0.426978i
\(890\) −22.9967 + 115.117i −0.0258390 + 0.129344i
\(891\) 48.5480 0.0544871
\(892\) 384.101 0.430607
\(893\) 47.3646i 0.0530398i
\(894\) 22.6302i 0.0253134i
\(895\) −199.413 + 998.218i −0.222807 + 1.11533i
\(896\) 779.764 446.812i 0.870272 0.498674i
\(897\) 248.169i 0.276666i
\(898\) 83.4666i 0.0929472i
\(899\) 2232.41i 2.48322i
\(900\) −242.813 101.045i −0.269792 0.112272i
\(901\) 719.963i 0.799071i
\(902\) −136.516 −0.151348
\(903\) 11.9632 6.85504i 0.0132483 0.00759141i
\(904\) −886.445 −0.980581
\(905\) −1433.87 286.442i −1.58438 0.316510i
\(906\) 99.8121i 0.110168i
\(907\) 158.597i 0.174859i 0.996171 + 0.0874293i \(0.0278652\pi\)
−0.996171 + 0.0874293i \(0.972135\pi\)
\(908\) 1295.68 1.42696
\(909\) 141.211i 0.155348i
\(910\) 97.8113 + 292.058i 0.107485 + 0.320943i
\(911\) 700.060 0.768452 0.384226 0.923239i \(-0.374468\pi\)
0.384226 + 0.923239i \(0.374468\pi\)
\(912\) 34.7120i 0.0380614i
\(913\) 760.238 0.832681
\(914\) 255.631 0.279684
\(915\) −403.866 80.6798i −0.441383 0.0881746i
\(916\) 1270.78i 1.38731i
\(917\) −1123.89 + 643.999i −1.22562 + 0.702290i
\(918\) 29.7331i 0.0323891i
\(919\) 91.7379 0.0998236 0.0499118 0.998754i \(-0.484106\pi\)
0.0499118 + 0.998754i \(0.484106\pi\)
\(920\) −59.0620 + 295.652i −0.0641979 + 0.321361i
\(921\) 667.344 0.724586
\(922\) 264.781 0.287181
\(923\) 660.648 0.715762
\(924\) −114.021 198.987i −0.123400 0.215354i
\(925\) 401.263 964.238i 0.433798 1.04242i
\(926\) 145.255 0.156863
\(927\) −440.417 −0.475099
\(928\) 1254.46i 1.35179i
\(929\) 411.879i 0.443358i −0.975120 0.221679i \(-0.928846\pi\)
0.975120 0.221679i \(-0.0711537\pi\)
\(930\) −60.1004 + 300.850i −0.0646241 + 0.323495i
\(931\) −82.0704 48.1000i −0.0881529 0.0516648i
\(932\) 98.6218i 0.105817i
\(933\) 205.875i 0.220659i
\(934\) 75.9272i 0.0812925i
\(935\) 43.0435 215.467i 0.0460359 0.230446i
\(936\) 198.176i 0.211727i
\(937\) 1257.62 1.34218 0.671091 0.741375i \(-0.265826\pi\)
0.671091 + 0.741375i \(0.265826\pi\)
\(938\) −256.491 447.621i −0.273444 0.477208i
\(939\) −296.384 −0.315638
\(940\) −83.7987 + 419.479i −0.0891476 + 0.446254i
\(941\) 1353.18i 1.43802i −0.694998 0.719012i \(-0.744595\pi\)
0.694998 0.719012i \(-0.255405\pi\)
\(942\) 163.105i 0.173148i
\(943\) 412.056 0.436963
\(944\) 484.388i 0.513123i
\(945\) 172.451 57.7546i 0.182488 0.0611160i
\(946\) 4.30877 0.00455473
\(947\) 413.235i 0.436362i −0.975908 0.218181i \(-0.929988\pi\)
0.975908 0.218181i \(-0.0700124\pi\)
\(948\) −463.583 −0.489012
\(949\) −929.925 −0.979899
\(950\) −31.4736 13.0976i −0.0331301 0.0137869i
\(951\) 259.462i 0.272831i
\(952\) −260.885 + 149.489i −0.274038 + 0.157026i
\(953\) 1488.70i 1.56212i −0.624455 0.781061i \(-0.714679\pi\)
0.624455 0.781061i \(-0.285321\pi\)
\(954\) −186.223 −0.195202
\(955\) −80.0706 + 400.816i −0.0838435 + 0.419703i
\(956\) −783.924 −0.820005
\(957\) 413.549 0.432131
\(958\) −308.338 −0.321856
\(959\) −982.186 + 562.801i −1.02418 + 0.586863i
\(960\) 36.2815 181.618i 0.0377933 0.189185i
\(961\) −1582.74 −1.64698
\(962\) 367.630 0.382151
\(963\) 334.921i 0.347789i
\(964\) 489.769i 0.508059i
\(965\) −1325.66 264.826i −1.37374 0.274431i
\(966\) −48.4204 84.5019i −0.0501246 0.0874761i
\(967\) 329.641i 0.340890i 0.985367 + 0.170445i \(0.0545205\pi\)
−0.985367 + 0.170445i \(0.945479\pi\)
\(968\) 484.566i 0.500584i
\(969\) 27.3935i 0.0282699i
\(970\) −416.586 83.2209i −0.429470 0.0857948i
\(971\) 1814.32i 1.86851i −0.356610 0.934253i \(-0.616067\pi\)
0.356610 0.934253i \(-0.383933\pi\)
\(972\) −54.6632 −0.0562378
\(973\) −1417.69 + 812.350i −1.45703 + 0.834892i
\(974\) −309.046 −0.317296
\(975\) 500.868 + 208.434i 0.513711 + 0.213778i
\(976\) 490.925i 0.502997i
\(977\) 1615.80i 1.65384i 0.562318 + 0.826921i \(0.309910\pi\)
−0.562318 + 0.826921i \(0.690090\pi\)
\(978\) −12.3514 −0.0126293
\(979\) 180.308i 0.184175i
\(980\) −641.747 571.193i −0.654844 0.582850i
\(981\) −225.108 −0.229467
\(982\) 78.5923i 0.0800329i
\(983\) 657.745 0.669120 0.334560 0.942374i \(-0.391412\pi\)
0.334560 + 0.942374i \(0.391412\pi\)
\(984\) 329.049 0.334399
\(985\) −200.293 40.0123i −0.203344 0.0406217i
\(986\) 253.278i 0.256874i
\(987\) −147.066 256.655i −0.149003 0.260035i
\(988\) 85.2912i 0.0863271i
\(989\) −13.0055 −0.0131502
\(990\) 55.7318 + 11.1335i 0.0562947 + 0.0112459i
\(991\) 1191.09 1.20191 0.600956 0.799282i \(-0.294787\pi\)
0.600956 + 0.799282i \(0.294787\pi\)
\(992\) −1429.41 −1.44094
\(993\) −481.864 −0.485261
\(994\) 224.952 128.899i 0.226310 0.129677i
\(995\) 61.3735 + 12.2605i 0.0616819 + 0.0123221i
\(996\) −855.999 −0.859436
\(997\) −1231.00 −1.23470 −0.617350 0.786689i \(-0.711794\pi\)
−0.617350 + 0.786689i \(0.711794\pi\)
\(998\) 55.3563i 0.0554672i
\(999\) 217.074i 0.217291i
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 105.3.e.a.34.7 16
3.2 odd 2 315.3.e.e.244.10 16
4.3 odd 2 1680.3.bd.c.769.14 16
5.2 odd 4 525.3.h.e.76.10 16
5.3 odd 4 525.3.h.e.76.7 16
5.4 even 2 inner 105.3.e.a.34.10 yes 16
7.6 odd 2 inner 105.3.e.a.34.8 yes 16
15.14 odd 2 315.3.e.e.244.7 16
20.19 odd 2 1680.3.bd.c.769.4 16
21.20 even 2 315.3.e.e.244.9 16
28.27 even 2 1680.3.bd.c.769.3 16
35.13 even 4 525.3.h.e.76.8 16
35.27 even 4 525.3.h.e.76.9 16
35.34 odd 2 inner 105.3.e.a.34.9 yes 16
105.104 even 2 315.3.e.e.244.8 16
140.139 even 2 1680.3.bd.c.769.13 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.e.a.34.7 16 1.1 even 1 trivial
105.3.e.a.34.8 yes 16 7.6 odd 2 inner
105.3.e.a.34.9 yes 16 35.34 odd 2 inner
105.3.e.a.34.10 yes 16 5.4 even 2 inner
315.3.e.e.244.7 16 15.14 odd 2
315.3.e.e.244.8 16 105.104 even 2
315.3.e.e.244.9 16 21.20 even 2
315.3.e.e.244.10 16 3.2 odd 2
525.3.h.e.76.7 16 5.3 odd 4
525.3.h.e.76.8 16 35.13 even 4
525.3.h.e.76.9 16 35.27 even 4
525.3.h.e.76.10 16 5.2 odd 4
1680.3.bd.c.769.3 16 28.27 even 2
1680.3.bd.c.769.4 16 20.19 odd 2
1680.3.bd.c.769.13 16 140.139 even 2
1680.3.bd.c.769.14 16 4.3 odd 2