Properties

Label 1045.2.b.c.419.13
Level $1045$
Weight $2$
Character 1045.419
Analytic conductor $8.344$
Analytic rank $0$
Dimension $20$
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] = [1045,2,Mod(419,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.419");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.b (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: \(8.34436701122\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 26 x^{18} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + 2753 x^{4} + 276 x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 419.13
Root \(0.712399i\) of defining polynomial
Character \(\chi\) \(=\) 1045.419
Dual form 1045.2.b.c.419.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.712399i q^{2} -3.32227i q^{3} +1.49249 q^{4} +(1.31011 - 1.81207i) q^{5} +2.36678 q^{6} -2.70450i q^{7} +2.48804i q^{8} -8.03747 q^{9} +O(q^{10})\) \(q+0.712399i q^{2} -3.32227i q^{3} +1.49249 q^{4} +(1.31011 - 1.81207i) q^{5} +2.36678 q^{6} -2.70450i q^{7} +2.48804i q^{8} -8.03747 q^{9} +(1.29092 + 0.933320i) q^{10} +1.00000 q^{11} -4.95845i q^{12} +3.93869i q^{13} +1.92668 q^{14} +(-6.02020 - 4.35253i) q^{15} +1.21250 q^{16} -4.53720i q^{17} -5.72588i q^{18} +1.00000 q^{19} +(1.95532 - 2.70450i) q^{20} -8.98508 q^{21} +0.712399i q^{22} -3.13766i q^{23} +8.26595 q^{24} +(-1.56723 - 4.74803i) q^{25} -2.80592 q^{26} +16.7358i q^{27} -4.03643i q^{28} +7.37268 q^{29} +(3.10074 - 4.28878i) q^{30} -6.00774 q^{31} +5.83987i q^{32} -3.32227i q^{33} +3.23229 q^{34} +(-4.90076 - 3.54319i) q^{35} -11.9958 q^{36} -7.56844i q^{37} +0.712399i q^{38} +13.0854 q^{39} +(4.50852 + 3.25961i) q^{40} -0.108411 q^{41} -6.40096i q^{42} +3.35317i q^{43} +1.49249 q^{44} +(-10.5300 + 14.5645i) q^{45} +2.23526 q^{46} +7.06218i q^{47} -4.02824i q^{48} -0.314322 q^{49} +(3.38249 - 1.11649i) q^{50} -15.0738 q^{51} +5.87844i q^{52} +12.1616i q^{53} -11.9226 q^{54} +(1.31011 - 1.81207i) q^{55} +6.72892 q^{56} -3.32227i q^{57} +5.25228i q^{58} -3.83960 q^{59} +(-8.98508 - 6.49610i) q^{60} -5.74344 q^{61} -4.27991i q^{62} +21.7373i q^{63} -1.73532 q^{64} +(7.13720 + 5.16011i) q^{65} +2.36678 q^{66} +15.8539i q^{67} -6.77171i q^{68} -10.4241 q^{69} +(2.52416 - 3.49129i) q^{70} -7.83511 q^{71} -19.9976i q^{72} -11.6635i q^{73} +5.39175 q^{74} +(-15.7742 + 5.20676i) q^{75} +1.49249 q^{76} -2.70450i q^{77} +9.32200i q^{78} +12.0695 q^{79} +(1.58850 - 2.19714i) q^{80} +31.4885 q^{81} -0.0772318i q^{82} +11.0121i q^{83} -13.4101 q^{84} +(-8.22174 - 5.94422i) q^{85} -2.38880 q^{86} -24.4940i q^{87} +2.48804i q^{88} +7.90725 q^{89} +(-10.3757 - 7.50153i) q^{90} +10.6522 q^{91} -4.68291i q^{92} +19.9593i q^{93} -5.03109 q^{94} +(1.31011 - 1.81207i) q^{95} +19.4016 q^{96} -19.3959i q^{97} -0.223922i q^{98} -8.03747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9} - 6 q^{10} + 20 q^{11} + 24 q^{14} - 6 q^{15} - 4 q^{16} + 20 q^{19} - 6 q^{20} - 30 q^{21} + 38 q^{24} + 2 q^{25} + 8 q^{26} + 50 q^{29} - 20 q^{30} - 50 q^{31} + 28 q^{34} + 6 q^{35} - 12 q^{36} + 48 q^{39} + 12 q^{40} - 34 q^{41} - 12 q^{44} - 18 q^{45} - 36 q^{46} - 6 q^{49} + 26 q^{50} - 40 q^{51} - 6 q^{54} - 40 q^{56} + 30 q^{59} - 30 q^{60} - 14 q^{61} + 36 q^{64} + 30 q^{65} - 8 q^{66} - 12 q^{69} - 54 q^{70} - 40 q^{71} + 50 q^{74} - 8 q^{75} - 12 q^{76} + 106 q^{79} + 8 q^{80} - 30 q^{84} - 22 q^{85} + 56 q^{86} + 36 q^{89} - 64 q^{90} - 56 q^{91} + 28 q^{94} + 66 q^{96} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(761\) \(837\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.712399i 0.503742i 0.967761 + 0.251871i \(0.0810459\pi\)
−0.967761 + 0.251871i \(0.918954\pi\)
\(3\) 3.32227i 1.91811i −0.283216 0.959056i \(-0.591401\pi\)
0.283216 0.959056i \(-0.408599\pi\)
\(4\) 1.49249 0.746244
\(5\) 1.31011 1.81207i 0.585898 0.810385i
\(6\) 2.36678 0.966234
\(7\) 2.70450i 1.02221i −0.859520 0.511103i \(-0.829237\pi\)
0.859520 0.511103i \(-0.170763\pi\)
\(8\) 2.48804i 0.879656i
\(9\) −8.03747 −2.67916
\(10\) 1.29092 + 0.933320i 0.408225 + 0.295142i
\(11\) 1.00000 0.301511
\(12\) 4.95845i 1.43138i
\(13\) 3.93869i 1.09240i 0.837656 + 0.546198i \(0.183925\pi\)
−0.837656 + 0.546198i \(0.816075\pi\)
\(14\) 1.92668 0.514928
\(15\) −6.02020 4.35253i −1.55441 1.12382i
\(16\) 1.21250 0.303124
\(17\) 4.53720i 1.10043i −0.835023 0.550216i \(-0.814545\pi\)
0.835023 0.550216i \(-0.185455\pi\)
\(18\) 5.72588i 1.34960i
\(19\) 1.00000 0.229416
\(20\) 1.95532 2.70450i 0.437223 0.604745i
\(21\) −8.98508 −1.96070
\(22\) 0.712399i 0.151884i
\(23\) 3.13766i 0.654246i −0.944982 0.327123i \(-0.893921\pi\)
0.944982 0.327123i \(-0.106079\pi\)
\(24\) 8.26595 1.68728
\(25\) −1.56723 4.74803i −0.313446 0.949606i
\(26\) −2.80592 −0.550285
\(27\) 16.7358i 3.22081i
\(28\) 4.03643i 0.762814i
\(29\) 7.37268 1.36907 0.684536 0.728979i \(-0.260005\pi\)
0.684536 + 0.728979i \(0.260005\pi\)
\(30\) 3.10074 4.28878i 0.566115 0.783021i
\(31\) −6.00774 −1.07902 −0.539511 0.841979i \(-0.681391\pi\)
−0.539511 + 0.841979i \(0.681391\pi\)
\(32\) 5.83987i 1.03235i
\(33\) 3.32227i 0.578333i
\(34\) 3.23229 0.554333
\(35\) −4.90076 3.54319i −0.828379 0.598908i
\(36\) −11.9958 −1.99930
\(37\) 7.56844i 1.24424i −0.782920 0.622122i \(-0.786271\pi\)
0.782920 0.622122i \(-0.213729\pi\)
\(38\) 0.712399i 0.115566i
\(39\) 13.0854 2.09534
\(40\) 4.50852 + 3.25961i 0.712860 + 0.515389i
\(41\) −0.108411 −0.0169309 −0.00846547 0.999964i \(-0.502695\pi\)
−0.00846547 + 0.999964i \(0.502695\pi\)
\(42\) 6.40096i 0.987689i
\(43\) 3.35317i 0.511354i 0.966762 + 0.255677i \(0.0822984\pi\)
−0.966762 + 0.255677i \(0.917702\pi\)
\(44\) 1.49249 0.225001
\(45\) −10.5300 + 14.5645i −1.56971 + 2.17115i
\(46\) 2.23526 0.329571
\(47\) 7.06218i 1.03013i 0.857152 + 0.515063i \(0.172231\pi\)
−0.857152 + 0.515063i \(0.827769\pi\)
\(48\) 4.02824i 0.581427i
\(49\) −0.314322 −0.0449031
\(50\) 3.38249 1.11649i 0.478356 0.157896i
\(51\) −15.0738 −2.11075
\(52\) 5.87844i 0.815193i
\(53\) 12.1616i 1.67053i 0.549847 + 0.835265i \(0.314686\pi\)
−0.549847 + 0.835265i \(0.685314\pi\)
\(54\) −11.9226 −1.62246
\(55\) 1.31011 1.81207i 0.176655 0.244340i
\(56\) 6.72892 0.899189
\(57\) 3.32227i 0.440045i
\(58\) 5.25228i 0.689659i
\(59\) −3.83960 −0.499873 −0.249937 0.968262i \(-0.580410\pi\)
−0.249937 + 0.968262i \(0.580410\pi\)
\(60\) −8.98508 6.49610i −1.15997 0.838643i
\(61\) −5.74344 −0.735372 −0.367686 0.929950i \(-0.619850\pi\)
−0.367686 + 0.929950i \(0.619850\pi\)
\(62\) 4.27991i 0.543549i
\(63\) 21.7373i 2.73865i
\(64\) −1.73532 −0.216915
\(65\) 7.13720 + 5.16011i 0.885260 + 0.640033i
\(66\) 2.36678 0.291330
\(67\) 15.8539i 1.93686i 0.249288 + 0.968430i \(0.419804\pi\)
−0.249288 + 0.968430i \(0.580196\pi\)
\(68\) 6.77171i 0.821190i
\(69\) −10.4241 −1.25492
\(70\) 2.52416 3.49129i 0.301695 0.417289i
\(71\) −7.83511 −0.929856 −0.464928 0.885348i \(-0.653920\pi\)
−0.464928 + 0.885348i \(0.653920\pi\)
\(72\) 19.9976i 2.35674i
\(73\) 11.6635i 1.36511i −0.730834 0.682556i \(-0.760868\pi\)
0.730834 0.682556i \(-0.239132\pi\)
\(74\) 5.39175 0.626778
\(75\) −15.7742 + 5.20676i −1.82145 + 0.601225i
\(76\) 1.49249 0.171200
\(77\) 2.70450i 0.308206i
\(78\) 9.32200i 1.05551i
\(79\) 12.0695 1.35792 0.678962 0.734174i \(-0.262430\pi\)
0.678962 + 0.734174i \(0.262430\pi\)
\(80\) 1.58850 2.19714i 0.177600 0.245647i
\(81\) 31.4885 3.49872
\(82\) 0.0772318i 0.00852882i
\(83\) 11.0121i 1.20874i 0.796705 + 0.604368i \(0.206575\pi\)
−0.796705 + 0.604368i \(0.793425\pi\)
\(84\) −13.4101 −1.46316
\(85\) −8.22174 5.94422i −0.891773 0.644741i
\(86\) −2.38880 −0.257591
\(87\) 24.4940i 2.62603i
\(88\) 2.48804i 0.265226i
\(89\) 7.90725 0.838167 0.419084 0.907948i \(-0.362351\pi\)
0.419084 + 0.907948i \(0.362351\pi\)
\(90\) −10.3757 7.50153i −1.09370 0.790730i
\(91\) 10.6522 1.11665
\(92\) 4.68291i 0.488228i
\(93\) 19.9593i 2.06969i
\(94\) −5.03109 −0.518917
\(95\) 1.31011 1.81207i 0.134414 0.185915i
\(96\) 19.4016 1.98017
\(97\) 19.3959i 1.96936i −0.174382 0.984678i \(-0.555793\pi\)
0.174382 0.984678i \(-0.444207\pi\)
\(98\) 0.223922i 0.0226196i
\(99\) −8.03747 −0.807796
\(100\) −2.33907 7.08638i −0.233907 0.708638i
\(101\) 6.19426 0.616352 0.308176 0.951329i \(-0.400281\pi\)
0.308176 + 0.951329i \(0.400281\pi\)
\(102\) 10.7385i 1.06327i
\(103\) 14.1287i 1.39215i −0.717971 0.696073i \(-0.754929\pi\)
0.717971 0.696073i \(-0.245071\pi\)
\(104\) −9.79963 −0.960932
\(105\) −11.7714 + 16.2816i −1.14877 + 1.58892i
\(106\) −8.66394 −0.841516
\(107\) 1.62430i 0.157027i 0.996913 + 0.0785134i \(0.0250173\pi\)
−0.996913 + 0.0785134i \(0.974983\pi\)
\(108\) 24.9780i 2.40351i
\(109\) 17.0381 1.63196 0.815978 0.578083i \(-0.196199\pi\)
0.815978 + 0.578083i \(0.196199\pi\)
\(110\) 1.29092 + 0.933320i 0.123084 + 0.0889885i
\(111\) −25.1444 −2.38660
\(112\) 3.27920i 0.309855i
\(113\) 0.922301i 0.0867627i −0.999059 0.0433814i \(-0.986187\pi\)
0.999059 0.0433814i \(-0.0138131\pi\)
\(114\) 2.36678 0.221669
\(115\) −5.68567 4.11067i −0.530191 0.383322i
\(116\) 11.0036 1.02166
\(117\) 31.6571i 2.92670i
\(118\) 2.73533i 0.251807i
\(119\) −12.2708 −1.12487
\(120\) 10.8293 14.9785i 0.988575 1.36735i
\(121\) 1.00000 0.0909091
\(122\) 4.09162i 0.370437i
\(123\) 0.360170i 0.0324754i
\(124\) −8.96648 −0.805214
\(125\) −10.6570 3.38050i −0.953194 0.302361i
\(126\) −15.4856 −1.37957
\(127\) 0.743724i 0.0659948i 0.999455 + 0.0329974i \(0.0105053\pi\)
−0.999455 + 0.0329974i \(0.989495\pi\)
\(128\) 10.4435i 0.923084i
\(129\) 11.1401 0.980835
\(130\) −3.67605 + 5.08453i −0.322411 + 0.445943i
\(131\) −4.73616 −0.413801 −0.206900 0.978362i \(-0.566338\pi\)
−0.206900 + 0.978362i \(0.566338\pi\)
\(132\) 4.95845i 0.431577i
\(133\) 2.70450i 0.234510i
\(134\) −11.2943 −0.975677
\(135\) 30.3266 + 21.9257i 2.61009 + 1.88707i
\(136\) 11.2887 0.968002
\(137\) 2.26917i 0.193869i 0.995291 + 0.0969343i \(0.0309037\pi\)
−0.995291 + 0.0969343i \(0.969096\pi\)
\(138\) 7.42614i 0.632155i
\(139\) −3.51232 −0.297911 −0.148955 0.988844i \(-0.547591\pi\)
−0.148955 + 0.988844i \(0.547591\pi\)
\(140\) −7.31432 5.28817i −0.618173 0.446932i
\(141\) 23.4625 1.97590
\(142\) 5.58172i 0.468407i
\(143\) 3.93869i 0.329370i
\(144\) −9.74541 −0.812117
\(145\) 9.65901 13.3598i 0.802137 1.10947i
\(146\) 8.30907 0.687664
\(147\) 1.04426i 0.0861292i
\(148\) 11.2958i 0.928510i
\(149\) 12.8508 1.05278 0.526390 0.850243i \(-0.323545\pi\)
0.526390 + 0.850243i \(0.323545\pi\)
\(150\) −3.70929 11.2375i −0.302862 0.917541i
\(151\) 11.8967 0.968139 0.484069 0.875030i \(-0.339158\pi\)
0.484069 + 0.875030i \(0.339158\pi\)
\(152\) 2.48804i 0.201807i
\(153\) 36.4676i 2.94823i
\(154\) 1.92668 0.155256
\(155\) −7.87079 + 10.8865i −0.632197 + 0.874423i
\(156\) 19.5298 1.56363
\(157\) 5.21525i 0.416222i 0.978105 + 0.208111i \(0.0667315\pi\)
−0.978105 + 0.208111i \(0.933268\pi\)
\(158\) 8.59828i 0.684043i
\(159\) 40.4042 3.20427
\(160\) 10.5823 + 7.65086i 0.836603 + 0.604854i
\(161\) −8.48579 −0.668774
\(162\) 22.4323i 1.76245i
\(163\) 7.87829i 0.617075i −0.951212 0.308538i \(-0.900160\pi\)
0.951212 0.308538i \(-0.0998396\pi\)
\(164\) −0.161802 −0.0126346
\(165\) −6.02020 4.35253i −0.468672 0.338844i
\(166\) −7.84502 −0.608891
\(167\) 17.4388i 1.34945i 0.738068 + 0.674726i \(0.235738\pi\)
−0.738068 + 0.674726i \(0.764262\pi\)
\(168\) 22.3553i 1.72475i
\(169\) −2.51325 −0.193327
\(170\) 4.23465 5.85715i 0.324783 0.449223i
\(171\) −8.03747 −0.614640
\(172\) 5.00457i 0.381595i
\(173\) 13.7948i 1.04880i −0.851473 0.524399i \(-0.824290\pi\)
0.851473 0.524399i \(-0.175710\pi\)
\(174\) 17.4495 1.32284
\(175\) −12.8410 + 4.23858i −0.970692 + 0.320406i
\(176\) 1.21250 0.0913954
\(177\) 12.7562i 0.958813i
\(178\) 5.63312i 0.422220i
\(179\) 5.68388 0.424833 0.212417 0.977179i \(-0.431867\pi\)
0.212417 + 0.977179i \(0.431867\pi\)
\(180\) −15.7158 + 21.7373i −1.17139 + 1.62020i
\(181\) −18.5723 −1.38047 −0.690234 0.723586i \(-0.742493\pi\)
−0.690234 + 0.723586i \(0.742493\pi\)
\(182\) 7.58860i 0.562504i
\(183\) 19.0812i 1.41053i
\(184\) 7.80662 0.575512
\(185\) −13.7146 9.91548i −1.00832 0.729001i
\(186\) −14.2190 −1.04259
\(187\) 4.53720i 0.331793i
\(188\) 10.5402i 0.768725i
\(189\) 45.2620 3.29233
\(190\) 1.29092 + 0.933320i 0.0936532 + 0.0677101i
\(191\) −3.63564 −0.263066 −0.131533 0.991312i \(-0.541990\pi\)
−0.131533 + 0.991312i \(0.541990\pi\)
\(192\) 5.76520i 0.416067i
\(193\) 18.8353i 1.35579i −0.735158 0.677896i \(-0.762892\pi\)
0.735158 0.677896i \(-0.237108\pi\)
\(194\) 13.8176 0.992047
\(195\) 17.1433 23.7117i 1.22765 1.69803i
\(196\) −0.469122 −0.0335087
\(197\) 0.0627922i 0.00447376i −0.999997 0.00223688i \(-0.999288\pi\)
0.999997 0.00223688i \(-0.000712021\pi\)
\(198\) 5.72588i 0.406921i
\(199\) −6.95332 −0.492908 −0.246454 0.969155i \(-0.579265\pi\)
−0.246454 + 0.969155i \(0.579265\pi\)
\(200\) 11.8133 3.89934i 0.835327 0.275725i
\(201\) 52.6708 3.71511
\(202\) 4.41278i 0.310482i
\(203\) 19.9394i 1.39947i
\(204\) −22.4974 −1.57514
\(205\) −0.142030 + 0.196449i −0.00991981 + 0.0137206i
\(206\) 10.0653 0.701282
\(207\) 25.2188i 1.75283i
\(208\) 4.77565i 0.331132i
\(209\) 1.00000 0.0691714
\(210\) −11.5990 8.38595i −0.800408 0.578685i
\(211\) 19.3587 1.33271 0.666353 0.745637i \(-0.267855\pi\)
0.666353 + 0.745637i \(0.267855\pi\)
\(212\) 18.1511i 1.24662i
\(213\) 26.0303i 1.78357i
\(214\) −1.15715 −0.0791009
\(215\) 6.07620 + 4.39302i 0.414394 + 0.299602i
\(216\) −41.6394 −2.83321
\(217\) 16.2479i 1.10298i
\(218\) 12.1379i 0.822084i
\(219\) −38.7493 −2.61844
\(220\) 1.95532 2.70450i 0.131828 0.182337i
\(221\) 17.8706 1.20211
\(222\) 17.9128i 1.20223i
\(223\) 3.97309i 0.266057i 0.991112 + 0.133029i \(0.0424703\pi\)
−0.991112 + 0.133029i \(0.957530\pi\)
\(224\) 15.7939 1.05528
\(225\) 12.5966 + 38.1621i 0.839771 + 2.54414i
\(226\) 0.657046 0.0437060
\(227\) 3.15396i 0.209336i −0.994507 0.104668i \(-0.966622\pi\)
0.994507 0.104668i \(-0.0333779\pi\)
\(228\) 4.95845i 0.328381i
\(229\) −0.468155 −0.0309365 −0.0154683 0.999880i \(-0.504924\pi\)
−0.0154683 + 0.999880i \(0.504924\pi\)
\(230\) 2.92844 4.05046i 0.193095 0.267080i
\(231\) −8.98508 −0.591175
\(232\) 18.3435i 1.20431i
\(233\) 15.5925i 1.02150i 0.859730 + 0.510749i \(0.170632\pi\)
−0.859730 + 0.510749i \(0.829368\pi\)
\(234\) 22.5524 1.47430
\(235\) 12.7972 + 9.25223i 0.834798 + 0.603549i
\(236\) −5.73056 −0.373027
\(237\) 40.0981i 2.60465i
\(238\) 8.74173i 0.566642i
\(239\) −8.71766 −0.563898 −0.281949 0.959429i \(-0.590981\pi\)
−0.281949 + 0.959429i \(0.590981\pi\)
\(240\) −7.29948 5.27743i −0.471179 0.340657i
\(241\) −14.8860 −0.958894 −0.479447 0.877571i \(-0.659163\pi\)
−0.479447 + 0.877571i \(0.659163\pi\)
\(242\) 0.712399i 0.0457947i
\(243\) 54.4057i 3.49013i
\(244\) −8.57201 −0.548767
\(245\) −0.411796 + 0.569575i −0.0263087 + 0.0363888i
\(246\) −0.256585 −0.0163592
\(247\) 3.93869i 0.250613i
\(248\) 14.9475i 0.949168i
\(249\) 36.5852 2.31849
\(250\) 2.40826 7.59205i 0.152312 0.480164i
\(251\) 6.95702 0.439123 0.219562 0.975599i \(-0.429537\pi\)
0.219562 + 0.975599i \(0.429537\pi\)
\(252\) 32.4427i 2.04370i
\(253\) 3.13766i 0.197263i
\(254\) −0.529828 −0.0332443
\(255\) −19.7483 + 27.3148i −1.23669 + 1.71052i
\(256\) −10.9106 −0.681911
\(257\) 17.2912i 1.07859i −0.842115 0.539297i \(-0.818690\pi\)
0.842115 0.539297i \(-0.181310\pi\)
\(258\) 7.93623i 0.494088i
\(259\) −20.4689 −1.27187
\(260\) 10.6522 + 7.70140i 0.660620 + 0.477621i
\(261\) −59.2576 −3.66796
\(262\) 3.37404i 0.208449i
\(263\) 8.88346i 0.547778i −0.961761 0.273889i \(-0.911690\pi\)
0.961761 0.273889i \(-0.0883100\pi\)
\(264\) 8.26595 0.508734
\(265\) 22.0378 + 15.9331i 1.35377 + 0.978761i
\(266\) 1.92668 0.118132
\(267\) 26.2700i 1.60770i
\(268\) 23.6617i 1.44537i
\(269\) 15.6372 0.953415 0.476707 0.879062i \(-0.341830\pi\)
0.476707 + 0.879062i \(0.341830\pi\)
\(270\) −15.6199 + 21.6046i −0.950595 + 1.31481i
\(271\) −6.18562 −0.375750 −0.187875 0.982193i \(-0.560160\pi\)
−0.187875 + 0.982193i \(0.560160\pi\)
\(272\) 5.50134i 0.333568i
\(273\) 35.3894i 2.14186i
\(274\) −1.61656 −0.0976597
\(275\) −1.56723 4.74803i −0.0945076 0.286317i
\(276\) −15.5579 −0.936475
\(277\) 13.5897i 0.816524i −0.912865 0.408262i \(-0.866135\pi\)
0.912865 0.408262i \(-0.133865\pi\)
\(278\) 2.50217i 0.150070i
\(279\) 48.2870 2.89087
\(280\) 8.81561 12.1933i 0.526833 0.728689i
\(281\) −9.70357 −0.578866 −0.289433 0.957198i \(-0.593467\pi\)
−0.289433 + 0.957198i \(0.593467\pi\)
\(282\) 16.7146i 0.995342i
\(283\) 1.54391i 0.0917760i 0.998947 + 0.0458880i \(0.0146117\pi\)
−0.998947 + 0.0458880i \(0.985388\pi\)
\(284\) −11.6938 −0.693900
\(285\) −6.02020 4.35253i −0.356606 0.257822i
\(286\) −2.80592 −0.165917
\(287\) 0.293197i 0.0173069i
\(288\) 46.9378i 2.76583i
\(289\) −3.58614 −0.210949
\(290\) 9.51753 + 6.88106i 0.558889 + 0.404070i
\(291\) −64.4384 −3.77745
\(292\) 17.4077i 1.01871i
\(293\) 22.2671i 1.30086i 0.759567 + 0.650430i \(0.225411\pi\)
−0.759567 + 0.650430i \(0.774589\pi\)
\(294\) −0.743930 −0.0433869
\(295\) −5.03029 + 6.95764i −0.292875 + 0.405090i
\(296\) 18.8306 1.09451
\(297\) 16.7358i 0.971111i
\(298\) 9.15490i 0.530329i
\(299\) 12.3582 0.714696
\(300\) −23.5429 + 7.77103i −1.35925 + 0.448661i
\(301\) 9.06866 0.522709
\(302\) 8.47519i 0.487692i
\(303\) 20.5790i 1.18223i
\(304\) 1.21250 0.0695415
\(305\) −7.52453 + 10.4075i −0.430853 + 0.595934i
\(306\) −25.9794 −1.48515
\(307\) 10.2910i 0.587340i −0.955907 0.293670i \(-0.905123\pi\)
0.955907 0.293670i \(-0.0948767\pi\)
\(308\) 4.03643i 0.229997i
\(309\) −46.9394 −2.67029
\(310\) −7.75551 5.60714i −0.440483 0.318464i
\(311\) 23.1134 1.31064 0.655320 0.755351i \(-0.272534\pi\)
0.655320 + 0.755351i \(0.272534\pi\)
\(312\) 32.5570i 1.84318i
\(313\) 8.71229i 0.492448i 0.969213 + 0.246224i \(0.0791899\pi\)
−0.969213 + 0.246224i \(0.920810\pi\)
\(314\) −3.71533 −0.209668
\(315\) 39.3897 + 28.4783i 2.21936 + 1.60457i
\(316\) 18.0136 1.01334
\(317\) 18.3723i 1.03189i 0.856621 + 0.515946i \(0.172560\pi\)
−0.856621 + 0.515946i \(0.827440\pi\)
\(318\) 28.7839i 1.61412i
\(319\) 7.37268 0.412791
\(320\) −2.27346 + 3.14453i −0.127090 + 0.175785i
\(321\) 5.39635 0.301195
\(322\) 6.04527i 0.336889i
\(323\) 4.53720i 0.252456i
\(324\) 46.9962 2.61090
\(325\) 18.7010 6.17283i 1.03734 0.342407i
\(326\) 5.61248 0.310847
\(327\) 56.6052i 3.13027i
\(328\) 0.269731i 0.0148934i
\(329\) 19.0997 1.05300
\(330\) 3.10074 4.28878i 0.170690 0.236090i
\(331\) −4.86106 −0.267188 −0.133594 0.991036i \(-0.542652\pi\)
−0.133594 + 0.991036i \(0.542652\pi\)
\(332\) 16.4355i 0.902013i
\(333\) 60.8311i 3.33352i
\(334\) −12.4234 −0.679775
\(335\) 28.7284 + 20.7703i 1.56960 + 1.13480i
\(336\) −10.8944 −0.594337
\(337\) 17.0842i 0.930634i 0.885144 + 0.465317i \(0.154060\pi\)
−0.885144 + 0.465317i \(0.845940\pi\)
\(338\) 1.79044i 0.0973870i
\(339\) −3.06413 −0.166421
\(340\) −12.2708 8.87168i −0.665480 0.481134i
\(341\) −6.00774 −0.325337
\(342\) 5.72588i 0.309620i
\(343\) 18.0814i 0.976305i
\(344\) −8.34285 −0.449816
\(345\) −13.6567 + 18.8893i −0.735255 + 1.01697i
\(346\) 9.82738 0.528323
\(347\) 18.9161i 1.01547i 0.861513 + 0.507736i \(0.169517\pi\)
−0.861513 + 0.507736i \(0.830483\pi\)
\(348\) 36.5570i 1.95966i
\(349\) −27.7295 −1.48433 −0.742163 0.670219i \(-0.766200\pi\)
−0.742163 + 0.670219i \(0.766200\pi\)
\(350\) −3.01956 9.14795i −0.161402 0.488978i
\(351\) −65.9171 −3.51840
\(352\) 5.83987i 0.311266i
\(353\) 5.23456i 0.278607i −0.990250 0.139304i \(-0.955514\pi\)
0.990250 0.139304i \(-0.0444864\pi\)
\(354\) −9.08748 −0.482994
\(355\) −10.2648 + 14.1978i −0.544801 + 0.753541i
\(356\) 11.8015 0.625477
\(357\) 40.7670i 2.15762i
\(358\) 4.04919i 0.214006i
\(359\) −5.96494 −0.314818 −0.157409 0.987534i \(-0.550314\pi\)
−0.157409 + 0.987534i \(0.550314\pi\)
\(360\) −36.2371 26.1990i −1.90986 1.38081i
\(361\) 1.00000 0.0526316
\(362\) 13.2309i 0.695400i
\(363\) 3.32227i 0.174374i
\(364\) 15.8983 0.833295
\(365\) −21.1352 15.2805i −1.10627 0.799817i
\(366\) −13.5934 −0.710541
\(367\) 5.90016i 0.307986i 0.988072 + 0.153993i \(0.0492133\pi\)
−0.988072 + 0.153993i \(0.950787\pi\)
\(368\) 3.80440i 0.198318i
\(369\) 0.871349 0.0453606
\(370\) 7.06378 9.77025i 0.367228 0.507931i
\(371\) 32.8912 1.70762
\(372\) 29.7891i 1.54449i
\(373\) 18.6800i 0.967215i 0.875285 + 0.483608i \(0.160674\pi\)
−0.875285 + 0.483608i \(0.839326\pi\)
\(374\) 3.23229 0.167138
\(375\) −11.2309 + 35.4055i −0.579962 + 1.82833i
\(376\) −17.5710 −0.906156
\(377\) 29.0387i 1.49557i
\(378\) 32.2446i 1.65848i
\(379\) −13.2052 −0.678306 −0.339153 0.940731i \(-0.610140\pi\)
−0.339153 + 0.940731i \(0.610140\pi\)
\(380\) 1.95532 2.70450i 0.100306 0.138738i
\(381\) 2.47085 0.126585
\(382\) 2.59002i 0.132517i
\(383\) 11.3980i 0.582411i 0.956661 + 0.291205i \(0.0940563\pi\)
−0.956661 + 0.291205i \(0.905944\pi\)
\(384\) 34.6961 1.77058
\(385\) −4.90076 3.54319i −0.249766 0.180578i
\(386\) 13.4182 0.682969
\(387\) 26.9510i 1.37000i
\(388\) 28.9482i 1.46962i
\(389\) −4.12316 −0.209052 −0.104526 0.994522i \(-0.533333\pi\)
−0.104526 + 0.994522i \(0.533333\pi\)
\(390\) 16.8922 + 12.2128i 0.855368 + 0.618421i
\(391\) −14.2362 −0.719953
\(392\) 0.782047i 0.0394993i
\(393\) 15.7348i 0.793716i
\(394\) 0.0447330 0.00225362
\(395\) 15.8123 21.8708i 0.795605 1.10044i
\(396\) −11.9958 −0.602813
\(397\) 20.5811i 1.03293i 0.856307 + 0.516467i \(0.172753\pi\)
−0.856307 + 0.516467i \(0.827247\pi\)
\(398\) 4.95354i 0.248298i
\(399\) −8.98508 −0.449816
\(400\) −1.90026 5.75697i −0.0950131 0.287849i
\(401\) 11.5597 0.577262 0.288631 0.957440i \(-0.406800\pi\)
0.288631 + 0.957440i \(0.406800\pi\)
\(402\) 37.5226i 1.87146i
\(403\) 23.6626i 1.17872i
\(404\) 9.24486 0.459949
\(405\) 41.2533 57.0595i 2.04989 2.83531i
\(406\) 14.2048 0.704973
\(407\) 7.56844i 0.375154i
\(408\) 37.5042i 1.85674i
\(409\) 14.8227 0.732935 0.366468 0.930431i \(-0.380567\pi\)
0.366468 + 0.930431i \(0.380567\pi\)
\(410\) −0.139950 0.101182i −0.00691162 0.00499702i
\(411\) 7.53880 0.371862
\(412\) 21.0870i 1.03888i
\(413\) 10.3842i 0.510973i
\(414\) −17.9658 −0.882973
\(415\) 19.9548 + 14.4271i 0.979542 + 0.708197i
\(416\) −23.0014 −1.12774
\(417\) 11.6689i 0.571426i
\(418\) 0.712399i 0.0348446i
\(419\) −4.58368 −0.223927 −0.111964 0.993712i \(-0.535714\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(420\) −17.5687 + 24.3001i −0.857265 + 1.18573i
\(421\) −5.07417 −0.247300 −0.123650 0.992326i \(-0.539460\pi\)
−0.123650 + 0.992326i \(0.539460\pi\)
\(422\) 13.7911i 0.671340i
\(423\) 56.7621i 2.75987i
\(424\) −30.2587 −1.46949
\(425\) −21.5427 + 7.11083i −1.04498 + 0.344926i
\(426\) −18.5440 −0.898458
\(427\) 15.5331i 0.751701i
\(428\) 2.42424i 0.117180i
\(429\) 13.0854 0.631768
\(430\) −3.12958 + 4.32868i −0.150922 + 0.208747i
\(431\) −27.5096 −1.32509 −0.662546 0.749021i \(-0.730524\pi\)
−0.662546 + 0.749021i \(0.730524\pi\)
\(432\) 20.2921i 0.976306i
\(433\) 13.1720i 0.633007i −0.948591 0.316503i \(-0.897491\pi\)
0.948591 0.316503i \(-0.102509\pi\)
\(434\) −11.5750 −0.555618
\(435\) −44.3850 32.0898i −2.12810 1.53859i
\(436\) 25.4292 1.21784
\(437\) 3.13766i 0.150094i
\(438\) 27.6050i 1.31902i
\(439\) 12.4523 0.594317 0.297159 0.954828i \(-0.403961\pi\)
0.297159 + 0.954828i \(0.403961\pi\)
\(440\) 4.50852 + 3.25961i 0.214935 + 0.155396i
\(441\) 2.52635 0.120302
\(442\) 12.7310i 0.605551i
\(443\) 17.1036i 0.812617i −0.913736 0.406309i \(-0.866816\pi\)
0.913736 0.406309i \(-0.133184\pi\)
\(444\) −37.5277 −1.78099
\(445\) 10.3594 14.3285i 0.491081 0.679238i
\(446\) −2.83042 −0.134024
\(447\) 42.6938i 2.01935i
\(448\) 4.69317i 0.221732i
\(449\) −1.69279 −0.0798876 −0.0399438 0.999202i \(-0.512718\pi\)
−0.0399438 + 0.999202i \(0.512718\pi\)
\(450\) −27.1867 + 8.97377i −1.28159 + 0.423028i
\(451\) −0.108411 −0.00510487
\(452\) 1.37652i 0.0647462i
\(453\) 39.5240i 1.85700i
\(454\) 2.24688 0.105451
\(455\) 13.9555 19.3025i 0.654245 0.904917i
\(456\) 8.26595 0.387089
\(457\) 16.2265i 0.759044i −0.925183 0.379522i \(-0.876088\pi\)
0.925183 0.379522i \(-0.123912\pi\)
\(458\) 0.333513i 0.0155840i
\(459\) 75.9337 3.54428
\(460\) −8.48579 6.13513i −0.395652 0.286052i
\(461\) 13.0705 0.608756 0.304378 0.952551i \(-0.401551\pi\)
0.304378 + 0.952551i \(0.401551\pi\)
\(462\) 6.40096i 0.297799i
\(463\) 36.5814i 1.70008i −0.526718 0.850040i \(-0.676578\pi\)
0.526718 0.850040i \(-0.323422\pi\)
\(464\) 8.93935 0.414999
\(465\) 36.1678 + 26.1489i 1.67724 + 1.21263i
\(466\) −11.1081 −0.514572
\(467\) 5.78204i 0.267561i 0.991011 + 0.133781i \(0.0427117\pi\)
−0.991011 + 0.133781i \(0.957288\pi\)
\(468\) 47.2478i 2.18403i
\(469\) 42.8768 1.97987
\(470\) −6.59128 + 9.11671i −0.304033 + 0.420523i
\(471\) 17.3264 0.798360
\(472\) 9.55309i 0.439717i
\(473\) 3.35317i 0.154179i
\(474\) 28.5658 1.31207
\(475\) −1.56723 4.74803i −0.0719095 0.217855i
\(476\) −18.3141 −0.839425
\(477\) 97.7488i 4.47561i
\(478\) 6.21045i 0.284059i
\(479\) −4.97976 −0.227531 −0.113765 0.993508i \(-0.536291\pi\)
−0.113765 + 0.993508i \(0.536291\pi\)
\(480\) 25.4182 35.1572i 1.16018 1.60470i
\(481\) 29.8097 1.35921
\(482\) 10.6048i 0.483035i
\(483\) 28.1921i 1.28278i
\(484\) 1.49249 0.0678404
\(485\) −35.1468 25.4107i −1.59594 1.15384i
\(486\) 38.7585 1.75812
\(487\) 15.2998i 0.693302i 0.937994 + 0.346651i \(0.112681\pi\)
−0.937994 + 0.346651i \(0.887319\pi\)
\(488\) 14.2899i 0.646874i
\(489\) −26.1738 −1.18362
\(490\) −0.405764 0.293363i −0.0183306 0.0132528i
\(491\) 11.6615 0.526275 0.263138 0.964758i \(-0.415243\pi\)
0.263138 + 0.964758i \(0.415243\pi\)
\(492\) 0.537549i 0.0242346i
\(493\) 33.4513i 1.50657i
\(494\) −2.80592 −0.126244
\(495\) −10.5300 + 14.5645i −0.473286 + 0.654625i
\(496\) −7.28437 −0.327078
\(497\) 21.1900i 0.950504i
\(498\) 26.0633i 1.16792i
\(499\) −21.2628 −0.951855 −0.475928 0.879484i \(-0.657888\pi\)
−0.475928 + 0.879484i \(0.657888\pi\)
\(500\) −15.9055 5.04535i −0.711315 0.225635i
\(501\) 57.9362 2.58840
\(502\) 4.95617i 0.221205i
\(503\) 26.1347i 1.16529i 0.812727 + 0.582645i \(0.197982\pi\)
−0.812727 + 0.582645i \(0.802018\pi\)
\(504\) −54.0834 −2.40907
\(505\) 8.11515 11.2245i 0.361120 0.499482i
\(506\) 2.23526 0.0993695
\(507\) 8.34970i 0.370823i
\(508\) 1.11000i 0.0492482i
\(509\) 24.9546 1.10609 0.553046 0.833151i \(-0.313465\pi\)
0.553046 + 0.833151i \(0.313465\pi\)
\(510\) −19.4590 14.0687i −0.861661 0.622971i
\(511\) −31.5440 −1.39542
\(512\) 13.1143i 0.579576i
\(513\) 16.7358i 0.738904i
\(514\) 12.3182 0.543333
\(515\) −25.6023 18.5102i −1.12817 0.815656i
\(516\) 16.6265 0.731942
\(517\) 7.06218i 0.310595i
\(518\) 14.5820i 0.640696i
\(519\) −45.8300 −2.01171
\(520\) −12.8386 + 17.7577i −0.563009 + 0.778725i
\(521\) −25.5480 −1.11928 −0.559640 0.828736i \(-0.689060\pi\)
−0.559640 + 0.828736i \(0.689060\pi\)
\(522\) 42.2151i 1.84770i
\(523\) 16.6070i 0.726172i 0.931756 + 0.363086i \(0.118277\pi\)
−0.931756 + 0.363086i \(0.881723\pi\)
\(524\) −7.06867 −0.308796
\(525\) 14.0817 + 42.6614i 0.614575 + 1.86190i
\(526\) 6.32857 0.275939
\(527\) 27.2583i 1.18739i
\(528\) 4.02824i 0.175307i
\(529\) 13.1551 0.571962
\(530\) −11.3507 + 15.6997i −0.493043 + 0.681952i
\(531\) 30.8607 1.33924
\(532\) 4.03643i 0.175002i
\(533\) 0.426996i 0.0184953i
\(534\) 18.7147 0.809865
\(535\) 2.94335 + 2.12801i 0.127252 + 0.0920017i
\(536\) −39.4451 −1.70377
\(537\) 18.8834i 0.814878i
\(538\) 11.1399i 0.480275i
\(539\) −0.314322 −0.0135388
\(540\) 45.2620 + 32.7239i 1.94777 + 1.40821i
\(541\) 33.1242 1.42412 0.712060 0.702119i \(-0.247762\pi\)
0.712060 + 0.702119i \(0.247762\pi\)
\(542\) 4.40663i 0.189281i
\(543\) 61.7022i 2.64789i
\(544\) 26.4966 1.13603
\(545\) 22.3218 30.8743i 0.956160 1.32251i
\(546\) 25.2114 1.07895
\(547\) 29.8988i 1.27838i 0.769049 + 0.639189i \(0.220730\pi\)
−0.769049 + 0.639189i \(0.779270\pi\)
\(548\) 3.38672i 0.144673i
\(549\) 46.1627 1.97017
\(550\) 3.38249 1.11649i 0.144230 0.0476074i
\(551\) 7.37268 0.314087
\(552\) 25.9357i 1.10390i
\(553\) 32.6419i 1.38808i
\(554\) 9.68126 0.411318
\(555\) −32.9419 + 45.5635i −1.39831 + 1.93406i
\(556\) −5.24209 −0.222314
\(557\) 18.2206i 0.772030i 0.922493 + 0.386015i \(0.126149\pi\)
−0.922493 + 0.386015i \(0.873851\pi\)
\(558\) 34.3996i 1.45625i
\(559\) −13.2071 −0.558601
\(560\) −5.94215 4.29611i −0.251102 0.181544i
\(561\) −15.0738 −0.636415
\(562\) 6.91281i 0.291599i
\(563\) 46.4723i 1.95858i 0.202473 + 0.979288i \(0.435102\pi\)
−0.202473 + 0.979288i \(0.564898\pi\)
\(564\) 35.0175 1.47450
\(565\) −1.67128 1.20831i −0.0703112 0.0508342i
\(566\) −1.09988 −0.0462314
\(567\) 85.1606i 3.57641i
\(568\) 19.4941i 0.817954i
\(569\) −33.2411 −1.39354 −0.696770 0.717295i \(-0.745380\pi\)
−0.696770 + 0.717295i \(0.745380\pi\)
\(570\) 3.10074 4.28878i 0.129876 0.179637i
\(571\) −25.3387 −1.06039 −0.530196 0.847875i \(-0.677882\pi\)
−0.530196 + 0.847875i \(0.677882\pi\)
\(572\) 5.87844i 0.245790i
\(573\) 12.0786i 0.504589i
\(574\) −0.208873 −0.00871820
\(575\) −14.8977 + 4.91743i −0.621276 + 0.205071i
\(576\) 13.9476 0.581149
\(577\) 2.07211i 0.0862632i −0.999069 0.0431316i \(-0.986267\pi\)
0.999069 0.0431316i \(-0.0137335\pi\)
\(578\) 2.55476i 0.106264i
\(579\) −62.5758 −2.60056
\(580\) 14.4160 19.9394i 0.598590 0.827939i
\(581\) 29.7823 1.23558
\(582\) 45.9058i 1.90286i
\(583\) 12.1616i 0.503684i
\(584\) 29.0193 1.20083
\(585\) −57.3650 41.4742i −2.37175 1.71475i
\(586\) −15.8631 −0.655297
\(587\) 8.27824i 0.341679i −0.985299 0.170840i \(-0.945352\pi\)
0.985299 0.170840i \(-0.0546480\pi\)
\(588\) 1.55855i 0.0642734i
\(589\) −6.00774 −0.247545
\(590\) −4.95661 3.58357i −0.204061 0.147533i
\(591\) −0.208612 −0.00858117
\(592\) 9.17672i 0.377161i
\(593\) 12.6945i 0.521301i 0.965433 + 0.260651i \(0.0839371\pi\)
−0.965433 + 0.260651i \(0.916063\pi\)
\(594\) −11.9226 −0.489189
\(595\) −16.0761 + 22.2357i −0.659058 + 0.911574i
\(596\) 19.1797 0.785631
\(597\) 23.1008i 0.945453i
\(598\) 8.80400i 0.360022i
\(599\) 44.5906 1.82192 0.910962 0.412491i \(-0.135341\pi\)
0.910962 + 0.412491i \(0.135341\pi\)
\(600\) −12.9546 39.2470i −0.528871 1.60225i
\(601\) 48.0310 1.95922 0.979612 0.200900i \(-0.0643865\pi\)
0.979612 + 0.200900i \(0.0643865\pi\)
\(602\) 6.46050i 0.263310i
\(603\) 127.425i 5.18915i
\(604\) 17.7557 0.722468
\(605\) 1.31011 1.81207i 0.0532635 0.0736713i
\(606\) 14.6604 0.595540
\(607\) 4.19205i 0.170150i 0.996375 + 0.0850751i \(0.0271130\pi\)
−0.996375 + 0.0850751i \(0.972887\pi\)
\(608\) 5.83987i 0.236838i
\(609\) −66.2440 −2.68434
\(610\) −7.41431 5.36046i −0.300197 0.217039i
\(611\) −27.8157 −1.12530
\(612\) 54.4274i 2.20010i
\(613\) 33.7644i 1.36373i −0.731477 0.681867i \(-0.761168\pi\)
0.731477 0.681867i \(-0.238832\pi\)
\(614\) 7.33132 0.295868
\(615\) 0.652655 + 0.471862i 0.0263176 + 0.0190273i
\(616\) 6.72892 0.271116
\(617\) 4.33391i 0.174477i −0.996187 0.0872383i \(-0.972196\pi\)
0.996187 0.0872383i \(-0.0278041\pi\)
\(618\) 33.4396i 1.34514i
\(619\) −34.8040 −1.39889 −0.699445 0.714686i \(-0.746570\pi\)
−0.699445 + 0.714686i \(0.746570\pi\)
\(620\) −11.7471 + 16.2479i −0.471773 + 0.652533i
\(621\) 52.5112 2.10720
\(622\) 16.4660i 0.660225i
\(623\) 21.3852i 0.856779i
\(624\) 15.8660 0.635148
\(625\) −20.0876 + 14.8825i −0.803503 + 0.595301i
\(626\) −6.20663 −0.248067
\(627\) 3.32227i 0.132679i
\(628\) 7.78369i 0.310603i
\(629\) −34.3395 −1.36921
\(630\) −20.2879 + 28.0611i −0.808288 + 1.11798i
\(631\) −15.6712 −0.623862 −0.311931 0.950105i \(-0.600976\pi\)
−0.311931 + 0.950105i \(0.600976\pi\)
\(632\) 30.0294i 1.19451i
\(633\) 64.3147i 2.55628i
\(634\) −13.0884 −0.519808
\(635\) 1.34768 + 0.974359i 0.0534812 + 0.0386662i
\(636\) 60.3029 2.39116
\(637\) 1.23802i 0.0490520i
\(638\) 5.25228i 0.207940i
\(639\) 62.9744 2.49123
\(640\) 18.9244 + 13.6821i 0.748053 + 0.540833i
\(641\) −41.6116 −1.64356 −0.821780 0.569805i \(-0.807019\pi\)
−0.821780 + 0.569805i \(0.807019\pi\)
\(642\) 3.84435i 0.151724i
\(643\) 38.0923i 1.50221i −0.660180 0.751107i \(-0.729520\pi\)
0.660180 0.751107i \(-0.270480\pi\)
\(644\) −12.6649 −0.499069
\(645\) 14.5948 20.1868i 0.574670 0.794854i
\(646\) 3.23229 0.127173
\(647\) 10.3871i 0.408359i 0.978934 + 0.204179i \(0.0654526\pi\)
−0.978934 + 0.204179i \(0.934547\pi\)
\(648\) 78.3447i 3.07767i
\(649\) −3.83960 −0.150717
\(650\) 4.39752 + 13.3226i 0.172485 + 0.522554i
\(651\) 53.9800 2.11564
\(652\) 11.7583i 0.460489i
\(653\) 38.8944i 1.52205i 0.648720 + 0.761027i \(0.275305\pi\)
−0.648720 + 0.761027i \(0.724695\pi\)
\(654\) 40.3255 1.57685
\(655\) −6.20489 + 8.58228i −0.242445 + 0.335338i
\(656\) −0.131448 −0.00513218
\(657\) 93.7451i 3.65735i
\(658\) 13.6066i 0.530440i
\(659\) −15.3578 −0.598253 −0.299127 0.954213i \(-0.596695\pi\)
−0.299127 + 0.954213i \(0.596695\pi\)
\(660\) −8.98508 6.49610i −0.349744 0.252860i
\(661\) −0.608689 −0.0236753 −0.0118376 0.999930i \(-0.503768\pi\)
−0.0118376 + 0.999930i \(0.503768\pi\)
\(662\) 3.46301i 0.134594i
\(663\) 59.3709i 2.30577i
\(664\) −27.3986 −1.06327
\(665\) −4.90076 3.54319i −0.190043 0.137399i
\(666\) −43.3360 −1.67924
\(667\) 23.1329i 0.895710i
\(668\) 26.0271i 1.00702i
\(669\) 13.1997 0.510328
\(670\) −14.7967 + 20.4661i −0.571648 + 0.790674i
\(671\) −5.74344 −0.221723
\(672\) 52.4717i 2.02414i
\(673\) 20.7131i 0.798432i 0.916857 + 0.399216i \(0.130718\pi\)
−0.916857 + 0.399216i \(0.869282\pi\)
\(674\) −12.1707 −0.468799
\(675\) 79.4622 26.2289i 3.05850 1.00955i
\(676\) −3.75100 −0.144269
\(677\) 18.6760i 0.717776i 0.933381 + 0.358888i \(0.116844\pi\)
−0.933381 + 0.358888i \(0.883156\pi\)
\(678\) 2.18288i 0.0838331i
\(679\) −52.4562 −2.01309
\(680\) 14.7895 20.4560i 0.567151 0.784453i
\(681\) −10.4783 −0.401529
\(682\) 4.27991i 0.163886i
\(683\) 44.6906i 1.71004i 0.518597 + 0.855019i \(0.326455\pi\)
−0.518597 + 0.855019i \(0.673545\pi\)
\(684\) −11.9958 −0.458672
\(685\) 4.11191 + 2.97286i 0.157108 + 0.113587i
\(686\) 12.8812 0.491806
\(687\) 1.55534i 0.0593397i
\(688\) 4.06572i 0.155004i
\(689\) −47.9009 −1.82488
\(690\) −13.4567 9.72905i −0.512289 0.370379i
\(691\) −33.2786 −1.26598 −0.632988 0.774162i \(-0.718172\pi\)
−0.632988 + 0.774162i \(0.718172\pi\)
\(692\) 20.5885i 0.782659i
\(693\) 21.7373i 0.825733i
\(694\) −13.4758 −0.511536
\(695\) −4.60152 + 6.36458i −0.174545 + 0.241422i
\(696\) 60.9422 2.31001
\(697\) 0.491881i 0.0186313i
\(698\) 19.7545i 0.747717i
\(699\) 51.8025 1.95935
\(700\) −19.1651 + 6.32602i −0.724373 + 0.239101i
\(701\) 22.7497 0.859244 0.429622 0.903009i \(-0.358647\pi\)
0.429622 + 0.903009i \(0.358647\pi\)
\(702\) 46.9593i 1.77236i
\(703\) 7.56844i 0.285449i
\(704\) −1.73532 −0.0654023
\(705\) 30.7384 42.5158i 1.15767 1.60124i
\(706\) 3.72909 0.140346
\(707\) 16.7524i 0.630038i
\(708\) 19.0384i 0.715509i
\(709\) 11.0298 0.414233 0.207116 0.978316i \(-0.433592\pi\)
0.207116 + 0.978316i \(0.433592\pi\)
\(710\) −10.1145 7.31266i −0.379590 0.274439i
\(711\) −97.0081 −3.63809
\(712\) 19.6736i 0.737299i
\(713\) 18.8502i 0.705946i
\(714\) −29.0424 −1.08688
\(715\) 7.13720 + 5.16011i 0.266916 + 0.192977i
\(716\) 8.48313 0.317029
\(717\) 28.9624i 1.08162i
\(718\) 4.24942i 0.158587i
\(719\) 8.03346 0.299598 0.149799 0.988717i \(-0.452137\pi\)
0.149799 + 0.988717i \(0.452137\pi\)
\(720\) −12.7675 + 17.6594i −0.475818 + 0.658127i
\(721\) −38.2112 −1.42306
\(722\) 0.712399i 0.0265127i
\(723\) 49.4554i 1.83927i
\(724\) −27.7189 −1.03017
\(725\) −11.5547 35.0057i −0.429130 1.30008i
\(726\) 2.36678 0.0878394
\(727\) 25.2120i 0.935060i 0.883977 + 0.467530i \(0.154856\pi\)
−0.883977 + 0.467530i \(0.845144\pi\)
\(728\) 26.5031i 0.982270i
\(729\) −86.2849 −3.19574
\(730\) 10.8858 15.0567i 0.402901 0.557272i
\(731\) 15.2140 0.562710
\(732\) 28.4785i 1.05260i
\(733\) 10.9045i 0.402766i −0.979513 0.201383i \(-0.935456\pi\)
0.979513 0.201383i \(-0.0645435\pi\)
\(734\) −4.20326 −0.155145
\(735\) 1.89228 + 1.36810i 0.0697978 + 0.0504630i
\(736\) 18.3235 0.675413
\(737\) 15.8539i 0.583985i
\(738\) 0.620748i 0.0228500i
\(739\) 3.13455 0.115306 0.0576531 0.998337i \(-0.481638\pi\)
0.0576531 + 0.998337i \(0.481638\pi\)
\(740\) −20.4689 14.7987i −0.752450 0.544012i
\(741\) 13.0854 0.480703
\(742\) 23.4316i 0.860202i
\(743\) 18.0854i 0.663489i 0.943369 + 0.331744i \(0.107637\pi\)
−0.943369 + 0.331744i \(0.892363\pi\)
\(744\) −49.6597 −1.82061
\(745\) 16.8360 23.2866i 0.616822 0.853156i
\(746\) −13.3076 −0.487227
\(747\) 88.5095i 3.23839i
\(748\) 6.77171i 0.247598i
\(749\) 4.39291 0.160513
\(750\) −25.2228 8.00089i −0.921008 0.292151i
\(751\) −37.8934 −1.38275 −0.691374 0.722497i \(-0.742994\pi\)
−0.691374 + 0.722497i \(0.742994\pi\)
\(752\) 8.56288i 0.312256i
\(753\) 23.1131i 0.842287i
\(754\) −20.6871 −0.753380
\(755\) 15.5860 21.5577i 0.567231 0.784565i
\(756\) 67.5530 2.45688
\(757\) 33.0357i 1.20070i 0.799736 + 0.600351i \(0.204973\pi\)
−0.799736 + 0.600351i \(0.795027\pi\)
\(758\) 9.40737i 0.341691i
\(759\) −10.4241 −0.378372
\(760\) 4.50852 + 3.25961i 0.163541 + 0.118238i
\(761\) −39.4886 −1.43146 −0.715731 0.698376i \(-0.753906\pi\)
−0.715731 + 0.698376i \(0.753906\pi\)
\(762\) 1.76023i 0.0637664i
\(763\) 46.0796i 1.66819i
\(764\) −5.42615 −0.196311
\(765\) 66.0819 + 47.7765i 2.38920 + 1.72736i
\(766\) −8.11992 −0.293385
\(767\) 15.1230i 0.546059i
\(768\) 36.2479i 1.30798i
\(769\) −39.2949 −1.41701 −0.708505 0.705706i \(-0.750630\pi\)
−0.708505 + 0.705706i \(0.750630\pi\)
\(770\) 2.52416 3.49129i 0.0909645 0.125817i
\(771\) −57.4460 −2.06887
\(772\) 28.1114i 1.01175i
\(773\) 1.29918i 0.0467281i −0.999727 0.0233640i \(-0.992562\pi\)
0.999727 0.0233640i \(-0.00743768\pi\)
\(774\) 19.1999 0.690125
\(775\) 9.41551 + 28.5249i 0.338215 + 1.02465i
\(776\) 48.2579 1.73236
\(777\) 68.0030i 2.43959i
\(778\) 2.93733i 0.105308i
\(779\) −0.108411 −0.00388422
\(780\) 25.5861 35.3894i 0.916130 1.26714i
\(781\) −7.83511 −0.280362
\(782\) 10.1418i 0.362671i
\(783\) 123.388i 4.40952i
\(784\) −0.381114 −0.0136112
\(785\) 9.45041 + 6.83254i 0.337300 + 0.243864i
\(786\) −11.2095 −0.399828
\(787\) 21.6621i 0.772170i 0.922463 + 0.386085i \(0.126173\pi\)
−0.922463 + 0.386085i \(0.873827\pi\)
\(788\) 0.0937165i 0.00333851i
\(789\) −29.5132 −1.05070
\(790\) 15.5807 + 11.2647i 0.554338 + 0.400780i
\(791\) −2.49436 −0.0886893
\(792\) 19.9976i 0.710583i
\(793\) 22.6216i 0.803316i
\(794\) −14.6619 −0.520332
\(795\) 52.9340 73.2155i 1.87737 2.59669i
\(796\) −10.3777 −0.367830
\(797\) 31.7834i 1.12582i −0.826517 0.562912i \(-0.809681\pi\)
0.826517 0.562912i \(-0.190319\pi\)
\(798\) 6.40096i 0.226591i
\(799\) 32.0425 1.13358
\(800\) 27.7279 9.15242i 0.980328 0.323587i
\(801\) −63.5543 −2.24558
\(802\) 8.23509i 0.290791i
\(803\) 11.6635i 0.411597i
\(804\) 78.6106 2.77238
\(805\) −11.1173 + 15.3769i −0.391834 + 0.541964i
\(806\) 16.8572 0.593770
\(807\) 51.9509i 1.82876i
\(808\) 15.4116i 0.542178i
\(809\) −26.2573 −0.923157 −0.461578 0.887099i \(-0.652717\pi\)
−0.461578 + 0.887099i \(0.652717\pi\)
\(810\) 40.6491 + 29.3888i 1.42826 + 1.03262i
\(811\) −36.5555 −1.28364 −0.641819 0.766856i \(-0.721820\pi\)
−0.641819 + 0.766856i \(0.721820\pi\)
\(812\) 29.7593i 1.04435i
\(813\) 20.5503i 0.720730i
\(814\) 5.39175 0.188981
\(815\) −14.2761 10.3214i −0.500068 0.361543i
\(816\) −18.2769 −0.639820
\(817\) 3.35317i 0.117313i
\(818\) 10.5597i 0.369210i
\(819\) −85.6165 −2.99168
\(820\) −0.211978 + 0.293197i −0.00740260 + 0.0102389i
\(821\) 17.3018 0.603837 0.301919 0.953334i \(-0.402373\pi\)
0.301919 + 0.953334i \(0.402373\pi\)
\(822\) 5.37063i 0.187322i
\(823\) 27.8154i 0.969582i 0.874630 + 0.484791i \(0.161104\pi\)
−0.874630 + 0.484791i \(0.838896\pi\)
\(824\) 35.1529 1.22461
\(825\) −15.7742 + 5.20676i −0.549188 + 0.181276i
\(826\) −7.39769 −0.257398
\(827\) 34.4103i 1.19656i 0.801285 + 0.598282i \(0.204150\pi\)
−0.801285 + 0.598282i \(0.795850\pi\)
\(828\) 37.6388i 1.30804i
\(829\) 2.94933 0.102434 0.0512172 0.998688i \(-0.483690\pi\)
0.0512172 + 0.998688i \(0.483690\pi\)
\(830\) −10.2778 + 14.2158i −0.356749 + 0.493436i
\(831\) −45.1485 −1.56619
\(832\) 6.83488i 0.236957i
\(833\) 1.42614i 0.0494128i
\(834\) −8.31288 −0.287851
\(835\) 31.6003 + 22.8467i 1.09357 + 0.790642i
\(836\) 1.49249 0.0516188
\(837\) 100.544i 3.47532i
\(838\) 3.26541i 0.112802i
\(839\) −25.9837 −0.897057 −0.448528 0.893769i \(-0.648052\pi\)
−0.448528 + 0.893769i \(0.648052\pi\)
\(840\) −40.5094 29.2878i −1.39771 1.01053i
\(841\) 25.3563 0.874357
\(842\) 3.61483i 0.124575i
\(843\) 32.2379i 1.11033i
\(844\) 28.8926 0.994524
\(845\) −3.29263 + 4.55420i −0.113270 + 0.156669i
\(846\) 40.4372 1.39026
\(847\) 2.70450i 0.0929277i
\(848\) 14.7460i 0.506378i
\(849\) 5.12929 0.176037
\(850\) −5.06575 15.3470i −0.173754 0.526398i
\(851\) −23.7472 −0.814042
\(852\) 38.8500i 1.33098i
\(853\) 31.9494i 1.09393i 0.837157 + 0.546963i \(0.184216\pi\)
−0.837157 + 0.546963i \(0.815784\pi\)
\(854\) −11.0658 −0.378663
\(855\) −10.5300 + 14.5645i −0.360117 + 0.498095i
\(856\) −4.04132 −0.138130
\(857\) 28.7090i 0.980682i 0.871531 + 0.490341i \(0.163128\pi\)
−0.871531 + 0.490341i \(0.836872\pi\)
\(858\) 9.32200i 0.318248i
\(859\) 18.4221 0.628552 0.314276 0.949332i \(-0.398238\pi\)
0.314276 + 0.949332i \(0.398238\pi\)
\(860\) 9.06866 + 6.55654i 0.309239 + 0.223576i
\(861\) 0.974080 0.0331966
\(862\) 19.5978i 0.667504i
\(863\) 17.4004i 0.592316i −0.955139 0.296158i \(-0.904294\pi\)
0.955139 0.296158i \(-0.0957055\pi\)
\(864\) −97.7350 −3.32501
\(865\) −24.9972 18.0727i −0.849929 0.614489i
\(866\) 9.38373 0.318872
\(867\) 11.9141i 0.404625i
\(868\) 24.2498i 0.823094i
\(869\) 12.0695 0.409429
\(870\) 22.8607 31.6198i 0.775052 1.07201i
\(871\) −62.4434 −2.11582
\(872\) 42.3916i 1.43556i
\(873\) 155.894i 5.27621i
\(874\) 2.23526 0.0756089
\(875\) −9.14255 + 28.8219i −0.309075 + 0.974359i
\(876\) −57.8329 −1.95399
\(877\) 6.68555i 0.225755i 0.993609 + 0.112877i \(0.0360067\pi\)
−0.993609 + 0.112877i \(0.963993\pi\)
\(878\) 8.87102i 0.299383i
\(879\) 73.9774 2.49519
\(880\) 1.58850 2.19714i 0.0535484 0.0740654i
\(881\) −23.4701 −0.790728 −0.395364 0.918525i \(-0.629382\pi\)
−0.395364 + 0.918525i \(0.629382\pi\)
\(882\) 1.79977i 0.0606014i
\(883\) 20.8333i 0.701096i 0.936545 + 0.350548i \(0.114005\pi\)
−0.936545 + 0.350548i \(0.885995\pi\)
\(884\) 26.6716 0.897065
\(885\) 23.1152 + 16.7120i 0.777007 + 0.561767i
\(886\) 12.1846 0.409349
\(887\) 5.03263i 0.168979i −0.996424 0.0844896i \(-0.973074\pi\)
0.996424 0.0844896i \(-0.0269260\pi\)
\(888\) 62.5604i 2.09939i
\(889\) 2.01140 0.0674602
\(890\) 10.2076 + 7.37999i 0.342160 + 0.247378i
\(891\) 31.4885 1.05490
\(892\) 5.92978i 0.198544i
\(893\) 7.06218i 0.236327i
\(894\) 30.4150 1.01723
\(895\) 7.44650 10.2996i 0.248909 0.344278i
\(896\) 28.2444 0.943581
\(897\) 41.0574i 1.37087i
\(898\) 1.20594i 0.0402427i
\(899\) −44.2931 −1.47726
\(900\) 18.8002 + 56.9565i 0.626674 + 1.89855i
\(901\) 55.1798 1.83830
\(902\) 0.0772318i 0.00257154i
\(903\) 30.1285i 1.00261i
\(904\) 2.29472 0.0763214
\(905\) −24.3317 + 33.6544i −0.808814 + 1.11871i
\(906\) 28.1568 0.935448
\(907\) 24.4295i 0.811169i −0.914058 0.405584i \(-0.867068\pi\)
0.914058 0.405584i \(-0.132932\pi\)
\(908\) 4.70725i 0.156215i
\(909\) −49.7862 −1.65130
\(910\) 13.7511 + 9.94189i 0.455845 + 0.329570i
\(911\) −23.8703 −0.790859 −0.395430 0.918496i \(-0.629404\pi\)
−0.395430 + 0.918496i \(0.629404\pi\)
\(912\) 4.02824i 0.133388i
\(913\) 11.0121i 0.364448i
\(914\) 11.5597 0.382362
\(915\) 34.5766 + 24.9985i 1.14307 + 0.826425i
\(916\) −0.698715 −0.0230862
\(917\) 12.8090i 0.422989i
\(918\) 54.0950i 1.78540i
\(919\) 56.2979 1.85710 0.928548 0.371213i \(-0.121058\pi\)
0.928548 + 0.371213i \(0.121058\pi\)
\(920\) 10.2275 14.1462i 0.337192 0.466386i
\(921\) −34.1896 −1.12658
\(922\) 9.31143i 0.306656i
\(923\) 30.8600i 1.01577i
\(924\) −13.4101 −0.441161
\(925\) −35.9352 + 11.8615i −1.18154 + 0.390003i
\(926\) 26.0605 0.856401
\(927\) 113.559i 3.72977i
\(928\) 43.0555i 1.41336i
\(929\) 52.6145 1.72623 0.863113 0.505011i \(-0.168512\pi\)
0.863113 + 0.505011i \(0.168512\pi\)
\(930\) −18.6284 + 25.7659i −0.610850 + 0.844897i
\(931\) −0.314322 −0.0103015
\(932\) 23.2716i 0.762288i
\(933\) 76.7889i 2.51396i
\(934\) −4.11912 −0.134782
\(935\) −8.22174 5.94422i −0.268880 0.194397i
\(936\) 78.7642 2.57449
\(937\) 38.7016i 1.26433i 0.774835 + 0.632163i \(0.217833\pi\)
−0.774835 + 0.632163i \(0.782167\pi\)
\(938\) 30.5454i 0.997342i
\(939\) 28.9446 0.944571
\(940\) 19.0997 + 13.8088i 0.622963 + 0.450395i
\(941\) 13.4504 0.438471 0.219235 0.975672i \(-0.429644\pi\)
0.219235 + 0.975672i \(0.429644\pi\)
\(942\) 12.3433i 0.402168i
\(943\) 0.340156i 0.0110770i
\(944\) −4.65550 −0.151524
\(945\) 59.2982 82.0182i 1.92897 2.66805i
\(946\) −2.38880 −0.0776665
\(947\) 45.0879i 1.46516i −0.680681 0.732580i \(-0.738316\pi\)
0.680681 0.732580i \(-0.261684\pi\)
\(948\) 59.8459i 1.94370i
\(949\) 45.9389 1.49124
\(950\) 3.38249 1.11649i 0.109742 0.0362238i
\(951\) 61.0378 1.97929
\(952\) 30.5304i 0.989496i
\(953\) 27.6756i 0.896502i 0.893908 + 0.448251i \(0.147953\pi\)
−0.893908 + 0.448251i \(0.852047\pi\)
\(954\) 69.6361 2.25455
\(955\) −4.76308 + 6.58805i −0.154130 + 0.213184i
\(956\) −13.0110 −0.420806
\(957\) 24.4940i 0.791779i
\(958\) 3.54757i 0.114617i
\(959\) 6.13698 0.198173
\(960\) 10.4470 + 7.55304i 0.337175 + 0.243773i
\(961\) 5.09294 0.164288
\(962\) 21.2364i 0.684689i
\(963\) 13.0552i 0.420699i
\(964\) −22.2172 −0.715569
\(965\) −34.1309 24.6762i −1.09871 0.794356i
\(966\) −20.0840 −0.646192
\(967\) 21.9186i 0.704855i 0.935839 + 0.352428i \(0.114644\pi\)
−0.935839 + 0.352428i \(0.885356\pi\)
\(968\) 2.48804i 0.0799688i
\(969\) −15.0738 −0.484240
\(970\) 18.1026 25.0386i 0.581239 0.803940i
\(971\) 38.2300 1.22686 0.613429 0.789750i \(-0.289790\pi\)
0.613429 + 0.789750i \(0.289790\pi\)
\(972\) 81.1999i 2.60449i
\(973\) 9.49906i 0.304526i
\(974\) −10.8996 −0.349245
\(975\) −20.5078 62.1297i −0.656775 1.98974i
\(976\) −6.96390 −0.222909
\(977\) 55.6928i 1.78177i −0.454227 0.890886i \(-0.650085\pi\)
0.454227 0.890886i \(-0.349915\pi\)
\(978\) 18.6462i 0.596239i
\(979\) 7.90725 0.252717
\(980\) −0.614600 + 0.850084i −0.0196327 + 0.0271549i
\(981\) −136.943 −4.37226
\(982\) 8.30762i 0.265107i
\(983\) 55.0897i 1.75709i −0.477660 0.878545i \(-0.658515\pi\)
0.477660 0.878545i \(-0.341485\pi\)
\(984\) −0.896119 −0.0285672
\(985\) −0.113784 0.0822645i −0.00362546 0.00262117i
\(986\) 23.8306 0.758922
\(987\) 63.4543i 2.01977i
\(988\) 5.87844i 0.187018i
\(989\) 10.5211 0.334552
\(990\) −10.3757 7.50153i −0.329762 0.238414i
\(991\) −39.1755 −1.24445 −0.622226 0.782838i \(-0.713771\pi\)
−0.622226 + 0.782838i \(0.713771\pi\)
\(992\) 35.0844i 1.11393i
\(993\) 16.1497i 0.512496i
\(994\) −15.0958 −0.478808
\(995\) −9.10961 + 12.5999i −0.288794 + 0.399445i
\(996\) 54.6030 1.73016
\(997\) 59.0338i 1.86962i −0.355148 0.934810i \(-0.615569\pi\)
0.355148 0.934810i \(-0.384431\pi\)
\(998\) 15.1476i 0.479489i
\(999\) 126.664 4.00747
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 1045.2.b.c.419.13 yes 20
5.2 odd 4 5225.2.a.ba.1.8 20
5.3 odd 4 5225.2.a.ba.1.13 20
5.4 even 2 inner 1045.2.b.c.419.8 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.b.c.419.8 20 5.4 even 2 inner
1045.2.b.c.419.13 yes 20 1.1 even 1 trivial
5225.2.a.ba.1.8 20 5.2 odd 4
5225.2.a.ba.1.13 20 5.3 odd 4