Properties

Label 637.2.h.m.471.1
Level $637$
Weight $2$
Character 637.471
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 8 x^{14} + 45 x^{12} + 124 x^{10} + 248 x^{8} + 250 x^{6} + 177 x^{4} + 14 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 471.1
Root \(0.558788 - 0.967849i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.m.165.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.33152 q^{2} +(-1.15450 + 1.99966i) q^{3} +3.43596 q^{4} +(-1.68556 + 2.91947i) q^{5} +(2.69174 - 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 - 2.01915i) q^{9} +O(q^{10})\) \(q-2.33152 q^{2} +(-1.15450 + 1.99966i) q^{3} +3.43596 q^{4} +(-1.68556 + 2.91947i) q^{5} +(2.69174 - 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 - 2.01915i) q^{9} +(3.92990 - 6.80679i) q^{10} +(-1.16576 + 2.01915i) q^{11} +(-3.96683 + 6.87075i) q^{12} +(0.408029 + 3.58239i) q^{13} +(-3.89197 - 6.74108i) q^{15} +0.933914 q^{16} -5.45734 q^{17} +(2.71798 + 4.70768i) q^{18} +(3.58410 + 6.20784i) q^{19} +(-5.79151 + 10.0312i) q^{20} +(2.71798 - 4.70768i) q^{22} -6.45242 q^{23} +(3.86524 - 6.69480i) q^{24} +(-3.18221 - 5.51175i) q^{25} +(-0.951325 - 8.35239i) q^{26} -1.54354 q^{27} +(4.22143 + 7.31174i) q^{29} +(9.07418 + 15.7169i) q^{30} +(1.52560 + 2.64242i) q^{31} +4.51850 q^{32} +(-2.69174 - 4.66224i) q^{33} +12.7239 q^{34} +(-4.00550 - 6.93773i) q^{36} +3.05653 q^{37} +(-8.35637 - 14.4737i) q^{38} +(-7.63463 - 3.31996i) q^{39} +(5.64320 - 9.77430i) q^{40} +(0.468833 + 0.812043i) q^{41} +(2.04605 - 3.54385i) q^{43} +(-4.00550 + 6.93773i) q^{44} +7.85981 q^{45} +15.0439 q^{46} +(1.73168 - 2.99936i) q^{47} +(-1.07821 + 1.86751i) q^{48} +(7.41937 + 12.8507i) q^{50} +(6.30052 - 10.9128i) q^{51} +(1.40197 + 12.3090i) q^{52} +(1.17194 + 2.02985i) q^{53} +3.59878 q^{54} +(-3.92990 - 6.80679i) q^{55} -16.5514 q^{57} +(-9.84233 - 17.0474i) q^{58} +7.24693 q^{59} +(-13.3726 - 23.1621i) q^{60} +(-3.19506 - 5.53401i) q^{61} +(-3.55697 - 6.16085i) q^{62} -12.4028 q^{64} +(-11.1464 - 4.84710i) q^{65} +(6.27584 + 10.8701i) q^{66} +(-2.30670 + 3.99532i) q^{67} -18.7512 q^{68} +(7.44934 - 12.9026i) q^{69} +(3.79370 - 6.57088i) q^{71} +(3.90292 + 6.76006i) q^{72} +(1.03498 + 1.79264i) q^{73} -7.12636 q^{74} +14.6955 q^{75} +(12.3148 + 21.3299i) q^{76} +(17.8002 + 7.74054i) q^{78} +(3.79434 - 6.57199i) q^{79} +(-1.57417 + 2.72654i) q^{80} +(5.27929 - 9.14400i) q^{81} +(-1.09309 - 1.89329i) q^{82} -2.89335 q^{83} +(9.19866 - 15.9326i) q^{85} +(-4.77039 + 8.26255i) q^{86} -19.4946 q^{87} +(3.90292 - 6.76006i) q^{88} +13.1597 q^{89} -18.3253 q^{90} -22.1703 q^{92} -7.04526 q^{93} +(-4.03744 + 6.99305i) q^{94} -24.1648 q^{95} +(-5.21663 + 9.03546i) q^{96} +(1.77856 - 3.08056i) q^{97} +5.43596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{2} + 24q^{4} + 24q^{8} - 4q^{9} + O(q^{10}) \) \( 16q - 8q^{2} + 24q^{4} + 24q^{8} - 4q^{9} - 4q^{11} - 8q^{15} + 8q^{16} + 28q^{18} + 28q^{22} - 24q^{23} + 12q^{25} + 8q^{29} + 28q^{30} + 4q^{36} + 16q^{37} + 20q^{39} + 32q^{43} + 4q^{44} + 8q^{46} + 36q^{50} + 44q^{51} + 4q^{53} - 96q^{57} - 48q^{58} - 64q^{60} - 64q^{64} - 68q^{65} + 20q^{67} + 8q^{71} + 28q^{72} - 152q^{74} + 28q^{78} + 4q^{79} + 56q^{81} + 36q^{85} - 4q^{86} + 28q^{88} - 160q^{92} - 16q^{93} - 104q^{95} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33152 −1.64863 −0.824315 0.566131i \(-0.808440\pi\)
−0.824315 + 0.566131i \(0.808440\pi\)
\(3\) −1.15450 + 1.99966i −0.666553 + 1.15450i 0.312309 + 0.949981i \(0.398898\pi\)
−0.978862 + 0.204523i \(0.934436\pi\)
\(4\) 3.43596 1.71798
\(5\) −1.68556 + 2.91947i −0.753804 + 1.30563i 0.192162 + 0.981363i \(0.438450\pi\)
−0.945966 + 0.324264i \(0.894883\pi\)
\(6\) 2.69174 4.66224i 1.09890 1.90335i
\(7\) 0 0
\(8\) −3.34797 −1.18369
\(9\) −1.16576 2.01915i −0.388586 0.673050i
\(10\) 3.92990 6.80679i 1.24274 2.15250i
\(11\) −1.16576 + 2.01915i −0.351489 + 0.608797i −0.986511 0.163697i \(-0.947658\pi\)
0.635021 + 0.772494i \(0.280991\pi\)
\(12\) −3.96683 + 6.87075i −1.14513 + 1.98342i
\(13\) 0.408029 + 3.58239i 0.113167 + 0.993576i
\(14\) 0 0
\(15\) −3.89197 6.74108i −1.00490 1.74054i
\(16\) 0.933914 0.233479
\(17\) −5.45734 −1.32360 −0.661800 0.749681i \(-0.730207\pi\)
−0.661800 + 0.749681i \(0.730207\pi\)
\(18\) 2.71798 + 4.70768i 0.640634 + 1.10961i
\(19\) 3.58410 + 6.20784i 0.822248 + 1.42418i 0.904004 + 0.427523i \(0.140614\pi\)
−0.0817564 + 0.996652i \(0.526053\pi\)
\(20\) −5.79151 + 10.0312i −1.29502 + 2.24304i
\(21\) 0 0
\(22\) 2.71798 4.70768i 0.579476 1.00368i
\(23\) −6.45242 −1.34542 −0.672711 0.739905i \(-0.734870\pi\)
−0.672711 + 0.739905i \(0.734870\pi\)
\(24\) 3.86524 6.69480i 0.788989 1.36657i
\(25\) −3.18221 5.51175i −0.636442 1.10235i
\(26\) −0.951325 8.35239i −0.186570 1.63804i
\(27\) −1.54354 −0.297054
\(28\) 0 0
\(29\) 4.22143 + 7.31174i 0.783900 + 1.35776i 0.929654 + 0.368434i \(0.120106\pi\)
−0.145753 + 0.989321i \(0.546561\pi\)
\(30\) 9.07418 + 15.7169i 1.65671 + 2.86951i
\(31\) 1.52560 + 2.64242i 0.274007 + 0.474593i 0.969884 0.243567i \(-0.0783176\pi\)
−0.695877 + 0.718161i \(0.744984\pi\)
\(32\) 4.51850 0.798766
\(33\) −2.69174 4.66224i −0.468572 0.811591i
\(34\) 12.7239 2.18213
\(35\) 0 0
\(36\) −4.00550 6.93773i −0.667583 1.15629i
\(37\) 3.05653 0.502491 0.251246 0.967923i \(-0.419160\pi\)
0.251246 + 0.967923i \(0.419160\pi\)
\(38\) −8.35637 14.4737i −1.35558 2.34794i
\(39\) −7.63463 3.31996i −1.22252 0.531620i
\(40\) 5.64320 9.77430i 0.892268 1.54545i
\(41\) 0.468833 + 0.812043i 0.0732194 + 0.126820i 0.900311 0.435248i \(-0.143339\pi\)
−0.827091 + 0.562068i \(0.810006\pi\)
\(42\) 0 0
\(43\) 2.04605 3.54385i 0.312019 0.540433i −0.666780 0.745254i \(-0.732328\pi\)
0.978799 + 0.204822i \(0.0656614\pi\)
\(44\) −4.00550 + 6.93773i −0.603852 + 1.04590i
\(45\) 7.85981 1.17167
\(46\) 15.0439 2.21810
\(47\) 1.73168 2.99936i 0.252591 0.437501i −0.711647 0.702537i \(-0.752050\pi\)
0.964239 + 0.265036i \(0.0853838\pi\)
\(48\) −1.07821 + 1.86751i −0.155626 + 0.269552i
\(49\) 0 0
\(50\) 7.41937 + 12.8507i 1.04926 + 1.81737i
\(51\) 6.30052 10.9128i 0.882249 1.52810i
\(52\) 1.40197 + 12.3090i 0.194418 + 1.70695i
\(53\) 1.17194 + 2.02985i 0.160978 + 0.278822i 0.935220 0.354068i \(-0.115202\pi\)
−0.774242 + 0.632890i \(0.781869\pi\)
\(54\) 3.59878 0.489732
\(55\) −3.92990 6.80679i −0.529908 0.917828i
\(56\) 0 0
\(57\) −16.5514 −2.19229
\(58\) −9.84233 17.0474i −1.29236 2.23844i
\(59\) 7.24693 0.943470 0.471735 0.881740i \(-0.343628\pi\)
0.471735 + 0.881740i \(0.343628\pi\)
\(60\) −13.3726 23.1621i −1.72640 2.99022i
\(61\) −3.19506 5.53401i −0.409086 0.708558i 0.585702 0.810527i \(-0.300819\pi\)
−0.994788 + 0.101969i \(0.967486\pi\)
\(62\) −3.55697 6.16085i −0.451736 0.782429i
\(63\) 0 0
\(64\) −12.4028 −1.55035
\(65\) −11.1464 4.84710i −1.38255 0.601208i
\(66\) 6.27584 + 10.8701i 0.772502 + 1.33801i
\(67\) −2.30670 + 3.99532i −0.281808 + 0.488106i −0.971830 0.235682i \(-0.924268\pi\)
0.690022 + 0.723788i \(0.257601\pi\)
\(68\) −18.7512 −2.27392
\(69\) 7.44934 12.9026i 0.896795 1.55329i
\(70\) 0 0
\(71\) 3.79370 6.57088i 0.450229 0.779819i −0.548171 0.836366i \(-0.684676\pi\)
0.998400 + 0.0565468i \(0.0180090\pi\)
\(72\) 3.90292 + 6.76006i 0.459964 + 0.796680i
\(73\) 1.03498 + 1.79264i 0.121136 + 0.209813i 0.920216 0.391412i \(-0.128013\pi\)
−0.799080 + 0.601224i \(0.794680\pi\)
\(74\) −7.12636 −0.828422
\(75\) 14.6955 1.69689
\(76\) 12.3148 + 21.3299i 1.41261 + 2.44671i
\(77\) 0 0
\(78\) 17.8002 + 7.74054i 2.01548 + 0.876444i
\(79\) 3.79434 6.57199i 0.426897 0.739407i −0.569699 0.821854i \(-0.692940\pi\)
0.996595 + 0.0824467i \(0.0262734\pi\)
\(80\) −1.57417 + 2.72654i −0.175997 + 0.304836i
\(81\) 5.27929 9.14400i 0.586588 1.01600i
\(82\) −1.09309 1.89329i −0.120712 0.209079i
\(83\) −2.89335 −0.317587 −0.158793 0.987312i \(-0.550760\pi\)
−0.158793 + 0.987312i \(0.550760\pi\)
\(84\) 0 0
\(85\) 9.19866 15.9326i 0.997735 1.72813i
\(86\) −4.77039 + 8.26255i −0.514404 + 0.890974i
\(87\) −19.4946 −2.09004
\(88\) 3.90292 6.76006i 0.416053 0.720624i
\(89\) 13.1597 1.39492 0.697461 0.716622i \(-0.254313\pi\)
0.697461 + 0.716622i \(0.254313\pi\)
\(90\) −18.3253 −1.93165
\(91\) 0 0
\(92\) −22.1703 −2.31141
\(93\) −7.04526 −0.730560
\(94\) −4.03744 + 6.99305i −0.416430 + 0.721278i
\(95\) −24.1648 −2.47926
\(96\) −5.21663 + 9.03546i −0.532420 + 0.922178i
\(97\) 1.77856 3.08056i 0.180585 0.312783i −0.761495 0.648171i \(-0.775534\pi\)
0.942080 + 0.335388i \(0.108867\pi\)
\(98\) 0 0
\(99\) 5.43596 0.546335
\(100\) −10.9340 18.9382i −1.09340 1.89382i
\(101\) −2.36432 + 4.09513i −0.235259 + 0.407481i −0.959348 0.282226i \(-0.908927\pi\)
0.724089 + 0.689707i \(0.242260\pi\)
\(102\) −14.6898 + 25.4434i −1.45450 + 2.51927i
\(103\) 2.99143 5.18131i 0.294754 0.510529i −0.680173 0.733051i \(-0.738096\pi\)
0.974928 + 0.222522i \(0.0714289\pi\)
\(104\) −1.36607 11.9937i −0.133954 1.17608i
\(105\) 0 0
\(106\) −2.73239 4.73263i −0.265393 0.459674i
\(107\) 13.1826 1.27441 0.637206 0.770694i \(-0.280090\pi\)
0.637206 + 0.770694i \(0.280090\pi\)
\(108\) −5.30353 −0.510333
\(109\) −2.05772 3.56408i −0.197094 0.341377i 0.750491 0.660881i \(-0.229817\pi\)
−0.947585 + 0.319504i \(0.896484\pi\)
\(110\) 9.16263 + 15.8701i 0.873623 + 1.51316i
\(111\) −3.52878 + 6.11203i −0.334937 + 0.580128i
\(112\) 0 0
\(113\) −7.14026 + 12.3673i −0.671699 + 1.16342i 0.305723 + 0.952121i \(0.401102\pi\)
−0.977422 + 0.211297i \(0.932231\pi\)
\(114\) 38.5899 3.61427
\(115\) 10.8759 18.8376i 1.01418 1.75662i
\(116\) 14.5047 + 25.1229i 1.34673 + 2.33260i
\(117\) 6.75772 5.00007i 0.624752 0.462257i
\(118\) −16.8963 −1.55543
\(119\) 0 0
\(120\) 13.0302 + 22.5689i 1.18949 + 2.06025i
\(121\) 2.78202 + 4.81860i 0.252911 + 0.438054i
\(122\) 7.44934 + 12.9026i 0.674431 + 1.16815i
\(123\) −2.16508 −0.195219
\(124\) 5.24192 + 9.07927i 0.470738 + 0.815343i
\(125\) 4.59963 0.411403
\(126\) 0 0
\(127\) 5.53854 + 9.59304i 0.491466 + 0.851244i 0.999952 0.00982616i \(-0.00312781\pi\)
−0.508486 + 0.861071i \(0.669794\pi\)
\(128\) 19.8803 1.75718
\(129\) 4.72433 + 8.18279i 0.415954 + 0.720454i
\(130\) 25.9881 + 11.3011i 2.27931 + 0.991170i
\(131\) 0.336006 0.581979i 0.0293570 0.0508478i −0.850974 0.525208i \(-0.823987\pi\)
0.880331 + 0.474361i \(0.157321\pi\)
\(132\) −9.24873 16.0193i −0.804998 1.39430i
\(133\) 0 0
\(134\) 5.37810 9.31515i 0.464597 0.804706i
\(135\) 2.60172 4.50631i 0.223920 0.387842i
\(136\) 18.2710 1.56673
\(137\) 7.83875 0.669709 0.334855 0.942270i \(-0.391313\pi\)
0.334855 + 0.942270i \(0.391313\pi\)
\(138\) −17.3682 + 30.0827i −1.47848 + 2.56081i
\(139\) −1.63760 + 2.83641i −0.138900 + 0.240581i −0.927080 0.374863i \(-0.877690\pi\)
0.788181 + 0.615444i \(0.211023\pi\)
\(140\) 0 0
\(141\) 3.99846 + 6.92554i 0.336731 + 0.583236i
\(142\) −8.84506 + 15.3201i −0.742261 + 1.28563i
\(143\) −7.70905 3.35233i −0.644663 0.280336i
\(144\) −1.08872 1.88571i −0.0907265 0.157143i
\(145\) −28.4619 −2.36363
\(146\) −2.41308 4.17957i −0.199708 0.345904i
\(147\) 0 0
\(148\) 10.5021 0.863270
\(149\) 7.08186 + 12.2661i 0.580169 + 1.00488i 0.995459 + 0.0951925i \(0.0303467\pi\)
−0.415290 + 0.909689i \(0.636320\pi\)
\(150\) −34.2628 −2.79754
\(151\) 0.673125 + 1.16589i 0.0547781 + 0.0948785i 0.892114 0.451810i \(-0.149222\pi\)
−0.837336 + 0.546689i \(0.815888\pi\)
\(152\) −11.9994 20.7836i −0.973283 1.68578i
\(153\) 6.36194 + 11.0192i 0.514332 + 0.890849i
\(154\) 0 0
\(155\) −10.2860 −0.826190
\(156\) −26.2323 11.4073i −2.10026 0.913313i
\(157\) 6.52006 + 11.2931i 0.520357 + 0.901285i 0.999720 + 0.0236682i \(0.00753454\pi\)
−0.479363 + 0.877617i \(0.659132\pi\)
\(158\) −8.84657 + 15.3227i −0.703795 + 1.21901i
\(159\) −5.41202 −0.429201
\(160\) −7.61620 + 13.1916i −0.602113 + 1.04289i
\(161\) 0 0
\(162\) −12.3087 + 21.3194i −0.967067 + 1.67501i
\(163\) −2.46628 4.27172i −0.193174 0.334587i 0.753127 0.657876i \(-0.228545\pi\)
−0.946300 + 0.323289i \(0.895211\pi\)
\(164\) 1.61089 + 2.79015i 0.125790 + 0.217874i
\(165\) 18.1484 1.41285
\(166\) 6.74590 0.523583
\(167\) −1.82128 3.15455i −0.140935 0.244107i 0.786914 0.617063i \(-0.211678\pi\)
−0.927849 + 0.372956i \(0.878344\pi\)
\(168\) 0 0
\(169\) −12.6670 + 2.92344i −0.974387 + 0.224880i
\(170\) −21.4468 + 37.1470i −1.64490 + 2.84904i
\(171\) 8.35637 14.4737i 0.639028 1.10683i
\(172\) 7.03014 12.1766i 0.536043 0.928453i
\(173\) −6.34584 10.9913i −0.482465 0.835654i 0.517332 0.855785i \(-0.326925\pi\)
−0.999797 + 0.0201306i \(0.993592\pi\)
\(174\) 45.4520 3.44571
\(175\) 0 0
\(176\) −1.08872 + 1.88571i −0.0820652 + 0.142141i
\(177\) −8.36661 + 14.4914i −0.628873 + 1.08924i
\(178\) −30.6820 −2.29971
\(179\) 4.39469 7.61183i 0.328475 0.568935i −0.653735 0.756724i \(-0.726799\pi\)
0.982209 + 0.187789i \(0.0601321\pi\)
\(180\) 27.0060 2.01291
\(181\) −17.1982 −1.27833 −0.639167 0.769068i \(-0.720721\pi\)
−0.639167 + 0.769068i \(0.720721\pi\)
\(182\) 0 0
\(183\) 14.7548 1.09071
\(184\) 21.6025 1.59256
\(185\) −5.15197 + 8.92347i −0.378780 + 0.656066i
\(186\) 16.4261 1.20442
\(187\) 6.36194 11.0192i 0.465231 0.805804i
\(188\) 5.94999 10.3057i 0.433947 0.751619i
\(189\) 0 0
\(190\) 56.3406 4.08738
\(191\) −0.533902 0.924745i −0.0386318 0.0669122i 0.846063 0.533083i \(-0.178967\pi\)
−0.884695 + 0.466171i \(0.845633\pi\)
\(192\) 14.3191 24.8013i 1.03339 1.78988i
\(193\) −1.57790 + 2.73300i −0.113580 + 0.196726i −0.917211 0.398402i \(-0.869565\pi\)
0.803631 + 0.595127i \(0.202898\pi\)
\(194\) −4.14674 + 7.18237i −0.297719 + 0.515664i
\(195\) 22.5611 16.6931i 1.61564 1.19542i
\(196\) 0 0
\(197\) 8.84783 + 15.3249i 0.630382 + 1.09185i 0.987474 + 0.157784i \(0.0504351\pi\)
−0.357092 + 0.934069i \(0.616232\pi\)
\(198\) −12.6740 −0.900704
\(199\) 12.9895 0.920803 0.460402 0.887711i \(-0.347705\pi\)
0.460402 + 0.887711i \(0.347705\pi\)
\(200\) 10.6539 + 18.4532i 0.753348 + 1.30484i
\(201\) −5.32619 9.22522i −0.375680 0.650697i
\(202\) 5.51246 9.54785i 0.387855 0.671785i
\(203\) 0 0
\(204\) 21.6484 37.4960i 1.51569 2.62525i
\(205\) −3.16098 −0.220773
\(206\) −6.97456 + 12.0803i −0.485941 + 0.841674i
\(207\) 7.52195 + 13.0284i 0.522812 + 0.905537i
\(208\) 0.381064 + 3.34565i 0.0264220 + 0.231979i
\(209\) −16.7127 −1.15605
\(210\) 0 0
\(211\) −13.7701 23.8505i −0.947974 1.64194i −0.749685 0.661795i \(-0.769795\pi\)
−0.198289 0.980144i \(-0.563538\pi\)
\(212\) 4.02673 + 6.97450i 0.276557 + 0.479011i
\(213\) 8.75967 + 15.1722i 0.600203 + 1.03958i
\(214\) −30.7355 −2.10103
\(215\) 6.89746 + 11.9467i 0.470403 + 0.814761i
\(216\) 5.16771 0.351618
\(217\) 0 0
\(218\) 4.79761 + 8.30971i 0.324935 + 0.562805i
\(219\) −4.77956 −0.322973
\(220\) −13.5030 23.3879i −0.910372 1.57681i
\(221\) −2.22675 19.5503i −0.149788 1.31510i
\(222\) 8.22740 14.2503i 0.552187 0.956416i
\(223\) 4.35098 + 7.53612i 0.291363 + 0.504656i 0.974132 0.225978i \(-0.0725578\pi\)
−0.682769 + 0.730634i \(0.739224\pi\)
\(224\) 0 0
\(225\) −7.41937 + 12.8507i −0.494625 + 0.856715i
\(226\) 16.6476 28.8345i 1.10738 1.91805i
\(227\) −21.9669 −1.45800 −0.728998 0.684516i \(-0.760013\pi\)
−0.728998 + 0.684516i \(0.760013\pi\)
\(228\) −56.8700 −3.76631
\(229\) −10.2594 + 17.7698i −0.677959 + 1.17426i 0.297636 + 0.954679i \(0.403802\pi\)
−0.975595 + 0.219580i \(0.929531\pi\)
\(230\) −25.3574 + 43.9203i −1.67202 + 2.89602i
\(231\) 0 0
\(232\) −14.1332 24.4795i −0.927892 1.60716i
\(233\) 8.64439 14.9725i 0.566313 0.980883i −0.430613 0.902537i \(-0.641703\pi\)
0.996926 0.0783463i \(-0.0249640\pi\)
\(234\) −15.7557 + 11.6577i −1.02998 + 0.762090i
\(235\) 5.83769 + 10.1112i 0.380809 + 0.659581i
\(236\) 24.9002 1.62086
\(237\) 8.76116 + 15.1748i 0.569099 + 0.985708i
\(238\) 0 0
\(239\) 3.25961 0.210847 0.105423 0.994427i \(-0.466380\pi\)
0.105423 + 0.994427i \(0.466380\pi\)
\(240\) −3.63476 6.29559i −0.234623 0.406379i
\(241\) 1.46571 0.0944149 0.0472074 0.998885i \(-0.484968\pi\)
0.0472074 + 0.998885i \(0.484968\pi\)
\(242\) −6.48632 11.2346i −0.416956 0.722190i
\(243\) 9.87462 + 17.1033i 0.633457 + 1.09718i
\(244\) −10.9781 19.0147i −0.702802 1.21729i
\(245\) 0 0
\(246\) 5.04791 0.321843
\(247\) −20.7765 + 15.3726i −1.32198 + 0.978135i
\(248\) −5.10768 8.84676i −0.324338 0.561770i
\(249\) 3.34039 5.78572i 0.211688 0.366655i
\(250\) −10.7241 −0.678252
\(251\) 8.55142 14.8115i 0.539761 0.934894i −0.459156 0.888356i \(-0.651848\pi\)
0.998917 0.0465376i \(-0.0148187\pi\)
\(252\) 0 0
\(253\) 7.52195 13.0284i 0.472901 0.819089i
\(254\) −12.9132 22.3663i −0.810246 1.40339i
\(255\) 21.2398 + 36.7884i 1.33009 + 2.30378i
\(256\) −21.5456 −1.34660
\(257\) −3.85011 −0.240163 −0.120082 0.992764i \(-0.538316\pi\)
−0.120082 + 0.992764i \(0.538316\pi\)
\(258\) −11.0149 19.0783i −0.685755 1.18776i
\(259\) 0 0
\(260\) −38.2988 16.6544i −2.37519 1.03286i
\(261\) 9.84233 17.0474i 0.609225 1.05521i
\(262\) −0.783403 + 1.35689i −0.0483988 + 0.0838292i
\(263\) 15.2579 26.4275i 0.940844 1.62959i 0.176978 0.984215i \(-0.443368\pi\)
0.763866 0.645375i \(-0.223299\pi\)
\(264\) 9.01187 + 15.6090i 0.554642 + 0.960669i
\(265\) −7.90147 −0.485383
\(266\) 0 0
\(267\) −15.1929 + 26.3149i −0.929790 + 1.61044i
\(268\) −7.92573 + 13.7278i −0.484141 + 0.838557i
\(269\) −16.7771 −1.02292 −0.511460 0.859307i \(-0.670895\pi\)
−0.511460 + 0.859307i \(0.670895\pi\)
\(270\) −6.06595 + 10.5065i −0.369162 + 0.639407i
\(271\) −31.1772 −1.89388 −0.946941 0.321407i \(-0.895844\pi\)
−0.946941 + 0.321407i \(0.895844\pi\)
\(272\) −5.09669 −0.309032
\(273\) 0 0
\(274\) −18.2762 −1.10410
\(275\) 14.8387 0.894810
\(276\) 25.5956 44.3330i 1.54068 2.66853i
\(277\) 0.395882 0.0237863 0.0118931 0.999929i \(-0.496214\pi\)
0.0118931 + 0.999929i \(0.496214\pi\)
\(278\) 3.81810 6.61314i 0.228994 0.396630i
\(279\) 3.55697 6.16085i 0.212950 0.368841i
\(280\) 0 0
\(281\) −22.9459 −1.36884 −0.684420 0.729088i \(-0.739944\pi\)
−0.684420 + 0.729088i \(0.739944\pi\)
\(282\) −9.32247 16.1470i −0.555145 0.961540i
\(283\) 9.67575 16.7589i 0.575164 0.996213i −0.420860 0.907126i \(-0.638272\pi\)
0.996024 0.0890873i \(-0.0283950\pi\)
\(284\) 13.0350 22.5773i 0.773485 1.33972i
\(285\) 27.8984 48.3214i 1.65256 2.86231i
\(286\) 17.9738 + 7.81600i 1.06281 + 0.462170i
\(287\) 0 0
\(288\) −5.26748 9.12354i −0.310389 0.537610i
\(289\) 12.7826 0.751916
\(290\) 66.3593 3.89675
\(291\) 4.10671 + 7.11303i 0.240740 + 0.416973i
\(292\) 3.55616 + 6.15945i 0.208109 + 0.360455i
\(293\) −7.88616 + 13.6592i −0.460715 + 0.797981i −0.998997 0.0447835i \(-0.985740\pi\)
0.538282 + 0.842765i \(0.319074\pi\)
\(294\) 0 0
\(295\) −12.2151 + 21.1572i −0.711192 + 1.23182i
\(296\) −10.2332 −0.594792
\(297\) 1.79939 3.11663i 0.104411 0.180845i
\(298\) −16.5115 28.5987i −0.956483 1.65668i
\(299\) −2.63277 23.1151i −0.152257 1.33678i
\(300\) 50.4932 2.91523
\(301\) 0 0
\(302\) −1.56940 2.71828i −0.0903089 0.156420i
\(303\) −5.45924 9.45568i −0.313625 0.543215i
\(304\) 3.34724 + 5.79759i 0.191977 + 0.332515i
\(305\) 21.5419 1.23348
\(306\) −14.8330 25.6914i −0.847943 1.46868i
\(307\) −19.2535 −1.09885 −0.549427 0.835542i \(-0.685154\pi\)
−0.549427 + 0.835542i \(0.685154\pi\)
\(308\) 0 0
\(309\) 6.90723 + 11.9637i 0.392939 + 0.680590i
\(310\) 23.9819 1.36208
\(311\) 1.53232 + 2.65405i 0.0868898 + 0.150498i 0.906195 0.422860i \(-0.138974\pi\)
−0.819305 + 0.573358i \(0.805641\pi\)
\(312\) 25.5605 + 11.1151i 1.44708 + 0.629271i
\(313\) −17.6376 + 30.5492i −0.996934 + 1.72674i −0.430705 + 0.902493i \(0.641735\pi\)
−0.566229 + 0.824248i \(0.691598\pi\)
\(314\) −15.2016 26.3300i −0.857877 1.48589i
\(315\) 0 0
\(316\) 13.0372 22.5811i 0.733401 1.27029i
\(317\) −16.3533 + 28.3247i −0.918490 + 1.59087i −0.116781 + 0.993158i \(0.537258\pi\)
−0.801709 + 0.597714i \(0.796076\pi\)
\(318\) 12.6182 0.707594
\(319\) −19.6847 −1.10213
\(320\) 20.9056 36.2096i 1.16866 2.02418i
\(321\) −15.2194 + 26.3607i −0.849463 + 1.47131i
\(322\) 0 0
\(323\) −19.5596 33.8783i −1.08833 1.88504i
\(324\) 18.1394 31.4184i 1.00775 1.74547i
\(325\) 18.4468 13.6489i 1.02324 0.757103i
\(326\) 5.75016 + 9.95958i 0.318472 + 0.551610i
\(327\) 9.50260 0.525495
\(328\) −1.56964 2.71869i −0.0866688 0.150115i
\(329\) 0 0
\(330\) −42.3132 −2.32926
\(331\) −2.38851 4.13703i −0.131285 0.227392i 0.792887 0.609368i \(-0.208577\pi\)
−0.924172 + 0.381977i \(0.875244\pi\)
\(332\) −9.94145 −0.545608
\(333\) −3.56318 6.17161i −0.195261 0.338202i
\(334\) 4.24635 + 7.35489i 0.232350 + 0.402442i
\(335\) −7.77615 13.4687i −0.424856 0.735873i
\(336\) 0 0
\(337\) 26.2392 1.42934 0.714669 0.699463i \(-0.246577\pi\)
0.714669 + 0.699463i \(0.246577\pi\)
\(338\) 29.5334 6.81603i 1.60640 0.370743i
\(339\) −16.4869 28.5562i −0.895447 1.55096i
\(340\) 31.6063 54.7437i 1.71409 2.96889i
\(341\) −7.11394 −0.385241
\(342\) −19.4830 + 33.7456i −1.05352 + 1.82475i
\(343\) 0 0
\(344\) −6.85010 + 11.8647i −0.369332 + 0.639702i
\(345\) 25.1126 + 43.4963i 1.35202 + 2.34176i
\(346\) 14.7954 + 25.6264i 0.795407 + 1.37768i
\(347\) −10.4442 −0.560675 −0.280338 0.959901i \(-0.590446\pi\)
−0.280338 + 0.959901i \(0.590446\pi\)
\(348\) −66.9829 −3.59066
\(349\) 11.7344 + 20.3246i 0.628128 + 1.08795i 0.987927 + 0.154920i \(0.0495118\pi\)
−0.359799 + 0.933030i \(0.617155\pi\)
\(350\) 0 0
\(351\) −0.629807 5.52955i −0.0336166 0.295145i
\(352\) −5.26748 + 9.12354i −0.280758 + 0.486286i
\(353\) 1.46567 2.53862i 0.0780099 0.135117i −0.824381 0.566035i \(-0.808477\pi\)
0.902391 + 0.430918i \(0.141810\pi\)
\(354\) 19.5069 33.7869i 1.03678 1.79575i
\(355\) 12.7890 + 22.1512i 0.678769 + 1.17566i
\(356\) 45.2162 2.39645
\(357\) 0 0
\(358\) −10.2463 + 17.7471i −0.541533 + 0.937963i
\(359\) 8.55069 14.8102i 0.451288 0.781654i −0.547178 0.837016i \(-0.684298\pi\)
0.998466 + 0.0553624i \(0.0176314\pi\)
\(360\) −26.3144 −1.38689
\(361\) −16.1915 + 28.0445i −0.852184 + 1.47603i
\(362\) 40.0979 2.10750
\(363\) −12.8474 −0.674314
\(364\) 0 0
\(365\) −6.97809 −0.365250
\(366\) −34.4012 −1.79818
\(367\) −0.524301 + 0.908115i −0.0273683 + 0.0474032i −0.879385 0.476111i \(-0.842046\pi\)
0.852017 + 0.523514i \(0.175379\pi\)
\(368\) −6.02600 −0.314127
\(369\) 1.09309 1.89329i 0.0569041 0.0985608i
\(370\) 12.0119 20.8052i 0.624468 1.08161i
\(371\) 0 0
\(372\) −24.2073 −1.25509
\(373\) 7.50536 + 12.9997i 0.388613 + 0.673098i 0.992263 0.124152i \(-0.0396210\pi\)
−0.603650 + 0.797249i \(0.706288\pi\)
\(374\) −14.8330 + 25.6914i −0.766994 + 1.32847i
\(375\) −5.31029 + 9.19768i −0.274222 + 0.474966i
\(376\) −5.79761 + 10.0418i −0.298989 + 0.517864i
\(377\) −24.4710 + 18.1062i −1.26032 + 0.932517i
\(378\) 0 0
\(379\) 13.5749 + 23.5123i 0.697294 + 1.20775i 0.969401 + 0.245481i \(0.0789459\pi\)
−0.272108 + 0.962267i \(0.587721\pi\)
\(380\) −83.0294 −4.25932
\(381\) −25.5771 −1.31035
\(382\) 1.24480 + 2.15606i 0.0636895 + 0.110314i
\(383\) −8.01320 13.8793i −0.409455 0.709197i 0.585373 0.810764i \(-0.300948\pi\)
−0.994829 + 0.101566i \(0.967615\pi\)
\(384\) −22.9519 + 39.7538i −1.17126 + 2.02868i
\(385\) 0 0
\(386\) 3.67890 6.37203i 0.187251 0.324328i
\(387\) −9.54077 −0.484985
\(388\) 6.11107 10.5847i 0.310242 0.537356i
\(389\) −3.99714 6.92324i −0.202663 0.351022i 0.746723 0.665136i \(-0.231626\pi\)
−0.949386 + 0.314113i \(0.898293\pi\)
\(390\) −52.6017 + 38.9202i −2.66359 + 1.97080i
\(391\) 35.2130 1.78080
\(392\) 0 0
\(393\) 0.775840 + 1.34379i 0.0391360 + 0.0677855i
\(394\) −20.6289 35.7302i −1.03927 1.80006i
\(395\) 12.7912 + 22.1550i 0.643593 + 1.11474i
\(396\) 18.6778 0.938593
\(397\) −6.10435 10.5731i −0.306369 0.530646i 0.671196 0.741280i \(-0.265781\pi\)
−0.977565 + 0.210633i \(0.932447\pi\)
\(398\) −30.2853 −1.51806
\(399\) 0 0
\(400\) −2.97191 5.14750i −0.148596 0.257375i
\(401\) 37.8412 1.88970 0.944850 0.327503i \(-0.106207\pi\)
0.944850 + 0.327503i \(0.106207\pi\)
\(402\) 12.4181 + 21.5087i 0.619358 + 1.07276i
\(403\) −8.84370 + 6.54349i −0.440536 + 0.325955i
\(404\) −8.12373 + 14.0707i −0.404171 + 0.700044i
\(405\) 17.7971 + 30.8255i 0.884345 + 1.53173i
\(406\) 0 0
\(407\) −3.56318 + 6.17161i −0.176620 + 0.305915i
\(408\) −21.0939 + 36.5358i −1.04431 + 1.80879i
\(409\) −0.235074 −0.0116237 −0.00581184 0.999983i \(-0.501850\pi\)
−0.00581184 + 0.999983i \(0.501850\pi\)
\(410\) 7.36988 0.363972
\(411\) −9.04986 + 15.6748i −0.446397 + 0.773182i
\(412\) 10.2784 17.8028i 0.506382 0.877080i
\(413\) 0 0
\(414\) −17.5375 30.3759i −0.861923 1.49290i
\(415\) 4.87692 8.44706i 0.239398 0.414650i
\(416\) 1.84368 + 16.1870i 0.0903938 + 0.793635i
\(417\) −3.78124 6.54930i −0.185168 0.320720i
\(418\) 38.9660 1.90589
\(419\) 0.222023 + 0.384555i 0.0108465 + 0.0187868i 0.871398 0.490577i \(-0.163214\pi\)
−0.860551 + 0.509364i \(0.829881\pi\)
\(420\) 0 0
\(421\) 9.45998 0.461051 0.230526 0.973066i \(-0.425955\pi\)
0.230526 + 0.973066i \(0.425955\pi\)
\(422\) 32.1052 + 55.6079i 1.56286 + 2.70695i
\(423\) −8.07488 −0.392614
\(424\) −3.92361 6.79588i −0.190547 0.330037i
\(425\) 17.3664 + 30.0795i 0.842395 + 1.45907i
\(426\) −20.4233 35.3742i −0.989513 1.71389i
\(427\) 0 0
\(428\) 45.2950 2.18942
\(429\) 15.6036 11.5452i 0.753351 0.557407i
\(430\) −16.0815 27.8540i −0.775520 1.34324i
\(431\) −10.7723 + 18.6582i −0.518883 + 0.898732i 0.480876 + 0.876789i \(0.340319\pi\)
−0.999759 + 0.0219436i \(0.993015\pi\)
\(432\) −1.44153 −0.0693557
\(433\) −6.57949 + 11.3960i −0.316190 + 0.547657i −0.979690 0.200519i \(-0.935737\pi\)
0.663500 + 0.748176i \(0.269070\pi\)
\(434\) 0 0
\(435\) 32.8593 56.9141i 1.57548 2.72882i
\(436\) −7.07026 12.2461i −0.338604 0.586479i
\(437\) −23.1261 40.0555i −1.10627 1.91612i
\(438\) 11.1436 0.532463
\(439\) 29.7847 1.42155 0.710773 0.703422i \(-0.248345\pi\)
0.710773 + 0.703422i \(0.248345\pi\)
\(440\) 13.1572 + 22.7889i 0.627245 + 1.08642i
\(441\) 0 0
\(442\) 5.19171 + 45.5819i 0.246944 + 2.16811i
\(443\) −7.42333 + 12.8576i −0.352693 + 0.610883i −0.986720 0.162428i \(-0.948067\pi\)
0.634027 + 0.773311i \(0.281401\pi\)
\(444\) −12.1248 + 21.0007i −0.575416 + 0.996649i
\(445\) −22.1814 + 38.4193i −1.05150 + 1.82125i
\(446\) −10.1444 17.5706i −0.480351 0.831992i
\(447\) −32.7041 −1.54685
\(448\) 0 0
\(449\) 13.1114 22.7095i 0.618763 1.07173i −0.370949 0.928653i \(-0.620968\pi\)
0.989712 0.143075i \(-0.0456992\pi\)
\(450\) 17.2984 29.9617i 0.815454 1.41241i
\(451\) −2.18618 −0.102943
\(452\) −24.5337 + 42.4936i −1.15397 + 1.99873i
\(453\) −3.10850 −0.146050
\(454\) 51.2162 2.40369
\(455\) 0 0
\(456\) 55.4136 2.59498
\(457\) −15.8708 −0.742406 −0.371203 0.928552i \(-0.621055\pi\)
−0.371203 + 0.928552i \(0.621055\pi\)
\(458\) 23.9199 41.4305i 1.11770 1.93592i
\(459\) 8.42361 0.393180
\(460\) 37.3693 64.7255i 1.74235 3.01784i
\(461\) 11.0443 19.1293i 0.514384 0.890940i −0.485476 0.874250i \(-0.661354\pi\)
0.999861 0.0166900i \(-0.00531285\pi\)
\(462\) 0 0
\(463\) 18.2887 0.849949 0.424974 0.905205i \(-0.360283\pi\)
0.424974 + 0.905205i \(0.360283\pi\)
\(464\) 3.94246 + 6.82854i 0.183024 + 0.317007i
\(465\) 11.8752 20.5685i 0.550699 0.953839i
\(466\) −20.1545 + 34.9087i −0.933641 + 1.61711i
\(467\) 2.26659 3.92585i 0.104885 0.181667i −0.808806 0.588076i \(-0.799886\pi\)
0.913691 + 0.406409i \(0.133219\pi\)
\(468\) 23.2193 17.1801i 1.07331 0.794148i
\(469\) 0 0
\(470\) −13.6107 23.5744i −0.627813 1.08740i
\(471\) −30.1097 −1.38738
\(472\) −24.2625 −1.11677
\(473\) 4.77039 + 8.26255i 0.219343 + 0.379912i
\(474\) −20.4268 35.3802i −0.938233 1.62507i
\(475\) 22.8107 39.5093i 1.04663 1.81281i
\(476\) 0 0
\(477\) 2.73239 4.73263i 0.125107 0.216692i
\(478\) −7.59984 −0.347609
\(479\) −5.22303 + 9.04655i −0.238646 + 0.413347i −0.960326 0.278880i \(-0.910037\pi\)
0.721680 + 0.692227i \(0.243370\pi\)
\(480\) −17.5859 30.4596i −0.802681 1.39028i
\(481\) 1.24715 + 10.9497i 0.0568653 + 0.499263i
\(482\) −3.41733 −0.155655
\(483\) 0 0
\(484\) 9.55891 + 16.5565i 0.434496 + 0.752569i
\(485\) 5.99573 + 10.3849i 0.272252 + 0.471555i
\(486\) −23.0228 39.8767i −1.04434 1.80884i
\(487\) 35.9143 1.62743 0.813715 0.581263i \(-0.197441\pi\)
0.813715 + 0.581263i \(0.197441\pi\)
\(488\) 10.6970 + 18.5277i 0.484229 + 0.838710i
\(489\) 11.3893 0.515042
\(490\) 0 0
\(491\) −3.85124 6.67054i −0.173804 0.301037i 0.765943 0.642909i \(-0.222273\pi\)
−0.939747 + 0.341871i \(0.888939\pi\)
\(492\) −7.43913 −0.335382
\(493\) −23.0378 39.9026i −1.03757 1.79712i
\(494\) 48.4407 35.8415i 2.17945 1.61258i
\(495\) −9.16263 + 15.8701i −0.411830 + 0.713310i
\(496\) 1.42478 + 2.46780i 0.0639747 + 0.110807i
\(497\) 0 0
\(498\) −7.78816 + 13.4895i −0.348996 + 0.604479i
\(499\) −4.24539 + 7.35323i −0.190050 + 0.329176i −0.945266 0.326299i \(-0.894198\pi\)
0.755217 + 0.655475i \(0.227532\pi\)
\(500\) 15.8041 0.706783
\(501\) 8.41071 0.375763
\(502\) −19.9378 + 34.5332i −0.889866 + 1.54129i
\(503\) 15.2000 26.3272i 0.677736 1.17387i −0.297924 0.954589i \(-0.596294\pi\)
0.975661 0.219285i \(-0.0703723\pi\)
\(504\) 0 0
\(505\) −7.97041 13.8052i −0.354679 0.614321i
\(506\) −17.5375 + 30.3759i −0.779639 + 1.35037i
\(507\) 8.77825 28.7048i 0.389856 1.27483i
\(508\) 19.0302 + 32.9613i 0.844330 + 1.46242i
\(509\) 15.5801 0.690578 0.345289 0.938496i \(-0.387781\pi\)
0.345289 + 0.938496i \(0.387781\pi\)
\(510\) −49.5209 85.7727i −2.19282 3.79808i
\(511\) 0 0
\(512\) 10.4733 0.462860
\(513\) −5.53218 9.58202i −0.244252 0.423057i
\(514\) 8.97660 0.395941
\(515\) 10.0845 + 17.4668i 0.444374 + 0.769678i
\(516\) 16.2326 + 28.1157i 0.714602 + 1.23773i
\(517\) 4.03744 + 6.99305i 0.177566 + 0.307554i
\(518\) 0 0
\(519\) 29.3052 1.28635
\(520\) 37.3179 + 16.2279i 1.63650 + 0.711642i
\(521\) 13.5787 + 23.5190i 0.594893 + 1.03039i 0.993562 + 0.113290i \(0.0361390\pi\)
−0.398669 + 0.917095i \(0.630528\pi\)
\(522\) −22.9476 + 39.7463i −1.00439 + 1.73965i
\(523\) 18.0575 0.789598 0.394799 0.918767i \(-0.370814\pi\)
0.394799 + 0.918767i \(0.370814\pi\)
\(524\) 1.15450 1.99966i 0.0504347 0.0873555i
\(525\) 0 0
\(526\) −35.5741 + 61.6161i −1.55110 + 2.68659i
\(527\) −8.32574 14.4206i −0.362675 0.628172i
\(528\) −2.51386 4.35413i −0.109402 0.189489i
\(529\) 18.6337 0.810160
\(530\) 18.4224 0.800217
\(531\) −8.44816 14.6326i −0.366619 0.635003i
\(532\) 0 0
\(533\) −2.71776 + 2.01088i −0.117719 + 0.0871009i
\(534\) 35.4225 61.3535i 1.53288 2.65503i
\(535\) −22.2201 + 38.4863i −0.960657 + 1.66391i
\(536\) 7.72276 13.3762i 0.333572 0.577764i
\(537\) 10.1474 + 17.5758i 0.437892 + 0.758451i
\(538\) 39.1162 1.68642
\(539\) 0 0
\(540\) 8.93941 15.4835i 0.384691 0.666305i
\(541\) −19.9941 + 34.6308i −0.859613 + 1.48889i 0.0126849 + 0.999920i \(0.495962\pi\)
−0.872298 + 0.488974i \(0.837371\pi\)
\(542\) 72.6902 3.12231
\(543\) 19.8554 34.3906i 0.852077 1.47584i
\(544\) −24.6590 −1.05725
\(545\) 13.8736 0.594282
\(546\) 0 0
\(547\) −22.6124 −0.966836 −0.483418 0.875390i \(-0.660605\pi\)
−0.483418 + 0.875390i \(0.660605\pi\)
\(548\) 26.9336 1.15055
\(549\) −7.44934 + 12.9026i −0.317930 + 0.550671i
\(550\) −34.5968 −1.47521
\(551\) −30.2600 + 52.4119i −1.28912 + 2.23282i
\(552\) −24.9402 + 43.1976i −1.06152 + 1.83861i
\(553\) 0 0
\(554\) −0.923005 −0.0392147
\(555\) −11.8959 20.6043i −0.504954 0.874606i
\(556\) −5.62674 + 9.74581i −0.238627 + 0.413314i
\(557\) 4.98686 8.63750i 0.211300 0.365983i −0.740822 0.671702i \(-0.765564\pi\)
0.952122 + 0.305719i \(0.0988969\pi\)
\(558\) −8.29313 + 14.3641i −0.351076 + 0.608082i
\(559\) 13.5303 + 5.88374i 0.572271 + 0.248856i
\(560\) 0 0
\(561\) 14.6898 + 25.4434i 0.620202 + 1.07422i
\(562\) 53.4988 2.25671
\(563\) 21.5279 0.907294 0.453647 0.891181i \(-0.350123\pi\)
0.453647 + 0.891181i \(0.350123\pi\)
\(564\) 13.7386 + 23.7959i 0.578498 + 1.00199i
\(565\) −24.0707 41.6916i −1.01266 1.75398i
\(566\) −22.5592 + 39.0736i −0.948232 + 1.64239i
\(567\) 0 0
\(568\) −12.7012 + 21.9991i −0.532930 + 0.923061i
\(569\) −33.1004 −1.38764 −0.693819 0.720149i \(-0.744073\pi\)
−0.693819 + 0.720149i \(0.744073\pi\)
\(570\) −65.0454 + 112.662i −2.72445 + 4.71889i
\(571\) −9.96786 17.2648i −0.417142 0.722511i 0.578509 0.815676i \(-0.303635\pi\)
−0.995651 + 0.0931651i \(0.970302\pi\)
\(572\) −26.4880 11.5185i −1.10752 0.481611i
\(573\) 2.46557 0.103001
\(574\) 0 0
\(575\) 20.5330 + 35.5641i 0.856283 + 1.48313i
\(576\) 14.4586 + 25.0431i 0.602443 + 1.04346i
\(577\) 14.7348 + 25.5214i 0.613416 + 1.06247i 0.990660 + 0.136354i \(0.0435385\pi\)
−0.377244 + 0.926114i \(0.623128\pi\)
\(578\) −29.8028 −1.23963
\(579\) −3.64338 6.31052i −0.151414 0.262256i
\(580\) −97.7939 −4.06067
\(581\) 0 0
\(582\) −9.57486 16.5841i −0.396891 0.687435i
\(583\) −5.46477 −0.226328
\(584\) −3.46509 6.00171i −0.143386 0.248353i
\(585\) 3.20703 + 28.1569i 0.132594 + 1.16414i
\(586\) 18.3867 31.8467i 0.759548 1.31558i
\(587\) 3.49429 + 6.05229i 0.144225 + 0.249805i 0.929084 0.369870i \(-0.120598\pi\)
−0.784859 + 0.619675i \(0.787264\pi\)
\(588\) 0 0
\(589\) −10.9358 + 18.9414i −0.450603 + 0.780467i
\(590\) 28.4797 49.3283i 1.17249 2.03082i
\(591\) −40.8594 −1.68073
\(592\) 2.85454 0.117321
\(593\) 0.485124 0.840259i 0.0199216 0.0345053i −0.855893 0.517153i \(-0.826992\pi\)
0.875814 + 0.482648i \(0.160325\pi\)
\(594\) −4.19530 + 7.26648i −0.172135 + 0.298147i
\(595\) 0 0
\(596\) 24.3330 + 42.1460i 0.996719 + 1.72637i
\(597\) −14.9965 + 25.9746i −0.613764 + 1.06307i
\(598\) 6.13835 + 53.8931i 0.251016 + 2.20385i
\(599\) 11.2999 + 19.5720i 0.461702 + 0.799692i 0.999046 0.0436716i \(-0.0139055\pi\)
−0.537344 + 0.843363i \(0.680572\pi\)
\(600\) −49.2001 −2.00858
\(601\) −15.2146 26.3525i −0.620617 1.07494i −0.989371 0.145414i \(-0.953549\pi\)
0.368754 0.929527i \(-0.379785\pi\)
\(602\) 0 0
\(603\) 10.7562 0.438027
\(604\) 2.31283 + 4.00594i 0.0941078 + 0.163000i
\(605\) −18.7570 −0.762581
\(606\) 12.7283 + 22.0461i 0.517052 + 0.895560i
\(607\) −16.0788 27.8493i −0.652618 1.13037i −0.982485 0.186340i \(-0.940337\pi\)
0.329868 0.944027i \(-0.392996\pi\)
\(608\) 16.1947 + 28.0501i 0.656784 + 1.13758i
\(609\) 0 0
\(610\) −50.2252 −2.03356
\(611\) 11.4514 + 4.97973i 0.463276 + 0.201458i
\(612\) 21.8594 + 37.8616i 0.883613 + 1.53046i
\(613\) −6.96043 + 12.0558i −0.281129 + 0.486930i −0.971663 0.236370i \(-0.924042\pi\)
0.690534 + 0.723300i \(0.257376\pi\)
\(614\) 44.8898 1.81160
\(615\) 3.64937 6.32089i 0.147157 0.254883i
\(616\) 0 0
\(617\) 5.08394 8.80565i 0.204672 0.354502i −0.745356 0.666666i \(-0.767721\pi\)
0.950028 + 0.312164i \(0.101054\pi\)
\(618\) −16.1043 27.8935i −0.647810 1.12204i
\(619\) −21.8952 37.9237i −0.880044 1.52428i −0.851291 0.524694i \(-0.824180\pi\)
−0.0287526 0.999587i \(-0.509154\pi\)
\(620\) −35.3422 −1.41938
\(621\) 9.95954 0.399663
\(622\) −3.57262 6.18796i −0.143249 0.248115i
\(623\) 0 0
\(624\) −7.13009 3.10056i −0.285432 0.124122i
\(625\) 8.15812 14.1303i 0.326325 0.565211i
\(626\) 41.1223 71.2258i 1.64358 2.84676i
\(627\) 19.2949 33.4198i 0.770565 1.33466i
\(628\) 22.4027 + 38.8026i 0.893964 + 1.54839i
\(629\) −16.6806 −0.665097
\(630\) 0 0
\(631\) −8.04464 + 13.9337i −0.320252 + 0.554693i −0.980540 0.196320i \(-0.937101\pi\)
0.660288 + 0.751013i \(0.270434\pi\)
\(632\) −12.7033 + 22.0028i −0.505312 + 0.875226i
\(633\) 63.5906 2.52750
\(634\) 38.1279 66.0394i 1.51425 2.62276i
\(635\) −37.3421 −1.48188
\(636\) −18.5955 −0.737359
\(637\) 0 0
\(638\) 45.8951 1.81700
\(639\) −17.6901 −0.699810
\(640\) −33.5094 + 58.0399i −1.32457 + 2.29423i
\(641\) −49.2508 −1.94529 −0.972645 0.232296i \(-0.925376\pi\)
−0.972645 + 0.232296i \(0.925376\pi\)
\(642\) 35.4842 61.4605i 1.40045 2.42565i
\(643\) −1.33579 + 2.31366i −0.0526784 + 0.0912417i −0.891162 0.453685i \(-0.850109\pi\)
0.838484 + 0.544927i \(0.183442\pi\)
\(644\) 0 0
\(645\) −31.8526 −1.25419
\(646\) 45.6036 + 78.9877i 1.79425 + 3.10773i
\(647\) −16.6814 + 28.8930i −0.655814 + 1.13590i 0.325876 + 0.945413i \(0.394341\pi\)
−0.981689 + 0.190490i \(0.938992\pi\)
\(648\) −17.6749 + 30.6138i −0.694336 + 1.20262i
\(649\) −8.44816 + 14.6326i −0.331619 + 0.574382i
\(650\) −43.0090 + 31.8226i −1.68695 + 1.24818i
\(651\) 0 0
\(652\) −8.47404 14.6775i −0.331869 0.574814i
\(653\) 23.8487 0.933274 0.466637 0.884449i \(-0.345466\pi\)
0.466637 + 0.884449i \(0.345466\pi\)
\(654\) −22.1554 −0.866347
\(655\) 1.13271 + 1.96192i 0.0442588 + 0.0766585i
\(656\) 0.437850 + 0.758379i 0.0170952 + 0.0296097i
\(657\) 2.41308 4.17957i 0.0941431 0.163061i
\(658\) 0 0
\(659\) 8.58114 14.8630i 0.334274 0.578979i −0.649071 0.760727i \(-0.724842\pi\)
0.983345 + 0.181749i \(0.0581757\pi\)
\(660\) 62.3571 2.42725
\(661\) 0.233201 0.403917i 0.00907048 0.0157105i −0.861455 0.507835i \(-0.830446\pi\)
0.870525 + 0.492124i \(0.163779\pi\)
\(662\) 5.56886 + 9.64554i 0.216440 + 0.374885i
\(663\) 41.6648 + 18.1182i 1.61813 + 0.703652i
\(664\) 9.68686 0.375923
\(665\) 0 0
\(666\) 8.30760 + 14.3892i 0.321913 + 0.557570i
\(667\) −27.2384 47.1784i −1.05468 1.82675i
\(668\) −6.25786 10.8389i −0.242124 0.419371i
\(669\) −20.0929 −0.776837
\(670\) 18.1302 + 31.4024i 0.700431 + 1.21318i
\(671\) 14.8987 0.575157
\(672\) 0 0
\(673\) −8.77061 15.1911i −0.338082 0.585576i 0.645990 0.763346i \(-0.276445\pi\)
−0.984072 + 0.177770i \(0.943112\pi\)
\(674\) −61.1770 −2.35645
\(675\) 4.91186 + 8.50759i 0.189058 + 0.327457i
\(676\) −43.5234 + 10.0448i −1.67398 + 0.386339i
\(677\) 4.85980 8.41743i 0.186777 0.323508i −0.757397 0.652955i \(-0.773529\pi\)
0.944174 + 0.329447i \(0.106862\pi\)
\(678\) 38.4395 + 66.5792i 1.47626 + 2.55696i
\(679\) 0 0
\(680\) −30.7968 + 53.3417i −1.18101 + 2.04556i
\(681\) 25.3609 43.9263i 0.971831 1.68326i
\(682\) 16.5863 0.635121
\(683\) −36.1154 −1.38192 −0.690960 0.722893i \(-0.742812\pi\)
−0.690960 + 0.722893i \(0.742812\pi\)
\(684\) 28.7122 49.7310i 1.09784 1.90151i
\(685\) −13.2127 + 22.8850i −0.504830 + 0.874391i
\(686\) 0 0
\(687\) −23.6890 41.0305i −0.903791 1.56541i
\(688\) 1.91083 3.30966i 0.0728498 0.126179i
\(689\) −6.79354 + 5.02657i −0.258813 + 0.191497i
\(690\) −58.5504 101.412i −2.22897 3.86070i
\(691\) −8.77269 −0.333729 −0.166864 0.985980i \(-0.553364\pi\)
−0.166864 + 0.985980i \(0.553364\pi\)
\(692\) −21.8041 37.7657i −0.828866 1.43564i
\(693\) 0 0
\(694\) 24.3509 0.924346
\(695\) −5.52055 9.56187i −0.209406 0.362703i
\(696\) 65.2674 2.47396
\(697\) −2.55858 4.43160i −0.0969132 0.167859i
\(698\) −27.3589 47.3870i −1.03555 1.79363i
\(699\) 19.9600 + 34.5717i 0.754955 + 1.30762i
\(700\) 0 0
\(701\) 1.51585 0.0572530 0.0286265 0.999590i \(-0.490887\pi\)
0.0286265 + 0.999590i \(0.490887\pi\)
\(702\) 1.46841 + 12.8922i 0.0554214 + 0.486586i
\(703\) 10.9549 + 18.9745i 0.413172 + 0.715636i
\(704\) 14.4586 25.0431i 0.544930 0.943847i
\(705\) −26.9586 −1.01532
\(706\) −3.41724 + 5.91883i −0.128609 + 0.222758i
\(707\) 0 0
\(708\) −28.7473 + 49.7919i −1.08039 + 1.87129i
\(709\) 7.55100 + 13.0787i 0.283584 + 0.491182i 0.972265 0.233883i \(-0.0751433\pi\)
−0.688681 + 0.725065i \(0.741810\pi\)
\(710\) −29.8177 51.6458i −1.11904 1.93823i
\(711\) −17.6931 −0.663544
\(712\) −44.0582 −1.65115
\(713\) −9.84384 17.0500i −0.368655 0.638528i
\(714\) 0 0
\(715\) 22.7811 16.8558i 0.851964 0.630372i
\(716\) 15.1000 26.1540i 0.564314 0.977420i
\(717\) −3.76324 + 6.51812i −0.140541 + 0.243424i
\(718\) −19.9361 + 34.5303i −0.744007 + 1.28866i
\(719\) 9.59946 + 16.6267i 0.357999 + 0.620073i 0.987626 0.156824i \(-0.0501257\pi\)
−0.629627 + 0.776897i \(0.716792\pi\)
\(720\) 7.34039 0.273560
\(721\) 0 0
\(722\) 37.7507 65.3861i 1.40494 2.43342i
\(723\) −1.69217 + 2.93093i −0.0629325 + 0.109002i
\(724\) −59.0925 −2.19615
\(725\) 26.8670 46.5350i 0.997815 1.72827i
\(726\) 29.9539 1.11169
\(727\) 2.41101 0.0894195 0.0447098 0.999000i \(-0.485764\pi\)
0.0447098 + 0.999000i \(0.485764\pi\)
\(728\) 0 0
\(729\) −13.9254 −0.515755
\(730\) 16.2695 0.602162
\(731\) −11.1660 + 19.3400i −0.412988 + 0.715317i
\(732\) 50.6971 1.87382
\(733\) −6.74959 + 11.6906i −0.249302 + 0.431804i −0.963332 0.268311i \(-0.913534\pi\)
0.714030 + 0.700115i \(0.246868\pi\)
\(734\) 1.22241 2.11728i 0.0451201 0.0781504i
\(735\) 0 0
\(736\) −29.1553 −1.07468
\(737\) −5.37810 9.31515i −0.198105 0.343128i
\(738\) −2.54856 + 4.41423i −0.0938138 + 0.162490i
\(739\) 0.0214096 0.0370824i 0.000787563 0.00136410i −0.865631 0.500682i \(-0.833083\pi\)
0.866419 + 0.499318i \(0.166416\pi\)
\(740\) −17.7020 + 30.6607i −0.650737 + 1.12711i
\(741\) −6.75345 59.2936i −0.248094 2.17820i
\(742\) 0 0
\(743\) 10.8254 + 18.7501i 0.397145 + 0.687875i 0.993372 0.114941i \(-0.0366678\pi\)
−0.596228 + 0.802815i \(0.703334\pi\)
\(744\) 23.5873 0.864753
\(745\) −47.7475 −1.74933
\(746\) −17.4989 30.3089i −0.640679 1.10969i
\(747\) 3.37295 + 5.84212i 0.123410 + 0.213752i
\(748\) 21.8594 37.8616i 0.799258 1.38436i
\(749\) 0 0
\(750\) 12.3810 21.4445i 0.452091 0.783044i
\(751\) −44.8858 −1.63791 −0.818953 0.573860i \(-0.805445\pi\)
−0.818953 + 0.573860i \(0.805445\pi\)
\(752\) 1.61724 2.80114i 0.0589747 0.102147i
\(753\) 19.7453 + 34.1999i 0.719559 + 1.24631i
\(754\) 57.0545 42.2149i 2.07780 1.53738i
\(755\) −4.53837 −0.165168
\(756\) 0 0
\(757\) 3.77726 + 6.54240i 0.137287 + 0.237788i 0.926469 0.376372i \(-0.122828\pi\)
−0.789182 + 0.614159i \(0.789495\pi\)
\(758\) −31.6500 54.8194i −1.14958 1.99113i
\(759\) 17.3682 + 30.0827i 0.630427 + 1.09193i
\(760\) 80.9030 2.93466
\(761\) 11.6946 + 20.2556i 0.423928 + 0.734265i 0.996320 0.0857157i \(-0.0273177\pi\)
−0.572392 + 0.819980i \(0.693984\pi\)
\(762\) 59.6333 2.16029
\(763\) 0 0
\(764\) −1.83447 3.17739i −0.0663687 0.114954i
\(765\) −42.8937 −1.55082
\(766\) 18.6829 + 32.3597i 0.675040 + 1.16920i
\(767\) 2.95696 + 25.9613i 0.106769 + 0.937409i
\(768\) 24.8745 43.0838i 0.897580 1.55465i
\(769\) −21.9255 37.9760i −0.790652 1.36945i −0.925564 0.378592i \(-0.876408\pi\)
0.134911 0.990858i \(-0.456925\pi\)
\(770\) 0 0
\(771\) 4.44497 7.69891i 0.160082 0.277270i
\(772\) −5.42160 + 9.39049i −0.195128 + 0.337971i
\(773\) 43.1225 1.55101 0.775505 0.631341i \(-0.217495\pi\)
0.775505 + 0.631341i \(0.217495\pi\)
\(774\) 22.2445 0.799560
\(775\) 9.70959 16.8175i 0.348779 0.604103i
\(776\) −5.95457 + 10.3136i −0.213756 + 0.370237i
\(777\) 0 0
\(778\) 9.31939 + 16.1417i 0.334116 + 0.578706i
\(779\) −3.36069 + 5.82088i −0.120409 + 0.208555i
\(780\) 77.5193 57.3568i 2.77563 2.05370i
\(781\) 8.84506 + 15.3201i 0.316501 + 0.548196i
\(782\) −82.0997 −2.93588
\(783\) −6.51594 11.2859i −0.232861 0.403326i