Properties

Label 637.2.h.m.471.2
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 471.2
Root \(-0.558788 + 0.967849i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.m.165.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{2} + 24 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} + 8 q^{16} + 28 q^{18} + 28 q^{22} - 24 q^{23} + 12 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} + 16 q^{37} + 20 q^{39} + 32 q^{43} + 4 q^{44} + 8 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} - 48 q^{58} - 64 q^{60} - 64 q^{64} - 68 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} - 152 q^{74} + 28 q^{78} + 4 q^{79} + 56 q^{81} + 36 q^{85} - 4 q^{86} + 28 q^{88} - 160 q^{92} - 16 q^{93} - 104 q^{95} + 56 q^{99} + O(q^{100}) \)

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 \(-0.601102\pi\)
0.978862 0.204523i \(-0.0655643\pi\)
\(4\) 3.43596 1.71798
\(5\) 1.68556 2.91947i 0.753804 1.30563i −0.192162 0.981363i \(-0.561550\pi\)
0.945966 0.324264i \(-0.105117\pi\)
\(6\) −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 \(-0.269793\pi\)
0.661800 + 0.749681i \(0.269793\pi\)
\(18\) 2.71798 + 4.70768i 0.640634 + 1.10961i
\(19\) −3.58410 6.20784i −0.822248 1.42418i −0.904004 0.427523i \(-0.859386\pi\)
0.0817564 0.996652i \(-0.473947\pi\)
\(20\) 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 0.695877 0.718161i \(-0.255016\pi\)
−0.969884 + 0.243567i \(0.921682\pi\)
\(32\) 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 0.827091 0.562068i \(-0.189994\pi\)
−0.900311 + 0.435248i \(0.856661\pi\)
\(42\) 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 −0.964239 0.265036i \(-0.914616\pi\)
0.711647 + 0.702537i \(0.247950\pi\)
\(48\) 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 \(-0.656372\pi\)
−0.471735 + 0.881740i \(0.656372\pi\)
\(60\) −13.3726 23.1621i −1.72640 2.99022i
\(61\) 3.19506 + 5.53401i 0.409086 + 0.708558i 0.994788 0.101969i \(-0.0325143\pi\)
−0.585702 + 0.810527i \(0.699181\pi\)
\(62\) 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 0.799080 0.601224i \(-0.205320\pi\)
−0.920216 + 0.391412i \(0.871987\pi\)
\(74\) −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 \(-0.449240\pi\)
0.158793 + 0.987312i \(0.449240\pi\)
\(84\) 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 \(-0.745687\pi\)
−0.697461 + 0.716622i \(0.745687\pi\)
\(90\) 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 −0.942080 0.335388i \(-0.891133\pi\)
0.761495 + 0.648171i \(0.224466\pi\)
\(98\) 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 −0.724089 0.689707i \(-0.757740\pi\)
0.959348 + 0.282226i \(0.0910728\pi\)
\(102\) −14.6898 + 25.4434i −1.45450 + 2.51927i
\(103\) −2.99143 + 5.18131i −0.294754 + 0.510529i −0.974928 0.222522i \(-0.928571\pi\)
0.680173 + 0.733051i \(0.261904\pi\)
\(104\) 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 −0.880331 0.474361i \(-0.842679\pi\)
0.850974 + 0.525208i \(0.176013\pi\)
\(132\) 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 −0.788181 0.615444i \(-0.788977\pi\)
0.927080 + 0.374863i \(0.122310\pi\)
\(140\) 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 \(-0.992465\pi\)
0.479363 0.877617i \(-0.340868\pi\)
\(158\) −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 0.927849 0.372956i \(-0.121656\pi\)
−0.786914 + 0.617063i \(0.788322\pi\)
\(168\) 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 0.999797 0.0201306i \(-0.00640819\pi\)
−0.517332 + 0.855785i \(0.673075\pi\)
\(174\) −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 \(-0.279279\pi\)
0.639167 + 0.769068i \(0.279279\pi\)
\(182\) 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 \(-0.652295\pi\)
−0.460402 + 0.887711i \(0.652295\pi\)
\(200\) 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 0.682769 0.730634i \(-0.260776\pi\)
−0.974132 + 0.225978i \(0.927442\pi\)
\(224\) 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 \(-0.239987\pi\)
0.728998 + 0.684516i \(0.239987\pi\)
\(228\) −56.8700 −3.76631
\(229\) 10.2594 17.7698i 0.677959 1.17426i −0.297636 0.954679i \(-0.596198\pi\)
0.975595 0.219580i \(-0.0704685\pi\)
\(230\) 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 \(-0.515032\pi\)
−0.0472074 + 0.998885i \(0.515032\pi\)
\(242\) −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 \(0.348152\pi\)
−0.998917 + 0.0465376i \(0.985181\pi\)
\(252\) 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 \(-0.461684\pi\)
0.120082 + 0.992764i \(0.461684\pi\)
\(258\) 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 \(-0.329105\pi\)
0.511460 + 0.859307i \(0.329105\pi\)
\(270\) −6.06595 + 10.5065i −0.369162 + 0.639407i
\(271\) 31.1772 1.89388 0.946941 0.321407i \(-0.104156\pi\)
0.946941 + 0.321407i \(0.104156\pi\)
\(272\) 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 \(0.361728\pi\)
−0.996024 + 0.0890873i \(0.971605\pi\)
\(284\) 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 −0.538282 0.842765i \(-0.680926\pi\)
0.998997 + 0.0447835i \(0.0142598\pi\)
\(294\) 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 \(-0.314846\pi\)
0.549427 + 0.835542i \(0.314846\pi\)
\(308\) 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 0.819305 0.573358i \(-0.194359\pi\)
−0.906195 + 0.422860i \(0.861026\pi\)
\(312\) 25.5605 + 11.1151i 1.44708 + 0.629271i
\(313\) 17.6376 30.5492i 0.996934 1.72674i 0.430705 0.902493i \(-0.358265\pi\)
0.566229 0.824248i \(-0.308402\pi\)
\(314\) 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 \(-0.950488\pi\)
0.359799 0.933030i \(-0.382845\pi\)
\(350\) 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 −0.902391 0.430918i \(-0.858190\pi\)
0.824381 + 0.566035i \(0.191523\pi\)
\(354\) 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 −0.852017 0.523514i \(-0.824621\pi\)
0.879385 + 0.476111i \(0.157954\pi\)
\(368\) −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 0.994829 0.101566i \(-0.0323854\pi\)
−0.585373 + 0.810764i \(0.699052\pi\)
\(384\) 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 0.977565 0.210633i \(-0.0675526\pi\)
−0.671196 + 0.741280i \(0.734219\pi\)
\(398\) 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 \(-0.498150\pi\)
0.00581184 + 0.999983i \(0.498150\pi\)
\(410\) 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 0.860551 0.509364i \(-0.170119\pi\)
−0.871398 + 0.490577i \(0.836786\pi\)
\(420\) 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 −0.663500 0.748176i \(-0.730930\pi\)
0.979690 + 0.200519i \(0.0642630\pi\)
\(434\) 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 \(-0.751655\pi\)
−0.710773 + 0.703422i \(0.751655\pi\)
\(440\) −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 \(0.338646\pi\)
−0.999861 + 0.0166900i \(0.994687\pi\)
\(462\) 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 −0.913691 0.406409i \(-0.866781\pi\)
0.808806 + 0.588076i \(0.200114\pi\)
\(468\) −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 −0.721680 0.692227i \(-0.756630\pi\)
0.960326 + 0.278880i \(0.0899630\pi\)
\(480\) −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 \(0.403706\pi\)
−0.975661 + 0.219285i \(0.929628\pi\)
\(504\) 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 \(-0.612219\pi\)
−0.345289 + 0.938496i \(0.612219\pi\)
\(510\) 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 \(-0.963861\pi\)
0.398669 0.917095i \(-0.369472\pi\)
\(522\) −22.9476 + 39.7463i −1.00439 + 1.73965i
\(523\) −18.0575 −0.789598 −0.394799 0.918767i \(-0.629186\pi\)
−0.394799 + 0.918767i \(0.629186\pi\)
\(524\) −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 \(-0.649877\pi\)
−0.453647 + 0.891181i \(0.649877\pi\)
\(564\) 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 \(-0.956462\pi\)
0.377244 0.926114i \(-0.376872\pi\)
\(578\) −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 0.784859 0.619675i \(-0.212736\pi\)
−0.929084 + 0.369870i \(0.879402\pi\)
\(588\) 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 −0.875814 0.482648i \(-0.839675\pi\)
0.855893 + 0.517153i \(0.173008\pi\)
\(594\) 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 \(0.0464513\pi\)
−0.368754 + 0.929527i \(0.620215\pi\)
\(602\) 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 \(0.0596626\pi\)
−0.329868 + 0.944027i \(0.607004\pi\)
\(608\) −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 \(0.175820\pi\)
0.0287526 + 0.999587i \(0.490846\pi\)
\(620\) −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 −0.838484 0.544927i \(-0.816558\pi\)
0.891162 + 0.453685i \(0.149891\pi\)
\(644\) 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 \(-0.605659\pi\)
0.981689 0.190490i \(-0.0610076\pi\)
\(648\) −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 −0.870525 0.492124i \(-0.836221\pi\)
0.861455 + 0.507835i \(0.169554\pi\)
\(662\) 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 −0.944174 0.329447i \(-0.893138\pi\)
0.757397 + 0.652955i \(0.226471\pi\)
\(678\) −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 \(-0.446636\pi\)
0.166864 + 0.985980i \(0.446636\pi\)
\(692\) 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 0.629627 0.776897i \(-0.283208\pi\)
−0.987626 + 0.156824i \(0.949874\pi\)
\(720\) −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 \(-0.514236\pi\)
−0.0447098 + 0.999000i \(0.514236\pi\)
\(728\) 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 −0.714030 0.700115i \(-0.753132\pi\)
0.963332 + 0.268311i \(0.0864655\pi\)
\(734\) −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 0.572392 0.819980i \(-0.306016\pi\)
−0.996320 + 0.0857157i \(0.972682\pi\)
\(762\) −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 \(0.123592\pi\)
−0.134911 + 0.990858i \(0.543075\pi\)
\(770\) 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 \(-0.782505\pi\)
−0.775505 + 0.631341i \(0.782505\pi\)
\(774\) 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 0.2328