Properties

Label 637.2.f.l.295.7
Level $637$
Weight $2$
Character 637.295
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.f (of order \(3\), degree \(2\), 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 295.7
Root \(-0.558788 - 0.967849i\) of defining polynomial
Character \(\chi\) \(=\) 637.295
Dual form 637.2.f.l.393.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.16576 - 2.01915i) q^{2} +(-1.15450 + 1.99966i) q^{3} +(-1.71798 - 2.97563i) q^{4} +3.37112 q^{5} +(2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 - 2.01915i) q^{9} +O(q^{10})\) \(q+(1.16576 - 2.01915i) q^{2} +(-1.15450 + 1.99966i) q^{3} +(-1.71798 - 2.97563i) q^{4} +3.37112 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} +7.93366 q^{12} +(0.408029 - 3.58239i) q^{13} +(-3.89197 + 6.74108i) q^{15} +(-0.466957 + 0.808794i) q^{16} +(2.72867 + 4.72620i) q^{17} -5.43596 q^{18} +(3.58410 + 6.20784i) q^{19} +(-5.79151 - 10.0312i) q^{20} +(2.71798 + 4.70768i) q^{22} +(3.22621 - 5.58796i) q^{23} +(3.86524 - 6.69480i) q^{24} +6.36442 q^{25} +(-6.75772 - 5.00007i) q^{26} -1.54354 q^{27} +(4.22143 - 7.31174i) q^{29} +(9.07418 + 15.7169i) q^{30} -3.05121 q^{31} +(-2.25925 - 3.91314i) q^{32} +(-2.69174 - 4.66224i) q^{33} +12.7239 q^{34} +(-4.00550 + 6.93773i) q^{36} +(-1.52827 + 2.64704i) q^{37} +16.7127 q^{38} +(6.69249 + 4.95180i) q^{39} -11.2864 q^{40} +(0.468833 - 0.812043i) q^{41} +(2.04605 + 3.54385i) q^{43} +8.01100 q^{44} +(-3.92990 - 6.80679i) q^{45} +(-7.52195 - 13.0284i) q^{46} -3.46336 q^{47} +(-1.07821 - 1.86751i) q^{48} +(7.41937 - 12.8507i) q^{50} -12.6010 q^{51} +(-11.3609 + 4.94034i) q^{52} -2.34387 q^{53} +(-1.79939 + 3.11663i) q^{54} +(-3.92990 + 6.80679i) q^{55} -16.5514 q^{57} +(-9.84233 - 17.0474i) q^{58} +(-3.62346 - 6.27602i) q^{59} +26.7453 q^{60} +(-3.19506 - 5.53401i) q^{61} +(-3.55697 + 6.16085i) q^{62} -12.4028 q^{64} +(1.37551 - 12.0766i) q^{65} -12.5517 q^{66} +(-2.30670 + 3.99532i) q^{67} +(9.37561 - 16.2390i) q^{68} +(7.44934 + 12.9026i) q^{69} +(3.79370 + 6.57088i) q^{71} +(3.90292 + 6.76006i) q^{72} -2.06996 q^{73} +(3.56318 + 6.17161i) q^{74} +(-7.34775 + 12.7267i) q^{75} +(12.3148 - 21.3299i) q^{76} +(17.8002 - 7.74054i) q^{78} -7.58868 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} +9.54077 q^{86} +(9.74732 + 16.8829i) q^{87} +(3.90292 - 6.76006i) q^{88} +(-6.57984 + 11.3966i) q^{89} -18.3253 q^{90} -22.1703 q^{92} +(3.52263 - 6.10138i) q^{93} +(-4.03744 + 6.99305i) q^{94} +(12.0824 + 20.9273i) q^{95} +10.4333 q^{96} +(1.77856 + 3.08056i) q^{97} +5.43596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} + O(q^{10}) \) \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16576 2.01915i 0.824315 1.42776i −0.0781266 0.996943i \(-0.524894\pi\)
0.902442 0.430812i \(-0.141773\pi\)
\(3\) −1.15450 + 1.99966i −0.666553 + 1.15450i 0.312309 + 0.949981i \(0.398898\pi\)
−0.978862 + 0.204523i \(0.934436\pi\)
\(4\) −1.71798 2.97563i −0.858991 1.48782i
\(5\) 3.37112 1.50761 0.753804 0.657099i \(-0.228217\pi\)
0.753804 + 0.657099i \(0.228217\pi\)
\(6\) 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 \(0.280991\pi\)
\(12\) 7.93366 2.29025
\(13\) 0.408029 3.58239i 0.113167 0.993576i
\(14\) 0 0
\(15\) −3.89197 + 6.74108i −1.00490 + 1.74054i
\(16\) −0.466957 + 0.808794i −0.116739 + 0.202198i
\(17\) 2.72867 + 4.72620i 0.661800 + 1.14627i 0.980142 + 0.198295i \(0.0635405\pi\)
−0.318343 + 0.947976i \(0.603126\pi\)
\(18\) −5.43596 −1.28127
\(19\) 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
\(23\) 3.22621 5.58796i 0.672711 1.16517i −0.304421 0.952537i \(-0.598463\pi\)
0.977132 0.212632i \(-0.0682036\pi\)
\(24\) 3.86524 6.69480i 0.788989 1.36657i
\(25\) 6.36442 1.27288
\(26\) −6.75772 5.00007i −1.32530 0.980594i
\(27\) −1.54354 −0.297054
\(28\) 0 0
\(29\) 4.22143 7.31174i 0.783900 1.35776i −0.145753 0.989321i \(-0.546561\pi\)
0.929654 0.368434i \(-0.120106\pi\)
\(30\) 9.07418 + 15.7169i 1.65671 + 2.86951i
\(31\) −3.05121 −0.548013 −0.274007 0.961728i \(-0.588349\pi\)
−0.274007 + 0.961728i \(0.588349\pi\)
\(32\) −2.25925 3.91314i −0.399383 0.691752i
\(33\) −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
\(37\) −1.52827 + 2.64704i −0.251246 + 0.435170i −0.963869 0.266377i \(-0.914174\pi\)
0.712623 + 0.701547i \(0.247507\pi\)
\(38\) 16.7127 2.71117
\(39\) 6.69249 + 4.95180i 1.07166 + 0.792923i
\(40\) −11.2864 −1.78454
\(41\) 0.468833 0.812043i 0.0732194 0.126820i −0.827091 0.562068i \(-0.810006\pi\)
0.900311 + 0.435248i \(0.143339\pi\)
\(42\) 0 0
\(43\) 2.04605 + 3.54385i 0.312019 + 0.540433i 0.978799 0.204822i \(-0.0656614\pi\)
−0.666780 + 0.745254i \(0.732328\pi\)
\(44\) 8.01100 1.20770
\(45\) −3.92990 6.80679i −0.585835 1.01470i
\(46\) −7.52195 13.0284i −1.10905 1.92093i
\(47\) −3.46336 −0.505183 −0.252591 0.967573i \(-0.581283\pi\)
−0.252591 + 0.967573i \(0.581283\pi\)
\(48\) −1.07821 1.86751i −0.155626 0.269552i
\(49\) 0 0
\(50\) 7.41937 12.8507i 1.04926 1.81737i
\(51\) −12.6010 −1.76450
\(52\) −11.3609 + 4.94034i −1.57547 + 0.685101i
\(53\) −2.34387 −0.321956 −0.160978 0.986958i \(-0.551465\pi\)
−0.160978 + 0.986958i \(0.551465\pi\)
\(54\) −1.79939 + 3.11663i −0.244866 + 0.424120i
\(55\) −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
\(59\) −3.62346 6.27602i −0.471735 0.817069i 0.527742 0.849405i \(-0.323039\pi\)
−0.999477 + 0.0323358i \(0.989705\pi\)
\(60\) 26.7453 3.45280
\(61\) −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
\(65\) 1.37551 12.0766i 0.170611 1.49792i
\(66\) −12.5517 −1.54500
\(67\) −2.30670 + 3.99532i −0.281808 + 0.488106i −0.971830 0.235682i \(-0.924268\pi\)
0.690022 + 0.723788i \(0.257601\pi\)
\(68\) 9.37561 16.2390i 1.13696 1.96927i
\(69\) 7.44934 + 12.9026i 0.896795 + 1.55329i
\(70\) 0 0
\(71\) 3.79370 + 6.57088i 0.450229 + 0.779819i 0.998400 0.0565468i \(-0.0180090\pi\)
−0.548171 + 0.836366i \(0.684676\pi\)
\(72\) 3.90292 + 6.76006i 0.459964 + 0.796680i
\(73\) −2.06996 −0.242271 −0.121136 0.992636i \(-0.538654\pi\)
−0.121136 + 0.992636i \(0.538654\pi\)
\(74\) 3.56318 + 6.17161i 0.414211 + 0.717435i
\(75\) −7.34775 + 12.7267i −0.848445 + 1.46955i
\(76\) 12.3148 21.3299i 1.41261 2.44671i
\(77\) 0 0
\(78\) 17.8002 7.74054i 2.01548 0.876444i
\(79\) −7.58868 −0.853794 −0.426897 0.904300i \(-0.640393\pi\)
−0.426897 + 0.904300i \(0.640393\pi\)
\(80\) −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
\(86\) 9.54077 1.02881
\(87\) 9.74732 + 16.8829i 1.04502 + 1.81003i
\(88\) 3.90292 6.76006i 0.416053 0.720624i
\(89\) −6.57984 + 11.3966i −0.697461 + 1.20804i 0.271882 + 0.962330i \(0.412354\pi\)
−0.969344 + 0.245708i \(0.920980\pi\)
\(90\) −18.3253 −1.93165
\(91\) 0 0
\(92\) −22.1703 −2.31141
\(93\) 3.52263 6.10138i 0.365280 0.632683i
\(94\) −4.03744 + 6.99305i −0.416430 + 0.721278i
\(95\) 12.0824 + 20.9273i 1.23963 + 2.14710i
\(96\) 10.4333 1.06484
\(97\) 1.77856 + 3.08056i 0.180585 + 0.312783i 0.942080 0.335388i \(-0.108867\pi\)
−0.761495 + 0.648171i \(0.775534\pi\)
\(98\) 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
\(103\) −5.98286 −0.589508 −0.294754 0.955573i \(-0.595238\pi\)
−0.294754 + 0.955573i \(0.595238\pi\)
\(104\) −1.36607 + 11.9937i −0.133954 + 1.17608i
\(105\) 0 0
\(106\) −2.73239 + 4.73263i −0.265393 + 0.459674i
\(107\) −6.59131 + 11.4165i −0.637206 + 1.10367i 0.348837 + 0.937183i \(0.386577\pi\)
−0.986043 + 0.166490i \(0.946757\pi\)
\(108\) 2.65177 + 4.59300i 0.255166 + 0.441961i
\(109\) 4.11545 0.394188 0.197094 0.980385i \(-0.436850\pi\)
0.197094 + 0.980385i \(0.436850\pi\)
\(110\) 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 −0.977422 0.211297i \(-0.932231\pi\)
0.305723 0.952121i \(-0.401102\pi\)
\(114\) −19.2949 + 33.4198i −1.80714 + 3.13005i
\(115\) 10.8759 18.8376i 1.01418 1.75662i
\(116\) −29.0094 −2.69345
\(117\) −7.70905 + 3.35233i −0.712702 + 0.309923i
\(118\) −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
\(122\) −14.8987 −1.34886
\(123\) 1.08254 + 1.87501i 0.0976093 + 0.169064i
\(124\) 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 −0.508486 0.861071i \(-0.669794\pi\)
0.999952 + 0.00982616i \(0.00312781\pi\)
\(128\) −9.94014 + 17.2168i −0.878592 + 1.52177i
\(129\) −9.44867 −0.831909
\(130\) −22.7811 16.8558i −1.99803 1.47835i
\(131\) −0.672012 −0.0587139 −0.0293570 0.999569i \(-0.509346\pi\)
−0.0293570 + 0.999569i \(0.509346\pi\)
\(132\) −9.24873 + 16.0193i −0.804998 + 1.39430i
\(133\) 0 0
\(134\) 5.37810 + 9.31515i 0.464597 + 0.804706i
\(135\) −5.20344 −0.447841
\(136\) −9.13550 15.8232i −0.783363 1.35682i
\(137\) −3.91937 6.78855i −0.334855 0.579985i 0.648602 0.761128i \(-0.275354\pi\)
−0.983457 + 0.181142i \(0.942021\pi\)
\(138\) 34.7365 2.95697
\(139\) −1.63760 2.83641i −0.138900 0.240581i 0.788181 0.615444i \(-0.211023\pi\)
−0.927080 + 0.374863i \(0.877690\pi\)
\(140\) 0 0
\(141\) 3.99846 6.92554i 0.336731 0.583236i
\(142\) 17.6901 1.48452
\(143\) 6.75772 + 5.00007i 0.565109 + 0.418127i
\(144\) 2.17744 0.181453
\(145\) 14.2309 24.6487i 1.18182 2.04696i
\(146\) −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 \(0.636320\pi\)
\(150\) 17.1314 + 29.6724i 1.39877 + 2.42274i
\(151\) −1.34625 −0.109556 −0.0547781 0.998499i \(-0.517445\pi\)
−0.0547781 + 0.998499i \(0.517445\pi\)
\(152\) −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
\(156\) 3.23716 28.4215i 0.259180 2.27554i
\(157\) −13.0401 −1.04071 −0.520357 0.853949i \(-0.674201\pi\)
−0.520357 + 0.853949i \(0.674201\pi\)
\(158\) −8.84657 + 15.3227i −0.703795 + 1.21901i
\(159\) 2.70601 4.68695i 0.214600 0.371699i
\(160\) −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 \(0.895211\pi\)
\(164\) −3.22179 −0.251579
\(165\) −9.07418 15.7169i −0.706424 1.22356i
\(166\) −3.37295 + 5.84212i −0.261792 + 0.453436i
\(167\) −1.82128 + 3.15455i −0.140935 + 0.244107i −0.927849 0.372956i \(-0.878344\pi\)
0.786914 + 0.617063i \(0.211678\pi\)
\(168\) 0 0
\(169\) −12.6670 2.92344i −0.974387 0.224880i
\(170\) 42.8937 3.28979
\(171\) 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
\(177\) 16.7332 1.25775
\(178\) 15.3410 + 26.5714i 1.14986 + 1.99161i
\(179\) 4.39469 7.61183i 0.328475 0.568935i −0.653735 0.756724i \(-0.726799\pi\)
0.982209 + 0.187789i \(0.0601321\pi\)
\(180\) −13.5030 + 23.3879i −1.00645 + 1.74323i
\(181\) −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
\(184\) −10.8012 + 18.7083i −0.796278 + 1.37919i
\(185\) −5.15197 + 8.92347i −0.378780 + 0.656066i
\(186\) −8.21307 14.2255i −0.602212 1.04306i
\(187\) −12.7239 −0.930462
\(188\) 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 \(0.202898\pi\)
\(194\) 8.29348 0.595437
\(195\) 22.5611 + 16.6931i 1.61564 + 1.19542i
\(196\) 0 0
\(197\) 8.84783 15.3249i 0.630382 1.09185i −0.357092 0.934069i \(-0.616232\pi\)
0.987474 0.157784i \(-0.0504351\pi\)
\(198\) 6.33701 10.9760i 0.450352 0.780033i
\(199\) −6.49476 11.2493i −0.460402 0.797439i 0.538579 0.842575i \(-0.318961\pi\)
−0.998981 + 0.0451359i \(0.985628\pi\)
\(200\) −21.3079 −1.50670
\(201\) −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
\(205\) 1.58049 2.73749i 0.110386 0.191195i
\(206\) −6.97456 + 12.0803i −0.485941 + 0.841674i
\(207\) −15.0439 −1.04562
\(208\) 2.70688 + 2.00283i 0.187688 + 0.138872i
\(209\) −16.7127 −1.15605
\(210\) 0 0
\(211\) −13.7701 + 23.8505i −0.947974 + 1.64194i −0.198289 + 0.980144i \(0.563538\pi\)
−0.749685 + 0.661795i \(0.769795\pi\)
\(212\) 4.02673 + 6.97450i 0.276557 + 0.479011i
\(213\) −17.5193 −1.20041
\(214\) 15.3677 + 26.6177i 1.05052 + 1.81955i
\(215\) 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
\(219\) 2.38978 4.13922i 0.161487 0.279703i
\(220\) 27.0060 1.82074
\(221\) 18.0445 7.84674i 1.21380 0.527829i
\(222\) −16.4548 −1.10437
\(223\) 4.35098 7.53612i 0.291363 0.504656i −0.682769 0.730634i \(-0.739224\pi\)
0.974132 + 0.225978i \(0.0725578\pi\)
\(224\) 0 0
\(225\) −7.41937 12.8507i −0.494625 0.856715i
\(226\) −33.2953 −2.21477
\(227\) 10.9835 + 19.0239i 0.728998 + 1.26266i 0.957307 + 0.289072i \(0.0933468\pi\)
−0.228310 + 0.973589i \(0.573320\pi\)
\(228\) 28.4350 + 49.2509i 1.88315 + 3.26172i
\(229\) 20.5188 1.35592 0.677959 0.735100i \(-0.262865\pi\)
0.677959 + 0.735100i \(0.262865\pi\)
\(230\) −25.3574 43.9203i −1.67202 2.89602i
\(231\) 0 0
\(232\) −14.1332 + 24.4795i −0.927892 + 1.60716i
\(233\) −17.2888 −1.13263 −0.566313 0.824190i \(-0.691631\pi\)
−0.566313 + 0.824190i \(0.691631\pi\)
\(234\) −2.21803 + 19.4737i −0.144997 + 1.27304i
\(235\) −11.6754 −0.761618
\(236\) −12.4501 + 21.5642i −0.810432 + 1.40371i
\(237\) 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
\(241\) −0.732856 1.26934i −0.0472074 0.0817657i 0.841456 0.540325i \(-0.181699\pi\)
−0.888664 + 0.458560i \(0.848366\pi\)
\(242\) 12.9726 0.833913
\(243\) 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
\(247\) 23.7013 10.3067i 1.50808 0.655797i
\(248\) 10.2154 0.648676
\(249\) 3.34039 5.78572i 0.211688 0.366655i
\(250\) 5.36205 9.28734i 0.339126 0.587383i
\(251\) 8.55142 + 14.8115i 0.539761 + 0.934894i 0.998917 + 0.0465376i \(0.0148187\pi\)
−0.459156 + 0.888356i \(0.651848\pi\)
\(252\) 0 0
\(253\) 7.52195 + 13.0284i 0.472901 + 0.819089i
\(254\) −12.9132 22.3663i −0.810246 1.40339i
\(255\) −42.4796 −2.66017
\(256\) 10.7728 + 18.6590i 0.673300 + 1.16619i
\(257\) 1.92506 3.33430i 0.120082 0.207988i −0.799718 0.600376i \(-0.795018\pi\)
0.919800 + 0.392388i \(0.128351\pi\)
\(258\) −11.0149 + 19.0783i −0.685755 + 1.18776i
\(259\) 0 0
\(260\) −38.2988 + 16.6544i −2.37519 + 1.03286i
\(261\) −19.6847 −1.21845
\(262\) −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
\(268\) 15.8515 0.968282
\(269\) 8.38857 + 14.5294i 0.511460 + 0.885875i 0.999912 + 0.0132842i \(0.00422861\pi\)
−0.488451 + 0.872591i \(0.662438\pi\)
\(270\) −6.06595 + 10.5065i −0.369162 + 0.639407i
\(271\) 15.5886 27.0003i 0.946941 1.64015i 0.195124 0.980779i \(-0.437489\pi\)
0.751817 0.659372i \(-0.229178\pi\)
\(272\) −5.09669 −0.309032
\(273\) 0 0
\(274\) −18.2762 −1.10410
\(275\) −7.41937 + 12.8507i −0.447405 + 0.774928i
\(276\) 25.5956 44.3330i 1.54068 2.66853i
\(277\) −0.197941 0.342844i −0.0118931 0.0205995i 0.860018 0.510264i \(-0.170452\pi\)
−0.871911 + 0.489665i \(0.837119\pi\)
\(278\) −7.63619 −0.457988
\(279\) 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
\(285\) −55.7967 −3.30511
\(286\) 17.9738 7.81600i 1.06281 0.462170i
\(287\) 0 0
\(288\) −5.26748 + 9.12354i −0.310389 + 0.537610i
\(289\) −6.39129 + 11.0700i −0.375958 + 0.651178i
\(290\) −33.1796 57.4688i −1.94838 3.37469i
\(291\) −8.21342 −0.481479
\(292\) 3.55616 + 6.15945i 0.208109 + 0.360455i
\(293\) −7.88616 13.6592i −0.460715 0.797981i 0.538282 0.842765i \(-0.319074\pi\)
−0.998997 + 0.0447835i \(0.985740\pi\)
\(294\) 0 0
\(295\) −12.2151 21.1572i −0.711192 1.23182i
\(296\) 5.11659 8.86220i 0.297396 0.515105i
\(297\) 1.79939 3.11663i 0.104411 0.180845i
\(298\) 33.0229 1.91297
\(299\) −18.7018 13.8376i −1.08156 0.800248i
\(300\) 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
\(304\) −6.69448 −0.383955
\(305\) −10.7709 18.6558i −0.616742 1.06823i
\(306\) −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
\(310\) −11.9910 + 20.7689i −0.681041 + 1.17960i
\(311\) −3.06464 −0.173780 −0.0868898 0.996218i \(-0.527693\pi\)
−0.0868898 + 0.996218i \(0.527693\pi\)
\(312\) −22.4062 16.5785i −1.26850 0.938571i
\(313\) 35.2751 1.99387 0.996934 0.0782450i \(-0.0249316\pi\)
0.996934 + 0.0782450i \(0.0249316\pi\)
\(314\) −15.2016 + 26.3300i −0.857877 + 1.48589i
\(315\) 0 0
\(316\) 13.0372 + 22.5811i 0.733401 + 1.27029i
\(317\) 32.7065 1.83698 0.918490 0.395444i \(-0.129409\pi\)
0.918490 + 0.395444i \(0.129409\pi\)
\(318\) −6.30910 10.9277i −0.353797 0.612794i
\(319\) 9.84233 + 17.0474i 0.551065 + 0.954472i
\(320\) −41.8112 −2.33732
\(321\) −15.2194 26.3607i −0.849463 1.47131i
\(322\) 0 0
\(323\) −19.5596 + 33.8783i −1.08833 + 1.88504i
\(324\) −36.2789 −2.01549
\(325\) 2.59687 22.7998i 0.144048 1.26471i
\(326\) −11.5003 −0.636944
\(327\) −4.75130 + 8.22949i −0.262747 + 0.455092i
\(328\) −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 \(0.875244\pi\)
\(332\) 4.97073 + 8.60955i 0.272804 + 0.472511i
\(333\) 7.12636 0.390522
\(334\) 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 \(0.246577\pi\)
\(338\) −20.6695 + 22.1686i −1.12427 + 1.20581i
\(339\) 32.9738 1.79089
\(340\) 31.6063 54.7437i 1.71409 2.96889i
\(341\) 3.55697 6.16085i 0.192621 0.333629i
\(342\) −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
\(346\) −29.5908 −1.59081
\(347\) 5.22211 + 9.04496i 0.280338 + 0.485559i 0.971468 0.237171i \(-0.0762202\pi\)
−0.691130 + 0.722730i \(0.742887\pi\)
\(348\) 33.4914 58.0088i 1.79533 3.10960i
\(349\) 11.7344 20.3246i 0.628128 1.08795i −0.359799 0.933030i \(-0.617155\pi\)
0.987927 0.154920i \(-0.0495118\pi\)
\(350\) 0 0
\(351\) −0.629807 + 5.52955i −0.0336166 + 0.295145i
\(352\) 10.5350 0.561515
\(353\) 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
\(359\) −17.1014 −0.902576 −0.451288 0.892378i \(-0.649035\pi\)
−0.451288 + 0.892378i \(0.649035\pi\)
\(360\) 13.1572 + 22.7889i 0.693445 + 1.20108i
\(361\) −16.1915 + 28.0445i −0.852184 + 1.47603i
\(362\) −20.0490 + 34.7258i −1.05375 + 1.82515i
\(363\) −12.8474 −0.674314
\(364\) 0 0
\(365\) −6.97809 −0.365250
\(366\) 17.2006 29.7923i 0.899089 1.55727i
\(367\) −0.524301 + 0.908115i −0.0273683 + 0.0474032i −0.879385 0.476111i \(-0.842046\pi\)
0.852017 + 0.523514i \(0.175379\pi\)
\(368\) 3.01300 + 5.21867i 0.157064 + 0.272042i
\(369\) −2.18618 −0.113808
\(370\) 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
\(376\) 11.5952 0.597978
\(377\) −24.4710 18.1062i −1.26032 0.932517i
\(378\) 0 0
\(379\) 13.5749 23.5123i 0.697294 1.20775i −0.272108 0.962267i \(-0.587721\pi\)
0.969401 0.245481i \(-0.0789459\pi\)
\(380\) 41.5147 71.9056i 2.12966 3.68868i
\(381\) 12.7885 + 22.1504i 0.655177 + 1.13480i
\(382\) −2.48960 −0.127379
\(383\) −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
\(387\) 4.77039 8.26255i 0.242492 0.420009i
\(388\) 6.11107 10.5847i 0.310242 0.537356i
\(389\) 7.99427 0.405326 0.202663 0.979249i \(-0.435040\pi\)
0.202663 + 0.979249i \(0.435040\pi\)
\(390\) 60.0067 26.0943i 3.03856 1.32133i
\(391\) 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
\(395\) −25.5823 −1.28719
\(396\) −9.33888 16.1754i −0.469297 0.812845i
\(397\) −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
\(401\) −18.9206 + 32.7715i −0.944850 + 1.63653i −0.188799 + 0.982016i \(0.560459\pi\)
−0.756051 + 0.654513i \(0.772874\pi\)
\(402\) −24.8362 −1.23872
\(403\) −1.24498 + 10.9306i −0.0620169 + 0.544493i
\(404\) 16.2475 0.808341
\(405\) 17.7971 30.8255i 0.884345 1.53173i
\(406\) 0 0
\(407\) −3.56318 6.17161i −0.176620 0.305915i
\(408\) 42.1879 2.08861
\(409\) 0.117537 + 0.203580i 0.00581184 + 0.0100664i 0.868917 0.494958i \(-0.164817\pi\)
−0.863105 + 0.505025i \(0.831483\pi\)
\(410\) −3.68494 6.38250i −0.181986 0.315209i
\(411\) 18.0997 0.892794
\(412\) 10.2784 + 17.8028i 0.506382 + 0.877080i
\(413\) 0 0
\(414\) −17.5375 + 30.3759i −0.861923 + 1.49290i
\(415\) −9.75383 −0.478797
\(416\) −14.9402 + 6.49684i −0.732505 + 0.318534i
\(417\) 7.56248 0.370336
\(418\) −19.4830 + 33.7456i −0.952945 + 1.65055i
\(419\) 0.222023 0.384555i 0.0108465 0.0187868i −0.860551 0.509364i \(-0.829881\pi\)
0.871398 + 0.490577i \(0.163214\pi\)
\(420\) 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
\(423\) 4.03744 + 6.99305i 0.196307 + 0.340014i
\(424\) 7.84721 0.381094
\(425\) 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
\(429\) −17.8002 + 7.74054i −0.859404 + 0.373717i
\(430\) 32.1630 1.55104
\(431\) −10.7723 + 18.6582i −0.518883 + 0.898732i 0.480876 + 0.876789i \(0.340319\pi\)
−0.999759 + 0.0219436i \(0.993015\pi\)
\(432\) 0.720766 1.24840i 0.0346778 0.0600638i
\(433\) −6.57949 11.3960i −0.316190 0.547657i 0.663500 0.748176i \(-0.269070\pi\)
−0.979690 + 0.200519i \(0.935737\pi\)
\(434\) 0 0
\(435\) 32.8593 + 56.9141i 1.57548 + 2.72882i
\(436\) −7.07026 12.2461i −0.338604 0.586479i
\(437\) 46.2522 2.21254
\(438\) −5.57181 9.65066i −0.266232 0.461127i
\(439\) −14.8923 + 25.7943i −0.710773 + 1.23109i 0.253795 + 0.967258i \(0.418321\pi\)
−0.964568 + 0.263836i \(0.915012\pi\)
\(440\) 13.1572 22.7889i 0.627245 1.08642i
\(441\) 0 0
\(442\) 5.19171 45.5819i 0.246944 2.16811i
\(443\) 14.8467 0.705387 0.352693 0.935739i \(-0.385266\pi\)
0.352693 + 0.935739i \(0.385266\pi\)
\(444\) −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 0.989712 + 0.143075i \(0.0456992\pi\)
−0.370949 + 0.928653i \(0.620968\pi\)
\(450\) −34.5968 −1.63091
\(451\) 1.09309 + 1.89329i 0.0514717 + 0.0891516i
\(452\) −24.5337 + 42.4936i −1.15397 + 1.99873i
\(453\) 1.55425 2.69204i 0.0730251 0.126483i
\(454\) 51.2162 2.40369
\(455\) 0 0
\(456\) 55.4136 2.59498
\(457\) 7.93542 13.7445i 0.371203 0.642943i −0.618548 0.785747i \(-0.712279\pi\)
0.989751 + 0.142804i \(0.0456120\pi\)
\(458\) 23.9199 41.4305i 1.11770 1.93592i
\(459\) −4.21180 7.29506i −0.196590 0.340504i
\(460\) −74.7385 −3.48470
\(461\) 11.0443 + 19.1293i 0.514384 + 0.890940i 0.999861 + 0.0166900i \(0.00531285\pi\)
−0.485476 + 0.874250i \(0.661354\pi\)
\(462\) 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
\(467\) −4.53318 −0.209771 −0.104885 0.994484i \(-0.533448\pi\)
−0.104885 + 0.994484i \(0.533448\pi\)
\(468\) 23.2193 + 17.1801i 1.07331 + 0.794148i
\(469\) 0 0
\(470\) −13.6107 + 23.5744i −0.627813 + 1.08740i
\(471\) 15.0549 26.0758i 0.693691 1.20151i
\(472\) 12.1312 + 21.0119i 0.558386 + 0.967153i
\(473\) −9.54077 −0.438685
\(474\) −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
\(478\) 3.79992 6.58165i 0.173804 0.301038i
\(479\) −5.22303 + 9.04655i −0.238646 + 0.413347i −0.960326 0.278880i \(-0.910037\pi\)
0.721680 + 0.692227i \(0.243370\pi\)
\(480\) 35.1717 1.60536
\(481\) 8.85914 + 6.55491i 0.403942 + 0.298878i
\(482\) −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
\(486\) 46.0456 2.08867
\(487\) −17.9571 31.1027i −0.813715 1.40940i −0.910247 0.414067i \(-0.864108\pi\)
0.0965311 0.995330i \(-0.469225\pi\)
\(488\) 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 −0.939747 0.341871i \(-0.888939\pi\)
0.765943 + 0.642909i \(0.222273\pi\)
\(492\) 3.71956 6.44247i 0.167691 0.290449i
\(493\) 46.0756 2.07514
\(494\) 6.81928 59.8716i 0.306814 2.69375i
\(495\) 18.3253 0.823659
\(496\) 1.42478 2.46780i 0.0639747 0.110807i
\(497\) 0 0
\(498\) −7.78816 13.4895i −0.348996 0.604479i
\(499\) 8.49078 0.380099 0.190050 0.981774i \(-0.439135\pi\)
0.190050 + 0.981774i \(0.439135\pi\)
\(500\) −7.90207 13.6868i −0.353391 0.612092i
\(501\) −4.20535 7.28389i −0.187881 0.325420i
\(502\) 39.8755 1.77973
\(503\) 15.2000 + 26.3272i 0.677736 + 1.17387i 0.975661 + 0.219285i \(0.0703723\pi\)
−0.297924 + 0.954589i \(0.596294\pi\)
\(504\) 0 0
\(505\) −7.97041 + 13.8052i −0.354679 + 0.614321i
\(506\) 35.0751 1.55928
\(507\) 20.4700 21.9546i 0.909105 0.975039i
\(508\) −38.0604 −1.68866
\(509\) −7.79007 + 13.4928i −0.345289 + 0.598058i −0.985406 0.170219i \(-0.945552\pi\)
0.640117 + 0.768277i \(0.278886\pi\)
\(510\) −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
\(514\) −4.48830 7.77396i −0.197970 0.342895i
\(515\) −20.1689 −0.888748
\(516\) 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
\(520\) −4.60517 + 40.4322i −0.201950 + 1.77307i
\(521\) −27.1574 −1.18979 −0.594893 0.803805i \(-0.702806\pi\)
−0.594893 + 0.803805i \(0.702806\pi\)
\(522\) −22.9476 + 39.7463i −1.00439 + 1.73965i
\(523\) −9.02874 + 15.6382i −0.394799 + 0.683812i −0.993076 0.117478i \(-0.962519\pi\)
0.598276 + 0.801290i \(0.295853\pi\)
\(524\) 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
\(528\) 5.02772 0.218803
\(529\) −9.31684 16.1372i −0.405080 0.701619i
\(530\) −9.21119 + 15.9543i −0.400109 + 0.693008i
\(531\) −8.44816 + 14.6326i −0.366619 + 0.635003i
\(532\) 0 0
\(533\) −2.71776 2.01088i −0.117719 0.0871009i
\(534\) −70.8449 −3.06576
\(535\) −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
\(541\) 39.9882 1.71923 0.859613 0.510945i \(-0.170705\pi\)
0.859613 + 0.510945i \(0.170705\pi\)
\(542\) −36.3451 62.9516i −1.56116 2.70400i
\(543\) 19.8554 34.3906i 0.852077 1.47584i
\(544\) 12.3295 21.3553i 0.528623 0.915602i
\(545\) 13.8736 0.594282
\(546\) 0 0
\(547\) −22.6124 −0.966836 −0.483418 0.875390i \(-0.660605\pi\)
−0.483418 + 0.875390i \(0.660605\pi\)
\(548\) −13.4668 + 23.3252i −0.575274 + 0.996404i
\(549\) −7.44934 + 12.9026i −0.317930 + 0.550671i
\(550\) 17.2984 + 29.9617i 0.737605 + 1.27757i
\(551\) 60.5201 2.57824
\(552\) −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 \(0.0988969\pi\)
\(558\) 16.5863 0.702152
\(559\) 13.5303 5.88374i 0.572271 0.248856i
\(560\) 0 0
\(561\) 14.6898 25.4434i 0.620202 1.07422i
\(562\) −26.7494 + 46.3313i −1.12836 + 1.95437i
\(563\) −10.7640 18.6437i −0.453647 0.785740i 0.544962 0.838461i \(-0.316544\pi\)
−0.998609 + 0.0527209i \(0.983211\pi\)
\(564\) −27.4771 −1.15700
\(565\) −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
\(569\) 16.5502 28.6657i 0.693819 1.20173i −0.276758 0.960940i \(-0.589260\pi\)
0.970577 0.240791i \(-0.0774068\pi\)
\(570\) −65.0454 + 112.662i −2.72445 + 4.71889i
\(571\) 19.9357 0.834284 0.417142 0.908841i \(-0.363032\pi\)
0.417142 + 0.908841i \(0.363032\pi\)
\(572\) 3.26872 28.6985i 0.136672 1.19995i
\(573\) 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
\(577\) −29.4695 −1.22683 −0.613416 0.789760i \(-0.710205\pi\)
−0.613416 + 0.789760i \(0.710205\pi\)
\(578\) 14.9014 + 25.8100i 0.619816 + 1.07355i
\(579\) −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
\(583\) 2.73239 4.73263i 0.113164 0.196006i
\(584\) 6.93018 0.286773
\(585\) −25.9881 + 11.3011i −1.07448 + 0.467242i
\(586\) −36.7734 −1.51910
\(587\) 3.49429 6.05229i 0.144225 0.249805i −0.784859 0.619675i \(-0.787264\pi\)
0.929084 + 0.369870i \(0.120598\pi\)
\(588\) 0 0
\(589\) −10.9358 18.9414i −0.450603 0.780467i
\(590\) −56.9595 −2.34498
\(591\) 20.4297 + 35.3853i 0.840366 + 1.45556i
\(592\) −1.42727 2.47211i −0.0586605 0.101603i
\(593\) −0.970248 −0.0398433 −0.0199216 0.999802i \(-0.506342\pi\)
−0.0199216 + 0.999802i \(0.506342\pi\)
\(594\) −4.19530 7.26648i −0.172135 0.298147i
\(595\) 0 0
\(596\) 24.3330 42.1460i 0.996719 1.72637i
\(597\) 29.9929 1.22753
\(598\) −49.7420 + 21.6306i −2.03410 + 0.884541i
\(599\) −22.5998 −0.923404 −0.461702 0.887035i \(-0.652761\pi\)
−0.461702 + 0.887035i \(0.652761\pi\)
\(600\) 24.6000 42.6085i 1.00429 1.73949i
\(601\) −15.2146 + 26.3525i −0.620617 + 1.07494i 0.368754 + 0.929527i \(0.379785\pi\)
−0.989371 + 0.145414i \(0.953549\pi\)
\(602\) 0 0
\(603\) 10.7562 0.438027
\(604\) 2.31283 + 4.00594i 0.0941078 + 0.163000i
\(605\) 9.37851 + 16.2441i 0.381291 + 0.660415i
\(606\) −25.4566 −1.03410
\(607\) −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
\(611\) −1.41315 + 12.4071i −0.0571699 + 0.501938i
\(612\) −43.7188 −1.76723
\(613\) −6.96043 + 12.0558i −0.281129 + 0.486930i −0.971663 0.236370i \(-0.924042\pi\)
0.690534 + 0.723300i \(0.257376\pi\)
\(614\) −22.4449 + 38.8757i −0.905801 + 1.56889i
\(615\) 3.64937 + 6.32089i 0.147157 + 0.254883i
\(616\) 0 0
\(617\) 5.08394 + 8.80565i 0.204672 + 0.354502i 0.950028 0.312164i \(-0.101054\pi\)
−0.745356 + 0.666666i \(0.767721\pi\)
\(618\) −16.1043 27.8935i −0.647810 1.12204i
\(619\) 43.7905 1.76009 0.880044 0.474893i \(-0.157513\pi\)
0.880044 + 0.474893i \(0.157513\pi\)
\(620\) 17.6711 + 30.6073i 0.709689 + 1.22922i
\(621\) −4.97977 + 8.62522i −0.199831 + 0.346118i
\(622\) −3.57262 + 6.18796i −0.143249 + 0.248115i
\(623\) 0 0
\(624\) −7.13009 + 3.10056i −0.285432 + 0.124122i
\(625\) −16.3162 −0.652650
\(626\) 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 0.660288 0.751013i \(-0.270434\pi\)
−0.980540 + 0.196320i \(0.937101\pi\)
\(632\) 25.4067 1.01062
\(633\) −31.7953 55.0711i −1.26375 2.18888i
\(634\) 38.1279 66.0394i 1.51425 2.62276i
\(635\) 18.6711 32.3392i 0.740939 1.28334i
\(636\) −18.5955 −0.737359
\(637\) 0 0
\(638\) 45.8951 1.81700
\(639\) 8.84506 15.3201i 0.349905 0.606054i
\(640\) −33.5094 + 58.0399i −1.32457 + 2.29423i
\(641\) 24.6254 + 42.6525i 0.972645 + 1.68467i 0.687497 + 0.726187i \(0.258709\pi\)
0.285148 + 0.958483i \(0.407957\pi\)
\(642\) −70.9684 −2.80090
\(643\) −1.33579 2.31366i −0.0526784 0.0912417i 0.838484 0.544927i \(-0.183442\pi\)
−0.891162 + 0.453685i \(0.850109\pi\)
\(644\) 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
\(649\) 16.8963 0.663239
\(650\) −43.0090 31.8226i −1.68695 1.24818i
\(651\) 0 0
\(652\) −8.47404 + 14.6775i −0.331869 + 0.574814i
\(653\) −11.9244 + 20.6536i −0.466637 + 0.808239i −0.999274 0.0381052i \(-0.987868\pi\)
0.532637 + 0.846344i \(0.321201\pi\)
\(654\) 11.0777 + 19.1872i 0.433173 + 0.750278i
\(655\) −2.26543 −0.0885177
\(656\) 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 0.983345 0.181749i \(-0.0581757\pi\)
−0.649071 + 0.760727i \(0.724842\pi\)
\(660\) −31.1785 + 54.0028i −1.21362 + 2.10206i
\(661\) 0.233201 0.403917i 0.00907048 0.0157105i −0.861455 0.507835i \(-0.830446\pi\)
0.870525 + 0.492124i \(0.163779\pi\)
\(662\) −11.1377 −0.432880
\(663\) −5.14159 + 45.1418i −0.199683 + 1.75316i
\(664\) 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
\(668\) 12.5157 0.484248
\(669\) 10.0465 + 17.4010i 0.388418 + 0.672760i
\(670\) 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 −0.984072 0.177770i \(-0.943112\pi\)
0.645990 + 0.763346i \(0.276445\pi\)
\(674\) 30.5885 52.9808i 1.17822 2.04075i
\(675\) −9.82372 −0.378115
\(676\) 13.0626 + 42.7148i 0.502410 + 1.64288i
\(677\) −9.71961 −0.373555 −0.186777 0.982402i \(-0.559804\pi\)
−0.186777 + 0.982402i \(0.559804\pi\)
\(678\) 38.4395 66.5792i 1.47626 2.55696i
\(679\) 0 0
\(680\) −30.7968 53.3417i −1.18101 2.04556i
\(681\) −50.7218 −1.94366
\(682\) −8.29313 14.3641i −0.317560 0.550031i
\(683\) 18.0577 + 31.2769i 0.690960 + 1.19678i 0.971524 + 0.236942i \(0.0761451\pi\)
−0.280564 + 0.959835i \(0.590522\pi\)
\(684\) −57.4244 −2.19568
\(685\) −13.2127 22.8850i −0.504830 0.874391i
\(686\) 0 0
\(687\) −23.6890 + 41.0305i −0.903791 + 1.56541i
\(688\) −3.82166 −0.145700
\(689\) −0.956367 + 8.39666i −0.0364347 + 0.319887i
\(690\) 117.101 4.45795
\(691\) 4.38634 7.59737i 0.166864 0.289018i −0.770451 0.637499i \(-0.779969\pi\)
0.937316 + 0.348481i \(0.113302\pi\)
\(692\) −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
\(696\) −32.6337 56.5233i −1.23698 2.14251i
\(697\) 5.11717 0.193826
\(698\) −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 \(0.490887\pi\)
\(702\) 10.4308 + 7.71779i 0.393685 + 0.291289i
\(703\) −21.9098 −0.826345
\(704\) 14.4586 25.0431i 0.544930 0.943847i
\(705\) 13.4793 23.3468i 0.507659 0.879291i
\(706\) −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 \(0.741810\pi\)
\(710\) 59.6355 2.23808
\(711\) 8.84657 + 15.3227i 0.331772 + 0.574646i
\(712\) 22.0291 38.1555i 0.825575 1.42994i
\(713\) −9.84384 + 17.0500i −0.368655 + 0.638528i
\(714\) 0 0
\(715\) 22.7811 + 16.8558i 0.851964 + 0.630372i
\(716\) −30.2000 −1.12863
\(717\) −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
\(723\) 3.38434 0.125865
\(724\) 29.5462 + 51.1756i 1.09808 + 1.90193i
\(725\) 26.8670 46.5350i 0.997815 1.72827i
\(726\) −14.9770 + 25.9409i −0.555847 + 0.962755i
\(727\) 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
\(730\) −8.13476 + 14.0898i −0.301081 + 0.521488i
\(731\) −11.1660 + 19.3400i −0.412988 + 0.715317i
\(732\) −25.3486 43.9050i −0.936910 1.62278i
\(733\) 13.4992 0.498604 0.249302 0.968426i \(-0.419799\pi\)
0.249302 + 0.968426i \(0.419799\pi\)
\(734\) 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 \(0.166416\pi\)
\(740\) 35.4039 1.30147
\(741\) −6.75345 + 59.2936i −0.248094 + 2.17820i
\(742\) 0 0
\(743\) 10.8254 18.7501i 0.397145 0.687875i −0.596228 0.802815i \(-0.703334\pi\)
0.993372 + 0.114941i \(0.0366678\pi\)
\(744\) −11.7937 + 20.4272i −0.432377 + 0.748898i
\(745\) 23.8738 + 41.3506i 0.874667 + 1.51497i
\(746\) 34.9977 1.28136
\(747\) 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
\(751\) 22.4429 38.8723i 0.818953 1.41847i −0.0875006 0.996164i \(-0.527888\pi\)
0.906454 0.422304i \(-0.138779\pi\)
\(752\) 1.61724 2.80114i 0.0589747 0.102147i
\(753\) −39.4906 −1.43912
\(754\) −65.0865 + 28.3032i −2.37031 + 1.03074i
\(755\) −4.53837 −0.165168
\(756\) 0 0
\(757\) 3.77726 6.54240i 0.137287 0.237788i −0.789182 0.614159i \(-0.789495\pi\)
0.926469 + 0.376372i \(0.122828\pi\)
\(758\) −31.6500 54.8194i −1.14958 1.99113i
\(759\) −34.7365 −1.26085
\(760\) −40.4515 70.0641i −1.46733 2.54149i
\(761\) 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
\(765\) 21.4468 37.1470i 0.775412 1.34305i
\(766\) −37.3658 −1.35008
\(767\) −23.9616 + 10.4199i −0.865205 + 0.376239i
\(768\) −49.7489 −1.79516
\(769\) −21.9255 + 37.9760i −0.790652 + 1.36945i 0.134911 + 0.990858i \(0.456925\pi\)
−0.925564 + 0.378592i \(0.876408\pi\)
\(770\) 0 0
\(771\) 4.44497 + 7.69891i 0.160082 + 0.277270i
\(772\) 10.8432 0.390255
\(773\) −21.5613 37.3452i −0.775505 1.34321i −0.934510 0.355936i \(-0.884162\pi\)
0.159005 0.987278i \(-0.449171\pi\)
\(774\) −11.1222 19.2643i −0.399780 0.692440i
\(775\) −19.4192 −0.697558
\(776\) −5.95457 10.3136i −0.213756 0.370237i
\(777\) 0 0
\(778\) 9.31939 16.1417i 0.334116 0.578706i
\(779\) 6.72137 0.240818
\(780\) 10.9128 95.8121i 0.390743 3.43062i
\(781\) −17.6901 −0.633002
\(782\) 41.0499 71.1005i 1.46794 2.54255i
\(783\) −6.51594 + 11.2859i −0.232861 + 0.403326i
\(784\) 0