Properties

Label 637.2.q.i.589.6
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 589.6
Root \(1.32725 + 0.488273i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.i.491.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.24179 + 1.29430i) q^{2} +(0.259233 - 0.449005i) q^{3} +(2.35043 + 4.07106i) q^{4} +1.61205i q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} +(1.36560 + 2.36528i) q^{9} +O(q^{10})\) \(q+(2.24179 + 1.29430i) q^{2} +(0.259233 - 0.449005i) q^{3} +(2.35043 + 4.07106i) q^{4} +1.61205i q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} +(1.36560 + 2.36528i) q^{9} +(-2.08648 + 3.61389i) q^{10} +(-2.34256 - 1.35248i) q^{11} +2.43723 q^{12} +(-2.36840 - 2.71858i) q^{13} +(0.723819 + 0.417897i) q^{15} +(-4.34816 + 7.53123i) q^{16} +(-1.56330 - 2.70772i) q^{17} +7.06997i q^{18} +(3.18828 - 1.84075i) q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} +(0.993019 - 1.71996i) q^{23} +(3.13918 + 1.81241i) q^{24} +2.40128 q^{25} +(-1.79081 - 9.15992i) q^{26} +2.97143 q^{27} +(2.68636 - 4.65290i) q^{29} +(1.08177 + 1.87368i) q^{30} +10.4780i q^{31} +(-7.38583 + 4.26421i) q^{32} +(-1.21454 + 0.701214i) q^{33} -8.09354i q^{34} +(-6.41947 + 11.1188i) q^{36} +(-5.15585 - 2.97673i) q^{37} +9.52994 q^{38} +(-1.83462 + 0.358678i) q^{39} -11.2706 q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} -12.7156i q^{44} +(-3.81296 + 2.20141i) q^{45} +(4.45229 - 2.57053i) q^{46} -1.05508i q^{47} +(2.25437 + 3.90469i) q^{48} +(5.38318 + 3.10798i) q^{50} -1.62104 q^{51} +(5.50074 - 16.0317i) q^{52} +7.26568 q^{53} +(6.66133 + 3.84592i) q^{54} +(2.18027 - 3.77633i) q^{55} -1.90873i q^{57} +(12.0445 - 6.95390i) q^{58} +(-9.89352 + 5.71203i) q^{59} +3.92895i q^{60} +(-1.46254 - 2.53319i) q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(4.38250 - 3.81799i) q^{65} -3.63033 q^{66} +(-11.7622 - 6.79091i) q^{67} +(7.34886 - 12.7286i) q^{68} +(-0.514846 - 0.891740i) q^{69} +(1.17009 - 0.675554i) q^{71} +(-16.5367 + 9.54747i) q^{72} -9.10335i q^{73} +(-7.70557 - 13.3464i) q^{74} +(0.622492 - 1.07819i) q^{75} +(14.9876 + 8.65311i) q^{76} +(-4.57708 - 1.57047i) q^{78} -6.20578 q^{79} +(-12.1407 - 7.00946i) q^{80} +(-3.32650 + 5.76166i) q^{81} +(9.96806 + 17.2652i) q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} -8.68734i q^{86} +(-1.39278 - 2.41237i) q^{87} +(9.45576 - 16.3779i) q^{88} +(1.52410 + 0.879938i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(4.70469 + 2.71625i) q^{93} +(1.36560 - 2.36528i) q^{94} +(2.96739 + 5.13967i) q^{95} +4.42170i q^{96} +(13.4078 - 7.74102i) q^{97} -7.38776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 3q^{3} + 4q^{4} + 9q^{6} - q^{9} + O(q^{10}) \) \( 12q + 3q^{3} + 4q^{4} + 9q^{6} - q^{9} - 12q^{10} - 12q^{11} - 2q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} + 9q^{19} + 3q^{20} - 15q^{22} + 3q^{23} + 15q^{24} + 10q^{25} - 15q^{26} - 12q^{27} - q^{29} + 11q^{30} - 18q^{32} - 6q^{33} - 13q^{36} - 15q^{37} + 38q^{38} + 5q^{39} - 2q^{40} + 6q^{41} + 11q^{43} - 9q^{45} + 30q^{46} - 19q^{48} + 18q^{50} - 8q^{51} + 40q^{52} + 16q^{53} + 6q^{54} + 15q^{55} + 24q^{58} + 27q^{59} - 5q^{61} - 41q^{62} + 2q^{64} - 18q^{65} - 68q^{66} - 15q^{67} + 11q^{68} - 7q^{69} + 30q^{71} - 57q^{72} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} + 70q^{79} - 63q^{80} + 14q^{81} - 5q^{82} - 21q^{85} - 10q^{87} - 14q^{88} + 48q^{89} - 66q^{92} + 81q^{93} - q^{94} + 2q^{95} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24179 + 1.29430i 1.58519 + 0.915209i 0.994084 + 0.108613i \(0.0346409\pi\)
0.591104 + 0.806596i \(0.298692\pi\)
\(3\) 0.259233 0.449005i 0.149668 0.259233i −0.781437 0.623985i \(-0.785513\pi\)
0.931105 + 0.364752i \(0.118846\pi\)
\(4\) 2.35043 + 4.07106i 1.17521 + 2.03553i
\(5\) 1.61205i 0.720932i 0.932772 + 0.360466i \(0.117382\pi\)
−0.932772 + 0.360466i \(0.882618\pi\)
\(6\) 1.16229 0.671051i 0.474504 0.273955i
\(7\) 0 0
\(8\) 6.99143i 2.47184i
\(9\) 1.36560 + 2.36528i 0.455199 + 0.788428i
\(10\) −2.08648 + 3.61389i −0.659803 + 1.14281i
\(11\) −2.34256 1.35248i −0.706309 0.407788i 0.103384 0.994642i \(-0.467033\pi\)
−0.809693 + 0.586854i \(0.800366\pi\)
\(12\) 2.43723 0.703568
\(13\) −2.36840 2.71858i −0.656876 0.753998i
\(14\) 0 0
\(15\) 0.723819 + 0.417897i 0.186889 + 0.107901i
\(16\) −4.34816 + 7.53123i −1.08704 + 1.88281i
\(17\) −1.56330 2.70772i −0.379157 0.656719i 0.611783 0.791026i \(-0.290453\pi\)
−0.990940 + 0.134307i \(0.957119\pi\)
\(18\) 7.06997i 1.66641i
\(19\) 3.18828 1.84075i 0.731441 0.422297i −0.0875083 0.996164i \(-0.527890\pi\)
0.818949 + 0.573866i \(0.194557\pi\)
\(20\) −6.56276 + 3.78901i −1.46748 + 0.847249i
\(21\) 0 0
\(22\) −3.50103 6.06396i −0.746421 1.29284i
\(23\) 0.993019 1.71996i 0.207059 0.358636i −0.743728 0.668482i \(-0.766944\pi\)
0.950787 + 0.309846i \(0.100278\pi\)
\(24\) 3.13918 + 1.81241i 0.640783 + 0.369956i
\(25\) 2.40128 0.480257
\(26\) −1.79081 9.15992i −0.351206 1.79641i
\(27\) 2.97143 0.571852
\(28\) 0 0
\(29\) 2.68636 4.65290i 0.498844 0.864023i −0.501155 0.865357i \(-0.667092\pi\)
0.999999 + 0.00133469i \(0.000424845\pi\)
\(30\) 1.08177 + 1.87368i 0.197503 + 0.342086i
\(31\) 10.4780i 1.88191i 0.338529 + 0.940956i \(0.390071\pi\)
−0.338529 + 0.940956i \(0.609929\pi\)
\(32\) −7.38583 + 4.26421i −1.30564 + 0.753813i
\(33\) −1.21454 + 0.701214i −0.211424 + 0.122066i
\(34\) 8.09354i 1.38803i
\(35\) 0 0
\(36\) −6.41947 + 11.1188i −1.06991 + 1.85314i
\(37\) −5.15585 2.97673i −0.847616 0.489371i 0.0122297 0.999925i \(-0.496107\pi\)
−0.859846 + 0.510554i \(0.829440\pi\)
\(38\) 9.52994 1.54596
\(39\) −1.83462 + 0.358678i −0.293775 + 0.0574344i
\(40\) −11.2706 −1.78203
\(41\) 6.66970 + 3.85075i 1.04163 + 0.601386i 0.920295 0.391225i \(-0.127949\pi\)
0.121337 + 0.992611i \(0.461282\pi\)
\(42\) 0 0
\(43\) −1.67800 2.90638i −0.255892 0.443219i 0.709245 0.704962i \(-0.249036\pi\)
−0.965138 + 0.261743i \(0.915703\pi\)
\(44\) 12.7156i 1.91695i
\(45\) −3.81296 + 2.20141i −0.568403 + 0.328168i
\(46\) 4.45229 2.57053i 0.656454 0.379004i
\(47\) 1.05508i 0.153900i −0.997035 0.0769500i \(-0.975482\pi\)
0.997035 0.0769500i \(-0.0245182\pi\)
\(48\) 2.25437 + 3.90469i 0.325390 + 0.563593i
\(49\) 0 0
\(50\) 5.38318 + 3.10798i 0.761297 + 0.439535i
\(51\) −1.62104 −0.226991
\(52\) 5.50074 16.0317i 0.762816 2.22320i
\(53\) 7.26568 0.998017 0.499009 0.866597i \(-0.333698\pi\)
0.499009 + 0.866597i \(0.333698\pi\)
\(54\) 6.66133 + 3.84592i 0.906492 + 0.523363i
\(55\) 2.18027 3.77633i 0.293987 0.509201i
\(56\) 0 0
\(57\) 1.90873i 0.252818i
\(58\) 12.0445 6.95390i 1.58152 0.913092i
\(59\) −9.89352 + 5.71203i −1.28803 + 0.743643i −0.978302 0.207183i \(-0.933570\pi\)
−0.309725 + 0.950826i \(0.600237\pi\)
\(60\) 3.92895i 0.507225i
\(61\) −1.46254 2.53319i −0.187259 0.324341i 0.757077 0.653326i \(-0.226627\pi\)
−0.944335 + 0.328985i \(0.893294\pi\)
\(62\) −13.5617 + 23.4896i −1.72234 + 2.98318i
\(63\) 0 0
\(64\) −4.68406 −0.585507
\(65\) 4.38250 3.81799i 0.543582 0.473563i
\(66\) −3.63033 −0.446862
\(67\) −11.7622 6.79091i −1.43698 0.829642i −0.439343 0.898320i \(-0.644789\pi\)
−0.997639 + 0.0686778i \(0.978122\pi\)
\(68\) 7.34886 12.7286i 0.891180 1.54357i
\(69\) −0.514846 0.891740i −0.0619802 0.107353i
\(70\) 0 0
\(71\) 1.17009 0.675554i 0.138865 0.0801736i −0.428958 0.903324i \(-0.641119\pi\)
0.567823 + 0.823151i \(0.307786\pi\)
\(72\) −16.5367 + 9.54747i −1.94887 + 1.12518i
\(73\) 9.10335i 1.06547i −0.846283 0.532733i \(-0.821165\pi\)
0.846283 0.532733i \(-0.178835\pi\)
\(74\) −7.70557 13.3464i −0.895754 1.55149i
\(75\) 0.622492 1.07819i 0.0718791 0.124498i
\(76\) 14.9876 + 8.65311i 1.71920 + 0.992579i
\(77\) 0 0
\(78\) −4.57708 1.57047i −0.518252 0.177821i
\(79\) −6.20578 −0.698205 −0.349102 0.937085i \(-0.613513\pi\)
−0.349102 + 0.937085i \(0.613513\pi\)
\(80\) −12.1407 7.00946i −1.35738 0.783682i
\(81\) −3.32650 + 5.76166i −0.369611 + 0.640185i
\(82\) 9.96806 + 17.2652i 1.10079 + 1.90662i
\(83\) 2.69672i 0.296003i −0.988987 0.148002i \(-0.952716\pi\)
0.988987 0.148002i \(-0.0472841\pi\)
\(84\) 0 0
\(85\) 4.36499 2.52013i 0.473450 0.273346i
\(86\) 8.68734i 0.936780i
\(87\) −1.39278 2.41237i −0.149322 0.258633i
\(88\) 9.45576 16.3779i 1.00799 1.74589i
\(89\) 1.52410 + 0.879938i 0.161554 + 0.0932732i 0.578597 0.815613i \(-0.303600\pi\)
−0.417043 + 0.908887i \(0.636934\pi\)
\(90\) −11.3972 −1.20137
\(91\) 0 0
\(92\) 9.33607 0.973353
\(93\) 4.70469 + 2.71625i 0.487853 + 0.281662i
\(94\) 1.36560 2.36528i 0.140851 0.243960i
\(95\) 2.96739 + 5.13967i 0.304448 + 0.527319i
\(96\) 4.42170i 0.451288i
\(97\) 13.4078 7.74102i 1.36136 0.785981i 0.371555 0.928411i \(-0.378825\pi\)
0.989805 + 0.142430i \(0.0454915\pi\)
\(98\) 0 0
\(99\) 7.38776i 0.742498i
\(100\) 5.64404 + 9.77576i 0.564404 + 0.977576i
\(101\) 0.639651 1.10791i 0.0636477 0.110241i −0.832446 0.554107i \(-0.813060\pi\)
0.896093 + 0.443866i \(0.146393\pi\)
\(102\) −3.63404 2.09811i −0.359823 0.207744i
\(103\) −11.4673 −1.12991 −0.564956 0.825121i \(-0.691107\pi\)
−0.564956 + 0.825121i \(0.691107\pi\)
\(104\) 19.0068 16.5585i 1.86377 1.62370i
\(105\) 0 0
\(106\) 16.2881 + 9.40397i 1.58204 + 0.913394i
\(107\) 2.56763 4.44726i 0.248222 0.429933i −0.714811 0.699318i \(-0.753487\pi\)
0.963033 + 0.269385i \(0.0868205\pi\)
\(108\) 6.98412 + 12.0969i 0.672048 + 1.16402i
\(109\) 1.72783i 0.165496i −0.996570 0.0827481i \(-0.973630\pi\)
0.996570 0.0827481i \(-0.0263697\pi\)
\(110\) 9.77542 5.64384i 0.932050 0.538119i
\(111\) −2.67313 + 1.54333i −0.253722 + 0.146487i
\(112\) 0 0
\(113\) 4.29556 + 7.44014i 0.404093 + 0.699909i 0.994215 0.107404i \(-0.0342540\pi\)
−0.590123 + 0.807314i \(0.700921\pi\)
\(114\) 2.47048 4.27899i 0.231381 0.400764i
\(115\) 2.77267 + 1.60080i 0.258552 + 0.149275i
\(116\) 25.2563 2.34499
\(117\) 3.19593 9.31442i 0.295464 0.861119i
\(118\) −29.5723 −2.72235
\(119\) 0 0
\(120\) −2.92170 + 5.06053i −0.266714 + 0.461961i
\(121\) −1.84160 3.18975i −0.167419 0.289977i
\(122\) 7.57184i 0.685522i
\(123\) 3.45801 1.99648i 0.311798 0.180017i
\(124\) −42.6567 + 24.6279i −3.83069 + 2.21165i
\(125\) 11.9313i 1.06716i
\(126\) 0 0
\(127\) −1.56206 + 2.70556i −0.138610 + 0.240080i −0.926971 0.375133i \(-0.877597\pi\)
0.788361 + 0.615214i \(0.210930\pi\)
\(128\) 4.27097 + 2.46585i 0.377504 + 0.217952i
\(129\) −1.73997 −0.153196
\(130\) 14.7663 2.88688i 1.29509 0.253196i
\(131\) −10.2092 −0.891982 −0.445991 0.895038i \(-0.647149\pi\)
−0.445991 + 0.895038i \(0.647149\pi\)
\(132\) −5.70937 3.29630i −0.496936 0.286906i
\(133\) 0 0
\(134\) −17.5790 30.4476i −1.51859 2.63028i
\(135\) 4.79010i 0.412266i
\(136\) 18.9308 10.9297i 1.62331 0.937216i
\(137\) −8.65385 + 4.99630i −0.739348 + 0.426863i −0.821832 0.569729i \(-0.807048\pi\)
0.0824839 + 0.996592i \(0.473715\pi\)
\(138\) 2.66546i 0.226899i
\(139\) −0.832100 1.44124i −0.0705778 0.122244i 0.828577 0.559875i \(-0.189151\pi\)
−0.899155 + 0.437631i \(0.855818\pi\)
\(140\) 0 0
\(141\) −0.473738 0.273513i −0.0398959 0.0230339i
\(142\) 3.49748 0.293502
\(143\) 1.87130 + 9.57165i 0.156486 + 0.800422i
\(144\) −23.7513 −1.97928
\(145\) 7.50073 + 4.33055i 0.622902 + 0.359633i
\(146\) 11.7825 20.4078i 0.975124 1.68897i
\(147\) 0 0
\(148\) 27.9863i 2.30046i
\(149\) −17.1456 + 9.89902i −1.40462 + 0.810959i −0.994863 0.101234i \(-0.967721\pi\)
−0.409760 + 0.912193i \(0.634387\pi\)
\(150\) 2.79100 1.61138i 0.227884 0.131569i
\(151\) 7.53493i 0.613184i 0.951841 + 0.306592i \(0.0991886\pi\)
−0.951841 + 0.306592i \(0.900811\pi\)
\(152\) 12.8695 + 22.2906i 1.04385 + 1.80801i
\(153\) 4.26968 7.39531i 0.345183 0.597875i
\(154\) 0 0
\(155\) −16.8912 −1.35673
\(156\) −5.77234 6.62581i −0.462157 0.530489i
\(157\) −14.0045 −1.11768 −0.558839 0.829276i \(-0.688753\pi\)
−0.558839 + 0.829276i \(0.688753\pi\)
\(158\) −13.9121 8.03214i −1.10679 0.639003i
\(159\) 1.88350 3.26232i 0.149371 0.258719i
\(160\) −6.87414 11.9064i −0.543448 0.941280i
\(161\) 0 0
\(162\) −14.9146 + 8.61097i −1.17181 + 0.676542i
\(163\) −6.20936 + 3.58498i −0.486355 + 0.280797i −0.723061 0.690784i \(-0.757265\pi\)
0.236706 + 0.971581i \(0.423932\pi\)
\(164\) 36.2036i 2.82703i
\(165\) −1.13039 1.95790i −0.0880011 0.152422i
\(166\) 3.49036 6.04548i 0.270904 0.469220i
\(167\) −15.5716 8.99027i −1.20497 0.695688i −0.243312 0.969948i \(-0.578234\pi\)
−0.961656 + 0.274260i \(0.911567\pi\)
\(168\) 0 0
\(169\) −1.78135 + 12.8774i −0.137027 + 0.990567i
\(170\) 13.0472 1.00068
\(171\) 8.70780 + 5.02745i 0.665902 + 0.384459i
\(172\) 7.88803 13.6625i 0.601456 1.04175i
\(173\) 6.40579 + 11.0952i 0.487023 + 0.843549i 0.999889 0.0149198i \(-0.00474930\pi\)
−0.512865 + 0.858469i \(0.671416\pi\)
\(174\) 7.21072i 0.546643i
\(175\) 0 0
\(176\) 20.3717 11.7616i 1.53557 0.886562i
\(177\) 5.92298i 0.445199i
\(178\) 2.27781 + 3.94528i 0.170729 + 0.295711i
\(179\) 0.920110 1.59368i 0.0687723 0.119117i −0.829589 0.558375i \(-0.811425\pi\)
0.898361 + 0.439258i \(0.144758\pi\)
\(180\) −17.9242 10.3485i −1.33599 0.771334i
\(181\) 3.29928 0.245234 0.122617 0.992454i \(-0.460871\pi\)
0.122617 + 0.992454i \(0.460871\pi\)
\(182\) 0 0
\(183\) −1.51655 −0.112107
\(184\) 12.0250 + 6.94262i 0.886493 + 0.511817i
\(185\) 4.79865 8.31150i 0.352804 0.611074i
\(186\) 7.03129 + 12.1786i 0.515560 + 0.892975i
\(187\) 8.45734i 0.618462i
\(188\) 4.29531 2.47990i 0.313268 0.180865i
\(189\) 0 0
\(190\) 15.3628i 1.11453i
\(191\) −2.44807 4.24018i −0.177136 0.306809i 0.763762 0.645498i \(-0.223350\pi\)
−0.940898 + 0.338689i \(0.890017\pi\)
\(192\) −1.21426 + 2.10316i −0.0876318 + 0.151783i
\(193\) −2.61462 1.50955i −0.188204 0.108660i 0.402937 0.915228i \(-0.367989\pi\)
−0.591142 + 0.806568i \(0.701323\pi\)
\(194\) 40.0768 2.87735
\(195\) −0.578207 2.95751i −0.0414063 0.211792i
\(196\) 0 0
\(197\) 4.02694 + 2.32496i 0.286908 + 0.165646i 0.636546 0.771238i \(-0.280362\pi\)
−0.349639 + 0.936885i \(0.613696\pi\)
\(198\) 9.56198 16.5618i 0.679540 1.17700i
\(199\) −0.205360 0.355694i −0.0145576 0.0252145i 0.858655 0.512554i \(-0.171301\pi\)
−0.873212 + 0.487340i \(0.837967\pi\)
\(200\) 16.7884i 1.18712i
\(201\) −6.09830 + 3.52085i −0.430141 + 0.248342i
\(202\) 2.86793 1.65580i 0.201787 0.116502i
\(203\) 0 0
\(204\) −3.81013 6.59934i −0.266763 0.462047i
\(205\) −6.20762 + 10.7519i −0.433559 + 0.750946i
\(206\) −25.7074 14.8422i −1.79112 1.03410i
\(207\) 5.42425 0.377012
\(208\) 30.7724 6.01616i 2.13368 0.417146i
\(209\) −9.95831 −0.688831
\(210\) 0 0
\(211\) 3.75800 6.50905i 0.258711 0.448101i −0.707186 0.707028i \(-0.750035\pi\)
0.965897 + 0.258927i \(0.0833688\pi\)
\(212\) 17.0774 + 29.5790i 1.17288 + 2.03149i
\(213\) 0.700504i 0.0479977i
\(214\) 11.5122 6.64656i 0.786956 0.454349i
\(215\) 4.68524 2.70502i 0.319531 0.184481i
\(216\) 20.7745i 1.41353i
\(217\) 0 0
\(218\) 2.23633 3.87344i 0.151464 0.262343i
\(219\) −4.08745 2.35989i −0.276204 0.159467i
\(220\) 20.4982 1.38199
\(221\) −3.65863 + 10.6629i −0.246106 + 0.717267i
\(222\) −7.99014 −0.536263
\(223\) 19.5544 + 11.2897i 1.30946 + 0.756016i 0.982006 0.188852i \(-0.0604766\pi\)
0.327452 + 0.944868i \(0.393810\pi\)
\(224\) 0 0
\(225\) 3.27918 + 5.67971i 0.218612 + 0.378648i
\(226\) 22.2390i 1.47932i
\(227\) 11.8401 6.83586i 0.785853 0.453712i −0.0526478 0.998613i \(-0.516766\pi\)
0.838500 + 0.544901i \(0.183433\pi\)
\(228\) 7.77057 4.48634i 0.514618 0.297115i
\(229\) 7.93086i 0.524086i −0.965056 0.262043i \(-0.915604\pi\)
0.965056 0.262043i \(-0.0843962\pi\)
\(230\) 4.14383 + 7.17733i 0.273236 + 0.473259i
\(231\) 0 0
\(232\) 32.5305 + 18.7815i 2.13573 + 1.23306i
\(233\) 6.57171 0.430527 0.215263 0.976556i \(-0.430939\pi\)
0.215263 + 0.976556i \(0.430939\pi\)
\(234\) 19.2203 16.7445i 1.25647 1.09462i
\(235\) 1.70085 0.110951
\(236\) −46.5080 26.8514i −3.02741 1.74788i
\(237\) −1.60874 + 2.78642i −0.104499 + 0.180998i
\(238\) 0 0
\(239\) 9.39284i 0.607572i 0.952740 + 0.303786i \(0.0982508\pi\)
−0.952740 + 0.303786i \(0.901749\pi\)
\(240\) −6.29456 + 3.63417i −0.406312 + 0.234584i
\(241\) 8.73460 5.04292i 0.562645 0.324843i −0.191562 0.981481i \(-0.561355\pi\)
0.754206 + 0.656637i \(0.228022\pi\)
\(242\) 9.53435i 0.612891i
\(243\) 6.18182 + 10.7072i 0.396564 + 0.686869i
\(244\) 6.87517 11.9081i 0.440137 0.762340i
\(245\) 0 0
\(246\) 10.3362 0.659012
\(247\) −12.5553 4.30794i −0.798878 0.274108i
\(248\) −73.2565 −4.65179
\(249\) −1.21084 0.699078i −0.0767337 0.0443022i
\(250\) −15.4426 + 26.7474i −0.976678 + 1.69166i
\(251\) 5.17427 + 8.96209i 0.326597 + 0.565682i 0.981834 0.189741i \(-0.0607648\pi\)
−0.655237 + 0.755423i \(0.727431\pi\)
\(252\) 0 0
\(253\) −4.65242 + 2.68607i −0.292495 + 0.168872i
\(254\) −7.00363 + 4.04355i −0.439447 + 0.253715i
\(255\) 2.61320i 0.163645i
\(256\) 11.0672 + 19.1689i 0.691697 + 1.19805i
\(257\) −3.99329 + 6.91658i −0.249095 + 0.431445i −0.963275 0.268517i \(-0.913466\pi\)
0.714180 + 0.699962i \(0.246800\pi\)
\(258\) −3.90065 2.25204i −0.242844 0.140206i
\(259\) 0 0
\(260\) 25.8440 + 8.86749i 1.60278 + 0.549939i
\(261\) 14.6739 0.908292
\(262\) −22.8869 13.2138i −1.41396 0.816349i
\(263\) −2.52967 + 4.38152i −0.155986 + 0.270176i −0.933418 0.358792i \(-0.883189\pi\)
0.777431 + 0.628968i \(0.216522\pi\)
\(264\) −4.90249 8.49136i −0.301727 0.522607i
\(265\) 11.7127i 0.719503i
\(266\) 0 0
\(267\) 0.790192 0.456218i 0.0483590 0.0279201i
\(268\) 63.8461i 3.90002i
\(269\) 6.94512 + 12.0293i 0.423451 + 0.733439i 0.996274 0.0862400i \(-0.0274852\pi\)
−0.572823 + 0.819679i \(0.694152\pi\)
\(270\) −6.19983 + 10.7384i −0.377310 + 0.653519i
\(271\) −7.21158 4.16361i −0.438072 0.252921i 0.264707 0.964329i \(-0.414725\pi\)
−0.702780 + 0.711408i \(0.748058\pi\)
\(272\) 27.1900 1.64863
\(273\) 0 0
\(274\) −25.8669 −1.56267
\(275\) −5.62515 3.24768i −0.339210 0.195843i
\(276\) 2.42022 4.19194i 0.145680 0.252325i
\(277\) −11.6058 20.1018i −0.697325 1.20780i −0.969391 0.245523i \(-0.921040\pi\)
0.272066 0.962279i \(-0.412293\pi\)
\(278\) 4.30795i 0.258374i
\(279\) −24.7835 + 14.3088i −1.48375 + 0.856644i
\(280\) 0 0
\(281\) 27.1595i 1.62020i 0.586292 + 0.810100i \(0.300587\pi\)
−0.586292 + 0.810100i \(0.699413\pi\)
\(282\) −0.708015 1.22632i −0.0421617 0.0730262i
\(283\) 8.07563 13.9874i 0.480046 0.831464i −0.519692 0.854354i \(-0.673953\pi\)
0.999738 + 0.0228894i \(0.00728654\pi\)
\(284\) 5.50044 + 3.17568i 0.326391 + 0.188442i
\(285\) 3.07698 0.182265
\(286\) −8.19351 + 23.8797i −0.484493 + 1.41204i
\(287\) 0 0
\(288\) −20.1721 11.6464i −1.18865 0.686270i
\(289\) 3.61216 6.25645i 0.212480 0.368027i
\(290\) 11.2101 + 19.4164i 0.658278 + 1.14017i
\(291\) 8.02691i 0.470546i
\(292\) 37.0603 21.3968i 2.16879 1.25215i
\(293\) 12.6831 7.32260i 0.740956 0.427791i −0.0814609 0.996677i \(-0.525959\pi\)
0.822417 + 0.568885i \(0.192625\pi\)
\(294\) 0 0
\(295\) −9.20810 15.9489i −0.536116 0.928580i
\(296\) 20.8116 36.0468i 1.20965 2.09517i
\(297\) −6.96075 4.01879i −0.403904 0.233194i
\(298\) −51.2492 −2.96879
\(299\) −7.02771 + 1.37395i −0.406423 + 0.0794577i
\(300\) 5.85248 0.337893
\(301\) 0 0
\(302\) −9.75246 + 16.8918i −0.561191 + 0.972011i
\(303\) −0.331637 0.574412i −0.0190521 0.0329991i
\(304\) 32.0155i 1.83622i
\(305\) 4.08363 2.35769i 0.233828 0.135001i
\(306\) 19.1435 11.0525i 1.09436 0.631830i
\(307\) 8.97844i 0.512427i 0.966620 + 0.256213i \(0.0824750\pi\)
−0.966620 + 0.256213i \(0.917525\pi\)
\(308\) 0 0
\(309\) −2.97271 + 5.14889i −0.169112 + 0.292910i
\(310\) −37.8665 21.8622i −2.15067 1.24169i
\(311\) 12.1816 0.690755 0.345378 0.938464i \(-0.387751\pi\)
0.345378 + 0.938464i \(0.387751\pi\)
\(312\) −2.50767 12.8266i −0.141969 0.726165i
\(313\) −13.1240 −0.741810 −0.370905 0.928671i \(-0.620953\pi\)
−0.370905 + 0.928671i \(0.620953\pi\)
\(314\) −31.3951 18.1260i −1.77173 1.02291i
\(315\) 0 0
\(316\) −14.5862 25.2641i −0.820540 1.42122i
\(317\) 16.7155i 0.938836i 0.882976 + 0.469418i \(0.155536\pi\)
−0.882976 + 0.469418i \(0.844464\pi\)
\(318\) 8.44485 4.87563i 0.473564 0.273412i
\(319\) −12.5859 + 7.26648i −0.704675 + 0.406845i
\(320\) 7.55095i 0.422111i
\(321\) −1.33123 2.30575i −0.0743018 0.128695i
\(322\) 0 0
\(323\) −9.96849 5.75531i −0.554661 0.320234i
\(324\) −31.2748 −1.73749
\(325\) −5.68720 6.52808i −0.315469 0.362113i
\(326\) −18.5601 −1.02795
\(327\) −0.775804 0.447911i −0.0429021 0.0247695i
\(328\) −26.9223 + 46.6307i −1.48653 + 2.57475i
\(329\) 0 0
\(330\) 5.85228i 0.322157i
\(331\) 3.43522 1.98332i 0.188817 0.109013i −0.402612 0.915371i \(-0.631898\pi\)
0.591428 + 0.806357i \(0.298564\pi\)
\(332\) 10.9785 6.33843i 0.602523 0.347867i
\(333\) 16.2600i 0.891045i
\(334\) −23.2722 40.3087i −1.27340 2.20559i
\(335\) 10.9473 18.9613i 0.598116 1.03597i
\(336\) 0 0
\(337\) −13.7032 −0.746461 −0.373230 0.927739i \(-0.621750\pi\)
−0.373230 + 0.927739i \(0.621750\pi\)
\(338\) −20.6606 + 26.5628i −1.12379 + 1.44483i
\(339\) 4.45421 0.241919
\(340\) 20.5192 + 11.8468i 1.11281 + 0.642481i
\(341\) 14.1713 24.5455i 0.767420 1.32921i
\(342\) 13.0141 + 22.5410i 0.703720 + 1.21888i
\(343\) 0 0
\(344\) 20.3197 11.7316i 1.09557 0.632526i
\(345\) 1.43753 0.829960i 0.0773942 0.0446835i
\(346\) 33.1641i 1.78291i
\(347\) 13.1989 + 22.8612i 0.708556 + 1.22725i 0.965393 + 0.260800i \(0.0839863\pi\)
−0.256837 + 0.966455i \(0.582680\pi\)
\(348\) 6.54727 11.3402i 0.350971 0.607899i
\(349\) 4.23507 + 2.44512i 0.226698 + 0.130884i 0.609048 0.793133i \(-0.291552\pi\)
−0.382350 + 0.924018i \(0.624885\pi\)
\(350\) 0 0
\(351\) −7.03753 8.07806i −0.375636 0.431175i
\(352\) 23.0690 1.22958
\(353\) −11.7413 6.77886i −0.624928 0.360802i 0.153857 0.988093i \(-0.450830\pi\)
−0.778785 + 0.627291i \(0.784164\pi\)
\(354\) −7.66612 + 13.2781i −0.407450 + 0.705724i
\(355\) 1.08903 + 1.88626i 0.0577997 + 0.100112i
\(356\) 8.27291i 0.438464i
\(357\) 0 0
\(358\) 4.12540 2.38180i 0.218034 0.125882i
\(359\) 8.58568i 0.453135i 0.973996 + 0.226567i \(0.0727503\pi\)
−0.973996 + 0.226567i \(0.927250\pi\)
\(360\) −15.3910 26.6581i −0.811179 1.40500i
\(361\) −2.72326 + 4.71683i −0.143330 + 0.248254i
\(362\) 7.39632 + 4.27026i 0.388742 + 0.224440i
\(363\) −1.90962 −0.100229
\(364\) 0 0
\(365\) 14.6751 0.768130
\(366\) −3.39979 1.96287i −0.177710 0.102601i
\(367\) −0.831612 + 1.44039i −0.0434098 + 0.0751880i −0.886914 0.461935i \(-0.847155\pi\)
0.843504 + 0.537123i \(0.180489\pi\)
\(368\) 8.63560 + 14.9573i 0.450162 + 0.779703i
\(369\) 21.0343i 1.09500i
\(370\) 21.5152 12.4218i 1.11852 0.645778i
\(371\) 0 0
\(372\) 25.5374i 1.32405i
\(373\) −6.98174 12.0927i −0.361501 0.626138i 0.626707 0.779255i \(-0.284402\pi\)
−0.988208 + 0.153117i \(0.951069\pi\)
\(374\) −10.9463 + 18.9596i −0.566022 + 0.980378i
\(375\) 5.35719 + 3.09298i 0.276644 + 0.159721i
\(376\) 7.37655 0.380417
\(377\) −19.0117 + 3.71687i −0.979150 + 0.191429i
\(378\) 0 0
\(379\) −27.3454 15.7879i −1.40464 0.810969i −0.409775 0.912187i \(-0.634393\pi\)
−0.994864 + 0.101218i \(0.967726\pi\)
\(380\) −13.9493 + 24.1608i −0.715582 + 1.23943i
\(381\) 0.809874 + 1.40274i 0.0414911 + 0.0718647i
\(382\) 12.6741i 0.648466i
\(383\) −27.6333 + 15.9541i −1.41200 + 0.815217i −0.995576 0.0939554i \(-0.970049\pi\)
−0.416420 + 0.909172i \(0.636716\pi\)
\(384\) 2.21435 1.27846i 0.113001 0.0652410i
\(385\) 0 0
\(386\) −3.90762 6.76820i −0.198893 0.344492i
\(387\) 4.58294 7.93788i 0.232964 0.403505i
\(388\) 63.0283 + 36.3894i 3.19978 + 1.84739i
\(389\) 25.4150 1.28859 0.644296 0.764776i \(-0.277150\pi\)
0.644296 + 0.764776i \(0.277150\pi\)
\(390\) 2.53168 7.37850i 0.128197 0.373625i
\(391\) −6.20956 −0.314031
\(392\) 0 0
\(393\) −2.64656 + 4.58398i −0.133501 + 0.231231i
\(394\) 6.01838 + 10.4241i 0.303202 + 0.525161i
\(395\) 10.0041i 0.503358i
\(396\) 30.0760 17.3644i 1.51138 0.872593i
\(397\) −3.60178 + 2.07949i −0.180768 + 0.104366i −0.587653 0.809113i \(-0.699948\pi\)
0.406885 + 0.913479i \(0.366615\pi\)
\(398\) 1.06319i 0.0532930i
\(399\) 0 0
\(400\) −10.4412 + 18.0846i −0.522058 + 0.904231i
\(401\) 16.9753 + 9.80067i 0.847704 + 0.489422i 0.859875 0.510504i \(-0.170541\pi\)
−0.0121716 + 0.999926i \(0.503874\pi\)
\(402\) −18.2282 −0.909139
\(403\) 28.4854 24.8162i 1.41896 1.23618i
\(404\) 6.01381 0.299198
\(405\) −9.28811 5.36249i −0.461530 0.266464i
\(406\) 0 0
\(407\) 8.05193 + 13.9463i 0.399119 + 0.691295i
\(408\) 11.3334i 0.561086i
\(409\) −15.2712 + 8.81685i −0.755114 + 0.435965i −0.827539 0.561409i \(-0.810260\pi\)
0.0724249 + 0.997374i \(0.476926\pi\)
\(410\) −27.8324 + 16.0690i −1.37454 + 0.793594i
\(411\) 5.18083i 0.255551i
\(412\) −26.9532 46.6842i −1.32789 2.29997i
\(413\) 0 0
\(414\) 12.1601 + 7.02061i 0.597634 + 0.345044i
\(415\) 4.34725 0.213398
\(416\) 29.0852 + 9.97961i 1.42602 + 0.489291i
\(417\) −0.862831 −0.0422530
\(418\) −22.3245 12.8890i −1.09193 0.630424i
\(419\) 14.9455 25.8864i 0.730137 1.26463i −0.226688 0.973968i \(-0.572790\pi\)
0.956824 0.290666i \(-0.0938770\pi\)
\(420\) 0 0
\(421\) 12.8528i 0.626407i 0.949686 + 0.313203i \(0.101402\pi\)
−0.949686 + 0.313203i \(0.898598\pi\)
\(422\) 16.8493 9.72796i 0.820212 0.473550i
\(423\) 2.49557 1.44082i 0.121339 0.0700551i
\(424\) 50.7975i 2.46694i
\(425\) −3.75393 6.50200i −0.182093 0.315394i
\(426\) 0.906662 1.57038i 0.0439279 0.0760854i
\(427\) 0 0
\(428\) 24.1401 1.16685
\(429\) 4.78282 + 1.64106i 0.230917 + 0.0792313i
\(430\) 14.0045 0.675355
\(431\) −7.76876 4.48530i −0.374208 0.216049i 0.301087 0.953597i \(-0.402650\pi\)
−0.675295 + 0.737547i \(0.735984\pi\)
\(432\) −12.9202 + 22.3785i −0.621625 + 1.07669i
\(433\) 1.72531 + 2.98833i 0.0829132 + 0.143610i 0.904500 0.426473i \(-0.140244\pi\)
−0.821587 + 0.570083i \(0.806911\pi\)
\(434\) 0 0
\(435\) 3.88887 2.24524i 0.186457 0.107651i
\(436\) 7.03410 4.06114i 0.336872 0.194493i
\(437\) 7.31161i 0.349762i
\(438\) −6.10881 10.5808i −0.291890 0.505569i
\(439\) 19.2572 33.3544i 0.919096 1.59192i 0.118304 0.992977i \(-0.462254\pi\)
0.800792 0.598943i \(-0.204412\pi\)
\(440\) 26.4020 + 15.2432i 1.25867 + 0.726691i
\(441\) 0 0
\(442\) −22.0029 + 19.1687i −1.04657 + 0.911764i
\(443\) −15.0399 −0.714569 −0.357284 0.933996i \(-0.616297\pi\)
−0.357284 + 0.933996i \(0.616297\pi\)
\(444\) −12.5660 7.25498i −0.596356 0.344306i
\(445\) −1.41851 + 2.45693i −0.0672437 + 0.116469i
\(446\) 29.2246 + 50.6185i 1.38382 + 2.39685i
\(447\) 10.2646i 0.485499i
\(448\) 0 0
\(449\) 33.7087 19.4617i 1.59081 0.918456i 0.597646 0.801760i \(-0.296103\pi\)
0.993168 0.116696i \(-0.0372304\pi\)
\(450\) 16.9770i 0.800303i
\(451\) −10.4161 18.0412i −0.490476 0.849529i
\(452\) −20.1928 + 34.9750i −0.949790 + 1.64509i
\(453\) 3.38322 + 1.95330i 0.158957 + 0.0917741i
\(454\) 35.3906 1.66097
\(455\) 0 0
\(456\) 13.3448 0.624927
\(457\) 12.0721 + 6.96982i 0.564708 + 0.326034i 0.755033 0.655687i \(-0.227621\pi\)
−0.190325 + 0.981721i \(0.560954\pi\)
\(458\) 10.2649 17.7793i 0.479648 0.830774i
\(459\) −4.64524 8.04580i −0.216821 0.375546i
\(460\) 15.0502i 0.701721i
\(461\) −32.4443 + 18.7317i −1.51108 + 0.872424i −0.511167 + 0.859481i \(0.670787\pi\)
−0.999916 + 0.0129430i \(0.995880\pi\)
\(462\) 0 0
\(463\) 6.75275i 0.313827i −0.987612 0.156913i \(-0.949846\pi\)
0.987612 0.156913i \(-0.0501544\pi\)
\(464\) 23.3614 + 40.4631i 1.08453 + 1.87845i
\(465\) −4.37875 + 7.58421i −0.203059 + 0.351709i
\(466\) 14.7324 + 8.50576i 0.682466 + 0.394022i
\(467\) 5.05032 0.233701 0.116851 0.993150i \(-0.462720\pi\)
0.116851 + 0.993150i \(0.462720\pi\)
\(468\) 45.4314 8.88205i 2.10006 0.410573i
\(469\) 0 0
\(470\) 3.81296 + 2.20141i 0.175879 + 0.101544i
\(471\) −3.63042 + 6.28807i −0.167281 + 0.289739i
\(472\) −39.9353 69.1699i −1.83817 3.18380i
\(473\) 9.07783i 0.417399i
\(474\) −7.21294 + 4.16439i −0.331301 + 0.191277i
\(475\) 7.65595 4.42017i 0.351279 0.202811i
\(476\) 0 0
\(477\) 9.92198 + 17.1854i 0.454296 + 0.786864i
\(478\) −12.1572 + 21.0568i −0.556055 + 0.963116i
\(479\) 8.18670 + 4.72659i 0.374060 + 0.215964i 0.675231 0.737607i \(-0.264044\pi\)
−0.301171 + 0.953570i \(0.597377\pi\)
\(480\) −7.12801 −0.325348
\(481\) 4.11864 + 21.0667i 0.187794 + 0.960558i
\(482\) 26.1082 1.18920
\(483\) 0 0
\(484\) 8.65711 14.9946i 0.393505 0.681571i
\(485\) 12.4789 + 21.6142i 0.566639 + 0.981448i
\(486\) 32.0045i 1.45175i
\(487\) −34.6407 + 19.9998i −1.56972 + 0.906277i −0.573517 + 0.819194i \(0.694421\pi\)
−0.996201 + 0.0870831i \(0.972245\pi\)
\(488\) 17.7106 10.2252i 0.801721 0.462874i
\(489\) 3.71737i 0.168105i
\(490\) 0 0
\(491\) −3.38049 + 5.85517i −0.152559 + 0.264240i −0.932168 0.362027i \(-0.882085\pi\)
0.779608 + 0.626267i \(0.215418\pi\)
\(492\) 16.2556 + 9.38518i 0.732859 + 0.423116i
\(493\) −16.7984 −0.756560
\(494\) −22.5707 25.9079i −1.01551 1.16565i
\(495\) 11.9095 0.535291
\(496\) −78.9125 45.5602i −3.54328 2.04571i
\(497\) 0 0
\(498\) −1.80963 3.13438i −0.0810916 0.140455i
\(499\) 11.3575i 0.508433i −0.967147 0.254217i \(-0.918182\pi\)
0.967147 0.254217i \(-0.0818176\pi\)
\(500\) −48.5729 + 28.0436i −2.17225 + 1.25415i
\(501\) −8.07335 + 4.66115i −0.360691 + 0.208245i
\(502\) 26.7882i 1.19562i
\(503\) −6.96423 12.0624i −0.310520 0.537836i 0.667955 0.744202i \(-0.267170\pi\)
−0.978475 + 0.206365i \(0.933836\pi\)
\(504\) 0 0
\(505\) 1.78601 + 1.03115i 0.0794763 + 0.0458857i
\(506\) −13.9063 −0.618212
\(507\) 5.32022 + 4.13807i 0.236279 + 0.183778i
\(508\) −14.6860 −0.651587
\(509\) 17.1602 + 9.90746i 0.760614 + 0.439141i 0.829516 0.558483i \(-0.188616\pi\)
−0.0689022 + 0.997623i \(0.521950\pi\)
\(510\) 3.38227 5.85826i 0.149769 0.259408i
\(511\) 0 0
\(512\) 47.4335i 2.09628i
\(513\) 9.47373 5.46966i 0.418276 0.241491i
\(514\) −17.9043 + 10.3370i −0.789724 + 0.455947i
\(515\) 18.4860i 0.814590i
\(516\) −4.08967 7.08352i −0.180038 0.311835i
\(517\) −1.42698 + 2.47160i −0.0627585 + 0.108701i
\(518\) 0 0
\(519\) 6.64237 0.291568
\(520\) 26.6932 + 30.6399i 1.17057 + 1.34365i
\(521\) 31.0951 1.36230 0.681151 0.732143i \(-0.261480\pi\)
0.681151 + 0.732143i \(0.261480\pi\)
\(522\) 32.8959 + 18.9924i 1.43981 + 0.831277i
\(523\) 11.3601 19.6763i 0.496742 0.860383i −0.503251 0.864140i \(-0.667863\pi\)
0.999993 + 0.00375758i \(0.00119608\pi\)
\(524\) −23.9960 41.5622i −1.04827 1.81565i
\(525\) 0 0
\(526\) −11.3420 + 6.54831i −0.494535 + 0.285520i
\(527\) 28.3716 16.3804i 1.23589 0.713540i
\(528\) 12.1960i 0.530761i
\(529\) 9.52783 + 16.5027i 0.414253 + 0.717508i
\(530\) −15.1597 + 26.2574i −0.658495 + 1.14055i
\(531\) −27.0211 15.6007i −1.17262 0.677011i
\(532\) 0 0
\(533\) −5.32794 27.2522i −0.230779 1.18043i
\(534\) 2.36193 0.102211
\(535\) 7.16922 + 4.13915i 0.309952 + 0.178951i
\(536\) 47.4782 82.2346i 2.05074 3.55199i
\(537\) −0.477046 0.826267i −0.0205860 0.0356561i
\(538\) 35.9563i 1.55018i
\(539\) 0 0
\(540\) −19.5008 + 11.2588i −0.839180 + 0.484501i
\(541\) 2.09872i 0.0902310i 0.998982 + 0.0451155i \(0.0143656\pi\)
−0.998982 + 0.0451155i \(0.985634\pi\)
\(542\) −10.7779 18.6679i −0.462951 0.801855i
\(543\) 0.855283 1.48139i 0.0367037 0.0635727i
\(544\) 23.0926 + 13.3325i 0.990087 + 0.571627i
\(545\) 2.78536 0.119312
\(546\) 0 0
\(547\) 25.3770 1.08504 0.542521 0.840042i \(-0.317470\pi\)
0.542521 + 0.840042i \(0.317470\pi\)
\(548\) −40.6805 23.4869i −1.73778 1.00331i
\(549\) 3.99447 6.91862i 0.170480 0.295280i
\(550\) −8.40696 14.5613i −0.358474 0.620895i
\(551\) 19.7797i 0.842642i
\(552\) 6.23454 3.59951i 0.265360 0.153205i
\(553\) 0 0
\(554\) 60.0855i 2.55279i
\(555\) −2.48794 4.30923i −0.105607 0.182917i
\(556\) 3.91158 6.77506i 0.165888 0.287327i
\(557\) 38.3219 + 22.1252i 1.62375 + 0.937473i 0.985904 + 0.167309i \(0.0535078\pi\)
0.637846 + 0.770164i \(0.279826\pi\)
\(558\) −74.0794 −3.13603
\(559\) −3.92705 + 11.4452i −0.166097 + 0.484082i
\(560\) 0 0
\(561\) 3.79738 + 2.19242i 0.160326 + 0.0925641i
\(562\) −35.1526 + 60.8860i −1.48282 + 2.56832i
\(563\) 19.4453 + 33.6803i 0.819523 + 1.41946i 0.906034 + 0.423205i \(0.139095\pi\)
−0.0865108 + 0.996251i \(0.527572\pi\)
\(564\) 2.57149i 0.108279i
\(565\) −11.9939 + 6.92468i −0.504587 + 0.291324i
\(566\) 36.2078 20.9046i 1.52193 0.878685i
\(567\) 0 0
\(568\) 4.72309 + 8.18063i 0.198177 + 0.343252i
\(569\) 23.0789 39.9739i 0.967520 1.67579i 0.264832 0.964294i \(-0.414683\pi\)
0.702687 0.711499i \(-0.251983\pi\)
\(570\) 6.89796 + 3.98254i 0.288924 + 0.166810i
\(571\) −21.1368 −0.884548 −0.442274 0.896880i \(-0.645828\pi\)
−0.442274 + 0.896880i \(0.645828\pi\)
\(572\) −34.5684 + 30.1157i −1.44538 + 1.25920i
\(573\) −2.53848 −0.106047
\(574\) 0 0
\(575\) 2.38452 4.13011i 0.0994413 0.172237i
\(576\) −6.39653 11.0791i −0.266522 0.461630i
\(577\) 25.3304i 1.05452i 0.849705 + 0.527259i \(0.176780\pi\)
−0.849705 + 0.527259i \(0.823220\pi\)
\(578\) 16.1955 9.35045i 0.673642 0.388927i
\(579\) −1.35559 + 0.782650i −0.0563364 + 0.0325258i
\(580\) 40.7146i 1.69058i
\(581\) 0 0
\(582\) 10.3892 17.9947i 0.430647 0.745903i
\(583\) −17.0203 9.82667i −0.704908 0.406979i
\(584\) 63.6455 2.63367
\(585\) 15.0153 + 5.15201i 0.620808 + 0.213009i
\(586\) 37.9106 1.56607
\(587\) −3.08554 1.78144i −0.127354 0.0735278i 0.434970 0.900445i \(-0.356759\pi\)
−0.562324 + 0.826917i \(0.690092\pi\)
\(588\) 0 0
\(589\) 19.2875 + 33.4069i 0.794727 + 1.37651i
\(590\) 47.6722i 1.96263i
\(591\) 2.08783 1.20541i 0.0858819 0.0495839i
\(592\) 44.8369 25.8866i 1.84278 1.06393i
\(593\) 25.3536i 1.04115i −0.853817 0.520573i \(-0.825718\pi\)
0.853817 0.520573i \(-0.174282\pi\)
\(594\) −10.4030 18.0186i −0.426842 0.739312i
\(595\) 0 0
\(596\) −80.5990 46.5338i −3.30146 1.90610i
\(597\) −0.212945 −0.00871524
\(598\) −17.5330 6.01585i −0.716977 0.246007i
\(599\) 10.9216 0.446243 0.223122 0.974791i \(-0.428375\pi\)
0.223122 + 0.974791i \(0.428375\pi\)
\(600\) 7.53807 + 4.35211i 0.307740 + 0.177674i
\(601\) 12.1282 21.0067i 0.494720 0.856880i −0.505262 0.862966i \(-0.668604\pi\)
0.999981 + 0.00608649i \(0.00193740\pi\)
\(602\) 0 0
\(603\) 37.0946i 1.51061i
\(604\) −30.6751 + 17.7103i −1.24815 + 0.720621i
\(605\) 5.14205 2.96876i 0.209054 0.120697i
\(606\) 1.71695i 0.0697464i
\(607\) −4.92724 8.53422i −0.199990 0.346393i 0.748535 0.663096i \(-0.230758\pi\)
−0.948525 + 0.316702i \(0.897424\pi\)
\(608\) −15.6987 + 27.1910i −0.636667 + 1.10274i
\(609\) 0 0
\(610\) 12.2062 0.494215
\(611\) −2.86833 + 2.49886i −0.116040 + 0.101093i
\(612\) 40.1423 1.62266
\(613\) 3.18428 + 1.83844i 0.128612 + 0.0742540i 0.562926 0.826508i \(-0.309676\pi\)
−0.434314 + 0.900762i \(0.643009\pi\)
\(614\) −11.6208 + 20.1278i −0.468977 + 0.812293i
\(615\) 3.21844 + 5.57450i 0.129780 + 0.224785i
\(616\) 0 0
\(617\) 16.2352 9.37341i 0.653605 0.377359i −0.136231 0.990677i \(-0.543499\pi\)
0.789836 + 0.613318i \(0.210166\pi\)
\(618\) −13.3284 + 7.69517i −0.536148 + 0.309545i
\(619\) 15.8945i 0.638854i 0.947611 + 0.319427i \(0.103490\pi\)
−0.947611 + 0.319427i \(0.896510\pi\)
\(620\) −39.7014 68.7649i −1.59445 2.76167i
\(621\) 2.95068 5.11073i 0.118407 0.205087i
\(622\) 27.3086 + 15.7667i 1.09498 + 0.632185i
\(623\) 0 0
\(624\) 5.27594 15.3765i 0.211207 0.615555i
\(625\) −7.22743 −0.289097
\(626\) −29.4212 16.9864i −1.17591 0.678911i
\(627\) −2.58152 + 4.47133i −0.103096 + 0.178568i
\(628\) −32.9165 57.0130i −1.31351 2.27507i
\(629\) 18.6141i 0.742194i
\(630\) 0 0
\(631\) −17.0998 + 9.87255i −0.680731 + 0.393020i −0.800130 0.599826i \(-0.795236\pi\)
0.119400 + 0.992846i \(0.461903\pi\)
\(632\) 43.3873i 1.72585i
\(633\) −1.94839 3.37472i −0.0774417 0.134133i
\(634\) −21.6349 + 37.4727i −0.859231 + 1.48823i
\(635\) −4.36151 2.51812i −0.173081 0.0999286i
\(636\) 17.7081 0.702173
\(637\) 0 0
\(638\) −37.6200 −1.48939
\(639\) 3.19575 + 1.84507i 0.126422 + 0.0729898i
\(640\) −3.97508 + 6.88504i −0.157129 + 0.272155i
\(641\) −14.8893 25.7890i −0.588092 1.01860i −0.994482 0.104905i \(-0.966546\pi\)
0.406390 0.913699i \(-0.366787\pi\)
\(642\) 6.89203i 0.272007i
\(643\) −10.0220 + 5.78623i −0.395231 + 0.228187i −0.684424 0.729084i \(-0.739946\pi\)
0.289193 + 0.957271i \(0.406613\pi\)
\(644\) 0 0
\(645\) 2.80493i 0.110444i
\(646\) −14.8982 25.8044i −0.586162 1.01526i
\(647\) −12.7533 + 22.0893i −0.501382 + 0.868420i 0.498616 + 0.866823i \(0.333842\pi\)
−0.999999 + 0.00159698i \(0.999492\pi\)
\(648\) −40.2823 23.2570i −1.58244 0.913620i
\(649\) 30.9016 1.21299
\(650\) −4.30024 21.9956i −0.168669 0.862737i
\(651\) 0 0
\(652\) −29.1893 16.8524i −1.14314 0.659993i
\(653\) 22.4146 38.8233i 0.877152 1.51927i 0.0227004 0.999742i \(-0.492774\pi\)
0.854452 0.519530i \(-0.173893\pi\)
\(654\) −1.15946 2.00825i −0.0453386 0.0785287i
\(655\) 16.4578i 0.643058i
\(656\) −58.0018 + 33.4874i −2.26459 + 1.30746i
\(657\) 21.5320 12.4315i 0.840043 0.484999i
\(658\) 0 0
\(659\) −20.5867 35.6572i −0.801944 1.38901i −0.918335 0.395805i \(-0.870466\pi\)
0.116390 0.993204i \(-0.462868\pi\)
\(660\) 5.31382 9.20380i 0.206840 0.358258i
\(661\) −18.9606 10.9469i −0.737481 0.425785i 0.0836719 0.996493i \(-0.473335\pi\)
−0.821153 + 0.570709i \(0.806669\pi\)
\(662\) 10.2681 0.399080
\(663\) 3.83927 + 4.40692i 0.149105 + 0.171151i
\(664\) 18.8539 0.731673
\(665\) 0 0
\(666\) 21.0454 36.4517i 0.815492 1.41247i
\(667\) −5.33520 9.24084i −0.206580 0.357807i
\(668\) 84.5239i 3.27033i
\(669\) 10.1383 5.85334i 0.391968 0.226303i
\(670\) 49.0832 28.3382i 1.89625 1.09480i
\(671\) 7.91219i 0.305447i
\(672\) 0 0
\(673\) 17.8344 30.8901i 0.687466 1.19073i −0.285189 0.958471i \(-0.592056\pi\)
0.972655 0.232254i \(-0.0746102\pi\)
\(674\) −30.7197 17.7361i −1.18328 0.683167i
\(675\) 7.13524 0.274635
\(676\) −56.6115 + 23.0153i −2.17736 + 0.885205i
\(677\) −2.55532 −0.0982089 −0.0491044 0.998794i \(-0.515637\pi\)
−0.0491044 + 0.998794i \(0.515637\pi\)
\(678\) 9.98541 + 5.76508i 0.383488 + 0.221407i
\(679\) 0 0
\(680\) 17.6193 + 30.5175i 0.675670 + 1.17029i
\(681\) 7.08832i 0.271625i
\(682\) 63.5384 36.6839i 2.43301 1.40470i
\(683\) 30.9517 17.8700i 1.18433 0.683775i 0.227320 0.973820i \(-0.427004\pi\)
0.957013 + 0.290045i \(0.0936704\pi\)
\(684\) 47.2666i 1.80728i
\(685\) −8.05431 13.9505i −0.307739 0.533020i
\(686\) 0 0
\(687\) −3.56099 2.05594i −0.135860 0.0784390i
\(688\) 29.1848 1.11266
\(689\) −17.2080 19.7523i −0.655574 0.752503i
\(690\) 4.29687 0.163579
\(691\) 22.5419 + 13.0146i 0.857536 + 0.495099i 0.863186 0.504885i \(-0.168465\pi\)
−0.00565028 + 0.999984i \(0.501799\pi\)
\(692\) −30.1127 + 52.1567i −1.14471 + 1.98270i
\(693\) 0 0
\(694\) 68.3335i 2.59391i
\(695\) 2.32336 1.34139i 0.0881299 0.0508818i
\(696\) 16.8659 9.73755i 0.639301 0.369101i
\(697\) 24.0796i 0.912079i
\(698\) 6.32944 + 10.9629i 0.239573 + 0.414952i
\(699\) 1.70360 2.95073i 0.0644362 0.111607i
\(700\) 0 0
\(701\) −1.12731 −0.0425779 −0.0212890 0.999773i \(-0.506777\pi\)
−0.0212890 + 0.999773i \(0.506777\pi\)
\(702\) −5.32126 27.2180i −0.200838 1.02728i
\(703\) −21.9177 −0.826641
\(704\) 10.9727 + 6.33509i 0.413549 + 0.238763i
\(705\) 0.440917 0.763691i 0.0166059 0.0287623i
\(706\) −17.5478 30.3936i −0.660419 1.14388i
\(707\) 0 0
\(708\) −24.1128 + 13.9215i −0.906215 + 0.523203i
\(709\) 5.23972 3.02515i 0.196782 0.113612i −0.398372 0.917224i \(-0.630425\pi\)
0.595153 + 0.803612i \(0.297091\pi\)
\(710\) 5.63813i 0.211595i
\(711\) −8.47459 14.6784i −0.317822 0.550484i
\(712\) −6.15202 + 10.6556i −0.230557 + 0.399336i
\(713\) 18.0218 + 10.4049i 0.674922 + 0.389666i
\(714\) 0 0
\(715\) −15.4300 + 3.01664i −0.577050 + 0.112816i
\(716\) 8.65061 0.323288
\(717\) 4.21743 + 2.43493i 0.157503 + 0.0909342i
\(718\) −11.1124 + 19.2473i −0.414713 + 0.718304i
\(719\) −23.5589 40.8052i −0.878597 1.52178i −0.852880 0.522106i \(-0.825146\pi\)
−0.0257170 0.999669i \(-0.508187\pi\)
\(720\) 38.2884i 1.42692i
\(721\) 0 0
\(722\) −12.2100 + 7.04944i −0.454409 + 0.262353i
\(723\) 5.22916i 0.194475i
\(724\) 7.75473 + 13.4316i 0.288202 + 0.499181i
\(725\) 6.45070 11.1729i 0.239573 0.414953i
\(726\) −4.28097 2.47162i −0.158882 0.0917303i
\(727\) −17.9215 −0.664671 −0.332335 0.943161i \(-0.607837\pi\)
−0.332335 + 0.943161i \(0.607837\pi\)
\(728\) 0 0
\(729\) −13.5489 −0.501810
\(730\) 32.8985 + 18.9940i 1.21763 + 0.702999i
\(731\) −5.24644 + 9.08711i −0.194047 + 0.336099i
\(732\) −3.56454 6.17396i −0.131749 0.228196i
\(733\) 45.2685i 1.67203i 0.548705 + 0.836016i \(0.315121\pi\)
−0.548705 + 0.836016i \(0.684879\pi\)
\(734\) −3.72861 + 2.15271i −0.137625 + 0.0794581i
\(735\) 0 0
\(736\) 16.9378i 0.624335i
\(737\) 18.3691 + 31.8163i 0.676635 + 1.17197i
\(738\) −27.2247 + 47.1546i −1.00215 + 1.73578i
\(739\) −16.6808 9.63066i −0.613613 0.354270i 0.160765 0.986993i \(-0.448604\pi\)
−0.774378 + 0.632723i \(0.781937\pi\)
\(740\) 45.1155 1.65848
\(741\) −5.18905 + 4.52065i −0.190624 + 0.166070i
\(742\) 0 0
\(743\) 30.2115 + 17.4426i 1.10835 + 0.639908i 0.938402 0.345545i \(-0.112306\pi\)
0.169951 + 0.985453i \(0.445639\pi\)
\(744\) −18.9905 + 32.8925i −0.696225 + 1.20590i
\(745\) −15.9577 27.6396i −0.584647 1.01264i
\(746\) 36.1459i 1.32339i
\(747\) 6.37850 3.68263i 0.233377 0.134740i
\(748\) −34.4303 + 19.8784i −1.25890 + 0.726825i
\(749\) 0 0
\(750\) 8.00648 + 13.8676i 0.292355 + 0.506374i
\(751\) −12.4834 + 21.6219i −0.455526 + 0.788993i −0.998718 0.0506146i \(-0.983882\pi\)
0.543193 + 0.839608i \(0.317215\pi\)
\(752\) 7.94609 + 4.58767i 0.289764 + 0.167295i
\(753\) 5.36536 0.195525
\(754\) −47.4310 16.2743i −1.72733 0.592676i
\(755\) −12.1467 −0.442064
\(756\) 0 0
\(757\) 5.30243 9.18408i 0.192720 0.333801i −0.753431 0.657527i \(-0.771602\pi\)
0.946151 + 0.323726i \(0.104936\pi\)
\(758\) −40.8685 70.7863i −1.48441 2.57108i
\(759\) 2.78527i 0.101099i
\(760\) −35.9337 + 20.7463i −1.30345 + 0.752548i
\(761\) 28.2660 16.3194i 1.02464 0.591578i 0.109198 0.994020i \(-0.465172\pi\)
0.915446 + 0.402442i \(0.131838\pi\)
\(762\) 4.19288i 0.151892i
\(763\) 0 0
\(764\) 11.5080 19.9325i 0.416345 0.721131i
\(765\) 11.9216 + 6.88296i 0.431028 + 0.248854i
\(766\) −82.5976 −2.98437
\(767\) 38.9604 + 13.3680i 1.40678 + 0.482689i
\(768\) 11.4759 0.414100
\(769\) 45.1851 + 26.0876i 1.62942 + 0.940744i 0.984267 + 0.176686i \(0.0565378\pi\)
0.645148 + 0.764057i \(0.276796\pi\)
\(770\) 0 0
\(771\) 2.07039 + 3.58601i 0.0745631 + 0.129147i
\(772\) 14.1924i 0.510794i
\(773\) −30.9221 + 17.8529i −1.11219 + 0.642123i −0.939396 0.342835i \(-0.888613\pi\)
−0.172794 + 0.984958i \(0.555279\pi\)
\(774\) 20.5480 11.8634i 0.738583 0.426421i
\(775\) 25.1607i 0.903800i
\(776\) 54.1208 + 93.7400i 1.94282 + 3.36507i
\(777\) 0 0
\(778\) 56.9752 + 32.8947i 2.04266 + 1.17933i
\(779\) 28.3531 1.01586
\(780\) 10.6812 9.30533i 0.382447 0.333184i
\(781\) −3.65469 −0.130775
\(782\) −13.9206 8.03703i