Properties

Label 637.2.k.i.459.6
Level $637$
Weight $2$
Character 637.459
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.k (of order \(6\), degree \(2\), not 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 459.6
Root \(1.21245 + 0.727987i\) of defining polynomial
Character \(\chi\) \(=\) 637.459
Dual form 637.2.k.i.569.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.30327i q^{2} +(-0.736680 - 1.27597i) q^{3} -3.30504 q^{4} +(-0.733776 + 0.423646i) q^{5} +(2.93889 - 1.69677i) q^{6} -3.00585i q^{8} +(0.414604 - 0.718115i) q^{9} +O(q^{10})\) \(q+2.30327i q^{2} +(-0.736680 - 1.27597i) q^{3} -3.30504 q^{4} +(-0.733776 + 0.423646i) q^{5} +(2.93889 - 1.69677i) q^{6} -3.00585i q^{8} +(0.414604 - 0.718115i) q^{9} +(-0.975769 - 1.69008i) q^{10} +(1.30198 - 0.751701i) q^{11} +(2.43476 + 4.21712i) q^{12} +(2.92329 - 2.11054i) q^{13} +(1.08112 + 0.624183i) q^{15} +0.313194 q^{16} +2.07140 q^{17} +(1.65401 + 0.954943i) q^{18} +(-0.0410731 - 0.0237136i) q^{19} +(2.42516 - 1.40016i) q^{20} +(1.73137 + 2.99882i) q^{22} +7.81870 q^{23} +(-3.83536 + 2.21435i) q^{24} +(-2.14105 + 3.70840i) q^{25} +(4.86115 + 6.73311i) q^{26} -5.64180 q^{27} +(-0.679854 + 1.17754i) q^{29} +(-1.43766 + 2.49010i) q^{30} +(6.80787 + 3.93052i) q^{31} -5.29033i q^{32} +(-1.91829 - 1.10753i) q^{33} +4.77099i q^{34} +(-1.37028 + 2.37340i) q^{36} -6.70219i q^{37} +(0.0546187 - 0.0946024i) q^{38} +(-4.84652 - 2.17522i) q^{39} +(1.27341 + 2.20562i) q^{40} +(8.67622 + 5.00922i) q^{41} +(4.63283 + 8.02430i) q^{43} +(-4.30311 + 2.48440i) q^{44} +0.702581i q^{45} +18.0086i q^{46} +(0.311781 - 0.180007i) q^{47} +(-0.230724 - 0.399625i) q^{48} +(-8.54144 - 4.93141i) q^{50} +(-1.52596 - 2.64304i) q^{51} +(-9.66157 + 6.97543i) q^{52} +(-1.35591 + 2.34850i) q^{53} -12.9946i q^{54} +(-0.636910 + 1.10316i) q^{55} +0.0698773i q^{57} +(-2.71219 - 1.56588i) q^{58} +1.64120i q^{59} +(-3.57313 - 2.06295i) q^{60} +(2.26097 - 3.91612i) q^{61} +(-9.05305 + 15.6803i) q^{62} +12.8114 q^{64} +(-1.25091 + 2.78711i) q^{65} +(2.55093 - 4.41834i) q^{66} +(-1.76900 + 1.02133i) q^{67} -6.84606 q^{68} +(-5.75988 - 9.97641i) q^{69} +(12.3096 - 7.10697i) q^{71} +(-2.15854 - 1.24624i) q^{72} +(-5.85563 - 3.38075i) q^{73} +15.4369 q^{74} +6.30907 q^{75} +(0.135748 + 0.0783743i) q^{76} +(5.01012 - 11.1628i) q^{78} +(-5.82952 - 10.0970i) q^{79} +(-0.229814 + 0.132683i) q^{80} +(2.91240 + 5.04442i) q^{81} +(-11.5376 + 19.9837i) q^{82} -11.5362i q^{83} +(-1.51994 + 0.877541i) q^{85} +(-18.4821 + 10.6706i) q^{86} +2.00334 q^{87} +(-2.25950 - 3.91357i) q^{88} -17.5112i q^{89} -1.61823 q^{90} -25.8411 q^{92} -11.5822i q^{93} +(0.414604 + 0.718115i) q^{94} +0.0401846 q^{95} +(-6.75029 + 3.89728i) q^{96} +(-0.369125 + 0.213115i) q^{97} -1.24663i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} + O(q^{10}) \) \( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} - 12 q^{10} + 12 q^{11} + q^{12} + 2 q^{13} - 12 q^{15} + 16 q^{16} + 34 q^{17} + 3 q^{18} - 9 q^{19} + 3 q^{20} - 15 q^{22} - 6 q^{23} - 15 q^{24} - 5 q^{25} + 6 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{31} + 6 q^{33} - 13 q^{36} - 19 q^{38} - 4 q^{39} + q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} + 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{55} - 24 q^{58} - 30 q^{60} - 5 q^{61} - 41 q^{62} + 2 q^{64} + 21 q^{65} + 34 q^{66} + 15 q^{67} - 22 q^{68} - 7 q^{69} + 30 q^{71} + 57 q^{72} - 42 q^{73} + 66 q^{74} + 2 q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} + 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 57 q^{86} + 20 q^{87} - 14 q^{88} - 66 q^{92} - q^{94} - 4 q^{95} - 21 q^{96} + 3 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30327i 1.62866i 0.580405 + 0.814328i \(0.302894\pi\)
−0.580405 + 0.814328i \(0.697106\pi\)
\(3\) −0.736680 1.27597i −0.425323 0.736680i 0.571128 0.820861i \(-0.306506\pi\)
−0.996451 + 0.0841807i \(0.973173\pi\)
\(4\) −3.30504 −1.65252
\(5\) −0.733776 + 0.423646i −0.328155 + 0.189460i −0.655022 0.755610i \(-0.727340\pi\)
0.326867 + 0.945070i \(0.394007\pi\)
\(6\) 2.93889 1.69677i 1.19980 0.692704i
\(7\) 0 0
\(8\) 3.00585i 1.06273i
\(9\) 0.414604 0.718115i 0.138201 0.239372i
\(10\) −0.975769 1.69008i −0.308565 0.534451i
\(11\) 1.30198 0.751701i 0.392563 0.226646i −0.290707 0.956812i \(-0.593890\pi\)
0.683270 + 0.730166i \(0.260557\pi\)
\(12\) 2.43476 + 4.21712i 0.702853 + 1.21738i
\(13\) 2.92329 2.11054i 0.810774 0.585360i
\(14\) 0 0
\(15\) 1.08112 + 0.624183i 0.279143 + 0.161163i
\(16\) 0.313194 0.0782985
\(17\) 2.07140 0.502389 0.251194 0.967937i \(-0.419177\pi\)
0.251194 + 0.967937i \(0.419177\pi\)
\(18\) 1.65401 + 0.954943i 0.389854 + 0.225082i
\(19\) −0.0410731 0.0237136i −0.00942282 0.00544027i 0.495281 0.868733i \(-0.335065\pi\)
−0.504704 + 0.863292i \(0.668398\pi\)
\(20\) 2.42516 1.40016i 0.542282 0.313086i
\(21\) 0 0
\(22\) 1.73137 + 2.99882i 0.369129 + 0.639350i
\(23\) 7.81870 1.63031 0.815156 0.579241i \(-0.196651\pi\)
0.815156 + 0.579241i \(0.196651\pi\)
\(24\) −3.83536 + 2.21435i −0.782891 + 0.452002i
\(25\) −2.14105 + 3.70840i −0.428210 + 0.741681i
\(26\) 4.86115 + 6.73311i 0.953349 + 1.32047i
\(27\) −5.64180 −1.08577
\(28\) 0 0
\(29\) −0.679854 + 1.17754i −0.126246 + 0.218664i −0.922219 0.386668i \(-0.873626\pi\)
0.795973 + 0.605331i \(0.206959\pi\)
\(30\) −1.43766 + 2.49010i −0.262480 + 0.454628i
\(31\) 6.80787 + 3.93052i 1.22273 + 0.705943i 0.965499 0.260407i \(-0.0838567\pi\)
0.257230 + 0.966350i \(0.417190\pi\)
\(32\) 5.29033i 0.935206i
\(33\) −1.91829 1.10753i −0.333932 0.192796i
\(34\) 4.77099i 0.818218i
\(35\) 0 0
\(36\) −1.37028 + 2.37340i −0.228380 + 0.395566i
\(37\) 6.70219i 1.10183i −0.834560 0.550917i \(-0.814278\pi\)
0.834560 0.550917i \(-0.185722\pi\)
\(38\) 0.0546187 0.0946024i 0.00886032 0.0153465i
\(39\) −4.84652 2.17522i −0.776064 0.348314i
\(40\) 1.27341 + 2.20562i 0.201345 + 0.348739i
\(41\) 8.67622 + 5.00922i 1.35500 + 0.782309i 0.988945 0.148285i \(-0.0473754\pi\)
0.366054 + 0.930594i \(0.380709\pi\)
\(42\) 0 0
\(43\) 4.63283 + 8.02430i 0.706500 + 1.22369i 0.966147 + 0.257991i \(0.0830604\pi\)
−0.259647 + 0.965704i \(0.583606\pi\)
\(44\) −4.30311 + 2.48440i −0.648718 + 0.374537i
\(45\) 0.702581i 0.104735i
\(46\) 18.0086i 2.65522i
\(47\) 0.311781 0.180007i 0.0454779 0.0262567i −0.477089 0.878855i \(-0.658308\pi\)
0.522567 + 0.852598i \(0.324975\pi\)
\(48\) −0.230724 0.399625i −0.0333021 0.0576810i
\(49\) 0 0
\(50\) −8.54144 4.93141i −1.20794 0.697406i
\(51\) −1.52596 2.64304i −0.213677 0.370100i
\(52\) −9.66157 + 6.97543i −1.33982 + 0.967318i
\(53\) −1.35591 + 2.34850i −0.186248 + 0.322591i −0.943996 0.329956i \(-0.892966\pi\)
0.757748 + 0.652547i \(0.226299\pi\)
\(54\) 12.9946i 1.76834i
\(55\) −0.636910 + 1.10316i −0.0858809 + 0.148750i
\(56\) 0 0
\(57\) 0.0698773i 0.00925548i
\(58\) −2.71219 1.56588i −0.356128 0.205611i
\(59\) 1.64120i 0.213666i 0.994277 + 0.106833i \(0.0340709\pi\)
−0.994277 + 0.106833i \(0.965929\pi\)
\(60\) −3.57313 2.06295i −0.461289 0.266325i
\(61\) 2.26097 3.91612i 0.289488 0.501407i −0.684200 0.729295i \(-0.739848\pi\)
0.973688 + 0.227887i \(0.0731817\pi\)
\(62\) −9.05305 + 15.6803i −1.14974 + 1.99140i
\(63\) 0 0
\(64\) 12.8114 1.60143
\(65\) −1.25091 + 2.78711i −0.155157 + 0.345698i
\(66\) 2.55093 4.41834i 0.313998 0.543860i
\(67\) −1.76900 + 1.02133i −0.216117 + 0.124775i −0.604151 0.796870i \(-0.706488\pi\)
0.388034 + 0.921645i \(0.373154\pi\)
\(68\) −6.84606 −0.830206
\(69\) −5.75988 9.97641i −0.693409 1.20102i
\(70\) 0 0
\(71\) 12.3096 7.10697i 1.46088 0.843442i 0.461832 0.886967i \(-0.347192\pi\)
0.999052 + 0.0435255i \(0.0138590\pi\)
\(72\) −2.15854 1.24624i −0.254387 0.146870i
\(73\) −5.85563 3.38075i −0.685349 0.395687i 0.116518 0.993189i \(-0.462827\pi\)
−0.801867 + 0.597502i \(0.796160\pi\)
\(74\) 15.4369 1.79451
\(75\) 6.30907 0.728509
\(76\) 0.135748 + 0.0783743i 0.0155714 + 0.00899015i
\(77\) 0 0
\(78\) 5.01012 11.1628i 0.567284 1.26394i
\(79\) −5.82952 10.0970i −0.655873 1.13600i −0.981674 0.190567i \(-0.938967\pi\)
0.325801 0.945438i \(-0.394366\pi\)
\(80\) −0.229814 + 0.132683i −0.0256940 + 0.0148344i
\(81\) 2.91240 + 5.04442i 0.323600 + 0.560491i
\(82\) −11.5376 + 19.9837i −1.27411 + 2.20683i
\(83\) 11.5362i 1.26627i −0.774043 0.633133i \(-0.781768\pi\)
0.774043 0.633133i \(-0.218232\pi\)
\(84\) 0 0
\(85\) −1.51994 + 0.877541i −0.164861 + 0.0951826i
\(86\) −18.4821 + 10.6706i −1.99298 + 1.15065i
\(87\) 2.00334 0.214781
\(88\) −2.25950 3.91357i −0.240863 0.417188i
\(89\) 17.5112i 1.85619i −0.372350 0.928093i \(-0.621448\pi\)
0.372350 0.928093i \(-0.378552\pi\)
\(90\) −1.61823 −0.170576
\(91\) 0 0
\(92\) −25.8411 −2.69412
\(93\) 11.5822i 1.20101i
\(94\) 0.414604 + 0.718115i 0.0427631 + 0.0740679i
\(95\) 0.0401846 0.00412286
\(96\) −6.75029 + 3.89728i −0.688948 + 0.397764i
\(97\) −0.369125 + 0.213115i −0.0374790 + 0.0216385i −0.518622 0.855003i \(-0.673555\pi\)
0.481143 + 0.876642i \(0.340222\pi\)
\(98\) 0 0
\(99\) 1.24663i 0.125291i
\(100\) 7.07624 12.2564i 0.707624 1.22564i
\(101\) −4.83499 8.37444i −0.481099 0.833288i 0.518666 0.854977i \(-0.326429\pi\)
−0.999765 + 0.0216891i \(0.993096\pi\)
\(102\) 6.08763 3.51469i 0.602765 0.348007i
\(103\) 4.98912 + 8.64140i 0.491592 + 0.851463i 0.999953 0.00968129i \(-0.00308170\pi\)
−0.508361 + 0.861144i \(0.669748\pi\)
\(104\) −6.34397 8.78695i −0.622078 0.861631i
\(105\) 0 0
\(106\) −5.40922 3.12301i −0.525390 0.303334i
\(107\) 9.86223 0.953417 0.476709 0.879061i \(-0.341830\pi\)
0.476709 + 0.879061i \(0.341830\pi\)
\(108\) 18.6464 1.79425
\(109\) −10.0507 5.80275i −0.962679 0.555803i −0.0656822 0.997841i \(-0.520922\pi\)
−0.896996 + 0.442038i \(0.854256\pi\)
\(110\) −2.54087 1.46697i −0.242263 0.139870i
\(111\) −8.55178 + 4.93737i −0.811699 + 0.468635i
\(112\) 0 0
\(113\) 1.73879 + 3.01167i 0.163572 + 0.283314i 0.936147 0.351609i \(-0.114365\pi\)
−0.772576 + 0.634923i \(0.781032\pi\)
\(114\) −0.160946 −0.0150740
\(115\) −5.73718 + 3.31236i −0.534994 + 0.308879i
\(116\) 2.24694 3.89182i 0.208623 0.361346i
\(117\) −0.303608 2.97429i −0.0280686 0.274974i
\(118\) −3.78011 −0.347987
\(119\) 0 0
\(120\) 1.87620 3.24967i 0.171273 0.296653i
\(121\) −4.36989 + 7.56887i −0.397263 + 0.688079i
\(122\) 9.01986 + 5.20762i 0.816620 + 0.471476i
\(123\) 14.7608i 1.33093i
\(124\) −22.5003 12.9905i −2.02058 1.16658i
\(125\) 7.86464i 0.703435i
\(126\) 0 0
\(127\) −7.84992 + 13.5965i −0.696567 + 1.20649i 0.273082 + 0.961991i \(0.411957\pi\)
−0.969649 + 0.244499i \(0.921376\pi\)
\(128\) 18.9275i 1.67297i
\(129\) 6.82583 11.8227i 0.600981 1.04093i
\(130\) −6.41945 2.88119i −0.563023 0.252697i
\(131\) −1.27259 2.20418i −0.111186 0.192580i 0.805063 0.593190i \(-0.202132\pi\)
−0.916249 + 0.400610i \(0.868798\pi\)
\(132\) 6.34003 + 3.66042i 0.551829 + 0.318598i
\(133\) 0 0
\(134\) −2.35240 4.07447i −0.203216 0.351981i
\(135\) 4.13982 2.39013i 0.356299 0.205709i
\(136\) 6.22632i 0.533902i
\(137\) 1.86472i 0.159314i 0.996822 + 0.0796571i \(0.0253825\pi\)
−0.996822 + 0.0796571i \(0.974617\pi\)
\(138\) 22.9783 13.2665i 1.95605 1.12932i
\(139\) 7.80462 + 13.5180i 0.661979 + 1.14658i 0.980095 + 0.198530i \(0.0636166\pi\)
−0.318116 + 0.948052i \(0.603050\pi\)
\(140\) 0 0
\(141\) −0.459366 0.265215i −0.0386856 0.0223351i
\(142\) 16.3692 + 28.3524i 1.37368 + 2.37928i
\(143\) 2.21957 4.94533i 0.185610 0.413550i
\(144\) 0.129851 0.224909i 0.0108209 0.0187424i
\(145\) 1.15207i 0.0956741i
\(146\) 7.78676 13.4871i 0.644437 1.11620i
\(147\) 0 0
\(148\) 22.1510i 1.82080i
\(149\) 5.51106 + 3.18181i 0.451484 + 0.260664i 0.708457 0.705754i \(-0.249392\pi\)
−0.256973 + 0.966419i \(0.582725\pi\)
\(150\) 14.5315i 1.18649i
\(151\) 0.575122 + 0.332047i 0.0468028 + 0.0270216i 0.523219 0.852198i \(-0.324731\pi\)
−0.476416 + 0.879220i \(0.658064\pi\)
\(152\) −0.0712794 + 0.123460i −0.00578152 + 0.0100139i
\(153\) 0.858811 1.48750i 0.0694307 0.120258i
\(154\) 0 0
\(155\) −6.66060 −0.534992
\(156\) 16.0179 + 7.18919i 1.28246 + 0.575596i
\(157\) −8.28798 + 14.3552i −0.661453 + 1.14567i 0.318781 + 0.947828i \(0.396727\pi\)
−0.980234 + 0.197842i \(0.936607\pi\)
\(158\) 23.2562 13.4269i 1.85016 1.06819i
\(159\) 3.99548 0.316862
\(160\) 2.24122 + 3.88191i 0.177184 + 0.306892i
\(161\) 0 0
\(162\) −11.6186 + 6.70802i −0.912846 + 0.527032i
\(163\) 7.83863 + 4.52563i 0.613969 + 0.354475i 0.774517 0.632553i \(-0.217993\pi\)
−0.160548 + 0.987028i \(0.551326\pi\)
\(164\) −28.6752 16.5557i −2.23916 1.29278i
\(165\) 1.87680 0.146108
\(166\) 26.5710 2.06231
\(167\) 2.30156 + 1.32880i 0.178100 + 0.102826i 0.586400 0.810022i \(-0.300545\pi\)
−0.408300 + 0.912848i \(0.633878\pi\)
\(168\) 0 0
\(169\) 4.09120 12.3395i 0.314708 0.949189i
\(170\) −2.02121 3.50084i −0.155020 0.268502i
\(171\) −0.0340582 + 0.0196635i −0.00260449 + 0.00150370i
\(172\) −15.3117 26.5206i −1.16750 2.02218i
\(173\) −9.79352 + 16.9629i −0.744588 + 1.28966i 0.205799 + 0.978594i \(0.434021\pi\)
−0.950387 + 0.311070i \(0.899313\pi\)
\(174\) 4.61423i 0.349804i
\(175\) 0 0
\(176\) 0.407774 0.235428i 0.0307371 0.0177461i
\(177\) 2.09411 1.20904i 0.157403 0.0908768i
\(178\) 40.3330 3.02309
\(179\) −1.44666 2.50569i −0.108129 0.187284i 0.806884 0.590711i \(-0.201152\pi\)
−0.915012 + 0.403426i \(0.867819\pi\)
\(180\) 2.32205i 0.173076i
\(181\) 1.36804 0.101686 0.0508429 0.998707i \(-0.483809\pi\)
0.0508429 + 0.998707i \(0.483809\pi\)
\(182\) 0 0
\(183\) −6.66245 −0.492503
\(184\) 23.5018i 1.73258i
\(185\) 2.83936 + 4.91791i 0.208754 + 0.361572i
\(186\) 26.6768 1.95604
\(187\) 2.69693 1.55707i 0.197219 0.113865i
\(188\) −1.03045 + 0.594929i −0.0751531 + 0.0433897i
\(189\) 0 0
\(190\) 0.0925559i 0.00671471i
\(191\) 0.756625 1.31051i 0.0547475 0.0948254i −0.837353 0.546663i \(-0.815898\pi\)
0.892100 + 0.451837i \(0.149231\pi\)
\(192\) −9.43792 16.3470i −0.681123 1.17974i
\(193\) −6.02229 + 3.47697i −0.433494 + 0.250278i −0.700834 0.713324i \(-0.747189\pi\)
0.267340 + 0.963602i \(0.413855\pi\)
\(194\) −0.490860 0.850194i −0.0352417 0.0610404i
\(195\) 4.47778 0.457080i 0.320661 0.0327322i
\(196\) 0 0
\(197\) −13.4037 7.73860i −0.954971 0.551353i −0.0603494 0.998177i \(-0.519221\pi\)
−0.894622 + 0.446825i \(0.852555\pi\)
\(198\) 2.87133 0.204056
\(199\) 6.61529 0.468945 0.234473 0.972123i \(-0.424664\pi\)
0.234473 + 0.972123i \(0.424664\pi\)
\(200\) 11.1469 + 6.43566i 0.788205 + 0.455070i
\(201\) 2.60637 + 1.50479i 0.183839 + 0.106140i
\(202\) 19.2886 11.1363i 1.35714 0.783545i
\(203\) 0 0
\(204\) 5.04336 + 8.73535i 0.353106 + 0.611597i
\(205\) −8.48854 −0.592865
\(206\) −19.9035 + 11.4913i −1.38674 + 0.800634i
\(207\) 3.24166 5.61473i 0.225311 0.390250i
\(208\) 0.915555 0.661010i 0.0634823 0.0458328i
\(209\) −0.0713021 −0.00493207
\(210\) 0 0
\(211\) 4.04714 7.00986i 0.278617 0.482578i −0.692424 0.721490i \(-0.743457\pi\)
0.971041 + 0.238912i \(0.0767907\pi\)
\(212\) 4.48132 7.76187i 0.307778 0.533088i
\(213\) −18.1365 10.4711i −1.24269 0.717470i
\(214\) 22.7153i 1.55279i
\(215\) −6.79892 3.92536i −0.463683 0.267707i
\(216\) 16.9584i 1.15387i
\(217\) 0 0
\(218\) 13.3653 23.1493i 0.905211 1.56787i
\(219\) 9.96212i 0.673178i
\(220\) 2.10501 3.64599i 0.141920 0.245812i
\(221\) 6.05530 4.37178i 0.407323 0.294078i
\(222\) −11.3721 19.6970i −0.763244 1.32198i
\(223\) −13.9067 8.02903i −0.931261 0.537664i −0.0440506 0.999029i \(-0.514026\pi\)
−0.887210 + 0.461366i \(0.847360\pi\)
\(224\) 0 0
\(225\) 1.77537 + 3.07504i 0.118358 + 0.205002i
\(226\) −6.93668 + 4.00490i −0.461421 + 0.266402i
\(227\) 1.29581i 0.0860057i −0.999075 0.0430029i \(-0.986308\pi\)
0.999075 0.0430029i \(-0.0136925\pi\)
\(228\) 0.230947i 0.0152948i
\(229\) −18.0285 + 10.4088i −1.19136 + 0.687831i −0.958614 0.284707i \(-0.908104\pi\)
−0.232743 + 0.972538i \(0.574770\pi\)
\(230\) −7.62925 13.2142i −0.503058 0.871322i
\(231\) 0 0
\(232\) 3.53951 + 2.04354i 0.232380 + 0.134165i
\(233\) −6.65213 11.5218i −0.435796 0.754820i 0.561565 0.827433i \(-0.310200\pi\)
−0.997360 + 0.0726127i \(0.976866\pi\)
\(234\) 6.85059 0.699290i 0.447837 0.0457140i
\(235\) −0.152518 + 0.264169i −0.00994920 + 0.0172325i
\(236\) 5.42421i 0.353086i
\(237\) −8.58899 + 14.8766i −0.557915 + 0.966337i
\(238\) 0 0
\(239\) 13.3652i 0.864525i 0.901748 + 0.432263i \(0.142285\pi\)
−0.901748 + 0.432263i \(0.857715\pi\)
\(240\) 0.338599 + 0.195490i 0.0218565 + 0.0126188i
\(241\) 0.834153i 0.0537325i −0.999639 0.0268663i \(-0.991447\pi\)
0.999639 0.0268663i \(-0.00855282\pi\)
\(242\) −17.4331 10.0650i −1.12064 0.647004i
\(243\) −4.17170 + 7.22559i −0.267614 + 0.463522i
\(244\) −7.47259 + 12.9429i −0.478384 + 0.828585i
\(245\) 0 0
\(246\) 33.9980 2.16763
\(247\) −0.170117 + 0.0173651i −0.0108243 + 0.00110491i
\(248\) 11.8146 20.4634i 0.750225 1.29943i
\(249\) −14.7199 + 8.49852i −0.932834 + 0.538572i
\(250\) 18.1144 1.14565
\(251\) −13.6360 23.6183i −0.860699 1.49078i −0.871255 0.490831i \(-0.836693\pi\)
0.0105555 0.999944i \(-0.496640\pi\)
\(252\) 0 0
\(253\) 10.1798 5.87733i 0.640000 0.369504i
\(254\) −31.3163 18.0804i −1.96496 1.13447i
\(255\) 2.23943 + 1.29293i 0.140238 + 0.0809667i
\(256\) −17.9721 −1.12326
\(257\) 6.55188 0.408695 0.204348 0.978898i \(-0.434493\pi\)
0.204348 + 0.978898i \(0.434493\pi\)
\(258\) 27.2308 + 15.7217i 1.69532 + 0.978791i
\(259\) 0 0
\(260\) 4.13432 9.21148i 0.256399 0.571272i
\(261\) 0.563740 + 0.976426i 0.0348946 + 0.0604393i
\(262\) 5.07682 2.93110i 0.313647 0.181084i
\(263\) 11.2945 + 19.5627i 0.696450 + 1.20629i 0.969689 + 0.244341i \(0.0785717\pi\)
−0.273239 + 0.961946i \(0.588095\pi\)
\(264\) −3.32906 + 5.76610i −0.204889 + 0.354879i
\(265\) 2.29770i 0.141146i
\(266\) 0 0
\(267\) −22.3437 + 12.9002i −1.36742 + 0.789478i
\(268\) 5.84660 3.37553i 0.357138 0.206194i
\(269\) −16.0013 −0.975617 −0.487808 0.872951i \(-0.662203\pi\)
−0.487808 + 0.872951i \(0.662203\pi\)
\(270\) 5.50510 + 9.53511i 0.335030 + 0.580288i
\(271\) 8.75935i 0.532093i 0.963960 + 0.266046i \(0.0857174\pi\)
−0.963960 + 0.266046i \(0.914283\pi\)
\(272\) 0.648750 0.0393363
\(273\) 0 0
\(274\) −4.29496 −0.259468
\(275\) 6.43771i 0.388209i
\(276\) 19.0366 + 32.9724i 1.14587 + 1.98471i
\(277\) 19.9183 1.19677 0.598387 0.801208i \(-0.295809\pi\)
0.598387 + 0.801208i \(0.295809\pi\)
\(278\) −31.1355 + 17.9761i −1.86739 + 1.07814i
\(279\) 5.64514 3.25922i 0.337965 0.195124i
\(280\) 0 0
\(281\) 14.0234i 0.836566i −0.908317 0.418283i \(-0.862632\pi\)
0.908317 0.418283i \(-0.137368\pi\)
\(282\) 0.610861 1.05804i 0.0363762 0.0630055i
\(283\) −0.506295 0.876929i −0.0300961 0.0521280i 0.850585 0.525838i \(-0.176248\pi\)
−0.880681 + 0.473710i \(0.842915\pi\)
\(284\) −40.6838 + 23.4888i −2.41414 + 1.39380i
\(285\) −0.0296032 0.0512743i −0.00175354 0.00303723i
\(286\) 11.3904 + 5.11227i 0.673530 + 0.302295i
\(287\) 0 0
\(288\) −3.79906 2.19339i −0.223862 0.129247i
\(289\) −12.7093 −0.747606
\(290\) 2.65352 0.155820
\(291\) 0.543855 + 0.313995i 0.0318813 + 0.0184067i
\(292\) 19.3531 + 11.1735i 1.13255 + 0.653879i
\(293\) 0.172543 0.0996176i 0.0100801 0.00581972i −0.494952 0.868921i \(-0.664814\pi\)
0.505032 + 0.863101i \(0.331481\pi\)
\(294\) 0 0
\(295\) −0.695286 1.20427i −0.0404811 0.0701153i
\(296\) −20.1458 −1.17095
\(297\) −7.34554 + 4.24095i −0.426232 + 0.246085i
\(298\) −7.32857 + 12.6935i −0.424532 + 0.735312i
\(299\) 22.8563 16.5017i 1.32181 0.954319i
\(300\) −20.8517 −1.20387
\(301\) 0 0
\(302\) −0.764792 + 1.32466i −0.0440088 + 0.0762256i
\(303\) −7.12368 + 12.3386i −0.409245 + 0.708833i
\(304\) −0.0128639 0.00742695i −0.000737793 0.000425965i
\(305\) 3.83140i 0.219386i
\(306\) 3.42612 + 1.97807i 0.195858 + 0.113079i
\(307\) 27.2004i 1.55241i 0.630482 + 0.776204i \(0.282857\pi\)
−0.630482 + 0.776204i \(0.717143\pi\)
\(308\) 0 0
\(309\) 7.35077 12.7319i 0.418171 0.724293i
\(310\) 15.3411i 0.871318i
\(311\) −13.5505 + 23.4701i −0.768376 + 1.33087i 0.170067 + 0.985432i \(0.445602\pi\)
−0.938443 + 0.345434i \(0.887732\pi\)
\(312\) −6.53839 + 14.5679i −0.370163 + 0.824744i
\(313\) −11.0392 19.1205i −0.623975 1.08076i −0.988738 0.149656i \(-0.952183\pi\)
0.364763 0.931100i \(-0.381150\pi\)
\(314\) −33.0639 19.0894i −1.86590 1.07728i
\(315\) 0 0
\(316\) 19.2668 + 33.3711i 1.08384 + 1.87727i
\(317\) −6.12126 + 3.53411i −0.343804 + 0.198496i −0.661953 0.749545i \(-0.730272\pi\)
0.318149 + 0.948041i \(0.396939\pi\)
\(318\) 9.20265i 0.516059i
\(319\) 2.04419i 0.114453i
\(320\) −9.40071 + 5.42750i −0.525516 + 0.303407i
\(321\) −7.26531 12.5839i −0.405510 0.702364i
\(322\) 0 0
\(323\) −0.0850789 0.0491204i −0.00473392 0.00273313i
\(324\) −9.62558 16.6720i −0.534754 0.926221i
\(325\) 1.56786 + 15.3595i 0.0869690 + 0.851992i
\(326\) −10.4237 + 18.0544i −0.577318 + 0.999943i
\(327\) 17.0991i 0.945582i
\(328\) 15.0569 26.0794i 0.831381 1.43999i
\(329\) 0 0
\(330\) 4.32276i 0.237960i
\(331\) 5.70588 + 3.29429i 0.313623 + 0.181071i 0.648547 0.761175i \(-0.275377\pi\)
−0.334923 + 0.942245i \(0.608710\pi\)
\(332\) 38.1277i 2.09253i
\(333\) −4.81294 2.77875i −0.263748 0.152275i
\(334\) −3.06059 + 5.30110i −0.167468 + 0.290063i
\(335\) 0.865365 1.49886i 0.0472799 0.0818912i
\(336\) 0 0
\(337\) −4.22290 −0.230036 −0.115018 0.993363i \(-0.536693\pi\)
−0.115018 + 0.993363i \(0.536693\pi\)
\(338\) 28.4210 + 9.42313i 1.54590 + 0.512551i
\(339\) 2.56187 4.43728i 0.139141 0.241000i
\(340\) 5.02347 2.90030i 0.272436 0.157291i
\(341\) 11.8183 0.639998
\(342\) −0.0452902 0.0784450i −0.00244902 0.00424182i
\(343\) 0 0
\(344\) 24.1198 13.9256i 1.30045 0.750817i
\(345\) 8.45293 + 4.88030i 0.455091 + 0.262747i
\(346\) −39.0700 22.5571i −2.10042 1.21268i
\(347\) −9.09478 −0.488233 −0.244117 0.969746i \(-0.578498\pi\)
−0.244117 + 0.969746i \(0.578498\pi\)
\(348\) −6.62111 −0.354929
\(349\) −7.98521 4.61026i −0.427439 0.246782i 0.270816 0.962631i \(-0.412706\pi\)
−0.698255 + 0.715849i \(0.746040\pi\)
\(350\) 0 0
\(351\) −16.4926 + 11.9073i −0.880310 + 0.635564i
\(352\) −3.97674 6.88792i −0.211961 0.367127i
\(353\) −1.86584 + 1.07724i −0.0993087 + 0.0573359i −0.548832 0.835933i \(-0.684927\pi\)
0.449523 + 0.893269i \(0.351594\pi\)
\(354\) 2.78473 + 4.82330i 0.148007 + 0.256356i
\(355\) −6.02167 + 10.4298i −0.319597 + 0.553559i
\(356\) 57.8752i 3.06738i
\(357\) 0 0
\(358\) 5.77128 3.33205i 0.305021 0.176104i
\(359\) −7.41107 + 4.27878i −0.391141 + 0.225825i −0.682654 0.730741i \(-0.739175\pi\)
0.291513 + 0.956567i \(0.405841\pi\)
\(360\) 2.11185 0.111304
\(361\) −9.49888 16.4525i −0.499941 0.865923i
\(362\) 3.15096i 0.165611i
\(363\) 12.8769 0.675860
\(364\) 0 0
\(365\) 5.72896 0.299867
\(366\) 15.3454i 0.802117i
\(367\) 1.14912 + 1.99033i 0.0599833 + 0.103894i 0.894458 0.447153i \(-0.147562\pi\)
−0.834474 + 0.551047i \(0.814229\pi\)
\(368\) 2.44877 0.127651
\(369\) 7.19439 4.15368i 0.374525 0.216232i
\(370\) −11.3273 + 6.53979i −0.588876 + 0.339988i
\(371\) 0 0
\(372\) 38.2795i 1.98470i
\(373\) −5.88418 + 10.1917i −0.304672 + 0.527707i −0.977188 0.212375i \(-0.931880\pi\)
0.672517 + 0.740082i \(0.265213\pi\)
\(374\) 3.58636 + 6.21175i 0.185446 + 0.321202i
\(375\) −10.0350 + 5.79373i −0.518207 + 0.299187i
\(376\) −0.541073 0.937166i −0.0279037 0.0483307i
\(377\) 0.497847 + 4.87715i 0.0256404 + 0.251186i
\(378\) 0 0
\(379\) −6.92034 3.99546i −0.355474 0.205233i 0.311619 0.950207i \(-0.399129\pi\)
−0.667094 + 0.744974i \(0.732462\pi\)
\(380\) −0.132812 −0.00681310
\(381\) 23.1315 1.18506
\(382\) 3.01846 + 1.74271i 0.154438 + 0.0891647i
\(383\) 24.4605 + 14.1223i 1.24988 + 0.721616i 0.971084 0.238736i \(-0.0767331\pi\)
0.278791 + 0.960352i \(0.410066\pi\)
\(384\) 24.1508 13.9435i 1.23244 0.711551i
\(385\) 0 0
\(386\) −8.00839 13.8709i −0.407616 0.706012i
\(387\) 7.68316 0.390557
\(388\) 1.21997 0.704352i 0.0619347 0.0357580i
\(389\) 3.84043 6.65182i 0.194717 0.337261i −0.752090 0.659060i \(-0.770954\pi\)
0.946808 + 0.321799i \(0.104288\pi\)
\(390\) 1.05278 + 10.3135i 0.0533094 + 0.522246i
\(391\) 16.1957 0.819050
\(392\) 0 0
\(393\) −1.87498 + 3.24756i −0.0945801 + 0.163818i
\(394\) 17.8241 30.8722i 0.897964 1.55532i
\(395\) 8.55513 + 4.93931i 0.430455 + 0.248524i
\(396\) 4.12017i 0.207046i
\(397\) −6.45433 3.72641i −0.323933 0.187023i 0.329211 0.944256i \(-0.393217\pi\)
−0.653144 + 0.757233i \(0.726551\pi\)
\(398\) 15.2368i 0.763750i
\(399\) 0 0
\(400\) −0.670563 + 1.16145i −0.0335282 + 0.0580725i
\(401\) 18.1982i 0.908777i −0.890804 0.454389i \(-0.849858\pi\)
0.890804 0.454389i \(-0.150142\pi\)
\(402\) −3.46593 + 6.00316i −0.172865 + 0.299411i
\(403\) 28.1969 2.87826i 1.40459 0.143376i
\(404\) 15.9798 + 27.6778i 0.795025 + 1.37702i
\(405\) −4.27409 2.46765i −0.212381 0.122618i
\(406\) 0 0
\(407\) −5.03804 8.72615i −0.249727 0.432539i
\(408\) −7.94458 + 4.58681i −0.393315 + 0.227081i
\(409\) 29.2825i 1.44793i −0.689838 0.723964i \(-0.742318\pi\)
0.689838 0.723964i \(-0.257682\pi\)
\(410\) 19.5514i 0.965573i
\(411\) 2.37933 1.37371i 0.117364 0.0677599i
\(412\) −16.4892 28.5602i −0.812365 1.40706i
\(413\) 0 0
\(414\) 12.9322 + 7.46641i 0.635583 + 0.366954i
\(415\) 4.88728 + 8.46502i 0.239907 + 0.415531i
\(416\) −11.1655 15.4651i −0.547432 0.758241i
\(417\) 11.4990 19.9169i 0.563109 0.975334i
\(418\) 0.164228i 0.00803264i
\(419\) −10.3697 + 17.9608i −0.506591 + 0.877441i 0.493380 + 0.869814i \(0.335761\pi\)
−0.999971 + 0.00762733i \(0.997572\pi\)
\(420\) 0 0
\(421\) 24.8696i 1.21207i −0.795437 0.606036i \(-0.792759\pi\)
0.795437 0.606036i \(-0.207241\pi\)
\(422\) 16.1456 + 9.32165i 0.785954 + 0.453771i
\(423\) 0.298526i 0.0145148i
\(424\) 7.05923 + 4.07565i 0.342826 + 0.197931i
\(425\) −4.43497 + 7.68159i −0.215128 + 0.372612i
\(426\) 24.1178 41.7733i 1.16851 2.02392i
\(427\) 0 0
\(428\) −32.5950 −1.57554
\(429\) −7.94520 + 0.811025i −0.383598 + 0.0391566i
\(430\) 9.04115 15.6597i 0.436003 0.755179i
\(431\) −18.3327 + 10.5844i −0.883055 + 0.509832i −0.871665 0.490103i \(-0.836959\pi\)
−0.0113906 + 0.999935i \(0.503626\pi\)
\(432\) −1.76698 −0.0850138
\(433\) 11.7148 + 20.2906i 0.562977 + 0.975105i 0.997235 + 0.0743163i \(0.0236774\pi\)
−0.434258 + 0.900789i \(0.642989\pi\)
\(434\) 0 0
\(435\) −1.47000 + 0.848707i −0.0704813 + 0.0406924i
\(436\) 33.2178 + 19.1783i 1.59084 + 0.918474i
\(437\) −0.321139 0.185409i −0.0153621 0.00886934i
\(438\) −22.9454 −1.09637
\(439\) −12.0384 −0.574561 −0.287280 0.957847i \(-0.592751\pi\)
−0.287280 + 0.957847i \(0.592751\pi\)
\(440\) 3.31593 + 1.91445i 0.158081 + 0.0912680i
\(441\) 0 0
\(442\) 10.0694 + 13.9470i 0.478952 + 0.663390i
\(443\) −7.86656 13.6253i −0.373752 0.647357i 0.616388 0.787443i \(-0.288595\pi\)
−0.990139 + 0.140086i \(0.955262\pi\)
\(444\) 28.2640 16.3182i 1.34135 0.774427i
\(445\) 7.41855 + 12.8493i 0.351673 + 0.609116i
\(446\) 18.4930 32.0308i 0.875669 1.51670i
\(447\) 9.37592i 0.443466i
\(448\) 0 0
\(449\) 22.5177 13.0006i 1.06268 0.613536i 0.136504 0.990640i \(-0.456413\pi\)
0.926171 + 0.377104i \(0.123080\pi\)
\(450\) −7.08263 + 4.08916i −0.333878 + 0.192765i
\(451\) 15.0617 0.709230
\(452\) −5.74676 9.95369i −0.270305 0.468182i
\(453\) 0.978449i 0.0459716i
\(454\) 2.98459 0.140074
\(455\) 0 0
\(456\) 0.210041 0.00983605
\(457\) 30.7958i 1.44057i 0.693679 + 0.720284i \(0.255989\pi\)
−0.693679 + 0.720284i \(0.744011\pi\)
\(458\) −23.9742 41.5245i −1.12024 1.94031i
\(459\) −11.6864 −0.545476
\(460\) 18.9616 10.9475i 0.884088 0.510429i
\(461\) 29.5278 17.0479i 1.37525 0.794000i 0.383665 0.923472i \(-0.374662\pi\)
0.991583 + 0.129472i \(0.0413284\pi\)
\(462\) 0 0
\(463\) 1.69184i 0.0786263i 0.999227 + 0.0393131i \(0.0125170\pi\)
−0.999227 + 0.0393131i \(0.987483\pi\)
\(464\) −0.212926 + 0.368799i −0.00988485 + 0.0171211i
\(465\) 4.90674 + 8.49871i 0.227544 + 0.394118i
\(466\) 26.5378 15.3216i 1.22934 0.709761i
\(467\) −14.1762 24.5539i −0.655996 1.13622i −0.981643 0.190727i \(-0.938916\pi\)
0.325647 0.945491i \(-0.394418\pi\)
\(468\) 1.00344 + 9.83015i 0.0463838 + 0.454399i
\(469\) 0 0
\(470\) −0.608453 0.351290i −0.0280658 0.0162038i
\(471\) 24.4224 1.12532
\(472\) 4.93318 0.227068
\(473\) 12.0637 + 6.96501i 0.554692 + 0.320251i
\(474\) −34.2647 19.7827i −1.57383 0.908651i
\(475\) 0.175879 0.101544i 0.00806989 0.00465915i
\(476\) 0 0
\(477\) 1.12433 + 1.94739i 0.0514794 + 0.0891650i
\(478\) −30.7837 −1.40801
\(479\) −5.44077 + 3.14123i −0.248595 + 0.143526i −0.619121 0.785296i \(-0.712511\pi\)
0.370526 + 0.928822i \(0.379178\pi\)
\(480\) 3.30213 5.71946i 0.150721 0.261056i
\(481\) −14.1453 19.5924i −0.644969 0.893338i
\(482\) 1.92128 0.0875117
\(483\) 0 0
\(484\) 14.4427 25.0154i 0.656484 1.13706i
\(485\) 0.180570 0.312757i 0.00819927 0.0142016i
\(486\) −16.6425 9.60853i −0.754917 0.435852i
\(487\) 13.0176i 0.589883i 0.955515 + 0.294942i \(0.0953002\pi\)
−0.955515 + 0.294942i \(0.904700\pi\)
\(488\) −11.7712 6.79613i −0.532859 0.307647i
\(489\) 13.3358i 0.603065i
\(490\) 0 0
\(491\) −6.17616 + 10.6974i −0.278726 + 0.482768i −0.971068 0.238801i \(-0.923246\pi\)
0.692342 + 0.721569i \(0.256579\pi\)
\(492\) 48.7849i 2.19939i
\(493\) −1.40825 + 2.43916i −0.0634244 + 0.109854i
\(494\) −0.0399964 0.391825i −0.00179952 0.0176290i
\(495\) 0.528131 + 0.914749i 0.0237377 + 0.0411149i
\(496\) 2.13218 + 1.23102i 0.0957378 + 0.0552743i
\(497\) 0 0
\(498\) −19.5744 33.9038i −0.877148 1.51926i
\(499\) 7.92708 4.57670i 0.354865 0.204881i −0.311961 0.950095i \(-0.600986\pi\)
0.666826 + 0.745214i \(0.267652\pi\)
\(500\) 25.9929i 1.16244i
\(501\) 3.91562i 0.174937i
\(502\) 54.3993 31.4074i 2.42796 1.40178i
\(503\) 11.2519 + 19.4888i 0.501696 + 0.868963i 0.999998 + 0.00195935i \(0.000623680\pi\)
−0.498302 + 0.867003i \(0.666043\pi\)
\(504\) 0 0
\(505\) 7.09559 + 4.09664i 0.315750 + 0.182298i
\(506\) 13.5370 + 23.4469i 0.601795 + 1.04234i
\(507\) −18.7587 + 3.86999i −0.833101 + 0.171872i
\(508\) 25.9443 44.9368i 1.15109 1.99375i
\(509\) 38.6606i 1.71360i 0.515649 + 0.856800i \(0.327551\pi\)
−0.515649 + 0.856800i \(0.672449\pi\)
\(510\) −2.97797 + 5.15800i −0.131867 + 0.228400i
\(511\) 0 0
\(512\) 3.53972i 0.156435i
\(513\) 0.231727 + 0.133787i 0.0102310 + 0.00590686i
\(514\) 15.0907i 0.665623i
\(515\) −7.32179 4.22724i −0.322637 0.186274i
\(516\) −22.5596 + 39.0744i −0.993132 + 1.72016i
\(517\) 0.270623 0.468732i 0.0119020 0.0206148i
\(518\) 0 0
\(519\) 28.8588 1.26676
\(520\) 8.37761 + 3.76006i 0.367383 + 0.164889i
\(521\) 20.1176 34.8446i 0.881366 1.52657i 0.0315430 0.999502i \(-0.489958\pi\)
0.849823 0.527068i \(-0.176709\pi\)
\(522\) −2.24897 + 1.29844i −0.0984348 + 0.0568313i
\(523\) 0.732146 0.0320145 0.0160073 0.999872i \(-0.494905\pi\)
0.0160073 + 0.999872i \(0.494905\pi\)
\(524\) 4.20594 + 7.28491i 0.183737 + 0.318243i
\(525\) 0 0
\(526\) −45.0581 + 26.0143i −1.96463 + 1.13428i
\(527\) 14.1018 + 8.14169i 0.614285 + 0.354658i
\(528\) −0.600798 0.346871i −0.0261464 0.0150956i
\(529\) 38.1321 1.65792
\(530\) 5.29221 0.229879
\(531\) 1.17857 + 0.680446i 0.0511455 + 0.0295288i
\(532\) 0 0
\(533\) 35.9353 3.66817i 1.55653 0.158886i
\(534\) −29.7125 51.4636i −1.28579 2.22705i
\(535\) −7.23667 + 4.17809i −0.312868 + 0.180635i
\(536\) 3.06996 + 5.31733i 0.132602 + 0.229674i
\(537\) −2.13146 + 3.69179i −0.0919791 + 0.159312i
\(538\) 36.8553i 1.58894i
\(539\) 0 0
\(540\) −13.6823 + 7.89946i −0.588791 + 0.339939i
\(541\) −20.4847 + 11.8268i −0.880705 + 0.508476i −0.870891 0.491476i \(-0.836457\pi\)
−0.00981448 + 0.999952i \(0.503124\pi\)
\(542\) −20.1751 −0.866595
\(543\) −1.00781 1.74558i −0.0432492 0.0749099i
\(544\) 10.9584i 0.469837i
\(545\) 9.83325 0.421210
\(546\) 0 0
\(547\) −12.9472 −0.553582 −0.276791 0.960930i \(-0.589271\pi\)
−0.276791 + 0.960930i \(0.589271\pi\)
\(548\) 6.16298i 0.263270i
\(549\) −1.87481 3.24727i −0.0800151 0.138590i
\(550\) −14.8278 −0.632258
\(551\) 0.0558475 0.0322436i 0.00237918 0.00137362i
\(552\) −29.9876 + 17.3133i −1.27636 + 0.736904i
\(553\) 0 0
\(554\) 45.8771i 1.94913i
\(555\) 4.18340 7.24585i 0.177575 0.307569i
\(556\) −25.7946 44.6775i −1.09393 1.89475i
\(557\) 5.54845 3.20340i 0.235096 0.135732i −0.377825 0.925877i \(-0.623328\pi\)
0.612921 + 0.790145i \(0.289995\pi\)
\(558\) 7.50685 + 13.0023i 0.317790 + 0.550429i
\(559\) 30.4787 + 13.6795i 1.28911 + 0.578582i
\(560\) 0 0
\(561\) −3.97355 2.29413i −0.167764 0.0968584i
\(562\) 32.2996 1.36248
\(563\) 7.32084 0.308537 0.154268 0.988029i \(-0.450698\pi\)
0.154268 + 0.988029i \(0.450698\pi\)
\(564\) 1.51822 + 0.876546i 0.0639287 + 0.0369092i
\(565\) −2.55176 1.47326i −0.107354 0.0619806i
\(566\) 2.01980 1.16613i 0.0848986 0.0490162i
\(567\) 0 0
\(568\) −21.3625 37.0009i −0.896349 1.55252i
\(569\) 4.31743 0.180996 0.0904981 0.995897i \(-0.471154\pi\)
0.0904981 + 0.995897i \(0.471154\pi\)
\(570\) 0.118098 0.0681842i 0.00494660 0.00285592i
\(571\) 17.0847 29.5916i 0.714974 1.23837i −0.247996 0.968761i \(-0.579772\pi\)
0.962970 0.269610i \(-0.0868946\pi\)
\(572\) −7.33577 + 16.3445i −0.306724 + 0.683398i
\(573\) −2.22956 −0.0931413
\(574\) 0 0
\(575\) −16.7402 + 28.9949i −0.698115 + 1.20917i
\(576\) 5.31166 9.20007i 0.221319 0.383336i
\(577\) 5.50494 + 3.17828i 0.229174 + 0.132314i 0.610191 0.792254i \(-0.291093\pi\)
−0.381017 + 0.924568i \(0.624426\pi\)
\(578\) 29.2729i 1.21759i
\(579\) 8.87301 + 5.12283i 0.368750 + 0.212898i
\(580\) 3.80763i 0.158103i
\(581\) 0 0
\(582\) −0.723214 + 1.25264i −0.0299782 + 0.0519237i
\(583\) 4.07695i 0.168850i
\(584\) −10.1620 + 17.6011i −0.420507 + 0.728339i
\(585\) 1.48283 + 2.05384i 0.0613074 + 0.0849160i
\(586\) 0.229446 + 0.397412i 0.00947832 + 0.0164169i
\(587\) −27.2036 15.7060i −1.12281 0.648256i −0.180695 0.983539i \(-0.557835\pi\)
−0.942118 + 0.335283i \(0.891168\pi\)
\(588\) 0 0
\(589\) −0.186414 0.322878i −0.00768104 0.0133040i
\(590\) 2.77376 1.60143i 0.114194 0.0659298i
\(591\) 22.8035i 0.938011i
\(592\) 2.09909i 0.0862719i
\(593\) −0.409641 + 0.236506i −0.0168219 + 0.00971215i −0.508387 0.861128i \(-0.669758\pi\)
0.491565 + 0.870841i \(0.336425\pi\)
\(594\) −9.76804 16.9187i −0.400787 0.694184i
\(595\) 0 0
\(596\) −18.2143 10.5160i −0.746086 0.430753i
\(597\) −4.87335 8.44089i −0.199453 0.345463i
\(598\) 38.0079 + 52.6442i 1.55426 + 2.15278i
\(599\) 4.81348 8.33719i 0.196673 0.340648i −0.750774 0.660559i \(-0.770320\pi\)
0.947448 + 0.319910i \(0.103653\pi\)
\(600\) 18.9641i 0.774207i
\(601\) −20.5399 + 35.5762i −0.837842 + 1.45118i 0.0538542 + 0.998549i \(0.482849\pi\)
−0.891696 + 0.452635i \(0.850484\pi\)
\(602\) 0 0
\(603\) 1.69379i 0.0689765i
\(604\) −1.90080 1.09743i −0.0773424 0.0446537i
\(605\) 7.40514i 0.301062i
\(606\) −28.4190 16.4077i −1.15444 0.666518i
\(607\) 9.54289 16.5288i 0.387334 0.670882i −0.604756 0.796411i \(-0.706729\pi\)
0.992090 + 0.125529i \(0.0400627\pi\)
\(608\) −0.125453 + 0.217290i −0.00508777 + 0.00881228i
\(609\) 0 0
\(610\) −8.82474 −0.357303
\(611\) 0.531513 1.18424i 0.0215027 0.0479092i
\(612\) −2.83840 + 4.91626i −0.114736 + 0.198728i
\(613\) −32.9131 + 19.0024i −1.32935 + 0.767500i −0.985199 0.171415i \(-0.945166\pi\)
−0.344149 + 0.938915i \(0.611833\pi\)
\(614\) −62.6498 −2.52834
\(615\) 6.25334 + 10.8311i 0.252159 + 0.436752i
\(616\) 0 0
\(617\) 7.20117 4.15759i 0.289908 0.167378i −0.347992 0.937497i \(-0.613136\pi\)
0.637900 + 0.770119i \(0.279803\pi\)
\(618\) 29.3250 + 16.9308i 1.17962 + 0.681056i
\(619\) 38.5146 + 22.2364i 1.54803 + 0.893756i 0.998292 + 0.0584199i \(0.0186062\pi\)
0.549739 + 0.835336i \(0.314727\pi\)
\(620\) 22.0135 0.884085
\(621\) −44.1116 −1.77014
\(622\) −54.0579 31.2103i −2.16752 1.25142i
\(623\) 0 0
\(624\) −1.51790 0.681266i −0.0607646 0.0272725i
\(625\) −7.37342 12.7711i −0.294937 0.510845i
\(626\) 44.0397 25.4263i 1.76018 1.01624i
\(627\) 0.0525269 + 0.0909792i 0.00209772 + 0.00363336i
\(628\) 27.3921 47.4445i 1.09306 1.89324i
\(629\) 13.8829i 0.553549i
\(630\) 0 0
\(631\) −10.1779 + 5.87622i −0.405177 + 0.233929i −0.688715 0.725032i \(-0.741825\pi\)
0.283539 + 0.958961i \(0.408492\pi\)
\(632\) −30.3501 + 17.5227i −1.20726 + 0.697014i
\(633\) −11.9258 −0.474008
\(634\) −8.14001 14.0989i −0.323281 0.559939i
\(635\) 13.3023i 0.527887i
\(636\) −13.2052 −0.523620
\(637\) 0 0
\(638\) −4.70831 −0.186404
\(639\) 11.7863i 0.466259i
\(640\) −8.01854 13.8885i −0.316961 0.548992i
\(641\) −10.4868 −0.414205 −0.207102 0.978319i \(-0.566403\pi\)
−0.207102 + 0.978319i \(0.566403\pi\)
\(642\) 28.9840 16.7339i 1.14391 0.660436i
\(643\) −27.0912 + 15.6411i −1.06837 + 0.616825i −0.927736 0.373237i \(-0.878248\pi\)
−0.140635 + 0.990061i \(0.544915\pi\)
\(644\) 0 0
\(645\) 11.5669i 0.455448i
\(646\) 0.113137 0.195959i 0.00445133 0.00770992i
\(647\) 13.4337 + 23.2679i 0.528135 + 0.914757i 0.999462 + 0.0327983i \(0.0104419\pi\)
−0.471327 + 0.881959i \(0.656225\pi\)
\(648\) 15.1627 8.75422i 0.595649 0.343898i
\(649\) 1.23369 + 2.13681i 0.0484265 + 0.0838772i
\(650\) −35.3770 + 3.61119i −1.38760 + 0.141643i
\(651\) 0 0
\(652\) −25.9070 14.9574i −1.01459 0.585776i
\(653\) −4.14161 −0.162074 −0.0810369 0.996711i \(-0.525823\pi\)
−0.0810369 + 0.996711i \(0.525823\pi\)
\(654\) −39.3838 −1.54003
\(655\) 1.86759 + 1.07825i 0.0729726 + 0.0421308i
\(656\) 2.71734 + 1.56886i 0.106094 + 0.0612536i
\(657\) −4.85553 + 2.80334i −0.189432 + 0.109369i
\(658\) 0 0
\(659\) −10.7276 18.5807i −0.417887 0.723801i 0.577840 0.816150i \(-0.303896\pi\)
−0.995727 + 0.0923492i \(0.970562\pi\)
\(660\) −6.20288 −0.241447
\(661\) 36.7084 21.1936i 1.42779 0.824335i 0.430844 0.902426i \(-0.358216\pi\)
0.996946 + 0.0780909i \(0.0248824\pi\)
\(662\) −7.58763 + 13.1422i −0.294902 + 0.510785i
\(663\) −10.0391 4.50576i −0.389885 0.174989i
\(664\) −34.6762 −1.34570
\(665\) 0 0
\(666\) 6.40021 11.0855i 0.248003 0.429554i
\(667\) −5.31558 + 9.20685i −0.205820 + 0.356491i
\(668\) −7.60673 4.39175i −0.294313 0.169922i
\(669\) 23.6593i 0.914722i
\(670\) 3.45226 + 1.99317i 0.133373 + 0.0770027i
\(671\) 6.79830i 0.262445i
\(672\) 0 0
\(673\) −14.7928 + 25.6219i −0.570220 + 0.987650i 0.426323 + 0.904571i \(0.359809\pi\)
−0.996543 + 0.0830790i \(0.973525\pi\)
\(674\) 9.72645i 0.374649i
\(675\) 12.0794 20.9221i 0.464935 0.805292i
\(676\) −13.5216 + 40.7823i −0.520061 + 1.56855i
\(677\) 16.0830 + 27.8565i 0.618118 + 1.07061i 0.989829 + 0.142263i \(0.0454380\pi\)
−0.371711 + 0.928349i \(0.621229\pi\)
\(678\) 10.2202 + 5.90066i 0.392506 + 0.226613i
\(679\) 0 0
\(680\) 2.63775 + 4.56872i 0.101153 + 0.175202i
\(681\) −1.65341 + 0.954596i −0.0633587 + 0.0365802i
\(682\) 27.2207i 1.04234i
\(683\) 8.60236i 0.329160i 0.986364 + 0.164580i \(0.0526269\pi\)
−0.986364 + 0.164580i \(0.947373\pi\)
\(684\) 0.112563 0.0649885i 0.00430397 0.00248490i
\(685\) −0.789983 1.36829i −0.0301837 0.0522797i
\(686\) 0 0
\(687\) 26.5625 + 15.3359i 1.01342 + 0.585100i
\(688\) 1.45097 + 2.51316i 0.0553179 + 0.0958134i
\(689\) 0.992909 + 9.72704i 0.0378268 + 0.370571i
\(690\) −11.2406 + 19.4694i −0.427924 + 0.741186i
\(691\) 20.4420i 0.777651i −0.921311 0.388826i \(-0.872881\pi\)
0.921311 0.388826i \(-0.127119\pi\)
\(692\) 32.3680 56.0629i 1.23044 2.13119i
\(693\) 0 0
\(694\) 20.9477i 0.795164i
\(695\) −11.4537 6.61279i −0.434463 0.250837i
\(696\) 6.02174i 0.228253i
\(697\) 17.9719 + 10.3761i 0.680736 + 0.393023i
\(698\) 10.6187 18.3921i 0.401922 0.696150i
\(699\) −9.80099 + 16.9758i −0.370708 + 0.642084i
\(700\) 0 0
\(701\) −25.1373 −0.949422 −0.474711 0.880142i \(-0.657447\pi\)
−0.474711 + 0.880142i \(0.657447\pi\)
\(702\) −27.4256 37.9869i −1.03511 1.43372i
\(703\) −0.158933 + 0.275280i −0.00599427 + 0.0103824i
\(704\) 16.6803 9.63036i 0.628661 0.362958i
\(705\) 0.449429 0.0169265
\(706\) −2.48118 4.29753i −0.0933804 0.161740i
\(707\) 0 0
\(708\) −6.92112 + 3.99591i −0.260112 + 0.150176i
\(709\) −25.5416 14.7464i −0.959234 0.553814i −0.0632970 0.997995i \(-0.520162\pi\)
−0.895937 + 0.444181i \(0.853495\pi\)
\(710\) −24.0227 13.8695i −0.901556 0.520514i
\(711\) −9.66777 −0.362570
\(712\) −52.6360 −1.97262
\(713\) 53.2287 + 30.7316i 1.99343 + 1.15091i
\(714\) 0 0
\(715\) 0.466399 + 4.56908i 0.0174423 + 0.170874i
\(716\) 4.78127 + 8.28140i 0.178684 + 0.309491i
\(717\) 17.0536 9.84591i 0.636879 0.367702i
\(718\) −9.85518 17.0697i −0.367792 0.637034i
\(719\) 4.16576 7.21531i 0.155357 0.269086i −0.777832 0.628472i \(-0.783681\pi\)
0.933189 + 0.359386i \(0.117014\pi\)
\(720\) 0.220044i 0.00820055i
\(721\) 0 0
\(722\) 37.8946 21.8784i 1.41029 0.814231i
\(723\) −1.06435 + 0.614504i −0.0395837 + 0.0228537i
\(724\) −4.52143 −0.168038
\(725\) −2.91120 5.04235i −0.108119 0.187268i
\(726\) 29.6588i 1.10074i
\(727\) −9.66141 −0.358322 −0.179161 0.983820i \(-0.557338\pi\)
−0.179161 + 0.983820i \(0.557338\pi\)
\(728\) 0 0
\(729\) 29.7672 1.10249
\(730\) 13.1953i 0.488381i
\(731\) 9.59645 + 16.6215i 0.354938 + 0.614770i
\(732\) 22.0197 0.813870
\(733\) 12.1398 7.00894i 0.448395 0.258881i −0.258757 0.965942i \(-0.583313\pi\)
0.707152 + 0.707061i \(0.249980\pi\)
\(734\) −4.58425 + 2.64672i −0.169208 + 0.0976921i
\(735\) 0 0
\(736\) 41.3635i 1.52468i
\(737\) −1.53547 + 2.65951i −0.0565598 + 0.0979644i
\(738\) 9.56704 + 16.5706i 0.352168 + 0.609972i
\(739\) 33.6145 19.4073i 1.23653 0.713910i 0.268146 0.963378i \(-0.413589\pi\)
0.968383 + 0.249468i \(0.0802559\pi\)
\(740\) −9.38417 16.2539i −0.344969 0.597504i
\(741\) 0.147479 + 0.204271i 0.00541779 + 0.00750410i
\(742\) 0 0
\(743\) 29.7863 + 17.1971i 1.09275 + 0.630901i 0.934308 0.356467i \(-0.116019\pi\)
0.158445 + 0.987368i \(0.449352\pi\)
\(744\) −34.8142 −1.27635
\(745\) −5.39185 −0.197542
\(746\) −23.4742 13.5528i −0.859452 0.496205i
\(747\) −8.28434 4.78297i −0.303108 0.175000i
\(748\) −8.91346 + 5.14619i −0.325908 + 0.188163i
\(749\) 0 0
\(750\) −13.3445 23.1134i −0.487272 0.843980i
\(751\) −48.1470 −1.75691 −0.878454 0.477827i \(-0.841425\pi\)
−0.878454 + 0.477827i \(0.841425\pi\)
\(752\) 0.0976479 0.0563770i 0.00356085 0.00205586i
\(753\) −20.0908 + 34.7983i −0.732150 + 1.26812i
\(754\) −11.2334 + 1.14667i −0.409096 + 0.0417594i
\(755\) −0.562681 −0.0204781
\(756\) 0 0
\(757\) 3.45319 5.98110i 0.125508 0.217387i −0.796423 0.604740i \(-0.793277\pi\)
0.921931 + 0.387353i \(0.126611\pi\)
\(758\) 9.20262 15.9394i 0.334254 0.578945i
\(759\) −14.9986 8.65942i −0.544413 0.314317i
\(760\) 0.120789i 0.00438147i
\(761\) 27.6895 + 15.9865i 1.00374 + 0.579511i 0.909353 0.416025i \(-0.136577\pi\)
0.0943888 + 0.995535i \(0.469910\pi\)
\(762\) 53.2781i 1.93006i
\(763\) 0 0
\(764\) −2.50067 + 4.33129i −0.0904712 + 0.156701i
\(765\) 1.45533i 0.0526174i
\(766\) −32.5274 + 56.3391i −1.17526 + 2.03562i
\(767\) 3.46382 + 4.79769i 0.125071 + 0.173234i
\(768\) 13.2397 + 22.9319i 0.477748 + 0.827483i
\(769\) −12.4665 7.19752i −0.449553 0.259549i 0.258089 0.966121i \(-0.416907\pi\)
−0.707641 + 0.706572i \(0.750241\pi\)
\(770\) 0 0
\(771\) −4.82664 8.35999i −0.173827 0.301078i
\(772\) 19.9039 11.4915i 0.716357 0.413589i
\(773\) 37.2771i 1.34076i −0.742016 0.670382i \(-0.766130\pi\)
0.742016 0.670382i \(-0.233870\pi\)
\(774\) 17.6964i 0.636083i
\(775\) −29.1520 + 16.8309i −1.04717 + 0.604583i
\(776\) 0.640590 + 1.10953i 0.0229958 + 0.0398300i
\(777\) 0 0
\(778\) 15.3209 + 8.84553i 0.549281 + 0.317128i
\(779\) −0.237573 0.411489i −0.00851194 0.0147431i
\(780\) −14.7992 + 1.51067i −0.529897 + 0.0540905i
\(781\) 10.6846 18.5063i 0.382326 0.662208i