Properties

Label 637.2.k.i.569.1
Level $637$
Weight $2$
Character 637.569
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 569.1
Root \(1.21245 - 0.727987i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.i.459.6

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30327i 1.62866i −0.580405 0.814328i \(-0.697106\pi\)
0.580405 0.814328i \(-0.302894\pi\)
\(3\) −0.736680 + 1.27597i −0.425323 + 0.736680i −0.996451 0.0841807i \(-0.973173\pi\)
0.571128 + 0.820861i \(0.306506\pi\)
\(4\) −3.30504 −1.65252
\(5\) −0.733776 0.423646i −0.328155 0.189460i 0.326867 0.945070i \(-0.394007\pi\)
−0.655022 + 0.755610i \(0.727340\pi\)
\(6\) 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 0.683270 0.730166i \(-0.260557\pi\)
−0.290707 + 0.956812i \(0.593890\pi\)
\(12\) 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 −0.504704 0.863292i \(-0.668398\pi\)
0.495281 + 0.868733i \(0.335065\pi\)
\(20\) 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 0.795973 0.605331i \(-0.206959\pi\)
−0.922219 + 0.386668i \(0.873626\pi\)
\(30\) −1.43766 2.49010i −0.262480 0.454628i
\(31\) 6.80787 3.93052i 1.22273 0.705943i 0.257230 0.966350i \(-0.417190\pi\)
0.965499 + 0.260407i \(0.0838567\pi\)
\(32\) 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 \(0.185722\pi\)
−0.834560 + 0.550917i \(0.814278\pi\)
\(38\) 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 0.366054 0.930594i \(-0.380709\pi\)
0.988945 + 0.148285i \(0.0473754\pi\)
\(42\) 0 0
\(43\) 4.63283 8.02430i 0.706500 1.22369i −0.259647 0.965704i \(-0.583606\pi\)
0.966147 0.257991i \(-0.0830604\pi\)
\(44\) −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 0.522567 0.852598i \(-0.324975\pi\)
−0.477089 + 0.878855i \(0.658308\pi\)
\(48\) −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 0.757748 0.652547i \(-0.226299\pi\)
−0.943996 + 0.329956i \(0.892966\pi\)
\(54\) 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 \(-0.965929\pi\)
0.994277 0.106833i \(-0.0340709\pi\)
\(60\) −3.57313 + 2.06295i −0.461289 + 0.266325i
\(61\) 2.26097 + 3.91612i 0.289488 + 0.501407i 0.973688 0.227887i \(-0.0731817\pi\)
−0.684200 + 0.729295i \(0.739848\pi\)
\(62\) −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 0.388034 0.921645i \(-0.373154\pi\)
−0.604151 + 0.796870i \(0.706488\pi\)
\(68\) −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 0.999052 0.0435255i \(-0.0138590\pi\)
0.461832 + 0.886967i \(0.347192\pi\)
\(72\) −2.15854 + 1.24624i −0.254387 + 0.146870i
\(73\) −5.85563 + 3.38075i −0.685349 + 0.395687i −0.801867 0.597502i \(-0.796160\pi\)
0.116518 + 0.993189i \(0.462827\pi\)
\(74\) 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 0.325801 + 0.945438i \(0.394366\pi\)
−0.981674 + 0.190567i \(0.938967\pi\)
\(80\) −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 \(0.218232\pi\)
−0.774043 + 0.633133i \(0.781768\pi\)
\(84\) 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 \(0.378552\pi\)
−0.372350 + 0.928093i \(0.621448\pi\)
\(90\) −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 0.481143 0.876642i \(-0.340222\pi\)
−0.518622 + 0.855003i \(0.673555\pi\)
\(98\) 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 −0.999765 0.0216891i \(-0.993096\pi\)
0.518666 + 0.854977i \(0.326429\pi\)
\(102\) 6.08763 + 3.51469i 0.602765 + 0.348007i
\(103\) 4.98912 8.64140i 0.491592 0.851463i −0.508361 0.861144i \(-0.669748\pi\)
0.999953 + 0.00968129i \(0.00308170\pi\)
\(104\) −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 −0.896996 0.442038i \(-0.854256\pi\)
−0.0656822 + 0.997841i \(0.520922\pi\)
\(110\) −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 −0.772576 0.634923i \(-0.781032\pi\)
0.936147 + 0.351609i \(0.114365\pi\)
\(114\) −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 −0.969649 0.244499i \(-0.921376\pi\)
0.273082 0.961991i \(-0.411957\pi\)
\(128\) 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 −0.916249 0.400610i \(-0.868798\pi\)
0.805063 + 0.593190i \(0.202132\pi\)
\(132\) 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 \(-0.974617\pi\)
0.996822 0.0796571i \(-0.0253825\pi\)
\(138\) 22.9783 + 13.2665i 1.95605 + 1.12932i
\(139\) 7.80462 13.5180i 0.661979 1.14658i −0.318116 0.948052i \(-0.603050\pi\)
0.980095 0.198530i \(-0.0636166\pi\)
\(140\) 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 −0.256973 0.966419i \(-0.582725\pi\)
0.708457 + 0.705754i \(0.249392\pi\)
\(150\) 14.5315i 1.18649i
\(151\) 0.575122 0.332047i 0.0468028 0.0270216i −0.476416 0.879220i \(-0.658064\pi\)
0.523219 + 0.852198i \(0.324731\pi\)
\(152\) −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 −0.980234 0.197842i \(-0.936607\pi\)
0.318781 0.947828i \(-0.396727\pi\)
\(158\) 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 −0.160548 0.987028i \(-0.551326\pi\)
0.774517 + 0.632553i \(0.217993\pi\)
\(164\) −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 −0.408300 0.912848i \(-0.633878\pi\)
0.586400 + 0.810022i \(0.300545\pi\)
\(168\) 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 −0.950387 0.311070i \(-0.899313\pi\)
0.205799 0.978594i \(-0.434021\pi\)
\(174\) 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 −0.915012 0.403426i \(-0.867819\pi\)
0.806884 + 0.590711i \(0.201152\pi\)
\(180\) 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 0.892100 0.451837i \(-0.149231\pi\)
−0.837353 + 0.546663i \(0.815898\pi\)
\(192\) −9.43792 + 16.3470i −0.681123 + 1.17974i
\(193\) −6.02229 3.47697i −0.433494 0.250278i 0.267340 0.963602i \(-0.413855\pi\)
−0.700834 + 0.713324i \(0.747189\pi\)
\(194\) −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 −0.894622 0.446825i \(-0.852555\pi\)
−0.0603494 + 0.998177i \(0.519221\pi\)
\(198\) 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 0.971041 0.238912i \(-0.0767907\pi\)
−0.692424 + 0.721490i \(0.743457\pi\)
\(212\) 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 −0.887210 0.461366i \(-0.847360\pi\)
−0.0440506 + 0.999029i \(0.514026\pi\)
\(224\) 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 \(0.0136925\pi\)
−0.999075 + 0.0430029i \(0.986308\pi\)
\(228\) 0.230947i 0.0152948i
\(229\) −18.0285 10.4088i −1.19136 0.687831i −0.232743 0.972538i \(-0.574770\pi\)
−0.958614 + 0.284707i \(0.908104\pi\)
\(230\) −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 −0.997360 0.0726127i \(-0.976866\pi\)
0.561565 + 0.827433i \(0.310200\pi\)
\(234\) 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 \(-0.857715\pi\)
0.901748 0.432263i \(-0.142285\pi\)
\(240\) 0.338599 0.195490i 0.0218565 0.0126188i
\(241\) 0.834153i 0.0537325i 0.999639 + 0.0268663i \(0.00855282\pi\)
−0.999639 + 0.0268663i \(0.991447\pi\)
\(242\) −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 0.0105555 + 0.999944i \(0.496640\pi\)
−0.871255 + 0.490831i \(0.836693\pi\)
\(252\) 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 −0.273239 0.961946i \(-0.588095\pi\)
0.969689 0.244341i \(-0.0785717\pi\)
\(264\) −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 \(-0.914283\pi\)
0.963960 0.266046i \(-0.0857174\pi\)
\(272\) 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 \(0.137368\pi\)
−0.908317 + 0.418283i \(0.862632\pi\)
\(282\) 0.610861 + 1.05804i 0.0363762 + 0.0630055i
\(283\) −0.506295 + 0.876929i −0.0300961 + 0.0521280i −0.880681 0.473710i \(-0.842915\pi\)
0.850585 + 0.525838i \(0.176248\pi\)
\(284\) −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 0.505032 0.863101i \(-0.331481\pi\)
−0.494952 + 0.868921i \(0.664814\pi\)
\(294\) 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 \(-0.717143\pi\)
0.630482 0.776204i \(-0.282857\pi\)
\(308\) 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 −0.938443 0.345434i \(-0.887732\pi\)
0.170067 0.985432i \(-0.445602\pi\)
\(312\) −6.53839 14.5679i −0.370163 0.824744i
\(313\) −11.0392 + 19.1205i −0.623975 + 1.08076i 0.364763 + 0.931100i \(0.381150\pi\)
−0.988738 + 0.149656i \(0.952183\pi\)
\(314\) −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 0.318149 0.948041i \(-0.396939\pi\)
−0.661953 + 0.749545i \(0.730272\pi\)
\(318\) 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 −0.334923 0.942245i \(-0.608710\pi\)
0.648547 + 0.761175i \(0.275377\pi\)
\(332\) 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 −0.698255 0.715849i \(-0.746040\pi\)
0.270816 + 0.962631i \(0.412706\pi\)
\(350\) 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 0.449523 0.893269i \(-0.351594\pi\)
−0.548832 + 0.835933i \(0.684927\pi\)
\(354\) 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 0.291513 0.956567i \(-0.405841\pi\)
−0.682654 + 0.730741i \(0.739175\pi\)
\(360\) 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 −0.834474 0.551047i \(-0.814229\pi\)
0.894458 + 0.447153i \(0.147562\pi\)
\(368\) 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 0.672517 0.740082i \(-0.265213\pi\)
−0.977188 + 0.212375i \(0.931880\pi\)
\(374\) 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 −0.667094 0.744974i \(-0.732462\pi\)
0.311619 + 0.950207i \(0.399129\pi\)
\(380\) −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 0.278791 0.960352i \(-0.410066\pi\)
0.971084 + 0.238736i \(0.0767331\pi\)
\(384\) 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 0.946808 0.321799i \(-0.104288\pi\)
−0.752090 + 0.659060i \(0.770954\pi\)
\(390\) 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 −0.653144 0.757233i \(-0.726551\pi\)
0.329211 + 0.944256i \(0.393217\pi\)
\(398\) 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 \(0.150142\pi\)
−0.890804 + 0.454389i \(0.849858\pi\)
\(402\) −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 \(0.257682\pi\)
−0.689838 + 0.723964i \(0.742318\pi\)
\(410\) 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 −0.999971 0.00762733i \(-0.997572\pi\)
0.493380 0.869814i \(-0.335761\pi\)
\(420\) 0 0
\(421\) 24.8696i 1.21207i 0.795437 + 0.606036i \(0.207241\pi\)
−0.795437 + 0.606036i \(0.792759\pi\)
\(422\) 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 −0.0113906 0.999935i \(-0.503626\pi\)
−0.871665 + 0.490103i \(0.836959\pi\)
\(432\) −1.76698 −0.0850138
\(433\) 11.7148 20.2906i 0.562977 0.975105i −0.434258 0.900789i \(-0.642989\pi\)
0.997235 0.0743163i \(-0.0236774\pi\)
\(434\) 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 −0.990139 0.140086i \(-0.955262\pi\)
0.616388 + 0.787443i \(0.288595\pi\)
\(444\) 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 0.926171 0.377104i \(-0.123080\pi\)
0.136504 + 0.990640i \(0.456413\pi\)
\(450\) −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 \(-0.744011\pi\)
0.693679 0.720284i \(-0.255989\pi\)
\(458\) −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 0.991583 0.129472i \(-0.0413284\pi\)
0.383665 + 0.923472i \(0.374662\pi\)
\(462\) 0 0
\(463\) 1.69184i 0.0786263i −0.999227 0.0393131i \(-0.987483\pi\)
0.999227 0.0393131i \(-0.0125170\pi\)
\(464\) −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 0.325647 + 0.945491i \(0.394418\pi\)
−0.981643 + 0.190727i \(0.938916\pi\)
\(468\) 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 0.370526 0.928822i \(-0.379178\pi\)
−0.619121 + 0.785296i \(0.712511\pi\)
\(480\) 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 \(-0.904700\pi\)
0.955515 0.294942i \(-0.0953002\pi\)
\(488\) −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 0.692342 0.721569i \(-0.256579\pi\)
−0.971068 + 0.238801i \(0.923246\pi\)
\(492\) 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 0.666826 0.745214i \(-0.267652\pi\)
−0.311961 + 0.950095i \(0.600986\pi\)
\(500\) 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 −0.498302 0.867003i \(-0.666043\pi\)
0.999998 0.00195935i \(-0.000623680\pi\)
\(504\) 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 \(-0.672449\pi\)
0.515649 0.856800i \(-0.327551\pi\)
\(510\) −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 0.849823 + 0.527068i \(0.176709\pi\)
0.0315430 + 0.999502i \(0.489958\pi\)
\(522\) −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 −0.00981448 0.999952i \(-0.503124\pi\)
−0.870891 + 0.491476i \(0.836457\pi\)
\(542\) −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 0.612921 0.790145i \(-0.289995\pi\)
−0.377825 + 0.925877i \(0.623328\pi\)
\(558\) 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 0.962970 + 0.269610i \(0.0868946\pi\)
−0.247996 + 0.968761i \(0.579772\pi\)
\(572\) −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 −0.381017 0.924568i \(-0.624426\pi\)
0.610191 + 0.792254i \(0.291093\pi\)
\(578\) 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 −0.942118 0.335283i \(-0.891168\pi\)
−0.180695 + 0.983539i \(0.557835\pi\)
\(588\) 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 0.491565 0.870841i \(-0.336425\pi\)
−0.508387 + 0.861128i \(0.669758\pi\)
\(594\) −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 0.947448 0.319910i \(-0.103653\pi\)
−0.750774 + 0.660559i \(0.770320\pi\)
\(600\) 18.9641i 0.774207i
\(601\) −20.5399 35.5762i −0.837842 1.45118i −0.891696 0.452635i \(-0.850484\pi\)
0.0538542 0.998549i \(-0.482849\pi\)
\(602\) 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 0.992090 0.125529i \(-0.0400627\pi\)
−0.604756 + 0.796411i \(0.706729\pi\)
\(608\) −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 −0.344149 0.938915i \(-0.611833\pi\)
−0.985199 + 0.171415i \(0.945166\pi\)
\(614\) −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 0.637900 0.770119i \(-0.279803\pi\)
−0.347992 + 0.937497i \(0.613136\pi\)
\(618\) 29.3250 16.9308i 1.17962 0.681056i
\(619\) 38.5146 22.2364i 1.54803 0.893756i 0.549739 0.835336i \(-0.314727\pi\)
0.998292 0.0584199i \(-0.0186062\pi\)
\(620\) 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 0.283539 0.958961i \(-0.408492\pi\)
−0.688715 + 0.725032i \(0.741825\pi\)
\(632\) −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 −0.140635 0.990061i \(-0.544915\pi\)
−0.927736 + 0.373237i \(0.878248\pi\)
\(644\) 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 −0.471327 0.881959i \(-0.656225\pi\)
0.999462 0.0327983i \(-0.0104419\pi\)
\(648\) 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 −0.995727 0.0923492i \(-0.970562\pi\)
0.577840 + 0.816150i \(0.303896\pi\)
\(660\) −6.20288 −0.241447
\(661\) 36.7084 + 21.1936i 1.42779 + 0.824335i 0.996946 0.0780909i \(-0.0248824\pi\)
0.430844 + 0.902426i \(0.358216\pi\)
\(662\) −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 −0.996543 0.0830790i \(-0.973525\pi\)
0.426323 0.904571i \(-0.359809\pi\)
\(674\) 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 −0.371711 0.928349i \(-0.621229\pi\)
0.989829 0.142263i \(-0.0454380\pi\)
\(678\) 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 \(-0.947373\pi\)
0.986364 0.164580i \(-0.0526269\pi\)
\(684\) 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 \(0.127119\pi\)
−0.921311 + 0.388826i \(0.872881\pi\)
\(692\) 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 −0.895937 0.444181i \(-0.853495\pi\)
−0.0632970 + 0.997995i \(0.520162\pi\)
\(710\) −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 0.933189 0.359386i \(-0.117014\pi\)
−0.777832 + 0.628472i \(0.783681\pi\)
\(720\) 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 0.707152 0.707061i \(-0.249980\pi\)
−0.258757 + 0.965942i \(0.583313\pi\)
\(734\) −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 0.968383 0.249468i \(-0.0802559\pi\)
0.268146 + 0.963378i \(0.413589\pi\)
\(740\) −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 0.158445 0.987368i \(-0.449352\pi\)
0.934308 + 0.356467i \(0.116019\pi\)
\(744\) −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 0.921931 0.387353i \(-0.126611\pi\)
−0.796423 + 0.604740i \(0.793277\pi\)
\(758\) 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 0.0943888 0.995535i \(-0.469910\pi\)
0.909353 + 0.416025i \(0.136577\pi\)
\(762\) 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 −0.707641 0.706572i \(-0.750241\pi\)
0.258089 + 0.966121i \(0.416907\pi\)
\(770\) 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 \(0.233870\pi\)
−0.742016 + 0.670382i \(0.766130\pi\)
\(774\) 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