Properties

Label 637.2.q.i.491.1
Level $637$
Weight $2$
Character 637.491
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 491.1
Root \(1.21245 + 0.727987i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.i.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.99469 + 1.15163i) q^{2} +(-0.736680 - 1.27597i) q^{3} +(1.65252 - 2.86225i) q^{4} +0.847292i q^{5} +(2.93889 + 1.69677i) q^{6} +3.00585i q^{8} +(0.414604 - 0.718115i) q^{9} +O(q^{10})\) \(q+(-1.99469 + 1.15163i) q^{2} +(-0.736680 - 1.27597i) q^{3} +(1.65252 - 2.86225i) q^{4} +0.847292i 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} -4.86951 q^{12} +(2.92329 + 2.11054i) q^{13} +(1.08112 - 0.624183i) q^{15} +(-0.156597 - 0.271234i) q^{16} +(-1.03570 + 1.79389i) q^{17} +1.90989i q^{18} +(0.0410731 + 0.0237136i) q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} +(-3.90935 - 6.77119i) q^{23} +(3.83536 - 2.21435i) q^{24} +4.28210 q^{25} +(-8.26161 - 0.843323i) q^{26} -5.64180 q^{27} +(-0.679854 - 1.17754i) q^{29} +(-1.43766 + 2.49010i) q^{30} +7.86105i q^{31} +(-4.58156 - 2.64516i) q^{32} +(1.91829 + 1.10753i) q^{33} -4.77099i q^{34} +(-1.37028 - 2.37340i) q^{36} +(5.80427 - 3.35110i) q^{37} -0.109237 q^{38} +(0.539460 - 5.28482i) q^{39} -2.54683 q^{40} +(8.67622 - 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +4.96880i q^{44} +(0.608453 + 0.351290i) q^{45} +(15.5959 + 9.00428i) q^{46} -0.360014i q^{47} +(-0.230724 + 0.399625i) q^{48} +(-8.54144 + 4.93141i) q^{50} +3.05192 q^{51} +(10.8717 - 4.87945i) q^{52} +2.71181 q^{53} +(11.2536 - 6.49729i) q^{54} +(-0.636910 - 1.10316i) q^{55} -0.0698773i q^{57} +(2.71219 + 1.56588i) q^{58} +(1.42132 + 0.820598i) q^{59} -4.12590i q^{60} +(2.26097 - 3.91612i) q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(-1.78825 + 2.47688i) q^{65} -5.10186 q^{66} +(1.76900 - 1.02133i) q^{67} +(3.42303 + 5.92886i) q^{68} +(-5.75988 + 9.97641i) q^{69} +(12.3096 + 7.10697i) q^{71} +(2.15854 + 1.24624i) q^{72} -6.76150i q^{73} +(-7.71847 + 13.3688i) q^{74} +(-3.15454 - 5.46382i) q^{75} +(0.135748 - 0.0783743i) q^{76} +(5.01012 + 11.1628i) q^{78} +11.6590 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} +21.3413i q^{86} +(-1.00167 + 1.73494i) q^{87} +(-2.25950 - 3.91357i) q^{88} +(15.1652 - 8.75561i) q^{89} -1.61823 q^{90} -25.8411 q^{92} +(10.0304 - 5.79108i) q^{93} +(0.414604 + 0.718115i) q^{94} +(-0.0200923 + 0.0348009i) q^{95} +7.79456i q^{96} +(-0.369125 - 0.213115i) q^{97} +1.24663i 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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99469 + 1.15163i −1.41046 + 0.814328i −0.995431 0.0954820i \(-0.969561\pi\)
−0.415026 + 0.909810i \(0.636227\pi\)
\(3\) −0.736680 1.27597i −0.425323 0.736680i 0.571128 0.820861i \(-0.306506\pi\)
−0.996451 + 0.0841807i \(0.973173\pi\)
\(4\) 1.65252 2.86225i 0.826259 1.43112i
\(5\) 0.847292i 0.378920i 0.981888 + 0.189460i \(0.0606738\pi\)
−0.981888 + 0.189460i \(0.939326\pi\)
\(6\) 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 \(-0.739443\pi\)
0.290707 + 0.956812i \(0.406110\pi\)
\(12\) −4.86951 −1.40571
\(13\) 2.92329 + 2.11054i 0.810774 + 0.585360i
\(14\) 0 0
\(15\) 1.08112 0.624183i 0.279143 0.161163i
\(16\) −0.156597 0.271234i −0.0391492 0.0678085i
\(17\) −1.03570 + 1.79389i −0.251194 + 0.435081i −0.963855 0.266428i \(-0.914157\pi\)
0.712661 + 0.701509i \(0.247490\pi\)
\(18\) 1.90989i 0.450164i
\(19\) 0.0410731 + 0.0237136i 0.00942282 + 0.00544027i 0.504704 0.863292i \(-0.331602\pi\)
−0.495281 + 0.868733i \(0.664935\pi\)
\(20\) 2.42516 + 1.40016i 0.542282 + 0.313086i
\(21\) 0 0
\(22\) 1.73137 2.99882i 0.369129 0.639350i
\(23\) −3.90935 6.77119i −0.815156 1.41189i −0.909216 0.416325i \(-0.863318\pi\)
0.0940598 0.995567i \(-0.470016\pi\)
\(24\) 3.83536 2.21435i 0.782891 0.452002i
\(25\) 4.28210 0.856419
\(26\) −8.26161 0.843323i −1.62024 0.165389i
\(27\) −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
\(31\) 7.86105i 1.41189i 0.708269 + 0.705943i \(0.249477\pi\)
−0.708269 + 0.705943i \(0.750523\pi\)
\(32\) −4.58156 2.64516i −0.809912 0.467603i
\(33\) 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
\(37\) 5.80427 3.35110i 0.954216 0.550917i 0.0598278 0.998209i \(-0.480945\pi\)
0.894388 + 0.447292i \(0.147612\pi\)
\(38\) −0.109237 −0.0177206
\(39\) 0.539460 5.28482i 0.0863827 0.846248i
\(40\) −2.54683 −0.402689
\(41\) 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 \(-0.0830604\pi\)
\(44\) 4.96880i 0.749075i
\(45\) 0.608453 + 0.351290i 0.0907028 + 0.0523673i
\(46\) 15.5959 + 9.00428i 2.29948 + 1.32761i
\(47\) 0.360014i 0.0525134i −0.999655 0.0262567i \(-0.991641\pi\)
0.999655 0.0262567i \(-0.00835873\pi\)
\(48\) −0.230724 + 0.399625i −0.0333021 + 0.0576810i
\(49\) 0 0
\(50\) −8.54144 + 4.93141i −1.20794 + 0.697406i
\(51\) 3.05192 0.427355
\(52\) 10.8717 4.87945i 1.50763 0.676658i
\(53\) 2.71181 0.372496 0.186248 0.982503i \(-0.440367\pi\)
0.186248 + 0.982503i \(0.440367\pi\)
\(54\) 11.2536 6.49729i 1.53143 0.884169i
\(55\) −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
\(59\) 1.42132 + 0.820598i 0.185040 + 0.106833i 0.589658 0.807653i \(-0.299262\pi\)
−0.404619 + 0.914486i \(0.632596\pi\)
\(60\) 4.12590i 0.532651i
\(61\) 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
\(65\) −1.78825 + 2.47688i −0.221805 + 0.307219i
\(66\) −5.10186 −0.627995
\(67\) 1.76900 1.02133i 0.216117 0.124775i −0.388034 0.921645i \(-0.626846\pi\)
0.604151 + 0.796870i \(0.293512\pi\)
\(68\) 3.42303 + 5.92886i 0.415103 + 0.718980i
\(69\) −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
\(73\) 6.76150i 0.791373i −0.918386 0.395687i \(-0.870507\pi\)
0.918386 0.395687i \(-0.129493\pi\)
\(74\) −7.71847 + 13.3688i −0.897253 + 1.55409i
\(75\) −3.15454 5.46382i −0.364255 0.630907i
\(76\) 0.135748 0.0783743i 0.0155714 0.00899015i
\(77\) 0 0
\(78\) 5.01012 + 11.1628i 0.567284 + 1.26394i
\(79\) 11.6590 1.31175 0.655873 0.754871i \(-0.272301\pi\)
0.655873 + 0.754871i \(0.272301\pi\)
\(80\) 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
\(86\) 21.3413i 2.30129i
\(87\) −1.00167 + 1.73494i −0.107390 + 0.186006i
\(88\) −2.25950 3.91357i −0.240863 0.417188i
\(89\) 15.1652 8.75561i 1.60750 0.928093i 0.617577 0.786510i \(-0.288114\pi\)
0.989927 0.141582i \(-0.0452189\pi\)
\(90\) −1.61823 −0.170576
\(91\) 0 0
\(92\) −25.8411 −2.69412
\(93\) 10.0304 5.79108i 1.04011 0.600507i
\(94\) 0.414604 + 0.718115i 0.0427631 + 0.0740679i
\(95\) −0.0200923 + 0.0348009i −0.00206143 + 0.00357050i
\(96\) 7.79456i 0.795529i
\(97\) −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 0.518666 0.854977i \(-0.326429\pi\)
−0.999765 + 0.0216891i \(0.993096\pi\)
\(102\) −6.08763 + 3.51469i −0.602765 + 0.348007i
\(103\) −9.97823 −0.983185 −0.491592 0.870825i \(-0.663585\pi\)
−0.491592 + 0.870825i \(0.663585\pi\)
\(104\) −6.34397 + 8.78695i −0.622078 + 0.861631i
\(105\) 0 0
\(106\) −5.40922 + 3.12301i −0.525390 + 0.303334i
\(107\) −4.93111 8.54094i −0.476709 0.825684i 0.522935 0.852373i \(-0.324837\pi\)
−0.999644 + 0.0266888i \(0.991504\pi\)
\(108\) −9.32319 + 16.1482i −0.897124 + 1.55386i
\(109\) 11.6055i 1.11161i −0.831314 0.555803i \(-0.812411\pi\)
0.831314 0.555803i \(-0.187589\pi\)
\(110\) 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 \(0.114365\pi\)
\(114\) 0.0804731 + 0.139383i 0.00753699 + 0.0130545i
\(115\) 5.73718 3.31236i 0.534994 0.308879i
\(116\) −4.49388 −0.417247
\(117\) 2.72762 1.22422i 0.252168 0.113179i
\(118\) −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
\(122\) 10.4152i 0.942951i
\(123\) −12.7832 7.38039i −1.15262 0.665467i
\(124\) 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 \(-0.411957\pi\)
\(128\) −16.3917 + 9.46373i −1.44883 + 0.836483i
\(129\) −13.6517 −1.20196
\(130\) 0.714541 7.00000i 0.0626694 0.613940i
\(131\) 2.54517 0.222373 0.111186 0.993800i \(-0.464535\pi\)
0.111186 + 0.993800i \(0.464535\pi\)
\(132\) 6.34003 3.66042i 0.551829 0.318598i
\(133\) 0 0
\(134\) −2.35240 + 4.07447i −0.203216 + 0.351981i
\(135\) 4.78025i 0.411419i
\(136\) −5.39215 3.11316i −0.462373 0.266951i
\(137\) 1.61490 + 0.932362i 0.137970 + 0.0796571i 0.567396 0.823445i \(-0.307951\pi\)
−0.429426 + 0.903102i \(0.641284\pi\)
\(138\) 26.5331i 2.25865i
\(139\) 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
\(142\) −32.7385 −2.74735
\(143\) −5.39257 0.550459i −0.450949 0.0460317i
\(144\) −0.259703 −0.0216419
\(145\) 0.997721 0.576035i 0.0828562 0.0478371i
\(146\) 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 \(-0.417275\pi\)
−0.708457 + 0.705754i \(0.750608\pi\)
\(150\) 12.5846 + 7.26574i 1.02753 + 0.593245i
\(151\) 0.664094i 0.0540432i 0.999635 + 0.0270216i \(0.00860228\pi\)
−0.999635 + 0.0270216i \(0.991398\pi\)
\(152\) −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
\(156\) −14.2350 10.2773i −1.13971 0.822844i
\(157\) 16.5760 1.32291 0.661453 0.749986i \(-0.269940\pi\)
0.661453 + 0.749986i \(0.269940\pi\)
\(158\) −23.2562 + 13.4269i −1.85016 + 1.06819i
\(159\) −1.99774 3.46019i −0.158431 0.274411i
\(160\) 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 \(-0.448674\pi\)
−0.774517 + 0.632553i \(0.782007\pi\)
\(164\) 33.1113i 2.58556i
\(165\) −0.938398 + 1.62535i −0.0730542 + 0.126534i
\(166\) −13.2855 23.0112i −1.03116 1.78601i
\(167\) 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
\(170\) 4.04242 0.310039
\(171\) 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
\(177\) 2.41807i 0.181754i
\(178\) −20.1665 + 34.9294i −1.51154 + 2.61807i
\(179\) −1.44666 2.50569i −0.108129 0.187284i 0.806884 0.590711i \(-0.201152\pi\)
−0.915012 + 0.403426i \(0.867819\pi\)
\(180\) 2.01096 1.16103i 0.149888 0.0865379i
\(181\) 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
\(184\) 20.3532 11.7509i 1.50046 0.866289i
\(185\) 2.83936 + 4.91791i 0.208754 + 0.361572i
\(186\) −13.3384 + 23.1028i −0.978019 + 1.69398i
\(187\) 3.11415i 0.227729i
\(188\) −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 −0.267340 0.963602i \(-0.586145\pi\)
0.700834 + 0.713324i \(0.252811\pi\)
\(194\) 0.981719 0.0704834
\(195\) 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 \(0.519221\pi\)
\(198\) −1.43566 2.48664i −0.102028 0.176718i
\(199\) −3.30764 + 5.72901i −0.234473 + 0.406118i −0.959119 0.283002i \(-0.908670\pi\)
0.724647 + 0.689121i \(0.242003\pi\)
\(200\) 12.8713i 0.910140i
\(201\) −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
\(205\) 4.24427 + 7.35129i 0.296433 + 0.513436i
\(206\) 19.9035 11.4913i 1.38674 0.800634i
\(207\) −6.48333 −0.450622
\(208\) 0.114674 1.12340i 0.00795118 0.0778937i
\(209\) −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
\(213\) 20.9423i 1.43494i
\(214\) 19.6721 + 11.3577i 1.34475 + 0.776394i
\(215\) 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
\(219\) −8.62745 + 4.98106i −0.582989 + 0.336589i
\(220\) −4.21002 −0.283840
\(221\) −6.81373 + 3.05815i −0.458341 + 0.205713i
\(222\) 22.7442 1.52649
\(223\) −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
\(226\) 8.00979i 0.532804i
\(227\) −1.12220 0.647903i −0.0744831 0.0430029i 0.462296 0.886726i \(-0.347026\pi\)
−0.536779 + 0.843723i \(0.680359\pi\)
\(228\) −0.200006 0.115474i −0.0132457 0.00764742i
\(229\) 20.8175i 1.37566i 0.725871 + 0.687831i \(0.241437\pi\)
−0.725871 + 0.687831i \(0.758563\pi\)
\(230\) −7.62925 + 13.2142i −0.503058 + 0.871322i
\(231\) 0 0
\(232\) 3.53951 2.04354i 0.232380 0.134165i
\(233\) 13.3043 0.871591 0.435796 0.900046i \(-0.356467\pi\)
0.435796 + 0.900046i \(0.356467\pi\)
\(234\) −4.03090 + 5.58314i −0.263508 + 0.364981i
\(235\) 0.305037 0.0198984
\(236\) 4.69751 2.71211i 0.305782 0.176543i
\(237\) −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
\(241\) −0.722398 0.417076i −0.0465337 0.0268663i 0.476553 0.879146i \(-0.341886\pi\)
−0.523086 + 0.852280i \(0.675219\pi\)
\(242\) 20.1300i 1.29401i
\(243\) −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
\(247\) 0.0700199 + 0.156008i 0.00445526 + 0.00992657i
\(248\) −23.6291 −1.50045
\(249\) 14.7199 8.49852i 0.932834 0.538572i
\(250\) −9.05718 15.6875i −0.572827 0.992165i
\(251\) −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
\(255\) 2.58587i 0.161933i
\(256\) 8.98607 15.5643i 0.561630 0.972771i
\(257\) −3.27594 5.67409i −0.204348 0.353940i 0.745577 0.666419i \(-0.232174\pi\)
−0.949925 + 0.312479i \(0.898841\pi\)
\(258\) 27.2308 15.7217i 1.69532 0.978791i
\(259\) 0 0
\(260\) 4.13432 + 9.21148i 0.256399 + 0.571272i
\(261\) −1.12748 −0.0697893
\(262\) −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
\(268\) 6.75107i 0.412387i
\(269\) 8.00065 13.8575i 0.487808 0.844909i −0.512093 0.858930i \(-0.671130\pi\)
0.999902 + 0.0140210i \(0.00446317\pi\)
\(270\) 5.50510 + 9.53511i 0.335030 + 0.580288i
\(271\) −7.58582 + 4.37967i −0.460806 + 0.266046i −0.712383 0.701791i \(-0.752384\pi\)
0.251577 + 0.967837i \(0.419051\pi\)
\(272\) 0.648750 0.0393363
\(273\) 0 0
\(274\) −4.29496 −0.259468
\(275\) −5.57522 + 3.21886i −0.336199 + 0.194104i
\(276\) 19.0366 + 32.9724i 1.14587 + 1.98471i
\(277\) −9.95914 + 17.2497i −0.598387 + 1.03644i 0.394673 + 0.918822i \(0.370858\pi\)
−0.993059 + 0.117614i \(0.962475\pi\)
\(278\) 35.9522i 2.15627i
\(279\) 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 0.850585 0.525838i \(-0.176248\pi\)
−0.880681 + 0.473710i \(0.842915\pi\)
\(284\) 40.6838 23.4888i 2.41414 1.39380i
\(285\) 0.0592065 0.00350709
\(286\) 11.3904 5.11227i 0.673530 0.302295i
\(287\) 0 0
\(288\) −3.79906 + 2.19339i −0.223862 + 0.129247i
\(289\) 6.35465 + 11.0066i 0.373803 + 0.647446i
\(290\) −1.32676 + 2.29802i −0.0779101 + 0.134944i
\(291\) 0.627989i 0.0368134i
\(292\) −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
\(296\) 10.0729 + 17.4467i 0.585474 + 1.01407i
\(297\) 7.34554 4.24095i 0.426232 0.246085i
\(298\) 14.6571 0.849065
\(299\) 2.86276 28.0450i 0.165558 1.62188i
\(300\) −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
\(304\) 0.0148539i 0.000851930i
\(305\) 3.31809 + 1.91570i 0.189993 + 0.109693i
\(306\) −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
\(310\) 13.2858 7.67057i 0.754584 0.435659i
\(311\) 27.1009 1.53675 0.768376 0.639999i \(-0.221065\pi\)
0.768376 + 0.639999i \(0.221065\pi\)
\(312\) 15.8854 + 1.62153i 0.899331 + 0.0918013i
\(313\) 22.0785 1.24795 0.623975 0.781445i \(-0.285517\pi\)
0.623975 + 0.781445i \(0.285517\pi\)
\(314\) −33.0639 + 19.0894i −1.86590 + 1.07728i
\(315\) 0 0
\(316\) 19.2668 33.3711i 1.08384 1.87727i
\(317\) 7.06823i 0.396991i 0.980102 + 0.198496i \(0.0636056\pi\)
−0.980102 + 0.198496i \(0.936394\pi\)
\(318\) 7.96973 + 4.60133i 0.446920 + 0.258030i
\(319\) 1.77032 + 1.02209i 0.0991188 + 0.0572263i
\(320\) 10.8550i 0.606813i
\(321\) −7.26531 + 12.5839i −0.405510 + 0.702364i
\(322\) 0 0
\(323\) −0.0850789 + 0.0491204i −0.00473392 + 0.00273313i
\(324\) 19.2512 1.06951
\(325\) 12.5178 + 9.03756i 0.694362 + 0.501313i
\(326\) 20.8475 1.15464
\(327\) −14.8082 + 8.54955i −0.818898 + 0.472791i
\(328\) 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 \(-0.391290\pi\)
−0.648547 + 0.761175i \(0.724623\pi\)
\(332\) 33.0195 + 19.0638i 1.81218 + 1.04626i
\(333\) 5.55751i 0.304550i
\(334\) −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 \(0.536693\pi\)
\(338\) −22.3712 19.9018i −1.21683 1.08251i
\(339\) −5.12373 −0.278283
\(340\) −5.02347 + 2.90030i −0.272436 + 0.157291i
\(341\) −5.90916 10.2350i −0.319999 0.554254i
\(342\) −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
\(346\) 45.1142i 2.42535i
\(347\) 4.54739 7.87631i 0.244117 0.422822i −0.717766 0.696284i \(-0.754835\pi\)
0.961883 + 0.273462i \(0.0881687\pi\)
\(348\) 3.31056 + 5.73405i 0.177464 + 0.307378i
\(349\) −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
\(352\) 7.95349 0.423922
\(353\) 1.86584 1.07724i 0.0993087 0.0573359i −0.449523 0.893269i \(-0.648406\pi\)
0.548832 + 0.835933i \(0.315073\pi\)
\(354\) 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
\(359\) 8.55756i 0.451651i 0.974168 + 0.225825i \(0.0725079\pi\)
−0.974168 + 0.225825i \(0.927492\pi\)
\(360\) −1.05593 + 1.82892i −0.0556521 + 0.0963923i
\(361\) −9.49888 16.4525i −0.499941 0.865923i
\(362\) −2.72881 + 1.57548i −0.143423 + 0.0828055i
\(363\) 12.8769 0.675860
\(364\) 0 0
\(365\) 5.72896 0.299867
\(366\) 13.2895 7.67270i 0.694654 0.401059i
\(367\) 1.14912 + 1.99033i 0.0599833 + 0.103894i 0.894458 0.447153i \(-0.147562\pi\)
−0.834474 + 0.551047i \(0.814229\pi\)
\(368\) −1.22438 + 2.12070i −0.0638255 + 0.110549i
\(369\) 8.30736i 0.432464i
\(370\) −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
\(376\) 1.08215 0.0558074
\(377\) 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 \(0.399129\pi\)
\(380\) 0.0664059 + 0.115018i 0.00340655 + 0.00590032i
\(381\) −11.5658 + 20.0325i −0.592532 + 1.02630i
\(382\) 3.48542i 0.178329i
\(383\) −24.4605 14.1223i −1.24988 0.721616i −0.278791 0.960352i \(-0.589934\pi\)
−0.971084 + 0.238736i \(0.923267\pi\)
\(384\) 24.1508 + 13.9435i 1.23244 + 0.711551i
\(385\) 0 0
\(386\) −8.00839 + 13.8709i −0.407616 + 0.706012i
\(387\) −3.84158 6.65381i −0.195278 0.338232i
\(388\) −1.21997 + 0.704352i −0.0619347 + 0.0357580i
\(389\) −7.68086 −0.389435 −0.194717 0.980859i \(-0.562379\pi\)
−0.194717 + 0.980859i \(0.562379\pi\)
\(390\) −9.45816 + 4.24503i −0.478933 + 0.214955i
\(391\) 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
\(395\) 9.87862i 0.497047i
\(396\) 3.56817 + 2.06008i 0.179307 + 0.103523i
\(397\) 6.45433 + 3.72641i 0.323933 + 0.187023i 0.653144 0.757233i \(-0.273449\pi\)
−0.329211 + 0.944256i \(0.606783\pi\)
\(398\) 15.2368i 0.763750i
\(399\) 0 0
\(400\) −0.670563 1.16145i −0.0335282 0.0580725i
\(401\) 15.7601 9.09912i 0.787024 0.454389i −0.0518898 0.998653i \(-0.516524\pi\)
0.838914 + 0.544264i \(0.183191\pi\)
\(402\) 6.93186 0.345730
\(403\) −16.5911 + 22.9801i −0.826461 + 1.14472i
\(404\) −31.9596 −1.59005
\(405\) −4.27409 + 2.46765i −0.212381 + 0.122618i
\(406\) 0 0
\(407\) −5.03804 + 8.72615i −0.249727 + 0.432539i
\(408\) 9.17361i 0.454161i
\(409\) −25.3594 14.6413i −1.25394 0.723964i −0.282053 0.959399i \(-0.591015\pi\)
−0.971890 + 0.235435i \(0.924349\pi\)
\(410\) −16.9320 9.77568i −0.836211 0.482787i
\(411\) 2.74741i 0.135520i
\(412\) −16.4892 + 28.5602i −0.812365 + 1.40706i
\(413\) 0 0
\(414\) 12.9322 7.46641i 0.635583 0.366954i
\(415\) −9.77456 −0.479814
\(416\) −7.81047 17.4021i −0.382940 0.853210i
\(417\) −22.9980 −1.12622
\(418\) 0.142225 0.0821139i 0.00695647 0.00401632i
\(419\) −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
\(423\) −0.258531 0.149263i −0.0125702 0.00725742i
\(424\) 8.15130i 0.395862i
\(425\) −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
\(429\) 3.27023 + 7.28626i 0.157888 + 0.351784i
\(430\) −18.0823 −0.872006
\(431\) 18.3327 10.5844i 0.883055 0.509832i 0.0113906 0.999935i \(-0.496374\pi\)
0.871665 + 0.490103i \(0.163041\pi\)
\(432\) 0.883489 + 1.53025i 0.0425069 + 0.0736241i
\(433\) 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
\(437\) 0.370819i 0.0177387i
\(438\) 11.4727 19.8713i 0.548187 0.949488i
\(439\) 6.01919 + 10.4256i 0.287280 + 0.497584i 0.973160 0.230131i \(-0.0739155\pi\)
−0.685879 + 0.727715i \(0.740582\pi\)
\(440\) 3.31593 1.91445i 0.158081 0.0912680i
\(441\) 0 0
\(442\) 10.0694 13.9470i 0.478952 0.663390i
\(443\) 15.7331 0.747503 0.373752 0.927529i \(-0.378071\pi\)
0.373752 + 0.927529i \(0.378071\pi\)
\(444\) −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 \(0.456413\pi\)
\(450\) 8.17832i 0.385530i
\(451\) −7.53087 + 13.0438i −0.354615 + 0.614211i
\(452\) −5.74676 9.95369i −0.270305 0.468182i
\(453\) 0.847362 0.489225i 0.0398125 0.0229858i
\(454\) 2.98459 0.140074
\(455\) 0 0
\(456\) 0.210041 0.00983605
\(457\) −26.6700 + 15.3979i −1.24757 + 0.720284i −0.970624 0.240602i \(-0.922655\pi\)
−0.276945 + 0.960886i \(0.589322\pi\)
\(458\) −23.9742 41.5245i −1.12024 1.94031i
\(459\) 5.84322 10.1208i 0.272738 0.472396i
\(460\) 21.8949i 1.02086i
\(461\) 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
\(467\) 28.3524 1.31199 0.655996 0.754764i \(-0.272249\pi\)
0.655996 + 0.754764i \(0.272249\pi\)
\(468\) 1.00344 9.83015i 0.0463838 0.454399i
\(469\) 0 0
\(470\) −0.608453 + 0.351290i −0.0280658 + 0.0162038i
\(471\) −12.2112 21.1504i −0.562662 0.974559i
\(472\) −2.46659 + 4.27226i −0.113534 + 0.196647i
\(473\) 13.9300i 0.640503i
\(474\) 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
\(478\) 15.3918 + 26.6595i 0.704007 + 1.21938i
\(479\) 5.44077 3.14123i 0.248595 0.143526i −0.370526 0.928822i \(-0.620822\pi\)
0.619121 + 0.785296i \(0.287489\pi\)
\(480\) −6.60426 −0.301442
\(481\) 24.0402 + 2.45396i 1.09614 + 0.111891i
\(482\) 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
\(486\) 19.2171i 0.871703i
\(487\) 11.2736 + 6.50879i 0.510854 + 0.294942i 0.733185 0.680030i \(-0.238033\pi\)
−0.222331 + 0.974971i \(0.571366\pi\)
\(488\) 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 \(0.923246\pi\)
\(492\) −42.2490 + 24.3925i −1.90473 + 1.09970i
\(493\) 2.81650 0.126849
\(494\) −0.319332 0.230550i −0.0143674 0.0103730i
\(495\) −1.05626 −0.0474754
\(496\) 2.13218 1.23102i 0.0957378 0.0552743i
\(497\) 0 0
\(498\) −19.5744 + 33.9038i −0.877148 + 1.51926i
\(499\) 9.15340i 0.409763i −0.978787 0.204881i \(-0.934319\pi\)
0.978787 0.204881i \(-0.0656808\pi\)
\(500\) 22.5105 + 12.9965i 1.00670 + 0.581220i
\(501\) −3.39102 1.95781i −0.151500 0.0874684i
\(502\) 62.8149i 2.80357i
\(503\) 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
\(506\) −27.0741 −1.20359
\(507\) 12.7308 14.3105i 0.565396 0.635551i
\(508\) −51.8885 −2.30218
\(509\) −33.4811 + 19.3303i −1.48402 + 0.856800i −0.999835 0.0181646i \(-0.994218\pi\)
−0.484187 + 0.874965i \(0.660884\pi\)
\(510\) −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
\(514\) 13.0690 + 7.54536i 0.576447 + 0.332812i
\(515\) 8.45447i 0.372549i
\(516\) −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
\(520\) −7.44511 5.37520i −0.326490 0.235718i
\(521\) −40.2351 −1.76273 −0.881366 0.472434i \(-0.843375\pi\)
−0.881366 + 0.472434i \(0.843375\pi\)
\(522\) 2.24897 1.29844i 0.0984348 0.0568313i
\(523\) −0.366073 0.634057i −0.0160073 0.0277254i 0.857911 0.513799i \(-0.171762\pi\)
−0.873918 + 0.486073i \(0.838429\pi\)
\(524\) 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
\(528\) 0.693741i 0.0301912i
\(529\) −19.0660 + 33.0234i −0.828959 + 1.43580i
\(530\) −2.64610 4.58319i −0.114939 0.199081i
\(531\) 1.17857 0.680446i 0.0511455 0.0295288i
\(532\) 0 0
\(533\) 35.9353 + 3.66817i 1.55653 + 0.158886i
\(534\) 59.4251 2.57157
\(535\) 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
\(541\) 23.6537i 1.01695i 0.861076 + 0.508476i \(0.169791\pi\)
−0.861076 + 0.508476i \(0.830209\pi\)
\(542\) 10.0876 17.4722i 0.433298 0.750494i
\(543\) −1.00781 1.74558i −0.0432492 0.0749099i
\(544\) 9.49024 5.47919i 0.406891 0.234918i
\(545\) 9.83325 0.421210
\(546\) 0 0
\(547\) −12.9472 −0.553582 −0.276791 0.960930i \(-0.589271\pi\)
−0.276791 + 0.960930i \(0.589271\pi\)
\(548\) 5.33730 3.08149i 0.227998 0.131635i
\(549\) −1.87481 3.24727i −0.0800151 0.138590i
\(550\) 7.41388 12.8412i 0.316129 0.547552i
\(551\) 0.0644871i 0.00274724i
\(552\) −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 \(-0.710005\pi\)
0.377825 + 0.925877i \(0.376672\pi\)
\(558\) −15.0137 −0.635581
\(559\) 30.4787 13.6795i 1.28911 0.578582i
\(560\) 0 0
\(561\) −3.97355 + 2.29413i −0.167764 + 0.0968584i
\(562\) −16.1498 27.9723i −0.681239 1.17994i
\(563\) −3.66042 + 6.34004i −0.154268 + 0.267201i −0.932792 0.360414i \(-0.882635\pi\)
0.778524 + 0.627615i \(0.215969\pi\)
\(564\) 1.75309i 0.0738185i
\(565\) 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
\(569\) −2.15872 3.73901i −0.0904981 0.156747i 0.817223 0.576322i \(-0.195513\pi\)
−0.907721 + 0.419575i \(0.862179\pi\)
\(570\) −0.118098 + 0.0681842i −0.00494660 + 0.00285592i
\(571\) −34.1695 −1.42995 −0.714974 0.699152i \(-0.753561\pi\)
−0.714974 + 0.699152i \(0.753561\pi\)
\(572\) −10.4869 + 14.5252i −0.438478 + 0.607330i
\(573\) −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
\(577\) 6.35656i 0.264627i 0.991208 + 0.132314i \(0.0422406\pi\)
−0.991208 + 0.132314i \(0.957759\pi\)
\(578\) −25.3511 14.6364i −1.05447 0.608796i
\(579\) −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
\(583\) −3.53074 + 2.03847i −0.146228 + 0.0844249i
\(584\) 20.3240 0.841014
\(585\) 1.03727 + 2.31109i 0.0428857 + 0.0955518i
\(586\) −0.458892 −0.0189566
\(587\) −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
\(590\) 3.20286i 0.131860i
\(591\) 19.7484 + 11.4018i 0.812342 + 0.469006i
\(592\) −1.81786 1.04954i −0.0747136 0.0431359i
\(593\) 0.473013i 0.0194243i 0.999953 + 0.00971215i \(0.00309152\pi\)
−0.999953 + 0.00971215i \(0.996908\pi\)
\(594\) −9.76804 + 16.9187i −0.400787 + 0.694184i
\(595\) 0 0
\(596\) −18.2143 + 10.5160i −0.746086 + 0.430753i
\(597\) 9.74670 0.398906
\(598\) 26.5872 + 59.2378i 1.08723 + 2.42242i
\(599\) −9.62695 −0.393347 −0.196673 0.980469i \(-0.563014\pi\)
−0.196673 + 0.980469i \(0.563014\pi\)
\(600\) 16.4234 9.48206i 0.670483 0.387103i
\(601\) −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
\(605\) −6.41304 3.70257i −0.260727 0.150531i
\(606\) 32.8155i 1.33304i
\(607\) 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
\(611\) 0.759825 1.05242i 0.0307392 0.0425765i
\(612\) 5.67680 0.229471
\(613\) 32.9131 19.0024i 1.32935 0.767500i 0.344149 0.938915i \(-0.388167\pi\)
0.985199 + 0.171415i \(0.0548340\pi\)
\(614\) 31.3249 + 54.2563i 1.26417 + 2.18961i
\(615\) 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
\(619\) 44.4728i 1.78751i 0.448553 + 0.893756i \(0.351940\pi\)
−0.448553 + 0.893756i \(0.648060\pi\)
\(620\) −11.0068 + 19.0643i −0.442042 + 0.765640i
\(621\) 22.0558 + 38.2018i 0.885069 + 1.53298i
\(622\) −54.0579 + 31.2103i −2.16752 + 1.25142i
\(623\) 0 0
\(624\) −1.51790 + 0.681266i −0.0607646 + 0.0272725i
\(625\) 14.7468 0.589874
\(626\) −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 \(0.741825\pi\)
\(632\) 35.0453i 1.39403i
\(633\) 5.96290 10.3280i 0.237004 0.410503i
\(634\) −8.14001 14.0989i −0.323281 0.559939i
\(635\) 11.5202 6.65117i 0.457164 0.263944i
\(636\) −13.2052 −0.523620
\(637\) 0 0
\(638\) −4.70831 −0.186404
\(639\) 10.2072 5.89315i 0.403792 0.233129i
\(640\) −8.01854 13.8885i −0.316961 0.548992i
\(641\) 5.24342 9.08186i 0.207102 0.358712i −0.743698 0.668516i \(-0.766930\pi\)
0.950801 + 0.309804i \(0.100263\pi\)
\(642\) 33.4679i 1.32087i
\(643\) −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 0.999462 + 0.0327983i \(0.0104419\pi\)
−0.471327 + 0.881959i \(0.656225\pi\)
\(648\) −15.1627 + 8.75422i −0.595649 + 0.343898i
\(649\) −2.46738 −0.0968530
\(650\) −35.3770 3.61119i −1.38760 0.141643i
\(651\) 0 0
\(652\) −25.9070 + 14.9574i −1.01459 + 0.585776i
\(653\) 2.07081 + 3.58674i 0.0810369 + 0.140360i 0.903696 0.428176i \(-0.140844\pi\)
−0.822659 + 0.568536i \(0.807510\pi\)
\(654\) 19.6919 34.1073i 0.770014 1.33370i
\(655\) 2.15650i 0.0842615i
\(656\) −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 \(0.303896\pi\)
\(660\) 3.10144 + 5.37185i 0.120723 + 0.209099i
\(661\) −36.7084 + 21.1936i −1.42779 + 0.824335i −0.996946 0.0780909i \(-0.975118\pi\)
−0.430844 + 0.902426i \(0.641784\pi\)
\(662\) 15.1753 0.589803
\(663\) 8.92164 + 6.44122i 0.346488 + 0.250156i
\(664\) −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
\(668\) 8.78349i 0.339844i
\(669\) 20.4896 + 11.8297i 0.792173 + 0.457361i
\(670\) −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 \(-0.359809\pi\)
\(674\) 8.42336 4.86323i 0.324456 0.187324i
\(675\) −24.1588 −0.929871
\(676\) 42.0793 + 8.68114i 1.61844 + 0.333890i
\(677\) −32.1659 −1.23624 −0.618118 0.786085i \(-0.712105\pi\)
−0.618118 + 0.786085i \(0.712105\pi\)
\(678\) 10.2202 5.90066i 0.392506 0.226613i
\(679\) 0 0
\(680\) 2.63775 4.56872i 0.101153 0.175202i
\(681\) 1.90919i 0.0731604i
\(682\) 23.5738 + 13.6104i 0.902689 + 0.521168i
\(683\) 7.44986 + 4.30118i 0.285061 + 0.164580i 0.635712 0.771926i \(-0.280706\pi\)
−0.350651 + 0.936506i \(0.614040\pi\)
\(684\) 0.129977i 0.00496980i
\(685\) −0.789983 + 1.36829i −0.0301837 + 0.0522797i
\(686\) 0 0
\(687\) 26.5625 15.3359i 1.01342 0.585100i
\(688\) −2.90195 −0.110636
\(689\) 7.92740 + 5.72340i 0.302010 + 0.218044i
\(690\) 22.4813 0.855847
\(691\) 17.7033 10.2210i 0.673466 0.388826i −0.123923 0.992292i \(-0.539548\pi\)
0.797388 + 0.603466i \(0.206214\pi\)
\(692\) 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
\(696\) −5.21498 3.01087i −0.197673 0.114127i
\(697\) 20.7522i 0.786046i
\(698\) 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 \(0.657447\pi\)
\(702\) 46.6104 + 4.75787i 1.75920 + 0.179574i
\(703\) 0.317866 0.0119885
\(704\) −16.6803 + 9.63036i −0.628661 + 0.362958i
\(705\) −0.224715 0.389217i −0.00846324 0.0146588i
\(706\) −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 \(-0.146505\pi\)
0.0632970 + 0.997995i \(0.479838\pi\)
\(710\) 27.7390i 1.04103i
\(711\) 4.83389 8.37254i 0.181285 0.313995i
\(712\) 26.3180 + 45.5841i 0.986309 + 1.70834i
\(713\) 53.2287 30.7316i 1.99343 1.15091i
\(714\) 0 0
\(715\) 0.466399 4.56908i 0.0174423 0.170874i
\(716\) −9.56254 −0.357369
\(717\) −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
\(723\) 1.22901i 0.0457073i
\(724\) 2.26071 3.91567i 0.0840188 0.145525i
\(725\) −2.91120 5.04235i −0.108119 0.187268i
\(726\) −25.6853 + 14.8294i −0.953271 + 0.550371i
\(727\) −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
\(730\) −11.4275 + 6.59766i −0.422950 + 0.244190i
\(731\) 9.59645 + 16.6215i 0.354938 + 0.614770i
\(732\) −11.0098 + 19.0696i −0.406935 + 0.704832i
\(733\) 14.0179i 0.517762i −0.965909 0.258881i \(-0.916646\pi\)
0.965909 0.258881i \(-0.0833538\pi\)
\(734\) −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 \(-0.919744\pi\)
−0.268146 + 0.963378i \(0.586411\pi\)
\(740\) 18.7683 0.689938
\(741\) 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 \(0.116019\pi\)
\(744\) 17.4071 + 30.1500i 0.638175 + 1.10535i
\(745\) 2.69592 4.66948i 0.0987710 0.171076i
\(746\) 27.1057i 0.992410i
\(747\) 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
\(751\) 24.0735 + 41.6965i 0.878454 + 1.52153i 0.853037 + 0.521850i \(0.174758\pi\)
0.0254165 + 0.999677i \(0.491909\pi\)
\(752\) −0.0976479 + 0.0563770i −0.00356085 + 0.00205586i
\(753\) 40.1816 1.46430
\(754\) 4.62364 + 10.3017i 0.168383 + 0.375167i
\(755\) −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
\(759\) 17.3188i 0.628634i
\(760\) −0.104606 0.0603945i −0.00379447 0.00219074i
\(761\) −27.6895 15.9865i −1.00374 0.579511i −0.0943888 0.995535i \(-0.530090\pi\)
−0.909353 + 0.416025i \(0.863423\pi\)
\(762\) 53.2781i 1.93006i
\(763\) 0 0
\(764\) −2.50067 4.33129i −0.0904712 0.156701i
\(765\) −1.26035 + 0.727663i −0.0455680 + 0.0263087i
\(766\) 65.0548 2.35053
\(767\) 2.42301 + 5.39860i 0.0874898 + 0.194932i
\(768\) −26.4795 −0.955495
\(769\) −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
\(772\) 22.9830i 0.827177i
\(773\) −32.2829 18.6385i −1.16114 0.670382i −0.209560 0.977796i \(-0.567203\pi\)
−0.951576 + 0.307414i \(0.900536\pi\)
\(774\) 15.3255 + 8.84818i 0.550864 + 0.318041i
\(775\) 33.6618i 1.20917i
\(776\) 0.640590 1.10953i 0.0229958 0.0398300i
\(777\) 0 0
\(778\) 15.3209 8.84553i 0.549281 0.317128i
\(779\) 0.475146 0.0170239
\(780\) 8.70789 12.0612i 0.311792 0.431859i
\(781\) −21.3693 −0.764652
\(7