Properties

Label 637.2.q.g.589.1
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 589.1
Root \(1.21245 - 0.727987i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.g.491.1

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99469 1.15163i −1.41046 0.814328i −0.415026 0.909810i \(-0.636227\pi\)
−0.995431 + 0.0954820i \(0.969561\pi\)
\(3\) 0.736680 1.27597i 0.425323 0.736680i −0.571128 0.820861i \(-0.693494\pi\)
0.996451 + 0.0841807i \(0.0268273\pi\)
\(4\) 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 0.290707 0.956812i \(-0.406110\pi\)
−0.683270 + 0.730166i \(0.739443\pi\)
\(12\) 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 \(-0.0858434\pi\)
−0.712661 + 0.701509i \(0.752510\pi\)
\(18\) 1.90989i 0.450164i
\(19\) −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
\(23\) −3.90935 + 6.77119i −0.815156 + 1.41189i 0.0940598 + 0.995567i \(0.470016\pi\)
−0.909216 + 0.416325i \(0.863318\pi\)
\(24\) −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 −0.922219 0.386668i \(-0.873626\pi\)
0.795973 + 0.605331i \(0.206959\pi\)
\(30\) −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 0.894388 0.447292i \(-0.147612\pi\)
0.0598278 + 0.998209i \(0.480945\pi\)
\(38\) 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 \(-0.619291\pi\)
−0.988945 + 0.148285i \(0.952625\pi\)
\(42\) 0 0
\(43\) 4.63283 + 8.02430i 0.706500 + 1.22369i 0.966147 + 0.257991i \(0.0830604\pi\)
−0.259647 + 0.965704i \(0.583606\pi\)
\(44\) 4.96880i 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 \(-0.700738\pi\)
0.404619 + 0.914486i \(0.367404\pi\)
\(60\) 4.12590i 0.532651i
\(61\) −2.26097 3.91612i −0.289488 0.501407i 0.684200 0.729295i \(-0.260152\pi\)
−0.973688 + 0.227887i \(0.926818\pi\)
\(62\) 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 0.604151 0.796870i \(-0.293512\pi\)
−0.388034 + 0.921645i \(0.626846\pi\)
\(68\) −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 0.461832 0.886967i \(-0.347192\pi\)
0.999052 + 0.0435255i \(0.0138590\pi\)
\(72\) 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 −0.989927 0.141582i \(-0.954781\pi\)
−0.617577 0.786510i \(-0.711886\pi\)
\(90\) 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 \(-0.659778\pi\)
0.518622 + 0.855003i \(0.326445\pi\)
\(98\) 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 \(-0.673571\pi\)
0.999765 + 0.0216891i \(0.00690441\pi\)
\(102\) −6.08763 3.51469i −0.602765 0.348007i
\(103\) 9.97823 0.983185 0.491592 0.870825i \(-0.336415\pi\)
0.491592 + 0.870825i \(0.336415\pi\)
\(104\) 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 −0.999644 0.0266888i \(-0.991504\pi\)
0.522935 + 0.852373i \(0.324837\pi\)
\(108\) 9.32319 + 16.1482i 0.897124 + 1.55386i
\(109\) 11.6055i 1.11161i 0.831314 + 0.555803i \(0.187589\pi\)
−0.831314 + 0.555803i \(0.812411\pi\)
\(110\) −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 \(0.781032\pi\)
\(114\) 0.0804731 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 0.273082 + 0.961991i \(0.411957\pi\)
−0.969649 + 0.244499i \(0.921376\pi\)
\(128\) −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 \(-0.535465\pi\)
−0.111186 + 0.993800i \(0.535465\pi\)
\(132\) −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 −0.429426 0.903102i \(-0.641284\pi\)
0.567396 + 0.823445i \(0.307951\pi\)
\(138\) 26.5331i 2.25865i
\(139\) −7.80462 13.5180i −0.661979 1.14658i −0.980095 0.198530i \(-0.936383\pi\)
0.318116 0.948052i \(-0.396950\pi\)
\(140\) 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 −0.708457 0.705754i \(-0.750608\pi\)
0.256973 + 0.966419i \(0.417275\pi\)
\(150\) −12.5846 + 7.26574i −1.02753 + 0.593245i
\(151\) 0.664094i 0.0540432i −0.999635 0.0270216i \(-0.991398\pi\)
0.999635 0.0270216i \(-0.00860228\pi\)
\(152\) 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 \(-0.730060\pi\)
−0.661453 + 0.749986i \(0.730060\pi\)
\(158\) −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 −0.774517 0.632553i \(-0.782007\pi\)
0.160548 + 0.987028i \(0.448674\pi\)
\(164\) 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 \(-0.366122\pi\)
−0.586400 + 0.810022i \(0.699455\pi\)
\(168\) 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 0.950387 + 0.311070i \(0.100687\pi\)
−0.205799 + 0.978594i \(0.565979\pi\)
\(174\) 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 −0.915012 0.403426i \(-0.867819\pi\)
0.806884 + 0.590711i \(0.201152\pi\)
\(180\) −2.01096 1.16103i −0.149888 0.0865379i
\(181\) −1.36804 −0.101686 −0.0508429 0.998707i \(-0.516191\pi\)
−0.0508429 + 0.998707i \(0.516191\pi\)
\(182\) 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 0.892100 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 0.700834 0.713324i \(-0.252811\pi\)
−0.267340 + 0.963602i \(0.586145\pi\)
\(194\) −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 −0.0603494 0.998177i \(-0.519221\pi\)
−0.894622 + 0.446825i \(0.852555\pi\)
\(198\) −1.43566 + 2.48664i −0.102028 + 0.176718i
\(199\) 3.30764 + 5.72901i 0.234473 + 0.406118i 0.959119 0.283002i \(-0.0913304\pi\)
−0.724647 + 0.689121i \(0.757997\pi\)
\(200\) 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 −0.692424 0.721490i \(-0.743457\pi\)
0.971041 + 0.238912i \(0.0767907\pi\)
\(212\) 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 \(-0.152640\pi\)
0.0440506 + 0.999029i \(0.485974\pi\)
\(224\) 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 \(-0.652974\pi\)
0.536779 + 0.843723i \(0.319641\pi\)
\(228\) −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 \(0.142285\pi\)
−0.901748 + 0.432263i \(0.857715\pi\)
\(240\) −0.338599 + 0.195490i −0.0218565 + 0.0126188i
\(241\) 0.722398 0.417076i 0.0465337 0.0268663i −0.476553 0.879146i \(-0.658114\pi\)
0.523086 + 0.852280i \(0.324781\pi\)
\(242\) 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 0.871255 + 0.490831i \(0.163307\pi\)
−0.0105555 + 0.999944i \(0.503360\pi\)
\(252\) 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 \(-0.767826\pi\)
0.949925 + 0.312479i \(0.101159\pi\)
\(258\) −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 −0.273239 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
\(268\) 6.75107i 0.412387i
\(269\) −8.00065 13.8575i −0.487808 0.844909i 0.512093 0.858930i \(-0.328870\pi\)
−0.999902 + 0.0140210i \(0.995537\pi\)
\(270\) 5.50510 9.53511i 0.335030 0.580288i
\(271\) 7.58582 + 4.37967i 0.460806 + 0.266046i 0.712383 0.701791i \(-0.247616\pi\)
−0.251577 + 0.967837i \(0.580949\pi\)
\(272\) −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 −0.993059 0.117614i \(-0.962475\pi\)
0.394673 0.918822i \(-0.370858\pi\)
\(278\) 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 \(-0.862632\pi\)
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 \(-0.823752\pi\)
0.880681 + 0.473710i \(0.157085\pi\)
\(284\) 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 \(-0.668519\pi\)
0.494952 + 0.868921i \(0.335186\pi\)
\(294\) 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 \(-0.778935\pi\)
−0.768376 + 0.639999i \(0.778935\pi\)
\(312\) 15.8854 1.62153i 0.899331 0.0918013i
\(313\) −22.0785 −1.24795 −0.623975 0.781445i \(-0.714483\pi\)
−0.623975 + 0.781445i \(0.714483\pi\)
\(314\) 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 \(-0.936394\pi\)
0.980102 0.198496i \(-0.0636056\pi\)
\(318\) −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 −0.648547 0.761175i \(-0.724623\pi\)
0.334923 + 0.942245i \(0.391290\pi\)
\(332\) −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 0.961883 0.273462i \(-0.0881687\pi\)
−0.717766 + 0.696284i \(0.754835\pi\)
\(348\) −3.31056 + 5.73405i −0.177464 + 0.307378i
\(349\) 7.98521 + 4.61026i 0.427439 + 0.246782i 0.698255 0.715849i \(-0.253960\pi\)
−0.270816 + 0.962631i \(0.587294\pi\)
\(350\) 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 \(-0.351594\pi\)
−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
\(359\) 8.55756i 0.451651i −0.974168 0.225825i \(-0.927492\pi\)
0.974168 0.225825i \(-0.0725079\pi\)
\(360\) 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 \(-0.852438\pi\)
0.834474 + 0.551047i \(0.185771\pi\)
\(368\) −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 0.672517 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
\(376\) −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 0.311619 0.950207i \(-0.399129\pi\)
−0.667094 + 0.744974i \(0.732462\pi\)
\(380\) 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 \(-0.410066\pi\)
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
\(387\) −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 \(-0.726551\pi\)
0.329211 + 0.944256i \(0.393217\pi\)
\(398\) 15.2368i 0.763750i
\(399\) 0 0
\(400\) −0.670563 + 1.16145i −0.0335282 + 0.0580725i
\(401\) 15.7601 + 9.09912i 0.787024 + 0.454389i 0.838914 0.544264i \(-0.183191\pi\)
−0.0518898 + 0.998653i \(0.516524\pi\)
\(402\) −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 \(-0.408985\pi\)
0.971890 + 0.235435i \(0.0756514\pi\)
\(410\) −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 −0.493380 0.869814i \(-0.664239\pi\)
0.999971 0.00762733i \(-0.00242788\pi\)
\(420\) 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
\(423\) 0.258531 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 0.871665 0.490103i \(-0.163041\pi\)
0.0113906 + 0.999935i \(0.496374\pi\)
\(432\) −0.883489 + 1.53025i −0.0425069 + 0.0736241i
\(433\) −11.7148 20.2906i −0.562977 0.975105i −0.997235 0.0743163i \(-0.976323\pi\)
0.434258 0.900789i \(-0.357011\pi\)
\(434\) 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 \(-0.926085\pi\)
0.685879 + 0.727715i \(0.259418\pi\)
\(440\) −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 0.136504 0.990640i \(-0.456413\pi\)
0.926171 + 0.377104i \(0.123080\pi\)
\(450\) 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 −0.276945 0.960886i \(-0.589322\pi\)
−0.970624 + 0.240602i \(0.922655\pi\)
\(458\) 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 \(-0.958672\pi\)
−0.383665 + 0.923472i \(0.625338\pi\)
\(462\) 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
\(467\) −28.3524 −1.31199 −0.655996 0.754764i \(-0.727751\pi\)
−0.655996 + 0.754764i \(0.727751\pi\)
\(468\) −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 \(-0.379178\pi\)
−0.619121 + 0.785296i \(0.712511\pi\)
\(480\) −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 −0.222331 0.974971i \(-0.571366\pi\)
0.733185 + 0.680030i \(0.238033\pi\)
\(488\) −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 \(0.256579\pi\)
\(492\) −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 \(0.0656808\pi\)
−0.978787 + 0.204881i \(0.934319\pi\)
\(500\) −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 −0.999998 0.00195935i \(-0.999376\pi\)
0.498302 0.867003i \(-0.333957\pi\)
\(504\) 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 \(-0.00578229\pi\)
0.484187 + 0.874965i \(0.339116\pi\)
\(510\) 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 \(-0.156625\pi\)
0.881366 + 0.472434i \(0.156625\pi\)
\(522\) 2.24897 + 1.29844i 0.0984348 + 0.0568313i
\(523\) 0.366073 0.634057i 0.0160073 0.0277254i −0.857911 0.513799i \(-0.828238\pi\)
0.873918 + 0.486073i \(0.161571\pi\)
\(524\) −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 \(-0.830209\pi\)
0.861076 0.508476i \(-0.169791\pi\)
\(542\) −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 0.377825 0.925877i \(-0.376672\pi\)
−0.612921 + 0.790145i \(0.710005\pi\)
\(558\) 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 \(-0.117365\pi\)
−0.778524 + 0.627615i \(0.784031\pi\)
\(564\) 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 −0.907721 0.419575i \(-0.862179\pi\)
0.817223 + 0.576322i \(0.195513\pi\)
\(570\) 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 \(-0.108832\pi\)
0.180695 + 0.983539i \(0.442165\pi\)
\(588\) 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 −0.0538542 0.998549i \(-0.517151\pi\)
0.891696 0.452635i \(-0.149516\pi\)
\(602\) 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 \(-0.293271\pi\)
−0.992090 + 0.125529i \(0.959937\pi\)
\(608\) 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 0.985199 0.171415i \(-0.0548340\pi\)
0.344149 + 0.938915i \(0.388167\pi\)
\(614\) −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 −0.347992 0.937497i \(-0.613136\pi\)
0.637900 + 0.770119i \(0.279803\pi\)
\(618\) −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 −0.688715 0.725032i \(-0.741825\pi\)
0.283539 + 0.958961i \(0.408492\pi\)
\(632\) 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 0.950801 0.309804i \(-0.100263\pi\)
−0.743698 + 0.668516i \(0.766930\pi\)
\(642\) 33.4679i 1.32087i
\(643\) 27.0912 15.6411i 1.06837 0.616825i 0.140635 0.990061i \(-0.455085\pi\)
0.927736 + 0.373237i \(0.121752\pi\)
\(644\) 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 \(0.343775\pi\)
−0.999462 + 0.0327983i \(0.989558\pi\)
\(648\) −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 −0.822659 0.568536i \(-0.807510\pi\)
0.903696 + 0.428176i \(0.140844\pi\)
\(654\) −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 0.577840 0.816150i \(-0.303896\pi\)
−0.995727 + 0.0923492i \(0.970562\pi\)
\(660\) 3.10144 5.37185i 0.120723 0.209099i
\(661\) 36.7084 + 21.1936i 1.42779 + 0.824335i 0.996946 0.0780909i \(-0.0248824\pi\)
0.430844 + 0.902426i \(0.358216\pi\)
\(662\) 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 0.426323 + 0.904571i \(0.359809\pi\)
−0.996543 + 0.0830790i \(0.973525\pi\)
\(674\) 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 \(-0.287895\pi\)
0.618118 + 0.786085i \(0.287895\pi\)
\(678\) −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 −0.350651 0.936506i \(-0.614040\pi\)
0.635712 + 0.771926i \(0.280706\pi\)
\(684\) 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 \(-0.460452\pi\)
−0.797388 + 0.603466i \(0.793786\pi\)
\(692\) −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 0.0632970 0.997995i \(-0.479838\pi\)
0.895937 + 0.444181i \(0.146505\pi\)
\(710\) 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 \(-0.216319\pi\)
−0.933189 + 0.359386i \(0.882986\pi\)
\(720\) 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 \(-0.442662\pi\)
0.179161 + 0.983820i \(0.442662\pi\)
\(728\) 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 −0.268146 0.963378i \(-0.586411\pi\)
−0.968383 + 0.249468i \(0.919744\pi\)
\(740\) −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 0.934308 0.356467i \(-0.116019\pi\)
0.158445 + 0.987368i \(0.449352\pi\)
\(744\) 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 0.0254165 0.999677i \(-0.491909\pi\)
0.853037 0.521850i \(-0.174758\pi\)
\(752\) 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 −0.796423 0.604740i \(-0.793277\pi\)
0.921931 + 0.387353i \(0.126611\pi\)
\(758\) 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 \(-0.469910\pi\)
0.909353 + 0.416025i \(0.136577\pi\)
\(762\) 53.2781i 1.93006i
\(763\) 0 0
\(764\) −2.50067 + 4.33129i −0.0904712 + 0.156701i
\(765\) −1.26035 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 \(-0.249759\pi\)
−0.258089 + 0.966121i \(0.583093\pi\)
\(770\) 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 \(-0.432797\pi\)
0.951576 + 0.307414i \(0.0994636\pi\)
\(774\) 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