Properties

Label 637.2.u.g.361.6
Level $637$
Weight $2$
Character 637.361
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.u (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 361.6
Root \(1.21245 - 0.727987i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.g.30.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.99469 + 1.15163i) q^{2} +1.47336 q^{3} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.93889 + 1.69677i) q^{6} +3.00585i q^{8} -0.829208 q^{9} +O(q^{10})\) \(q+(1.99469 + 1.15163i) q^{2} +1.47336 q^{3} +(1.65252 + 2.86225i) q^{4} +(0.733776 - 0.423646i) q^{5} +(2.93889 + 1.69677i) q^{6} +3.00585i q^{8} -0.829208 q^{9} +1.95154 q^{10} -1.50340i q^{11} +(2.43476 + 4.21712i) 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} +(-1.65401 - 0.954943i) q^{18} -0.0474272i q^{19} +(2.42516 + 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} +(-3.90935 + 6.77119i) q^{23} +4.42870i q^{24} +(-2.14105 + 3.70840i) q^{25} +(3.40047 + 7.57643i) q^{26} -5.64180 q^{27} +(-0.679854 - 1.17754i) q^{29} +2.87532 q^{30} +(-6.80787 - 3.93052i) q^{31} +(4.58156 - 2.64516i) q^{32} -2.21505i q^{33} -4.77099i q^{34} +(-1.37028 - 2.37340i) q^{36} +(-5.80427 - 3.35110i) q^{37} +(0.0546187 - 0.0946024i) q^{38} +(4.30706 + 3.10959i) 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} +(-0.608453 + 0.351290i) q^{45} +(-15.5959 + 9.00428i) 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} +(-1.21011 + 11.8549i) q^{52} +(-1.35591 + 2.34850i) q^{53} +(-11.2536 - 6.49729i) q^{54} +(-0.636910 - 1.10316i) q^{55} -0.0698773i q^{57} -3.13177i q^{58} +(-1.42132 + 0.820598i) q^{59} +(3.57313 + 2.06295i) q^{60} -4.52194 q^{61} +(-9.05305 - 15.6803i) q^{62} +12.8114 q^{64} +(3.03916 + 0.310229i) q^{65} +(2.55093 - 4.41834i) q^{66} +2.04266i q^{67} +(3.42303 - 5.92886i) q^{68} +(-5.75988 + 9.97641i) q^{69} +(12.3096 + 7.10697i) q^{71} -2.49247i q^{72} +(5.85563 + 3.38075i) 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} +(-5.82952 - 10.0970i) q^{79} +0.265367i q^{80} -5.82479 q^{81} +23.0751 q^{82} +11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +(18.4821 - 10.6706i) q^{86} +(-1.00167 - 1.73494i) q^{87} +4.51900 q^{88} +(-15.1652 - 8.75561i) q^{89} -1.61823 q^{90} -25.8411 q^{92} +(-10.0304 - 5.79108i) q^{93} -0.829208 q^{94} +(-0.0200923 - 0.0348009i) q^{95} +(6.75029 - 3.89728i) q^{96} +(-0.369125 - 0.213115i) q^{97} +1.24663i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + 24q^{10} + q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} - 3q^{18} + 3q^{20} - 15q^{22} + 3q^{23} - 5q^{25} + 9q^{26} - 12q^{27} - q^{29} - 22q^{30} + 18q^{31} + 18q^{32} - 13q^{36} + 15q^{37} - 19q^{38} - q^{39} + q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 9q^{45} - 30q^{46} - 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} - 47q^{52} - 8q^{53} - 6q^{54} + 15q^{55} - 27q^{59} + 30q^{60} + 10q^{61} - 41q^{62} + 2q^{64} - 3q^{65} + 34q^{66} + 11q^{68} - 7q^{69} + 30q^{71} + 42q^{73} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} - 35q^{79} - 28q^{81} + 10q^{82} - 21q^{85} + 57q^{86} - 10q^{87} + 28q^{88} - 48q^{89} - 66q^{92} - 81q^{93} + 2q^{94} + 2q^{95} + 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.99469 + 1.15163i 1.41046 + 0.814328i 0.995431 0.0954820i \(-0.0304392\pi\)
0.415026 + 0.909810i \(0.363773\pi\)
\(3\) 1.47336 0.850645 0.425323 0.905042i \(-0.360161\pi\)
0.425323 + 0.905042i \(0.360161\pi\)
\(4\) 1.65252 + 2.86225i 0.826259 + 1.43112i
\(5\) 0.733776 0.423646i 0.328155 0.189460i −0.326867 0.945070i \(-0.605993\pi\)
0.655022 + 0.755610i \(0.272660\pi\)
\(6\) 2.93889 + 1.69677i 1.19980 + 0.692704i
\(7\) 0 0
\(8\) 3.00585i 1.06273i
\(9\) −0.829208 −0.276403
\(10\) 1.95154 0.617131
\(11\) 1.50340i 0.453293i −0.973977 0.226646i \(-0.927224\pi\)
0.973977 0.226646i \(-0.0727762\pi\)
\(12\) 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
\(16\) −0.156597 + 0.271234i −0.0391492 + 0.0678085i
\(17\) −1.03570 1.79389i −0.251194 0.435081i 0.712661 0.701509i \(-0.247490\pi\)
−0.963855 + 0.266428i \(0.914157\pi\)
\(18\) −1.65401 0.954943i −0.389854 0.225082i
\(19\) 0.0474272i 0.0108805i −0.999985 0.00544027i \(-0.998268\pi\)
0.999985 0.00544027i \(-0.00173170\pi\)
\(20\) 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 \(0.863318\pi\)
\(24\) 4.42870i 0.904004i
\(25\) −2.14105 + 3.70840i −0.428210 + 0.741681i
\(26\) 3.40047 + 7.57643i 0.666887 + 1.48586i
\(27\) −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 \(0.873626\pi\)
\(30\) 2.87532 0.524959
\(31\) −6.80787 3.93052i −1.22273 0.705943i −0.257230 0.966350i \(-0.582810\pi\)
−0.965499 + 0.260407i \(0.916143\pi\)
\(32\) 4.58156 2.64516i 0.809912 0.467603i
\(33\) 2.21505i 0.385591i
\(34\) 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 \(-0.519055\pi\)
−0.894388 + 0.447292i \(0.852388\pi\)
\(38\) 0.0546187 0.0946024i 0.00886032 0.0153465i
\(39\) 4.30706 + 3.10959i 0.689681 + 0.497934i
\(40\) 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
\(45\) −0.608453 + 0.351290i −0.0907028 + 0.0523673i
\(46\) −15.5959 + 9.00428i −2.29948 + 1.32761i
\(47\) −0.311781 + 0.180007i −0.0454779 + 0.0262567i −0.522567 0.852598i \(-0.675025\pi\)
0.477089 + 0.878855i \(0.341692\pi\)
\(48\) −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
\(52\) −1.21011 + 11.8549i −0.167813 + 1.64398i
\(53\) −1.35591 + 2.34850i −0.186248 + 0.322591i −0.943996 0.329956i \(-0.892966\pi\)
0.757748 + 0.652547i \(0.226299\pi\)
\(54\) −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
\(58\) 3.13177i 0.411222i
\(59\) −1.42132 + 0.820598i −0.185040 + 0.106833i −0.589658 0.807653i \(-0.700738\pi\)
0.404619 + 0.914486i \(0.367404\pi\)
\(60\) 3.57313 + 2.06295i 0.461289 + 0.266325i
\(61\) −4.52194 −0.578975 −0.289488 0.957182i \(-0.593485\pi\)
−0.289488 + 0.957182i \(0.593485\pi\)
\(62\) −9.05305 15.6803i −1.14974 1.99140i
\(63\) 0 0
\(64\) 12.8114 1.60143
\(65\) 3.03916 + 0.310229i 0.376962 + 0.0384792i
\(66\) 2.55093 4.41834i 0.313998 0.543860i
\(67\) 2.04266i 0.249551i 0.992185 + 0.124775i \(0.0398210\pi\)
−0.992185 + 0.124775i \(0.960179\pi\)
\(68\) 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 \(0.347192\pi\)
\(72\) 2.49247i 0.293741i
\(73\) 5.85563 + 3.38075i 0.685349 + 0.395687i 0.801867 0.597502i \(-0.203840\pi\)
−0.116518 + 0.993189i \(0.537173\pi\)
\(74\) −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
\(79\) −5.82952 10.0970i −0.655873 1.13600i −0.981674 0.190567i \(-0.938967\pi\)
0.325801 0.945438i \(-0.394366\pi\)
\(80\) 0.265367i 0.0296689i
\(81\) −5.82479 −0.647199
\(82\) 23.0751 2.54822
\(83\) 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
\(87\) −1.00167 1.73494i −0.107390 0.186006i
\(88\) 4.51900 0.481727
\(89\) −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
\(94\) −0.829208 −0.0855262
\(95\) −0.0200923 0.0348009i −0.00206143 0.00357050i
\(96\) 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
\(100\) −14.1525 −1.41525
\(101\) 9.66997 0.962198 0.481099 0.876666i \(-0.340238\pi\)
0.481099 + 0.876666i \(0.340238\pi\)
\(102\) 7.02939i 0.696013i
\(103\) 4.98912 + 8.64140i 0.491592 + 0.851463i 0.999953 0.00968129i \(-0.00308170\pi\)
−0.508361 + 0.861144i \(0.669748\pi\)
\(104\) −6.34397 + 8.78695i −0.622078 + 0.861631i
\(105\) 0 0
\(106\) −5.40922 + 3.12301i −0.525390 + 0.303334i
\(107\) −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
\(109\) 10.0507 + 5.80275i 0.962679 + 0.555803i 0.896996 0.442038i \(-0.145744\pi\)
0.0656822 + 0.997841i \(0.479078\pi\)
\(110\) 2.93395i 0.279741i
\(111\) −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
\(115\) 6.62472i 0.617758i
\(116\) 2.24694 3.89182i 0.208623 0.361346i
\(117\) −2.42401 1.75008i −0.224100 0.161795i
\(118\) −3.78011 −0.347987
\(119\) 0 0
\(120\) 1.87620 + 3.24967i 0.171273 + 0.296653i
\(121\) 8.73978 0.794526
\(122\) −9.01986 5.20762i −0.816620 0.471476i
\(123\) 12.7832 7.38039i 1.15262 0.665467i
\(124\) 25.9811i 2.33317i
\(125\) 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
\(129\) 6.82583 11.8227i 0.600981 1.04093i
\(130\) 5.70491 + 4.11881i 0.500353 + 0.361243i
\(131\) −1.27259 2.20418i −0.111186 0.192580i 0.805063 0.593190i \(-0.202132\pi\)
−0.916249 + 0.400610i \(0.868798\pi\)
\(132\) 6.34003 3.66042i 0.551829 0.318598i
\(133\) 0 0
\(134\) −2.35240 + 4.07447i −0.203216 + 0.351981i
\(135\) −4.13982 + 2.39013i −0.356299 + 0.205709i
\(136\) 5.39215 3.11316i 0.462373 0.266951i
\(137\) −1.61490 + 0.932362i −0.137970 + 0.0796571i −0.567396 0.823445i \(-0.692049\pi\)
0.429426 + 0.903102i \(0.358716\pi\)
\(138\) −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
\(143\) 3.17300 4.39487i 0.265339 0.367518i
\(144\) 0.129851 0.224909i 0.0108209 0.0187424i
\(145\) −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
\(149\) 6.36363i 0.521329i 0.965429 + 0.260664i \(0.0839416\pi\)
−0.965429 + 0.260664i \(0.916058\pi\)
\(150\) −12.5846 + 7.26574i −1.02753 + 0.593245i
\(151\) −0.575122 0.332047i −0.0468028 0.0270216i 0.476416 0.879220i \(-0.341936\pi\)
−0.523219 + 0.852198i \(0.675269\pi\)
\(152\) 0.142559 0.0115630
\(153\) 0.858811 + 1.48750i 0.0694307 + 0.120258i
\(154\) 0 0
\(155\) −6.66060 −0.534992
\(156\) −1.78293 + 17.4665i −0.142749 + 1.39844i
\(157\) −8.28798 + 14.3552i −0.661453 + 1.14567i 0.318781 + 0.947828i \(0.396727\pi\)
−0.980234 + 0.197842i \(0.936607\pi\)
\(158\) 26.8539i 2.13638i
\(159\) −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
\(163\) 9.05127i 0.708950i 0.935065 + 0.354475i \(0.115340\pi\)
−0.935065 + 0.354475i \(0.884660\pi\)
\(164\) 28.6752 + 16.5557i 2.23916 + 1.29278i
\(165\) −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
\(170\) −2.02121 3.50084i −0.155020 0.268502i
\(171\) 0.0393270i 0.00300741i
\(172\) 30.6234 2.33501
\(173\) 19.5870 1.48918 0.744588 0.667525i \(-0.232646\pi\)
0.744588 + 0.667525i \(0.232646\pi\)
\(174\) 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
\(178\) −20.1665 34.9294i −1.51154 2.61807i
\(179\) 2.89332 0.216257 0.108129 0.994137i \(-0.465514\pi\)
0.108129 + 0.994137i \(0.465514\pi\)
\(180\) −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
\(185\) −5.67871 −0.417507
\(186\) −13.3384 23.1028i −0.978019 1.69398i
\(187\) −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
\(191\) −1.51325 −0.109495 −0.0547475 0.998500i \(-0.517435\pi\)
−0.0547475 + 0.998500i \(0.517435\pi\)
\(192\) 18.8758 1.36225
\(193\) 6.95394i 0.500556i 0.968174 + 0.250278i \(0.0805220\pi\)
−0.968174 + 0.250278i \(0.919478\pi\)
\(194\) −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 \(0.519221\pi\)
\(198\) −1.43566 + 2.48664i −0.102028 + 0.176718i
\(199\) −3.30764 5.72901i −0.234473 0.406118i 0.724647 0.689121i \(-0.242003\pi\)
−0.959119 + 0.283002i \(0.908670\pi\)
\(200\) −11.1469 6.43566i −0.788205 0.455070i
\(201\) 3.00958i 0.212279i
\(202\) 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
\(206\) 22.9825i 1.60127i
\(207\) 3.24166 5.61473i 0.225311 0.390250i
\(208\) −1.03023 + 0.462389i −0.0714335 + 0.0320609i
\(209\) −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 \(0.743457\pi\)
\(212\) −8.96264 −0.615557
\(213\) 18.1365 + 10.4711i 1.24269 + 0.717470i
\(214\) −19.6721 + 11.3577i −1.34475 + 0.776394i
\(215\) 7.85072i 0.535415i
\(216\) 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
\(220\) 2.10501 3.64599i 0.141920 0.245812i
\(221\) 0.758428 7.42993i 0.0510174 0.499791i
\(222\) −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
\(227\) 1.12220 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
\(229\) 18.0285 10.4088i 1.19136 0.687831i 0.232743 0.972538i \(-0.425230\pi\)
0.958614 + 0.284707i \(0.0918965\pi\)
\(230\) −7.62925 + 13.2142i −0.503058 + 0.871322i
\(231\) 0 0
\(232\) 3.53951 2.04354i 0.232380 0.134165i
\(233\) −6.65213 11.5218i −0.435796 0.754820i 0.561565 0.827433i \(-0.310200\pi\)
−0.997360 + 0.0726127i \(0.976866\pi\)
\(234\) −2.81969 6.28243i −0.184329 0.410696i
\(235\) −0.152518 + 0.264169i −0.00994920 + 0.0172325i
\(236\) −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 \(-0.142285\pi\)
\(240\) 0.390981i 0.0252377i
\(241\) 0.722398 0.417076i 0.0465337 0.0268663i −0.476553 0.879146i \(-0.658114\pi\)
0.523086 + 0.852280i \(0.324781\pi\)
\(242\) 17.4331 + 10.0650i 1.12064 + 0.647004i
\(243\) 8.34339 0.535229
\(244\) −7.47259 12.9429i −0.478384 0.828585i
\(245\) 0 0
\(246\) 33.9980 2.16763
\(247\) 0.100097 0.138643i 0.00636903 0.00882165i
\(248\) 11.8146 20.4634i 0.750225 1.29943i
\(249\) 16.9970i 1.07714i
\(250\) −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
\(254\) 36.1609i 2.26894i
\(255\) −2.23943 1.29293i −0.140238 0.0809667i
\(256\) 8.98607 + 15.5643i 0.561630 + 0.972771i
\(257\) −3.27594 + 5.67409i −0.204348 + 0.353940i −0.949925 0.312479i \(-0.898841\pi\)
0.745577 + 0.666419i \(0.232174\pi\)
\(258\) 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
\(262\) 5.86221i 0.362168i
\(263\) −22.5891 −1.39290 −0.696450 0.717605i \(-0.745238\pi\)
−0.696450 + 0.717605i \(0.745238\pi\)
\(264\) 6.65811 0.409779
\(265\) 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
\(269\) 8.00065 + 13.8575i 0.487808 + 0.844909i 0.999902 0.0140210i \(-0.00446317\pi\)
−0.512093 + 0.858930i \(0.671130\pi\)
\(270\) −11.0102 −0.670059
\(271\) 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
\(276\) −38.0733 −2.29174
\(277\) −9.95914 17.2497i −0.598387 1.03644i −0.993059 0.117614i \(-0.962475\pi\)
0.394673 0.918822i \(-0.370858\pi\)
\(278\) 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 \(0.862632\pi\)
\(282\) −1.22172 −0.0727525
\(283\) 1.01259 0.0601922 0.0300961 0.999547i \(-0.490419\pi\)
0.0300961 + 0.999547i \(0.490419\pi\)
\(284\) 46.9776i 2.78761i
\(285\) −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
\(289\) 6.35465 11.0066i 0.373803 0.647446i
\(290\) −1.32676 2.29802i −0.0779101 0.134944i
\(291\) −0.543855 0.313995i −0.0318813 0.0184067i
\(292\) 22.3470i 1.30776i
\(293\) 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
\(297\) 8.48190i 0.492170i
\(298\) −7.32857 + 12.6935i −0.424532 + 0.735312i
\(299\) −25.7191 + 11.5433i −1.48737 + 0.667565i
\(300\) −20.8517 −1.20387
\(301\) 0 0
\(302\) −0.764792 1.32466i −0.0440088 0.0762256i
\(303\) 14.2474 0.818489
\(304\) 0.0128639 + 0.00742695i 0.000737793 + 0.000425965i
\(305\) −3.31809 + 1.91570i −0.189993 + 0.109693i
\(306\) 3.95614i 0.226157i
\(307\) 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
\(311\) −13.5505 + 23.4701i −0.768376 + 1.33087i 0.170067 + 0.985432i \(0.445602\pi\)
−0.938443 + 0.345434i \(0.887732\pi\)
\(312\) −9.34696 + 12.9464i −0.529168 + 0.732943i
\(313\) −11.0392 19.1205i −0.623975 1.08076i −0.988738 0.149656i \(-0.952183\pi\)
0.364763 0.931100i \(-0.381150\pi\)
\(314\) −33.0639 + 19.0894i −1.86590 + 1.07728i
\(315\) 0 0
\(316\) 19.2668 33.3711i 1.08384 1.87727i
\(317\) 6.12126 3.53411i 0.343804 0.198496i −0.318149 0.948041i \(-0.603061\pi\)
0.661953 + 0.749545i \(0.269728\pi\)
\(318\) −7.96973 + 4.60133i −0.446920 + 0.258030i
\(319\) −1.77032 + 1.02209i −0.0991188 + 0.0572263i
\(320\) 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
\(325\) −14.0857 + 6.32195i −0.781331 + 0.350679i
\(326\) −10.4237 + 18.0544i −0.577318 + 0.999943i
\(327\) 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
\(331\) 6.58858i 0.362141i 0.983470 + 0.181071i \(0.0579563\pi\)
−0.983470 + 0.181071i \(0.942044\pi\)
\(332\) −33.0195 + 19.0638i −1.81218 + 1.04626i
\(333\) 4.81294 + 2.77875i 0.263748 + 0.152275i
\(334\) 6.12118 0.334936
\(335\) 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 \(0.536693\pi\)
\(338\) −6.04985 + 29.3249i −0.329069 + 1.59506i
\(339\) 2.56187 4.43728i 0.139141 0.241000i
\(340\) 5.80061i 0.314582i
\(341\) −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
\(345\) 9.76060i 0.525493i
\(346\) 39.0700 + 22.5571i 2.10042 + 1.21268i
\(347\) 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 \(-0.746040\pi\)
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
\(353\) 2.15449i 0.114672i 0.998355 + 0.0573359i \(0.0182606\pi\)
−0.998355 + 0.0573359i \(0.981739\pi\)
\(354\) −5.56947 −0.296014
\(355\) 12.0433 0.639195
\(356\) 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 \(-0.594159\pi\)
0.682654 + 0.730741i \(0.260825\pi\)
\(360\) −1.05593 1.82892i −0.0556521 0.0963923i
\(361\) 18.9978 0.999882
\(362\) 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
\(367\) −2.29823 −0.119967 −0.0599833 0.998199i \(-0.519105\pi\)
−0.0599833 + 0.998199i \(0.519105\pi\)
\(368\) −1.22438 2.12070i −0.0638255 0.110549i
\(369\) −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
\(373\) 11.7684 0.609343 0.304672 0.952457i \(-0.401453\pi\)
0.304672 + 0.952457i \(0.401453\pi\)
\(374\) −7.17271 −0.370892
\(375\) 11.5875i 0.598374i
\(376\) −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 \(0.399129\pi\)
\(380\) 0.0664059 0.115018i 0.00340655 0.00590032i
\(381\) −11.5658 20.0325i −0.592532 1.02630i
\(382\) −3.01846 1.74271i −0.154438 0.0891647i
\(383\) 28.2446i 1.44323i 0.692294 + 0.721616i \(0.256600\pi\)
−0.692294 + 0.721616i \(0.743400\pi\)
\(384\) 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
\(388\) 1.40870i 0.0715161i
\(389\) 3.84043 6.65182i 0.194717 0.337261i −0.752090 0.659060i \(-0.770954\pi\)
0.946808 + 0.321799i \(0.104288\pi\)
\(390\) 8.40538 + 6.06849i 0.425623 + 0.307290i
\(391\) 16.1957 0.819050
\(392\) 0 0
\(393\) −1.87498 3.24756i −0.0945801 0.163818i
\(394\) −35.6481 −1.79593
\(395\) −8.55513 4.93931i −0.430455 0.248524i
\(396\) −3.56817 + 2.06008i −0.179307 + 0.103523i
\(397\) 7.45281i 0.374046i −0.982356 0.187023i \(-0.940116\pi\)
0.982356 0.187023i \(-0.0598839\pi\)
\(398\) 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 \(-0.483476\pi\)
−0.838914 + 0.544264i \(0.816809\pi\)
\(402\) −3.46593 + 6.00316i −0.172865 + 0.299411i
\(403\) −11.6058 25.8584i −0.578126 1.28810i
\(404\) 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
\(409\) 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
\(411\) −2.37933 + 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
\(416\) 18.9759 + 1.93701i 0.930372 + 0.0949698i
\(417\) 11.4990 19.9169i 0.563109 0.975334i
\(418\) −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 \(0.792759\pi\)
\(422\) 18.6433i 0.907541i
\(423\) 0.258531 0.149263i 0.0125702 0.00725742i
\(424\) −7.05923 4.07565i −0.342826 0.197931i
\(425\) 8.86994 0.430255
\(426\) 24.1178 + 41.7733i 1.16851 + 2.02392i
\(427\) 0 0
\(428\) −32.5950 −1.57554
\(429\) 4.67497 6.47524i 0.225710 0.312627i
\(430\) 9.04115 15.6597i 0.436003 0.755179i
\(431\) 21.1688i 1.01966i 0.860274 + 0.509832i \(0.170292\pi\)
−0.860274 + 0.509832i \(0.829708\pi\)
\(432\) 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
\(436\) 38.3566i 1.83695i
\(437\) 0.321139 + 0.185409i 0.0153621 + 0.00886934i
\(438\) 11.4727 + 19.8713i 0.548187 + 0.949488i
\(439\) 6.01919 10.4256i 0.287280 0.497584i −0.685879 0.727715i \(-0.740582\pi\)
0.973160 + 0.230131i \(0.0739155\pi\)
\(440\) 3.31593 1.91445i 0.158081 0.0912680i
\(441\) 0 0
\(442\) 10.0694 13.9470i 0.478952 0.663390i
\(443\) −7.86656 13.6253i −0.373752 0.647357i 0.616388 0.787443i \(-0.288595\pi\)
−0.990139 + 0.140086i \(0.955262\pi\)
\(444\) 32.6364i 1.54885i
\(445\) −14.8371 −0.703346
\(446\) −36.9860 −1.75134
\(447\) 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
\(451\) −7.53087 13.0438i −0.354615 0.614211i
\(452\) 11.4935 0.540610
\(453\) −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 \(-0.0773448\pi\)
0.276945 + 0.960886i \(0.410678\pi\)
\(458\) 47.9483 2.24048
\(459\) 5.84322 + 10.1208i 0.272738 + 0.472396i
\(460\) −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 \(-0.0125170\pi\)
\(464\) 0.425852 0.0197697
\(465\) −9.81347 −0.455089
\(466\) 30.6433i 1.41952i
\(467\) −14.1762 24.5539i −0.655996 1.13622i −0.981643 0.190727i \(-0.938916\pi\)
0.325647 0.945491i \(-0.394418\pi\)
\(468\) 1.00344 9.83015i 0.0463838 0.454399i
\(469\) 0 0
\(470\) −0.608453 + 0.351290i −0.0280658 + 0.0162038i
\(471\) −12.2112 + 21.1504i −0.562662 + 0.974559i
\(472\) −2.46659 4.27226i −0.113534 0.196647i
\(473\) −12.0637 6.96501i −0.554692 0.320251i
\(474\) 39.5655i 1.81730i
\(475\) 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
\(479\) 6.28246i 0.287053i 0.989646 + 0.143526i \(0.0458442\pi\)
−0.989646 + 0.143526i \(0.954156\pi\)
\(480\) 3.30213 5.71946i 0.150721 0.261056i
\(481\) −9.89490 22.0464i −0.451169 1.00523i
\(482\) 1.92128 0.0875117
\(483\) 0 0
\(484\) 14.4427 + 25.0154i 0.656484 + 1.13706i
\(485\) −0.361140 −0.0163985
\(486\) 16.6425 + 9.60853i 0.754917 + 0.435852i
\(487\) −11.2736 + 6.50879i −0.510854 + 0.294942i −0.733185 0.680030i \(-0.761967\pi\)
0.222331 + 0.974971i \(0.428634\pi\)
\(488\) 13.5923i 0.615293i
\(489\) 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
\(493\) −1.40825 + 2.43916i −0.0634244 + 0.109854i
\(494\) 0.359329 0.161275i 0.0161670 0.00725609i
\(495\) 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 \(-0.732348\pi\)
0.311961 + 0.950095i \(0.399014\pi\)
\(500\) −22.5105 + 12.9965i −1.00670 + 0.581220i
\(501\) 3.39102 1.95781i 0.151500 0.0874684i
\(502\) −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
\(507\) 6.02782 + 18.1805i 0.267705 + 0.807423i
\(508\) 25.9443 44.9368i 1.15109 1.99375i
\(509\) 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
\(513\) 0.267575i 0.0118137i
\(514\) −13.0690 + 7.54536i −0.576447 + 0.332812i
\(515\) 7.32179 + 4.22724i 0.322637 + 0.186274i
\(516\) 45.1193 1.98626
\(517\) 0.270623 + 0.468732i 0.0119020 + 0.0206148i
\(518\) 0 0
\(519\) 28.8588 1.26676
\(520\) −0.932502 + 9.13525i −0.0408929 + 0.400607i
\(521\) 20.1176 34.8446i 0.881366 1.52657i 0.0315430 0.999502i \(-0.489958\pi\)
0.849823 0.527068i \(-0.176709\pi\)
\(522\) 2.59689i 0.113663i
\(523\) −0.366073 + 0.634057i −0.0160073 + 0.0277254i −0.873918 0.486073i \(-0.838429\pi\)
0.857911 + 0.513799i \(0.171762\pi\)
\(524\) 4.20594 7.28491i 0.183737 0.318243i
\(525\) 0 0
\(526\) −45.0581 26.0143i −1.96463 1.13428i
\(527\) 16.2834i 0.709316i
\(528\) 0.600798 + 0.346871i 0.0261464 + 0.0150956i
\(529\) −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
\(534\) −29.7125 51.4636i −1.28579 2.22705i
\(535\) 8.35618i 0.361269i
\(536\) −6.13993 −0.265204
\(537\) 4.26291 0.183958
\(538\) 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 \(-0.496876\pi\)
0.870891 + 0.491476i \(0.163543\pi\)
\(542\) 10.0876 + 17.4722i 0.433298 + 0.750494i
\(543\) 2.01562 0.0864985
\(544\) −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
\(549\) 3.74963 0.160030
\(550\) 7.41388 + 12.8412i 0.316129 + 0.547552i
\(551\) −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
\(555\) −8.36679 −0.355150
\(556\) 51.5891 2.18787
\(557\) 6.40680i 0.271465i −0.990746 0.135732i \(-0.956661\pi\)
0.990746 0.135732i \(-0.0433388\pi\)
\(558\) 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
\(562\) −16.1498 + 27.9723i −0.681239 + 1.17994i
\(563\) −3.66042 6.34004i −0.154268 0.267201i 0.778524 0.627615i \(-0.215969\pi\)
−0.932792 + 0.360414i \(0.882635\pi\)
\(564\) −1.51822 0.876546i −0.0639287 0.0369092i
\(565\) 2.94652i 0.123961i
\(566\) 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 \(0.195513\pi\)
\(570\) 0.136368i 0.00571184i
\(571\) 17.0847 29.5916i 0.714974 1.23837i −0.247996 0.968761i \(-0.579772\pi\)
0.962970 0.269610i \(-0.0868946\pi\)
\(572\) 17.8226 + 1.81929i 0.745202 + 0.0760682i
\(573\) −2.22956 −0.0931413
\(574\) 0 0
\(575\) −16.7402 28.9949i −0.698115 1.20917i
\(576\) −10.6233 −0.442639
\(577\) −5.50494 3.17828i −0.229174 0.132314i 0.381017 0.924568i \(-0.375574\pi\)
−0.610191 + 0.792254i \(0.708907\pi\)
\(578\) 25.3511 14.6364i 1.05447 0.608796i
\(579\) 10.2457i 0.425795i
\(580\) 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
\(584\) −10.1620 + 17.6011i −0.420507 + 0.728339i
\(585\) −2.52010 0.257244i −0.104193 0.0106358i
\(586\) 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
\(591\) −19.7484 + 11.4018i −0.812342 + 0.469006i
\(592\) 1.81786 1.04954i 0.0747136 0.0431359i
\(593\) 0.409641 0.236506i 0.0168219 0.00971215i −0.491565 0.870841i \(-0.663575\pi\)
0.508387 + 0.861128i \(0.330242\pi\)
\(594\) −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
\(598\) −64.5951 6.59369i −2.64149 0.269636i
\(599\) 4.81348 8.33719i 0.196673 0.340648i −0.750774 0.660559i \(-0.770320\pi\)
0.947448 + 0.319910i \(0.103653\pi\)
\(600\) −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
\(604\) 2.19485i 0.0893073i
\(605\) 6.41304 3.70257i 0.260727 0.150531i
\(606\) 28.4190 + 16.4077i 1.15444 + 0.666518i
\(607\) −19.0858 −0.774668 −0.387334 0.921939i \(-0.626604\pi\)
−0.387334 + 0.921939i \(0.626604\pi\)
\(608\) −0.125453 0.217290i −0.00508777 0.00881228i
\(609\) 0 0
\(610\) −8.82474 −0.357303
\(611\) −1.29134 0.131816i −0.0522419 0.00533271i
\(612\) −2.83840 + 4.91626i −0.114736 + 0.198728i
\(613\) 38.0048i 1.53500i 0.641049 + 0.767500i \(0.278499\pi\)
−0.641049 + 0.767500i \(0.721501\pi\)
\(614\) 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 \(0.613136\pi\)
\(618\) 33.8616i 1.36211i
\(619\) −38.5146 22.2364i −1.54803 0.893756i −0.998292 0.0584199i \(-0.981394\pi\)
−0.549739 0.835336i \(-0.685273\pi\)
\(620\) −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
\(625\) −7.37342 12.7711i −0.294937 0.510845i
\(626\) 50.8526i 2.03248i
\(627\) −0.105054 −0.00419544
\(628\) −54.7842 −2.18613
\(629\) 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
\(633\) 5.96290 + 10.3280i 0.237004 + 0.410503i
\(634\) 16.2800 0.646562
\(635\) −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
\(640\) 16.0371 0.633921
\(641\) 5.24342 + 9.08186i 0.207102 + 0.358712i 0.950801 0.309804i \(-0.100263\pi\)
−0.743698 + 0.668516i \(0.766930\pi\)
\(642\) −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
\(646\) −0.226275 −0.00890265
\(647\) −26.8675 −1.05627 −0.528135 0.849160i \(-0.677109\pi\)
−0.528135 + 0.849160i \(0.677109\pi\)
\(648\) 17.5084i 0.687796i
\(649\) 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
\(653\) 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
\(655\) −1.86759 1.07825i −0.0729726 0.0421308i
\(656\) 3.13771i 0.122507i
\(657\) −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
\(661\) 42.3872i 1.64867i −0.566102 0.824335i \(-0.691549\pi\)
0.566102 0.824335i \(-0.308451\pi\)
\(662\) −7.58763 + 13.1422i −0.294902 + 0.510785i
\(663\) 1.11744 10.9470i 0.0433977 0.425145i
\(664\) −34.6762 −1.34570
\(665\) 0 0
\(666\) 6.40021 + 11.0855i 0.248003 + 0.429554i
\(667\) 10.6312 0.411640
\(668\) 7.60673 + 4.39175i 0.294313 + 0.169922i
\(669\) −20.4896 + 11.8297i −0.792173 + 0.457361i
\(670\) 3.98633i 0.154005i
\(671\) 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
\(675\) 12.0794 20.9221i 0.464935 0.805292i
\(676\) −28.5578 + 32.1012i −1.09838 + 1.23466i
\(677\) 16.0830 + 27.8565i 0.618118 + 1.07061i 0.989829 + 0.142263i \(0.0454380\pi\)
−0.371711 + 0.928349i \(0.621229\pi\)
\(678\) 10.2202 5.90066i 0.392506 0.226613i
\(679\) 0 0
\(680\) 2.63775 4.56872i 0.101153 0.175202i
\(681\) 1.65341 0.954596i 0.0633587 0.0365802i
\(682\) −23.5738 + 13.6104i −0.902689 + 0.521168i
\(683\) −7.44986 + 4.30118i −0.285061 + 0.164580i −0.635712 0.771926i \(-0.719294\pi\)
0.350651 + 0.936506i \(0.385960\pi\)
\(684\) −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
\(689\) −8.92031 + 4.00363i −0.339837 + 0.152526i
\(690\) −11.2406 + 19.4694i −0.427924 + 0.741186i
\(691\) −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
\(695\) 13.2256i 0.501675i
\(696\) 5.21498 3.01087i 0.197673 0.114127i
\(697\) −17.9719 10.3761i −0.680736 0.393023i
\(698\) −21.2373 −0.803845
\(699\) −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 \(0.657447\pi\)
\(702\) −19.1848 42.7447i −0.724083 1.61330i
\(703\) −0.158933 + 0.275280i −0.00599427 + 0.0103824i
\(704\) 19.2607i 0.725915i
\(705\) −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
\(709\) 29.4929i 1.10763i −0.832640 0.553814i \(-0.813172\pi\)
0.832640 0.553814i \(-0.186828\pi\)
\(710\) 24.0227 + 13.8695i 0.901556 + 0.520514i
\(711\) 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
\(716\) 4.78127 + 8.28140i 0.178684 + 0.309491i
\(717\) 19.6918i 0.735404i
\(718\) 19.7104 0.735584
\(719\) −8.33153 −0.310713 −0.155357 0.987858i \(-0.549653\pi\)
−0.155357 + 0.987858i \(0.549653\pi\)
\(720\) 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
\(724\) 2.26071 + 3.91567i 0.0840188 + 0.145525i
\(725\) 5.82240 0.216239
\(726\) 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
\(731\) −19.1929 −0.709875
\(732\) −11.0098 19.0696i −0.406935 0.704832i
\(733\) −12.1398 + 7.00894i −0.448395 + 0.258881i −0.707152 0.707061i \(-0.750020\pi\)
0.258757 + 0.965942i \(0.416687\pi\)
\(734\) −4.58425 2.64672i −0.169208 0.0976921i
\(735\) 0 0
\(736\) 41.3635i 1.52468i
\(737\) 3.07094 0.113120
\(738\) −19.1341 −0.704335
\(739\) 38.8147i 1.42782i −0.700237 0.713910i \(-0.746923\pi\)
0.700237 0.713910i \(-0.253077\pi\)
\(740\) −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 \(0.116019\pi\)
\(744\) 17.4071 30.1500i 0.638175 1.10535i
\(745\) 2.69592 + 4.66948i 0.0987710 + 0.171076i
\(746\) 23.4742 + 13.5528i 0.859452 + 0.496205i
\(747\) 9.56594i 0.349999i
\(748\) −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 \(-0.174758\pi\)
\(752\) 0.112754i 0.00411172i
\(753\) −20.0908 + 34.7983i −0.732150 + 1.26812i
\(754\) 6.60974 9.15506i 0.240713 0.333408i
\(755\) −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 \(0.793277\pi\)
\(758\) −18.4052 −0.668508
\(759\) 14.9986 + 8.65942i 0.544413 + 0.314317i
\(760\) 0.104606 0.0603945i 0.00379447 0.00219074i
\(761\) 31.9730i 1.15902i 0.814965 + 0.579511i \(0.196756\pi\)
−0.814965 + 0.579511i \(0.803244\pi\)
\(762\) 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
\(766\) −32.5274 + 56.3391i −1.17526 + 2.03562i
\(767\) −5.88683 0.600911i −0.212561 0.0216976i
\(768\) 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
\(773\) 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
\(775\) 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
\(780\) 6.09134 + 13.5718i 0.218105 + 0.485950i
\(781\)