Properties

Label 637.2.u.g.30.6
Level $637$
Weight $2$
Character 637.30
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.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 30.6
Root \(1.21245 + 0.727987i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.g.361.6

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.99469 1.15163i 1.41046 0.814328i 0.415026 0.909810i \(-0.363773\pi\)
0.995431 + 0.0954820i \(0.0304392\pi\)
\(3\) 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 0.655022 0.755610i \(-0.272660\pi\)
−0.326867 + 0.945070i \(0.605993\pi\)
\(6\) 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 \(0.0727762\pi\)
−0.973977 + 0.226646i \(0.927224\pi\)
\(12\) 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 −0.963855 0.266428i \(-0.914157\pi\)
0.712661 + 0.701509i \(0.247490\pi\)
\(18\) −1.65401 + 0.954943i −0.389854 + 0.225082i
\(19\) 0.0474272i 0.0108805i 0.999985 + 0.00544027i \(0.00173170\pi\)
−0.999985 + 0.00544027i \(0.998268\pi\)
\(20\) 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 \(-0.470016\pi\)
\(24\) 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 −0.922219 0.386668i \(-0.873626\pi\)
0.795973 + 0.605331i \(0.206959\pi\)
\(30\) 2.87532 0.524959
\(31\) −6.80787 + 3.93052i −1.22273 + 0.705943i −0.965499 0.260407i \(-0.916143\pi\)
−0.257230 + 0.966350i \(0.582810\pi\)
\(32\) 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 −0.894388 0.447292i \(-0.852388\pi\)
−0.0598278 + 0.998209i \(0.519055\pi\)
\(38\) 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 0.988945 0.148285i \(-0.0473754\pi\)
0.366054 + 0.930594i \(0.380709\pi\)
\(42\) 0 0
\(43\) 4.63283 + 8.02430i 0.706500 + 1.22369i 0.966147 + 0.257991i \(0.0830604\pi\)
−0.259647 + 0.965704i \(0.583606\pi\)
\(44\) 4.30311 + 2.48440i 0.648718 + 0.374537i
\(45\) −0.608453 0.351290i −0.0907028 0.0523673i
\(46\) −15.5959 9.00428i −2.29948 1.32761i
\(47\) −0.311781 0.180007i −0.0454779 0.0262567i 0.477089 0.878855i \(-0.341692\pi\)
−0.522567 + 0.852598i \(0.675025\pi\)
\(48\) −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 0.757748 0.652547i \(-0.226299\pi\)
−0.943996 + 0.329956i \(0.892966\pi\)
\(54\) −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 0.404619 0.914486i \(-0.367404\pi\)
−0.589658 + 0.807653i \(0.700738\pi\)
\(60\) 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 \(-0.960179\pi\)
0.992185 0.124775i \(-0.0398210\pi\)
\(68\) 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 \(0.0138590\pi\)
\(72\) 2.49247i 0.293741i
\(73\) 5.85563 3.38075i 0.685349 0.395687i −0.116518 0.993189i \(-0.537173\pi\)
0.801867 + 0.597502i \(0.203840\pi\)
\(74\) −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 0.325801 + 0.945438i \(0.394366\pi\)
−0.981674 + 0.190567i \(0.938967\pi\)
\(80\) 0.265367i 0.0296689i
\(81\) −5.82479 −0.647199
\(82\) 23.0751 2.54822
\(83\) 11.5362i 1.26627i −0.774043 0.633133i \(-0.781768\pi\)
0.774043 0.633133i \(-0.218232\pi\)
\(84\) 0 0
\(85\) −1.51994 + 0.877541i −0.164861 + 0.0951826i
\(86\) 18.4821 + 10.6706i 1.99298 + 1.15065i
\(87\) −1.00167 + 1.73494i −0.107390 + 0.186006i
\(88\) 4.51900 0.481727
\(89\) −15.1652 + 8.75561i −1.60750 + 0.928093i −0.617577 + 0.786510i \(0.711886\pi\)
−0.989927 + 0.141582i \(0.954781\pi\)
\(90\) −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 −0.518622 0.855003i \(-0.673555\pi\)
0.481143 + 0.876642i \(0.340222\pi\)
\(98\) 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 −0.508361 0.861144i \(-0.669748\pi\)
0.999953 + 0.00968129i \(0.00308170\pi\)
\(104\) −6.34397 8.78695i −0.622078 0.861631i
\(105\) 0 0
\(106\) −5.40922 3.12301i −0.525390 0.303334i
\(107\) −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
\(109\) 10.0507 5.80275i 0.962679 0.555803i 0.0656822 0.997841i \(-0.479078\pi\)
0.896996 + 0.442038i \(0.145744\pi\)
\(110\) 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 0.936147 0.351609i \(-0.114365\pi\)
−0.772576 + 0.634923i \(0.781032\pi\)
\(114\) 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 0.273082 + 0.961991i \(0.411957\pi\)
−0.969649 + 0.244499i \(0.921376\pi\)
\(128\) 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 −0.916249 0.400610i \(-0.868798\pi\)
0.805063 + 0.593190i \(0.202132\pi\)
\(132\) 6.34003 + 3.66042i 0.551829 + 0.318598i
\(133\) 0 0
\(134\) −2.35240 4.07447i −0.203216 0.351981i
\(135\) −4.13982 2.39013i −0.356299 0.205709i
\(136\) 5.39215 + 3.11316i 0.462373 + 0.266951i
\(137\) −1.61490 0.932362i −0.137970 0.0796571i 0.429426 0.903102i \(-0.358716\pi\)
−0.567396 + 0.823445i \(0.692049\pi\)
\(138\) −22.9783 13.2665i −1.95605 1.12932i
\(139\) 7.80462 + 13.5180i 0.661979 + 1.14658i 0.980095 + 0.198530i \(0.0636166\pi\)
−0.318116 + 0.948052i \(0.603050\pi\)
\(140\) 0 0
\(141\) −0.459366 0.265215i −0.0386856 0.0223351i
\(142\) 16.3692 28.3524i 1.37368 2.37928i
\(143\) 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 \(-0.916058\pi\)
0.965429 0.260664i \(-0.0839416\pi\)
\(150\) −12.5846 7.26574i −1.02753 0.593245i
\(151\) −0.575122 + 0.332047i −0.0468028 + 0.0270216i −0.523219 0.852198i \(-0.675269\pi\)
0.476416 + 0.879220i \(0.341936\pi\)
\(152\) 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 −0.980234 0.197842i \(-0.936607\pi\)
0.318781 0.947828i \(-0.396727\pi\)
\(158\) 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 \(-0.884660\pi\)
0.935065 0.354475i \(-0.115340\pi\)
\(164\) 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 0.586400 0.810022i \(-0.300545\pi\)
−0.408300 + 0.912848i \(0.633878\pi\)
\(168\) 0 0
\(169\) 4.09120 12.3395i 0.314708 0.949189i
\(170\) −2.02121 + 3.50084i −0.155020 + 0.268502i
\(171\) 0.0393270i 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 \(-0.919478\pi\)
0.968174 0.250278i \(-0.0805220\pi\)
\(194\) −0.490860 + 0.850194i −0.0352417 + 0.0610404i
\(195\) 4.47778 0.457080i 0.320661 0.0327322i
\(196\) 0 0
\(197\) −13.4037 7.73860i −0.954971 0.551353i −0.0603494 0.998177i \(-0.519221\pi\)
−0.894622 + 0.446825i \(0.852555\pi\)
\(198\) −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 \(0.242003\pi\)
\(200\) −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 −0.692424 0.721490i \(-0.743457\pi\)
0.971041 + 0.238912i \(0.0767907\pi\)
\(212\) −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 −0.0440506 0.999029i \(-0.514026\pi\)
−0.887210 + 0.461366i \(0.847360\pi\)
\(224\) 0 0
\(225\) 1.77537 + 3.07504i 0.118358 + 0.205002i
\(226\) 6.93668 + 4.00490i 0.461421 + 0.266402i
\(227\) 1.12220 + 0.647903i 0.0744831 + 0.0430029i 0.536779 0.843723i \(-0.319641\pi\)
−0.462296 + 0.886726i \(0.652974\pi\)
\(228\) 0.200006 + 0.115474i 0.0132457 + 0.00764742i
\(229\) 18.0285 + 10.4088i 1.19136 + 0.687831i 0.958614 0.284707i \(-0.0918965\pi\)
0.232743 + 0.972538i \(0.425230\pi\)
\(230\) −7.62925 13.2142i −0.503058 0.871322i
\(231\) 0 0
\(232\) 3.53951 + 2.04354i 0.232380 + 0.134165i
\(233\) −6.65213 + 11.5218i −0.435796 + 0.754820i −0.997360 0.0726127i \(-0.976866\pi\)
0.561565 + 0.827433i \(0.310200\pi\)
\(234\) −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 \(0.142285\pi\)
−0.901748 + 0.432263i \(0.857715\pi\)
\(240\) 0.390981i 0.0252377i
\(241\) 0.722398 + 0.417076i 0.0465337 + 0.0268663i 0.523086 0.852280i \(-0.324781\pi\)
−0.476553 + 0.879146i \(0.658114\pi\)
\(242\) 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 −0.871255 0.490831i \(-0.836693\pi\)
0.0105555 0.999944i \(-0.496640\pi\)
\(252\) 0 0
\(253\) 10.1798 5.87733i 0.640000 0.369504i
\(254\) 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 0.745577 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
\(261\) 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 −0.512093 0.858930i \(-0.671130\pi\)
0.999902 + 0.0140210i \(0.00446317\pi\)
\(270\) −11.0102 −0.670059
\(271\) 7.58582 4.37967i 0.460806 0.266046i −0.251577 0.967837i \(-0.580949\pi\)
0.712383 + 0.701791i \(0.247616\pi\)
\(272\) 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 0.394673 + 0.918822i \(0.370858\pi\)
−0.993059 + 0.117614i \(0.962475\pi\)
\(278\) 31.1355 + 17.9761i 1.86739 + 1.07814i
\(279\) 5.64514 3.25922i 0.337965 0.195124i
\(280\) 0 0
\(281\) 14.0234i 0.836566i −0.908317 0.418283i \(-0.862632\pi\)
0.908317 0.418283i \(-0.137368\pi\)
\(282\) −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 −0.494952 0.868921i \(-0.664814\pi\)
0.505032 + 0.863101i \(0.331481\pi\)
\(294\) 0 0
\(295\) −0.695286 1.20427i −0.0404811 0.0701153i
\(296\) 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 \(0.282857\pi\)
−0.630482 + 0.776204i \(0.717143\pi\)
\(308\) 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 −0.938443 0.345434i \(-0.887732\pi\)
0.170067 0.985432i \(-0.445602\pi\)
\(312\) −9.34696 12.9464i −0.529168 0.732943i
\(313\) −11.0392 + 19.1205i −0.623975 + 1.08076i 0.364763 + 0.931100i \(0.381150\pi\)
−0.988738 + 0.149656i \(0.952183\pi\)
\(314\) −33.0639 19.0894i −1.86590 1.07728i
\(315\) 0 0
\(316\) 19.2668 + 33.3711i 1.08384 + 1.87727i
\(317\) 6.12126 + 3.53411i 0.343804 + 0.198496i 0.661953 0.749545i \(-0.269728\pi\)
−0.318149 + 0.948041i \(0.603061\pi\)
\(318\) −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 \(-0.942044\pi\)
0.983470 0.181071i \(-0.0579563\pi\)
\(332\) −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 −0.717766 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 0.270816 0.962631i \(-0.412706\pi\)
−0.698255 + 0.715849i \(0.746040\pi\)
\(350\) 0 0
\(351\) −16.4926 + 11.9073i −0.880310 + 0.635564i
\(352\) −3.97674 + 6.88792i −0.211961 + 0.367127i
\(353\) 2.15449i 0.114672i −0.998355 0.0573359i \(-0.981739\pi\)
0.998355 0.0573359i \(-0.0182606\pi\)
\(354\) −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 0.682654 0.730741i \(-0.260825\pi\)
−0.291513 + 0.956567i \(0.594159\pi\)
\(360\) −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 0.311619 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
\(382\) −3.01846 + 1.74271i −0.154438 + 0.0891647i
\(383\) 28.2446i 1.44323i −0.692294 0.721616i \(-0.743400\pi\)
0.692294 0.721616i \(-0.256600\pi\)
\(384\) 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 0.946808 0.321799i \(-0.104288\pi\)
−0.752090 + 0.659060i \(0.770954\pi\)
\(390\) 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 \(0.0598839\pi\)
−0.982356 + 0.187023i \(0.940116\pi\)
\(398\) 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 \(-0.816809\pi\)
0.0518898 + 0.998653i \(0.483476\pi\)
\(402\) −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 0.971890 0.235435i \(-0.0756514\pi\)
0.282053 + 0.959399i \(0.408985\pi\)
\(410\) 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 0.493380 + 0.869814i \(0.335761\pi\)
−0.999971 + 0.00762733i \(0.997572\pi\)
\(420\) 0 0
\(421\) 24.8696i 1.21207i −0.795437 0.606036i \(-0.792759\pi\)
0.795437 0.606036i \(-0.207241\pi\)
\(422\) 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 \(-0.829708\pi\)
0.860274 0.509832i \(-0.170292\pi\)
\(432\) 0.883489 + 1.53025i 0.0425069 + 0.0736241i
\(433\) 11.7148 + 20.2906i 0.562977 + 0.975105i 0.997235 + 0.0743163i \(0.0236774\pi\)
−0.434258 + 0.900789i \(0.642989\pi\)
\(434\) 0 0
\(435\) −1.47000 + 0.848707i −0.0704813 + 0.0406924i
\(436\) 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 0.973160 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
\(443\) −7.86656 + 13.6253i −0.373752 + 0.647357i −0.990139 0.140086i \(-0.955262\pi\)
0.616388 + 0.787443i \(0.288595\pi\)
\(444\) 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 0.136504 0.990640i \(-0.456413\pi\)
0.926171 + 0.377104i \(0.123080\pi\)
\(450\) 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 0.276945 0.960886i \(-0.410678\pi\)
0.970624 + 0.240602i \(0.0773448\pi\)
\(458\) 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 0.383665 0.923472i \(-0.374662\pi\)
0.991583 + 0.129472i \(0.0413284\pi\)
\(462\) 0 0
\(463\) 1.69184i 0.0786263i 0.999227 + 0.0393131i \(0.0125170\pi\)
−0.999227 + 0.0393131i \(0.987483\pi\)
\(464\) 0.425852 0.0197697
\(465\) −9.81347 −0.455089
\(466\) 30.6433i 1.41952i
\(467\) −14.1762 + 24.5539i −0.655996 + 1.13622i 0.325647 + 0.945491i \(0.394418\pi\)
−0.981643 + 0.190727i \(0.938916\pi\)
\(468\) 1.00344 + 9.83015i 0.0463838 + 0.454399i
\(469\) 0 0
\(470\) −0.608453 0.351290i −0.0280658 0.0162038i
\(471\) −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 \(-0.954156\pi\)
0.989646 0.143526i \(-0.0458442\pi\)
\(480\) 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 0.222331 0.974971i \(-0.428634\pi\)
−0.733185 + 0.680030i \(0.761967\pi\)
\(488\) 13.5923i 0.615293i
\(489\) 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
\(493\) −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 0.311961 0.950095i \(-0.399014\pi\)
−0.666826 + 0.745214i \(0.732348\pi\)
\(500\) −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 0.999998 + 0.00195935i \(0.000623680\pi\)
−0.498302 + 0.867003i \(0.666043\pi\)
\(504\) 0 0
\(505\) 7.09559 + 4.09664i 0.315750 + 0.182298i
\(506\) 13.5370 23.4469i 0.601795 1.04234i
\(507\) 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 0.484187 0.874965i \(-0.339116\pi\)
0.999835 + 0.0181646i \(0.00578229\pi\)
\(510\) −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 0.849823 + 0.527068i \(0.176709\pi\)
0.0315430 + 0.999502i \(0.489958\pi\)
\(522\) 2.59689i 0.113663i
\(523\) −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
\(527\) 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 0.870891 0.491476i \(-0.163543\pi\)
0.00981448 + 0.999952i \(0.496876\pi\)
\(542\) 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 \(0.0433388\pi\)
−0.990746 + 0.135732i \(0.956661\pi\)
\(558\) 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 −0.932792 0.360414i \(-0.882635\pi\)
0.778524 + 0.627615i \(0.215969\pi\)
\(564\) −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 0.817223 0.576322i \(-0.195513\pi\)
−0.907721 + 0.419575i \(0.862179\pi\)
\(570\) 0.136368i 0.00571184i
\(571\) 17.0847 + 29.5916i 0.714974 + 1.23837i 0.962970 + 0.269610i \(0.0868946\pi\)
−0.247996 + 0.968761i \(0.579772\pi\)
\(572\) 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 −0.610191 0.792254i \(-0.708907\pi\)
0.381017 + 0.924568i \(0.375574\pi\)
\(578\) 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 −0.180695 0.983539i \(-0.557835\pi\)
−0.942118 + 0.335283i \(0.891168\pi\)
\(588\) 0 0
\(589\) −0.186414 0.322878i −0.00768104 0.0133040i
\(590\) −2.77376 1.60143i −0.114194 0.0659298i
\(591\) −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 0.508387 0.861128i \(-0.330242\pi\)
−0.491565 + 0.870841i \(0.663575\pi\)
\(594\) −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 0.947448 0.319910i \(-0.103653\pi\)
−0.750774 + 0.660559i \(0.770320\pi\)
\(600\) −16.4234 + 9.48206i −0.670483 + 0.387103i
\(601\) −20.5399 + 35.5762i −0.837842 + 1.45118i 0.0538542 + 0.998549i \(0.482849\pi\)
−0.891696 + 0.452635i \(0.850484\pi\)
\(602\) 0 0
\(603\) 1.69379i 0.0689765i
\(604\) 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 \(-0.721501\pi\)
0.641049 0.767500i \(-0.278499\pi\)
\(614\) 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 \(0.279803\pi\)
\(618\) 33.8616i 1.36211i
\(619\) −38.5146 + 22.2364i −1.54803 + 0.893756i −0.549739 + 0.835336i \(0.685273\pi\)
−0.998292 + 0.0584199i \(0.981394\pi\)
\(620\) −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 −0.688715 0.725032i \(-0.741825\pi\)
0.283539 + 0.958961i \(0.408492\pi\)
\(632\) 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 −0.743698 0.668516i \(-0.766930\pi\)
0.950801 + 0.309804i \(0.100263\pi\)
\(642\) −28.9840 16.7339i −1.14391 0.660436i
\(643\) −27.0912 + 15.6411i −1.06837 + 0.616825i −0.927736 0.373237i \(-0.878248\pi\)
−0.140635 + 0.990061i \(0.544915\pi\)
\(644\) 0 0
\(645\) 11.5669i 0.455448i
\(646\) −0.226275 −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 0.903696 0.428176i \(-0.140844\pi\)
−0.822659 + 0.568536i \(0.807510\pi\)
\(654\) 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 0.577840 0.816150i \(-0.303896\pi\)
−0.995727 + 0.0923492i \(0.970562\pi\)
\(660\) 3.10144 + 5.37185i 0.120723 + 0.209099i
\(661\) 42.3872i 1.64867i 0.566102 + 0.824335i \(0.308451\pi\)
−0.566102 + 0.824335i \(0.691549\pi\)
\(662\) −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 0.426323 + 0.904571i \(0.359809\pi\)
−0.996543 + 0.0830790i \(0.973525\pi\)
\(674\) −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 −0.371711 0.928349i \(-0.621229\pi\)
0.989829 0.142263i \(-0.0454380\pi\)
\(678\) 10.2202 + 5.90066i 0.392506 + 0.226613i
\(679\) 0 0
\(680\) 2.63775 + 4.56872i 0.101153 + 0.175202i
\(681\) 1.65341 + 0.954596i 0.0633587 + 0.0365802i
\(682\) −23.5738 13.6104i −0.902689 0.521168i
\(683\) −7.44986 4.30118i −0.285061 0.164580i 0.350651 0.936506i \(-0.385960\pi\)
−0.635712 + 0.771926i \(0.719294\pi\)
\(684\) −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 −0.797388 0.603466i \(-0.793786\pi\)
0.123923 + 0.992292i \(0.460452\pi\)
\(692\) 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 \(0.186828\pi\)
−0.832640 + 0.553814i \(0.813172\pi\)
\(710\) 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 0.258757 0.965942i \(-0.416687\pi\)
−0.707152 + 0.707061i \(0.750020\pi\)
\(734\) −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 \(0.253077\pi\)
−0.700237 + 0.713910i \(0.746923\pi\)
\(740\) −9.38417 + 16.2539i −0.344969 + 0.597504i
\(741\) 0.147479 + 0.204271i 0.00541779 + 0.00750410i
\(742\) 0 0
\(743\) 29.7863 + 17.1971i 1.09275 + 0.630901i 0.934308 0.356467i \(-0.116019\pi\)
0.158445 + 0.987368i \(0.449352\pi\)
\(744\) 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 0.853037 + 0.521850i \(0.174758\pi\)
0.0254165 + 0.999677i \(0.491909\pi\)
\(752\) 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 −0.796423 0.604740i \(-0.793277\pi\)
0.921931 + 0.387353i \(0.126611\pi\)
\(758\) −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 \(-0.803244\pi\)
0.814965 0.579511i \(-0.196756\pi\)
\(762\) 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 0.258089 0.966121i \(-0.416907\pi\)
−0.707641 + 0.706572i \(0.750241\pi\)
\(770\) 0 0
\(771\) −4.82664 8.35999i −0.173827 0.301078i
\(772\) −19.9039 11.4915i −0.716357 0.413589i
\(773\) 32.2829 + 18.6385i 1.16114 + 0.670382i 0.951576 0.307414i \(-0.0994636\pi\)
0.209560 + 0.977796i \(0.432797\pi\)
\(774\) −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
\(781\) 10.6846 + 18.5063i