Properties

Label 637.2.q.h.491.5
Level $637$
Weight $2$
Character 637.491
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: 12.0.58891012706304.1
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 491.5
Root \(1.40744 + 0.138282i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.h.589.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.10554 - 0.638282i) q^{2} +(-0.583963 - 1.01145i) q^{3} +(-0.185192 + 0.320762i) q^{4} +1.81487i q^{5} +(-1.29118 - 0.745466i) q^{6} +3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +O(q^{10})\) \(q+(1.10554 - 0.638282i) q^{2} +(-0.583963 - 1.01145i) q^{3} +(-0.185192 + 0.320762i) q^{4} +1.81487i q^{5} +(-1.29118 - 0.745466i) q^{6} +3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +(1.15840 + 2.00641i) q^{10} +(-2.40625 + 1.38925i) q^{11} +0.432581 q^{12} +(3.58305 + 0.402155i) q^{13} +(1.83566 - 1.05982i) q^{15} +(1.56102 + 2.70377i) q^{16} +(-1.37198 + 2.37634i) q^{17} -2.08840i q^{18} +(5.08351 + 2.93497i) q^{19} +(-0.582143 - 0.336100i) q^{20} +(-1.77346 + 3.07173i) q^{22} +(3.49955 + 6.06139i) q^{23} +(3.06060 - 1.76704i) q^{24} +1.70623 q^{25} +(4.21789 - 1.84240i) q^{26} -5.41444 q^{27} +(1.75806 + 3.04505i) q^{29} +(1.35293 - 2.34334i) q^{30} -2.06697i q^{31} +(-1.78956 - 1.03320i) q^{32} +(2.81031 + 1.62254i) q^{33} +3.50284i q^{34} +(0.302965 + 0.524751i) q^{36} +(1.50950 - 0.871512i) q^{37} +7.49334 q^{38} +(-1.68561 - 3.85893i) q^{39} -5.49171 q^{40} +(-5.51406 + 3.18355i) q^{41} +(4.55195 - 7.88422i) q^{43} -1.02911i q^{44} +(2.57127 + 1.48452i) q^{45} +(7.73776 + 4.46740i) q^{46} -6.65932i q^{47} +(1.82316 - 3.15780i) q^{48} +(1.88631 - 1.08906i) q^{50} +3.20474 q^{51} +(-0.792549 + 1.07483i) q^{52} -10.4879 q^{53} +(-5.98587 + 3.45594i) q^{54} +(-2.52131 - 4.36703i) q^{55} -6.85564i q^{57} +(3.88720 + 2.24427i) q^{58} +(-2.66212 - 1.53698i) q^{59} +0.785080i q^{60} +(0.540892 - 0.936853i) q^{61} +(-1.31931 - 2.28511i) q^{62} -8.88199 q^{64} +(-0.729860 + 6.50279i) q^{65} +4.14254 q^{66} +(4.34568 - 2.50898i) q^{67} +(-0.508159 - 0.880158i) q^{68} +(4.08721 - 7.07925i) q^{69} +(2.35453 + 1.35939i) q^{71} +(4.28709 + 2.47515i) q^{72} +7.67213i q^{73} +(1.11254 - 1.92698i) q^{74} +(-0.996377 - 1.72578i) q^{75} +(-1.88285 + 1.08706i) q^{76} +(-4.32659 - 3.19030i) q^{78} -15.7399 q^{79} +(-4.90700 + 2.83306i) q^{80} +(0.707906 + 1.22613i) q^{81} +(-4.06400 + 7.03905i) q^{82} -7.97408i q^{83} +(-4.31275 - 2.48997i) q^{85} -11.6217i q^{86} +(2.05328 - 3.55639i) q^{87} +(-4.20379 - 7.28117i) q^{88} +(13.9118 - 8.03198i) q^{89} +3.79017 q^{90} -2.59235 q^{92} +(-2.09064 + 1.20703i) q^{93} +(-4.25052 - 7.36212i) q^{94} +(-5.32659 + 9.22592i) q^{95} +2.41340i q^{96} +(12.3209 + 7.11347i) q^{97} +4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10554 0.638282i 0.781733 0.451334i −0.0553113 0.998469i \(-0.517615\pi\)
0.837044 + 0.547136i \(0.184282\pi\)
\(3\) −0.583963 1.01145i −0.337151 0.583963i 0.646745 0.762707i \(-0.276130\pi\)
−0.983896 + 0.178744i \(0.942797\pi\)
\(4\) −0.185192 + 0.320762i −0.0925960 + 0.160381i
\(5\) 1.81487i 0.811636i 0.913954 + 0.405818i \(0.133013\pi\)
−0.913954 + 0.405818i \(0.866987\pi\)
\(6\) −1.29118 0.745466i −0.527124 0.304335i
\(7\) 0 0
\(8\) 3.02595i 1.06983i
\(9\) 0.817975 1.41677i 0.272658 0.472258i
\(10\) 1.15840 + 2.00641i 0.366319 + 0.634482i
\(11\) −2.40625 + 1.38925i −0.725510 + 0.418874i −0.816777 0.576953i \(-0.804242\pi\)
0.0912671 + 0.995826i \(0.470908\pi\)
\(12\) 0.432581 0.124875
\(13\) 3.58305 + 0.402155i 0.993760 + 0.111538i
\(14\) 0 0
\(15\) 1.83566 1.05982i 0.473965 0.273644i
\(16\) 1.56102 + 2.70377i 0.390256 + 0.675943i
\(17\) −1.37198 + 2.37634i −0.332754 + 0.576347i −0.983051 0.183334i \(-0.941311\pi\)
0.650297 + 0.759680i \(0.274645\pi\)
\(18\) 2.08840i 0.492240i
\(19\) 5.08351 + 2.93497i 1.16624 + 0.673327i 0.952791 0.303628i \(-0.0981979\pi\)
0.213446 + 0.976955i \(0.431531\pi\)
\(20\) −0.582143 0.336100i −0.130171 0.0751543i
\(21\) 0 0
\(22\) −1.77346 + 3.07173i −0.378103 + 0.654894i
\(23\) 3.49955 + 6.06139i 0.729706 + 1.26389i 0.957007 + 0.290063i \(0.0936763\pi\)
−0.227302 + 0.973824i \(0.572990\pi\)
\(24\) 3.06060 1.76704i 0.624743 0.360696i
\(25\) 1.70623 0.341247
\(26\) 4.21789 1.84240i 0.827195 0.361325i
\(27\) −5.41444 −1.04201
\(28\) 0 0
\(29\) 1.75806 + 3.04505i 0.326463 + 0.565451i 0.981807 0.189879i \(-0.0608097\pi\)
−0.655344 + 0.755330i \(0.727476\pi\)
\(30\) 1.35293 2.34334i 0.247009 0.427833i
\(31\) 2.06697i 0.371238i −0.982622 0.185619i \(-0.940571\pi\)
0.982622 0.185619i \(-0.0594290\pi\)
\(32\) −1.78956 1.03320i −0.316352 0.182646i
\(33\) 2.81031 + 1.62254i 0.489213 + 0.282447i
\(34\) 3.50284i 0.600732i
\(35\) 0 0
\(36\) 0.302965 + 0.524751i 0.0504942 + 0.0874585i
\(37\) 1.50950 0.871512i 0.248161 0.143276i −0.370761 0.928728i \(-0.620903\pi\)
0.618922 + 0.785453i \(0.287570\pi\)
\(38\) 7.49334 1.21558
\(39\) −1.68561 3.85893i −0.269913 0.617924i
\(40\) −5.49171 −0.868316
\(41\) −5.51406 + 3.18355i −0.861152 + 0.497186i −0.864398 0.502808i \(-0.832300\pi\)
0.00324599 + 0.999995i \(0.498967\pi\)
\(42\) 0 0
\(43\) 4.55195 7.88422i 0.694167 1.20233i −0.276294 0.961073i \(-0.589106\pi\)
0.970461 0.241259i \(-0.0775603\pi\)
\(44\) 1.02911i 0.155144i
\(45\) 2.57127 + 1.48452i 0.383302 + 0.221299i
\(46\) 7.73776 + 4.46740i 1.14087 + 0.658681i
\(47\) 6.65932i 0.971361i −0.874136 0.485681i \(-0.838572\pi\)
0.874136 0.485681i \(-0.161428\pi\)
\(48\) 1.82316 3.15780i 0.263150 0.455790i
\(49\) 0 0
\(50\) 1.88631 1.08906i 0.266764 0.154016i
\(51\) 3.20474 0.448753
\(52\) −0.792549 + 1.07483i −0.109907 + 0.149052i
\(53\) −10.4879 −1.44063 −0.720313 0.693649i \(-0.756002\pi\)
−0.720313 + 0.693649i \(0.756002\pi\)
\(54\) −5.98587 + 3.45594i −0.814573 + 0.470294i
\(55\) −2.52131 4.36703i −0.339973 0.588850i
\(56\) 0 0
\(57\) 6.85564i 0.908052i
\(58\) 3.88720 + 2.24427i 0.510414 + 0.294688i
\(59\) −2.66212 1.53698i −0.346579 0.200097i 0.316598 0.948560i \(-0.397459\pi\)
−0.663177 + 0.748462i \(0.730793\pi\)
\(60\) 0.785080i 0.101353i
\(61\) 0.540892 0.936853i 0.0692541 0.119952i −0.829319 0.558775i \(-0.811271\pi\)
0.898573 + 0.438824i \(0.144605\pi\)
\(62\) −1.31931 2.28511i −0.167552 0.290209i
\(63\) 0 0
\(64\) −8.88199 −1.11025
\(65\) −0.729860 + 6.50279i −0.0905280 + 0.806572i
\(66\) 4.14254 0.509912
\(67\) 4.34568 2.50898i 0.530910 0.306521i −0.210477 0.977599i \(-0.567502\pi\)
0.741387 + 0.671078i \(0.234168\pi\)
\(68\) −0.508159 0.880158i −0.0616234 0.106735i
\(69\) 4.08721 7.07925i 0.492042 0.852242i
\(70\) 0 0
\(71\) 2.35453 + 1.35939i 0.279431 + 0.161330i 0.633166 0.774016i \(-0.281755\pi\)
−0.353735 + 0.935346i \(0.615088\pi\)
\(72\) 4.28709 + 2.47515i 0.505238 + 0.291699i
\(73\) 7.67213i 0.897955i 0.893543 + 0.448978i \(0.148212\pi\)
−0.893543 + 0.448978i \(0.851788\pi\)
\(74\) 1.11254 1.92698i 0.129330 0.224006i
\(75\) −0.996377 1.72578i −0.115052 0.199275i
\(76\) −1.88285 + 1.08706i −0.215978 + 0.124695i
\(77\) 0 0
\(78\) −4.32659 3.19030i −0.489890 0.361230i
\(79\) −15.7399 −1.77087 −0.885436 0.464761i \(-0.846140\pi\)
−0.885436 + 0.464761i \(0.846140\pi\)
\(80\) −4.90700 + 2.83306i −0.548620 + 0.316746i
\(81\) 0.707906 + 1.22613i 0.0786563 + 0.136237i
\(82\) −4.06400 + 7.03905i −0.448794 + 0.777333i
\(83\) 7.97408i 0.875269i −0.899153 0.437635i \(-0.855816\pi\)
0.899153 0.437635i \(-0.144184\pi\)
\(84\) 0 0
\(85\) −4.31275 2.48997i −0.467784 0.270075i
\(86\) 11.6217i 1.25320i
\(87\) 2.05328 3.55639i 0.220135 0.381285i
\(88\) −4.20379 7.28117i −0.448125 0.776176i
\(89\) 13.9118 8.03198i 1.47465 0.851388i 0.475055 0.879956i \(-0.342428\pi\)
0.999592 + 0.0285683i \(0.00909482\pi\)
\(90\) 3.79017 0.399519
\(91\) 0 0
\(92\) −2.59235 −0.270271
\(93\) −2.09064 + 1.20703i −0.216789 + 0.125163i
\(94\) −4.25052 7.36212i −0.438408 0.759345i
\(95\) −5.32659 + 9.22592i −0.546497 + 0.946560i
\(96\) 2.41340i 0.246317i
\(97\) 12.3209 + 7.11347i 1.25100 + 0.722263i 0.971307 0.237827i \(-0.0764353\pi\)
0.279689 + 0.960091i \(0.409769\pi\)
\(98\) 0 0
\(99\) 4.54548i 0.456838i
\(100\) −0.315981 + 0.547295i −0.0315981 + 0.0547295i
\(101\) 0.0365612 + 0.0633259i 0.00363798 + 0.00630117i 0.867839 0.496846i \(-0.165509\pi\)
−0.864201 + 0.503147i \(0.832175\pi\)
\(102\) 3.54296 2.04553i 0.350805 0.202537i
\(103\) −12.9196 −1.27301 −0.636503 0.771275i \(-0.719620\pi\)
−0.636503 + 0.771275i \(0.719620\pi\)
\(104\) −1.21690 + 10.8421i −0.119327 + 1.06316i
\(105\) 0 0
\(106\) −11.5948 + 6.69425i −1.12618 + 0.650203i
\(107\) −2.00427 3.47150i −0.193761 0.335603i 0.752733 0.658326i \(-0.228735\pi\)
−0.946493 + 0.322723i \(0.895402\pi\)
\(108\) 1.00271 1.73675i 0.0964860 0.167119i
\(109\) 1.98589i 0.190214i −0.995467 0.0951071i \(-0.969681\pi\)
0.995467 0.0951071i \(-0.0303194\pi\)
\(110\) −5.57479 3.21861i −0.531536 0.306882i
\(111\) −1.76299 1.01786i −0.167335 0.0966110i
\(112\) 0 0
\(113\) 5.28711 9.15754i 0.497369 0.861469i −0.502626 0.864504i \(-0.667633\pi\)
0.999995 + 0.00303506i \(0.000966090\pi\)
\(114\) −4.37583 7.57916i −0.409834 0.709854i
\(115\) −11.0007 + 6.35123i −1.02582 + 0.592256i
\(116\) −1.30231 −0.120917
\(117\) 3.50061 4.74743i 0.323632 0.438900i
\(118\) −3.92410 −0.361243
\(119\) 0 0
\(120\) 3.20695 + 5.55461i 0.292753 + 0.507064i
\(121\) −1.63999 + 2.84054i −0.149090 + 0.258231i
\(122\) 1.38097i 0.125027i
\(123\) 6.44001 + 3.71814i 0.580676 + 0.335254i
\(124\) 0.663004 + 0.382786i 0.0595395 + 0.0343752i
\(125\) 12.1710i 1.08860i
\(126\) 0 0
\(127\) 5.63478 + 9.75972i 0.500006 + 0.866035i 1.00000 6.53271e-6i \(2.07943e-6\pi\)
−0.499994 + 0.866029i \(0.666665\pi\)
\(128\) −6.24025 + 3.60281i −0.551566 + 0.318447i
\(129\) −10.6327 −0.936156
\(130\) 3.34373 + 7.65493i 0.293264 + 0.671382i
\(131\) −3.06481 −0.267774 −0.133887 0.990997i \(-0.542746\pi\)
−0.133887 + 0.990997i \(0.542746\pi\)
\(132\) −1.04090 + 0.600962i −0.0905984 + 0.0523070i
\(133\) 0 0
\(134\) 3.20288 5.54754i 0.276686 0.479235i
\(135\) 9.82653i 0.845733i
\(136\) −7.19067 4.15154i −0.616595 0.355991i
\(137\) 18.9512 + 10.9415i 1.61911 + 0.934796i 0.987150 + 0.159799i \(0.0510845\pi\)
0.631965 + 0.774997i \(0.282249\pi\)
\(138\) 10.4352i 0.888300i
\(139\) 5.53535 9.58750i 0.469502 0.813201i −0.529890 0.848066i \(-0.677767\pi\)
0.999392 + 0.0348652i \(0.0111002\pi\)
\(140\) 0 0
\(141\) −6.73559 + 3.88879i −0.567239 + 0.327495i
\(142\) 3.47069 0.291254
\(143\) −9.18040 + 4.01006i −0.767703 + 0.335338i
\(144\) 5.10752 0.425626
\(145\) −5.52637 + 3.19065i −0.458940 + 0.264969i
\(146\) 4.89699 + 8.48183i 0.405277 + 0.701961i
\(147\) 0 0
\(148\) 0.645588i 0.0530670i
\(149\) −1.99824 1.15369i −0.163702 0.0945136i 0.415911 0.909406i \(-0.363463\pi\)
−0.579613 + 0.814892i \(0.696796\pi\)
\(150\) −2.20306 1.27194i −0.179879 0.103853i
\(151\) 20.6158i 1.67769i −0.544371 0.838845i \(-0.683232\pi\)
0.544371 0.838845i \(-0.316768\pi\)
\(152\) −8.88105 + 15.3824i −0.720348 + 1.24768i
\(153\) 2.24449 + 3.88757i 0.181456 + 0.314292i
\(154\) 0 0
\(155\) 3.75128 0.301310
\(156\) 1.54996 + 0.173964i 0.124096 + 0.0139283i
\(157\) −2.89649 −0.231165 −0.115582 0.993298i \(-0.536873\pi\)
−0.115582 + 0.993298i \(0.536873\pi\)
\(158\) −17.4010 + 10.0465i −1.38435 + 0.799254i
\(159\) 6.12455 + 10.6080i 0.485709 + 0.841272i
\(160\) 1.87513 3.24782i 0.148242 0.256763i
\(161\) 0 0
\(162\) 1.56523 + 0.903688i 0.122976 + 0.0710004i
\(163\) −20.2944 11.7170i −1.58958 0.917743i −0.993376 0.114907i \(-0.963343\pi\)
−0.596201 0.802835i \(-0.703324\pi\)
\(164\) 2.35827i 0.184150i
\(165\) −2.94470 + 5.10037i −0.229244 + 0.397063i
\(166\) −5.08971 8.81564i −0.395038 0.684226i
\(167\) −6.58349 + 3.80098i −0.509446 + 0.294129i −0.732606 0.680653i \(-0.761696\pi\)
0.223160 + 0.974782i \(0.428363\pi\)
\(168\) 0 0
\(169\) 12.6765 + 2.88188i 0.975119 + 0.221683i
\(170\) −6.35721 −0.487576
\(171\) 8.31637 4.80146i 0.635969 0.367177i
\(172\) 1.68597 + 2.92019i 0.128554 + 0.222662i
\(173\) −2.69861 + 4.67412i −0.205171 + 0.355367i −0.950187 0.311679i \(-0.899108\pi\)
0.745016 + 0.667047i \(0.232442\pi\)
\(174\) 5.24229i 0.397417i
\(175\) 0 0
\(176\) −7.51241 4.33729i −0.566269 0.326936i
\(177\) 3.59015i 0.269852i
\(178\) 10.2533 17.7593i 0.768520 1.33112i
\(179\) −6.14571 10.6447i −0.459352 0.795621i 0.539575 0.841938i \(-0.318585\pi\)
−0.998927 + 0.0463168i \(0.985252\pi\)
\(180\) −0.952357 + 0.549843i −0.0709845 + 0.0409829i
\(181\) 21.8525 1.62428 0.812140 0.583463i \(-0.198303\pi\)
0.812140 + 0.583463i \(0.198303\pi\)
\(182\) 0 0
\(183\) −1.26344 −0.0933964
\(184\) −18.3415 + 10.5894i −1.35215 + 0.780664i
\(185\) 1.58168 + 2.73956i 0.116288 + 0.201416i
\(186\) −1.54085 + 2.66883i −0.112981 + 0.195688i
\(187\) 7.62407i 0.557527i
\(188\) 2.13606 + 1.23325i 0.155788 + 0.0899442i
\(189\) 0 0
\(190\) 13.5995i 0.986609i
\(191\) −1.37858 + 2.38777i −0.0997507 + 0.172773i −0.911581 0.411120i \(-0.865138\pi\)
0.811831 + 0.583893i \(0.198471\pi\)
\(192\) 5.18675 + 8.98371i 0.374321 + 0.648344i
\(193\) 11.2491 6.49467i 0.809728 0.467497i −0.0371334 0.999310i \(-0.511823\pi\)
0.846861 + 0.531814i \(0.178489\pi\)
\(194\) 18.1616 1.30393
\(195\) 7.00347 3.05917i 0.501529 0.219071i
\(196\) 0 0
\(197\) 16.4772 9.51312i 1.17395 0.677781i 0.219344 0.975648i \(-0.429608\pi\)
0.954608 + 0.297866i \(0.0962749\pi\)
\(198\) 2.90130 + 5.02519i 0.206186 + 0.357125i
\(199\) 10.0159 17.3480i 0.710006 1.22977i −0.254848 0.966981i \(-0.582025\pi\)
0.964854 0.262786i \(-0.0846412\pi\)
\(200\) 5.16298i 0.365078i
\(201\) −5.07543 2.93030i −0.357993 0.206688i
\(202\) 0.0808396 + 0.0466728i 0.00568785 + 0.00328388i
\(203\) 0 0
\(204\) −0.593492 + 1.02796i −0.0415528 + 0.0719715i
\(205\) −5.77773 10.0073i −0.403534 0.698942i
\(206\) −14.2831 + 8.24634i −0.995150 + 0.574550i
\(207\) 11.4502 0.795842
\(208\) 4.50590 + 10.3155i 0.312428 + 0.715254i
\(209\) −16.3096 −1.12816
\(210\) 0 0
\(211\) −5.00015 8.66052i −0.344225 0.596215i 0.640988 0.767551i \(-0.278525\pi\)
−0.985213 + 0.171336i \(0.945192\pi\)
\(212\) 1.94228 3.36413i 0.133396 0.231049i
\(213\) 3.17532i 0.217570i
\(214\) −4.43160 2.55858i −0.302938 0.174901i
\(215\) 14.3089 + 8.26122i 0.975856 + 0.563411i
\(216\) 16.3838i 1.11478i
\(217\) 0 0
\(218\) −1.26756 2.19548i −0.0858501 0.148697i
\(219\) 7.76000 4.48024i 0.524372 0.302747i
\(220\) 1.86770 0.125921
\(221\) −5.87153 + 7.96280i −0.394962 + 0.535636i
\(222\) −2.59873 −0.174415
\(223\) −7.25954 + 4.19130i −0.486135 + 0.280670i −0.722970 0.690880i \(-0.757223\pi\)
0.236835 + 0.971550i \(0.423890\pi\)
\(224\) 0 0
\(225\) 1.39566 2.41735i 0.0930439 0.161157i
\(226\) 13.4987i 0.897918i
\(227\) 0.796500 + 0.459860i 0.0528656 + 0.0305220i 0.526200 0.850361i \(-0.323616\pi\)
−0.473334 + 0.880883i \(0.656950\pi\)
\(228\) 2.19903 + 1.26961i 0.145634 + 0.0840820i
\(229\) 24.6208i 1.62699i −0.581574 0.813494i \(-0.697563\pi\)
0.581574 0.813494i \(-0.302437\pi\)
\(230\) −8.10776 + 14.0430i −0.534610 + 0.925971i
\(231\) 0 0
\(232\) −9.21415 + 5.31979i −0.604939 + 0.349261i
\(233\) 17.2769 1.13185 0.565925 0.824457i \(-0.308519\pi\)
0.565925 + 0.824457i \(0.308519\pi\)
\(234\) 0.839858 7.48283i 0.0549032 0.489168i
\(235\) 12.0858 0.788392
\(236\) 0.986008 0.569272i 0.0641837 0.0370565i
\(237\) 9.19149 + 15.9201i 0.597051 + 1.03412i
\(238\) 0 0
\(239\) 14.4828i 0.936816i 0.883512 + 0.468408i \(0.155172\pi\)
−0.883512 + 0.468408i \(0.844828\pi\)
\(240\) 5.73101 + 3.30880i 0.369935 + 0.213582i
\(241\) 7.30441 + 4.21720i 0.470518 + 0.271654i 0.716457 0.697632i \(-0.245763\pi\)
−0.245938 + 0.969285i \(0.579096\pi\)
\(242\) 4.18710i 0.269157i
\(243\) −7.29488 + 12.6351i −0.467967 + 0.810543i
\(244\) 0.200338 + 0.346995i 0.0128253 + 0.0222141i
\(245\) 0 0
\(246\) 9.49290 0.605245
\(247\) 17.0342 + 12.5605i 1.08386 + 0.799205i
\(248\) 6.25453 0.397163
\(249\) −8.06541 + 4.65657i −0.511124 + 0.295098i
\(250\) 7.76851 + 13.4555i 0.491324 + 0.850998i
\(251\) 7.33631 12.7069i 0.463064 0.802050i −0.536048 0.844188i \(-0.680083\pi\)
0.999112 + 0.0421373i \(0.0134167\pi\)
\(252\) 0 0
\(253\) −16.8415 9.72346i −1.05882 0.611309i
\(254\) 12.4589 + 7.19315i 0.781742 + 0.451339i
\(255\) 5.81620i 0.364224i
\(256\) 4.28277 7.41797i 0.267673 0.463623i
\(257\) −14.6643 25.3993i −0.914733 1.58436i −0.807292 0.590152i \(-0.799068\pi\)
−0.107441 0.994211i \(-0.534266\pi\)
\(258\) −11.7548 + 6.78665i −0.731824 + 0.422519i
\(259\) 0 0
\(260\) −1.95068 1.43838i −0.120976 0.0892043i
\(261\) 5.75219 0.356052
\(262\) −3.38826 + 1.95622i −0.209328 + 0.120855i
\(263\) −9.95747 17.2468i −0.614004 1.06349i −0.990558 0.137091i \(-0.956225\pi\)
0.376555 0.926394i \(-0.377109\pi\)
\(264\) −4.90971 + 8.50386i −0.302172 + 0.523377i
\(265\) 19.0342i 1.16926i
\(266\) 0 0
\(267\) −16.2479 9.38075i −0.994357 0.574092i
\(268\) 1.85857i 0.113530i
\(269\) −11.1625 + 19.3340i −0.680589 + 1.17881i 0.294213 + 0.955740i \(0.404943\pi\)
−0.974801 + 0.223074i \(0.928391\pi\)
\(270\) −6.27210 10.8636i −0.381708 0.661137i
\(271\) 8.14054 4.69994i 0.494502 0.285501i −0.231938 0.972731i \(-0.574507\pi\)
0.726440 + 0.687230i \(0.241173\pi\)
\(272\) −8.56677 −0.519437
\(273\) 0 0
\(274\) 27.9351 1.68762
\(275\) −4.10562 + 2.37038i −0.247578 + 0.142939i
\(276\) 1.51384 + 2.62204i 0.0911223 + 0.157828i
\(277\) −7.17133 + 12.4211i −0.430883 + 0.746312i −0.996950 0.0780478i \(-0.975131\pi\)
0.566066 + 0.824360i \(0.308465\pi\)
\(278\) 14.1324i 0.847608i
\(279\) −2.92842 1.69073i −0.175320 0.101221i
\(280\) 0 0
\(281\) 0.0988416i 0.00589640i 0.999996 + 0.00294820i \(0.000938442\pi\)
−0.999996 + 0.00294820i \(0.999062\pi\)
\(282\) −4.96429 + 8.59841i −0.295619 + 0.512028i
\(283\) 0.310336 + 0.537518i 0.0184476 + 0.0319521i 0.875102 0.483939i \(-0.160794\pi\)
−0.856654 + 0.515891i \(0.827461\pi\)
\(284\) −0.872079 + 0.503495i −0.0517484 + 0.0298769i
\(285\) 12.4421 0.737007
\(286\) −7.58972 + 10.2930i −0.448789 + 0.608635i
\(287\) 0 0
\(288\) −2.92763 + 1.69027i −0.172512 + 0.0995998i
\(289\) 4.73534 + 8.20186i 0.278550 + 0.482462i
\(290\) −4.07307 + 7.05477i −0.239179 + 0.414270i
\(291\) 16.6160i 0.974047i
\(292\) −2.46093 1.42082i −0.144015 0.0831471i
\(293\) −21.5586 12.4469i −1.25947 0.727153i −0.286496 0.958082i \(-0.592490\pi\)
−0.972971 + 0.230928i \(0.925824\pi\)
\(294\) 0 0
\(295\) 2.78942 4.83142i 0.162406 0.281296i
\(296\) 2.63715 + 4.56767i 0.153281 + 0.265491i
\(297\) 13.0285 7.52200i 0.755989 0.436471i
\(298\) −2.94551 −0.170629
\(299\) 10.1014 + 23.1256i 0.584182 + 1.33739i
\(300\) 0.738085 0.0426133
\(301\) 0 0
\(302\) −13.1587 22.7915i −0.757197 1.31150i
\(303\) 0.0427008 0.0739599i 0.00245310 0.00424889i
\(304\) 18.3262i 1.05108i
\(305\) 1.70027 + 0.981651i 0.0973571 + 0.0562091i
\(306\) 4.96274 + 2.86524i 0.283701 + 0.163795i
\(307\) 9.89767i 0.564890i −0.959284 0.282445i \(-0.908855\pi\)
0.959284 0.282445i \(-0.0911455\pi\)
\(308\) 0 0
\(309\) 7.54456 + 13.0676i 0.429195 + 0.743387i
\(310\) 4.14718 2.39437i 0.235544 0.135991i
\(311\) 7.23790 0.410423 0.205212 0.978718i \(-0.434212\pi\)
0.205212 + 0.978718i \(0.434212\pi\)
\(312\) 11.6769 5.10056i 0.661076 0.288763i
\(313\) −32.6606 −1.84609 −0.923043 0.384696i \(-0.874306\pi\)
−0.923043 + 0.384696i \(0.874306\pi\)
\(314\) −3.20217 + 1.84877i −0.180709 + 0.104332i
\(315\) 0 0
\(316\) 2.91490 5.04875i 0.163976 0.284014i
\(317\) 17.1744i 0.964608i 0.876004 + 0.482304i \(0.160200\pi\)
−0.876004 + 0.482304i \(0.839800\pi\)
\(318\) 13.5418 + 7.81838i 0.759388 + 0.438433i
\(319\) −8.46064 4.88475i −0.473705 0.273494i
\(320\) 16.1197i 0.901118i
\(321\) −2.34084 + 4.05446i −0.130653 + 0.226298i
\(322\) 0 0
\(323\) −13.9489 + 8.05342i −0.776140 + 0.448105i
\(324\) −0.524395 −0.0291330
\(325\) 6.11353 + 0.686170i 0.339118 + 0.0380619i
\(326\) −29.9149 −1.65683
\(327\) −2.00864 + 1.15969i −0.111078 + 0.0641309i
\(328\) −9.63324 16.6853i −0.531907 0.921289i
\(329\) 0 0
\(330\) 7.51819i 0.413863i
\(331\) 17.2633 + 9.96698i 0.948877 + 0.547835i 0.892732 0.450588i \(-0.148786\pi\)
0.0561454 + 0.998423i \(0.482119\pi\)
\(332\) 2.55778 + 1.47674i 0.140377 + 0.0810465i
\(333\) 2.85150i 0.156261i
\(334\) −4.85219 + 8.40424i −0.265500 + 0.459860i
\(335\) 4.55348 + 7.88687i 0.248783 + 0.430905i
\(336\) 0 0
\(337\) 1.27189 0.0692842 0.0346421 0.999400i \(-0.488971\pi\)
0.0346421 + 0.999400i \(0.488971\pi\)
\(338\) 15.8538 4.90518i 0.862335 0.266807i
\(339\) −12.3499 −0.670754
\(340\) 1.59738 0.922245i 0.0866298 0.0500158i
\(341\) 2.87152 + 4.97363i 0.155502 + 0.269337i
\(342\) 6.12937 10.6164i 0.331438 0.574068i
\(343\) 0 0
\(344\) 23.8572 + 13.7740i 1.28630 + 0.742643i
\(345\) 12.8479 + 7.41777i 0.691710 + 0.399359i
\(346\) 6.88989i 0.370403i
\(347\) −12.9417 + 22.4156i −0.694744 + 1.20333i 0.275522 + 0.961295i \(0.411149\pi\)
−0.970267 + 0.242038i \(0.922184\pi\)
\(348\) 0.760503 + 1.31723i 0.0407672 + 0.0706109i
\(349\) 14.9967 8.65837i 0.802757 0.463472i −0.0416774 0.999131i \(-0.513270\pi\)
0.844434 + 0.535659i \(0.179937\pi\)
\(350\) 0 0
\(351\) −19.4002 2.17744i −1.03551 0.116223i
\(352\) 5.74148 0.306022
\(353\) 21.9533 12.6747i 1.16846 0.674608i 0.215140 0.976583i \(-0.430979\pi\)
0.953316 + 0.301975i \(0.0976459\pi\)
\(354\) 2.29153 + 3.96904i 0.121793 + 0.210952i
\(355\) −2.46711 + 4.27317i −0.130941 + 0.226796i
\(356\) 5.94983i 0.315341i
\(357\) 0 0
\(358\) −13.5886 7.84539i −0.718181 0.414642i
\(359\) 5.27044i 0.278163i −0.990281 0.139082i \(-0.955585\pi\)
0.990281 0.139082i \(-0.0444151\pi\)
\(360\) −4.49208 + 7.78052i −0.236754 + 0.410069i
\(361\) 7.72804 + 13.3854i 0.406739 + 0.704493i
\(362\) 24.1587 13.9480i 1.26975 0.733092i
\(363\) 3.83077 0.201063
\(364\) 0 0
\(365\) −13.9240 −0.728813
\(366\) −1.39678 + 0.806433i −0.0730110 + 0.0421529i
\(367\) 12.6588 + 21.9257i 0.660783 + 1.14451i 0.980410 + 0.196967i \(0.0631092\pi\)
−0.319627 + 0.947544i \(0.603557\pi\)
\(368\) −10.9257 + 18.9240i −0.569544 + 0.986479i
\(369\) 10.4162i 0.542248i
\(370\) 3.49722 + 2.01912i 0.181812 + 0.104969i
\(371\) 0 0
\(372\) 0.894130i 0.0463585i
\(373\) 3.39391 5.87842i 0.175730 0.304373i −0.764684 0.644406i \(-0.777105\pi\)
0.940414 + 0.340033i \(0.110438\pi\)
\(374\) −4.86631 8.42869i −0.251631 0.435837i
\(375\) 12.3104 7.10739i 0.635704 0.367024i
\(376\) 20.1507 1.03920
\(377\) 5.07464 + 11.6176i 0.261357 + 0.598336i
\(378\) 0 0
\(379\) 10.6717 6.16130i 0.548168 0.316485i −0.200215 0.979752i \(-0.564164\pi\)
0.748383 + 0.663267i \(0.230831\pi\)
\(380\) −1.97288 3.41714i −0.101207 0.175295i
\(381\) 6.58100 11.3986i 0.337155 0.583969i
\(382\) 3.51970i 0.180083i
\(383\) 6.28662 + 3.62958i 0.321232 + 0.185463i 0.651941 0.758269i \(-0.273955\pi\)
−0.330710 + 0.943732i \(0.607288\pi\)
\(384\) 7.28815 + 4.20782i 0.371922 + 0.214729i
\(385\) 0 0
\(386\) 8.29086 14.3602i 0.421994 0.730915i
\(387\) −7.44677 12.8982i −0.378541 0.655652i
\(388\) −4.56346 + 2.63472i −0.231675 + 0.133757i
\(389\) 7.14811 0.362424 0.181212 0.983444i \(-0.441998\pi\)
0.181212 + 0.983444i \(0.441998\pi\)
\(390\) 5.78999 7.85221i 0.293187 0.397612i
\(391\) −19.2052 −0.971250
\(392\) 0 0
\(393\) 1.78974 + 3.09991i 0.0902802 + 0.156370i
\(394\) 12.1441 21.0342i 0.611811 1.05969i
\(395\) 28.5659i 1.43730i
\(396\) −1.45802 0.841786i −0.0732681 0.0423014i
\(397\) 19.4520 + 11.2306i 0.976266 + 0.563647i 0.901141 0.433527i \(-0.142731\pi\)
0.0751252 + 0.997174i \(0.476064\pi\)
\(398\) 25.5718i 1.28180i
\(399\) 0 0
\(400\) 2.66347 + 4.61327i 0.133174 + 0.230663i
\(401\) −2.64547 + 1.52736i −0.132108 + 0.0762729i −0.564598 0.825366i \(-0.690969\pi\)
0.432489 + 0.901639i \(0.357635\pi\)
\(402\) −7.48144 −0.373140
\(403\) 0.831240 7.40605i 0.0414070 0.368921i
\(404\) −0.0270834 −0.00134745
\(405\) −2.22527 + 1.28476i −0.110575 + 0.0638403i
\(406\) 0 0
\(407\) −2.42149 + 4.19414i −0.120029 + 0.207896i
\(408\) 9.69737i 0.480091i
\(409\) −4.85482 2.80293i −0.240055 0.138596i 0.375147 0.926965i \(-0.377592\pi\)
−0.615202 + 0.788369i \(0.710926\pi\)
\(410\) −12.7750 7.37564i −0.630912 0.364257i
\(411\) 25.5577i 1.26067i
\(412\) 2.39261 4.14412i 0.117875 0.204166i
\(413\) 0 0
\(414\) 12.6586 7.30844i 0.622136 0.359190i
\(415\) 14.4719 0.710400
\(416\) −5.99657 4.42169i −0.294006 0.216791i
\(417\) −12.9297 −0.633172
\(418\) −18.0308 + 10.4101i −0.881916 + 0.509175i
\(419\) 3.06969 + 5.31687i 0.149964 + 0.259746i 0.931214 0.364473i \(-0.118751\pi\)
−0.781250 + 0.624219i \(0.785417\pi\)
\(420\) 0 0
\(421\) 1.92589i 0.0938622i −0.998898 0.0469311i \(-0.985056\pi\)
0.998898 0.0469311i \(-0.0149441\pi\)
\(422\) −11.0557 6.38302i −0.538184 0.310720i
\(423\) −9.43475 5.44716i −0.458733 0.264850i
\(424\) 31.7359i 1.54123i
\(425\) −2.34092 + 4.05459i −0.113551 + 0.196677i
\(426\) −2.02675 3.51044i −0.0981965 0.170081i
\(427\) 0 0
\(428\) 1.48470 0.0717658
\(429\) 9.41700 + 6.94381i 0.454657 + 0.335250i
\(430\) 21.0920 1.01714
\(431\) 9.30923 5.37469i 0.448410 0.258890i −0.258749 0.965945i \(-0.583310\pi\)
0.707158 + 0.707055i \(0.249977\pi\)
\(432\) −8.45207 14.6394i −0.406651 0.704340i
\(433\) −20.1328 + 34.8710i −0.967520 + 1.67579i −0.264835 + 0.964294i \(0.585318\pi\)
−0.702685 + 0.711501i \(0.748016\pi\)
\(434\) 0 0
\(435\) 6.45439 + 3.72644i 0.309464 + 0.178669i
\(436\) 0.637000 + 0.367772i 0.0305068 + 0.0176131i
\(437\) 41.0842i 1.96532i
\(438\) 5.71931 9.90614i 0.273279 0.473334i
\(439\) 10.9754 + 19.0099i 0.523826 + 0.907294i 0.999615 + 0.0277345i \(0.00882930\pi\)
−0.475789 + 0.879560i \(0.657837\pi\)
\(440\) 13.2144 7.62934i 0.629972 0.363715i
\(441\) 0 0
\(442\) −1.40868 + 12.5509i −0.0670042 + 0.596984i
\(443\) −27.8963 −1.32539 −0.662697 0.748887i \(-0.730588\pi\)
−0.662697 + 0.748887i \(0.730588\pi\)
\(444\) 0.652982 0.376999i 0.0309892 0.0178916i
\(445\) 14.5770 + 25.2481i 0.691017 + 1.19688i
\(446\) −5.35046 + 9.26727i −0.253352 + 0.438818i
\(447\) 2.69484i 0.127461i
\(448\) 0 0
\(449\) 19.1056 + 11.0306i 0.901648 + 0.520567i 0.877734 0.479147i \(-0.159054\pi\)
0.0239134 + 0.999714i \(0.492387\pi\)
\(450\) 3.56329i 0.167975i
\(451\) 8.84546 15.3208i 0.416516 0.721427i
\(452\) 1.95826 + 3.39181i 0.0921088 + 0.159537i
\(453\) −20.8519 + 12.0389i −0.979708 + 0.565635i
\(454\) 1.17408 0.0551023
\(455\) 0 0
\(456\) 20.7448 0.971464
\(457\) 4.77724 2.75814i 0.223470 0.129020i −0.384086 0.923297i \(-0.625483\pi\)
0.607556 + 0.794277i \(0.292150\pi\)
\(458\) −15.7150 27.2192i −0.734314 1.27187i
\(459\) 7.42851 12.8665i 0.346733 0.600559i
\(460\) 4.70479i 0.219362i
\(461\) −25.0092 14.4391i −1.16479 0.672494i −0.212346 0.977195i \(-0.568110\pi\)
−0.952448 + 0.304700i \(0.901444\pi\)
\(462\) 0 0
\(463\) 14.2284i 0.661251i 0.943762 + 0.330625i \(0.107260\pi\)
−0.943762 + 0.330625i \(0.892740\pi\)
\(464\) −5.48874 + 9.50678i −0.254808 + 0.441341i
\(465\) −2.19061 3.79424i −0.101587 0.175954i
\(466\) 19.1003 11.0276i 0.884804 0.510842i
\(467\) −4.54326 −0.210237 −0.105118 0.994460i \(-0.533522\pi\)
−0.105118 + 0.994460i \(0.533522\pi\)
\(468\) 0.874509 + 2.00205i 0.0404242 + 0.0925448i
\(469\) 0 0
\(470\) 13.3613 7.71416i 0.616312 0.355828i
\(471\) 1.69144 + 2.92966i 0.0779374 + 0.134992i
\(472\) 4.65081 8.05545i 0.214071 0.370782i
\(473\) 25.2951i 1.16307i
\(474\) 20.3231 + 11.7335i 0.933469 + 0.538939i
\(475\) 8.67366 + 5.00774i 0.397975 + 0.229771i
\(476\) 0 0
\(477\) −8.57886 + 14.8590i −0.392799 + 0.680348i
\(478\) 9.24413 + 16.0113i 0.422817 + 0.732340i
\(479\) 1.44239 0.832764i 0.0659044 0.0380499i −0.466686 0.884423i \(-0.654552\pi\)
0.532590 + 0.846373i \(0.321219\pi\)
\(480\) −4.38002 −0.199920
\(481\) 5.75911 2.51562i 0.262593 0.114702i
\(482\) 10.7671 0.490426
\(483\) 0 0
\(484\) −0.607426 1.05209i −0.0276103 0.0478224i
\(485\) −12.9100 + 22.3608i −0.586215 + 1.01535i
\(486\) 18.6248i 0.844837i
\(487\) −1.28598 0.742463i −0.0582735 0.0336442i 0.470580 0.882357i \(-0.344045\pi\)
−0.528854 + 0.848713i \(0.677378\pi\)
\(488\) 2.83487 + 1.63671i 0.128328 + 0.0740904i
\(489\) 27.3691i 1.23767i
\(490\) 0 0
\(491\) 7.99791 + 13.8528i 0.360941 + 0.625167i 0.988116 0.153711i \(-0.0491224\pi\)
−0.627175 + 0.778878i \(0.715789\pi\)
\(492\) −2.38528 + 1.37714i −0.107537 + 0.0620863i
\(493\) −9.64808 −0.434528
\(494\) 26.8490 + 3.01348i 1.20800 + 0.135583i
\(495\) −8.24947 −0.370786
\(496\) 5.58860 3.22658i 0.250936 0.144878i
\(497\) 0 0
\(498\) −5.94440 + 10.2960i −0.266375 + 0.461375i
\(499\) 17.7199i 0.793253i −0.917980 0.396627i \(-0.870181\pi\)
0.917980 0.396627i \(-0.129819\pi\)
\(500\) −3.90398 2.25397i −0.174591 0.100800i
\(501\) 7.68902 + 4.43926i 0.343520 + 0.198331i
\(502\) 18.7305i 0.835985i
\(503\) −0.598451 + 1.03655i −0.0266836 + 0.0462174i −0.879059 0.476713i \(-0.841828\pi\)
0.852375 + 0.522931i \(0.175161\pi\)
\(504\) 0 0
\(505\) −0.114929 + 0.0663540i −0.00511425 + 0.00295272i
\(506\) −24.8253 −1.10362
\(507\) −4.48774 14.5046i −0.199307 0.644174i
\(508\) −4.17406 −0.185194
\(509\) −5.44396 + 3.14307i −0.241299 + 0.139314i −0.615774 0.787923i \(-0.711156\pi\)
0.374474 + 0.927237i \(0.377823\pi\)
\(510\) 3.71237 + 6.43002i 0.164387 + 0.284726i
\(511\) 0 0
\(512\) 25.3457i 1.12013i
\(513\) −27.5244 15.8912i −1.21523 0.701614i
\(514\) −32.4238 18.7199i −1.43015 0.825699i
\(515\) 23.4474i 1.03322i
\(516\) 1.96909 3.41056i 0.0866843 0.150142i
\(517\) 9.25143 + 16.0240i 0.406878 + 0.704733i
\(518\) 0 0
\(519\) 6.30354 0.276695
\(520\) −19.6771 2.20852i −0.862898 0.0968499i
\(521\) 10.8473 0.475230 0.237615 0.971359i \(-0.423634\pi\)
0.237615 + 0.971359i \(0.423634\pi\)
\(522\) 6.35926 3.67152i 0.278337 0.160698i
\(523\) 0.673629 + 1.16676i 0.0294557 + 0.0510188i 0.880377 0.474274i \(-0.157289\pi\)
−0.850922 + 0.525292i \(0.823956\pi\)
\(524\) 0.567579 0.983076i 0.0247948 0.0429459i
\(525\) 0 0
\(526\) −22.0167 12.7113i −0.959974 0.554241i
\(527\) 4.91181 + 2.83583i 0.213962 + 0.123531i
\(528\) 10.1313i 0.440907i
\(529\) −12.9936 + 22.5057i −0.564941 + 0.978507i
\(530\) −12.1492 21.0431i −0.527728 0.914052i
\(531\) −4.35510 + 2.51442i −0.188995 + 0.109117i
\(532\) 0 0
\(533\) −21.0375 + 9.18931i −0.911233 + 0.398033i
\(534\) −23.9502 −1.03643
\(535\) 6.30034 3.63750i 0.272388 0.157263i
\(536\) 7.59205 + 13.1498i 0.327926 + 0.567985i
\(537\) −7.17773 + 12.4322i −0.309742 + 0.536489i
\(538\) 28.4993i 1.22869i
\(539\) 0 0
\(540\) 3.15198 + 1.81980i 0.135640 + 0.0783115i
\(541\) 20.1571i 0.866621i −0.901245 0.433310i \(-0.857345\pi\)
0.901245 0.433310i \(-0.142655\pi\)
\(542\) 5.99978 10.3919i 0.257712 0.446371i
\(543\) −12.7610 22.1027i −0.547628 0.948519i
\(544\) 4.91047 2.83506i 0.210535 0.121552i
\(545\) 3.60415 0.154385
\(546\) 0 0
\(547\) −3.42286 −0.146351 −0.0731755 0.997319i \(-0.523313\pi\)
−0.0731755 + 0.997319i \(0.523313\pi\)
\(548\) −7.01924 + 4.05256i −0.299847 + 0.173117i
\(549\) −0.884873 1.53264i −0.0377654 0.0654117i
\(550\) −3.02594 + 5.24109i −0.129027 + 0.223481i
\(551\) 20.6394i 0.879266i
\(552\) 21.4214 + 12.3677i 0.911757 + 0.526403i
\(553\) 0 0
\(554\) 18.3093i 0.777889i
\(555\) 1.84729 3.19960i 0.0784130 0.135815i
\(556\) 2.05020 + 3.55106i 0.0869480 + 0.150598i
\(557\) −20.4948 + 11.8327i −0.868394 + 0.501367i −0.866814 0.498631i \(-0.833836\pi\)
−0.00157977 + 0.999999i \(0.500503\pi\)
\(558\) −4.31664 −0.182738
\(559\) 19.4806 26.4190i 0.823940 1.11740i
\(560\) 0 0
\(561\) −7.71139 + 4.45217i −0.325575 + 0.187971i
\(562\) 0.0630888 + 0.109273i 0.00266124 + 0.00460941i
\(563\) −14.4037 + 24.9480i −0.607045 + 1.05143i 0.384680 + 0.923050i \(0.374312\pi\)
−0.991725 + 0.128382i \(0.959022\pi\)
\(564\) 2.88069i 0.121299i
\(565\) 16.6198 + 9.59543i 0.699199 + 0.403683i
\(566\) 0.686177 + 0.396164i 0.0288422 + 0.0166520i
\(567\) 0 0
\(568\) −4.11343 + 7.12467i −0.172596 + 0.298945i
\(569\) −13.8361 23.9648i −0.580040 1.00466i −0.995474 0.0950353i \(-0.969704\pi\)
0.415434 0.909623i \(-0.363630\pi\)
\(570\) 13.7552 7.94158i 0.576143 0.332636i
\(571\) −12.9655 −0.542588 −0.271294 0.962497i \(-0.587452\pi\)
−0.271294 + 0.962497i \(0.587452\pi\)
\(572\) 0.413861 3.68736i 0.0173044 0.154176i
\(573\) 3.22016 0.134524
\(574\) 0 0
\(575\) 5.97105 + 10.3422i 0.249010 + 0.431298i
\(576\) −7.26525 + 12.5838i −0.302719 + 0.524324i
\(577\) 9.46047i 0.393844i 0.980419 + 0.196922i \(0.0630947\pi\)
−0.980419 + 0.196922i \(0.936905\pi\)
\(578\) 10.4702 + 6.04497i 0.435503 + 0.251438i
\(579\) −13.1381 7.58529i −0.546001 0.315234i
\(580\) 2.36354i 0.0981405i
\(581\) 0 0
\(582\) −10.6057 18.3696i −0.439620 0.761444i
\(583\) 25.2365 14.5703i 1.04519 0.603440i
\(584\) −23.2155 −0.960663
\(585\) 8.61598 + 6.35317i 0.356227 + 0.262671i
\(586\) −31.7784 −1.31275
\(587\) 18.6673 10.7776i 0.770481 0.444837i −0.0625654 0.998041i \(-0.519928\pi\)
0.833046 + 0.553204i \(0.186595\pi\)
\(588\) 0 0
\(589\) 6.06647 10.5074i 0.249965 0.432951i
\(590\) 7.12175i 0.293198i
\(591\) −19.2441 11.1106i −0.791598 0.457029i
\(592\) 4.71274 + 2.72090i 0.193692 + 0.111828i
\(593\) 3.97234i 0.163124i 0.996668 + 0.0815622i \(0.0259909\pi\)
−0.996668 + 0.0815622i \(0.974009\pi\)
\(594\) 9.60231 16.6317i 0.393988 0.682407i
\(595\) 0 0
\(596\) 0.740117 0.427307i 0.0303164 0.0175032i
\(597\) −23.3956 −0.957517
\(598\) 25.9282 + 19.1187i 1.06028 + 0.781821i
\(599\) −19.5049 −0.796950 −0.398475 0.917179i \(-0.630460\pi\)
−0.398475 + 0.917179i \(0.630460\pi\)
\(600\) 5.22211 3.01498i 0.213192 0.123086i
\(601\) −13.4368 23.2733i −0.548100 0.949336i −0.998405 0.0564616i \(-0.982018\pi\)
0.450305 0.892875i \(-0.351315\pi\)
\(602\) 0 0
\(603\) 8.20914i 0.334302i
\(604\) 6.61276 + 3.81788i 0.269070 + 0.155347i
\(605\) −5.15523 2.97637i −0.209590 0.121007i
\(606\) 0.109021i 0.00442866i
\(607\) 12.5102 21.6682i 0.507772 0.879487i −0.492187 0.870489i \(-0.663803\pi\)
0.999960 0.00899773i \(-0.00286411\pi\)
\(608\) −6.06482 10.5046i −0.245961 0.426016i
\(609\) 0 0
\(610\) 2.50628 0.101476
\(611\) 2.67808 23.8607i 0.108343 0.965300i
\(612\) −1.66265 −0.0672086
\(613\) −18.4970 + 10.6793i −0.747088 + 0.431332i −0.824641 0.565657i \(-0.808623\pi\)
0.0775527 + 0.996988i \(0.475289\pi\)
\(614\) −6.31751 10.9422i −0.254954 0.441593i
\(615\) −6.74796 + 11.6878i −0.272104 + 0.471298i
\(616\) 0 0
\(617\) −28.5425 16.4790i −1.14908 0.663420i −0.200415 0.979711i \(-0.564229\pi\)
−0.948662 + 0.316291i \(0.897562\pi\)
\(618\) 16.6816 + 9.63111i 0.671031 + 0.387420i
\(619\) 48.9117i 1.96593i −0.183795 0.982965i \(-0.558838\pi\)
0.183795 0.982965i \(-0.441162\pi\)
\(620\) −0.694707 + 1.20327i −0.0279001 + 0.0483244i
\(621\) −18.9481 32.8191i −0.760361 1.31698i
\(622\) 8.00176 4.61982i 0.320841 0.185238i
\(623\) 0 0
\(624\) 7.80240 10.5814i 0.312346 0.423595i
\(625\) −13.5576 −0.542304
\(626\) −36.1075 + 20.8467i −1.44315 + 0.833201i
\(627\) 9.52417 + 16.4964i 0.380359 + 0.658801i
\(628\) 0.536406 0.929083i 0.0214049 0.0370744i
\(629\) 4.78278i 0.190702i
\(630\) 0 0
\(631\) 4.65076 + 2.68512i 0.185144 + 0.106893i 0.589707 0.807617i \(-0.299243\pi\)
−0.404563 + 0.914510i \(0.632576\pi\)
\(632\) 47.6280i 1.89454i
\(633\) −5.83981 + 10.1148i −0.232111 + 0.402029i
\(634\) 10.9621 + 18.9869i 0.435360 + 0.754066i
\(635\) −17.7127 + 10.2264i −0.702905 + 0.405823i
\(636\) −4.53687 −0.179899
\(637\) 0 0
\(638\) −12.4714 −0.493747
\(639\) 3.85189 2.22389i 0.152378 0.0879757i
\(640\) −6.53865 11.3253i −0.258463 0.447671i
\(641\) 19.8510 34.3829i 0.784066 1.35804i −0.145489 0.989360i \(-0.546475\pi\)
0.929555 0.368683i \(-0.120191\pi\)
\(642\) 5.97647i 0.235872i
\(643\) −27.8388 16.0727i −1.09785 0.633847i −0.162198 0.986758i \(-0.551858\pi\)
−0.935657 + 0.352911i \(0.885192\pi\)
\(644\) 0 0
\(645\) 19.2970i 0.759818i
\(646\) −10.2807 + 17.8067i −0.404489 + 0.700596i
\(647\) 9.92502 + 17.1906i 0.390193 + 0.675833i 0.992475 0.122450i \(-0.0390751\pi\)
−0.602282 + 0.798283i \(0.705742\pi\)
\(648\) −3.71020 + 2.14209i −0.145751 + 0.0841491i
\(649\) 8.54096 0.335262
\(650\) 7.19670 3.14357i 0.282278 0.123301i
\(651\) 0 0
\(652\) 7.51671 4.33977i 0.294377 0.169959i
\(653\) 9.50024 + 16.4549i 0.371773 + 0.643930i 0.989838 0.142197i \(-0.0454165\pi\)
−0.618065 + 0.786127i \(0.712083\pi\)
\(654\) −1.48042 + 2.56416i −0.0578889 + 0.100266i
\(655\) 5.56225i 0.217335i
\(656\) −17.2152 9.93918i −0.672139 0.388060i
\(657\) 10.8697 + 6.27562i 0.424067 + 0.244835i
\(658\) 0 0
\(659\) 3.60729 6.24801i 0.140520 0.243388i −0.787173 0.616733i \(-0.788456\pi\)
0.927693 + 0.373345i \(0.121789\pi\)
\(660\) −1.09067 1.88909i −0.0424542 0.0735329i
\(661\) −14.5068 + 8.37548i −0.564248 + 0.325769i −0.754849 0.655899i \(-0.772290\pi\)
0.190601 + 0.981668i \(0.438956\pi\)
\(662\) 25.4470 0.989025
\(663\) 11.4828 + 1.28880i 0.445953 + 0.0500529i
\(664\) 24.1291 0.936393
\(665\) 0 0
\(666\) −1.82006 3.15244i −0.0705259 0.122155i
\(667\) −12.3048 + 21.3126i −0.476444 + 0.825226i
\(668\) 2.81564i 0.108941i
\(669\) 8.47860 + 4.89512i 0.327802 + 0.189256i
\(670\) 10.0681 + 5.81281i 0.388964 + 0.224569i
\(671\) 3.00573i 0.116035i
\(672\) 0 0
\(673\) −18.6684 32.3346i −0.719614 1.24641i −0.961153 0.276016i \(-0.910986\pi\)
0.241539 0.970391i \(-0.422348\pi\)
\(674\) 1.40612 0.811824i 0.0541618 0.0312703i
\(675\) −9.23831 −0.355583
\(676\) −3.27199 + 3.53245i −0.125846 + 0.135864i
\(677\) −28.1341 −1.08128 −0.540641 0.841253i \(-0.681818\pi\)
−0.540641 + 0.841253i \(0.681818\pi\)
\(678\) −13.6533 + 7.88271i −0.524350 + 0.302734i
\(679\) 0 0
\(680\) 7.53452 13.0502i 0.288935 0.500451i
\(681\) 1.07416i 0.0411620i
\(682\) 6.34915 + 3.66568i 0.243122 + 0.140366i
\(683\) −1.79295 1.03516i −0.0686053 0.0396093i 0.465305 0.885150i \(-0.345945\pi\)
−0.533910 + 0.845541i \(0.679278\pi\)
\(684\) 3.55677i 0.135996i
\(685\) −19.8574 + 34.3941i −0.758714 + 1.31413i
\(686\) 0 0
\(687\) −24.9028 + 14.3776i −0.950100 + 0.548540i
\(688\) 28.4228 1.08361
\(689\) −37.5788 4.21776i −1.43164 0.160684i
\(690\) 18.9385 0.720977
\(691\) −31.0542 + 17.9291i −1.18136 + 0.682057i −0.956328 0.292295i \(-0.905581\pi\)
−0.225029 + 0.974352i \(0.572248\pi\)
\(692\) −0.999521 1.73122i −0.0379961 0.0658112i
\(693\) 0 0
\(694\) 33.0417i 1.25425i
\(695\) 17.4001 + 10.0460i 0.660023 + 0.381065i
\(696\) 10.7614 + 6.21312i 0.407911 + 0.235508i
\(697\) 17.4710i 0.661763i
\(698\) 11.0530 19.1443i 0.418361 0.724622i
\(699\) −10.0891 17.4748i −0.381604 0.660958i
\(700\) 0 0
\(701\) −44.8940 −1.69562 −0.847812 0.530297i \(-0.822081\pi\)
−0.847812 + 0.530297i \(0.822081\pi\)
\(702\) −22.8375 + 9.97558i −0.861946 + 0.376504i
\(703\) 10.2314 0.385885
\(704\) 21.3722 12.3393i 0.805497 0.465054i
\(705\) −7.05767 12.2242i −0.265807 0.460391i
\(706\) 16.1801 28.0248i 0.608947 1.05473i
\(707\) 0 0
\(708\) −1.15158 0.664867i −0.0432792 0.0249872i
\(709\) −14.0864 8.13279i −0.529026 0.305433i 0.211594 0.977358i \(-0.432135\pi\)
−0.740620 + 0.671924i \(0.765468\pi\)
\(710\) 6.29886i 0.236392i
\(711\) −12.8748 + 22.2998i −0.482843 + 0.836309i
\(712\) 24.3043 + 42.0963i 0.910843 + 1.57763i
\(713\) 12.5287 7.23344i 0.469203 0.270894i
\(714\) 0 0
\(715\) −7.27775 16.6613i −0.272173 0.623096i
\(716\) 4.55255 0.170137
\(717\) 14.6487 8.45743i 0.547066 0.315849i
\(718\) −3.36403 5.82667i −0.125544 0.217449i
\(719\) 5.00744 8.67314i 0.186746 0.323454i −0.757417 0.652931i \(-0.773539\pi\)
0.944164 + 0.329477i \(0.106873\pi\)
\(720\) 9.26949i 0.345454i
\(721\) 0 0
\(722\) 17.0873 + 9.86534i 0.635922 + 0.367150i
\(723\) 9.85076i 0.366354i
\(724\) −4.04690 + 7.00944i −0.150402 + 0.260504i
\(725\) 2.99966 + 5.19556i 0.111405 + 0.192958i
\(726\) 4.23506 2.44511i 0.157178 0.0907466i
\(727\) −34.5299 −1.28064 −0.640322 0.768106i \(-0.721199\pi\)
−0.640322 + 0.768106i \(0.721199\pi\)
\(728\) 0 0
\(729\) 21.2872 0.788415
\(730\) −15.3934 + 8.88741i −0.569737 + 0.328938i
\(731\) 12.4904 + 21.6340i 0.461973 + 0.800161i
\(732\) 0.233980 0.405265i 0.00864814 0.0149790i
\(733\) 33.1360i 1.22391i −0.790894 0.611953i \(-0.790384\pi\)
0.790894 0.611953i \(-0.209616\pi\)
\(734\) 27.9895 + 16.1598i 1.03311 + 0.596468i
\(735\) 0 0
\(736\) 14.4629i 0.533111i
\(737\) −6.97119 + 12.0745i −0.256787 + 0.444768i
\(738\) 6.64850 + 11.5155i 0.244735 + 0.423893i
\(739\) −3.47767 + 2.00784i −0.127928 + 0.0738594i −0.562598 0.826730i \(-0.690198\pi\)
0.434670 + 0.900590i \(0.356865\pi\)
\(740\) −1.17166 −0.0430711
\(741\) 2.75703 24.5641i 0.101282 0.902386i
\(742\) 0 0
\(743\) 10.8361 6.25622i 0.397538 0.229519i −0.287883 0.957666i \(-0.592952\pi\)
0.685421 + 0.728147i \(0.259618\pi\)
\(744\) −3.65241 6.32616i −0.133904 0.231928i
\(745\) 2.09379 3.62656i 0.0767107 0.132867i
\(746\) 8.66508i 0.317251i
\(747\) −11.2975 6.52260i −0.413353 0.238650i
\(748\) 2.44551 + 1.41192i 0.0894168 + 0.0516248i
\(749\) 0 0
\(750\) 9.07304 15.7150i 0.331300 0.573829i
\(751\) 18.7579 + 32.4896i 0.684486 + 1.18556i 0.973598 + 0.228269i \(0.0733065\pi\)
−0.289112 + 0.957295i \(0.593360\pi\)
\(752\) 18.0053 10.3954i 0.656585 0.379080i
\(753\) −17.1365 −0.624490
\(754\) 13.0255 + 9.60461i 0.474360 + 0.349779i
\(755\) 37.4150 1.36167
\(756\) 0 0
\(757\) 17.5223 + 30.3496i 0.636860 + 1.10307i 0.986118 + 0.166047i \(0.0531004\pi\)
−0.349258 + 0.937027i \(0.613566\pi\)
\(758\) 7.86530 13.6231i 0.285680 0.494813i
\(759\) 22.7126i 0.824414i
\(760\) −27.9172 16.1180i −1.01266 0.584661i
\(761\) 3.72586 + 2.15113i 0.135062 + 0.0779782i 0.566009 0.824399i \(-0.308487\pi\)
−0.430946 + 0.902378i \(0.641820\pi\)
\(762\) 16.8021i 0.608677i
\(763\) 0 0
\(764\) −0.510605 0.884394i −0.0184730 0.0319962i
\(765\) −7.05545 + 4.07347i −0.255090 + 0.147277i
\(766\) 9.26679 0.334823
\(767\) −8.92043 6.57766i −0.322098 0.237506i
\(768\) −10.0039 −0.360985
\(769\) −10.6146 + 6.12834i −0.382772 + 0.220994i −0.679024 0.734116i \(-0.737597\pi\)
0.296251 + 0.955110i \(0.404263\pi\)
\(770\) 0 0
\(771\) −17.1268 + 29.6645i −0.616806 + 1.06834i
\(772\) 4.81105i 0.173153i
\(773\) 3.29372 + 1.90163i 0.118467 + 0.0683970i 0.558063 0.829799i \(-0.311545\pi\)
−0.439596 + 0.898196i \(0.644878\pi\)
\(774\) −16.4654 9.50628i −0.591835 0.341696i
\(775\) 3.52673i 0.126684i
\(776\) −21.5250 + 37.2824i −0.772702 + 1.33836i
\(777\) 0 0
\(778\) 7.90250 4.56251i 0.283318 0.163574i
\(779\) −37.3744