Properties

Label 637.2.q.h.589.5
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
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 589.5
Root \(1.40744 - 0.138282i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.h.491.5

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10554 + 0.638282i 0.781733 + 0.451334i 0.837044 0.547136i \(-0.184282\pi\)
−0.0553113 + 0.998469i \(0.517615\pi\)
\(3\) −0.583963 + 1.01145i −0.337151 + 0.583963i −0.983896 0.178744i \(-0.942797\pi\)
0.646745 + 0.762707i \(0.276130\pi\)
\(4\) −0.185192 0.320762i −0.0925960 0.160381i
\(5\) 1.81487i 0.811636i −0.913954 0.405818i \(-0.866987\pi\)
0.913954 0.405818i \(-0.133013\pi\)
\(6\) −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 0.0912671 0.995826i \(-0.470908\pi\)
−0.816777 + 0.576953i \(0.804242\pi\)
\(12\) 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 0.650297 0.759680i \(-0.274645\pi\)
−0.983051 + 0.183334i \(0.941311\pi\)
\(18\) 2.08840i 0.492240i
\(19\) 5.08351 2.93497i 1.16624 0.673327i 0.213446 0.976955i \(-0.431531\pi\)
0.952791 + 0.303628i \(0.0981979\pi\)
\(20\) −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 −0.227302 0.973824i \(-0.572990\pi\)
0.957007 0.290063i \(-0.0936763\pi\)
\(24\) 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 −0.655344 0.755330i \(-0.727476\pi\)
0.981807 + 0.189879i \(0.0608097\pi\)
\(30\) 1.35293 + 2.34334i 0.247009 + 0.427833i
\(31\) 2.06697i 0.371238i 0.982622 + 0.185619i \(0.0594290\pi\)
−0.982622 + 0.185619i \(0.940571\pi\)
\(32\) −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 0.618922 0.785453i \(-0.287570\pi\)
−0.370761 + 0.928728i \(0.620903\pi\)
\(38\) 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 0.00324599 0.999995i \(-0.498967\pi\)
−0.864398 + 0.502808i \(0.832300\pi\)
\(42\) 0 0
\(43\) 4.55195 + 7.88422i 0.694167 + 1.20233i 0.970461 + 0.241259i \(0.0775603\pi\)
−0.276294 + 0.961073i \(0.589106\pi\)
\(44\) 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 \(0.161428\pi\)
−0.874136 + 0.485681i \(0.838572\pi\)
\(48\) 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 −0.663177 0.748462i \(-0.730793\pi\)
0.316598 + 0.948560i \(0.397459\pi\)
\(60\) 0.785080i 0.101353i
\(61\) 0.540892 + 0.936853i 0.0692541 + 0.119952i 0.898573 0.438824i \(-0.144605\pi\)
−0.829319 + 0.558775i \(0.811271\pi\)
\(62\) −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 0.741387 0.671078i \(-0.234168\pi\)
−0.210477 + 0.977599i \(0.567502\pi\)
\(68\) −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 −0.353735 0.935346i \(-0.615088\pi\)
0.633166 + 0.774016i \(0.281755\pi\)
\(72\) 4.28709 2.47515i 0.505238 0.291699i
\(73\) 7.67213i 0.897955i −0.893543 0.448978i \(-0.851788\pi\)
0.893543 0.448978i \(-0.148212\pi\)
\(74\) 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 \(0.144184\pi\)
−0.899153 + 0.437635i \(0.855816\pi\)
\(84\) 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 0.999592 0.0285683i \(-0.00909482\pi\)
0.475055 + 0.879956i \(0.342428\pi\)
\(90\) 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 0.279689 0.960091i \(-0.409769\pi\)
0.971307 + 0.237827i \(0.0764353\pi\)
\(98\) 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 −0.864201 0.503147i \(-0.832175\pi\)
0.867839 + 0.496846i \(0.165509\pi\)
\(102\) 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 −0.946493 0.322723i \(-0.895402\pi\)
0.752733 + 0.658326i \(0.228735\pi\)
\(108\) 1.00271 + 1.73675i 0.0964860 + 0.167119i
\(109\) 1.98589i 0.190214i 0.995467 + 0.0951071i \(0.0303194\pi\)
−0.995467 + 0.0951071i \(0.969681\pi\)
\(110\) −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 0.999995 0.00303506i \(-0.000966090\pi\)
−0.502626 + 0.864504i \(0.667633\pi\)
\(114\) −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 −0.499994 0.866029i \(-0.666665\pi\)
1.00000 6.53271e-6i \(-2.07943e-6\pi\)
\(128\) −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 0.631965 0.774997i \(-0.282249\pi\)
0.987150 0.159799i \(-0.0510845\pi\)
\(138\) 10.4352i 0.888300i
\(139\) 5.53535 + 9.58750i 0.469502 + 0.813201i 0.999392 0.0348652i \(-0.0111002\pi\)
−0.529890 + 0.848066i \(0.677767\pi\)
\(140\) 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 −0.579613 0.814892i \(-0.696796\pi\)
0.415911 + 0.909406i \(0.363463\pi\)
\(150\) −2.20306 + 1.27194i −0.179879 + 0.103853i
\(151\) 20.6158i 1.67769i 0.544371 + 0.838845i \(0.316768\pi\)
−0.544371 + 0.838845i \(0.683232\pi\)
\(152\) −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 −0.596201 + 0.802835i \(0.703324\pi\)
−0.993376 + 0.114907i \(0.963343\pi\)
\(164\) 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 0.223160 0.974782i \(-0.428363\pi\)
−0.732606 + 0.680653i \(0.761696\pi\)
\(168\) 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 0.745016 0.667047i \(-0.232442\pi\)
−0.950187 + 0.311679i \(0.899108\pi\)
\(174\) 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 −0.998927 0.0463168i \(-0.985252\pi\)
0.539575 + 0.841938i \(0.318585\pi\)
\(180\) −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 0.811831 0.583893i \(-0.198471\pi\)
−0.911581 + 0.411120i \(0.865138\pi\)
\(192\) 5.18675 8.98371i 0.374321 0.648344i
\(193\) 11.2491 + 6.49467i 0.809728 + 0.467497i 0.846861 0.531814i \(-0.178489\pi\)
−0.0371334 + 0.999310i \(0.511823\pi\)
\(194\) 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 0.954608 0.297866i \(-0.0962749\pi\)
0.219344 + 0.975648i \(0.429608\pi\)
\(198\) 2.90130 5.02519i 0.206186 0.357125i
\(199\) 10.0159 + 17.3480i 0.710006 + 1.22977i 0.964854 + 0.262786i \(0.0846412\pi\)
−0.254848 + 0.966981i \(0.582025\pi\)
\(200\) 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 −0.985213 0.171336i \(-0.945192\pi\)
0.640988 + 0.767551i \(0.278525\pi\)
\(212\) 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 0.236835 0.971550i \(-0.423890\pi\)
−0.722970 + 0.690880i \(0.757223\pi\)
\(224\) 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 −0.473334 0.880883i \(-0.656950\pi\)
0.526200 + 0.850361i \(0.323616\pi\)
\(228\) 2.19903 1.26961i 0.145634 0.0840820i
\(229\) 24.6208i 1.62699i 0.581574 + 0.813494i \(0.302437\pi\)
−0.581574 + 0.813494i \(0.697563\pi\)
\(230\) −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 \(-0.844828\pi\)
0.883512 0.468408i \(-0.155172\pi\)
\(240\) 5.73101 3.30880i 0.369935 0.213582i
\(241\) 7.30441 4.21720i 0.470518 0.271654i −0.245938 0.969285i \(-0.579096\pi\)
0.716457 + 0.697632i \(0.245763\pi\)
\(242\) 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 0.999112 0.0421373i \(-0.0134167\pi\)
−0.536048 + 0.844188i \(0.680083\pi\)
\(252\) 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 −0.107441 + 0.994211i \(0.534266\pi\)
−0.807292 + 0.590152i \(0.799068\pi\)
\(258\) −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 0.376555 + 0.926394i \(0.377109\pi\)
−0.990558 + 0.137091i \(0.956225\pi\)
\(264\) −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 −0.974801 0.223074i \(-0.928391\pi\)
0.294213 0.955740i \(-0.404943\pi\)
\(270\) −6.27210 + 10.8636i −0.381708 + 0.661137i
\(271\) 8.14054 + 4.69994i 0.494502 + 0.285501i 0.726440 0.687230i \(-0.241173\pi\)
−0.231938 + 0.972731i \(0.574507\pi\)
\(272\) −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 0.566066 0.824360i \(-0.308465\pi\)
−0.996950 + 0.0780478i \(0.975131\pi\)
\(278\) 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 \(-0.999062\pi\)
0.999996 0.00294820i \(-0.000938442\pi\)
\(282\) −4.96429 8.59841i −0.295619 0.512028i
\(283\) 0.310336 0.537518i 0.0184476 0.0319521i −0.856654 0.515891i \(-0.827461\pi\)
0.875102 + 0.483939i \(0.160794\pi\)
\(284\) −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 −0.972971 0.230928i \(-0.925824\pi\)
−0.286496 + 0.958082i \(0.592490\pi\)
\(294\) 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 \(0.0911455\pi\)
−0.959284 + 0.282445i \(0.908855\pi\)
\(308\) 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 \(-0.839800\pi\)
0.876004 0.482304i \(-0.160200\pi\)
\(318\) 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 0.0561454 0.998423i \(-0.482119\pi\)
0.892732 + 0.450588i \(0.148786\pi\)
\(332\) 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 −0.970267 0.242038i \(-0.922184\pi\)
0.275522 0.961295i \(-0.411149\pi\)
\(348\) 0.760503 1.31723i 0.0407672 0.0706109i
\(349\) 14.9967 + 8.65837i 0.802757 + 0.463472i 0.844434 0.535659i \(-0.179937\pi\)
−0.0416774 + 0.999131i \(0.513270\pi\)
\(350\) 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 0.953316 0.301975i \(-0.0976459\pi\)
0.215140 + 0.976583i \(0.430979\pi\)
\(354\) 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 \(0.0444151\pi\)
−0.990281 + 0.139082i \(0.955585\pi\)
\(360\) −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 −0.319627 0.947544i \(-0.603557\pi\)
0.980410 0.196967i \(-0.0631092\pi\)
\(368\) −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 0.940414 0.340033i \(-0.110438\pi\)
−0.764684 + 0.644406i \(0.777105\pi\)
\(374\) −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 0.748383 0.663267i \(-0.230831\pi\)
−0.200215 + 0.979752i \(0.564164\pi\)
\(380\) −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 −0.330710 0.943732i \(-0.607288\pi\)
0.651941 + 0.758269i \(0.273955\pi\)
\(384\) 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 0.0751252 0.997174i \(-0.476064\pi\)
0.901141 + 0.433527i \(0.142731\pi\)
\(398\) 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 0.432489 0.901639i \(-0.357635\pi\)
−0.564598 + 0.825366i \(0.690969\pi\)
\(402\) −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 −0.615202 0.788369i \(-0.710926\pi\)
0.375147 + 0.926965i \(0.377592\pi\)
\(410\) −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 −0.781250 0.624219i \(-0.785417\pi\)
0.931214 + 0.364473i \(0.118751\pi\)
\(420\) 0 0
\(421\) 1.92589i 0.0938622i 0.998898 + 0.0469311i \(0.0149441\pi\)
−0.998898 + 0.0469311i \(0.985056\pi\)
\(422\) −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 0.707158 0.707055i \(-0.249977\pi\)
−0.258749 + 0.965945i \(0.583310\pi\)
\(432\) −8.45207 + 14.6394i −0.406651 + 0.704340i
\(433\) −20.1328 34.8710i −0.967520 1.67579i −0.702685 0.711501i \(-0.748016\pi\)
−0.264835 0.964294i \(-0.585318\pi\)
\(434\) 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 −0.475789 0.879560i \(-0.657837\pi\)
0.999615 0.0277345i \(-0.00882930\pi\)
\(440\) 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 0.0239134 0.999714i \(-0.492387\pi\)
0.877734 + 0.479147i \(0.159054\pi\)
\(450\) 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 0.607556 0.794277i \(-0.292150\pi\)
−0.384086 + 0.923297i \(0.625483\pi\)
\(458\) −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 −0.952448 0.304700i \(-0.901444\pi\)
−0.212346 + 0.977195i \(0.568110\pi\)
\(462\) 0 0
\(463\) 14.2284i 0.661251i −0.943762 0.330625i \(-0.892740\pi\)
0.943762 0.330625i \(-0.107260\pi\)
\(464\) −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 0.532590 0.846373i \(-0.321219\pi\)
−0.466686 + 0.884423i \(0.654552\pi\)
\(480\) −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 −0.528854 0.848713i \(-0.677378\pi\)
0.470580 + 0.882357i \(0.344045\pi\)
\(488\) 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 −0.627175 0.778878i \(-0.715789\pi\)
0.988116 + 0.153711i \(0.0491224\pi\)
\(492\) −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 \(0.129819\pi\)
−0.917980 + 0.396627i \(0.870181\pi\)
\(500\) −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 0.852375 0.522931i \(-0.175161\pi\)
−0.879059 + 0.476713i \(0.841828\pi\)
\(504\) 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 0.374474 0.927237i \(-0.377823\pi\)
−0.615774 + 0.787923i \(0.711156\pi\)
\(510\) 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 −0.850922 0.525292i \(-0.823956\pi\)
0.880377 + 0.474274i \(0.157289\pi\)
\(524\) 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 \(0.142655\pi\)
−0.901245 + 0.433310i \(0.857345\pi\)
\(542\) 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 −0.00157977 0.999999i \(-0.500503\pi\)
−0.866814 + 0.498631i \(0.833836\pi\)
\(558\) −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 −0.991725 0.128382i \(-0.959022\pi\)
0.384680 0.923050i \(-0.374312\pi\)
\(564\) 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 0.415434 + 0.909623i \(0.363630\pi\)
−0.995474 + 0.0950353i \(0.969704\pi\)
\(570\) 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 \(-0.936905\pi\)
0.980419 0.196922i \(-0.0630947\pi\)
\(578\) 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 0.833046 0.553204i \(-0.186595\pi\)
−0.0625654 + 0.998041i \(0.519928\pi\)
\(588\) 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 \(-0.974009\pi\)
0.996668 0.0815622i \(-0.0259909\pi\)
\(594\) 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 0.450305 + 0.892875i \(0.351315\pi\)
−0.998405 + 0.0564616i \(0.982018\pi\)
\(602\) 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 0.999960 + 0.00899773i \(0.00286411\pi\)
−0.492187 + 0.870489i \(0.663803\pi\)
\(608\) −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 0.0775527 0.996988i \(-0.475289\pi\)
−0.824641 + 0.565657i \(0.808623\pi\)
\(614\) −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 −0.948662 0.316291i \(-0.897562\pi\)
−0.200415 + 0.979711i \(0.564229\pi\)
\(618\) 16.6816 9.63111i 0.671031 0.387420i
\(619\) 48.9117i 1.96593i 0.183795 + 0.982965i \(0.441162\pi\)
−0.183795 + 0.982965i \(0.558838\pi\)
\(620\) −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 −0.404563 0.914510i \(-0.632576\pi\)
0.589707 + 0.807617i \(0.299243\pi\)
\(632\) 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 0.929555 + 0.368683i \(0.120191\pi\)
−0.145489 + 0.989360i \(0.546475\pi\)
\(642\) 5.97647i 0.235872i
\(643\) −27.8388 + 16.0727i −1.09785 + 0.633847i −0.935657 0.352911i \(-0.885192\pi\)
−0.162198 + 0.986758i \(0.551858\pi\)
\(644\) 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 −0.602282 0.798283i \(-0.705742\pi\)
0.992475 + 0.122450i \(0.0390751\pi\)
\(648\) −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 −0.618065 0.786127i \(-0.712083\pi\)
0.989838 + 0.142197i \(0.0454165\pi\)
\(654\) −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 0.927693 0.373345i \(-0.121789\pi\)
−0.787173 + 0.616733i \(0.788456\pi\)
\(660\) −1.09067 + 1.88909i −0.0424542 + 0.0735329i
\(661\) −14.5068 8.37548i −0.564248 0.325769i 0.190601 0.981668i \(-0.438956\pi\)
−0.754849 + 0.655899i \(0.772290\pi\)
\(662\) 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 0.241539 + 0.970391i \(0.422348\pi\)
−0.961153 + 0.276016i \(0.910986\pi\)
\(674\) 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 −0.533910 0.845541i \(-0.679278\pi\)
0.465305 + 0.885150i \(0.345945\pi\)
\(684\) 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 −0.225029 0.974352i \(-0.572248\pi\)
−0.956328 + 0.292295i \(0.905581\pi\)
\(692\) −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 −0.740620 0.671924i \(-0.765468\pi\)
0.211594 + 0.977358i \(0.432135\pi\)
\(710\) 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 0.944164 0.329477i \(-0.106873\pi\)
−0.757417 + 0.652931i \(0.773539\pi\)
\(720\) 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 \(0.209616\pi\)
−0.790894 + 0.611953i \(0.790384\pi\)
\(734\) 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 0.434670 0.900590i \(-0.356865\pi\)
−0.562598 + 0.826730i \(0.690198\pi\)
\(740\) −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 0.685421 0.728147i \(-0.259618\pi\)
−0.287883 + 0.957666i \(0.592952\pi\)
\(744\) −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 −0.289112 0.957295i \(-0.593360\pi\)
0.973598 0.228269i \(-0.0733065\pi\)
\(752\) 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 −0.349258 0.937027i \(-0.613566\pi\)
0.986118 0.166047i \(-0.0531004\pi\)
\(758\) 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 −0.430946 0.902378i \(-0.641820\pi\)
0.566009 + 0.824399i \(0.308487\pi\)
\(762\) 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 0.296251 0.955110i \(-0.404263\pi\)
−0.679024 + 0.734116i \(0.737597\pi\)
\(770\) 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 −0.439596 0.898196i \(-0.644878\pi\)
0.558063 + 0.829799i \(0.311545\pi\)
\(774\) −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 −1.33908
\(780\) −0.315723 2.81298i −0.0113047 0.100721i
\(781\)