Properties

Label 637.2.q.i.589.2
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 589.2
Root \(0.874681 + 1.11128i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.i.491.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16500 - 0.672613i) q^{2} +(1.02505 - 1.77544i) q^{3} +(-0.0951832 - 0.164862i) q^{4} -3.56778i q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +(-0.601462 - 1.04176i) q^{9} +O(q^{10})\) \(q+(-1.16500 - 0.672613i) q^{2} +(1.02505 - 1.77544i) q^{3} +(-0.0951832 - 0.164862i) q^{4} -3.56778i q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +(-0.601462 - 1.04176i) q^{9} +(-2.39973 + 4.15646i) q^{10} +(1.10736 + 0.639336i) q^{11} -0.390271 q^{12} +(-3.57420 - 0.474474i) q^{13} +(-6.33438 - 3.65716i) q^{15} +(1.79151 - 3.10299i) q^{16} +(-3.86960 - 6.70234i) q^{17} +1.61821i q^{18} +(0.817422 - 0.471939i) q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} +(0.823637 - 1.42658i) q^{23} +(5.23141 + 3.02035i) q^{24} -7.72903 q^{25} +(3.84480 + 2.95681i) q^{26} +3.68419 q^{27} +(-2.02242 + 3.50293i) q^{29} +(4.91970 + 8.52117i) q^{30} +5.15220i q^{31} +(0.929326 - 0.536547i) q^{32} +(2.27021 - 1.31071i) q^{33} +10.4110i q^{34} +(-0.114498 + 0.198317i) q^{36} +(-0.914594 - 0.528041i) q^{37} -1.26973 q^{38} +(-4.50614 + 5.85942i) q^{39} +10.5126 q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} -0.243416i q^{44} +(-3.71678 + 2.14588i) q^{45} +(-1.91908 + 1.10798i) q^{46} -0.894217i q^{47} +(-3.67279 - 6.36146i) q^{48} +(9.00432 + 5.19865i) q^{50} -15.8662 q^{51} +(0.261981 + 0.634412i) q^{52} -0.0799923 q^{53} +(-4.29208 - 2.47804i) q^{54} +(2.28101 - 3.95082i) q^{55} -1.93505i q^{57} +(4.71224 - 2.72061i) q^{58} +(9.68627 - 5.59237i) q^{59} +1.39240i q^{60} +(-3.81196 - 6.60251i) q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(-1.69282 + 12.7519i) q^{65} -3.52639 q^{66} +(-5.47418 - 3.16052i) q^{67} +(-0.736641 + 1.27590i) q^{68} +(-1.68854 - 2.92464i) q^{69} +(9.89346 - 5.71199i) q^{71} +(3.06959 - 1.77223i) q^{72} +0.760506i q^{73} +(0.710335 + 1.23034i) q^{74} +(-7.92265 + 13.7224i) q^{75} +(-0.155610 - 0.0898413i) q^{76} +(9.19077 - 3.79533i) q^{78} -2.85531 q^{79} +(-11.0708 - 6.39172i) q^{80} +(5.58087 - 9.66636i) q^{81} +(-2.82418 - 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} -5.15308i q^{86} +(4.14617 + 7.18137i) q^{87} +(-1.88383 + 3.26289i) q^{88} +(6.56124 + 3.78813i) q^{89} +5.77339 q^{90} -0.313586 q^{92} +(9.14742 + 5.28127i) q^{93} +(-0.601462 + 1.04176i) q^{94} +(-1.68377 - 2.91638i) q^{95} -2.19995i q^{96} +(0.414443 - 0.239279i) q^{97} -1.53815i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 3q^{3} + 4q^{4} + 9q^{6} - q^{9} + O(q^{10}) \) \( 12q + 3q^{3} + 4q^{4} + 9q^{6} - q^{9} - 12q^{10} - 12q^{11} - 2q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} + 9q^{19} + 3q^{20} - 15q^{22} + 3q^{23} + 15q^{24} + 10q^{25} - 15q^{26} - 12q^{27} - q^{29} + 11q^{30} - 18q^{32} - 6q^{33} - 13q^{36} - 15q^{37} + 38q^{38} + 5q^{39} - 2q^{40} + 6q^{41} + 11q^{43} - 9q^{45} + 30q^{46} - 19q^{48} + 18q^{50} - 8q^{51} + 40q^{52} + 16q^{53} + 6q^{54} + 15q^{55} + 24q^{58} + 27q^{59} - 5q^{61} - 41q^{62} + 2q^{64} - 18q^{65} - 68q^{66} - 15q^{67} + 11q^{68} - 7q^{69} + 30q^{71} - 57q^{72} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} + 70q^{79} - 63q^{80} + 14q^{81} - 5q^{82} - 21q^{85} - 10q^{87} - 14q^{88} + 48q^{89} - 66q^{92} + 81q^{93} - q^{94} + 2q^{95} + 3q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16500 0.672613i −0.823779 0.475609i 0.0279386 0.999610i \(-0.491106\pi\)
−0.851718 + 0.524000i \(0.824439\pi\)
\(3\) 1.02505 1.77544i 0.591814 1.02505i −0.402174 0.915563i \(-0.631745\pi\)
0.993988 0.109489i \(-0.0349213\pi\)
\(4\) −0.0951832 0.164862i −0.0475916 0.0824311i
\(5\) 3.56778i 1.59556i −0.602950 0.797779i \(-0.706008\pi\)
0.602950 0.797779i \(-0.293992\pi\)
\(6\) −2.38837 + 1.37893i −0.975048 + 0.562944i
\(7\) 0 0
\(8\) 2.94654i 1.04176i
\(9\) −0.601462 1.04176i −0.200487 0.347254i
\(10\) −2.39973 + 4.15646i −0.758862 + 1.31439i
\(11\) 1.10736 + 0.639336i 0.333882 + 0.192767i 0.657563 0.753399i \(-0.271587\pi\)
−0.323681 + 0.946166i \(0.604920\pi\)
\(12\) −0.390271 −0.112661
\(13\) −3.57420 0.474474i −0.991304 0.131595i
\(14\) 0 0
\(15\) −6.33438 3.65716i −1.63553 0.944273i
\(16\) 1.79151 3.10299i 0.447878 0.775748i
\(17\) −3.86960 6.70234i −0.938515 1.62556i −0.768242 0.640159i \(-0.778868\pi\)
−0.170273 0.985397i \(-0.554465\pi\)
\(18\) 1.61821i 0.381415i
\(19\) 0.817422 0.471939i 0.187530 0.108270i −0.403296 0.915070i \(-0.632135\pi\)
0.590826 + 0.806799i \(0.298802\pi\)
\(20\) −0.588191 + 0.339592i −0.131524 + 0.0759352i
\(21\) 0 0
\(22\) −0.860052 1.48965i −0.183364 0.317595i
\(23\) 0.823637 1.42658i 0.171740 0.297463i −0.767288 0.641303i \(-0.778394\pi\)
0.939028 + 0.343840i \(0.111728\pi\)
\(24\) 5.23141 + 3.02035i 1.06786 + 0.616527i
\(25\) −7.72903 −1.54581
\(26\) 3.84480 + 2.95681i 0.754027 + 0.579879i
\(27\) 3.68419 0.709023
\(28\) 0 0
\(29\) −2.02242 + 3.50293i −0.375554 + 0.650478i −0.990410 0.138161i \(-0.955881\pi\)
0.614856 + 0.788639i \(0.289214\pi\)
\(30\) 4.91970 + 8.52117i 0.898210 + 1.55575i
\(31\) 5.15220i 0.925362i 0.886525 + 0.462681i \(0.153112\pi\)
−0.886525 + 0.462681i \(0.846888\pi\)
\(32\) 0.929326 0.536547i 0.164283 0.0948490i
\(33\) 2.27021 1.31071i 0.395192 0.228164i
\(34\) 10.4110i 1.78547i
\(35\) 0 0
\(36\) −0.114498 + 0.198317i −0.0190830 + 0.0330528i
\(37\) −0.914594 0.528041i −0.150358 0.0868094i 0.422933 0.906161i \(-0.361000\pi\)
−0.573292 + 0.819351i \(0.694334\pi\)
\(38\) −1.26973 −0.205977
\(39\) −4.50614 + 5.85942i −0.721559 + 0.938257i
\(40\) 10.5126 1.66219
\(41\) 3.63629 + 2.09941i 0.567893 + 0.327873i 0.756307 0.654217i \(-0.227002\pi\)
−0.188415 + 0.982090i \(0.560335\pi\)
\(42\) 0 0
\(43\) 1.91532 + 3.31744i 0.292084 + 0.505904i 0.974302 0.225244i \(-0.0723180\pi\)
−0.682218 + 0.731148i \(0.738985\pi\)
\(44\) 0.243416i 0.0366964i
\(45\) −3.71678 + 2.14588i −0.554064 + 0.319889i
\(46\) −1.91908 + 1.10798i −0.282952 + 0.163363i
\(47\) 0.894217i 0.130435i −0.997871 0.0652175i \(-0.979226\pi\)
0.997871 0.0652175i \(-0.0207741\pi\)
\(48\) −3.67279 6.36146i −0.530121 0.918197i
\(49\) 0 0
\(50\) 9.00432 + 5.19865i 1.27340 + 0.735200i
\(51\) −15.8662 −2.22171
\(52\) 0.261981 + 0.634412i 0.0363302 + 0.0879770i
\(53\) −0.0799923 −0.0109878 −0.00549389 0.999985i \(-0.501749\pi\)
−0.00549389 + 0.999985i \(0.501749\pi\)
\(54\) −4.29208 2.47804i −0.584079 0.337218i
\(55\) 2.28101 3.95082i 0.307571 0.532729i
\(56\) 0 0
\(57\) 1.93505i 0.256303i
\(58\) 4.71224 2.72061i 0.618747 0.357234i
\(59\) 9.68627 5.59237i 1.26104 0.728064i 0.287768 0.957700i \(-0.407087\pi\)
0.973277 + 0.229636i \(0.0737535\pi\)
\(60\) 1.39240i 0.179758i
\(61\) −3.81196 6.60251i −0.488072 0.845365i 0.511834 0.859084i \(-0.328966\pi\)
−0.999906 + 0.0137195i \(0.995633\pi\)
\(62\) 3.46543 6.00231i 0.440111 0.762294i
\(63\) 0 0
\(64\) −8.60961 −1.07620
\(65\) −1.69282 + 12.7519i −0.209968 + 1.58168i
\(66\) −3.52639 −0.434069
\(67\) −5.47418 3.16052i −0.668777 0.386119i 0.126836 0.991924i \(-0.459518\pi\)
−0.795613 + 0.605805i \(0.792851\pi\)
\(68\) −0.736641 + 1.27590i −0.0893309 + 0.154726i
\(69\) −1.68854 2.92464i −0.203277 0.352085i
\(70\) 0 0
\(71\) 9.89346 5.71199i 1.17414 0.677889i 0.219487 0.975616i \(-0.429562\pi\)
0.954651 + 0.297727i \(0.0962285\pi\)
\(72\) 3.06959 1.77223i 0.361755 0.208859i
\(73\) 0.760506i 0.0890105i 0.999009 + 0.0445052i \(0.0141711\pi\)
−0.999009 + 0.0445052i \(0.985829\pi\)
\(74\) 0.710335 + 1.23034i 0.0825747 + 0.143024i
\(75\) −7.92265 + 13.7224i −0.914829 + 1.58453i
\(76\) −0.155610 0.0898413i −0.0178497 0.0103055i
\(77\) 0 0
\(78\) 9.19077 3.79533i 1.04065 0.429737i
\(79\) −2.85531 −0.321247 −0.160624 0.987016i \(-0.551351\pi\)
−0.160624 + 0.987016i \(0.551351\pi\)
\(80\) −11.0708 6.39172i −1.23775 0.714616i
\(81\) 5.58087 9.66636i 0.620097 1.07404i
\(82\) −2.82418 4.89163i −0.311879 0.540190i
\(83\) 2.32483i 0.255183i 0.991827 + 0.127591i \(0.0407246\pi\)
−0.991827 + 0.127591i \(0.959275\pi\)
\(84\) 0 0
\(85\) −23.9125 + 13.8059i −2.59367 + 1.49746i
\(86\) 5.15308i 0.555671i
\(87\) 4.14617 + 7.18137i 0.444516 + 0.769924i
\(88\) −1.88383 + 3.26289i −0.200817 + 0.347825i
\(89\) 6.56124 + 3.78813i 0.695490 + 0.401541i 0.805665 0.592371i \(-0.201808\pi\)
−0.110176 + 0.993912i \(0.535141\pi\)
\(90\) 5.77339 0.608569
\(91\) 0 0
\(92\) −0.313586 −0.0326936
\(93\) 9.14742 + 5.28127i 0.948544 + 0.547642i
\(94\) −0.601462 + 1.04176i −0.0620361 + 0.107450i
\(95\) −1.68377 2.91638i −0.172751 0.299214i
\(96\) 2.19995i 0.224532i
\(97\) 0.414443 0.239279i 0.0420803 0.0242951i −0.478812 0.877917i \(-0.658933\pi\)
0.520893 + 0.853622i \(0.325599\pi\)
\(98\) 0 0
\(99\) 1.53815i 0.154589i
\(100\) 0.735674 + 1.27422i 0.0735674 + 0.127422i
\(101\) −1.43918 + 2.49273i −0.143204 + 0.248036i −0.928701 0.370829i \(-0.879074\pi\)
0.785498 + 0.618865i \(0.212407\pi\)
\(102\) 18.4841 + 10.6718i 1.83020 + 1.05666i
\(103\) −11.3351 −1.11688 −0.558441 0.829544i \(-0.688600\pi\)
−0.558441 + 0.829544i \(0.688600\pi\)
\(104\) 1.39806 10.5315i 0.137091 1.03270i
\(105\) 0 0
\(106\) 0.0931910 + 0.0538039i 0.00905151 + 0.00522589i
\(107\) 3.28603 5.69157i 0.317673 0.550225i −0.662329 0.749213i \(-0.730432\pi\)
0.980002 + 0.198988i \(0.0637653\pi\)
\(108\) −0.350673 0.607384i −0.0337435 0.0584455i
\(109\) 5.83914i 0.559288i 0.960104 + 0.279644i \(0.0902165\pi\)
−0.960104 + 0.279644i \(0.909784\pi\)
\(110\) −5.31475 + 3.06847i −0.506741 + 0.292567i
\(111\) −1.87501 + 1.08254i −0.177968 + 0.102750i
\(112\) 0 0
\(113\) −3.26617 5.65717i −0.307255 0.532181i 0.670506 0.741904i \(-0.266077\pi\)
−0.977761 + 0.209723i \(0.932744\pi\)
\(114\) −1.30154 + 2.25433i −0.121900 + 0.211137i
\(115\) −5.08973 2.93855i −0.474619 0.274022i
\(116\) 0.770001 0.0714928
\(117\) 1.65545 + 4.00884i 0.153047 + 0.370618i
\(118\) −15.0460 −1.38510
\(119\) 0 0
\(120\) 10.7759 18.6645i 0.983705 1.70383i
\(121\) −4.68250 8.11033i −0.425682 0.737302i
\(122\) 10.2559i 0.928525i
\(123\) 7.45477 4.30401i 0.672174 0.388080i
\(124\) 0.849402 0.490402i 0.0762786 0.0440394i
\(125\) 9.73656i 0.870865i
\(126\) 0 0
\(127\) 7.35818 12.7447i 0.652932 1.13091i −0.329475 0.944164i \(-0.606872\pi\)
0.982408 0.186748i \(-0.0597948\pi\)
\(128\) 8.17154 + 4.71784i 0.722269 + 0.417002i
\(129\) 7.85322 0.691437
\(130\) 10.5492 13.7174i 0.925230 1.20309i
\(131\) −11.1867 −0.977386 −0.488693 0.872456i \(-0.662526\pi\)
−0.488693 + 0.872456i \(0.662526\pi\)
\(132\) −0.432171 0.249514i −0.0376157 0.0217174i
\(133\) 0 0
\(134\) 4.25161 + 7.36400i 0.367283 + 0.636153i
\(135\) 13.1444i 1.13129i
\(136\) 19.7487 11.4019i 1.69344 0.977706i
\(137\) 15.2687 8.81541i 1.30450 0.753151i 0.323324 0.946288i \(-0.395200\pi\)
0.981172 + 0.193137i \(0.0618662\pi\)
\(138\) 4.54294i 0.386721i
\(139\) −2.92855 5.07240i −0.248396 0.430235i 0.714685 0.699447i \(-0.246570\pi\)
−0.963081 + 0.269212i \(0.913237\pi\)
\(140\) 0 0
\(141\) −1.58763 0.916619i −0.133703 0.0771932i
\(142\) −15.3678 −1.28964
\(143\) −3.65458 2.81053i −0.305612 0.235028i
\(144\) −4.31011 −0.359176
\(145\) 12.4977 + 7.21554i 1.03788 + 0.599218i
\(146\) 0.511526 0.885989i 0.0423342 0.0733250i
\(147\) 0 0
\(148\) 0.201043i 0.0165256i
\(149\) −9.07505 + 5.23948i −0.743457 + 0.429235i −0.823325 0.567570i \(-0.807884\pi\)
0.0798677 + 0.996805i \(0.474550\pi\)
\(150\) 18.4598 10.6578i 1.50724 0.870203i
\(151\) 4.71406i 0.383625i 0.981432 + 0.191812i \(0.0614365\pi\)
−0.981432 + 0.191812i \(0.938564\pi\)
\(152\) 1.39059 + 2.40857i 0.112791 + 0.195361i
\(153\) −4.65483 + 8.06241i −0.376321 + 0.651807i
\(154\) 0 0
\(155\) 18.3819 1.47647
\(156\) 1.39490 + 0.185173i 0.111682 + 0.0148257i
\(157\) −9.00210 −0.718445 −0.359223 0.933252i \(-0.616958\pi\)
−0.359223 + 0.933252i \(0.616958\pi\)
\(158\) 3.32643 + 1.92052i 0.264637 + 0.152788i
\(159\) −0.0819962 + 0.142022i −0.00650272 + 0.0112630i
\(160\) −1.91428 3.31563i −0.151337 0.262123i
\(161\) 0 0
\(162\) −13.0034 + 7.50754i −1.02165 + 0.589848i
\(163\) −10.4203 + 6.01619i −0.816185 + 0.471224i −0.849099 0.528234i \(-0.822854\pi\)
0.0329144 + 0.999458i \(0.489521\pi\)
\(164\) 0.799315i 0.0624160i
\(165\) −4.67630 8.09959i −0.364050 0.630553i
\(166\) 1.56371 2.70842i 0.121367 0.210214i
\(167\) 16.8199 + 9.71099i 1.30157 + 0.751459i 0.980672 0.195657i \(-0.0626838\pi\)
0.320893 + 0.947116i \(0.396017\pi\)
\(168\) 0 0
\(169\) 12.5497 + 3.39173i 0.965365 + 0.260902i
\(170\) 37.1440 2.84882
\(171\) −0.983297 0.567707i −0.0751946 0.0434136i
\(172\) 0.364613 0.631528i 0.0278015 0.0481536i
\(173\) −7.18976 12.4530i −0.546627 0.946786i −0.998503 0.0547049i \(-0.982578\pi\)
0.451875 0.892081i \(-0.350755\pi\)
\(174\) 11.1551i 0.845663i
\(175\) 0 0
\(176\) 3.96771 2.29076i 0.299077 0.172672i
\(177\) 22.9299i 1.72351i
\(178\) −5.09589 8.82635i −0.381953 0.661563i
\(179\) 2.71303 4.69911i 0.202781 0.351228i −0.746642 0.665226i \(-0.768335\pi\)
0.949424 + 0.313998i \(0.101669\pi\)
\(180\) 0.707550 + 0.408504i 0.0527376 + 0.0304481i
\(181\) 15.4902 1.15138 0.575688 0.817669i \(-0.304734\pi\)
0.575688 + 0.817669i \(0.304734\pi\)
\(182\) 0 0
\(183\) −15.6298 −1.15539
\(184\) 4.20348 + 2.42688i 0.309885 + 0.178912i
\(185\) −1.88393 + 3.26307i −0.138509 + 0.239905i
\(186\) −7.10450 12.3054i −0.520927 0.902272i
\(187\) 9.89589i 0.723659i
\(188\) −0.147423 + 0.0851144i −0.0107519 + 0.00620761i
\(189\) 0 0
\(190\) 4.53011i 0.328649i
\(191\) −2.37311 4.11035i −0.171712 0.297414i 0.767306 0.641281i \(-0.221597\pi\)
−0.939019 + 0.343866i \(0.888263\pi\)
\(192\) −8.82529 + 15.2859i −0.636911 + 1.10316i
\(193\) −18.2204 10.5196i −1.31154 0.757215i −0.329185 0.944266i \(-0.606774\pi\)
−0.982350 + 0.187050i \(0.940107\pi\)
\(194\) −0.643768 −0.0462198
\(195\) 20.9051 + 16.0769i 1.49704 + 1.15129i
\(196\) 0 0
\(197\) 5.03342 + 2.90604i 0.358616 + 0.207047i 0.668474 0.743736i \(-0.266948\pi\)
−0.309857 + 0.950783i \(0.600281\pi\)
\(198\) −1.03458 + 1.79194i −0.0735242 + 0.127348i
\(199\) −5.30909 9.19562i −0.376352 0.651860i 0.614177 0.789168i \(-0.289488\pi\)
−0.990528 + 0.137309i \(0.956155\pi\)
\(200\) 22.7739i 1.61036i
\(201\) −11.2226 + 6.47939i −0.791583 + 0.457021i
\(202\) 3.35329 1.93602i 0.235936 0.136218i
\(203\) 0 0
\(204\) 1.51019 + 2.61573i 0.105735 + 0.183138i
\(205\) 7.49023 12.9735i 0.523140 0.906106i
\(206\) 13.2054 + 7.62414i 0.920064 + 0.531199i
\(207\) −1.98155 −0.137727
\(208\) −7.87551 + 10.2407i −0.546068 + 0.710063i
\(209\) 1.20691 0.0834837
\(210\) 0 0
\(211\) 2.33275 4.04043i 0.160593 0.278155i −0.774489 0.632588i \(-0.781993\pi\)
0.935081 + 0.354433i \(0.115326\pi\)
\(212\) 0.00761392 + 0.0131877i 0.000522926 + 0.000905735i
\(213\) 23.4203i 1.60474i
\(214\) −7.65645 + 4.42046i −0.523384 + 0.302176i
\(215\) 11.8359 6.83344i 0.807200 0.466037i
\(216\) 10.8556i 0.738631i
\(217\) 0 0
\(218\) 3.92748 6.80260i 0.266003 0.460730i
\(219\) 1.35023 + 0.779558i 0.0912403 + 0.0526776i
\(220\) −0.868455 −0.0585512
\(221\) 10.6506 + 25.7915i 0.716438 + 1.73492i
\(222\) 2.91252 0.195475
\(223\) −20.9798 12.1127i −1.40491 0.811126i −0.410020 0.912076i \(-0.634478\pi\)
−0.994891 + 0.100950i \(0.967812\pi\)
\(224\) 0 0
\(225\) 4.64872 + 8.05182i 0.309915 + 0.536788i
\(226\) 8.78747i 0.584534i
\(227\) −13.3154 + 7.68764i −0.883773 + 0.510247i −0.871901 0.489683i \(-0.837113\pi\)
−0.0118726 + 0.999930i \(0.503779\pi\)
\(228\) −0.319016 + 0.184184i −0.0211274 + 0.0121979i
\(229\) 16.3515i 1.08054i 0.841493 + 0.540268i \(0.181677\pi\)
−0.841493 + 0.540268i \(0.818323\pi\)
\(230\) 3.95302 + 6.84683i 0.260654 + 0.451467i
\(231\) 0 0
\(232\) −10.3215 5.95913i −0.677641 0.391236i
\(233\) 29.1107 1.90711 0.953554 0.301223i \(-0.0973947\pi\)
0.953554 + 0.301223i \(0.0973947\pi\)
\(234\) 0.767796 5.78378i 0.0501924 0.378098i
\(235\) −3.19037 −0.208117
\(236\) −1.84394 1.06460i −0.120030 0.0692995i
\(237\) −2.92684 + 5.06943i −0.190119 + 0.329295i
\(238\) 0 0
\(239\) 8.65409i 0.559787i 0.960031 + 0.279893i \(0.0902991\pi\)
−0.960031 + 0.279893i \(0.909701\pi\)
\(240\) −22.6963 + 13.1037i −1.46504 + 0.845840i
\(241\) 15.7601 9.09909i 1.01520 0.586124i 0.102487 0.994734i \(-0.467320\pi\)
0.912709 + 0.408611i \(0.133987\pi\)
\(242\) 12.5980i 0.809833i
\(243\) −5.91508 10.2452i −0.379453 0.657231i
\(244\) −0.725669 + 1.25690i −0.0464562 + 0.0804645i
\(245\) 0 0
\(246\) −11.5797 −0.738297
\(247\) −3.14555 + 1.29896i −0.200147 + 0.0826506i
\(248\) −15.1811 −0.964003
\(249\) 4.12759 + 2.38307i 0.261576 + 0.151021i
\(250\) 6.54894 11.3431i 0.414191 0.717400i
\(251\) −7.93598 13.7455i −0.500915 0.867610i −0.999999 0.00105678i \(-0.999664\pi\)
0.499085 0.866553i \(-0.333670\pi\)
\(252\) 0 0
\(253\) 1.82413 1.05316i 0.114682 0.0662117i
\(254\) −17.1446 + 9.89841i −1.07574 + 0.621082i
\(255\) 56.6069i 3.54486i
\(256\) 2.26304 + 3.91971i 0.141440 + 0.244982i
\(257\) 12.1634 21.0676i 0.758730 1.31416i −0.184769 0.982782i \(-0.559154\pi\)
0.943499 0.331376i \(-0.107513\pi\)
\(258\) −9.14900 5.28218i −0.569592 0.328854i
\(259\) 0 0
\(260\) 2.26344 0.934688i 0.140372 0.0579669i
\(261\) 4.86563 0.301175
\(262\) 13.0325 + 7.52432i 0.805150 + 0.464854i
\(263\) −7.71727 + 13.3667i −0.475867 + 0.824226i −0.999618 0.0276456i \(-0.991199\pi\)
0.523751 + 0.851872i \(0.324532\pi\)
\(264\) 3.86204 + 6.68925i 0.237692 + 0.411695i
\(265\) 0.285395i 0.0175317i
\(266\) 0 0
\(267\) 13.4512 7.76606i 0.823201 0.475275i
\(268\) 1.20331i 0.0735040i
\(269\) −6.52035 11.2936i −0.397553 0.688582i 0.595870 0.803081i \(-0.296807\pi\)
−0.993423 + 0.114499i \(0.963474\pi\)
\(270\) −8.84108 + 15.3132i −0.538051 + 0.931931i
\(271\) 23.3572 + 13.4853i 1.41885 + 0.819174i 0.996198 0.0871168i \(-0.0277653\pi\)
0.422654 + 0.906291i \(0.361099\pi\)
\(272\) −27.7298 −1.68136
\(273\) 0 0
\(274\) −23.7174 −1.43282
\(275\) −8.55884 4.94145i −0.516117 0.297980i
\(276\) −0.321442 + 0.556753i −0.0193485 + 0.0335126i
\(277\) 6.35073 + 10.9998i 0.381578 + 0.660913i 0.991288 0.131712i \(-0.0420474\pi\)
−0.609710 + 0.792625i \(0.708714\pi\)
\(278\) 7.87912i 0.472558i
\(279\) 5.36737 3.09885i 0.321336 0.185523i
\(280\) 0 0
\(281\) 26.7216i 1.59408i 0.603930 + 0.797038i \(0.293601\pi\)
−0.603930 + 0.797038i \(0.706399\pi\)
\(282\) 1.23306 + 2.13572i 0.0734276 + 0.127180i
\(283\) −7.37113 + 12.7672i −0.438168 + 0.758929i −0.997548 0.0699819i \(-0.977706\pi\)
0.559380 + 0.828911i \(0.311039\pi\)
\(284\) −1.88338 1.08737i −0.111758 0.0645236i
\(285\) −6.90382 −0.408947
\(286\) 2.36719 + 5.73238i 0.139975 + 0.338963i
\(287\) 0 0
\(288\) −1.11791 0.645425i −0.0658734 0.0380320i
\(289\) −21.4476 + 37.1483i −1.26162 + 2.18519i
\(290\) −9.70653 16.8122i −0.569987 0.987247i
\(291\) 0.981092i 0.0575126i
\(292\) 0.125379 0.0723874i 0.00733723 0.00423615i
\(293\) 10.0312 5.79153i 0.586030 0.338345i −0.177496 0.984121i \(-0.556800\pi\)
0.763526 + 0.645777i \(0.223466\pi\)
\(294\) 0 0
\(295\) −19.9523 34.5584i −1.16167 2.01207i
\(296\) 1.55589 2.69489i 0.0904344 0.156637i
\(297\) 4.07974 + 2.35544i 0.236730 + 0.136676i
\(298\) 14.0966 0.816593
\(299\) −3.62072 + 4.70809i −0.209391 + 0.272276i
\(300\) 3.01641 0.174153
\(301\) 0 0
\(302\) 3.17074 5.49188i 0.182455 0.316022i
\(303\) 2.95047 + 5.11036i 0.169500 + 0.293582i
\(304\) 3.38194i 0.193968i
\(305\) −23.5563 + 13.6002i −1.34883 + 0.778746i
\(306\) 10.8458 6.26180i 0.620011 0.357963i
\(307\) 29.3335i 1.67415i −0.547086 0.837076i \(-0.684263\pi\)
0.547086 0.837076i \(-0.315737\pi\)
\(308\) 0 0
\(309\) −11.6191 + 20.1248i −0.660986 + 1.14486i
\(310\) −21.4149 12.3639i −1.21628 0.702222i
\(311\) −0.150654 −0.00854282 −0.00427141 0.999991i \(-0.501360\pi\)
−0.00427141 + 0.999991i \(0.501360\pi\)
\(312\) −17.2650 13.2775i −0.977438 0.751691i
\(313\) 10.5211 0.594690 0.297345 0.954770i \(-0.403899\pi\)
0.297345 + 0.954770i \(0.403899\pi\)
\(314\) 10.4874 + 6.05493i 0.591841 + 0.341699i
\(315\) 0 0
\(316\) 0.271777 + 0.470732i 0.0152887 + 0.0264808i
\(317\) 1.50676i 0.0846281i 0.999104 + 0.0423140i \(0.0134730\pi\)
−0.999104 + 0.0423140i \(0.986527\pi\)
\(318\) 0.191051 0.110303i 0.0107136 0.00618551i
\(319\) −4.47910 + 2.58601i −0.250782 + 0.144789i
\(320\) 30.7172i 1.71714i
\(321\) −6.73671 11.6683i −0.376006 0.651262i
\(322\) 0 0
\(323\) −6.32619 3.65243i −0.351999 0.203227i
\(324\) −2.12482 −0.118046
\(325\) 27.6251 + 3.66722i 1.53236 + 0.203421i
\(326\) 16.1863 0.896475
\(327\) 10.3671 + 5.98542i 0.573299 + 0.330995i
\(328\) −6.18600 + 10.7145i −0.341565 + 0.591607i
\(329\) 0 0
\(330\) 12.5814i 0.692582i
\(331\) 21.8679 12.6254i 1.20197 0.693957i 0.240976 0.970531i \(-0.422533\pi\)
0.960993 + 0.276574i \(0.0891992\pi\)
\(332\) 0.383276 0.221284i 0.0210350 0.0121446i
\(333\) 1.27039i 0.0696167i
\(334\) −13.0635 22.6266i −0.714802 1.23807i
\(335\) −11.2760 + 19.5306i −0.616075 + 1.06707i
\(336\) 0 0
\(337\) 32.1811 1.75302 0.876509 0.481386i \(-0.159866\pi\)
0.876509 + 0.481386i \(0.159866\pi\)
\(338\) −12.3391 12.3925i −0.671161 0.674062i
\(339\) −13.3920 −0.727351
\(340\) 4.55213 + 2.62817i 0.246874 + 0.142533i
\(341\) −3.29398 + 5.70535i −0.178379 + 0.308962i
\(342\) 0.763694 + 1.32276i 0.0412959 + 0.0715265i
\(343\) 0 0
\(344\) −9.77495 + 5.64357i −0.527030 + 0.304281i
\(345\) −10.4345 + 6.02434i −0.561773 + 0.324340i
\(346\) 19.3437i 1.03992i
\(347\) −12.3819 21.4461i −0.664695 1.15128i −0.979368 0.202085i \(-0.935228\pi\)
0.314673 0.949200i \(-0.398105\pi\)
\(348\) 0.789291 1.36709i 0.0423104 0.0732838i
\(349\) 10.0075 + 5.77782i 0.535688 + 0.309280i 0.743330 0.668925i \(-0.233245\pi\)
−0.207642 + 0.978205i \(0.566579\pi\)
\(350\) 0 0
\(351\) −13.1680 1.74805i −0.702857 0.0933042i
\(352\) 1.37213 0.0731350
\(353\) −17.3971 10.0442i −0.925953 0.534599i −0.0404237 0.999183i \(-0.512871\pi\)
−0.885529 + 0.464583i \(0.846204\pi\)
\(354\) −15.4229 + 26.7133i −0.819719 + 1.41980i
\(355\) −20.3791 35.2977i −1.08161 1.87340i
\(356\) 1.44227i 0.0764399i
\(357\) 0 0
\(358\) −6.32136 + 3.64964i −0.334094 + 0.192890i
\(359\) 15.0510i 0.794363i 0.917740 + 0.397181i \(0.130012\pi\)
−0.917740 + 0.397181i \(0.869988\pi\)
\(360\) −6.32292 10.9516i −0.333247 0.577201i
\(361\) −9.05455 + 15.6829i −0.476555 + 0.825418i
\(362\) −18.0461 10.4189i −0.948481 0.547606i
\(363\) −19.1992 −1.00770
\(364\) 0 0
\(365\) 2.71331 0.142021
\(366\) 18.2087 + 10.5128i 0.951787 + 0.549514i
\(367\) 4.50178 7.79731i 0.234991 0.407016i −0.724279 0.689507i \(-0.757827\pi\)
0.959270 + 0.282491i \(0.0911607\pi\)
\(368\) −2.95112 5.11148i −0.153838 0.266454i
\(369\) 5.05087i 0.262938i
\(370\) 4.38956 2.53431i 0.228202 0.131753i
\(371\) 0 0
\(372\) 2.01075i 0.104253i
\(373\) 8.06953 + 13.9768i 0.417824 + 0.723693i 0.995720 0.0924174i \(-0.0294594\pi\)
−0.577896 + 0.816110i \(0.696126\pi\)
\(374\) −6.65611 + 11.5287i −0.344179 + 0.596136i
\(375\) 17.2867 + 9.98048i 0.892681 + 0.515390i
\(376\) 2.63484 0.135882
\(377\) 8.89057 11.5606i 0.457888 0.595400i
\(378\) 0 0
\(379\) −13.5668 7.83277i −0.696878 0.402342i 0.109306 0.994008i \(-0.465137\pi\)
−0.806183 + 0.591666i \(0.798471\pi\)
\(380\) −0.320534 + 0.555181i −0.0164430 + 0.0284802i
\(381\) −15.0850 26.1280i −0.772829 1.33858i
\(382\) 6.38474i 0.326672i
\(383\) 21.3327 12.3164i 1.09005 0.629339i 0.156459 0.987685i \(-0.449992\pi\)
0.933589 + 0.358345i \(0.116659\pi\)
\(384\) 16.7525 9.67207i 0.854898 0.493576i
\(385\) 0 0
\(386\) 14.1512 + 24.5106i 0.720277 + 1.24756i
\(387\) 2.30399 3.99062i 0.117118 0.202855i
\(388\) −0.0788960 0.0455506i −0.00400534 0.00231248i
\(389\) 18.8567 0.956071 0.478036 0.878340i \(-0.341349\pi\)
0.478036 + 0.878340i \(0.341349\pi\)
\(390\) −13.5409 32.7906i −0.685670 1.66042i
\(391\) −12.7486 −0.644724
\(392\) 0 0
\(393\) −11.4669 + 19.8613i −0.578431 + 1.00187i
\(394\) −3.90929 6.77108i −0.196947 0.341122i
\(395\) 10.1871i 0.512569i
\(396\) −0.253582 + 0.146406i −0.0127430 + 0.00735716i
\(397\) −12.5600 + 7.25149i −0.630366 + 0.363942i −0.780894 0.624664i \(-0.785236\pi\)
0.150528 + 0.988606i \(0.451903\pi\)
\(398\) 14.2839i 0.715985i
\(399\) 0 0
\(400\) −13.8467 + 23.9831i −0.692333 + 1.19916i
\(401\) −18.1770 10.4945i −0.907714 0.524069i −0.0280189 0.999607i \(-0.508920\pi\)
−0.879695 + 0.475539i \(0.842253\pi\)
\(402\) 17.4325 0.869453
\(403\) 2.44458 18.4150i 0.121773 0.917314i
\(404\) 0.547943 0.0272612
\(405\) −34.4874 19.9113i −1.71369 0.989401i
\(406\) 0 0
\(407\) −0.675191 1.16947i −0.0334680 0.0579683i
\(408\) 46.7502i 2.31448i
\(409\) −18.5568 + 10.7138i −0.917576 + 0.529763i −0.882861 0.469635i \(-0.844386\pi\)
−0.0347148 + 0.999397i \(0.511052\pi\)
\(410\) −17.4522 + 10.0761i −0.861905 + 0.497621i
\(411\) 36.1450i 1.78290i
\(412\) 1.07891 + 1.86873i 0.0531542 + 0.0920657i
\(413\) 0 0
\(414\) 2.30850 + 1.33281i 0.113457 + 0.0655043i
\(415\) 8.29446 0.407159
\(416\) −3.57617 + 1.47678i −0.175336 + 0.0724052i
\(417\) −12.0077 −0.588018
\(418\) −1.40605 0.811784i −0.0687722 0.0397056i
\(419\) 3.98203 6.89708i 0.194535 0.336944i −0.752213 0.658920i \(-0.771014\pi\)
0.946748 + 0.321976i \(0.104347\pi\)
\(420\) 0 0
\(421\) 2.81786i 0.137334i −0.997640 0.0686670i \(-0.978125\pi\)
0.997640 0.0686670i \(-0.0218746\pi\)
\(422\) −5.43530 + 3.13807i −0.264586 + 0.152759i
\(423\) −0.931562 + 0.537838i −0.0452941 + 0.0261506i
\(424\) 0.235700i 0.0114466i
\(425\) 29.9082 + 51.8026i 1.45076 + 2.51279i
\(426\) −15.7528 + 27.2847i −0.763227 + 1.32195i
\(427\) 0 0
\(428\) −1.25110 −0.0604742
\(429\) −8.73606 + 3.60756i −0.421781 + 0.174175i
\(430\) −18.3851 −0.886606
\(431\) −4.96775 2.86813i −0.239288 0.138153i 0.375561 0.926797i \(-0.377450\pi\)
−0.614849 + 0.788645i \(0.710783\pi\)
\(432\) 6.60028 11.4320i 0.317556 0.550023i
\(433\) 12.2628 + 21.2398i 0.589314 + 1.02072i 0.994322 + 0.106409i \(0.0339351\pi\)
−0.405009 + 0.914313i \(0.632732\pi\)
\(434\) 0 0
\(435\) 25.6215 14.7926i 1.22846 0.709251i
\(436\) 0.962653 0.555788i 0.0461027 0.0266174i
\(437\) 1.55483i 0.0743774i
\(438\) −1.04868 1.81637i −0.0501079 0.0867895i
\(439\) −18.3211 + 31.7332i −0.874420 + 1.51454i −0.0170416 + 0.999855i \(0.505425\pi\)
−0.857379 + 0.514686i \(0.827909\pi\)
\(440\) 11.6412 + 6.72108i 0.554975 + 0.320415i
\(441\) 0 0
\(442\) 4.93973 37.2108i 0.234959 1.76994i
\(443\) 27.0933 1.28724 0.643622 0.765344i \(-0.277431\pi\)
0.643622 + 0.765344i \(0.277431\pi\)
\(444\) 0.356939 + 0.206079i 0.0169396 + 0.00978008i
\(445\) 13.5152 23.4090i 0.640682 1.10969i
\(446\) 16.2943 + 28.2226i 0.771558 + 1.33638i
\(447\) 21.4830i 1.01611i
\(448\) 0 0
\(449\) 23.7571 13.7162i 1.12117 0.647307i 0.179470 0.983764i \(-0.442562\pi\)
0.941699 + 0.336456i \(0.109228\pi\)
\(450\) 12.5072i 0.589593i
\(451\) 2.68446 + 4.64962i 0.126406 + 0.218942i
\(452\) −0.621768 + 1.07693i −0.0292455 + 0.0506547i
\(453\) 8.36953 + 4.83215i 0.393235 + 0.227034i
\(454\) 20.6832 0.970712
\(455\) 0 0
\(456\) 5.70169 0.267006
\(457\) 34.3500 + 19.8320i 1.60682 + 0.927700i 0.990075 + 0.140539i \(0.0448835\pi\)
0.616748 + 0.787161i \(0.288450\pi\)
\(458\) 10.9982 19.0495i 0.513913 0.890123i
\(459\) −14.2563 24.6927i −0.665429 1.15256i
\(460\) 1.11880i 0.0521645i
\(461\) 4.23988 2.44790i 0.197471 0.114010i −0.398004 0.917384i \(-0.630297\pi\)
0.595475 + 0.803374i \(0.296964\pi\)
\(462\) 0 0
\(463\) 4.71193i 0.218982i 0.993988 + 0.109491i \(0.0349221\pi\)
−0.993988 + 0.109491i \(0.965078\pi\)
\(464\) 7.24638 + 12.5511i 0.336405 + 0.582670i
\(465\) 18.8424 32.6360i 0.873794 1.51346i
\(466\) −33.9140 19.5803i −1.57104 0.907038i
\(467\) 32.0161 1.48153 0.740765 0.671764i \(-0.234463\pi\)
0.740765 + 0.671764i \(0.234463\pi\)
\(468\) 0.503335 0.654496i 0.0232667 0.0302541i
\(469\) 0 0
\(470\) 3.71678 + 2.14588i 0.171442 + 0.0989822i
\(471\) −9.22761 + 15.9827i −0.425186 + 0.736444i
\(472\) 16.4781 + 28.5410i 0.758467 + 1.31370i
\(473\) 4.89814i 0.225217i
\(474\) 6.81953 3.93726i 0.313232 0.180844i
\(475\) −6.31788 + 3.64763i −0.289884 + 0.167365i
\(476\) 0 0
\(477\) 0.0481123 + 0.0833330i 0.00220291 + 0.00381556i
\(478\) 5.82086 10.0820i 0.266240 0.461141i
\(479\) 15.6097 + 9.01224i 0.713224 + 0.411780i 0.812254 0.583305i \(-0.198241\pi\)
−0.0990298 + 0.995084i \(0.531574\pi\)
\(480\) −7.84894 −0.358253
\(481\) 3.01840 + 2.32127i 0.137627 + 0.105841i
\(482\) −24.4807 −1.11506
\(483\) 0 0
\(484\) −0.891390 + 1.54393i −0.0405177 + 0.0701788i
\(485\) −0.853693 1.47864i −0.0387642 0.0671416i
\(486\) 15.9142i 0.721885i
\(487\) 15.2424 8.80020i 0.690699 0.398775i −0.113175 0.993575i \(-0.536102\pi\)
0.803874 + 0.594800i \(0.202769\pi\)
\(488\) 19.4545 11.2321i 0.880666 0.508453i
\(489\) 24.6676i 1.11551i
\(490\) 0 0
\(491\) 1.93180 3.34598i 0.0871810 0.151002i −0.819138 0.573597i \(-0.805547\pi\)
0.906318 + 0.422595i \(0.138881\pi\)
\(492\) −1.41914 0.819339i −0.0639796 0.0369387i
\(493\) 31.3038 1.40985
\(494\) 4.53826 + 0.602454i 0.204186 + 0.0271057i
\(495\) −5.48776 −0.246656
\(496\) 15.9872 + 9.23023i 0.717848 + 0.414450i
\(497\) 0 0
\(498\) −3.20576 5.55255i −0.143654 0.248816i
\(499\) 12.6473i 0.566169i −0.959095 0.283084i \(-0.908642\pi\)
0.959095 0.283084i \(-0.0913577\pi\)
\(500\) 1.60519 0.926757i 0.0717863 0.0414458i
\(501\) 34.4826 19.9085i 1.54057 0.889448i
\(502\) 21.3514i 0.952959i
\(503\) 11.0180 + 19.0837i 0.491268 + 0.850902i 0.999949 0.0100533i \(-0.00320011\pi\)
−0.508681 + 0.860955i \(0.669867\pi\)
\(504\) 0 0
\(505\) 8.89351 + 5.13467i 0.395756 + 0.228490i
\(506\) −2.83348 −0.125964
\(507\) 18.8860 18.8047i 0.838755 0.835144i
\(508\) −2.80150 −0.124296
\(509\) −13.5708 7.83509i −0.601514 0.347284i 0.168123 0.985766i \(-0.446229\pi\)
−0.769637 + 0.638482i \(0.779563\pi\)
\(510\) 38.0745 65.9470i 1.68597 2.92018i
\(511\) 0 0
\(512\) 24.9600i 1.10309i
\(513\) 3.01154 1.73871i 0.132963 0.0767661i
\(514\) −28.3406 + 16.3625i −1.25005 + 0.721718i
\(515\) 40.4411i 1.78205i
\(516\) −0.747495 1.29470i −0.0329066 0.0569959i
\(517\) 0.571705 0.990222i 0.0251436 0.0435499i
\(518\) 0 0
\(519\) −29.4795 −1.29401
\(520\) −37.5741 4.98795i −1.64773 0.218736i
\(521\) 25.2415 1.10585 0.552925 0.833231i \(-0.313512\pi\)
0.552925 + 0.833231i \(0.313512\pi\)
\(522\) −5.66846 3.27269i −0.248102 0.143242i
\(523\) −6.62383 + 11.4728i −0.289640 + 0.501671i −0.973724 0.227733i \(-0.926869\pi\)
0.684084 + 0.729403i \(0.260202\pi\)
\(524\) 1.06479 + 1.84426i 0.0465154 + 0.0805670i
\(525\) 0 0
\(526\) 17.9812 10.3815i 0.784019 0.452654i
\(527\) 34.5318 19.9369i 1.50423 0.868466i
\(528\) 9.39259i 0.408760i
\(529\) 10.1432 + 17.5686i 0.441011 + 0.763853i
\(530\) 0.191960 0.332485i 0.00833822 0.0144422i
\(531\) −11.6518 6.72720i −0.505647 0.291935i
\(532\) 0 0
\(533\) −12.0007 9.22903i −0.519807 0.399754i
\(534\) −20.8942 −0.904181
\(535\) −20.3063 11.7238i −0.877916 0.506865i
\(536\) 9.31258 16.1299i 0.402242 0.696704i
\(537\) −5.56200 9.63366i −0.240018 0.415723i
\(538\) 17.5427i 0.756320i
\(539\) 0 0
\(540\) −2.16701 + 1.25112i −0.0932532 + 0.0538398i
\(541\) 14.4034i 0.619250i −0.950859 0.309625i \(-0.899796\pi\)
0.950859 0.309625i \(-0.100204\pi\)
\(542\) −18.1408 31.4208i −0.779214 1.34964i
\(543\) 15.8782 27.5019i 0.681401 1.18022i
\(544\) −7.19224 4.15244i −0.308365 0.178034i
\(545\) 20.8328 0.892377
\(546\) 0 0
\(547\) 2.00679 0.0858042 0.0429021 0.999079i \(-0.486340\pi\)
0.0429021 + 0.999079i \(0.486340\pi\)
\(548\) −2.90665 1.67816i −0.124166 0.0716873i
\(549\) −4.58550 + 7.94232i −0.195704 + 0.338970i
\(550\) 6.64736 + 11.5136i 0.283445 + 0.490940i
\(551\) 3.81783i 0.162645i
\(552\) 8.61757 4.97535i 0.366788 0.211765i
\(553\) 0 0
\(554\) 17.0863i 0.725928i
\(555\) 3.86226 + 6.68962i 0.163944 + 0.283959i
\(556\) −0.557497 + 0.965614i −0.0236432 + 0.0409512i
\(557\) 7.42977 + 4.28958i 0.314810 + 0.181755i 0.649077 0.760723i \(-0.275155\pi\)
−0.334267 + 0.942478i \(0.608489\pi\)
\(558\) −8.33731 −0.352946
\(559\) −5.27170 12.7659i −0.222969 0.539942i
\(560\) 0 0
\(561\) −17.5696 10.1438i −0.741788 0.428272i
\(562\) 17.9733 31.1306i 0.758157 1.31317i
\(563\) 6.38718 + 11.0629i 0.269188 + 0.466247i 0.968652 0.248421i \(-0.0799115\pi\)
−0.699465 + 0.714667i \(0.746578\pi\)
\(564\) 0.348987i 0.0146950i
\(565\) −20.1835 + 11.6530i −0.849126 + 0.490243i
\(566\) 17.1747 9.91583i 0.721908 0.416794i
\(567\) 0 0
\(568\) 16.8306 + 29.1515i 0.706196 + 1.22317i
\(569\) −2.89558 + 5.01530i −0.121389 + 0.210252i −0.920316 0.391176i \(-0.872068\pi\)
0.798927 + 0.601429i \(0.205402\pi\)
\(570\) 8.04295 + 4.64360i 0.336882 + 0.194499i
\(571\) 44.1332 1.84692 0.923458 0.383700i \(-0.125350\pi\)
0.923458 + 0.383700i \(0.125350\pi\)
\(572\) −0.115495 + 0.870017i −0.00482907 + 0.0363772i
\(573\) −9.73025 −0.406487
\(574\) 0 0
\(575\) −6.36592 + 11.0261i −0.265477 + 0.459820i
\(576\) 5.17835 + 8.96917i 0.215765 + 0.373715i
\(577\) 11.9330i 0.496776i 0.968661 + 0.248388i \(0.0799009\pi\)
−0.968661 + 0.248388i \(0.920099\pi\)
\(578\) 49.9729 28.8518i 2.07860 1.20008i
\(579\) −37.3538 + 21.5662i −1.55237 + 0.896261i
\(580\) 2.74719i 0.114071i
\(581\) 0 0
\(582\) −0.659895 + 1.14297i −0.0273535 + 0.0473777i
\(583\) −0.0885805 0.0511420i −0.00366863 0.00211808i
\(584\) −2.24086 −0.0927274
\(585\) 14.3027 5.90629i 0.591342 0.244195i
\(586\) −15.5818 −0.643679
\(587\) −17.6250 10.1758i −0.727462 0.420000i 0.0900312 0.995939i \(-0.471303\pi\)
−0.817493 + 0.575939i \(0.804637\pi\)
\(588\) 0 0
\(589\) 2.43152 + 4.21152i 0.100189 + 0.173533i
\(590\) 53.6808i 2.21000i
\(591\) 10.3190 5.95769i 0.424468 0.245067i
\(592\) −3.27701 + 1.89199i −0.134684 + 0.0777601i
\(593\) 18.1800i 0.746563i −0.927718 0.373282i \(-0.878232\pi\)
0.927718 0.373282i \(-0.121768\pi\)
\(594\) −3.16859 5.48817i −0.130009 0.225182i
\(595\) 0 0
\(596\) 1.72759 + 0.997422i 0.0707646 + 0.0408560i
\(597\) −21.7684 −0.890920
\(598\) 7.38486 3.04958i 0.301989 0.124707i
\(599\) −38.2682 −1.56359 −0.781797 0.623532i \(-0.785697\pi\)
−0.781797 + 0.623532i \(0.785697\pi\)
\(600\) −40.4337 23.3444i −1.65070 0.953031i
\(601\) −13.4360 + 23.2718i −0.548064 + 0.949275i 0.450343 + 0.892856i \(0.351302\pi\)
−0.998407 + 0.0564195i \(0.982032\pi\)
\(602\) 0 0
\(603\) 7.60372i 0.309648i
\(604\) 0.777170 0.448699i 0.0316226 0.0182573i
\(605\) −28.9358 + 16.7061i −1.17641 + 0.679200i
\(606\) 7.93809i 0.322463i
\(607\) −4.70105 8.14245i −0.190810 0.330492i 0.754709 0.656059i \(-0.227778\pi\)
−0.945519 + 0.325568i \(0.894445\pi\)
\(608\) 0.506435 0.877171i 0.0205386 0.0355740i
\(609\) 0 0
\(610\) 36.5908 1.48152
\(611\) −0.424283 + 3.19611i −0.0171646 + 0.129301i
\(612\) 1.77225 0.0716389
\(613\) −11.5089 6.64469i −0.464842 0.268376i 0.249236 0.968443i \(-0.419820\pi\)
−0.714078 + 0.700066i \(0.753154\pi\)
\(614\) −19.7301 + 34.1735i −0.796242 + 1.37913i
\(615\) −15.3557 26.5969i −0.619204 1.07249i
\(616\) 0 0
\(617\) −9.72211 + 5.61306i −0.391397 + 0.225973i −0.682765 0.730638i \(-0.739223\pi\)
0.291368 + 0.956611i \(0.405890\pi\)
\(618\) 27.0724 15.6303i 1.08901 0.628742i
\(619\) 9.28505i 0.373198i −0.982436 0.186599i \(-0.940254\pi\)
0.982436 0.186599i \(-0.0597465\pi\)
\(620\) −1.74965 3.03048i −0.0702675 0.121707i
\(621\) 3.03444 5.25580i 0.121768 0.210908i
\(622\) 0.175512 + 0.101332i 0.00703740 + 0.00406304i
\(623\) 0 0
\(624\) 10.1089 + 24.4797i 0.404681 + 0.979974i
\(625\) −3.90726 −0.156290
\(626\) −12.2571 7.07665i −0.489893 0.282840i
\(627\) 1.23715 2.14280i 0.0494068 0.0855752i
\(628\) 0.856848 + 1.48410i 0.0341920 + 0.0592222i
\(629\) 8.17322i 0.325888i
\(630\) 0 0
\(631\) 9.00894 5.20132i 0.358640 0.207061i −0.309844 0.950787i \(-0.600277\pi\)
0.668484 + 0.743726i \(0.266943\pi\)
\(632\) 8.41327i 0.334662i
\(633\) −4.78237 8.28331i −0.190082 0.329232i
\(634\) 1.01347 1.75538i 0.0402499 0.0697149i
\(635\) −45.4704 26.2523i −1.80444 1.04179i
\(636\) 0.0312187 0.00123790
\(637\) 0 0
\(638\) 6.95754 0.275452
\(639\) −11.9011 6.87109i −0.470800 0.271816i
\(640\) 16.8322 29.1542i 0.665351 1.15242i
\(641\) 7.42955 + 12.8684i 0.293449 + 0.508269i 0.974623 0.223853i \(-0.0718634\pi\)
−0.681174 + 0.732122i \(0.738530\pi\)
\(642\) 18.1248i 0.715328i
\(643\) −1.98945 + 1.14861i −0.0784563 + 0.0452968i −0.538715 0.842488i \(-0.681090\pi\)
0.460259 + 0.887785i \(0.347757\pi\)
\(644\) 0 0
\(645\) 28.0185i 1.10323i
\(646\) 4.91334 + 8.51016i 0.193313 + 0.334828i
\(647\) −3.99932 + 6.92703i −0.157230 + 0.272330i −0.933869 0.357616i \(-0.883590\pi\)
0.776639 + 0.629946i \(0.216923\pi\)
\(648\) 28.4823 + 16.4443i 1.11889 + 0.645991i
\(649\) 14.3016 0.561387
\(650\) −29.7166 22.8533i −1.16558 0.896380i
\(651\) 0 0
\(652\) 1.98368 + 1.14528i 0.0776871 + 0.0448526i
\(653\) −1.99222 + 3.45062i −0.0779615 + 0.135033i −0.902370 0.430962i \(-0.858174\pi\)
0.824409 + 0.565995i \(0.191508\pi\)
\(654\) −8.05175 13.9460i −0.314848 0.545333i
\(655\) 39.9116i 1.55948i
\(656\) 13.0289 7.52225i 0.508694 0.293695i
\(657\) 0.792267 0.457415i 0.0309093 0.0178455i
\(658\) 0 0
\(659\) 13.7501 + 23.8159i 0.535629 + 0.927737i 0.999133 + 0.0416417i \(0.0132588\pi\)
−0.463504 + 0.886095i \(0.653408\pi\)
\(660\) −0.890211 + 1.54189i −0.0346514 + 0.0600180i
\(661\) 6.05023 + 3.49310i 0.235327 + 0.135866i 0.613027 0.790062i \(-0.289952\pi\)
−0.377700 + 0.925928i \(0.623285\pi\)
\(662\) −33.9681 −1.32021
\(663\) 56.7087 + 7.52808i 2.20238 + 0.292366i
\(664\) −6.85019 −0.265839
\(665\) 0 0
\(666\) 0.854479 1.48000i 0.0331104 0.0573488i
\(667\) 3.33148 + 5.77029i 0.128995 + 0.223427i
\(668\) 3.69729i 0.143053i
\(669\) −43.0108 + 24.8323i −1.66289 + 0.960071i
\(670\) 26.2731 15.1688i 1.01502 0.586022i
\(671\) 9.74849i 0.376336i
\(672\) 0 0
\(673\) 2.72783 4.72474i 0.105150 0.182125i −0.808649 0.588291i \(-0.799801\pi\)
0.913800 + 0.406166i \(0.133134\pi\)
\(674\) −37.4910 21.6455i −1.44410 0.833752i
\(675\) −28.4752 −1.09601
\(676\) −0.635358 2.39181i −0.0244369 0.0919928i
\(677\) −33.7922 −1.29874 −0.649371 0.760472i \(-0.724968\pi\)
−0.649371 + 0.760472i \(0.724968\pi\)
\(678\) 15.6016 + 9.00761i 0.599177 + 0.345935i
\(679\) 0 0
\(680\) −40.6795 70.4590i −1.55999 2.70198i
\(681\) 31.5209i 1.20788i
\(682\) 7.67498 4.43115i 0.293890 0.169678i
\(683\) 10.6511 6.14942i 0.407553 0.235301i −0.282185 0.959360i \(-0.591059\pi\)
0.689738 + 0.724059i \(0.257726\pi\)
\(684\) 0.216145i 0.00826450i
\(685\) −31.4514 54.4754i −1.20170 2.08140i
\(686\) 0 0
\(687\) 29.0311 + 16.7611i 1.10760 + 0.639476i
\(688\) 13.7253 0.523272
\(689\) 0.285908 + 0.0379543i 0.0108922 + 0.00144594i
\(690\) 16.2082 0.617036
\(691\) 9.60393 + 5.54483i 0.365351 + 0.210935i 0.671425 0.741072i \(-0.265682\pi\)
−0.306075 + 0.952008i \(0.599016\pi\)
\(692\) −1.36869 + 2.37064i −0.0520297 + 0.0901181i
\(693\) 0 0
\(694\) 33.3129i 1.26454i
\(695\) −18.0972 + 10.4484i −0.686465 + 0.396331i
\(696\) −21.1602 + 12.2168i −0.802075 + 0.463078i
\(697\) 32.4955i 1.23086i
\(698\) −7.77247 13.4623i −0.294193 0.509556i
\(699\) 29.8400 51.6844i 1.12865 1.95488i
\(700\) 0 0
\(701\) 10.6470 0.402133 0.201066 0.979578i \(-0.435559\pi\)
0.201066 + 0.979578i \(0.435559\pi\)
\(702\) 14.1650 + 10.8935i 0.534623 + 0.411147i
\(703\) −0.996813 −0.0375955
\(704\) −9.53396 5.50443i −0.359325 0.207456i
\(705\) −3.27029 + 5.66431i −0.123166 + 0.213330i
\(706\) 13.5117 + 23.4030i 0.508521 + 0.880784i
\(707\) 0 0
\(708\) −3.78027 + 2.18254i −0.142071 + 0.0820248i
\(709\) −35.2532 + 20.3535i −1.32396 + 0.764391i −0.984358 0.176178i \(-0.943627\pi\)
−0.339605 + 0.940568i \(0.610293\pi\)
\(710\) 54.8290i 2.05770i
\(711\) 1.71736 + 2.97455i 0.0644060 + 0.111554i
\(712\) −11.1619 + 19.3329i −0.418309 + 0.724532i
\(713\) 7.35003 + 4.24354i 0.275261 + 0.158922i
\(714\) 0 0
\(715\) −10.0273 + 13.0387i −0.375001 + 0.487621i
\(716\) −1.03294 −0.0386028
\(717\) 15.3648 + 8.87089i 0.573810 + 0.331290i
\(718\) 10.1235 17.5344i 0.377806 0.654380i
\(719\) 4.88769 + 8.46572i 0.182280 + 0.315718i 0.942657 0.333764i \(-0.108319\pi\)
−0.760377 + 0.649482i \(0.774986\pi\)
\(720\) 15.3775i 0.573086i
\(721\) 0 0
\(722\) 21.0971 12.1804i 0.785153 0.453308i
\(723\) 37.3081i 1.38750i
\(724\) −1.47441 2.55375i −0.0547959 0.0949092i
\(725\) 15.6313 27.0743i 0.580533 1.00551i
\(726\) 22.3671 + 12.9136i 0.830120 + 0.479270i
\(727\) 12.2091 0.452811 0.226406 0.974033i \(-0.427303\pi\)
0.226406 + 0.974033i \(0.427303\pi\)
\(728\) 0 0
\(729\) 9.23219 0.341933
\(730\) −3.16101 1.82501i −0.116994 0.0675467i
\(731\) 14.8231 25.6743i 0.548251 0.949598i
\(732\) 1.48770 + 2.57677i 0.0549869 + 0.0952400i
\(733\) 22.3153i 0.824236i 0.911131 + 0.412118i \(0.135211\pi\)
−0.911131 + 0.412118i \(0.864789\pi\)
\(734\) −10.4891 + 6.05591i −0.387161 + 0.223528i
\(735\) 0 0
\(736\) 1.76768i 0.0651576i
\(737\) −4.04126 6.99968i −0.148862 0.257836i
\(738\) −3.39728 + 5.88426i −0.125056 + 0.216603i
\(739\) 36.6960 + 21.1865i 1.34989 + 0.779357i 0.988233 0.152956i \(-0.0488793\pi\)
0.361653 + 0.932313i \(0.382213\pi\)
\(740\) 0.717275 0.0263675
\(741\) −0.918130 + 6.91624i −0.0337283 + 0.254074i
\(742\) 0 0
\(743\) −26.8296 15.4901i −0.984282 0.568276i −0.0807220 0.996737i \(-0.525723\pi\)
−0.903560 + 0.428461i \(0.859056\pi\)
\(744\) −15.5615 + 26.9532i −0.570511 + 0.988153i
\(745\) 18.6933 + 32.3778i 0.684870 + 1.18623i
\(746\) 21.7107i 0.794885i
\(747\) 2.42192 1.39830i 0.0886133 0.0511609i
\(748\) −1.63146 + 0.941923i −0.0596520 + 0.0344401i
\(749\) 0 0
\(750\) −13.4260 23.2545i −0.490248 0.849135i
\(751\) 11.2830 19.5427i 0.411722 0.713123i −0.583356 0.812216i \(-0.698261\pi\)
0.995078 + 0.0990930i \(0.0315941\pi\)
\(752\) −2.77475 1.60200i −0.101185 0.0584190i
\(753\) −32.5392 −1.18579
\(754\) −18.1333 + 7.48816i −0.660376 + 0.272703i
\(755\) 16.8187 0.612095
\(756\) 0 0
\(757\) −16.1404 + 27.9560i −0.586633 + 1.01608i 0.408037 + 0.912965i \(0.366213\pi\)
−0.994670 + 0.103112i \(0.967120\pi\)
\(758\) 10.5368 + 18.2504i 0.382716 + 0.662883i
\(759\) 4.31818i 0.156740i
\(760\) 8.59323 4.96130i 0.311709 0.179965i
\(761\) −25.7657 + 14.8758i −0.934006 + 0.539249i −0.888076 0.459696i \(-0.847958\pi\)
−0.0459296 + 0.998945i \(0.514625\pi\)
\(762\) 40.5855i 1.47026i
\(763\) 0 0
\(764\) −0.451761 + 0.782473i −0.0163441 + 0.0283089i
\(765\) 28.7649 + 16.6074i 1.04000 + 0.600442i
\(766\) −33.1367 −1.19728
\(767\) −37.2740 + 15.3923i −1.34589 + 0.555785i
\(768\) 9.27895 0.334825
\(769\) 36.2090 + 20.9053i 1.30573 + 0.753863i 0.981380 0.192075i \(-0.0615215\pi\)
0.324349 + 0.945938i \(0.394855\pi\)
\(770\) 0 0
\(771\) −24.9361 43.1907i −0.898053 1.55547i
\(772\) 4.00514i 0.144148i
\(773\) 35.8826 20.7168i 1.29061 0.745132i 0.311845 0.950133i \(-0.399053\pi\)
0.978762 + 0.205001i \(0.0657198\pi\)
\(774\) −5.36829 + 3.09938i −0.192959 + 0.111405i
\(775\) 39.8215i 1.43043i
\(776\) 0.705044 + 1.22117i 0.0253096 + 0.0438375i
\(777\) 0 0
\(778\) −21.9680 12.6832i −0.787592 0.454716i
\(779\) 3.96318 0.141996
\(780\) 0.660657 4.97671i 0.0236553 0.178195i
\(781\) 14.6075 0.522698
\(782\) 14.8521