Properties

Label 637.2.q.g.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.g.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 \(0.368255\pi\)
−0.993988 + 0.109489i \(0.965079\pi\)
\(4\) −0.0951832 0.164862i −0.0475916 0.0824311i
\(5\) 3.56778i 1.59556i 0.602950 + 0.797779i \(0.293992\pi\)
−0.602950 + 0.797779i \(0.706008\pi\)
\(6\) 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 \(0.221132\pi\)
0.170273 + 0.985397i \(0.445535\pi\)
\(18\) 1.61821i 0.381415i
\(19\) −0.817422 + 0.471939i −0.187530 + 0.108270i −0.590826 0.806799i \(-0.701198\pi\)
0.403296 + 0.915070i \(0.367865\pi\)
\(20\) 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 \(-0.846888\pi\)
0.886525 0.462681i \(-0.153112\pi\)
\(32\) 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 0.188415 0.982090i \(-0.439665\pi\)
−0.756307 + 0.654217i \(0.772998\pi\)
\(42\) 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 \(0.0207741\pi\)
−0.997871 + 0.0652175i \(0.979226\pi\)
\(48\) 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 −0.973277 0.229636i \(-0.926246\pi\)
−0.287768 + 0.957700i \(0.592913\pi\)
\(60\) 1.39240i 0.179758i
\(61\) 3.81196 + 6.60251i 0.488072 + 0.845365i 0.999906 0.0137195i \(-0.00436719\pi\)
−0.511834 + 0.859084i \(0.671034\pi\)
\(62\) −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 \(-0.985829\pi\)
0.999009 0.0445052i \(-0.0141711\pi\)
\(74\) 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 \(-0.959275\pi\)
0.991827 0.127591i \(-0.0407246\pi\)
\(84\) 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 0.110176 0.993912i \(-0.464859\pi\)
−0.805665 + 0.592371i \(0.798192\pi\)
\(90\) −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 −0.520893 0.853622i \(-0.674401\pi\)
0.478812 + 0.877917i \(0.341067\pi\)
\(98\) 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 −0.785498 0.618865i \(-0.787593\pi\)
0.928701 + 0.370829i \(0.120926\pi\)
\(102\) 18.4841 + 10.6718i 1.83020 + 1.05666i
\(103\) 11.3351 1.11688 0.558441 0.829544i \(-0.311400\pi\)
0.558441 + 0.829544i \(0.311400\pi\)
\(104\) −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 \(-0.337474\pi\)
0.488693 + 0.872456i \(0.337474\pi\)
\(132\) 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 0.963081 0.269212i \(-0.0867631\pi\)
−0.714685 + 0.699447i \(0.753430\pi\)
\(140\) 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 \(-0.383042\pi\)
0.359223 + 0.933252i \(0.383042\pi\)
\(158\) 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 −0.320893 0.947116i \(-0.603983\pi\)
−0.980672 + 0.195657i \(0.937316\pi\)
\(168\) 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 \(0.0174218\pi\)
−0.451875 + 0.892081i \(0.649245\pi\)
\(174\) 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 \(-0.695266\pi\)
−0.575688 + 0.817669i \(0.695266\pi\)
\(182\) 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 0.990528 0.137309i \(-0.0438452\pi\)
−0.614177 + 0.789168i \(0.710512\pi\)
\(200\) 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 0.994891 0.100950i \(-0.0321883\pi\)
0.410020 + 0.912076i \(0.365522\pi\)
\(224\) 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 0.0118726 0.999930i \(-0.496221\pi\)
0.871901 + 0.489683i \(0.162887\pi\)
\(228\) −0.319016 + 0.184184i −0.0211274 + 0.0121979i
\(229\) 16.3515i 1.08054i −0.841493 0.540268i \(-0.818323\pi\)
0.841493 0.540268i \(-0.181677\pi\)
\(230\) −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 −0.912709 0.408611i \(-0.866013\pi\)
−0.102487 + 0.994734i \(0.532680\pi\)
\(242\) 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 \(0.000336383\pi\)
−0.499085 + 0.866553i \(0.666330\pi\)
\(252\) 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 \(0.440846\pi\)
−0.943499 + 0.331376i \(0.892487\pi\)
\(258\) 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 0.993423 0.114499i \(-0.0365261\pi\)
−0.595870 + 0.803081i \(0.703193\pi\)
\(270\) −8.84108 + 15.3132i −0.538051 + 0.931931i
\(271\) −23.3572 13.4853i −1.41885 0.819174i −0.422654 0.906291i \(-0.638901\pi\)
−0.996198 + 0.0871168i \(0.972235\pi\)
\(272\) 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 −0.559380 0.828911i \(-0.688961\pi\)
0.997548 + 0.0699819i \(0.0222941\pi\)
\(284\) −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 −0.763526 0.645777i \(-0.776534\pi\)
0.177496 + 0.984121i \(0.443200\pi\)
\(294\) 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 \(0.315737\pi\)
−0.547086 + 0.837076i \(0.684263\pi\)
\(308\) 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 \(-0.498640\pi\)
0.00427141 + 0.999991i \(0.498640\pi\)
\(312\) −17.2650 13.2775i −0.977438 0.751691i
\(313\) −10.5211 −0.594690 −0.297345 0.954770i \(-0.596101\pi\)
−0.297345 + 0.954770i \(0.596101\pi\)
\(314\) −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 0.207642 0.978205i \(-0.433421\pi\)
−0.743330 + 0.668925i \(0.766755\pi\)
\(350\) 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 0.885529 0.464583i \(-0.153796\pi\)
0.0404237 + 0.999183i \(0.487129\pi\)
\(354\) −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 −0.959270 0.282491i \(-0.908839\pi\)
0.724279 + 0.689507i \(0.242173\pi\)
\(368\) −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 −0.933589 0.358345i \(-0.883341\pi\)
−0.156459 + 0.987685i \(0.550008\pi\)
\(384\) −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 −0.150528 0.988606i \(-0.548097\pi\)
0.780894 + 0.624664i \(0.214764\pi\)
\(398\) 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 0.0347148 0.999397i \(-0.488948\pi\)
0.882861 + 0.469635i \(0.155614\pi\)
\(410\) −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 −0.946748 0.321976i \(-0.895653\pi\)
0.752213 + 0.658920i \(0.228986\pi\)
\(420\) 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 \(-0.966065\pi\)
0.405009 0.914313i \(-0.367268\pi\)
\(434\) 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 \(-0.494575\pi\)
0.857379 0.514686i \(-0.172091\pi\)
\(440\) −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 −0.595475 0.803374i \(-0.703036\pi\)
0.398004 + 0.917384i \(0.369703\pi\)
\(462\) 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 \(-0.765537\pi\)
−0.740765 + 0.671764i \(0.765537\pi\)
\(468\) −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 0.0990298 0.995084i \(-0.468426\pi\)
−0.812254 + 0.583305i \(0.801759\pi\)
\(480\) −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 0.508681 0.860955i \(-0.330133\pi\)
−0.999949 + 0.0100533i \(0.996800\pi\)
\(504\) 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 0.769637 0.638482i \(-0.220437\pi\)
−0.168123 + 0.985766i \(0.553771\pi\)
\(510\) −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 \(-0.686488\pi\)
−0.552925 + 0.833231i \(0.686488\pi\)
\(522\) −5.66846 3.27269i −0.248102 0.143242i
\(523\) 6.62383 11.4728i 0.289640 0.501671i −0.684084 0.729403i \(-0.739798\pi\)
0.973724 + 0.227733i \(0.0731312\pi\)
\(524\) −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 0.699465 0.714667i \(-0.253422\pi\)
−0.968652 + 0.248421i \(0.920088\pi\)
\(564\) 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 \(-0.920099\pi\)
0.968661 0.248388i \(-0.0799009\pi\)
\(578\) 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 0.817493 0.575939i \(-0.195363\pi\)
−0.0900312 + 0.995939i \(0.528697\pi\)
\(588\) 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 \(0.121768\pi\)
−0.927718 + 0.373282i \(0.878232\pi\)
\(594\) 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 \(-0.648698\pi\)
0.998407 0.0564195i \(-0.0179684\pi\)
\(602\) 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 0.945519 0.325568i \(-0.105555\pi\)
−0.754709 + 0.656059i \(0.772222\pi\)
\(608\) −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 \(0.0597465\pi\)
−0.982436 + 0.186599i \(0.940254\pi\)
\(620\) −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 −0.460259 0.887785i \(-0.652243\pi\)
0.538715 + 0.842488i \(0.318910\pi\)
\(644\) 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 −0.776639 0.629946i \(-0.783077\pi\)
0.933869 + 0.357616i \(0.116410\pi\)
\(648\) 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 0.377700 0.925928i \(-0.376715\pi\)
−0.613027 + 0.790062i \(0.710048\pi\)
\(662\) −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 \(-0.275032\pi\)
0.649371 + 0.760472i \(0.275032\pi\)
\(678\) −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 0.306075 0.952008i \(-0.400984\pi\)
−0.671425 + 0.741072i \(0.734318\pi\)
\(692\) 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 0.760377 0.649482i \(-0.225014\pi\)
−0.942657 + 0.333764i \(0.891681\pi\)
\(720\) 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 \(-0.572697\pi\)
−0.226406 + 0.974033i \(0.572697\pi\)
\(728\) 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 \(-0.864789\pi\)
0.911131 0.412118i \(-0.135211\pi\)
\(734\) 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 0.0459296 0.998945i \(-0.485375\pi\)
0.888076 + 0.459696i \(0.152042\pi\)
\(762\) 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 −0.324349 0.945938i \(-0.605145\pi\)
−0.981380 + 0.192075i \(0.938478\pi\)
\(770\) 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 −0.978762 0.205001i \(-0.934280\pi\)
−0.311845 + 0.950133i \(0.600947\pi\)
\(774\) −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
\(782\)