Properties

Label 637.2.q.g.491.2
Level $637$
Weight $2$
Character 637.491
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
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 491.2
Root \(0.874681 - 1.11128i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.g.589.2

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16500 + 0.672613i −0.823779 + 0.475609i −0.851718 0.524000i \(-0.824439\pi\)
0.0279386 + 0.999610i \(0.491106\pi\)
\(3\) −1.02505 1.77544i −0.591814 1.02505i −0.993988 0.109489i \(-0.965079\pi\)
0.402174 0.915563i \(-0.368255\pi\)
\(4\) −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 −0.323681 0.946166i \(-0.604920\pi\)
0.657563 + 0.753399i \(0.271587\pi\)
\(12\) 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 0.170273 0.985397i \(-0.445535\pi\)
0.768242 0.640159i \(-0.221132\pi\)
\(18\) 1.61821i 0.381415i
\(19\) −0.817422 0.471939i −0.187530 0.108270i 0.403296 0.915070i \(-0.367865\pi\)
−0.590826 + 0.806799i \(0.701198\pi\)
\(20\) 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 0.939028 0.343840i \(-0.111728\pi\)
−0.767288 + 0.641303i \(0.778394\pi\)
\(24\) −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 0.614856 0.788639i \(-0.289214\pi\)
−0.990410 + 0.138161i \(0.955881\pi\)
\(30\) 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 −0.573292 0.819351i \(-0.694334\pi\)
0.422933 + 0.906161i \(0.361000\pi\)
\(38\) 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 \(-0.772998\pi\)
0.188415 + 0.982090i \(0.439665\pi\)
\(42\) 0 0
\(43\) 1.91532 3.31744i 0.292084 0.505904i −0.682218 0.731148i \(-0.738985\pi\)
0.974302 + 0.225244i \(0.0723180\pi\)
\(44\) 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 \(-0.592913\pi\)
−0.973277 + 0.229636i \(0.926246\pi\)
\(60\) 1.39240i 0.179758i
\(61\) 3.81196 6.60251i 0.488072 0.845365i −0.511834 0.859084i \(-0.671034\pi\)
0.999906 + 0.0137195i \(0.00436719\pi\)
\(62\) −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 −0.795613 0.605805i \(-0.792851\pi\)
0.126836 + 0.991924i \(0.459518\pi\)
\(68\) 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 0.954651 0.297727i \(-0.0962285\pi\)
0.219487 + 0.975616i \(0.429562\pi\)
\(72\) 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 \(-0.798192\pi\)
0.110176 + 0.993912i \(0.464859\pi\)
\(90\) −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 \(-0.341067\pi\)
−0.520893 + 0.853622i \(0.674401\pi\)
\(98\) 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 \(-0.120926\pi\)
−0.785498 + 0.618865i \(0.787593\pi\)
\(102\) 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 0.980002 0.198988i \(-0.0637653\pi\)
−0.662329 + 0.749213i \(0.730432\pi\)
\(108\) 0.350673 0.607384i 0.0337435 0.0584455i
\(109\) 5.83914i 0.559288i −0.960104 0.279644i \(-0.909784\pi\)
0.960104 0.279644i \(-0.0902165\pi\)
\(110\) 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 −0.977761 0.209723i \(-0.932744\pi\)
0.670506 + 0.741904i \(0.266077\pi\)
\(114\) −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 0.982408 + 0.186748i \(0.0597948\pi\)
−0.329475 + 0.944164i \(0.606872\pi\)
\(128\) 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 0.981172 0.193137i \(-0.0618662\pi\)
0.323324 + 0.946288i \(0.395200\pi\)
\(138\) 4.54294i 0.386721i
\(139\) 2.92855 5.07240i 0.248396 0.430235i −0.714685 0.699447i \(-0.753430\pi\)
0.963081 + 0.269212i \(0.0867631\pi\)
\(140\) 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 0.0798677 0.996805i \(-0.474550\pi\)
−0.823325 + 0.567570i \(0.807884\pi\)
\(150\) −18.4598 10.6578i −1.50724 0.870203i
\(151\) 4.71406i 0.383625i −0.981432 0.191812i \(-0.938564\pi\)
0.981432 0.191812i \(-0.0614365\pi\)
\(152\) −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 0.0329144 0.999458i \(-0.489521\pi\)
−0.849099 + 0.528234i \(0.822854\pi\)
\(164\) 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 \(-0.937316\pi\)
−0.320893 + 0.947116i \(0.603983\pi\)
\(168\) 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 −0.451875 0.892081i \(-0.649245\pi\)
0.998503 0.0547049i \(-0.0174218\pi\)
\(174\) 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 0.949424 0.313998i \(-0.101669\pi\)
−0.746642 + 0.665226i \(0.768335\pi\)
\(180\) −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 −0.939019 0.343866i \(-0.888263\pi\)
0.767306 + 0.641281i \(0.221597\pi\)
\(192\) 8.82529 + 15.2859i 0.636911 + 1.10316i
\(193\) −18.2204 + 10.5196i −1.31154 + 0.757215i −0.982350 0.187050i \(-0.940107\pi\)
−0.329185 + 0.944266i \(0.606774\pi\)
\(194\) 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 −0.309857 0.950783i \(-0.600281\pi\)
0.668474 + 0.743736i \(0.266948\pi\)
\(198\) −1.03458 1.79194i −0.0735242 0.127348i
\(199\) 5.30909 9.19562i 0.376352 0.651860i −0.614177 0.789168i \(-0.710512\pi\)
0.990528 + 0.137309i \(0.0438452\pi\)
\(200\) 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 0.935081 0.354433i \(-0.115326\pi\)
−0.774489 + 0.632588i \(0.781993\pi\)
\(212\) 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 \(-0.365522\pi\)
0.994891 + 0.100950i \(0.0321883\pi\)
\(224\) 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 \(-0.162887\pi\)
0.0118726 + 0.999930i \(0.496221\pi\)
\(228\) −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 \(-0.909701\pi\)
0.960031 0.279893i \(-0.0902991\pi\)
\(240\) −22.6963 13.1037i −1.46504 0.845840i
\(241\) −15.7601 9.09909i −1.01520 0.586124i −0.102487 0.994734i \(-0.532680\pi\)
−0.912709 + 0.408611i \(0.866013\pi\)
\(242\) 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 −0.499085 0.866553i \(-0.666330\pi\)
0.999999 0.00105678i \(-0.000336383\pi\)
\(252\) 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 −0.943499 0.331376i \(-0.892487\pi\)
0.184769 0.982782i \(-0.440846\pi\)
\(258\) 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 0.523751 0.851872i \(-0.324532\pi\)
−0.999618 + 0.0276456i \(0.991199\pi\)
\(264\) −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 \(-0.703193\pi\)
0.993423 + 0.114499i \(0.0365261\pi\)
\(270\) −8.84108 15.3132i −0.538051 0.931931i
\(271\) −23.3572 + 13.4853i −1.41885 + 0.819174i −0.996198 0.0871168i \(-0.972235\pi\)
−0.422654 + 0.906291i \(0.638901\pi\)
\(272\) 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 −0.609710 0.792625i \(-0.708714\pi\)
0.991288 + 0.131712i \(0.0420474\pi\)
\(278\) 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 \(-0.706399\pi\)
0.603930 0.797038i \(-0.293601\pi\)
\(282\) 1.23306 2.13572i 0.0734276 0.127180i
\(283\) 7.37113 + 12.7672i 0.438168 + 0.758929i 0.997548 0.0699819i \(-0.0222941\pi\)
−0.559380 + 0.828911i \(0.688961\pi\)
\(284\) −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 \(-0.443200\pi\)
−0.763526 + 0.645777i \(0.776534\pi\)
\(294\) 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 \(-0.498640\pi\)
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 \(-0.986527\pi\)
0.999104 0.0423140i \(-0.0134730\pi\)
\(318\) −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 0.960993 0.276574i \(-0.0891992\pi\)
0.240976 + 0.970531i \(0.422533\pi\)
\(332\) −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 0.314673 + 0.949200i \(0.398105\pi\)
−0.979368 + 0.202085i \(0.935228\pi\)
\(348\) −0.789291 1.36709i −0.0423104 0.0732838i
\(349\) −10.0075 + 5.77782i −0.535688 + 0.309280i −0.743330 0.668925i \(-0.766755\pi\)
0.207642 + 0.978205i \(0.433421\pi\)
\(350\) 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 \(-0.487129\pi\)
0.885529 + 0.464583i \(0.153796\pi\)
\(354\) −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 \(-0.869988\pi\)
0.917740 0.397181i \(-0.130012\pi\)
\(360\) 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 \(-0.242173\pi\)
−0.959270 + 0.282491i \(0.908839\pi\)
\(368\) −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 −0.577896 0.816110i \(-0.696126\pi\)
0.995720 + 0.0924174i \(0.0294594\pi\)
\(374\) 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 −0.806183 0.591666i \(-0.798471\pi\)
0.109306 + 0.994008i \(0.465137\pi\)
\(380\) −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 \(-0.550008\pi\)
−0.933589 + 0.358345i \(0.883341\pi\)
\(384\) −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 \(-0.214764\pi\)
−0.150528 + 0.988606i \(0.548097\pi\)
\(398\) 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 −0.879695 0.475539i \(-0.842253\pi\)
−0.0280189 + 0.999607i \(0.508920\pi\)
\(402\) −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 \(-0.155614\pi\)
0.0347148 + 0.999397i \(0.488948\pi\)
\(410\) −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 \(-0.228986\pi\)
−0.946748 + 0.321976i \(0.895653\pi\)
\(420\) 0 0
\(421\) 2.81786i 0.137334i 0.997640 + 0.0686670i \(0.0218746\pi\)
−0.997640 + 0.0686670i \(0.978125\pi\)
\(422\) −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 −0.614849 0.788645i \(-0.710783\pi\)
0.375561 + 0.926797i \(0.377450\pi\)
\(432\) −6.60028 11.4320i −0.317556 0.550023i
\(433\) −12.2628 + 21.2398i −0.589314 + 1.02072i 0.405009 + 0.914313i \(0.367268\pi\)
−0.994322 + 0.106409i \(0.966065\pi\)
\(434\) 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 0.857379 + 0.514686i \(0.172091\pi\)
0.0170416 + 0.999855i \(0.494575\pi\)
\(440\) −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 0.941699 0.336456i \(-0.109228\pi\)
0.179470 + 0.983764i \(0.442562\pi\)
\(450\) 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 0.616748 0.787161i \(-0.288450\pi\)
0.990075 0.140539i \(-0.0448835\pi\)
\(458\) −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 \(-0.369703\pi\)
−0.595475 + 0.803374i \(0.703036\pi\)
\(462\) 0 0
\(463\) 4.71193i 0.218982i −0.993988 0.109491i \(-0.965078\pi\)
0.993988 0.109491i \(-0.0349221\pi\)
\(464\) 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 −0.812254 0.583305i \(-0.801759\pi\)
0.0990298 + 0.995084i \(0.468426\pi\)
\(480\) −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 0.803874 0.594800i \(-0.202769\pi\)
−0.113175 + 0.993575i \(0.536102\pi\)
\(488\) −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 0.906318 0.422595i \(-0.138881\pi\)
−0.819138 + 0.573597i \(0.805547\pi\)
\(492\) −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 \(0.0913577\pi\)
−0.959095 + 0.283084i \(0.908642\pi\)
\(500\) −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 \(-0.996800\pi\)
0.508681 + 0.860955i \(0.330133\pi\)
\(504\) 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 \(-0.553771\pi\)
0.769637 + 0.638482i \(0.220437\pi\)
\(510\) −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 0.973724 0.227733i \(-0.0731312\pi\)
−0.684084 + 0.729403i \(0.739798\pi\)
\(524\) −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 \(0.100204\pi\)
−0.950859 + 0.309625i \(0.899796\pi\)
\(542\) 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 −0.334267 0.942478i \(-0.608489\pi\)
0.649077 + 0.760723i \(0.275155\pi\)
\(558\) 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 \(-0.920088\pi\)
0.699465 + 0.714667i \(0.253422\pi\)
\(564\) 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 0.798927 0.601429i \(-0.205402\pi\)
−0.920316 + 0.391176i \(0.872068\pi\)
\(570\) −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 \(-0.528697\pi\)
0.817493 + 0.575939i \(0.195363\pi\)
\(588\) 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 0.998407 + 0.0564195i \(0.0179684\pi\)
−0.450343 + 0.892856i \(0.648698\pi\)
\(602\) 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 \(-0.772222\pi\)
0.945519 + 0.325568i \(0.105555\pi\)
\(608\) −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 −0.714078 0.700066i \(-0.753154\pi\)
0.249236 + 0.968443i \(0.419820\pi\)
\(614\) 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 0.291368 0.956611i \(-0.405890\pi\)
−0.682765 + 0.730638i \(0.739223\pi\)
\(618\) 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 0.668484 0.743726i \(-0.266943\pi\)
−0.309844 + 0.950787i \(0.600277\pi\)
\(632\) 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 −0.681174 0.732122i \(-0.738530\pi\)
0.974623 + 0.223853i \(0.0718634\pi\)
\(642\) 18.1248i 0.715328i
\(643\) 1.98945 + 1.14861i 0.0784563 + 0.0452968i 0.538715 0.842488i \(-0.318910\pi\)
−0.460259 + 0.887785i \(0.652243\pi\)
\(644\) 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 \(-0.116410\pi\)
−0.776639 + 0.629946i \(0.783077\pi\)
\(648\) 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 0.824409 0.565995i \(-0.191508\pi\)
−0.902370 + 0.430962i \(0.858174\pi\)
\(654\) 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 −0.463504 0.886095i \(-0.653408\pi\)
0.999133 0.0416417i \(-0.0132588\pi\)
\(660\) −0.890211 1.54189i −0.0346514 0.0600180i
\(661\) −6.05023 + 3.49310i −0.235327 + 0.135866i −0.613027 0.790062i \(-0.710048\pi\)
0.377700 + 0.925928i \(0.376715\pi\)
\(662\) −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 0.913800 0.406166i \(-0.133134\pi\)
−0.808649 + 0.588291i \(0.799801\pi\)
\(674\) −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 0.689738 0.724059i \(-0.257726\pi\)
−0.282185 + 0.959360i \(0.591059\pi\)
\(684\) 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 \(-0.734318\pi\)
0.306075 + 0.952008i \(0.400984\pi\)
\(692\) 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 −0.339605 0.940568i \(-0.610293\pi\)
−0.984358 + 0.176178i \(0.943627\pi\)
\(710\) 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 \(-0.891681\pi\)
0.760377 + 0.649482i \(0.225014\pi\)
\(720\) 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 \(0.135211\pi\)
−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 0.361653 0.932313i \(-0.382213\pi\)
0.988233 + 0.152956i \(0.0488793\pi\)
\(740\) −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 −0.903560 0.428461i \(-0.859056\pi\)
−0.0807220 + 0.996737i \(0.525723\pi\)
\(744\) −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 0.995078 0.0990930i \(-0.0315941\pi\)
−0.583356 + 0.812216i \(0.698261\pi\)
\(752\) 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 −0.994670 0.103112i \(-0.967120\pi\)
0.408037 0.912965i \(-0.366213\pi\)
\(758\) 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 \(-0.152042\pi\)
0.0459296 + 0.998945i \(0.485375\pi\)
\(762\) 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 \(-0.938478\pi\)
−0.324349 + 0.945938i \(0.605145\pi\)
\(770\) 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 \(-0.600947\pi\)
−0.978762 + 0.205001i \(0.934280\pi\)
\(774\) −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