Properties

Label 637.2.f.j.393.2
Level $637$
Weight $2$
Character 637.393
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.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.2
Root \(-1.02197 + 1.77010i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.j.295.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.777343 - 1.34640i) q^{2} +(-0.244626 - 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} +1.19151 q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +O(q^{10})\) \(q+(-0.777343 - 1.34640i) q^{2} +(-0.244626 - 0.423704i) q^{3} +(-0.208526 + 0.361177i) q^{4} +1.19151 q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 - 2.39078i) q^{9} +(-0.926214 - 1.60425i) q^{10} +(-1.05807 - 1.83263i) q^{11} +0.204043 q^{12} +(-2.86133 + 2.19381i) q^{13} +(-0.291474 - 0.504848i) q^{15} +(2.33009 + 4.03583i) q^{16} +(-0.453151 + 0.784881i) q^{17} -4.29192 q^{18} +(3.34514 - 5.79395i) q^{19} +(-0.248461 + 0.430346i) q^{20} +(-1.64497 + 2.84917i) q^{22} +(-1.79866 - 3.11538i) q^{23} +(0.602021 + 1.04273i) q^{24} -3.58030 q^{25} +(5.17797 + 2.14715i) q^{26} -2.81840 q^{27} +(-4.25772 - 7.37459i) q^{29} +(-0.453151 + 0.784881i) q^{30} +5.28780 q^{31} +(1.16156 - 2.01189i) q^{32} +(-0.517662 + 0.896617i) q^{33} +1.40902 q^{34} +(0.575663 + 0.997077i) q^{36} +(-2.49579 - 4.32284i) q^{37} -10.4013 q^{38} +(1.62948 + 0.675696i) q^{39} -2.93230 q^{40} +(0.768181 + 1.33053i) q^{41} +(-2.71636 + 4.70488i) q^{43} +0.882538 q^{44} +(1.64466 - 2.84864i) q^{45} +(-2.79636 + 4.84344i) q^{46} +3.18673 q^{47} +(1.14000 - 1.97453i) q^{48} +(2.78312 + 4.82051i) q^{50} +0.443410 q^{51} +(-0.195692 - 1.49091i) q^{52} -2.82477 q^{53} +(2.19086 + 3.79469i) q^{54} +(-1.26070 - 2.18360i) q^{55} -3.27323 q^{57} +(-6.61943 + 11.4652i) q^{58} +(-5.12298 + 8.87327i) q^{59} +0.243120 q^{60} +(-4.13423 + 7.16069i) q^{61} +(-4.11044 - 7.11949i) q^{62} +5.70861 q^{64} +(-3.40931 + 2.61395i) q^{65} +1.60960 q^{66} +(1.87182 + 3.24208i) q^{67} +(-0.188987 - 0.327336i) q^{68} +(-0.880000 + 1.52420i) q^{69} +(1.26510 - 2.19122i) q^{71} +(-3.39694 + 5.88368i) q^{72} +5.73044 q^{73} +(-3.88018 + 6.72066i) q^{74} +(0.875834 + 1.51699i) q^{75} +(1.39510 + 2.41638i) q^{76} +(-0.356910 - 2.71918i) q^{78} +6.07240 q^{79} +(2.77632 + 4.80873i) q^{80} +(-3.45150 - 5.97817i) q^{81} +(1.19428 - 2.06856i) q^{82} +11.6309 q^{83} +(-0.539935 + 0.935195i) q^{85} +8.44619 q^{86} +(-2.08310 + 3.60803i) q^{87} +(2.60390 + 4.51008i) q^{88} +(-8.87557 - 15.3729i) q^{89} -5.11387 q^{90} +1.50027 q^{92} +(-1.29353 - 2.24046i) q^{93} +(-2.47719 - 4.29061i) q^{94} +(3.98577 - 6.90356i) q^{95} -1.13659 q^{96} +(3.10217 - 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - q^{3} - 4q^{4} + 2q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q + 2q^{2} - q^{3} - 4q^{4} + 2q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} + 10q^{12} + 2q^{13} - 2q^{15} + 8q^{16} - 5q^{17} - 6q^{18} + q^{19} + q^{20} - 5q^{22} - q^{23} + 11q^{24} - 14q^{25} - 11q^{26} + 8q^{27} + 3q^{29} - 5q^{30} + 32q^{31} + 8q^{32} - 16q^{33} - 32q^{34} - 21q^{36} - 13q^{37} - 34q^{38} + 43q^{39} - 10q^{40} + 8q^{41} - 11q^{43} - 42q^{44} + 7q^{45} + 16q^{46} - 2q^{47} - 21q^{48} + 6q^{50} + 40q^{51} + 16q^{52} + 4q^{53} + 18q^{54} - 9q^{55} + 42q^{57} - 8q^{58} - 13q^{59} - 40q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 14q^{65} + 36q^{66} - 11q^{67} - 29q^{68} - 23q^{69} + 6q^{71} + 25q^{72} - 60q^{73} - 3q^{74} + 3q^{75} + 9q^{76} + 16q^{78} - 14q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} + 14q^{86} - 16q^{87} - 4q^{89} + 16q^{90} + 54q^{92} - 7q^{93} - 45q^{94} - 6q^{95} + 38q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.777343 1.34640i −0.549665 0.952047i −0.998297 0.0583310i \(-0.981422\pi\)
0.448632 0.893716i \(-0.351911\pi\)
\(3\) −0.244626 0.423704i −0.141235 0.244626i 0.786727 0.617301i \(-0.211774\pi\)
−0.927962 + 0.372675i \(0.878441\pi\)
\(4\) −0.208526 + 0.361177i −0.104263 + 0.180588i
\(5\) 1.19151 0.532860 0.266430 0.963854i \(-0.414156\pi\)
0.266430 + 0.963854i \(0.414156\pi\)
\(6\) −0.380316 + 0.658727i −0.155264 + 0.268924i
\(7\) 0 0
\(8\) −2.46099 −0.870091
\(9\) 1.38032 2.39078i 0.460105 0.796926i
\(10\) −0.926214 1.60425i −0.292894 0.507308i
\(11\) −1.05807 1.83263i −0.319020 0.552559i 0.661264 0.750153i \(-0.270020\pi\)
−0.980284 + 0.197595i \(0.936687\pi\)
\(12\) 0.204043 0.0589021
\(13\) −2.86133 + 2.19381i −0.793590 + 0.608453i
\(14\) 0 0
\(15\) −0.291474 0.504848i −0.0752584 0.130351i
\(16\) 2.33009 + 4.03583i 0.582521 + 1.00896i
\(17\) −0.453151 + 0.784881i −0.109905 + 0.190362i −0.915732 0.401790i \(-0.868388\pi\)
0.805826 + 0.592152i \(0.201721\pi\)
\(18\) −4.29192 −1.01162
\(19\) 3.34514 5.79395i 0.767428 1.32922i −0.171525 0.985180i \(-0.554870\pi\)
0.938953 0.344045i \(-0.111797\pi\)
\(20\) −0.248461 + 0.430346i −0.0555575 + 0.0962284i
\(21\) 0 0
\(22\) −1.64497 + 2.84917i −0.350708 + 0.607444i
\(23\) −1.79866 3.11538i −0.375048 0.649601i 0.615287 0.788303i \(-0.289040\pi\)
−0.990334 + 0.138702i \(0.955707\pi\)
\(24\) 0.602021 + 1.04273i 0.122887 + 0.212847i
\(25\) −3.58030 −0.716060
\(26\) 5.17797 + 2.14715i 1.01548 + 0.421091i
\(27\) −2.81840 −0.542401
\(28\) 0 0
\(29\) −4.25772 7.37459i −0.790639 1.36943i −0.925572 0.378573i \(-0.876415\pi\)
0.134932 0.990855i \(-0.456918\pi\)
\(30\) −0.453151 + 0.784881i −0.0827337 + 0.143299i
\(31\) 5.28780 0.949717 0.474859 0.880062i \(-0.342499\pi\)
0.474859 + 0.880062i \(0.342499\pi\)
\(32\) 1.16156 2.01189i 0.205337 0.355655i
\(33\) −0.517662 + 0.896617i −0.0901134 + 0.156081i
\(34\) 1.40902 0.241644
\(35\) 0 0
\(36\) 0.575663 + 0.997077i 0.0959438 + 0.166180i
\(37\) −2.49579 4.32284i −0.410306 0.710670i 0.584617 0.811309i \(-0.301245\pi\)
−0.994923 + 0.100639i \(0.967911\pi\)
\(38\) −10.4013 −1.68731
\(39\) 1.62948 + 0.675696i 0.260926 + 0.108198i
\(40\) −2.93230 −0.463637
\(41\) 0.768181 + 1.33053i 0.119970 + 0.207794i 0.919755 0.392492i \(-0.128387\pi\)
−0.799786 + 0.600286i \(0.795054\pi\)
\(42\) 0 0
\(43\) −2.71636 + 4.70488i −0.414242 + 0.717488i −0.995349 0.0963397i \(-0.969286\pi\)
0.581107 + 0.813827i \(0.302620\pi\)
\(44\) 0.882538 0.133048
\(45\) 1.64466 2.84864i 0.245172 0.424650i
\(46\) −2.79636 + 4.84344i −0.412301 + 0.714126i
\(47\) 3.18673 0.464833 0.232416 0.972616i \(-0.425337\pi\)
0.232416 + 0.972616i \(0.425337\pi\)
\(48\) 1.14000 1.97453i 0.164545 0.284999i
\(49\) 0 0
\(50\) 2.78312 + 4.82051i 0.393593 + 0.681723i
\(51\) 0.443410 0.0620898
\(52\) −0.195692 1.49091i −0.0271376 0.206752i
\(53\) −2.82477 −0.388012 −0.194006 0.981000i \(-0.562148\pi\)
−0.194006 + 0.981000i \(0.562148\pi\)
\(54\) 2.19086 + 3.79469i 0.298139 + 0.516391i
\(55\) −1.26070 2.18360i −0.169993 0.294436i
\(56\) 0 0
\(57\) −3.27323 −0.433550
\(58\) −6.61943 + 11.4652i −0.869173 + 1.50545i
\(59\) −5.12298 + 8.87327i −0.666956 + 1.15520i 0.311795 + 0.950149i \(0.399070\pi\)
−0.978751 + 0.205052i \(0.934264\pi\)
\(60\) 0.243120 0.0313866
\(61\) −4.13423 + 7.16069i −0.529333 + 0.916832i 0.470081 + 0.882623i \(0.344225\pi\)
−0.999415 + 0.0342093i \(0.989109\pi\)
\(62\) −4.11044 7.11949i −0.522026 0.904176i
\(63\) 0 0
\(64\) 5.70861 0.713576
\(65\) −3.40931 + 2.61395i −0.422873 + 0.324220i
\(66\) 1.60960 0.198129
\(67\) 1.87182 + 3.24208i 0.228679 + 0.396083i 0.957417 0.288709i \(-0.0932261\pi\)
−0.728738 + 0.684793i \(0.759893\pi\)
\(68\) −0.188987 0.327336i −0.0229181 0.0396953i
\(69\) −0.880000 + 1.52420i −0.105939 + 0.183493i
\(70\) 0 0
\(71\) 1.26510 2.19122i 0.150140 0.260050i −0.781139 0.624357i \(-0.785361\pi\)
0.931279 + 0.364307i \(0.118694\pi\)
\(72\) −3.39694 + 5.88368i −0.400334 + 0.693398i
\(73\) 5.73044 0.670697 0.335349 0.942094i \(-0.391146\pi\)
0.335349 + 0.942094i \(0.391146\pi\)
\(74\) −3.88018 + 6.72066i −0.451061 + 0.781261i
\(75\) 0.875834 + 1.51699i 0.101133 + 0.175167i
\(76\) 1.39510 + 2.41638i 0.160028 + 0.277177i
\(77\) 0 0
\(78\) −0.356910 2.71918i −0.0404121 0.307886i
\(79\) 6.07240 0.683198 0.341599 0.939846i \(-0.389031\pi\)
0.341599 + 0.939846i \(0.389031\pi\)
\(80\) 2.77632 + 4.80873i 0.310402 + 0.537633i
\(81\) −3.45150 5.97817i −0.383500 0.664241i
\(82\) 1.19428 2.06856i 0.131886 0.228434i
\(83\) 11.6309 1.27665 0.638327 0.769766i \(-0.279627\pi\)
0.638327 + 0.769766i \(0.279627\pi\)
\(84\) 0 0
\(85\) −0.539935 + 0.935195i −0.0585642 + 0.101436i
\(86\) 8.44619 0.910776
\(87\) −2.08310 + 3.60803i −0.223331 + 0.386821i
\(88\) 2.60390 + 4.51008i 0.277576 + 0.480776i
\(89\) −8.87557 15.3729i −0.940808 1.62953i −0.763934 0.645295i \(-0.776735\pi\)
−0.176875 0.984233i \(-0.556599\pi\)
\(90\) −5.11387 −0.539049
\(91\) 0 0
\(92\) 1.50027 0.156414
\(93\) −1.29353 2.24046i −0.134133 0.232325i
\(94\) −2.47719 4.29061i −0.255502 0.442543i
\(95\) 3.98577 6.90356i 0.408932 0.708291i
\(96\) −1.13659 −0.116003
\(97\) 3.10217 5.37312i 0.314978 0.545557i −0.664455 0.747328i \(-0.731336\pi\)
0.979433 + 0.201771i \(0.0646696\pi\)
\(98\) 0 0
\(99\) −5.84188 −0.587131
\(100\) 0.746584 1.29312i 0.0746584 0.129312i
\(101\) −3.61133 6.25501i −0.359341 0.622397i 0.628510 0.777802i \(-0.283665\pi\)
−0.987851 + 0.155405i \(0.950332\pi\)
\(102\) −0.344682 0.597007i −0.0341286 0.0591125i
\(103\) −9.92645 −0.978082 −0.489041 0.872261i \(-0.662653\pi\)
−0.489041 + 0.872261i \(0.662653\pi\)
\(104\) 7.04170 5.39894i 0.690496 0.529409i
\(105\) 0 0
\(106\) 2.19582 + 3.80327i 0.213277 + 0.369406i
\(107\) 1.10003 + 1.90531i 0.106344 + 0.184193i 0.914287 0.405068i \(-0.132752\pi\)
−0.807942 + 0.589261i \(0.799419\pi\)
\(108\) 0.587708 1.01794i 0.0565523 0.0979514i
\(109\) 13.7458 1.31661 0.658305 0.752751i \(-0.271274\pi\)
0.658305 + 0.752751i \(0.271274\pi\)
\(110\) −1.96000 + 3.39481i −0.186878 + 0.323683i
\(111\) −1.22107 + 2.11496i −0.115899 + 0.200743i
\(112\) 0 0
\(113\) 8.04736 13.9384i 0.757032 1.31122i −0.187326 0.982298i \(-0.559982\pi\)
0.944358 0.328920i \(-0.106685\pi\)
\(114\) 2.54442 + 4.40707i 0.238307 + 0.412760i
\(115\) −2.14313 3.71201i −0.199848 0.346147i
\(116\) 3.55138 0.329737
\(117\) 1.29536 + 9.86895i 0.119756 + 0.912385i
\(118\) 15.9293 1.46641
\(119\) 0 0
\(120\) 0.717315 + 1.24243i 0.0654816 + 0.113418i
\(121\) 3.26098 5.64818i 0.296453 0.513471i
\(122\) 12.8549 1.16382
\(123\) 0.375834 0.650963i 0.0338878 0.0586954i
\(124\) −1.10264 + 1.90983i −0.0990202 + 0.171508i
\(125\) −10.2235 −0.914420
\(126\) 0 0
\(127\) 7.83921 + 13.5779i 0.695617 + 1.20484i 0.969972 + 0.243216i \(0.0782023\pi\)
−0.274355 + 0.961628i \(0.588464\pi\)
\(128\) −6.76067 11.7098i −0.597565 1.03501i
\(129\) 2.65797 0.234021
\(130\) 6.16962 + 2.55835i 0.541111 + 0.224382i
\(131\) 9.53769 0.833312 0.416656 0.909064i \(-0.363202\pi\)
0.416656 + 0.909064i \(0.363202\pi\)
\(132\) −0.215892 0.373935i −0.0187910 0.0325469i
\(133\) 0 0
\(134\) 2.91009 5.04042i 0.251393 0.435426i
\(135\) −3.35815 −0.289024
\(136\) 1.11520 1.93158i 0.0956277 0.165632i
\(137\) 1.38231 2.39422i 0.118098 0.204552i −0.800916 0.598777i \(-0.795654\pi\)
0.919014 + 0.394225i \(0.128987\pi\)
\(138\) 2.73625 0.232925
\(139\) −11.3983 + 19.7425i −0.966795 + 1.67454i −0.262081 + 0.965046i \(0.584409\pi\)
−0.704714 + 0.709492i \(0.748925\pi\)
\(140\) 0 0
\(141\) −0.779557 1.35023i −0.0656505 0.113710i
\(142\) −3.93368 −0.330107
\(143\) 7.04792 + 2.92256i 0.589377 + 0.244397i
\(144\) 12.8650 1.07209
\(145\) −5.07312 8.78691i −0.421300 0.729713i
\(146\) −4.45452 7.71546i −0.368659 0.638536i
\(147\) 0 0
\(148\) 2.08175 0.171119
\(149\) 7.20581 12.4808i 0.590323 1.02247i −0.403866 0.914818i \(-0.632334\pi\)
0.994189 0.107651i \(-0.0343329\pi\)
\(150\) 1.36165 2.35844i 0.111178 0.192566i
\(151\) 15.2580 1.24168 0.620840 0.783937i \(-0.286792\pi\)
0.620840 + 0.783937i \(0.286792\pi\)
\(152\) −8.23236 + 14.2589i −0.667732 + 1.15655i
\(153\) 1.25098 + 2.16677i 0.101136 + 0.175173i
\(154\) 0 0
\(155\) 6.30048 0.506067
\(156\) −0.583834 + 0.447631i −0.0467442 + 0.0358392i
\(157\) 11.4149 0.911008 0.455504 0.890234i \(-0.349459\pi\)
0.455504 + 0.890234i \(0.349459\pi\)
\(158\) −4.72034 8.17587i −0.375530 0.650437i
\(159\) 0.691012 + 1.19687i 0.0548008 + 0.0949178i
\(160\) 1.38402 2.39719i 0.109416 0.189514i
\(161\) 0 0
\(162\) −5.36600 + 9.29418i −0.421592 + 0.730220i
\(163\) 7.20385 12.4774i 0.564249 0.977308i −0.432870 0.901456i \(-0.642499\pi\)
0.997119 0.0758514i \(-0.0241675\pi\)
\(164\) −0.640742 −0.0500335
\(165\) −0.616800 + 1.06833i −0.0480178 + 0.0831693i
\(166\) −9.04118 15.6598i −0.701731 1.21543i
\(167\) 3.88595 + 6.73066i 0.300704 + 0.520834i 0.976296 0.216442i \(-0.0694452\pi\)
−0.675592 + 0.737276i \(0.736112\pi\)
\(168\) 0 0
\(169\) 3.37442 12.5544i 0.259571 0.965724i
\(170\) 1.67886 0.128763
\(171\) −9.23471 15.9950i −0.706196 1.22317i
\(172\) −1.13286 1.96218i −0.0863800 0.149615i
\(173\) 3.04731 5.27809i 0.231682 0.401286i −0.726621 0.687039i \(-0.758910\pi\)
0.958303 + 0.285753i \(0.0922436\pi\)
\(174\) 6.47713 0.491030
\(175\) 0 0
\(176\) 4.93078 8.54037i 0.371672 0.643754i
\(177\) 5.01286 0.376789
\(178\) −13.7987 + 23.9001i −1.03426 + 1.79139i
\(179\) −9.26488 16.0472i −0.692490 1.19943i −0.971020 0.239000i \(-0.923181\pi\)
0.278530 0.960428i \(-0.410153\pi\)
\(180\) 0.685909 + 1.18803i 0.0511246 + 0.0885504i
\(181\) 5.60520 0.416631 0.208316 0.978062i \(-0.433202\pi\)
0.208316 + 0.978062i \(0.433202\pi\)
\(182\) 0 0
\(183\) 4.04535 0.299041
\(184\) 4.42650 + 7.66692i 0.326326 + 0.565212i
\(185\) −2.97377 5.15071i −0.218636 0.378688i
\(186\) −2.01104 + 3.48322i −0.147456 + 0.255402i
\(187\) 1.91786 0.140248
\(188\) −0.664516 + 1.15097i −0.0484648 + 0.0839435i
\(189\) 0 0
\(190\) −12.3933 −0.899102
\(191\) −0.251851 + 0.436219i −0.0182233 + 0.0315637i −0.874993 0.484135i \(-0.839134\pi\)
0.856770 + 0.515699i \(0.172468\pi\)
\(192\) −1.39647 2.41876i −0.100782 0.174559i
\(193\) 1.85622 + 3.21507i 0.133614 + 0.231426i 0.925067 0.379804i \(-0.124009\pi\)
−0.791453 + 0.611230i \(0.790675\pi\)
\(194\) −9.64581 −0.692529
\(195\) 1.94154 + 0.805100i 0.139037 + 0.0576544i
\(196\) 0 0
\(197\) 3.72225 + 6.44713i 0.265200 + 0.459339i 0.967616 0.252427i \(-0.0812288\pi\)
−0.702416 + 0.711766i \(0.747895\pi\)
\(198\) 4.54115 + 7.86550i 0.322725 + 0.558977i
\(199\) 3.75278 6.50001i 0.266028 0.460773i −0.701805 0.712369i \(-0.747622\pi\)
0.967832 + 0.251596i \(0.0809554\pi\)
\(200\) 8.81108 0.623038
\(201\) 0.915789 1.58619i 0.0645948 0.111881i
\(202\) −5.61449 + 9.72458i −0.395034 + 0.684219i
\(203\) 0 0
\(204\) −0.0924624 + 0.160149i −0.00647366 + 0.0112127i
\(205\) 0.915297 + 1.58534i 0.0639271 + 0.110725i
\(206\) 7.71626 + 13.3650i 0.537617 + 0.931181i
\(207\) −9.93091 −0.690246
\(208\) −15.5210 6.43608i −1.07619 0.446262i
\(209\) −14.1576 −0.979299
\(210\) 0 0
\(211\) −1.89531 3.28278i −0.130479 0.225996i 0.793383 0.608723i \(-0.208318\pi\)
−0.923861 + 0.382728i \(0.874985\pi\)
\(212\) 0.589037 1.02024i 0.0404553 0.0700706i
\(213\) −1.23791 −0.0848200
\(214\) 1.71020 2.96216i 0.116907 0.202489i
\(215\) −3.23658 + 5.60592i −0.220733 + 0.382320i
\(216\) 6.93605 0.471938
\(217\) 0 0
\(218\) −10.6852 18.5073i −0.723695 1.25348i
\(219\) −1.40181 2.42801i −0.0947258 0.164070i
\(220\) 1.05155 0.0708958
\(221\) −0.425262 3.23993i −0.0286062 0.217941i
\(222\) 3.79676 0.254822
\(223\) 2.43440 + 4.21650i 0.163019 + 0.282358i 0.935950 0.352133i \(-0.114543\pi\)
−0.772931 + 0.634490i \(0.781210\pi\)
\(224\) 0 0
\(225\) −4.94195 + 8.55971i −0.329463 + 0.570647i
\(226\) −25.0223 −1.66446
\(227\) 12.0884 20.9376i 0.802332 1.38968i −0.115745 0.993279i \(-0.536925\pi\)
0.918077 0.396402i \(-0.129741\pi\)
\(228\) 0.682552 1.18222i 0.0452031 0.0782941i
\(229\) 21.7123 1.43479 0.717394 0.696668i \(-0.245335\pi\)
0.717394 + 0.696668i \(0.245335\pi\)
\(230\) −3.33190 + 5.77101i −0.219699 + 0.380529i
\(231\) 0 0
\(232\) 10.4782 + 18.1488i 0.687928 + 1.19153i
\(233\) 3.79684 0.248739 0.124370 0.992236i \(-0.460309\pi\)
0.124370 + 0.992236i \(0.460309\pi\)
\(234\) 12.2806 9.41564i 0.802808 0.615520i
\(235\) 3.79703 0.247691
\(236\) −2.13655 3.70061i −0.139077 0.240889i
\(237\) −1.48547 2.57290i −0.0964914 0.167128i
\(238\) 0 0
\(239\) 21.9100 1.41724 0.708619 0.705592i \(-0.249319\pi\)
0.708619 + 0.705592i \(0.249319\pi\)
\(240\) 1.35832 2.35268i 0.0876792 0.151865i
\(241\) −10.3744 + 17.9690i −0.668273 + 1.15748i 0.310114 + 0.950699i \(0.399633\pi\)
−0.978387 + 0.206783i \(0.933701\pi\)
\(242\) −10.1396 −0.651798
\(243\) −5.91625 + 10.2472i −0.379527 + 0.657361i
\(244\) −1.72418 2.98637i −0.110380 0.191183i
\(245\) 0 0
\(246\) −1.16861 −0.0745077
\(247\) 3.13926 + 23.9170i 0.199747 + 1.52180i
\(248\) −13.0132 −0.826341
\(249\) −2.84521 4.92805i −0.180308 0.312302i
\(250\) 7.94719 + 13.7649i 0.502624 + 0.870571i
\(251\) 6.62891 11.4816i 0.418413 0.724713i −0.577367 0.816485i \(-0.695920\pi\)
0.995780 + 0.0917718i \(0.0292530\pi\)
\(252\) 0 0
\(253\) −3.80622 + 6.59257i −0.239295 + 0.414472i
\(254\) 12.1875 21.1094i 0.764713 1.32452i
\(255\) 0.528328 0.0330852
\(256\) −4.80213 + 8.31753i −0.300133 + 0.519845i
\(257\) −6.58555 11.4065i −0.410795 0.711518i 0.584182 0.811623i \(-0.301416\pi\)
−0.994977 + 0.100105i \(0.968082\pi\)
\(258\) −2.06616 3.57869i −0.128633 0.222799i
\(259\) 0 0
\(260\) −0.233169 1.77644i −0.0144605 0.110170i
\(261\) −23.5080 −1.45511
\(262\) −7.41406 12.8415i −0.458042 0.793352i
\(263\) 9.57028 + 16.5762i 0.590129 + 1.02213i 0.994215 + 0.107412i \(0.0342564\pi\)
−0.404086 + 0.914721i \(0.632410\pi\)
\(264\) 1.27396 2.20657i 0.0784069 0.135805i
\(265\) −3.36575 −0.206756
\(266\) 0 0
\(267\) −4.34239 + 7.52123i −0.265750 + 0.460292i
\(268\) −1.56129 −0.0953708
\(269\) −14.2411 + 24.6663i −0.868296 + 1.50393i −0.00455867 + 0.999990i \(0.501451\pi\)
−0.863737 + 0.503943i \(0.831882\pi\)
\(270\) 2.61044 + 4.52141i 0.158866 + 0.275164i
\(271\) 8.97371 + 15.5429i 0.545114 + 0.944165i 0.998600 + 0.0529014i \(0.0168469\pi\)
−0.453486 + 0.891263i \(0.649820\pi\)
\(272\) −4.22353 −0.256089
\(273\) 0 0
\(274\) −4.29811 −0.259658
\(275\) 3.78821 + 6.56137i 0.228437 + 0.395665i
\(276\) −0.367005 0.635671i −0.0220911 0.0382629i
\(277\) −6.71943 + 11.6384i −0.403732 + 0.699284i −0.994173 0.107797i \(-0.965620\pi\)
0.590441 + 0.807081i \(0.298954\pi\)
\(278\) 35.4417 2.12565
\(279\) 7.29884 12.6420i 0.436970 0.756855i
\(280\) 0 0
\(281\) −29.9530 −1.78685 −0.893424 0.449214i \(-0.851704\pi\)
−0.893424 + 0.449214i \(0.851704\pi\)
\(282\) −1.21197 + 2.09919i −0.0721716 + 0.125005i
\(283\) −4.94561 8.56604i −0.293986 0.509199i 0.680763 0.732504i \(-0.261649\pi\)
−0.974748 + 0.223306i \(0.928315\pi\)
\(284\) 0.527613 + 0.913852i 0.0313080 + 0.0542271i
\(285\) −3.90009 −0.231021
\(286\) −1.54373 11.7611i −0.0912824 0.695451i
\(287\) 0 0
\(288\) −3.20665 5.55408i −0.188954 0.327277i
\(289\) 8.08931 + 14.0111i 0.475842 + 0.824182i
\(290\) −7.88712 + 13.6609i −0.463148 + 0.802195i
\(291\) −3.03548 −0.177943
\(292\) −1.19494 + 2.06970i −0.0699288 + 0.121120i
\(293\) 3.95529 6.85076i 0.231071 0.400226i −0.727053 0.686581i \(-0.759111\pi\)
0.958123 + 0.286356i \(0.0924438\pi\)
\(294\) 0 0
\(295\) −6.10409 + 10.5726i −0.355394 + 0.615561i
\(296\) 6.14212 + 10.6385i 0.357003 + 0.618348i
\(297\) 2.98206 + 5.16508i 0.173037 + 0.299708i
\(298\) −22.4056 −1.29792
\(299\) 11.9811 + 4.96821i 0.692886 + 0.287319i
\(300\) −0.730535 −0.0421775
\(301\) 0 0
\(302\) −11.8607 20.5434i −0.682508 1.18214i
\(303\) −1.76685 + 3.06027i −0.101503 + 0.175808i
\(304\) 31.1779 1.78817
\(305\) −4.92598 + 8.53204i −0.282061 + 0.488543i
\(306\) 1.94489 3.36865i 0.111182 0.192573i
\(307\) −1.27238 −0.0726187 −0.0363094 0.999341i \(-0.511560\pi\)
−0.0363094 + 0.999341i \(0.511560\pi\)
\(308\) 0 0
\(309\) 2.42827 + 4.20588i 0.138139 + 0.239264i
\(310\) −4.89763 8.48295i −0.278167 0.481799i
\(311\) −24.7635 −1.40421 −0.702103 0.712075i \(-0.747756\pi\)
−0.702103 + 0.712075i \(0.747756\pi\)
\(312\) −4.01013 1.66288i −0.227029 0.0941421i
\(313\) −2.37651 −0.134328 −0.0671642 0.997742i \(-0.521395\pi\)
−0.0671642 + 0.997742i \(0.521395\pi\)
\(314\) −8.87330 15.3690i −0.500749 0.867323i
\(315\) 0 0
\(316\) −1.26625 + 2.19321i −0.0712322 + 0.123378i
\(317\) −19.7796 −1.11093 −0.555466 0.831539i \(-0.687460\pi\)
−0.555466 + 0.831539i \(0.687460\pi\)
\(318\) 1.07431 1.86076i 0.0602442 0.104346i
\(319\) −9.00993 + 15.6057i −0.504459 + 0.873749i
\(320\) 6.80187 0.380236
\(321\) 0.538192 0.932176i 0.0300390 0.0520290i
\(322\) 0 0
\(323\) 3.03171 + 5.25108i 0.168689 + 0.292178i
\(324\) 2.87890 0.159939
\(325\) 10.2444 7.85449i 0.568258 0.435689i
\(326\) −22.3995 −1.24059
\(327\) −3.36258 5.82416i −0.185951 0.322077i
\(328\) −1.89049 3.27442i −0.104385 0.180799i
\(329\) 0 0
\(330\) 1.91786 0.105575
\(331\) −1.96386 + 3.40151i −0.107944 + 0.186964i −0.914937 0.403596i \(-0.867760\pi\)
0.806993 + 0.590561i \(0.201093\pi\)
\(332\) −2.42533 + 4.20080i −0.133107 + 0.230549i
\(333\) −13.7799 −0.755136
\(334\) 6.04143 10.4641i 0.330572 0.572568i
\(335\) 2.23029 + 3.86298i 0.121854 + 0.211057i
\(336\) 0 0
\(337\) −7.14099 −0.388995 −0.194497 0.980903i \(-0.562308\pi\)
−0.194497 + 0.980903i \(0.562308\pi\)
\(338\) −19.5263 + 5.21577i −1.06209 + 0.283701i
\(339\) −7.87437 −0.427677
\(340\) −0.225181 0.390024i −0.0122121 0.0211520i
\(341\) −5.59486 9.69059i −0.302979 0.524775i
\(342\) −14.3571 + 24.8672i −0.776342 + 1.34466i
\(343\) 0 0
\(344\) 6.68494 11.5787i 0.360428 0.624280i
\(345\) −1.04853 + 1.81611i −0.0564509 + 0.0977759i
\(346\) −9.47522 −0.509391
\(347\) −5.03498 + 8.72085i −0.270292 + 0.468160i −0.968937 0.247309i \(-0.920454\pi\)
0.698644 + 0.715469i \(0.253787\pi\)
\(348\) −0.868758 1.50473i −0.0465703 0.0806622i
\(349\) −3.14418 5.44588i −0.168304 0.291512i 0.769520 0.638623i \(-0.220496\pi\)
−0.937824 + 0.347112i \(0.887162\pi\)
\(350\) 0 0
\(351\) 8.06437 6.18302i 0.430444 0.330025i
\(352\) −4.91606 −0.262027
\(353\) 17.0836 + 29.5897i 0.909269 + 1.57490i 0.815083 + 0.579345i \(0.196692\pi\)
0.0941861 + 0.995555i \(0.469975\pi\)
\(354\) −3.89671 6.74930i −0.207108 0.358721i
\(355\) 1.50738 2.61087i 0.0800036 0.138570i
\(356\) 7.40313 0.392365
\(357\) 0 0
\(358\) −14.4040 + 24.9484i −0.761274 + 1.31857i
\(359\) 18.6865 0.986238 0.493119 0.869962i \(-0.335857\pi\)
0.493119 + 0.869962i \(0.335857\pi\)
\(360\) −4.04750 + 7.01047i −0.213322 + 0.369484i
\(361\) −12.8799 22.3087i −0.677891 1.17414i
\(362\) −4.35716 7.54683i −0.229007 0.396653i
\(363\) −3.19088 −0.167478
\(364\) 0 0
\(365\) 6.82788 0.357388
\(366\) −3.14463 5.44666i −0.164372 0.284701i
\(367\) −15.5305 26.8997i −0.810687 1.40415i −0.912384 0.409336i \(-0.865760\pi\)
0.101696 0.994816i \(-0.467573\pi\)
\(368\) 8.38209 14.5182i 0.436946 0.756813i
\(369\) 4.24133 0.220795
\(370\) −4.62327 + 8.00775i −0.240353 + 0.416303i
\(371\) 0 0
\(372\) 1.07894 0.0559404
\(373\) 1.46852 2.54355i 0.0760371 0.131700i −0.825500 0.564403i \(-0.809107\pi\)
0.901537 + 0.432702i \(0.142440\pi\)
\(374\) −1.49084 2.58221i −0.0770894 0.133523i
\(375\) 2.50094 + 4.33175i 0.129148 + 0.223691i
\(376\) −7.84252 −0.404447
\(377\) 28.3612 + 11.7605i 1.46068 + 0.605698i
\(378\) 0 0
\(379\) −5.04254 8.73394i −0.259018 0.448632i 0.706961 0.707252i \(-0.250066\pi\)
−0.965979 + 0.258620i \(0.916732\pi\)
\(380\) 1.66227 + 2.87914i 0.0852727 + 0.147697i
\(381\) 3.83534 6.64301i 0.196491 0.340332i
\(382\) 0.783100 0.0400669
\(383\) 1.84466 3.19504i 0.0942576 0.163259i −0.815041 0.579403i \(-0.803286\pi\)
0.909299 + 0.416144i \(0.136619\pi\)
\(384\) −3.30767 + 5.72905i −0.168794 + 0.292360i
\(385\) 0 0
\(386\) 2.88584 4.99842i 0.146885 0.254413i
\(387\) 7.49888 + 12.9884i 0.381190 + 0.660240i
\(388\) 1.29376 + 2.24086i 0.0656809 + 0.113763i
\(389\) 22.6667 1.14925 0.574623 0.818418i \(-0.305149\pi\)
0.574623 + 0.818418i \(0.305149\pi\)
\(390\) −0.425262 3.23993i −0.0215340 0.164060i
\(391\) 3.26027 0.164879
\(392\) 0 0
\(393\) −2.33316 4.04116i −0.117693 0.203849i
\(394\) 5.78694 10.0233i 0.291542 0.504965i
\(395\) 7.23533 0.364049
\(396\) 1.21818 2.10995i 0.0612160 0.106029i
\(397\) −14.5680 + 25.2325i −0.731146 + 1.26638i 0.225248 + 0.974302i \(0.427681\pi\)
−0.956394 + 0.292080i \(0.905652\pi\)
\(398\) −11.6688 −0.584904
\(399\) 0 0
\(400\) −8.34241 14.4495i −0.417120 0.722474i
\(401\) −4.06026 7.03258i −0.202760 0.351190i 0.746657 0.665209i \(-0.231658\pi\)
−0.949417 + 0.314019i \(0.898324\pi\)
\(402\) −2.84753 −0.142022
\(403\) −15.1302 + 11.6004i −0.753687 + 0.577858i
\(404\) 3.01222 0.149864
\(405\) −4.11250 7.12305i −0.204352 0.353947i
\(406\) 0 0
\(407\) −5.28144 + 9.14773i −0.261791 + 0.453436i
\(408\) −1.09123 −0.0540238
\(409\) −4.16131 + 7.20759i −0.205763 + 0.356393i −0.950376 0.311105i \(-0.899301\pi\)
0.744612 + 0.667497i \(0.232634\pi\)
\(410\) 1.42300 2.46471i 0.0702769 0.121723i
\(411\) −1.35259 −0.0667184
\(412\) 2.06992 3.58520i 0.101978 0.176630i
\(413\) 0 0
\(414\) 7.71973 + 13.3710i 0.379404 + 0.657147i
\(415\) 13.8583 0.680278
\(416\) 1.09007 + 8.30492i 0.0534453 + 0.407182i
\(417\) 11.1533 0.546180
\(418\) 11.0053 + 19.0617i 0.538286 + 0.932339i
\(419\) −6.50832 11.2727i −0.317952 0.550710i 0.662108 0.749408i \(-0.269662\pi\)
−0.980061 + 0.198699i \(0.936329\pi\)
\(420\) 0 0
\(421\) −8.89681 −0.433604 −0.216802 0.976216i \(-0.569563\pi\)
−0.216802 + 0.976216i \(0.569563\pi\)
\(422\) −2.94662 + 5.10369i −0.143439 + 0.248444i
\(423\) 4.39870 7.61877i 0.213872 0.370437i
\(424\) 6.95174 0.337606
\(425\) 1.62242 2.81011i 0.0786988 0.136310i
\(426\) 0.962279 + 1.66672i 0.0466225 + 0.0807526i
\(427\) 0 0
\(428\) −0.917539 −0.0443509
\(429\) −0.485802 3.70117i −0.0234548 0.178694i
\(430\) 10.0637 0.485316
\(431\) 4.47872 + 7.75736i 0.215732 + 0.373659i 0.953499 0.301397i \(-0.0974529\pi\)
−0.737767 + 0.675056i \(0.764120\pi\)
\(432\) −6.56711 11.3746i −0.315960 0.547259i
\(433\) −0.0864547 + 0.149744i −0.00415475 + 0.00719624i −0.868095 0.496398i \(-0.834656\pi\)
0.863941 + 0.503594i \(0.167989\pi\)
\(434\) 0 0
\(435\) −2.48203 + 4.29901i −0.119004 + 0.206122i
\(436\) −2.86636 + 4.96467i −0.137274 + 0.237765i
\(437\) −24.0671 −1.15129
\(438\) −2.17938 + 3.77480i −0.104135 + 0.180367i
\(439\) 4.77080 + 8.26327i 0.227698 + 0.394384i 0.957125 0.289674i \(-0.0935468\pi\)
−0.729428 + 0.684058i \(0.760213\pi\)
\(440\) 3.10257 + 5.37382i 0.147909 + 0.256187i
\(441\) 0 0
\(442\) −4.03166 + 3.09111i −0.191767 + 0.147029i
\(443\) −13.8735 −0.659151 −0.329576 0.944129i \(-0.606906\pi\)
−0.329576 + 0.944129i \(0.606906\pi\)
\(444\) −0.509249 0.882045i −0.0241679 0.0418600i
\(445\) −10.5753 18.3170i −0.501319 0.868310i
\(446\) 3.78473 6.55534i 0.179212 0.310404i
\(447\) −7.05091 −0.333496
\(448\) 0 0
\(449\) 10.6456 18.4388i 0.502398 0.870180i −0.497598 0.867408i \(-0.665784\pi\)
0.999996 0.00277167i \(-0.000882252\pi\)
\(450\) 15.3664 0.724377
\(451\) 1.62558 2.81558i 0.0765455 0.132581i
\(452\) 3.35616 + 5.81304i 0.157861 + 0.273423i
\(453\) −3.73251 6.46489i −0.175368 0.303747i
\(454\) −37.5872 −1.76406
\(455\) 0 0
\(456\) 8.05539 0.377228
\(457\) −4.84282 8.38801i −0.226538 0.392375i 0.730242 0.683189i \(-0.239407\pi\)
−0.956780 + 0.290814i \(0.906074\pi\)
\(458\) −16.8779 29.2334i −0.788652 1.36599i
\(459\) 1.27716 2.21211i 0.0596128 0.103252i
\(460\) 1.78759 0.0833468
\(461\) −0.687178 + 1.19023i −0.0320051 + 0.0554344i −0.881584 0.472027i \(-0.843523\pi\)
0.849579 + 0.527461i \(0.176856\pi\)
\(462\) 0 0
\(463\) 31.7710 1.47653 0.738263 0.674513i \(-0.235646\pi\)
0.738263 + 0.674513i \(0.235646\pi\)
\(464\) 19.8417 34.3669i 0.921128 1.59544i
\(465\) −1.54126 2.66954i −0.0714742 0.123797i
\(466\) −2.95145 5.11206i −0.136723 0.236812i
\(467\) 29.1209 1.34756 0.673778 0.738934i \(-0.264670\pi\)
0.673778 + 0.738934i \(0.264670\pi\)
\(468\) −3.83456 1.59007i −0.177252 0.0735012i
\(469\) 0 0
\(470\) −2.95160 5.11231i −0.136147 0.235813i
\(471\) −2.79238 4.83654i −0.128666 0.222856i
\(472\) 12.6076 21.8370i 0.580312 1.00513i
\(473\) 11.4964 0.528605
\(474\) −2.30943 + 4.00006i −0.106076 + 0.183729i
\(475\) −11.9766 + 20.7441i −0.549525 + 0.951804i
\(476\) 0 0
\(477\) −3.89908 + 6.75341i −0.178527 + 0.309217i
\(478\) −17.0316 29.4995i −0.779005 1.34928i
\(479\) 4.86092 + 8.41936i 0.222101 + 0.384690i 0.955446 0.295167i \(-0.0953752\pi\)
−0.733345 + 0.679857i \(0.762042\pi\)
\(480\) −1.35426 −0.0618134
\(481\) 16.6248 + 6.89379i 0.758024 + 0.314330i
\(482\) 32.2578 1.46930
\(483\) 0 0
\(484\) 1.36000 + 2.35558i 0.0618180 + 0.107072i
\(485\) 3.69627 6.40213i 0.167839 0.290706i
\(486\) 18.3958 0.834452
\(487\) 8.55666 14.8206i 0.387739 0.671584i −0.604406 0.796676i \(-0.706589\pi\)
0.992145 + 0.125093i \(0.0399228\pi\)
\(488\) 10.1743 17.6224i 0.460568 0.797728i
\(489\) −7.04899 −0.318766
\(490\) 0 0
\(491\) 12.8607 + 22.2753i 0.580394 + 1.00527i 0.995432 + 0.0954681i \(0.0304348\pi\)
−0.415038 + 0.909804i \(0.636232\pi\)
\(492\) 0.156742 + 0.271485i 0.00706647 + 0.0122395i
\(493\) 7.71757 0.347582
\(494\) 29.7615 22.8184i 1.33903 1.02665i
\(495\) −6.96067 −0.312859
\(496\) 12.3210 + 21.3407i 0.553231 + 0.958224i
\(497\) 0 0
\(498\) −4.42341 + 7.66157i −0.198218 + 0.343323i
\(499\) 5.40396 0.241914 0.120957 0.992658i \(-0.461404\pi\)
0.120957 + 0.992658i \(0.461404\pi\)
\(500\) 2.13187 3.69250i 0.0953400 0.165134i
\(501\) 1.90121 3.29299i 0.0849396 0.147120i
\(502\) −20.6118 −0.919948
\(503\) −6.30847 + 10.9266i −0.281281 + 0.487193i −0.971700 0.236216i \(-0.924093\pi\)
0.690420 + 0.723409i \(0.257426\pi\)
\(504\) 0 0
\(505\) −4.30294 7.45292i −0.191478 0.331650i
\(506\) 11.8350 0.526129
\(507\) −6.14483 + 1.64138i −0.272901 + 0.0728960i
\(508\) −6.53870 −0.290108
\(509\) −0.979379 1.69633i −0.0434102 0.0751887i 0.843504 0.537123i \(-0.180489\pi\)
−0.886914 + 0.461934i \(0.847156\pi\)
\(510\) −0.410692 0.711340i −0.0181858 0.0314987i
\(511\) 0 0
\(512\) −12.1111 −0.535240
\(513\) −9.42794 + 16.3297i −0.416254 + 0.720973i
\(514\) −10.2385 + 17.7335i −0.451599 + 0.782193i
\(515\) −11.8275 −0.521181
\(516\) −0.554255 + 0.959998i −0.0243997 + 0.0422615i
\(517\) −3.37178 5.84010i −0.148291 0.256847i
\(518\) 0 0
\(519\) −2.98180 −0.130886
\(520\) 8.39027 6.43289i 0.367938 0.282101i
\(521\) 39.0954 1.71280 0.856401 0.516312i \(-0.172695\pi\)
0.856401 + 0.516312i \(0.172695\pi\)
\(522\) 18.2738 + 31.6512i 0.799823 + 1.38533i
\(523\) −4.35634 7.54540i −0.190489 0.329937i 0.754923 0.655813i \(-0.227674\pi\)
−0.945413 + 0.325876i \(0.894341\pi\)
\(524\) −1.98885 + 3.44479i −0.0868834 + 0.150486i
\(525\) 0 0
\(526\) 14.8788 25.7708i 0.648746 1.12366i
\(527\) −2.39618 + 4.15030i −0.104379 + 0.180790i
\(528\) −4.82479 −0.209972
\(529\) 5.02961 8.71154i 0.218679 0.378763i
\(530\) 2.61634 + 4.53164i 0.113647 + 0.196842i
\(531\) 14.1427 + 24.4958i 0.613740 + 1.06303i
\(532\) 0 0
\(533\) −5.11694 2.12184i −0.221639 0.0919072i
\(534\) 13.5021 0.584293
\(535\) 1.31070 + 2.27020i 0.0566665 + 0.0981493i
\(536\) −4.60652 7.97873i −0.198971 0.344629i
\(537\) −4.53286 + 7.85114i −0.195607 + 0.338802i
\(538\) 44.2809 1.90909
\(539\) 0 0
\(540\) 0.700261 1.21289i 0.0301344 0.0521944i
\(541\) −21.4994 −0.924330 −0.462165 0.886794i \(-0.652927\pi\)
−0.462165 + 0.886794i \(0.652927\pi\)
\(542\) 13.9513 24.1644i 0.599260 1.03795i
\(543\) −1.37118 2.37495i −0.0588428 0.101919i
\(544\) 1.05273 + 1.82338i 0.0451353 + 0.0781767i
\(545\) 16.3783 0.701569
\(546\) 0 0
\(547\) −30.2968 −1.29540 −0.647699 0.761896i \(-0.724269\pi\)
−0.647699 + 0.761896i \(0.724269\pi\)
\(548\) 0.576493 + 0.998514i 0.0246265 + 0.0426544i
\(549\) 11.4131 + 19.7680i 0.487098 + 0.843679i
\(550\) 5.88947 10.2009i 0.251128 0.434967i
\(551\) −56.9707 −2.42703
\(552\) 2.16567 3.75105i 0.0921770 0.159655i
\(553\) 0 0
\(554\) 20.8932 0.887668
\(555\) −1.45492 + 2.51999i −0.0617579 + 0.106968i
\(556\) −4.75369 8.23364i −0.201601 0.349184i
\(557\) 8.84201 + 15.3148i 0.374648 + 0.648909i 0.990274 0.139129i \(-0.0444302\pi\)
−0.615626 + 0.788038i \(0.711097\pi\)
\(558\) −22.6948 −0.960749
\(559\) −2.54918 19.4214i −0.107819 0.821437i
\(560\) 0 0
\(561\) −0.469159 0.812606i −0.0198079 0.0343083i
\(562\) 23.2838 + 40.3287i 0.982167 + 1.70116i
\(563\) −20.8695 + 36.1471i −0.879545 + 1.52342i −0.0277042 + 0.999616i \(0.508820\pi\)
−0.851841 + 0.523801i \(0.824514\pi\)
\(564\) 0.650230 0.0273796
\(565\) 9.58852 16.6078i 0.403392 0.698696i
\(566\) −7.68887 + 13.3175i −0.323187 + 0.559777i
\(567\) 0 0
\(568\) −3.11340 + 5.39257i −0.130636 + 0.226267i
\(569\) −2.73388 4.73521i −0.114610 0.198510i 0.803014 0.595960i \(-0.203229\pi\)
−0.917624 + 0.397450i \(0.869895\pi\)
\(570\) 3.03171 + 5.25108i 0.126984 + 0.219943i
\(571\) 9.35242 0.391387 0.195693 0.980665i \(-0.437304\pi\)
0.195693 + 0.980665i \(0.437304\pi\)
\(572\) −2.52523 + 1.93612i −0.105585 + 0.0809532i
\(573\) 0.246437 0.0102951
\(574\) 0 0
\(575\) 6.43976 + 11.1540i 0.268557 + 0.465154i
\(576\) 7.87968 13.6480i 0.328320 0.568667i
\(577\) 3.36925 0.140264 0.0701318 0.997538i \(-0.477658\pi\)
0.0701318 + 0.997538i \(0.477658\pi\)
\(578\) 12.5763 21.7829i 0.523107 0.906048i
\(579\) 0.908159 1.57298i 0.0377418 0.0653707i
\(580\) 4.23151 0.175704
\(581\) 0 0
\(582\) 2.35961 + 4.08697i 0.0978091 + 0.169410i
\(583\) 2.98881 + 5.17676i 0.123784 + 0.214400i
\(584\) −14.1026 −0.583568
\(585\) 1.54344 + 11.7590i 0.0638134 + 0.486174i
\(586\) −12.2985 −0.508045
\(587\) −6.57639 11.3906i −0.271437 0.470142i 0.697793 0.716299i \(-0.254165\pi\)
−0.969230 + 0.246157i \(0.920832\pi\)
\(588\) 0 0
\(589\) 17.6884 30.6373i 0.728840 1.26239i
\(590\) 18.9799 0.781390
\(591\) 1.82112 3.15427i 0.0749108 0.129749i
\(592\) 11.6308 20.1452i 0.478024 0.827961i
\(593\) −38.5916 −1.58477 −0.792384 0.610022i \(-0.791161\pi\)
−0.792384 + 0.610022i \(0.791161\pi\)
\(594\) 4.63617 8.03008i 0.190224 0.329478i
\(595\) 0 0
\(596\) 3.00519 + 5.20515i 0.123097 + 0.213211i
\(597\) −3.67211 −0.150289
\(598\) −2.62426 19.9934i −0.107314 0.817589i
\(599\) 18.4152 0.752426 0.376213 0.926533i \(-0.377226\pi\)
0.376213 + 0.926533i \(0.377226\pi\)
\(600\) −2.15542 3.73329i −0.0879946 0.152411i
\(601\) −20.7018 35.8566i −0.844445 1.46262i −0.886102 0.463490i \(-0.846597\pi\)
0.0416571 0.999132i \(-0.486736\pi\)
\(602\) 0 0
\(603\) 10.3348 0.420865
\(604\) −3.18169 + 5.51085i −0.129461 + 0.224233i
\(605\) 3.88549 6.72987i 0.157968 0.273608i
\(606\) 5.49380 0.223170
\(607\) 6.15255 10.6565i 0.249724 0.432535i −0.713725 0.700426i \(-0.752993\pi\)
0.963449 + 0.267891i \(0.0863266\pi\)
\(608\) −7.77119 13.4601i −0.315163 0.545879i
\(609\) 0 0
\(610\) 15.3167 0.620155
\(611\) −9.11830 + 6.99108i −0.368887 + 0.282829i
\(612\) −1.04345 −0.0421789
\(613\) −13.1112 22.7093i −0.529556 0.917219i −0.999406 0.0344720i \(-0.989025\pi\)
0.469849 0.882747i \(-0.344308\pi\)
\(614\) 0.989078 + 1.71313i 0.0399160 + 0.0691365i
\(615\) 0.447810 0.775630i 0.0180575 0.0312764i
\(616\) 0 0
\(617\) 9.41259 16.3031i 0.378936 0.656337i −0.611971 0.790880i \(-0.709623\pi\)
0.990908 + 0.134543i \(0.0429565\pi\)
\(618\) 3.77519 6.53882i 0.151860 0.263030i
\(619\) 15.8083 0.635389 0.317695 0.948193i \(-0.397091\pi\)
0.317695 + 0.948193i \(0.397091\pi\)
\(620\) −1.31381 + 2.27559i −0.0527639 + 0.0913898i
\(621\) 5.06935 + 8.78038i 0.203426 + 0.352344i
\(622\) 19.2497 + 33.3415i 0.771843 + 1.33687i
\(623\) 0 0
\(624\) 1.06984 + 8.15073i 0.0428277 + 0.326290i
\(625\) 5.72006 0.228802
\(626\) 1.84737 + 3.19973i 0.0738356 + 0.127887i
\(627\) 3.46331 + 5.99862i 0.138311 + 0.239562i
\(628\) −2.38030 + 4.12280i −0.0949843 + 0.164518i
\(629\) 4.52389 0.180379
\(630\) 0 0
\(631\) 8.33817 14.4421i 0.331937 0.574933i −0.650954 0.759117i \(-0.725631\pi\)
0.982892 + 0.184184i \(0.0589644\pi\)
\(632\) −14.9441 −0.594445
\(633\) −0.927285 + 1.60610i −0.0368563 + 0.0638369i
\(634\) 15.3755 + 26.6312i 0.610640 + 1.05766i
\(635\) 9.34050 + 16.1782i 0.370667 + 0.642013i
\(636\) −0.576375 −0.0228548
\(637\) 0 0
\(638\) 28.0152 1.10913
\(639\) −3.49248 6.04916i −0.138161 0.239301i
\(640\) −8.05542 13.9524i −0.318418 0.551517i
\(641\) −24.6232 + 42.6487i −0.972559 + 1.68452i −0.284792 + 0.958589i \(0.591925\pi\)
−0.687767 + 0.725932i \(0.741409\pi\)
\(642\) −1.67344 −0.0660454
\(643\) 21.4355 37.1275i 0.845335 1.46416i −0.0399940 0.999200i \(-0.512734\pi\)
0.885330 0.464964i \(-0.153933\pi\)
\(644\) 0 0
\(645\) 3.16700 0.124701
\(646\) 4.71336 8.16378i 0.185445 0.321200i
\(647\) 2.12929 + 3.68804i 0.0837112 + 0.144992i 0.904841 0.425749i \(-0.139989\pi\)
−0.821130 + 0.570741i \(0.806656\pi\)
\(648\) 8.49410 + 14.7122i 0.333680 + 0.577950i
\(649\) 21.6819 0.851089
\(650\) −18.5387 7.68744i −0.727148 0.301526i
\(651\) 0 0
\(652\) 3.00437 + 5.20373i 0.117660 + 0.203794i
\(653\) 1.04776 + 1.81477i 0.0410020 + 0.0710176i 0.885798 0.464071i \(-0.153612\pi\)
−0.844796 + 0.535088i \(0.820278\pi\)
\(654\) −5.22776 + 9.05475i −0.204422 + 0.354069i
\(655\) 11.3643 0.444038
\(656\) −3.57986 + 6.20049i −0.139770 + 0.242089i
\(657\) 7.90982 13.7002i 0.308592 0.534496i
\(658\) 0 0
\(659\) −12.7259 + 22.0419i −0.495732 + 0.858632i −0.999988 0.00492170i \(-0.998433\pi\)
0.504256 + 0.863554i \(0.331767\pi\)
\(660\) −0.257237 0.445548i −0.0100129 0.0173429i
\(661\) 13.9054 + 24.0848i 0.540857 + 0.936792i 0.998855 + 0.0478387i \(0.0152333\pi\)
−0.457998 + 0.888953i \(0.651433\pi\)
\(662\) 6.10639 0.237332
\(663\) −1.26874 + 0.972756i −0.0492739 + 0.0377787i
\(664\) −28.6234 −1.11080
\(665\) 0 0
\(666\) 10.7117 + 18.5533i 0.415072 + 0.718925i
\(667\) −15.3164 + 26.5288i −0.593055 + 1.02720i
\(668\) −3.24128 −0.125409
\(669\) 1.19103 2.06293i 0.0460480 0.0797574i
\(670\) 3.46740 6.00572i 0.133957 0.232021i
\(671\) 17.4972 0.675472
\(672\) 0 0
\(673\) −7.76033 13.4413i −0.299139 0.518124i 0.676800 0.736167i \(-0.263366\pi\)
−0.975939 + 0.218043i \(0.930033\pi\)
\(674\) 5.55100 + 9.61462i 0.213817 + 0.370341i
\(675\) 10.0907 0.388392
\(676\) 3.83071 + 3.83668i 0.147335 + 0.147565i
\(677\) −34.5626 −1.32835 −0.664175 0.747577i \(-0.731217\pi\)
−0.664175 + 0.747577i \(0.731217\pi\)
\(678\) 6.12109 + 10.6020i 0.235079 + 0.407169i
\(679\) 0 0
\(680\) 1.32877 2.30150i 0.0509562 0.0882587i
\(681\) −11.8285 −0.453269
\(682\) −8.69826 + 15.0658i −0.333074 + 0.576900i
\(683\) −23.5032 + 40.7087i −0.899325 + 1.55768i −0.0709661 + 0.997479i \(0.522608\pi\)
−0.828359 + 0.560198i \(0.810725\pi\)
\(684\) 7.70269 0.294520
\(685\) 1.64703 2.85275i 0.0629299 0.108998i
\(686\) 0 0
\(687\) −5.31138 9.19958i −0.202642 0.350986i
\(688\) −25.3174 −0.965218
\(689\) 8.08261 6.19701i 0.307923 0.236087i
\(690\) 3.26027 0.124116
\(691\) 9.50301 + 16.4597i 0.361512 + 0.626156i 0.988210 0.153106i \(-0.0489275\pi\)
−0.626698 + 0.779262i \(0.715594\pi\)
\(692\) 1.27088 + 2.20123i 0.0483117 + 0.0836784i
\(693\) 0 0
\(694\) 15.6556 0.594280
\(695\) −13.5813 + 23.5234i −0.515166 + 0.892294i
\(696\) 5.12648 8.87933i 0.194319 0.336570i
\(697\) −1.39241 −0.0527413
\(698\) −4.88822 + 8.46665i −0.185022 + 0.320467i
\(699\) −0.928805 1.60874i −0.0351306 0.0608480i
\(700\) 0 0
\(701\) −45.4648 −1.71718 −0.858591 0.512662i \(-0.828659\pi\)
−0.858591 + 0.512662i \(0.828659\pi\)
\(702\) −14.5936 6.05152i −0.550800 0.228400i
\(703\) −33.3951 −1.25952
\(704\) −6.04010 10.4618i −0.227645 0.394293i
\(705\) −0.928851 1.60882i −0.0349826 0.0605916i
\(706\) 26.5597 46.0027i 0.999586 1.73133i
\(707\) 0 0
\(708\) −1.04531 + 1.81053i −0.0392851 + 0.0680438i
\(709\) 4.89390 8.47648i 0.183794 0.318341i −0.759375 0.650653i \(-0.774495\pi\)
0.943170 + 0.332312i \(0.107829\pi\)
\(710\) −4.68702 −0.175901
\(711\) 8.38183 14.5178i 0.314343 0.544459i
\(712\) 21.8427 + 37.8326i 0.818589 + 1.41784i
\(713\) −9.51099 16.4735i −0.356189 0.616938i
\(714\) 0 0
\(715\) 8.39768 + 3.48226i 0.314055 + 0.130229i
\(716\) 7.72786 0.288804
\(717\) −5.35974 9.28334i −0.200163 0.346693i
\(718\) −14.5259 25.1595i −0.542100 0.938945i
\(719\) −13.9201 + 24.1104i −0.519133 + 0.899165i 0.480620 + 0.876929i \(0.340412\pi\)
−0.999753 + 0.0222358i \(0.992922\pi\)
\(720\) 15.3288 0.571271
\(721\) 0 0
\(722\) −20.0243 + 34.6830i −0.745226 + 1.29077i
\(723\) 10.1514 0.377533
\(724\) −1.16883 + 2.02447i −0.0434391 + 0.0752388i
\(725\) 15.2439 + 26.4033i 0.566145 + 0.980592i
\(726\) 2.48041 + 4.29619i 0.0920566 + 0.159447i
\(727\) 14.5650 0.540186 0.270093 0.962834i \(-0.412945\pi\)
0.270093 + 0.962834i \(0.412945\pi\)
\(728\) 0 0
\(729\) −14.9199 −0.552589
\(730\) −5.30761 9.19305i −0.196444 0.340250i
\(731\) −2.46185 4.26405i −0.0910547 0.157711i
\(732\) −0.843560 + 1.46109i −0.0311789 + 0.0540034i
\(733\) −17.6606 −0.652309 −0.326155 0.945316i \(-0.605753\pi\)
−0.326155 + 0.945316i \(0.605753\pi\)
\(734\) −24.1451 + 41.8206i −0.891213 + 1.54363i
\(735\) 0 0
\(736\) −8.35705 −0.308045
\(737\) 3.96102 6.86069i 0.145906 0.252717i
\(738\) −3.29697 5.71052i −0.121363 0.210207i
\(739\) −4.48279 7.76443i −0.164902 0.285619i 0.771718 0.635964i \(-0.219398\pi\)
−0.936621 + 0.350345i \(0.886064\pi\)
\(740\) 2.48042 0.0911822
\(741\) 9.36579 7.18084i 0.344061 0.263795i
\(742\) 0 0
\(743\) 13.1839 + 22.8352i 0.483671 + 0.837743i 0.999824 0.0187532i \(-0.00596968\pi\)
−0.516153 + 0.856497i \(0.672636\pi\)
\(744\) 3.18337 + 5.51376i 0.116708 + 0.202144i
\(745\) 8.58580 14.8710i 0.314560 0.544833i
\(746\) −4.56618 −0.167180
\(747\) 16.0543 27.8068i 0.587395 1.01740i
\(748\) −0.399923 + 0.692688i −0.0146226 + 0.0253272i
\(749\) 0 0
\(750\) 3.88818 6.73452i 0.141976 0.245910i
\(751\) 10.1438 + 17.5696i 0.370152 + 0.641123i 0.989589 0.143924i \(-0.0459721\pi\)
−0.619436 + 0.785047i \(0.712639\pi\)
\(752\) 7.42536 + 12.8611i 0.270775 + 0.468996i
\(753\) −6.48641 −0.236378
\(754\) −6.21203 47.3274i −0.226229 1.72356i
\(755\) 18.1801 0.661642
\(756\) 0 0
\(757\) −12.4992 21.6493i −0.454292 0.786857i 0.544355 0.838855i \(-0.316774\pi\)
−0.998647 + 0.0519981i \(0.983441\pi\)
\(758\) −7.83957 + 13.5785i −0.284746 + 0.493195i
\(759\) 3.72440 0.135187
\(760\) −9.80895 + 16.9896i −0.355808 + 0.616277i
\(761\) 10.0711 17.4436i 0.365077 0.632332i −0.623712 0.781655i \(-0.714376\pi\)
0.988789 + 0.149323i \(0.0477094\pi\)
\(762\) −11.9255 −0.432016
\(763\) 0 0
\(764\) −0.105035 0.181926i −0.00380003 0.00658184i
\(765\) 1.49056 + 2.58173i 0.0538914 + 0.0933426i
\(766\) −5.73573 −0.207240
\(767\) −4.80769 36.6282i −0.173596 1.32257i
\(768\) 4.69889 0.169557
\(769\) 4.33610 + 7.51034i 0.156364 + 0.270830i 0.933555 0.358435i \(-0.116689\pi\)
−0.777191 + 0.629265i \(0.783356\pi\)
\(770\) 0 0
\(771\) −3.22199 + 5.58065i −0.116037 + 0.200982i
\(772\) −1.54828 −0.0557237
\(773\) 1.17283 2.03141i 0.0421839 0.0730647i −0.844163 0.536087i \(-0.819902\pi\)
0.886346 + 0.463023i \(0.153235\pi\)
\(774\) 11.6584 20.1930i 0.419053 0.725821i
\(775\) −18.9319 −0.680055
\(776\) −7.63441 + 13.2232i −0.274059 + 0.474685i
\(777\) 0 0
\(778\) −17.6198 30.5184i −0.631701 1.09414i
\(779\) 10.2787 0.368273
\(780\) −0.695645 + 0.533357i −0.0249081 + 0.0190973i
\(781\) −5.35426 −0.191591
\(782\) −2.53435 4.38962i −0.0906281 0.156973i
\(783\) 12.0000 + 20.7845i 0.428844 + 0.742779i