Properties

Label 1183.2.e.d.508.2
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
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 508.2
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.d.170.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.190983 - 0.330792i) q^{2} +(-1.11803 + 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +0.854102 q^{6} +(2.00000 - 1.73205i) q^{7} -1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.190983 - 0.330792i) q^{2} +(-1.11803 + 1.93649i) q^{3} +(0.927051 - 1.60570i) q^{4} +(-1.11803 - 1.93649i) q^{5} +0.854102 q^{6} +(2.00000 - 1.73205i) q^{7} -1.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(-0.427051 + 0.739674i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(2.07295 + 3.59045i) q^{12} +(-0.954915 - 0.330792i) q^{14} +5.00000 q^{15} +(-1.57295 - 2.72443i) q^{16} +(3.73607 - 6.47106i) q^{17} +(-0.381966 + 0.661585i) q^{18} +(1.50000 + 2.59808i) q^{19} -4.14590 q^{20} +(1.11803 + 5.80948i) q^{21} +1.14590 q^{22} +(1.88197 + 3.25966i) q^{23} +(1.64590 - 2.85078i) q^{24} -2.23607 q^{27} +(-0.927051 - 4.81710i) q^{28} -4.47214 q^{29} +(-0.954915 - 1.65396i) q^{30} +(2.50000 - 4.33013i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(-3.35410 - 5.80948i) q^{33} -2.85410 q^{34} +(-5.59017 - 1.93649i) q^{35} -3.70820 q^{36} +(-4.35410 - 7.54153i) q^{37} +(0.572949 - 0.992377i) q^{38} +(1.64590 + 2.85078i) q^{40} -4.47214 q^{41} +(1.70820 - 1.47935i) q^{42} -8.00000 q^{43} +(2.78115 + 4.81710i) q^{44} +(-2.23607 + 3.87298i) q^{45} +(0.718847 - 1.24508i) q^{46} +(0.736068 + 1.27491i) q^{47} +7.03444 q^{48} +(1.00000 - 6.92820i) q^{49} +(8.35410 + 14.4697i) q^{51} +(-0.736068 + 1.27491i) q^{53} +(0.427051 + 0.739674i) q^{54} +6.70820 q^{55} +(-2.94427 + 2.54981i) q^{56} -6.70820 q^{57} +(0.854102 + 1.47935i) q^{58} +(3.73607 - 6.47106i) q^{59} +(4.63525 - 8.02850i) q^{60} +(-1.50000 - 2.59808i) q^{61} -1.90983 q^{62} +(-5.00000 - 1.73205i) q^{63} -4.70820 q^{64} +(-1.28115 + 2.21902i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-6.92705 - 11.9980i) q^{68} -8.41641 q^{69} +(0.427051 + 2.21902i) q^{70} -8.94427 q^{71} +(1.47214 + 2.54981i) q^{72} +(5.35410 - 9.27358i) q^{73} +(-1.66312 + 2.88061i) q^{74} +5.56231 q^{76} +(1.50000 + 7.79423i) q^{77} +(-5.35410 - 9.27358i) q^{79} +(-3.51722 + 6.09201i) q^{80} +(5.50000 - 9.52628i) q^{81} +(0.854102 + 1.47935i) q^{82} +(10.3647 + 3.59045i) q^{84} -16.7082 q^{85} +(1.52786 + 2.64634i) q^{86} +(5.00000 - 8.66025i) q^{87} +(2.20820 - 3.82472i) q^{88} +(-1.11803 - 1.93649i) q^{89} +1.70820 q^{90} +6.97871 q^{92} +(5.59017 + 9.68246i) q^{93} +(0.281153 - 0.486971i) q^{94} +(3.35410 - 5.80948i) q^{95} +(-4.63525 - 8.02850i) q^{96} +17.4164 q^{97} +(-2.48278 + 0.992377i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{2} - 3q^{4} - 10q^{6} + 8q^{7} + 12q^{8} - 4q^{9} + O(q^{10}) \) \( 4q - 3q^{2} - 3q^{4} - 10q^{6} + 8q^{7} + 12q^{8} - 4q^{9} + 5q^{10} - 6q^{11} + 15q^{12} - 15q^{14} + 20q^{15} - 13q^{16} + 6q^{17} - 6q^{18} + 6q^{19} - 30q^{20} + 18q^{22} + 12q^{23} + 20q^{24} + 3q^{28} - 15q^{30} + 10q^{31} - 15q^{32} + 2q^{34} + 12q^{36} - 4q^{37} + 9q^{38} + 20q^{40} - 20q^{42} - 32q^{43} - 9q^{44} + 23q^{46} - 6q^{47} - 30q^{48} + 4q^{49} + 20q^{51} + 6q^{53} - 5q^{54} + 24q^{56} - 10q^{58} + 6q^{59} - 15q^{60} - 6q^{61} - 30q^{62} - 20q^{63} + 8q^{64} + 15q^{66} - 6q^{67} - 21q^{68} + 20q^{69} - 5q^{70} - 12q^{72} + 8q^{73} + 9q^{74} - 18q^{76} + 6q^{77} - 8q^{79} + 15q^{80} + 22q^{81} - 10q^{82} + 75q^{84} - 40q^{85} + 24q^{86} + 20q^{87} - 18q^{88} - 20q^{90} - 66q^{92} - 19q^{94} + 15q^{96} + 16q^{97} - 39q^{98} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.190983 0.330792i −0.135045 0.233905i 0.790569 0.612372i \(-0.209785\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) −1.11803 + 1.93649i −0.645497 + 1.11803i 0.338689 + 0.940898i \(0.390016\pi\)
−0.984186 + 0.177136i \(0.943317\pi\)
\(4\) 0.927051 1.60570i 0.463525 0.802850i
\(5\) −1.11803 1.93649i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(6\) 0.854102 0.348686
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) −1.47214 −0.520479
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) −0.427051 + 0.739674i −0.135045 + 0.233905i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 2.07295 + 3.59045i 0.598409 + 1.03647i
\(13\) 0 0
\(14\) −0.954915 0.330792i −0.255212 0.0884080i
\(15\) 5.00000 1.29099
\(16\) −1.57295 2.72443i −0.393237 0.681107i
\(17\) 3.73607 6.47106i 0.906130 1.56946i 0.0867359 0.996231i \(-0.472356\pi\)
0.819394 0.573231i \(-0.194310\pi\)
\(18\) −0.381966 + 0.661585i −0.0900303 + 0.155937i
\(19\) 1.50000 + 2.59808i 0.344124 + 0.596040i 0.985194 0.171442i \(-0.0548427\pi\)
−0.641071 + 0.767482i \(0.721509\pi\)
\(20\) −4.14590 −0.927051
\(21\) 1.11803 + 5.80948i 0.243975 + 1.26773i
\(22\) 1.14590 0.244306
\(23\) 1.88197 + 3.25966i 0.392417 + 0.679686i 0.992768 0.120051i \(-0.0383057\pi\)
−0.600351 + 0.799737i \(0.704972\pi\)
\(24\) 1.64590 2.85078i 0.335968 0.581913i
\(25\) 0 0
\(26\) 0 0
\(27\) −2.23607 −0.430331
\(28\) −0.927051 4.81710i −0.175196 0.910346i
\(29\) −4.47214 −0.830455 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(30\) −0.954915 1.65396i −0.174343 0.301971i
\(31\) 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i \(-0.685109\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) −2.07295 + 3.59045i −0.366449 + 0.634708i
\(33\) −3.35410 5.80948i −0.583874 1.01130i
\(34\) −2.85410 −0.489474
\(35\) −5.59017 1.93649i −0.944911 0.327327i
\(36\) −3.70820 −0.618034
\(37\) −4.35410 7.54153i −0.715810 1.23982i −0.962646 0.270762i \(-0.912724\pi\)
0.246836 0.969057i \(-0.420609\pi\)
\(38\) 0.572949 0.992377i 0.0929446 0.160985i
\(39\) 0 0
\(40\) 1.64590 + 2.85078i 0.260239 + 0.450748i
\(41\) −4.47214 −0.698430 −0.349215 0.937043i \(-0.613552\pi\)
−0.349215 + 0.937043i \(0.613552\pi\)
\(42\) 1.70820 1.47935i 0.263582 0.228268i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 2.78115 + 4.81710i 0.419275 + 0.726205i
\(45\) −2.23607 + 3.87298i −0.333333 + 0.577350i
\(46\) 0.718847 1.24508i 0.105988 0.183577i
\(47\) 0.736068 + 1.27491i 0.107367 + 0.185964i 0.914703 0.404128i \(-0.132425\pi\)
−0.807336 + 0.590092i \(0.799091\pi\)
\(48\) 7.03444 1.01533
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 8.35410 + 14.4697i 1.16981 + 2.02617i
\(52\) 0 0
\(53\) −0.736068 + 1.27491i −0.101107 + 0.175122i −0.912141 0.409877i \(-0.865572\pi\)
0.811034 + 0.584999i \(0.198905\pi\)
\(54\) 0.427051 + 0.739674i 0.0581143 + 0.100657i
\(55\) 6.70820 0.904534
\(56\) −2.94427 + 2.54981i −0.393445 + 0.340733i
\(57\) −6.70820 −0.888523
\(58\) 0.854102 + 1.47935i 0.112149 + 0.194248i
\(59\) 3.73607 6.47106i 0.486395 0.842460i −0.513483 0.858100i \(-0.671645\pi\)
0.999878 + 0.0156395i \(0.00497842\pi\)
\(60\) 4.63525 8.02850i 0.598409 1.03647i
\(61\) −1.50000 2.59808i −0.192055 0.332650i 0.753876 0.657017i \(-0.228182\pi\)
−0.945931 + 0.324367i \(0.894849\pi\)
\(62\) −1.90983 −0.242549
\(63\) −5.00000 1.73205i −0.629941 0.218218i
\(64\) −4.70820 −0.588525
\(65\) 0 0
\(66\) −1.28115 + 2.21902i −0.157699 + 0.273143i
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) −6.92705 11.9980i −0.840028 1.45497i
\(69\) −8.41641 −1.01322
\(70\) 0.427051 + 2.21902i 0.0510424 + 0.265224i
\(71\) −8.94427 −1.06149 −0.530745 0.847532i \(-0.678088\pi\)
−0.530745 + 0.847532i \(0.678088\pi\)
\(72\) 1.47214 + 2.54981i 0.173493 + 0.300498i
\(73\) 5.35410 9.27358i 0.626650 1.08539i −0.361569 0.932345i \(-0.617759\pi\)
0.988219 0.153045i \(-0.0489079\pi\)
\(74\) −1.66312 + 2.88061i −0.193334 + 0.334864i
\(75\) 0 0
\(76\) 5.56231 0.638040
\(77\) 1.50000 + 7.79423i 0.170941 + 0.888235i
\(78\) 0 0
\(79\) −5.35410 9.27358i −0.602384 1.04336i −0.992459 0.122576i \(-0.960884\pi\)
0.390076 0.920783i \(-0.372449\pi\)
\(80\) −3.51722 + 6.09201i −0.393237 + 0.681107i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0.854102 + 1.47935i 0.0943198 + 0.163367i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 10.3647 + 3.59045i 1.13089 + 0.391751i
\(85\) −16.7082 −1.81226
\(86\) 1.52786 + 2.64634i 0.164754 + 0.285362i
\(87\) 5.00000 8.66025i 0.536056 0.928477i
\(88\) 2.20820 3.82472i 0.235395 0.407717i
\(89\) −1.11803 1.93649i −0.118511 0.205268i 0.800667 0.599110i \(-0.204479\pi\)
−0.919178 + 0.393842i \(0.871146\pi\)
\(90\) 1.70820 0.180061
\(91\) 0 0
\(92\) 6.97871 0.727581
\(93\) 5.59017 + 9.68246i 0.579674 + 1.00402i
\(94\) 0.281153 0.486971i 0.0289987 0.0502272i
\(95\) 3.35410 5.80948i 0.344124 0.596040i
\(96\) −4.63525 8.02850i −0.473084 0.819405i
\(97\) 17.4164 1.76837 0.884184 0.467139i \(-0.154715\pi\)
0.884184 + 0.467139i \(0.154715\pi\)
\(98\) −2.48278 + 0.992377i −0.250799 + 0.100245i
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) 3.19098 5.52694i 0.315954 0.547249i
\(103\) −5.35410 9.27358i −0.527555 0.913753i −0.999484 0.0321160i \(-0.989775\pi\)
0.471929 0.881637i \(-0.343558\pi\)
\(104\) 0 0
\(105\) 10.0000 8.66025i 0.975900 0.845154i
\(106\) 0.562306 0.0546160
\(107\) 7.11803 + 12.3288i 0.688126 + 1.19187i 0.972443 + 0.233139i \(0.0748999\pi\)
−0.284317 + 0.958730i \(0.591767\pi\)
\(108\) −2.07295 + 3.59045i −0.199470 + 0.345492i
\(109\) 5.35410 9.27358i 0.512830 0.888248i −0.487059 0.873369i \(-0.661930\pi\)
0.999889 0.0148787i \(-0.00473620\pi\)
\(110\) −1.28115 2.21902i −0.122153 0.211575i
\(111\) 19.4721 1.84821
\(112\) −7.86475 2.72443i −0.743149 0.257434i
\(113\) −14.9443 −1.40584 −0.702919 0.711269i \(-0.748121\pi\)
−0.702919 + 0.711269i \(0.748121\pi\)
\(114\) 1.28115 + 2.21902i 0.119991 + 0.207830i
\(115\) 4.20820 7.28882i 0.392417 0.679686i
\(116\) −4.14590 + 7.18091i −0.384937 + 0.666730i
\(117\) 0 0
\(118\) −2.85410 −0.262741
\(119\) −3.73607 19.4132i −0.342485 1.77960i
\(120\) −7.36068 −0.671935
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −0.572949 + 0.992377i −0.0518724 + 0.0898456i
\(123\) 5.00000 8.66025i 0.450835 0.780869i
\(124\) −4.63525 8.02850i −0.416258 0.720980i
\(125\) −11.1803 −1.00000
\(126\) 0.381966 + 1.98475i 0.0340282 + 0.176816i
\(127\) 15.4164 1.36798 0.683992 0.729489i \(-0.260242\pi\)
0.683992 + 0.729489i \(0.260242\pi\)
\(128\) 5.04508 + 8.73834i 0.445927 + 0.772368i
\(129\) 8.94427 15.4919i 0.787499 1.36399i
\(130\) 0 0
\(131\) 1.88197 + 3.25966i 0.164428 + 0.284798i 0.936452 0.350796i \(-0.114089\pi\)
−0.772024 + 0.635593i \(0.780755\pi\)
\(132\) −12.4377 −1.08256
\(133\) 7.50000 + 2.59808i 0.650332 + 0.225282i
\(134\) 1.14590 0.0989905
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) −5.50000 + 9.52628i −0.471621 + 0.816872i
\(137\) −1.88197 + 3.25966i −0.160787 + 0.278492i −0.935151 0.354249i \(-0.884737\pi\)
0.774364 + 0.632740i \(0.218070\pi\)
\(138\) 1.60739 + 2.78408i 0.136830 + 0.236997i
\(139\) 3.41641 0.289776 0.144888 0.989448i \(-0.453718\pi\)
0.144888 + 0.989448i \(0.453718\pi\)
\(140\) −8.29180 + 7.18091i −0.700785 + 0.606897i
\(141\) −3.29180 −0.277219
\(142\) 1.70820 + 2.95870i 0.143349 + 0.248288i
\(143\) 0 0
\(144\) −3.14590 + 5.44886i −0.262158 + 0.454071i
\(145\) 5.00000 + 8.66025i 0.415227 + 0.719195i
\(146\) −4.09017 −0.338505
\(147\) 12.2984 + 9.68246i 1.01435 + 0.798596i
\(148\) −16.1459 −1.32718
\(149\) −6.35410 11.0056i −0.520548 0.901616i −0.999715 0.0238920i \(-0.992394\pi\)
0.479166 0.877724i \(-0.340939\pi\)
\(150\) 0 0
\(151\) −3.20820 + 5.55677i −0.261080 + 0.452204i −0.966529 0.256557i \(-0.917412\pi\)
0.705449 + 0.708760i \(0.250745\pi\)
\(152\) −2.20820 3.82472i −0.179109 0.310226i
\(153\) −14.9443 −1.20817
\(154\) 2.29180 1.98475i 0.184678 0.159936i
\(155\) −11.1803 −0.898027
\(156\) 0 0
\(157\) −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) −2.04508 + 3.54219i −0.162698 + 0.281802i
\(159\) −1.64590 2.85078i −0.130528 0.226081i
\(160\) 9.27051 0.732898
\(161\) 9.40983 + 3.25966i 0.741598 + 0.256897i
\(162\) −4.20163 −0.330111
\(163\) 5.20820 + 9.02087i 0.407938 + 0.706569i 0.994659 0.103220i \(-0.0329146\pi\)
−0.586721 + 0.809789i \(0.699581\pi\)
\(164\) −4.14590 + 7.18091i −0.323740 + 0.560735i
\(165\) −7.50000 + 12.9904i −0.583874 + 1.01130i
\(166\) 0 0
\(167\) −13.5279 −1.04682 −0.523409 0.852082i \(-0.675340\pi\)
−0.523409 + 0.852082i \(0.675340\pi\)
\(168\) −1.64590 8.55234i −0.126984 0.659827i
\(169\) 0 0
\(170\) 3.19098 + 5.52694i 0.244737 + 0.423897i
\(171\) 3.00000 5.19615i 0.229416 0.397360i
\(172\) −7.41641 + 12.8456i −0.565496 + 0.979467i
\(173\) −5.20820 9.02087i −0.395972 0.685844i 0.597252 0.802053i \(-0.296259\pi\)
−0.993225 + 0.116209i \(0.962926\pi\)
\(174\) −3.81966 −0.289568
\(175\) 0 0
\(176\) 9.43769 0.711393
\(177\) 8.35410 + 14.4697i 0.627933 + 1.08761i
\(178\) −0.427051 + 0.739674i −0.0320088 + 0.0554409i
\(179\) −10.0623 + 17.4284i −0.752092 + 1.30266i 0.194715 + 0.980860i \(0.437622\pi\)
−0.946807 + 0.321802i \(0.895712\pi\)
\(180\) 4.14590 + 7.18091i 0.309017 + 0.535233i
\(181\) 1.41641 0.105281 0.0526404 0.998614i \(-0.483236\pi\)
0.0526404 + 0.998614i \(0.483236\pi\)
\(182\) 0 0
\(183\) 6.70820 0.495885
\(184\) −2.77051 4.79866i −0.204245 0.353762i
\(185\) −9.73607 + 16.8634i −0.715810 + 1.23982i
\(186\) 2.13525 3.69837i 0.156564 0.271178i
\(187\) 11.2082 + 19.4132i 0.819625 + 1.41963i
\(188\) 2.72949 0.199069
\(189\) −4.47214 + 3.87298i −0.325300 + 0.281718i
\(190\) −2.56231 −0.185889
\(191\) 5.59017 + 9.68246i 0.404491 + 0.700598i 0.994262 0.106972i \(-0.0341155\pi\)
−0.589772 + 0.807570i \(0.700782\pi\)
\(192\) 5.26393 9.11740i 0.379892 0.657992i
\(193\) −6.35410 + 11.0056i −0.457378 + 0.792202i −0.998821 0.0485349i \(-0.984545\pi\)
0.541443 + 0.840737i \(0.317878\pi\)
\(194\) −3.32624 5.76121i −0.238810 0.413631i
\(195\) 0 0
\(196\) −10.1976 8.02850i −0.728397 0.573464i
\(197\) 26.9443 1.91970 0.959850 0.280514i \(-0.0905049\pi\)
0.959850 + 0.280514i \(0.0905049\pi\)
\(198\) −1.14590 1.98475i −0.0814354 0.141050i
\(199\) 3.64590 6.31488i 0.258451 0.447650i −0.707376 0.706837i \(-0.750121\pi\)
0.965827 + 0.259187i \(0.0834547\pi\)
\(200\) 0 0
\(201\) −3.35410 5.80948i −0.236580 0.409769i
\(202\) −3.43769 −0.241875
\(203\) −8.94427 + 7.74597i −0.627765 + 0.543660i
\(204\) 30.9787 2.16894
\(205\) 5.00000 + 8.66025i 0.349215 + 0.604858i
\(206\) −2.04508 + 3.54219i −0.142488 + 0.246796i
\(207\) 3.76393 6.51932i 0.261611 0.453124i
\(208\) 0 0
\(209\) −9.00000 −0.622543
\(210\) −4.77458 1.65396i −0.329477 0.114134i
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 1.36475 + 2.36381i 0.0937311 + 0.162347i
\(213\) 10.0000 17.3205i 0.685189 1.18678i
\(214\) 2.71885 4.70918i 0.185857 0.321913i
\(215\) 8.94427 + 15.4919i 0.609994 + 1.05654i
\(216\) 3.29180 0.223978
\(217\) −2.50000 12.9904i −0.169711 0.881845i
\(218\) −4.09017 −0.277021
\(219\) 11.9721 + 20.7363i 0.809002 + 1.40123i
\(220\) 6.21885 10.7714i 0.419275 0.726205i
\(221\) 0 0
\(222\) −3.71885 6.44123i −0.249593 0.432307i
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 2.07295 + 10.7714i 0.138505 + 0.719692i
\(225\) 0 0
\(226\) 2.85410 + 4.94345i 0.189852 + 0.328833i
\(227\) −5.97214 + 10.3440i −0.396385 + 0.686558i −0.993277 0.115763i \(-0.963069\pi\)
0.596892 + 0.802321i \(0.296402\pi\)
\(228\) −6.21885 + 10.7714i −0.411853 + 0.713351i
\(229\) −8.06231 13.9643i −0.532772 0.922788i −0.999268 0.0382649i \(-0.987817\pi\)
0.466495 0.884524i \(-0.345516\pi\)
\(230\) −3.21478 −0.211976
\(231\) −16.7705 5.80948i −1.10342 0.382235i
\(232\) 6.58359 0.432234
\(233\) 2.97214 + 5.14789i 0.194711 + 0.337250i 0.946806 0.321806i \(-0.104290\pi\)
−0.752095 + 0.659055i \(0.770956\pi\)
\(234\) 0 0
\(235\) 1.64590 2.85078i 0.107367 0.185964i
\(236\) −6.92705 11.9980i −0.450913 0.781004i
\(237\) 23.9443 1.55535
\(238\) −5.70820 + 4.94345i −0.370008 + 0.320436i
\(239\) 7.41641 0.479728 0.239864 0.970807i \(-0.422897\pi\)
0.239864 + 0.970807i \(0.422897\pi\)
\(240\) −7.86475 13.6221i −0.507667 0.879305i
\(241\) −4.35410 + 7.54153i −0.280472 + 0.485792i −0.971501 0.237035i \(-0.923824\pi\)
0.691029 + 0.722827i \(0.257158\pi\)
\(242\) 0.381966 0.661585i 0.0245537 0.0425283i
\(243\) 8.94427 + 15.4919i 0.573775 + 0.993808i
\(244\) −5.56231 −0.356090
\(245\) −14.5344 + 5.80948i −0.928571 + 0.371154i
\(246\) −3.81966 −0.243533
\(247\) 0 0
\(248\) −3.68034 + 6.37454i −0.233702 + 0.404783i
\(249\) 0 0
\(250\) 2.13525 + 3.69837i 0.135045 + 0.233905i
\(251\) 10.4721 0.660995 0.330498 0.943807i \(-0.392783\pi\)
0.330498 + 0.943807i \(0.392783\pi\)
\(252\) −7.41641 + 6.42280i −0.467190 + 0.404598i
\(253\) −11.2918 −0.709909
\(254\) −2.94427 5.09963i −0.184740 0.319979i
\(255\) 18.6803 32.3553i 1.16981 2.02617i
\(256\) −2.78115 + 4.81710i −0.173822 + 0.301069i
\(257\) 8.97214 + 15.5402i 0.559666 + 0.969371i 0.997524 + 0.0703264i \(0.0224041\pi\)
−0.437858 + 0.899044i \(0.644263\pi\)
\(258\) −6.83282 −0.425393
\(259\) −21.7705 7.54153i −1.35275 0.468608i
\(260\) 0 0
\(261\) 4.47214 + 7.74597i 0.276818 + 0.479463i
\(262\) 0.718847 1.24508i 0.0444105 0.0769213i
\(263\) 7.06231 12.2323i 0.435480 0.754274i −0.561854 0.827236i \(-0.689912\pi\)
0.997335 + 0.0729620i \(0.0232452\pi\)
\(264\) 4.93769 + 8.55234i 0.303894 + 0.526360i
\(265\) 3.29180 0.202213
\(266\) −0.572949 2.97713i −0.0351298 0.182540i
\(267\) 5.00000 0.305995
\(268\) 2.78115 + 4.81710i 0.169886 + 0.294251i
\(269\) −2.26393 + 3.92125i −0.138034 + 0.239083i −0.926753 0.375672i \(-0.877412\pi\)
0.788718 + 0.614755i \(0.210745\pi\)
\(270\) 0.954915 1.65396i 0.0581143 0.100657i
\(271\) 3.20820 + 5.55677i 0.194885 + 0.337550i 0.946863 0.321638i \(-0.104233\pi\)
−0.751978 + 0.659188i \(0.770900\pi\)
\(272\) −23.5066 −1.42530
\(273\) 0 0
\(274\) 1.43769 0.0868543
\(275\) 0 0
\(276\) −7.80244 + 13.5142i −0.469652 + 0.813461i
\(277\) −13.2082 + 22.8773i −0.793604 + 1.37456i 0.130118 + 0.991499i \(0.458464\pi\)
−0.923722 + 0.383064i \(0.874869\pi\)
\(278\) −0.652476 1.13012i −0.0391329 0.0677802i
\(279\) −10.0000 −0.598684
\(280\) 8.22949 + 2.85078i 0.491806 + 0.170367i
\(281\) −9.05573 −0.540219 −0.270110 0.962830i \(-0.587060\pi\)
−0.270110 + 0.962830i \(0.587060\pi\)
\(282\) 0.628677 + 1.08890i 0.0374372 + 0.0648431i
\(283\) 7.06231 12.2323i 0.419811 0.727133i −0.576110 0.817372i \(-0.695430\pi\)
0.995920 + 0.0902393i \(0.0287632\pi\)
\(284\) −8.29180 + 14.3618i −0.492028 + 0.852217i
\(285\) 7.50000 + 12.9904i 0.444262 + 0.769484i
\(286\) 0 0
\(287\) −8.94427 + 7.74597i −0.527964 + 0.457230i
\(288\) 8.29180 0.488599
\(289\) −19.4164 33.6302i −1.14214 1.97825i
\(290\) 1.90983 3.30792i 0.112149 0.194248i
\(291\) −19.4721 + 33.7267i −1.14148 + 1.97710i
\(292\) −9.92705 17.1942i −0.580937 1.00621i
\(293\) −2.94427 −0.172006 −0.0860031 0.996295i \(-0.527409\pi\)
−0.0860031 + 0.996295i \(0.527409\pi\)
\(294\) 0.854102 5.91739i 0.0498122 0.345109i
\(295\) −16.7082 −0.972789
\(296\) 6.40983 + 11.1022i 0.372564 + 0.645299i
\(297\) 3.35410 5.80948i 0.194625 0.337100i
\(298\) −2.42705 + 4.20378i −0.140595 + 0.243518i
\(299\) 0 0
\(300\) 0 0
\(301\) −16.0000 + 13.8564i −0.922225 + 0.798670i
\(302\) 2.45085 0.141031
\(303\) 10.0623 + 17.4284i 0.578064 + 1.00124i
\(304\) 4.71885 8.17328i 0.270644 0.468770i
\(305\) −3.35410 + 5.80948i −0.192055 + 0.332650i
\(306\) 2.85410 + 4.94345i 0.163158 + 0.282598i
\(307\) 7.41641 0.423277 0.211638 0.977348i \(-0.432120\pi\)
0.211638 + 0.977348i \(0.432120\pi\)
\(308\) 13.9058 + 4.81710i 0.792354 + 0.274480i
\(309\) 23.9443 1.36214
\(310\) 2.13525 + 3.69837i 0.121274 + 0.210053i
\(311\) 16.1180 27.9173i 0.913970 1.58304i 0.105567 0.994412i \(-0.466334\pi\)
0.808403 0.588630i \(-0.200333\pi\)
\(312\) 0 0
\(313\) 16.2082 + 28.0734i 0.916142 + 1.58680i 0.805221 + 0.592975i \(0.202047\pi\)
0.110921 + 0.993829i \(0.464620\pi\)
\(314\) 2.67376 0.150889
\(315\) 2.23607 + 11.6190i 0.125988 + 0.654654i
\(316\) −19.8541 −1.11688
\(317\) −1.88197 3.25966i −0.105702 0.183081i 0.808323 0.588739i \(-0.200376\pi\)
−0.914025 + 0.405659i \(0.867042\pi\)
\(318\) −0.628677 + 1.08890i −0.0352545 + 0.0610625i
\(319\) 6.70820 11.6190i 0.375587 0.650536i
\(320\) 5.26393 + 9.11740i 0.294263 + 0.509678i
\(321\) −31.8328 −1.77673
\(322\) −0.718847 3.73524i −0.0400598 0.208157i
\(323\) 22.4164 1.24728
\(324\) −10.1976 17.6627i −0.566531 0.981261i
\(325\) 0 0
\(326\) 1.98936 3.44567i 0.110180 0.190838i
\(327\) 11.9721 + 20.7363i 0.662061 + 1.14672i
\(328\) 6.58359 0.363518
\(329\) 3.68034 + 1.27491i 0.202904 + 0.0702879i
\(330\) 5.72949 0.315398
\(331\) −14.2082 24.6093i −0.780954 1.35265i −0.931387 0.364031i \(-0.881400\pi\)
0.150433 0.988620i \(-0.451933\pi\)
\(332\) 0 0
\(333\) −8.70820 + 15.0831i −0.477207 + 0.826546i
\(334\) 2.58359 + 4.47491i 0.141368 + 0.244856i
\(335\) 6.70820 0.366508
\(336\) 14.0689 12.1840i 0.767521 0.664692i
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) 16.7082 28.9395i 0.907465 1.57178i
\(340\) −15.4894 + 26.8284i −0.840028 + 1.45497i
\(341\) 7.50000 + 12.9904i 0.406148 + 0.703469i
\(342\) −2.29180 −0.123926
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 11.7771 0.634978
\(345\) 9.40983 + 16.2983i 0.506608 + 0.877471i
\(346\) −1.98936 + 3.44567i −0.106948 + 0.185240i
\(347\) 17.5344 30.3705i 0.941298 1.63038i 0.178299 0.983976i \(-0.442940\pi\)
0.762999 0.646400i \(-0.223726\pi\)
\(348\) −9.27051 16.0570i −0.496951 0.860745i
\(349\) 2.58359 0.138297 0.0691483 0.997606i \(-0.477972\pi\)
0.0691483 + 0.997606i \(0.477972\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −6.21885 10.7714i −0.331466 0.574115i
\(353\) 15.3541 26.5941i 0.817216 1.41546i −0.0905091 0.995896i \(-0.528849\pi\)
0.907725 0.419565i \(-0.137817\pi\)
\(354\) 3.19098 5.52694i 0.169599 0.293754i
\(355\) 10.0000 + 17.3205i 0.530745 + 0.919277i
\(356\) −4.14590 −0.219732
\(357\) 41.7705 + 14.4697i 2.21073 + 0.765819i
\(358\) 7.68692 0.406266
\(359\) −2.97214 5.14789i −0.156863 0.271695i 0.776873 0.629658i \(-0.216805\pi\)
−0.933736 + 0.357963i \(0.883472\pi\)
\(360\) 3.29180 5.70156i 0.173493 0.300498i
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) −0.270510 0.468537i −0.0142177 0.0246257i
\(363\) −4.47214 −0.234726
\(364\) 0 0
\(365\) −23.9443 −1.25330
\(366\) −1.28115 2.21902i −0.0669669 0.115990i
\(367\) −0.354102 + 0.613323i −0.0184840 + 0.0320152i −0.875119 0.483907i \(-0.839217\pi\)
0.856635 + 0.515922i \(0.172551\pi\)
\(368\) 5.92047 10.2546i 0.308626 0.534556i
\(369\) 4.47214 + 7.74597i 0.232810 + 0.403239i
\(370\) 7.43769 0.386667
\(371\) 0.736068 + 3.82472i 0.0382147 + 0.198570i
\(372\) 20.7295 1.07477
\(373\) 14.2082 + 24.6093i 0.735673 + 1.27422i 0.954427 + 0.298443i \(0.0964673\pi\)
−0.218755 + 0.975780i \(0.570199\pi\)
\(374\) 4.28115 7.41517i 0.221373 0.383430i
\(375\) 12.5000 21.6506i 0.645497 1.11803i
\(376\) −1.08359 1.87684i −0.0558820 0.0967905i
\(377\) 0 0
\(378\) 2.13525 + 0.739674i 0.109826 + 0.0380447i
\(379\) −11.4164 −0.586421 −0.293211 0.956048i \(-0.594724\pi\)
−0.293211 + 0.956048i \(0.594724\pi\)
\(380\) −6.21885 10.7714i −0.319020 0.552559i
\(381\) −17.2361 + 29.8537i −0.883031 + 1.52945i
\(382\) 2.13525 3.69837i 0.109249 0.189225i
\(383\) 7.50000 + 12.9904i 0.383232 + 0.663777i 0.991522 0.129937i \(-0.0414776\pi\)
−0.608290 + 0.793715i \(0.708144\pi\)
\(384\) −22.5623 −1.15138
\(385\) 13.4164 11.6190i 0.683763 0.592157i
\(386\) 4.85410 0.247067
\(387\) 8.00000 + 13.8564i 0.406663 + 0.704361i
\(388\) 16.1459 27.9655i 0.819684 1.41973i
\(389\) 3.73607 6.47106i 0.189426 0.328096i −0.755633 0.654995i \(-0.772671\pi\)
0.945059 + 0.326900i \(0.106004\pi\)
\(390\) 0 0
\(391\) 28.1246 1.42232
\(392\) −1.47214 + 10.1993i −0.0743541 + 0.515140i
\(393\) −8.41641 −0.424552
\(394\) −5.14590 8.91296i −0.259247 0.449028i
\(395\) −11.9721 + 20.7363i −0.602384 + 1.04336i
\(396\) 5.56231 9.63420i 0.279516 0.484137i
\(397\) 7.06231 + 12.2323i 0.354447 + 0.613920i 0.987023 0.160578i \(-0.0513358\pi\)
−0.632576 + 0.774498i \(0.718002\pi\)
\(398\) −2.78522 −0.139610
\(399\) −13.4164 + 11.6190i −0.671660 + 0.581675i
\(400\) 0 0
\(401\) 4.88197 + 8.45581i 0.243794 + 0.422263i 0.961792 0.273782i \(-0.0882747\pi\)
−0.717998 + 0.696045i \(0.754941\pi\)
\(402\) −1.28115 + 2.21902i −0.0638981 + 0.110675i
\(403\) 0 0
\(404\) −8.34346 14.4513i −0.415103 0.718979i
\(405\) −24.5967 −1.22222
\(406\) 4.27051 + 1.47935i 0.211942 + 0.0734188i
\(407\) 26.1246 1.29495
\(408\) −12.2984 21.3014i −0.608860 1.05458i
\(409\) −2.35410 + 4.07742i −0.116403 + 0.201616i −0.918340 0.395793i \(-0.870470\pi\)
0.801937 + 0.597409i \(0.203803\pi\)
\(410\) 1.90983 3.30792i 0.0943198 0.163367i
\(411\) −4.20820 7.28882i −0.207575 0.359531i
\(412\) −19.8541 −0.978141
\(413\) −3.73607 19.4132i −0.183840 0.955260i
\(414\) −2.87539 −0.141318
\(415\) 0 0
\(416\) 0 0
\(417\) −3.81966 + 6.61585i −0.187050 + 0.323979i
\(418\) 1.71885 + 2.97713i 0.0840716 + 0.145616i
\(419\) 15.0557 0.735520 0.367760 0.929921i \(-0.380125\pi\)
0.367760 + 0.929921i \(0.380125\pi\)
\(420\) −4.63525 24.0855i −0.226177 1.17525i
\(421\) 13.4164 0.653876 0.326938 0.945046i \(-0.393983\pi\)
0.326938 + 0.945046i \(0.393983\pi\)
\(422\) −0.763932 1.32317i −0.0371876 0.0644109i
\(423\) 1.47214 2.54981i 0.0715777 0.123976i
\(424\) 1.08359 1.87684i 0.0526239 0.0911472i
\(425\) 0 0
\(426\) −7.63932 −0.370126
\(427\) −7.50000 2.59808i −0.362950 0.125730i
\(428\) 26.3951 1.27586
\(429\) 0 0
\(430\) 3.41641 5.91739i 0.164754 0.285362i
\(431\) 6.68034 11.5707i 0.321781 0.557340i −0.659075 0.752077i \(-0.729052\pi\)
0.980856 + 0.194737i \(0.0623853\pi\)
\(432\) 3.51722 + 6.09201i 0.169222 + 0.293102i
\(433\) 2.58359 0.124160 0.0620798 0.998071i \(-0.480227\pi\)
0.0620798 + 0.998071i \(0.480227\pi\)
\(434\) −3.81966 + 3.30792i −0.183350 + 0.158785i
\(435\) −22.3607 −1.07211
\(436\) −9.92705 17.1942i −0.475420 0.823451i
\(437\) −5.64590 + 9.77898i −0.270080 + 0.467792i
\(438\) 4.57295 7.92058i 0.218504 0.378460i
\(439\) 8.06231 + 13.9643i 0.384793 + 0.666481i 0.991740 0.128261i \(-0.0409395\pi\)
−0.606948 + 0.794742i \(0.707606\pi\)
\(440\) −9.87539 −0.470791
\(441\) −13.0000 + 5.19615i −0.619048 + 0.247436i
\(442\) 0 0
\(443\) 1.11803 + 1.93649i 0.0531194 + 0.0920055i 0.891362 0.453291i \(-0.149750\pi\)
−0.838243 + 0.545297i \(0.816417\pi\)
\(444\) 18.0517 31.2664i 0.856694 1.48384i
\(445\) −2.50000 + 4.33013i −0.118511 + 0.205268i
\(446\) −0.763932 1.32317i −0.0361732 0.0626539i
\(447\) 28.4164 1.34405
\(448\) −9.41641 + 8.15485i −0.444883 + 0.385280i
\(449\) −10.3607 −0.488951 −0.244475 0.969656i \(-0.578616\pi\)
−0.244475 + 0.969656i \(0.578616\pi\)
\(450\) 0 0
\(451\) 6.70820 11.6190i 0.315877 0.547115i
\(452\) −13.8541 + 23.9960i −0.651642 + 1.12868i
\(453\) −7.17376 12.4253i −0.337053 0.583792i
\(454\) 4.56231 0.214120
\(455\) 0 0
\(456\) 9.87539 0.462457
\(457\) 17.0623 + 29.5528i 0.798141 + 1.38242i 0.920825 + 0.389975i \(0.127516\pi\)
−0.122684 + 0.992446i \(0.539150\pi\)
\(458\) −3.07953 + 5.33390i −0.143897 + 0.249237i
\(459\) −8.35410 + 14.4697i −0.389936 + 0.675389i
\(460\) −7.80244 13.5142i −0.363791 0.630104i
\(461\) 10.3607 0.482545 0.241272 0.970457i \(-0.422435\pi\)
0.241272 + 0.970457i \(0.422435\pi\)
\(462\) 1.28115 + 6.65707i 0.0596046 + 0.309715i
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 7.03444 + 12.1840i 0.326566 + 0.565628i
\(465\) 12.5000 21.6506i 0.579674 1.00402i
\(466\) 1.13525 1.96632i 0.0525897 0.0910880i
\(467\) 10.8262 + 18.7516i 0.500979 + 0.867720i 0.999999 + 0.00113029i \(0.000359784\pi\)
−0.499021 + 0.866590i \(0.666307\pi\)
\(468\) 0 0
\(469\) 1.50000 + 7.79423i 0.0692636 + 0.359904i
\(470\) −1.25735 −0.0579974
\(471\) −7.82624 13.5554i −0.360614 0.624602i
\(472\) −5.50000 + 9.52628i −0.253158 + 0.438483i
\(473\) 12.0000 20.7846i 0.551761 0.955677i
\(474\) −4.57295 7.92058i −0.210043 0.363804i
\(475\) 0 0
\(476\) −34.6353 11.9980i −1.58750 0.549928i
\(477\) 2.94427 0.134809
\(478\) −1.41641 2.45329i −0.0647850 0.112211i
\(479\) −14.9164 + 25.8360i −0.681548 + 1.18048i 0.292960 + 0.956125i \(0.405360\pi\)
−0.974508 + 0.224351i \(0.927974\pi\)
\(480\) −10.3647 + 17.9523i −0.473084 + 0.819405i
\(481\) 0 0
\(482\) 3.32624 0.151506
\(483\) −16.8328 + 14.5776i −0.765920 + 0.663306i
\(484\) 3.70820 0.168555
\(485\) −19.4721 33.7267i −0.884184 1.53145i
\(486\) 3.41641 5.91739i 0.154971 0.268418i
\(487\) 15.9164 27.5680i 0.721241 1.24923i −0.239261 0.970955i \(-0.576905\pi\)
0.960503 0.278271i \(-0.0897614\pi\)
\(488\) 2.20820 + 3.82472i 0.0999607 + 0.173137i
\(489\) −23.2918 −1.05329
\(490\) 4.69756 + 3.69837i 0.212214 + 0.167075i
\(491\) −34.4721 −1.55571 −0.777853 0.628446i \(-0.783691\pi\)
−0.777853 + 0.628446i \(0.783691\pi\)
\(492\) −9.27051 16.0570i −0.417947 0.723905i
\(493\) −16.7082 + 28.9395i −0.752500 + 1.30337i
\(494\) 0 0
\(495\) −6.70820 11.6190i −0.301511 0.522233i
\(496\) −15.7295 −0.706275
\(497\) −17.8885 + 15.4919i −0.802411 + 0.694908i
\(498\) 0 0
\(499\) −0.208204 0.360620i −0.00932049 0.0161436i 0.861328 0.508050i \(-0.169634\pi\)
−0.870648 + 0.491907i \(0.836300\pi\)
\(500\) −10.3647 + 17.9523i −0.463525 + 0.802850i
\(501\) 15.1246 26.1966i 0.675718 1.17038i
\(502\) −2.00000 3.46410i −0.0892644 0.154610i
\(503\) 3.05573 0.136248 0.0681241 0.997677i \(-0.478299\pi\)
0.0681241 + 0.997677i \(0.478299\pi\)
\(504\) 7.36068 + 2.54981i 0.327871 + 0.113578i
\(505\) −20.1246 −0.895533
\(506\) 2.15654 + 3.73524i 0.0958699 + 0.166052i
\(507\) 0 0
\(508\) 14.2918 24.7541i 0.634096 1.09829i
\(509\) −7.88197 13.6520i −0.349362 0.605113i 0.636774 0.771050i \(-0.280268\pi\)
−0.986136 + 0.165938i \(0.946935\pi\)
\(510\) −14.2705 −0.631909
\(511\) −5.35410 27.8207i −0.236852 1.23072i
\(512\) 22.3050 0.985749
\(513\) −3.35410 5.80948i −0.148087 0.256495i
\(514\) 3.42705 5.93583i 0.151161 0.261818i
\(515\) −11.9721 + 20.7363i −0.527555 + 0.913753i
\(516\) −16.5836 28.7236i −0.730052 1.26449i
\(517\) −4.41641 −0.194233
\(518\) 1.66312 + 8.64182i 0.0730733 + 0.379700i
\(519\) 23.2918 1.02240
\(520\) 0 0
\(521\) 0.0278640 0.0482619i 0.00122075 0.00211439i −0.865414 0.501057i \(-0.832945\pi\)
0.866635 + 0.498942i \(0.166278\pi\)
\(522\) 1.70820 2.95870i 0.0747661 0.129499i
\(523\) −9.64590 16.7072i −0.421786 0.730554i 0.574329 0.818625i \(-0.305263\pi\)
−0.996114 + 0.0880707i \(0.971930\pi\)
\(524\) 6.97871 0.304867
\(525\) 0 0
\(526\) −5.39512 −0.235238
\(527\) −18.6803 32.3553i −0.813728 1.40942i
\(528\) −10.5517 + 18.2760i −0.459202 + 0.795362i
\(529\) 4.41641 7.64944i 0.192018 0.332584i
\(530\) −0.628677 1.08890i −0.0273080 0.0472988i
\(531\) −14.9443 −0.648526
\(532\) 11.1246 9.63420i 0.482313 0.417695i
\(533\) 0 0
\(534\) −0.954915 1.65396i −0.0413232 0.0715739i
\(535\) 15.9164 27.5680i 0.688126 1.19187i
\(536\) 2.20820 3.82472i 0.0953799 0.165203i
\(537\) −22.5000 38.9711i −0.970947 1.68173i
\(538\) 1.72949 0.0745636
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) 9.27051 0.398939
\(541\) 7.35410 + 12.7377i 0.316178 + 0.547636i 0.979687 0.200532i \(-0.0642671\pi\)
−0.663510 + 0.748168i \(0.730934\pi\)
\(542\) 1.22542 2.12250i 0.0526365 0.0911691i
\(543\) −1.58359 + 2.74286i −0.0679584 + 0.117707i
\(544\) 15.4894 + 26.8284i 0.664101 + 1.15026i
\(545\) −23.9443 −1.02566
\(546\) 0 0
\(547\) −31.4164 −1.34327 −0.671634 0.740883i \(-0.734407\pi\)
−0.671634 + 0.740883i \(0.734407\pi\)
\(548\) 3.48936 + 6.04374i 0.149058 + 0.258176i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) 0 0
\(551\) −6.70820 11.6190i −0.285779 0.494984i
\(552\) 12.3901 0.527358
\(553\) −26.7705 9.27358i −1.13840 0.394353i
\(554\) 10.0902 0.428690
\(555\) −21.7705 37.7076i −0.924107 1.60060i
\(556\) 3.16718 5.48572i 0.134319 0.232647i
\(557\) −2.64590 + 4.58283i −0.112110 + 0.194181i −0.916621 0.399758i \(-0.869094\pi\)
0.804511 + 0.593938i \(0.202428\pi\)
\(558\) 1.90983 + 3.30792i 0.0808496 + 0.140036i
\(559\) 0 0
\(560\) 3.51722 + 18.2760i 0.148630 + 0.772303i
\(561\) −50.1246 −2.11626
\(562\) 1.72949 + 2.99556i 0.0729541 + 0.126360i
\(563\) 18.2984 31.6937i 0.771185 1.33573i −0.165730 0.986171i \(-0.552998\pi\)
0.936914 0.349560i \(-0.113669\pi\)
\(564\) −3.05166 + 5.28563i −0.128498 + 0.222565i
\(565\) 16.7082 + 28.9395i 0.702919 + 1.21749i
\(566\) −5.39512 −0.226774
\(567\) −5.50000 28.5788i −0.230978 1.20020i
\(568\) 13.1672 0.552483
\(569\) −8.26393 14.3136i −0.346442 0.600055i 0.639173 0.769063i \(-0.279277\pi\)
−0.985615 + 0.169008i \(0.945944\pi\)
\(570\) 2.86475 4.96188i 0.119991 0.207830i
\(571\) −2.06231 + 3.57202i −0.0863048 + 0.149484i −0.905946 0.423392i \(-0.860839\pi\)
0.819642 + 0.572877i \(0.194173\pi\)
\(572\) 0 0
\(573\) −25.0000 −1.04439
\(574\) 4.27051 + 1.47935i 0.178248 + 0.0617468i
\(575\) 0 0
\(576\) 4.70820 + 8.15485i 0.196175 + 0.339785i
\(577\) −16.3541 + 28.3261i −0.680830 + 1.17923i 0.293898 + 0.955837i \(0.405047\pi\)
−0.974728 + 0.223396i \(0.928286\pi\)
\(578\) −7.41641 + 12.8456i −0.308482 + 0.534306i
\(579\) −14.2082 24.6093i −0.590473 1.02273i
\(580\) 18.5410 0.769874
\(581\) 0 0
\(582\) 14.8754 0.616605
\(583\) −2.20820 3.82472i −0.0914545 0.158404i
\(584\) −7.88197 + 13.6520i −0.326158 + 0.564922i
\(585\) 0 0
\(586\) 0.562306 + 0.973942i 0.0232286 + 0.0402332i
\(587\) 41.8885 1.72893 0.864463 0.502697i \(-0.167659\pi\)
0.864463 + 0.502697i \(0.167659\pi\)
\(588\) 26.9483 10.7714i 1.11133 0.444203i
\(589\) 15.0000 0.618064
\(590\) 3.19098 + 5.52694i 0.131371 + 0.227541i
\(591\) −30.1246 + 52.1774i −1.23916 + 2.14629i
\(592\) −13.6976 + 23.7249i −0.562966 + 0.975086i
\(593\) 16.1180 + 27.9173i 0.661888 + 1.14642i 0.980119 + 0.198411i \(0.0635780\pi\)
−0.318231 + 0.948013i \(0.603089\pi\)
\(594\) −2.56231 −0.105133
\(595\) −33.4164 + 28.9395i −1.36994 + 1.18640i
\(596\) −23.5623 −0.965150
\(597\) 8.15248 + 14.1205i 0.333659 + 0.577914i
\(598\) 0 0
\(599\) −20.5344 + 35.5667i −0.839015 + 1.45322i 0.0517049 + 0.998662i \(0.483534\pi\)
−0.890719 + 0.454553i \(0.849799\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 7.63932 + 2.64634i 0.311355 + 0.107857i
\(603\) 6.00000 0.244339
\(604\) 5.94834 + 10.3028i 0.242034 + 0.419216i
\(605\) 2.23607 3.87298i 0.0909091 0.157459i
\(606\) 3.84346 6.65707i 0.156130 0.270425i
\(607\) 8.06231 + 13.9643i 0.327239 + 0.566794i 0.981963 0.189074i \(-0.0605485\pi\)
−0.654724 + 0.755868i \(0.727215\pi\)
\(608\) −12.4377 −0.504415
\(609\) −5.00000 25.9808i −0.202610 1.05279i
\(610\) 2.56231 0.103745
\(611\) 0 0
\(612\) −13.8541 + 23.9960i −0.560019 + 0.969981i
\(613\) 11.0623 19.1605i 0.446802 0.773884i −0.551373 0.834259i \(-0.685896\pi\)
0.998176 + 0.0603742i \(0.0192294\pi\)
\(614\) −1.41641 2.45329i −0.0571616 0.0990067i
\(615\) −22.3607 −0.901670
\(616\) −2.20820 11.4742i −0.0889711 0.462307i
\(617\) −4.47214 −0.180041 −0.0900207 0.995940i \(-0.528693\pi\)
−0.0900207 + 0.995940i \(0.528693\pi\)
\(618\) −4.57295 7.92058i −0.183951 0.318612i
\(619\) 8.50000 14.7224i 0.341644 0.591744i −0.643094 0.765787i \(-0.722350\pi\)
0.984738 + 0.174042i \(0.0556830\pi\)
\(620\) −10.3647 + 17.9523i −0.416258 + 0.720980i
\(621\) −4.20820 7.28882i −0.168869 0.292490i
\(622\) −12.3131 −0.493710
\(623\) −5.59017 1.93649i −0.223965 0.0775839i
\(624\) 0 0
\(625\) 12.5000 + 21.6506i 0.500000 + 0.866025i
\(626\) 6.19098 10.7231i 0.247441 0.428581i
\(627\) 10.0623 17.4284i 0.401850 0.696024i
\(628\) 6.48936 + 11.2399i 0.258954 + 0.448521i
\(629\) −65.0689 −2.59447
\(630\) 3.41641 2.95870i 0.136113 0.117877i
\(631\) 30.8328 1.22744 0.613718 0.789526i \(-0.289673\pi\)
0.613718 + 0.789526i \(0.289673\pi\)
\(632\) 7.88197 + 13.6520i 0.313528 + 0.543046i
\(633\) −4.47214 + 7.74597i −0.177751 + 0.307875i
\(634\) −0.718847 + 1.24508i −0.0285491 + 0.0494484i
\(635\) −17.2361 29.8537i −0.683992 1.18471i
\(636\) −6.10333 −0.242013
\(637\) 0 0
\(638\) −5.12461 −0.202885
\(639\) 8.94427 + 15.4919i 0.353830 + 0.612851i
\(640\) 11.2812 19.5395i 0.445927 0.772368i
\(641\) 2.97214 5.14789i 0.117392 0.203329i −0.801341 0.598208i \(-0.795880\pi\)
0.918734 + 0.394878i \(0.129213\pi\)
\(642\) 6.07953 + 10.5300i 0.239940 + 0.415588i
\(643\) 18.8328 0.742694 0.371347 0.928494i \(-0.378896\pi\)
0.371347 + 0.928494i \(0.378896\pi\)
\(644\) 13.9574 12.0875i 0.550000 0.476314i
\(645\) −40.0000 −1.57500
\(646\) −4.28115 7.41517i −0.168440 0.291746i
\(647\) −7.88197 + 13.6520i −0.309872 + 0.536714i −0.978334 0.207032i \(-0.933620\pi\)
0.668462 + 0.743746i \(0.266953\pi\)
\(648\) −8.09675 + 14.0240i −0.318070 + 0.550914i
\(649\) 11.2082 + 19.4132i 0.439960 + 0.762034i
\(650\) 0 0
\(651\) 27.9508 + 9.68246i 1.09548 + 0.379485i
\(652\) 19.3131 0.756359
\(653\) −6.73607 11.6672i −0.263603 0.456573i 0.703594 0.710602i \(-0.251577\pi\)
−0.967197 + 0.254029i \(0.918244\pi\)
\(654\) 4.57295 7.92058i 0.178816 0.309719i
\(655\) 4.20820 7.28882i 0.164428 0.284798i
\(656\) 7.03444 + 12.1840i 0.274649 + 0.475706i
\(657\) −21.4164 −0.835534
\(658\) −0.281153 1.46091i −0.0109605 0.0569523i
\(659\) 8.94427 0.348419 0.174210 0.984709i \(-0.444263\pi\)
0.174210 + 0.984709i \(0.444263\pi\)
\(660\) 13.9058 + 24.0855i 0.541281 + 0.937526i
\(661\) 3.35410 5.80948i 0.130459 0.225962i −0.793394 0.608708i \(-0.791688\pi\)
0.923854 + 0.382746i \(0.125021\pi\)
\(662\) −5.42705 + 9.39993i −0.210928 + 0.365339i
\(663\) 0 0
\(664\) 0 0
\(665\) −3.35410 17.4284i −0.130066 0.675845i
\(666\) 6.65248 0.257778
\(667\) −8.41641 14.5776i −0.325885 0.564449i
\(668\) −12.5410 + 21.7217i −0.485227 + 0.840437i
\(669\) −4.47214 + 7.74597i −0.172903 + 0.299476i
\(670\) −1.28115 2.21902i −0.0494953 0.0857283i
\(671\) 9.00000 0.347441
\(672\) −23.1763 8.02850i −0.894044 0.309706i
\(673\) 17.4164 0.671353 0.335677 0.941977i \(-0.391035\pi\)
0.335677 + 0.941977i \(0.391035\pi\)
\(674\) −3.43769 5.95426i −0.132415 0.229350i
\(675\) 0 0
\(676\) 0 0
\(677\) −16.4443 28.4823i −0.632005 1.09466i −0.987141 0.159850i \(-0.948899\pi\)
0.355137 0.934814i \(-0.384434\pi\)
\(678\) −12.7639 −0.490196
\(679\) 34.8328 30.1661i 1.33676 1.15767i
\(680\) 24.5967 0.943242
\(681\) −13.3541 23.1300i −0.511730 0.886343i
\(682\) 2.86475 4.96188i 0.109697 0.190000i
\(683\) −2.26393 + 3.92125i −0.0866270 + 0.150042i −0.906083 0.423099i \(-0.860942\pi\)
0.819456 + 0.573142i \(0.194275\pi\)
\(684\) −5.56231 9.63420i −0.212680 0.368373i
\(685\) 8.41641 0.321574
\(686\) −3.24671 + 6.28505i −0.123960 + 0.239964i
\(687\) 36.0557 1.37561
\(688\) 12.5836 + 21.7954i 0.479745 + 0.830943i
\(689\) 0 0
\(690\) 3.59424 6.22540i 0.136830 0.236997i
\(691\) 0.916408 + 1.58726i 0.0348618 + 0.0603824i 0.882930 0.469505i \(-0.155568\pi\)
−0.848068 + 0.529887i \(0.822234\pi\)
\(692\) −19.3131 −0.734173
\(693\) 12.0000 10.3923i 0.455842 0.394771i
\(694\) −13.3951 −0.508472
\(695\) −3.81966 6.61585i −0.144888 0.250953i
\(696\) −7.36068 + 12.7491i −0.279006 + 0.483252i
\(697\) −16.7082 + 28.9395i −0.632868 + 1.09616i
\(698\) −0.493422 0.854632i −0.0186763 0.0323483i
\(699\) −13.2918 −0.502742
\(700\) 0 0
\(701\) 22.3607 0.844551 0.422276 0.906467i \(-0.361231\pi\)
0.422276 + 0.906467i \(0.361231\pi\)
\(702\) 0 0
\(703\) 13.0623 22.6246i 0.492654 0.853302i
\(704\) 7.06231 12.2323i 0.266171 0.461021i
\(705\) 3.68034 + 6.37454i 0.138610 + 0.240079i
\(706\) −11.7295 −0.441445
\(707\) −4.50000 23.3827i −0.169240 0.879396i
\(708\) 30.9787 1.16425
\(709\) −4.93769 8.55234i −0.185439 0.321190i 0.758285 0.651923i \(-0.226037\pi\)
−0.943724 + 0.330733i \(0.892704\pi\)
\(710\) 3.81966 6.61585i 0.143349 0.248288i
\(711\) −10.7082 + 18.5472i −0.401589 + 0.695573i
\(712\) 1.64590 + 2.85078i 0.0616826 + 0.106837i
\(713\) 18.8197 0.704802
\(714\) −3.19098 16.5808i −0.119420 0.620522i
\(715\) 0 0
\(716\) 18.6565 + 32.3141i 0.697228 + 1.20763i
\(717\) −8.29180 + 14.3618i −0.309663 + 0.536352i
\(718\) −1.13525 + 1.96632i −0.0423673 + 0.0733824i
\(719\) −5.64590 9.77898i −0.210556 0.364694i 0.741332 0.671138i \(-0.234194\pi\)
−0.951889 + 0.306444i \(0.900861\pi\)
\(720\) 14.0689 0.524316
\(721\) −26.7705 9.27358i −0.996986 0.345366i
\(722\) −3.81966 −0.142153
\(723\) −9.73607 16.8634i −0.362088 0.627155i
\(724\) 1.31308 2.27433i 0.0488003 0.0845246i
\(725\) 0 0
\(726\) 0.854102 + 1.47935i 0.0316987 + 0.0549038i
\(727\) 14.8328 0.550119 0.275059 0.961427i \(-0.411302\pi\)
0.275059 + 0.961427i \(0.411302\pi\)
\(728\) 0 0
\(729\) −7.00000 −0.259259
\(730\) 4.57295 + 7.92058i 0.169252 + 0.293154i
\(731\) −29.8885 + 51.7685i −1.10547 + 1.91473i
\(732\) 6.21885 10.7714i 0.229855 0.398121i
\(733\) 7.64590 + 13.2431i 0.282408 + 0.489144i 0.971977 0.235075i \(-0.0755336\pi\)
−0.689570 + 0.724219i \(0.742200\pi\)
\(734\) 0.270510 0.00998470
\(735\) 5.00000 34.6410i 0.184428 1.27775i
\(736\) −15.6049 −0.575203
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) 1.70820 2.95870i 0.0628799 0.108911i
\(739\) 17.9164 31.0321i 0.659066 1.14154i −0.321792 0.946810i \(-0.604285\pi\)
0.980858 0.194725i \(-0.0623814\pi\)
\(740\) 18.0517 + 31.2664i 0.663592 + 1.14938i
\(741\) 0 0
\(742\) 1.12461 0.973942i 0.0412858 0.0357545i
\(743\) −15.0557 −0.552341 −0.276171 0.961109i \(-0.589065\pi\)
−0.276171 + 0.961109i \(0.589065\pi\)
\(744\) −8.22949 14.2539i −0.301708 0.522573i
\(745\) −14.2082 + 24.6093i −0.520548 + 0.901616i
\(746\) 5.42705 9.39993i 0.198698 0.344156i
\(747\) 0 0
\(748\) 41.5623 1.51967
\(749\) 35.5902 + 12.3288i 1.30044 + 0.450484i
\(750\) −9.54915 −0.348686
\(751\) −15.0623 26.0887i −0.549631 0.951989i −0.998300 0.0582911i \(-0.981435\pi\)
0.448668 0.893698i \(-0.351898\pi\)
\(752\) 2.31559 4.01073i 0.0844411 0.146256i
\(753\) −11.7082 + 20.2792i −0.426671 + 0.739015i
\(754\) 0 0
\(755\) 14.3475 0.522160
\(756\) 2.07295 + 10.7714i 0.0753924 + 0.391751i
\(757\) 0.832816 0.0302692 0.0151346 0.999885i \(-0.495182\pi\)
0.0151346 + 0.999885i \(0.495182\pi\)
\(758\) 2.18034 + 3.77646i 0.0791935 + 0.137167i
\(759\) 12.6246 21.8665i 0.458244 0.793703i
\(760\) −4.93769 + 8.55234i −0.179109 + 0.310226i
\(761\) 16.7705 + 29.0474i 0.607931 + 1.05297i 0.991581 + 0.129488i \(0.0413334\pi\)
−0.383650 + 0.923478i \(0.625333\pi\)
\(762\) 13.1672 0.476997
\(763\) −5.35410 27.8207i −0.193832 1.00718i
\(764\) 20.7295 0.749967
\(765\) 16.7082 + 28.9395i 0.604086 + 1.04631i
\(766\) 2.86475 4.96188i 0.103507 0.179280i
\(767\) 0 0
\(768\) −6.21885 10.7714i −0.224403 0.388678i
\(769\) −46.0000 −1.65880 −0.829401 0.558653i \(-0.811318\pi\)
−0.829401 + 0.558653i \(0.811318\pi\)
\(770\) −6.40576 2.21902i −0.230848 0.0799680i
\(771\) −40.1246 −1.44505
\(772\) 11.7812 + 20.4056i 0.424013 + 0.734412i
\(773\) 5.53444 9.58593i 0.199060 0.344782i −0.749164 0.662385i \(-0.769544\pi\)
0.948224 + 0.317603i \(0.102878\pi\)
\(774\) 3.05573 5.29268i 0.109836 0.190241i
\(775\) 0 0
\(776\) −25.6393 −0.920398
\(777\) 38.9443 33.7267i 1.39712 1.20994i
\(778\) −2.85410 −0.102325
\(779\) −6.70820 11.6190i −0.240346 0.416292i
\(780\)