Properties

Label 65.2.k.a.8.1
Level 65
Weight 2
Character 65.8
Analytic conductor 0.519
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 65.k (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.1
Root \(1.00000i\)
Character \(\chi\) = 65.8
Dual form 65.2.k.a.57.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.00000 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +(1.00000 + 1.00000i) q^{6} +2.00000i q^{7} -3.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.00000 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +(1.00000 + 1.00000i) q^{6} +2.00000i q^{7} -3.00000 q^{8} -1.00000i q^{9} +(-1.00000 - 2.00000i) q^{10} +(-1.00000 + 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{12} +(3.00000 - 2.00000i) q^{13} +2.00000i q^{14} +(1.00000 - 3.00000i) q^{15} -1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} -1.00000i q^{18} +(-5.00000 + 5.00000i) q^{19} +(1.00000 + 2.00000i) q^{20} +(-2.00000 + 2.00000i) q^{21} +(-1.00000 + 1.00000i) q^{22} +(3.00000 - 3.00000i) q^{23} +(-3.00000 - 3.00000i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(3.00000 - 2.00000i) q^{26} +(4.00000 - 4.00000i) q^{27} -2.00000i q^{28} +(1.00000 - 3.00000i) q^{30} +(5.00000 + 5.00000i) q^{31} +5.00000 q^{32} -2.00000 q^{33} +(1.00000 + 1.00000i) q^{34} +(4.00000 - 2.00000i) q^{35} +1.00000i q^{36} +(-5.00000 + 5.00000i) q^{38} +(5.00000 + 1.00000i) q^{39} +(3.00000 + 6.00000i) q^{40} +(-7.00000 - 7.00000i) q^{41} +(-2.00000 + 2.00000i) q^{42} +(-1.00000 + 1.00000i) q^{43} +(1.00000 - 1.00000i) q^{44} +(-2.00000 + 1.00000i) q^{45} +(3.00000 - 3.00000i) q^{46} -6.00000i q^{47} +(-1.00000 - 1.00000i) q^{48} +3.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} +2.00000i q^{51} +(-3.00000 + 2.00000i) q^{52} +(5.00000 + 5.00000i) q^{53} +(4.00000 - 4.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} -6.00000i q^{56} -10.0000 q^{57} +(-7.00000 - 7.00000i) q^{59} +(-1.00000 + 3.00000i) q^{60} -14.0000 q^{61} +(5.00000 + 5.00000i) q^{62} +2.00000 q^{63} +7.00000 q^{64} +(-7.00000 - 4.00000i) q^{65} -2.00000 q^{66} -4.00000 q^{67} +(-1.00000 - 1.00000i) q^{68} +6.00000 q^{69} +(4.00000 - 2.00000i) q^{70} +(1.00000 + 1.00000i) q^{71} +3.00000i q^{72} -10.0000 q^{73} +(-7.00000 + 1.00000i) q^{75} +(5.00000 - 5.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +(5.00000 + 1.00000i) q^{78} +2.00000i q^{79} +(1.00000 + 2.00000i) q^{80} +5.00000 q^{81} +(-7.00000 - 7.00000i) q^{82} +6.00000i q^{83} +(2.00000 - 2.00000i) q^{84} +(1.00000 - 3.00000i) q^{85} +(-1.00000 + 1.00000i) q^{86} +(3.00000 - 3.00000i) q^{88} +(5.00000 + 5.00000i) q^{89} +(-2.00000 + 1.00000i) q^{90} +(4.00000 + 6.00000i) q^{91} +(-3.00000 + 3.00000i) q^{92} +10.0000i q^{93} -6.00000i q^{94} +(15.0000 + 5.00000i) q^{95} +(5.00000 + 5.00000i) q^{96} +2.00000 q^{97} +3.00000 q^{98} +(1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 6q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 6q^{8} - 2q^{10} - 2q^{11} - 2q^{12} + 6q^{13} + 2q^{15} - 2q^{16} + 2q^{17} - 10q^{19} + 2q^{20} - 4q^{21} - 2q^{22} + 6q^{23} - 6q^{24} - 6q^{25} + 6q^{26} + 8q^{27} + 2q^{30} + 10q^{31} + 10q^{32} - 4q^{33} + 2q^{34} + 8q^{35} - 10q^{38} + 10q^{39} + 6q^{40} - 14q^{41} - 4q^{42} - 2q^{43} + 2q^{44} - 4q^{45} + 6q^{46} - 2q^{48} + 6q^{49} - 6q^{50} - 6q^{52} + 10q^{53} + 8q^{54} + 6q^{55} - 20q^{57} - 14q^{59} - 2q^{60} - 28q^{61} + 10q^{62} + 4q^{63} + 14q^{64} - 14q^{65} - 4q^{66} - 8q^{67} - 2q^{68} + 12q^{69} + 8q^{70} + 2q^{71} - 20q^{73} - 14q^{75} + 10q^{76} - 4q^{77} + 10q^{78} + 2q^{80} + 10q^{81} - 14q^{82} + 4q^{84} + 2q^{85} - 2q^{86} + 6q^{88} + 10q^{89} - 4q^{90} + 8q^{91} - 6q^{92} + 30q^{95} + 10q^{96} + 4q^{97} + 6q^{98} + 2q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i \(-0.116140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 1.00000 + 1.00000i 0.408248 + 0.408248i
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) −3.00000 −1.06066
\(9\) 1.00000i 0.333333i
\(10\) −1.00000 2.00000i −0.316228 0.632456i
\(11\) −1.00000 + 1.00000i −0.301511 + 0.301511i −0.841605 0.540094i \(-0.818389\pi\)
0.540094 + 0.841605i \(0.318389\pi\)
\(12\) −1.00000 1.00000i −0.288675 0.288675i
\(13\) 3.00000 2.00000i 0.832050 0.554700i
\(14\) 2.00000i 0.534522i
\(15\) 1.00000 3.00000i 0.258199 0.774597i
\(16\) −1.00000 −0.250000
\(17\) 1.00000 + 1.00000i 0.242536 + 0.242536i 0.817898 0.575363i \(-0.195139\pi\)
−0.575363 + 0.817898i \(0.695139\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −5.00000 + 5.00000i −1.14708 + 1.14708i −0.159954 + 0.987124i \(0.551135\pi\)
−0.987124 + 0.159954i \(0.948865\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) −2.00000 + 2.00000i −0.436436 + 0.436436i
\(22\) −1.00000 + 1.00000i −0.213201 + 0.213201i
\(23\) 3.00000 3.00000i 0.625543 0.625543i −0.321400 0.946943i \(-0.604153\pi\)
0.946943 + 0.321400i \(0.104153\pi\)
\(24\) −3.00000 3.00000i −0.612372 0.612372i
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 3.00000 2.00000i 0.588348 0.392232i
\(27\) 4.00000 4.00000i 0.769800 0.769800i
\(28\) 2.00000i 0.377964i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 1.00000 3.00000i 0.182574 0.547723i
\(31\) 5.00000 + 5.00000i 0.898027 + 0.898027i 0.995261 0.0972349i \(-0.0309998\pi\)
−0.0972349 + 0.995261i \(0.531000\pi\)
\(32\) 5.00000 0.883883
\(33\) −2.00000 −0.348155
\(34\) 1.00000 + 1.00000i 0.171499 + 0.171499i
\(35\) 4.00000 2.00000i 0.676123 0.338062i
\(36\) 1.00000i 0.166667i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −5.00000 + 5.00000i −0.811107 + 0.811107i
\(39\) 5.00000 + 1.00000i 0.800641 + 0.160128i
\(40\) 3.00000 + 6.00000i 0.474342 + 0.948683i
\(41\) −7.00000 7.00000i −1.09322 1.09322i −0.995183 0.0980332i \(-0.968745\pi\)
−0.0980332 0.995183i \(-0.531255\pi\)
\(42\) −2.00000 + 2.00000i −0.308607 + 0.308607i
\(43\) −1.00000 + 1.00000i −0.152499 + 0.152499i −0.779233 0.626734i \(-0.784391\pi\)
0.626734 + 0.779233i \(0.284391\pi\)
\(44\) 1.00000 1.00000i 0.150756 0.150756i
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) 3.00000 3.00000i 0.442326 0.442326i
\(47\) 6.00000i 0.875190i −0.899172 0.437595i \(-0.855830\pi\)
0.899172 0.437595i \(-0.144170\pi\)
\(48\) −1.00000 1.00000i −0.144338 0.144338i
\(49\) 3.00000 0.428571
\(50\) −3.00000 + 4.00000i −0.424264 + 0.565685i
\(51\) 2.00000i 0.280056i
\(52\) −3.00000 + 2.00000i −0.416025 + 0.277350i
\(53\) 5.00000 + 5.00000i 0.686803 + 0.686803i 0.961524 0.274721i \(-0.0885855\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 4.00000 4.00000i 0.544331 0.544331i
\(55\) 3.00000 + 1.00000i 0.404520 + 0.134840i
\(56\) 6.00000i 0.801784i
\(57\) −10.0000 −1.32453
\(58\) 0 0
\(59\) −7.00000 7.00000i −0.911322 0.911322i 0.0850540 0.996376i \(-0.472894\pi\)
−0.996376 + 0.0850540i \(0.972894\pi\)
\(60\) −1.00000 + 3.00000i −0.129099 + 0.387298i
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 5.00000 + 5.00000i 0.635001 + 0.635001i
\(63\) 2.00000 0.251976
\(64\) 7.00000 0.875000
\(65\) −7.00000 4.00000i −0.868243 0.496139i
\(66\) −2.00000 −0.246183
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −1.00000 1.00000i −0.121268 0.121268i
\(69\) 6.00000 0.722315
\(70\) 4.00000 2.00000i 0.478091 0.239046i
\(71\) 1.00000 + 1.00000i 0.118678 + 0.118678i 0.763952 0.645273i \(-0.223257\pi\)
−0.645273 + 0.763952i \(0.723257\pi\)
\(72\) 3.00000i 0.353553i
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) −7.00000 + 1.00000i −0.808290 + 0.115470i
\(76\) 5.00000 5.00000i 0.573539 0.573539i
\(77\) −2.00000 2.00000i −0.227921 0.227921i
\(78\) 5.00000 + 1.00000i 0.566139 + 0.113228i
\(79\) 2.00000i 0.225018i 0.993651 + 0.112509i \(0.0358886\pi\)
−0.993651 + 0.112509i \(0.964111\pi\)
\(80\) 1.00000 + 2.00000i 0.111803 + 0.223607i
\(81\) 5.00000 0.555556
\(82\) −7.00000 7.00000i −0.773021 0.773021i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 2.00000 2.00000i 0.218218 0.218218i
\(85\) 1.00000 3.00000i 0.108465 0.325396i
\(86\) −1.00000 + 1.00000i −0.107833 + 0.107833i
\(87\) 0 0
\(88\) 3.00000 3.00000i 0.319801 0.319801i
\(89\) 5.00000 + 5.00000i 0.529999 + 0.529999i 0.920572 0.390573i \(-0.127723\pi\)
−0.390573 + 0.920572i \(0.627723\pi\)
\(90\) −2.00000 + 1.00000i −0.210819 + 0.105409i
\(91\) 4.00000 + 6.00000i 0.419314 + 0.628971i
\(92\) −3.00000 + 3.00000i −0.312772 + 0.312772i
\(93\) 10.0000i 1.03695i
\(94\) 6.00000i 0.618853i
\(95\) 15.0000 + 5.00000i 1.53897 + 0.512989i
\(96\) 5.00000 + 5.00000i 0.510310 + 0.510310i
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 3.00000 0.303046
\(99\) 1.00000 + 1.00000i 0.100504 + 0.100504i
\(100\) 3.00000 4.00000i 0.300000 0.400000i
\(101\) 12.0000i 1.19404i −0.802225 0.597022i \(-0.796350\pi\)
0.802225 0.597022i \(-0.203650\pi\)
\(102\) 2.00000i 0.198030i
\(103\) 7.00000 7.00000i 0.689730 0.689730i −0.272442 0.962172i \(-0.587831\pi\)
0.962172 + 0.272442i \(0.0878312\pi\)
\(104\) −9.00000 + 6.00000i −0.882523 + 0.588348i
\(105\) 6.00000 + 2.00000i 0.585540 + 0.195180i
\(106\) 5.00000 + 5.00000i 0.485643 + 0.485643i
\(107\) 7.00000 7.00000i 0.676716 0.676716i −0.282540 0.959256i \(-0.591177\pi\)
0.959256 + 0.282540i \(0.0911770\pi\)
\(108\) −4.00000 + 4.00000i −0.384900 + 0.384900i
\(109\) 9.00000 9.00000i 0.862044 0.862044i −0.129532 0.991575i \(-0.541347\pi\)
0.991575 + 0.129532i \(0.0413474\pi\)
\(110\) 3.00000 + 1.00000i 0.286039 + 0.0953463i
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) 5.00000 + 5.00000i 0.470360 + 0.470360i 0.902031 0.431671i \(-0.142076\pi\)
−0.431671 + 0.902031i \(0.642076\pi\)
\(114\) −10.0000 −0.936586
\(115\) −9.00000 3.00000i −0.839254 0.279751i
\(116\) 0 0
\(117\) −2.00000 3.00000i −0.184900 0.277350i
\(118\) −7.00000 7.00000i −0.644402 0.644402i
\(119\) −2.00000 + 2.00000i −0.183340 + 0.183340i
\(120\) −3.00000 + 9.00000i −0.273861 + 0.821584i
\(121\) 9.00000i 0.818182i
\(122\) −14.0000 −1.26750
\(123\) 14.0000i 1.26234i
\(124\) −5.00000 5.00000i −0.449013 0.449013i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 2.00000 0.178174
\(127\) 9.00000 + 9.00000i 0.798621 + 0.798621i 0.982878 0.184257i \(-0.0589879\pi\)
−0.184257 + 0.982878i \(0.558988\pi\)
\(128\) −3.00000 −0.265165
\(129\) −2.00000 −0.176090
\(130\) −7.00000 4.00000i −0.613941 0.350823i
\(131\) −20.0000 −1.74741 −0.873704 0.486458i \(-0.838289\pi\)
−0.873704 + 0.486458i \(0.838289\pi\)
\(132\) 2.00000 0.174078
\(133\) −10.0000 10.0000i −0.867110 0.867110i
\(134\) −4.00000 −0.345547
\(135\) −12.0000 4.00000i −1.03280 0.344265i
\(136\) −3.00000 3.00000i −0.257248 0.257248i
\(137\) 16.0000i 1.36697i 0.729964 + 0.683486i \(0.239537\pi\)
−0.729964 + 0.683486i \(0.760463\pi\)
\(138\) 6.00000 0.510754
\(139\) 14.0000i 1.18746i 0.804663 + 0.593732i \(0.202346\pi\)
−0.804663 + 0.593732i \(0.797654\pi\)
\(140\) −4.00000 + 2.00000i −0.338062 + 0.169031i
\(141\) 6.00000 6.00000i 0.505291 0.505291i
\(142\) 1.00000 + 1.00000i 0.0839181 + 0.0839181i
\(143\) −1.00000 + 5.00000i −0.0836242 + 0.418121i
\(144\) 1.00000i 0.0833333i
\(145\) 0 0
\(146\) −10.0000 −0.827606
\(147\) 3.00000 + 3.00000i 0.247436 + 0.247436i
\(148\) 0 0
\(149\) −3.00000 + 3.00000i −0.245770 + 0.245770i −0.819232 0.573462i \(-0.805600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) −7.00000 + 1.00000i −0.571548 + 0.0816497i
\(151\) 7.00000 7.00000i 0.569652 0.569652i −0.362379 0.932031i \(-0.618035\pi\)
0.932031 + 0.362379i \(0.118035\pi\)
\(152\) 15.0000 15.0000i 1.21666 1.21666i
\(153\) 1.00000 1.00000i 0.0808452 0.0808452i
\(154\) −2.00000 2.00000i −0.161165 0.161165i
\(155\) 5.00000 15.0000i 0.401610 1.20483i
\(156\) −5.00000 1.00000i −0.400320 0.0800641i
\(157\) 13.0000 13.0000i 1.03751 1.03751i 0.0382445 0.999268i \(-0.487823\pi\)
0.999268 0.0382445i \(-0.0121766\pi\)
\(158\) 2.00000i 0.159111i
\(159\) 10.0000i 0.793052i
\(160\) −5.00000 10.0000i −0.395285 0.790569i
\(161\) 6.00000 + 6.00000i 0.472866 + 0.472866i
\(162\) 5.00000 0.392837
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 7.00000 + 7.00000i 0.546608 + 0.546608i
\(165\) 2.00000 + 4.00000i 0.155700 + 0.311400i
\(166\) 6.00000i 0.465690i
\(167\) 18.0000i 1.39288i 0.717614 + 0.696441i \(0.245234\pi\)
−0.717614 + 0.696441i \(0.754766\pi\)
\(168\) 6.00000 6.00000i 0.462910 0.462910i
\(169\) 5.00000 12.0000i 0.384615 0.923077i
\(170\) 1.00000 3.00000i 0.0766965 0.230089i
\(171\) 5.00000 + 5.00000i 0.382360 + 0.382360i
\(172\) 1.00000 1.00000i 0.0762493 0.0762493i
\(173\) −11.0000 + 11.0000i −0.836315 + 0.836315i −0.988372 0.152057i \(-0.951410\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(174\) 0 0
\(175\) −8.00000 6.00000i −0.604743 0.453557i
\(176\) 1.00000 1.00000i 0.0753778 0.0753778i
\(177\) 14.0000i 1.05230i
\(178\) 5.00000 + 5.00000i 0.374766 + 0.374766i
\(179\) −20.0000 −1.49487 −0.747435 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 2.00000 1.00000i 0.149071 0.0745356i
\(181\) 8.00000i 0.594635i 0.954779 + 0.297318i \(0.0960920\pi\)
−0.954779 + 0.297318i \(0.903908\pi\)
\(182\) 4.00000 + 6.00000i 0.296500 + 0.444750i
\(183\) −14.0000 14.0000i −1.03491 1.03491i
\(184\) −9.00000 + 9.00000i −0.663489 + 0.663489i
\(185\) 0 0
\(186\) 10.0000i 0.733236i
\(187\) −2.00000 −0.146254
\(188\) 6.00000i 0.437595i
\(189\) 8.00000 + 8.00000i 0.581914 + 0.581914i
\(190\) 15.0000 + 5.00000i 1.08821 + 0.362738i
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 7.00000 + 7.00000i 0.505181 + 0.505181i
\(193\) 18.0000 1.29567 0.647834 0.761781i \(-0.275675\pi\)
0.647834 + 0.761781i \(0.275675\pi\)
\(194\) 2.00000 0.143592
\(195\) −3.00000 11.0000i −0.214834 0.787726i
\(196\) −3.00000 −0.214286
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 1.00000 + 1.00000i 0.0710669 + 0.0710669i
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 9.00000 12.0000i 0.636396 0.848528i
\(201\) −4.00000 4.00000i −0.282138 0.282138i
\(202\) 12.0000i 0.844317i
\(203\) 0 0
\(204\) 2.00000i 0.140028i
\(205\) −7.00000 + 21.0000i −0.488901 + 1.46670i
\(206\) 7.00000 7.00000i 0.487713 0.487713i
\(207\) −3.00000 3.00000i −0.208514 0.208514i
\(208\) −3.00000 + 2.00000i −0.208013 + 0.138675i
\(209\) 10.0000i 0.691714i
\(210\) 6.00000 + 2.00000i 0.414039 + 0.138013i
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −5.00000 5.00000i −0.343401 0.343401i
\(213\) 2.00000i 0.137038i
\(214\) 7.00000 7.00000i 0.478510 0.478510i
\(215\) 3.00000 + 1.00000i 0.204598 + 0.0681994i
\(216\) −12.0000 + 12.0000i −0.816497 + 0.816497i
\(217\) −10.0000 + 10.0000i −0.678844 + 0.678844i
\(218\) 9.00000 9.00000i 0.609557 0.609557i
\(219\) −10.0000 10.0000i −0.675737 0.675737i
\(220\) −3.00000 1.00000i −0.202260 0.0674200i
\(221\) 5.00000 + 1.00000i 0.336336 + 0.0672673i
\(222\) 0 0
\(223\) 2.00000i 0.133930i 0.997755 + 0.0669650i \(0.0213316\pi\)
−0.997755 + 0.0669650i \(0.978668\pi\)
\(224\) 10.0000i 0.668153i
\(225\) 4.00000 + 3.00000i 0.266667 + 0.200000i
\(226\) 5.00000 + 5.00000i 0.332595 + 0.332595i
\(227\) −12.0000 −0.796468 −0.398234 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 10.0000 0.662266
\(229\) −3.00000 3.00000i −0.198246 0.198246i 0.601002 0.799248i \(-0.294768\pi\)
−0.799248 + 0.601002i \(0.794768\pi\)
\(230\) −9.00000 3.00000i −0.593442 0.197814i
\(231\) 4.00000i 0.263181i
\(232\) 0 0
\(233\) 1.00000 1.00000i 0.0655122 0.0655122i −0.673592 0.739104i \(-0.735249\pi\)
0.739104 + 0.673592i \(0.235249\pi\)
\(234\) −2.00000 3.00000i −0.130744 0.196116i
\(235\) −12.0000 + 6.00000i −0.782794 + 0.391397i
\(236\) 7.00000 + 7.00000i 0.455661 + 0.455661i
\(237\) −2.00000 + 2.00000i −0.129914 + 0.129914i
\(238\) −2.00000 + 2.00000i −0.129641 + 0.129641i
\(239\) 3.00000 3.00000i 0.194054 0.194054i −0.603391 0.797445i \(-0.706184\pi\)
0.797445 + 0.603391i \(0.206184\pi\)
\(240\) −1.00000 + 3.00000i −0.0645497 + 0.193649i
\(241\) 17.0000 17.0000i 1.09507 1.09507i 0.100088 0.994979i \(-0.468088\pi\)
0.994979 0.100088i \(-0.0319123\pi\)
\(242\) 9.00000i 0.578542i
\(243\) −7.00000 7.00000i −0.449050 0.449050i
\(244\) 14.0000 0.896258
\(245\) −3.00000 6.00000i −0.191663 0.383326i
\(246\) 14.0000i 0.892607i
\(247\) −5.00000 + 25.0000i −0.318142 + 1.59071i
\(248\) −15.0000 15.0000i −0.952501 0.952501i
\(249\) −6.00000 + 6.00000i −0.380235 + 0.380235i
\(250\) 11.0000 + 2.00000i 0.695701 + 0.126491i
\(251\) 2.00000i 0.126239i −0.998006 0.0631194i \(-0.979895\pi\)
0.998006 0.0631194i \(-0.0201049\pi\)
\(252\) −2.00000 −0.125988
\(253\) 6.00000i 0.377217i
\(254\) 9.00000 + 9.00000i 0.564710 + 0.564710i
\(255\) 4.00000 2.00000i 0.250490 0.125245i
\(256\) −17.0000 −1.06250
\(257\) −11.0000 11.0000i −0.686161 0.686161i 0.275220 0.961381i \(-0.411249\pi\)
−0.961381 + 0.275220i \(0.911249\pi\)
\(258\) −2.00000 −0.124515
\(259\) 0 0
\(260\) 7.00000 + 4.00000i 0.434122 + 0.248069i
\(261\) 0 0
\(262\) −20.0000 −1.23560
\(263\) 1.00000 + 1.00000i 0.0616626 + 0.0616626i 0.737266 0.675603i \(-0.236117\pi\)
−0.675603 + 0.737266i \(0.736117\pi\)
\(264\) 6.00000 0.369274
\(265\) 5.00000 15.0000i 0.307148 0.921443i
\(266\) −10.0000 10.0000i −0.613139 0.613139i
\(267\) 10.0000i 0.611990i
\(268\) 4.00000 0.244339
\(269\) 12.0000i 0.731653i −0.930683 0.365826i \(-0.880786\pi\)
0.930683 0.365826i \(-0.119214\pi\)
\(270\) −12.0000 4.00000i −0.730297 0.243432i
\(271\) −9.00000 + 9.00000i −0.546711 + 0.546711i −0.925488 0.378777i \(-0.876345\pi\)
0.378777 + 0.925488i \(0.376345\pi\)
\(272\) −1.00000 1.00000i −0.0606339 0.0606339i
\(273\) −2.00000 + 10.0000i −0.121046 + 0.605228i
\(274\) 16.0000i 0.966595i
\(275\) −1.00000 7.00000i −0.0603023 0.422116i
\(276\) −6.00000 −0.361158
\(277\) −15.0000 15.0000i −0.901263 0.901263i 0.0942828 0.995545i \(-0.469944\pi\)
−0.995545 + 0.0942828i \(0.969944\pi\)
\(278\) 14.0000i 0.839664i
\(279\) 5.00000 5.00000i 0.299342 0.299342i
\(280\) −12.0000 + 6.00000i −0.717137 + 0.358569i
\(281\) 1.00000 1.00000i 0.0596550 0.0596550i −0.676650 0.736305i \(-0.736569\pi\)
0.736305 + 0.676650i \(0.236569\pi\)
\(282\) 6.00000 6.00000i 0.357295 0.357295i
\(283\) −9.00000 + 9.00000i −0.534994 + 0.534994i −0.922055 0.387060i \(-0.873491\pi\)
0.387060 + 0.922055i \(0.373491\pi\)
\(284\) −1.00000 1.00000i −0.0593391 0.0593391i
\(285\) 10.0000 + 20.0000i 0.592349 + 1.18470i
\(286\) −1.00000 + 5.00000i −0.0591312 + 0.295656i
\(287\) 14.0000 14.0000i 0.826394 0.826394i
\(288\) 5.00000i 0.294628i
\(289\) 15.0000i 0.882353i
\(290\) 0 0
\(291\) 2.00000 + 2.00000i 0.117242 + 0.117242i
\(292\) 10.0000 0.585206
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 3.00000 + 3.00000i 0.174964 + 0.174964i
\(295\) −7.00000 + 21.0000i −0.407556 + 1.22267i
\(296\) 0 0
\(297\) 8.00000i 0.464207i
\(298\) −3.00000 + 3.00000i −0.173785 + 0.173785i
\(299\) 3.00000 15.0000i 0.173494 0.867472i
\(300\) 7.00000 1.00000i 0.404145 0.0577350i
\(301\) −2.00000 2.00000i −0.115278 0.115278i
\(302\) 7.00000 7.00000i 0.402805 0.402805i
\(303\) 12.0000 12.0000i 0.689382 0.689382i
\(304\) 5.00000 5.00000i 0.286770 0.286770i
\(305\) 14.0000 + 28.0000i 0.801638 + 1.60328i
\(306\) 1.00000 1.00000i 0.0571662 0.0571662i
\(307\) 18.0000i 1.02731i −0.857996 0.513657i \(-0.828290\pi\)
0.857996 0.513657i \(-0.171710\pi\)
\(308\) 2.00000 + 2.00000i 0.113961 + 0.113961i
\(309\) 14.0000 0.796432
\(310\) 5.00000 15.0000i 0.283981 0.851943i
\(311\) 6.00000i 0.340229i −0.985424 0.170114i \(-0.945586\pi\)
0.985424 0.170114i \(-0.0544137\pi\)
\(312\) −15.0000 3.00000i −0.849208 0.169842i
\(313\) 9.00000 + 9.00000i 0.508710 + 0.508710i 0.914130 0.405420i \(-0.132875\pi\)
−0.405420 + 0.914130i \(0.632875\pi\)
\(314\) 13.0000 13.0000i 0.733632 0.733632i
\(315\) −2.00000 4.00000i −0.112687 0.225374i
\(316\) 2.00000i 0.112509i
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 10.0000i 0.560772i
\(319\) 0 0
\(320\) −7.00000 14.0000i −0.391312 0.782624i
\(321\) 14.0000 0.781404
\(322\) 6.00000 + 6.00000i 0.334367 + 0.334367i
\(323\) −10.0000 −0.556415
\(324\) −5.00000 −0.277778
\(325\) −1.00000 + 18.0000i −0.0554700 + 0.998460i
\(326\) 4.00000 0.221540
\(327\) 18.0000 0.995402
\(328\) 21.0000 + 21.0000i 1.15953 + 1.15953i
\(329\) 12.0000 0.661581
\(330\) 2.00000 + 4.00000i 0.110096 + 0.220193i
\(331\) −3.00000 3.00000i −0.164895 0.164895i 0.619836 0.784731i \(-0.287199\pi\)
−0.784731 + 0.619836i \(0.787199\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 0 0
\(334\) 18.0000i 0.984916i
\(335\) 4.00000 + 8.00000i 0.218543 + 0.437087i
\(336\) 2.00000 2.00000i 0.109109 0.109109i
\(337\) 13.0000 + 13.0000i 0.708155 + 0.708155i 0.966147 0.257992i \(-0.0830608\pi\)
−0.257992 + 0.966147i \(0.583061\pi\)
\(338\) 5.00000 12.0000i 0.271964 0.652714i
\(339\) 10.0000i 0.543125i
\(340\) −1.00000 + 3.00000i −0.0542326 + 0.162698i
\(341\) −10.0000 −0.541530
\(342\) 5.00000 + 5.00000i 0.270369 + 0.270369i
\(343\) 20.0000i 1.07990i
\(344\) 3.00000 3.00000i 0.161749 0.161749i
\(345\) −6.00000 12.0000i −0.323029 0.646058i
\(346\) −11.0000 + 11.0000i −0.591364 + 0.591364i
\(347\) 3.00000 3.00000i 0.161048 0.161048i −0.621983 0.783031i \(-0.713673\pi\)
0.783031 + 0.621983i \(0.213673\pi\)
\(348\) 0 0
\(349\) 9.00000 + 9.00000i 0.481759 + 0.481759i 0.905693 0.423934i \(-0.139351\pi\)
−0.423934 + 0.905693i \(0.639351\pi\)
\(350\) −8.00000 6.00000i −0.427618 0.320713i
\(351\) 4.00000 20.0000i 0.213504 1.06752i
\(352\) −5.00000 + 5.00000i −0.266501 + 0.266501i
\(353\) 12.0000i 0.638696i −0.947638 0.319348i \(-0.896536\pi\)
0.947638 0.319348i \(-0.103464\pi\)
\(354\) 14.0000i 0.744092i
\(355\) 1.00000 3.00000i 0.0530745 0.159223i
\(356\) −5.00000 5.00000i −0.264999 0.264999i
\(357\) −4.00000 −0.211702
\(358\) −20.0000 −1.05703
\(359\) 1.00000 + 1.00000i 0.0527780 + 0.0527780i 0.733003 0.680225i \(-0.238118\pi\)
−0.680225 + 0.733003i \(0.738118\pi\)
\(360\) 6.00000 3.00000i 0.316228 0.158114i
\(361\) 31.0000i 1.63158i
\(362\) 8.00000i 0.420471i
\(363\) −9.00000 + 9.00000i −0.472377 + 0.472377i
\(364\) −4.00000 6.00000i −0.209657 0.314485i
\(365\) 10.0000 + 20.0000i 0.523424 + 1.04685i
\(366\) −14.0000 14.0000i −0.731792 0.731792i
\(367\) −1.00000 + 1.00000i −0.0521996 + 0.0521996i −0.732725 0.680525i \(-0.761752\pi\)
0.680525 + 0.732725i \(0.261752\pi\)
\(368\) −3.00000 + 3.00000i −0.156386 + 0.156386i
\(369\) −7.00000 + 7.00000i −0.364405 + 0.364405i
\(370\) 0 0
\(371\) −10.0000 + 10.0000i −0.519174 + 0.519174i
\(372\) 10.0000i 0.518476i
\(373\) −15.0000 15.0000i −0.776671 0.776671i 0.202593 0.979263i \(-0.435063\pi\)
−0.979263 + 0.202593i \(0.935063\pi\)
\(374\) −2.00000 −0.103418
\(375\) 9.00000 + 13.0000i 0.464758 + 0.671317i
\(376\) 18.0000i 0.928279i
\(377\) 0 0
\(378\) 8.00000 + 8.00000i 0.411476 + 0.411476i
\(379\) −1.00000 + 1.00000i −0.0513665 + 0.0513665i −0.732323 0.680957i \(-0.761564\pi\)
0.680957 + 0.732323i \(0.261564\pi\)
\(380\) −15.0000 5.00000i −0.769484 0.256495i
\(381\) 18.0000i 0.922168i
\(382\) 8.00000 0.409316
\(383\) 30.0000i 1.53293i −0.642287 0.766464i \(-0.722014\pi\)
0.642287 0.766464i \(-0.277986\pi\)
\(384\) −3.00000 3.00000i −0.153093 0.153093i
\(385\) −2.00000 + 6.00000i −0.101929 + 0.305788i
\(386\) 18.0000 0.916176
\(387\) 1.00000 + 1.00000i 0.0508329 + 0.0508329i
\(388\) −2.00000 −0.101535
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) −3.00000 11.0000i −0.151911 0.557007i
\(391\) 6.00000 0.303433
\(392\) −9.00000 −0.454569
\(393\) −20.0000 20.0000i −1.00887 1.00887i
\(394\) 6.00000 0.302276
\(395\) 4.00000 2.00000i 0.201262 0.100631i
\(396\) −1.00000 1.00000i −0.0502519 0.0502519i
\(397\) 16.0000i 0.803017i −0.915855 0.401508i \(-0.868486\pi\)
0.915855 0.401508i \(-0.131514\pi\)
\(398\) −8.00000 −0.401004
\(399\) 20.0000i 1.00125i
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) −11.0000 + 11.0000i −0.549314 + 0.549314i −0.926242 0.376929i \(-0.876980\pi\)
0.376929 + 0.926242i \(0.376980\pi\)
\(402\) −4.00000 4.00000i −0.199502 0.199502i
\(403\) 25.0000 + 5.00000i 1.24534 + 0.249068i
\(404\) 12.0000i 0.597022i
\(405\) −5.00000 10.0000i −0.248452 0.496904i
\(406\) 0 0
\(407\) 0 0
\(408\) 6.00000i 0.297044i
\(409\) −7.00000 + 7.00000i −0.346128 + 0.346128i −0.858665 0.512537i \(-0.828706\pi\)
0.512537 + 0.858665i \(0.328706\pi\)
\(410\) −7.00000 + 21.0000i −0.345705 + 1.03712i
\(411\) −16.0000 + 16.0000i −0.789222 + 0.789222i
\(412\) −7.00000 + 7.00000i −0.344865 + 0.344865i
\(413\) 14.0000 14.0000i 0.688895 0.688895i
\(414\) −3.00000 3.00000i −0.147442 0.147442i
\(415\) 12.0000 6.00000i 0.589057 0.294528i
\(416\) 15.0000 10.0000i 0.735436 0.490290i
\(417\) −14.0000 + 14.0000i −0.685583 + 0.685583i
\(418\) 10.0000i 0.489116i
\(419\) 38.0000i 1.85642i 0.372055 + 0.928211i \(0.378653\pi\)
−0.372055 + 0.928211i \(0.621347\pi\)
\(420\) −6.00000 2.00000i −0.292770 0.0975900i
\(421\) −11.0000 11.0000i −0.536107 0.536107i 0.386276 0.922383i \(-0.373761\pi\)
−0.922383 + 0.386276i \(0.873761\pi\)
\(422\) 4.00000 0.194717
\(423\) −6.00000 −0.291730
\(424\) −15.0000 15.0000i −0.728464 0.728464i
\(425\) −7.00000 + 1.00000i −0.339550 + 0.0485071i
\(426\) 2.00000i 0.0969003i
\(427\) 28.0000i 1.35501i
\(428\) −7.00000 + 7.00000i −0.338358 + 0.338358i
\(429\) −6.00000 + 4.00000i −0.289683 + 0.193122i
\(430\) 3.00000 + 1.00000i 0.144673 + 0.0482243i
\(431\) 13.0000 + 13.0000i 0.626188 + 0.626188i 0.947107 0.320919i \(-0.103992\pi\)
−0.320919 + 0.947107i \(0.603992\pi\)
\(432\) −4.00000 + 4.00000i −0.192450 + 0.192450i
\(433\) 17.0000 17.0000i 0.816968 0.816968i −0.168700 0.985668i \(-0.553957\pi\)
0.985668 + 0.168700i \(0.0539568\pi\)
\(434\) −10.0000 + 10.0000i −0.480015 + 0.480015i
\(435\) 0 0
\(436\) −9.00000 + 9.00000i −0.431022 + 0.431022i
\(437\) 30.0000i 1.43509i
\(438\) −10.0000 10.0000i −0.477818 0.477818i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −9.00000 3.00000i −0.429058 0.143019i
\(441\) 3.00000i 0.142857i
\(442\) 5.00000 + 1.00000i 0.237826 + 0.0475651i
\(443\) 25.0000 + 25.0000i 1.18779 + 1.18779i 0.977678 + 0.210108i \(0.0673814\pi\)
0.210108 + 0.977678i \(0.432619\pi\)
\(444\) 0 0
\(445\) 5.00000 15.0000i 0.237023 0.711068i
\(446\) 2.00000i 0.0947027i
\(447\) −6.00000 −0.283790
\(448\) 14.0000i 0.661438i
\(449\) −3.00000 3.00000i −0.141579 0.141579i 0.632765 0.774344i \(-0.281920\pi\)
−0.774344 + 0.632765i \(0.781920\pi\)
\(450\) 4.00000 + 3.00000i 0.188562 + 0.141421i
\(451\) 14.0000 0.659234
\(452\) −5.00000 5.00000i −0.235180 0.235180i
\(453\) 14.0000 0.657777
\(454\) −12.0000 −0.563188
\(455\) 8.00000 14.0000i 0.375046 0.656330i
\(456\) 30.0000 1.40488
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) −3.00000 3.00000i −0.140181 0.140181i
\(459\) 8.00000 0.373408
\(460\) 9.00000 + 3.00000i 0.419627 + 0.139876i
\(461\) 17.0000 + 17.0000i 0.791769 + 0.791769i 0.981782 0.190013i \(-0.0608529\pi\)
−0.190013 + 0.981782i \(0.560853\pi\)
\(462\) 4.00000i 0.186097i
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 0 0
\(465\) 20.0000 10.0000i 0.927478 0.463739i
\(466\) 1.00000 1.00000i 0.0463241 0.0463241i
\(467\) 9.00000 + 9.00000i 0.416470 + 0.416470i 0.883985 0.467515i \(-0.154851\pi\)
−0.467515 + 0.883985i \(0.654851\pi\)
\(468\) 2.00000 + 3.00000i 0.0924500 + 0.138675i
\(469\) 8.00000i 0.369406i
\(470\) −12.0000 + 6.00000i −0.553519 + 0.276759i
\(471\) 26.0000 1.19802
\(472\) 21.0000 + 21.0000i 0.966603 + 0.966603i
\(473\) 2.00000i 0.0919601i
\(474\) −2.00000 + 2.00000i −0.0918630 + 0.0918630i
\(475\) −5.00000 35.0000i −0.229416 1.60591i
\(476\) 2.00000 2.00000i 0.0916698 0.0916698i
\(477\) 5.00000 5.00000i 0.228934 0.228934i
\(478\) 3.00000 3.00000i 0.137217 0.137217i
\(479\) −7.00000 7.00000i −0.319838 0.319838i 0.528867 0.848705i \(-0.322617\pi\)
−0.848705 + 0.528867i \(0.822617\pi\)
\(480\) 5.00000 15.0000i 0.228218 0.684653i
\(481\) 0 0
\(482\) 17.0000 17.0000i 0.774329 0.774329i
\(483\) 12.0000i 0.546019i
\(484\) 9.00000i 0.409091i
\(485\) −2.00000 4.00000i −0.0908153 0.181631i
\(486\) −7.00000 7.00000i −0.317526 0.317526i
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 42.0000 1.90125
\(489\) 4.00000 + 4.00000i 0.180886 + 0.180886i
\(490\) −3.00000 6.00000i −0.135526 0.271052i
\(491\) 22.0000i 0.992846i 0.868081 + 0.496423i \(0.165354\pi\)
−0.868081 + 0.496423i \(0.834646\pi\)
\(492\) 14.0000i 0.631169i
\(493\) 0 0
\(494\) −5.00000 + 25.0000i −0.224961 + 1.12480i
\(495\) 1.00000 3.00000i 0.0449467 0.134840i
\(496\) −5.00000 5.00000i −0.224507 0.224507i
\(497\) −2.00000 + 2.00000i −0.0897123 + 0.0897123i
\(498\) −6.00000 + 6.00000i −0.268866 + 0.268866i
\(499\) 3.00000 3.00000i 0.134298 0.134298i −0.636762 0.771060i \(-0.719727\pi\)
0.771060 + 0.636762i \(0.219727\pi\)
\(500\) −11.0000 2.00000i −0.491935 0.0894427i
\(501\) −18.0000 + 18.0000i −0.804181 + 0.804181i
\(502\) 2.00000i 0.0892644i
\(503\) −3.00000 3.00000i −0.133763 0.133763i 0.637055 0.770818i \(-0.280152\pi\)
−0.770818 + 0.637055i \(0.780152\pi\)
\(504\) −6.00000 −0.267261
\(505\) −24.0000 + 12.0000i −1.06799 + 0.533993i
\(506\) 6.00000i 0.266733i
\(507\) 17.0000 7.00000i 0.754997 0.310881i
\(508\) −9.00000 9.00000i −0.399310 0.399310i
\(509\) 13.0000 13.0000i 0.576215 0.576215i −0.357643 0.933858i \(-0.616420\pi\)
0.933858 + 0.357643i \(0.116420\pi\)
\(510\) 4.00000 2.00000i 0.177123 0.0885615i
\(511\) 20.0000i 0.884748i
\(512\) −11.0000 −0.486136
\(513\) 40.0000i 1.76604i
\(514\) −11.0000 11.0000i −0.485189 0.485189i
\(515\) −21.0000 7.00000i −0.925371 0.308457i
\(516\) 2.00000 0.0880451
\(517\) 6.00000 + 6.00000i 0.263880 + 0.263880i
\(518\) 0 0
\(519\) −22.0000 −0.965693
\(520\) 21.0000 + 12.0000i 0.920911 + 0.526235i
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 0 0
\(523\) 9.00000 + 9.00000i 0.393543 + 0.393543i 0.875948 0.482405i \(-0.160237\pi\)
−0.482405 + 0.875948i \(0.660237\pi\)
\(524\) 20.0000 0.873704
\(525\) −2.00000 14.0000i −0.0872872 0.611010i
\(526\) 1.00000 + 1.00000i 0.0436021 + 0.0436021i
\(527\) 10.0000i 0.435607i
\(528\) 2.00000 0.0870388
\(529\) 5.00000i 0.217391i
\(530\) 5.00000 15.0000i 0.217186 0.651558i
\(531\) −7.00000 + 7.00000i −0.303774 + 0.303774i
\(532\) 10.0000 + 10.0000i 0.433555 + 0.433555i
\(533\) −35.0000 7.00000i −1.51602 0.303204i
\(534\) 10.0000i 0.432742i
\(535\) −21.0000 7.00000i −0.907909 0.302636i
\(536\) 12.0000 0.518321
\(537\) −20.0000 20.0000i −0.863064 0.863064i
\(538\) 12.0000i 0.517357i
\(539\) −3.00000 + 3.00000i −0.129219 + 0.129219i
\(540\) 12.0000 + 4.00000i 0.516398 + 0.172133i
\(541\) 9.00000 9.00000i 0.386940 0.386940i −0.486654 0.873595i \(-0.661783\pi\)
0.873595 + 0.486654i \(0.161783\pi\)
\(542\) −9.00000 + 9.00000i −0.386583 + 0.386583i
\(543\) −8.00000 + 8.00000i −0.343313 + 0.343313i
\(544\) 5.00000 + 5.00000i 0.214373 + 0.214373i
\(545\) −27.0000 9.00000i −1.15655 0.385518i
\(546\) −2.00000 + 10.0000i −0.0855921 + 0.427960i
\(547\) −9.00000 + 9.00000i −0.384812 + 0.384812i −0.872832 0.488020i \(-0.837719\pi\)
0.488020 + 0.872832i \(0.337719\pi\)
\(548\) 16.0000i 0.683486i
\(549\) 14.0000i 0.597505i
\(550\) −1.00000 7.00000i −0.0426401 0.298481i
\(551\) 0 0
\(552\) −18.0000 −0.766131
\(553\) −4.00000 −0.170097
\(554\) −15.0000 15.0000i −0.637289 0.637289i
\(555\) 0 0
\(556\) 14.0000i 0.593732i
\(557\) 24.0000i 1.01691i −0.861088 0.508456i \(-0.830216\pi\)
0.861088 0.508456i \(-0.169784\pi\)
\(558\) 5.00000 5.00000i 0.211667 0.211667i
\(559\) −1.00000 + 5.00000i −0.0422955 + 0.211477i
\(560\) −4.00000 + 2.00000i −0.169031 + 0.0845154i
\(561\) −2.00000 2.00000i −0.0844401 0.0844401i
\(562\) 1.00000 1.00000i 0.0421825 0.0421825i
\(563\) 15.0000 15.0000i 0.632175 0.632175i −0.316438 0.948613i \(-0.602487\pi\)
0.948613 + 0.316438i \(0.102487\pi\)
\(564\) −6.00000 + 6.00000i −0.252646 + 0.252646i
\(565\) 5.00000 15.0000i 0.210352 0.631055i
\(566\) −9.00000 + 9.00000i −0.378298 + 0.378298i
\(567\) 10.0000i 0.419961i
\(568\) −3.00000 3.00000i −0.125877 0.125877i
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 10.0000 + 20.0000i 0.418854 + 0.837708i
\(571\) 6.00000i 0.251092i 0.992088 + 0.125546i \(0.0400683\pi\)
−0.992088 + 0.125546i \(0.959932\pi\)
\(572\) 1.00000 5.00000i 0.0418121 0.209061i
\(573\) 8.00000 + 8.00000i 0.334205 + 0.334205i
\(574\) 14.0000 14.0000i 0.584349 0.584349i
\(575\) 3.00000 + 21.0000i 0.125109 + 0.875761i
\(576\) 7.00000i 0.291667i
\(577\) 46.0000 1.91501 0.957503 0.288425i \(-0.0931316\pi\)
0.957503 + 0.288425i \(0.0931316\pi\)
\(578\) 15.0000i 0.623918i
\(579\) 18.0000 + 18.0000i 0.748054 + 0.748054i
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) 2.00000 + 2.00000i 0.0829027 + 0.0829027i
\(583\) −10.0000 −0.414158
\(584\) 30.0000 1.24141
\(585\) −4.00000 + 7.00000i −0.165380 + 0.289414i
\(586\) −6.00000 −0.247858
\(587\) −4.00000 −0.165098 −0.0825488 0.996587i \(-0.526306\pi\)
−0.0825488 + 0.996587i \(0.526306\pi\)
\(588\) −3.00000 3.00000i −0.123718 0.123718i
\(589\) −50.0000 −2.06021
\(590\) −7.00000 + 21.0000i −0.288185 + 0.864556i
\(591\) 6.00000 + 6.00000i 0.246807 + 0.246807i
\(592\) 0 0
\(593\) 10.0000 0.410651 0.205325 0.978694i \(-0.434175\pi\)
0.205325 + 0.978694i \(0.434175\pi\)
\(594\) 8.00000i 0.328244i
\(595\) 6.00000 + 2.00000i 0.245976 + 0.0819920i
\(596\) 3.00000 3.00000i 0.122885 0.122885i
\(597\) −8.00000 8.00000i −0.327418 0.327418i
\(598\) 3.00000 15.0000i 0.122679 0.613396i
\(599\) 30.0000i 1.22577i −0.790173 0.612883i \(-0.790010\pi\)
0.790173 0.612883i \(-0.209990\pi\)
\(600\) 21.0000 3.00000i 0.857321 0.122474i
\(601\) −38.0000 −1.55005 −0.775026 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) −2.00000 2.00000i −0.0815139 0.0815139i
\(603\) 4.00000i 0.162893i
\(604\) −7.00000 + 7.00000i −0.284826 + 0.284826i
\(605\) 18.0000 9.00000i 0.731804 0.365902i
\(606\) 12.0000 12.0000i 0.487467 0.487467i
\(607\) −13.0000 + 13.0000i −0.527654 + 0.527654i −0.919872 0.392218i \(-0.871708\pi\)
0.392218 + 0.919872i \(0.371708\pi\)
\(608\) −25.0000 + 25.0000i −1.01388 + 1.01388i
\(609\) 0 0
\(610\) 14.0000 + 28.0000i 0.566843 + 1.13369i
\(611\) −12.0000 18.0000i −0.485468 0.728202i
\(612\) −1.00000 + 1.00000i −0.0404226 + 0.0404226i
\(613\) 20.0000i 0.807792i −0.914805 0.403896i \(-0.867656\pi\)
0.914805 0.403896i \(-0.132344\pi\)
\(614\) 18.0000i 0.726421i
\(615\) −28.0000 + 14.0000i −1.12907 + 0.564534i
\(616\) 6.00000 + 6.00000i 0.241747 + 0.241747i
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 14.0000 0.563163
\(619\) 25.0000 + 25.0000i 1.00483 + 1.00483i 0.999988 + 0.00484658i \(0.00154272\pi\)
0.00484658 + 0.999988i \(0.498457\pi\)
\(620\) −5.00000 + 15.0000i −0.200805 + 0.602414i
\(621\) 24.0000i 0.963087i
\(622\) 6.00000i 0.240578i
\(623\) −10.0000 + 10.0000i −0.400642 + 0.400642i
\(624\) −5.00000 1.00000i −0.200160 0.0400320i
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 9.00000 + 9.00000i 0.359712 + 0.359712i
\(627\) 10.0000 10.0000i 0.399362 0.399362i
\(628\) −13.0000 + 13.0000i −0.518756 + 0.518756i
\(629\) 0 0
\(630\) −2.00000 4.00000i −0.0796819 0.159364i
\(631\) 11.0000 11.0000i 0.437903 0.437903i −0.453403 0.891306i \(-0.649790\pi\)
0.891306 + 0.453403i \(0.149790\pi\)
\(632\) 6.00000i 0.238667i
\(633\) 4.00000 + 4.00000i 0.158986 + 0.158986i
\(634\) −14.0000 −0.556011
\(635\) 9.00000 27.0000i 0.357154 1.07146i
\(636\) 10.0000i 0.396526i
\(637\) 9.00000 6.00000i 0.356593 0.237729i
\(638\) 0 0
\(639\) 1.00000 1.00000i 0.0395594 0.0395594i
\(640\) 3.00000 + 6.00000i 0.118585 + 0.237171i
\(641\) 24.0000i 0.947943i 0.880540 + 0.473972i \(0.157180\pi\)
−0.880540 + 0.473972i \(0.842820\pi\)
\(642\) 14.0000 0.552536
\(643\) 34.0000i 1.34083i −0.741987 0.670415i \(-0.766116\pi\)
0.741987 0.670415i \(-0.233884\pi\)
\(644\) −6.00000 6.00000i −0.236433 0.236433i
\(645\) 2.00000 + 4.00000i 0.0787499 + 0.157500i
\(646\) −10.0000 −0.393445
\(647\) 1.00000 + 1.00000i 0.0393141 + 0.0393141i 0.726491 0.687176i \(-0.241150\pi\)
−0.687176 + 0.726491i \(0.741150\pi\)
\(648\) −15.0000 −0.589256
\(649\) 14.0000 0.549548
\(650\) −1.00000 + 18.0000i −0.0392232 + 0.706018i
\(651\) −20.0000 −0.783862
\(652\) −4.00000 −0.156652
\(653\) 13.0000 + 13.0000i 0.508729 + 0.508729i 0.914136 0.405407i \(-0.132870\pi\)
−0.405407 + 0.914136i \(0.632870\pi\)
\(654\) 18.0000 0.703856
\(655\) 20.0000 + 40.0000i 0.781465 + 1.56293i
\(656\) 7.00000 + 7.00000i 0.273304 + 0.273304i
\(657\) 10.0000i 0.390137i
\(658\) 12.0000 0.467809
\(659\) 26.0000i 1.01282i −0.862294 0.506408i \(-0.830973\pi\)
0.862294 0.506408i \(-0.169027\pi\)
\(660\) −2.00000 4.00000i −0.0778499 0.155700i
\(661\) 17.0000 17.0000i 0.661223 0.661223i −0.294445 0.955668i \(-0.595135\pi\)
0.955668 + 0.294445i \(0.0951348\pi\)
\(662\) −3.00000 3.00000i −0.116598 0.116598i
\(663\) 4.00000 + 6.00000i 0.155347 + 0.233021i
\(664\) 18.0000i 0.698535i
\(665\) −10.0000 + 30.0000i −0.387783 + 1.16335i
\(666\) 0 0
\(667\) 0 0
\(668\) 18.0000i 0.696441i
\(669\) −2.00000 + 2.00000i −0.0773245 + 0.0773245i
\(670\) 4.00000 + 8.00000i 0.154533 + 0.309067i
\(671\) 14.0000 14.0000i 0.540464 0.540464i
\(672\) −10.0000 + 10.0000i −0.385758 + 0.385758i
\(673\) −15.0000 + 15.0000i −0.578208 + 0.578208i −0.934409 0.356202i \(-0.884072\pi\)
0.356202 + 0.934409i \(0.384072\pi\)
\(674\) 13.0000 + 13.0000i 0.500741 + 0.500741i
\(675\) 4.00000 + 28.0000i 0.153960 + 1.07772i
\(676\) −5.00000 + 12.0000i −0.192308 + 0.461538i
\(677\) −23.0000 + 23.0000i −0.883962 + 0.883962i −0.993935 0.109973i \(-0.964924\pi\)
0.109973 + 0.993935i \(0.464924\pi\)
\(678\) 10.0000i 0.384048i
\(679\) 4.00000i 0.153506i
\(680\) −3.00000 + 9.00000i −0.115045 + 0.345134i
\(681\) −12.0000 12.0000i −0.459841 0.459841i
\(682\) −10.0000 −0.382920
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) −5.00000 5.00000i −0.191180 0.191180i
\(685\) 32.0000 16.0000i 1.22266 0.611329i
\(686\) 20.0000i 0.763604i
\(687\) 6.00000i 0.228914i
\(688\) 1.00000 1.00000i 0.0381246 0.0381246i
\(689\) 25.0000 + 5.00000i 0.952424 + 0.190485i
\(690\) −6.00000 12.0000i −0.228416 0.456832i
\(691\) −3.00000 3.00000i −0.114125 0.114125i 0.647738 0.761863i \(-0.275715\pi\)
−0.761863 + 0.647738i \(0.775715\pi\)
\(692\) 11.0000 11.0000i 0.418157 0.418157i
\(693\) −2.00000 + 2.00000i −0.0759737 + 0.0759737i
\(694\) 3.00000 3.00000i 0.113878 0.113878i
\(695\) 28.0000 14.0000i 1.06210 0.531050i
\(696\) 0 0
\(697\) 14.0000i 0.530288i
\(698\) 9.00000 + 9.00000i 0.340655 + 0.340655i
\(699\) 2.00000 0.0756469
\(700\) 8.00000 + 6.00000i 0.302372 + 0.226779i
\(701\) 12.0000i 0.453234i −0.973984 0.226617i \(-0.927233\pi\)
0.973984 0.226617i \(-0.0727665\pi\)
\(702\) 4.00000 20.0000i 0.150970 0.754851i
\(703\) 0 0
\(704\) −7.00000 + 7.00000i −0.263822 + 0.263822i
\(705\) −18.0000 6.00000i −0.677919 0.225973i
\(706\) 12.0000i 0.451626i
\(707\) 24.0000 0.902613
\(708\) 14.0000i 0.526152i
\(709\) 29.0000 + 29.0000i 1.08912 + 1.08912i 0.995619 + 0.0934984i \(0.0298050\pi\)
0.0934984 + 0.995619i \(0.470195\pi\)
\(710\) 1.00000 3.00000i 0.0375293 0.112588i
\(711\) 2.00000 0.0750059
\(712\) −15.0000 15.0000i −0.562149 0.562149i
\(713\) 30.0000 1.12351
\(714\) −4.00000 −0.149696
\(715\) 11.0000 3.00000i 0.411377 0.112194i
\(716\) 20.0000 0.747435
\(717\) 6.00000 0.224074
\(718\) 1.00000 + 1.00000i 0.0373197 + 0.0373197i
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 2.00000 1.00000i 0.0745356 0.0372678i
\(721\) 14.0000 + 14.0000i 0.521387 + 0.521387i
\(722\) 31.0000i 1.15370i
\(723\) 34.0000 1.26447
\(724\) 8.00000i 0.297318i
\(725\) 0 0
\(726\) −9.00000 + 9.00000i −0.334021 + 0.334021i
\(727\) −35.0000 35.0000i −1.29808 1.29808i −0.929660 0.368418i \(-0.879900\pi\)
−0.368418 0.929660i \(-0.620100\pi\)
\(728\) −12.0000 18.0000i −0.444750 0.667124i
\(729\) 29.0000i 1.07407i
\(730\) 10.0000 + 20.0000i 0.370117 + 0.740233i
\(731\) −2.00000 −0.0739727
\(732\) 14.0000 + 14.0000i 0.517455 + 0.517455i
\(733\) 4.00000i 0.147743i −0.997268 0.0738717i \(-0.976464\pi\)
0.997268 0.0738717i \(-0.0235355\pi\)
\(734\) −1.00000 + 1.00000i −0.0369107 + 0.0369107i
\(735\) 3.00000 9.00000i 0.110657 0.331970i
\(736\) 15.0000 15.0000i 0.552907 0.552907i
\(737\) 4.00000 4.00000i 0.147342 0.147342i
\(738\) −7.00000 + 7.00000i −0.257674 + 0.257674i
\(739\) −3.00000 3.00000i −0.110357 0.110357i 0.649772 0.760129i \(-0.274864\pi\)
−0.760129 + 0.649772i \(0.774864\pi\)
\(740\) 0 0
\(741\) −30.0000 + 20.0000i −1.10208 + 0.734718i
\(742\) −10.0000 + 10.0000i −0.367112 + 0.367112i
\(743\) 34.0000i 1.24734i 0.781688 + 0.623670i \(0.214359\pi\)
−0.781688 + 0.623670i \(0.785641\pi\)
\(744\) 30.0000i 1.09985i
\(745\) 9.00000 + 3.00000i 0.329734 + 0.109911i
\(746\) −15.0000 15.0000i −0.549189 0.549189i
\(747\) 6.00000 0.219529
\(748\) 2.00000 0.0731272
\(749\) 14.0000 + 14.0000i 0.511549 + 0.511549i
\(750\) 9.00000 + 13.0000i 0.328634 + 0.474693i
\(751\) 50.0000i 1.82453i 0.409605 + 0.912263i \(0.365667\pi\)
−0.409605 + 0.912263i \(0.634333\pi\)
\(752\) 6.00000i 0.218797i
\(753\) 2.00000 2.00000i 0.0728841 0.0728841i
\(754\) 0 0
\(755\) −21.0000 7.00000i −0.764268 0.254756i
\(756\) −8.00000 8.00000i −0.290957 0.290957i
\(757\) −35.0000 + 35.0000i −1.27210 + 1.27210i −0.327111 + 0.944986i \(0.606075\pi\)
−0.944986 + 0.327111i \(0.893925\pi\)
\(758\) −1.00000 + 1.00000i −0.0363216 + 0.0363216i
\(759\) −6.00000 + 6.00000i −0.217786 + 0.217786i
\(760\) −45.0000 15.0000i −1.63232 0.544107i
\(761\) −7.00000 + 7.00000i −0.253750 + 0.253750i −0.822506 0.568756i \(-0.807425\pi\)
0.568756 + 0.822506i \(0.307425\pi\)
\(762\) 18.0000i 0.652071i
\(763\) 18.0000 + 18.0000i 0.651644 + 0.651644i
\(764\) −8.00000 −0.289430
\(765\) −3.00000 1.00000i −0.108465 0.0361551i
\(766\) 30.0000i 1.08394i
\(767\) −35.0000 7.00000i −1.26378 0.252755i
\(768\) −17.0000 17.0000i −0.613435 0.613435i
\(769\) −15.0000 + 15.0000i −0.540914 + 0.540914i −0.923797 0.382883i \(-0.874931\pi\)
0.382883 + 0.923797i \(0.374931\pi\)
\(770\) −2.00000 + 6.00000i −0.0720750 + 0.216225i
\(771\) 22.0000i 0.792311i
\(772\) −18.0000 −0.647834
\(773\) 32.0000i 1.15096i −0.817816 0.575480i \(-0.804815\pi\)
0.817816 0.575480i \(-0.195185\pi\)
\(774\) 1.00000 + 1.00000i 0.0359443 + 0.0359443i
\(775\) −35.0000 + 5.00000i −1.25724 + 0.179605i
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) 70.0000 2.50801
\(780\) 3.00000 + 11.0000i 0.107417 + 0.393863i
\(781\) −2.00000 −0.0715656
\(782\) 6.00000 0.214560
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) −39.0000 13.0000i −1.39197 0.463990i
\(786\) −20.0000 20.0000i −0.713376 0.713376i
\(787\) 22.0000i 0.784215i 0.919919 + 0.392108i \(0.128254\pi\)
−0.919919 + 0.392108i \(0.871746\pi\)
\(788\) −6.00000 −0.213741
\(789\) 2.00000i 0.0712019i
\(790\) 4.00000 2.00000i 0.142314 0.0711568i
\(791\) −10.0000 + 10.0000i −0.355559 + 0.355559i
\(792\) −3.00000 3.00000i −0.106600 0.106600i
\(793\) −42.0000 + 28.0000i