Properties

Label 1110.2.u.f.401.11
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.11
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.f.191.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.72471 + 0.159268i) q^{6} -3.17089 q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.549384 + 2.94927i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.72471 + 0.159268i) q^{6} -3.17089 q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.549384 + 2.94927i) q^{9} -1.00000 q^{10} -4.29438 q^{11} +(-1.10694 + 1.33218i) q^{12} +(0.469209 - 0.469209i) q^{13} +(-2.24216 + 2.24216i) q^{14} +(0.159268 + 1.72471i) q^{15} -1.00000 q^{16} +(4.17376 + 4.17376i) q^{17} +(2.47392 + 1.69697i) q^{18} +(2.35319 - 2.35319i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(4.22419 + 3.50998i) q^{21} +(-3.03659 + 3.03659i) q^{22} +(2.43772 + 2.43772i) q^{23} +(0.159268 + 1.72471i) q^{24} +1.00000i q^{25} -0.663562i q^{26} +(2.53278 - 4.53707i) q^{27} +3.17089i q^{28} +(-3.28489 + 3.28489i) q^{29} +(1.33218 + 1.10694i) q^{30} +(-0.0756563 - 0.0756563i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.72087 + 4.75361i) q^{33} +5.90259 q^{34} +(2.24216 + 2.24216i) q^{35} +(2.94927 - 0.549384i) q^{36} +(3.36709 + 5.06584i) q^{37} -3.32791i q^{38} +(-1.14445 + 0.105684i) q^{39} +1.00000i q^{40} -6.28349 q^{41} +(5.46888 - 0.505022i) q^{42} +(2.94167 - 2.94167i) q^{43} +4.29438i q^{44} +(1.69697 - 2.47392i) q^{45} +3.44746 q^{46} +0.554395i q^{47} +(1.33218 + 1.10694i) q^{48} +3.05457 q^{49} +(0.707107 + 0.707107i) q^{50} +(-0.940094 - 10.1803i) q^{51} +(-0.469209 - 0.469209i) q^{52} +10.4161i q^{53} +(-1.41725 - 4.99914i) q^{54} +(3.03659 + 3.03659i) q^{55} +(2.24216 + 2.24216i) q^{56} +(-5.73969 + 0.530030i) q^{57} +4.64554i q^{58} +(-5.42735 - 5.42735i) q^{59} +(1.72471 - 0.159268i) q^{60} +(-3.80832 - 3.80832i) q^{61} -0.106994 q^{62} +(-1.74204 - 9.35181i) q^{63} +1.00000i q^{64} -0.663562 q^{65} +(7.40657 - 0.683958i) q^{66} -7.22479i q^{67} +(4.17376 - 4.17376i) q^{68} +(-0.549071 - 5.94588i) q^{69} +3.17089 q^{70} +8.00969i q^{71} +(1.69697 - 2.47392i) q^{72} +12.0206i q^{73} +(5.96298 + 1.20120i) q^{74} +(1.10694 - 1.33218i) q^{75} +(-2.35319 - 2.35319i) q^{76} +13.6170 q^{77} +(-0.734521 + 0.883981i) q^{78} +(-2.36673 + 2.36673i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-8.39636 + 3.24056i) q^{81} +(-4.44310 + 4.44310i) q^{82} +10.3371i q^{83} +(3.50998 - 4.22419i) q^{84} -5.90259i q^{85} -4.16015i q^{86} +(8.01221 - 0.739886i) q^{87} +(3.03659 + 3.03659i) q^{88} +(-2.62728 + 2.62728i) q^{89} +(-0.549384 - 2.94927i) q^{90} +(-1.48781 + 1.48781i) q^{91} +(2.43772 - 2.43772i) q^{92} +(0.0170408 + 0.184534i) q^{93} +(0.392017 + 0.392017i) q^{94} -3.32791 q^{95} +(1.72471 - 0.159268i) q^{96} +(-0.130832 + 0.130832i) q^{97} +(2.15991 - 2.15991i) q^{98} +(-2.35926 - 12.6653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q + 24q^{7} - 8q^{9} - 40q^{10} + 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 16q^{22} - 8q^{31} + 24q^{33} + 24q^{34} + 32q^{37} + 16q^{39} + 12q^{42} + 32q^{43} + 8q^{45} - 56q^{46} - 32q^{49} - 44q^{51} - 16q^{52} - 24q^{54} + 16q^{55} + 8q^{57} - 72q^{61} + 24q^{63} - 28q^{66} + 16q^{69} - 24q^{70} + 8q^{72} - 16q^{76} - 48q^{79} + 120q^{81} - 24q^{82} - 24q^{84} + 20q^{87} + 16q^{88} + 8q^{90} - 92q^{93} - 8q^{94} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −1.33218 1.10694i −0.769132 0.639090i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) −1.72471 + 0.159268i −0.704111 + 0.0650209i
\(7\) −3.17089 −1.19849 −0.599243 0.800567i \(-0.704532\pi\)
−0.599243 + 0.800567i \(0.704532\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.549384 + 2.94927i 0.183128 + 0.983089i
\(10\) −1.00000 −0.316228
\(11\) −4.29438 −1.29480 −0.647402 0.762149i \(-0.724145\pi\)
−0.647402 + 0.762149i \(0.724145\pi\)
\(12\) −1.10694 + 1.33218i −0.319545 + 0.384566i
\(13\) 0.469209 0.469209i 0.130135 0.130135i −0.639039 0.769174i \(-0.720668\pi\)
0.769174 + 0.639039i \(0.220668\pi\)
\(14\) −2.24216 + 2.24216i −0.599243 + 0.599243i
\(15\) 0.159268 + 1.72471i 0.0411229 + 0.445319i
\(16\) −1.00000 −0.250000
\(17\) 4.17376 + 4.17376i 1.01229 + 1.01229i 0.999924 + 0.0123615i \(0.00393489\pi\)
0.0123615 + 0.999924i \(0.496065\pi\)
\(18\) 2.47392 + 1.69697i 0.583108 + 0.399981i
\(19\) 2.35319 2.35319i 0.539859 0.539859i −0.383629 0.923487i \(-0.625326\pi\)
0.923487 + 0.383629i \(0.125326\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) 4.22419 + 3.50998i 0.921793 + 0.765940i
\(22\) −3.03659 + 3.03659i −0.647402 + 0.647402i
\(23\) 2.43772 + 2.43772i 0.508301 + 0.508301i 0.914005 0.405704i \(-0.132974\pi\)
−0.405704 + 0.914005i \(0.632974\pi\)
\(24\) 0.159268 + 1.72471i 0.0325105 + 0.352055i
\(25\) 1.00000i 0.200000i
\(26\) 0.663562i 0.130135i
\(27\) 2.53278 4.53707i 0.487433 0.873160i
\(28\) 3.17089i 0.599243i
\(29\) −3.28489 + 3.28489i −0.609989 + 0.609989i −0.942943 0.332954i \(-0.891955\pi\)
0.332954 + 0.942943i \(0.391955\pi\)
\(30\) 1.33218 + 1.10694i 0.243221 + 0.202098i
\(31\) −0.0756563 0.0756563i −0.0135883 0.0135883i 0.700280 0.713868i \(-0.253058\pi\)
−0.713868 + 0.700280i \(0.753058\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 5.72087 + 4.75361i 0.995875 + 0.827497i
\(34\) 5.90259 1.01229
\(35\) 2.24216 + 2.24216i 0.378994 + 0.378994i
\(36\) 2.94927 0.549384i 0.491545 0.0915639i
\(37\) 3.36709 + 5.06584i 0.553546 + 0.832819i
\(38\) 3.32791i 0.539859i
\(39\) −1.14445 + 0.105684i −0.183259 + 0.0169230i
\(40\) 1.00000i 0.158114i
\(41\) −6.28349 −0.981316 −0.490658 0.871352i \(-0.663244\pi\)
−0.490658 + 0.871352i \(0.663244\pi\)
\(42\) 5.46888 0.505022i 0.843867 0.0779266i
\(43\) 2.94167 2.94167i 0.448600 0.448600i −0.446289 0.894889i \(-0.647255\pi\)
0.894889 + 0.446289i \(0.147255\pi\)
\(44\) 4.29438i 0.647402i
\(45\) 1.69697 2.47392i 0.252970 0.368790i
\(46\) 3.44746 0.508301
\(47\) 0.554395i 0.0808669i 0.999182 + 0.0404334i \(0.0128739\pi\)
−0.999182 + 0.0404334i \(0.987126\pi\)
\(48\) 1.33218 + 1.10694i 0.192283 + 0.159773i
\(49\) 3.05457 0.436367
\(50\) 0.707107 + 0.707107i 0.100000 + 0.100000i
\(51\) −0.940094 10.1803i −0.131639 1.42552i
\(52\) −0.469209 0.469209i −0.0650676 0.0650676i
\(53\) 10.4161i 1.43075i 0.698738 + 0.715377i \(0.253745\pi\)
−0.698738 + 0.715377i \(0.746255\pi\)
\(54\) −1.41725 4.99914i −0.192864 0.680297i
\(55\) 3.03659 + 3.03659i 0.409453 + 0.409453i
\(56\) 2.24216 + 2.24216i 0.299621 + 0.299621i
\(57\) −5.73969 + 0.530030i −0.760241 + 0.0702043i
\(58\) 4.64554i 0.609989i
\(59\) −5.42735 5.42735i −0.706580 0.706580i 0.259234 0.965814i \(-0.416530\pi\)
−0.965814 + 0.259234i \(0.916530\pi\)
\(60\) 1.72471 0.159268i 0.222659 0.0205614i
\(61\) −3.80832 3.80832i −0.487606 0.487606i 0.419944 0.907550i \(-0.362050\pi\)
−0.907550 + 0.419944i \(0.862050\pi\)
\(62\) −0.106994 −0.0135883
\(63\) −1.74204 9.35181i −0.219476 1.17822i
\(64\) 1.00000i 0.125000i
\(65\) −0.663562 −0.0823047
\(66\) 7.40657 0.683958i 0.911686 0.0841894i
\(67\) 7.22479i 0.882649i −0.897348 0.441324i \(-0.854509\pi\)
0.897348 0.441324i \(-0.145491\pi\)
\(68\) 4.17376 4.17376i 0.506143 0.506143i
\(69\) −0.549071 5.94588i −0.0661004 0.715800i
\(70\) 3.17089 0.378994
\(71\) 8.00969i 0.950575i 0.879831 + 0.475287i \(0.157656\pi\)
−0.879831 + 0.475287i \(0.842344\pi\)
\(72\) 1.69697 2.47392i 0.199990 0.291554i
\(73\) 12.0206i 1.40691i 0.710741 + 0.703453i \(0.248360\pi\)
−0.710741 + 0.703453i \(0.751640\pi\)
\(74\) 5.96298 + 1.20120i 0.693182 + 0.139636i
\(75\) 1.10694 1.33218i 0.127818 0.153826i
\(76\) −2.35319 2.35319i −0.269929 0.269929i
\(77\) 13.6170 1.55180
\(78\) −0.734521 + 0.883981i −0.0831681 + 0.100091i
\(79\) −2.36673 + 2.36673i −0.266278 + 0.266278i −0.827599 0.561320i \(-0.810294\pi\)
0.561320 + 0.827599i \(0.310294\pi\)
\(80\) 0.707107 + 0.707107i 0.0790569 + 0.0790569i
\(81\) −8.39636 + 3.24056i −0.932928 + 0.360062i
\(82\) −4.44310 + 4.44310i −0.490658 + 0.490658i
\(83\) 10.3371i 1.13464i 0.823496 + 0.567321i \(0.192020\pi\)
−0.823496 + 0.567321i \(0.807980\pi\)
\(84\) 3.50998 4.22419i 0.382970 0.460897i
\(85\) 5.90259i 0.640225i
\(86\) 4.16015i 0.448600i
\(87\) 8.01221 0.739886i 0.859000 0.0793241i
\(88\) 3.03659 + 3.03659i 0.323701 + 0.323701i
\(89\) −2.62728 + 2.62728i −0.278491 + 0.278491i −0.832506 0.554016i \(-0.813095\pi\)
0.554016 + 0.832506i \(0.313095\pi\)
\(90\) −0.549384 2.94927i −0.0579101 0.310880i
\(91\) −1.48781 + 1.48781i −0.155965 + 0.155965i
\(92\) 2.43772 2.43772i 0.254150 0.254150i
\(93\) 0.0170408 + 0.184534i 0.00176704 + 0.0191353i
\(94\) 0.392017 + 0.392017i 0.0404334 + 0.0404334i
\(95\) −3.32791 −0.341437
\(96\) 1.72471 0.159268i 0.176028 0.0162552i
\(97\) −0.130832 + 0.130832i −0.0132840 + 0.0132840i −0.713718 0.700434i \(-0.752990\pi\)
0.700434 + 0.713718i \(0.252990\pi\)
\(98\) 2.15991 2.15991i 0.218183 0.218183i
\(99\) −2.35926 12.6653i −0.237115 1.27291i
\(100\) 1.00000 0.100000
\(101\) 15.3310 1.52549 0.762744 0.646700i \(-0.223852\pi\)
0.762744 + 0.646700i \(0.223852\pi\)
\(102\) −7.86328 6.53379i −0.778581 0.646941i
\(103\) 7.22462 + 7.22462i 0.711863 + 0.711863i 0.966925 0.255062i \(-0.0820959\pi\)
−0.255062 + 0.966925i \(0.582096\pi\)
\(104\) −0.663562 −0.0650676
\(105\) −0.505022 5.46888i −0.0492851 0.533708i
\(106\) 7.36526 + 7.36526i 0.715377 + 0.715377i
\(107\) 0.283834i 0.0274393i 0.999906 + 0.0137196i \(0.00436724\pi\)
−0.999906 + 0.0137196i \(0.995633\pi\)
\(108\) −4.53707 2.53278i −0.436580 0.243716i
\(109\) −7.09218 + 7.09218i −0.679307 + 0.679307i −0.959843 0.280536i \(-0.909488\pi\)
0.280536 + 0.959843i \(0.409488\pi\)
\(110\) 4.29438 0.409453
\(111\) 1.12201 10.4757i 0.106496 0.994313i
\(112\) 3.17089 0.299621
\(113\) −10.1290 + 10.1290i −0.952860 + 0.952860i −0.998938 0.0460778i \(-0.985328\pi\)
0.0460778 + 0.998938i \(0.485328\pi\)
\(114\) −3.68379 + 4.43336i −0.345018 + 0.415223i
\(115\) 3.44746i 0.321477i
\(116\) 3.28489 + 3.28489i 0.304994 + 0.304994i
\(117\) 1.64160 + 1.12605i 0.151766 + 0.104103i
\(118\) −7.67543 −0.706580
\(119\) −13.2345 13.2345i −1.21321 1.21321i
\(120\) 1.10694 1.33218i 0.101049 0.121610i
\(121\) 7.44170 0.676518
\(122\) −5.38578 −0.487606
\(123\) 8.37071 + 6.95543i 0.754762 + 0.627150i
\(124\) −0.0756563 + 0.0756563i −0.00679413 + 0.00679413i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) −7.84454 5.38092i −0.698847 0.479371i
\(127\) −11.8818 −1.05434 −0.527169 0.849761i \(-0.676747\pi\)
−0.527169 + 0.849761i \(0.676747\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −7.17506 + 0.662579i −0.631728 + 0.0583368i
\(130\) −0.469209 + 0.469209i −0.0411524 + 0.0411524i
\(131\) −14.8606 + 14.8606i −1.29838 + 1.29838i −0.368917 + 0.929462i \(0.620271\pi\)
−0.929462 + 0.368917i \(0.879729\pi\)
\(132\) 4.75361 5.72087i 0.413748 0.497938i
\(133\) −7.46172 + 7.46172i −0.647013 + 0.647013i
\(134\) −5.10870 5.10870i −0.441324 0.441324i
\(135\) −4.99914 + 1.41725i −0.430257 + 0.121978i
\(136\) 5.90259i 0.506143i
\(137\) 20.7659i 1.77415i −0.461628 0.887074i \(-0.652735\pi\)
0.461628 0.887074i \(-0.347265\pi\)
\(138\) −4.59262 3.81612i −0.390950 0.324850i
\(139\) 10.4767i 0.888618i −0.895874 0.444309i \(-0.853449\pi\)
0.895874 0.444309i \(-0.146551\pi\)
\(140\) 2.24216 2.24216i 0.189497 0.189497i
\(141\) 0.613680 0.738552i 0.0516812 0.0621973i
\(142\) 5.66370 + 5.66370i 0.475287 + 0.475287i
\(143\) −2.01496 + 2.01496i −0.168500 + 0.168500i
\(144\) −0.549384 2.94927i −0.0457820 0.245772i
\(145\) 4.64554 0.385791
\(146\) 8.49986 + 8.49986i 0.703453 + 0.703453i
\(147\) −4.06922 3.38121i −0.335624 0.278878i
\(148\) 5.06584 3.36709i 0.416409 0.276773i
\(149\) 13.4251i 1.09982i −0.835223 0.549911i \(-0.814661\pi\)
0.835223 0.549911i \(-0.185339\pi\)
\(150\) −0.159268 1.72471i −0.0130042 0.140822i
\(151\) 11.6822i 0.950682i 0.879802 + 0.475341i \(0.157675\pi\)
−0.879802 + 0.475341i \(0.842325\pi\)
\(152\) −3.32791 −0.269929
\(153\) −10.0165 + 14.6025i −0.809789 + 1.18054i
\(154\) 9.62869 9.62869i 0.775902 0.775902i
\(155\) 0.106994i 0.00859397i
\(156\) 0.105684 + 1.14445i 0.00846151 + 0.0916296i
\(157\) −4.59753 −0.366923 −0.183461 0.983027i \(-0.558730\pi\)
−0.183461 + 0.983027i \(0.558730\pi\)
\(158\) 3.34706i 0.266278i
\(159\) 11.5299 13.8760i 0.914381 1.10044i
\(160\) 1.00000 0.0790569
\(161\) −7.72976 7.72976i −0.609191 0.609191i
\(162\) −3.64570 + 8.22854i −0.286433 + 0.646495i
\(163\) 12.8094 + 12.8094i 1.00331 + 1.00331i 0.999995 + 0.00331536i \(0.00105531\pi\)
0.00331536 + 0.999995i \(0.498945\pi\)
\(164\) 6.28349i 0.490658i
\(165\) −0.683958 7.40657i −0.0532461 0.576601i
\(166\) 7.30943 + 7.30943i 0.567321 + 0.567321i
\(167\) −2.59545 2.59545i −0.200842 0.200842i 0.599519 0.800361i \(-0.295359\pi\)
−0.800361 + 0.599519i \(0.795359\pi\)
\(168\) −0.505022 5.46888i −0.0389633 0.421933i
\(169\) 12.5597i 0.966130i
\(170\) −4.17376 4.17376i −0.320113 0.320113i
\(171\) 8.23299 + 5.64738i 0.629592 + 0.431866i
\(172\) −2.94167 2.94167i −0.224300 0.224300i
\(173\) −5.26417 −0.400228 −0.200114 0.979773i \(-0.564131\pi\)
−0.200114 + 0.979773i \(0.564131\pi\)
\(174\) 5.14231 6.18867i 0.389838 0.469162i
\(175\) 3.17089i 0.239697i
\(176\) 4.29438 0.323701
\(177\) 1.22245 + 13.2379i 0.0918850 + 0.995022i
\(178\) 3.71553i 0.278491i
\(179\) −9.64682 + 9.64682i −0.721037 + 0.721037i −0.968816 0.247780i \(-0.920299\pi\)
0.247780 + 0.968816i \(0.420299\pi\)
\(180\) −2.47392 1.69697i −0.184395 0.126485i
\(181\) 1.74294 0.129552 0.0647760 0.997900i \(-0.479367\pi\)
0.0647760 + 0.997900i \(0.479367\pi\)
\(182\) 2.10408i 0.155965i
\(183\) 0.857784 + 9.28893i 0.0634092 + 0.686657i
\(184\) 3.44746i 0.254150i
\(185\) 1.20120 5.96298i 0.0883139 0.438407i
\(186\) 0.142535 + 0.118436i 0.0104512 + 0.00868413i
\(187\) −17.9237 17.9237i −1.31071 1.31071i
\(188\) 0.554395 0.0404334
\(189\) −8.03116 + 14.3866i −0.584181 + 1.04647i
\(190\) −2.35319 + 2.35319i −0.170718 + 0.170718i
\(191\) −17.6905 17.6905i −1.28004 1.28004i −0.940643 0.339399i \(-0.889776\pi\)
−0.339399 0.940643i \(-0.610224\pi\)
\(192\) 1.10694 1.33218i 0.0798863 0.0961415i
\(193\) 2.31213 2.31213i 0.166431 0.166431i −0.618978 0.785409i \(-0.712453\pi\)
0.785409 + 0.618978i \(0.212453\pi\)
\(194\) 0.185024i 0.0132840i
\(195\) 0.883981 + 0.734521i 0.0633032 + 0.0526001i
\(196\) 3.05457i 0.218183i
\(197\) 24.2094i 1.72485i −0.506185 0.862425i \(-0.668945\pi\)
0.506185 0.862425i \(-0.331055\pi\)
\(198\) −10.6240 7.28745i −0.755011 0.517897i
\(199\) 15.4468 + 15.4468i 1.09500 + 1.09500i 0.994986 + 0.100010i \(0.0318874\pi\)
0.100010 + 0.994986i \(0.468113\pi\)
\(200\) 0.707107 0.707107i 0.0500000 0.0500000i
\(201\) −7.99739 + 9.62469i −0.564092 + 0.678873i
\(202\) 10.8406 10.8406i 0.762744 0.762744i
\(203\) 10.4160 10.4160i 0.731063 0.731063i
\(204\) −10.1803 + 0.940094i −0.712761 + 0.0658197i
\(205\) 4.44310 + 4.44310i 0.310320 + 0.310320i
\(206\) 10.2172 0.711863
\(207\) −5.85025 + 8.52874i −0.406621 + 0.592789i
\(208\) −0.469209 + 0.469209i −0.0325338 + 0.0325338i
\(209\) −10.1055 + 10.1055i −0.699011 + 0.699011i
\(210\) −4.22419 3.50998i −0.291497 0.242211i
\(211\) −26.2503 −1.80714 −0.903571 0.428437i \(-0.859064\pi\)
−0.903571 + 0.428437i \(0.859064\pi\)
\(212\) 10.4161 0.715377
\(213\) 8.86621 10.6703i 0.607503 0.731117i
\(214\) 0.200701 + 0.200701i 0.0137196 + 0.0137196i
\(215\) −4.16015 −0.283720
\(216\) −4.99914 + 1.41725i −0.340148 + 0.0964319i
\(217\) 0.239898 + 0.239898i 0.0162853 + 0.0162853i
\(218\) 10.0299i 0.679307i
\(219\) 13.3061 16.0136i 0.899140 1.08210i
\(220\) 3.03659 3.03659i 0.204727 0.204727i
\(221\) 3.91673 0.263468
\(222\) −6.61409 8.20085i −0.443908 0.550405i
\(223\) −16.7598 −1.12232 −0.561160 0.827707i \(-0.689645\pi\)
−0.561160 + 0.827707i \(0.689645\pi\)
\(224\) 2.24216 2.24216i 0.149811 0.149811i
\(225\) −2.94927 + 0.549384i −0.196618 + 0.0366256i
\(226\) 14.3246i 0.952860i
\(227\) −2.30277 2.30277i −0.152840 0.152840i 0.626545 0.779385i \(-0.284468\pi\)
−0.779385 + 0.626545i \(0.784468\pi\)
\(228\) 0.530030 + 5.73969i 0.0351021 + 0.380120i
\(229\) 2.83286 0.187200 0.0936002 0.995610i \(-0.470162\pi\)
0.0936002 + 0.995610i \(0.470162\pi\)
\(230\) −2.43772 2.43772i −0.160739 0.160739i
\(231\) −18.1403 15.0732i −1.19354 0.991742i
\(232\) 4.64554 0.304994
\(233\) 13.0719 0.856372 0.428186 0.903691i \(-0.359153\pi\)
0.428186 + 0.903691i \(0.359153\pi\)
\(234\) 1.95702 0.364550i 0.127934 0.0238314i
\(235\) 0.392017 0.392017i 0.0255724 0.0255724i
\(236\) −5.42735 + 5.42735i −0.353290 + 0.353290i
\(237\) 5.77273 0.533081i 0.374979 0.0346273i
\(238\) −18.7165 −1.21321
\(239\) −6.64308 6.64308i −0.429705 0.429705i 0.458823 0.888528i \(-0.348271\pi\)
−0.888528 + 0.458823i \(0.848271\pi\)
\(240\) −0.159268 1.72471i −0.0102807 0.111330i
\(241\) −5.79053 + 5.79053i −0.373001 + 0.373001i −0.868569 0.495568i \(-0.834960\pi\)
0.495568 + 0.868569i \(0.334960\pi\)
\(242\) 5.26208 5.26208i 0.338259 0.338259i
\(243\) 14.7725 + 4.97724i 0.947657 + 0.319290i
\(244\) −3.80832 + 3.80832i −0.243803 + 0.243803i
\(245\) −2.15991 2.15991i −0.137991 0.137991i
\(246\) 10.8372 1.00076i 0.690956 0.0638061i
\(247\) 2.20828i 0.140509i
\(248\) 0.106994i 0.00679413i
\(249\) 11.4425 13.7708i 0.725139 0.872690i
\(250\) 1.00000i 0.0632456i
\(251\) 3.57449 3.57449i 0.225620 0.225620i −0.585240 0.810860i \(-0.699000\pi\)
0.810860 + 0.585240i \(0.199000\pi\)
\(252\) −9.35181 + 1.74204i −0.589109 + 0.109738i
\(253\) −10.4685 10.4685i −0.658150 0.658150i
\(254\) −8.40169 + 8.40169i −0.527169 + 0.527169i
\(255\) −6.53379 + 7.86328i −0.409162 + 0.492418i
\(256\) 1.00000 0.0625000
\(257\) 2.58770 + 2.58770i 0.161416 + 0.161416i 0.783194 0.621778i \(-0.213589\pi\)
−0.621778 + 0.783194i \(0.713589\pi\)
\(258\) −4.60502 + 5.54204i −0.286696 + 0.345033i
\(259\) −10.6767 16.0632i −0.663416 0.998121i
\(260\) 0.663562i 0.0411524i
\(261\) −11.4927 7.88335i −0.711379 0.487967i
\(262\) 21.0161i 1.29838i
\(263\) 10.2023 0.629102 0.314551 0.949241i \(-0.398146\pi\)
0.314551 + 0.949241i \(0.398146\pi\)
\(264\) −0.683958 7.40657i −0.0420947 0.455843i
\(265\) 7.36526 7.36526i 0.452444 0.452444i
\(266\) 10.5525i 0.647013i
\(267\) 6.40822 0.591765i 0.392177 0.0362154i
\(268\) −7.22479 −0.441324
\(269\) 22.2257i 1.35513i −0.735465 0.677563i \(-0.763036\pi\)
0.735465 0.677563i \(-0.236964\pi\)
\(270\) −2.53278 + 4.53707i −0.154140 + 0.276118i
\(271\) −0.400523 −0.0243300 −0.0121650 0.999926i \(-0.503872\pi\)
−0.0121650 + 0.999926i \(0.503872\pi\)
\(272\) −4.17376 4.17376i −0.253071 0.253071i
\(273\) 3.62894 0.335114i 0.219633 0.0202820i
\(274\) −14.6837 14.6837i −0.887074 0.887074i
\(275\) 4.29438i 0.258961i
\(276\) −5.94588 + 0.549071i −0.357900 + 0.0330502i
\(277\) −5.22843 5.22843i −0.314146 0.314146i 0.532367 0.846513i \(-0.321302\pi\)
−0.846513 + 0.532367i \(0.821302\pi\)
\(278\) −7.40811 7.40811i −0.444309 0.444309i
\(279\) 0.181566 0.264695i 0.0108701 0.0158469i
\(280\) 3.17089i 0.189497i
\(281\) −7.32785 7.32785i −0.437143 0.437143i 0.453906 0.891049i \(-0.350030\pi\)
−0.891049 + 0.453906i \(0.850030\pi\)
\(282\) −0.0882975 0.956173i −0.00525804 0.0569393i
\(283\) −7.08939 7.08939i −0.421421 0.421421i 0.464272 0.885693i \(-0.346316\pi\)
−0.885693 + 0.464272i \(0.846316\pi\)
\(284\) 8.00969 0.475287
\(285\) 4.43336 + 3.68379i 0.262610 + 0.218209i
\(286\) 2.84959i 0.168500i
\(287\) 19.9243 1.17609
\(288\) −2.47392 1.69697i −0.145777 0.0999952i
\(289\) 17.8405i 1.04944i
\(290\) 3.28489 3.28489i 0.192895 0.192895i
\(291\) 0.319114 0.0294685i 0.0187068 0.00172747i
\(292\) 12.0206 0.703453
\(293\) 27.9995i 1.63575i 0.575399 + 0.817873i \(0.304847\pi\)
−0.575399 + 0.817873i \(0.695153\pi\)
\(294\) −5.26825 + 0.486495i −0.307251 + 0.0283730i
\(295\) 7.67543i 0.446881i
\(296\) 1.20120 5.96298i 0.0698182 0.346591i
\(297\) −10.8767 + 19.4839i −0.631130 + 1.13057i
\(298\) −9.49294 9.49294i −0.549911 0.549911i
\(299\) 2.28760 0.132296
\(300\) −1.33218 1.10694i −0.0769132 0.0639090i
\(301\) −9.32772 + 9.32772i −0.537641 + 0.537641i
\(302\) 8.26055 + 8.26055i 0.475341 + 0.475341i
\(303\) −20.4235 16.9704i −1.17330 0.974924i
\(304\) −2.35319 + 2.35319i −0.134965 + 0.134965i
\(305\) 5.38578i 0.308389i
\(306\) 3.24278 + 17.4083i 0.185378 + 0.995166i
\(307\) 12.1710i 0.694637i 0.937747 + 0.347319i \(0.112908\pi\)
−0.937747 + 0.347319i \(0.887092\pi\)
\(308\) 13.6170i 0.775902i
\(309\) −1.62727 17.6216i −0.0925720 1.00246i
\(310\) 0.0756563 + 0.0756563i 0.00429699 + 0.00429699i
\(311\) −10.9987 + 10.9987i −0.623678 + 0.623678i −0.946470 0.322792i \(-0.895379\pi\)
0.322792 + 0.946470i \(0.395379\pi\)
\(312\) 0.883981 + 0.734521i 0.0500456 + 0.0415840i
\(313\) −24.6477 + 24.6477i −1.39317 + 1.39317i −0.575057 + 0.818113i \(0.695020\pi\)
−0.818113 + 0.575057i \(0.804980\pi\)
\(314\) −3.25094 + 3.25094i −0.183461 + 0.183461i
\(315\) −5.38092 + 7.84454i −0.303181 + 0.441990i
\(316\) 2.36673 + 2.36673i 0.133139 + 0.133139i
\(317\) 24.9951 1.40386 0.701932 0.712244i \(-0.252321\pi\)
0.701932 + 0.712244i \(0.252321\pi\)
\(318\) −1.65895 17.9647i −0.0930290 1.00741i
\(319\) 14.1066 14.1066i 0.789816 0.789816i
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) 0.314186 0.378117i 0.0175362 0.0211044i
\(322\) −10.9315 −0.609191
\(323\) 19.6433 1.09298
\(324\) 3.24056 + 8.39636i 0.180031 + 0.466464i
\(325\) 0.469209 + 0.469209i 0.0260270 + 0.0260270i
\(326\) 18.1152 1.00331
\(327\) 17.2986 1.59744i 0.956615 0.0883384i
\(328\) 4.44310 + 4.44310i 0.245329 + 0.245329i
\(329\) 1.75793i 0.0969178i
\(330\) −5.72087 4.75361i −0.314923 0.261677i
\(331\) 18.9528 18.9528i 1.04174 1.04174i 0.0426473 0.999090i \(-0.486421\pi\)
0.999090 0.0426473i \(-0.0135792\pi\)
\(332\) 10.3371 0.567321
\(333\) −13.0907 + 12.7135i −0.717365 + 0.696697i
\(334\) −3.67053 −0.200842
\(335\) −5.10870 + 5.10870i −0.279118 + 0.279118i
\(336\) −4.22419 3.50998i −0.230448 0.191485i
\(337\) 3.52403i 0.191966i 0.995383 + 0.0959832i \(0.0305995\pi\)
−0.995383 + 0.0959832i \(0.969400\pi\)
\(338\) 8.88104 + 8.88104i 0.483065 + 0.483065i
\(339\) 24.7059 2.28146i 1.34184 0.123912i
\(340\) −5.90259 −0.320113
\(341\) 0.324897 + 0.324897i 0.0175941 + 0.0175941i
\(342\) 9.81490 1.82830i 0.530729 0.0988632i
\(343\) 12.5105 0.675506
\(344\) −4.16015 −0.224300
\(345\) −3.81612 + 4.59262i −0.205453 + 0.247259i
\(346\) −3.72233 + 3.72233i −0.200114 + 0.200114i
\(347\) −6.24635 + 6.24635i −0.335322 + 0.335322i −0.854603 0.519281i \(-0.826200\pi\)
0.519281 + 0.854603i \(0.326200\pi\)
\(348\) −0.739886 8.01221i −0.0396620 0.429500i
\(349\) 32.9526 1.76391 0.881957 0.471330i \(-0.156226\pi\)
0.881957 + 0.471330i \(0.156226\pi\)
\(350\) −2.24216 2.24216i −0.119849 0.119849i
\(351\) −0.940435 3.31724i −0.0501967 0.177061i
\(352\) 3.03659 3.03659i 0.161851 0.161851i
\(353\) 13.3438 13.3438i 0.710218 0.710218i −0.256362 0.966581i \(-0.582524\pi\)
0.966581 + 0.256362i \(0.0825240\pi\)
\(354\) 10.2250 + 8.49621i 0.543453 + 0.451568i
\(355\) 5.66370 5.66370i 0.300598 0.300598i
\(356\) 2.62728 + 2.62728i 0.139245 + 0.139245i
\(357\) 2.98094 + 32.2805i 0.157768 + 1.70847i
\(358\) 13.6427i 0.721037i
\(359\) 0.209030i 0.0110322i −0.999985 0.00551610i \(-0.998244\pi\)
0.999985 0.00551610i \(-0.00175584\pi\)
\(360\) −2.94927 + 0.549384i −0.155440 + 0.0289551i
\(361\) 7.92500i 0.417105i
\(362\) 1.23245 1.23245i 0.0647760 0.0647760i
\(363\) −9.91365 8.23749i −0.520332 0.432356i
\(364\) 1.48781 + 1.48781i 0.0779825 + 0.0779825i
\(365\) 8.49986 8.49986i 0.444903 0.444903i
\(366\) 7.17481 + 5.96172i 0.375033 + 0.311624i
\(367\) 14.8095 0.773048 0.386524 0.922279i \(-0.373676\pi\)
0.386524 + 0.922279i \(0.373676\pi\)
\(368\) −2.43772 2.43772i −0.127075 0.127075i
\(369\) −3.45205 18.5317i −0.179706 0.964722i
\(370\) −3.36709 5.06584i −0.175047 0.263360i
\(371\) 33.0282i 1.71474i
\(372\) 0.184534 0.0170408i 0.00956765 0.000883522i
\(373\) 3.56845i 0.184767i 0.995723 + 0.0923836i \(0.0294486\pi\)
−0.995723 + 0.0923836i \(0.970551\pi\)
\(374\) −25.3479 −1.31071
\(375\) −1.72471 + 0.159268i −0.0890638 + 0.00822457i
\(376\) 0.392017 0.392017i 0.0202167 0.0202167i
\(377\) 3.08260i 0.158762i
\(378\) 4.49396 + 15.8517i 0.231144 + 0.815326i
\(379\) −6.69408 −0.343852 −0.171926 0.985110i \(-0.554999\pi\)
−0.171926 + 0.985110i \(0.554999\pi\)
\(380\) 3.32791i 0.170718i
\(381\) 15.8286 + 13.1524i 0.810925 + 0.673817i
\(382\) −25.0182 −1.28004
\(383\) −10.2592 10.2592i −0.524221 0.524221i 0.394622 0.918843i \(-0.370875\pi\)
−0.918843 + 0.394622i \(0.870875\pi\)
\(384\) −0.159268 1.72471i −0.00812762 0.0880139i
\(385\) −9.62869 9.62869i −0.490723 0.490723i
\(386\) 3.26985i 0.166431i
\(387\) 10.2919 + 7.05966i 0.523165 + 0.358863i
\(388\) 0.130832 + 0.130832i 0.00664199 + 0.00664199i
\(389\) −11.2832 11.2832i −0.572079 0.572079i 0.360630 0.932709i \(-0.382562\pi\)
−0.932709 + 0.360630i \(0.882562\pi\)
\(390\) 1.14445 0.105684i 0.0579516 0.00535153i
\(391\) 20.3489i 1.02909i
\(392\) −2.15991 2.15991i −0.109092 0.109092i
\(393\) 36.2467 3.34720i 1.82841 0.168844i
\(394\) −17.1186 17.1186i −0.862425 0.862425i
\(395\) 3.34706 0.168409
\(396\) −12.6653 + 2.35926i −0.636454 + 0.118557i
\(397\) 15.5131i 0.778580i 0.921115 + 0.389290i \(0.127280\pi\)
−0.921115 + 0.389290i \(0.872720\pi\)
\(398\) 21.8451 1.09500
\(399\) 18.2000 1.68067i 0.911138 0.0841388i
\(400\) 1.00000i 0.0500000i
\(401\) −1.36032 + 1.36032i −0.0679314 + 0.0679314i −0.740256 0.672325i \(-0.765296\pi\)
0.672325 + 0.740256i \(0.265296\pi\)
\(402\) 1.15068 + 12.4607i 0.0573907 + 0.621483i
\(403\) −0.0709972 −0.00353662
\(404\) 15.3310i 0.762744i
\(405\) 8.22854 + 3.64570i 0.408879 + 0.181156i
\(406\) 14.7305i 0.731063i
\(407\) −14.4596 21.7546i −0.716733 1.07834i
\(408\) −6.53379 + 7.86328i −0.323471 + 0.389290i
\(409\) −9.43162 9.43162i −0.466363 0.466363i 0.434371 0.900734i \(-0.356971\pi\)
−0.900734 + 0.434371i \(0.856971\pi\)
\(410\) 6.28349 0.310320
\(411\) −22.9865 + 27.6638i −1.13384 + 1.36455i
\(412\) 7.22462 7.22462i 0.355931 0.355931i
\(413\) 17.2095 + 17.2095i 0.846826 + 0.846826i
\(414\) 1.89398 + 10.1675i 0.0930840 + 0.499705i
\(415\) 7.30943 7.30943i 0.358806 0.358806i
\(416\) 0.663562i 0.0325338i
\(417\) −11.5970 + 13.9567i −0.567907 + 0.683464i
\(418\) 14.2913i 0.699011i
\(419\) 30.3868i 1.48449i 0.670128 + 0.742246i \(0.266239\pi\)
−0.670128 + 0.742246i \(0.733761\pi\)
\(420\) −5.46888 + 0.505022i −0.266854 + 0.0246426i
\(421\) 7.53525 + 7.53525i 0.367246 + 0.367246i 0.866472 0.499226i \(-0.166382\pi\)
−0.499226 + 0.866472i \(0.666382\pi\)
\(422\) −18.5617 + 18.5617i −0.903571 + 0.903571i
\(423\) −1.63506 + 0.304576i −0.0794994 + 0.0148090i
\(424\) 7.36526 7.36526i 0.357689 0.357689i
\(425\) −4.17376 + 4.17376i −0.202457 + 0.202457i
\(426\) −1.27569 13.8144i −0.0618073 0.669310i
\(427\) 12.0758 + 12.0758i 0.584389 + 0.584389i
\(428\) 0.283834 0.0137196
\(429\) 4.91472 0.453848i 0.237285 0.0219120i
\(430\) −2.94167 + 2.94167i −0.141860 + 0.141860i
\(431\) 13.1264 13.1264i 0.632279 0.632279i −0.316360 0.948639i \(-0.602461\pi\)
0.948639 + 0.316360i \(0.102461\pi\)
\(432\) −2.53278 + 4.53707i −0.121858 + 0.218290i
\(433\) 21.3135 1.02426 0.512131 0.858907i \(-0.328856\pi\)
0.512131 + 0.858907i \(0.328856\pi\)
\(434\) 0.339267 0.0162853
\(435\) −6.18867 5.14231i −0.296724 0.246555i
\(436\) 7.09218 + 7.09218i 0.339654 + 0.339654i
\(437\) 11.4729 0.548821
\(438\) −1.91450 20.7321i −0.0914784 0.990619i
\(439\) 1.95249 + 1.95249i 0.0931874 + 0.0931874i 0.752164 0.658976i \(-0.229010\pi\)
−0.658976 + 0.752164i \(0.729010\pi\)
\(440\) 4.29438i 0.204727i
\(441\) 1.67813 + 9.00874i 0.0799109 + 0.428987i
\(442\) 2.76955 2.76955i 0.131734 0.131734i
\(443\) −40.7519 −1.93618 −0.968089 0.250605i \(-0.919371\pi\)
−0.968089 + 0.250605i \(0.919371\pi\)
\(444\) −10.4757 1.12201i −0.497157 0.0532482i
\(445\) 3.71553 0.176133
\(446\) −11.8510 + 11.8510i −0.561160 + 0.561160i
\(447\) −14.8607 + 17.8845i −0.702886 + 0.845909i
\(448\) 3.17089i 0.149811i
\(449\) −16.4400 16.4400i −0.775853 0.775853i 0.203269 0.979123i \(-0.434843\pi\)
−0.979123 + 0.203269i \(0.934843\pi\)
\(450\) −1.69697 + 2.47392i −0.0799961 + 0.116622i
\(451\) 26.9837 1.27061
\(452\) 10.1290 + 10.1290i 0.476430 + 0.476430i
\(453\) 12.9314 15.5627i 0.607572 0.731200i
\(454\) −3.25660 −0.152840
\(455\) 2.10408 0.0986410
\(456\) 4.43336 + 3.68379i 0.207611 + 0.172509i
\(457\) −13.7781 + 13.7781i −0.644512 + 0.644512i −0.951661 0.307149i \(-0.900625\pi\)
0.307149 + 0.951661i \(0.400625\pi\)
\(458\) 2.00313 2.00313i 0.0936002 0.0936002i
\(459\) 29.5078 8.36546i 1.37731 0.390466i
\(460\) −3.44746 −0.160739
\(461\) 14.2992 + 14.2992i 0.665979 + 0.665979i 0.956783 0.290804i \(-0.0939226\pi\)
−0.290804 + 0.956783i \(0.593923\pi\)
\(462\) −23.4855 + 2.16876i −1.09264 + 0.100900i
\(463\) 22.7343 22.7343i 1.05655 1.05655i 0.0582522 0.998302i \(-0.481447\pi\)
0.998302 0.0582522i \(-0.0185528\pi\)
\(464\) 3.28489 3.28489i 0.152497 0.152497i
\(465\) 0.118436 0.142535i 0.00549232 0.00660990i
\(466\) 9.24326 9.24326i 0.428186 0.428186i
\(467\) −25.3750 25.3750i −1.17422 1.17422i −0.981194 0.193022i \(-0.938171\pi\)
−0.193022 0.981194i \(-0.561829\pi\)
\(468\) 1.12605 1.64160i 0.0520515 0.0758829i
\(469\) 22.9090i 1.05784i
\(470\) 0.554395i 0.0255724i
\(471\) 6.12471 + 5.08917i 0.282212 + 0.234497i
\(472\) 7.67543i 0.353290i
\(473\) −12.6326 + 12.6326i −0.580849 + 0.580849i
\(474\) 3.70499 4.45888i 0.170176 0.204803i
\(475\) 2.35319 + 2.35319i 0.107972 + 0.107972i
\(476\) −13.2345 + 13.2345i −0.606604 + 0.606604i
\(477\) −30.7197 + 5.72241i −1.40656 + 0.262011i
\(478\) −9.39473 −0.429705
\(479\) 28.4324 + 28.4324i 1.29911 + 1.29911i 0.928981 + 0.370127i \(0.120686\pi\)
0.370127 + 0.928981i \(0.379314\pi\)
\(480\) −1.33218 1.10694i −0.0608052 0.0505245i
\(481\) 3.95681 + 0.797069i 0.180415 + 0.0363432i
\(482\) 8.18905i 0.373001i
\(483\) 1.74105 + 18.8538i 0.0792203 + 0.857876i
\(484\) 7.44170i 0.338259i
\(485\) 0.185024 0.00840152
\(486\) 13.9652 6.92630i 0.633474 0.314183i
\(487\) −8.44631 + 8.44631i −0.382739 + 0.382739i −0.872088 0.489349i \(-0.837234\pi\)
0.489349 + 0.872088i \(0.337234\pi\)
\(488\) 5.38578i 0.243803i
\(489\) −2.88518 31.2436i −0.130472 1.41288i
\(490\) −3.05457 −0.137991
\(491\) 21.3703i 0.964426i −0.876054 0.482213i \(-0.839833\pi\)
0.876054 0.482213i \(-0.160167\pi\)
\(492\) 6.95543 8.37071i 0.313575 0.377381i
\(493\) −27.4207 −1.23497
\(494\) −1.56149 1.56149i −0.0702546 0.0702546i
\(495\) −7.28745 + 10.6240i −0.327547 + 0.477511i
\(496\) 0.0756563 + 0.0756563i 0.00339707 + 0.00339707i
\(497\) 25.3979i 1.13925i
\(498\) −1.64637 17.8285i −0.0737756 0.798915i
\(499\) −23.8771 23.8771i −1.06888 1.06888i −0.997445 0.0714387i \(-0.977241\pi\)
−0.0714387 0.997445i \(-0.522759\pi\)
\(500\) −0.707107 0.707107i −0.0316228 0.0316228i
\(501\) 0.584598 + 6.33060i 0.0261179 + 0.282831i
\(502\) 5.05509i 0.225620i
\(503\) −17.4364 17.4364i −0.777452 0.777452i 0.201945 0.979397i \(-0.435274\pi\)
−0.979397 + 0.201945i \(0.935274\pi\)
\(504\) −5.38092 + 7.84454i −0.239685 + 0.349423i
\(505\) −10.8406 10.8406i −0.482402 0.482402i
\(506\) −14.8047 −0.658150
\(507\) 13.9028 16.7317i 0.617444 0.743081i
\(508\) 11.8818i 0.527169i
\(509\) 27.3051 1.21028 0.605139 0.796120i \(-0.293118\pi\)
0.605139 + 0.796120i \(0.293118\pi\)
\(510\) 0.940094 + 10.1803i 0.0416281 + 0.450790i
\(511\) 38.1161i 1.68616i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −4.71649 16.6367i −0.208238 0.734528i
\(514\) 3.65956 0.161416
\(515\) 10.2172i 0.450221i
\(516\) 0.662579 + 7.17506i 0.0291684 + 0.315864i
\(517\) 2.38078i 0.104707i
\(518\) −18.9080 3.80887i −0.830769 0.167352i
\(519\) 7.01280 + 5.82710i 0.307828 + 0.255781i
\(520\) 0.469209 + 0.469209i 0.0205762 + 0.0205762i
\(521\) 33.5578 1.47019 0.735097 0.677962i \(-0.237137\pi\)
0.735097 + 0.677962i \(0.237137\pi\)
\(522\) −13.7009 + 2.55218i −0.599673 + 0.111706i
\(523\) −3.03654 + 3.03654i −0.132779 + 0.132779i −0.770373 0.637594i \(-0.779930\pi\)
0.637594 + 0.770373i \(0.279930\pi\)
\(524\) 14.8606 + 14.8606i 0.649190 + 0.649190i
\(525\) −3.50998 + 4.22419i −0.153188 + 0.184359i
\(526\) 7.21413 7.21413i 0.314551 0.314551i
\(527\) 0.631542i 0.0275104i
\(528\) −5.72087 4.75361i −0.248969 0.206874i
\(529\) 11.1150i 0.483261i
\(530\) 10.4161i 0.452444i
\(531\) 13.0250 18.9884i 0.565237 0.824026i
\(532\) 7.46172 + 7.46172i 0.323506 + 0.323506i
\(533\) −2.94827 + 2.94827i −0.127704 + 0.127704i
\(534\) 4.11285 4.94974i 0.177981 0.214196i
\(535\) 0.200701 0.200701i 0.00867707 0.00867707i
\(536\) −5.10870 + 5.10870i −0.220662 + 0.220662i
\(537\) 23.5297 2.17284i 1.01538 0.0937650i
\(538\) −15.7160 15.7160i −0.677563 0.677563i
\(539\) −13.1175 −0.565010
\(540\) 1.41725 + 4.99914i 0.0609889 + 0.215129i
\(541\) −5.18238 + 5.18238i −0.222808 + 0.222808i −0.809680 0.586872i \(-0.800359\pi\)
0.586872 + 0.809680i \(0.300359\pi\)
\(542\) −0.283212 + 0.283212i −0.0121650 + 0.0121650i
\(543\) −2.32191 1.92933i −0.0996425 0.0827953i
\(544\) −5.90259 −0.253071
\(545\) 10.0299 0.429632
\(546\) 2.32909 2.80301i 0.0996757 0.119958i
\(547\) −2.14503 2.14503i −0.0917148 0.0917148i 0.659761 0.751476i \(-0.270658\pi\)
−0.751476 + 0.659761i \(0.770658\pi\)
\(548\) −20.7659 −0.887074
\(549\) 9.13954 13.3240i 0.390066 0.568654i
\(550\) −3.03659 3.03659i −0.129480 0.129480i
\(551\) 15.4599i 0.658616i
\(552\) −3.81612 + 4.59262i −0.162425 + 0.195475i
\(553\) 7.50466 7.50466i 0.319130 0.319130i
\(554\) −7.39412 −0.314146
\(555\) −8.20085 + 6.61409i −0.348107 + 0.280752i
\(556\) −10.4767 −0.444309
\(557\) 4.77952 4.77952i 0.202515 0.202515i −0.598562 0.801077i \(-0.704261\pi\)
0.801077 + 0.598562i \(0.204261\pi\)
\(558\) −0.0587808 0.315554i −0.00248839 0.0133585i
\(559\) 2.76051i 0.116757i
\(560\) −2.24216 2.24216i −0.0947486 0.0947486i
\(561\) 4.03712 + 43.7179i 0.170447 + 1.84577i
\(562\) −10.3631 −0.437143
\(563\) 20.9149 + 20.9149i 0.881459 + 0.881459i 0.993683 0.112224i \(-0.0357973\pi\)
−0.112224 + 0.993683i \(0.535797\pi\)
\(564\) −0.738552 0.613680i −0.0310987 0.0258406i
\(565\) 14.3246 0.602642
\(566\) −10.0259 −0.421421
\(567\) 26.6240 10.2755i 1.11810 0.431529i
\(568\) 5.66370 5.66370i 0.237644 0.237644i
\(569\) −23.7328 + 23.7328i −0.994929 + 0.994929i −0.999987 0.00505843i \(-0.998390\pi\)
0.00505843 + 0.999987i \(0.498390\pi\)
\(570\) 5.73969 0.530030i 0.240409 0.0222005i
\(571\) 47.2125 1.97578 0.987890 0.155154i \(-0.0495873\pi\)
0.987890 + 0.155154i \(0.0495873\pi\)
\(572\) 2.01496 + 2.01496i 0.0842498 + 0.0842498i
\(573\) 3.98460 + 43.1492i 0.166459 + 1.80258i
\(574\) 14.0886 14.0886i 0.588047 0.588047i
\(575\) −2.43772 + 2.43772i −0.101660 + 0.101660i
\(576\) −2.94927 + 0.549384i −0.122886 + 0.0228910i
\(577\) 13.8837 13.8837i 0.577985 0.577985i −0.356363 0.934348i \(-0.615983\pi\)
0.934348 + 0.356363i \(0.115983\pi\)
\(578\) 12.6152 + 12.6152i 0.524721 + 0.524721i
\(579\) −5.63955 + 0.520783i −0.234372 + 0.0216430i
\(580\) 4.64554i 0.192895i
\(581\) 32.7778i 1.35985i
\(582\) 0.204810 0.246485i 0.00848965 0.0102171i
\(583\) 44.7305i 1.85255i
\(584\) 8.49986 8.49986i 0.351727 0.351727i
\(585\) −0.364550 1.95702i −0.0150723 0.0809129i
\(586\) 19.7986 + 19.7986i 0.817873 + 0.817873i
\(587\) −28.2138 + 28.2138i −1.16451 + 1.16451i −0.181033 + 0.983477i \(0.557944\pi\)
−0.983477 + 0.181033i \(0.942056\pi\)
\(588\) −3.38121 + 4.06922i −0.139439 + 0.167812i
\(589\) −0.356067 −0.0146715
\(590\) 5.42735 + 5.42735i 0.223440 + 0.223440i
\(591\) −26.7983 + 32.2512i −1.10233 + 1.32664i
\(592\) −3.36709 5.06584i −0.138386 0.208205i
\(593\) 6.81280i 0.279768i 0.990168 + 0.139884i \(0.0446730\pi\)
−0.990168 + 0.139884i \(0.955327\pi\)
\(594\) 6.08622 + 21.4682i 0.249721 + 0.880851i
\(595\) 18.7165i 0.767301i
\(596\) −13.4251 −0.549911
\(597\) −3.47923 37.6765i −0.142395 1.54200i
\(598\) 1.61758 1.61758i 0.0661478 0.0661478i
\(599\) 35.3959i 1.44624i 0.690724 + 0.723119i \(0.257292\pi\)
−0.690724 + 0.723119i \(0.742708\pi\)
\(600\) −1.72471 + 0.159268i −0.0704111 + 0.00650209i
\(601\) −9.54349 −0.389287 −0.194643 0.980874i \(-0.562355\pi\)
−0.194643 + 0.980874i \(0.562355\pi\)
\(602\) 13.1914i 0.537641i
\(603\) 21.3078 3.96918i 0.867722 0.161638i
\(604\) 11.6822 0.475341
\(605\) −5.26208 5.26208i −0.213934 0.213934i
\(606\) −26.4415 + 2.44173i −1.07411 + 0.0991887i
\(607\) 14.5767 + 14.5767i 0.591650 + 0.591650i 0.938077 0.346427i \(-0.112605\pi\)
−0.346427 + 0.938077i \(0.612605\pi\)
\(608\) 3.32791i 0.134965i
\(609\) −25.4059 + 2.34610i −1.02950 + 0.0950688i
\(610\) 3.80832 + 3.80832i 0.154195 + 0.154195i
\(611\) 0.260127 + 0.260127i 0.0105236 + 0.0105236i
\(612\) 14.6025 + 10.0165i 0.590272 + 0.404894i
\(613\) 46.0780i 1.86107i −0.366198 0.930537i \(-0.619341\pi\)
0.366198 0.930537i \(-0.380659\pi\)
\(614\) 8.60622 + 8.60622i 0.347319 + 0.347319i
\(615\) −1.00076 10.8372i −0.0403545 0.436999i
\(616\) −9.62869 9.62869i −0.387951 0.387951i
\(617\) −8.81089 −0.354713 −0.177357 0.984147i \(-0.556755\pi\)
−0.177357 + 0.984147i \(0.556755\pi\)
\(618\) −13.6110 11.3097i −0.547516 0.454944i
\(619\) 31.5228i 1.26701i −0.773740 0.633504i \(-0.781616\pi\)
0.773740 0.633504i \(-0.218384\pi\)
\(620\) 0.106994 0.00429699
\(621\) 17.2343 4.88593i 0.691590 0.196065i
\(622\) 15.5545i 0.623678i
\(623\) 8.33081 8.33081i 0.333767 0.333767i
\(624\) 1.14445 0.105684i 0.0458148 0.00423076i
\(625\) −1.00000 −0.0400000
\(626\) 34.8571i 1.39317i
\(627\) 24.6484 2.27615i 0.984363 0.0909008i
\(628\) 4.59753i 0.183461i
\(629\) −7.09018 + 35.1970i −0.282704 + 1.40340i
\(630\) 1.74204 + 9.35181i 0.0694044 + 0.372585i
\(631\) −18.7269 18.7269i −0.745504 0.745504i 0.228127 0.973631i \(-0.426740\pi\)
−0.973631 + 0.228127i \(0.926740\pi\)
\(632\) 3.34706 0.133139
\(633\) 34.9700 + 29.0574i 1.38993 + 1.15493i
\(634\) 17.6742 17.6742i 0.701932 0.701932i
\(635\) 8.40169 + 8.40169i 0.333411 + 0.333411i
\(636\) −13.8760 11.5299i −0.550220 0.457191i
\(637\) 1.43323 1.43323i 0.0567867 0.0567867i
\(638\) 19.9497i 0.789816i
\(639\) −23.6227 + 4.40039i −0.934500 + 0.174077i
\(640\) 1.00000i 0.0395285i
\(641\) 12.3332i 0.487131i 0.969884 + 0.243565i \(0.0783170\pi\)
−0.969884 + 0.243565i \(0.921683\pi\)
\(642\) −0.0452057 0.489532i −0.00178413 0.0193203i
\(643\) 17.2628 + 17.2628i 0.680776 + 0.680776i 0.960175 0.279399i \(-0.0901351\pi\)
−0.279399 + 0.960175i \(0.590135\pi\)
\(644\) −7.72976 + 7.72976i −0.304595 + 0.304595i
\(645\) 5.54204 + 4.60502i 0.218218 + 0.181322i
\(646\) 13.8899 13.8899i 0.546491 0.546491i
\(647\) 9.42234 9.42234i 0.370430 0.370430i −0.497204 0.867634i \(-0.665640\pi\)
0.867634 + 0.497204i \(0.165640\pi\)
\(648\) 8.22854 + 3.64570i 0.323248 + 0.143217i
\(649\) 23.3071 + 23.3071i 0.914883 + 0.914883i
\(650\) 0.663562 0.0260270
\(651\) −0.0540344 0.585138i −0.00211778 0.0229334i
\(652\) 12.8094 12.8094i 0.501655 0.501655i
\(653\) −5.72159 + 5.72159i −0.223903 + 0.223903i −0.810140 0.586237i \(-0.800609\pi\)
0.586237 + 0.810140i \(0.300609\pi\)
\(654\) 11.1024 13.3615i 0.434138 0.522477i
\(655\) 21.0161 0.821167
\(656\) 6.28349 0.245329
\(657\) −35.4520 + 6.60393i −1.38311 + 0.257644i
\(658\) −1.24304 1.24304i −0.0484589 0.0484589i
\(659\) −5.42404 −0.211291 −0.105645 0.994404i \(-0.533691\pi\)
−0.105645 + 0.994404i \(0.533691\pi\)
\(660\) −7.40657 + 0.683958i −0.288300 + 0.0266230i
\(661\) 11.0748 + 11.0748i 0.430758 + 0.430758i 0.888886 0.458128i \(-0.151480\pi\)
−0.458128 + 0.888886i \(0.651480\pi\)
\(662\) 26.8032i 1.04174i
\(663\) −5.21777 4.33557i −0.202641 0.168380i
\(664\) 7.30943 7.30943i 0.283661 0.283661i
\(665\) 10.5525 0.409207
\(666\) −0.266692 + 18.2463i −0.0103341 + 0.707031i
\(667\) −16.0153 −0.620115
\(668\) −2.59545 + 2.59545i −0.100421 + 0.100421i
\(669\) 22.3270 + 18.5520i 0.863212 + 0.717264i
\(670\) 7.22479i 0.279118i
\(671\) 16.3544 + 16.3544i 0.631354 + 0.631354i
\(672\) −5.46888 + 0.505022i −0.210967 + 0.0194817i
\(673\) −24.4076 −0.940843 −0.470422 0.882442i \(-0.655898\pi\)
−0.470422 + 0.882442i \(0.655898\pi\)
\(674\) 2.49187 + 2.49187i 0.0959832 + 0.0959832i
\(675\) 4.53707 + 2.53278i 0.174632 + 0.0974866i
\(676\) 12.5597 0.483065
\(677\) 25.9755 0.998319 0.499160 0.866510i \(-0.333642\pi\)
0.499160 + 0.866510i \(0.333642\pi\)
\(678\) 15.8565 19.0829i 0.608963 0.732875i
\(679\) 0.414854 0.414854i 0.0159206 0.0159206i
\(680\) −4.17376 + 4.17376i −0.160056 + 0.160056i
\(681\) 0.518673 + 5.61670i 0.0198756 + 0.215233i
\(682\) 0.459473 0.0175941
\(683\) 17.5140 + 17.5140i 0.670156 + 0.670156i 0.957752 0.287596i \(-0.0928561\pi\)
−0.287596 + 0.957752i \(0.592856\pi\)
\(684\) 5.64738 8.23299i 0.215933 0.314796i
\(685\) −14.6837 + 14.6837i −0.561035 + 0.561035i
\(686\) 8.84629 8.84629i 0.337753 0.337753i
\(687\) −3.77386 3.13579i −0.143982 0.119638i
\(688\) −2.94167 + 2.94167i −0.112150 + 0.112150i
\(689\) 4.88731 + 4.88731i 0.186192 + 0.186192i
\(690\) 0.549071 + 5.94588i 0.0209028 + 0.226356i
\(691\) 27.6376i 1.05138i −0.850675 0.525692i \(-0.823807\pi\)
0.850675 0.525692i \(-0.176193\pi\)
\(692\) 5.26417i 0.200114i
\(693\) 7.48097 + 40.1602i 0.284179 + 1.52556i
\(694\) 8.83368i 0.335322i
\(695\) −7.40811 + 7.40811i −0.281006 + 0.281006i
\(696\) −6.18867 5.14231i −0.234581 0.194919i
\(697\) −26.2258 26.2258i −0.993372 0.993372i
\(698\) 23.3010 23.3010i 0.881957 0.881957i
\(699\) −17.4141 14.4698i −0.658663 0.547299i
\(700\) −3.17089 −0.119849
\(701\) −0.160630 0.160630i −0.00606691 0.00606691i 0.704067 0.710134i \(-0.251366\pi\)
−0.710134 + 0.704067i \(0.751366\pi\)
\(702\) −3.01063 1.68065i −0.113629 0.0634322i
\(703\) 19.8443 + 3.99748i 0.748441 + 0.150768i
\(704\) 4.29438i 0.161851i
\(705\) −0.956173 + 0.0882975i −0.0360116 + 0.00332548i
\(706\) 18.8710i 0.710218i
\(707\) −48.6129 −1.82828
\(708\) 13.2379 1.22245i 0.497511 0.0459425i
\(709\) −9.93985 + 9.93985i −0.373299 + 0.373299i −0.868677 0.495378i \(-0.835029\pi\)
0.495378 + 0.868677i \(0.335029\pi\)
\(710\) 8.00969i 0.300598i
\(711\) −8.28037 5.67988i −0.310538 0.213012i
\(712\) 3.71553 0.139245
\(713\) 0.368858i 0.0138138i
\(714\) 24.9336 + 20.7179i 0.933118 + 0.775350i
\(715\) 2.84959 0.106568
\(716\) 9.64682 + 9.64682i 0.360518 + 0.360518i
\(717\) 1.49628 + 16.2032i 0.0558797 + 0.605120i
\(718\) −0.147807 0.147807i −0.00551610 0.00551610i
\(719\) 4.09595i 0.152753i −0.997079 0.0763766i \(-0.975665\pi\)
0.997079 0.0763766i \(-0.0243351\pi\)
\(720\) −1.69697 + 2.47392i −0.0632425 + 0.0921975i
\(721\) −22.9085 22.9085i −0.853157 0.853157i
\(722\) 5.60382 + 5.60382i 0.208553 + 0.208553i
\(723\) 14.1238 1.30425i 0.525268 0.0485057i
\(724\) 1.74294i 0.0647760i
\(725\) −3.28489 3.28489i −0.121998 0.121998i
\(726\) −12.8348 + 1.18523i −0.476344 + 0.0439879i
\(727\) 18.7410 + 18.7410i 0.695066 + 0.695066i 0.963342 0.268276i \(-0.0864540\pi\)
−0.268276 + 0.963342i \(0.586454\pi\)
\(728\) 2.10408 0.0779825
\(729\) −14.1701 22.9828i −0.524818 0.851214i
\(730\) 12.0206i 0.444903i
\(731\) 24.5556 0.908222
\(732\) 9.28893 0.857784i 0.343329 0.0317046i
\(733\) 16.3805i 0.605026i −0.953145 0.302513i \(-0.902174\pi\)
0.953145 0.302513i \(-0.0978255\pi\)
\(734\) 10.4719 10.4719i 0.386524 0.386524i
\(735\) 0.486495 + 5.26825i 0.0179447 + 0.194322i
\(736\) −3.44746 −0.127075
\(737\) 31.0260i 1.14286i
\(738\) −15.5449 10.6629i −0.572214 0.392508i
\(739\) 46.1239i 1.69670i 0.529439 + 0.848348i \(0.322403\pi\)
−0.529439 + 0.848348i \(0.677597\pi\)
\(740\) −5.96298 1.20120i −0.219203 0.0441569i
\(741\) −2.44442 + 2.94181i −0.0897980 + 0.108070i
\(742\) −23.3545 23.3545i −0.857369 0.857369i
\(743\) −39.6883 −1.45602 −0.728012 0.685565i \(-0.759555\pi\)
−0.728012 + 0.685565i \(0.759555\pi\)
\(744\) 0.118436 0.142535i 0.00434206 0.00522558i
\(745\) −9.49294 + 9.49294i −0.347795 + 0.347795i
\(746\) 2.52327 + 2.52327i 0.0923836 + 0.0923836i
\(747\) −30.4868 + 5.67903i −1.11546 + 0.207785i
\(748\) −17.9237 + 17.9237i −0.655356 + 0.655356i
\(749\) 0.900008i 0.0328856i
\(750\) −1.10694 + 1.33218i −0.0404196 + 0.0486442i
\(751\) 46.3282i 1.69054i 0.534339 + 0.845270i \(0.320560\pi\)
−0.534339 + 0.845270i \(0.679440\pi\)
\(752\) 0.554395i 0.0202167i
\(753\) −8.71858 + 0.805115i −0.317723 + 0.0293400i
\(754\) 2.17973 + 2.17973i 0.0793810 + 0.0793810i
\(755\) 8.26055 8.26055i 0.300632 0.300632i
\(756\) 14.3866 + 8.03116i 0.523235 + 0.292091i
\(757\) 6.01198 6.01198i 0.218509 0.218509i −0.589361 0.807870i \(-0.700620\pi\)
0.807870 + 0.589361i \(0.200620\pi\)
\(758\) −4.73343 + 4.73343i −0.171926 + 0.171926i
\(759\) 2.35792 + 25.5339i 0.0855870 + 0.926821i
\(760\) 2.35319 + 2.35319i 0.0853592 + 0.0853592i
\(761\) 1.71775 0.0622685 0.0311343 0.999515i \(-0.490088\pi\)
0.0311343 + 0.999515i \(0.490088\pi\)
\(762\) 20.4927 1.89239i 0.742371 0.0685540i
\(763\) 22.4885 22.4885i 0.814140 0.814140i
\(764\) −17.6905 + 17.6905i −0.640021 + 0.640021i
\(765\) 17.4083 3.24278i 0.629399 0.117243i
\(766\) −14.5087 −0.524221
\(767\) −5.09312 −0.183902
\(768\) −1.33218 1.10694i −0.0480707 0.0399431i
\(769\) −28.0211 28.0211i −1.01047 1.01047i −0.999945 0.0105221i \(-0.996651\pi\)
−0.0105221 0.999945i \(-0.503349\pi\)
\(770\) −13.6170 −0.490723
\(771\) −0.582851 6.31169i −0.0209909 0.227310i
\(772\) −2.31213 2.31213i −0.0832155 0.0832155i
\(773\) 23.3393i 0.839457i 0.907650 + 0.419729i \(0.137875\pi\)
−0.907650 + 0.419729i \(0.862125\pi\)
\(774\) 12.2694 2.28552i 0.441014 0.0821512i
\(775\) 0.0756563 0.0756563i 0.00271765 0.00271765i
\(776\) 0.185024 0.00664199
\(777\) −3.55777 + 33.2175i −0.127634 + 1.19167i
\(778\) −15.9568 −0.572079
\(779\) −14.7862 + 14.7862i