Properties

Label 1110.2.u.f.401.5
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 401.5
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.f.191.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.159268 + 1.72471i) q^{6} -3.17089 q^{7} +(0.707107 + 0.707107i) q^{8} +(0.549384 - 2.94927i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.33218 - 1.10694i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.159268 + 1.72471i) 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} +(1.72471 + 0.159268i) q^{15} -1.00000 q^{16} +(-4.17376 - 4.17376i) q^{17} +(1.69697 + 2.47392i) 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} +(1.72471 + 0.159268i) 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} +(0.105684 - 1.14445i) q^{39} +1.00000i q^{40} +6.28349 q^{41} +(0.505022 - 5.46888i) q^{42} +(2.94167 - 2.94167i) q^{43} -4.29438i q^{44} +(2.47392 - 1.69697i) 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} +(-10.1803 - 0.940094i) q^{51} +(-0.469209 - 0.469209i) q^{52} -10.4161i q^{53} +(4.99914 + 1.41725i) q^{54} +(3.03659 + 3.03659i) q^{55} +(-2.24216 - 2.24216i) q^{56} +(0.530030 - 5.73969i) q^{57} +4.64554i q^{58} +(5.42735 + 5.42735i) q^{59} +(0.159268 - 1.72471i) 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} +(-0.683958 + 7.40657i) q^{66} -7.22479i q^{67} +(-4.17376 + 4.17376i) q^{68} +(-5.94588 - 0.549071i) q^{69} +3.17089 q^{70} -8.00969i q^{71} +(2.47392 - 1.69697i) 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} +(0.739886 - 8.01221i) 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} +(-0.184534 - 0.0170408i) q^{93} +(0.392017 + 0.392017i) q^{94} +3.32791 q^{95} +(0.159268 - 1.72471i) 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
\(6\) −0.159268 + 1.72471i −0.0650209 + 0.704111i
\(7\) −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 \(-0.275855\pi\)
0.647402 + 0.762149i \(0.275855\pi\)
\(12\) −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
\(15\) 1.72471 + 0.159268i 0.445319 + 0.0411229i
\(16\) −1.00000 −0.250000
\(17\) −4.17376 4.17376i −1.01229 1.01229i −0.999924 0.0123615i \(-0.996065\pi\)
−0.0123615 0.999924i \(-0.503935\pi\)
\(18\) 1.69697 + 2.47392i 0.399981 + 0.583108i
\(19\) 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 0.405704 0.914005i \(-0.367026\pi\)
−0.914005 + 0.405704i \(0.867026\pi\)
\(24\) 1.72471 + 0.159268i 0.352055 + 0.0325105i
\(25\) 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 −0.332954 0.942943i \(-0.608045\pi\)
0.942943 + 0.332954i \(0.108045\pi\)
\(30\) −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
\(39\) 0.105684 1.14445i 0.0169230 0.183259i
\(40\) 1.00000i 0.158114i
\(41\) 6.28349 0.981316 0.490658 0.871352i \(-0.336756\pi\)
0.490658 + 0.871352i \(0.336756\pi\)
\(42\) 0.505022 5.46888i 0.0779266 0.843867i
\(43\) 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
\(45\) 2.47392 1.69697i 0.368790 0.252970i
\(46\) 3.44746 0.508301
\(47\) 0.554395i 0.0808669i −0.999182 0.0404334i \(-0.987126\pi\)
0.999182 0.0404334i \(-0.0128739\pi\)
\(48\) −1.33218 + 1.10694i −0.192283 + 0.159773i
\(49\) 3.05457 0.436367
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) −10.1803 0.940094i −1.42552 0.131639i
\(52\) −0.469209 0.469209i −0.0650676 0.0650676i
\(53\) 10.4161i 1.43075i −0.698738 0.715377i \(-0.746255\pi\)
0.698738 0.715377i \(-0.253745\pi\)
\(54\) 4.99914 + 1.41725i 0.680297 + 0.192864i
\(55\) 3.03659 + 3.03659i 0.409453 + 0.409453i
\(56\) −2.24216 2.24216i −0.299621 0.299621i
\(57\) 0.530030 5.73969i 0.0702043 0.760241i
\(58\) 4.64554i 0.609989i
\(59\) 5.42735 + 5.42735i 0.706580 + 0.706580i 0.965814 0.259234i \(-0.0834701\pi\)
−0.259234 + 0.965814i \(0.583470\pi\)
\(60\) 0.159268 1.72471i 0.0205614 0.222659i
\(61\) −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
\(66\) −0.683958 + 7.40657i −0.0841894 + 0.911686i
\(67\) 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
\(69\) −5.94588 0.549071i −0.715800 0.0661004i
\(70\) 3.17089 0.378994
\(71\) 8.00969i 0.950575i −0.879831 0.475287i \(-0.842344\pi\)
0.879831 0.475287i \(-0.157656\pi\)
\(72\) 2.47392 1.69697i 0.291554 0.199990i
\(73\) 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 \(-0.807980\pi\)
0.823496 0.567321i \(-0.192020\pi\)
\(84\) 3.50998 + 4.22419i 0.382970 + 0.460897i
\(85\) 5.90259i 0.640225i
\(86\) 4.16015i 0.448600i
\(87\) 0.739886 8.01221i 0.0793241 0.859000i
\(88\) 3.03659 + 3.03659i 0.323701 + 0.323701i
\(89\) 2.62728 2.62728i 0.278491 0.278491i −0.554016 0.832506i \(-0.686905\pi\)
0.832506 + 0.554016i \(0.186905\pi\)
\(90\) −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
\(93\) −0.184534 0.0170408i −0.0191353 0.00176704i
\(94\) 0.392017 + 0.392017i 0.0404334 + 0.0404334i
\(95\) 3.32791 0.341437
\(96\) 0.159268 1.72471i 0.0162552 0.176028i
\(97\) −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 \(-0.776148\pi\)
−0.762744 + 0.646700i \(0.776148\pi\)
\(102\) 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
\(105\) −5.46888 0.505022i −0.533708 0.0492851i
\(106\) 7.36526 + 7.36526i 0.715377 + 0.715377i
\(107\) 0.283834i 0.0274393i −0.999906 0.0137196i \(-0.995633\pi\)
0.999906 0.0137196i \(-0.00436724\pi\)
\(108\) −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
\(111\) 10.0931 + 3.02143i 0.957996 + 0.286782i
\(112\) 3.17089 0.299621
\(113\) 10.1290 10.1290i 0.952860 0.952860i −0.0460778 0.998938i \(-0.514672\pi\)
0.998938 + 0.0460778i \(0.0146722\pi\)
\(114\) 3.68379 + 4.43336i 0.345018 + 0.415223i
\(115\) 3.44746i 0.321477i
\(116\) −3.28489 3.28489i −0.304994 0.304994i
\(117\) −1.12605 1.64160i −0.104103 0.151766i
\(118\) −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
\(126\) −5.38092 7.84454i −0.479371 0.698847i
\(127\) −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
\(129\) 0.662579 7.17506i 0.0583368 0.631728i
\(130\) −0.469209 + 0.469209i −0.0411524 + 0.0411524i
\(131\) 14.8606 14.8606i 1.29838 1.29838i 0.368917 0.929462i \(-0.379729\pi\)
0.929462 0.368917i \(-0.120271\pi\)
\(132\) −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
\(135\) 1.41725 4.99914i 0.121978 0.430257i
\(136\) 5.90259i 0.506143i
\(137\) 20.7659i 1.77415i 0.461628 + 0.887074i \(0.347265\pi\)
−0.461628 + 0.887074i \(0.652735\pi\)
\(138\) 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 \(0.185339\pi\)
−0.835223 + 0.549911i \(0.814661\pi\)
\(150\) −1.72471 0.159268i −0.140822 0.0130042i
\(151\) 11.6822i 0.950682i 0.879802 + 0.475341i \(0.157675\pi\)
−0.879802 + 0.475341i \(0.842325\pi\)
\(152\) 3.32791 0.269929
\(153\) −14.6025 + 10.0165i −1.18054 + 0.809789i
\(154\) 9.62869 9.62869i 0.775902 0.775902i
\(155\) 0.106994i 0.00859397i
\(156\) −1.14445 0.105684i −0.0916296 0.00846151i
\(157\) −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
\(162\) 8.22854 3.64570i 0.646495 0.286433i
\(163\) 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
\(165\) 7.40657 + 0.683958i 0.576601 + 0.0532461i
\(166\) 7.30943 + 7.30943i 0.567321 + 0.567321i
\(167\) 2.59545 + 2.59545i 0.200842 + 0.200842i 0.800361 0.599519i \(-0.204641\pi\)
−0.599519 + 0.800361i \(0.704641\pi\)
\(168\) −5.46888 0.505022i −0.421933 0.0389633i
\(169\) 12.5597i 0.966130i
\(170\) 4.17376 + 4.17376i 0.320113 + 0.320113i
\(171\) −5.64738 8.23299i −0.431866 0.629592i
\(172\) −2.94167 2.94167i −0.224300 0.224300i
\(173\) 5.26417 0.400228 0.200114 0.979773i \(-0.435869\pi\)
0.200114 + 0.979773i \(0.435869\pi\)
\(174\) 5.14231 + 6.18867i 0.389838 + 0.469162i
\(175\) 3.17089i 0.239697i
\(176\) −4.29438 −0.323701
\(177\) 13.2379 + 1.22245i 0.995022 + 0.0918850i
\(178\) 3.71553i 0.278491i
\(179\) 9.64682 9.64682i 0.721037 0.721037i −0.247780 0.968816i \(-0.579701\pi\)
0.968816 + 0.247780i \(0.0797009\pi\)
\(180\) −1.69697 2.47392i −0.126485 0.184395i
\(181\) 1.74294 0.129552 0.0647760 0.997900i \(-0.479367\pi\)
0.0647760 + 0.997900i \(0.479367\pi\)
\(182\) 2.10408i 0.155965i
\(183\) −9.28893 0.857784i −0.686657 0.0634092i
\(184\) 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 \(0.110224\pi\)
0.339399 + 0.940643i \(0.389776\pi\)
\(192\) 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 \(0.331055\pi\)
−0.506185 + 0.862425i \(0.668945\pi\)
\(198\) 7.28745 + 10.6240i 0.517897 + 0.755011i
\(199\) 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
\(204\) −0.940094 + 10.1803i −0.0658197 + 0.712761i
\(205\) 4.44310 + 4.44310i 0.310320 + 0.310320i
\(206\) −10.2172 −0.711863
\(207\) −8.52874 + 5.85025i −0.592789 + 0.406621i
\(208\) −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
\(216\) 1.41725 4.99914i 0.0964319 0.340148i
\(217\) 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
\(222\) −9.27339 + 5.00043i −0.622389 + 0.335607i
\(223\) −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 0.779385 0.626545i \(-0.215532\pi\)
−0.626545 + 0.779385i \(0.715532\pi\)
\(228\) −5.73969 0.530030i −0.380120 0.0351021i
\(229\) 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 \(-0.640847\pi\)
−0.428186 + 0.903691i \(0.640847\pi\)
\(234\) 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
\(237\) −0.533081 + 5.77273i −0.0346273 + 0.374979i
\(238\) −18.7165 −1.21321
\(239\) 6.64308 + 6.64308i 0.429705 + 0.429705i 0.888528 0.458823i \(-0.151729\pi\)
−0.458823 + 0.888528i \(0.651729\pi\)
\(240\) −1.72471 0.159268i −0.111330 0.0102807i
\(241\) −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
\(246\) −1.00076 + 10.8372i −0.0638061 + 0.690956i
\(247\) 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 −0.810860 0.585240i \(-0.801000\pi\)
0.585240 + 0.810860i \(0.301000\pi\)
\(252\) 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 0.621778 0.783194i \(-0.286411\pi\)
−0.783194 + 0.621778i \(0.786411\pi\)
\(258\) 4.60502 + 5.54204i 0.286696 + 0.345033i
\(259\) −10.6767 16.0632i −0.663416 0.998121i
\(260\) 0.663562i 0.0411524i
\(261\) −7.88335 11.4927i −0.487967 0.711379i
\(262\) 21.0161i 1.29838i
\(263\) −10.2023 −0.629102 −0.314551 0.949241i \(-0.601854\pi\)
−0.314551 + 0.949241i \(0.601854\pi\)
\(264\) 7.40657 + 0.683958i 0.455843 + 0.0420947i
\(265\) 7.36526 7.36526i 0.452444 0.452444i
\(266\) 10.5525i 0.647013i
\(267\) 0.591765 6.40822i 0.0362154 0.392177i
\(268\) −7.22479 −0.441324
\(269\) 22.2257i 1.35513i 0.735465 + 0.677563i \(0.236964\pi\)
−0.735465 + 0.677563i \(0.763036\pi\)
\(270\) 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
\(273\) −0.335114 + 3.62894i −0.0202820 + 0.219633i
\(274\) −14.6837 14.6837i −0.887074 0.887074i
\(275\) 4.29438i 0.258961i
\(276\) −0.549071 + 5.94588i −0.0330502 + 0.357900i
\(277\) −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
\(279\) −0.264695 + 0.181566i −0.0158469 + 0.0108701i
\(280\) 3.17089i 0.189497i
\(281\) 7.32785 + 7.32785i 0.437143 + 0.437143i 0.891049 0.453906i \(-0.149970\pi\)
−0.453906 + 0.891049i \(0.649970\pi\)
\(282\) 0.956173 + 0.0882975i 0.0569393 + 0.00525804i
\(283\) −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
\(288\) −1.69697 2.47392i −0.0999952 0.145777i
\(289\) 17.8405i 1.04944i
\(290\) −3.28489 + 3.28489i −0.192895 + 0.192895i
\(291\) −0.0294685 + 0.319114i −0.00172747 + 0.0187068i
\(292\) 12.0206 0.703453
\(293\) 27.9995i 1.63575i −0.575399 0.817873i \(-0.695153\pi\)
0.575399 0.817873i \(-0.304847\pi\)
\(294\) −0.486495 + 5.26825i −0.0283730 + 0.307251i
\(295\) 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
\(309\) 17.6216 + 1.62727i 1.00246 + 0.0925720i
\(310\) 0.0756563 + 0.0756563i 0.00429699 + 0.00429699i
\(311\) 10.9987 10.9987i 0.623678 0.623678i −0.322792 0.946470i \(-0.604621\pi\)
0.946470 + 0.322792i \(0.104621\pi\)
\(312\) 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
\(315\) −7.84454 + 5.38092i −0.441990 + 0.303181i
\(316\) 2.36673 + 2.36673i 0.133139 + 0.133139i
\(317\) −24.9951 −1.40386 −0.701932 0.712244i \(-0.747679\pi\)
−0.701932 + 0.712244i \(0.747679\pi\)
\(318\) 17.9647 + 1.65895i 1.00741 + 0.0930290i
\(319\) 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
\(327\) −1.59744 + 17.2986i −0.0883384 + 0.956615i
\(328\) 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
\(333\) 16.7903 7.14735i 0.920105 0.391673i
\(334\) −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
\(339\) 2.28146 24.7059i 0.123912 1.34184i
\(340\) −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 −0.519281 0.854603i \(-0.673800\pi\)
0.854603 + 0.519281i \(0.173800\pi\)
\(348\) −8.01221 0.739886i −0.429500 0.0396620i
\(349\) 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
\(351\) −3.31724 0.940435i −0.177061 0.0501967i
\(352\) 3.03659 3.03659i 0.161851 0.161851i
\(353\) −13.3438 + 13.3438i −0.710218 + 0.710218i −0.966581 0.256362i \(-0.917476\pi\)
0.256362 + 0.966581i \(0.417476\pi\)
\(354\) −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
\(357\) 32.2805 + 2.98094i 1.70847 + 0.157768i
\(358\) 13.6427i 0.721037i
\(359\) 0.209030i 0.0110322i 0.999985 + 0.00551610i \(0.00175584\pi\)
−0.999985 + 0.00551610i \(0.998244\pi\)
\(360\) 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
\(372\) −0.0170408 + 0.184534i −0.000883522 + 0.00956765i
\(373\) 3.56845i 0.184767i 0.995723 + 0.0923836i \(0.0294486\pi\)
−0.995723 + 0.0923836i \(0.970551\pi\)
\(374\) 25.3479 1.31071
\(375\) −0.159268 + 1.72471i −0.00822457 + 0.0890638i
\(376\) 0.392017 0.392017i 0.0202167 0.0202167i
\(377\) 3.08260i 0.158762i
\(378\) −15.8517 4.49396i −0.815326 0.231144i
\(379\) −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 0.918843 0.394622i \(-0.129125\pi\)
−0.394622 + 0.918843i \(0.629125\pi\)
\(384\) −1.72471 0.159268i −0.0880139 0.00812762i
\(385\) −9.62869 9.62869i −0.490723 0.490723i
\(386\) 3.26985i 0.166431i
\(387\) −7.05966 10.2919i −0.358863 0.523165i
\(388\) 0.130832 + 0.130832i 0.00664199 + 0.00664199i
\(389\) 11.2832 + 11.2832i 0.572079 + 0.572079i 0.932709 0.360630i \(-0.117438\pi\)
−0.360630 + 0.932709i \(0.617438\pi\)
\(390\) −0.105684 + 1.14445i −0.00535153 + 0.0579516i
\(391\) 20.3489i 1.02909i
\(392\) 2.15991 + 2.15991i 0.109092 + 0.109092i
\(393\) 3.34720 36.2467i 0.168844 1.82841i
\(394\) −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
\(399\) −1.68067 + 18.2000i −0.0841388 + 0.911138i
\(400\) 1.00000i 0.0500000i
\(401\) 1.36032 1.36032i 0.0679314 0.0679314i −0.672325 0.740256i \(-0.734704\pi\)
0.740256 + 0.672325i \(0.234704\pi\)
\(402\) 12.4607 + 1.15068i 0.621483 + 0.0573907i
\(403\) −0.0709972 −0.00353662
\(404\) 15.3310i 0.762744i
\(405\) −3.64570 8.22854i −0.181156 0.408879i
\(406\) 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 \(-0.733761\pi\)
0.670128 0.742246i \(-0.266239\pi\)
\(420\) −0.505022 + 5.46888i −0.0246426 + 0.266854i
\(421\) 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
\(426\) 13.8144 + 1.27569i 0.669310 + 0.0618073i
\(427\) 12.0758 + 12.0758i 0.584389 + 0.584389i
\(428\) −0.283834 −0.0137196
\(429\) 0.453848 4.91472i 0.0219120 0.237285i
\(430\) −2.94167 + 2.94167i −0.141860 + 0.141860i
\(431\) −13.1264 + 13.1264i −0.632279 + 0.632279i −0.948639 0.316360i \(-0.897539\pi\)
0.316360 + 0.948639i \(0.397539\pi\)
\(432\) 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
\(438\) −20.7321 1.91450i −0.990619 0.0914784i
\(439\) 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 \(-0.0806295\pi\)
0.968089 + 0.250605i \(0.0806295\pi\)
\(444\) 3.02143 10.0931i 0.143391 0.478998i
\(445\) 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 0.979123 0.203269i \(-0.0651567\pi\)
−0.203269 + 0.979123i \(0.565157\pi\)
\(450\) −2.47392 + 1.69697i −0.116622 + 0.0799961i
\(451\) 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
\(459\) −8.36546 + 29.5078i −0.390466 + 1.37731i
\(460\) −3.44746 −0.160739
\(461\) −14.2992 14.2992i −0.665979 0.665979i 0.290804 0.956783i \(-0.406077\pi\)
−0.956783 + 0.290804i \(0.906077\pi\)
\(462\) 2.16876 23.4855i 0.100900 1.09264i
\(463\) 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 \(0.0618289\pi\)
0.193022 + 0.981194i \(0.438171\pi\)
\(468\) −1.64160 + 1.12605i −0.0758829 + 0.0520515i
\(469\) 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 \(-0.879314\pi\)
−0.370127 0.928981i \(-0.620686\pi\)
\(480\) 1.33218 1.10694i 0.0608052 0.0505245i
\(481\) 3.95681 + 0.797069i 0.180415 + 0.0363432i
\(482\) 8.18905i 0.373001i
\(483\) 18.8538 + 1.74105i 0.857876 + 0.0792203i
\(484\) 7.44170i 0.338259i
\(485\) −0.185024 −0.00840152
\(486\) 6.92630 13.9652i 0.314183 0.633474i
\(487\) −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
\(489\) 31.2436 + 2.88518i 1.41288 + 0.130472i
\(490\) −3.05457 −0.137991
\(491\) 21.3703i 0.964426i 0.876054 + 0.482213i \(0.160167\pi\)
−0.876054 + 0.482213i \(0.839833\pi\)
\(492\) −6.95543 8.37071i −0.313575 0.377381i
\(493\) −27.4207 −1.23497
\(494\) 1.56149 + 1.56149i 0.0702546 + 0.0702546i
\(495\) 10.6240 7.28745i 0.477511 0.327547i
\(496\) 0.0756563 + 0.0756563i 0.00339707 + 0.00339707i
\(497\) 25.3979i 1.13925i
\(498\) 17.8285 + 1.64637i 0.798915 + 0.0737756i
\(499\) −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
\(501\) 6.33060 + 0.584598i 0.282831 + 0.0261179i
\(502\) 5.05509i 0.225620i
\(503\) 17.4364 + 17.4364i 0.777452 + 0.777452i 0.979397 0.201945i \(-0.0647261\pi\)
−0.201945 + 0.979397i \(0.564726\pi\)
\(504\) −7.84454 + 5.38092i −0.349423 + 0.239685i
\(505\) −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 \(-0.706882\pi\)
−0.605139 + 0.796120i \(0.706882\pi\)
\(510\) 10.1803 + 0.940094i 0.450790 + 0.0416281i
\(511\) 38.1161i 1.68616i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −16.6367 4.71649i −0.734528 0.208238i
\(514\) 3.65956 0.161416
\(515\) 10.2172i 0.450221i
\(516\) −7.17506 0.662579i −0.315864 0.0291684i
\(517\) 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 \(-0.762863\pi\)
−0.735097 + 0.677962i \(0.762863\pi\)
\(522\) 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
\(531\) 18.9884 13.0250i 0.824026 0.565237i
\(532\) 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
\(537\) 2.17284 23.5297i 0.0937650 1.01538i
\(538\) −15.7160 15.7160i −0.677563 0.677563i
\(539\) 13.1175 0.565010
\(540\) −4.99914 1.41725i −0.215129 0.0609889i
\(541\) −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
\(549\) −13.3240 + 9.13954i −0.568654 + 0.390066i
\(550\) −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
\(555\) 5.00043 + 9.27339i 0.212257 + 0.393633i
\(556\) −10.4767 −0.444309
\(557\) −4.77952 + 4.77952i −0.202515 + 0.202515i −0.801077 0.598562i \(-0.795739\pi\)
0.598562 + 0.801077i \(0.295739\pi\)
\(558\) 0.0587808 0.315554i 0.00248839 0.0133585i
\(559\) 2.76051i 0.116757i
\(560\) 2.24216 + 2.24216i 0.0947486 + 0.0947486i
\(561\) −43.7179 4.03712i −1.84577 0.170447i
\(562\) −10.3631 −0.437143
\(563\) −20.9149 20.9149i −0.881459 0.881459i 0.112224 0.993683i \(-0.464203\pi\)
−0.993683 + 0.112224i \(0.964203\pi\)
\(564\) −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 −0.00505843 0.999987i \(-0.501610\pi\)
0.999987 + 0.00505843i \(0.00161016\pi\)
\(570\) −0.530030 + 5.73969i −0.0222005 + 0.240409i
\(571\) 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
\(573\) 43.1492 + 3.98460i 1.80258 + 0.166459i
\(574\) 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
\(579\) 0.520783 5.63955i 0.0216430 0.234372i
\(580\) 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 \(-0.442056\pi\)
0.983477 0.181033i \(-0.0579440\pi\)
\(588\) −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 \(-0.955327\pi\)
0.990168 0.139884i \(-0.0446730\pi\)
\(594\) 21.4682 + 6.08622i 0.880851 + 0.249721i
\(595\) 18.7165i 0.767301i
\(596\) 13.4251 0.549911
\(597\) 37.6765 + 3.47923i 1.54200 + 0.142395i
\(598\) 1.61758 1.61758i 0.0661478 0.0661478i
\(599\) 35.3959i 1.44624i −0.690724 0.723119i \(-0.742708\pi\)
0.690724 0.723119i \(-0.257292\pi\)
\(600\) −0.159268 + 1.72471i −0.00650209 + 0.0704111i
\(601\) −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
\(606\) 2.44173 26.4415i 0.0991887 1.07411i
\(607\) 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
\(609\) −2.34610 + 25.4059i −0.0950688 + 1.02950i
\(610\) 3.80832 + 3.80832i 0.154195 + 0.154195i
\(611\) −0.260127 0.260127i −0.0105236 0.0105236i
\(612\) 10.0165 + 14.6025i 0.404894 + 0.590272i
\(613\) 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
\(615\) 10.8372 + 1.00076i 0.436999 + 0.0403545i
\(616\) −9.62869 9.62869i −0.387951 0.387951i
\(617\) 8.81089 0.354713 0.177357 0.984147i \(-0.443245\pi\)
0.177357 + 0.984147i \(0.443245\pi\)
\(618\) −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
\(621\) −4.88593 + 17.2343i −0.196065 + 0.691590i
\(622\) 15.5545i 0.623678i
\(623\) −8.33081 + 8.33081i −0.333767 + 0.333767i
\(624\) −0.105684 + 1.14445i −0.00423076 + 0.0458148i
\(625\) −1.00000 −0.0400000
\(626\) 34.8571i 1.39317i
\(627\) 2.27615 24.6484i 0.0909008 0.984363i
\(628\) 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 \(-0.921683\pi\)
0.969884 0.243565i \(-0.0783170\pi\)
\(642\) 0.489532 + 0.0452057i 0.0193203 + 0.00178413i
\(643\) 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 −0.867634 0.497204i \(-0.834360\pi\)
0.497204 + 0.867634i \(0.334360\pi\)
\(648\) −3.64570 8.22854i −0.143217 0.323248i
\(649\) 23.3071 + 23.3071i 0.914883 + 0.914883i
\(650\) −0.663562 −0.0260270
\(651\) 0.585138 + 0.0540344i 0.0229334 + 0.00211778i
\(652\) 12.8094 12.8094i 0.501655 0.501655i
\(653\) 5.72159 5.72159i 0.223903 0.223903i −0.586237 0.810140i \(-0.699391\pi\)
0.810140 + 0.586237i \(0.199391\pi\)
\(654\) −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 \(-0.466309\pi\)
0.105645 + 0.994404i \(0.466309\pi\)
\(660\) 0.683958 7.40657i 0.0266230 0.288300i
\(661\) 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
\(666\) −6.81862 + 16.9265i −0.264216 + 0.655889i
\(667\) −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
\(672\) −0.505022 + 5.46888i −0.0194817 + 0.210967i
\(673\) −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 \(-0.666358\pi\)
−0.499160 + 0.866510i \(0.666358\pi\)
\(678\) 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
\(681\) 5.61670 + 0.518673i 0.215233 + 0.0198756i
\(682\) 0.459473 0.0175941
\(683\) −17.5140 17.5140i −0.670156 0.670156i 0.287596 0.957752i \(-0.407144\pi\)
−0.957752 + 0.287596i \(0.907144\pi\)
\(684\) −8.23299 + 5.64738i −0.314796 + 0.215933i
\(685\) −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
\(690\) 5.94588 + 0.549071i 0.226356 + 0.0209028i
\(691\) 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 0.710134 0.704067i \(-0.248634\pi\)
−0.704067 + 0.710134i \(0.748634\pi\)
\(702\) 3.01063 1.68065i 0.113629 0.0634322i
\(703\) 19.8443 + 3.99748i 0.748441 + 0.150768i
\(704\) 4.29438i 0.161851i
\(705\) 0.0882975 0.956173i 0.00332548 0.0360116i
\(706\) 18.8710i 0.710218i
\(707\) 48.6129 1.82828
\(708\) 1.22245 13.2379i 0.0459425 0.497511i
\(709\) −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
\(711\) 5.67988 + 8.28037i 0.213012 + 0.310538i
\(712\) 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
\(717\) 16.2032 + 1.49628i 0.605120 + 0.0558797i
\(718\) −0.147807 0.147807i −0.00551610 0.00551610i
\(719\) 4.09595i 0.152753i 0.997079 + 0.0763766i \(0.0243351\pi\)
−0.997079 + 0.0763766i \(0.975665\pi\)
\(720\) −2.47392 + 1.69697i −0.0921975 + 0.0632425i
\(721\) −22.9085 22.9085i −0.853157 0.853157i
\(722\) −5.60382 5.60382i −0.208553 0.208553i
\(723\) −1.30425 + 14.1238i −0.0485057 + 0.525268i
\(724\) 1.74294i 0.0647760i
\(725\) 3.28489 + 3.28489i 0.121998 + 0.121998i
\(726\) −1.18523 + 12.8348i −0.0439879 + 0.476344i
\(727\) 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
\(732\) −0.857784 + 9.28893i −0.0317046 + 0.343329i
\(733\) 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
\(735\) 5.26825 + 0.486495i 0.194322 + 0.0179447i
\(736\) −3.44746 −0.127075
\(737\) 31.0260i 1.14286i
\(738\) 10.6629 + 15.5449i 0.392508 + 0.572214i
\(739\) 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 \(-0.240445\pi\)
0.728012 + 0.685565i \(0.240445\pi\)
\(744\) −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
\(753\) −0.805115 + 8.71858i −0.0293400 + 0.317723i
\(754\) 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
\(759\) −25.5339 2.35792i −0.926821 0.0855870i
\(760\) 2.35319 + 2.35319i 0.0853592 + 0.0853592i
\(761\) −1.71775 −0.0622685 −0.0311343 0.999515i \(-0.509912\pi\)
−0.0311343 + 0.999515i \(0.509912\pi\)
\(762\) 1.89239 20.4927i 0.0685540 0.742371i
\(763\) 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
\(771\) −6.31169 0.582851i −0.227310 0.0209909i
\(772\) −2.31213 2.31213i −0.0832155 0.0832155i
\(773\) 23.3393i 0.839457i −0.907650 0.419729i \(-0.862125\pi\)
0.907650 0.419729i \(-0.137875\pi\)
\(774\) 12.2694 + 2.28552i 0.441014 + 0.0821512i
\(775\) 0.0756563 0.0756563i 0.00271765 0.00271765i
\(776\) −0.185024 −0.00664199
\(777\) −32.0042 9.58065i −1.14814 0.343704i
\(778\) −15.9568 −0.572079
\(779\) 14.7862