Properties

Label 76.3.b.b.39.2
Level $76$
Weight $3$
Character 76.39
Analytic conductor $2.071$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.2
Root \(-1.92254 - 0.551226i\) of defining polynomial
Character \(\chi\) \(=\) 76.39
Dual form 76.3.b.b.39.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.92254 + 0.551226i) q^{2} -0.644704i q^{3} +(3.39230 - 2.11950i) q^{4} -2.32715 q^{5} +(0.355377 + 1.23947i) q^{6} -8.62924i q^{7} +(-5.35350 + 5.94475i) q^{8} +8.58436 q^{9} +O(q^{10})\) \(q+(-1.92254 + 0.551226i) q^{2} -0.644704i q^{3} +(3.39230 - 2.11950i) q^{4} -2.32715 q^{5} +(0.355377 + 1.23947i) q^{6} -8.62924i q^{7} +(-5.35350 + 5.94475i) q^{8} +8.58436 q^{9} +(4.47404 - 1.28279i) q^{10} -19.2717i q^{11} +(-1.36645 - 2.18703i) q^{12} +13.8067 q^{13} +(4.75666 + 16.5900i) q^{14} +1.50032i q^{15} +(7.01540 - 14.3800i) q^{16} -12.5180 q^{17} +(-16.5037 + 4.73192i) q^{18} -4.35890i q^{19} +(-7.89440 + 4.93241i) q^{20} -5.56330 q^{21} +(10.6231 + 37.0506i) q^{22} +37.4981i q^{23} +(3.83260 + 3.45142i) q^{24} -19.5844 q^{25} +(-26.5438 + 7.61058i) q^{26} -11.3367i q^{27} +(-18.2897 - 29.2730i) q^{28} -6.36930 q^{29} +(-0.827018 - 2.88443i) q^{30} +5.44851i q^{31} +(-5.56075 + 31.5131i) q^{32} -12.4245 q^{33} +(24.0663 - 6.90025i) q^{34} +20.0816i q^{35} +(29.1207 - 18.1946i) q^{36} +20.9250 q^{37} +(2.40274 + 8.38015i) q^{38} -8.90120i q^{39} +(12.4584 - 13.8343i) q^{40} +72.8337 q^{41} +(10.6957 - 3.06664i) q^{42} -10.1553i q^{43} +(-40.8465 - 65.3755i) q^{44} -19.9771 q^{45} +(-20.6699 - 72.0914i) q^{46} +32.4450i q^{47} +(-9.27083 - 4.52286i) q^{48} -25.4638 q^{49} +(37.6517 - 10.7954i) q^{50} +8.07040i q^{51} +(46.8363 - 29.2633i) q^{52} -42.9339 q^{53} +(6.24908 + 21.7952i) q^{54} +44.8482i q^{55} +(51.2987 + 46.1966i) q^{56} -2.81020 q^{57} +(12.2452 - 3.51092i) q^{58} -38.9728i q^{59} +(3.17994 + 5.08955i) q^{60} +25.5611 q^{61} +(-3.00336 - 10.4750i) q^{62} -74.0765i q^{63} +(-6.68010 - 63.6504i) q^{64} -32.1302 q^{65} +(23.8867 - 6.84873i) q^{66} +65.3183i q^{67} +(-42.4648 + 26.5320i) q^{68} +24.1751 q^{69} +(-11.0695 - 38.6076i) q^{70} +18.7557i q^{71} +(-45.9563 + 51.0319i) q^{72} +72.8251 q^{73} +(-40.2292 + 11.5344i) q^{74} +12.6261i q^{75} +(-9.23871 - 14.7867i) q^{76} -166.300 q^{77} +(4.90657 + 17.1129i) q^{78} +139.874i q^{79} +(-16.3259 + 33.4644i) q^{80} +69.9504 q^{81} +(-140.026 + 40.1478i) q^{82} -94.7116i q^{83} +(-18.8724 + 11.7914i) q^{84} +29.1313 q^{85} +(5.59789 + 19.5240i) q^{86} +4.10631i q^{87} +(114.566 + 103.171i) q^{88} +33.3546 q^{89} +(38.4068 - 11.0119i) q^{90} -119.141i q^{91} +(79.4773 + 127.205i) q^{92} +3.51267 q^{93} +(-17.8845 - 62.3766i) q^{94} +10.1438i q^{95} +(20.3166 + 3.58504i) q^{96} -150.817 q^{97} +(48.9551 - 14.0363i) q^{98} -165.435i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} + O(q^{10}) \) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} - 12q^{10} + 4q^{12} + 54q^{13} + 30q^{14} + 58q^{16} + 34q^{17} + 36q^{18} + 32q^{20} - 38q^{21} + 36q^{22} - 98q^{24} - 86q^{25} - 16q^{26} + 18q^{28} + 54q^{29} - 204q^{30} + 72q^{32} + 20q^{33} - 82q^{34} + 96q^{36} + 100q^{37} - 148q^{40} + 224q^{41} + 224q^{42} - 96q^{44} - 168q^{45} + 46q^{46} + 296q^{48} - 220q^{49} - 58q^{50} - 288q^{52} + 14q^{53} - 128q^{54} + 12q^{56} + 38q^{57} - 72q^{58} + 188q^{60} + 28q^{61} + 396q^{62} - 118q^{64} - 472q^{65} - 32q^{66} + 30q^{68} + 122q^{69} + 156q^{70} + 80q^{72} + 70q^{73} - 224q^{74} + 228q^{77} + 274q^{78} - 348q^{80} + 334q^{81} - 400q^{82} - 216q^{84} + 48q^{85} - 124q^{86} + 472q^{88} + 416q^{90} + 126q^{92} - 176q^{93} - 88q^{94} - 106q^{96} + 308q^{97} + 68q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92254 + 0.551226i −0.961269 + 0.275613i
\(3\) 0.644704i 0.214901i −0.994210 0.107451i \(-0.965731\pi\)
0.994210 0.107451i \(-0.0342688\pi\)
\(4\) 3.39230 2.11950i 0.848075 0.529876i
\(5\) −2.32715 −0.465431 −0.232715 0.972545i \(-0.574761\pi\)
−0.232715 + 0.972545i \(0.574761\pi\)
\(6\) 0.355377 + 1.23947i 0.0592296 + 0.206578i
\(7\) 8.62924i 1.23275i −0.787453 0.616374i \(-0.788601\pi\)
0.787453 0.616374i \(-0.211399\pi\)
\(8\) −5.35350 + 5.94475i −0.669187 + 0.743094i
\(9\) 8.58436 0.953817
\(10\) 4.47404 1.28279i 0.447404 0.128279i
\(11\) 19.2717i 1.75197i −0.482334 0.875987i \(-0.660211\pi\)
0.482334 0.875987i \(-0.339789\pi\)
\(12\) −1.36645 2.18703i −0.113871 0.182252i
\(13\) 13.8067 1.06205 0.531025 0.847356i \(-0.321807\pi\)
0.531025 + 0.847356i \(0.321807\pi\)
\(14\) 4.75666 + 16.5900i 0.339761 + 1.18500i
\(15\) 1.50032i 0.100022i
\(16\) 7.01540 14.3800i 0.438463 0.898749i
\(17\) −12.5180 −0.736353 −0.368177 0.929756i \(-0.620018\pi\)
−0.368177 + 0.929756i \(0.620018\pi\)
\(18\) −16.5037 + 4.73192i −0.916875 + 0.262884i
\(19\) 4.35890i 0.229416i
\(20\) −7.89440 + 4.93241i −0.394720 + 0.246621i
\(21\) −5.56330 −0.264919
\(22\) 10.6231 + 37.0506i 0.482867 + 1.68412i
\(23\) 37.4981i 1.63035i 0.579214 + 0.815175i \(0.303360\pi\)
−0.579214 + 0.815175i \(0.696640\pi\)
\(24\) 3.83260 + 3.45142i 0.159692 + 0.143809i
\(25\) −19.5844 −0.783374
\(26\) −26.5438 + 7.61058i −1.02092 + 0.292715i
\(27\) 11.3367i 0.419878i
\(28\) −18.2897 29.2730i −0.653204 1.04546i
\(29\) −6.36930 −0.219631 −0.109816 0.993952i \(-0.535026\pi\)
−0.109816 + 0.993952i \(0.535026\pi\)
\(30\) −0.827018 2.88443i −0.0275673 0.0961477i
\(31\) 5.44851i 0.175758i 0.996131 + 0.0878791i \(0.0280089\pi\)
−0.996131 + 0.0878791i \(0.971991\pi\)
\(32\) −5.56075 + 31.5131i −0.173774 + 0.984786i
\(33\) −12.4245 −0.376502
\(34\) 24.0663 6.90025i 0.707833 0.202948i
\(35\) 20.0816i 0.573759i
\(36\) 29.1207 18.1946i 0.808909 0.505405i
\(37\) 20.9250 0.565542 0.282771 0.959187i \(-0.408746\pi\)
0.282771 + 0.959187i \(0.408746\pi\)
\(38\) 2.40274 + 8.38015i 0.0632299 + 0.220530i
\(39\) 8.90120i 0.228236i
\(40\) 12.4584 13.8343i 0.311460 0.345859i
\(41\) 72.8337 1.77643 0.888216 0.459425i \(-0.151945\pi\)
0.888216 + 0.459425i \(0.151945\pi\)
\(42\) 10.6957 3.06664i 0.254659 0.0730152i
\(43\) 10.1553i 0.236171i −0.993003 0.118085i \(-0.962324\pi\)
0.993003 0.118085i \(-0.0376757\pi\)
\(44\) −40.8465 65.3755i −0.928329 1.48581i
\(45\) −19.9771 −0.443936
\(46\) −20.6699 72.0914i −0.449346 1.56721i
\(47\) 32.4450i 0.690318i 0.938544 + 0.345159i \(0.112175\pi\)
−0.938544 + 0.345159i \(0.887825\pi\)
\(48\) −9.27083 4.52286i −0.193142 0.0942262i
\(49\) −25.4638 −0.519669
\(50\) 37.6517 10.7954i 0.753033 0.215908i
\(51\) 8.07040i 0.158243i
\(52\) 46.8363 29.2633i 0.900698 0.562755i
\(53\) −42.9339 −0.810074 −0.405037 0.914300i \(-0.632741\pi\)
−0.405037 + 0.914300i \(0.632741\pi\)
\(54\) 6.24908 + 21.7952i 0.115724 + 0.403615i
\(55\) 44.8482i 0.815423i
\(56\) 51.2987 + 46.1966i 0.916048 + 0.824940i
\(57\) −2.81020 −0.0493017
\(58\) 12.2452 3.51092i 0.211125 0.0605332i
\(59\) 38.9728i 0.660556i −0.943884 0.330278i \(-0.892858\pi\)
0.943884 0.330278i \(-0.107142\pi\)
\(60\) 3.17994 + 5.08955i 0.0529991 + 0.0848258i
\(61\) 25.5611 0.419034 0.209517 0.977805i \(-0.432811\pi\)
0.209517 + 0.977805i \(0.432811\pi\)
\(62\) −3.00336 10.4750i −0.0484412 0.168951i
\(63\) 74.0765i 1.17582i
\(64\) −6.68010 63.6504i −0.104377 0.994538i
\(65\) −32.1302 −0.494311
\(66\) 23.8867 6.84873i 0.361919 0.103769i
\(67\) 65.3183i 0.974900i 0.873151 + 0.487450i \(0.162073\pi\)
−0.873151 + 0.487450i \(0.837927\pi\)
\(68\) −42.4648 + 26.5320i −0.624483 + 0.390176i
\(69\) 24.1751 0.350364
\(70\) −11.0695 38.6076i −0.158135 0.551537i
\(71\) 18.7557i 0.264165i 0.991239 + 0.132083i \(0.0421665\pi\)
−0.991239 + 0.132083i \(0.957834\pi\)
\(72\) −45.9563 + 51.0319i −0.638283 + 0.708776i
\(73\) 72.8251 0.997604 0.498802 0.866716i \(-0.333773\pi\)
0.498802 + 0.866716i \(0.333773\pi\)
\(74\) −40.2292 + 11.5344i −0.543638 + 0.155871i
\(75\) 12.6261i 0.168348i
\(76\) −9.23871 14.7867i −0.121562 0.194562i
\(77\) −166.300 −2.15974
\(78\) 4.90657 + 17.1129i 0.0629048 + 0.219396i
\(79\) 139.874i 1.77056i 0.465060 + 0.885279i \(0.346033\pi\)
−0.465060 + 0.885279i \(0.653967\pi\)
\(80\) −16.3259 + 33.4644i −0.204074 + 0.418306i
\(81\) 69.9504 0.863585
\(82\) −140.026 + 40.1478i −1.70763 + 0.489608i
\(83\) 94.7116i 1.14110i −0.821262 0.570552i \(-0.806729\pi\)
0.821262 0.570552i \(-0.193271\pi\)
\(84\) −18.8724 + 11.7914i −0.224671 + 0.140374i
\(85\) 29.1313 0.342721
\(86\) 5.59789 + 19.5240i 0.0650917 + 0.227024i
\(87\) 4.10631i 0.0471990i
\(88\) 114.566 + 103.171i 1.30188 + 1.17240i
\(89\) 33.3546 0.374770 0.187385 0.982287i \(-0.439999\pi\)
0.187385 + 0.982287i \(0.439999\pi\)
\(90\) 38.4068 11.0119i 0.426742 0.122354i
\(91\) 119.141i 1.30924i
\(92\) 79.4773 + 127.205i 0.863884 + 1.38266i
\(93\) 3.51267 0.0377707
\(94\) −17.8845 62.3766i −0.190261 0.663581i
\(95\) 10.1438i 0.106777i
\(96\) 20.3166 + 3.58504i 0.211632 + 0.0373441i
\(97\) −150.817 −1.55482 −0.777408 0.628996i \(-0.783466\pi\)
−0.777408 + 0.628996i \(0.783466\pi\)
\(98\) 48.9551 14.0363i 0.499542 0.143228i
\(99\) 165.435i 1.67106i
\(100\) −66.4360 + 41.5091i −0.664360 + 0.415091i
\(101\) 77.7745 0.770045 0.385022 0.922907i \(-0.374194\pi\)
0.385022 + 0.922907i \(0.374194\pi\)
\(102\) −4.44862 15.5157i −0.0436139 0.152114i
\(103\) 14.9481i 0.145127i 0.997364 + 0.0725637i \(0.0231180\pi\)
−0.997364 + 0.0725637i \(0.976882\pi\)
\(104\) −73.9139 + 82.0771i −0.710711 + 0.789203i
\(105\) 12.9467 0.123302
\(106\) 82.5420 23.6663i 0.778698 0.223267i
\(107\) 80.5205i 0.752528i 0.926512 + 0.376264i \(0.122792\pi\)
−0.926512 + 0.376264i \(0.877208\pi\)
\(108\) −24.0282 38.4575i −0.222483 0.356088i
\(109\) 53.8512 0.494048 0.247024 0.969009i \(-0.420547\pi\)
0.247024 + 0.969009i \(0.420547\pi\)
\(110\) −24.7215 86.2224i −0.224741 0.783840i
\(111\) 13.4905i 0.121536i
\(112\) −124.088 60.5376i −1.10793 0.540514i
\(113\) 105.921 0.937355 0.468677 0.883369i \(-0.344731\pi\)
0.468677 + 0.883369i \(0.344731\pi\)
\(114\) 5.40271 1.54905i 0.0473922 0.0135882i
\(115\) 87.2638i 0.758815i
\(116\) −21.6066 + 13.4998i −0.186264 + 0.116377i
\(117\) 118.521 1.01300
\(118\) 21.4828 + 74.9266i 0.182058 + 0.634972i
\(119\) 108.021i 0.907739i
\(120\) −8.91905 8.03199i −0.0743254 0.0669332i
\(121\) −250.399 −2.06941
\(122\) −49.1421 + 14.0899i −0.402804 + 0.115491i
\(123\) 46.9562i 0.381758i
\(124\) 11.5481 + 18.4830i 0.0931301 + 0.149056i
\(125\) 103.755 0.830037
\(126\) 40.8329 + 142.415i 0.324070 + 1.13028i
\(127\) 17.1409i 0.134968i −0.997720 0.0674839i \(-0.978503\pi\)
0.997720 0.0674839i \(-0.0214971\pi\)
\(128\) 47.9285 + 118.688i 0.374441 + 0.927251i
\(129\) −6.54719 −0.0507534
\(130\) 61.7715 17.7110i 0.475166 0.136238i
\(131\) 229.336i 1.75066i −0.483526 0.875330i \(-0.660644\pi\)
0.483526 0.875330i \(-0.339356\pi\)
\(132\) −42.1478 + 26.3339i −0.319302 + 0.199499i
\(133\) −37.6140 −0.282812
\(134\) −36.0051 125.577i −0.268695 0.937141i
\(135\) 26.3822i 0.195424i
\(136\) 67.0151 74.4164i 0.492758 0.547179i
\(137\) −120.567 −0.880054 −0.440027 0.897985i \(-0.645031\pi\)
−0.440027 + 0.897985i \(0.645031\pi\)
\(138\) −46.4776 + 13.3260i −0.336794 + 0.0965650i
\(139\) 145.864i 1.04938i 0.851292 + 0.524692i \(0.175819\pi\)
−0.851292 + 0.524692i \(0.824181\pi\)
\(140\) 42.5630 + 68.1227i 0.304021 + 0.486591i
\(141\) 20.9174 0.148350
\(142\) −10.3387 36.0586i −0.0728074 0.253934i
\(143\) 266.078i 1.86069i
\(144\) 60.2227 123.443i 0.418213 0.857243i
\(145\) 14.8223 0.102223
\(146\) −140.009 + 40.1431i −0.958966 + 0.274953i
\(147\) 16.4166i 0.111678i
\(148\) 70.9840 44.3507i 0.479622 0.299667i
\(149\) 19.2547 0.129226 0.0646132 0.997910i \(-0.479419\pi\)
0.0646132 + 0.997910i \(0.479419\pi\)
\(150\) −6.95984 24.2742i −0.0463989 0.161828i
\(151\) 165.526i 1.09620i 0.836414 + 0.548099i \(0.184648\pi\)
−0.836414 + 0.548099i \(0.815352\pi\)
\(152\) 25.9126 + 23.3354i 0.170477 + 0.153522i
\(153\) −107.459 −0.702347
\(154\) 319.719 91.6690i 2.07609 0.595253i
\(155\) 12.6795i 0.0818033i
\(156\) −18.8661 30.1956i −0.120937 0.193561i
\(157\) 149.449 0.951907 0.475954 0.879470i \(-0.342103\pi\)
0.475954 + 0.879470i \(0.342103\pi\)
\(158\) −77.1022 268.913i −0.487989 1.70198i
\(159\) 27.6796i 0.174086i
\(160\) 12.9407 73.3359i 0.0808795 0.458349i
\(161\) 323.580 2.00981
\(162\) −134.482 + 38.5585i −0.830137 + 0.238015i
\(163\) 146.763i 0.900384i 0.892932 + 0.450192i \(0.148644\pi\)
−0.892932 + 0.450192i \(0.851356\pi\)
\(164\) 247.074 154.371i 1.50655 0.941289i
\(165\) 28.9138 0.175235
\(166\) 52.2075 + 182.087i 0.314503 + 1.09691i
\(167\) 213.493i 1.27840i 0.769040 + 0.639201i \(0.220735\pi\)
−0.769040 + 0.639201i \(0.779265\pi\)
\(168\) 29.7831 33.0724i 0.177281 0.196860i
\(169\) 21.6237 0.127951
\(170\) −56.0061 + 16.0579i −0.329447 + 0.0944584i
\(171\) 37.4183i 0.218821i
\(172\) −21.5243 34.4500i −0.125141 0.200291i
\(173\) −280.715 −1.62263 −0.811314 0.584610i \(-0.801247\pi\)
−0.811314 + 0.584610i \(0.801247\pi\)
\(174\) −2.26351 7.89454i −0.0130087 0.0453709i
\(175\) 168.998i 0.965704i
\(176\) −277.127 135.199i −1.57459 0.768175i
\(177\) −25.1259 −0.141954
\(178\) −64.1254 + 18.3859i −0.360255 + 0.103292i
\(179\) 35.1878i 0.196580i −0.995158 0.0982899i \(-0.968663\pi\)
0.995158 0.0982899i \(-0.0313372\pi\)
\(180\) −67.7684 + 42.3416i −0.376491 + 0.235231i
\(181\) −345.539 −1.90906 −0.954529 0.298120i \(-0.903641\pi\)
−0.954529 + 0.298120i \(0.903641\pi\)
\(182\) 65.6736 + 229.053i 0.360844 + 1.25853i
\(183\) 16.4793i 0.0900509i
\(184\) −222.917 200.746i −1.21150 1.09101i
\(185\) −48.6958 −0.263220
\(186\) −6.75324 + 1.93628i −0.0363078 + 0.0104101i
\(187\) 241.244i 1.29007i
\(188\) 68.7672 + 110.063i 0.365783 + 0.585442i
\(189\) −97.8271 −0.517604
\(190\) −5.59154 19.5019i −0.0294292 0.102642i
\(191\) 100.233i 0.524782i −0.964962 0.262391i \(-0.915489\pi\)
0.964962 0.262391i \(-0.0845110\pi\)
\(192\) −41.0357 + 4.30669i −0.213727 + 0.0224307i
\(193\) 168.119 0.871085 0.435543 0.900168i \(-0.356557\pi\)
0.435543 + 0.900168i \(0.356557\pi\)
\(194\) 289.952 83.1343i 1.49460 0.428528i
\(195\) 20.7145i 0.106228i
\(196\) −86.3808 + 53.9706i −0.440719 + 0.275360i
\(197\) 216.705 1.10002 0.550012 0.835157i \(-0.314623\pi\)
0.550012 + 0.835157i \(0.314623\pi\)
\(198\) 91.1922 + 318.056i 0.460567 + 1.60634i
\(199\) 82.2545i 0.413339i 0.978411 + 0.206670i \(0.0662625\pi\)
−0.978411 + 0.206670i \(0.933738\pi\)
\(200\) 104.845 116.424i 0.524224 0.582121i
\(201\) 42.1109 0.209507
\(202\) −149.524 + 42.8713i −0.740220 + 0.212234i
\(203\) 54.9623i 0.270750i
\(204\) 17.1053 + 27.3772i 0.0838493 + 0.134202i
\(205\) −169.495 −0.826806
\(206\) −8.23978 28.7383i −0.0399990 0.139506i
\(207\) 321.897i 1.55506i
\(208\) 96.8592 198.540i 0.465669 0.954517i
\(209\) −84.0035 −0.401931
\(210\) −24.8904 + 7.13653i −0.118526 + 0.0339835i
\(211\) 16.4195i 0.0778173i 0.999243 + 0.0389087i \(0.0123881\pi\)
−0.999243 + 0.0389087i \(0.987612\pi\)
\(212\) −145.645 + 90.9986i −0.687003 + 0.429239i
\(213\) 12.0919 0.0567695
\(214\) −44.3850 154.804i −0.207407 0.723382i
\(215\) 23.6331i 0.109921i
\(216\) 67.3938 + 60.6910i 0.312009 + 0.280977i
\(217\) 47.0165 0.216666
\(218\) −103.531 + 29.6842i −0.474913 + 0.136166i
\(219\) 46.9506i 0.214386i
\(220\) 95.0561 + 152.139i 0.432073 + 0.691540i
\(221\) −172.832 −0.782044
\(222\) 7.43629 + 25.9359i 0.0334968 + 0.116828i
\(223\) 195.225i 0.875450i −0.899109 0.437725i \(-0.855784\pi\)
0.899109 0.437725i \(-0.144216\pi\)
\(224\) 271.934 + 47.9851i 1.21399 + 0.214219i
\(225\) −168.119 −0.747196
\(226\) −203.637 + 58.3864i −0.901050 + 0.258347i
\(227\) 305.403i 1.34539i −0.739920 0.672695i \(-0.765137\pi\)
0.739920 0.672695i \(-0.234863\pi\)
\(228\) −9.53304 + 5.95623i −0.0418116 + 0.0261238i
\(229\) −229.686 −1.00300 −0.501499 0.865158i \(-0.667218\pi\)
−0.501499 + 0.865158i \(0.667218\pi\)
\(230\) 48.1020 + 167.768i 0.209139 + 0.729425i
\(231\) 107.214i 0.464132i
\(232\) 34.0981 37.8639i 0.146974 0.163207i
\(233\) 187.667 0.805436 0.402718 0.915324i \(-0.368065\pi\)
0.402718 + 0.915324i \(0.368065\pi\)
\(234\) −227.862 + 65.3320i −0.973767 + 0.279196i
\(235\) 75.5044i 0.321295i
\(236\) −82.6030 132.207i −0.350013 0.560201i
\(237\) 90.1774 0.380495
\(238\) −59.5439 207.674i −0.250184 0.872581i
\(239\) 69.8504i 0.292261i −0.989265 0.146130i \(-0.953318\pi\)
0.989265 0.146130i \(-0.0466819\pi\)
\(240\) 21.5747 + 10.5254i 0.0898944 + 0.0438557i
\(241\) 297.561 1.23469 0.617346 0.786691i \(-0.288208\pi\)
0.617346 + 0.786691i \(0.288208\pi\)
\(242\) 481.402 138.026i 1.98926 0.570357i
\(243\) 147.128i 0.605463i
\(244\) 86.7109 54.1768i 0.355372 0.222036i
\(245\) 59.2582 0.241870
\(246\) 25.8835 + 90.2750i 0.105217 + 0.366972i
\(247\) 60.1818i 0.243651i
\(248\) −32.3900 29.1686i −0.130605 0.117615i
\(249\) −61.0609 −0.245225
\(250\) −199.472 + 57.1922i −0.797889 + 0.228769i
\(251\) 36.4667i 0.145286i −0.997358 0.0726429i \(-0.976857\pi\)
0.997358 0.0726429i \(-0.0231433\pi\)
\(252\) −157.005 251.290i −0.623037 0.997181i
\(253\) 722.652 2.85633
\(254\) 9.44851 + 32.9540i 0.0371988 + 0.129740i
\(255\) 18.7811i 0.0736513i
\(256\) −157.568 201.763i −0.615501 0.788136i
\(257\) −175.943 −0.684604 −0.342302 0.939590i \(-0.611207\pi\)
−0.342302 + 0.939590i \(0.611207\pi\)
\(258\) 12.5872 3.60898i 0.0487877 0.0139883i
\(259\) 180.567i 0.697171i
\(260\) −108.995 + 68.1001i −0.419213 + 0.261924i
\(261\) −54.6764 −0.209488
\(262\) 126.416 + 440.908i 0.482504 + 1.68285i
\(263\) 444.887i 1.69158i −0.533512 0.845792i \(-0.679128\pi\)
0.533512 0.845792i \(-0.320872\pi\)
\(264\) 66.5148 73.8608i 0.251950 0.279776i
\(265\) 99.9138 0.377033
\(266\) 72.3143 20.7338i 0.271858 0.0779466i
\(267\) 21.5038i 0.0805386i
\(268\) 138.442 + 221.579i 0.516576 + 0.826788i
\(269\) 149.744 0.556670 0.278335 0.960484i \(-0.410217\pi\)
0.278335 + 0.960484i \(0.410217\pi\)
\(270\) −14.5426 50.7208i −0.0538614 0.187855i
\(271\) 439.685i 1.62245i −0.584731 0.811227i \(-0.698800\pi\)
0.584731 0.811227i \(-0.301200\pi\)
\(272\) −87.8188 + 180.009i −0.322863 + 0.661797i
\(273\) −76.8106 −0.281358
\(274\) 231.795 66.4598i 0.845968 0.242554i
\(275\) 377.424i 1.37245i
\(276\) 82.0094 51.2393i 0.297135 0.185650i
\(277\) 83.2452 0.300524 0.150262 0.988646i \(-0.451988\pi\)
0.150262 + 0.988646i \(0.451988\pi\)
\(278\) −80.4042 280.430i −0.289224 1.00874i
\(279\) 46.7719i 0.167641i
\(280\) −119.380 107.507i −0.426357 0.383952i
\(281\) −12.9851 −0.0462105 −0.0231052 0.999733i \(-0.507355\pi\)
−0.0231052 + 0.999733i \(0.507355\pi\)
\(282\) −40.2144 + 11.5302i −0.142604 + 0.0408872i
\(283\) 111.022i 0.392303i −0.980574 0.196152i \(-0.937156\pi\)
0.980574 0.196152i \(-0.0628445\pi\)
\(284\) 39.7529 + 63.6251i 0.139975 + 0.224032i
\(285\) 6.53976 0.0229465
\(286\) 146.669 + 511.545i 0.512829 + 1.78862i
\(287\) 628.500i 2.18990i
\(288\) −47.7355 + 270.520i −0.165748 + 0.939306i
\(289\) −132.300 −0.457784
\(290\) −28.4965 + 8.17046i −0.0982639 + 0.0281740i
\(291\) 97.2324i 0.334132i
\(292\) 247.045 154.353i 0.846043 0.528607i
\(293\) −141.572 −0.483179 −0.241590 0.970378i \(-0.577669\pi\)
−0.241590 + 0.970378i \(0.577669\pi\)
\(294\) −9.04926 31.5615i −0.0307798 0.107352i
\(295\) 90.6956i 0.307443i
\(296\) −112.022 + 124.394i −0.378453 + 0.420251i
\(297\) −218.478 −0.735615
\(298\) −37.0179 + 10.6137i −0.124221 + 0.0356165i
\(299\) 517.723i 1.73151i
\(300\) 26.7611 + 42.8315i 0.0892036 + 0.142772i
\(301\) −87.6329 −0.291139
\(302\) −91.2421 318.229i −0.302126 1.05374i
\(303\) 50.1415i 0.165484i
\(304\) −62.6809 30.5794i −0.206187 0.100590i
\(305\) −59.4846 −0.195031
\(306\) 206.594 59.2342i 0.675144 0.193576i
\(307\) 357.744i 1.16529i −0.812727 0.582645i \(-0.802018\pi\)
0.812727 0.582645i \(-0.197982\pi\)
\(308\) −564.141 + 352.474i −1.83163 + 1.14440i
\(309\) 9.63710 0.0311880
\(310\) 6.98927 + 24.3768i 0.0225460 + 0.0786349i
\(311\) 472.383i 1.51892i 0.650557 + 0.759458i \(0.274536\pi\)
−0.650557 + 0.759458i \(0.725464\pi\)
\(312\) 52.9154 + 47.6526i 0.169601 + 0.152733i
\(313\) 63.7596 0.203705 0.101852 0.994800i \(-0.467523\pi\)
0.101852 + 0.994800i \(0.467523\pi\)
\(314\) −287.322 + 82.3804i −0.915039 + 0.262358i
\(315\) 172.387i 0.547261i
\(316\) 296.464 + 474.495i 0.938177 + 1.50157i
\(317\) 198.721 0.626880 0.313440 0.949608i \(-0.398519\pi\)
0.313440 + 0.949608i \(0.398519\pi\)
\(318\) −15.2577 53.2151i −0.0479803 0.167343i
\(319\) 122.747i 0.384788i
\(320\) 15.5456 + 148.124i 0.0485801 + 0.462888i
\(321\) 51.9119 0.161719
\(322\) −622.094 + 178.366i −1.93197 + 0.553930i
\(323\) 54.5647i 0.168931i
\(324\) 237.293 148.260i 0.732385 0.457593i
\(325\) −270.394 −0.831983
\(326\) −80.8993 282.156i −0.248157 0.865511i
\(327\) 34.7181i 0.106172i
\(328\) −389.915 + 432.978i −1.18877 + 1.32006i
\(329\) 279.975 0.850989
\(330\) −55.5879 + 15.9380i −0.168448 + 0.0482971i
\(331\) 438.736i 1.32549i 0.748846 + 0.662744i \(0.230608\pi\)
−0.748846 + 0.662744i \(0.769392\pi\)
\(332\) −200.742 321.290i −0.604644 0.967742i
\(333\) 179.628 0.539424
\(334\) −117.683 410.449i −0.352344 1.22889i
\(335\) 152.006i 0.453748i
\(336\) −39.0288 + 80.0003i −0.116157 + 0.238096i
\(337\) −538.699 −1.59851 −0.799257 0.600989i \(-0.794773\pi\)
−0.799257 + 0.600989i \(0.794773\pi\)
\(338\) −41.5724 + 11.9196i −0.122995 + 0.0352650i
\(339\) 68.2877i 0.201439i
\(340\) 98.8222 61.7440i 0.290653 0.181600i
\(341\) 105.002 0.307924
\(342\) 20.6260 + 71.9382i 0.0603098 + 0.210346i
\(343\) 203.100i 0.592127i
\(344\) 60.3710 + 54.3666i 0.175497 + 0.158043i
\(345\) −56.2593 −0.163070
\(346\) 539.685 154.737i 1.55978 0.447217i
\(347\) 584.405i 1.68417i 0.539349 + 0.842083i \(0.318671\pi\)
−0.539349 + 0.842083i \(0.681329\pi\)
\(348\) 8.70335 + 13.9299i 0.0250096 + 0.0400283i
\(349\) −300.832 −0.861983 −0.430991 0.902356i \(-0.641836\pi\)
−0.430991 + 0.902356i \(0.641836\pi\)
\(350\) −93.1561 324.905i −0.266160 0.928301i
\(351\) 156.522i 0.445931i
\(352\) 607.312 + 107.165i 1.72532 + 0.304447i
\(353\) −316.023 −0.895250 −0.447625 0.894221i \(-0.647730\pi\)
−0.447625 + 0.894221i \(0.647730\pi\)
\(354\) 48.3055 13.8500i 0.136456 0.0391244i
\(355\) 43.6475i 0.122951i
\(356\) 113.149 70.6951i 0.317833 0.198582i
\(357\) 69.6415 0.195074
\(358\) 19.3964 + 67.6498i 0.0541799 + 0.188966i
\(359\) 116.055i 0.323272i 0.986850 + 0.161636i \(0.0516770\pi\)
−0.986850 + 0.161636i \(0.948323\pi\)
\(360\) 106.947 118.759i 0.297076 0.329886i
\(361\) −19.0000 −0.0526316
\(362\) 664.312 190.470i 1.83512 0.526161i
\(363\) 161.433i 0.444720i
\(364\) −252.520 404.162i −0.693736 1.11033i
\(365\) −169.475 −0.464316
\(366\) 9.08383 + 31.6821i 0.0248192 + 0.0865632i
\(367\) 67.8773i 0.184952i 0.995715 + 0.0924759i \(0.0294781\pi\)
−0.995715 + 0.0924759i \(0.970522\pi\)
\(368\) 539.222 + 263.064i 1.46528 + 0.714848i
\(369\) 625.231 1.69439
\(370\) 93.6195 26.8424i 0.253026 0.0725470i
\(371\) 370.487i 0.998617i
\(372\) 11.9160 7.44512i 0.0320324 0.0200138i
\(373\) −267.337 −0.716721 −0.358361 0.933583i \(-0.616664\pi\)
−0.358361 + 0.933583i \(0.616664\pi\)
\(374\) −132.980 463.800i −0.355561 1.24011i
\(375\) 66.8910i 0.178376i
\(376\) −192.877 173.694i −0.512971 0.461952i
\(377\) −87.9388 −0.233259
\(378\) 188.076 53.9248i 0.497556 0.142658i
\(379\) 372.834i 0.983731i 0.870671 + 0.491866i \(0.163685\pi\)
−0.870671 + 0.491866i \(0.836315\pi\)
\(380\) 21.4999 + 34.4109i 0.0565786 + 0.0905550i
\(381\) −11.0508 −0.0290047
\(382\) 55.2512 + 192.702i 0.144637 + 0.504457i
\(383\) 19.6246i 0.0512392i −0.999672 0.0256196i \(-0.991844\pi\)
0.999672 0.0256196i \(-0.00815587\pi\)
\(384\) 76.5186 30.8997i 0.199267 0.0804679i
\(385\) 387.006 1.00521
\(386\) −323.216 + 92.6718i −0.837347 + 0.240082i
\(387\) 87.1771i 0.225264i
\(388\) −511.617 + 319.658i −1.31860 + 0.823860i
\(389\) 198.727 0.510867 0.255434 0.966827i \(-0.417782\pi\)
0.255434 + 0.966827i \(0.417782\pi\)
\(390\) −11.4183 39.8243i −0.0292778 0.102114i
\(391\) 469.401i 1.20051i
\(392\) 136.320 151.376i 0.347756 0.386163i
\(393\) −147.854 −0.376219
\(394\) −416.623 + 119.453i −1.05742 + 0.303181i
\(395\) 325.509i 0.824072i
\(396\) −350.641 561.206i −0.885457 1.41719i
\(397\) 295.448 0.744203 0.372101 0.928192i \(-0.378637\pi\)
0.372101 + 0.928192i \(0.378637\pi\)
\(398\) −45.3408 158.137i −0.113922 0.397330i
\(399\) 24.2499i 0.0607766i
\(400\) −137.392 + 281.623i −0.343480 + 0.704057i
\(401\) −63.9986 −0.159597 −0.0797987 0.996811i \(-0.525428\pi\)
−0.0797987 + 0.996811i \(0.525428\pi\)
\(402\) −80.9599 + 23.2126i −0.201393 + 0.0577429i
\(403\) 75.2256i 0.186664i
\(404\) 263.835 164.843i 0.653056 0.408028i
\(405\) −162.785 −0.401939
\(406\) −30.2966 105.667i −0.0746222 0.260264i
\(407\) 403.262i 0.990815i
\(408\) −47.9765 43.2049i −0.117590 0.105894i
\(409\) 504.473 1.23343 0.616715 0.787186i \(-0.288463\pi\)
0.616715 + 0.787186i \(0.288463\pi\)
\(410\) 325.861 93.4302i 0.794783 0.227878i
\(411\) 77.7302i 0.189125i
\(412\) 31.6826 + 50.7085i 0.0768995 + 0.123079i
\(413\) −336.306 −0.814299
\(414\) −177.438 618.859i −0.428594 1.49483i
\(415\) 220.408i 0.531105i
\(416\) −76.7754 + 435.091i −0.184556 + 1.04589i
\(417\) 94.0393 0.225514
\(418\) 161.500 46.3049i 0.386363 0.110777i
\(419\) 470.299i 1.12243i 0.827670 + 0.561215i \(0.189666\pi\)
−0.827670 + 0.561215i \(0.810334\pi\)
\(420\) 43.9190 27.4405i 0.104569 0.0653345i
\(421\) −470.034 −1.11647 −0.558235 0.829683i \(-0.688521\pi\)
−0.558235 + 0.829683i \(0.688521\pi\)
\(422\) −9.05083 31.5670i −0.0214475 0.0748033i
\(423\) 278.519i 0.658437i
\(424\) 229.847 255.231i 0.542091 0.601961i
\(425\) 245.157 0.576840
\(426\) −23.2471 + 6.66537i −0.0545707 + 0.0156464i
\(427\) 220.573i 0.516564i
\(428\) 170.664 + 273.150i 0.398747 + 0.638201i
\(429\) −171.541 −0.399864
\(430\) −13.0271 45.4354i −0.0302957 0.105664i
\(431\) 224.005i 0.519733i 0.965645 + 0.259866i \(0.0836785\pi\)
−0.965645 + 0.259866i \(0.916321\pi\)
\(432\) −163.022 79.5315i −0.377365 0.184101i
\(433\) 180.128 0.415999 0.207999 0.978129i \(-0.433305\pi\)
0.207999 + 0.978129i \(0.433305\pi\)
\(434\) −90.3909 + 25.9167i −0.208274 + 0.0597159i
\(435\) 9.55602i 0.0219679i
\(436\) 182.680 114.138i 0.418990 0.261784i
\(437\) 163.450 0.374028
\(438\) 25.8804 + 90.2643i 0.0590877 + 0.206083i
\(439\) 590.004i 1.34397i 0.740563 + 0.671987i \(0.234559\pi\)
−0.740563 + 0.671987i \(0.765441\pi\)
\(440\) −266.612 240.095i −0.605936 0.545671i
\(441\) −218.590 −0.495670
\(442\) 332.276 95.2693i 0.751755 0.215541i
\(443\) 157.459i 0.355439i 0.984081 + 0.177719i \(0.0568720\pi\)
−0.984081 + 0.177719i \(0.943128\pi\)
\(444\) −28.5931 45.7637i −0.0643988 0.103071i
\(445\) −77.6212 −0.174430
\(446\) 107.613 + 375.328i 0.241285 + 0.841543i
\(447\) 12.4136i 0.0277709i
\(448\) −549.255 + 57.6442i −1.22602 + 0.128670i
\(449\) −715.434 −1.59339 −0.796697 0.604379i \(-0.793421\pi\)
−0.796697 + 0.604379i \(0.793421\pi\)
\(450\) 323.215 92.6716i 0.718256 0.205937i
\(451\) 1403.63i 3.11226i
\(452\) 359.316 224.500i 0.794947 0.496682i
\(453\) 106.715 0.235574
\(454\) 168.346 + 587.149i 0.370807 + 1.29328i
\(455\) 277.259i 0.609361i
\(456\) 15.0444 16.7059i 0.0329921 0.0366358i
\(457\) 31.3497 0.0685988 0.0342994 0.999412i \(-0.489080\pi\)
0.0342994 + 0.999412i \(0.489080\pi\)
\(458\) 441.581 126.609i 0.964150 0.276439i
\(459\) 141.913i 0.309178i
\(460\) −184.956 296.025i −0.402078 0.643532i
\(461\) 368.719 0.799824 0.399912 0.916554i \(-0.369041\pi\)
0.399912 + 0.916554i \(0.369041\pi\)
\(462\) −59.0994 206.124i −0.127921 0.446155i
\(463\) 817.405i 1.76545i −0.469887 0.882726i \(-0.655705\pi\)
0.469887 0.882726i \(-0.344295\pi\)
\(464\) −44.6832 + 91.5905i −0.0963001 + 0.197393i
\(465\) −8.17453 −0.0175796
\(466\) −360.796 + 103.447i −0.774241 + 0.221989i
\(467\) 86.9194i 0.186123i 0.995660 + 0.0930614i \(0.0296653\pi\)
−0.995660 + 0.0930614i \(0.970335\pi\)
\(468\) 402.060 251.206i 0.859102 0.536766i
\(469\) 563.647 1.20181
\(470\) 41.6200 + 145.160i 0.0885531 + 0.308851i
\(471\) 96.3506i 0.204566i
\(472\) 231.683 + 208.641i 0.490855 + 0.442036i
\(473\) −195.711 −0.413765
\(474\) −173.369 + 49.7081i −0.365758 + 0.104869i
\(475\) 85.3662i 0.179718i
\(476\) 228.951 + 366.439i 0.480989 + 0.769830i
\(477\) −368.560 −0.772662
\(478\) 38.5033 + 134.290i 0.0805509 + 0.280941i
\(479\) 333.107i 0.695421i −0.937602 0.347710i \(-0.886959\pi\)
0.937602 0.347710i \(-0.113041\pi\)
\(480\) −47.2799 8.34293i −0.0984999 0.0173811i
\(481\) 288.905 0.600634
\(482\) −572.072 + 164.023i −1.18687 + 0.340297i
\(483\) 208.613i 0.431911i
\(484\) −849.429 + 530.722i −1.75502 + 1.09653i
\(485\) 350.975 0.723659
\(486\) 81.1005 + 282.858i 0.166873 + 0.582013i
\(487\) 264.690i 0.543511i −0.962366 0.271755i \(-0.912396\pi\)
0.962366 0.271755i \(-0.0876042\pi\)
\(488\) −136.841 + 151.954i −0.280412 + 0.311382i
\(489\) 94.6183 0.193494
\(490\) −113.926 + 32.6646i −0.232502 + 0.0666625i
\(491\) 402.874i 0.820518i 0.911969 + 0.410259i \(0.134562\pi\)
−0.911969 + 0.410259i \(0.865438\pi\)
\(492\) −99.5238 159.289i −0.202284 0.323759i
\(493\) 79.7310 0.161726
\(494\) 33.1738 + 115.702i 0.0671534 + 0.234214i
\(495\) 384.993i 0.777764i
\(496\) 78.3495 + 38.2235i 0.157963 + 0.0770634i
\(497\) 161.848 0.325650
\(498\) 117.392 33.6584i 0.235727 0.0675871i
\(499\) 350.536i 0.702477i 0.936286 + 0.351238i \(0.114239\pi\)
−0.936286 + 0.351238i \(0.885761\pi\)
\(500\) 351.967 219.908i 0.703934 0.439817i
\(501\) 137.640 0.274730
\(502\) 20.1014 + 70.1086i 0.0400426 + 0.139659i
\(503\) 339.615i 0.675179i −0.941293 0.337589i \(-0.890388\pi\)
0.941293 0.337589i \(-0.109612\pi\)
\(504\) 440.366 + 396.568i 0.873742 + 0.786842i
\(505\) −180.993 −0.358403
\(506\) −1389.33 + 398.345i −2.74570 + 0.787242i
\(507\) 13.9409i 0.0274969i
\(508\) −36.3302 58.1471i −0.0715162 0.114463i
\(509\) −933.003 −1.83301 −0.916506 0.400020i \(-0.869003\pi\)
−0.916506 + 0.400020i \(0.869003\pi\)
\(510\) 10.3526 + 36.1073i 0.0202992 + 0.0707986i
\(511\) 628.426i 1.22980i
\(512\) 414.148 + 301.041i 0.808882 + 0.587971i
\(513\) −49.4155 −0.0963266
\(514\) 338.257 96.9844i 0.658088 0.188686i
\(515\) 34.7866i 0.0675467i
\(516\) −22.2100 + 13.8768i −0.0430427 + 0.0268930i
\(517\) 625.270 1.20942
\(518\) 99.5333 + 347.147i 0.192149 + 0.670169i
\(519\) 180.978i 0.348705i
\(520\) 172.009 191.006i 0.330787 0.367319i
\(521\) −415.284 −0.797091 −0.398545 0.917149i \(-0.630485\pi\)
−0.398545 + 0.917149i \(0.630485\pi\)
\(522\) 105.117 30.1390i 0.201374 0.0577376i
\(523\) 241.598i 0.461947i −0.972960 0.230973i \(-0.925809\pi\)
0.972960 0.230973i \(-0.0741911\pi\)
\(524\) −486.080 777.978i −0.927633 1.48469i
\(525\) 108.954 0.207531
\(526\) 245.233 + 855.311i 0.466223 + 1.62607i
\(527\) 68.2044i 0.129420i
\(528\) −87.1632 + 178.665i −0.165082 + 0.338381i
\(529\) −877.105 −1.65804
\(530\) −192.088 + 55.0750i −0.362430 + 0.103915i
\(531\) 334.556i 0.630050i
\(532\) −127.598 + 79.7230i −0.239846 + 0.149855i
\(533\) 1005.59 1.88666
\(534\) 11.8535 + 41.3419i 0.0221975 + 0.0774192i
\(535\) 187.384i 0.350250i
\(536\) −388.301 349.681i −0.724442 0.652391i
\(537\) −22.6857 −0.0422452
\(538\) −287.889 + 82.5428i −0.535109 + 0.153425i
\(539\) 490.731i 0.910447i
\(540\) 55.9173 + 89.4965i 0.103551 + 0.165734i
\(541\) −304.787 −0.563377 −0.281689 0.959506i \(-0.590894\pi\)
−0.281689 + 0.959506i \(0.590894\pi\)
\(542\) 242.366 + 845.311i 0.447169 + 1.55961i
\(543\) 222.770i 0.410259i
\(544\) 69.6095 394.482i 0.127959 0.725150i
\(545\) −125.320 −0.229945
\(546\) 147.671 42.3400i 0.270460 0.0775458i
\(547\) 555.915i 1.01630i 0.861269 + 0.508149i \(0.169670\pi\)
−0.861269 + 0.508149i \(0.830330\pi\)
\(548\) −409.001 + 255.543i −0.746352 + 0.466319i
\(549\) 219.425 0.399682
\(550\) −208.046 725.612i −0.378265 1.31930i
\(551\) 27.7632i 0.0503869i
\(552\) −129.422 + 143.715i −0.234459 + 0.260354i
\(553\) 1207.01 2.18265
\(554\) −160.042 + 45.8869i −0.288885 + 0.0828283i
\(555\) 31.3944i 0.0565664i
\(556\) 309.160 + 494.816i 0.556043 + 0.889956i
\(557\) −192.055 −0.344802 −0.172401 0.985027i \(-0.555152\pi\)
−0.172401 + 0.985027i \(0.555152\pi\)
\(558\) −25.7819 89.9208i −0.0462041 0.161148i
\(559\) 140.211i 0.250825i
\(560\) 288.773 + 140.880i 0.515666 + 0.251572i
\(561\) 155.531 0.277238
\(562\) 24.9644 7.15775i 0.0444207 0.0127362i
\(563\) 107.771i 0.191423i −0.995409 0.0957114i \(-0.969487\pi\)
0.995409 0.0957114i \(-0.0305126\pi\)
\(564\) 70.9580 44.3345i 0.125812 0.0786072i
\(565\) −246.495 −0.436274
\(566\) 61.1981 + 213.444i 0.108124 + 0.377109i
\(567\) 603.619i 1.06458i
\(568\) −111.498 100.409i −0.196300 0.176776i
\(569\) −647.934 −1.13872 −0.569362 0.822087i \(-0.692810\pi\)
−0.569362 + 0.822087i \(0.692810\pi\)
\(570\) −12.5729 + 3.60489i −0.0220578 + 0.00632436i
\(571\) 285.402i 0.499828i −0.968268 0.249914i \(-0.919598\pi\)
0.968268 0.249914i \(-0.0804023\pi\)
\(572\) −563.953 902.616i −0.985933 1.57800i
\(573\) −64.6208 −0.112776
\(574\) 346.445 + 1208.31i 0.603563 + 2.10508i
\(575\) 734.376i 1.27717i
\(576\) −57.3444 546.398i −0.0995562 0.948608i
\(577\) −92.4624 −0.160247 −0.0801234 0.996785i \(-0.525531\pi\)
−0.0801234 + 0.996785i \(0.525531\pi\)
\(578\) 254.351 72.9269i 0.440053 0.126171i
\(579\) 108.387i 0.187197i
\(580\) 50.2819 31.4160i 0.0866929 0.0541656i
\(581\) −817.289 −1.40669
\(582\) −53.5970 186.933i −0.0920911 0.321191i
\(583\) 827.410i 1.41923i
\(584\) −389.869 + 432.927i −0.667584 + 0.741314i
\(585\) −275.817 −0.471482
\(586\) 272.177 78.0379i 0.464465 0.133170i
\(587\) 654.717i 1.11536i 0.830056 + 0.557681i \(0.188309\pi\)
−0.830056 + 0.557681i \(0.811691\pi\)
\(588\) 34.7951 + 55.6901i 0.0591753 + 0.0947110i
\(589\) 23.7495 0.0403217
\(590\) −49.9938 174.366i −0.0847352 0.295535i
\(591\) 139.710i 0.236396i
\(592\) 146.798 300.902i 0.247969 0.508280i
\(593\) 106.297 0.179253 0.0896264 0.995975i \(-0.471433\pi\)
0.0896264 + 0.995975i \(0.471433\pi\)
\(594\) 420.032 120.431i 0.707124 0.202745i
\(595\) 251.381i 0.422489i
\(596\) 65.3178 40.8105i 0.109594 0.0684740i
\(597\) 53.0298 0.0888271
\(598\) −285.382 995.342i −0.477228 1.66445i
\(599\) 478.675i 0.799124i 0.916706 + 0.399562i \(0.130838\pi\)
−0.916706 + 0.399562i \(0.869162\pi\)
\(600\) −75.0591 67.5939i −0.125098 0.112656i
\(601\) 808.024 1.34447 0.672233 0.740340i \(-0.265335\pi\)
0.672233 + 0.740340i \(0.265335\pi\)
\(602\) 168.478 48.3055i 0.279863 0.0802418i
\(603\) 560.715i 0.929876i
\(604\) 350.833 + 561.513i 0.580849 + 0.929657i
\(605\) 582.717 0.963169
\(606\) 27.6393 + 96.3990i 0.0456094 + 0.159074i
\(607\) 694.694i 1.14447i −0.820089 0.572236i \(-0.806076\pi\)
0.820089 0.572236i \(-0.193924\pi\)
\(608\) 137.363 + 24.2388i 0.225925 + 0.0398664i
\(609\) 35.4344 0.0581845
\(610\) 114.361 32.7894i 0.187478 0.0537531i
\(611\) 447.956i 0.733153i
\(612\) −364.533 + 227.760i −0.595643 + 0.372157i
\(613\) −496.830 −0.810489 −0.405245 0.914208i \(-0.632814\pi\)
−0.405245 + 0.914208i \(0.632814\pi\)
\(614\) 197.198 + 687.776i 0.321169 + 1.12016i
\(615\) 109.274i 0.177682i
\(616\) 890.289 988.614i 1.44527 1.60489i
\(617\) 387.951 0.628770 0.314385 0.949296i \(-0.398202\pi\)
0.314385 + 0.949296i \(0.398202\pi\)
\(618\) −18.5277 + 5.31222i −0.0299801 + 0.00859583i
\(619\) 882.105i 1.42505i −0.701647 0.712525i \(-0.747552\pi\)
0.701647 0.712525i \(-0.252448\pi\)
\(620\) −26.8743 43.0127i −0.0433456 0.0693753i
\(621\) 425.104 0.684548
\(622\) −260.389 908.173i −0.418633 1.46009i
\(623\) 287.824i 0.461998i
\(624\) −127.999 62.4455i −0.205127 0.100073i
\(625\) 248.156 0.397050
\(626\) −122.580 + 35.1459i −0.195815 + 0.0561437i
\(627\) 54.1574i 0.0863754i
\(628\) 506.977 316.759i 0.807289 0.504393i
\(629\) −261.940 −0.416439
\(630\) −95.0243 331.421i −0.150832 0.526065i
\(631\) 502.601i 0.796515i 0.917274 + 0.398258i \(0.130385\pi\)
−0.917274 + 0.398258i \(0.869615\pi\)
\(632\) −831.517 748.816i −1.31569 1.18484i
\(633\) 10.5857 0.0167230
\(634\) −382.048 + 109.540i −0.602600 + 0.172776i
\(635\) 39.8895i 0.0628181i
\(636\) 58.6671 + 93.8977i 0.0922439 + 0.147638i
\(637\) −351.570 −0.551915
\(638\) −67.6616 235.987i −0.106053 0.369885i
\(639\) 161.006i 0.251966i
\(640\) −111.537 276.205i −0.174277 0.431571i
\(641\) 385.625 0.601600 0.300800 0.953687i \(-0.402746\pi\)
0.300800 + 0.953687i \(0.402746\pi\)
\(642\) −99.8026 + 28.6152i −0.155456 + 0.0445719i
\(643\) 925.293i 1.43902i −0.694480 0.719512i \(-0.744365\pi\)
0.694480 0.719512i \(-0.255635\pi\)
\(644\) 1097.68 685.829i 1.70447 1.06495i
\(645\) 15.2363 0.0236222
\(646\) −30.0775 104.903i −0.0465596 0.162388i
\(647\) 656.956i 1.01539i 0.861538 + 0.507694i \(0.169502\pi\)
−0.861538 + 0.507694i \(0.830498\pi\)
\(648\) −374.479 + 415.838i −0.577900 + 0.641725i
\(649\) −751.073 −1.15728
\(650\) 519.843 149.048i 0.799759 0.229305i
\(651\) 30.3117i 0.0465617i
\(652\) 311.064 + 497.863i 0.477092 + 0.763593i
\(653\) 392.897 0.601680 0.300840 0.953675i \(-0.402733\pi\)
0.300840 + 0.953675i \(0.402733\pi\)
\(654\) 19.1375 + 66.7468i 0.0292622 + 0.102059i
\(655\) 533.701i 0.814811i
\(656\) 510.958 1047.35i 0.778899 1.59657i
\(657\) 625.157 0.951533
\(658\) −538.263 + 154.330i −0.818029 + 0.234543i
\(659\) 695.576i 1.05550i −0.849399 0.527751i \(-0.823035\pi\)
0.849399 0.527751i \(-0.176965\pi\)
\(660\) 98.0844 61.2830i 0.148613 0.0928530i
\(661\) 1179.05 1.78373 0.891866 0.452299i \(-0.149396\pi\)
0.891866 + 0.452299i \(0.149396\pi\)
\(662\) −241.843 843.487i −0.365322 1.27415i
\(663\) 111.425i 0.168062i
\(664\) 563.037 + 507.038i 0.847947 + 0.763612i
\(665\) 87.5335 0.131629
\(666\) −345.342 + 99.0156i −0.518531 + 0.148672i
\(667\) 238.837i 0.358076i
\(668\) 452.500 + 724.233i 0.677395 + 1.08418i
\(669\) −125.863 −0.188135
\(670\) 83.7894 + 292.237i 0.125059 + 0.436174i
\(671\) 492.606i 0.734137i
\(672\) 30.9362 175.317i 0.0460359 0.260889i
\(673\) −881.170 −1.30932 −0.654658 0.755925i \(-0.727187\pi\)
−0.654658 + 0.755925i \(0.727187\pi\)
\(674\) 1035.67 296.945i 1.53660 0.440571i
\(675\) 222.022i 0.328921i
\(676\) 73.3542 45.8316i 0.108512 0.0677982i
\(677\) −126.536 −0.186907 −0.0934533 0.995624i \(-0.529791\pi\)
−0.0934533 + 0.995624i \(0.529791\pi\)
\(678\) 37.6420 + 131.286i 0.0555191 + 0.193637i
\(679\) 1301.44i 1.91670i
\(680\) −155.954 + 173.178i −0.229345 + 0.254674i
\(681\) −196.895 −0.289126
\(682\) −201.870 + 57.8798i −0.295998 + 0.0848678i
\(683\) 873.042i 1.27825i 0.769105 + 0.639123i \(0.220702\pi\)
−0.769105 + 0.639123i \(0.779298\pi\)
\(684\) −79.3083 126.934i −0.115948 0.185576i
\(685\) 280.579 0.409604
\(686\) 111.954 + 390.467i 0.163198 + 0.569193i
\(687\) 148.080i 0.215545i
\(688\) −146.034 71.2439i −0.212258 0.103552i
\(689\) −592.774 −0.860339
\(690\) 108.161 31.0116i 0.156754 0.0449443i
\(691\) 610.841i 0.883996i 0.897016 + 0.441998i \(0.145730\pi\)
−0.897016 + 0.441998i \(0.854270\pi\)
\(692\) −952.269 + 594.976i −1.37611 + 0.859792i
\(693\) −1427.58 −2.06000
\(694\) −322.139 1123.54i −0.464178 1.61894i
\(695\) 339.449i 0.488415i
\(696\) −24.4110 21.9831i −0.0350733 0.0315850i
\(697\) −911.733 −1.30808
\(698\) 578.361 165.826i 0.828597 0.237574i
\(699\) 120.989i 0.173089i
\(700\) 358.192 + 573.292i 0.511703 + 0.818989i
\(701\) −506.393 −0.722387 −0.361193 0.932491i \(-0.617631\pi\)
−0.361193 + 0.932491i \(0.617631\pi\)
\(702\) 86.2789 + 300.919i 0.122904 + 0.428660i
\(703\) 91.2102i 0.129744i
\(704\) −1226.65 + 128.737i −1.74241 + 0.182865i
\(705\) −48.6780 −0.0690467
\(706\) 607.566 174.200i 0.860576 0.246742i
\(707\) 671.135i 0.949272i
\(708\) −85.2346 + 53.2545i −0.120388 + 0.0752182i
\(709\) −1036.42 −1.46180 −0.730902 0.682483i \(-0.760900\pi\)
−0.730902 + 0.682483i \(0.760900\pi\)
\(710\) 24.0596 + 83.9140i 0.0338868 + 0.118189i
\(711\) 1200.73i 1.68879i
\(712\) −178.564 + 198.284i −0.250792 + 0.278489i
\(713\) −204.308 −0.286548
\(714\) −133.888 + 38.3882i −0.187519 + 0.0537649i
\(715\) 619.204i 0.866020i
\(716\) −74.5806 119.367i −0.104163 0.166714i
\(717\) −45.0328 −0.0628072
\(718\) −63.9722 223.119i −0.0890978 0.310751i
\(719\) 834.943i 1.16126i 0.814169 + 0.580628i \(0.197193\pi\)
−0.814169 + 0.580628i \(0.802807\pi\)
\(720\) −140.148 + 287.271i −0.194649 + 0.398987i
\(721\) 128.991 0.178905
\(722\) 36.5282 10.4733i 0.0505931 0.0145059i
\(723\) 191.839i 0.265337i
\(724\) −1172.17 + 732.372i −1.61902 + 1.01156i
\(725\) 124.739 0.172053
\(726\) −88.9862 310.362i −0.122571 0.427495i
\(727\) 225.252i 0.309838i 0.987927 + 0.154919i \(0.0495116\pi\)
−0.987927 + 0.154919i \(0.950488\pi\)
\(728\) 708.263 + 637.821i 0.972889 + 0.876128i
\(729\) 534.700 0.733470
\(730\) 325.822 93.4191i 0.446332 0.127971i
\(731\) 127.125i 0.173905i
\(732\) −34.9280 55.9028i −0.0477158 0.0763700i
\(733\) 697.401 0.951434 0.475717 0.879598i \(-0.342189\pi\)
0.475717 + 0.879598i \(0.342189\pi\)
\(734\) −37.4157 130.497i −0.0509751 0.177788i
\(735\) 38.2040i 0.0519782i
\(736\) −1181.68 208.517i −1.60555 0.283312i
\(737\) 1258.80 1.70800
\(738\) −1202.03 + 344.643i −1.62877 + 0.466996i
\(739\) 1065.87i 1.44231i 0.692772 + 0.721157i \(0.256389\pi\)
−0.692772 + 0.721157i \(0.743611\pi\)
\(740\) −165.191 + 103.211i −0.223231 + 0.139474i
\(741\) −38.7994 −0.0523609
\(742\) −204.222 712.275i −0.275232 0.959939i
\(743\) 1050.43i 1.41376i 0.707332 + 0.706881i \(0.249898\pi\)
−0.707332 + 0.706881i \(0.750102\pi\)
\(744\) −18.8051 + 20.8820i −0.0252756 + 0.0280671i
\(745\) −44.8087 −0.0601459
\(746\) 513.966 147.363i 0.688962 0.197538i
\(747\) 813.038i 1.08840i
\(748\) 511.317 + 818.370i 0.683578 + 1.09408i
\(749\) 694.831 0.927678
\(750\) 36.8720 + 128.600i 0.0491627 + 0.171467i
\(751\) 26.6606i 0.0355002i 0.999842 + 0.0177501i \(0.00565033\pi\)
−0.999842 + 0.0177501i \(0.994350\pi\)
\(752\) 466.558 + 227.614i 0.620423 + 0.302679i
\(753\) −23.5102 −0.0312221
\(754\) 169.066 48.4741i 0.224225 0.0642893i
\(755\) 385.204i 0.510204i
\(756\) −331.859 + 207.345i −0.438967 + 0.274266i
\(757\) 445.989 0.589153 0.294577 0.955628i \(-0.404821\pi\)
0.294577 + 0.955628i \(0.404821\pi\)
\(758\) −205.516 716.788i −0.271129 0.945630i
\(759\) 465.897i 0.613830i
\(760\) −60.3025 54.3050i −0.0793454 0.0714539i
\(761\) 294.799 0.387384 0.193692 0.981062i \(-0.437954\pi\)
0.193692 + 0.981062i \(0.437954\pi\)
\(762\) 21.2456 6.09149i 0.0278813 0.00799408i
\(763\) 464.695i 0.609037i
\(764\) −212.445 340.022i −0.278070 0.445055i
\(765\) 250.074 0.326894
\(766\) 10.8176 + 37.7291i 0.0141222 + 0.0492547i
\(767\) 538.084i 0.701543i
\(768\) −130.077 + 101.585i −0.169371 + 0.132272i
\(769\) −279.363 −0.363281 −0.181641 0.983365i \(-0.558141\pi\)
−0.181641 + 0.983365i \(0.558141\pi\)
\(770\) −744.034 + 213.328i −0.966278 + 0.277049i
\(771\) 113.431i 0.147122i
\(772\) 570.312 356.330i 0.738746 0.461567i
\(773\) −1092.48 −1.41329 −0.706647 0.707566i \(-0.749793\pi\)
−0.706647 + 0.707566i \(0.749793\pi\)
\(774\) 48.0543 + 167.601i 0.0620856 + 0.216539i
\(775\) 106.705i 0.137684i
\(776\) 807.400 896.571i 1.04046 1.15537i
\(777\) −116.412 −0.149823
\(778\) −382.061 + 109.544i −0.491081 + 0.140802i
\(779\) 317.475i 0.407542i