Properties

Label 48.3.l.a.43.3
Level $48$
Weight $3$
Character 48.43
Analytic conductor $1.308$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.30790526893\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.3
Root \(1.78012 - 0.911682i\) of defining polynomial
Character \(\chi\) \(=\) 48.43
Dual form 48.3.l.a.19.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.78012 - 0.911682i) q^{2} +(1.22474 + 1.22474i) q^{3} +(2.33767 + 3.24581i) q^{4} +(1.00772 + 1.00772i) q^{5} +(-1.06362 - 3.29677i) q^{6} +10.0236 q^{7} +(-1.20220 - 7.90915i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.78012 - 0.911682i) q^{2} +(1.22474 + 1.22474i) q^{3} +(2.33767 + 3.24581i) q^{4} +(1.00772 + 1.00772i) q^{5} +(-1.06362 - 3.29677i) q^{6} +10.0236 q^{7} +(-1.20220 - 7.90915i) q^{8} +3.00000i q^{9} +(-0.875146 - 2.71259i) q^{10} +(2.26517 - 2.26517i) q^{11} +(-1.11224 + 6.83834i) q^{12} +(-6.88229 + 6.88229i) q^{13} +(-17.8432 - 9.13830i) q^{14} +2.46840i q^{15} +(-5.07058 + 15.1753i) q^{16} -22.3801 q^{17} +(2.73505 - 5.34037i) q^{18} +(-16.8918 - 16.8918i) q^{19} +(-0.915151 + 5.62660i) q^{20} +(12.2763 + 12.2763i) q^{21} +(-6.09740 + 1.96717i) q^{22} +33.2007 q^{23} +(8.21431 - 11.1591i) q^{24} -22.9690i q^{25} +(18.5258 - 5.97686i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(23.4318 + 32.5346i) q^{28} +(-24.6412 + 24.6412i) q^{29} +(2.25040 - 4.39406i) q^{30} -41.3761i q^{31} +(22.8613 - 22.3911i) q^{32} +5.54852 q^{33} +(39.8394 + 20.4036i) q^{34} +(10.1010 + 10.1010i) q^{35} +(-9.73743 + 7.01302i) q^{36} +(-6.60031 - 6.60031i) q^{37} +(14.6695 + 45.4693i) q^{38} -16.8581 q^{39} +(6.75875 - 9.18170i) q^{40} -47.1477i q^{41} +(-10.6612 - 33.0454i) q^{42} +(-48.8218 + 48.8218i) q^{43} +(12.6475 + 2.05709i) q^{44} +(-3.02316 + 3.02316i) q^{45} +(-59.1013 - 30.2685i) q^{46} +45.6048i q^{47} +(-24.7960 + 12.3757i) q^{48} +51.4717 q^{49} +(-20.9404 + 40.8876i) q^{50} +(-27.4100 - 27.4100i) q^{51} +(-38.4271 - 6.25007i) q^{52} +(25.1401 + 25.1401i) q^{53} +(9.89032 - 3.19085i) q^{54} +4.56532 q^{55} +(-12.0503 - 79.2779i) q^{56} -41.3762i q^{57} +(66.3292 - 21.3994i) q^{58} +(6.23974 - 6.23974i) q^{59} +(-8.01197 + 5.77032i) q^{60} +(35.9513 - 35.9513i) q^{61} +(-37.7219 + 73.6546i) q^{62} +30.0707i q^{63} +(-61.1095 + 19.0167i) q^{64} -13.8709 q^{65} +(-9.87704 - 5.05848i) q^{66} +(10.2045 + 10.2045i) q^{67} +(-52.3174 - 72.6417i) q^{68} +(40.6624 + 40.6624i) q^{69} +(-8.77208 - 27.1898i) q^{70} +11.9529 q^{71} +(23.7275 - 3.60659i) q^{72} +111.332i q^{73} +(5.73197 + 17.7667i) q^{74} +(28.1312 - 28.1312i) q^{75} +(15.3401 - 94.3149i) q^{76} +(22.7051 - 22.7051i) q^{77} +(30.0095 + 15.3692i) q^{78} +4.46031i q^{79} +(-20.4022 + 10.1827i) q^{80} -9.00000 q^{81} +(-42.9837 + 83.9287i) q^{82} +(10.1751 + 10.1751i) q^{83} +(-11.1486 + 68.5445i) q^{84} +(-22.5530 - 22.5530i) q^{85} +(131.419 - 42.3988i) q^{86} -60.3583 q^{87} +(-20.6388 - 15.1924i) q^{88} -21.9364i q^{89} +(8.13777 - 2.62544i) q^{90} +(-68.9850 + 68.9850i) q^{91} +(77.6124 + 107.763i) q^{92} +(50.6752 - 50.6752i) q^{93} +(41.5771 - 81.1821i) q^{94} -34.0444i q^{95} +(55.4226 + 0.575837i) q^{96} +107.309 q^{97} +(-91.6260 - 46.9259i) q^{98} +(6.79552 + 6.79552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} - 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} - 12q^{8} - 56q^{10} + 32q^{11} - 24q^{12} - 44q^{14} + 32q^{16} + 12q^{18} - 32q^{19} + 80q^{20} + 32q^{22} - 128q^{23} + 36q^{24} - 100q^{26} - 120q^{28} + 32q^{29} + 72q^{30} + 160q^{32} + 96q^{34} + 96q^{35} + 12q^{36} - 96q^{37} + 168q^{38} + 48q^{40} - 60q^{42} + 160q^{43} + 88q^{44} + 136q^{46} - 144q^{48} + 112q^{49} - 236q^{50} - 96q^{51} - 48q^{52} - 160q^{53} - 36q^{54} - 256q^{55} - 224q^{56} + 144q^{58} - 128q^{59} - 72q^{60} - 32q^{61} - 276q^{62} - 408q^{64} - 32q^{65} + 72q^{66} + 320q^{67} - 448q^{68} + 96q^{69} - 384q^{70} + 512q^{71} + 60q^{72} + 348q^{74} + 192q^{75} + 72q^{76} + 224q^{77} + 396q^{78} + 552q^{80} - 144q^{81} - 40q^{82} - 160q^{83} + 72q^{84} + 160q^{85} + 528q^{86} + 480q^{88} - 24q^{90} - 480q^{91} + 496q^{92} + 312q^{94} - 480q^{96} - 440q^{98} + 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.78012 0.911682i −0.890061 0.455841i
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 2.33767 + 3.24581i 0.584418 + 0.811453i
\(5\) 1.00772 + 1.00772i 0.201544 + 0.201544i 0.800661 0.599117i \(-0.204482\pi\)
−0.599117 + 0.800661i \(0.704482\pi\)
\(6\) −1.06362 3.29677i −0.177270 0.549462i
\(7\) 10.0236 1.43194 0.715969 0.698133i \(-0.245985\pi\)
0.715969 + 0.698133i \(0.245985\pi\)
\(8\) −1.20220 7.90915i −0.150274 0.988644i
\(9\) 3.00000i 0.333333i
\(10\) −0.875146 2.71259i −0.0875146 0.271259i
\(11\) 2.26517 2.26517i 0.205925 0.205925i −0.596608 0.802533i \(-0.703485\pi\)
0.802533 + 0.596608i \(0.203485\pi\)
\(12\) −1.11224 + 6.83834i −0.0926865 + 0.569862i
\(13\) −6.88229 + 6.88229i −0.529407 + 0.529407i −0.920395 0.390989i \(-0.872133\pi\)
0.390989 + 0.920395i \(0.372133\pi\)
\(14\) −17.8432 9.13830i −1.27451 0.652736i
\(15\) 2.46840i 0.164560i
\(16\) −5.07058 + 15.1753i −0.316911 + 0.948455i
\(17\) −22.3801 −1.31648 −0.658240 0.752809i \(-0.728699\pi\)
−0.658240 + 0.752809i \(0.728699\pi\)
\(18\) 2.73505 5.34037i 0.151947 0.296687i
\(19\) −16.8918 16.8918i −0.889041 0.889041i 0.105390 0.994431i \(-0.466391\pi\)
−0.994431 + 0.105390i \(0.966391\pi\)
\(20\) −0.915151 + 5.62660i −0.0457575 + 0.281330i
\(21\) 12.2763 + 12.2763i 0.584586 + 0.584586i
\(22\) −6.09740 + 1.96717i −0.277155 + 0.0894167i
\(23\) 33.2007 1.44351 0.721755 0.692149i \(-0.243336\pi\)
0.721755 + 0.692149i \(0.243336\pi\)
\(24\) 8.21431 11.1591i 0.342263 0.464962i
\(25\) 22.9690i 0.918760i
\(26\) 18.5258 5.97686i 0.712530 0.229879i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 23.4318 + 32.5346i 0.836850 + 1.16195i
\(29\) −24.6412 + 24.6412i −0.849696 + 0.849696i −0.990095 0.140399i \(-0.955161\pi\)
0.140399 + 0.990095i \(0.455161\pi\)
\(30\) 2.25040 4.39406i 0.0750133 0.146469i
\(31\) 41.3761i 1.33471i −0.744738 0.667357i \(-0.767426\pi\)
0.744738 0.667357i \(-0.232574\pi\)
\(32\) 22.8613 22.3911i 0.714415 0.699722i
\(33\) 5.54852 0.168137
\(34\) 39.8394 + 20.4036i 1.17175 + 0.600105i
\(35\) 10.1010 + 10.1010i 0.288599 + 0.288599i
\(36\) −9.73743 + 7.01302i −0.270484 + 0.194806i
\(37\) −6.60031 6.60031i −0.178387 0.178387i 0.612266 0.790652i \(-0.290258\pi\)
−0.790652 + 0.612266i \(0.790258\pi\)
\(38\) 14.6695 + 45.4693i 0.386039 + 1.19656i
\(39\) −16.8581 −0.432259
\(40\) 6.75875 9.18170i 0.168969 0.229543i
\(41\) 47.1477i 1.14994i −0.818173 0.574972i \(-0.805013\pi\)
0.818173 0.574972i \(-0.194987\pi\)
\(42\) −10.6612 33.0454i −0.253839 0.786795i
\(43\) −48.8218 + 48.8218i −1.13539 + 1.13539i −0.146124 + 0.989266i \(0.546680\pi\)
−0.989266 + 0.146124i \(0.953320\pi\)
\(44\) 12.6475 + 2.05709i 0.287444 + 0.0467521i
\(45\) −3.02316 + 3.02316i −0.0671814 + 0.0671814i
\(46\) −59.1013 30.2685i −1.28481 0.658011i
\(47\) 45.6048i 0.970315i 0.874427 + 0.485157i \(0.161238\pi\)
−0.874427 + 0.485157i \(0.838762\pi\)
\(48\) −24.7960 + 12.3757i −0.516584 + 0.257827i
\(49\) 51.4717 1.05044
\(50\) −20.9404 + 40.8876i −0.418808 + 0.817752i
\(51\) −27.4100 27.4100i −0.537450 0.537450i
\(52\) −38.4271 6.25007i −0.738983 0.120194i
\(53\) 25.1401 + 25.1401i 0.474341 + 0.474341i 0.903316 0.428975i \(-0.141125\pi\)
−0.428975 + 0.903316i \(0.641125\pi\)
\(54\) 9.89032 3.19085i 0.183154 0.0590899i
\(55\) 4.56532 0.0830059
\(56\) −12.0503 79.2779i −0.215184 1.41568i
\(57\) 41.3762i 0.725899i
\(58\) 66.3292 21.3994i 1.14361 0.368955i
\(59\) 6.23974 6.23974i 0.105758 0.105758i −0.652248 0.758006i \(-0.726174\pi\)
0.758006 + 0.652248i \(0.226174\pi\)
\(60\) −8.01197 + 5.77032i −0.133533 + 0.0961720i
\(61\) 35.9513 35.9513i 0.589366 0.589366i −0.348093 0.937460i \(-0.613171\pi\)
0.937460 + 0.348093i \(0.113171\pi\)
\(62\) −37.7219 + 73.6546i −0.608417 + 1.18798i
\(63\) 30.0707i 0.477312i
\(64\) −61.1095 + 19.0167i −0.954835 + 0.297136i
\(65\) −13.8709 −0.213398
\(66\) −9.87704 5.05848i −0.149652 0.0766437i
\(67\) 10.2045 + 10.2045i 0.152307 + 0.152307i 0.779147 0.626841i \(-0.215652\pi\)
−0.626841 + 0.779147i \(0.715652\pi\)
\(68\) −52.3174 72.6417i −0.769374 1.06826i
\(69\) 40.6624 + 40.6624i 0.589310 + 0.589310i
\(70\) −8.77208 27.1898i −0.125315 0.388426i
\(71\) 11.9529 0.168350 0.0841752 0.996451i \(-0.473174\pi\)
0.0841752 + 0.996451i \(0.473174\pi\)
\(72\) 23.7275 3.60659i 0.329548 0.0500915i
\(73\) 111.332i 1.52510i 0.646929 + 0.762550i \(0.276053\pi\)
−0.646929 + 0.762550i \(0.723947\pi\)
\(74\) 5.73197 + 17.7667i 0.0774591 + 0.240091i
\(75\) 28.1312 28.1312i 0.375082 0.375082i
\(76\) 15.3401 94.3149i 0.201843 1.24099i
\(77\) 22.7051 22.7051i 0.294871 0.294871i
\(78\) 30.0095 + 15.3692i 0.384737 + 0.197041i
\(79\) 4.46031i 0.0564596i 0.999601 + 0.0282298i \(0.00898702\pi\)
−0.999601 + 0.0282298i \(0.991013\pi\)
\(80\) −20.4022 + 10.1827i −0.255027 + 0.127284i
\(81\) −9.00000 −0.111111
\(82\) −42.9837 + 83.9287i −0.524192 + 1.02352i
\(83\) 10.1751 + 10.1751i 0.122592 + 0.122592i 0.765741 0.643149i \(-0.222373\pi\)
−0.643149 + 0.765741i \(0.722373\pi\)
\(84\) −11.1486 + 68.5445i −0.132721 + 0.816006i
\(85\) −22.5530 22.5530i −0.265329 0.265329i
\(86\) 131.419 42.3988i 1.52812 0.493010i
\(87\) −60.3583 −0.693774
\(88\) −20.6388 15.1924i −0.234532 0.172641i
\(89\) 21.9364i 0.246476i −0.992377 0.123238i \(-0.960672\pi\)
0.992377 0.123238i \(-0.0393279\pi\)
\(90\) 8.13777 2.62544i 0.0904196 0.0291715i
\(91\) −68.9850 + 68.9850i −0.758077 + 0.758077i
\(92\) 77.6124 + 107.763i 0.843613 + 1.17134i
\(93\) 50.6752 50.6752i 0.544895 0.544895i
\(94\) 41.5771 81.1821i 0.442309 0.863640i
\(95\) 34.0444i 0.358362i
\(96\) 55.4226 + 0.575837i 0.577319 + 0.00599830i
\(97\) 107.309 1.10628 0.553140 0.833088i \(-0.313429\pi\)
0.553140 + 0.833088i \(0.313429\pi\)
\(98\) −91.6260 46.9259i −0.934959 0.478835i
\(99\) 6.79552 + 6.79552i 0.0686416 + 0.0686416i
\(100\) 74.5530 53.6940i 0.745530 0.536940i
\(101\) −100.780 100.780i −0.997824 0.997824i 0.00217389 0.999998i \(-0.499308\pi\)
−0.999998 + 0.00217389i \(0.999308\pi\)
\(102\) 23.8039 + 73.7823i 0.233372 + 0.723356i
\(103\) 58.0562 0.563653 0.281826 0.959465i \(-0.409060\pi\)
0.281826 + 0.959465i \(0.409060\pi\)
\(104\) 62.7069 + 46.1592i 0.602951 + 0.443839i
\(105\) 24.7422i 0.235640i
\(106\) −21.8327 67.6722i −0.205968 0.638417i
\(107\) 112.747 112.747i 1.05371 1.05371i 0.0552381 0.998473i \(-0.482408\pi\)
0.998473 0.0552381i \(-0.0175918\pi\)
\(108\) −20.5150 3.33671i −0.189954 0.0308955i
\(109\) −81.1384 + 81.1384i −0.744389 + 0.744389i −0.973419 0.229030i \(-0.926445\pi\)
0.229030 + 0.973419i \(0.426445\pi\)
\(110\) −8.12684 4.16212i −0.0738803 0.0378375i
\(111\) 16.1674i 0.145652i
\(112\) −50.8252 + 152.110i −0.453797 + 1.35813i
\(113\) −171.844 −1.52074 −0.760371 0.649489i \(-0.774983\pi\)
−0.760371 + 0.649489i \(0.774983\pi\)
\(114\) −37.7219 + 73.6547i −0.330894 + 0.646094i
\(115\) 33.4571 + 33.4571i 0.290931 + 0.290931i
\(116\) −137.584 22.3776i −1.18607 0.192910i
\(117\) −20.6469 20.6469i −0.176469 0.176469i
\(118\) −16.7962 + 5.41884i −0.142340 + 0.0459224i
\(119\) −224.329 −1.88512
\(120\) 19.5230 2.96750i 0.162692 0.0247292i
\(121\) 110.738i 0.915190i
\(122\) −96.7740 + 31.2216i −0.793230 + 0.255915i
\(123\) 57.7439 57.7439i 0.469463 0.469463i
\(124\) 134.299 96.7238i 1.08306 0.780031i
\(125\) 48.3394 48.3394i 0.386715 0.386715i
\(126\) 27.4149 53.5295i 0.217579 0.424837i
\(127\) 36.8333i 0.290026i −0.989430 0.145013i \(-0.953678\pi\)
0.989430 0.145013i \(-0.0463224\pi\)
\(128\) 126.119 + 21.8603i 0.985309 + 0.170784i
\(129\) −119.588 −0.927042
\(130\) 24.6918 + 12.6458i 0.189937 + 0.0972754i
\(131\) −12.3686 12.3686i −0.0944170 0.0944170i 0.658321 0.752738i \(-0.271267\pi\)
−0.752738 + 0.658321i \(0.771267\pi\)
\(132\) 12.9706 + 18.0094i 0.0982622 + 0.136435i
\(133\) −169.316 169.316i −1.27305 1.27305i
\(134\) −8.86204 27.4686i −0.0661347 0.204990i
\(135\) −7.40521 −0.0548534
\(136\) 26.9053 + 177.008i 0.197833 + 1.30153i
\(137\) 145.679i 1.06335i 0.846949 + 0.531674i \(0.178437\pi\)
−0.846949 + 0.531674i \(0.821563\pi\)
\(138\) −35.3129 109.455i −0.255890 0.793154i
\(139\) 82.5709 82.5709i 0.594035 0.594035i −0.344684 0.938719i \(-0.612014\pi\)
0.938719 + 0.344684i \(0.112014\pi\)
\(140\) −9.17307 + 56.3985i −0.0655219 + 0.402847i
\(141\) −55.8542 + 55.8542i −0.396129 + 0.396129i
\(142\) −21.2776 10.8972i −0.149842 0.0767410i
\(143\) 31.1791i 0.218036i
\(144\) −45.5259 15.2117i −0.316152 0.105637i
\(145\) −49.6629 −0.342503
\(146\) 101.500 198.185i 0.695203 1.35743i
\(147\) 63.0398 + 63.0398i 0.428842 + 0.428842i
\(148\) 5.99399 36.8527i 0.0405000 0.249005i
\(149\) 196.248 + 196.248i 1.31710 + 1.31710i 0.916059 + 0.401043i \(0.131352\pi\)
0.401043 + 0.916059i \(0.368648\pi\)
\(150\) −75.7236 + 24.4302i −0.504824 + 0.162868i
\(151\) 64.5007 0.427157 0.213578 0.976926i \(-0.431488\pi\)
0.213578 + 0.976926i \(0.431488\pi\)
\(152\) −113.292 + 153.907i −0.745345 + 1.01254i
\(153\) 67.1404i 0.438826i
\(154\) −61.1177 + 19.7180i −0.396868 + 0.128039i
\(155\) 41.6956 41.6956i 0.269004 0.269004i
\(156\) −39.4087 54.7182i −0.252620 0.350758i
\(157\) 54.4202 54.4202i 0.346625 0.346625i −0.512226 0.858851i \(-0.671179\pi\)
0.858851 + 0.512226i \(0.171179\pi\)
\(158\) 4.06638 7.93990i 0.0257366 0.0502525i
\(159\) 61.5803i 0.387298i
\(160\) 45.6018 + 0.473799i 0.285011 + 0.00296124i
\(161\) 332.789 2.06701
\(162\) 16.0211 + 8.20514i 0.0988957 + 0.0506490i
\(163\) 104.803 + 104.803i 0.642961 + 0.642961i 0.951282 0.308321i \(-0.0997671\pi\)
−0.308321 + 0.951282i \(0.599767\pi\)
\(164\) 153.033 110.216i 0.933126 0.672048i
\(165\) 5.59136 + 5.59136i 0.0338870 + 0.0338870i
\(166\) −8.83647 27.3894i −0.0532317 0.164996i
\(167\) 53.3110 0.319228 0.159614 0.987180i \(-0.448975\pi\)
0.159614 + 0.987180i \(0.448975\pi\)
\(168\) 82.3367 111.854i 0.490099 0.665796i
\(169\) 74.2683i 0.439457i
\(170\) 19.5859 + 60.7081i 0.115211 + 0.357107i
\(171\) 50.6753 50.6753i 0.296347 0.296347i
\(172\) −272.596 44.3370i −1.58486 0.257773i
\(173\) −41.5780 + 41.5780i −0.240335 + 0.240335i −0.816989 0.576654i \(-0.804358\pi\)
0.576654 + 0.816989i \(0.304358\pi\)
\(174\) 107.445 + 55.0276i 0.617501 + 0.316251i
\(175\) 230.231i 1.31561i
\(176\) 22.8889 + 45.8604i 0.130051 + 0.260570i
\(177\) 15.2842 0.0863513
\(178\) −19.9990 + 39.0495i −0.112354 + 0.219379i
\(179\) 53.0709 + 53.0709i 0.296486 + 0.296486i 0.839636 0.543150i \(-0.182769\pi\)
−0.543150 + 0.839636i \(0.682769\pi\)
\(180\) −16.8798 2.74545i −0.0937766 0.0152525i
\(181\) −66.6042 66.6042i −0.367979 0.367979i 0.498761 0.866740i \(-0.333789\pi\)
−0.866740 + 0.498761i \(0.833789\pi\)
\(182\) 185.694 59.9094i 1.02030 0.329172i
\(183\) 88.0625 0.481216
\(184\) −39.9138 262.590i −0.216923 1.42712i
\(185\) 13.3025i 0.0719056i
\(186\) −136.408 + 44.0084i −0.733375 + 0.236604i
\(187\) −50.6949 + 50.6949i −0.271096 + 0.271096i
\(188\) −148.025 + 106.609i −0.787365 + 0.567070i
\(189\) −36.8289 + 36.8289i −0.194862 + 0.194862i
\(190\) −31.0377 + 60.6032i −0.163356 + 0.318964i
\(191\) 113.753i 0.595567i 0.954633 + 0.297784i \(0.0962474\pi\)
−0.954633 + 0.297784i \(0.903753\pi\)
\(192\) −98.1341 51.5529i −0.511115 0.268505i
\(193\) −26.5596 −0.137615 −0.0688073 0.997630i \(-0.521919\pi\)
−0.0688073 + 0.997630i \(0.521919\pi\)
\(194\) −191.023 97.8318i −0.984657 0.504288i
\(195\) −16.9883 16.9883i −0.0871193 0.0871193i
\(196\) 120.324 + 167.068i 0.613898 + 0.852386i
\(197\) 51.8935 + 51.8935i 0.263419 + 0.263419i 0.826442 0.563023i \(-0.190362\pi\)
−0.563023 + 0.826442i \(0.690362\pi\)
\(198\) −5.90150 18.2922i −0.0298056 0.0923848i
\(199\) −136.741 −0.687140 −0.343570 0.939127i \(-0.611636\pi\)
−0.343570 + 0.939127i \(0.611636\pi\)
\(200\) −181.665 + 27.6132i −0.908327 + 0.138066i
\(201\) 24.9959i 0.124358i
\(202\) 87.5216 + 271.281i 0.433275 + 1.34297i
\(203\) −246.992 + 246.992i −1.21671 + 1.21671i
\(204\) 24.8921 153.043i 0.122020 0.750211i
\(205\) 47.5118 47.5118i 0.231765 0.231765i
\(206\) −103.347 52.9288i −0.501686 0.256936i
\(207\) 99.6022i 0.481170i
\(208\) −69.5435 139.338i −0.334344 0.669893i
\(209\) −76.5255 −0.366151
\(210\) 22.5570 44.0441i 0.107414 0.209734i
\(211\) −141.171 141.171i −0.669057 0.669057i 0.288441 0.957498i \(-0.406863\pi\)
−0.957498 + 0.288441i \(0.906863\pi\)
\(212\) −22.8307 + 140.369i −0.107692 + 0.662119i
\(213\) 14.6392 + 14.6392i 0.0687288 + 0.0687288i
\(214\) −303.493 + 97.9142i −1.41819 + 0.457543i
\(215\) −98.3975 −0.457663
\(216\) 33.4772 + 24.6429i 0.154987 + 0.114088i
\(217\) 414.736i 1.91123i
\(218\) 218.409 70.4639i 1.00188 0.323229i
\(219\) −136.354 + 136.354i −0.622620 + 0.622620i
\(220\) 10.6722 + 14.8182i 0.0485101 + 0.0673554i
\(221\) 154.027 154.027i 0.696953 0.696953i
\(222\) −14.7395 + 28.7799i −0.0663942 + 0.129639i
\(223\) 122.607i 0.549806i 0.961472 + 0.274903i \(0.0886457\pi\)
−0.961472 + 0.274903i \(0.911354\pi\)
\(224\) 229.151 224.439i 1.02300 1.00196i
\(225\) 68.9070 0.306253
\(226\) 305.903 + 156.667i 1.35355 + 0.693216i
\(227\) −295.844 295.844i −1.30328 1.30328i −0.926168 0.377112i \(-0.876917\pi\)
−0.377112 0.926168i \(-0.623083\pi\)
\(228\) 134.299 96.7240i 0.589032 0.424228i
\(229\) 73.3817 + 73.3817i 0.320444 + 0.320444i 0.848937 0.528493i \(-0.177243\pi\)
−0.528493 + 0.848937i \(0.677243\pi\)
\(230\) −29.0555 90.0599i −0.126328 0.391565i
\(231\) 55.6159 0.240761
\(232\) 224.514 + 165.267i 0.967735 + 0.712359i
\(233\) 156.229i 0.670509i −0.942128 0.335255i \(-0.891178\pi\)
0.942128 0.335255i \(-0.108822\pi\)
\(234\) 17.9306 + 55.5773i 0.0766264 + 0.237510i
\(235\) −45.9569 + 45.9569i −0.195561 + 0.195561i
\(236\) 34.8395 + 5.66655i 0.147625 + 0.0240108i
\(237\) −5.46274 + 5.46274i −0.0230495 + 0.0230495i
\(238\) 399.333 + 204.516i 1.67787 + 0.859313i
\(239\) 13.1716i 0.0551113i 0.999620 + 0.0275557i \(0.00877235\pi\)
−0.999620 + 0.0275557i \(0.991228\pi\)
\(240\) −37.4587 12.5162i −0.156078 0.0521510i
\(241\) −189.519 −0.786386 −0.393193 0.919456i \(-0.628630\pi\)
−0.393193 + 0.919456i \(0.628630\pi\)
\(242\) 100.958 197.127i 0.417181 0.814575i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 200.734 + 32.6488i 0.822679 + 0.133807i
\(245\) 51.8692 + 51.8692i 0.211711 + 0.211711i
\(246\) −155.435 + 50.1472i −0.631851 + 0.203850i
\(247\) 232.508 0.941328
\(248\) −327.250 + 49.7422i −1.31956 + 0.200573i
\(249\) 24.9238i 0.100096i
\(250\) −130.120 + 41.9799i −0.520481 + 0.167920i
\(251\) −27.4434 + 27.4434i −0.109336 + 0.109336i −0.759658 0.650322i \(-0.774634\pi\)
0.650322 + 0.759658i \(0.274634\pi\)
\(252\) −97.6037 + 70.2954i −0.387316 + 0.278950i
\(253\) 75.2053 75.2053i 0.297254 0.297254i
\(254\) −33.5802 + 65.5678i −0.132206 + 0.258141i
\(255\) 55.2432i 0.216640i
\(256\) −204.578 153.895i −0.799135 0.601152i
\(257\) 135.375 0.526752 0.263376 0.964693i \(-0.415164\pi\)
0.263376 + 0.964693i \(0.415164\pi\)
\(258\) 212.882 + 109.027i 0.825125 + 0.422584i
\(259\) −66.1586 66.1586i −0.255438 0.255438i
\(260\) −32.4255 45.0222i −0.124714 0.173162i
\(261\) −73.9236 73.9236i −0.283232 0.283232i
\(262\) 10.7414 + 33.2939i 0.0409978 + 0.127076i
\(263\) 31.6123 0.120199 0.0600994 0.998192i \(-0.480858\pi\)
0.0600994 + 0.998192i \(0.480858\pi\)
\(264\) −6.67040 43.8841i −0.0252667 0.166228i
\(265\) 50.6684i 0.191201i
\(266\) 147.041 + 455.765i 0.552784 + 1.71340i
\(267\) 26.8665 26.8665i 0.100624 0.100624i
\(268\) −9.26715 + 56.9769i −0.0345789 + 0.212600i
\(269\) −194.213 + 194.213i −0.721981 + 0.721981i −0.969008 0.247028i \(-0.920546\pi\)
0.247028 + 0.969008i \(0.420546\pi\)
\(270\) 13.1822 + 6.75120i 0.0488229 + 0.0250044i
\(271\) 291.647i 1.07619i 0.842884 + 0.538095i \(0.180856\pi\)
−0.842884 + 0.538095i \(0.819144\pi\)
\(272\) 113.480 339.625i 0.417207 1.24862i
\(273\) −168.978 −0.618967
\(274\) 132.813 259.326i 0.484717 0.946444i
\(275\) −52.0287 52.0287i −0.189195 0.189195i
\(276\) −36.9271 + 227.038i −0.133794 + 0.822601i
\(277\) 305.166 + 305.166i 1.10168 + 1.10168i 0.994208 + 0.107475i \(0.0342765\pi\)
0.107475 + 0.994208i \(0.465723\pi\)
\(278\) −222.265 + 71.7079i −0.799513 + 0.257942i
\(279\) 124.128 0.444905
\(280\) 67.7467 92.0333i 0.241952 0.328691i
\(281\) 211.861i 0.753955i −0.926222 0.376978i \(-0.876963\pi\)
0.926222 0.376978i \(-0.123037\pi\)
\(282\) 150.349 48.5061i 0.533151 0.172007i
\(283\) 105.325 105.325i 0.372175 0.372175i −0.496094 0.868269i \(-0.665233\pi\)
0.868269 + 0.496094i \(0.165233\pi\)
\(284\) 27.9419 + 38.7968i 0.0983870 + 0.136608i
\(285\) 41.6957 41.6957i 0.146301 0.146301i
\(286\) 28.4254 55.5027i 0.0993897 0.194065i
\(287\) 472.588i 1.64665i
\(288\) 67.1733 + 68.5838i 0.233241 + 0.238138i
\(289\) 211.871 0.733117
\(290\) 88.4060 + 45.2768i 0.304848 + 0.156127i
\(291\) 131.426 + 131.426i 0.451637 + 0.451637i
\(292\) −361.364 + 260.258i −1.23755 + 0.891296i
\(293\) −171.289 171.289i −0.584603 0.584603i 0.351562 0.936165i \(-0.385651\pi\)
−0.936165 + 0.351562i \(0.885651\pi\)
\(294\) −54.7463 169.691i −0.186212 0.577179i
\(295\) 12.5758 0.0426300
\(296\) −44.2680 + 60.1377i −0.149554 + 0.203168i
\(297\) 16.6455i 0.0560456i
\(298\) −170.430 528.262i −0.571912 1.77269i
\(299\) −228.497 + 228.497i −0.764204 + 0.764204i
\(300\) 157.070 + 25.5470i 0.523566 + 0.0851566i
\(301\) −489.368 + 489.368i −1.62581 + 1.62581i
\(302\) −114.819 58.8041i −0.380196 0.194716i
\(303\) 246.860i 0.814720i
\(304\) 341.988 170.686i 1.12496 0.561468i
\(305\) 72.4579 0.237567
\(306\) −61.2107 + 119.518i −0.200035 + 0.390582i
\(307\) −27.1124 27.1124i −0.0883140 0.0883140i 0.661570 0.749884i \(-0.269891\pi\)
−0.749884 + 0.661570i \(0.769891\pi\)
\(308\) 126.773 + 20.6194i 0.411602 + 0.0669460i
\(309\) 71.1041 + 71.1041i 0.230110 + 0.230110i
\(310\) −112.236 + 36.2102i −0.362053 + 0.116807i
\(311\) 371.124 1.19333 0.596663 0.802492i \(-0.296493\pi\)
0.596663 + 0.802492i \(0.296493\pi\)
\(312\) 20.2667 + 133.333i 0.0649575 + 0.427350i
\(313\) 374.501i 1.19649i −0.801313 0.598245i \(-0.795865\pi\)
0.801313 0.598245i \(-0.204135\pi\)
\(314\) −146.488 + 47.2607i −0.466524 + 0.150512i
\(315\) −30.3029 + 30.3029i −0.0961996 + 0.0961996i
\(316\) −14.4773 + 10.4267i −0.0458143 + 0.0329960i
\(317\) −48.5840 + 48.5840i −0.153262 + 0.153262i −0.779573 0.626311i \(-0.784564\pi\)
0.626311 + 0.779573i \(0.284564\pi\)
\(318\) 56.1417 109.621i 0.176546 0.344719i
\(319\) 111.633i 0.349947i
\(320\) −80.7448 42.4178i −0.252328 0.132555i
\(321\) 276.173 0.860352
\(322\) −592.406 303.398i −1.83977 0.942230i
\(323\) 378.040 + 378.040i 1.17040 + 1.17040i
\(324\) −21.0391 29.2123i −0.0649353 0.0901614i
\(325\) 158.079 + 158.079i 0.486398 + 0.486398i
\(326\) −91.0149 282.108i −0.279187 0.865363i
\(327\) −198.748 −0.607791
\(328\) −372.899 + 56.6808i −1.13689 + 0.172807i
\(329\) 457.122i 1.38943i
\(330\) −4.85576 15.0508i −0.0147144 0.0456086i
\(331\) −1.88883 + 1.88883i −0.00570644 + 0.00570644i −0.709954 0.704248i \(-0.751284\pi\)
0.704248 + 0.709954i \(0.251284\pi\)
\(332\) −9.24040 + 56.8125i −0.0278325 + 0.171122i
\(333\) 19.8009 19.8009i 0.0594622 0.0594622i
\(334\) −94.9001 48.6027i −0.284132 0.145517i
\(335\) 20.5667i 0.0613931i
\(336\) −248.544 + 124.048i −0.739715 + 0.369192i
\(337\) −386.980 −1.14831 −0.574154 0.818747i \(-0.694669\pi\)
−0.574154 + 0.818747i \(0.694669\pi\)
\(338\) 67.7090 132.207i 0.200323 0.391144i
\(339\) −210.465 210.465i −0.620840 0.620840i
\(340\) 20.4812 125.924i 0.0602388 0.370365i
\(341\) −93.7240 93.7240i −0.274851 0.274851i
\(342\) −136.408 + 44.0085i −0.398854 + 0.128680i
\(343\) 24.7757 0.0722325
\(344\) 444.832 + 327.446i 1.29312 + 0.951877i
\(345\) 81.9528i 0.237544i
\(346\) 111.920 36.1080i 0.323468 0.104358i
\(347\) 441.887 441.887i 1.27345 1.27345i 0.329183 0.944266i \(-0.393227\pi\)
0.944266 0.329183i \(-0.106773\pi\)
\(348\) −141.098 195.912i −0.405454 0.562965i
\(349\) 119.382 119.382i 0.342068 0.342068i −0.515076 0.857144i \(-0.672236\pi\)
0.857144 + 0.515076i \(0.172236\pi\)
\(350\) −209.898 + 409.840i −0.599707 + 1.17097i
\(351\) 50.5743i 0.144086i
\(352\) 1.06501 102.504i 0.00302560 0.291206i
\(353\) −515.642 −1.46074 −0.730371 0.683050i \(-0.760653\pi\)
−0.730371 + 0.683050i \(0.760653\pi\)
\(354\) −27.2077 13.9343i −0.0768580 0.0393625i
\(355\) 12.0452 + 12.0452i 0.0339301 + 0.0339301i
\(356\) 71.2014 51.2801i 0.200004 0.144045i
\(357\) −274.745 274.745i −0.769595 0.769595i
\(358\) −46.0890 142.857i −0.128740 0.399041i
\(359\) 428.264 1.19294 0.596468 0.802637i \(-0.296570\pi\)
0.596468 + 0.802637i \(0.296570\pi\)
\(360\) 27.5451 + 20.2762i 0.0765142 + 0.0563229i
\(361\) 209.664i 0.580786i
\(362\) 57.8418 + 179.286i 0.159784 + 0.495264i
\(363\) −135.626 + 135.626i −0.373625 + 0.373625i
\(364\) −385.177 62.6480i −1.05818 0.172110i
\(365\) −112.192 + 112.192i −0.307375 + 0.307375i
\(366\) −156.762 80.2850i −0.428311 0.219358i
\(367\) 219.482i 0.598043i 0.954246 + 0.299021i \(0.0966602\pi\)
−0.954246 + 0.299021i \(0.903340\pi\)
\(368\) −168.347 + 503.830i −0.457464 + 1.36910i
\(369\) 141.443 0.383315
\(370\) −12.1277 + 23.6802i −0.0327775 + 0.0640004i
\(371\) 251.993 + 251.993i 0.679226 + 0.679226i
\(372\) 282.944 + 46.0201i 0.760602 + 0.123710i
\(373\) 425.005 + 425.005i 1.13942 + 1.13942i 0.988554 + 0.150870i \(0.0482075\pi\)
0.150870 + 0.988554i \(0.451793\pi\)
\(374\) 136.461 44.0255i 0.364868 0.117715i
\(375\) 118.407 0.315752
\(376\) 360.695 54.8259i 0.959296 0.145814i
\(377\) 339.175i 0.899669i
\(378\) 99.1362 31.9837i 0.262265 0.0846130i
\(379\) 365.916 365.916i 0.965476 0.965476i −0.0339473 0.999424i \(-0.510808\pi\)
0.999424 + 0.0339473i \(0.0108078\pi\)
\(380\) 110.502 79.5846i 0.290794 0.209433i
\(381\) 45.1114 45.1114i 0.118403 0.118403i
\(382\) 103.707 202.495i 0.271484 0.530091i
\(383\) 213.276i 0.556857i 0.960457 + 0.278428i \(0.0898135\pi\)
−0.960457 + 0.278428i \(0.910187\pi\)
\(384\) 127.691 + 181.238i 0.332528 + 0.471973i
\(385\) 45.7608 0.118859
\(386\) 47.2793 + 24.2139i 0.122485 + 0.0627303i
\(387\) −146.465 146.465i −0.378464 0.378464i
\(388\) 250.854 + 348.305i 0.646530 + 0.897694i
\(389\) −210.798 210.798i −0.541898 0.541898i 0.382187 0.924085i \(-0.375171\pi\)
−0.924085 + 0.382187i \(0.875171\pi\)
\(390\) 14.7533 + 45.7291i 0.0378290 + 0.117254i
\(391\) −743.037 −1.90035
\(392\) −61.8791 407.098i −0.157855 1.03852i
\(393\) 30.2968i 0.0770912i
\(394\) −45.0665 139.687i −0.114382 0.354536i
\(395\) −4.49475 + 4.49475i −0.0113791 + 0.0113791i
\(396\) −6.17127 + 37.9426i −0.0155840 + 0.0958148i
\(397\) 392.907 392.907i 0.989690 0.989690i −0.0102579 0.999947i \(-0.503265\pi\)
0.999947 + 0.0102579i \(0.00326524\pi\)
\(398\) 243.415 + 124.664i 0.611597 + 0.313226i
\(399\) 414.737i 1.03944i
\(400\) 348.561 + 116.466i 0.871403 + 0.291165i
\(401\) 29.3290 0.0731396 0.0365698 0.999331i \(-0.488357\pi\)
0.0365698 + 0.999331i \(0.488357\pi\)
\(402\) 22.7883 44.4958i 0.0566874 0.110686i
\(403\) 284.762 + 284.762i 0.706606 + 0.706606i
\(404\) 91.5224 562.705i 0.226541 1.39283i
\(405\) −9.06949 9.06949i −0.0223938 0.0223938i
\(406\) 664.855 214.498i 1.63757 0.528321i
\(407\) −29.9017 −0.0734684
\(408\) −183.838 + 249.742i −0.450582 + 0.612112i
\(409\) 601.115i 1.46972i 0.678219 + 0.734860i \(0.262752\pi\)
−0.678219 + 0.734860i \(0.737248\pi\)
\(410\) −127.892 + 41.2612i −0.311933 + 0.100637i
\(411\) −178.419 + 178.419i −0.434110 + 0.434110i
\(412\) 135.716 + 188.440i 0.329409 + 0.457378i
\(413\) 62.5444 62.5444i 0.151439 0.151439i
\(414\) 90.8055 177.304i 0.219337 0.428271i
\(415\) 20.5073i 0.0494153i
\(416\) −3.23584 + 311.440i −0.00777845 + 0.748654i
\(417\) 202.257 0.485028
\(418\) 136.225 + 69.7669i 0.325897 + 0.166907i
\(419\) −518.885 518.885i −1.23839 1.23839i −0.960659 0.277729i \(-0.910418\pi\)
−0.277729 0.960659i \(-0.589582\pi\)
\(420\) −80.3085 + 57.8391i −0.191211 + 0.137712i
\(421\) −411.213 411.213i −0.976754 0.976754i 0.0229817 0.999736i \(-0.492684\pi\)
−0.999736 + 0.0229817i \(0.992684\pi\)
\(422\) 122.599 + 380.005i 0.290518 + 0.900485i
\(423\) −136.814 −0.323438
\(424\) 168.613 229.060i 0.397673 0.540236i
\(425\) 514.049i 1.20953i
\(426\) −12.7133 39.4059i −0.0298434 0.0925022i
\(427\) 360.360 360.360i 0.843936 0.843936i
\(428\) 629.522 + 102.390i 1.47084 + 0.239229i
\(429\) −38.1865 + 38.1865i −0.0890128 + 0.0890128i
\(430\) 175.160 + 89.7072i 0.407348 + 0.208622i
\(431\) 41.1083i 0.0953789i 0.998862 + 0.0476895i \(0.0151858\pi\)
−0.998862 + 0.0476895i \(0.984814\pi\)
\(432\) −37.1271 74.3880i −0.0859423 0.172195i
\(433\) −351.682 −0.812199 −0.406100 0.913829i \(-0.633111\pi\)
−0.406100 + 0.913829i \(0.633111\pi\)
\(434\) −378.107 + 738.281i −0.871215 + 1.70111i
\(435\) −60.8244 60.8244i −0.139826 0.139826i
\(436\) −453.035 73.6850i −1.03907 0.169002i
\(437\) −560.819 560.819i −1.28334 1.28334i
\(438\) 367.037 118.415i 0.837985 0.270354i
\(439\) −775.613 −1.76677 −0.883386 0.468646i \(-0.844742\pi\)
−0.883386 + 0.468646i \(0.844742\pi\)
\(440\) −5.48841 36.1079i −0.0124737 0.0820633i
\(441\) 154.415i 0.350148i
\(442\) −414.609 + 133.763i −0.938030 + 0.302631i
\(443\) −241.372 + 241.372i −0.544858 + 0.544858i −0.924949 0.380091i \(-0.875893\pi\)
0.380091 + 0.924949i \(0.375893\pi\)
\(444\) 52.4763 37.7940i 0.118190 0.0851217i
\(445\) 22.1058 22.1058i 0.0496759 0.0496759i
\(446\) 111.778 218.255i 0.250624 0.489361i
\(447\) 480.708i 1.07541i
\(448\) −612.534 + 190.615i −1.36726 + 0.425480i
\(449\) 266.360 0.593228 0.296614 0.954997i \(-0.404142\pi\)
0.296614 + 0.954997i \(0.404142\pi\)
\(450\) −122.663 62.8213i −0.272584 0.139603i
\(451\) −106.798 106.798i −0.236802 0.236802i
\(452\) −401.714 557.772i −0.888749 1.23401i
\(453\) 78.9969 + 78.9969i 0.174386 + 0.174386i
\(454\) 256.923 + 796.355i 0.565910 + 1.75409i
\(455\) −139.035 −0.305572
\(456\) −327.251 + 49.7423i −0.717655 + 0.109084i
\(457\) 515.244i 1.12745i −0.825963 0.563725i \(-0.809368\pi\)
0.825963 0.563725i \(-0.190632\pi\)
\(458\) −63.7277 197.529i −0.139143 0.431287i
\(459\) 82.2299 82.2299i 0.179150 0.179150i
\(460\) −30.3837 + 186.807i −0.0660514 + 0.406102i
\(461\) 5.67717 5.67717i 0.0123149 0.0123149i −0.700923 0.713237i \(-0.747228\pi\)
0.713237 + 0.700923i \(0.247228\pi\)
\(462\) −99.0031 50.7040i −0.214292 0.109749i
\(463\) 464.510i 1.00326i −0.865082 0.501631i \(-0.832733\pi\)
0.865082 0.501631i \(-0.167267\pi\)
\(464\) −248.992 498.882i −0.536621 1.07518i
\(465\) 102.133 0.219641
\(466\) −142.431 + 278.106i −0.305646 + 0.596794i
\(467\) 495.985 + 495.985i 1.06207 + 1.06207i 0.997942 + 0.0641248i \(0.0204256\pi\)
0.0641248 + 0.997942i \(0.479574\pi\)
\(468\) 18.7502 115.281i 0.0400646 0.246328i
\(469\) 102.286 + 102.286i 0.218094 + 0.218094i
\(470\) 123.707 39.9109i 0.263207 0.0849167i
\(471\) 133.302 0.283018
\(472\) −56.8525 41.8497i −0.120450 0.0886646i
\(473\) 221.180i 0.467610i
\(474\) 14.7046 4.74407i 0.0310224 0.0100086i
\(475\) −387.987 + 387.987i −0.816815 + 0.816815i
\(476\) −524.407 728.129i −1.10170 1.52968i
\(477\) −75.4202 + 75.4202i −0.158114 + 0.158114i
\(478\) 12.0083 23.4471i 0.0251220 0.0490525i
\(479\) 378.802i 0.790818i −0.918505 0.395409i \(-0.870603\pi\)
0.918505 0.395409i \(-0.129397\pi\)
\(480\) 55.2703 + 56.4309i 0.115146 + 0.117564i
\(481\) 90.8504 0.188878
\(482\) 337.367 + 172.781i 0.699932 + 0.358467i
\(483\) 407.582 + 407.582i 0.843855 + 0.843855i
\(484\) −359.435 + 258.869i −0.742633 + 0.534854i
\(485\) 108.138 + 108.138i 0.222964 + 0.222964i
\(486\) 9.57256 + 29.6710i 0.0196966 + 0.0610514i
\(487\) 147.446 0.302764 0.151382 0.988475i \(-0.451628\pi\)
0.151382 + 0.988475i \(0.451628\pi\)
\(488\) −327.565 241.124i −0.671240 0.494107i
\(489\) 256.713i 0.524976i
\(490\) −45.0453 139.622i −0.0919292 0.284942i
\(491\) 109.547 109.547i 0.223110 0.223110i −0.586697 0.809807i \(-0.699572\pi\)
0.809807 + 0.586697i \(0.199572\pi\)
\(492\) 322.412 + 52.4395i 0.655310 + 0.106584i
\(493\) 551.473 551.473i 1.11861 1.11861i
\(494\) −413.893 211.973i −0.837840 0.429096i
\(495\) 13.6960i 0.0276686i
\(496\) 627.894 + 209.801i 1.26592 + 0.422985i
\(497\) 119.810 0.241067
\(498\) 22.7226 44.3674i 0.0456277 0.0890912i
\(499\) −360.523 360.523i −0.722491 0.722491i 0.246621 0.969112i \(-0.420680\pi\)
−0.969112 + 0.246621i \(0.920680\pi\)
\(500\) 269.902 + 43.8989i 0.539804 + 0.0877977i
\(501\) 65.2924 + 65.2924i 0.130324 + 0.130324i
\(502\) 73.8722 23.8329i 0.147156 0.0474760i
\(503\) −927.420 −1.84378 −0.921889 0.387454i \(-0.873355\pi\)
−0.921889 + 0.387454i \(0.873355\pi\)
\(504\) 237.834 36.1508i 0.471892 0.0717279i
\(505\) 203.117i 0.402211i
\(506\) −202.438 + 65.3114i −0.400075 + 0.129074i
\(507\) −90.9597 + 90.9597i −0.179408 + 0.179408i
\(508\) 119.554 86.1042i 0.235342 0.169496i
\(509\) 677.931 677.931i 1.33189 1.33189i 0.428208 0.903680i \(-0.359145\pi\)
0.903680 0.428208i \(-0.140855\pi\)
\(510\) −50.3642 + 98.3397i −0.0987534 + 0.192823i
\(511\) 1115.95i 2.18385i
\(512\) 223.872 + 460.462i 0.437249 + 0.899340i
\(513\) 124.129 0.241966
\(514\) −240.984 123.419i −0.468841 0.240115i
\(515\) 58.5045 + 58.5045i 0.113601 + 0.113601i
\(516\) −279.559 388.162i −0.541780 0.752251i
\(517\) 103.303 + 103.303i 0.199812 + 0.199812i
\(518\) 57.4548 + 178.086i 0.110917 + 0.343795i
\(519\) −101.845 −0.196233
\(520\) 16.6755 + 109.707i 0.0320682 + 0.210974i
\(521\) 143.173i 0.274804i −0.990515 0.137402i \(-0.956125\pi\)
0.990515 0.137402i \(-0.0438753\pi\)
\(522\) 64.1982 + 198.988i 0.122985 + 0.381203i
\(523\) 226.187 226.187i 0.432481 0.432481i −0.456991 0.889471i \(-0.651073\pi\)
0.889471 + 0.456991i \(0.151073\pi\)
\(524\) 11.2324 69.0600i 0.0214359 0.131794i
\(525\) 281.974 281.974i 0.537094 0.537094i
\(526\) −56.2738 28.8204i −0.106984 0.0547916i
\(527\) 926.004i 1.75712i
\(528\) −28.1342 + 84.2003i −0.0532844 + 0.159470i
\(529\) 573.288 1.08372
\(530\) 46.1934 90.1959i 0.0871574 0.170181i
\(531\) 18.7192 + 18.7192i 0.0352528 + 0.0352528i
\(532\) 153.762 945.371i 0.289027 1.77701i
\(533\) 324.484 + 324.484i 0.608788 + 0.608788i
\(534\) −72.3193 + 23.3319i −0.135429 + 0.0436928i
\(535\) 227.235 0.424739
\(536\) 68.4415 92.9772i 0.127689 0.173465i
\(537\) 129.997i 0.242080i
\(538\) 522.783 168.662i 0.971716 0.313499i
\(539\) 116.592 116.592i 0.216312 0.216312i
\(540\) −17.3110 24.0359i −0.0320573 0.0445109i
\(541\) −156.708 + 156.708i −0.289663 + 0.289663i −0.836947 0.547284i \(-0.815662\pi\)
0.547284 + 0.836947i \(0.315662\pi\)
\(542\) 265.890 519.168i 0.490571 0.957875i
\(543\) 163.146i 0.300454i
\(544\) −511.639 + 501.116i −0.940512 + 0.921170i
\(545\) −163.530 −0.300055
\(546\) 300.802 + 154.054i 0.550919 + 0.282151i
\(547\) 247.357 + 247.357i 0.452207 + 0.452207i 0.896086 0.443880i \(-0.146398\pi\)
−0.443880 + 0.896086i \(0.646398\pi\)
\(548\) −472.845 + 340.549i −0.862856 + 0.621440i
\(549\) 107.854 + 107.854i 0.196455 + 0.196455i
\(550\) 45.1839 + 140.051i 0.0821525 + 0.254638i
\(551\) 832.466 1.51083
\(552\) 272.721 370.489i 0.494060 0.671177i
\(553\) 44.7082i 0.0808466i
\(554\) −265.019 821.447i −0.478373 1.48276i
\(555\) 16.2922 16.2922i 0.0293553 0.0293553i
\(556\) 461.033 + 74.9858i 0.829196 + 0.134867i
\(557\) −661.193 + 661.193i −1.18706 + 1.18706i −0.209184 + 0.977876i \(0.567081\pi\)
−0.977876 + 0.209184i \(0.932919\pi\)
\(558\) −220.964 113.166i −0.395992 0.202806i
\(559\) 672.011i 1.20217i
\(560\) −204.503 + 102.067i −0.365183 + 0.182263i
\(561\) −124.177 −0.221349
\(562\) −193.150 + 377.139i −0.343684 + 0.671066i
\(563\) 246.685 + 246.685i 0.438162 + 0.438162i 0.891393 0.453231i \(-0.149729\pi\)
−0.453231 + 0.891393i \(0.649729\pi\)
\(564\) −311.861 50.7234i −0.552945 0.0899351i
\(565\) −173.171 173.171i −0.306497 0.306497i
\(566\) −283.516 + 91.4689i −0.500911 + 0.161606i
\(567\) −90.2120 −0.159104
\(568\) −14.3697 94.5372i −0.0252988 0.166439i
\(569\) 243.567i 0.428061i −0.976827 0.214030i \(-0.931341\pi\)
0.976827 0.214030i \(-0.0686592\pi\)
\(570\) −112.237 + 36.2102i −0.196906 + 0.0635267i
\(571\) 59.9229 59.9229i 0.104944 0.104944i −0.652685 0.757629i \(-0.726358\pi\)
0.757629 + 0.652685i \(0.226358\pi\)
\(572\) −101.202 + 72.8866i −0.176926 + 0.127424i
\(573\) −139.319 + 139.319i −0.243139 + 0.243139i
\(574\) −430.850 + 841.265i −0.750610 + 1.46562i
\(575\) 762.587i 1.32624i
\(576\) −57.0501 183.328i −0.0990453 0.318278i
\(577\) 136.609 0.236757 0.118378 0.992969i \(-0.462230\pi\)
0.118378 + 0.992969i \(0.462230\pi\)
\(578\) −377.156 193.159i −0.652519 0.334185i
\(579\) −32.5287 32.5287i −0.0561809 0.0561809i
\(580\) −116.096 161.196i −0.200165 0.277925i
\(581\) 101.991 + 101.991i 0.175543 + 0.175543i
\(582\) −114.136 353.774i −0.196110 0.607859i
\(583\) 113.893 0.195357
\(584\) 880.544 133.843i 1.50778 0.229184i
\(585\) 41.6126i 0.0711326i
\(586\) 148.754 + 461.076i 0.253846 + 0.786818i
\(587\) −331.817 + 331.817i −0.565276 + 0.565276i −0.930801 0.365525i \(-0.880889\pi\)
0.365525 + 0.930801i \(0.380889\pi\)
\(588\) −57.2488 + 351.981i −0.0973620 + 0.598608i
\(589\) −698.916 + 698.916i −1.18661 + 1.18661i
\(590\) −22.3865 11.4652i −0.0379433 0.0194325i
\(591\) 127.113i 0.215081i
\(592\) 133.629 66.6942i 0.225724 0.112659i
\(593\) 131.285 0.221391 0.110695 0.993854i \(-0.464692\pi\)
0.110695 + 0.993854i \(0.464692\pi\)
\(594\) 15.1754 29.6311i 0.0255479 0.0498840i
\(595\) −226.061 226.061i −0.379934 0.379934i
\(596\) −178.221 + 1095.75i −0.299028 + 1.83850i
\(597\) −167.473 167.473i −0.280524 0.280524i
\(598\) 615.069 198.436i 1.02854 0.331833i
\(599\) −136.119 −0.227243 −0.113621 0.993524i \(-0.536245\pi\)
−0.113621 + 0.993524i \(0.536245\pi\)
\(600\) −256.313 188.675i −0.427188 0.314458i
\(601\) 498.566i 0.829561i −0.909922 0.414780i \(-0.863858\pi\)
0.909922 0.414780i \(-0.136142\pi\)
\(602\) 1317.28 424.987i 2.18818 0.705959i
\(603\) −30.6136 + 30.6136i −0.0507689 + 0.0507689i
\(604\) 150.781 + 209.357i 0.249638 + 0.346617i
\(605\) −111.593 + 111.593i −0.184451 + 0.184451i
\(606\) −225.058 + 439.441i −0.371383 + 0.725150i
\(607\) 568.740i 0.936969i −0.883472 0.468484i \(-0.844800\pi\)
0.883472 0.468484i \(-0.155200\pi\)
\(608\) −764.393 7.94198i −1.25723 0.0130625i
\(609\) −605.005 −0.993441
\(610\) −128.984 66.0585i −0.211449 0.108293i
\(611\) −313.865 313.865i −0.513691 0.513691i
\(612\) 217.925 156.952i 0.356087 0.256458i
\(613\) −168.441 168.441i −0.274782 0.274782i 0.556240 0.831022i \(-0.312244\pi\)
−0.831022 + 0.556240i \(0.812244\pi\)
\(614\) 23.5455 + 72.9813i 0.0383478 + 0.118862i
\(615\) 116.380 0.189235
\(616\) −206.874 152.282i −0.335834 0.247211i
\(617\) 599.157i 0.971081i 0.874214 + 0.485541i \(0.161377\pi\)
−0.874214 + 0.485541i \(0.838623\pi\)
\(618\) −61.7497 191.398i −0.0999186 0.309706i
\(619\) 126.719 126.719i 0.204715 0.204715i −0.597301 0.802017i \(-0.703760\pi\)
0.802017 + 0.597301i \(0.203760\pi\)
\(620\) 232.807 + 37.8654i 0.375495 + 0.0610732i
\(621\) −121.987 + 121.987i −0.196437 + 0.196437i
\(622\) −660.647 338.347i −1.06213 0.543967i
\(623\) 219.881i 0.352939i
\(624\) 85.4802 255.826i 0.136988 0.409978i
\(625\) −476.800 −0.762879
\(626\) −341.426 + 666.658i −0.545409 + 1.06495i
\(627\) −93.7242 93.7242i −0.149480 0.149480i
\(628\) 303.854 + 49.4210i 0.483844 + 0.0786959i
\(629\) 147.716 + 147.716i 0.234842 + 0.234842i
\(630\) 81.5694 26.3162i 0.129475 0.0417718i
\(631\) 668.283 1.05909 0.529543 0.848283i \(-0.322363\pi\)
0.529543 + 0.848283i \(0.322363\pi\)
\(632\) 35.2773 5.36216i 0.0558185 0.00848444i
\(633\) 345.797i 0.546283i
\(634\) 130.779 42.1923i 0.206275 0.0665494i
\(635\) 37.1177 37.1177i 0.0584531 0.0584531i
\(636\) −199.878 + 143.955i −0.314274 + 0.226344i
\(637\) −354.243 + 354.243i −0.556112 + 0.556112i
\(638\) 101.774 198.720i 0.159520 0.311474i
\(639\) 35.8586i 0.0561168i
\(640\) 105.064 + 149.122i 0.164163 + 0.233004i
\(641\) 484.574 0.755966 0.377983 0.925813i \(-0.376618\pi\)
0.377983 + 0.925813i \(0.376618\pi\)
\(642\) −491.622 251.782i −0.765766 0.392184i
\(643\) 75.2980 + 75.2980i 0.117104 + 0.117104i 0.763230 0.646126i \(-0.223612\pi\)
−0.646126 + 0.763230i \(0.723612\pi\)
\(644\) 777.952 + 1080.17i 1.20800 + 1.67728i
\(645\) −120.512 120.512i −0.186840 0.186840i
\(646\) −328.306 1017.61i −0.508213 1.57525i
\(647\) −582.307 −0.900011 −0.450006 0.893026i \(-0.648578\pi\)
−0.450006 + 0.893026i \(0.648578\pi\)
\(648\) 10.8198 + 71.1824i 0.0166972 + 0.109849i
\(649\) 28.2682i 0.0435565i
\(650\) −137.282 425.518i −0.211204 0.654644i
\(651\) 507.946 507.946i 0.780255 0.780255i
\(652\) −95.1754 + 585.164i −0.145974 + 0.897491i
\(653\) 457.453 457.453i 0.700541 0.700541i −0.263986 0.964527i \(-0.585037\pi\)
0.964527 + 0.263986i \(0.0850371\pi\)
\(654\) 353.795 + 181.195i 0.540972 + 0.277056i
\(655\) 24.9283i 0.0380584i
\(656\) 715.480 + 239.066i 1.09067 + 0.364430i
\(657\) −333.997 −0.508367
\(658\) 416.750 813.734i 0.633359 1.23668i
\(659\) −430.079 430.079i −0.652623 0.652623i 0.301001 0.953624i \(-0.402679\pi\)
−0.953624 + 0.301001i \(0.902679\pi\)
\(660\) −5.07773 + 31.2193i −0.00769353 + 0.0473019i
\(661\) −513.622 513.622i −0.777038 0.777038i 0.202288 0.979326i \(-0.435162\pi\)
−0.979326 + 0.202288i \(0.935162\pi\)
\(662\) 5.08436 1.64034i 0.00768031 0.00247785i
\(663\) 377.287 0.569060
\(664\) 68.2440 92.7089i 0.102777 0.139622i
\(665\) 341.246i 0.513152i
\(666\) −53.3002 + 17.1959i −0.0800303 + 0.0258197i
\(667\) −818.105 + 818.105i −1.22654 + 1.22654i
\(668\) 124.624 + 173.037i 0.186562 + 0.259038i
\(669\) −150.162 + 150.162i −0.224457 + 0.224457i
\(670\) 18.7503 36.6112i 0.0279855 0.0546436i
\(671\) 162.872i 0.242730i
\(672\) 555.532 + 5.77193i 0.826685 + 0.00858919i
\(673\) −1112.68 −1.65332 −0.826659 0.562703i \(-0.809761\pi\)
−0.826659 + 0.562703i \(0.809761\pi\)
\(674\) 688.871 + 352.802i 1.02206 + 0.523446i
\(675\) 84.3935 + 84.3935i 0.125027 + 0.125027i
\(676\) −241.061 + 173.615i −0.356599 + 0.256827i
\(677\) 633.271 + 633.271i 0.935408 + 0.935408i 0.998037 0.0626291i \(-0.0199485\pi\)
−0.0626291 + 0.998037i \(0.519949\pi\)
\(678\) 182.776 + 566.530i 0.269581 + 0.835590i
\(679\) 1075.62 1.58412
\(680\) −151.262 + 205.488i −0.222444 + 0.302188i
\(681\) 724.668i 1.06412i
\(682\) 81.3937 + 252.287i 0.119346 + 0.369922i
\(683\) −429.651 + 429.651i −0.629065 + 0.629065i −0.947833 0.318768i \(-0.896731\pi\)
0.318768 + 0.947833i \(0.396731\pi\)
\(684\) 282.945 + 46.0202i 0.413662 + 0.0672810i
\(685\) −146.803 + 146.803i −0.214312 + 0.214312i
\(686\) −44.1038 22.5876i −0.0642913 0.0329265i
\(687\) 179.748i 0.261642i
\(688\) −493.330 988.439i −0.717049 1.43668i
\(689\) −346.042 −0.502239
\(690\) 74.7148 145.886i 0.108282 0.211429i
\(691\) −151.617 151.617i −0.219417 0.219417i 0.588836 0.808253i \(-0.299586\pi\)
−0.808253 + 0.588836i \(0.799586\pi\)
\(692\) −232.150 37.7586i −0.335477 0.0545644i
\(693\) 68.1153 + 68.1153i 0.0982904 + 0.0982904i
\(694\) −1189.47 + 383.753i −1.71394 + 0.552958i
\(695\) 166.417 0.239449
\(696\) 72.5625 + 477.383i 0.104257 + 0.685896i
\(697\) 1055.17i 1.51388i
\(698\) −321.353 + 103.676i −0.460391 + 0.148533i
\(699\) 191.340 191.340i 0.273734 0.273734i
\(700\) 747.287 538.205i 1.06755 0.768864i
\(701\) −920.704 + 920.704i −1.31341 + 1.31341i −0.394533 + 0.918882i \(0.629094\pi\)
−0.918882 + 0.394533i \(0.870906\pi\)
\(702\) −46.1076 + 90.0284i −0.0656804 + 0.128246i
\(703\) 222.982i 0.317186i
\(704\) −95.3473 + 181.500i −0.135437 + 0.257812i
\(705\) −112.571 −0.159675
\(706\) 917.906 + 470.102i 1.30015 + 0.665866i
\(707\) −1010.18 1010.18i −1.42882 1.42882i
\(708\) 35.7294 + 49.6096i 0.0504653 + 0.0700700i
\(709\) 405.348 + 405.348i 0.571718 + 0.571718i 0.932608 0.360890i \(-0.117527\pi\)
−0.360890 + 0.932608i \(0.617527\pi\)
\(710\) −10.4605 32.4233i −0.0147331 0.0456666i
\(711\) −13.3809 −0.0188199
\(712\) −173.498 + 26.3718i −0.243677 + 0.0370391i
\(713\) 1373.72i 1.92667i
\(714\) 238.600 + 739.561i 0.334174 + 1.03580i
\(715\) −31.4199 + 31.4199i −0.0439439 + 0.0439439i
\(716\) −48.1958 + 296.321i −0.0673125 + 0.413856i
\(717\) −16.1319 + 16.1319i −0.0224991 + 0.0224991i
\(718\) −762.363 390.441i −1.06179 0.543789i
\(719\) 880.704i 1.22490i 0.790509 + 0.612450i \(0.209816\pi\)
−0.790509 + 0.612450i \(0.790184\pi\)
\(720\) −30.5482 61.2066i −0.0424280 0.0850091i
\(721\) 581.930 0.807115
\(722\) 191.147 373.227i 0.264746 0.516935i
\(723\) −232.112 232.112i −0.321041 0.321041i
\(724\) 60.4859 371.884i 0.0835440 0.513651i
\(725\) 565.983 + 565.983i 0.780667 + 0.780667i
\(726\) 365.078 117.783i 0.502862 0.162235i
\(727\) 1000.46 1.37615 0.688077 0.725637i \(-0.258455\pi\)
0.688077 + 0.725637i \(0.258455\pi\)
\(728\) 628.547 + 462.680i 0.863388 + 0.635549i
\(729\) 27.0000i 0.0370370i
\(730\) 301.999 97.4320i 0.413697 0.133469i
\(731\) 1092.64 1092.64i 1.49472 1.49472i
\(732\) 205.861 + 285.834i 0.281231 + 0.390484i
\(733\) 540.306 540.306i 0.737116 0.737116i −0.234903 0.972019i \(-0.575477\pi\)
0.972019 + 0.234903i \(0.0754772\pi\)
\(734\) 200.097 390.704i 0.272612 0.532295i
\(735\) 127.053i 0.172861i
\(736\) 759.011 743.401i 1.03126 1.01006i
\(737\) 46.2301 0.0627274
\(738\) −251.786 128.951i −0.341174 0.174731i
\(739\) 893.726 + 893.726i 1.20937 + 1.20937i 0.971230 + 0.238142i \(0.0765384\pi\)
0.238142 + 0.971230i \(0.423462\pi\)
\(740\) 43.1775 31.0970i 0.0583480 0.0420229i
\(741\) 284.763 + 284.763i 0.384296 + 0.384296i
\(742\) −218.841 678.316i −0.294934 0.914172i
\(743\) 1295.75 1.74394 0.871969 0.489561i \(-0.162843\pi\)
0.871969 + 0.489561i \(0.162843\pi\)
\(744\) −461.719 339.876i −0.620591 0.456823i
\(745\) 395.527i 0.530909i
\(746\) −369.092 1144.03i −0.494761 1.53355i
\(747\) −30.5253 + 30.5253i −0.0408639 + 0.0408639i
\(748\) −283.054 46.0380i −0.378414 0.0615481i
\(749\) 1130.13 1130.13i 1.50885 1.50885i
\(750\) −210.779 107.949i −0.281038 0.143932i
\(751\) 229.818i 0.306016i −0.988225 0.153008i \(-0.951104\pi\)
0.988225 0.153008i \(-0.0488961\pi\)
\(752\) −692.066 231.243i −0.920300 0.307504i
\(753\) −67.2223 −0.0892726
\(754\) −309.220 + 603.774i −0.410106 + 0.800761i
\(755\) 64.9987 + 64.9987i 0.0860910 + 0.0860910i
\(756\) −205.634 33.4458i −0.272002 0.0442404i
\(757\) −373.678 373.678i −0.493630 0.493630i 0.415818 0.909448i \(-0.363495\pi\)
−0.909448 + 0.415818i \(0.863495\pi\)
\(758\) −984.973 + 317.776i −1.29944 + 0.419229i
\(759\) 184.215 0.242707
\(760\) −269.262 + 40.9280i −0.354293 + 0.0538527i
\(761\) 384.012i 0.504615i 0.967647 + 0.252307i \(0.0811894\pi\)
−0.967647 + 0.252307i \(0.918811\pi\)
\(762\) −121.431 + 39.1766i −0.159358 + 0.0514128i
\(763\) −813.296 + 813.296i −1.06592 + 1.06592i
\(764\) −369.222 + 265.918i −0.483275 + 0.348060i
\(765\) 67.6589 67.6589i 0.0884429 0.0884429i
\(766\) 194.440 379.658i 0.253838 0.495637i
\(767\) 85.8874i 0.111978i
\(768\) −62.0745 439.038i −0.0808261 0.571665i
\(769\) 865.026 1.12487 0.562436 0.826841i \(-0.309864\pi\)
0.562436 + 0.826841i \(0.309864\pi\)
\(770\) −81.4598 41.7193i −0.105792 0.0541809i
\(771\) 165.800 + 165.800i 0.215045 + 0.215045i