Properties

Label 76.3.b.b.39.3
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 39.3
Root \(-1.89728 + 0.632718i\) of defining polynomial
Character \(\chi\) \(=\) 76.39
Dual form 76.3.b.b.39.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.89728 - 0.632718i) q^{2} -5.34370i q^{3} +(3.19934 + 2.40089i) q^{4} +5.79268 q^{5} +(-3.38106 + 10.1385i) q^{6} -5.87536i q^{7} +(-4.55095 - 6.57943i) q^{8} -19.5551 q^{9} +O(q^{10})\) \(q+(-1.89728 - 0.632718i) q^{2} -5.34370i q^{3} +(3.19934 + 2.40089i) q^{4} +5.79268 q^{5} +(-3.38106 + 10.1385i) q^{6} -5.87536i q^{7} +(-4.55095 - 6.57943i) q^{8} -19.5551 q^{9} +(-10.9903 - 3.66514i) q^{10} +8.07883i q^{11} +(12.8296 - 17.0963i) q^{12} -14.0396 q^{13} +(-3.71745 + 11.1472i) q^{14} -30.9544i q^{15} +(4.47149 + 15.3625i) q^{16} +29.9906 q^{17} +(37.1016 + 12.3729i) q^{18} -4.35890i q^{19} +(18.5327 + 13.9076i) q^{20} -31.3962 q^{21} +(5.11162 - 15.3278i) q^{22} +8.74865i q^{23} +(-35.1585 + 24.3189i) q^{24} +8.55515 q^{25} +(26.6370 + 8.88309i) q^{26} +56.4036i q^{27} +(14.1061 - 18.7973i) q^{28} +13.4473 q^{29} +(-19.5854 + 58.7291i) q^{30} -7.65793i q^{31} +(1.23646 - 31.9761i) q^{32} +43.1708 q^{33} +(-56.9006 - 18.9756i) q^{34} -34.0341i q^{35} +(-62.5635 - 46.9497i) q^{36} +25.1221 q^{37} +(-2.75796 + 8.27005i) q^{38} +75.0232i q^{39} +(-26.3622 - 38.1125i) q^{40} +49.6861 q^{41} +(59.5673 + 19.8649i) q^{42} -47.2402i q^{43} +(-19.3963 + 25.8469i) q^{44} -113.277 q^{45} +(5.53543 - 16.5986i) q^{46} +46.8391i q^{47} +(82.0925 - 23.8943i) q^{48} +14.4801 q^{49} +(-16.2315 - 5.41300i) q^{50} -160.261i q^{51} +(-44.9173 - 33.7074i) q^{52} -14.1940 q^{53} +(35.6876 - 107.013i) q^{54} +46.7981i q^{55} +(-38.6565 + 26.7385i) q^{56} -23.2927 q^{57} +(-25.5133 - 8.50835i) q^{58} +100.107i q^{59} +(74.3179 - 99.0334i) q^{60} -31.1928 q^{61} +(-4.84532 + 14.5292i) q^{62} +114.894i q^{63} +(-22.5778 + 59.8853i) q^{64} -81.3267 q^{65} +(-81.9071 - 27.3150i) q^{66} +34.5861i q^{67} +(95.9501 + 72.0041i) q^{68} +46.7502 q^{69} +(-21.5340 + 64.5722i) q^{70} -66.0243i q^{71} +(88.9944 + 128.662i) q^{72} -27.5063 q^{73} +(-47.6636 - 15.8952i) q^{74} -45.7162i q^{75} +(10.4652 - 13.9456i) q^{76} +47.4661 q^{77} +(47.4686 - 142.340i) q^{78} +40.9739i q^{79} +(25.9019 + 88.9899i) q^{80} +125.408 q^{81} +(-94.2684 - 31.4373i) q^{82} -87.8564i q^{83} +(-100.447 - 75.3787i) q^{84} +173.726 q^{85} +(-29.8898 + 89.6279i) q^{86} -71.8584i q^{87} +(53.1541 - 36.7663i) q^{88} +28.6482 q^{89} +(214.918 + 71.6723i) q^{90} +82.4875i q^{91} +(-21.0045 + 27.9899i) q^{92} -40.9217 q^{93} +(29.6360 - 88.8669i) q^{94} -25.2497i q^{95} +(-170.871 - 6.60728i) q^{96} +9.35629 q^{97} +(-27.4728 - 9.16182i) q^{98} -157.983i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.89728 0.632718i −0.948639 0.316359i
\(3\) 5.34370i 1.78123i −0.454754 0.890617i \(-0.650273\pi\)
0.454754 0.890617i \(-0.349727\pi\)
\(4\) 3.19934 + 2.40089i 0.799834 + 0.600222i
\(5\) 5.79268 1.15854 0.579268 0.815137i \(-0.303338\pi\)
0.579268 + 0.815137i \(0.303338\pi\)
\(6\) −3.38106 + 10.1385i −0.563510 + 1.68975i
\(7\) 5.87536i 0.839338i −0.907677 0.419669i \(-0.862146\pi\)
0.907677 0.419669i \(-0.137854\pi\)
\(8\) −4.55095 6.57943i −0.568868 0.822429i
\(9\) −19.5551 −2.17279
\(10\) −10.9903 3.66514i −1.09903 0.366514i
\(11\) 8.07883i 0.734439i 0.930134 + 0.367219i \(0.119690\pi\)
−0.930134 + 0.367219i \(0.880310\pi\)
\(12\) 12.8296 17.0963i 1.06914 1.42469i
\(13\) −14.0396 −1.07997 −0.539983 0.841676i \(-0.681569\pi\)
−0.539983 + 0.841676i \(0.681569\pi\)
\(14\) −3.71745 + 11.1472i −0.265532 + 0.796229i
\(15\) 30.9544i 2.06362i
\(16\) 4.47149 + 15.3625i 0.279468 + 0.960155i
\(17\) 29.9906 1.76415 0.882077 0.471104i \(-0.156145\pi\)
0.882077 + 0.471104i \(0.156145\pi\)
\(18\) 37.1016 + 12.3729i 2.06120 + 0.687383i
\(19\) 4.35890i 0.229416i
\(20\) 18.5327 + 13.9076i 0.926636 + 0.695378i
\(21\) −31.3962 −1.49506
\(22\) 5.11162 15.3278i 0.232346 0.696718i
\(23\) 8.74865i 0.380376i 0.981748 + 0.190188i \(0.0609098\pi\)
−0.981748 + 0.190188i \(0.939090\pi\)
\(24\) −35.1585 + 24.3189i −1.46494 + 1.01329i
\(25\) 8.55515 0.342206
\(26\) 26.6370 + 8.88309i 1.02450 + 0.341657i
\(27\) 56.4036i 2.08902i
\(28\) 14.1061 18.7973i 0.503789 0.671331i
\(29\) 13.4473 0.463700 0.231850 0.972752i \(-0.425522\pi\)
0.231850 + 0.972752i \(0.425522\pi\)
\(30\) −19.5854 + 58.7291i −0.652846 + 1.95764i
\(31\) 7.65793i 0.247030i −0.992343 0.123515i \(-0.960583\pi\)
0.992343 0.123515i \(-0.0394167\pi\)
\(32\) 1.23646 31.9761i 0.0386394 0.999253i
\(33\) 43.1708 1.30821
\(34\) −56.9006 18.9756i −1.67355 0.558107i
\(35\) 34.0341i 0.972403i
\(36\) −62.5635 46.9497i −1.73787 1.30416i
\(37\) 25.1221 0.678975 0.339488 0.940611i \(-0.389746\pi\)
0.339488 + 0.940611i \(0.389746\pi\)
\(38\) −2.75796 + 8.27005i −0.0725778 + 0.217633i
\(39\) 75.0232i 1.92367i
\(40\) −26.3622 38.1125i −0.659054 0.952813i
\(41\) 49.6861 1.21186 0.605928 0.795519i \(-0.292802\pi\)
0.605928 + 0.795519i \(0.292802\pi\)
\(42\) 59.5673 + 19.8649i 1.41827 + 0.472975i
\(43\) 47.2402i 1.09861i −0.835622 0.549305i \(-0.814892\pi\)
0.835622 0.549305i \(-0.185108\pi\)
\(44\) −19.3963 + 25.8469i −0.440826 + 0.587429i
\(45\) −113.277 −2.51726
\(46\) 5.53543 16.5986i 0.120336 0.360840i
\(47\) 46.8391i 0.996577i 0.867011 + 0.498289i \(0.166038\pi\)
−0.867011 + 0.498289i \(0.833962\pi\)
\(48\) 82.0925 23.8943i 1.71026 0.497798i
\(49\) 14.4801 0.295512
\(50\) −16.2315 5.41300i −0.324630 0.108260i
\(51\) 160.261i 3.14237i
\(52\) −44.9173 33.7074i −0.863793 0.648219i
\(53\) −14.1940 −0.267811 −0.133906 0.990994i \(-0.542752\pi\)
−0.133906 + 0.990994i \(0.542752\pi\)
\(54\) 35.6876 107.013i 0.660881 1.98173i
\(55\) 46.7981i 0.850874i
\(56\) −38.6565 + 26.7385i −0.690295 + 0.477473i
\(57\) −23.2927 −0.408643
\(58\) −25.5133 8.50835i −0.439884 0.146696i
\(59\) 100.107i 1.69673i 0.529415 + 0.848363i \(0.322411\pi\)
−0.529415 + 0.848363i \(0.677589\pi\)
\(60\) 74.3179 99.0334i 1.23863 1.65056i
\(61\) −31.1928 −0.511357 −0.255678 0.966762i \(-0.582299\pi\)
−0.255678 + 0.966762i \(0.582299\pi\)
\(62\) −4.84532 + 14.5292i −0.0781503 + 0.234343i
\(63\) 114.894i 1.82371i
\(64\) −22.5778 + 59.8853i −0.352778 + 0.935707i
\(65\) −81.3267 −1.25118
\(66\) −81.9071 27.3150i −1.24102 0.413863i
\(67\) 34.5861i 0.516210i 0.966117 + 0.258105i \(0.0830981\pi\)
−0.966117 + 0.258105i \(0.916902\pi\)
\(68\) 95.9501 + 72.0041i 1.41103 + 1.05888i
\(69\) 46.7502 0.677539
\(70\) −21.5340 + 64.5722i −0.307629 + 0.922460i
\(71\) 66.0243i 0.929919i −0.885332 0.464960i \(-0.846069\pi\)
0.885332 0.464960i \(-0.153931\pi\)
\(72\) 88.9944 + 128.662i 1.23603 + 1.78697i
\(73\) −27.5063 −0.376798 −0.188399 0.982093i \(-0.560330\pi\)
−0.188399 + 0.982093i \(0.560330\pi\)
\(74\) −47.6636 15.8952i −0.644103 0.214800i
\(75\) 45.7162i 0.609549i
\(76\) 10.4652 13.9456i 0.137700 0.183494i
\(77\) 47.4661 0.616442
\(78\) 47.4686 142.340i 0.608571 1.82487i
\(79\) 40.9739i 0.518657i 0.965789 + 0.259329i \(0.0835013\pi\)
−0.965789 + 0.259329i \(0.916499\pi\)
\(80\) 25.9019 + 88.9899i 0.323774 + 1.11237i
\(81\) 125.408 1.54824
\(82\) −94.2684 31.4373i −1.14961 0.383382i
\(83\) 87.8564i 1.05851i −0.848463 0.529255i \(-0.822471\pi\)
0.848463 0.529255i \(-0.177529\pi\)
\(84\) −100.447 75.3787i −1.19580 0.897365i
\(85\) 173.726 2.04384
\(86\) −29.8898 + 89.6279i −0.347555 + 1.04219i
\(87\) 71.8584i 0.825958i
\(88\) 53.1541 36.7663i 0.604024 0.417799i
\(89\) 28.6482 0.321890 0.160945 0.986963i \(-0.448546\pi\)
0.160945 + 0.986963i \(0.448546\pi\)
\(90\) 214.918 + 71.6723i 2.38797 + 0.796359i
\(91\) 82.4875i 0.906457i
\(92\) −21.0045 + 27.9899i −0.228310 + 0.304238i
\(93\) −40.9217 −0.440018
\(94\) 29.6360 88.8669i 0.315276 0.945393i
\(95\) 25.2497i 0.265786i
\(96\) −170.871 6.60728i −1.77990 0.0688258i
\(97\) 9.35629 0.0964566 0.0482283 0.998836i \(-0.484642\pi\)
0.0482283 + 0.998836i \(0.484642\pi\)
\(98\) −27.4728 9.16182i −0.280334 0.0934879i
\(99\) 157.983i 1.59578i
\(100\) 27.3708 + 20.5399i 0.273708 + 0.205399i
\(101\) −86.6846 −0.858263 −0.429132 0.903242i \(-0.641180\pi\)
−0.429132 + 0.903242i \(0.641180\pi\)
\(102\) −101.400 + 304.060i −0.994118 + 2.98098i
\(103\) 139.602i 1.35536i 0.735358 + 0.677679i \(0.237014\pi\)
−0.735358 + 0.677679i \(0.762986\pi\)
\(104\) 63.8933 + 92.3723i 0.614359 + 0.888195i
\(105\) −181.868 −1.73208
\(106\) 26.9300 + 8.98081i 0.254057 + 0.0847246i
\(107\) 53.5627i 0.500586i −0.968170 0.250293i \(-0.919473\pi\)
0.968170 0.250293i \(-0.0805269\pi\)
\(108\) −135.419 + 180.454i −1.25388 + 1.67087i
\(109\) −154.519 −1.41760 −0.708802 0.705408i \(-0.750764\pi\)
−0.708802 + 0.705408i \(0.750764\pi\)
\(110\) 29.6100 88.7890i 0.269182 0.807173i
\(111\) 134.245i 1.20941i
\(112\) 90.2602 26.2716i 0.805894 0.234568i
\(113\) −66.0050 −0.584115 −0.292057 0.956401i \(-0.594340\pi\)
−0.292057 + 0.956401i \(0.594340\pi\)
\(114\) 44.1927 + 14.7377i 0.387655 + 0.129278i
\(115\) 50.6782i 0.440680i
\(116\) 43.0224 + 32.2854i 0.370883 + 0.278323i
\(117\) 274.546 2.34654
\(118\) 63.3394 189.931i 0.536775 1.60958i
\(119\) 176.206i 1.48072i
\(120\) −203.662 + 140.872i −1.69718 + 1.17393i
\(121\) 55.7325 0.460600
\(122\) 59.1814 + 19.7362i 0.485093 + 0.161772i
\(123\) 265.508i 2.15860i
\(124\) 18.3858 24.5003i 0.148273 0.197583i
\(125\) −95.2598 −0.762078
\(126\) 72.6953 217.985i 0.576947 1.73004i
\(127\) 222.988i 1.75581i 0.478833 + 0.877906i \(0.341060\pi\)
−0.478833 + 0.877906i \(0.658940\pi\)
\(128\) 80.7268 99.3337i 0.630678 0.776044i
\(129\) −252.438 −1.95688
\(130\) 154.299 + 51.4569i 1.18692 + 0.395822i
\(131\) 199.333i 1.52163i 0.648971 + 0.760813i \(0.275200\pi\)
−0.648971 + 0.760813i \(0.724800\pi\)
\(132\) 138.118 + 103.648i 1.04635 + 0.785214i
\(133\) −25.6101 −0.192557
\(134\) 21.8833 65.6195i 0.163308 0.489698i
\(135\) 326.728i 2.42021i
\(136\) −136.486 197.321i −1.00357 1.45089i
\(137\) −6.01427 −0.0438998 −0.0219499 0.999759i \(-0.506987\pi\)
−0.0219499 + 0.999759i \(0.506987\pi\)
\(138\) −88.6982 29.5797i −0.642740 0.214346i
\(139\) 77.3080i 0.556172i −0.960556 0.278086i \(-0.910300\pi\)
0.960556 0.278086i \(-0.0897001\pi\)
\(140\) 81.7120 108.887i 0.583657 0.777761i
\(141\) 250.294 1.77514
\(142\) −41.7748 + 125.266i −0.294188 + 0.882158i
\(143\) 113.423i 0.793169i
\(144\) −87.4406 300.416i −0.607227 2.08622i
\(145\) 77.8959 0.537213
\(146\) 52.1870 + 17.4037i 0.357445 + 0.119203i
\(147\) 77.3773i 0.526376i
\(148\) 80.3740 + 60.3153i 0.543067 + 0.407536i
\(149\) 250.996 1.68454 0.842270 0.539056i \(-0.181219\pi\)
0.842270 + 0.539056i \(0.181219\pi\)
\(150\) −28.9255 + 86.7363i −0.192836 + 0.578242i
\(151\) 62.0159i 0.410701i −0.978688 0.205351i \(-0.934167\pi\)
0.978688 0.205351i \(-0.0658335\pi\)
\(152\) −28.6791 + 19.8371i −0.188678 + 0.130507i
\(153\) −586.471 −3.83315
\(154\) −90.0564 30.0326i −0.584782 0.195017i
\(155\) 44.3600i 0.286193i
\(156\) −180.122 + 240.024i −1.15463 + 1.53862i
\(157\) −100.150 −0.637898 −0.318949 0.947772i \(-0.603330\pi\)
−0.318949 + 0.947772i \(0.603330\pi\)
\(158\) 25.9250 77.7390i 0.164082 0.492019i
\(159\) 75.8485i 0.477035i
\(160\) 7.16242 185.227i 0.0447651 1.15767i
\(161\) 51.4015 0.319264
\(162\) −237.933 79.3476i −1.46872 0.489800i
\(163\) 187.915i 1.15285i −0.817150 0.576425i \(-0.804447\pi\)
0.817150 0.576425i \(-0.195553\pi\)
\(164\) 158.963 + 119.291i 0.969284 + 0.727382i
\(165\) 250.075 1.51561
\(166\) −55.5883 + 166.688i −0.334869 + 1.00414i
\(167\) 24.2604i 0.145272i 0.997359 + 0.0726361i \(0.0231412\pi\)
−0.997359 + 0.0726361i \(0.976859\pi\)
\(168\) 142.882 + 206.569i 0.850490 + 1.22958i
\(169\) 28.1093 0.166327
\(170\) −329.607 109.920i −1.93886 0.646587i
\(171\) 85.2389i 0.498473i
\(172\) 113.418 151.137i 0.659410 0.878706i
\(173\) −250.771 −1.44954 −0.724772 0.688989i \(-0.758055\pi\)
−0.724772 + 0.688989i \(0.758055\pi\)
\(174\) −45.4661 + 136.335i −0.261299 + 0.783537i
\(175\) 50.2646i 0.287226i
\(176\) −124.111 + 36.1244i −0.705175 + 0.205252i
\(177\) 534.941 3.02227
\(178\) −54.3537 18.1263i −0.305358 0.101833i
\(179\) 62.4162i 0.348694i 0.984684 + 0.174347i \(0.0557815\pi\)
−0.984684 + 0.174347i \(0.944219\pi\)
\(180\) −362.410 271.965i −2.01339 1.51091i
\(181\) −66.6789 −0.368392 −0.184196 0.982890i \(-0.558968\pi\)
−0.184196 + 0.982890i \(0.558968\pi\)
\(182\) 52.1914 156.502i 0.286766 0.859900i
\(183\) 166.685i 0.910846i
\(184\) 57.5612 39.8147i 0.312832 0.216384i
\(185\) 145.524 0.786617
\(186\) 77.6399 + 25.8919i 0.417419 + 0.139204i
\(187\) 242.289i 1.29566i
\(188\) −112.455 + 149.854i −0.598167 + 0.797096i
\(189\) 331.392 1.75339
\(190\) −15.9760 + 47.9057i −0.0840840 + 0.252135i
\(191\) 218.487i 1.14391i 0.820285 + 0.571955i \(0.193815\pi\)
−0.820285 + 0.571955i \(0.806185\pi\)
\(192\) 320.009 + 120.649i 1.66671 + 0.628380i
\(193\) 61.9485 0.320977 0.160488 0.987038i \(-0.448693\pi\)
0.160488 + 0.987038i \(0.448693\pi\)
\(194\) −17.7515 5.91990i −0.0915025 0.0305149i
\(195\) 434.586i 2.22864i
\(196\) 46.3267 + 34.7651i 0.236361 + 0.177373i
\(197\) −355.348 −1.80380 −0.901898 0.431950i \(-0.857826\pi\)
−0.901898 + 0.431950i \(0.857826\pi\)
\(198\) −99.9585 + 299.737i −0.504841 + 1.51382i
\(199\) 208.471i 1.04759i 0.851843 + 0.523797i \(0.175485\pi\)
−0.851843 + 0.523797i \(0.824515\pi\)
\(200\) −38.9340 56.2880i −0.194670 0.281440i
\(201\) 184.818 0.919491
\(202\) 164.465 + 54.8469i 0.814183 + 0.271519i
\(203\) 79.0078i 0.389201i
\(204\) 384.768 512.729i 1.88612 2.51338i
\(205\) 287.816 1.40398
\(206\) 88.3286 264.864i 0.428780 1.28575i
\(207\) 171.081i 0.826479i
\(208\) −62.7777 215.682i −0.301816 1.03694i
\(209\) 35.2148 0.168492
\(210\) 345.055 + 115.071i 1.64312 + 0.547959i
\(211\) 275.150i 1.30403i −0.758206 0.652015i \(-0.773924\pi\)
0.758206 0.652015i \(-0.226076\pi\)
\(212\) −45.4114 34.0782i −0.214205 0.160746i
\(213\) −352.814 −1.65640
\(214\) −33.8901 + 101.623i −0.158365 + 0.474876i
\(215\) 273.648i 1.27278i
\(216\) 371.103 256.690i 1.71807 1.18838i
\(217\) −44.9932 −0.207342
\(218\) 293.165 + 97.7669i 1.34479 + 0.448472i
\(219\) 146.985i 0.671165i
\(220\) −112.357 + 149.723i −0.510713 + 0.680558i
\(221\) −421.055 −1.90523
\(222\) −84.9392 + 254.700i −0.382609 + 1.14730i
\(223\) 237.911i 1.06687i 0.845842 + 0.533434i \(0.179099\pi\)
−0.845842 + 0.533434i \(0.820901\pi\)
\(224\) −187.871 7.26466i −0.838711 0.0324315i
\(225\) −167.297 −0.743543
\(226\) 125.230 + 41.7626i 0.554114 + 0.184790i
\(227\) 157.067i 0.691924i −0.938249 0.345962i \(-0.887553\pi\)
0.938249 0.345962i \(-0.112447\pi\)
\(228\) −74.5210 55.9230i −0.326847 0.245276i
\(229\) −177.569 −0.775412 −0.387706 0.921783i \(-0.626732\pi\)
−0.387706 + 0.921783i \(0.626732\pi\)
\(230\) 32.0650 96.1506i 0.139413 0.418046i
\(231\) 253.644i 1.09803i
\(232\) −61.1979 88.4756i −0.263784 0.381360i
\(233\) 75.5890 0.324416 0.162208 0.986757i \(-0.448138\pi\)
0.162208 + 0.986757i \(0.448138\pi\)
\(234\) −520.890 173.710i −2.22602 0.742351i
\(235\) 271.324i 1.15457i
\(236\) −240.345 + 320.275i −1.01841 + 1.35710i
\(237\) 218.952 0.923850
\(238\) −111.489 + 334.312i −0.468440 + 1.40467i
\(239\) 1.99543i 0.00834909i −0.999991 0.00417454i \(-0.998671\pi\)
0.999991 0.00417454i \(-0.00132880\pi\)
\(240\) 475.536 138.412i 1.98140 0.576717i
\(241\) −64.6551 −0.268278 −0.134139 0.990962i \(-0.542827\pi\)
−0.134139 + 0.990962i \(0.542827\pi\)
\(242\) −105.740 35.2630i −0.436943 0.145715i
\(243\) 162.508i 0.668758i
\(244\) −99.7961 74.8903i −0.409000 0.306927i
\(245\) 83.8785 0.342361
\(246\) −167.992 + 503.742i −0.682893 + 2.04773i
\(247\) 61.1970i 0.247761i
\(248\) −50.3848 + 34.8508i −0.203165 + 0.140528i
\(249\) −469.478 −1.88545
\(250\) 180.734 + 60.2726i 0.722937 + 0.241090i
\(251\) 245.790i 0.979245i 0.871935 + 0.489622i \(0.162865\pi\)
−0.871935 + 0.489622i \(0.837135\pi\)
\(252\) −275.847 + 367.583i −1.09463 + 1.45866i
\(253\) −70.6789 −0.279363
\(254\) 141.089 423.071i 0.555467 1.66563i
\(255\) 928.341i 3.64055i
\(256\) −216.012 + 137.386i −0.843795 + 0.536665i
\(257\) 276.853 1.07725 0.538625 0.842546i \(-0.318944\pi\)
0.538625 + 0.842546i \(0.318944\pi\)
\(258\) 478.945 + 159.722i 1.85638 + 0.619078i
\(259\) 147.601i 0.569890i
\(260\) −260.191 195.256i −1.00074 0.750985i
\(261\) −262.964 −1.00752
\(262\) 126.122 378.190i 0.481380 1.44347i
\(263\) 95.4157i 0.362797i −0.983410 0.181399i \(-0.941938\pi\)
0.983410 0.181399i \(-0.0580624\pi\)
\(264\) −196.468 284.040i −0.744198 1.07591i
\(265\) −82.2213 −0.310269
\(266\) 48.5895 + 16.2040i 0.182667 + 0.0609173i
\(267\) 153.088i 0.573362i
\(268\) −83.0373 + 110.653i −0.309841 + 0.412882i
\(269\) −128.844 −0.478974 −0.239487 0.970900i \(-0.576979\pi\)
−0.239487 + 0.970900i \(0.576979\pi\)
\(270\) 206.727 619.894i 0.765654 2.29590i
\(271\) 317.491i 1.17155i −0.810472 0.585777i \(-0.800789\pi\)
0.810472 0.585777i \(-0.199211\pi\)
\(272\) 134.103 + 460.730i 0.493025 + 1.69386i
\(273\) 440.789 1.61461
\(274\) 11.4107 + 3.80534i 0.0416450 + 0.0138881i
\(275\) 69.1156i 0.251329i
\(276\) 149.570 + 112.242i 0.541919 + 0.406674i
\(277\) −29.1910 −0.105383 −0.0526913 0.998611i \(-0.516780\pi\)
−0.0526913 + 0.998611i \(0.516780\pi\)
\(278\) −48.9142 + 146.675i −0.175950 + 0.527607i
\(279\) 149.752i 0.536746i
\(280\) −223.925 + 154.887i −0.799732 + 0.553169i
\(281\) 204.530 0.727866 0.363933 0.931425i \(-0.381434\pi\)
0.363933 + 0.931425i \(0.381434\pi\)
\(282\) −474.878 158.366i −1.68397 0.561581i
\(283\) 502.549i 1.77579i −0.460044 0.887896i \(-0.652166\pi\)
0.460044 0.887896i \(-0.347834\pi\)
\(284\) 158.517 211.234i 0.558158 0.743781i
\(285\) −134.927 −0.473428
\(286\) −71.7649 + 215.195i −0.250926 + 0.752432i
\(287\) 291.924i 1.01716i
\(288\) −24.1792 + 625.297i −0.0839555 + 2.17117i
\(289\) 610.438 2.11224
\(290\) −147.790 49.2862i −0.509622 0.169952i
\(291\) 49.9972i 0.171812i
\(292\) −88.0017 66.0394i −0.301376 0.226162i
\(293\) 239.563 0.817623 0.408811 0.912619i \(-0.365943\pi\)
0.408811 + 0.912619i \(0.365943\pi\)
\(294\) −48.9580 + 146.806i −0.166524 + 0.499341i
\(295\) 579.887i 1.96572i
\(296\) −114.329 165.289i −0.386248 0.558409i
\(297\) −455.675 −1.53426
\(298\) −476.210 158.810i −1.59802 0.532919i
\(299\) 122.827i 0.410794i
\(300\) 109.759 146.261i 0.365864 0.487538i
\(301\) −277.554 −0.922105
\(302\) −39.2386 + 117.661i −0.129929 + 0.389608i
\(303\) 463.217i 1.52877i
\(304\) 66.9635 19.4908i 0.220275 0.0641144i
\(305\) −180.690 −0.592425
\(306\) 1112.70 + 371.071i 3.63627 + 1.21265i
\(307\) 310.436i 1.01119i −0.862771 0.505595i \(-0.831273\pi\)
0.862771 0.505595i \(-0.168727\pi\)
\(308\) 151.860 + 113.961i 0.493051 + 0.370002i
\(309\) 745.990 2.41421
\(310\) −28.0674 + 84.1632i −0.0905399 + 0.271494i
\(311\) 219.552i 0.705956i −0.935632 0.352978i \(-0.885169\pi\)
0.935632 0.352978i \(-0.114831\pi\)
\(312\) 493.610 341.427i 1.58208 1.09432i
\(313\) 322.681 1.03093 0.515465 0.856911i \(-0.327619\pi\)
0.515465 + 0.856911i \(0.327619\pi\)
\(314\) 190.013 + 63.3668i 0.605136 + 0.201805i
\(315\) 665.542i 2.11283i
\(316\) −98.3738 + 131.089i −0.311309 + 0.414840i
\(317\) −53.6396 −0.169210 −0.0846050 0.996415i \(-0.526963\pi\)
−0.0846050 + 0.996415i \(0.526963\pi\)
\(318\) 47.9908 143.906i 0.150914 0.452534i
\(319\) 108.638i 0.340559i
\(320\) −130.786 + 346.896i −0.408706 + 1.08405i
\(321\) −286.223 −0.891661
\(322\) −97.5231 32.5227i −0.302867 0.101002i
\(323\) 130.726i 0.404725i
\(324\) 401.221 + 301.089i 1.23834 + 0.929288i
\(325\) −120.111 −0.369571
\(326\) −118.897 + 356.526i −0.364715 + 1.09364i
\(327\) 825.702i 2.52508i
\(328\) −226.119 326.906i −0.689387 0.996665i
\(329\) 275.197 0.836465
\(330\) −474.462 158.227i −1.43776 0.479476i
\(331\) 165.098i 0.498786i 0.968402 + 0.249393i \(0.0802310\pi\)
−0.968402 + 0.249393i \(0.919769\pi\)
\(332\) 210.933 281.082i 0.635341 0.846632i
\(333\) −491.266 −1.47527
\(334\) 15.3500 46.0288i 0.0459582 0.137811i
\(335\) 200.346i 0.598048i
\(336\) −140.388 482.323i −0.417821 1.43549i
\(337\) −374.211 −1.11042 −0.555210 0.831710i \(-0.687362\pi\)
−0.555210 + 0.831710i \(0.687362\pi\)
\(338\) −53.3312 17.7853i −0.157785 0.0526191i
\(339\) 352.711i 1.04045i
\(340\) 555.808 + 417.097i 1.63473 + 1.22676i
\(341\) 61.8671 0.181429
\(342\) 53.9322 161.722i 0.157697 0.472871i
\(343\) 372.969i 1.08737i
\(344\) −310.814 + 214.988i −0.903529 + 0.624965i
\(345\) 270.809 0.784954
\(346\) 475.783 + 158.667i 1.37509 + 0.458577i
\(347\) 442.710i 1.27582i 0.770110 + 0.637911i \(0.220201\pi\)
−0.770110 + 0.637911i \(0.779799\pi\)
\(348\) 172.524 229.899i 0.495758 0.660629i
\(349\) −163.363 −0.468090 −0.234045 0.972226i \(-0.575196\pi\)
−0.234045 + 0.972226i \(0.575196\pi\)
\(350\) −31.8033 + 95.3660i −0.0908667 + 0.272474i
\(351\) 791.881i 2.25607i
\(352\) 258.329 + 9.98915i 0.733890 + 0.0283783i
\(353\) 410.271 1.16224 0.581120 0.813818i \(-0.302615\pi\)
0.581120 + 0.813818i \(0.302615\pi\)
\(354\) −1014.93 338.467i −2.86704 0.956121i
\(355\) 382.457i 1.07734i
\(356\) 91.6553 + 68.7812i 0.257459 + 0.193206i
\(357\) −941.592 −2.63751
\(358\) 39.4919 118.421i 0.110313 0.330785i
\(359\) 124.552i 0.346941i 0.984839 + 0.173470i \(0.0554981\pi\)
−0.984839 + 0.173470i \(0.944502\pi\)
\(360\) 515.516 + 745.296i 1.43199 + 2.07027i
\(361\) −19.0000 −0.0526316
\(362\) 126.508 + 42.1890i 0.349471 + 0.116544i
\(363\) 297.818i 0.820436i
\(364\) −198.043 + 263.905i −0.544075 + 0.725015i
\(365\) −159.335 −0.436534
\(366\) 105.465 316.248i 0.288155 0.864065i
\(367\) 288.749i 0.786782i −0.919371 0.393391i \(-0.871302\pi\)
0.919371 0.393391i \(-0.128698\pi\)
\(368\) −134.401 + 39.1195i −0.365220 + 0.106303i
\(369\) −971.619 −2.63311
\(370\) −276.100 92.0758i −0.746216 0.248854i
\(371\) 83.3950i 0.224784i
\(372\) −130.922 98.2484i −0.351942 0.264109i
\(373\) 380.740 1.02075 0.510376 0.859952i \(-0.329506\pi\)
0.510376 + 0.859952i \(0.329506\pi\)
\(374\) 153.301 459.690i 0.409895 1.22912i
\(375\) 509.040i 1.35744i
\(376\) 308.175 213.162i 0.819614 0.566921i
\(377\) −188.794 −0.500780
\(378\) −628.742 209.677i −1.66334 0.554702i
\(379\) 176.366i 0.465345i 0.972555 + 0.232673i \(0.0747471\pi\)
−0.972555 + 0.232673i \(0.925253\pi\)
\(380\) 60.6217 80.7823i 0.159531 0.212585i
\(381\) 1191.58 3.12751
\(382\) 138.241 414.530i 0.361886 1.08516i
\(383\) 389.993i 1.01826i −0.860690 0.509129i \(-0.829968\pi\)
0.860690 0.509129i \(-0.170032\pi\)
\(384\) −530.809 431.380i −1.38232 1.12339i
\(385\) 274.956 0.714171
\(386\) −117.534 39.1960i −0.304491 0.101544i
\(387\) 923.790i 2.38705i
\(388\) 29.9339 + 22.4634i 0.0771493 + 0.0578953i
\(389\) 5.08380 0.0130689 0.00653445 0.999979i \(-0.497920\pi\)
0.00653445 + 0.999979i \(0.497920\pi\)
\(390\) 274.970 824.530i 0.705052 2.11418i
\(391\) 262.378i 0.671043i
\(392\) −65.8981 95.2707i −0.168107 0.243038i
\(393\) 1065.18 2.71037
\(394\) 674.194 + 224.835i 1.71115 + 0.570647i
\(395\) 237.349i 0.600883i
\(396\) 379.298 505.439i 0.957824 1.27636i
\(397\) 320.541 0.807409 0.403705 0.914889i \(-0.367722\pi\)
0.403705 + 0.914889i \(0.367722\pi\)
\(398\) 131.904 395.528i 0.331416 0.993789i
\(399\) 136.853i 0.342990i
\(400\) 38.2543 + 131.428i 0.0956356 + 0.328571i
\(401\) −428.362 −1.06823 −0.534117 0.845410i \(-0.679356\pi\)
−0.534117 + 0.845410i \(0.679356\pi\)
\(402\) −350.651 116.938i −0.872266 0.290890i
\(403\) 107.514i 0.266784i
\(404\) −277.333 208.120i −0.686468 0.515148i
\(405\) 726.446 1.79369
\(406\) −49.9897 + 149.900i −0.123127 + 0.369211i
\(407\) 202.957i 0.498666i
\(408\) −1054.43 + 729.339i −2.58438 + 1.78760i
\(409\) 109.550 0.267849 0.133925 0.990992i \(-0.457242\pi\)
0.133925 + 0.990992i \(0.457242\pi\)
\(410\) −546.067 182.106i −1.33187 0.444162i
\(411\) 32.1385i 0.0781957i
\(412\) −335.168 + 446.633i −0.813515 + 1.08406i
\(413\) 588.164 1.42413
\(414\) −108.246 + 324.589i −0.261464 + 0.784031i
\(415\) 508.924i 1.22632i
\(416\) −17.3594 + 448.930i −0.0417292 + 1.07916i
\(417\) −413.111 −0.990673
\(418\) −66.8123 22.2810i −0.159838 0.0533039i
\(419\) 305.115i 0.728199i 0.931360 + 0.364099i \(0.118623\pi\)
−0.931360 + 0.364099i \(0.881377\pi\)
\(420\) −581.857 436.645i −1.38537 1.03963i
\(421\) −721.115 −1.71286 −0.856431 0.516261i \(-0.827323\pi\)
−0.856431 + 0.516261i \(0.827323\pi\)
\(422\) −174.093 + 522.037i −0.412542 + 1.23705i
\(423\) 915.946i 2.16536i
\(424\) 64.5962 + 93.3885i 0.152349 + 0.220256i
\(425\) 256.574 0.603704
\(426\) 669.386 + 223.232i 1.57133 + 0.524018i
\(427\) 183.269i 0.429201i
\(428\) 128.598 171.365i 0.300462 0.400386i
\(429\) −606.100 −1.41282
\(430\) −173.142 + 519.186i −0.402656 + 1.20741i
\(431\) 275.396i 0.638971i 0.947591 + 0.319485i \(0.103510\pi\)
−0.947591 + 0.319485i \(0.896490\pi\)
\(432\) −866.499 + 252.208i −2.00578 + 0.583815i
\(433\) −445.559 −1.02900 −0.514502 0.857489i \(-0.672023\pi\)
−0.514502 + 0.857489i \(0.672023\pi\)
\(434\) 85.3646 + 28.4680i 0.196693 + 0.0655945i
\(435\) 416.253i 0.956903i
\(436\) −494.357 370.982i −1.13385 0.850876i
\(437\) 38.1345 0.0872643
\(438\) 93.0002 278.872i 0.212329 0.636694i
\(439\) 501.542i 1.14246i −0.820788 0.571232i \(-0.806466\pi\)
0.820788 0.571232i \(-0.193534\pi\)
\(440\) 307.905 212.975i 0.699783 0.484035i
\(441\) −283.160 −0.642087
\(442\) 798.859 + 266.409i 1.80737 + 0.602736i
\(443\) 297.237i 0.670964i −0.942047 0.335482i \(-0.891101\pi\)
0.942047 0.335482i \(-0.108899\pi\)
\(444\) 322.307 429.495i 0.725916 0.967330i
\(445\) 165.950 0.372922
\(446\) 150.531 451.384i 0.337513 1.01207i
\(447\) 1341.25i 3.00056i
\(448\) 351.848 + 132.653i 0.785374 + 0.296100i
\(449\) −286.813 −0.638782 −0.319391 0.947623i \(-0.603478\pi\)
−0.319391 + 0.947623i \(0.603478\pi\)
\(450\) 317.409 + 105.852i 0.705354 + 0.235227i
\(451\) 401.405i 0.890034i
\(452\) −211.172 158.470i −0.467195 0.350598i
\(453\) −331.395 −0.731555
\(454\) −99.3789 + 297.999i −0.218896 + 0.656386i
\(455\) 477.824i 1.05016i
\(456\) 106.004 + 153.252i 0.232464 + 0.336080i
\(457\) 254.383 0.556637 0.278318 0.960489i \(-0.410223\pi\)
0.278318 + 0.960489i \(0.410223\pi\)
\(458\) 336.899 + 112.351i 0.735587 + 0.245309i
\(459\) 1691.58i 3.68536i
\(460\) −121.673 + 162.136i −0.264505 + 0.352470i
\(461\) −77.6648 −0.168470 −0.0842351 0.996446i \(-0.526845\pi\)
−0.0842351 + 0.996446i \(0.526845\pi\)
\(462\) −160.485 + 481.234i −0.347371 + 1.04163i
\(463\) 543.071i 1.17294i −0.809971 0.586470i \(-0.800517\pi\)
0.809971 0.586470i \(-0.199483\pi\)
\(464\) 60.1295 + 206.584i 0.129589 + 0.445224i
\(465\) −237.046 −0.509777
\(466\) −143.413 47.8265i −0.307754 0.102632i
\(467\) 384.665i 0.823694i −0.911253 0.411847i \(-0.864884\pi\)
0.911253 0.411847i \(-0.135116\pi\)
\(468\) 878.364 + 659.153i 1.87685 + 1.40845i
\(469\) 203.206 0.433275
\(470\) 171.672 514.778i 0.365259 1.09527i
\(471\) 535.172i 1.13625i
\(472\) 658.646 455.581i 1.39544 0.965213i
\(473\) 381.646 0.806862
\(474\) −415.414 138.535i −0.876401 0.292268i
\(475\) 37.2910i 0.0785074i
\(476\) 423.050 563.742i 0.888761 1.18433i
\(477\) 277.566 0.581899
\(478\) −1.26255 + 3.78589i −0.00264131 + 0.00792027i
\(479\) 661.184i 1.38034i −0.723646 0.690171i \(-0.757535\pi\)
0.723646 0.690171i \(-0.242465\pi\)
\(480\) −989.800 38.2738i −2.06208 0.0797372i
\(481\) −352.703 −0.733270
\(482\) 122.669 + 40.9085i 0.254500 + 0.0848724i
\(483\) 274.674i 0.568684i
\(484\) 178.307 + 133.808i 0.368403 + 0.276462i
\(485\) 54.1980 0.111748
\(486\) −102.822 + 308.323i −0.211568 + 0.634410i
\(487\) 626.822i 1.28711i −0.765401 0.643554i \(-0.777459\pi\)
0.765401 0.643554i \(-0.222541\pi\)
\(488\) 141.957 + 205.231i 0.290895 + 0.420555i
\(489\) −1004.16 −2.05350
\(490\) −159.141 53.0715i −0.324778 0.108309i
\(491\) 973.335i 1.98235i 0.132555 + 0.991176i \(0.457682\pi\)
−0.132555 + 0.991176i \(0.542318\pi\)
\(492\) 637.454 849.448i 1.29564 1.72652i
\(493\) 403.293 0.818039
\(494\) 38.7205 116.108i 0.0783815 0.235036i
\(495\) 915.143i 1.84877i
\(496\) 117.645 34.2424i 0.237187 0.0690370i
\(497\) −387.917 −0.780516
\(498\) 890.731 + 297.047i 1.78862 + 0.596481i
\(499\) 171.966i 0.344621i −0.985043 0.172311i \(-0.944877\pi\)
0.985043 0.172311i \(-0.0551233\pi\)
\(500\) −304.768 228.708i −0.609536 0.457416i
\(501\) 129.641 0.258764
\(502\) 155.516 466.333i 0.309793 0.928950i
\(503\) 806.197i 1.60278i 0.598145 + 0.801388i \(0.295905\pi\)
−0.598145 + 0.801388i \(0.704095\pi\)
\(504\) 755.935 522.875i 1.49987 1.03745i
\(505\) −502.136 −0.994329
\(506\) 134.098 + 44.7198i 0.265015 + 0.0883791i
\(507\) 150.208i 0.296268i
\(508\) −535.369 + 713.414i −1.05388 + 1.40436i
\(509\) 944.065 1.85475 0.927373 0.374139i \(-0.122062\pi\)
0.927373 + 0.374139i \(0.122062\pi\)
\(510\) −587.378 + 1761.32i −1.15172 + 3.45357i
\(511\) 161.609i 0.316261i
\(512\) 496.761 123.986i 0.970236 0.242160i
\(513\) 245.857 0.479254
\(514\) −525.268 175.170i −1.02192 0.340798i
\(515\) 808.669i 1.57023i
\(516\) −807.633 606.074i −1.56518 1.17456i
\(517\) −378.405 −0.731925
\(518\) −93.3901 + 280.041i −0.180290 + 0.540620i
\(519\) 1340.05i 2.58198i
\(520\) 370.113 + 535.083i 0.711757 + 1.02901i
\(521\) 168.936 0.324253 0.162126 0.986770i \(-0.448165\pi\)
0.162126 + 0.986770i \(0.448165\pi\)
\(522\) 498.916 + 166.382i 0.955778 + 0.318740i
\(523\) 391.361i 0.748300i −0.927368 0.374150i \(-0.877935\pi\)
0.927368 0.374150i \(-0.122065\pi\)
\(524\) −478.576 + 637.733i −0.913313 + 1.21705i
\(525\) −268.599 −0.511617
\(526\) −60.3712 + 181.030i −0.114774 + 0.344164i
\(527\) 229.666i 0.435799i
\(528\) 193.038 + 663.211i 0.365602 + 1.25608i
\(529\) 452.461 0.855314
\(530\) 155.997 + 52.0230i 0.294334 + 0.0981565i
\(531\) 1957.60i 3.68664i
\(532\) −81.9354 61.4870i −0.154014 0.115577i
\(533\) −697.571 −1.30876
\(534\) −96.8614 + 290.450i −0.181388 + 0.543914i
\(535\) 310.272i 0.579947i
\(536\) 227.557 157.399i 0.424546 0.293656i
\(537\) 333.534 0.621106
\(538\) 244.453 + 81.5220i 0.454374 + 0.151528i
\(539\) 116.982i 0.217036i
\(540\) −784.436 + 1045.31i −1.45266 + 1.93576i
\(541\) −561.849 −1.03854 −0.519269 0.854611i \(-0.673796\pi\)
−0.519269 + 0.854611i \(0.673796\pi\)
\(542\) −200.883 + 602.370i −0.370632 + 1.11138i
\(543\) 356.312i 0.656192i
\(544\) 37.0822 958.984i 0.0681659 1.76284i
\(545\) −895.078 −1.64234
\(546\) −836.299 278.895i −1.53168 0.510797i
\(547\) 630.789i 1.15318i −0.817034 0.576590i \(-0.804383\pi\)
0.817034 0.576590i \(-0.195617\pi\)
\(548\) −19.2417 14.4396i −0.0351125 0.0263496i
\(549\) 609.979 1.11107
\(550\) 43.7307 131.132i 0.0795103 0.238421i
\(551\) 58.6154i 0.106380i
\(552\) −212.758 307.590i −0.385431 0.557228i
\(553\) 240.737 0.435329
\(554\) 55.3834 + 18.4697i 0.0999700 + 0.0333387i
\(555\) 777.638i 1.40115i
\(556\) 185.608 247.334i 0.333827 0.444845i
\(557\) 123.847 0.222346 0.111173 0.993801i \(-0.464539\pi\)
0.111173 + 0.993801i \(0.464539\pi\)
\(558\) 94.7509 284.121i 0.169804 0.509178i
\(559\) 663.232i 1.18646i
\(560\) 522.848 152.183i 0.933658 0.271756i
\(561\) 1294.72 2.30788
\(562\) −388.051 129.410i −0.690483 0.230267i
\(563\) 935.582i 1.66178i 0.556437 + 0.830890i \(0.312168\pi\)
−0.556437 + 0.830890i \(0.687832\pi\)
\(564\) 800.775 + 600.928i 1.41981 + 1.06548i
\(565\) −382.346 −0.676718
\(566\) −317.972 + 953.476i −0.561788 + 1.68459i
\(567\) 736.815i 1.29950i
\(568\) −434.402 + 300.473i −0.764792 + 0.529001i
\(569\) 373.028 0.655586 0.327793 0.944750i \(-0.393695\pi\)
0.327793 + 0.944750i \(0.393695\pi\)
\(570\) 255.994 + 85.3707i 0.449112 + 0.149773i
\(571\) 435.521i 0.762733i 0.924424 + 0.381367i \(0.124546\pi\)
−0.924424 + 0.381367i \(0.875454\pi\)
\(572\) 272.316 362.879i 0.476077 0.634404i
\(573\) 1167.53 2.03757
\(574\) −184.706 + 553.861i −0.321787 + 0.964915i
\(575\) 74.8460i 0.130167i
\(576\) 441.512 1171.07i 0.766514 2.03310i
\(577\) −807.758 −1.39993 −0.699964 0.714178i \(-0.746801\pi\)
−0.699964 + 0.714178i \(0.746801\pi\)
\(578\) −1158.17 386.235i −2.00376 0.668227i
\(579\) 331.034i 0.571735i
\(580\) 249.215 + 187.019i 0.429681 + 0.322447i
\(581\) −516.188 −0.888448
\(582\) −31.6342 + 94.8587i −0.0543542 + 0.162987i
\(583\) 114.671i 0.196691i
\(584\) 125.179 + 180.975i 0.214348 + 0.309889i
\(585\) 1590.36 2.71856
\(586\) −454.519 151.576i −0.775629 0.258662i
\(587\) 311.402i 0.530498i −0.964180 0.265249i \(-0.914546\pi\)
0.964180 0.265249i \(-0.0854542\pi\)
\(588\) 185.774 247.556i 0.315942 0.421013i
\(589\) −33.3802 −0.0566726
\(590\) 366.905 1100.21i 0.621873 1.86476i
\(591\) 1898.87i 3.21298i
\(592\) 112.333 + 385.938i 0.189752 + 0.651922i
\(593\) −1048.73 −1.76851 −0.884255 0.467005i \(-0.845333\pi\)
−0.884255 + 0.467005i \(0.845333\pi\)
\(594\) 864.542 + 288.314i 1.45546 + 0.485377i
\(595\) 1020.70i 1.71547i
\(596\) 803.021 + 602.614i 1.34735 + 1.01110i
\(597\) 1114.01 1.86601
\(598\) −77.7151 + 233.038i −0.129958 + 0.389695i
\(599\) 20.9544i 0.0349822i 0.999847 + 0.0174911i \(0.00556788\pi\)
−0.999847 + 0.0174911i \(0.994432\pi\)
\(600\) −300.786 + 208.052i −0.501310 + 0.346753i
\(601\) 4.04669 0.00673326 0.00336663 0.999994i \(-0.498928\pi\)
0.00336663 + 0.999994i \(0.498928\pi\)
\(602\) 526.597 + 175.613i 0.874745 + 0.291716i
\(603\) 676.336i 1.12162i
\(604\) 148.893 198.410i 0.246512 0.328493i
\(605\) 322.841 0.533621
\(606\) 293.086 878.851i 0.483640 1.45025i
\(607\) 718.845i 1.18426i 0.805843 + 0.592129i \(0.201712\pi\)
−0.805843 + 0.592129i \(0.798288\pi\)
\(608\) −139.381 5.38961i −0.229244 0.00886449i
\(609\) −422.194 −0.693258
\(610\) 342.819 + 114.326i 0.561998 + 0.187419i
\(611\) 657.601i 1.07627i
\(612\) −1876.32 1408.05i −3.06588 2.30074i
\(613\) −568.157 −0.926847 −0.463424 0.886137i \(-0.653379\pi\)
−0.463424 + 0.886137i \(0.653379\pi\)
\(614\) −196.418 + 588.983i −0.319899 + 0.959255i
\(615\) 1538.00i 2.50082i
\(616\) −216.015 312.300i −0.350674 0.506980i
\(617\) 344.297 0.558017 0.279009 0.960289i \(-0.409994\pi\)
0.279009 + 0.960289i \(0.409994\pi\)
\(618\) −1415.35 472.002i −2.29021 0.763757i
\(619\) 269.442i 0.435286i −0.976028 0.217643i \(-0.930163\pi\)
0.976028 0.217643i \(-0.0698368\pi\)
\(620\) 106.503 141.922i 0.171779 0.228907i
\(621\) −493.455 −0.794614
\(622\) −138.915 + 416.552i −0.223336 + 0.669698i
\(623\) 168.319i 0.270175i
\(624\) −1152.54 + 335.466i −1.84702 + 0.537605i
\(625\) −765.688 −1.22510
\(626\) −612.216 204.166i −0.977980 0.326144i
\(627\) 188.177i 0.300123i
\(628\) −320.414 240.449i −0.510213 0.382880i
\(629\) 753.427 1.19782
\(630\) 421.101 1262.72i 0.668414 2.00432i
\(631\) 916.217i 1.45201i −0.687691 0.726004i \(-0.741375\pi\)
0.687691 0.726004i \(-0.258625\pi\)
\(632\) 269.585 186.470i 0.426559 0.295048i
\(633\) −1470.32 −2.32278
\(634\) 101.769 + 33.9387i 0.160519 + 0.0535311i
\(635\) 1291.70i 2.03417i
\(636\) −182.104 + 242.665i −0.286327 + 0.381549i
\(637\) −203.294 −0.319143
\(638\) 68.7375 206.117i 0.107739 0.323068i
\(639\) 1291.11i 2.02052i
\(640\) 467.625 575.408i 0.730664 0.899075i
\(641\) 809.161 1.26234 0.631171 0.775644i \(-0.282575\pi\)
0.631171 + 0.775644i \(0.282575\pi\)
\(642\) 543.045 + 181.099i 0.845864 + 0.282085i
\(643\) 611.403i 0.950859i 0.879754 + 0.475430i \(0.157707\pi\)
−0.879754 + 0.475430i \(0.842293\pi\)
\(644\) 164.451 + 123.409i 0.255358 + 0.191629i
\(645\) −1462.29 −2.26712
\(646\) −82.7128 + 248.024i −0.128038 + 0.383938i
\(647\) 375.179i 0.579875i −0.957046 0.289938i \(-0.906365\pi\)
0.957046 0.289938i \(-0.0936345\pi\)
\(648\) −570.723 825.110i −0.880745 1.27332i
\(649\) −808.746 −1.24614
\(650\) 227.883 + 75.9961i 0.350590 + 0.116917i
\(651\) 240.430i 0.369324i
\(652\) 451.161 601.202i 0.691965 0.922088i
\(653\) 122.859 0.188146 0.0940729 0.995565i \(-0.470011\pi\)
0.0940729 + 0.995565i \(0.470011\pi\)
\(654\) 522.437 1566.59i 0.798833 2.39539i
\(655\) 1154.67i 1.76286i
\(656\) 222.171 + 763.302i 0.338675 + 1.16357i
\(657\) 537.889 0.818704
\(658\) −522.125 174.122i −0.793504 0.264623i
\(659\) 104.791i 0.159015i −0.996834 0.0795074i \(-0.974665\pi\)
0.996834 0.0795074i \(-0.0253347\pi\)
\(660\) 800.073 + 600.401i 1.21223 + 0.909699i
\(661\) −1185.52 −1.79352 −0.896762 0.442514i \(-0.854087\pi\)
−0.896762 + 0.442514i \(0.854087\pi\)
\(662\) 104.461 313.237i 0.157795 0.473168i
\(663\) 2249.99i 3.39366i
\(664\) −578.045 + 399.830i −0.870549 + 0.602153i
\(665\) −148.351 −0.223085
\(666\) 932.069 + 310.833i 1.39950 + 0.466716i
\(667\) 117.646i 0.176381i
\(668\) −58.2466 + 77.6173i −0.0871955 + 0.116194i
\(669\) 1271.33 1.90034
\(670\) 126.763 380.113i 0.189198 0.567332i
\(671\) 252.001i 0.375560i
\(672\) −38.8202 + 1003.93i −0.0577681 + 1.49394i
\(673\) 86.7624 0.128919 0.0644594 0.997920i \(-0.479468\pi\)
0.0644594 + 0.997920i \(0.479468\pi\)
\(674\) 709.983 + 236.770i 1.05339 + 0.351291i
\(675\) 482.541i 0.714875i
\(676\) 89.9310 + 67.4872i 0.133034 + 0.0998332i
\(677\) −566.786 −0.837202 −0.418601 0.908170i \(-0.637479\pi\)
−0.418601 + 0.908170i \(0.637479\pi\)
\(678\) 223.167 669.191i 0.329154 0.987007i
\(679\) 54.9716i 0.0809597i
\(680\) −790.618 1143.02i −1.16267 1.68091i
\(681\) −839.317 −1.23248
\(682\) −117.379 39.1445i −0.172110 0.0573966i
\(683\) 192.839i 0.282341i −0.989985 0.141170i \(-0.954913\pi\)
0.989985 0.141170i \(-0.0450865\pi\)
\(684\) −204.649 + 272.708i −0.299194 + 0.398696i
\(685\) −34.8387 −0.0508595
\(686\) −235.984 + 707.626i −0.344000 + 1.03152i
\(687\) 948.878i 1.38119i
\(688\) 725.727 211.234i 1.05484 0.307026i
\(689\) 199.278 0.289227
\(690\) −513.800 171.346i −0.744638 0.248327i
\(691\) 639.216i 0.925059i 0.886604 + 0.462530i \(0.153058\pi\)
−0.886604 + 0.462530i \(0.846942\pi\)
\(692\) −802.301 602.073i −1.15939 0.870048i
\(693\) −928.206 −1.33940
\(694\) 280.111 839.945i 0.403618 1.21029i
\(695\) 447.820i 0.644346i
\(696\) −472.787 + 327.024i −0.679292 + 0.469861i
\(697\) 1490.12 2.13790
\(698\) 309.946 + 103.363i 0.444049 + 0.148085i
\(699\) 403.925i 0.577861i
\(700\) 120.680 160.813i 0.172399 0.229733i
\(701\) 109.111 0.155650 0.0778250 0.996967i \(-0.475202\pi\)
0.0778250 + 0.996967i \(0.475202\pi\)
\(702\) −501.038 + 1502.42i −0.713729 + 2.14020i
\(703\) 109.505i 0.155768i
\(704\) −483.803 182.402i −0.687220 0.259094i
\(705\) 1449.88 2.05656
\(706\) −778.398 259.586i −1.10255 0.367685i
\(707\) 509.304i 0.720373i
\(708\) 1711.46 + 1284.33i 2.41731 + 1.81403i
\(709\) 1381.83 1.94898 0.974489 0.224434i \(-0.0720532\pi\)
0.974489 + 0.224434i \(0.0720532\pi\)
\(710\) −241.988 + 725.628i −0.340828 + 1.02201i
\(711\) 801.251i 1.12694i
\(712\) −130.377 188.489i −0.183113 0.264732i
\(713\) 66.9966 0.0939644
\(714\) 1786.46 + 595.762i 2.50205 + 0.834401i
\(715\) 657.024i 0.918915i
\(716\) −149.854 + 199.690i −0.209294 + 0.278897i
\(717\) −10.6630 −0.0148717
\(718\) 78.8062 236.309i 0.109758 0.329122i
\(719\) 844.528i 1.17459i −0.809374 0.587293i \(-0.800194\pi\)
0.809374 0.587293i \(-0.199806\pi\)
\(720\) −506.516 1740.21i −0.703494 2.41696i
\(721\) 820.211 1.13760
\(722\) 36.0483 + 12.0216i 0.0499284 + 0.0166505i
\(723\) 345.498i 0.477867i
\(724\) −213.328 160.088i −0.294652 0.221117i
\(725\) 115.044 0.158681
\(726\) −188.435 + 565.044i −0.259552 + 0.778298i
\(727\) 926.186i 1.27398i 0.770871 + 0.636992i \(0.219821\pi\)
−0.770871 + 0.636992i \(0.780179\pi\)
\(728\) 542.721 375.396i 0.745496 0.515654i
\(729\) 260.272 0.357026
\(730\) 302.303 + 100.814i 0.414113 + 0.138102i
\(731\) 1416.76i 1.93812i
\(732\) −400.191 + 533.281i −0.546710 + 0.728526i
\(733\) 108.418 0.147910 0.0739551 0.997262i \(-0.476438\pi\)
0.0739551 + 0.997262i \(0.476438\pi\)
\(734\) −182.697 + 547.837i −0.248906 + 0.746372i
\(735\) 448.222i 0.609826i
\(736\) 279.748 + 10.8174i 0.380092 + 0.0146975i
\(737\) −279.415 −0.379125
\(738\) 1843.43 + 614.761i 2.49788 + 0.833010i
\(739\) 209.058i 0.282893i 0.989946 + 0.141447i \(0.0451753\pi\)
−0.989946 + 0.141447i \(0.954825\pi\)
\(740\) 465.581 + 349.387i 0.629163 + 0.472145i
\(741\) 327.019 0.441321
\(742\) 52.7655 158.224i 0.0711126 0.213239i
\(743\) 862.421i 1.16073i −0.814357 0.580364i \(-0.802910\pi\)
0.814357 0.580364i \(-0.197090\pi\)
\(744\) 186.233 + 269.242i 0.250313 + 0.361884i
\(745\) 1453.94 1.95160
\(746\) −722.371 240.901i −0.968325 0.322924i
\(747\) 1718.04i 2.29993i
\(748\) −581.709 + 775.164i −0.777685 + 1.03632i
\(749\) −314.700 −0.420161
\(750\) 322.079 965.791i 0.429438 1.28772i
\(751\) 167.423i 0.222933i 0.993768 + 0.111467i \(0.0355548\pi\)
−0.993768 + 0.111467i \(0.964445\pi\)
\(752\) −719.565 + 209.441i −0.956869 + 0.278512i
\(753\) 1313.43 1.74426
\(754\) 358.195 + 119.454i 0.475060 + 0.158426i
\(755\) 359.238i 0.475812i
\(756\) 1060.23 + 795.633i 1.40242 + 1.05243i
\(757\) 347.592 0.459171 0.229586 0.973288i \(-0.426263\pi\)
0.229586 + 0.973288i \(0.426263\pi\)
\(758\) 111.590 334.615i 0.147216 0.441445i
\(759\) 377.687i 0.497611i
\(760\) −166.129 + 114.910i −0.218590 + 0.151197i
\(761\) 1395.24 1.83343 0.916714 0.399544i \(-0.130832\pi\)
0.916714 + 0.399544i \(0.130832\pi\)
\(762\) −2260.76 753.936i −2.96688 0.989417i
\(763\) 907.854i 1.18985i
\(764\) −524.562 + 699.012i −0.686599 + 0.914937i
\(765\) −3397.24 −4.44084
\(766\) −246.756 + 739.925i −0.322135 + 0.965960i
\(767\) 1405.46i 1.83241i
\(768\) 734.152 + 1154.30i 0.955926 + 1.50300i
\(769\) 1104.80 1.43667 0.718333 0.695700i \(-0.244906\pi\)
0.718333 + 0.695700i \(0.244906\pi\)
\(770\) −521.668 173.970i −0.677490 0.225934i
\(771\) 1479.42i 1.91883i
\(772\) 198.194 + 148.731i 0.256728 + 0.192657i
\(773\) −1508.32 −1.95125 −0.975627 0.219436i \(-0.929578\pi\)
−0.975627 + 0.219436i \(0.929578\pi\)
\(774\) 584.499 1752.69i 0.755166 2.26445i
\(775\) 65.5148i 0.0845352i
\(776\) −42.5800 61.5591i −0.0548711 0.0793287i
\(777\) −788.738 −1.01511
\(778\) −9.64539 3.21661i −0.0123977 0.00413447i
\(779\) 216.577i 0.278019i
\(780\)