Properties

Label 105.3.h.a.76.8
Level 105
Weight 3
Character 105.76
Analytic conductor 2.861
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.8
Root \(-1.74681 - 3.02556i\) of \(x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} - 5472 x^{3} + 4950 x^{2} - 1638 x + 441\)
Character \(\chi\) \(=\) 105.76
Dual form 105.3.h.a.76.7

$q$-expansion

\(f(q)\) \(=\) \(q-0.112974 q^{2} +1.73205i q^{3} -3.98724 q^{4} +2.23607i q^{5} -0.195676i q^{6} +(-6.71303 - 1.98374i) q^{7} +0.902349 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-0.112974 q^{2} +1.73205i q^{3} -3.98724 q^{4} +2.23607i q^{5} -0.195676i q^{6} +(-6.71303 - 1.98374i) q^{7} +0.902349 q^{8} -3.00000 q^{9} -0.252617i q^{10} -15.8613 q^{11} -6.90610i q^{12} +13.3044i q^{13} +(0.758397 + 0.224110i) q^{14} -3.87298 q^{15} +15.8470 q^{16} -15.6784i q^{17} +0.338921 q^{18} +30.8816i q^{19} -8.91573i q^{20} +(3.43593 - 11.6273i) q^{21} +1.79192 q^{22} +3.63638 q^{23} +1.56291i q^{24} -5.00000 q^{25} -1.50305i q^{26} -5.19615i q^{27} +(26.7664 + 7.90963i) q^{28} +14.5640 q^{29} +0.437546 q^{30} +11.3504i q^{31} -5.39969 q^{32} -27.4726i q^{33} +1.77125i q^{34} +(4.43577 - 15.0108i) q^{35} +11.9617 q^{36} +17.3820 q^{37} -3.48881i q^{38} -23.0439 q^{39} +2.01771i q^{40} +27.9286i q^{41} +(-0.388171 + 1.31358i) q^{42} -12.1944 q^{43} +63.2429 q^{44} -6.70820i q^{45} -0.410816 q^{46} -80.5893i q^{47} +27.4478i q^{48} +(41.1296 + 26.6338i) q^{49} +0.564869 q^{50} +27.1557 q^{51} -53.0477i q^{52} -55.9152 q^{53} +0.587029i q^{54} -35.4670i q^{55} +(-6.05750 - 1.79002i) q^{56} -53.4885 q^{57} -1.64536 q^{58} +79.5439i q^{59} +15.4425 q^{60} +94.5743i q^{61} -1.28230i q^{62} +(20.1391 + 5.95121i) q^{63} -62.7780 q^{64} -29.7495 q^{65} +3.10369i q^{66} -103.457 q^{67} +62.5134i q^{68} +6.29840i q^{69} +(-0.501126 + 1.69583i) q^{70} -113.803 q^{71} -2.70705 q^{72} -20.3444i q^{73} -1.96371 q^{74} -8.66025i q^{75} -123.132i q^{76} +(106.478 + 31.4647i) q^{77} +2.60336 q^{78} -1.27532 q^{79} +35.4350i q^{80} +9.00000 q^{81} -3.15520i q^{82} +19.7667i q^{83} +(-13.6999 + 46.3608i) q^{84} +35.0579 q^{85} +1.37765 q^{86} +25.2257i q^{87} -14.3125 q^{88} -131.258i q^{89} +0.757851i q^{90} +(26.3924 - 89.3128i) q^{91} -14.4991 q^{92} -19.6595 q^{93} +9.10448i q^{94} -69.0533 q^{95} -9.35254i q^{96} +12.4236i q^{97} +(-4.64657 - 3.00892i) q^{98} +47.5840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10}) \) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} - 16q^{11} - 40q^{14} + 92q^{16} + 12q^{18} + 36q^{21} - 88q^{22} - 64q^{23} - 60q^{25} + 88q^{28} + 104q^{29} - 228q^{32} + 60q^{35} - 132q^{36} + 32q^{37} - 24q^{39} - 60q^{42} + 152q^{43} + 192q^{44} + 200q^{46} + 60q^{49} + 20q^{50} + 24q^{51} + 176q^{53} - 368q^{56} - 240q^{57} - 400q^{58} + 24q^{63} - 20q^{64} - 240q^{65} + 168q^{67} - 60q^{70} + 32q^{71} - 12q^{72} + 184q^{74} + 8q^{77} + 456q^{78} + 120q^{79} + 108q^{81} + 108q^{84} + 120q^{85} + 400q^{86} - 536q^{88} + 24q^{91} + 192q^{92} + 48q^{93} + 884q^{98} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.112974 −0.0564869 −0.0282435 0.999601i \(-0.508991\pi\)
−0.0282435 + 0.999601i \(0.508991\pi\)
\(3\) 1.73205i 0.577350i
\(4\) −3.98724 −0.996809
\(5\) 2.23607i 0.447214i
\(6\) 0.195676i 0.0326127i
\(7\) −6.71303 1.98374i −0.959004 0.283391i
\(8\) 0.902349 0.112794
\(9\) −3.00000 −0.333333
\(10\) 0.252617i 0.0252617i
\(11\) −15.8613 −1.44194 −0.720970 0.692966i \(-0.756303\pi\)
−0.720970 + 0.692966i \(0.756303\pi\)
\(12\) 6.90610i 0.575508i
\(13\) 13.3044i 1.02341i 0.859160 + 0.511707i \(0.170987\pi\)
−0.859160 + 0.511707i \(0.829013\pi\)
\(14\) 0.758397 + 0.224110i 0.0541712 + 0.0160079i
\(15\) −3.87298 −0.258199
\(16\) 15.8470 0.990438
\(17\) 15.6784i 0.922257i −0.887333 0.461129i \(-0.847445\pi\)
0.887333 0.461129i \(-0.152555\pi\)
\(18\) 0.338921 0.0188290
\(19\) 30.8816i 1.62535i 0.582719 + 0.812673i \(0.301989\pi\)
−0.582719 + 0.812673i \(0.698011\pi\)
\(20\) 8.91573i 0.445787i
\(21\) 3.43593 11.6273i 0.163616 0.553681i
\(22\) 1.79192 0.0814507
\(23\) 3.63638 0.158104 0.0790518 0.996871i \(-0.474811\pi\)
0.0790518 + 0.996871i \(0.474811\pi\)
\(24\) 1.56291i 0.0651214i
\(25\) −5.00000 −0.200000
\(26\) 1.50305i 0.0578095i
\(27\) 5.19615i 0.192450i
\(28\) 26.7664 + 7.90963i 0.955944 + 0.282487i
\(29\) 14.5640 0.502208 0.251104 0.967960i \(-0.419206\pi\)
0.251104 + 0.967960i \(0.419206\pi\)
\(30\) 0.437546 0.0145849
\(31\) 11.3504i 0.366142i 0.983100 + 0.183071i \(0.0586038\pi\)
−0.983100 + 0.183071i \(0.941396\pi\)
\(32\) −5.39969 −0.168740
\(33\) 27.4726i 0.832504i
\(34\) 1.77125i 0.0520955i
\(35\) 4.43577 15.0108i 0.126736 0.428880i
\(36\) 11.9617 0.332270
\(37\) 17.3820 0.469784 0.234892 0.972021i \(-0.424526\pi\)
0.234892 + 0.972021i \(0.424526\pi\)
\(38\) 3.48881i 0.0918108i
\(39\) −23.0439 −0.590869
\(40\) 2.01771i 0.0504428i
\(41\) 27.9286i 0.681186i 0.940211 + 0.340593i \(0.110628\pi\)
−0.940211 + 0.340593i \(0.889372\pi\)
\(42\) −0.388171 + 1.31358i −0.00924216 + 0.0312758i
\(43\) −12.1944 −0.283591 −0.141796 0.989896i \(-0.545288\pi\)
−0.141796 + 0.989896i \(0.545288\pi\)
\(44\) 63.2429 1.43734
\(45\) 6.70820i 0.149071i
\(46\) −0.410816 −0.00893078
\(47\) 80.5893i 1.71467i −0.514762 0.857333i \(-0.672120\pi\)
0.514762 0.857333i \(-0.327880\pi\)
\(48\) 27.4478i 0.571830i
\(49\) 41.1296 + 26.6338i 0.839379 + 0.543546i
\(50\) 0.564869 0.0112974
\(51\) 27.1557 0.532465
\(52\) 53.0477i 1.02015i
\(53\) −55.9152 −1.05500 −0.527502 0.849554i \(-0.676871\pi\)
−0.527502 + 0.849554i \(0.676871\pi\)
\(54\) 0.587029i 0.0108709i
\(55\) 35.4670i 0.644855i
\(56\) −6.05750 1.79002i −0.108170 0.0319647i
\(57\) −53.4885 −0.938395
\(58\) −1.64536 −0.0283682
\(59\) 79.5439i 1.34820i 0.738640 + 0.674101i \(0.235469\pi\)
−0.738640 + 0.674101i \(0.764531\pi\)
\(60\) 15.4425 0.257375
\(61\) 94.5743i 1.55040i 0.631717 + 0.775199i \(0.282350\pi\)
−0.631717 + 0.775199i \(0.717650\pi\)
\(62\) 1.28230i 0.0206822i
\(63\) 20.1391 + 5.95121i 0.319668 + 0.0944637i
\(64\) −62.7780 −0.980906
\(65\) −29.7495 −0.457685
\(66\) 3.10369i 0.0470256i
\(67\) −103.457 −1.54414 −0.772068 0.635540i \(-0.780778\pi\)
−0.772068 + 0.635540i \(0.780778\pi\)
\(68\) 62.5134i 0.919314i
\(69\) 6.29840i 0.0912811i
\(70\) −0.501126 + 1.69583i −0.00715894 + 0.0242261i
\(71\) −113.803 −1.60286 −0.801431 0.598087i \(-0.795928\pi\)
−0.801431 + 0.598087i \(0.795928\pi\)
\(72\) −2.70705 −0.0375979
\(73\) 20.3444i 0.278690i −0.990244 0.139345i \(-0.955500\pi\)
0.990244 0.139345i \(-0.0444998\pi\)
\(74\) −1.96371 −0.0265367
\(75\) 8.66025i 0.115470i
\(76\) 123.132i 1.62016i
\(77\) 106.478 + 31.4647i 1.38283 + 0.408633i
\(78\) 2.60336 0.0333763
\(79\) −1.27532 −0.0161433 −0.00807165 0.999967i \(-0.502569\pi\)
−0.00807165 + 0.999967i \(0.502569\pi\)
\(80\) 35.4350i 0.442937i
\(81\) 9.00000 0.111111
\(82\) 3.15520i 0.0384781i
\(83\) 19.7667i 0.238153i 0.992885 + 0.119076i \(0.0379934\pi\)
−0.992885 + 0.119076i \(0.962007\pi\)
\(84\) −13.6999 + 46.3608i −0.163094 + 0.551915i
\(85\) 35.0579 0.412446
\(86\) 1.37765 0.0160192
\(87\) 25.2257i 0.289950i
\(88\) −14.3125 −0.162642
\(89\) 131.258i 1.47481i −0.675450 0.737406i \(-0.736051\pi\)
0.675450 0.737406i \(-0.263949\pi\)
\(90\) 0.757851i 0.00842057i
\(91\) 26.3924 89.3128i 0.290026 0.981459i
\(92\) −14.4991 −0.157599
\(93\) −19.6595 −0.211392
\(94\) 9.10448i 0.0968562i
\(95\) −69.0533 −0.726877
\(96\) 9.35254i 0.0974223i
\(97\) 12.4236i 0.128078i 0.997947 + 0.0640391i \(0.0203982\pi\)
−0.997947 + 0.0640391i \(0.979602\pi\)
\(98\) −4.64657 3.00892i −0.0474139 0.0307033i
\(99\) 47.5840 0.480647
\(100\) 19.9362 0.199362
\(101\) 15.0668i 0.149176i −0.997214 0.0745882i \(-0.976236\pi\)
0.997214 0.0745882i \(-0.0237642\pi\)
\(102\) −3.06789 −0.0300773
\(103\) 69.5863i 0.675595i 0.941219 + 0.337798i \(0.109682\pi\)
−0.941219 + 0.337798i \(0.890318\pi\)
\(104\) 12.0052i 0.115435i
\(105\) 25.9995 + 7.68298i 0.247614 + 0.0731712i
\(106\) 6.31696 0.0595939
\(107\) 104.493 0.976569 0.488285 0.872684i \(-0.337623\pi\)
0.488285 + 0.872684i \(0.337623\pi\)
\(108\) 20.7183i 0.191836i
\(109\) −19.2137 −0.176273 −0.0881363 0.996108i \(-0.528091\pi\)
−0.0881363 + 0.996108i \(0.528091\pi\)
\(110\) 4.00685i 0.0364259i
\(111\) 30.1065i 0.271230i
\(112\) −106.381 31.4363i −0.949834 0.280681i
\(113\) 208.552 1.84559 0.922795 0.385291i \(-0.125899\pi\)
0.922795 + 0.385291i \(0.125899\pi\)
\(114\) 6.04280 0.0530070
\(115\) 8.13119i 0.0707060i
\(116\) −58.0703 −0.500606
\(117\) 39.9132i 0.341138i
\(118\) 8.98637i 0.0761557i
\(119\) −31.1018 + 105.249i −0.261359 + 0.884449i
\(120\) −3.49478 −0.0291232
\(121\) 130.582 1.07919
\(122\) 10.6844i 0.0875772i
\(123\) −48.3738 −0.393283
\(124\) 45.2567i 0.364974i
\(125\) 11.1803i 0.0894427i
\(126\) −2.27519 0.672331i −0.0180571 0.00533596i
\(127\) 65.1002 0.512600 0.256300 0.966597i \(-0.417496\pi\)
0.256300 + 0.966597i \(0.417496\pi\)
\(128\) 28.6910 0.224149
\(129\) 21.1213i 0.163731i
\(130\) 3.36092 0.0258532
\(131\) 160.360i 1.22412i 0.790812 + 0.612060i \(0.209659\pi\)
−0.790812 + 0.612060i \(0.790341\pi\)
\(132\) 109.540i 0.829848i
\(133\) 61.2610 207.309i 0.460609 1.55871i
\(134\) 11.6879 0.0872235
\(135\) 11.6190 0.0860663
\(136\) 14.1474i 0.104025i
\(137\) 158.451 1.15658 0.578289 0.815832i \(-0.303721\pi\)
0.578289 + 0.815832i \(0.303721\pi\)
\(138\) 0.711554i 0.00515619i
\(139\) 243.471i 1.75159i −0.482684 0.875794i \(-0.660338\pi\)
0.482684 0.875794i \(-0.339662\pi\)
\(140\) −17.6865 + 59.8516i −0.126332 + 0.427511i
\(141\) 139.585 0.989963
\(142\) 12.8568 0.0905408
\(143\) 211.025i 1.47570i
\(144\) −47.5410 −0.330146
\(145\) 32.5662i 0.224594i
\(146\) 2.29838i 0.0157424i
\(147\) −46.1311 + 71.2385i −0.313817 + 0.484616i
\(148\) −69.3062 −0.468285
\(149\) −134.390 −0.901948 −0.450974 0.892537i \(-0.648923\pi\)
−0.450974 + 0.892537i \(0.648923\pi\)
\(150\) 0.978382i 0.00652255i
\(151\) 1.60056 0.0105997 0.00529987 0.999986i \(-0.498313\pi\)
0.00529987 + 0.999986i \(0.498313\pi\)
\(152\) 27.8660i 0.183329i
\(153\) 47.0351i 0.307419i
\(154\) −12.0292 3.55469i −0.0781116 0.0230824i
\(155\) −25.3803 −0.163744
\(156\) 91.8814 0.588983
\(157\) 252.462i 1.60804i 0.594602 + 0.804020i \(0.297310\pi\)
−0.594602 + 0.804020i \(0.702690\pi\)
\(158\) 0.144078 0.000911885
\(159\) 96.8480i 0.609107i
\(160\) 12.0741i 0.0754630i
\(161\) −24.4111 7.21362i −0.151622 0.0448051i
\(162\) −1.01676 −0.00627632
\(163\) −239.023 −1.46640 −0.733199 0.680014i \(-0.761974\pi\)
−0.733199 + 0.680014i \(0.761974\pi\)
\(164\) 111.358i 0.679013i
\(165\) 61.4307 0.372307
\(166\) 2.23312i 0.0134525i
\(167\) 170.456i 1.02070i 0.859968 + 0.510348i \(0.170483\pi\)
−0.859968 + 0.510348i \(0.829517\pi\)
\(168\) 3.10041 10.4919i 0.0184548 0.0624517i
\(169\) −8.00675 −0.0473772
\(170\) −3.96063 −0.0232978
\(171\) 92.6448i 0.541782i
\(172\) 48.6220 0.282686
\(173\) 269.554i 1.55812i −0.626952 0.779058i \(-0.715698\pi\)
0.626952 0.779058i \(-0.284302\pi\)
\(174\) 2.84984i 0.0163784i
\(175\) 33.5652 + 9.91868i 0.191801 + 0.0566782i
\(176\) −251.355 −1.42815
\(177\) −137.774 −0.778384
\(178\) 14.8287i 0.0833076i
\(179\) 132.675 0.741199 0.370599 0.928793i \(-0.379152\pi\)
0.370599 + 0.928793i \(0.379152\pi\)
\(180\) 26.7472i 0.148596i
\(181\) 231.384i 1.27836i 0.769056 + 0.639182i \(0.220727\pi\)
−0.769056 + 0.639182i \(0.779273\pi\)
\(182\) −2.98165 + 10.0900i −0.0163827 + 0.0554396i
\(183\) −163.807 −0.895123
\(184\) 3.28128 0.0178331
\(185\) 38.8674i 0.210094i
\(186\) 2.22101 0.0119409
\(187\) 248.680i 1.32984i
\(188\) 321.329i 1.70920i
\(189\) −10.3078 + 34.8819i −0.0545386 + 0.184560i
\(190\) 7.80122 0.0410591
\(191\) −304.129 −1.59230 −0.796150 0.605099i \(-0.793133\pi\)
−0.796150 + 0.605099i \(0.793133\pi\)
\(192\) 108.735i 0.566326i
\(193\) 138.227 0.716202 0.358101 0.933683i \(-0.383424\pi\)
0.358101 + 0.933683i \(0.383424\pi\)
\(194\) 1.40354i 0.00723474i
\(195\) 51.5277i 0.264244i
\(196\) −163.993 106.195i −0.836701 0.541812i
\(197\) −26.9115 −0.136607 −0.0683034 0.997665i \(-0.521759\pi\)
−0.0683034 + 0.997665i \(0.521759\pi\)
\(198\) −5.37575 −0.0271502
\(199\) 251.997i 1.26632i 0.774023 + 0.633158i \(0.218241\pi\)
−0.774023 + 0.633158i \(0.781759\pi\)
\(200\) −4.51174 −0.0225587
\(201\) 179.193i 0.891507i
\(202\) 1.70216i 0.00842651i
\(203\) −97.7689 28.8912i −0.481620 0.142321i
\(204\) −108.276 −0.530766
\(205\) −62.4503 −0.304636
\(206\) 7.86143i 0.0381623i
\(207\) −10.9091 −0.0527012
\(208\) 210.835i 1.01363i
\(209\) 489.823i 2.34365i
\(210\) −2.93726 0.867976i −0.0139869 0.00413322i
\(211\) 235.692 1.11702 0.558511 0.829497i \(-0.311373\pi\)
0.558511 + 0.829497i \(0.311373\pi\)
\(212\) 222.947 1.05164
\(213\) 197.113i 0.925413i
\(214\) −11.8050 −0.0551634
\(215\) 27.2675i 0.126826i
\(216\) 4.68874i 0.0217071i
\(217\) 22.5162 76.1956i 0.103761 0.351132i
\(218\) 2.17065 0.00995709
\(219\) 35.2375 0.160902
\(220\) 141.415i 0.642797i
\(221\) 208.591 0.943851
\(222\) 3.40125i 0.0153210i
\(223\) 142.790i 0.640314i 0.947365 + 0.320157i \(0.103736\pi\)
−0.947365 + 0.320157i \(0.896264\pi\)
\(224\) 36.2483 + 10.7116i 0.161823 + 0.0478195i
\(225\) 15.0000 0.0666667
\(226\) −23.5609 −0.104252
\(227\) 30.6210i 0.134894i −0.997723 0.0674472i \(-0.978515\pi\)
0.997723 0.0674472i \(-0.0214854\pi\)
\(228\) 213.271 0.935400
\(229\) 210.682i 0.920007i 0.887917 + 0.460004i \(0.152152\pi\)
−0.887917 + 0.460004i \(0.847848\pi\)
\(230\) 0.918612i 0.00399397i
\(231\) −54.4985 + 184.425i −0.235924 + 0.798375i
\(232\) 13.1418 0.0566459
\(233\) −182.891 −0.784940 −0.392470 0.919765i \(-0.628379\pi\)
−0.392470 + 0.919765i \(0.628379\pi\)
\(234\) 4.50914i 0.0192698i
\(235\) 180.203 0.766822
\(236\) 317.160i 1.34390i
\(237\) 2.20892i 0.00932034i
\(238\) 3.51369 11.8904i 0.0147634 0.0499598i
\(239\) 122.511 0.512597 0.256299 0.966598i \(-0.417497\pi\)
0.256299 + 0.966598i \(0.417497\pi\)
\(240\) −61.3752 −0.255730
\(241\) 149.941i 0.622160i −0.950384 0.311080i \(-0.899309\pi\)
0.950384 0.311080i \(-0.100691\pi\)
\(242\) −14.7524 −0.0609601
\(243\) 15.5885i 0.0641500i
\(244\) 377.090i 1.54545i
\(245\) −59.5549 + 91.9685i −0.243081 + 0.375382i
\(246\) 5.46497 0.0222153
\(247\) −410.861 −1.66340
\(248\) 10.2420i 0.0412985i
\(249\) −34.2369 −0.137498
\(250\) 1.26309i 0.00505234i
\(251\) 229.388i 0.913896i 0.889493 + 0.456948i \(0.151058\pi\)
−0.889493 + 0.456948i \(0.848942\pi\)
\(252\) −80.2993 23.7289i −0.318648 0.0941622i
\(253\) −57.6779 −0.227976
\(254\) −7.35462 −0.0289552
\(255\) 60.7221i 0.238126i
\(256\) 247.871 0.968245
\(257\) 48.6524i 0.189309i 0.995510 + 0.0946545i \(0.0301746\pi\)
−0.995510 + 0.0946545i \(0.969825\pi\)
\(258\) 2.38616i 0.00924868i
\(259\) −116.686 34.4814i −0.450525 0.133133i
\(260\) 118.618 0.456225
\(261\) −43.6921 −0.167403
\(262\) 18.1164i 0.0691467i
\(263\) −37.6942 −0.143324 −0.0716620 0.997429i \(-0.522830\pi\)
−0.0716620 + 0.997429i \(0.522830\pi\)
\(264\) 24.7899i 0.0939012i
\(265\) 125.030i 0.471812i
\(266\) −6.92088 + 23.4205i −0.0260184 + 0.0880470i
\(267\) 227.346 0.851483
\(268\) 412.508 1.53921
\(269\) 291.724i 1.08448i 0.840225 + 0.542238i \(0.182423\pi\)
−0.840225 + 0.542238i \(0.817577\pi\)
\(270\) −1.31264 −0.00486162
\(271\) 102.880i 0.379631i 0.981820 + 0.189815i \(0.0607890\pi\)
−0.981820 + 0.189815i \(0.939211\pi\)
\(272\) 248.455i 0.913438i
\(273\) 154.694 + 45.7130i 0.566646 + 0.167447i
\(274\) −17.9008 −0.0653316
\(275\) 79.3067 0.288388
\(276\) 25.1132i 0.0909898i
\(277\) 381.417 1.37696 0.688479 0.725256i \(-0.258279\pi\)
0.688479 + 0.725256i \(0.258279\pi\)
\(278\) 27.5058i 0.0989418i
\(279\) 34.0512i 0.122047i
\(280\) 4.00261 13.5450i 0.0142950 0.0483749i
\(281\) 17.4853 0.0622251 0.0311126 0.999516i \(-0.490095\pi\)
0.0311126 + 0.999516i \(0.490095\pi\)
\(282\) −15.7694 −0.0559200
\(283\) 343.358i 1.21328i −0.794977 0.606640i \(-0.792517\pi\)
0.794977 0.606640i \(-0.207483\pi\)
\(284\) 453.760 1.59775
\(285\) 119.604i 0.419663i
\(286\) 23.8403i 0.0833579i
\(287\) 55.4031 187.486i 0.193042 0.653260i
\(288\) 16.1991 0.0562468
\(289\) 43.1887 0.149442
\(290\) 3.67913i 0.0126866i
\(291\) −21.5183 −0.0739460
\(292\) 81.1179i 0.277801i
\(293\) 244.504i 0.834486i 0.908795 + 0.417243i \(0.137004\pi\)
−0.908795 + 0.417243i \(0.862996\pi\)
\(294\) 5.21160 8.04809i 0.0177265 0.0273744i
\(295\) −177.865 −0.602934
\(296\) 15.6846 0.0529887
\(297\) 82.4179i 0.277501i
\(298\) 15.1826 0.0509482
\(299\) 48.3798i 0.161805i
\(300\) 34.5305i 0.115102i
\(301\) 81.8615 + 24.1905i 0.271965 + 0.0803672i
\(302\) −0.180822 −0.000598747
\(303\) 26.0965 0.0861270
\(304\) 489.381i 1.60981i
\(305\) −211.475 −0.693359
\(306\) 5.31374i 0.0173652i
\(307\) 347.793i 1.13287i −0.824105 0.566437i \(-0.808321\pi\)
0.824105 0.566437i \(-0.191679\pi\)
\(308\) −424.552 125.457i −1.37841 0.407329i
\(309\) −120.527 −0.390055
\(310\) 2.86731 0.00924938
\(311\) 105.360i 0.338778i −0.985549 0.169389i \(-0.945821\pi\)
0.985549 0.169389i \(-0.0541794\pi\)
\(312\) −20.7936 −0.0666462
\(313\) 165.880i 0.529967i 0.964253 + 0.264984i \(0.0853666\pi\)
−0.964253 + 0.264984i \(0.914633\pi\)
\(314\) 28.5216i 0.0908333i
\(315\) −13.3073 + 45.0324i −0.0422454 + 0.142960i
\(316\) 5.08500 0.0160918
\(317\) −96.7933 −0.305342 −0.152671 0.988277i \(-0.548787\pi\)
−0.152671 + 0.988277i \(0.548787\pi\)
\(318\) 10.9413i 0.0344066i
\(319\) −231.005 −0.724154
\(320\) 140.376i 0.438675i
\(321\) 180.987i 0.563823i
\(322\) 2.75782 + 0.814951i 0.00856466 + 0.00253090i
\(323\) 484.173 1.49899
\(324\) −35.8851 −0.110757
\(325\) 66.5219i 0.204683i
\(326\) 27.0033 0.0828323
\(327\) 33.2791i 0.101771i
\(328\) 25.2014i 0.0768334i
\(329\) −159.868 + 540.999i −0.485921 + 1.64437i
\(330\) −6.94006 −0.0210305
\(331\) −193.682 −0.585141 −0.292571 0.956244i \(-0.594511\pi\)
−0.292571 + 0.956244i \(0.594511\pi\)
\(332\) 78.8145i 0.237393i
\(333\) −52.1461 −0.156595
\(334\) 19.2571i 0.0576559i
\(335\) 231.337i 0.690559i
\(336\) 54.4493 184.258i 0.162051 0.548387i
\(337\) −238.742 −0.708433 −0.354216 0.935163i \(-0.615252\pi\)
−0.354216 + 0.935163i \(0.615252\pi\)
\(338\) 0.904554 0.00267619
\(339\) 361.222i 1.06555i
\(340\) −139.784 −0.411130
\(341\) 180.033i 0.527955i
\(342\) 10.4664i 0.0306036i
\(343\) −223.270 260.384i −0.650932 0.759136i
\(344\) −11.0036 −0.0319873
\(345\) −14.0836 −0.0408222
\(346\) 30.4526i 0.0880132i
\(347\) −533.787 −1.53829 −0.769145 0.639074i \(-0.779318\pi\)
−0.769145 + 0.639074i \(0.779318\pi\)
\(348\) 100.581i 0.289025i
\(349\) 230.498i 0.660454i −0.943902 0.330227i \(-0.892875\pi\)
0.943902 0.330227i \(-0.107125\pi\)
\(350\) −3.79198 1.12055i −0.0108342 0.00320158i
\(351\) 69.1316 0.196956
\(352\) 85.6463 0.243313
\(353\) 12.3883i 0.0350944i 0.999846 + 0.0175472i \(0.00558574\pi\)
−0.999846 + 0.0175472i \(0.994414\pi\)
\(354\) 15.5649 0.0439685
\(355\) 254.472i 0.716822i
\(356\) 523.358i 1.47011i
\(357\) −182.297 53.8698i −0.510637 0.150896i
\(358\) −14.9888 −0.0418680
\(359\) −442.447 −1.23244 −0.616222 0.787572i \(-0.711338\pi\)
−0.616222 + 0.787572i \(0.711338\pi\)
\(360\) 6.05314i 0.0168143i
\(361\) −592.673 −1.64175
\(362\) 26.1403i 0.0722108i
\(363\) 226.175i 0.623071i
\(364\) −105.233 + 356.111i −0.289101 + 0.978327i
\(365\) 45.4915 0.124634
\(366\) 18.5060 0.0505627
\(367\) 567.114i 1.54527i −0.634851 0.772635i \(-0.718938\pi\)
0.634851 0.772635i \(-0.281062\pi\)
\(368\) 57.6257 0.156592
\(369\) 83.7859i 0.227062i
\(370\) 4.39100i 0.0118676i
\(371\) 375.361 + 110.921i 1.01175 + 0.298979i
\(372\) 78.3870 0.210718
\(373\) −106.146 −0.284574 −0.142287 0.989825i \(-0.545446\pi\)
−0.142287 + 0.989825i \(0.545446\pi\)
\(374\) 28.0943i 0.0751185i
\(375\) 19.3649 0.0516398
\(376\) 72.7197i 0.193403i
\(377\) 193.766i 0.513967i
\(378\) 1.16451 3.94075i 0.00308072 0.0104253i
\(379\) 715.733 1.88848 0.944239 0.329262i \(-0.106800\pi\)
0.944239 + 0.329262i \(0.106800\pi\)
\(380\) 275.332 0.724558
\(381\) 112.757i 0.295950i
\(382\) 34.3587 0.0899441
\(383\) 571.840i 1.49305i 0.665355 + 0.746527i \(0.268280\pi\)
−0.665355 + 0.746527i \(0.731720\pi\)
\(384\) 49.6943i 0.129412i
\(385\) −70.3573 + 238.091i −0.182746 + 0.618419i
\(386\) −15.6160 −0.0404560
\(387\) 36.5832 0.0945304
\(388\) 49.5358i 0.127670i
\(389\) −12.6584 −0.0325409 −0.0162705 0.999868i \(-0.505179\pi\)
−0.0162705 + 0.999868i \(0.505179\pi\)
\(390\) 5.82128i 0.0149264i
\(391\) 57.0125i 0.145812i
\(392\) 37.1132 + 24.0330i 0.0946766 + 0.0613086i
\(393\) −277.751 −0.706745
\(394\) 3.04030 0.00771650
\(395\) 2.85170i 0.00721950i
\(396\) −189.729 −0.479113
\(397\) 29.1232i 0.0733582i 0.999327 + 0.0366791i \(0.0116779\pi\)
−0.999327 + 0.0366791i \(0.988322\pi\)
\(398\) 28.4690i 0.0715302i
\(399\) 359.070 + 106.107i 0.899925 + 0.265933i
\(400\) −79.2350 −0.198088
\(401\) 144.012 0.359133 0.179567 0.983746i \(-0.442530\pi\)
0.179567 + 0.983746i \(0.442530\pi\)
\(402\) 20.2441i 0.0503585i
\(403\) −151.010 −0.374715
\(404\) 60.0749i 0.148700i
\(405\) 20.1246i 0.0496904i
\(406\) 11.0453 + 3.26395i 0.0272052 + 0.00803929i
\(407\) −275.702 −0.677401
\(408\) 24.5039 0.0600587
\(409\) 338.914i 0.828641i −0.910131 0.414320i \(-0.864019\pi\)
0.910131 0.414320i \(-0.135981\pi\)
\(410\) 7.05525 0.0172079
\(411\) 274.446i 0.667751i
\(412\) 277.457i 0.673440i
\(413\) 157.794 533.980i 0.382068 1.29293i
\(414\) 1.23245 0.00297693
\(415\) −44.1997 −0.106505
\(416\) 71.8396i 0.172691i
\(417\) 421.704 1.01128
\(418\) 55.3372i 0.132386i
\(419\) 101.585i 0.242446i 0.992625 + 0.121223i \(0.0386816\pi\)
−0.992625 + 0.121223i \(0.961318\pi\)
\(420\) −103.666 30.6339i −0.246824 0.0729378i
\(421\) −145.700 −0.346081 −0.173041 0.984915i \(-0.555359\pi\)
−0.173041 + 0.984915i \(0.555359\pi\)
\(422\) −26.6270 −0.0630972
\(423\) 241.768i 0.571555i
\(424\) −50.4550 −0.118998
\(425\) 78.3919i 0.184451i
\(426\) 22.2686i 0.0522737i
\(427\) 187.610 634.880i 0.439369 1.48684i
\(428\) −416.638 −0.973453
\(429\) 365.507 0.851997
\(430\) 3.08052i 0.00716400i
\(431\) 497.669 1.15468 0.577342 0.816502i \(-0.304090\pi\)
0.577342 + 0.816502i \(0.304090\pi\)
\(432\) 82.3435i 0.190610i
\(433\) 605.000i 1.39723i 0.715499 + 0.698614i \(0.246199\pi\)
−0.715499 + 0.698614i \(0.753801\pi\)
\(434\) −2.54374 + 8.60811i −0.00586116 + 0.0198344i
\(435\) −56.4063 −0.129670
\(436\) 76.6096 0.175710
\(437\) 112.297i 0.256973i
\(438\) −3.98092 −0.00908886
\(439\) 211.605i 0.482015i −0.970523 0.241008i \(-0.922522\pi\)
0.970523 0.241008i \(-0.0774779\pi\)
\(440\) 32.0036i 0.0727355i
\(441\) −123.389 79.9013i −0.279793 0.181182i
\(442\) −23.5653 −0.0533152
\(443\) 794.013 1.79235 0.896177 0.443697i \(-0.146334\pi\)
0.896177 + 0.443697i \(0.146334\pi\)
\(444\) 120.042i 0.270365i
\(445\) 293.502 0.659556
\(446\) 16.1315i 0.0361693i
\(447\) 232.771i 0.520740i
\(448\) 421.431 + 124.535i 0.940693 + 0.277980i
\(449\) −486.171 −1.08279 −0.541393 0.840769i \(-0.682103\pi\)
−0.541393 + 0.840769i \(0.682103\pi\)
\(450\) −1.69461 −0.00376579
\(451\) 442.985i 0.982229i
\(452\) −831.545 −1.83970
\(453\) 2.77226i 0.00611977i
\(454\) 3.45938i 0.00761977i
\(455\) 199.709 + 59.0152i 0.438922 + 0.129704i
\(456\) −48.2653 −0.105845
\(457\) 114.609 0.250786 0.125393 0.992107i \(-0.459981\pi\)
0.125393 + 0.992107i \(0.459981\pi\)
\(458\) 23.8015i 0.0519684i
\(459\) −81.4672 −0.177488
\(460\) 32.4210i 0.0704804i
\(461\) 352.184i 0.763957i −0.924171 0.381978i \(-0.875243\pi\)
0.924171 0.381978i \(-0.124757\pi\)
\(462\) 6.15690 20.8352i 0.0133266 0.0450978i
\(463\) −226.624 −0.489468 −0.244734 0.969590i \(-0.578701\pi\)
−0.244734 + 0.969590i \(0.578701\pi\)
\(464\) 230.796 0.497406
\(465\) 43.9599i 0.0945375i
\(466\) 20.6619 0.0443388
\(467\) 405.655i 0.868641i −0.900758 0.434320i \(-0.856989\pi\)
0.900758 0.434320i \(-0.143011\pi\)
\(468\) 159.143i 0.340050i
\(469\) 694.511 + 205.232i 1.48083 + 0.437594i
\(470\) −20.3582 −0.0433154
\(471\) −437.278 −0.928403
\(472\) 71.7763i 0.152068i
\(473\) 193.420 0.408921
\(474\) 0.249550i 0.000526477i
\(475\) 154.408i 0.325069i
\(476\) 124.010 419.654i 0.260525 0.881627i
\(477\) 167.746 0.351668
\(478\) −13.8405 −0.0289550
\(479\) 900.420i 1.87979i 0.341463 + 0.939895i \(0.389078\pi\)
−0.341463 + 0.939895i \(0.610922\pi\)
\(480\) 20.9129 0.0435686
\(481\) 231.257i 0.480784i
\(482\) 16.9394i 0.0351439i
\(483\) 12.4944 42.2813i 0.0258682 0.0875390i
\(484\) −520.661 −1.07575
\(485\) −27.7800 −0.0572783
\(486\) 1.76109i 0.00362364i
\(487\) 55.4219 0.113803 0.0569014 0.998380i \(-0.481878\pi\)
0.0569014 + 0.998380i \(0.481878\pi\)
\(488\) 85.3390i 0.174875i
\(489\) 414.000i 0.846625i
\(490\) 6.72815 10.3900i 0.0137309 0.0212042i
\(491\) 616.592 1.25579 0.627894 0.778299i \(-0.283917\pi\)
0.627894 + 0.778299i \(0.283917\pi\)
\(492\) 192.878 0.392028
\(493\) 228.340i 0.463165i
\(494\) 46.4165 0.0939605
\(495\) 106.401i 0.214952i
\(496\) 179.870i 0.362641i
\(497\) 763.965 + 225.756i 1.53715 + 0.454237i
\(498\) 3.86788 0.00776682
\(499\) 624.620 1.25174 0.625872 0.779926i \(-0.284743\pi\)
0.625872 + 0.779926i \(0.284743\pi\)
\(500\) 44.5787i 0.0891573i
\(501\) −295.239 −0.589299
\(502\) 25.9148i 0.0516232i
\(503\) 226.444i 0.450187i 0.974337 + 0.225093i \(0.0722687\pi\)
−0.974337 + 0.225093i \(0.927731\pi\)
\(504\) 18.1725 + 5.37007i 0.0360565 + 0.0106549i
\(505\) 33.6904 0.0667137
\(506\) 6.51609 0.0128776
\(507\) 13.8681i 0.0273533i
\(508\) −259.570 −0.510965
\(509\) 468.169i 0.919781i −0.887976 0.459891i \(-0.847889\pi\)
0.887976 0.459891i \(-0.152111\pi\)
\(510\) 6.86000i 0.0134510i
\(511\) −40.3579 + 136.573i −0.0789783 + 0.267265i
\(512\) −142.767 −0.278842
\(513\) 160.465 0.312798
\(514\) 5.49645i 0.0106935i
\(515\) −155.600 −0.302135
\(516\) 84.2158i 0.163209i
\(517\) 1278.25i 2.47245i
\(518\) 13.1825 + 3.89549i 0.0254488 + 0.00752025i
\(519\) 466.881 0.899579
\(520\) −26.8444 −0.0516239
\(521\) 458.100i 0.879271i −0.898176 0.439635i \(-0.855108\pi\)
0.898176 0.439635i \(-0.144892\pi\)
\(522\) 4.93607 0.00945607
\(523\) 256.863i 0.491135i −0.969380 0.245567i \(-0.921026\pi\)
0.969380 0.245567i \(-0.0789742\pi\)
\(524\) 639.392i 1.22021i
\(525\) −17.1797 + 58.1366i −0.0327232 + 0.110736i
\(526\) 4.25846 0.00809593
\(527\) 177.956 0.337677
\(528\) 435.359i 0.824544i
\(529\) −515.777 −0.975003
\(530\) 14.1251i 0.0266512i
\(531\) 238.632i 0.449400i
\(532\) −244.262 + 826.590i −0.459139 + 1.55374i
\(533\) −371.573 −0.697136
\(534\) −25.6841 −0.0480976
\(535\) 233.653i 0.436735i
\(536\) −93.3544 −0.174169
\(537\) 229.799i 0.427931i
\(538\) 32.9572i 0.0612587i
\(539\) −652.370 422.447i −1.21033 0.783761i
\(540\) −46.3275 −0.0857917
\(541\) −57.7912 −0.106823 −0.0534115 0.998573i \(-0.517009\pi\)
−0.0534115 + 0.998573i \(0.517009\pi\)
\(542\) 11.6227i 0.0214442i
\(543\) −400.768 −0.738063
\(544\) 84.6584i 0.155622i
\(545\) 42.9632i 0.0788315i
\(546\) −17.4764 5.16437i −0.0320081 0.00945856i
\(547\) 658.275 1.20343 0.601714 0.798712i \(-0.294485\pi\)
0.601714 + 0.798712i \(0.294485\pi\)
\(548\) −631.783 −1.15289
\(549\) 283.723i 0.516799i
\(550\) −8.95958 −0.0162901
\(551\) 449.761i 0.816263i
\(552\) 5.68335i 0.0102959i
\(553\) 8.56126 + 2.52990i 0.0154815 + 0.00457486i
\(554\) −43.0902 −0.0777801
\(555\) −67.3203 −0.121298
\(556\) 970.776i 1.74600i
\(557\) −782.705 −1.40521 −0.702607 0.711578i \(-0.747981\pi\)
−0.702607 + 0.711578i \(0.747981\pi\)
\(558\) 3.84690i 0.00689408i
\(559\) 162.239i 0.290231i
\(560\) 70.2937 237.876i 0.125524 0.424779i
\(561\) −430.726 −0.767783
\(562\) −1.97538 −0.00351491
\(563\) 632.083i 1.12271i −0.827577 0.561353i \(-0.810281\pi\)
0.827577 0.561353i \(-0.189719\pi\)
\(564\) −556.558 −0.986804
\(565\) 466.336i 0.825373i
\(566\) 38.7905i 0.0685345i
\(567\) −60.4173 17.8536i −0.106556 0.0314879i
\(568\) −102.690 −0.180793
\(569\) −603.746 −1.06107 −0.530533 0.847665i \(-0.678008\pi\)
−0.530533 + 0.847665i \(0.678008\pi\)
\(570\) 13.5121i 0.0237055i
\(571\) −638.070 −1.11746 −0.558730 0.829349i \(-0.688711\pi\)
−0.558730 + 0.829349i \(0.688711\pi\)
\(572\) 841.408i 1.47099i
\(573\) 526.767i 0.919315i
\(574\) −6.25909 + 21.1810i −0.0109043 + 0.0369007i
\(575\) −18.1819 −0.0316207
\(576\) 188.334 0.326969
\(577\) 449.363i 0.778792i 0.921070 + 0.389396i \(0.127316\pi\)
−0.921070 + 0.389396i \(0.872684\pi\)
\(578\) −4.87919 −0.00844151
\(579\) 239.416i 0.413499i
\(580\) 129.849i 0.223878i
\(581\) 39.2119 132.694i 0.0674904 0.228390i
\(582\) 2.43100 0.00417698
\(583\) 886.890 1.52125
\(584\) 18.3577i 0.0314345i
\(585\) 89.2486 0.152562
\(586\) 27.6226i 0.0471375i
\(587\) 133.202i 0.226920i −0.993543 0.113460i \(-0.963807\pi\)
0.993543 0.113460i \(-0.0361935\pi\)
\(588\) 183.935 284.045i 0.312815 0.483069i
\(589\) −350.519 −0.595108
\(590\) 20.0941 0.0340579
\(591\) 46.6122i 0.0788700i
\(592\) 275.453 0.465292
\(593\) 444.341i 0.749310i −0.927164 0.374655i \(-0.877761\pi\)
0.927164 0.374655i \(-0.122239\pi\)
\(594\) 9.31107i 0.0156752i
\(595\) −235.345 69.5457i −0.395537 0.116883i
\(596\) 535.846 0.899070
\(597\) −436.471 −0.731107
\(598\) 5.46565i 0.00913989i
\(599\) −230.917 −0.385504 −0.192752 0.981247i \(-0.561741\pi\)
−0.192752 + 0.981247i \(0.561741\pi\)
\(600\) 7.81457i 0.0130243i
\(601\) 147.957i 0.246185i 0.992395 + 0.123092i \(0.0392812\pi\)
−0.992395 + 0.123092i \(0.960719\pi\)
\(602\) −9.24821 2.73289i −0.0153625 0.00453969i
\(603\) 310.371 0.514712
\(604\) −6.38182 −0.0105659
\(605\) 291.990i 0.482629i
\(606\) −2.94822 −0.00486505
\(607\) 1036.13i 1.70697i −0.521119 0.853484i \(-0.674485\pi\)
0.521119 0.853484i \(-0.325515\pi\)
\(608\) 166.751i 0.274262i
\(609\) 50.0411 169.341i 0.0821692 0.278063i
\(610\) 23.8911 0.0391657
\(611\) 1072.19 1.75481
\(612\) 187.540i 0.306438i
\(613\) −175.987 −0.287091 −0.143545 0.989644i \(-0.545850\pi\)
−0.143545 + 0.989644i \(0.545850\pi\)
\(614\) 39.2915i 0.0639926i
\(615\) 108.167i 0.175881i
\(616\) 96.0800 + 28.3922i 0.155974 + 0.0460912i
\(617\) −635.690 −1.03029 −0.515146 0.857103i \(-0.672262\pi\)
−0.515146 + 0.857103i \(0.672262\pi\)
\(618\) 13.6164 0.0220330
\(619\) 581.258i 0.939027i 0.882925 + 0.469514i \(0.155571\pi\)
−0.882925 + 0.469514i \(0.844429\pi\)
\(620\) 101.197 0.163221
\(621\) 18.8952i 0.0304270i
\(622\) 11.9029i 0.0191365i
\(623\) −260.382 + 881.141i −0.417948 + 1.41435i
\(624\) −365.176 −0.585219
\(625\) 25.0000 0.0400000
\(626\) 18.7401i 0.0299362i
\(627\) 848.399 1.35311
\(628\) 1006.63i 1.60291i
\(629\) 272.522i 0.433262i
\(630\) 1.50338 5.08748i 0.00238631 0.00807537i
\(631\) −550.845 −0.872972 −0.436486 0.899711i \(-0.643777\pi\)
−0.436486 + 0.899711i \(0.643777\pi\)
\(632\) −1.15078 −0.00182086
\(633\) 408.230i 0.644913i
\(634\) 10.9351 0.0172478
\(635\) 145.569i 0.229242i
\(636\) 386.156i 0.607163i
\(637\) −354.346 + 547.204i −0.556273 + 0.859033i
\(638\) 26.0975 0.0409052
\(639\) 341.410 0.534287
\(640\) 64.1551i 0.100242i
\(641\) −64.8667 −0.101196 −0.0505981 0.998719i \(-0.516113\pi\)
−0.0505981 + 0.998719i \(0.516113\pi\)
\(642\) 20.4468i 0.0318486i
\(643\) 812.068i 1.26294i 0.775402 + 0.631468i \(0.217547\pi\)
−0.775402 + 0.631468i \(0.782453\pi\)
\(644\) 97.3330 + 28.7624i 0.151138 + 0.0446621i
\(645\) 47.2288 0.0732229
\(646\) −54.6989 −0.0846732
\(647\) 618.282i 0.955613i 0.878465 + 0.477807i \(0.158568\pi\)
−0.878465 + 0.477807i \(0.841432\pi\)
\(648\) 8.12114 0.0125326
\(649\) 1261.67i 1.94402i
\(650\) 7.51524i 0.0115619i
\(651\) 131.975 + 38.9992i 0.202726 + 0.0599066i
\(652\) 953.041 1.46172
\(653\) −694.281 −1.06322 −0.531609 0.846990i \(-0.678412\pi\)
−0.531609 + 0.846990i \(0.678412\pi\)
\(654\) 3.75967i 0.00574873i
\(655\) −358.575 −0.547443
\(656\) 442.585i 0.674672i
\(657\) 61.0332i 0.0928968i
\(658\) 18.0609 61.1187i 0.0274482 0.0928855i
\(659\) 514.683 0.781007 0.390503 0.920601i \(-0.372301\pi\)
0.390503 + 0.920601i \(0.372301\pi\)
\(660\) −244.939 −0.371119
\(661\) 347.998i 0.526472i −0.964731 0.263236i \(-0.915210\pi\)
0.964731 0.263236i \(-0.0847899\pi\)
\(662\) 21.8810 0.0330528
\(663\) 361.290i 0.544933i
\(664\) 17.8364i 0.0268621i
\(665\) 463.557 + 136.984i 0.697079 + 0.205990i
\(666\) 5.89114 0.00884556
\(667\) 52.9604 0.0794009
\(668\) 679.649i 1.01744i
\(669\) −247.319 −0.369685
\(670\) 26.1350i 0.0390075i
\(671\) 1500.07i 2.23558i
\(672\) −18.5530 + 62.7839i −0.0276086 + 0.0934284i
\(673\) 478.656 0.711227 0.355614 0.934633i \(-0.384272\pi\)
0.355614 + 0.934633i \(0.384272\pi\)
\(674\) 26.9716 0.0400172
\(675\) 25.9808i 0.0384900i
\(676\) 31.9248 0.0472261
\(677\) 276.403i 0.408277i 0.978942 + 0.204138i \(0.0654393\pi\)
−0.978942 + 0.204138i \(0.934561\pi\)
\(678\) 40.8087i 0.0601898i
\(679\) 24.6451 83.3999i 0.0362962 0.122828i
\(680\) 31.6345 0.0465213
\(681\) 53.0372 0.0778814
\(682\) 20.3390i 0.0298225i
\(683\) 311.395 0.455922 0.227961 0.973670i \(-0.426794\pi\)
0.227961 + 0.973670i \(0.426794\pi\)
\(684\) 369.397i 0.540054i
\(685\) 354.308i 0.517238i
\(686\) 25.2236 + 29.4165i 0.0367691 + 0.0428812i
\(687\) −364.911 −0.531166
\(688\) −193.245 −0.280879
\(689\) 743.918i 1.07971i
\(690\) 1.59108 0.00230592
\(691\) 569.213i 0.823752i −0.911240 0.411876i \(-0.864874\pi\)
0.911240 0.411876i \(-0.135126\pi\)
\(692\) 1074.78i 1.55314i
\(693\) −319.433 94.3942i −0.460942 0.136211i
\(694\) 60.3039 0.0868933
\(695\) 544.417 0.783334
\(696\) 22.7623i 0.0327045i
\(697\) 437.875 0.628229
\(698\) 26.0403i 0.0373070i
\(699\) 316.776i 0.453185i
\(700\) −133.832 39.5481i −0.191189 0.0564973i
\(701\) −446.061 −0.636321 −0.318160 0.948037i \(-0.603065\pi\)
−0.318160 + 0.948037i \(0.603065\pi\)
\(702\) −7.81007 −0.0111254
\(703\) 536.785i 0.763563i
\(704\) 995.743 1.41441
\(705\) 312.121i 0.442725i
\(706\) 1.39956i 0.00198238i
\(707\) −29.8886 + 101.144i −0.0422752 + 0.143061i
\(708\) 549.338 0.775901
\(709\) −480.480 −0.677686 −0.338843 0.940843i \(-0.610036\pi\)
−0.338843 + 0.940843i \(0.610036\pi\)
\(710\) 28.7486i 0.0404911i
\(711\) 3.82596 0.00538110
\(712\) 118.441i 0.166349i
\(713\) 41.2744i 0.0578883i
\(714\) 20.5948 + 6.08588i 0.0288443 + 0.00852364i
\(715\) 471.867 0.659954
\(716\) −529.005 −0.738834
\(717\) 212.195i 0.295948i
\(718\) 49.9850 0.0696170
\(719\) 330.338i 0.459441i 0.973257 + 0.229721i \(0.0737813\pi\)
−0.973257 + 0.229721i \(0.926219\pi\)
\(720\) 106.305i 0.147646i
\(721\) 138.041 467.135i 0.191458 0.647899i
\(722\) 66.9565 0.0927375
\(723\) 259.705 0.359204
\(724\) 922.582i 1.27428i
\(725\) −72.8202 −0.100442
\(726\) 25.5518i 0.0351953i
\(727\) 327.774i 0.450858i 0.974260 + 0.225429i \(0.0723783\pi\)
−0.974260 + 0.225429i \(0.927622\pi\)
\(728\) 23.8152 80.5913i 0.0327131 0.110702i
\(729\) −27.0000 −0.0370370
\(730\) −5.13934 −0.00704020
\(731\) 191.189i 0.261544i
\(732\) 653.139 0.892267
\(733\) 124.845i 0.170320i 0.996367 + 0.0851601i \(0.0271402\pi\)
−0.996367 + 0.0851601i \(0.972860\pi\)
\(734\) 64.0690i 0.0872875i
\(735\) −159.294 103.152i −0.216727 0.140343i
\(736\) −19.6353 −0.0266784
\(737\) 1640.97 2.22655
\(738\) 9.46561i 0.0128260i
\(739\) 759.049 1.02713 0.513565 0.858051i \(-0.328325\pi\)
0.513565 + 0.858051i \(0.328325\pi\)
\(740\) 154.973i 0.209424i
\(741\) 711.632i 0.960367i
\(742\) −42.4059 12.5312i −0.0571508 0.0168884i
\(743\) 658.165 0.885820 0.442910 0.896566i \(-0.353946\pi\)
0.442910 + 0.896566i \(0.353946\pi\)
\(744\) −17.7397 −0.0238437
\(745\) 300.506i 0.403363i
\(746\) 11.9917 0.0160747
\(747\) 59.3001i 0.0793843i
\(748\) 991.546i 1.32560i
\(749\) −701.464 207.286i −0.936534 0.276751i
\(750\) −2.18773 −0.00291697
\(751\) −15.4050 −0.0205127 −0.0102564 0.999947i \(-0.503265\pi\)
−0.0102564 + 0.999947i \(0.503265\pi\)
\(752\) 1277.10i 1.69827i
\(753\) −397.312 −0.527638
\(754\) 21.8904i 0.0290324i
\(755\) 3.57897i 0.00474035i
\(756\) 41.0996 139.083i 0.0543646 0.183972i
\(757\) −732.280 −0.967345 −0.483673 0.875249i \(-0.660697\pi\)
−0.483673 + 0.875249i \(0.660697\pi\)
\(758\) −80.8591 −0.106674
\(759\) 99.9010i 0.131622i
\(760\) −62.3102 −0.0819871
\(761\) 969.037i 1.27337i 0.771123 + 0.636686i \(0.219695\pi\)
−0.771123 + 0.636686i \(0.780305\pi\)
\(762\) 12.7386i 0.0167173i
\(763\) 128.982 + 38.1149i 0.169046 + 0.0499541i
\(764\) 1212.64 1.58722
\(765\) −105.174 −0.137482
\(766\) 64.6029i 0.0843380i
\(767\) −1058.28 −1.37977
\(768\) 429.325i 0.559016i
\(769\) 1090.28i 1.41778i 0.705317 + 0.708892i \(0.250805\pi\)
−0.705317 + 0.708892i \(0.749195\pi\)
\(770\) 7.94853 26.8981i 0.0103228 0.0349326i
\(771\) −84.2685 −0.109298
\(772\) −551.144 −0.713917
\(773\) 1490.66i 1.92841i 0.265155 + 0.964206i \(0.414577\pi\)
−0.265155 + 0.964206i \(0.585423\pi\)
\(774\) −4.13295 −0.00533973
\(775\) 56.7520i 0.0732284i
\(776\) 11.2104i 0.0144464i
\(777\) 59.7235 202.106i 0.0768642 0.260111i
\(778\) 1.43007 0.00183814
\(779\) −862.481 −1.10716
\(780\) 205.453i 0.263401i
\(781\) 1805.07 2.31123
\(782\) 6.44092i 0.00823647i
\(783\) 75.6770i 0.0966500i
\(784\) 651.781 + 422.066i 0.831353 + 0.538349i
\(785\) −564.523 −0.719138
\(786\) 31.3786 0.0399219