Properties

Label 105.4.d.b.64.5
Level $105$
Weight $4$
Character 105.64
Analytic conductor $6.195$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 37 x^{8} + 398 x^{6} + 1149 x^{4} + 1040 x^{2} + 100\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.5
Root \(0.329739i\) of defining polynomial
Character \(\chi\) \(=\) 105.64
Dual form 105.4.d.b.64.6

$q$-expansion

\(f(q)\) \(=\) \(q-0.428319i q^{2} +3.00000i q^{3} +7.81654 q^{4} +(-1.76884 + 11.0395i) q^{5} +1.28496 q^{6} +7.00000i q^{7} -6.77452i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q-0.428319i q^{2} +3.00000i q^{3} +7.81654 q^{4} +(-1.76884 + 11.0395i) q^{5} +1.28496 q^{6} +7.00000i q^{7} -6.77452i q^{8} -9.00000 q^{9} +(4.72844 + 0.757628i) q^{10} -27.4721 q^{11} +23.4496i q^{12} +46.5524i q^{13} +2.99823 q^{14} +(-33.1186 - 5.30652i) q^{15} +59.6307 q^{16} +5.20546i q^{17} +3.85487i q^{18} +91.0007 q^{19} +(-13.8262 + 86.2910i) q^{20} -21.0000 q^{21} +11.7668i q^{22} +111.563i q^{23} +20.3236 q^{24} +(-118.742 - 39.0544i) q^{25} +19.9393 q^{26} -27.0000i q^{27} +54.7158i q^{28} -0.0763413 q^{29} +(-2.27288 + 14.1853i) q^{30} +201.784 q^{31} -79.7371i q^{32} -82.4163i q^{33} +2.22960 q^{34} +(-77.2767 - 12.3819i) q^{35} -70.3489 q^{36} -312.859i q^{37} -38.9773i q^{38} -139.657 q^{39} +(74.7876 + 11.9831i) q^{40} +102.432 q^{41} +8.99470i q^{42} -257.280i q^{43} -214.737 q^{44} +(15.9196 - 99.3558i) q^{45} +47.7847 q^{46} -350.994i q^{47} +178.892i q^{48} -49.0000 q^{49} +(-16.7277 + 50.8596i) q^{50} -15.6164 q^{51} +363.879i q^{52} -196.260i q^{53} -11.5646 q^{54} +(48.5938 - 303.279i) q^{55} +47.4217 q^{56} +273.002i q^{57} +0.0326984i q^{58} -881.060 q^{59} +(-258.873 - 41.4787i) q^{60} +737.897 q^{61} -86.4280i q^{62} -63.0000i q^{63} +442.893 q^{64} +(-513.917 - 82.3439i) q^{65} -35.3004 q^{66} +365.021i q^{67} +40.6887i q^{68} -334.690 q^{69} +(-5.30340 + 33.0991i) q^{70} +1112.53 q^{71} +60.9707i q^{72} -261.995i q^{73} -134.004 q^{74} +(117.163 - 356.227i) q^{75} +711.311 q^{76} -192.305i q^{77} +59.8179i q^{78} -273.829 q^{79} +(-105.477 + 658.295i) q^{80} +81.0000 q^{81} -43.8735i q^{82} +87.1353i q^{83} -164.147 q^{84} +(-57.4658 - 9.20763i) q^{85} -110.198 q^{86} -0.229024i q^{87} +186.110i q^{88} +1090.99 q^{89} +(-42.5559 - 6.81865i) q^{90} -325.867 q^{91} +872.039i q^{92} +605.353i q^{93} -150.337 q^{94} +(-160.966 + 1004.61i) q^{95} +239.211 q^{96} +228.830i q^{97} +20.9876i q^{98} +247.249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + O(q^{10}) \) \( 10q - 54q^{4} - 14q^{5} - 6q^{6} - 90q^{9} + 92q^{10} + 132q^{11} - 14q^{14} + 310q^{16} - 348q^{19} + 366q^{20} - 210q^{21} + 198q^{24} - 374q^{25} + 892q^{26} - 740q^{29} - 378q^{30} + 684q^{31} - 224q^{34} + 486q^{36} - 12q^{39} - 2156q^{40} + 1604q^{41} - 580q^{44} + 126q^{45} + 1280q^{46} - 490q^{49} - 2504q^{50} - 648q^{51} + 54q^{54} - 452q^{55} + 462q^{56} - 1408q^{59} - 852q^{60} + 1300q^{61} - 150q^{64} - 3296q^{65} + 3036q^{66} - 696q^{69} - 882q^{70} + 2940q^{71} + 2624q^{74} - 408q^{75} + 8740q^{76} + 1640q^{79} - 4126q^{80} + 810q^{81} + 1134q^{84} - 1704q^{85} + 1664q^{86} - 572q^{89} - 828q^{90} - 28q^{91} - 5080q^{94} + 1268q^{95} + 330q^{96} - 1188q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.428319i 0.151434i −0.997129 0.0757168i \(-0.975876\pi\)
0.997129 0.0757168i \(-0.0241245\pi\)
\(3\) 3.00000i 0.577350i
\(4\) 7.81654 0.977068
\(5\) −1.76884 + 11.0395i −0.158210 + 0.987405i
\(6\) 1.28496 0.0874302
\(7\) 7.00000i 0.377964i
\(8\) 6.77452i 0.299394i
\(9\) −9.00000 −0.333333
\(10\) 4.72844 + 0.757628i 0.149526 + 0.0239583i
\(11\) −27.4721 −0.753013 −0.376507 0.926414i \(-0.622875\pi\)
−0.376507 + 0.926414i \(0.622875\pi\)
\(12\) 23.4496i 0.564110i
\(13\) 46.5524i 0.993179i 0.867986 + 0.496589i \(0.165414\pi\)
−0.867986 + 0.496589i \(0.834586\pi\)
\(14\) 2.99823 0.0572365
\(15\) −33.1186 5.30652i −0.570079 0.0913426i
\(16\) 59.6307 0.931729
\(17\) 5.20546i 0.0742653i 0.999310 + 0.0371326i \(0.0118224\pi\)
−0.999310 + 0.0371326i \(0.988178\pi\)
\(18\) 3.85487i 0.0504779i
\(19\) 91.0007 1.09879 0.549395 0.835563i \(-0.314858\pi\)
0.549395 + 0.835563i \(0.314858\pi\)
\(20\) −13.8262 + 86.2910i −0.154582 + 0.964762i
\(21\) −21.0000 −0.218218
\(22\) 11.7668i 0.114032i
\(23\) 111.563i 1.01142i 0.862705 + 0.505708i \(0.168769\pi\)
−0.862705 + 0.505708i \(0.831231\pi\)
\(24\) 20.3236 0.172855
\(25\) −118.742 39.0544i −0.949939 0.312435i
\(26\) 19.9393 0.150401
\(27\) 27.0000i 0.192450i
\(28\) 54.7158i 0.369297i
\(29\) −0.0763413 −0.000488835 −0.000244418 1.00000i \(-0.500078\pi\)
−0.000244418 1.00000i \(0.500078\pi\)
\(30\) −2.27288 + 14.1853i −0.0138323 + 0.0863291i
\(31\) 201.784 1.16908 0.584541 0.811364i \(-0.301275\pi\)
0.584541 + 0.811364i \(0.301275\pi\)
\(32\) 79.7371i 0.440490i
\(33\) 82.4163i 0.434752i
\(34\) 2.22960 0.0112463
\(35\) −77.2767 12.3819i −0.373204 0.0597978i
\(36\) −70.3489 −0.325689
\(37\) 312.859i 1.39010i −0.718960 0.695051i \(-0.755382\pi\)
0.718960 0.695051i \(-0.244618\pi\)
\(38\) 38.9773i 0.166394i
\(39\) −139.657 −0.573412
\(40\) 74.7876 + 11.9831i 0.295624 + 0.0473672i
\(41\) 102.432 0.390175 0.195087 0.980786i \(-0.437501\pi\)
0.195087 + 0.980786i \(0.437501\pi\)
\(42\) 8.99470i 0.0330455i
\(43\) 257.280i 0.912439i −0.889867 0.456219i \(-0.849203\pi\)
0.889867 0.456219i \(-0.150797\pi\)
\(44\) −214.737 −0.735745
\(45\) 15.9196 99.3558i 0.0527367 0.329135i
\(46\) 47.7847 0.153162
\(47\) 350.994i 1.08931i −0.838659 0.544657i \(-0.816660\pi\)
0.838659 0.544657i \(-0.183340\pi\)
\(48\) 178.892i 0.537934i
\(49\) −49.0000 −0.142857
\(50\) −16.7277 + 50.8596i −0.0473131 + 0.143853i
\(51\) −15.6164 −0.0428771
\(52\) 363.879i 0.970403i
\(53\) 196.260i 0.508649i −0.967119 0.254324i \(-0.918147\pi\)
0.967119 0.254324i \(-0.0818531\pi\)
\(54\) −11.5646 −0.0291434
\(55\) 48.5938 303.279i 0.119134 0.743530i
\(56\) 47.4217 0.113160
\(57\) 273.002i 0.634386i
\(58\) 0.0326984i 7.40261e-5i
\(59\) −881.060 −1.94414 −0.972070 0.234692i \(-0.924592\pi\)
−0.972070 + 0.234692i \(0.924592\pi\)
\(60\) −258.873 41.4787i −0.557006 0.0892479i
\(61\) 737.897 1.54882 0.774410 0.632684i \(-0.218047\pi\)
0.774410 + 0.632684i \(0.218047\pi\)
\(62\) 86.4280i 0.177038i
\(63\) 63.0000i 0.125988i
\(64\) 442.893 0.865025
\(65\) −513.917 82.3439i −0.980670 0.157131i
\(66\) −35.3004 −0.0658361
\(67\) 365.021i 0.665589i 0.942999 + 0.332794i \(0.107991\pi\)
−0.942999 + 0.332794i \(0.892009\pi\)
\(68\) 40.6887i 0.0725622i
\(69\) −334.690 −0.583941
\(70\) −5.30340 + 33.0991i −0.00905539 + 0.0565157i
\(71\) 1112.53 1.85962 0.929809 0.368042i \(-0.119972\pi\)
0.929809 + 0.368042i \(0.119972\pi\)
\(72\) 60.9707i 0.0997982i
\(73\) 261.995i 0.420057i −0.977695 0.210029i \(-0.932644\pi\)
0.977695 0.210029i \(-0.0673558\pi\)
\(74\) −134.004 −0.210508
\(75\) 117.163 356.227i 0.180384 0.548448i
\(76\) 711.311 1.07359
\(77\) 192.305i 0.284612i
\(78\) 59.8179i 0.0868338i
\(79\) −273.829 −0.389977 −0.194988 0.980806i \(-0.562467\pi\)
−0.194988 + 0.980806i \(0.562467\pi\)
\(80\) −105.477 + 658.295i −0.147409 + 0.919995i
\(81\) 81.0000 0.111111
\(82\) 43.8735i 0.0590856i
\(83\) 87.1353i 0.115233i 0.998339 + 0.0576165i \(0.0183501\pi\)
−0.998339 + 0.0576165i \(0.981650\pi\)
\(84\) −164.147 −0.213214
\(85\) −57.4658 9.20763i −0.0733299 0.0117495i
\(86\) −110.198 −0.138174
\(87\) 0.229024i 0.000282229i
\(88\) 186.110i 0.225448i
\(89\) 1090.99 1.29938 0.649690 0.760199i \(-0.274899\pi\)
0.649690 + 0.760199i \(0.274899\pi\)
\(90\) −42.5559 6.81865i −0.0498421 0.00798610i
\(91\) −325.867 −0.375386
\(92\) 872.039i 0.988221i
\(93\) 605.353i 0.674969i
\(94\) −150.337 −0.164959
\(95\) −160.966 + 1004.61i −0.173839 + 1.08495i
\(96\) 239.211 0.254317
\(97\) 228.830i 0.239527i 0.992802 + 0.119764i \(0.0382137\pi\)
−0.992802 + 0.119764i \(0.961786\pi\)
\(98\) 20.9876i 0.0216334i
\(99\) 247.249 0.251004
\(100\) −928.155 305.270i −0.928155 0.305270i
\(101\) −590.728 −0.581976 −0.290988 0.956727i \(-0.593984\pi\)
−0.290988 + 0.956727i \(0.593984\pi\)
\(102\) 6.68879i 0.00649303i
\(103\) 1471.06i 1.40726i 0.710568 + 0.703629i \(0.248438\pi\)
−0.710568 + 0.703629i \(0.751562\pi\)
\(104\) 315.371 0.297352
\(105\) 37.1457 231.830i 0.0345243 0.215470i
\(106\) −84.0619 −0.0770265
\(107\) 1223.29i 1.10523i 0.833435 + 0.552617i \(0.186371\pi\)
−0.833435 + 0.552617i \(0.813629\pi\)
\(108\) 211.047i 0.188037i
\(109\) −1280.64 −1.12535 −0.562674 0.826679i \(-0.690227\pi\)
−0.562674 + 0.826679i \(0.690227\pi\)
\(110\) −129.900 20.8136i −0.112595 0.0180409i
\(111\) 938.578 0.802576
\(112\) 417.415i 0.352161i
\(113\) 1805.38i 1.50297i −0.659748 0.751487i \(-0.729337\pi\)
0.659748 0.751487i \(-0.270663\pi\)
\(114\) 116.932 0.0960674
\(115\) −1231.61 197.338i −0.998677 0.160016i
\(116\) −0.596725 −0.000477625
\(117\) 418.972i 0.331060i
\(118\) 377.375i 0.294408i
\(119\) −36.4382 −0.0280696
\(120\) −35.9492 + 224.363i −0.0273475 + 0.170678i
\(121\) −576.284 −0.432971
\(122\) 316.055i 0.234543i
\(123\) 307.296i 0.225268i
\(124\) 1577.26 1.14227
\(125\) 641.178 1241.78i 0.458790 0.888545i
\(126\) −26.9841 −0.0190788
\(127\) 1642.42i 1.14757i −0.819005 0.573786i \(-0.805474\pi\)
0.819005 0.573786i \(-0.194526\pi\)
\(128\) 827.596i 0.571483i
\(129\) 771.841 0.526797
\(130\) −35.2694 + 220.120i −0.0237949 + 0.148506i
\(131\) 2371.85 1.58190 0.790951 0.611879i \(-0.209586\pi\)
0.790951 + 0.611879i \(0.209586\pi\)
\(132\) 644.210i 0.424783i
\(133\) 637.005i 0.415303i
\(134\) 156.345 0.100792
\(135\) 298.067 + 47.7587i 0.190026 + 0.0304475i
\(136\) 35.2645 0.0222346
\(137\) 762.828i 0.475714i −0.971300 0.237857i \(-0.923555\pi\)
0.971300 0.237857i \(-0.0764450\pi\)
\(138\) 143.354i 0.0884283i
\(139\) −2025.84 −1.23618 −0.618092 0.786105i \(-0.712094\pi\)
−0.618092 + 0.786105i \(0.712094\pi\)
\(140\) −604.037 96.7836i −0.364646 0.0584265i
\(141\) 1052.98 0.628916
\(142\) 476.517i 0.281609i
\(143\) 1278.89i 0.747877i
\(144\) −536.676 −0.310576
\(145\) 0.135036 0.842772i 7.73386e−5 0.000482679i
\(146\) −112.217 −0.0636108
\(147\) 147.000i 0.0824786i
\(148\) 2445.48i 1.35822i
\(149\) 10.7903 0.00593272 0.00296636 0.999996i \(-0.499056\pi\)
0.00296636 + 0.999996i \(0.499056\pi\)
\(150\) −152.579 50.1832i −0.0830534 0.0273162i
\(151\) −2404.48 −1.29585 −0.647925 0.761704i \(-0.724363\pi\)
−0.647925 + 0.761704i \(0.724363\pi\)
\(152\) 616.487i 0.328972i
\(153\) 46.8491i 0.0247551i
\(154\) −82.3677 −0.0430999
\(155\) −356.924 + 2227.60i −0.184960 + 1.15436i
\(156\) −1091.64 −0.560262
\(157\) 396.624i 0.201618i −0.994906 0.100809i \(-0.967857\pi\)
0.994906 0.100809i \(-0.0321431\pi\)
\(158\) 117.286i 0.0590556i
\(159\) 588.780 0.293669
\(160\) 880.260 + 141.042i 0.434942 + 0.0696899i
\(161\) −780.943 −0.382279
\(162\) 34.6938i 0.0168260i
\(163\) 2751.69i 1.32226i 0.750270 + 0.661132i \(0.229923\pi\)
−0.750270 + 0.661132i \(0.770077\pi\)
\(164\) 800.663 0.381227
\(165\) 909.837 + 145.781i 0.429277 + 0.0687822i
\(166\) 37.3217 0.0174501
\(167\) 2079.43i 0.963541i 0.876297 + 0.481771i \(0.160006\pi\)
−0.876297 + 0.481771i \(0.839994\pi\)
\(168\) 142.265i 0.0653332i
\(169\) 29.8706 0.0135961
\(170\) −3.94380 + 24.6137i −0.00177927 + 0.0111046i
\(171\) −819.007 −0.366263
\(172\) 2011.04i 0.891515i
\(173\) 1929.59i 0.848000i −0.905662 0.424000i \(-0.860626\pi\)
0.905662 0.424000i \(-0.139374\pi\)
\(174\) −0.0980953 −4.27390e−5
\(175\) 273.380 831.197i 0.118089 0.359043i
\(176\) −1638.18 −0.701605
\(177\) 2643.18i 1.12245i
\(178\) 467.292i 0.196770i
\(179\) −1638.15 −0.684027 −0.342014 0.939695i \(-0.611109\pi\)
−0.342014 + 0.939695i \(0.611109\pi\)
\(180\) 124.436 776.619i 0.0515273 0.321587i
\(181\) −36.6604 −0.0150550 −0.00752749 0.999972i \(-0.502396\pi\)
−0.00752749 + 0.999972i \(0.502396\pi\)
\(182\) 139.575i 0.0568461i
\(183\) 2213.69i 0.894212i
\(184\) 755.788 0.302812
\(185\) 3453.82 + 553.399i 1.37259 + 0.219928i
\(186\) 259.284 0.102213
\(187\) 143.005i 0.0559227i
\(188\) 2743.56i 1.06433i
\(189\) 189.000 0.0727393
\(190\) 430.291 + 68.9447i 0.164298 + 0.0263251i
\(191\) 1054.82 0.399603 0.199801 0.979836i \(-0.435970\pi\)
0.199801 + 0.979836i \(0.435970\pi\)
\(192\) 1328.68i 0.499422i
\(193\) 213.661i 0.0796873i −0.999206 0.0398436i \(-0.987314\pi\)
0.999206 0.0398436i \(-0.0126860\pi\)
\(194\) 98.0121 0.0362725
\(195\) 247.032 1541.75i 0.0907195 0.566190i
\(196\) −383.011 −0.139581
\(197\) 3953.62i 1.42987i 0.699193 + 0.714933i \(0.253543\pi\)
−0.699193 + 0.714933i \(0.746457\pi\)
\(198\) 105.901i 0.0380105i
\(199\) −929.168 −0.330990 −0.165495 0.986211i \(-0.552922\pi\)
−0.165495 + 0.986211i \(0.552922\pi\)
\(200\) −264.575 + 804.423i −0.0935413 + 0.284407i
\(201\) −1095.06 −0.384278
\(202\) 253.020i 0.0881308i
\(203\) 0.534389i 0.000184762i
\(204\) −122.066 −0.0418938
\(205\) −181.186 + 1130.80i −0.0617295 + 0.385261i
\(206\) 630.081 0.213106
\(207\) 1004.07i 0.337138i
\(208\) 2775.95i 0.925374i
\(209\) −2499.98 −0.827403
\(210\) −99.2972 15.9102i −0.0326293 0.00522813i
\(211\) −926.806 −0.302388 −0.151194 0.988504i \(-0.548312\pi\)
−0.151194 + 0.988504i \(0.548312\pi\)
\(212\) 1534.07i 0.496984i
\(213\) 3337.59i 1.07365i
\(214\) 523.959 0.167370
\(215\) 2840.25 + 455.088i 0.900947 + 0.144357i
\(216\) −182.912 −0.0576185
\(217\) 1412.49i 0.441871i
\(218\) 548.521i 0.170415i
\(219\) 785.985 0.242520
\(220\) 379.835 2370.59i 0.116402 0.726479i
\(221\) −242.327 −0.0737587
\(222\) 402.011i 0.121537i
\(223\) 5351.73i 1.60708i 0.595253 + 0.803538i \(0.297052\pi\)
−0.595253 + 0.803538i \(0.702948\pi\)
\(224\) 558.160 0.166489
\(225\) 1068.68 + 351.489i 0.316646 + 0.104145i
\(226\) −773.279 −0.227601
\(227\) 6016.48i 1.75915i 0.475758 + 0.879576i \(0.342174\pi\)
−0.475758 + 0.879576i \(0.657826\pi\)
\(228\) 2133.93i 0.619839i
\(229\) −1210.84 −0.349408 −0.174704 0.984621i \(-0.555897\pi\)
−0.174704 + 0.984621i \(0.555897\pi\)
\(230\) −84.5235 + 527.520i −0.0242318 + 0.151233i
\(231\) 576.914 0.164321
\(232\) 0.517176i 0.000146355i
\(233\) 3517.31i 0.988957i −0.869190 0.494478i \(-0.835359\pi\)
0.869190 0.494478i \(-0.164641\pi\)
\(234\) −179.454 −0.0501335
\(235\) 3874.81 + 620.853i 1.07559 + 0.172340i
\(236\) −6886.84 −1.89956
\(237\) 821.487i 0.225153i
\(238\) 15.6072i 0.00425068i
\(239\) 6715.89 1.81764 0.908818 0.417194i \(-0.136986\pi\)
0.908818 + 0.417194i \(0.136986\pi\)
\(240\) −1974.88 316.432i −0.531159 0.0851066i
\(241\) −1715.70 −0.458582 −0.229291 0.973358i \(-0.573641\pi\)
−0.229291 + 0.973358i \(0.573641\pi\)
\(242\) 246.833i 0.0655663i
\(243\) 243.000i 0.0641500i
\(244\) 5767.80 1.51330
\(245\) 86.6732 540.937i 0.0226014 0.141058i
\(246\) 131.620 0.0341131
\(247\) 4236.31i 1.09129i
\(248\) 1366.99i 0.350017i
\(249\) −261.406 −0.0665298
\(250\) −531.877 274.629i −0.134556 0.0694762i
\(251\) −2464.48 −0.619748 −0.309874 0.950778i \(-0.600287\pi\)
−0.309874 + 0.950778i \(0.600287\pi\)
\(252\) 492.442i 0.123099i
\(253\) 3064.88i 0.761609i
\(254\) −703.482 −0.173781
\(255\) 27.6229 172.397i 0.00678358 0.0423370i
\(256\) 3188.67 0.778483
\(257\) 1873.99i 0.454850i −0.973796 0.227425i \(-0.926969\pi\)
0.973796 0.227425i \(-0.0730307\pi\)
\(258\) 330.594i 0.0797747i
\(259\) 2190.02 0.525409
\(260\) −4017.05 643.644i −0.958181 0.153527i
\(261\) 0.687072 0.000162945
\(262\) 1015.91i 0.239553i
\(263\) 2064.39i 0.484013i −0.970275 0.242007i \(-0.922194\pi\)
0.970275 0.242007i \(-0.0778056\pi\)
\(264\) −558.331 −0.130162
\(265\) 2166.62 + 347.153i 0.502243 + 0.0804733i
\(266\) 272.841 0.0628909
\(267\) 3272.97i 0.750197i
\(268\) 2853.20i 0.650325i
\(269\) −5649.86 −1.28059 −0.640294 0.768130i \(-0.721188\pi\)
−0.640294 + 0.768130i \(0.721188\pi\)
\(270\) 20.4560 127.668i 0.00461078 0.0287764i
\(271\) −3094.93 −0.693739 −0.346870 0.937913i \(-0.612755\pi\)
−0.346870 + 0.937913i \(0.612755\pi\)
\(272\) 310.405i 0.0691951i
\(273\) 977.601i 0.216729i
\(274\) −326.734 −0.0720391
\(275\) 3262.10 + 1072.90i 0.715317 + 0.235268i
\(276\) −2616.12 −0.570550
\(277\) 8962.93i 1.94415i −0.234665 0.972076i \(-0.575399\pi\)
0.234665 0.972076i \(-0.424601\pi\)
\(278\) 867.706i 0.187200i
\(279\) −1816.06 −0.389694
\(280\) −83.8814 + 523.513i −0.0179031 + 0.111735i
\(281\) −5858.94 −1.24383 −0.621913 0.783086i \(-0.713644\pi\)
−0.621913 + 0.783086i \(0.713644\pi\)
\(282\) 451.012i 0.0952390i
\(283\) 5819.46i 1.22237i −0.791487 0.611186i \(-0.790693\pi\)
0.791487 0.611186i \(-0.209307\pi\)
\(284\) 8696.13 1.81697
\(285\) −3013.82 482.898i −0.626397 0.100366i
\(286\) −547.774 −0.113254
\(287\) 717.023i 0.147472i
\(288\) 717.634i 0.146830i
\(289\) 4885.90 0.994485
\(290\) −0.360975 0.0578383i −7.30938e−5 1.17117e-5i
\(291\) −686.489 −0.138291
\(292\) 2047.90i 0.410425i
\(293\) 5678.78i 1.13228i −0.824310 0.566139i \(-0.808436\pi\)
0.824310 0.566139i \(-0.191564\pi\)
\(294\) −62.9629 −0.0124900
\(295\) 1558.46 9726.49i 0.307582 1.91965i
\(296\) −2119.47 −0.416189
\(297\) 741.746i 0.144917i
\(298\) 4.62169i 0.000898413i
\(299\) −5193.54 −1.00452
\(300\) 915.810 2784.47i 0.176248 0.535871i
\(301\) 1800.96 0.344869
\(302\) 1029.88i 0.196235i
\(303\) 1772.18i 0.336004i
\(304\) 5426.44 1.02377
\(305\) −1305.22 + 8146.04i −0.245039 + 1.52931i
\(306\) −20.0664 −0.00374875
\(307\) 9184.53i 1.70745i 0.520720 + 0.853727i \(0.325663\pi\)
−0.520720 + 0.853727i \(0.674337\pi\)
\(308\) 1503.16i 0.278086i
\(309\) −4413.17 −0.812480
\(310\) 954.125 + 152.877i 0.174808 + 0.0280092i
\(311\) 4410.22 0.804119 0.402059 0.915614i \(-0.368295\pi\)
0.402059 + 0.915614i \(0.368295\pi\)
\(312\) 946.112i 0.171676i
\(313\) 4405.28i 0.795530i 0.917487 + 0.397765i \(0.130214\pi\)
−0.917487 + 0.397765i \(0.869786\pi\)
\(314\) −169.882 −0.0305318
\(315\) 695.490 + 111.437i 0.124401 + 0.0199326i
\(316\) −2140.40 −0.381034
\(317\) 7486.86i 1.32651i −0.748393 0.663256i \(-0.769174\pi\)
0.748393 0.663256i \(-0.230826\pi\)
\(318\) 252.186i 0.0444713i
\(319\) 2.09726 0.000368100
\(320\) −783.407 + 4889.33i −0.136856 + 0.854130i
\(321\) −3669.87 −0.638107
\(322\) 334.493i 0.0578899i
\(323\) 473.701i 0.0816019i
\(324\) 633.140 0.108563
\(325\) 1818.08 5527.75i 0.310304 0.943459i
\(326\) 1178.60 0.200235
\(327\) 3841.91i 0.649719i
\(328\) 693.927i 0.116816i
\(329\) 2456.96 0.411722
\(330\) 62.4409 389.700i 0.0104159 0.0650070i
\(331\) 8860.56 1.47136 0.735680 0.677329i \(-0.236863\pi\)
0.735680 + 0.677329i \(0.236863\pi\)
\(332\) 681.097i 0.112590i
\(333\) 2815.74i 0.463367i
\(334\) 890.660 0.145912
\(335\) −4029.66 645.665i −0.657206 0.105303i
\(336\) −1252.24 −0.203320
\(337\) 8742.01i 1.41308i −0.707674 0.706539i \(-0.750255\pi\)
0.707674 0.706539i \(-0.249745\pi\)
\(338\) 12.7942i 0.00205891i
\(339\) 5416.15 0.867742
\(340\) −449.184 71.9719i −0.0716483 0.0114801i
\(341\) −5543.44 −0.880334
\(342\) 350.796i 0.0554646i
\(343\) 343.000i 0.0539949i
\(344\) −1742.95 −0.273179
\(345\) 592.013 3694.82i 0.0923853 0.576586i
\(346\) −826.480 −0.128416
\(347\) 7285.82i 1.12716i −0.826063 0.563579i \(-0.809424\pi\)
0.826063 0.563579i \(-0.190576\pi\)
\(348\) 1.79018i 0.000275757i
\(349\) −12610.9 −1.93423 −0.967117 0.254330i \(-0.918145\pi\)
−0.967117 + 0.254330i \(0.918145\pi\)
\(350\) −356.017 117.094i −0.0543712 0.0178827i
\(351\) 1256.92 0.191137
\(352\) 2190.55i 0.331695i
\(353\) 1202.59i 0.181325i 0.995882 + 0.0906623i \(0.0288984\pi\)
−0.995882 + 0.0906623i \(0.971102\pi\)
\(354\) −1132.12 −0.169977
\(355\) −1967.89 + 12281.8i −0.294210 + 1.83620i
\(356\) 8527.78 1.26958
\(357\) 109.315i 0.0162060i
\(358\) 701.649i 0.103585i
\(359\) −3216.35 −0.472848 −0.236424 0.971650i \(-0.575975\pi\)
−0.236424 + 0.971650i \(0.575975\pi\)
\(360\) −673.088 107.848i −0.0985413 0.0157891i
\(361\) 1422.14 0.207339
\(362\) 15.7024i 0.00227983i
\(363\) 1728.85i 0.249976i
\(364\) −2547.15 −0.366778
\(365\) 2892.30 + 463.428i 0.414767 + 0.0664573i
\(366\) 948.166 0.135414
\(367\) 1259.66i 0.179165i −0.995979 0.0895824i \(-0.971447\pi\)
0.995979 0.0895824i \(-0.0285532\pi\)
\(368\) 6652.59i 0.942365i
\(369\) −921.887 −0.130058
\(370\) 237.031 1479.34i 0.0333045 0.207857i
\(371\) 1373.82 0.192251
\(372\) 4731.77i 0.659491i
\(373\) 386.230i 0.0536145i 0.999641 + 0.0268073i \(0.00853404\pi\)
−0.999641 + 0.0268073i \(0.991466\pi\)
\(374\) −61.2517 −0.00846858
\(375\) 3725.34 + 1923.53i 0.513002 + 0.264882i
\(376\) −2377.82 −0.326135
\(377\) 3.55387i 0.000485501i
\(378\) 80.9523i 0.0110152i
\(379\) −14246.0 −1.93079 −0.965395 0.260794i \(-0.916016\pi\)
−0.965395 + 0.260794i \(0.916016\pi\)
\(380\) −1258.20 + 7852.54i −0.169853 + 1.06007i
\(381\) 4927.27 0.662551
\(382\) 451.800i 0.0605133i
\(383\) 9298.85i 1.24060i −0.784365 0.620299i \(-0.787011\pi\)
0.784365 0.620299i \(-0.212989\pi\)
\(384\) 2482.79 0.329946
\(385\) 2122.95 + 340.156i 0.281028 + 0.0450285i
\(386\) −91.5150 −0.0120673
\(387\) 2315.52i 0.304146i
\(388\) 1788.66i 0.234034i
\(389\) 1043.80 0.136049 0.0680244 0.997684i \(-0.478330\pi\)
0.0680244 + 0.997684i \(0.478330\pi\)
\(390\) −660.361 105.808i −0.0857402 0.0137380i
\(391\) −580.738 −0.0751130
\(392\) 331.952i 0.0427706i
\(393\) 7115.54i 0.913312i
\(394\) 1693.41 0.216530
\(395\) 484.360 3022.94i 0.0616982 0.385065i
\(396\) 1932.63 0.245248
\(397\) 4482.04i 0.566617i 0.959029 + 0.283309i \(0.0914321\pi\)
−0.959029 + 0.283309i \(0.908568\pi\)
\(398\) 397.980i 0.0501230i
\(399\) −1911.02 −0.239776
\(400\) −7080.69 2328.84i −0.885086 0.291105i
\(401\) 12686.2 1.57984 0.789921 0.613209i \(-0.210122\pi\)
0.789921 + 0.613209i \(0.210122\pi\)
\(402\) 469.036i 0.0581926i
\(403\) 9393.55i 1.16111i
\(404\) −4617.45 −0.568630
\(405\) −143.276 + 894.202i −0.0175789 + 0.109712i
\(406\) −0.228889 −2.79792e−5
\(407\) 8594.90i 1.04677i
\(408\) 105.794i 0.0128372i
\(409\) 6836.54 0.826516 0.413258 0.910614i \(-0.364391\pi\)
0.413258 + 0.910614i \(0.364391\pi\)
\(410\) 484.343 + 77.6052i 0.0583414 + 0.00934793i
\(411\) 2288.48 0.274654
\(412\) 11498.6i 1.37499i
\(413\) 6167.42i 0.734816i
\(414\) −430.062 −0.0510541
\(415\) −961.932 154.128i −0.113782 0.0182310i
\(416\) 3711.96 0.437485
\(417\) 6077.53i 0.713712i
\(418\) 1070.79i 0.125297i
\(419\) 5091.64 0.593659 0.296829 0.954930i \(-0.404071\pi\)
0.296829 + 0.954930i \(0.404071\pi\)
\(420\) 290.351 1812.11i 0.0337325 0.210528i
\(421\) 8373.48 0.969355 0.484677 0.874693i \(-0.338937\pi\)
0.484677 + 0.874693i \(0.338937\pi\)
\(422\) 396.968i 0.0457918i
\(423\) 3158.95i 0.363105i
\(424\) −1329.57 −0.152287
\(425\) 203.296 618.109i 0.0232031 0.0705475i
\(426\) 1429.55 0.162587
\(427\) 5165.28i 0.585399i
\(428\) 9561.91i 1.07989i
\(429\) 3836.68 0.431787
\(430\) 194.923 1216.53i 0.0218605 0.136434i
\(431\) 6027.75 0.673657 0.336829 0.941566i \(-0.390646\pi\)
0.336829 + 0.941566i \(0.390646\pi\)
\(432\) 1610.03i 0.179311i
\(433\) 11927.5i 1.32379i −0.749597 0.661894i \(-0.769753\pi\)
0.749597 0.661894i \(-0.230247\pi\)
\(434\) 604.996 0.0669141
\(435\) 2.52832 + 0.405107i 0.000278675 + 4.46515e-5i
\(436\) −10010.2 −1.09954
\(437\) 10152.3i 1.11133i
\(438\) 336.652i 0.0367257i
\(439\) −7914.93 −0.860499 −0.430250 0.902710i \(-0.641574\pi\)
−0.430250 + 0.902710i \(0.641574\pi\)
\(440\) −2054.57 329.200i −0.222609 0.0356681i
\(441\) 441.000 0.0476190
\(442\) 103.793i 0.0111695i
\(443\) 2522.71i 0.270559i 0.990807 + 0.135279i \(0.0431932\pi\)
−0.990807 + 0.135279i \(0.956807\pi\)
\(444\) 7336.44 0.784171
\(445\) −1929.79 + 12044.0i −0.205575 + 1.28302i
\(446\) 2292.24 0.243365
\(447\) 32.3709i 0.00342526i
\(448\) 3100.25i 0.326949i
\(449\) 5339.89 0.561258 0.280629 0.959816i \(-0.409457\pi\)
0.280629 + 0.959816i \(0.409457\pi\)
\(450\) 150.549 457.737i 0.0157710 0.0479509i
\(451\) −2814.02 −0.293807
\(452\) 14111.8i 1.46851i
\(453\) 7213.43i 0.748160i
\(454\) 2576.97 0.266395
\(455\) 576.407 3597.42i 0.0593899 0.370658i
\(456\) 1849.46 0.189932
\(457\) 13765.8i 1.40905i −0.709679 0.704526i \(-0.751160\pi\)
0.709679 0.704526i \(-0.248840\pi\)
\(458\) 518.625i 0.0529122i
\(459\) 140.547 0.0142924
\(460\) −9626.90 1542.50i −0.975775 0.156346i
\(461\) −12501.1 −1.26298 −0.631489 0.775384i \(-0.717556\pi\)
−0.631489 + 0.775384i \(0.717556\pi\)
\(462\) 247.103i 0.0248837i
\(463\) 3566.32i 0.357972i −0.983852 0.178986i \(-0.942718\pi\)
0.983852 0.178986i \(-0.0572817\pi\)
\(464\) −4.55229 −0.000455462
\(465\) −6682.81 1070.77i −0.666469 0.106787i
\(466\) −1506.53 −0.149761
\(467\) 4078.17i 0.404101i −0.979375 0.202050i \(-0.935240\pi\)
0.979375 0.202050i \(-0.0647605\pi\)
\(468\) 3274.91i 0.323468i
\(469\) −2555.15 −0.251569
\(470\) 265.923 1659.65i 0.0260981 0.162881i
\(471\) 1189.87 0.116404
\(472\) 5968.76i 0.582065i
\(473\) 7068.03i 0.687079i
\(474\) −351.858 −0.0340958
\(475\) −10805.6 3553.98i −1.04378 0.343300i
\(476\) −284.821 −0.0274259
\(477\) 1766.34i 0.169550i
\(478\) 2876.54i 0.275251i
\(479\) −19078.0 −1.81982 −0.909911 0.414803i \(-0.863850\pi\)
−0.909911 + 0.414803i \(0.863850\pi\)
\(480\) −423.127 + 2640.78i −0.0402355 + 0.251114i
\(481\) 14564.4 1.38062
\(482\) 734.868i 0.0694447i
\(483\) 2342.83i 0.220709i
\(484\) −4504.55 −0.423042
\(485\) −2526.17 404.764i −0.236511 0.0378956i
\(486\) 104.081 0.00971447
\(487\) 15616.4i 1.45307i −0.687128 0.726537i \(-0.741129\pi\)
0.687128 0.726537i \(-0.258871\pi\)
\(488\) 4998.90i 0.463708i
\(489\) −8255.07 −0.763409
\(490\) −231.693 37.1238i −0.0213609 0.00342262i
\(491\) 7547.46 0.693711 0.346856 0.937919i \(-0.387249\pi\)
0.346856 + 0.937919i \(0.387249\pi\)
\(492\) 2401.99i 0.220102i
\(493\) 0.397392i 3.63035e-5i
\(494\) 1814.49 0.165259
\(495\) −437.344 + 2729.51i −0.0397114 + 0.247843i
\(496\) 12032.5 1.08927
\(497\) 7787.70i 0.702870i
\(498\) 111.965i 0.0100748i
\(499\) −3288.10 −0.294982 −0.147491 0.989063i \(-0.547120\pi\)
−0.147491 + 0.989063i \(0.547120\pi\)
\(500\) 5011.80 9706.42i 0.448269 0.868169i
\(501\) −6238.30 −0.556301
\(502\) 1055.58i 0.0938506i
\(503\) 1044.67i 0.0926032i −0.998928 0.0463016i \(-0.985256\pi\)
0.998928 0.0463016i \(-0.0147435\pi\)
\(504\) −426.795 −0.0377202
\(505\) 1044.90 6521.36i 0.0920745 0.574647i
\(506\) −1312.74 −0.115333
\(507\) 89.6119i 0.00784972i
\(508\) 12838.1i 1.12126i
\(509\) 8783.91 0.764912 0.382456 0.923974i \(-0.375078\pi\)
0.382456 + 0.923974i \(0.375078\pi\)
\(510\) −73.8411 11.8314i −0.00641125 0.00102726i
\(511\) 1833.97 0.158767
\(512\) 7986.54i 0.689372i
\(513\) 2457.02i 0.211462i
\(514\) −802.666 −0.0688796
\(515\) −16239.8 2602.07i −1.38953 0.222642i
\(516\) 6033.13 0.514716
\(517\) 9642.54i 0.820268i
\(518\) 938.025i 0.0795646i
\(519\) 5788.77 0.489593
\(520\) −557.841 + 3481.54i −0.0470441 + 0.293607i
\(521\) 9983.79 0.839535 0.419767 0.907632i \(-0.362112\pi\)
0.419767 + 0.907632i \(0.362112\pi\)
\(522\) 0.294286i 2.46754e-5i
\(523\) 8177.52i 0.683706i 0.939754 + 0.341853i \(0.111054\pi\)
−0.939754 + 0.341853i \(0.888946\pi\)
\(524\) 18539.6 1.54563
\(525\) 2493.59 + 820.141i 0.207294 + 0.0681789i
\(526\) −884.215 −0.0732958
\(527\) 1050.38i 0.0868221i
\(528\) 4914.54i 0.405072i
\(529\) −279.364 −0.0229608
\(530\) 148.692 928.003i 0.0121864 0.0760564i
\(531\) 7929.54 0.648046
\(532\) 4979.18i 0.405780i
\(533\) 4768.45i 0.387513i
\(534\) 1401.88 0.113605
\(535\) −13504.6 2163.81i −1.09131 0.174859i
\(536\) 2472.85 0.199274
\(537\) 4914.44i 0.394923i
\(538\) 2419.94i 0.193924i
\(539\) 1346.13 0.107573
\(540\) 2329.86 + 373.308i 0.185669 + 0.0297493i
\(541\) −3425.16 −0.272198 −0.136099 0.990695i \(-0.543457\pi\)
−0.136099 + 0.990695i \(0.543457\pi\)
\(542\) 1325.61i 0.105055i
\(543\) 109.981i 0.00869199i
\(544\) 415.068 0.0327131
\(545\) 2265.24 14137.6i 0.178041 1.11117i
\(546\) −418.725 −0.0328201
\(547\) 5955.72i 0.465536i −0.972532 0.232768i \(-0.925222\pi\)
0.972532 0.232768i \(-0.0747783\pi\)
\(548\) 5962.68i 0.464805i
\(549\) −6641.07 −0.516273
\(550\) 459.545 1397.22i 0.0356274 0.108323i
\(551\) −6.94712 −0.000537127
\(552\) 2267.36i 0.174829i
\(553\) 1916.80i 0.147397i
\(554\) −3838.99 −0.294410
\(555\) −1660.20 + 10361.5i −0.126976 + 0.792468i
\(556\) −15835.1 −1.20784
\(557\) 2506.35i 0.190660i −0.995446 0.0953298i \(-0.969609\pi\)
0.995446 0.0953298i \(-0.0303906\pi\)
\(558\) 777.852i 0.0590127i
\(559\) 11977.0 0.906215
\(560\) −4608.06 738.341i −0.347725 0.0557153i
\(561\) 429.015 0.0322870
\(562\) 2509.50i 0.188357i
\(563\) 3460.79i 0.259068i −0.991575 0.129534i \(-0.958652\pi\)
0.991575 0.129534i \(-0.0413481\pi\)
\(564\) 8230.68 0.614493
\(565\) 19930.6 + 3193.43i 1.48404 + 0.237786i
\(566\) −2492.59 −0.185108
\(567\) 567.000i 0.0419961i
\(568\) 7536.86i 0.556760i
\(569\) −22561.2 −1.66224 −0.831119 0.556095i \(-0.812299\pi\)
−0.831119 + 0.556095i \(0.812299\pi\)
\(570\) −206.834 + 1290.87i −0.0151988 + 0.0948575i
\(571\) −992.585 −0.0727467 −0.0363734 0.999338i \(-0.511581\pi\)
−0.0363734 + 0.999338i \(0.511581\pi\)
\(572\) 9996.52i 0.730726i
\(573\) 3164.46i 0.230711i
\(574\) 307.114 0.0223322
\(575\) 4357.03 13247.3i 0.316001 0.960783i
\(576\) −3986.03 −0.288342
\(577\) 9202.70i 0.663975i 0.943284 + 0.331987i \(0.107719\pi\)
−0.943284 + 0.331987i \(0.892281\pi\)
\(578\) 2092.72i 0.150598i
\(579\) 640.983 0.0460075
\(580\) 1.05551 6.58756i 7.55651e−5 0.000471610i
\(581\) −609.947 −0.0435540
\(582\) 294.036i 0.0209419i
\(583\) 5391.67i 0.383019i
\(584\) −1774.89 −0.125763
\(585\) 4625.25 + 741.095i 0.326890 + 0.0523769i
\(586\) −2432.33 −0.171465
\(587\) 27046.3i 1.90174i 0.309593 + 0.950869i \(0.399807\pi\)
−0.309593 + 0.950869i \(0.600193\pi\)
\(588\) 1149.03i 0.0805872i
\(589\) 18362.5 1.28457
\(590\) −4166.04 667.516i −0.290700 0.0465783i
\(591\) −11860.9 −0.825534
\(592\) 18656.0i 1.29520i
\(593\) 26364.0i 1.82570i 0.408298 + 0.912849i \(0.366123\pi\)
−0.408298 + 0.912849i \(0.633877\pi\)
\(594\) 317.704 0.0219454
\(595\) 64.4534 402.261i 0.00444090 0.0277161i
\(596\) 84.3428 0.00579667
\(597\) 2787.50i 0.191097i
\(598\) 2224.49i 0.152117i
\(599\) −6624.09 −0.451841 −0.225921 0.974146i \(-0.572539\pi\)
−0.225921 + 0.974146i \(0.572539\pi\)
\(600\) −2413.27 793.724i −0.164202 0.0540061i
\(601\) −3984.03 −0.270403 −0.135201 0.990818i \(-0.543168\pi\)
−0.135201 + 0.990818i \(0.543168\pi\)
\(602\) 771.386i 0.0522248i
\(603\) 3285.19i 0.221863i
\(604\) −18794.7 −1.26613
\(605\) 1019.36 6361.91i 0.0685003 0.427518i
\(606\) −759.060 −0.0508823
\(607\) 8605.79i 0.575450i −0.957713 0.287725i \(-0.907101\pi\)
0.957713 0.287725i \(-0.0928990\pi\)
\(608\) 7256.14i 0.484005i
\(609\) 1.60317 0.000106673
\(610\) 3489.10 + 559.052i 0.231589 + 0.0371071i
\(611\) 16339.6 1.08188
\(612\) 366.198i 0.0241874i
\(613\) 22070.4i 1.45418i 0.686541 + 0.727091i \(0.259128\pi\)
−0.686541 + 0.727091i \(0.740872\pi\)
\(614\) 3933.91 0.258566
\(615\) −3392.40 543.557i −0.222430 0.0356396i
\(616\) −1302.77 −0.0852114
\(617\) 17328.8i 1.13068i 0.824858 + 0.565340i \(0.191255\pi\)
−0.824858 + 0.565340i \(0.808745\pi\)
\(618\) 1890.24i 0.123037i
\(619\) −1240.99 −0.0805808 −0.0402904 0.999188i \(-0.512828\pi\)
−0.0402904 + 0.999188i \(0.512828\pi\)
\(620\) −2789.91 + 17412.2i −0.180719 + 1.12789i
\(621\) 3012.21 0.194647
\(622\) 1888.98i 0.121771i
\(623\) 7636.94i 0.491119i
\(624\) −8327.86 −0.534265
\(625\) 12574.5 + 9274.82i 0.804769 + 0.593588i
\(626\) 1886.86 0.120470
\(627\) 7499.94i 0.477701i
\(628\) 3100.23i 0.196995i
\(629\) 1628.58 0.103236
\(630\) 47.7306 297.892i 0.00301846 0.0188386i
\(631\) 10004.0 0.631143 0.315572 0.948902i \(-0.397804\pi\)
0.315572 + 0.948902i \(0.397804\pi\)
\(632\) 1855.06i 0.116757i
\(633\) 2780.42i 0.174584i
\(634\) −3206.76 −0.200878
\(635\) 18131.6 + 2905.19i 1.13312 + 0.181557i
\(636\) 4602.22 0.286934
\(637\) 2281.07i 0.141883i
\(638\) 0.898294i 5.57426e-5i
\(639\) −10012.8 −0.619873
\(640\) 9136.27 + 1463.89i 0.564286 + 0.0904144i
\(641\) −23107.3 −1.42384 −0.711921 0.702260i \(-0.752174\pi\)
−0.711921 + 0.702260i \(0.752174\pi\)
\(642\) 1571.88i 0.0966308i
\(643\) 11629.9i 0.713281i −0.934242 0.356641i \(-0.883922\pi\)
0.934242 0.356641i \(-0.116078\pi\)
\(644\) −6104.27 −0.373513
\(645\) −1365.26 + 8520.76i −0.0833445 + 0.520162i
\(646\) 202.895 0.0123573
\(647\) 6371.50i 0.387156i 0.981085 + 0.193578i \(0.0620092\pi\)
−0.981085 + 0.193578i \(0.937991\pi\)
\(648\) 548.736i 0.0332661i
\(649\) 24204.6 1.46396
\(650\) −2367.64 778.716i −0.142871 0.0469904i
\(651\) −4237.47 −0.255114
\(652\) 21508.7i 1.29194i
\(653\) 20264.5i 1.21441i 0.794544 + 0.607207i \(0.207710\pi\)
−0.794544 + 0.607207i \(0.792290\pi\)
\(654\) −1645.56 −0.0983893
\(655\) −4195.42 + 26184.1i −0.250273 + 1.56198i
\(656\) 6108.08 0.363537
\(657\) 2357.96i 0.140019i
\(658\) 1052.36i 0.0623485i
\(659\) 7132.74 0.421627 0.210813 0.977526i \(-0.432389\pi\)
0.210813 + 0.977526i \(0.432389\pi\)
\(660\) 7111.78 + 1139.51i 0.419433 + 0.0672049i
\(661\) 10555.8 0.621140 0.310570 0.950550i \(-0.399480\pi\)
0.310570 + 0.950550i \(0.399480\pi\)
\(662\) 3795.14i 0.222813i
\(663\) 726.980i 0.0425846i
\(664\) 590.300 0.0345001
\(665\) −7032.24 1126.76i −0.410073 0.0657052i
\(666\) 1206.03 0.0701694
\(667\) 8.51689i 0.000494416i
\(668\) 16254.0i 0.941445i
\(669\) −16055.2 −0.927846
\(670\) −276.550 + 1725.98i −0.0159464 + 0.0995231i
\(671\) −20271.6 −1.16628
\(672\) 1674.48i 0.0961227i
\(673\) 3828.08i 0.219259i −0.993973 0.109630i \(-0.965034\pi\)
0.993973 0.109630i \(-0.0349665\pi\)
\(674\) −3744.37 −0.213988
\(675\) −1054.47 + 3206.04i −0.0601281 + 0.182816i
\(676\) 233.485 0.0132843
\(677\) 24660.6i 1.39998i −0.714154 0.699989i \(-0.753188\pi\)
0.714154 0.699989i \(-0.246812\pi\)
\(678\) 2319.84i 0.131405i
\(679\) −1601.81 −0.0905328
\(680\) −62.3773 + 389.304i −0.00351774 + 0.0219546i
\(681\) −18049.4 −1.01565
\(682\) 2374.36i 0.133312i
\(683\) 18562.2i 1.03992i 0.854192 + 0.519958i \(0.174052\pi\)
−0.854192 + 0.519958i \(0.825948\pi\)
\(684\) −6401.80 −0.357864
\(685\) 8421.26 + 1349.32i 0.469723 + 0.0752627i
\(686\) −146.913 −0.00817665
\(687\) 3632.52i 0.201731i
\(688\) 15341.8i 0.850146i
\(689\) 9136.38 0.505179
\(690\) −1582.56 253.570i −0.0873146 0.0139902i
\(691\) 27335.9 1.50493 0.752465 0.658632i \(-0.228865\pi\)
0.752465 + 0.658632i \(0.228865\pi\)
\(692\) 15082.7i 0.828554i
\(693\) 1730.74i 0.0948708i
\(694\) −3120.66 −0.170689
\(695\) 3583.39 22364.3i 0.195577 1.22062i
\(696\) −1.55153 −8.44979e−5
\(697\) 533.205i 0.0289764i
\(698\) 5401.50i 0.292908i
\(699\) 10551.9 0.570974
\(700\) 2136.89 6497.09i 0.115381 0.350810i
\(701\) −30924.1 −1.66617 −0.833087 0.553142i \(-0.813429\pi\)
−0.833087 + 0.553142i \(0.813429\pi\)
\(702\) 538.361i 0.0289446i
\(703\) 28470.4i 1.52743i
\(704\) −12167.2 −0.651375
\(705\) −1862.56 + 11624.4i −0.0995008 + 0.620995i
\(706\) 515.093 0.0274586
\(707\) 4135.09i 0.219966i
\(708\) 20660.5i 1.09671i
\(709\) 28329.0 1.50059 0.750295 0.661103i \(-0.229912\pi\)
0.750295 + 0.661103i \(0.229912\pi\)
\(710\) 5260.53 + 842.883i 0.278062 + 0.0445533i
\(711\) 2464.46 0.129992
\(712\) 7390.95i 0.389027i
\(713\) 22511.7i 1.18243i
\(714\) −46.8215 −0.00245413
\(715\) 14118.4 + 2262.16i 0.738458 + 0.118322i
\(716\) −12804.6 −0.668341
\(717\) 20147.7i 1.04941i
\(718\) 1377.62i 0.0716051i
\(719\) 12563.4 0.651651 0.325825 0.945430i \(-0.394358\pi\)
0.325825 + 0.945430i \(0.394358\pi\)
\(720\) 949.295 5924.65i 0.0491363 0.306665i
\(721\) −10297.4 −0.531893
\(722\) 609.127i 0.0313980i
\(723\) 5147.11i 0.264762i
\(724\) −286.558 −0.0147097
\(725\) 9.06495 + 2.98146i 0.000464364 + 0.000152729i
\(726\) −740.500 −0.0378547
\(727\) 13523.2i 0.689888i −0.938623 0.344944i \(-0.887898\pi\)
0.938623 0.344944i \(-0.112102\pi\)
\(728\) 2207.59i 0.112389i
\(729\) −729.000 −0.0370370
\(730\) 198.495 1238.83i 0.0100639 0.0628097i
\(731\) 1339.26 0.0677625
\(732\) 17303.4i 0.873706i
\(733\) 21325.0i 1.07457i −0.843402 0.537284i \(-0.819450\pi\)
0.843402 0.537284i \(-0.180550\pi\)
\(734\) −539.534 −0.0271316
\(735\) 1622.81 + 260.020i 0.0814398 + 0.0130489i
\(736\) 8895.74 0.445518
\(737\) 10027.9i 0.501197i
\(738\) 394.861i 0.0196952i
\(739\) 7403.75 0.368540 0.184270 0.982876i \(-0.441008\pi\)
0.184270 + 0.982876i \(0.441008\pi\)
\(740\) 26996.9 + 4325.67i 1.34112 + 0.214885i
\(741\) −12708.9 −0.630059
\(742\) 588.433i 0.0291133i
\(743\) 27131.6i 1.33965i −0.742519 0.669825i \(-0.766369\pi\)
0.742519 0.669825i \(-0.233631\pi\)
\(744\) 4100.98 0.202082
\(745\) −19.0863 + 119.120i −0.000938616 + 0.00585800i
\(746\) 165.430 0.00811904
\(747\) 784.217i 0.0384110i
\(748\) 1117.80i 0.0546403i
\(749\) −8563.04 −0.417739
\(750\) 823.886 1595.63i 0.0401121 0.0776857i
\(751\) −29393.3 −1.42820 −0.714098 0.700046i \(-0.753163\pi\)
−0.714098 + 0.700046i \(0.753163\pi\)
\(752\) 20930.0i 1.01495i
\(753\) 7393.44i 0.357811i
\(754\) −1.52219 −7.35211e−5
\(755\) 4253.14 26544.3i 0.205017 1.27953i
\(756\) 1477.33 0.0710712
\(757\) 37648.5i 1.80761i 0.427946 + 0.903804i \(0.359237\pi\)
−0.427946 + 0.903804i \(0.640763\pi\)
\(758\) 6101.84i 0.292386i
\(759\) 9194.63 0.439715
\(760\) 6805.72 + 1090.47i 0.324828 + 0.0520466i
\(761\) −35633.2 −1.69738 −0.848688 0.528894i \(-0.822607\pi\)
−0.848688 + 0.528894i \(0.822607\pi\)
\(762\) 2110.44i 0.100332i
\(763\) 8964.46i 0.425341i
\(764\) 8245.05 0.390439
\(765\) 517.192 + 82.8687i 0.0244433 + 0.00391650i
\(766\) −3982.87 −0.187868
\(767\) 41015.5i 1.93088i
\(768\) 9566.00i 0.449457i
\(769\) 3571.28 0.167469 0.0837345 0.996488i \(-0.473315\pi\)
0.0837345 + 0.996488i \(0.473315\pi\)
\(770\) 145.695 909.301i 0.00681883 0.0425570i
\(771\) 5621.98 0.262608
\(772\) 1670.09i 0.0778599i
\(773\) 16250.3i 0.756122i −0.925781 0.378061i \(-0.876591\pi\)
0.925781 0.378061i \(-0.123409\pi\)
\(774\) 991.782 0.0460580
\(775\) −23960.3 7880.55i −1.11056 0.365262i
\(776\) 1550.21 0.0717131
\(777\) 6570.05i 0.303345i
\(778\) 447.081i 0.0206024i
\(779\) 9321.37 0.428720
\(780\) 1930.93 12051.2i 0.0886391 0.553206i
\(781\) −30563.5 −1.40032
\(782\) 248.741i 0.0113746i
\(783\) 2.06122i 9.40764e-5i