Properties

Label 60.7.c.a.31.12
Level $60$
Weight $7$
Character 60.31
Analytic conductor $13.803$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.8032450172\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.12
Character \(\chi\) \(=\) 60.31
Dual form 60.7.c.a.31.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.331992 + 7.99311i) q^{2} +15.5885i q^{3} +(-63.7796 + 5.30729i) q^{4} -55.9017 q^{5} +(-124.600 + 5.17524i) q^{6} +552.003i q^{7} +(-63.5960 - 508.035i) q^{8} -243.000 q^{9} +O(q^{10})\) \(q+(0.331992 + 7.99311i) q^{2} +15.5885i q^{3} +(-63.7796 + 5.30729i) q^{4} -55.9017 q^{5} +(-124.600 + 5.17524i) q^{6} +552.003i q^{7} +(-63.5960 - 508.035i) q^{8} -243.000 q^{9} +(-18.5589 - 446.828i) q^{10} -1284.63i q^{11} +(-82.7325 - 994.225i) q^{12} -2513.57 q^{13} +(-4412.22 + 183.260i) q^{14} -871.421i q^{15} +(4039.67 - 676.993i) q^{16} +4597.01 q^{17} +(-80.6740 - 1942.33i) q^{18} -9800.21i q^{19} +(3565.39 - 296.687i) q^{20} -8604.88 q^{21} +(10268.2 - 426.487i) q^{22} +15217.2i q^{23} +(7919.48 - 991.364i) q^{24} +3125.00 q^{25} +(-834.485 - 20091.2i) q^{26} -3788.00i q^{27} +(-2929.64 - 35206.5i) q^{28} -14380.1 q^{29} +(6965.36 - 289.305i) q^{30} -34497.8i q^{31} +(6752.42 + 32064.7i) q^{32} +20025.4 q^{33} +(1526.17 + 36744.4i) q^{34} -30857.9i q^{35} +(15498.4 - 1289.67i) q^{36} -71409.5 q^{37} +(78334.2 - 3253.59i) q^{38} -39182.7i q^{39} +(3555.13 + 28400.0i) q^{40} -37657.2 q^{41} +(-2856.75 - 68779.7i) q^{42} -1535.15i q^{43} +(6817.91 + 81933.1i) q^{44} +13584.1 q^{45} +(-121633. + 5052.00i) q^{46} +131297. i q^{47} +(10553.3 + 62972.2i) q^{48} -187058. q^{49} +(1037.47 + 24978.5i) q^{50} +71660.4i q^{51} +(160314. - 13340.3i) q^{52} -228206. q^{53} +(30277.9 - 1257.58i) q^{54} +71813.0i q^{55} +(280437. - 35105.2i) q^{56} +152770. q^{57} +(-4774.07 - 114942. i) q^{58} +271199. i q^{59} +(4624.89 + 55578.9i) q^{60} -252456. q^{61} +(275745. - 11453.0i) q^{62} -134137. i q^{63} +(-254055. + 64618.0i) q^{64} +140513. q^{65} +(6648.27 + 160065. i) q^{66} -71786.4i q^{67} +(-293196. + 24397.7i) q^{68} -237213. q^{69} +(246651. - 10244.6i) q^{70} -193845. i q^{71} +(15453.8 + 123453. i) q^{72} +125558. q^{73} +(-23707.4 - 570784. i) q^{74} +48713.9i q^{75} +(52012.6 + 625053. i) q^{76} +709120. q^{77} +(313192. - 13008.3i) q^{78} +609914. i q^{79} +(-225824. + 37845.1i) q^{80} +59049.0 q^{81} +(-12501.9 - 300998. i) q^{82} -592195. i q^{83} +(548815. - 45668.6i) q^{84} -256981. q^{85} +(12270.6 - 509.657i) q^{86} -224163. i q^{87} +(-652637. + 81697.4i) q^{88} -154289. q^{89} +(4509.81 + 108579. i) q^{90} -1.38750e6i q^{91} +(-80762.4 - 970549. i) q^{92} +537768. q^{93} +(-1.04947e6 + 43589.6i) q^{94} +547849. i q^{95} +(-499840. + 105260. i) q^{96} -1.46175e6 q^{97} +(-62101.9 - 1.49518e6i) q^{98} +312165. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} + O(q^{10}) \) \( 24q + 20q^{2} - 246q^{4} + 162q^{6} - 340q^{8} - 5832q^{9} - 750q^{10} + 5040q^{13} - 2596q^{14} + 4194q^{16} - 4860q^{18} + 7000q^{20} + 19440q^{21} + 45780q^{22} + 24786q^{24} + 75000q^{25} + 75852q^{26} + 54300q^{28} + 132800q^{29} - 10700q^{32} - 173484q^{34} + 59778q^{36} - 69840q^{37} + 215800q^{38} - 14250q^{40} - 70448q^{41} - 189540q^{42} - 395668q^{44} - 158760q^{46} + 252720q^{48} - 642984q^{49} + 62500q^{50} - 210240q^{52} - 644320q^{53} - 39366q^{54} - 917708q^{56} + 408240q^{57} - 1345020q^{58} + 222750q^{60} - 222864q^{61} + 1948520q^{62} + 935922q^{64} + 266000q^{65} - 640548q^{66} + 572680q^{68} - 541728q^{69} + 220500q^{70} + 82620q^{72} + 771120q^{73} - 589164q^{74} - 191544q^{76} + 1383840q^{77} - 693360q^{78} - 946000q^{80} + 1417176q^{81} + 2672520q^{82} + 1256796q^{84} - 372000q^{85} + 1781528q^{86} + 956940q^{88} - 1566224q^{89} + 182250q^{90} - 3040560q^{92} + 1496880q^{93} - 3788352q^{94} - 413262q^{96} - 1666800q^{97} - 2709660q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.331992 + 7.99311i 0.0414990 + 0.999139i
\(3\) 15.5885i 0.577350i
\(4\) −63.7796 + 5.30729i −0.996556 + 0.0829264i
\(5\) −55.9017 −0.447214
\(6\) −124.600 + 5.17524i −0.576853 + 0.0239594i
\(7\) 552.003i 1.60934i 0.593723 + 0.804669i \(0.297657\pi\)
−0.593723 + 0.804669i \(0.702343\pi\)
\(8\) −63.5960 508.035i −0.124211 0.992256i
\(9\) −243.000 −0.333333
\(10\) −18.5589 446.828i −0.0185589 0.446828i
\(11\) 1284.63i 0.965162i −0.875851 0.482581i \(-0.839699\pi\)
0.875851 0.482581i \(-0.160301\pi\)
\(12\) −82.7325 994.225i −0.0478776 0.575362i
\(13\) −2513.57 −1.14409 −0.572046 0.820221i \(-0.693850\pi\)
−0.572046 + 0.820221i \(0.693850\pi\)
\(14\) −4412.22 + 183.260i −1.60795 + 0.0667859i
\(15\) 871.421i 0.258199i
\(16\) 4039.67 676.993i 0.986246 0.165282i
\(17\) 4597.01 0.935684 0.467842 0.883812i \(-0.345032\pi\)
0.467842 + 0.883812i \(0.345032\pi\)
\(18\) −80.6740 1942.33i −0.0138330 0.333046i
\(19\) 9800.21i 1.42881i −0.699732 0.714405i \(-0.746697\pi\)
0.699732 0.714405i \(-0.253303\pi\)
\(20\) 3565.39 296.687i 0.445673 0.0370858i
\(21\) −8604.88 −0.929152
\(22\) 10268.2 426.487i 0.964330 0.0400532i
\(23\) 15217.2i 1.25070i 0.780345 + 0.625349i \(0.215043\pi\)
−0.780345 + 0.625349i \(0.784957\pi\)
\(24\) 7919.48 991.364i 0.572879 0.0717133i
\(25\) 3125.00 0.200000
\(26\) −834.485 20091.2i −0.0474787 1.14311i
\(27\) 3788.00i 0.192450i
\(28\) −2929.64 35206.5i −0.133457 1.60380i
\(29\) −14380.1 −0.589614 −0.294807 0.955557i \(-0.595255\pi\)
−0.294807 + 0.955557i \(0.595255\pi\)
\(30\) 6965.36 289.305i 0.257976 0.0107150i
\(31\) 34497.8i 1.15800i −0.815329 0.578998i \(-0.803444\pi\)
0.815329 0.578998i \(-0.196556\pi\)
\(32\) 6752.42 + 32064.7i 0.206067 + 0.978538i
\(33\) 20025.4 0.557236
\(34\) 1526.17 + 36744.4i 0.0388299 + 0.934878i
\(35\) 30857.9i 0.719718i
\(36\) 15498.4 1289.67i 0.332185 0.0276421i
\(37\) −71409.5 −1.40978 −0.704889 0.709318i \(-0.749003\pi\)
−0.704889 + 0.709318i \(0.749003\pi\)
\(38\) 78334.2 3253.59i 1.42758 0.0592942i
\(39\) 39182.7i 0.660542i
\(40\) 3555.13 + 28400.0i 0.0555489 + 0.443750i
\(41\) −37657.2 −0.546383 −0.273191 0.961960i \(-0.588079\pi\)
−0.273191 + 0.961960i \(0.588079\pi\)
\(42\) −2856.75 68779.7i −0.0385588 0.928352i
\(43\) 1535.15i 0.0193083i −0.999953 0.00965417i \(-0.996927\pi\)
0.999953 0.00965417i \(-0.00307307\pi\)
\(44\) 6817.91 + 81933.1i 0.0800374 + 0.961837i
\(45\) 13584.1 0.149071
\(46\) −121633. + 5052.00i −1.24962 + 0.0519027i
\(47\) 131297.i 1.26463i 0.774713 + 0.632313i \(0.217894\pi\)
−0.774713 + 0.632313i \(0.782106\pi\)
\(48\) 10553.3 + 62972.2i 0.0954254 + 0.569410i
\(49\) −187058. −1.58997
\(50\) 1037.47 + 24978.5i 0.00829979 + 0.199828i
\(51\) 71660.4i 0.540217i
\(52\) 160314. 13340.3i 1.14015 0.0948755i
\(53\) −228206. −1.53285 −0.766424 0.642336i \(-0.777966\pi\)
−0.766424 + 0.642336i \(0.777966\pi\)
\(54\) 30277.9 1257.58i 0.192284 0.00798648i
\(55\) 71813.0i 0.431633i
\(56\) 280437. 35105.2i 1.59688 0.199898i
\(57\) 152770. 0.824924
\(58\) −4774.07 114942.i −0.0244684 0.589106i
\(59\) 271199.i 1.32048i 0.751053 + 0.660241i \(0.229546\pi\)
−0.751053 + 0.660241i \(0.770454\pi\)
\(60\) 4624.89 + 55578.9i 0.0214115 + 0.257310i
\(61\) −252456. −1.11223 −0.556116 0.831105i \(-0.687709\pi\)
−0.556116 + 0.831105i \(0.687709\pi\)
\(62\) 275745. 11453.0i 1.15700 0.0480556i
\(63\) 134137.i 0.536446i
\(64\) −254055. + 64618.0i −0.969143 + 0.246498i
\(65\) 140513. 0.511654
\(66\) 6648.27 + 160065.i 0.0231247 + 0.556756i
\(67\) 71786.4i 0.238681i −0.992853 0.119340i \(-0.961922\pi\)
0.992853 0.119340i \(-0.0380780\pi\)
\(68\) −293196. + 24397.7i −0.932461 + 0.0775929i
\(69\) −237213. −0.722091
\(70\) 246651. 10244.6i 0.719098 0.0298676i
\(71\) 193845.i 0.541601i −0.962635 0.270801i \(-0.912712\pi\)
0.962635 0.270801i \(-0.0872884\pi\)
\(72\) 15453.8 + 123453.i 0.0414037 + 0.330752i
\(73\) 125558. 0.322758 0.161379 0.986893i \(-0.448406\pi\)
0.161379 + 0.986893i \(0.448406\pi\)
\(74\) −23707.4 570784.i −0.0585043 1.40856i
\(75\) 48713.9i 0.115470i
\(76\) 52012.6 + 625053.i 0.118486 + 1.42389i
\(77\) 709120. 1.55327
\(78\) 313192. 13008.3i 0.659973 0.0274118i
\(79\) 609914.i 1.23705i 0.785765 + 0.618525i \(0.212270\pi\)
−0.785765 + 0.618525i \(0.787730\pi\)
\(80\) −225824. + 37845.1i −0.441063 + 0.0739162i
\(81\) 59049.0 0.111111
\(82\) −12501.9 300998.i −0.0226743 0.545912i
\(83\) 592195.i 1.03569i −0.855474 0.517846i \(-0.826734\pi\)
0.855474 0.517846i \(-0.173266\pi\)
\(84\) 548815. 45668.6i 0.925952 0.0770513i
\(85\) −256981. −0.418451
\(86\) 12270.6 509.657i 0.0192917 0.000801276i
\(87\) 224163.i 0.340414i
\(88\) −652637. + 81697.4i −0.957687 + 0.119884i
\(89\) −154289. −0.218859 −0.109429 0.993995i \(-0.534902\pi\)
−0.109429 + 0.993995i \(0.534902\pi\)
\(90\) 4509.81 + 108579.i 0.00618630 + 0.148943i
\(91\) 1.38750e6i 1.84123i
\(92\) −80762.4 970549.i −0.103716 1.24639i
\(93\) 537768. 0.668569
\(94\) −1.04947e6 + 43589.6i −1.26354 + 0.0524807i
\(95\) 547849.i 0.638984i
\(96\) −499840. + 105260.i −0.564959 + 0.118973i
\(97\) −1.46175e6 −1.60162 −0.800810 0.598919i \(-0.795597\pi\)
−0.800810 + 0.598919i \(0.795597\pi\)
\(98\) −62101.9 1.49518e6i −0.0659821 1.58860i
\(99\) 312165.i 0.321721i
\(100\) −199311. + 16585.3i −0.199311 + 0.0165853i
\(101\) 963761. 0.935417 0.467708 0.883883i \(-0.345080\pi\)
0.467708 + 0.883883i \(0.345080\pi\)
\(102\) −572789. + 23790.6i −0.539752 + 0.0224185i
\(103\) 1.01542e6i 0.929250i −0.885508 0.464625i \(-0.846189\pi\)
0.885508 0.464625i \(-0.153811\pi\)
\(104\) 159853. + 1.27698e6i 0.142109 + 1.13523i
\(105\) 481027. 0.415529
\(106\) −75762.4 1.82407e6i −0.0636116 1.53153i
\(107\) 509249.i 0.415699i 0.978161 + 0.207849i \(0.0666463\pi\)
−0.978161 + 0.207849i \(0.933354\pi\)
\(108\) 20104.0 + 241597.i 0.0159592 + 0.191787i
\(109\) 2.13481e6 1.64846 0.824231 0.566254i \(-0.191608\pi\)
0.824231 + 0.566254i \(0.191608\pi\)
\(110\) −574009. + 23841.3i −0.431262 + 0.0179123i
\(111\) 1.11316e6i 0.813936i
\(112\) 373703. + 2.22991e6i 0.265994 + 1.58720i
\(113\) 178688. 0.123840 0.0619200 0.998081i \(-0.480278\pi\)
0.0619200 + 0.998081i \(0.480278\pi\)
\(114\) 50718.4 + 1.22111e6i 0.0342335 + 0.824214i
\(115\) 850670.i 0.559329i
\(116\) 917156. 76319.3i 0.587583 0.0488946i
\(117\) 610798. 0.381364
\(118\) −2.16773e6 + 90036.0i −1.31935 + 0.0547987i
\(119\) 2.53757e6i 1.50583i
\(120\) −442712. + 55418.9i −0.256199 + 0.0320711i
\(121\) 121287. 0.0684633
\(122\) −83813.2 2.01790e6i −0.0461565 1.11127i
\(123\) 587018.i 0.315454i
\(124\) 183090. + 2.20026e6i 0.0960284 + 1.15401i
\(125\) −174693. −0.0894427
\(126\) 1.07217e6 44532.3i 0.535984 0.0222620i
\(127\) 1.94450e6i 0.949286i 0.880178 + 0.474643i \(0.157423\pi\)
−0.880178 + 0.474643i \(0.842577\pi\)
\(128\) −600843. 2.00924e6i −0.286504 0.958079i
\(129\) 23930.6 0.0111477
\(130\) 46649.1 + 1.12313e6i 0.0212331 + 0.511213i
\(131\) 3.66180e6i 1.62885i 0.580270 + 0.814424i \(0.302947\pi\)
−0.580270 + 0.814424i \(0.697053\pi\)
\(132\) −1.27721e6 + 106281.i −0.555317 + 0.0462096i
\(133\) 5.40975e6 2.29944
\(134\) 573796. 23832.5i 0.238475 0.00990501i
\(135\) 211755.i 0.0860663i
\(136\) −292352. 2.33544e6i −0.116222 0.928438i
\(137\) 477013. 0.185510 0.0927552 0.995689i \(-0.470433\pi\)
0.0927552 + 0.995689i \(0.470433\pi\)
\(138\) −78752.9 1.89607e6i −0.0299660 0.721469i
\(139\) 874957.i 0.325793i 0.986643 + 0.162897i \(0.0520837\pi\)
−0.986643 + 0.162897i \(0.947916\pi\)
\(140\) 163772. + 1.96810e6i 0.0596837 + 0.717239i
\(141\) −2.04672e6 −0.730132
\(142\) 1.54942e6 64354.9i 0.541135 0.0224759i
\(143\) 3.22901e6i 1.10423i
\(144\) −981639. + 164509.i −0.328749 + 0.0550939i
\(145\) 803871. 0.263683
\(146\) 41684.3 + 1.00360e6i 0.0133941 + 0.322480i
\(147\) 2.91595e6i 0.917970i
\(148\) 4.55447e6 378991.i 1.40492 0.116908i
\(149\) −2.52851e6 −0.764375 −0.382187 0.924085i \(-0.624829\pi\)
−0.382187 + 0.924085i \(0.624829\pi\)
\(150\) −389376. + 16172.6i −0.115371 + 0.00479189i
\(151\) 3.24281e6i 0.941869i −0.882168 0.470934i \(-0.843917\pi\)
0.882168 0.470934i \(-0.156083\pi\)
\(152\) −4.97885e6 + 623255.i −1.41775 + 0.177474i
\(153\) −1.11707e6 −0.311895
\(154\) 235422. + 5.66807e6i 0.0644592 + 1.55193i
\(155\) 1.92849e6i 0.517871i
\(156\) 207954. + 2.49906e6i 0.0547764 + 0.658267i
\(157\) −5.96596e6 −1.54164 −0.770818 0.637056i \(-0.780152\pi\)
−0.770818 + 0.637056i \(0.780152\pi\)
\(158\) −4.87511e6 + 202487.i −1.23599 + 0.0513363i
\(159\) 3.55737e6i 0.884990i
\(160\) −377472. 1.79247e6i −0.0921562 0.437615i
\(161\) −8.39997e6 −2.01280
\(162\) 19603.8 + 471985.i 0.00461100 + 0.111015i
\(163\) 4.08504e6i 0.943265i −0.881795 0.471632i \(-0.843665\pi\)
0.881795 0.471632i \(-0.156335\pi\)
\(164\) 2.40176e6 199858.i 0.544501 0.0453096i
\(165\) −1.11945e6 −0.249204
\(166\) 4.73348e6 196604.i 1.03480 0.0429801i
\(167\) 2.47808e6i 0.532067i −0.963964 0.266034i \(-0.914287\pi\)
0.963964 0.266034i \(-0.0857132\pi\)
\(168\) 547236. + 4.37158e6i 0.115411 + 0.921957i
\(169\) 1.49123e6 0.308948
\(170\) −85315.5 2.05408e6i −0.0173653 0.418090i
\(171\) 2.38145e6i 0.476270i
\(172\) 8147.48 + 97911.1i 0.00160117 + 0.0192418i
\(173\) 8.20504e6 1.58468 0.792341 0.610078i \(-0.208862\pi\)
0.792341 + 0.610078i \(0.208862\pi\)
\(174\) 1.79176e6 74420.4i 0.340120 0.0141268i
\(175\) 1.72501e6i 0.321868i
\(176\) −869686. 5.18948e6i −0.159523 0.951887i
\(177\) −4.22758e6 −0.762381
\(178\) −51222.6 1.23325e6i −0.00908241 0.218670i
\(179\) 3.09966e6i 0.540450i 0.962797 + 0.270225i \(0.0870981\pi\)
−0.962797 + 0.270225i \(0.912902\pi\)
\(180\) −866389. + 72094.8i −0.148558 + 0.0123619i
\(181\) −2.47886e6 −0.418038 −0.209019 0.977912i \(-0.567027\pi\)
−0.209019 + 0.977912i \(0.567027\pi\)
\(182\) 1.10904e7 460638.i 1.83965 0.0764092i
\(183\) 3.93539e6i 0.642148i
\(184\) 7.73089e6 967757.i 1.24101 0.155351i
\(185\) 3.99191e6 0.630472
\(186\) 178535. + 4.29844e6i 0.0277449 + 0.667993i
\(187\) 5.90546e6i 0.903086i
\(188\) −696833. 8.37408e6i −0.104871 1.26027i
\(189\) 2.09099e6 0.309717
\(190\) −4.37901e6 + 181881.i −0.638433 + 0.0265172i
\(191\) 1.42970e6i 0.205185i 0.994723 + 0.102592i \(0.0327137\pi\)
−0.994723 + 0.102592i \(0.967286\pi\)
\(192\) −1.00730e6 3.96033e6i −0.142316 0.559535i
\(193\) −1.81356e6 −0.252266 −0.126133 0.992013i \(-0.540257\pi\)
−0.126133 + 0.992013i \(0.540257\pi\)
\(194\) −485291. 1.16840e7i −0.0664656 1.60024i
\(195\) 2.19038e6i 0.295403i
\(196\) 1.19305e7 992774.i 1.58449 0.131851i
\(197\) −8.69647e6 −1.13748 −0.568740 0.822517i \(-0.692569\pi\)
−0.568740 + 0.822517i \(0.692569\pi\)
\(198\) −2.49517e6 + 103636.i −0.321443 + 0.0133511i
\(199\) 5.01570e6i 0.636462i 0.948013 + 0.318231i \(0.103089\pi\)
−0.948013 + 0.318231i \(0.896911\pi\)
\(200\) −198738. 1.58761e6i −0.0248422 0.198451i
\(201\) 1.11904e6 0.137802
\(202\) 319961. + 7.70344e6i 0.0388188 + 0.934611i
\(203\) 7.93785e6i 0.948888i
\(204\) −380322. 4.57047e6i −0.0447983 0.538357i
\(205\) 2.10510e6 0.244350
\(206\) 8.11634e6 337110.i 0.928450 0.0385629i
\(207\) 3.69779e6i 0.416899i
\(208\) −1.01540e7 + 1.70167e6i −1.12836 + 0.189097i
\(209\) −1.25896e7 −1.37903
\(210\) 159697. + 3.84490e6i 0.0172440 + 0.415171i
\(211\) 6.77795e6i 0.721525i −0.932658 0.360762i \(-0.882517\pi\)
0.932658 0.360762i \(-0.117483\pi\)
\(212\) 1.45549e7 1.21115e6i 1.52757 0.127114i
\(213\) 3.02175e6 0.312694
\(214\) −4.07048e6 + 169066.i −0.415340 + 0.0172511i
\(215\) 85817.4i 0.00863495i
\(216\) −1.92443e6 + 240902.i −0.190960 + 0.0239044i
\(217\) 1.90429e7 1.86361
\(218\) 708738. + 1.70637e7i 0.0684095 + 1.64704i
\(219\) 1.95726e6i 0.186344i
\(220\) −381133. 4.58020e6i −0.0357938 0.430147i
\(221\) −1.15549e7 −1.07051
\(222\) 8.89764e6 369561.i 0.813235 0.0337775i
\(223\) 1.21767e7i 1.09803i 0.835812 + 0.549016i \(0.184997\pi\)
−0.835812 + 0.549016i \(0.815003\pi\)
\(224\) −1.76998e7 + 3.72736e6i −1.57480 + 0.331632i
\(225\) −759375. −0.0666667
\(226\) 59323.1 + 1.42828e6i 0.00513923 + 0.123733i
\(227\) 8.92756e6i 0.763230i 0.924321 + 0.381615i \(0.124632\pi\)
−0.924321 + 0.381615i \(0.875368\pi\)
\(228\) −9.74362e6 + 810796.i −0.822083 + 0.0684080i
\(229\) −1.61284e7 −1.34302 −0.671512 0.740994i \(-0.734355\pi\)
−0.671512 + 0.740994i \(0.734355\pi\)
\(230\) 6.79950e6 282415.i 0.558847 0.0232116i
\(231\) 1.10541e7i 0.896782i
\(232\) 914517. + 7.30559e6i 0.0732365 + 0.585048i
\(233\) 5.66976e6 0.448226 0.224113 0.974563i \(-0.428052\pi\)
0.224113 + 0.974563i \(0.428052\pi\)
\(234\) 202780. + 4.88217e6i 0.0158262 + 0.381036i
\(235\) 7.33974e6i 0.565558i
\(236\) −1.43933e6 1.72970e7i −0.109503 1.31593i
\(237\) −9.50762e6 −0.714212
\(238\) −2.02830e7 + 842451.i −1.50453 + 0.0624905i
\(239\) 1.01650e7i 0.744583i −0.928116 0.372291i \(-0.878572\pi\)
0.928116 0.372291i \(-0.121428\pi\)
\(240\) −589947. 3.52025e6i −0.0426755 0.254648i
\(241\) −1.87229e7 −1.33759 −0.668795 0.743447i \(-0.733189\pi\)
−0.668795 + 0.743447i \(0.733189\pi\)
\(242\) 40266.2 + 969459.i 0.00284115 + 0.0684043i
\(243\) 920483.i 0.0641500i
\(244\) 1.61015e7 1.33986e6i 1.10840 0.0922335i
\(245\) 1.04569e7 0.711057
\(246\) 4.69210e6 194885.i 0.315182 0.0130910i
\(247\) 2.46335e7i 1.63469i
\(248\) −1.75261e7 + 2.19393e6i −1.14903 + 0.143836i
\(249\) 9.23140e6 0.597957
\(250\) −57996.6 1.39634e6i −0.00371178 0.0893657i
\(251\) 3.39034e6i 0.214398i 0.994238 + 0.107199i \(0.0341883\pi\)
−0.994238 + 0.107199i \(0.965812\pi\)
\(252\) 711903. + 8.55518e6i 0.0444856 + 0.534599i
\(253\) 1.95485e7 1.20713
\(254\) −1.55426e7 + 645559.i −0.948468 + 0.0393944i
\(255\) 4.00594e6i 0.241593i
\(256\) 1.58606e7 5.46965e6i 0.945364 0.326017i
\(257\) 2.79800e7 1.64835 0.824173 0.566338i \(-0.191640\pi\)
0.824173 + 0.566338i \(0.191640\pi\)
\(258\) 7944.76 + 191280.i 0.000462617 + 0.0111381i
\(259\) 3.94183e7i 2.26881i
\(260\) −8.96185e6 + 745743.i −0.509891 + 0.0424296i
\(261\) 3.49436e6 0.196538
\(262\) −2.92692e7 + 1.21569e6i −1.62745 + 0.0675955i
\(263\) 2.67037e7i 1.46793i 0.679189 + 0.733963i \(0.262331\pi\)
−0.679189 + 0.733963i \(0.737669\pi\)
\(264\) −1.27354e6 1.01736e7i −0.0692149 0.552921i
\(265\) 1.27571e7 0.685510
\(266\) 1.79599e6 + 4.32407e7i 0.0954244 + 2.29746i
\(267\) 2.40512e6i 0.126358i
\(268\) 380991. + 4.57850e6i 0.0197929 + 0.237859i
\(269\) 2.74962e7 1.41259 0.706295 0.707917i \(-0.250365\pi\)
0.706295 + 0.707917i \(0.250365\pi\)
\(270\) −1.69258e6 + 70301.0i −0.0859922 + 0.00357166i
\(271\) 7.82244e6i 0.393038i 0.980500 + 0.196519i \(0.0629637\pi\)
−0.980500 + 0.196519i \(0.937036\pi\)
\(272\) 1.85704e7 3.11215e6i 0.922815 0.154651i
\(273\) 2.16290e7 1.06304
\(274\) 158364. + 3.81281e6i 0.00769849 + 0.185351i
\(275\) 4.01447e6i 0.193032i
\(276\) 1.51294e7 1.25896e6i 0.719604 0.0598804i
\(277\) −3.48863e7 −1.64140 −0.820702 0.571356i \(-0.806418\pi\)
−0.820702 + 0.571356i \(0.806418\pi\)
\(278\) −6.99362e6 + 290478.i −0.325513 + 0.0135201i
\(279\) 8.38297e6i 0.385998i
\(280\) −1.56769e7 + 1.96244e6i −0.714144 + 0.0893969i
\(281\) −2.43392e6 −0.109695 −0.0548476 0.998495i \(-0.517467\pi\)
−0.0548476 + 0.998495i \(0.517467\pi\)
\(282\) −679495. 1.63597e7i −0.0302997 0.729503i
\(283\) 3.82558e7i 1.68787i 0.536447 + 0.843934i \(0.319766\pi\)
−0.536447 + 0.843934i \(0.680234\pi\)
\(284\) 1.02879e6 + 1.23634e7i 0.0449131 + 0.539736i
\(285\) −8.54011e6 −0.368917
\(286\) −2.58098e7 + 1.07200e6i −1.10328 + 0.0458246i
\(287\) 2.07869e7i 0.879315i
\(288\) −1.64084e6 7.79173e6i −0.0686891 0.326179i
\(289\) −3.00503e6 −0.124496
\(290\) 266879. + 6.42543e6i 0.0109426 + 0.263456i
\(291\) 2.27865e7i 0.924695i
\(292\) −8.00805e6 + 666374.i −0.321646 + 0.0267651i
\(293\) 2.04358e7 0.812436 0.406218 0.913776i \(-0.366847\pi\)
0.406218 + 0.913776i \(0.366847\pi\)
\(294\) 2.33075e7 968072.i 0.917179 0.0380948i
\(295\) 1.51605e7i 0.590538i
\(296\) 4.54136e6 + 3.62785e7i 0.175110 + 1.39886i
\(297\) −4.86617e6 −0.185745
\(298\) −839445. 2.02107e7i −0.0317208 0.763716i
\(299\) 3.82496e7i 1.43091i
\(300\) −258539. 3.10695e6i −0.00957552 0.115072i
\(301\) 847407. 0.0310737
\(302\) 2.59201e7 1.07659e6i 0.941058 0.0390866i
\(303\) 1.50235e7i 0.540063i
\(304\) −6.63468e6 3.95896e7i −0.236156 1.40916i
\(305\) 1.41127e7 0.497405
\(306\) −370859. 8.92890e6i −0.0129433 0.311626i
\(307\) 9.54158e6i 0.329765i −0.986313 0.164883i \(-0.947275\pi\)
0.986313 0.164883i \(-0.0527246\pi\)
\(308\) −4.52273e7 + 3.76351e6i −1.54792 + 0.128807i
\(309\) 1.58288e7 0.536503
\(310\) −1.54146e7 + 640242.i −0.517425 + 0.0214911i
\(311\) 2.91657e6i 0.0969595i 0.998824 + 0.0484798i \(0.0154376\pi\)
−0.998824 + 0.0484798i \(0.984562\pi\)
\(312\) −1.99062e7 + 2.49186e6i −0.655427 + 0.0820466i
\(313\) 1.93741e7 0.631814 0.315907 0.948790i \(-0.397691\pi\)
0.315907 + 0.948790i \(0.397691\pi\)
\(314\) −1.98065e6 4.76866e7i −0.0639763 1.54031i
\(315\) 7.49847e6i 0.239906i
\(316\) −3.23699e6 3.89001e7i −0.102584 1.23279i
\(317\) 6.50536e6 0.204218 0.102109 0.994773i \(-0.467441\pi\)
0.102109 + 0.994773i \(0.467441\pi\)
\(318\) 2.84345e7 1.18102e6i 0.884227 0.0367262i
\(319\) 1.84731e7i 0.569072i
\(320\) 1.42021e7 3.61226e6i 0.433414 0.110237i
\(321\) −7.93840e6 −0.240004
\(322\) −2.78872e6 6.71419e7i −0.0835290 2.01106i
\(323\) 4.50517e7i 1.33692i
\(324\) −3.76612e6 + 313390.i −0.110728 + 0.00921405i
\(325\) −7.85491e6 −0.228818
\(326\) 3.26522e7 1.35620e6i 0.942452 0.0391445i
\(327\) 3.32783e7i 0.951740i
\(328\) 2.39485e6 + 1.91312e7i 0.0678668 + 0.542151i
\(329\) −7.24765e7 −2.03521
\(330\) −371649. 8.94792e6i −0.0103417 0.248989i
\(331\) 2.30862e7i 0.636603i 0.947990 + 0.318301i \(0.103112\pi\)
−0.947990 + 0.318301i \(0.896888\pi\)
\(332\) 3.14295e6 + 3.77699e7i 0.0858862 + 1.03212i
\(333\) 1.73525e7 0.469926
\(334\) 1.98076e7 822703.i 0.531609 0.0220802i
\(335\) 4.01298e6i 0.106741i
\(336\) −3.47608e7 + 5.82545e6i −0.916373 + 0.153572i
\(337\) −4.43828e7 −1.15965 −0.579823 0.814743i \(-0.696878\pi\)
−0.579823 + 0.814743i \(0.696878\pi\)
\(338\) 495076. + 1.19196e7i 0.0128210 + 0.308681i
\(339\) 2.78548e6i 0.0714991i
\(340\) 1.63901e7 1.36387e6i 0.417009 0.0347006i
\(341\) −4.43170e7 −1.11765
\(342\) −1.90352e7 + 790622.i −0.475860 + 0.0197647i
\(343\) 3.83142e7i 0.949463i
\(344\) −779909. + 97629.4i −0.0191588 + 0.00239831i
\(345\) 1.32606e7 0.322929
\(346\) 2.72400e6 + 6.55838e7i 0.0657627 + 1.58332i
\(347\) 2.62548e7i 0.628376i −0.949361 0.314188i \(-0.898268\pi\)
0.949361 0.314188i \(-0.101732\pi\)
\(348\) 1.18970e6 + 1.42970e7i 0.0282293 + 0.339241i
\(349\) 7.54811e7 1.77567 0.887834 0.460164i \(-0.152209\pi\)
0.887834 + 0.460164i \(0.152209\pi\)
\(350\) −1.37882e7 + 572689.i −0.321590 + 0.0133572i
\(351\) 9.52140e6i 0.220181i
\(352\) 4.11913e7 8.67436e6i 0.944447 0.198888i
\(353\) −7.31900e6 −0.166390 −0.0831951 0.996533i \(-0.526512\pi\)
−0.0831951 + 0.996533i \(0.526512\pi\)
\(354\) −1.40352e6 3.37915e7i −0.0316380 0.761724i
\(355\) 1.08363e7i 0.242211i
\(356\) 9.84046e6 818855.i 0.218105 0.0181492i
\(357\) −3.95567e7 −0.869393
\(358\) −2.47759e7 + 1.02906e6i −0.539984 + 0.0224281i
\(359\) 4.02979e7i 0.870961i 0.900198 + 0.435480i \(0.143421\pi\)
−0.900198 + 0.435480i \(0.856579\pi\)
\(360\) −863896. 6.90120e6i −0.0185163 0.147917i
\(361\) −4.89983e7 −1.04150
\(362\) −822960. 1.98138e7i −0.0173482 0.417678i
\(363\) 1.89067e6i 0.0395273i
\(364\) 7.36386e6 + 8.84941e7i 0.152687 + 1.83489i
\(365\) −7.01892e6 −0.144342
\(366\) 3.14560e7 1.30652e6i 0.641594 0.0266485i
\(367\) 2.15750e7i 0.436469i 0.975896 + 0.218234i \(0.0700297\pi\)
−0.975896 + 0.218234i \(0.929970\pi\)
\(368\) 1.03020e7 + 6.14726e7i 0.206717 + 1.23350i
\(369\) 9.15071e6 0.182128
\(370\) 1.32528e6 + 3.19078e7i 0.0261639 + 0.629929i
\(371\) 1.25970e8i 2.46687i
\(372\) −3.42986e7 + 2.85409e6i −0.666266 + 0.0554420i
\(373\) 5.20071e7 1.00216 0.501079 0.865401i \(-0.332937\pi\)
0.501079 + 0.865401i \(0.332937\pi\)
\(374\) 4.72030e7 1.96056e6i 0.902308 0.0374771i
\(375\) 2.72319e6i 0.0516398i
\(376\) 6.67036e7 8.34999e6i 1.25483 0.157081i
\(377\) 3.61454e7 0.674573
\(378\) 694190. + 1.67135e7i 0.0128529 + 0.309451i
\(379\) 9.39645e6i 0.172602i 0.996269 + 0.0863010i \(0.0275047\pi\)
−0.996269 + 0.0863010i \(0.972495\pi\)
\(380\) −2.90759e6 3.49415e7i −0.0529886 0.636783i
\(381\) −3.03118e7 −0.548071
\(382\) −1.14277e7 + 474649.i −0.205008 + 0.00851495i
\(383\) 1.54516e7i 0.275028i −0.990500 0.137514i \(-0.956089\pi\)
0.990500 0.137514i \(-0.0439112\pi\)
\(384\) 3.13209e7 9.36622e6i 0.553147 0.165413i
\(385\) −3.96410e7 −0.694644
\(386\) −602086. 1.44960e7i −0.0104688 0.252049i
\(387\) 373041.i 0.00643612i
\(388\) 9.32301e7 7.75796e6i 1.59610 0.132817i
\(389\) −5.51480e7 −0.936873 −0.468437 0.883497i \(-0.655183\pi\)
−0.468437 + 0.883497i \(0.655183\pi\)
\(390\) −1.75079e7 + 727188.i −0.295149 + 0.0122589i
\(391\) 6.99539e7i 1.17026i
\(392\) 1.18962e7 + 9.50322e7i 0.197492 + 1.57766i
\(393\) −5.70818e7 −0.940416
\(394\) −2.88715e6 6.95118e7i −0.0472043 1.13650i
\(395\) 3.40952e7i 0.553226i
\(396\) −1.65675e6 1.99098e7i −0.0266791 0.320612i
\(397\) −9.29579e7 −1.48564 −0.742822 0.669489i \(-0.766513\pi\)
−0.742822 + 0.669489i \(0.766513\pi\)
\(398\) −4.00910e7 + 1.66517e6i −0.635914 + 0.0264125i
\(399\) 8.43296e7i 1.32758i
\(400\) 1.26240e7 2.11560e6i 0.197249 0.0330563i
\(401\) 1.17915e8 1.82867 0.914334 0.404960i \(-0.132715\pi\)
0.914334 + 0.404960i \(0.132715\pi\)
\(402\) 371512. + 8.94460e6i 0.00571866 + 0.137684i
\(403\) 8.67128e7i 1.32485i
\(404\) −6.14682e7 + 5.11496e6i −0.932195 + 0.0775708i
\(405\) −3.30094e6 −0.0496904
\(406\) 6.34481e7 2.63530e6i 0.948071 0.0393779i
\(407\) 9.17348e7i 1.36066i
\(408\) 3.64060e7 4.55732e6i 0.536034 0.0671009i
\(409\) 6.08808e7 0.889836 0.444918 0.895571i \(-0.353233\pi\)
0.444918 + 0.895571i \(0.353233\pi\)
\(410\) 698877. + 1.68263e7i 0.0101403 + 0.244139i
\(411\) 7.43589e6i 0.107104i
\(412\) 5.38911e6 + 6.47628e7i 0.0770594 + 0.926050i
\(413\) −1.49703e8 −2.12510
\(414\) 2.95568e7 1.22764e6i 0.416540 0.0173009i
\(415\) 3.31047e7i 0.463175i
\(416\) −1.69727e7 8.05970e7i −0.235760 1.11954i
\(417\) −1.36392e7 −0.188097
\(418\) −4.17966e6 1.00630e8i −0.0572285 1.37785i
\(419\) 3.24991e7i 0.441803i 0.975296 + 0.220902i \(0.0709000\pi\)
−0.975296 + 0.220902i \(0.929100\pi\)
\(420\) −3.06797e7 + 2.55295e6i −0.414098 + 0.0344584i
\(421\) 4.14006e7 0.554830 0.277415 0.960750i \(-0.410522\pi\)
0.277415 + 0.960750i \(0.410522\pi\)
\(422\) 5.41769e7 2.25022e6i 0.720903 0.0299425i
\(423\) 3.19052e7i 0.421542i
\(424\) 1.45130e7 + 1.15936e8i 0.190397 + 1.52098i
\(425\) 1.43657e7 0.187137
\(426\) 1.00319e6 + 2.41531e7i 0.0129765 + 0.312424i
\(427\) 1.39356e8i 1.78996i
\(428\) −2.70273e6 3.24797e7i −0.0344724 0.414267i
\(429\) −5.03353e7 −0.637530
\(430\) −685948. + 28490.7i −0.00862752 + 0.000358342i
\(431\) 2.64521e7i 0.330391i 0.986261 + 0.165196i \(0.0528255\pi\)
−0.986261 + 0.165196i \(0.947174\pi\)
\(432\) −2.56445e6 1.53022e7i −0.0318085 0.189803i
\(433\) −2.52090e7 −0.310521 −0.155261 0.987874i \(-0.549622\pi\)
−0.155261 + 0.987874i \(0.549622\pi\)
\(434\) 6.32209e6 + 1.52212e8i 0.0773377 + 1.86200i
\(435\) 1.25311e7i 0.152238i
\(436\) −1.36157e8 + 1.13300e7i −1.64278 + 0.136701i
\(437\) 1.49132e8 1.78701
\(438\) −1.56446e7 + 649794.i −0.186184 + 0.00773309i
\(439\) 1.58533e8i 1.87381i −0.349589 0.936903i \(-0.613679\pi\)
0.349589 0.936903i \(-0.386321\pi\)
\(440\) 3.64835e7 4.56702e6i 0.428291 0.0536136i
\(441\) 4.54552e7 0.529990
\(442\) −3.83614e6 9.23598e7i −0.0444250 1.06959i
\(443\) 1.05332e8i 1.21157i −0.795627 0.605787i \(-0.792858\pi\)
0.795627 0.605787i \(-0.207142\pi\)
\(444\) 5.90789e6 + 7.09971e7i 0.0674968 + 0.811132i
\(445\) 8.62500e6 0.0978766
\(446\) −9.73297e7 + 4.04256e6i −1.09709 + 0.0455672i
\(447\) 3.94156e7i 0.441312i
\(448\) −3.56694e7 1.40239e8i −0.396699 1.55968i
\(449\) −1.45273e8 −1.60490 −0.802448 0.596722i \(-0.796470\pi\)
−0.802448 + 0.596722i \(0.796470\pi\)
\(450\) −252106. 6.06977e6i −0.00276660 0.0666092i
\(451\) 4.83756e7i 0.527348i
\(452\) −1.13967e7 + 948351.i −0.123413 + 0.0102696i
\(453\) 5.05504e7 0.543788
\(454\) −7.13590e7 + 2.96388e6i −0.762572 + 0.0316732i
\(455\) 7.75636e7i 0.823424i
\(456\) −9.71558e6 7.76126e7i −0.102465 0.818536i
\(457\) 1.00926e8 1.05744 0.528718 0.848797i \(-0.322673\pi\)
0.528718 + 0.848797i \(0.322673\pi\)
\(458\) −5.35448e6 1.28916e8i −0.0557341 1.34187i
\(459\) 1.74135e7i 0.180072i
\(460\) 4.51475e6 + 5.42554e7i 0.0463832 + 0.557403i
\(461\) −1.04798e8 −1.06968 −0.534838 0.844955i \(-0.679627\pi\)
−0.534838 + 0.844955i \(0.679627\pi\)
\(462\) −8.83565e7 + 3.66986e6i −0.896009 + 0.0372155i
\(463\) 8.32165e7i 0.838430i 0.907887 + 0.419215i \(0.137695\pi\)
−0.907887 + 0.419215i \(0.862305\pi\)
\(464\) −5.80907e7 + 9.73523e6i −0.581504 + 0.0974523i
\(465\) −3.00621e7 −0.298993
\(466\) 1.88231e6 + 4.53190e7i 0.0186009 + 0.447840i
\(467\) 7.13276e6i 0.0700337i 0.999387 + 0.0350168i \(0.0111485\pi\)
−0.999387 + 0.0350168i \(0.988852\pi\)
\(468\) −3.89564e7 + 3.24168e6i −0.380051 + 0.0316252i
\(469\) 3.96263e7 0.384118
\(470\) 5.86673e7 2.43673e6i 0.565071 0.0234701i
\(471\) 9.30002e7i 0.890064i
\(472\) 1.37779e8 1.72472e7i 1.31026 0.164019i
\(473\) −1.97210e6 −0.0186357
\(474\) −3.15645e6 7.59955e7i −0.0296390 0.713596i
\(475\) 3.06257e7i 0.285762i
\(476\) −1.34676e7 1.61845e8i −0.124873 1.50065i
\(477\) 5.54540e7 0.510949
\(478\) 8.12498e7 3.37469e6i 0.743941 0.0308994i
\(479\) 1.02247e8i 0.930346i 0.885220 + 0.465173i \(0.154008\pi\)
−0.885220 + 0.465173i \(0.845992\pi\)
\(480\) 2.79419e7 5.88420e6i 0.252657 0.0532064i
\(481\) 1.79493e8 1.61292
\(482\) −6.21586e6 1.49654e8i −0.0555086 1.33644i
\(483\) 1.30943e8i 1.16209i
\(484\) −7.73562e6 + 643705.i −0.0682274 + 0.00567741i
\(485\) 8.17146e7 0.716266
\(486\) −7.35752e6 + 305593.i −0.0640948 + 0.00266216i
\(487\) 7.59619e6i 0.0657671i −0.999459 0.0328836i \(-0.989531\pi\)
0.999459 0.0328836i \(-0.0104691\pi\)
\(488\) 1.60552e7 + 1.28256e8i 0.138152 + 1.10362i
\(489\) 6.36795e7 0.544594
\(490\) 3.47160e6 + 8.35830e7i 0.0295081 + 0.710444i
\(491\) 4.78138e7i 0.403932i 0.979393 + 0.201966i \(0.0647331\pi\)
−0.979393 + 0.201966i \(0.935267\pi\)
\(492\) 3.11548e6 + 3.74398e7i 0.0261595 + 0.314368i
\(493\) −6.61055e7 −0.551692
\(494\) −1.96899e8 + 8.17813e6i −1.63328 + 0.0678380i
\(495\) 1.74506e7i 0.143878i
\(496\) −2.33548e7 1.39360e8i −0.191395 1.14207i
\(497\) 1.07003e8 0.871620
\(498\) 3.06475e6 + 7.37876e7i 0.0248146 + 0.597441i
\(499\) 7.03458e7i 0.566157i −0.959097 0.283078i \(-0.908644\pi\)
0.959097 0.283078i \(-0.0913556\pi\)
\(500\) 1.11418e7 927146.i 0.0891346 0.00741717i
\(501\) 3.86295e7 0.307189
\(502\) −2.70993e7 + 1.12556e6i −0.214214 + 0.00889731i
\(503\) 1.29972e7i 0.102128i −0.998695 0.0510639i \(-0.983739\pi\)
0.998695 0.0510639i \(-0.0162612\pi\)
\(504\) −6.81462e7 + 8.53057e6i −0.532292 + 0.0666325i
\(505\) −5.38759e7 −0.418331
\(506\) 6.48995e6 + 1.56254e8i 0.0500945 + 1.20609i
\(507\) 2.32460e7i 0.178371i
\(508\) −1.03200e7 1.24019e8i −0.0787209 0.946017i
\(509\) 1.39419e8 1.05723 0.528616 0.848861i \(-0.322711\pi\)
0.528616 + 0.848861i \(0.322711\pi\)
\(510\) 3.20199e7 1.32994e6i 0.241384 0.0100258i
\(511\) 6.93085e7i 0.519426i
\(512\) 4.89851e7 + 1.24959e8i 0.364968 + 0.931020i
\(513\) −3.71232e7 −0.274975
\(514\) 9.28913e6 + 2.23647e8i 0.0684047 + 1.64693i
\(515\) 5.67635e7i 0.415573i
\(516\) −1.52628e6 + 127007.i −0.0111093 + 0.000924437i
\(517\) 1.68668e8 1.22057
\(518\) 3.15074e8 1.30865e7i 2.26686 0.0941533i
\(519\) 1.27904e8i 0.914917i
\(520\) −8.93606e6 7.13855e7i −0.0635530 0.507691i
\(521\) −1.76371e6 −0.0124714 −0.00623570 0.999981i \(-0.501985\pi\)
−0.00623570 + 0.999981i \(0.501985\pi\)
\(522\) 1.16010e6 + 2.79308e7i 0.00815612 + 0.196369i
\(523\) 2.26098e8i 1.58049i −0.612792 0.790244i \(-0.709954\pi\)
0.612792 0.790244i \(-0.290046\pi\)
\(524\) −1.94342e7 2.33548e8i −0.135075 1.62324i
\(525\) −2.68902e7 −0.185830
\(526\) −2.13446e8 + 8.86541e6i −1.46666 + 0.0609174i
\(527\) 1.58587e8i 1.08352i
\(528\) 8.08959e7 1.35571e7i 0.549572 0.0921009i
\(529\) −8.35287e7 −0.564246
\(530\) 4.23525e6 + 1.01969e8i 0.0284480 + 0.684920i
\(531\) 6.59015e7i 0.440161i
\(532\) −3.45031e8 + 2.87111e7i −2.29152 + 0.190684i
\(533\) 9.46542e7 0.625112
\(534\) 1.92244e7 798481.i 0.126249 0.00524373i
\(535\) 2.84679e7i 0.185906i
\(536\) −3.64700e7 + 4.56533e6i −0.236832 + 0.0296468i
\(537\) −4.83190e7 −0.312029
\(538\) 9.12852e6 + 2.19780e8i 0.0586210 + 1.41137i
\(539\) 2.40301e8i 1.53458i
\(540\) −1.12385e6 1.35057e7i −0.00713717 0.0857699i
\(541\) 1.06341e8 0.671596 0.335798 0.941934i \(-0.390994\pi\)
0.335798 + 0.941934i \(0.390994\pi\)
\(542\) −6.25256e7 + 2.59699e6i −0.392699 + 0.0163107i
\(543\) 3.86416e7i 0.241354i
\(544\) 3.10410e7 + 1.47402e8i 0.192814 + 0.915602i
\(545\) −1.19339e8 −0.737215
\(546\) 7.18064e6 + 1.72883e8i 0.0441149 + 1.06212i
\(547\) 1.70542e7i 0.104200i 0.998642 + 0.0521002i \(0.0165915\pi\)
−0.998642 + 0.0521002i \(0.983408\pi\)
\(548\) −3.04237e7 + 2.53165e6i −0.184871 + 0.0153837i
\(549\) 6.13467e7 0.370744
\(550\) 3.20881e7 1.33277e6i 0.192866 0.00801064i
\(551\) 1.40928e8i 0.842446i
\(552\) 1.50858e7 + 1.20513e8i 0.0896917 + 0.716499i
\(553\) −3.36675e8 −1.99083
\(554\) −1.15820e7 2.78850e8i −0.0681166 1.63999i
\(555\) 6.22278e7i 0.364003i
\(556\) −4.64365e6 5.58043e7i −0.0270169 0.324671i
\(557\) −1.31701e8 −0.762118 −0.381059 0.924551i \(-0.624441\pi\)
−0.381059 + 0.924551i \(0.624441\pi\)
\(558\) −6.70060e7 + 2.78308e6i −0.385666 + 0.0160185i
\(559\) 3.85871e6i 0.0220905i
\(560\) −2.08906e7 1.24656e8i −0.118956 0.709819i
\(561\) 9.20571e7 0.521397
\(562\) −808042. 1.94546e7i −0.00455224 0.109601i
\(563\) 9.70061e7i 0.543593i 0.962355 + 0.271797i \(0.0876178\pi\)
−0.962355 + 0.271797i \(0.912382\pi\)
\(564\) 1.30539e8 1.08626e7i 0.727617 0.0605473i
\(565\) −9.98898e6 −0.0553829
\(566\) −3.05783e8 + 1.27006e7i −1.68641 + 0.0700448i
\(567\) 3.25952e7i 0.178815i
\(568\) −9.84801e7 + 1.23278e7i −0.537407 + 0.0672728i
\(569\) 2.37401e8 1.28868 0.644341 0.764738i \(-0.277132\pi\)
0.644341 + 0.764738i \(0.277132\pi\)
\(570\) −2.83525e6 6.82621e7i −0.0153097 0.368600i
\(571\) 8.85844e7i 0.475827i −0.971286 0.237913i \(-0.923537\pi\)
0.971286 0.237913i \(-0.0764635\pi\)
\(572\) −1.71373e7 2.05945e8i −0.0915702 1.10043i
\(573\) −2.22868e7 −0.118463
\(574\) 1.66152e8 6.90108e6i 0.878557 0.0364907i
\(575\) 4.75539e7i 0.250140i
\(576\) 6.17354e7 1.57022e7i 0.323048 0.0821661i
\(577\) −2.33160e8 −1.21374 −0.606871 0.794800i \(-0.707576\pi\)
−0.606871 + 0.794800i \(0.707576\pi\)
\(578\) −997644. 2.40195e7i −0.00516645 0.124389i
\(579\) 2.82706e7i 0.145646i
\(580\) −5.12706e7 + 4.26638e6i −0.262775 + 0.0218663i
\(581\) 3.26893e8 1.66678
\(582\) 1.82135e8 7.56493e6i 0.923899 0.0383739i
\(583\) 2.93160e8i 1.47945i
\(584\) −7.98500e6 6.37880e7i −0.0400901 0.320258i
\(585\) −3.41446e7 −0.170551
\(586\) 6.78452e6 + 1.63346e8i 0.0337152 + 0.811736i
\(587\) 3.20487e8i 1.58451i 0.610187 + 0.792257i \(0.291094\pi\)
−0.610187 + 0.792257i \(0.708906\pi\)
\(588\) 1.54758e7 + 1.85978e8i 0.0761240 + 0.914808i
\(589\) −3.38086e8 −1.65456
\(590\) 1.21180e8 5.03316e6i 0.590029 0.0245067i
\(591\) 1.35564e8i 0.656725i
\(592\) −2.88470e8 + 4.83438e7i −1.39039 + 0.233010i
\(593\) −2.06932e8 −0.992345 −0.496173 0.868224i \(-0.665262\pi\)
−0.496173 + 0.868224i \(0.665262\pi\)
\(594\) −1.61553e6 3.88958e7i −0.00770824 0.185585i
\(595\) 1.41854e8i 0.673429i
\(596\) 1.61267e8 1.34196e7i 0.761742 0.0633869i
\(597\) −7.81871e7 −0.367462
\(598\) 3.05733e8 1.26986e7i 1.42968 0.0593815i
\(599\) 1.70428e8i 0.792976i 0.918040 + 0.396488i \(0.129771\pi\)
−0.918040 + 0.396488i \(0.870229\pi\)
\(600\) 2.47484e7 3.09801e6i 0.114576 0.0143427i
\(601\) −2.51778e8 −1.15983 −0.579914 0.814678i \(-0.696914\pi\)
−0.579914 + 0.814678i \(0.696914\pi\)
\(602\) 281332. + 6.77342e6i 0.00128953 + 0.0310469i
\(603\) 1.74441e7i 0.0795603i
\(604\) 1.72105e7 + 2.06825e8i 0.0781058 + 0.938625i
\(605\) −6.78014e6 −0.0306177
\(606\) −1.20085e8 + 4.98769e6i −0.539598 + 0.0224121i
\(607\) 3.60842e8i 1.61343i 0.590940 + 0.806716i \(0.298757\pi\)
−0.590940 + 0.806716i \(0.701243\pi\)
\(608\) 3.14241e8 6.61751e7i 1.39815 0.294431i
\(609\) 1.23739e8 0.547841
\(610\) 4.68530e6 + 1.12804e8i 0.0206418 + 0.496977i
\(611\) 3.30025e8i 1.44685i
\(612\) 7.12465e7 5.92864e6i 0.310820 0.0258643i
\(613\) 2.76049e6 0.0119841 0.00599203 0.999982i \(-0.498093\pi\)
0.00599203 + 0.999982i \(0.498093\pi\)
\(614\) 7.62669e7 3.16773e6i 0.329481 0.0136849i
\(615\) 3.28153e7i 0.141075i
\(616\) −4.50972e7 3.60258e8i −0.192933 1.54124i
\(617\) −5.86892e7 −0.249863 −0.124932 0.992165i \(-0.539871\pi\)
−0.124932 + 0.992165i \(0.539871\pi\)
\(618\) 5.25502e6 + 1.26521e8i 0.0222643 + 0.536041i
\(619\) 2.86112e8i 1.20632i −0.797619 0.603161i \(-0.793907\pi\)
0.797619 0.603161i \(-0.206093\pi\)
\(620\) −1.02350e7 1.22998e8i −0.0429452 0.516087i
\(621\) 5.76429e7 0.240697
\(622\) −2.33124e7 + 968275.i −0.0968760 + 0.00402372i
\(623\) 8.51678e7i 0.352218i
\(624\) −2.65264e7 1.58285e8i −0.109175 0.651457i
\(625\) 9.76562e6 0.0400000
\(626\) 6.43205e6 + 1.54859e8i 0.0262196 + 0.631269i
\(627\) 1.96253e8i 0.796185i
\(628\) 3.80507e8 3.16631e7i 1.53633 0.127842i
\(629\) −3.28270e8 −1.31911
\(630\) −5.99361e7 + 2.48943e6i −0.239699 + 0.00995585i
\(631\) 2.43261e8i 0.968244i −0.875001 0.484122i \(-0.839139\pi\)
0.875001 0.484122i \(-0.160861\pi\)
\(632\) 3.09858e8 3.87881e7i 1.22747 0.153655i
\(633\) 1.05658e8 0.416572
\(634\) 2.15972e6 + 5.19980e7i 0.00847482 + 0.204042i
\(635\) 1.08701e8i 0.424534i
\(636\) 1.88800e7 + 2.26888e8i 0.0733890 + 0.881941i
\(637\) 4.70185e8 1.81907
\(638\) −1.47657e8 + 6.13291e6i −0.568582 + 0.0236159i
\(639\) 4.71043e7i 0.180534i
\(640\) 3.35882e7 + 1.12320e8i 0.128129 + 0.428466i
\(641\) 1.54539e8 0.586766 0.293383 0.955995i \(-0.405219\pi\)
0.293383 + 0.955995i \(0.405219\pi\)
\(642\) −2.63548e6 6.34525e7i −0.00995990 0.239797i
\(643\) 1.73101e8i 0.651130i 0.945520 + 0.325565i \(0.105555\pi\)
−0.945520 + 0.325565i \(0.894445\pi\)
\(644\) 5.35746e8 4.45811e7i 2.00586 0.166914i
\(645\) −1.33776e6 −0.00498539
\(646\) 3.60103e8 1.49568e7i 1.33576 0.0554806i
\(647\) 2.97783e8i 1.09948i −0.835336 0.549740i \(-0.814727\pi\)
0.835336 0.549740i \(-0.185273\pi\)
\(648\) −3.75528e6 2.99990e7i −0.0138012 0.110251i
\(649\) 3.48391e8 1.27448
\(650\) −2.60777e6 6.27851e7i −0.00949573 0.228621i
\(651\) 2.96850e8i 1.07595i
\(652\) 2.16805e7 + 2.60542e8i 0.0782216 + 0.940016i
\(653\) −4.67892e8 −1.68038 −0.840188 0.542296i \(-0.817555\pi\)
−0.840188 + 0.542296i \(0.817555\pi\)
\(654\) −2.65997e8 + 1.10481e7i −0.950920 + 0.0394962i
\(655\) 2.04701e8i 0.728443i
\(656\) −1.52123e8 + 2.54937e7i −0.538868 + 0.0903070i
\(657\) −3.05106e7 −0.107586
\(658\) −2.40616e7 5.79313e8i −0.0844592 2.03346i
\(659\) 3.65042e8i 1.27552i −0.770236 0.637759i \(-0.779862\pi\)
0.770236 0.637759i \(-0.220138\pi\)
\(660\) 7.13983e7 5.94127e6i 0.248345 0.0206656i
\(661\) 2.50270e7 0.0866573 0.0433287 0.999061i \(-0.486204\pi\)
0.0433287 + 0.999061i \(0.486204\pi\)
\(662\) −1.84530e8 + 7.66443e6i −0.636054 + 0.0264183i
\(663\) 1.80123e8i 0.618059i
\(664\) −3.00856e8 + 3.76612e7i −1.02767 + 0.128644i
\(665\) −3.02414e8 −1.02834
\(666\) 5.76089e6 + 1.38700e8i 0.0195014 + 0.469521i
\(667\) 2.18825e8i 0.737429i
\(668\) 1.31519e7 + 1.58051e8i 0.0441224 + 0.530234i
\(669\) −1.89816e8 −0.633949
\(670\) −3.20762e7 + 1.33228e6i −0.106649 + 0.00442965i
\(671\) 3.24312e8i 1.07348i
\(672\) −5.81037e7 2.75913e8i −0.191468 0.909210i
\(673\) −4.07582e8 −1.33712 −0.668559 0.743659i \(-0.733088\pi\)
−0.668559 + 0.743659i \(0.733088\pi\)
\(674\) −1.47347e7 3.54757e8i −0.0481241 1.15865i
\(675\) 1.18375e7i 0.0384900i
\(676\) −9.51101e7 + 7.91440e6i −0.307883 + 0.0256199i
\(677\) −3.08100e8 −0.992946 −0.496473 0.868052i \(-0.665372\pi\)
−0.496473 + 0.868052i \(0.665372\pi\)
\(678\) −2.22646e7 + 924755.i −0.0714375 + 0.00296714i
\(679\) 8.06893e8i 2.57755i
\(680\) 1.63430e7 + 1.30555e8i 0.0519762 + 0.415210i
\(681\) −1.39167e8 −0.440651
\(682\) −1.47129e7 3.54230e8i −0.0463814 1.11669i
\(683\) 2.86032e8i 0.897744i 0.893596 + 0.448872i \(0.148174\pi\)
−0.893596 + 0.448872i \(0.851826\pi\)
\(684\) −1.26391e7 1.51888e8i −0.0394954 0.474630i
\(685\) −2.66658e7 −0.0829628
\(686\) 3.06250e8 1.27200e7i 0.948645 0.0394017i
\(687\) 2.51416e8i 0.775395i
\(688\) −1.03929e6 6.20149e6i −0.00319131 0.0190428i
\(689\) 5.73611e8 1.75372
\(690\) 4.40242e6 + 1.05994e8i 0.0134012 + 0.322651i
\(691\) 6.17632e8i 1.87196i 0.352059 + 0.935978i \(0.385482\pi\)
−0.352059 + 0.935978i \(0.614518\pi\)
\(692\) −5.23314e8 + 4.35465e7i −1.57922 + 0.131412i
\(693\) −1.72316e8 −0.517757
\(694\) 2.09857e8 8.71636e6i 0.627835 0.0260770i
\(695\) 4.89116e7i 0.145699i
\(696\) −1.13883e8 + 1.42559e7i −0.337777 + 0.0422831i
\(697\) −1.73111e8 −0.511241
\(698\) 2.50591e7 + 6.03328e8i 0.0736884 + 1.77414i
\(699\) 8.83828e7i 0.258783i
\(700\) −9.15513e6 1.10020e8i −0.0266913 0.320759i
\(701\) −2.90668e8 −0.843808 −0.421904 0.906641i \(-0.638638\pi\)
−0.421904 + 0.906641i \(0.638638\pi\)
\(702\) −7.61055e7 + 3.16102e6i −0.219991 + 0.00913727i
\(703\) 6.99828e8i 2.01431i
\(704\) 8.30103e7 + 3.26367e8i 0.237911 + 0.935380i
\(705\) 1.14415e8 0.326525
\(706\) −2.42985e6 5.85016e7i −0.00690502 0.166247i
\(707\) 5.31999e8i 1.50540i
\(708\) 2.69633e8 2.24370e7i 0.759755 0.0632216i
\(709\) 5.33660e7 0.149736 0.0748679 0.997193i \(-0.476146\pi\)
0.0748679 + 0.997193i \(0.476146\pi\)
\(710\) −8.66155e7 + 3.59755e6i −0.242003 + 0.0100515i
\(711\) 1.48209e8i 0.412350i
\(712\) 9.81215e6 + 7.83840e7i 0.0271847 + 0.217164i
\(713\) 5.24962e8 1.44830
\(714\) −1.31325e7 3.16181e8i −0.0360789 0.868644i
\(715\) 1.80507e8i 0.493828i
\(716\) −1.64508e7 1.97695e8i −0.0448176 0.538588i
\(717\) 1.58456e8 0.429885
\(718\) −3.22105e8 + 1.33786e7i −0.870210 + 0.0361440i
\(719\) 8.54538e7i 0.229903i 0.993371 + 0.114951i \(0.0366713\pi\)
−0.993371 + 0.114951i \(0.963329\pi\)
\(720\) 5.48753e7 9.19636e6i 0.147021 0.0246387i
\(721\) 5.60513e8 1.49548
\(722\) −1.62670e7 3.91649e8i −0.0432212 1.04060i
\(723\) 2.91862e8i 0.772258i
\(724\) 1.58100e8 1.31560e7i 0.416598 0.0346664i
\(725\) −4.49378e7 −0.117923
\(726\) −1.51124e7 + 627688.i −0.0394932 + 0.00164034i
\(727\) 4.69711e8i 1.22244i 0.791461 + 0.611220i \(0.209321\pi\)
−0.791461 + 0.611220i \(0.790679\pi\)
\(728\) −7.04898e8 + 8.82395e7i −1.82697 + 0.228701i
\(729\) −1.43489e7 −0.0370370
\(730\) −2.33022e6 5.61030e7i −0.00599003 0.144217i
\(731\) 7.05710e6i 0.0180665i
\(732\) 2.08863e7 + 2.50998e8i 0.0532510 + 0.639936i
\(733\) 3.65700e8 0.928567 0.464283 0.885687i \(-0.346312\pi\)
0.464283 + 0.885687i \(0.346312\pi\)
\(734\) −1.72452e8 + 7.16273e6i −0.436093 + 0.0181130i
\(735\) 1.63007e8i 0.410529i
\(736\) −4.87937e8 + 1.02753e8i −1.22386 + 0.257728i
\(737\) −9.22189e7 −0.230366
\(738\) 3.03796e6 + 7.31426e7i 0.00755811 + 0.181971i
\(739\) 4.87643e8i 1.20828i −0.796877 0.604142i \(-0.793516\pi\)
0.796877 0.604142i \(-0.206484\pi\)
\(740\) −2.54602e8 + 2.11862e7i −0.628300 + 0.0522828i
\(741\) −3.83999e8 −0.943790
\(742\) 1.00689e9 4.18211e7i 2.46474 0.102373i
\(743\) 7.13753e8i 1.74013i −0.492939 0.870064i \(-0.664077\pi\)
0.492939 0.870064i \(-0.335923\pi\)
\(744\) −3.41999e7 2.73205e8i −0.0830436 0.663391i
\(745\) 1.41348e8 0.341839
\(746\) 1.72659e7 + 4.15699e8i 0.0415885 + 1.00129i
\(747\) 1.43903e8i 0.345230i
\(748\) 3.13420e7 + 3.76648e8i 0.0748897 + 0.899975i
\(749\) −2.81107e8 −0.669000
\(750\) 2.17668e7 904077.i 0.0515953 0.00214300i
\(751\) 3.91873e8i 0.925180i −0.886572 0.462590i \(-0.846920\pi\)
0.886572 0.462590i \(-0.153080\pi\)
\(752\) 8.88874e7 + 5.30397e8i 0.209019 + 1.24723i
\(753\) −5.28501e7 −0.123783
\(754\) 1.20000e7 + 2.88914e8i 0.0279941 + 0.673991i
\(755\) 1.81279e8i 0.421217i
\(756\) −1.33362e8 + 1.10975e7i −0.308651 + 0.0256838i
\(757\) 2.04521e7 0.0471466 0.0235733 0.999722i \(-0.492496\pi\)
0.0235733 + 0.999722i \(0.492496\pi\)
\(758\) −7.51068e7 + 3.11954e6i −0.172453 + 0.00716281i
\(759\) 3.04731e8i 0.696934i
\(760\) 2.78326e8 3.48410e7i 0.634035 0.0793688i
\(761\) 5.17521e8 1.17429 0.587143 0.809483i \(-0.300252\pi\)
0.587143 + 0.809483i \(0.300252\pi\)
\(762\) −1.00633e7 2.42285e8i −0.0227444 0.547599i
\(763\) 1.17842e9i 2.65293i
\(764\) −7.58784e6 9.11857e7i −0.0170152 0.204478i
\(765\) 6.24464e7 0.139484
\(766\) 1.23506e8 5.12980e6i 0.274791 0.0114134i
\(767\) 6.81679e8i 1.51075i
\(768\) 8.52635e7 + 2.47242e8i 0.188226 + 0.545806i
\(769\) −2.63067e8 −0.578478 −0.289239 0.957257i \(-0.593402\pi\)
−0.289239 + 0.957257i \(0.593402\pi\)
\(770\) −1.31605e7 3.16855e8i −0.0288270 0.694046i
\(771\) 4.36165e8i 0.951673i
\(772\) 1.15668e8 9.62508e6i 0.251397 0.0209196i
\(773\) 5.41479e8 1.17231