Properties

Label 6.19.b.a.5.5
Level 6
Weight 19
Character 6.5
Analytic conductor 12.323
Analytic rank 0
Dimension 6
CM No
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 19 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(12.3231682626\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{31}\cdot 3^{14} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.5
Root \(85.4804 - 88.2031i\)
Character \(\chi\) = 6.5
Dual form 6.19.b.a.5.2

$q$-expansion

\(f(q)\) \(=\) \(q+362.039i q^{2} +(-3612.02 + 19348.7i) q^{3} -131072. q^{4} -3.69488e6i q^{5} +(-7.00499e6 - 1.30769e6i) q^{6} +3.18077e7 q^{7} -4.74531e7i q^{8} +(-3.61327e8 - 1.39776e8i) q^{9} +O(q^{10})\) \(q+362.039i q^{2} +(-3612.02 + 19348.7i) q^{3} -131072. q^{4} -3.69488e6i q^{5} +(-7.00499e6 - 1.30769e6i) q^{6} +3.18077e7 q^{7} -4.74531e7i q^{8} +(-3.61327e8 - 1.39776e8i) q^{9} +1.33769e9 q^{10} +7.02311e8i q^{11} +(4.73435e8 - 2.53608e9i) q^{12} +8.10908e9 q^{13} +1.15156e10i q^{14} +(7.14912e10 + 1.33460e10i) q^{15} +1.71799e10 q^{16} -1.82909e11i q^{17} +(5.06044e10 - 1.30814e11i) q^{18} +2.50983e11 q^{19} +4.84295e11i q^{20} +(-1.14890e11 + 6.15439e11i) q^{21} -2.54264e11 q^{22} -9.32089e11i q^{23} +(9.18158e11 + 1.71402e11i) q^{24} -9.83742e12 q^{25} +2.93580e12i q^{26} +(4.00962e12 - 6.48635e12i) q^{27} -4.16910e12 q^{28} -8.17010e12i q^{29} +(-4.83176e12 + 2.58826e13i) q^{30} +2.87019e13 q^{31} +6.21978e12i q^{32} +(-1.35888e13 - 2.53676e12i) q^{33} +6.62202e13 q^{34} -1.17525e14i q^{35} +(4.73599e13 + 1.83207e13i) q^{36} +3.99953e13 q^{37} +9.08655e13i q^{38} +(-2.92902e13 + 1.56900e14i) q^{39} -1.75333e14 q^{40} -3.68995e14i q^{41} +(-2.22813e14 - 4.15947e13i) q^{42} -2.11773e14 q^{43} -9.20533e13i q^{44} +(-5.16456e14 + 1.33506e15i) q^{45} +3.37452e14 q^{46} -2.53857e14i q^{47} +(-6.20541e13 + 3.32409e14i) q^{48} -6.16685e14 q^{49} -3.56153e15i q^{50} +(3.53906e15 + 6.60673e14i) q^{51} -1.06287e15 q^{52} -2.48752e14i q^{53} +(2.34831e15 + 1.45164e15i) q^{54} +2.59495e15 q^{55} -1.50937e15i q^{56} +(-9.06556e14 + 4.85620e15i) q^{57} +2.95789e15 q^{58} +1.21495e14i q^{59} +(-9.37050e15 - 1.74928e15i) q^{60} +7.62514e14 q^{61} +1.03912e16i q^{62} +(-1.14930e16 - 4.44596e15i) q^{63} -2.25180e15 q^{64} -2.99621e16i q^{65} +(9.18406e14 - 4.91968e15i) q^{66} -4.78338e16 q^{67} +2.39743e16i q^{68} +(1.80347e16 + 3.36673e15i) q^{69} +4.25488e16 q^{70} +6.41967e16i q^{71} +(-6.63282e15 + 1.71461e16i) q^{72} +7.57613e16 q^{73} +1.44799e16i q^{74} +(3.55330e16 - 1.90342e17i) q^{75} -3.28968e16 q^{76} +2.23389e16i q^{77} +(-5.68040e16 - 1.06042e16i) q^{78} +1.35483e16 q^{79} -6.34775e16i q^{80} +(1.11020e17 + 1.01010e17i) q^{81} +1.33590e17 q^{82} +2.11746e17i q^{83} +(1.50589e16 - 8.06668e16i) q^{84} -6.75827e17 q^{85} -7.66699e16i q^{86} +(1.58081e17 + 2.95106e16i) q^{87} +3.33268e16 q^{88} +1.30497e17i q^{89} +(-4.83343e17 - 1.86977e17i) q^{90} +2.57931e17 q^{91} +1.22171e17i q^{92} +(-1.03672e17 + 5.55346e17i) q^{93} +9.19059e16 q^{94} -9.27351e17i q^{95} +(-1.20345e17 - 2.24660e16i) q^{96} +9.26791e17 q^{97} -2.23264e17i q^{98} +(9.81663e16 - 2.53764e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6258q^{3} - 786432q^{4} - 15753216q^{6} + 28233804q^{7} + 695971638q^{9} + O(q^{10}) \) \( 6q - 6258q^{3} - 786432q^{4} - 15753216q^{6} + 28233804q^{7} + 695971638q^{9} - 434257920q^{10} + 820248576q^{12} + 29566196220q^{13} + 119627095680q^{15} + 103079215104q^{16} + 315939373056q^{18} - 438814047012q^{19} + 2876527406172q^{21} - 2844452929536q^{22} + 2064805527552q^{24} - 25696048717290q^{25} + 11197265522814q^{27} - 3700661157888q^{28} + 13072787619840q^{30} + 21775814927148q^{31} - 962560003968q^{33} + 99067611119616q^{34} - 91222394535936q^{36} + 638446564817436q^{37} - 736541155104180q^{39} + 56919054090240q^{40} - 203954622480384q^{42} - 1688313718883652q^{43} + 390590504075520q^{45} + 1979247919104q^{46} - 107511621353472q^{48} - 895767896448270q^{49} + 9636273526722048q^{51} - 3875300470947840q^{52} + 2993011804200960q^{54} - 1259959207783680q^{55} + 4023767318253996q^{57} + 21251172660756480q^{58} - 15679762684968960q^{60} - 16279597277700036q^{61} - 32525159214131028q^{63} - 13510798882111488q^{64} - 60047751762690048q^{66} + 11153724314613276q^{67} + 3612037794746112q^{69} + 161904998736691200q^{70} - 41410805505196032q^{72} - 78910243347781140q^{73} + 348225828845090910q^{75} + 57516234769956864q^{76} - 168903906208235520q^{78} - 476518976428926228q^{79} + 630680446106425062q^{81} + 396536393269149696q^{82} - 377032200181776384q^{84} - 967978669078932480q^{85} + 419256510981966720q^{87} + 372828134380142592q^{88} - 2046848246643179520q^{90} - 1032060167365562760q^{91} + 764294136047005116q^{93} + 2566175766871080960q^{94} - 270638190107295744q^{96} + 834695417243310348q^{97} + 761688154713814272q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 362.039i 0.707107i
\(3\) −3612.02 + 19348.7i −0.183510 + 0.983018i
\(4\) −131072. −0.500000
\(5\) 3.69488e6i 1.89178i −0.324492 0.945889i \(-0.605193\pi\)
0.324492 0.945889i \(-0.394807\pi\)
\(6\) −7.00499e6 1.30769e6i −0.695099 0.129761i
\(7\) 3.18077e7 0.788224 0.394112 0.919062i \(-0.371052\pi\)
0.394112 + 0.919062i \(0.371052\pi\)
\(8\) 4.74531e7i 0.353553i
\(9\) −3.61327e8 1.39776e8i −0.932648 0.360787i
\(10\) 1.33769e9 1.33769
\(11\) 7.02311e8i 0.297848i 0.988849 + 0.148924i \(0.0475810\pi\)
−0.988849 + 0.148924i \(0.952419\pi\)
\(12\) 4.73435e8 2.53608e9i 0.0917549 0.491509i
\(13\) 8.10908e9 0.764683 0.382342 0.924021i \(-0.375118\pi\)
0.382342 + 0.924021i \(0.375118\pi\)
\(14\) 1.15156e10i 0.557359i
\(15\) 7.14912e10 + 1.33460e10i 1.85965 + 0.347160i
\(16\) 1.71799e10 0.250000
\(17\) 1.82909e11i 1.54239i −0.636596 0.771197i \(-0.719658\pi\)
0.636596 0.771197i \(-0.280342\pi\)
\(18\) 5.06044e10 1.30814e11i 0.255115 0.659482i
\(19\) 2.50983e11 0.777789 0.388894 0.921282i \(-0.372857\pi\)
0.388894 + 0.921282i \(0.372857\pi\)
\(20\) 4.84295e11i 0.945889i
\(21\) −1.14890e11 + 6.15439e11i −0.144647 + 0.774838i
\(22\) −2.54264e11 −0.210611
\(23\) 9.32089e11i 0.517496i −0.965945 0.258748i \(-0.916690\pi\)
0.965945 0.258748i \(-0.0833099\pi\)
\(24\) 9.18158e11 + 1.71402e11i 0.347549 + 0.0648805i
\(25\) −9.83742e12 −2.57882
\(26\) 2.93580e12i 0.540713i
\(27\) 4.00962e12 6.48635e12i 0.525810 0.850602i
\(28\) −4.16910e12 −0.394112
\(29\) 8.17010e12i 0.563178i −0.959535 0.281589i \(-0.909139\pi\)
0.959535 0.281589i \(-0.0908614\pi\)
\(30\) −4.83176e12 + 2.58826e13i −0.245479 + 1.31497i
\(31\) 2.87019e13 1.08557 0.542783 0.839873i \(-0.317371\pi\)
0.542783 + 0.839873i \(0.317371\pi\)
\(32\) 6.21978e12i 0.176777i
\(33\) −1.35888e13 2.53676e12i −0.292790 0.0546581i
\(34\) 6.62202e13 1.09064
\(35\) 1.17525e14i 1.49114i
\(36\) 4.73599e13 + 1.83207e13i 0.466324 + 0.180393i
\(37\) 3.99953e13 0.307747 0.153874 0.988091i \(-0.450825\pi\)
0.153874 + 0.988091i \(0.450825\pi\)
\(38\) 9.08655e13i 0.549980i
\(39\) −2.92902e13 + 1.56900e14i −0.140327 + 0.751697i
\(40\) −1.75333e14 −0.668844
\(41\) 3.68995e14i 1.12711i −0.826079 0.563554i \(-0.809434\pi\)
0.826079 0.563554i \(-0.190566\pi\)
\(42\) −2.22813e14 4.15947e13i −0.547893 0.102281i
\(43\) −2.11773e14 −0.421361 −0.210680 0.977555i \(-0.567568\pi\)
−0.210680 + 0.977555i \(0.567568\pi\)
\(44\) 9.20533e13i 0.148924i
\(45\) −5.16456e14 + 1.33506e15i −0.682528 + 1.76436i
\(46\) 3.37452e14 0.365925
\(47\) 2.53857e14i 0.226834i −0.993547 0.113417i \(-0.963820\pi\)
0.993547 0.113417i \(-0.0361796\pi\)
\(48\) −6.20541e13 + 3.32409e14i −0.0458774 + 0.245754i
\(49\) −6.16685e14 −0.378703
\(50\) 3.56153e15i 1.82350i
\(51\) 3.53906e15 + 6.60673e14i 1.51620 + 0.283044i
\(52\) −1.06287e15 −0.382342
\(53\) 2.48752e14i 0.0753848i −0.999289 0.0376924i \(-0.987999\pi\)
0.999289 0.0376924i \(-0.0120007\pi\)
\(54\) 2.34831e15 + 1.45164e15i 0.601466 + 0.371804i
\(55\) 2.59495e15 0.563463
\(56\) 1.50937e15i 0.278679i
\(57\) −9.06556e14 + 4.85620e15i −0.142732 + 0.764580i
\(58\) 2.95789e15 0.398227
\(59\) 1.21495e14i 0.0140246i 0.999975 + 0.00701231i \(0.00223211\pi\)
−0.999975 + 0.00701231i \(0.997768\pi\)
\(60\) −9.37050e15 1.74928e15i −0.929825 0.173580i
\(61\) 7.62514e14 0.0652047 0.0326024 0.999468i \(-0.489621\pi\)
0.0326024 + 0.999468i \(0.489621\pi\)
\(62\) 1.03912e16i 0.767611i
\(63\) −1.14930e16 4.44596e15i −0.735136 0.284381i
\(64\) −2.25180e15 −0.125000
\(65\) 2.99621e16i 1.44661i
\(66\) 9.18406e14 4.91968e15i 0.0386491 0.207034i
\(67\) −4.78338e16 −1.75817 −0.879086 0.476663i \(-0.841846\pi\)
−0.879086 + 0.476663i \(0.841846\pi\)
\(68\) 2.39743e16i 0.771197i
\(69\) 1.80347e16 + 3.36673e15i 0.508707 + 0.0949655i
\(70\) 4.25488e16 1.05440
\(71\) 6.41967e16i 1.40019i 0.714048 + 0.700096i \(0.246860\pi\)
−0.714048 + 0.700096i \(0.753140\pi\)
\(72\) −6.63282e15 + 1.71461e16i −0.127557 + 0.329741i
\(73\) 7.57613e16 1.28689 0.643446 0.765492i \(-0.277504\pi\)
0.643446 + 0.765492i \(0.277504\pi\)
\(74\) 1.44799e16i 0.217610i
\(75\) 3.55330e16 1.90342e17i 0.473239 2.53503i
\(76\) −3.28968e16 −0.388894
\(77\) 2.23389e16i 0.234771i
\(78\) −5.68040e16 1.06042e16i −0.531530 0.0992260i
\(79\) 1.35483e16 0.113042 0.0565209 0.998401i \(-0.481999\pi\)
0.0565209 + 0.998401i \(0.481999\pi\)
\(80\) 6.34775e16i 0.472944i
\(81\) 1.11020e17 + 1.01010e17i 0.739666 + 0.672974i
\(82\) 1.33590e17 0.796986
\(83\) 2.11746e17i 1.13269i 0.824168 + 0.566346i \(0.191643\pi\)
−0.824168 + 0.566346i \(0.808357\pi\)
\(84\) 1.50589e16 8.06668e16i 0.0723234 0.387419i
\(85\) −6.75827e17 −2.91787
\(86\) 7.66699e16i 0.297947i
\(87\) 1.58081e17 + 2.95106e16i 0.553614 + 0.103349i
\(88\) 3.33268e16 0.105305
\(89\) 1.30497e17i 0.372470i 0.982505 + 0.186235i \(0.0596285\pi\)
−0.982505 + 0.186235i \(0.940371\pi\)
\(90\) −4.83343e17 1.86977e17i −1.24759 0.482620i
\(91\) 2.57931e17 0.602742
\(92\) 1.22171e17i 0.258748i
\(93\) −1.03672e17 + 5.55346e17i −0.199212 + 1.06713i
\(94\) 9.19059e16 0.160396
\(95\) 9.27351e17i 1.47140i
\(96\) −1.20345e17 2.24660e16i −0.173775 0.0324403i
\(97\) 9.26791e17 1.21909 0.609545 0.792751i \(-0.291352\pi\)
0.609545 + 0.792751i \(0.291352\pi\)
\(98\) 2.23264e17i 0.267783i
\(99\) 9.81663e16 2.53764e17i 0.107460 0.277788i
\(100\) 1.28941e18 1.28941
\(101\) 4.46291e16i 0.0408062i 0.999792 + 0.0204031i \(0.00649495\pi\)
−0.999792 + 0.0204031i \(0.993505\pi\)
\(102\) −2.39189e17 + 1.28128e18i −0.200143 + 1.07212i
\(103\) −1.64674e18 −1.26209 −0.631043 0.775747i \(-0.717373\pi\)
−0.631043 + 0.775747i \(0.717373\pi\)
\(104\) 3.84801e17i 0.270356i
\(105\) 2.27397e18 + 4.24505e17i 1.46582 + 0.273640i
\(106\) 9.00579e16 0.0533051
\(107\) 2.30785e18i 1.25532i −0.778488 0.627660i \(-0.784013\pi\)
0.778488 0.627660i \(-0.215987\pi\)
\(108\) −5.25548e17 + 8.50179e17i −0.262905 + 0.425301i
\(109\) −1.97197e18 −0.907951 −0.453975 0.891014i \(-0.649995\pi\)
−0.453975 + 0.891014i \(0.649995\pi\)
\(110\) 9.39473e17i 0.398428i
\(111\) −1.44464e17 + 7.73860e17i −0.0564746 + 0.302521i
\(112\) 5.46452e17 0.197056
\(113\) 1.28812e18i 0.428794i 0.976747 + 0.214397i \(0.0687787\pi\)
−0.976747 + 0.214397i \(0.931221\pi\)
\(114\) −1.75813e18 3.28208e17i −0.540640 0.100927i
\(115\) −3.44395e18 −0.978986
\(116\) 1.07087e18i 0.281589i
\(117\) −2.93003e18 1.13346e18i −0.713180 0.275888i
\(118\) −4.39860e16 −0.00991691
\(119\) 5.81792e18i 1.21575i
\(120\) 6.33309e17 3.39248e18i 0.122739 0.657486i
\(121\) 5.06668e18 0.911286
\(122\) 2.76059e17i 0.0461067i
\(123\) 7.13958e18 + 1.33282e18i 1.10797 + 0.206835i
\(124\) −3.76202e18 −0.542783
\(125\) 2.22532e19i 2.98678i
\(126\) 1.60961e18 4.16090e18i 0.201088 0.519820i
\(127\) 2.56743e18 0.298721 0.149360 0.988783i \(-0.452279\pi\)
0.149360 + 0.988783i \(0.452279\pi\)
\(128\) 8.15239e17i 0.0883883i
\(129\) 7.64928e17 4.09754e18i 0.0773238 0.414205i
\(130\) 1.08474e19 1.02291
\(131\) 9.70264e18i 0.853981i −0.904256 0.426990i \(-0.859574\pi\)
0.904256 0.426990i \(-0.140426\pi\)
\(132\) 1.78112e18 + 3.32499e17i 0.146395 + 0.0273290i
\(133\) 7.98318e18 0.613072
\(134\) 1.73177e19i 1.24322i
\(135\) −2.39663e19 1.48150e19i −1.60915 0.994715i
\(136\) −8.67962e18 −0.545319
\(137\) 2.13367e19i 1.25500i 0.778618 + 0.627498i \(0.215921\pi\)
−0.778618 + 0.627498i \(0.784079\pi\)
\(138\) −1.21888e18 + 6.52927e18i −0.0671508 + 0.359710i
\(139\) 1.11915e19 0.577770 0.288885 0.957364i \(-0.406716\pi\)
0.288885 + 0.957364i \(0.406716\pi\)
\(140\) 1.54043e19i 0.745572i
\(141\) 4.91181e18 + 9.16936e17i 0.222982 + 0.0416262i
\(142\) −2.32417e19 −0.990086
\(143\) 5.69509e18i 0.227760i
\(144\) −6.20755e18 2.40134e18i −0.233162 0.0901967i
\(145\) −3.01875e19 −1.06541
\(146\) 2.74285e19i 0.909969i
\(147\) 2.22748e18 1.19321e19i 0.0694957 0.372272i
\(148\) −5.24227e18 −0.153874
\(149\) 3.51402e19i 0.970796i −0.874293 0.485398i \(-0.838675\pi\)
0.874293 0.485398i \(-0.161325\pi\)
\(150\) 6.89111e19 + 1.28643e19i 1.79253 + 0.334630i
\(151\) −1.32025e19 −0.323491 −0.161746 0.986832i \(-0.551712\pi\)
−0.161746 + 0.986832i \(0.551712\pi\)
\(152\) 1.19099e19i 0.274990i
\(153\) −2.55664e19 + 6.60901e19i −0.556476 + 1.43851i
\(154\) −8.08754e18 −0.166008
\(155\) 1.06050e20i 2.05365i
\(156\) 3.83912e18 2.05653e19i 0.0701634 0.375849i
\(157\) 6.77852e19 1.16960 0.584801 0.811177i \(-0.301173\pi\)
0.584801 + 0.811177i \(0.301173\pi\)
\(158\) 4.90499e18i 0.0799327i
\(159\) 4.81304e18 + 8.98498e17i 0.0741046 + 0.0138338i
\(160\) 2.29813e19 0.334422
\(161\) 2.96476e19i 0.407902i
\(162\) −3.65695e19 + 4.01935e19i −0.475865 + 0.523023i
\(163\) 1.40045e20 1.72416 0.862081 0.506770i \(-0.169161\pi\)
0.862081 + 0.506770i \(0.169161\pi\)
\(164\) 4.83649e19i 0.563554i
\(165\) −9.37303e18 + 5.02091e19i −0.103401 + 0.553894i
\(166\) −7.66601e19 −0.800934
\(167\) 1.49329e20i 1.47808i 0.673664 + 0.739038i \(0.264720\pi\)
−0.673664 + 0.739038i \(0.735280\pi\)
\(168\) 2.92045e19 + 5.45189e18i 0.273947 + 0.0511404i
\(169\) −4.66982e19 −0.415260
\(170\) 2.44676e20i 2.06324i
\(171\) −9.06869e19 3.50814e19i −0.725403 0.280616i
\(172\) 2.77575e19 0.210680
\(173\) 6.62161e19i 0.477033i −0.971138 0.238517i \(-0.923339\pi\)
0.971138 0.238517i \(-0.0766611\pi\)
\(174\) −1.06840e19 + 5.72315e19i −0.0730785 + 0.391464i
\(175\) −3.12906e20 −2.03269
\(176\) 1.20656e19i 0.0744621i
\(177\) −2.35078e18 4.38844e17i −0.0137865 0.00257366i
\(178\) −4.72450e19 −0.263376
\(179\) 3.08840e20i 1.63703i 0.574485 + 0.818515i \(0.305202\pi\)
−0.574485 + 0.818515i \(0.694798\pi\)
\(180\) 6.76929e19 1.74989e20i 0.341264 0.882181i
\(181\) 2.66841e20 1.27981 0.639904 0.768455i \(-0.278974\pi\)
0.639904 + 0.768455i \(0.278974\pi\)
\(182\) 9.33810e19i 0.426203i
\(183\) −2.75422e18 + 1.47537e19i −0.0119657 + 0.0640974i
\(184\) −4.42305e19 −0.182962
\(185\) 1.47778e20i 0.582189i
\(186\) −2.01057e20 3.75333e19i −0.754575 0.140864i
\(187\) 1.28459e20 0.459400
\(188\) 3.32735e19i 0.113417i
\(189\) 1.27537e20 2.06316e20i 0.414456 0.670465i
\(190\) 3.35737e20 1.04044
\(191\) 7.13917e19i 0.211032i −0.994418 0.105516i \(-0.966351\pi\)
0.994418 0.105516i \(-0.0336494\pi\)
\(192\) 8.13355e18 4.35695e19i 0.0229387 0.122877i
\(193\) −3.84509e20 −1.03488 −0.517441 0.855719i \(-0.673115\pi\)
−0.517441 + 0.855719i \(0.673115\pi\)
\(194\) 3.35534e20i 0.862027i
\(195\) 5.79728e20 + 1.08224e20i 1.42204 + 0.265467i
\(196\) 8.08301e19 0.189351
\(197\) 1.85603e20i 0.415325i 0.978201 + 0.207663i \(0.0665856\pi\)
−0.978201 + 0.207663i \(0.933414\pi\)
\(198\) 9.18723e19 + 3.55400e19i 0.196426 + 0.0759855i
\(199\) 2.31039e20 0.472071 0.236035 0.971744i \(-0.424152\pi\)
0.236035 + 0.971744i \(0.424152\pi\)
\(200\) 4.66816e20i 0.911751i
\(201\) 1.72777e20 9.25523e20i 0.322642 1.72831i
\(202\) −1.61575e19 −0.0288543
\(203\) 2.59872e20i 0.443910i
\(204\) −4.63872e20 8.65957e19i −0.758101 0.141522i
\(205\) −1.36339e21 −2.13224
\(206\) 5.96183e20i 0.892430i
\(207\) −1.30284e20 + 3.36789e20i −0.186706 + 0.482641i
\(208\) 1.39313e20 0.191171
\(209\) 1.76268e20i 0.231663i
\(210\) −1.53687e20 + 8.23265e20i −0.193492 + 1.03649i
\(211\) 2.14795e20 0.259108 0.129554 0.991572i \(-0.458645\pi\)
0.129554 + 0.991572i \(0.458645\pi\)
\(212\) 3.26044e19i 0.0376924i
\(213\) −1.24213e21 2.31880e20i −1.37641 0.256949i
\(214\) 8.35533e20 0.887645
\(215\) 7.82474e20i 0.797120i
\(216\) −3.07798e20 1.90269e20i −0.300733 0.185902i
\(217\) 9.12942e20 0.855669
\(218\) 7.13930e20i 0.642018i
\(219\) −2.73652e20 + 1.46589e21i −0.236157 + 1.26504i
\(220\) −3.40126e20 −0.281731
\(221\) 1.48323e21i 1.17944i
\(222\) −2.80167e20 5.23016e19i −0.213915 0.0399336i
\(223\) −3.18670e20 −0.233667 −0.116833 0.993152i \(-0.537274\pi\)
−0.116833 + 0.993152i \(0.537274\pi\)
\(224\) 1.97837e20i 0.139340i
\(225\) 3.55453e21 + 1.37504e21i 2.40513 + 0.930404i
\(226\) −4.66348e20 −0.303203
\(227\) 6.91420e20i 0.432025i −0.976391 0.216013i \(-0.930695\pi\)
0.976391 0.216013i \(-0.0693052\pi\)
\(228\) 1.18824e20 6.36512e20i 0.0713659 0.382290i
\(229\) 9.82621e20 0.567371 0.283685 0.958917i \(-0.408443\pi\)
0.283685 + 0.958917i \(0.408443\pi\)
\(230\) 1.24684e21i 0.692248i
\(231\) −4.32229e20 8.06885e19i −0.230784 0.0430828i
\(232\) −3.87697e20 −0.199113
\(233\) 1.17159e21i 0.578856i −0.957200 0.289428i \(-0.906535\pi\)
0.957200 0.289428i \(-0.0934651\pi\)
\(234\) 4.10355e20 1.06078e21i 0.195082 0.504295i
\(235\) −9.37969e20 −0.429119
\(236\) 1.59246e19i 0.00701231i
\(237\) −4.89366e19 + 2.62142e20i −0.0207443 + 0.111122i
\(238\) 2.10631e21 0.859667
\(239\) 1.92312e21i 0.755832i 0.925840 + 0.377916i \(0.123359\pi\)
−0.925840 + 0.377916i \(0.876641\pi\)
\(240\) 1.22821e21 + 2.29282e20i 0.464913 + 0.0867899i
\(241\) −1.72968e21 −0.630685 −0.315342 0.948978i \(-0.602119\pi\)
−0.315342 + 0.948978i \(0.602119\pi\)
\(242\) 1.83433e21i 0.644377i
\(243\) −2.35542e21 + 1.78324e21i −0.797282 + 0.603607i
\(244\) −9.99442e19 −0.0326024
\(245\) 2.27858e21i 0.716421i
\(246\) −4.82531e20 + 2.58481e21i −0.146255 + 0.783451i
\(247\) 2.03524e21 0.594762
\(248\) 1.36200e21i 0.383805i
\(249\) −4.09701e21 7.64830e20i −1.11346 0.207860i
\(250\) −8.05653e21 −2.11197
\(251\) 4.72980e21i 1.19613i −0.801447 0.598066i \(-0.795936\pi\)
0.801447 0.598066i \(-0.204064\pi\)
\(252\) 1.50641e21 + 5.82740e20i 0.367568 + 0.142190i
\(253\) 6.54616e20 0.154135
\(254\) 9.29510e20i 0.211228i
\(255\) 2.44110e21 1.30764e22i 0.535457 2.86831i
\(256\) 2.95148e20 0.0625000
\(257\) 1.96395e21i 0.401543i 0.979638 + 0.200771i \(0.0643449\pi\)
−0.979638 + 0.200771i \(0.935655\pi\)
\(258\) 1.48347e21 + 2.76934e20i 0.292887 + 0.0546762i
\(259\) 1.27216e21 0.242574
\(260\) 3.92719e21i 0.723305i
\(261\) −1.14199e21 + 2.95208e21i −0.203187 + 0.525247i
\(262\) 3.51273e21 0.603856
\(263\) 7.44618e21i 1.23689i 0.785827 + 0.618446i \(0.212238\pi\)
−0.785827 + 0.618446i \(0.787762\pi\)
\(264\) −1.20377e20 + 6.44833e20i −0.0193246 + 0.103517i
\(265\) −9.19108e20 −0.142611
\(266\) 2.89022e21i 0.433507i
\(267\) −2.52495e21 4.71358e20i −0.366144 0.0683518i
\(268\) 6.26967e21 0.879086
\(269\) 1.76444e21i 0.239241i −0.992820 0.119621i \(-0.961832\pi\)
0.992820 0.119621i \(-0.0381678\pi\)
\(270\) 5.36362e21 8.67671e21i 0.703370 1.13784i
\(271\) 1.35817e22 1.72279 0.861394 0.507937i \(-0.169592\pi\)
0.861394 + 0.507937i \(0.169592\pi\)
\(272\) 3.14236e21i 0.385599i
\(273\) −9.31653e20 + 4.99064e21i −0.110609 + 0.592506i
\(274\) −7.72472e21 −0.887417
\(275\) 6.90893e21i 0.768097i
\(276\) −2.36385e21 4.41283e20i −0.254354 0.0474828i
\(277\) 9.98253e21 1.03973 0.519867 0.854247i \(-0.325981\pi\)
0.519867 + 0.854247i \(0.325981\pi\)
\(278\) 4.05175e21i 0.408545i
\(279\) −1.03708e22 4.01185e21i −1.01245 0.391658i
\(280\) −5.57695e21 −0.527199
\(281\) 1.38066e22i 1.26395i 0.774988 + 0.631976i \(0.217756\pi\)
−0.774988 + 0.631976i \(0.782244\pi\)
\(282\) −3.31966e20 + 1.77826e21i −0.0294342 + 0.157672i
\(283\) −1.74078e22 −1.49509 −0.747543 0.664213i \(-0.768767\pi\)
−0.747543 + 0.664213i \(0.768767\pi\)
\(284\) 8.41439e21i 0.700096i
\(285\) 1.79431e22 + 3.34961e21i 1.44642 + 0.270017i
\(286\) −2.06184e21 −0.161050
\(287\) 1.17369e22i 0.888413i
\(288\) 8.69377e20 2.24737e21i 0.0637787 0.164870i
\(289\) −1.93927e22 −1.37898
\(290\) 1.09290e22i 0.753356i
\(291\) −3.34759e21 + 1.79322e22i −0.223715 + 1.19839i
\(292\) −9.93019e21 −0.643446
\(293\) 9.25225e21i 0.581352i 0.956822 + 0.290676i \(0.0938801\pi\)
−0.956822 + 0.290676i \(0.906120\pi\)
\(294\) 4.31987e21 + 8.06434e20i 0.263236 + 0.0491409i
\(295\) 4.48910e20 0.0265315
\(296\) 1.89790e21i 0.108805i
\(297\) 4.55543e21 + 2.81600e21i 0.253350 + 0.156612i
\(298\) 1.27221e22 0.686456
\(299\) 7.55838e21i 0.395720i
\(300\) −4.65738e21 + 2.49485e22i −0.236619 + 1.26751i
\(301\) −6.73600e21 −0.332127
\(302\) 4.77980e21i 0.228743i
\(303\) −8.63517e20 1.61201e20i −0.0401132 0.00748833i
\(304\) 4.31185e21 0.194447
\(305\) 2.81739e21i 0.123353i
\(306\) −2.39272e22 9.25601e21i −1.01718 0.393488i
\(307\) 3.43877e22 1.41957 0.709787 0.704416i \(-0.248791\pi\)
0.709787 + 0.704416i \(0.248791\pi\)
\(308\) 2.92800e21i 0.117386i
\(309\) 5.94805e21 3.18623e22i 0.231605 1.24065i
\(310\) 3.83942e22 1.45215
\(311\) 1.60564e22i 0.589934i −0.955507 0.294967i \(-0.904691\pi\)
0.955507 0.294967i \(-0.0953086\pi\)
\(312\) 7.44542e21 + 1.38991e21i 0.265765 + 0.0496130i
\(313\) 2.72444e21 0.0944884 0.0472442 0.998883i \(-0.484956\pi\)
0.0472442 + 0.998883i \(0.484956\pi\)
\(314\) 2.45409e22i 0.827033i
\(315\) −1.64273e22 + 4.24651e22i −0.537985 + 1.39071i
\(316\) −1.77580e21 −0.0565209
\(317\) 2.47426e22i 0.765440i −0.923864 0.382720i \(-0.874987\pi\)
0.923864 0.382720i \(-0.125013\pi\)
\(318\) −3.25291e20 + 1.74251e21i −0.00978201 + 0.0523999i
\(319\) 5.73795e21 0.167741
\(320\) 8.32012e21i 0.236472i
\(321\) 4.46541e22 + 8.33602e21i 1.23400 + 0.230363i
\(322\) 1.07336e22 0.288431
\(323\) 4.59071e22i 1.19966i
\(324\) −1.45516e22 1.32396e22i −0.369833 0.336487i
\(325\) −7.97724e22 −1.97198
\(326\) 5.07016e22i 1.21917i
\(327\) 7.12281e21 3.81552e22i 0.166618 0.892532i
\(328\) −1.75100e22 −0.398493
\(329\) 8.07459e21i 0.178796i
\(330\) −1.81776e22 3.39340e21i −0.391662 0.0731155i
\(331\) −1.10986e22 −0.232711 −0.116356 0.993208i \(-0.537121\pi\)
−0.116356 + 0.993208i \(0.537121\pi\)
\(332\) 2.77539e22i 0.566346i
\(333\) −1.44514e22 5.59040e21i −0.287020 0.111031i
\(334\) −5.40630e22 −1.04516
\(335\) 1.76740e23i 3.32607i
\(336\) −1.97380e21 + 1.05732e22i −0.0361617 + 0.193710i
\(337\) 4.70594e22 0.839415 0.419708 0.907659i \(-0.362133\pi\)
0.419708 + 0.907659i \(0.362133\pi\)
\(338\) 1.69066e22i 0.293633i
\(339\) −2.49234e22 4.65270e21i −0.421512 0.0786879i
\(340\) 8.85820e22 1.45893
\(341\) 2.01577e22i 0.323334i
\(342\) 1.27008e22 3.28322e22i 0.198425 0.512938i
\(343\) −7.14114e22 −1.08673
\(344\) 1.00493e22i 0.148973i
\(345\) 1.24396e22 6.66362e22i 0.179654 0.962361i
\(346\) 2.39728e22 0.337313
\(347\) 2.23558e22i 0.306496i −0.988188 0.153248i \(-0.951027\pi\)
0.988188 0.153248i \(-0.0489733\pi\)
\(348\) −2.07200e22 3.86801e21i −0.276807 0.0516743i
\(349\) −9.63172e22 −1.25394 −0.626968 0.779045i \(-0.715704\pi\)
−0.626968 + 0.779045i \(0.715704\pi\)
\(350\) 1.13284e23i 1.43733i
\(351\) 3.25143e22 5.25983e22i 0.402078 0.650441i
\(352\) −4.36822e21 −0.0526526
\(353\) 2.12429e22i 0.249599i 0.992182 + 0.124799i \(0.0398287\pi\)
−0.992182 + 0.124799i \(0.960171\pi\)
\(354\) 1.58878e20 8.51073e20i 0.00181985 0.00974850i
\(355\) 2.37199e23 2.64885
\(356\) 1.71045e22i 0.186235i
\(357\) 1.12569e23 + 2.10145e22i 1.19511 + 0.223102i
\(358\) −1.11812e23 −1.15756
\(359\) 1.79251e23i 1.80972i 0.425705 + 0.904862i \(0.360026\pi\)
−0.425705 + 0.904862i \(0.639974\pi\)
\(360\) 6.33527e22 + 2.45075e22i 0.623796 + 0.241310i
\(361\) −4.11350e22 −0.395045
\(362\) 9.66066e22i 0.904961i
\(363\) −1.83010e22 + 9.80338e22i −0.167230 + 0.895811i
\(364\) −3.38075e22 −0.301371
\(365\) 2.79929e23i 2.43451i
\(366\) −5.34140e21 9.97133e20i −0.0453237 0.00846103i
\(367\) 2.02891e23 1.67984 0.839922 0.542706i \(-0.182600\pi\)
0.839922 + 0.542706i \(0.182600\pi\)
\(368\) 1.60132e22i 0.129374i
\(369\) −5.15767e22 + 1.33328e23i −0.406646 + 1.05120i
\(370\) 5.35013e22 0.411670
\(371\) 7.91223e21i 0.0594201i
\(372\) 1.35885e22 7.27904e22i 0.0996059 0.533565i
\(373\) −1.15346e23 −0.825319 −0.412659 0.910885i \(-0.635400\pi\)
−0.412659 + 0.910885i \(0.635400\pi\)
\(374\) 4.65072e22i 0.324845i
\(375\) −4.30572e23 8.03792e22i −2.93606 0.548103i
\(376\) −1.20463e22 −0.0801979
\(377\) 6.62520e22i 0.430652i
\(378\) 7.46943e22 + 4.61732e22i 0.474090 + 0.293065i
\(379\) −1.01983e23 −0.632086 −0.316043 0.948745i \(-0.602354\pi\)
−0.316043 + 0.948745i \(0.602354\pi\)
\(380\) 1.21550e23i 0.735701i
\(381\) −9.27363e21 + 4.96766e22i −0.0548182 + 0.293648i
\(382\) 2.58466e22 0.149222
\(383\) 2.38227e23i 1.34339i −0.740828 0.671695i \(-0.765567\pi\)
0.740828 0.671695i \(-0.234433\pi\)
\(384\) 1.57738e22 + 2.94466e21i 0.0868873 + 0.0162201i
\(385\) 8.25394e22 0.444135
\(386\) 1.39207e23i 0.731773i
\(387\) 7.65192e22 + 2.96008e22i 0.392981 + 0.152021i
\(388\) −1.21476e23 −0.609545
\(389\) 8.49618e20i 0.00416560i −0.999998 0.00208280i \(-0.999337\pi\)
0.999998 0.00208280i \(-0.000662976\pi\)
\(390\) −3.91811e22 + 2.09884e23i −0.187714 + 1.00554i
\(391\) −1.70488e23 −0.798182
\(392\) 2.92636e22i 0.133892i
\(393\) 1.87734e23 + 3.50461e22i 0.839478 + 0.156714i
\(394\) −6.71954e22 −0.293679
\(395\) 5.00591e22i 0.213850i
\(396\) −1.28669e22 + 3.32613e22i −0.0537299 + 0.138894i
\(397\) 2.52796e23 1.03194 0.515971 0.856606i \(-0.327431\pi\)
0.515971 + 0.856606i \(0.327431\pi\)
\(398\) 8.36450e22i 0.333804i
\(399\) −2.88354e22 + 1.54465e23i −0.112505 + 0.602660i
\(400\) −1.69006e23 −0.644705
\(401\) 2.33535e23i 0.871068i 0.900172 + 0.435534i \(0.143440\pi\)
−0.900172 + 0.435534i \(0.856560\pi\)
\(402\) 3.35075e23 + 6.25518e22i 1.22210 + 0.228142i
\(403\) 2.32746e23 0.830113
\(404\) 5.84963e21i 0.0204031i
\(405\) 3.73219e23 4.10205e23i 1.27312 1.39928i
\(406\) 9.40837e22 0.313892
\(407\) 2.80892e22i 0.0916620i
\(408\) 3.13510e22 1.67940e23i 0.100071 0.536058i
\(409\) −4.91082e23 −1.53336 −0.766680 0.642029i \(-0.778093\pi\)
−0.766680 + 0.642029i \(0.778093\pi\)
\(410\) 4.93600e23i 1.50772i
\(411\) −4.12839e23 7.70687e22i −1.23368 0.230304i
\(412\) 2.15841e23 0.631043
\(413\) 3.86448e21i 0.0110545i
\(414\) −1.21931e23 4.71678e22i −0.341279 0.132021i
\(415\) 7.82374e23 2.14280
\(416\) 5.04367e22i 0.135178i
\(417\) −4.04239e22 + 2.16541e23i −0.106026 + 0.567958i
\(418\) −6.38158e22 −0.163811
\(419\) 2.92094e23i 0.733832i −0.930254 0.366916i \(-0.880414\pi\)
0.930254 0.366916i \(-0.119586\pi\)
\(420\) −2.98054e23 5.56407e22i −0.732911 0.136820i
\(421\) −3.49420e23 −0.841026 −0.420513 0.907287i \(-0.638150\pi\)
−0.420513 + 0.907287i \(0.638150\pi\)
\(422\) 7.77640e22i 0.183217i
\(423\) −3.54831e22 + 9.17253e22i −0.0818387 + 0.211556i
\(424\) −1.18041e22 −0.0266526
\(425\) 1.79936e24i 3.97756i
\(426\) 8.39496e22 4.49698e23i 0.181690 0.973272i
\(427\) 2.42538e22 0.0513959
\(428\) 3.02495e23i 0.627660i
\(429\) −1.10193e23 2.05708e22i −0.223892 0.0417961i
\(430\) −2.83286e23 −0.563649
\(431\) 8.50240e23i 1.65671i −0.560205 0.828354i \(-0.689277\pi\)
0.560205 0.828354i \(-0.310723\pi\)
\(432\) 6.88847e22 1.11435e23i 0.131452 0.212651i
\(433\) −6.80853e23 −1.27251 −0.636257 0.771477i \(-0.719518\pi\)
−0.636257 + 0.771477i \(0.719518\pi\)
\(434\) 3.30520e23i 0.605049i
\(435\) 1.09038e23 5.84090e23i 0.195513 1.04731i
\(436\) 2.58470e23 0.453975
\(437\) 2.33938e23i 0.402502i
\(438\) −5.30707e23 9.90725e22i −0.894516 0.166988i
\(439\) −6.56128e23 −1.08345 −0.541724 0.840556i \(-0.682228\pi\)
−0.541724 + 0.840556i \(0.682228\pi\)
\(440\) 1.23139e23i 0.199214i
\(441\) 2.22825e23 + 8.61979e22i 0.353197 + 0.136631i
\(442\) 5.36985e23 0.833992
\(443\) 9.77752e23i 1.48797i 0.668194 + 0.743987i \(0.267068\pi\)
−0.668194 + 0.743987i \(0.732932\pi\)
\(444\) 1.89352e22 1.01431e23i 0.0282373 0.151260i
\(445\) 4.82171e23 0.704629
\(446\) 1.15371e23i 0.165227i
\(447\) 6.79919e23 + 1.26927e23i 0.954310 + 0.178151i
\(448\) −7.16245e22 −0.0985280
\(449\) 8.18355e23i 1.10338i −0.834050 0.551689i \(-0.813983\pi\)
0.834050 0.551689i \(-0.186017\pi\)
\(450\) −4.97817e23 + 1.28688e24i −0.657895 + 1.70069i
\(451\) 2.59149e23 0.335707
\(452\) 1.68836e23i 0.214397i
\(453\) 4.76876e22 2.55451e23i 0.0593638 0.317998i
\(454\) 2.50321e23 0.305488
\(455\) 9.53024e23i 1.14025i
\(456\) 2.30442e23 + 4.30189e22i 0.270320 + 0.0504633i
\(457\) 9.22885e23 1.06146 0.530728 0.847542i \(-0.321919\pi\)
0.530728 + 0.847542i \(0.321919\pi\)
\(458\) 3.55747e23i 0.401192i
\(459\) −1.18641e24 7.33396e23i −1.31196 0.811006i
\(460\) 4.51406e23 0.489493
\(461\) 2.88458e23i 0.306743i −0.988169 0.153371i \(-0.950987\pi\)
0.988169 0.153371i \(-0.0490130\pi\)
\(462\) 2.92124e22 1.56484e23i 0.0304641 0.163189i
\(463\) 1.02160e22 0.0104485 0.00522423 0.999986i \(-0.498337\pi\)
0.00522423 + 0.999986i \(0.498337\pi\)
\(464\) 1.40361e23i 0.140794i
\(465\) 2.05194e24 + 3.83056e23i 2.01877 + 0.376864i
\(466\) 4.24159e23 0.409313
\(467\) 3.70628e23i 0.350822i 0.984495 + 0.175411i \(0.0561254\pi\)
−0.984495 + 0.175411i \(0.943875\pi\)
\(468\) 3.84045e23 + 1.48564e23i 0.356590 + 0.137944i
\(469\) −1.52148e24 −1.38583
\(470\) 3.39581e23i 0.303433i
\(471\) −2.44842e23 + 1.31156e24i −0.214633 + 1.14974i
\(472\) 5.76533e21 0.00495845
\(473\) 1.48730e23i 0.125502i
\(474\) −9.49054e22 1.77169e22i −0.0785753 0.0146684i
\(475\) −2.46902e24 −2.00578
\(476\) 7.62566e23i 0.607876i
\(477\) −3.47696e22 + 8.98808e22i −0.0271978 + 0.0703075i
\(478\) −6.96243e23 −0.534454
\(479\) 6.56672e23i 0.494685i 0.968928 + 0.247343i \(0.0795573\pi\)
−0.968928 + 0.247343i \(0.920443\pi\)
\(480\) −8.30090e22 + 4.44659e23i −0.0613697 + 0.328743i
\(481\) 3.24325e23 0.235329
\(482\) 6.26211e23i 0.445961i
\(483\) 5.73643e23 + 1.07088e23i 0.400975 + 0.0748541i
\(484\) −6.64099e23 −0.455643
\(485\) 3.42438e24i 2.30625i
\(486\) −6.45604e23 8.52753e23i −0.426815 0.563763i
\(487\) 2.28426e24 1.48247 0.741233 0.671248i \(-0.234242\pi\)
0.741233 + 0.671248i \(0.234242\pi\)
\(488\) 3.61837e22i 0.0230534i
\(489\) −5.05845e23 + 2.70969e24i −0.316401 + 1.69488i
\(490\) −8.24932e23 −0.506586
\(491\) 2.05495e23i 0.123899i 0.998079 + 0.0619496i \(0.0197318\pi\)
−0.998079 + 0.0619496i \(0.980268\pi\)
\(492\) −9.35799e23 1.74695e23i −0.553984 0.103418i
\(493\) −1.49439e24 −0.868642
\(494\) 7.36836e23i 0.420560i
\(495\) −9.37626e23 3.62713e23i −0.525512 0.203290i
\(496\) 4.93096e23 0.271391
\(497\) 2.04195e24i 1.10367i
\(498\) 2.76898e23 1.48328e24i 0.146979 0.787332i
\(499\) 2.98859e24 1.55798 0.778989 0.627037i \(-0.215733\pi\)
0.778989 + 0.627037i \(0.215733\pi\)
\(500\) 2.91677e24i 1.49339i
\(501\) −2.88933e24 5.39381e23i −1.45298 0.271241i
\(502\) 1.71237e24 0.845793
\(503\) 1.72827e24i 0.838494i 0.907872 + 0.419247i \(0.137706\pi\)
−0.907872 + 0.419247i \(0.862294\pi\)
\(504\) −2.10975e23 + 5.45378e23i −0.100544 + 0.259910i
\(505\) 1.64899e23 0.0771962
\(506\) 2.36996e23i 0.108990i
\(507\) 1.68675e23 9.03552e23i 0.0762043 0.408208i
\(508\) −3.36519e23 −0.149360
\(509\) 1.92080e24i 0.837574i −0.908084 0.418787i \(-0.862455\pi\)
0.908084 0.418787i \(-0.137545\pi\)
\(510\) 4.73417e24 + 8.83774e23i 2.02820 + 0.378625i
\(511\) 2.40979e24 1.01436
\(512\) 1.06855e23i 0.0441942i
\(513\) 1.00634e24 1.62796e24i 0.408969 0.661589i
\(514\) −7.11025e23 −0.283934
\(515\) 6.08449e24i 2.38759i
\(516\) −1.00261e23 + 5.37072e23i −0.0386619 + 0.207103i
\(517\) 1.78286e23 0.0675621
\(518\) 4.60571e23i 0.171525i
\(519\) 1.28120e24 + 2.39174e23i 0.468932 + 0.0875402i
\(520\) −1.42179e24 −0.511454
\(521\) 2.22359e24i 0.786166i 0.919503 + 0.393083i \(0.128592\pi\)
−0.919503 + 0.393083i \(0.871408\pi\)
\(522\) −1.06877e24 4.13443e23i −0.371405 0.143675i
\(523\) −4.28781e23 −0.146461 −0.0732303 0.997315i \(-0.523331\pi\)
−0.0732303 + 0.997315i \(0.523331\pi\)
\(524\) 1.27174e24i 0.426990i
\(525\) 1.13022e24 6.05433e24i 0.373018 1.99817i
\(526\) −2.69581e24 −0.874615
\(527\) 5.24985e24i 1.67437i
\(528\) −2.33454e23 4.35813e22i −0.0731976 0.0136645i
\(529\) 2.37536e24 0.732198
\(530\) 3.32753e23i 0.100841i
\(531\) 1.69821e22 4.38995e22i 0.00505990 0.0130800i
\(532\) −1.04637e24 −0.306536
\(533\) 2.99221e24i 0.861880i
\(534\) 1.70650e23 9.14131e23i 0.0483320 0.258903i
\(535\) −8.52724e24 −2.37479
\(536\) 2.26986e24i 0.621608i
\(537\) −5.97567e24 1.11554e24i −1.60923 0.300411i
\(538\) 6.38795e23 0.169169
\(539\) 4.33104e23i 0.112796i
\(540\) 3.14131e24 + 1.94184e24i 0.804575 + 0.497358i
\(541\) 3.73835e24 0.941683 0.470842 0.882218i \(-0.343950\pi\)
0.470842 + 0.882218i \(0.343950\pi\)
\(542\) 4.91712e24i 1.21820i
\(543\) −9.63834e23 + 5.16303e24i −0.234857 + 1.25807i
\(544\) 1.13765e24 0.272659
\(545\) 7.28619e24i 1.71764i
\(546\) −1.80681e24 3.37294e23i −0.418965 0.0782124i
\(547\) −1.53228e24 −0.349503 −0.174752 0.984613i \(-0.555912\pi\)
−0.174752 + 0.984613i \(0.555912\pi\)
\(548\) 2.79665e24i 0.627498i
\(549\) −2.75517e23 1.06581e23i −0.0608131 0.0235250i
\(550\) 2.50130e24 0.543127
\(551\) 2.05055e24i 0.438033i
\(552\) 1.59762e23 8.55805e23i 0.0335754 0.179855i
\(553\) 4.30938e23 0.0891023
\(554\) 3.61406e24i 0.735204i
\(555\) 2.85932e24 + 5.33777e23i 0.572302 + 0.106837i
\(556\) −1.46689e24 −0.288885
\(557\) 5.08097e24i 0.984578i −0.870432 0.492289i \(-0.836160\pi\)
0.870432 0.492289i \(-0.163840\pi\)
\(558\) 1.45244e24 3.75463e24i 0.276944 0.715911i
\(559\) −1.71728e24 −0.322207
\(560\) 2.01907e24i 0.372786i
\(561\) −4.63997e23 + 2.48552e24i −0.0843043 + 0.451598i
\(562\) −4.99853e24 −0.893749
\(563\) 6.50158e24i 1.14405i −0.820238 0.572023i \(-0.806159\pi\)
0.820238 0.572023i \(-0.193841\pi\)
\(564\) −6.43800e23 1.20185e23i −0.111491 0.0208131i
\(565\) 4.75943e24 0.811183
\(566\) 6.30230e24i 1.05719i
\(567\) 3.53128e24 + 3.21289e24i 0.583022 + 0.530455i
\(568\) 3.04634e24 0.495043
\(569\) 2.38767e24i 0.381913i −0.981598 0.190957i \(-0.938841\pi\)
0.981598 0.190957i \(-0.0611590\pi\)
\(570\) −1.21269e24 + 6.49608e24i −0.190931 + 1.02277i
\(571\) 9.17508e24 1.42195 0.710976 0.703216i \(-0.248253\pi\)
0.710976 + 0.703216i \(0.248253\pi\)
\(572\) 7.46467e23i 0.113880i
\(573\) 1.38134e24 + 2.57869e23i 0.207448 + 0.0387264i
\(574\) 4.24920e24 0.628203
\(575\) 9.16935e24i 1.33453i
\(576\) 8.13636e23 + 3.14748e23i 0.116581 + 0.0450984i
\(577\) −4.46121e24 −0.629318 −0.314659 0.949205i \(-0.601890\pi\)
−0.314659 + 0.949205i \(0.601890\pi\)
\(578\) 7.02091e24i 0.975087i
\(579\) 1.38886e24 7.43977e24i 0.189911 1.01731i
\(580\) 3.95674e24 0.532703
\(581\) 6.73514e24i 0.892815i
\(582\) −6.49216e24 1.21196e24i −0.847388 0.158190i
\(583\) 1.74701e23 0.0224532
\(584\) 3.59511e24i 0.454985i
\(585\) −4.18798e24 + 1.08261e25i −0.521918 + 1.34918i
\(586\) −3.34967e24 −0.411078
\(587\) 5.98733e24i 0.723586i −0.932258 0.361793i \(-0.882165\pi\)
0.932258 0.361793i \(-0.117835\pi\)
\(588\) −2.91960e23 + 1.56396e24i −0.0347478 + 0.186136i
\(589\) 7.20369e24 0.844340
\(590\) 1.62523e23i 0.0187606i
\(591\) −3.59118e24 6.70401e23i −0.408272 0.0762162i
\(592\) 6.87115e23 0.0769368
\(593\) 9.26339e24i 1.02159i 0.859702 + 0.510796i \(0.170649\pi\)
−0.859702 + 0.510796i \(0.829351\pi\)
\(594\) −1.01950e24 + 1.64924e24i −0.110741 + 0.179146i
\(595\) −2.14965e25 −2.29993
\(596\) 4.60590e24i 0.485398i
\(597\) −8.34517e23 + 4.47031e24i −0.0866296 + 0.464054i
\(598\) 2.73643e24 0.279816
\(599\) 7.25144e24i 0.730437i −0.930922 0.365219i \(-0.880994\pi\)
0.930922 0.365219i \(-0.119006\pi\)
\(600\) −9.03231e24 1.68615e24i −0.896267 0.167315i
\(601\) −8.01360e23 −0.0783352 −0.0391676 0.999233i \(-0.512471\pi\)
−0.0391676 + 0.999233i \(0.512471\pi\)
\(602\) 2.43869e24i 0.234849i
\(603\) 1.72836e25 + 6.68602e24i 1.63976 + 0.634325i
\(604\) 1.73047e24 0.161746
\(605\) 1.87207e25i 1.72395i
\(606\) 5.83611e22 3.12627e23i 0.00529505 0.0283643i
\(607\) −1.52554e25 −1.36372 −0.681861 0.731482i \(-0.738829\pi\)
−0.681861 + 0.731482i \(0.738829\pi\)
\(608\) 1.56106e24i 0.137495i
\(609\) 5.02819e24 + 9.38663e23i 0.436372 + 0.0814618i
\(610\) 1.02001e24 0.0872236
\(611\) 2.05854e24i 0.173456i
\(612\) 3.35103e24 8.66256e24i 0.278238 0.719256i
\(613\) −2.34840e25 −1.92145 −0.960723 0.277509i \(-0.910491\pi\)
−0.960723 + 0.277509i \(0.910491\pi\)
\(614\) 1.24497e25i 1.00379i
\(615\) 4.92460e24 2.63799e25i 0.391286 2.09603i
\(616\) 1.06005e24 0.0830042
\(617\) 2.25430e25i 1.73958i 0.493421 + 0.869790i \(0.335746\pi\)
−0.493421 + 0.869790i \(0.664254\pi\)
\(618\) 1.15354e25 + 2.15343e24i 0.877275 + 0.163770i
\(619\) 3.04763e24 0.228427 0.114213 0.993456i \(-0.463565\pi\)
0.114213 + 0.993456i \(0.463565\pi\)
\(620\) 1.39002e25i 1.02682i
\(621\) −6.04585e24 3.73732e24i −0.440183 0.272104i
\(622\) 5.81302e24 0.417146
\(623\) 4.15081e24i 0.293589i
\(624\) −5.03202e23 + 2.69553e24i −0.0350817 + 0.187924i
\(625\) 4.46961e25 3.07150
\(626\) 9.86353e23i 0.0668134i
\(627\) −3.41056e24 6.36684e23i −0.227729 0.0425124i
\(628\) −8.88474e24 −0.584801
\(629\) 7.31552e24i 0.474667i
\(630\) −1.53740e25 5.94731e24i −0.983383 0.380413i
\(631\) 1.65170e25 1.04152 0.520760 0.853703i \(-0.325649\pi\)
0.520760 + 0.853703i \(0.325649\pi\)
\(632\) 6.42907e23i 0.0399663i
\(633\) −7.75844e23 + 4.15601e24i −0.0475489 + 0.254708i
\(634\) 8.95776e24 0.541248
\(635\) 9.48635e24i 0.565113i
\(636\) −6.30855e23 1.17768e23i −0.0370523 0.00691692i
\(637\) −5.00075e24 −0.289588
\(638\) 2.07736e24i 0.118611i
\(639\) 8.97318e24 2.31960e25i 0.505171 1.30589i
\(640\) −3.01221e24 −0.167211
\(641\) 1.10098e25i 0.602636i −0.953524 0.301318i \(-0.902573\pi\)
0.953524 0.301318i \(-0.0974266\pi\)
\(642\) −3.01796e24 + 1.61665e25i −0.162892 + 0.872571i
\(643\) 1.18166e24 0.0628920 0.0314460 0.999505i \(-0.489989\pi\)
0.0314460 + 0.999505i \(0.489989\pi\)
\(644\) 3.88597e24i 0.203951i
\(645\) −1.51399e25 2.82632e24i −0.783584 0.146279i
\(646\) 1.66201e25 0.848285
\(647\) 3.86630e25i 1.94606i 0.230674 + 0.973031i \(0.425907\pi\)
−0.230674 + 0.973031i \(0.574093\pi\)
\(648\) 4.79323e24 5.26824e24i 0.237932 0.261511i
\(649\) −8.53274e22 −0.00417721
\(650\) 2.88807e25i 1.39440i
\(651\) −3.29757e24 + 1.76643e25i −0.157024 + 0.841138i
\(652\) −1.83559e25 −0.862081
\(653\) 3.72586e25i 1.72587i 0.505315 + 0.862935i \(0.331376\pi\)
−0.505315 + 0.862935i \(0.668624\pi\)
\(654\) 1.38136e25 + 2.57873e24i 0.631115 + 0.117817i
\(655\) −3.58501e25 −1.61554
\(656\) 6.33928e24i 0.281777i
\(657\) −2.73746e25 1.05896e25i −1.20022 0.464293i
\(658\) 2.92331e24 0.126428
\(659\) 1.32111e25i 0.563597i −0.959474 0.281799i \(-0.909069\pi\)
0.959474 0.281799i \(-0.0909310\pi\)
\(660\) 1.22854e24 6.58100e24i 0.0517005 0.276947i
\(661\) −1.10139e25 −0.457222 −0.228611 0.973518i \(-0.573418\pi\)
−0.228611 + 0.973518i \(0.573418\pi\)
\(662\) 4.01814e24i 0.164552i
\(663\) 2.86986e25 + 5.35745e24i 1.15941 + 0.216439i
\(664\) 1.00480e25 0.400467
\(665\) 2.94969e25i 1.15979i
\(666\) 2.02394e24 5.23197e24i 0.0785108 0.202954i
\(667\) −7.61526e24 −0.291442
\(668\) 1.95729e25i 0.739038i
\(669\) 1.15104e24 6.16586e24i 0.0428802 0.229699i
\(670\) −6.39867e25 −2.35189
\(671\) 5.35522e23i 0.0194211i
\(672\) −3.82789e24 7.14591e23i −0.136973 0.0255702i
\(673\) 2.97930e25 1.05191 0.525955 0.850513i \(-0.323708\pi\)
0.525955 + 0.850513i \(0.323708\pi\)
\(674\) 1.70373e25i 0.593556i
\(675\) −3.94443e25 + 6.38089e25i −1.35597 + 2.19355i
\(676\) 6.12083e24 0.207630
\(677\) 4.34240e24i 0.145356i −0.997355 0.0726778i \(-0.976846\pi\)
0.997355 0.0726778i \(-0.0231545\pi\)
\(678\) 1.68446e24 9.02324e24i 0.0556408 0.298054i
\(679\) 2.94791e25 0.960917
\(680\) 3.20701e25i 1.03162i
\(681\) 1.33781e25 + 2.49742e24i 0.424689 + 0.0792809i
\(682\) −7.29786e24 −0.228632
\(683\) 2.86178e24i 0.0884810i −0.999021 0.0442405i \(-0.985913\pi\)
0.999021 0.0442405i \(-0.0140868\pi\)
\(684\) 1.18865e25 + 4.59819e24i 0.362702 + 0.140308i
\(685\) 7.88366e25 2.37417
\(686\) 2.58537e25i 0.768432i
\(687\) −3.54925e24 + 1.90125e25i −0.104118 + 0.557736i
\(688\) −3.63823e24 −0.105340
\(689\) 2.01715e24i 0.0576455i
\(690\) 2.41249e25 + 4.50363e24i 0.680492 + 0.127034i
\(691\) −1.68395e25 −0.468842 −0.234421 0.972135i \(-0.575319\pi\)
−0.234421 + 0.972135i \(0.575319\pi\)
\(692\) 8.67907e24i 0.238517i
\(693\) 3.12244e24 8.07164e24i 0.0847024 0.218959i
\(694\) 8.09366e24 0.216725
\(695\) 4.13512e25i 1.09301i
\(696\) 1.40037e24 7.50144e24i 0.0365392 0.195732i
\(697\) −6.74926e25 −1.73844
\(698\) 3.48706e25i 0.886666i
\(699\) 2.26687e25 + 4.23179e24i 0.569026 + 0.106226i
\(700\) 4.10132e25 1.01634
\(701\) 4.96096e25i 1.21368i −0.794825 0.606839i \(-0.792437\pi\)
0.794825 0.606839i \(-0.207563\pi\)
\(702\) 1.90426e25 + 1.17714e25i 0.459931 + 0.284312i
\(703\) 1.00381e25 0.239362
\(704\) 1.58146e24i 0.0372310i
\(705\) 3.38797e24 1.81485e25i 0.0787476 0.421832i
\(706\) −7.69076e24 −0.176493
\(707\) 1.41955e24i 0.0321644i
\(708\) 3.08121e23 + 5.75201e22i 0.00689323 + 0.00128683i
\(709\) −1.44322e25 −0.318799 −0.159400 0.987214i \(-0.550956\pi\)
−0.159400 + 0.987214i \(0.550956\pi\)
\(710\) 8.58752e25i 1.87302i
\(711\) −4.89535e24 1.89372e24i −0.105428 0.0407840i
\(712\) 6.19250e24 0.131688
\(713\) 2.67527e25i 0.561775i
\(714\) −7.60805e24 + 4.07545e25i −0.157757 + 0.845068i
\(715\) 2.10427e25 0.430870
\(716\) 4.04803e25i 0.818515i
\(717\) −3.72099e25 6.94635e24i −0.742996 0.138702i
\(718\) −6.48959e25 −1.27967
\(719\) 5.43271e25i 1.05793i 0.848644 + 0.528965i \(0.177420\pi\)
−0.848644 + 0.528965i \(0.822580\pi\)
\(720\) −8.87264e24 + 2.29361e25i −0.170632 + 0.441091i
\(721\) −5.23789e25 −0.994807
\(722\) 1.48925e25i 0.279339i
\(723\) 6.24764e24 3.34671e25i 0.115737 0.619974i
\(724\) −3.49753e25 −0.639904
\(725\) 8.03727e25i 1.45233i
\(726\) −3.54920e25 6.62565e24i −0.633434 0.118249i
\(727\) 6.60270e25 1.16389 0.581945 0.813228i \(-0.302292\pi\)
0.581945 + 0.813228i \(0.302292\pi\)
\(728\) 1.22396e25i 0.213101i
\(729\) −2.59957e25 5.20155e25i −0.447048 0.894510i
\(730\) 1.01345e26 1.72146
\(731\) 3.87352e25i 0.649904i
\(732\) 3.61001e23 1.93379e24i 0.00598285 0.0320487i
\(733\) 2.07863e25 0.340284 0.170142 0.985420i \(-0.445577\pi\)
0.170142 + 0.985420i \(0.445577\pi\)
\(734\) 7.34546e25i 1.18783i
\(735\) −4.40876e25 8.23027e24i −0.704255 0.131470i
\(736\) 5.79738e24 0.0914812
\(737\) 3.35942e25i 0.523669i
\(738\) −4.82698e25 1.86728e25i −0.743307 0.287542i
\(739\) −2.13791e25 −0.325229 −0.162614 0.986690i \(-0.551993\pi\)
−0.162614 + 0.986690i \(0.551993\pi\)
\(740\) 1.93695e25i 0.291094i
\(741\) −7.35133e24 + 3.93793e25i −0.109145 + 0.584661i
\(742\) 2.86453e24 0.0420164
\(743\) 1.95124e25i 0.282756i 0.989956 + 0.141378i \(0.0451534\pi\)
−0.989956 + 0.141378i \(0.954847\pi\)
\(744\) 2.63529e25 + 4.91956e24i 0.377287 + 0.0704320i
\(745\) −1.29839e26 −1.83653
\(746\) 4.17596e25i 0.583588i
\(747\) 2.95970e25 7.65094e25i 0.408660 1.05640i
\(748\) −1.68374e25 −0.229700
\(749\) 7.34075e25i 0.989473i
\(750\) 2.91004e25 1.55884e26i 0.387567 2.07610i
\(751\) 8.83451e25 1.16258 0.581290 0.813696i \(-0.302548\pi\)
0.581290 + 0.813696i \(0.302548\pi\)
\(752\) 4.36122e24i 0.0567085i
\(753\) 9.15157e25 + 1.70841e25i 1.17582 + 0.219502i
\(754\) 2.39858e25 0.304517
\(755\) 4.87815e25i 0.611973i
\(756\) −1.67165e25 + 2.70422e25i −0.207228 + 0.335232i
\(757\) 4.11022e25 0.503504 0.251752 0.967792i \(-0.418993\pi\)
0.251752 + 0.967792i \(0.418993\pi\)
\(758\) 3.69219e25i 0.446953i
\(759\) −2.36449e24 + 1.26660e25i −0.0282853 + 0.151518i
\(760\) −4.40057e25 −0.520219
\(761\) 9.29992e25i 1.08647i 0.839581 + 0.543235i \(0.182801\pi\)
−0.839581 + 0.543235i \(0.817199\pi\)
\(762\) −1.79848e25 3.35741e24i −0.207640 0.0387623i
\(763\) −6.27239e25 −0.715668
\(764\) 9.35746e24i 0.105516i
\(765\) 2.44195e26 + 9.44646e25i 2.72134 + 1.05273i
\(766\) 8.62474e25 0.949920
\(767\) 9.85215e23i 0.0107244i
\(768\) −1.06608e24 + 5.71074e24i −0.0114694 + 0.0614386i
\(769\) 1.12638e26 1.19770 0.598850 0.800861i \(-0.295624\pi\)
0.598850 + 0.800861i \(0.295624\pi\)
\(770\) 2.98825e25i 0.314051i
\(771\) −3.79999e25 7.09383e24i −0.394724 0.0736871i
\(772\)