Properties

Label 21.22.c.b.20.12
Level $21$
Weight $22$
Character 21.20
Analytic conductor $58.690$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(58.6902423003\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.12
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.11

$q$-expansion

\(f(q)\) \(=\) \(q+1704.62i q^{2} +(-65800.8 + 78298.2i) q^{3} -808569. q^{4} -2.49846e7 q^{5} +(-1.33469e8 - 1.12165e8i) q^{6} +(7.21028e7 - 7.43873e8i) q^{7} +2.19654e9i q^{8} +(-1.80087e9 - 1.03042e10i) q^{9} +O(q^{10})\) \(q+1704.62i q^{2} +(-65800.8 + 78298.2i) q^{3} -808569. q^{4} -2.49846e7 q^{5} +(-1.33469e8 - 1.12165e8i) q^{6} +(7.21028e7 - 7.43873e8i) q^{7} +2.19654e9i q^{8} +(-1.80087e9 - 1.03042e10i) q^{9} -4.25893e10i q^{10} +5.38334e10i q^{11} +(5.32045e10 - 6.33095e10i) q^{12} -8.15234e11i q^{13} +(1.26802e12 + 1.22908e11i) q^{14} +(1.64401e12 - 1.95625e12i) q^{15} -5.43995e12 q^{16} +7.14032e12 q^{17} +(1.75647e13 - 3.06979e12i) q^{18} +2.64515e13i q^{19} +2.02018e13 q^{20} +(5.34995e13 + 5.45929e13i) q^{21} -9.17654e13 q^{22} -9.27517e13i q^{23} +(-1.71985e14 - 1.44534e14i) q^{24} +1.47395e14 q^{25} +1.38966e15 q^{26} +(9.25296e14 + 5.37017e14i) q^{27} +(-5.83001e13 + 6.01473e14i) q^{28} +2.96948e15i q^{29} +(3.33466e15 + 2.80241e15i) q^{30} -4.95268e15i q^{31} -4.66656e15i q^{32} +(-4.21506e15 - 3.54228e15i) q^{33} +1.21715e16i q^{34} +(-1.80146e15 + 1.85854e16i) q^{35} +(1.45613e15 + 8.33163e15i) q^{36} +3.48905e16 q^{37} -4.50897e16 q^{38} +(6.38314e16 + 5.36430e16i) q^{39} -5.48798e16i q^{40} +8.41304e15 q^{41} +(-9.30601e16 + 9.11962e16i) q^{42} -7.53851e15 q^{43} -4.35281e16i q^{44} +(4.49940e16 + 2.57446e17i) q^{45} +1.58106e17 q^{46} +2.39922e17 q^{47} +(3.57953e17 - 4.25939e17i) q^{48} +(-5.48148e17 - 1.07271e17i) q^{49} +2.51253e17i q^{50} +(-4.69838e17 + 5.59074e17i) q^{51} +6.59173e17i q^{52} -1.77085e18i q^{53} +(-9.15409e17 + 1.57728e18i) q^{54} -1.34501e18i q^{55} +(1.63395e18 + 1.58377e17i) q^{56} +(-2.07111e18 - 1.74053e18i) q^{57} -5.06183e18 q^{58} -6.53938e18 q^{59} +(-1.32929e18 + 1.58177e18i) q^{60} -4.21755e17i q^{61} +8.44243e18 q^{62} +(-7.79484e18 + 5.96658e17i) q^{63} -3.45371e18 q^{64} +2.03683e19i q^{65} +(6.03824e18 - 7.18507e18i) q^{66} -1.30627e19 q^{67} -5.77344e18 q^{68} +(7.26229e18 + 6.10313e18i) q^{69} +(-3.16810e19 - 3.07081e18i) q^{70} +3.56914e19i q^{71} +(2.26335e19 - 3.95568e18i) q^{72} +3.10669e19i q^{73} +5.94750e19i q^{74} +(-9.69872e18 + 1.15408e19i) q^{75} -2.13879e19i q^{76} +(4.00452e19 + 3.88154e18i) q^{77} +(-9.14408e19 + 1.08808e20i) q^{78} +1.16544e20 q^{79} +1.35915e20 q^{80} +(-1.02933e20 + 3.71129e19i) q^{81} +1.43410e19i q^{82} -1.17516e19 q^{83} +(-4.32580e19 - 4.41422e19i) q^{84} -1.78398e20 q^{85} -1.28503e19i q^{86} +(-2.32505e20 - 1.95394e20i) q^{87} -1.18247e20 q^{88} -8.40556e19 q^{89} +(-4.38847e20 + 7.66976e19i) q^{90} +(-6.06430e20 - 5.87807e19i) q^{91} +7.49961e19i q^{92} +(3.87786e20 + 3.25890e20i) q^{93} +4.08975e20i q^{94} -6.60882e20i q^{95} +(3.65383e20 + 3.07063e20i) q^{96} +4.28920e20i q^{97} +(1.82856e20 - 9.34383e20i) q^{98} +(5.54709e20 - 9.69469e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 58720260q^{4} + 1422287188q^{7} + 10150644696q^{9} + O(q^{10}) \) \( 52q - 58720260q^{4} + 1422287188q^{7} + 10150644696q^{9} - 687153165468q^{15} + 36241782390404q^{16} + 36759093002772q^{18} + 79412641656180q^{21} + 228880341648112q^{22} + 4502168959229812q^{25} - 328465100861772q^{28} - 2422487119598196q^{30} + 94669723666911312q^{36} - 111253244635261912q^{37} - 198389110134084780q^{39} - 125754675449474820q^{42} + 808208758088766656q^{43} - 1124214920076830456q^{46} + 760563680048831596q^{49} + 4341973540932052200q^{51} - 13080454499124088812q^{57} - 10814528487339424568q^{58} + 13643758017961015644q^{60} - 38182310822257441896q^{63} - 30480555033993680900q^{64} - 25547251957658589040q^{67} + 73727169165159410040q^{70} + 39846964674222889428q^{72} + 45848199464273536260q^{78} + 199210197493083963080q^{79} + 235499606962845306588q^{81} - 373919224753720758924q^{84} - 570842672309470848672q^{85} - 1060053674241923431168q^{88} - 923077800435233893128q^{91} - 2832166256981601869904q^{93} + 1525182290356701596928q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1704.62i 1.17710i 0.808462 + 0.588548i \(0.200300\pi\)
−0.808462 + 0.588548i \(0.799700\pi\)
\(3\) −65800.8 + 78298.2i −0.643366 + 0.765559i
\(4\) −808569. −0.385556
\(5\) −2.49846e7 −1.14416 −0.572082 0.820197i \(-0.693864\pi\)
−0.572082 + 0.820197i \(0.693864\pi\)
\(6\) −1.33469e8 1.12165e8i −0.901137 0.757303i
\(7\) 7.21028e7 7.43873e8i 0.0964768 0.995335i
\(8\) 2.19654e9i 0.723260i
\(9\) −1.80087e9 1.03042e10i −0.172161 0.985069i
\(10\) 4.25893e10i 1.34679i
\(11\) 5.38334e10i 0.625790i 0.949788 + 0.312895i \(0.101299\pi\)
−0.949788 + 0.312895i \(0.898701\pi\)
\(12\) 5.32045e10 6.33095e10i 0.248053 0.295166i
\(13\) 8.15234e11i 1.64013i −0.572274 0.820063i \(-0.693939\pi\)
0.572274 0.820063i \(-0.306061\pi\)
\(14\) 1.26802e12 + 1.22908e11i 1.17161 + 0.113562i
\(15\) 1.64401e12 1.95625e12i 0.736116 0.875925i
\(16\) −5.43995e12 −1.23690
\(17\) 7.14032e12 0.859021 0.429510 0.903062i \(-0.358686\pi\)
0.429510 + 0.903062i \(0.358686\pi\)
\(18\) 1.75647e13 3.06979e12i 1.15952 0.202650i
\(19\) 2.64515e13i 0.989778i 0.868956 + 0.494889i \(0.164791\pi\)
−0.868956 + 0.494889i \(0.835209\pi\)
\(20\) 2.02018e13 0.441139
\(21\) 5.34995e13 + 5.45929e13i 0.699918 + 0.714223i
\(22\) −9.17654e13 −0.736616
\(23\) 9.27517e13i 0.466852i −0.972375 0.233426i \(-0.925006\pi\)
0.972375 0.233426i \(-0.0749937\pi\)
\(24\) −1.71985e14 1.44534e14i −0.553698 0.465321i
\(25\) 1.47395e14 0.309110
\(26\) 1.38966e15 1.93059
\(27\) 9.25296e14 + 5.37017e14i 0.864891 + 0.501960i
\(28\) −5.83001e13 + 6.01473e14i −0.0371972 + 0.383757i
\(29\) 2.96948e15i 1.31069i 0.755328 + 0.655347i \(0.227478\pi\)
−0.755328 + 0.655347i \(0.772522\pi\)
\(30\) 3.33466e15 + 2.80241e15i 1.03105 + 0.866479i
\(31\) 4.95268e15i 1.08528i −0.839965 0.542641i \(-0.817424\pi\)
0.839965 0.542641i \(-0.182576\pi\)
\(32\) 4.66656e15i 0.732693i
\(33\) −4.21506e15 3.54228e15i −0.479080 0.402612i
\(34\) 1.21715e16i 1.01115i
\(35\) −1.80146e15 + 1.85854e16i −0.110385 + 1.13883i
\(36\) 1.45613e15 + 8.33163e15i 0.0663778 + 0.379799i
\(37\) 3.48905e16 1.19286 0.596430 0.802665i \(-0.296585\pi\)
0.596430 + 0.802665i \(0.296585\pi\)
\(38\) −4.50897e16 −1.16506
\(39\) 6.38314e16 + 5.36430e16i 1.25561 + 1.05520i
\(40\) 5.48798e16i 0.827528i
\(41\) 8.41304e15 0.0978864 0.0489432 0.998802i \(-0.484415\pi\)
0.0489432 + 0.998802i \(0.484415\pi\)
\(42\) −9.30601e16 + 9.11962e16i −0.840709 + 0.823871i
\(43\) −7.53851e15 −0.0531945 −0.0265973 0.999646i \(-0.508467\pi\)
−0.0265973 + 0.999646i \(0.508467\pi\)
\(44\) 4.35281e16i 0.241277i
\(45\) 4.49940e16 + 2.57446e17i 0.196981 + 1.12708i
\(46\) 1.58106e17 0.549530
\(47\) 2.39922e17 0.665337 0.332669 0.943044i \(-0.392051\pi\)
0.332669 + 0.943044i \(0.392051\pi\)
\(48\) 3.57953e17 4.25939e17i 0.795781 0.946922i
\(49\) −5.48148e17 1.07271e17i −0.981384 0.192054i
\(50\) 2.51253e17i 0.363853i
\(51\) −4.69838e17 + 5.59074e17i −0.552665 + 0.657631i
\(52\) 6.59173e17i 0.632360i
\(53\) 1.77085e18i 1.39086i −0.718592 0.695432i \(-0.755213\pi\)
0.718592 0.695432i \(-0.244787\pi\)
\(54\) −9.15409e17 + 1.57728e18i −0.590855 + 1.01806i
\(55\) 1.34501e18i 0.716007i
\(56\) 1.63395e18 + 1.58377e17i 0.719886 + 0.0697778i
\(57\) −2.07111e18 1.74053e18i −0.757733 0.636789i
\(58\) −5.06183e18 −1.54281
\(59\) −6.53938e18 −1.66567 −0.832837 0.553518i \(-0.813285\pi\)
−0.832837 + 0.553518i \(0.813285\pi\)
\(60\) −1.32929e18 + 1.58177e18i −0.283814 + 0.337718i
\(61\) 4.21755e17i 0.0757003i −0.999283 0.0378501i \(-0.987949\pi\)
0.999283 0.0378501i \(-0.0120510\pi\)
\(62\) 8.44243e18 1.27748
\(63\) −7.79484e18 + 5.96658e17i −0.997083 + 0.0763219i
\(64\) −3.45371e18 −0.374452
\(65\) 2.03683e19i 1.87657i
\(66\) 6.03824e18 7.18507e18i 0.473913 0.563923i
\(67\) −1.30627e19 −0.875479 −0.437740 0.899102i \(-0.644221\pi\)
−0.437740 + 0.899102i \(0.644221\pi\)
\(68\) −5.77344e18 −0.331200
\(69\) 7.26229e18 + 6.10313e18i 0.357403 + 0.300357i
\(70\) −3.16810e19 3.07081e18i −1.34051 0.129934i
\(71\) 3.56914e19i 1.30122i 0.759411 + 0.650611i \(0.225487\pi\)
−0.759411 + 0.650611i \(0.774513\pi\)
\(72\) 2.26335e19 3.95568e18i 0.712461 0.124517i
\(73\) 3.10669e19i 0.846074i 0.906112 + 0.423037i \(0.139036\pi\)
−0.906112 + 0.423037i \(0.860964\pi\)
\(74\) 5.94750e19i 1.40411i
\(75\) −9.69872e18 + 1.15408e19i −0.198871 + 0.236642i
\(76\) 2.13879e19i 0.381615i
\(77\) 4.00452e19 + 3.88154e18i 0.622871 + 0.0603743i
\(78\) −9.14408e19 + 1.08808e20i −1.24207 + 1.47798i
\(79\) 1.16544e20 1.38486 0.692429 0.721486i \(-0.256541\pi\)
0.692429 + 0.721486i \(0.256541\pi\)
\(80\) 1.35915e20 1.41522
\(81\) −1.02933e20 + 3.71129e19i −0.940721 + 0.339181i
\(82\) 1.43410e19i 0.115222i
\(83\) −1.17516e19 −0.0831339 −0.0415670 0.999136i \(-0.513235\pi\)
−0.0415670 + 0.999136i \(0.513235\pi\)
\(84\) −4.32580e19 4.41422e19i −0.269857 0.275373i
\(85\) −1.78398e20 −0.982860
\(86\) 1.28503e19i 0.0626151i
\(87\) −2.32505e20 1.95394e20i −1.00341 0.843256i
\(88\) −1.18247e20 −0.452609
\(89\) −8.40556e19 −0.285740 −0.142870 0.989741i \(-0.545633\pi\)
−0.142870 + 0.989741i \(0.545633\pi\)
\(90\) −4.38847e20 + 7.66976e19i −1.32668 + 0.231865i
\(91\) −6.06430e20 5.87807e19i −1.63247 0.158234i
\(92\) 7.49961e19i 0.179998i
\(93\) 3.87786e20 + 3.25890e20i 0.830848 + 0.698234i
\(94\) 4.08975e20i 0.783166i
\(95\) 6.60882e20i 1.13247i
\(96\) 3.65383e20 + 3.07063e20i 0.560920 + 0.471390i
\(97\) 4.28920e20i 0.590573i 0.955409 + 0.295286i \(0.0954150\pi\)
−0.955409 + 0.295286i \(0.904585\pi\)
\(98\) 1.82856e20 9.34383e20i 0.226065 1.15518i
\(99\) 5.54709e20 9.69469e19i 0.616447 0.107737i
\(100\) −1.19179e20 −0.119179
\(101\) 9.89833e20 0.891636 0.445818 0.895124i \(-0.352913\pi\)
0.445818 + 0.895124i \(0.352913\pi\)
\(102\) −9.53007e20 8.00895e20i −0.774095 0.650539i
\(103\) 2.36391e21i 1.73316i −0.499035 0.866582i \(-0.666312\pi\)
0.499035 0.866582i \(-0.333688\pi\)
\(104\) 1.79069e21 1.18624
\(105\) −1.33667e21 1.36399e21i −0.800821 0.817188i
\(106\) 3.01862e21 1.63718
\(107\) 1.14232e21i 0.561381i 0.959798 + 0.280690i \(0.0905634\pi\)
−0.959798 + 0.280690i \(0.909437\pi\)
\(108\) −7.48166e20 4.34216e20i −0.333464 0.193533i
\(109\) 4.60801e21 1.86438 0.932192 0.361964i \(-0.117894\pi\)
0.932192 + 0.361964i \(0.117894\pi\)
\(110\) 2.29273e21 0.842809
\(111\) −2.29582e21 + 2.73187e21i −0.767445 + 0.913204i
\(112\) −3.92236e20 + 4.04664e21i −0.119332 + 1.23113i
\(113\) 4.28982e21i 1.18882i 0.804162 + 0.594410i \(0.202614\pi\)
−0.804162 + 0.594410i \(0.797386\pi\)
\(114\) 2.96694e21 3.53044e21i 0.749562 0.891925i
\(115\) 2.31737e21i 0.534155i
\(116\) 2.40103e21i 0.505346i
\(117\) −8.40031e21 + 1.46813e21i −1.61564 + 0.282366i
\(118\) 1.11471e22i 1.96066i
\(119\) 5.14837e20 5.31149e21i 0.0828756 0.855014i
\(120\) 4.29699e21 + 3.61113e21i 0.633521 + 0.532403i
\(121\) 4.50221e21 0.608386
\(122\) 7.18932e20 0.0891065
\(123\) −5.53585e20 + 6.58726e20i −0.0629768 + 0.0749378i
\(124\) 4.00459e21i 0.418437i
\(125\) 8.23099e21 0.790491
\(126\) −1.01707e21 1.32872e22i −0.0898383 1.17366i
\(127\) 5.81932e21 0.473079 0.236539 0.971622i \(-0.423987\pi\)
0.236539 + 0.971622i \(0.423987\pi\)
\(128\) 1.56737e22i 1.17346i
\(129\) 4.96040e20 5.90252e20i 0.0342235 0.0407235i
\(130\) −3.47202e22 −2.20891
\(131\) 4.60586e21 0.270372 0.135186 0.990820i \(-0.456837\pi\)
0.135186 + 0.990820i \(0.456837\pi\)
\(132\) 3.40817e21 + 2.86418e21i 0.184712 + 0.155229i
\(133\) 1.96766e22 + 1.90723e21i 0.985161 + 0.0954906i
\(134\) 2.22668e22i 1.03052i
\(135\) −2.31182e22 1.34172e22i −0.989577 0.574324i
\(136\) 1.56840e22i 0.621296i
\(137\) 3.64031e22i 1.33528i 0.744485 + 0.667640i \(0.232695\pi\)
−0.744485 + 0.667640i \(0.767305\pi\)
\(138\) −1.04035e22 + 1.23794e22i −0.353549 + 0.420698i
\(139\) 4.77330e22i 1.50371i 0.659329 + 0.751854i \(0.270840\pi\)
−0.659329 + 0.751854i \(0.729160\pi\)
\(140\) 1.45661e21 1.50276e22i 0.0425597 0.439081i
\(141\) −1.57870e22 + 1.87854e22i −0.428055 + 0.509355i
\(142\) −6.08402e22 −1.53166
\(143\) 4.38868e22 1.02637
\(144\) 9.79664e21 + 5.60542e22i 0.212947 + 1.21843i
\(145\) 7.41914e22i 1.49965i
\(146\) −5.29572e22 −0.995910
\(147\) 4.44677e22 3.58605e22i 0.778417 0.627747i
\(148\) −2.82114e22 −0.459914
\(149\) 5.73702e22i 0.871426i 0.900086 + 0.435713i \(0.143504\pi\)
−0.900086 + 0.435713i \(0.856496\pi\)
\(150\) −1.96726e22 1.65326e22i −0.278551 0.234090i
\(151\) 3.45094e22 0.455701 0.227850 0.973696i \(-0.426830\pi\)
0.227850 + 0.973696i \(0.426830\pi\)
\(152\) −5.81018e22 −0.715867
\(153\) −1.28588e22 7.35750e22i −0.147890 0.846195i
\(154\) −6.61655e21 + 6.82618e22i −0.0710663 + 0.733180i
\(155\) 1.23741e23i 1.24174i
\(156\) −5.16121e22 4.33741e22i −0.484109 0.406838i
\(157\) 3.31549e21i 0.0290805i 0.999894 + 0.0145402i \(0.00462847\pi\)
−0.999894 + 0.0145402i \(0.995372\pi\)
\(158\) 1.98663e23i 1.63011i
\(159\) 1.38654e23 + 1.16523e23i 1.06479 + 0.894834i
\(160\) 1.16592e23i 0.838321i
\(161\) −6.89955e22 6.68766e21i −0.464675 0.0450404i
\(162\) −6.32633e22 1.75461e23i −0.399249 1.10732i
\(163\) 2.61004e23 1.54411 0.772055 0.635556i \(-0.219229\pi\)
0.772055 + 0.635556i \(0.219229\pi\)
\(164\) −6.80252e21 −0.0377407
\(165\) 1.05312e23 + 8.85027e22i 0.548145 + 0.460654i
\(166\) 2.00320e22i 0.0978566i
\(167\) −1.31835e23 −0.604653 −0.302327 0.953204i \(-0.597763\pi\)
−0.302327 + 0.953204i \(0.597763\pi\)
\(168\) −1.19916e23 + 1.17514e23i −0.516569 + 0.506223i
\(169\) −4.17542e23 −1.69001
\(170\) 3.04101e23i 1.15692i
\(171\) 2.72561e23 4.76357e22i 0.974999 0.170401i
\(172\) 6.09541e21 0.0205094
\(173\) −5.55338e22 −0.175822 −0.0879110 0.996128i \(-0.528019\pi\)
−0.0879110 + 0.996128i \(0.528019\pi\)
\(174\) 3.33072e23 3.96332e23i 0.992593 1.18111i
\(175\) 1.06276e22 1.09643e23i 0.0298220 0.307668i
\(176\) 2.92851e23i 0.774042i
\(177\) 4.30296e23 5.12021e23i 1.07164 1.27517i
\(178\) 1.43283e23i 0.336344i
\(179\) 2.31473e23i 0.512323i 0.966634 + 0.256162i \(0.0824579\pi\)
−0.966634 + 0.256162i \(0.917542\pi\)
\(180\) −3.63808e22 2.08163e23i −0.0759470 0.434552i
\(181\) 1.00558e24i 1.98057i 0.139053 + 0.990285i \(0.455594\pi\)
−0.139053 + 0.990285i \(0.544406\pi\)
\(182\) 1.00199e23 1.03373e24i 0.186257 1.92158i
\(183\) 3.30227e22 + 2.77518e22i 0.0579530 + 0.0487030i
\(184\) 2.03733e23 0.337656
\(185\) −8.71727e23 −1.36483
\(186\) −5.55519e23 + 6.61027e23i −0.821888 + 0.977988i
\(187\) 3.84388e23i 0.537567i
\(188\) −1.93993e23 −0.256525
\(189\) 4.66189e23 6.49583e23i 0.583060 0.812429i
\(190\) 1.12655e24 1.33302
\(191\) 9.60897e23i 1.07604i −0.842933 0.538018i \(-0.819173\pi\)
0.842933 0.538018i \(-0.180827\pi\)
\(192\) 2.27257e23 2.70419e23i 0.240909 0.286665i
\(193\) 6.33104e23 0.635512 0.317756 0.948173i \(-0.397071\pi\)
0.317756 + 0.948173i \(0.397071\pi\)
\(194\) −7.31145e23 −0.695161
\(195\) −1.59480e24 1.34025e24i −1.43663 1.20732i
\(196\) 4.43216e23 + 8.67358e22i 0.378378 + 0.0740473i
\(197\) 1.44208e24i 1.16706i 0.812091 + 0.583531i \(0.198330\pi\)
−0.812091 + 0.583531i \(0.801670\pi\)
\(198\) 1.65257e23 + 9.45566e23i 0.126817 + 0.725617i
\(199\) 7.52755e23i 0.547894i −0.961745 0.273947i \(-0.911671\pi\)
0.961745 0.273947i \(-0.0883292\pi\)
\(200\) 3.23760e23i 0.223567i
\(201\) 8.59533e23 1.02278e24i 0.563253 0.670231i
\(202\) 1.68729e24i 1.04954i
\(203\) 2.20892e24 + 2.14108e23i 1.30458 + 0.126452i
\(204\) 3.79897e23 4.52050e23i 0.213083 0.253554i
\(205\) −2.10197e23 −0.111998
\(206\) 4.02956e24 2.04010
\(207\) −9.55729e23 + 1.67034e23i −0.459882 + 0.0803739i
\(208\) 4.43484e24i 2.02867i
\(209\) −1.42398e24 −0.619394
\(210\) 2.32507e24 2.27850e24i 0.961909 0.942643i
\(211\) 2.43940e24 0.960100 0.480050 0.877241i \(-0.340619\pi\)
0.480050 + 0.877241i \(0.340619\pi\)
\(212\) 1.43185e24i 0.536256i
\(213\) −2.79458e24 2.34852e24i −0.996162 0.837161i
\(214\) −1.94722e24 −0.660799
\(215\) 1.88347e23 0.0608632
\(216\) −1.17958e24 + 2.03245e24i −0.363047 + 0.625541i
\(217\) −3.68417e24 3.57103e23i −1.08022 0.104705i
\(218\) 7.85490e24i 2.19456i
\(219\) −2.43249e24 2.04423e24i −0.647719 0.544335i
\(220\) 1.08753e24i 0.276060i
\(221\) 5.82103e24i 1.40890i
\(222\) −4.65679e24 3.91350e24i −1.07493 0.903356i
\(223\) 4.17894e24i 0.920164i 0.887876 + 0.460082i \(0.152180\pi\)
−0.887876 + 0.460082i \(0.847820\pi\)
\(224\) −3.47133e24 3.36472e23i −0.729275 0.0706879i
\(225\) −2.65439e23 1.51879e24i −0.0532168 0.304495i
\(226\) −7.31251e24 −1.39935
\(227\) 8.20116e24 1.49832 0.749159 0.662391i \(-0.230458\pi\)
0.749159 + 0.662391i \(0.230458\pi\)
\(228\) 1.67463e24 + 1.40734e24i 0.292148 + 0.245518i
\(229\) 2.44570e24i 0.407504i 0.979023 + 0.203752i \(0.0653136\pi\)
−0.979023 + 0.203752i \(0.934686\pi\)
\(230\) −3.95023e24 −0.628752
\(231\) −2.93893e24 + 2.88006e24i −0.446954 + 0.438002i
\(232\) −6.52259e24 −0.947973
\(233\) 6.61945e23i 0.0919570i −0.998942 0.0459785i \(-0.985359\pi\)
0.998942 0.0459785i \(-0.0146406\pi\)
\(234\) −2.50260e24 1.43193e25i −0.332372 1.90176i
\(235\) −5.99436e24 −0.761255
\(236\) 5.28754e24 0.642210
\(237\) −7.66868e24 + 9.12519e24i −0.890970 + 1.06019i
\(238\) 9.05406e24 + 8.77600e23i 1.00643 + 0.0975526i
\(239\) 1.32177e25i 1.40597i −0.711204 0.702986i \(-0.751850\pi\)
0.711204 0.702986i \(-0.248150\pi\)
\(240\) −8.94333e24 + 1.06419e25i −0.910503 + 1.08343i
\(241\) 1.06254e25i 1.03554i 0.855519 + 0.517772i \(0.173238\pi\)
−0.855519 + 0.517772i \(0.826762\pi\)
\(242\) 7.67455e24i 0.716129i
\(243\) 3.86718e24 1.05015e25i 0.345564 0.938395i
\(244\) 3.41018e23i 0.0291867i
\(245\) 1.36953e25 + 2.68012e24i 1.12286 + 0.219741i
\(246\) −1.12288e24 9.43650e23i −0.0882091 0.0741297i
\(247\) 2.15642e25 1.62336
\(248\) 1.08788e25 0.784942
\(249\) 7.73266e23 9.20132e23i 0.0534855 0.0636439i
\(250\) 1.40307e25i 0.930484i
\(251\) −1.49038e25 −0.947815 −0.473907 0.880575i \(-0.657157\pi\)
−0.473907 + 0.880575i \(0.657157\pi\)
\(252\) 6.30267e24 4.82439e23i 0.384431 0.0294264i
\(253\) 4.99314e24 0.292152
\(254\) 9.91972e24i 0.556859i
\(255\) 1.17387e25 1.39683e25i 0.632339 0.752438i
\(256\) 1.94748e25 1.00682
\(257\) −3.02992e25 −1.50360 −0.751801 0.659390i \(-0.770814\pi\)
−0.751801 + 0.659390i \(0.770814\pi\)
\(258\) 1.00615e24 + 8.45558e23i 0.0479355 + 0.0402844i
\(259\) 2.51570e24 2.59541e25i 0.115083 1.18730i
\(260\) 1.64692e25i 0.723523i
\(261\) 3.05980e25 5.34764e24i 1.29112 0.225651i
\(262\) 7.85123e24i 0.318254i
\(263\) 2.50284e25i 0.974760i −0.873190 0.487380i \(-0.837953\pi\)
0.873190 0.487380i \(-0.162047\pi\)
\(264\) 7.78077e24 9.25856e24i 0.291193 0.346499i
\(265\) 4.42440e25i 1.59138i
\(266\) −3.25110e24 + 3.35410e25i −0.112402 + 1.15963i
\(267\) 5.53093e24 6.58141e24i 0.183836 0.218751i
\(268\) 1.05621e25 0.337546
\(269\) 2.63526e25 0.809886 0.404943 0.914342i \(-0.367291\pi\)
0.404943 + 0.914342i \(0.367291\pi\)
\(270\) 2.28712e25 3.94077e25i 0.676035 1.16483i
\(271\) 1.18404e25i 0.336658i 0.985731 + 0.168329i \(0.0538371\pi\)
−0.985731 + 0.168329i \(0.946163\pi\)
\(272\) −3.88430e25 −1.06253
\(273\) 4.45060e25 4.36146e25i 1.17142 1.14795i
\(274\) −6.20533e25 −1.57175
\(275\) 7.93479e24i 0.193438i
\(276\) −5.87206e24 4.93480e24i −0.137799 0.115804i
\(277\) 5.94698e25 1.34356 0.671782 0.740749i \(-0.265529\pi\)
0.671782 + 0.740749i \(0.265529\pi\)
\(278\) −8.13666e25 −1.77001
\(279\) −5.10333e25 + 8.91913e24i −1.06908 + 0.186844i
\(280\) −4.08236e25 3.95699e24i −0.823668 0.0798372i
\(281\) 5.39388e25i 1.04830i −0.851626 0.524149i \(-0.824383\pi\)
0.851626 0.524149i \(-0.175617\pi\)
\(282\) −3.20220e25 2.69108e25i −0.599560 0.503862i
\(283\) 8.93895e25i 1.61261i −0.591501 0.806304i \(-0.701465\pi\)
0.591501 0.806304i \(-0.298535\pi\)
\(284\) 2.88590e25i 0.501694i
\(285\) 5.17459e25 + 4.34865e25i 0.866971 + 0.728591i
\(286\) 7.48103e25i 1.20814i
\(287\) 6.06604e23 6.25823e24i 0.00944377 0.0974298i
\(288\) −4.80850e25 + 8.40386e24i −0.721753 + 0.126141i
\(289\) −1.81078e25 −0.262083
\(290\) 1.26468e26 1.76523
\(291\) −3.35837e25 2.82233e25i −0.452118 0.379954i
\(292\) 2.51198e25i 0.326209i
\(293\) −4.40075e25 −0.551336 −0.275668 0.961253i \(-0.588899\pi\)
−0.275668 + 0.961253i \(0.588899\pi\)
\(294\) 6.11285e25 + 7.58004e25i 0.738919 + 0.916272i
\(295\) 1.63384e26 1.90580
\(296\) 7.66385e25i 0.862748i
\(297\) −2.89095e25 + 4.98119e25i −0.314122 + 0.541241i
\(298\) −9.77942e25 −1.02575
\(299\) −7.56143e25 −0.765696
\(300\) 7.84209e24 9.33152e24i 0.0766758 0.0912387i
\(301\) −5.43548e23 + 5.60769e24i −0.00513203 + 0.0529464i
\(302\) 5.88254e25i 0.536404i
\(303\) −6.51318e25 + 7.75022e25i −0.573648 + 0.682600i
\(304\) 1.43895e26i 1.22426i
\(305\) 1.05374e25i 0.0866135i
\(306\) 1.25417e26 2.19193e25i 0.996053 0.174081i
\(307\) 8.79033e25i 0.674609i 0.941396 + 0.337305i \(0.109515\pi\)
−0.941396 + 0.337305i \(0.890485\pi\)
\(308\) −3.23793e25 3.13850e24i −0.240152 0.0232776i
\(309\) 1.85090e26 + 1.55547e26i 1.32684 + 1.11506i
\(310\) −2.10931e26 −1.46165
\(311\) 5.79802e25 0.388414 0.194207 0.980961i \(-0.437787\pi\)
0.194207 + 0.980961i \(0.437787\pi\)
\(312\) −1.17829e26 + 1.40208e26i −0.763184 + 0.908134i
\(313\) 1.53921e26i 0.964013i −0.876168 0.482006i \(-0.839908\pi\)
0.876168 0.482006i \(-0.160092\pi\)
\(314\) −5.65165e24 −0.0342305
\(315\) 1.94751e26 1.49073e25i 1.14083 0.0873248i
\(316\) −9.42338e25 −0.533940
\(317\) 2.62029e24i 0.0143624i −0.999974 0.00718121i \(-0.997714\pi\)
0.999974 0.00718121i \(-0.00228587\pi\)
\(318\) −1.98628e26 + 2.36353e26i −1.05331 + 1.25336i
\(319\) −1.59857e26 −0.820220
\(320\) 8.62897e25 0.428434
\(321\) −8.94415e25 7.51654e25i −0.429770 0.361173i
\(322\) 1.13999e25 1.17611e26i 0.0530169 0.546967i
\(323\) 1.88872e26i 0.850240i
\(324\) 8.32282e25 3.00083e25i 0.362700 0.130773i
\(325\) 1.20162e26i 0.506979i
\(326\) 4.44913e26i 1.81757i
\(327\) −3.03211e26 + 3.60799e26i −1.19948 + 1.42730i
\(328\) 1.84796e25i 0.0707973i
\(329\) 1.72990e25 1.78471e26i 0.0641896 0.662234i
\(330\) −1.50863e26 + 1.79516e26i −0.542234 + 0.645220i
\(331\) 4.00443e26 1.39427 0.697135 0.716940i \(-0.254458\pi\)
0.697135 + 0.716940i \(0.254458\pi\)
\(332\) 9.50200e24 0.0320528
\(333\) −6.28332e25 3.59518e26i −0.205364 1.17505i
\(334\) 2.24727e26i 0.711735i
\(335\) 3.26366e26 1.00169
\(336\) −2.91035e26 2.96983e26i −0.865730 0.883424i
\(337\) −8.65529e25 −0.249556 −0.124778 0.992185i \(-0.539822\pi\)
−0.124778 + 0.992185i \(0.539822\pi\)
\(338\) 7.11749e26i 1.98931i
\(339\) −3.35886e26 2.82274e26i −0.910111 0.764845i
\(340\) 1.44247e26 0.378947
\(341\) 2.66620e26 0.679160
\(342\) 8.12006e25 + 4.64612e26i 0.200579 + 1.14767i
\(343\) −1.19319e26 + 4.00018e26i −0.285838 + 0.958278i
\(344\) 1.65586e25i 0.0384735i
\(345\) −1.81446e26 1.52485e26i −0.408928 0.343657i
\(346\) 9.46638e25i 0.206959i
\(347\) 3.69203e26i 0.783078i −0.920161 0.391539i \(-0.871943\pi\)
0.920161 0.391539i \(-0.128057\pi\)
\(348\) 1.87996e26 + 1.57990e26i 0.386872 + 0.325122i
\(349\) 5.13323e26i 1.02500i −0.858687 0.512500i \(-0.828720\pi\)
0.858687 0.512500i \(-0.171280\pi\)
\(350\) 1.86900e26 + 1.81160e25i 0.362155 + 0.0351033i
\(351\) 4.37795e26 7.54333e26i 0.823277 1.41853i
\(352\) 2.51217e26 0.458513
\(353\) 7.67815e26 1.36026 0.680130 0.733091i \(-0.261923\pi\)
0.680130 + 0.733091i \(0.261923\pi\)
\(354\) 8.72801e26 + 7.33490e26i 1.50100 + 1.26142i
\(355\) 8.91738e26i 1.48881i
\(356\) 6.79648e25 0.110169
\(357\) 3.82003e26 + 3.89811e26i 0.601244 + 0.613533i
\(358\) −3.94573e26 −0.603054
\(359\) 4.03983e25i 0.0599614i 0.999550 + 0.0299807i \(0.00954458\pi\)
−0.999550 + 0.0299807i \(0.990455\pi\)
\(360\) −5.65491e26 + 9.88313e25i −0.815172 + 0.142468i
\(361\) 1.45267e25 0.0203395
\(362\) −1.71412e27 −2.33132
\(363\) −2.96249e26 + 3.52515e26i −0.391415 + 0.465756i
\(364\) 4.90341e26 + 4.75282e25i 0.629410 + 0.0610080i
\(365\) 7.76196e26i 0.968047i
\(366\) −4.73063e25 + 5.62911e25i −0.0573281 + 0.0682163i
\(367\) 9.04216e26i 1.06483i 0.846485 + 0.532413i \(0.178715\pi\)
−0.846485 + 0.532413i \(0.821285\pi\)
\(368\) 5.04565e26i 0.577451i
\(369\) −1.51508e25 8.66894e25i −0.0168523 0.0964249i
\(370\) 1.48596e27i 1.60653i
\(371\) −1.31729e27 1.27683e26i −1.38438 0.134186i
\(372\) −3.13552e26 2.63505e26i −0.320338 0.269208i
\(373\) 1.38478e27 1.37542 0.687712 0.725984i \(-0.258615\pi\)
0.687712 + 0.725984i \(0.258615\pi\)
\(374\) −6.55234e26 −0.632768
\(375\) −5.41605e26 + 6.44472e26i −0.508575 + 0.605167i
\(376\) 5.26998e26i 0.481212i
\(377\) 2.42082e27 2.14970
\(378\) 1.10729e27 + 7.94674e26i 0.956307 + 0.686318i
\(379\) −3.97744e26 −0.334112 −0.167056 0.985947i \(-0.553426\pi\)
−0.167056 + 0.985947i \(0.553426\pi\)
\(380\) 5.34368e26i 0.436629i
\(381\) −3.82916e26 + 4.55643e26i −0.304363 + 0.362170i
\(382\) 1.63796e27 1.26660
\(383\) 4.37995e25 0.0329520 0.0164760 0.999864i \(-0.494755\pi\)
0.0164760 + 0.999864i \(0.494755\pi\)
\(384\) 1.22723e27 + 1.03134e27i 0.898352 + 0.754963i
\(385\) −1.00052e27 9.69790e25i −0.712667 0.0690780i
\(386\) 1.07920e27i 0.748058i
\(387\) 1.35759e25 + 7.76781e25i 0.00915803 + 0.0524002i
\(388\) 3.46812e26i 0.227699i
\(389\) 6.30559e26i 0.402954i 0.979493 + 0.201477i \(0.0645741\pi\)
−0.979493 + 0.201477i \(0.935426\pi\)
\(390\) 2.28462e27 2.71853e27i 1.42113 1.69105i
\(391\) 6.62276e26i 0.401036i
\(392\) 2.35624e26 1.20403e27i 0.138905 0.709796i
\(393\) −3.03069e26 + 3.60631e26i −0.173948 + 0.206986i
\(394\) −2.45820e27 −1.37375
\(395\) −2.91181e27 −1.58450
\(396\) −4.48520e26 + 7.83883e25i −0.237675 + 0.0415386i
\(397\) 9.29130e26i 0.479486i −0.970836 0.239743i \(-0.922937\pi\)
0.970836 0.239743i \(-0.0770633\pi\)
\(398\) 1.28316e27 0.644924
\(399\) −1.44407e27 + 1.41514e27i −0.706922 + 0.692763i
\(400\) −8.01823e26 −0.382339
\(401\) 1.41731e27i 0.658337i −0.944271 0.329168i \(-0.893232\pi\)
0.944271 0.329168i \(-0.106768\pi\)
\(402\) 1.74345e27 + 1.46517e27i 0.788927 + 0.663003i
\(403\) −4.03760e27 −1.78000
\(404\) −8.00348e26 −0.343775
\(405\) 2.57174e27 9.27252e26i 1.07634 0.388079i
\(406\) −3.64972e26 + 3.76536e27i −0.148846 + 1.53562i
\(407\) 1.87828e27i 0.746480i
\(408\) −1.22803e27 1.03202e27i −0.475638 0.399720i
\(409\) 2.56372e27i 0.967780i 0.875129 + 0.483890i \(0.160776\pi\)
−0.875129 + 0.483890i \(0.839224\pi\)
\(410\) 3.58305e26i 0.131833i
\(411\) −2.85030e27 2.39535e27i −1.02224 0.859073i
\(412\) 1.91138e27i 0.668231i
\(413\) −4.71507e26 + 4.86447e27i −0.160699 + 1.65790i
\(414\) −2.84728e26 1.62915e27i −0.0946078 0.541325i
\(415\) 2.93610e26 0.0951188
\(416\) −3.80434e27 −1.20171
\(417\) −3.73741e27 3.14087e27i −1.15118 0.967435i
\(418\) 2.42733e27i 0.729086i
\(419\) −2.76286e26 −0.0809303 −0.0404651 0.999181i \(-0.512884\pi\)
−0.0404651 + 0.999181i \(0.512884\pi\)
\(420\) 1.08079e27 + 1.10288e27i 0.308761 + 0.315072i
\(421\) 7.66524e26 0.213581 0.106791 0.994282i \(-0.465943\pi\)
0.106791 + 0.994282i \(0.465943\pi\)
\(422\) 4.15824e27i 1.13013i
\(423\) −4.32067e26 2.47219e27i −0.114545 0.655403i
\(424\) 3.88974e27 1.00596
\(425\) 1.05245e27 0.265532
\(426\) 4.00334e27 4.76368e27i 0.985420 1.17258i
\(427\) −3.13733e26 3.04098e25i −0.0753472 0.00730332i
\(428\) 9.23643e26i 0.216444i
\(429\) −2.88779e27 + 3.43626e27i −0.660334 + 0.785750i
\(430\) 3.21060e26i 0.0716419i
\(431\) 7.46042e27i 1.62462i −0.583225 0.812311i \(-0.698209\pi\)
0.583225 0.812311i \(-0.301791\pi\)
\(432\) −5.03357e27 2.92135e27i −1.06979 0.620875i
\(433\) 5.21226e27i 1.08119i 0.841282 + 0.540596i \(0.181801\pi\)
−0.841282 + 0.540596i \(0.818199\pi\)
\(434\) 6.08723e26 6.28010e27i 0.123247 1.27152i
\(435\) 5.80905e27 + 4.88185e27i 1.14807 + 0.964823i
\(436\) −3.72590e27 −0.718824
\(437\) 2.45342e27 0.462080
\(438\) 3.48463e27 4.14646e27i 0.640735 0.762428i
\(439\) 4.85066e26i 0.0870809i −0.999052 0.0435405i \(-0.986136\pi\)
0.999052 0.0435405i \(-0.0138637\pi\)
\(440\) 2.95437e27 0.517859
\(441\) −1.18193e26 + 5.84139e27i −0.0202295 + 0.999795i
\(442\) 9.92262e27 1.65841
\(443\) 1.00313e28i 1.63726i 0.574324 + 0.818628i \(0.305265\pi\)
−0.574324 + 0.818628i \(0.694735\pi\)
\(444\) 1.85633e27 2.20890e27i 0.295893 0.352091i
\(445\) 2.10010e27 0.326934
\(446\) −7.12350e27 −1.08312
\(447\) −4.49198e27 3.77500e27i −0.667128 0.560645i
\(448\) −2.49022e26 + 2.56912e27i −0.0361259 + 0.372705i
\(449\) 1.26558e27i 0.179350i −0.995971 0.0896752i \(-0.971417\pi\)
0.995971 0.0896752i \(-0.0285829\pi\)
\(450\) 2.58895e27 4.52473e26i 0.358420 0.0626413i
\(451\) 4.52903e26i 0.0612564i
\(452\) 3.46862e27i 0.458356i
\(453\) −2.27075e27 + 2.70203e27i −0.293182 + 0.348866i
\(454\) 1.39798e28i 1.76366i
\(455\) 1.51514e28 + 1.46861e27i 1.86782 + 0.181046i
\(456\) 3.82315e27 4.54927e27i 0.460564 0.548038i
\(457\) 1.22284e28 1.43963 0.719813 0.694168i \(-0.244227\pi\)
0.719813 + 0.694168i \(0.244227\pi\)
\(458\) −4.16899e27 −0.479671
\(459\) 6.60691e27 + 3.83447e27i 0.742959 + 0.431194i
\(460\) 1.87375e27i 0.205947i
\(461\) 1.60244e28 1.72156 0.860782 0.508973i \(-0.169975\pi\)
0.860782 + 0.508973i \(0.169975\pi\)
\(462\) −4.90941e27 5.00975e27i −0.515571 0.526108i
\(463\) −1.36001e28 −1.39618 −0.698092 0.716008i \(-0.745968\pi\)
−0.698092 + 0.716008i \(0.745968\pi\)
\(464\) 1.61538e28i 1.62120i
\(465\) −9.68870e27 8.14226e27i −0.950626 0.798893i
\(466\) 1.12836e27 0.108242
\(467\) 3.65637e27 0.342944 0.171472 0.985189i \(-0.445148\pi\)
0.171472 + 0.985189i \(0.445148\pi\)
\(468\) 6.79223e27 1.18708e27i 0.622918 0.108868i
\(469\) −9.41854e26 + 9.71695e27i −0.0844634 + 0.871395i
\(470\) 1.02181e28i 0.896070i
\(471\) −2.59597e26 2.18162e26i −0.0222628 0.0187094i
\(472\) 1.43640e28i 1.20472i
\(473\) 4.05824e26i 0.0332886i
\(474\) −1.55550e28 1.30722e28i −1.24795 1.04876i
\(475\) 3.89883e27i 0.305951i
\(476\) −4.16281e26 + 4.29470e27i −0.0319532 + 0.329655i
\(477\) −1.82471e28 + 3.18906e27i −1.37010 + 0.239453i
\(478\) 2.25310e28 1.65496
\(479\) −1.10483e28 −0.793912 −0.396956 0.917838i \(-0.629933\pi\)
−0.396956 + 0.917838i \(0.629933\pi\)
\(480\) −9.12898e27 7.67187e27i −0.641784 0.539347i
\(481\) 2.84439e28i 1.95644i
\(482\) −1.81123e28 −1.21893
\(483\) 5.06359e27 4.96217e27i 0.333437 0.326758i
\(484\) −3.64035e27 −0.234567
\(485\) 1.07164e28i 0.675712i
\(486\) 1.79011e28 + 6.59207e27i 1.10458 + 0.406762i
\(487\) −1.02733e28 −0.620375 −0.310187 0.950675i \(-0.600392\pi\)
−0.310187 + 0.950675i \(0.600392\pi\)
\(488\) 9.26403e26 0.0547510
\(489\) −1.71743e28 + 2.04362e28i −0.993427 + 1.18211i
\(490\) −4.56858e27 + 2.33452e28i −0.258656 + 1.32172i
\(491\) 4.32085e27i 0.239450i 0.992807 + 0.119725i \(0.0382012\pi\)
−0.992807 + 0.119725i \(0.961799\pi\)
\(492\) 4.47611e26 5.32625e26i 0.0242811 0.0288927i
\(493\) 2.12030e28i 1.12591i
\(494\) 3.67587e28i 1.91085i
\(495\) −1.38592e28 + 2.42218e27i −0.705316 + 0.123269i
\(496\) 2.69424e28i 1.34239i
\(497\) 2.65499e28 + 2.57345e27i 1.29515 + 0.125538i
\(498\) 1.56847e27 + 1.31812e27i 0.0749150 + 0.0629576i
\(499\) −2.48378e28 −1.16160 −0.580802 0.814045i \(-0.697261\pi\)
−0.580802 + 0.814045i \(0.697261\pi\)
\(500\) −6.65532e27 −0.304778
\(501\) 8.67481e27 1.03224e28i 0.389013 0.462898i
\(502\) 2.54053e28i 1.11567i
\(503\) 1.16976e28 0.503074 0.251537 0.967848i \(-0.419064\pi\)
0.251537 + 0.967848i \(0.419064\pi\)
\(504\) −1.31058e27 1.71217e28i −0.0552006 0.721150i
\(505\) −2.47306e28 −1.02018
\(506\) 8.51140e27i 0.343891i
\(507\) 2.74746e28 3.26928e28i 1.08729 1.29380i
\(508\) −4.70532e27 −0.182398
\(509\) −2.68759e28 −1.02053 −0.510266 0.860016i \(-0.670453\pi\)
−0.510266 + 0.860016i \(0.670453\pi\)
\(510\) 2.38105e28 + 2.00101e28i 0.885692 + 0.744324i
\(511\) 2.31098e28 + 2.24001e27i 0.842127 + 0.0816265i
\(512\) 3.26836e26i 0.0116680i
\(513\) −1.42049e28 + 2.44755e28i −0.496829 + 0.856050i
\(514\) 5.16485e28i 1.76988i
\(515\) 5.90614e28i 1.98302i
\(516\) −4.01082e26 + 4.77259e26i −0.0131951 + 0.0157012i
\(517\) 1.29158e28i 0.416362i
\(518\) 4.42418e28 + 4.28831e27i 1.39756 + 0.135464i
\(519\) 3.65416e27 4.34819e27i 0.113118 0.134602i
\(520\) −4.47399e28 −1.35725
\(521\) 9.47556e27 0.281714 0.140857 0.990030i \(-0.455014\pi\)
0.140857 + 0.990030i \(0.455014\pi\)
\(522\) 9.11568e27 + 5.21579e28i 0.265613 + 1.51978i
\(523\) 7.28173e27i 0.207954i −0.994580 0.103977i \(-0.966843\pi\)
0.994580 0.103977i \(-0.0331568\pi\)
\(524\) −3.72416e27 −0.104244
\(525\) 7.88557e27 + 8.04674e27i 0.216352 + 0.220774i
\(526\) 4.26639e28 1.14739
\(527\) 3.53637e28i 0.932281i
\(528\) 2.29297e28 + 1.92699e28i 0.592575 + 0.497992i
\(529\) 3.08687e28 0.782049
\(530\) −7.54191e28 −1.87320
\(531\) 1.17766e28 + 6.73828e28i 0.286765 + 1.64080i
\(532\) −1.59099e28 1.54213e27i −0.379834 0.0368170i
\(533\) 6.85859e27i 0.160546i
\(534\) 1.12188e28 + 9.42811e27i 0.257491 + 0.216392i
\(535\) 2.85404e28i 0.642311i
\(536\) 2.86927e28i 0.633199i
\(537\) −1.81239e28 1.52311e28i −0.392214 0.329611i
\(538\) 4.49210e28i 0.953313i
\(539\) 5.77475e27 2.95087e28i 0.120185 0.614141i
\(540\) 1.86927e28 + 1.08487e28i 0.381537 + 0.221434i
\(541\) −4.20480e28 −0.841733 −0.420867 0.907123i \(-0.638274\pi\)
−0.420867 + 0.907123i \(0.638274\pi\)
\(542\) −2.01833e28 −0.396279
\(543\) −7.87349e28 6.61677e28i −1.51624 1.27423i
\(544\) 3.33207e28i 0.629399i
\(545\) −1.15130e29 −2.13316
\(546\) 7.43462e28 + 7.58657e28i 1.35125 + 1.37887i
\(547\) 4.84337e28 0.863537 0.431768 0.901984i \(-0.357890\pi\)
0.431768 + 0.901984i \(0.357890\pi\)
\(548\) 2.94344e28i 0.514825i
\(549\) −4.34584e27 + 7.59526e26i −0.0745700 + 0.0130327i
\(550\) −1.35258e28 −0.227695
\(551\) −7.85473e28 −1.29730
\(552\) −1.34058e28 + 1.59519e28i −0.217236 + 0.258495i
\(553\) 8.40315e27 8.66939e28i 0.133607 1.37840i
\(554\) 1.01373e29i 1.58151i
\(555\) 5.73603e28 6.82547e28i 0.878082 1.04486i
\(556\) 3.85955e28i 0.579764i
\(557\) 1.13096e28i 0.166712i −0.996520 0.0833560i \(-0.973436\pi\)
0.996520 0.0833560i \(-0.0265639\pi\)
\(558\) −1.52037e28 8.69922e28i −0.219933 1.25841i
\(559\) 6.14565e27i 0.0872456i
\(560\) 9.79988e27 1.01104e29i 0.136536 1.40862i
\(561\) −3.00969e28 2.52930e28i −0.411539 0.345852i
\(562\) 9.19451e28 1.23395
\(563\) 1.20262e29 1.58412 0.792062 0.610441i \(-0.209008\pi\)
0.792062 + 0.610441i \(0.209008\pi\)
\(564\) 1.27649e28 1.51893e28i 0.165039 0.196385i
\(565\) 1.07180e29i 1.36020i
\(566\) 1.52375e29 1.89819
\(567\) 2.01855e28 + 7.92448e28i 0.246841 + 0.969056i
\(568\) −7.83977e28 −0.941122
\(569\) 9.26804e28i 1.09222i −0.837714 0.546109i \(-0.816109\pi\)
0.837714 0.546109i \(-0.183891\pi\)
\(570\) −7.41279e28 + 8.82069e28i −0.857622 + 1.02051i
\(571\) −9.42718e27 −0.107079 −0.0535393 0.998566i \(-0.517050\pi\)
−0.0535393 + 0.998566i \(0.517050\pi\)
\(572\) −3.54855e28 −0.395725
\(573\) 7.52365e28 + 6.32278e28i 0.823769 + 0.692284i
\(574\) 1.06679e28 + 1.03403e27i 0.114684 + 0.0111162i
\(575\) 1.36712e28i 0.144309i
\(576\) 6.21967e27 + 3.55876e28i 0.0644661 + 0.368861i
\(577\) 1.82632e28i 0.185879i 0.995672 + 0.0929395i \(0.0296263\pi\)
−0.995672 + 0.0929395i \(0.970374\pi\)
\(578\) 3.08669e28i 0.308497i
\(579\) −4.16588e28 + 4.95709e28i −0.408866 + 0.486522i
\(580\) 5.99889e28i 0.578198i
\(581\) −8.47326e26 + 8.74172e27i −0.00802049 + 0.0827461i
\(582\) 4.81099e28 5.72473e28i 0.447243 0.532187i
\(583\) 9.53309e28 0.870390
\(584\) −6.82398e28 −0.611931
\(585\) 2.09879e29 3.66807e28i 1.84855 0.323073i
\(586\) 7.50160e28i 0.648976i
\(587\) 1.02461e29 0.870684 0.435342 0.900265i \(-0.356628\pi\)
0.435342 + 0.900265i \(0.356628\pi\)
\(588\) −3.59552e28 + 2.89957e28i −0.300123 + 0.242032i
\(589\) 1.31006e29 1.07419
\(590\) 2.78507e29i 2.24332i
\(591\) −1.12912e29 9.48901e28i −0.893456 0.750848i
\(592\) −1.89803e29 −1.47545
\(593\) 9.65141e28 0.737084 0.368542 0.929611i \(-0.379857\pi\)
0.368542 + 0.929611i \(0.379857\pi\)
\(594\) −8.49102e28 4.92796e28i −0.637092 0.369751i
\(595\) −1.28630e28 + 1.32706e29i −0.0948232 + 0.978276i
\(596\) 4.63877e28i 0.335983i
\(597\) 5.89394e28 + 4.95319e28i 0.419445 + 0.352496i
\(598\) 1.28893e29i 0.901298i
\(599\) 1.55669e29i 1.06960i 0.844979 + 0.534799i \(0.179613\pi\)
−0.844979 + 0.534799i \(0.820387\pi\)
\(600\) −2.53498e28 2.13036e28i −0.171154 0.143835i
\(601\) 4.35706e28i 0.289076i −0.989499 0.144538i \(-0.953830\pi\)
0.989499 0.144538i \(-0.0461695\pi\)
\(602\) −9.55897e27 9.26541e26i −0.0623230 0.00604090i
\(603\) 2.35241e28 + 1.34600e29i 0.150724 + 0.862407i
\(604\) −2.79033e28 −0.175698
\(605\) −1.12486e29 −0.696093
\(606\) −1.32112e29 1.11025e29i −0.803486 0.675239i
\(607\) 4.72217e28i 0.282267i −0.989991 0.141134i \(-0.954925\pi\)
0.989991 0.141134i \(-0.0450747\pi\)
\(608\) 1.23438e29 0.725204
\(609\) −1.62113e29 + 1.58866e29i −0.936128 + 0.917379i
\(610\) −1.79623e28 −0.101952
\(611\) 1.95592e29i 1.09124i
\(612\) 1.03972e28 + 5.94905e28i 0.0570199 + 0.326255i
\(613\) 2.58348e29 1.39274 0.696370 0.717682i \(-0.254797\pi\)
0.696370 + 0.717682i \(0.254797\pi\)
\(614\) −1.49842e29 −0.794080
\(615\) 1.38311e28 1.64580e28i 0.0720557 0.0857411i
\(616\) −8.52597e27 + 8.79610e28i −0.0436663 + 0.450498i
\(617\) 4.81699e28i 0.242539i 0.992620 + 0.121269i \(0.0386965\pi\)
−0.992620 + 0.121269i \(0.961304\pi\)
\(618\) −2.65148e29 + 3.15507e29i −1.31253 + 1.56182i
\(619\) 6.83865e28i 0.332827i −0.986056 0.166414i \(-0.946781\pi\)
0.986056 0.166414i \(-0.0532187\pi\)
\(620\) 1.00053e29i 0.478760i
\(621\) 4.98093e28 8.58228e28i 0.234341 0.403776i
\(622\) 9.88340e28i 0.457201i
\(623\) −6.06065e27 + 6.25267e28i −0.0275673 + 0.284408i
\(624\) −3.47240e29 2.91816e29i −1.55307 1.30518i
\(625\) −2.75932e29 −1.21356
\(626\) 2.62377e29 1.13474
\(627\) 9.36987e28 1.11495e29i 0.398497 0.474182i
\(628\) 2.68080e27i 0.0112121i
\(629\) 2.49129e29 1.02469
\(630\) 2.54112e28 + 3.31976e29i 0.102790 + 1.34286i
\(631\) −2.90971e29 −1.15755 −0.578777 0.815486i \(-0.696470\pi\)
−0.578777 + 0.815486i \(0.696470\pi\)
\(632\) 2.55994e29i 1.00161i
\(633\) −1.60514e29 + 1.91000e29i −0.617695 + 0.735013i
\(634\) 4.46660e27 0.0169059
\(635\) −1.45394e29 −0.541279
\(636\) −1.12112e29 9.42170e28i −0.410535 0.345008i
\(637\) −8.74507e28 + 4.46869e29i −0.314992 + 1.60959i
\(638\) 2.72496e29i 0.965478i
\(639\) 3.67770e29 6.42756e28i 1.28179 0.224020i
\(640\) 3.91603e29i 1.34263i
\(641\) 1.64057e29i 0.553332i −0.960966 0.276666i \(-0.910770\pi\)
0.960966 0.276666i \(-0.0892296\pi\)
\(642\) 1.28128e29 1.52463e29i 0.425135 0.505881i
\(643\) 1.74137e29i 0.568427i −0.958761 0.284214i \(-0.908267\pi\)
0.958761 0.284214i \(-0.0917325\pi\)
\(644\) 5.57876e28 + 5.40743e27i 0.179158 + 0.0173656i
\(645\) −1.23934e28 + 1.47472e28i −0.0391573 + 0.0465944i
\(646\) −3.21955e29 −1.00081
\(647\) −8.97286e28 −0.274433 −0.137216 0.990541i \(-0.543816\pi\)
−0.137216 + 0.990541i \(0.543816\pi\)
\(648\) −8.15200e28 2.26096e29i −0.245316 0.680386i
\(649\) 3.52037e29i 1.04236i
\(650\) 2.04830e29 0.596764
\(651\) 2.70382e29 2.64966e29i 0.775134 0.759609i
\(652\) −2.11040e29 −0.595340
\(653\) 5.20171e29i 1.44397i −0.691910 0.721984i \(-0.743230\pi\)
0.691910 0.721984i \(-0.256770\pi\)
\(654\) −6.15025e29 5.16858e29i −1.68007 1.41190i
\(655\) −1.15076e29 −0.309350
\(656\) −4.57666e28 −0.121076
\(657\) 3.20119e29 5.59474e28i 0.833441 0.145661i
\(658\) 3.04225e29 + 2.94882e28i 0.779513 + 0.0755573i
\(659\) 6.00874e29i 1.51526i 0.652685 + 0.757629i \(0.273642\pi\)
−0.652685 + 0.757629i \(0.726358\pi\)
\(660\) −8.51519e28 7.15605e28i −0.211341 0.177608i
\(661\) 2.78191e29i 0.679559i 0.940505 + 0.339779i \(0.110352\pi\)
−0.940505 + 0.339779i \(0.889648\pi\)
\(662\) 6.82602e29i 1.64119i
\(663\) 4.55776e29 + 3.83028e29i 1.07860 + 0.906439i
\(664\) 2.58129e28i 0.0601274i
\(665\) −4.91612e29 4.76514e28i −1.12719 0.109257i
\(666\) 6.12840e29 1.07107e29i 1.38315 0.241733i
\(667\) 2.75424e29 0.611901
\(668\) 1.06597e29 0.233127
\(669\) −3.27204e29 2.74978e29i −0.704440 0.592002i
\(670\) 5.56329e29i 1.17909i
\(671\) 2.27046e28 0.0473725
\(672\) 2.54761e29 2.49659e29i 0.523307 0.512825i
\(673\) 8.91219e29 1.80230 0.901149 0.433510i \(-0.142725\pi\)
0.901149 + 0.433510i \(0.142725\pi\)
\(674\) 1.47540e29i 0.293751i
\(675\) 1.36384e29 + 7.91538e28i 0.267347 + 0.155161i
\(676\) 3.37611e29 0.651593
\(677\) −4.37738e29 −0.831827 −0.415914 0.909404i \(-0.636538\pi\)
−0.415914 + 0.909404i \(0.636538\pi\)
\(678\) 4.81169e29 5.72556e29i 0.900297 1.07129i
\(679\) 3.19062e29 + 3.09264e28i 0.587818 + 0.0569765i
\(680\) 3.91859e29i 0.710864i
\(681\) −5.39643e29 + 6.42136e29i −0.963966 + 1.14705i
\(682\) 4.54485e29i 0.799436i
\(683\) 1.06104e30i 1.83787i 0.394414 + 0.918933i \(0.370948\pi\)
−0.394414 + 0.918933i \(0.629052\pi\)
\(684\) −2.20384e29 + 3.85167e28i −0.375917 + 0.0656993i
\(685\) 9.09518e29i 1.52778i
\(686\) −6.81878e29 2.03393e29i −1.12799 0.336459i
\(687\) −1.91494e29 1.60929e29i −0.311968 0.262174i
\(688\) 4.10092e28 0.0657964
\(689\) −1.44366e30 −2.28119
\(690\) 2.59928e29 3.09296e29i 0.404518 0.481347i
\(691\) 1.29496e29i 0.198490i −0.995063 0.0992448i \(-0.968357\pi\)
0.995063 0.0992448i \(-0.0316427\pi\)
\(692\) 4.49029e28 0.0677891
\(693\) −3.21201e28 4.19623e29i −0.0477615 0.623965i
\(694\) 6.29349e29 0.921759
\(695\) 1.19259e30i 1.72049i
\(696\) 4.29191e29 5.10707e29i 0.609893 0.725729i
\(697\) 6.00718e28 0.0840865
\(698\) 8.75019e29 1.20652
\(699\) 5.18291e28 + 4.35565e28i 0.0703985 + 0.0591620i
\(700\) −8.59316e27 + 8.86542e28i −0.0114980 + 0.118623i
\(701\) 5.98641e28i 0.0789091i 0.999221 + 0.0394545i \(0.0125620\pi\)
−0.999221 + 0.0394545i \(0.987438\pi\)
\(702\) 1.28585e30 + 7.46273e29i 1.66975 + 0.969076i
\(703\) 9.22907e29i 1.18067i
\(704\) 1.85925e29i 0.234328i
\(705\) 3.94433e29 4.69347e29i 0.489765 0.582785i
\(706\) 1.30883e30i 1.60116i
\(707\) 7.13698e28 7.36310e29i 0.0860222 0.887476i
\(708\) −3.47924e29 + 4.14005e29i −0.413176 + 0.491650i
\(709\) 3.11942e29 0.364996 0.182498 0.983206i \(-0.441582\pi\)
0.182498 + 0.983206i \(0.441582\pi\)
\(710\) 1.52007e30 1.75247
\(711\) −2.09880e29 1.20089e30i −0.238419 1.36418i
\(712\) 1.84632e29i 0.206665i
\(713\) −4.59370e29 −0.506667
\(714\) −6.64478e29 + 6.51170e29i −0.722187 + 0.707722i
\(715\) −1.09650e30 −1.17434
\(716\) 1.87162e29i 0.197529i
\(717\) 1.03492e30 + 8.69732e29i 1.07635 + 0.904554i
\(718\) −6.88637e28 −0.0705803
\(719\) 6.52660e29 0.659225 0.329613 0.944116i \(-0.393082\pi\)
0.329613 + 0.944116i \(0.393082\pi\)
\(720\) −2.44766e29 1.40049e30i −0.243646 1.39409i
\(721\) −1.75845e30 1.70444e29i −1.72508 0.167210i
\(722\) 2.47624e28i 0.0239416i
\(723\) −8.31953e29 6.99163e29i −0.792769 0.666233i
\(724\) 8.13078e29i 0.763620i
\(725\) 4.37687e29i 0.405149i
\(726\) −6.00903e29 5.04991e29i −0.548239 0.460733i
\(727\) 2.41749e29i 0.217397i −0.994075 0.108698i \(-0.965332\pi\)
0.994075 0.108698i \(-0.0346682\pi\)
\(728\) 1.29114e29 1.33205e30i 0.114444 1.18070i
\(729\) 5.67786e29 + 9.93801e29i 0.496073 + 0.868281i
\(730\) 1.32312e30 1.13948
\(731\) −5.38273e28 −0.0456952
\(732\) −2.67011e28 2.24393e28i −0.0223441 0.0187777i
\(733\) 1.91838e30i 1.58250i 0.611493 + 0.791250i \(0.290569\pi\)
−0.611493 + 0.791250i \(0.709431\pi\)
\(734\) −1.54134e30 −1.25340
\(735\) −1.11101e30 + 8.95963e29i −0.890637 + 0.718245i
\(736\) −4.32832e29 −0.342060
\(737\) 7.03208e29i 0.547867i
\(738\) 1.47772e29 2.58263e28i 0.113501 0.0198367i
\(739\) −1.83945e30 −1.39290 −0.696452 0.717604i \(-0.745239\pi\)
−0.696452 + 0.717604i \(0.745239\pi\)
\(740\) 7.04851e29 0.526217
\(741\) −1.41894e30 + 1.68844e30i −1.04441 + 1.24278i
\(742\) 2.17651e29 2.24547e30i 0.157950 1.62954i
\(743\) 1.87045e30i 1.33833i 0.743115 + 0.669164i \(0.233348\pi\)
−0.743115 + 0.669164i \(0.766652\pi\)
\(744\) −7.15832e29 + 8.51789e29i −0.505004 + 0.600919i
\(745\) 1.43337e30i 0.997053i
\(746\) 2.36051e30i 1.61901i
\(747\) 2.11631e28 + 1.21091e29i 0.0143124 + 0.0818926i
\(748\) 3.10804e29i 0.207262i
\(749\) 8.49740e29 + 8.23644e28i 0.558762 + 0.0541602i
\(750\) −1.09858e30 9.23230e29i −0.712340 0.598641i
\(751\) −2.87327e29 −0.183721 −0.0918603 0.995772i \(-0.529281\pi\)
−0.0918603 + 0.995772i \(0.529281\pi\)
\(752\) −1.30516e30 −0.822957
\(753\) 9.80683e29 1.16694e30i 0.609791 0.725608i
\(754\) 4.12657e30i 2.53041i
\(755\) −8.62206e29 −0.521396
\(756\) −3.76946e29 + 5.25232e29i −0.224802 + 0.313237i
\(757\) −9.46707e29 −0.556812 −0.278406 0.960463i \(-0.589806\pi\)
−0.278406 + 0.960463i \(0.589806\pi\)
\(758\) 6.78001e29i 0.393282i
\(759\) −3.28553e29 + 3.90954e29i −0.187960 + 0.223659i
\(760\) 1.45165e30 0.819069
\(761\)