Properties

Label 16.12.e.a.5.13
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM No

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(12.293490889\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.13
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.13

$q$-expansion

\(f(q)\) \(=\) \(q+(16.6669 - 42.0739i) q^{2} +(-491.248 + 491.248i) q^{3} +(-1492.43 - 1402.49i) q^{4} +(6777.57 + 6777.57i) q^{5} +(12481.1 + 28856.3i) q^{6} -47511.7i q^{7} +(-83882.3 + 39417.0i) q^{8} -305503. i q^{9} +O(q^{10})\) \(q+(16.6669 - 42.0739i) q^{2} +(-491.248 + 491.248i) q^{3} +(-1492.43 - 1402.49i) q^{4} +(6777.57 + 6777.57i) q^{5} +(12481.1 + 28856.3i) q^{6} -47511.7i q^{7} +(-83882.3 + 39417.0i) q^{8} -305503. i q^{9} +(398120. - 172197. i) q^{10} +(-348627. - 348627. i) q^{11} +(1.42212e6 - 44182.6i) q^{12} +(623712. - 623712. i) q^{13} +(-1.99900e6 - 791875. i) q^{14} -6.65894e6 q^{15} +(260367. + 4.18621e6i) q^{16} -447898. q^{17} +(-1.28537e7 - 5.09180e6i) q^{18} +(1.39118e7 - 1.39118e7i) q^{19} +(-609571. - 1.96205e7i) q^{20} +(2.33400e7 + 2.33400e7i) q^{21} +(-2.04786e7 + 8.85754e6i) q^{22} -4.84106e7i q^{23} +(2.18435e7 - 6.05706e7i) q^{24} +4.30427e7i q^{25} +(-1.58466e7 - 3.66373e7i) q^{26} +(6.30548e7 + 6.30548e7i) q^{27} +(-6.66345e7 + 7.09077e7i) q^{28} +(-4.44473e6 + 4.44473e6i) q^{29} +(-1.10984e8 + 2.80168e8i) q^{30} -1.41505e8 q^{31} +(1.80470e8 + 5.88168e7i) q^{32} +3.42525e8 q^{33} +(-7.46509e6 + 1.88448e7i) q^{34} +(3.22014e8 - 3.22014e8i) q^{35} +(-4.28464e8 + 4.55941e8i) q^{36} +(4.51599e7 + 4.51599e7i) q^{37} +(-3.53455e8 - 8.17188e8i) q^{38} +6.12795e8i q^{39} +(-8.35669e8 - 3.01366e8i) q^{40} +3.91782e8i q^{41} +(1.37101e9 - 5.92999e8i) q^{42} +(8.76450e8 + 8.76450e8i) q^{43} +(3.13553e7 + 1.00924e9i) q^{44} +(2.07057e9 - 2.07057e9i) q^{45} +(-2.03682e9 - 8.06856e8i) q^{46} -1.57121e9 q^{47} +(-2.18438e9 - 1.92857e9i) q^{48} -2.80034e8 q^{49} +(1.81097e9 + 7.17391e8i) q^{50} +(2.20029e8 - 2.20029e8i) q^{51} +(-1.80559e9 + 5.60963e7i) q^{52} +(-3.45392e9 - 3.45392e9i) q^{53} +(3.70389e9 - 1.60203e9i) q^{54} -4.72568e9i q^{55} +(1.87277e9 + 3.98539e9i) q^{56} +1.36683e10i q^{57} +(1.12927e8 + 2.61087e8i) q^{58} +(-5.84309e9 - 5.84309e9i) q^{59} +(9.93797e9 + 9.33907e9i) q^{60} +(1.80673e9 - 1.80673e9i) q^{61} +(-2.35845e9 + 5.95365e9i) q^{62} -1.45150e10 q^{63} +(5.48253e9 - 6.61278e9i) q^{64} +8.45450e9 q^{65} +(5.70884e9 - 1.44113e10i) q^{66} +(-5.33925e9 + 5.33925e9i) q^{67} +(6.68454e8 + 6.28171e8i) q^{68} +(2.37816e10 + 2.37816e10i) q^{69} +(-8.18139e9 - 1.89154e10i) q^{70} +6.24617e9i q^{71} +(1.20420e10 + 2.56263e10i) q^{72} -2.44700e10i q^{73} +(2.65273e9 - 1.14737e9i) q^{74} +(-2.11447e10 - 2.11447e10i) q^{75} +(-4.02733e10 + 1.25122e9i) q^{76} +(-1.65638e10 + 1.65638e10i) q^{77} +(2.57827e10 + 1.02134e10i) q^{78} -2.55656e8 q^{79} +(-2.66077e10 + 3.01370e10i) q^{80} -7.83214e9 q^{81} +(1.64838e10 + 6.52981e9i) q^{82} +(5.06400e8 - 5.06400e8i) q^{83} +(-2.09919e9 - 6.75674e10i) q^{84} +(-3.03566e9 - 3.03566e9i) q^{85} +(5.14834e10 - 2.22679e10i) q^{86} -4.36694e9i q^{87} +(4.29854e10 + 1.55018e10i) q^{88} -4.97326e10i q^{89} +(-5.26068e10 - 1.21627e11i) q^{90} +(-2.96336e10 - 2.96336e10i) q^{91} +(-6.78952e10 + 7.22492e10i) q^{92} +(6.95139e10 - 6.95139e10i) q^{93} +(-2.61873e10 + 6.61069e10i) q^{94} +1.88576e11 q^{95} +(-1.17549e11 + 5.97619e10i) q^{96} +5.39948e10 q^{97} +(-4.66730e9 + 1.17821e10i) q^{98} +(-1.06507e11 + 1.06507e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} + O(q^{10}) \) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} - 988948q^{10} - 540846q^{11} + 2300260q^{12} - 2q^{13} - 1829956q^{14} - 6075004q^{15} - 3721448q^{16} - 4q^{17} - 32219106q^{18} - 11291290q^{19} + 68655164q^{20} + 354292q^{21} - 85011388q^{22} - 66180944q^{24} + 305685384q^{26} - 66463304q^{27} - 322075880q^{28} + 77673206q^{29} + 290643636q^{30} + 343549808q^{31} + 404698568q^{32} - 4q^{33} - 882461836q^{34} - 434731684q^{35} + 1854387628q^{36} - 522762058q^{37} - 1276252832q^{38} - 483241016q^{40} + 2372079160q^{42} + 3824193658q^{43} - 2657283740q^{44} + 97301954q^{45} - 1032658964q^{46} - 4586900144q^{47} - 1058870552q^{48} - 8474257474q^{49} + 6515930886q^{50} + 7074245796q^{51} - 13915491564q^{52} - 2100608058q^{53} + 4385621536q^{54} + 12910845976q^{56} - 21491153128q^{58} + 955824746q^{59} + 25615752768q^{60} + 2150827022q^{61} - 15814519760q^{62} + 27758037828q^{63} + 9674332160q^{64} - 1884965292q^{65} + 10932459412q^{66} - 3186519018q^{67} + 13817664656q^{68} - 16193060732q^{69} - 27206453120q^{70} - 20773133628q^{72} + 14141420908q^{74} + 28890034486q^{75} - 11786004940q^{76} - 22711870540q^{77} + 37031200508q^{78} + 48011833792q^{79} - 8952586328q^{80} - 90656394430q^{81} - 81555388352q^{82} + 55713221118q^{83} + 61178517160q^{84} - 84575506252q^{85} + 10047297860q^{86} - 162855622152q^{88} + 160133627736q^{90} - 147369662716q^{91} - 169766721928q^{92} - 69689773328q^{93} + 160320530128q^{94} + 375702304500q^{95} + 230764310192q^{96} - 4q^{97} - 108887063494q^{98} - 286271331106q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.6669 42.0739i 0.368291 0.929711i
\(3\) −491.248 + 491.248i −1.16717 + 1.16717i −0.184301 + 0.982870i \(0.559002\pi\)
−0.982870 + 0.184301i \(0.940998\pi\)
\(4\) −1492.43 1402.49i −0.728724 0.684808i
\(5\) 6777.57 + 6777.57i 0.969927 + 0.969927i 0.999561 0.0296343i \(-0.00943427\pi\)
−0.0296343 + 0.999561i \(0.509434\pi\)
\(6\) 12481.1 + 28856.3i 0.655273 + 1.51499i
\(7\) 47511.7i 1.06847i −0.845337 0.534234i \(-0.820600\pi\)
0.845337 0.534234i \(-0.179400\pi\)
\(8\) −83882.3 + 39417.0i −0.905055 + 0.425294i
\(9\) 305503.i 1.72457i
\(10\) 398120. 172197.i 1.25897 0.544536i
\(11\) −348627. 348627.i −0.652681 0.652681i 0.300957 0.953638i \(-0.402694\pi\)
−0.953638 + 0.300957i \(0.902694\pi\)
\(12\) 1.42212e6 44182.6i 1.64983 0.0512572i
\(13\) 623712. 623712.i 0.465903 0.465903i −0.434681 0.900584i \(-0.643139\pi\)
0.900584 + 0.434681i \(0.143139\pi\)
\(14\) −1.99900e6 791875.i −0.993365 0.393507i
\(15\) −6.65894e6 −2.26414
\(16\) 260367. + 4.18621e6i 0.0620763 + 0.998071i
\(17\) −447898. −0.0765085 −0.0382543 0.999268i \(-0.512180\pi\)
−0.0382543 + 0.999268i \(0.512180\pi\)
\(18\) −1.28537e7 5.09180e6i −1.60335 0.635145i
\(19\) 1.39118e7 1.39118e7i 1.28895 1.28895i 0.353529 0.935423i \(-0.384981\pi\)
0.935423 0.353529i \(-0.115019\pi\)
\(20\) −609571. 1.96205e7i −0.0425951 1.37102i
\(21\) 2.33400e7 + 2.33400e7i 1.24708 + 1.24708i
\(22\) −2.04786e7 + 8.85754e6i −0.847180 + 0.366428i
\(23\) 4.84106e7i 1.56833i −0.620553 0.784165i \(-0.713092\pi\)
0.620553 0.784165i \(-0.286908\pi\)
\(24\) 2.18435e7 6.05706e7i 0.559964 1.55274i
\(25\) 4.30427e7i 0.881515i
\(26\) −1.58466e7 3.66373e7i −0.261567 0.604743i
\(27\) 6.30548e7 + 6.30548e7i 0.845702 + 0.845702i
\(28\) −6.66345e7 + 7.09077e7i −0.731695 + 0.778617i
\(29\) −4.44473e6 + 4.44473e6i −0.0402399 + 0.0402399i −0.726940 0.686701i \(-0.759058\pi\)
0.686701 + 0.726940i \(0.259058\pi\)
\(30\) −1.10984e8 + 2.80168e8i −0.833862 + 2.10499i
\(31\) −1.41505e8 −0.887731 −0.443865 0.896094i \(-0.646393\pi\)
−0.443865 + 0.896094i \(0.646393\pi\)
\(32\) 1.80470e8 + 5.88168e7i 0.950780 + 0.309868i
\(33\) 3.42525e8 1.52358
\(34\) −7.46509e6 + 1.88448e7i −0.0281774 + 0.0711308i
\(35\) 3.22014e8 3.22014e8i 1.03633 1.03633i
\(36\) −4.28464e8 + 4.55941e8i −1.18100 + 1.25674i
\(37\) 4.51599e7 + 4.51599e7i 0.107064 + 0.107064i 0.758610 0.651546i \(-0.225879\pi\)
−0.651546 + 0.758610i \(0.725879\pi\)
\(38\) −3.53455e8 8.17188e8i −0.723643 1.67306i
\(39\) 6.12795e8i 1.08758i
\(40\) −8.35669e8 3.01366e8i −1.29034 0.465334i
\(41\) 3.91782e8i 0.528121i 0.964506 + 0.264060i \(0.0850618\pi\)
−0.964506 + 0.264060i \(0.914938\pi\)
\(42\) 1.37101e9 5.92999e8i 1.61872 0.700137i
\(43\) 8.76450e8 + 8.76450e8i 0.909182 + 0.909182i 0.996206 0.0870244i \(-0.0277358\pi\)
−0.0870244 + 0.996206i \(0.527736\pi\)
\(44\) 3.13553e7 + 1.00924e9i 0.0286630 + 0.922585i
\(45\) 2.07057e9 2.07057e9i 1.67271 1.67271i
\(46\) −2.03682e9 8.06856e8i −1.45809 0.577601i
\(47\) −1.57121e9 −0.999300 −0.499650 0.866227i \(-0.666538\pi\)
−0.499650 + 0.866227i \(0.666538\pi\)
\(48\) −2.18438e9 1.92857e9i −1.23737 1.09247i
\(49\) −2.80034e8 −0.141622
\(50\) 1.81097e9 + 7.17391e8i 0.819554 + 0.324654i
\(51\) 2.20029e8 2.20029e8i 0.0892985 0.0892985i
\(52\) −1.80559e9 + 5.60963e7i −0.658568 + 0.0204605i
\(53\) −3.45392e9 3.45392e9i −1.13448 1.13448i −0.989424 0.145052i \(-0.953665\pi\)
−0.145052 0.989424i \(-0.546335\pi\)
\(54\) 3.70389e9 1.60203e9i 1.09772 0.474794i
\(55\) 4.72568e9i 1.26610i
\(56\) 1.87277e9 + 3.98539e9i 0.454412 + 0.967022i
\(57\) 1.36683e10i 3.00886i
\(58\) 1.12927e8 + 2.61087e8i 0.0225915 + 0.0522314i
\(59\) −5.84309e9 5.84309e9i −1.06404 1.06404i −0.997804 0.0662320i \(-0.978902\pi\)
−0.0662320 0.997804i \(-0.521098\pi\)
\(60\) 9.93797e9 + 9.33907e9i 1.64993 + 1.55050i
\(61\) 1.80673e9 1.80673e9i 0.273891 0.273891i −0.556773 0.830665i \(-0.687961\pi\)
0.830665 + 0.556773i \(0.187961\pi\)
\(62\) −2.35845e9 + 5.95365e9i −0.326943 + 0.825333i
\(63\) −1.45150e10 −1.84265
\(64\) 5.48253e9 6.61278e9i 0.638251 0.769829i
\(65\) 8.45450e9 0.903783
\(66\) 5.70884e9 1.44113e10i 0.561120 1.41649i
\(67\) −5.33925e9 + 5.33925e9i −0.483135 + 0.483135i −0.906131 0.422996i \(-0.860978\pi\)
0.422996 + 0.906131i \(0.360978\pi\)
\(68\) 6.68454e8 + 6.28171e8i 0.0557536 + 0.0523936i
\(69\) 2.37816e10 + 2.37816e10i 1.83051 + 1.83051i
\(70\) −8.18139e9 1.89154e10i −0.581819 1.34516i
\(71\) 6.24617e9i 0.410859i 0.978672 + 0.205430i \(0.0658592\pi\)
−0.978672 + 0.205430i \(0.934141\pi\)
\(72\) 1.20420e10 + 2.56263e10i 0.733450 + 1.56084i
\(73\) 2.44700e10i 1.38152i −0.723084 0.690760i \(-0.757276\pi\)
0.723084 0.690760i \(-0.242724\pi\)
\(74\) 2.65273e9 1.14737e9i 0.138969 0.0601078i
\(75\) −2.11447e10 2.11447e10i −1.02888 1.02888i
\(76\) −4.02733e10 + 1.25122e9i −1.82198 + 0.0566053i
\(77\) −1.65638e10 + 1.65638e10i −0.697368 + 0.697368i
\(78\) 2.57827e10 + 1.02134e10i 1.01113 + 0.400544i
\(79\) −2.55656e8 −0.00934773 −0.00467387 0.999989i \(-0.501488\pi\)
−0.00467387 + 0.999989i \(0.501488\pi\)
\(80\) −2.66077e10 + 3.01370e10i −0.907846 + 1.02827i
\(81\) −7.83214e9 −0.249582
\(82\) 1.64838e10 + 6.52981e9i 0.490999 + 0.194502i
\(83\) 5.06400e8 5.06400e8i 0.0141112 0.0141112i −0.700016 0.714127i \(-0.746824\pi\)
0.714127 + 0.700016i \(0.246824\pi\)
\(84\) −2.09919e9 6.75674e10i −0.0547666 1.76279i
\(85\) −3.03566e9 3.03566e9i −0.0742076 0.0742076i
\(86\) 5.14834e10 2.22679e10i 1.18012 0.510433i
\(87\) 4.36694e9i 0.0939336i
\(88\) 4.29854e10 + 1.55018e10i 0.868293 + 0.313131i
\(89\) 4.97326e10i 0.944053i −0.881584 0.472026i \(-0.843523\pi\)
0.881584 0.472026i \(-0.156477\pi\)
\(90\) −5.26068e10 1.21627e11i −0.939093 2.17118i
\(91\) −2.96336e10 2.96336e10i −0.497802 0.497802i
\(92\) −6.78952e10 + 7.22492e10i −1.07400 + 1.14288i
\(93\) 6.95139e10 6.95139e10i 1.03613 1.03613i
\(94\) −2.61873e10 + 6.61069e10i −0.368033 + 0.929060i
\(95\) 1.88576e11 2.50038
\(96\) −1.17549e11 + 5.97619e10i −1.47139 + 0.748054i
\(97\) 5.39948e10 0.638421 0.319211 0.947684i \(-0.396582\pi\)
0.319211 + 0.947684i \(0.396582\pi\)
\(98\) −4.66730e9 + 1.17821e10i −0.0521582 + 0.131668i
\(99\) −1.06507e11 + 1.06507e11i −1.12560 + 1.12560i
\(100\) 6.03668e10 6.42381e10i 0.603668 0.642381i
\(101\) 8.42977e10 + 8.42977e10i 0.798083 + 0.798083i 0.982793 0.184710i \(-0.0591347\pi\)
−0.184710 + 0.982793i \(0.559135\pi\)
\(102\) −5.59027e9 1.29247e10i −0.0501339 0.115910i
\(103\) 1.11053e11i 0.943903i 0.881625 + 0.471951i \(0.156450\pi\)
−0.881625 + 0.471951i \(0.843550\pi\)
\(104\) −2.77335e10 + 7.69032e10i −0.223522 + 0.619813i
\(105\) 3.16377e11i 2.41916i
\(106\) −2.02886e11 + 8.77536e10i −1.47255 + 0.636917i
\(107\) −6.29435e10 6.29435e10i −0.433851 0.433851i 0.456085 0.889936i \(-0.349251\pi\)
−0.889936 + 0.456085i \(0.849251\pi\)
\(108\) −5.67111e9 1.82538e11i −0.0371396 1.19543i
\(109\) 9.16501e10 9.16501e10i 0.570541 0.570541i −0.361738 0.932280i \(-0.617817\pi\)
0.932280 + 0.361738i \(0.117817\pi\)
\(110\) −1.98828e11 7.87626e10i −1.17711 0.466295i
\(111\) −4.43694e10 −0.249924
\(112\) 1.98894e11 1.23705e10i 1.06641 0.0663265i
\(113\) −2.46974e11 −1.26101 −0.630507 0.776184i \(-0.717153\pi\)
−0.630507 + 0.776184i \(0.717153\pi\)
\(114\) 5.75077e11 + 2.27808e11i 2.79736 + 1.10813i
\(115\) 3.28106e11 3.28106e11i 1.52116 1.52116i
\(116\) 1.28671e10 3.99757e8i 0.0568803 0.00176717i
\(117\) −1.90546e11 1.90546e11i −0.803484 0.803484i
\(118\) −3.43228e11 + 1.48455e11i −1.38112 + 0.597371i
\(119\) 2.12804e10i 0.0817469i
\(120\) 5.58567e11 2.62476e11i 2.04917 0.962924i
\(121\) 4.22307e10i 0.148016i
\(122\) −4.59034e10 1.06129e11i −0.153768 0.355511i
\(123\) −1.92462e11 1.92462e11i −0.616407 0.616407i
\(124\) 2.11185e11 + 1.98458e11i 0.646910 + 0.607925i
\(125\) 3.92110e10 3.92110e10i 0.114922 0.114922i
\(126\) −2.41920e11 + 6.10701e11i −0.678632 + 1.71313i
\(127\) 1.69815e11 0.456094 0.228047 0.973650i \(-0.426766\pi\)
0.228047 + 0.973650i \(0.426766\pi\)
\(128\) −1.86848e11 3.40886e11i −0.480656 0.876909i
\(129\) −8.61110e11 −2.12234
\(130\) 1.40911e11 3.55714e11i 0.332855 0.840257i
\(131\) −8.41543e10 + 8.41543e10i −0.190583 + 0.190583i −0.795948 0.605365i \(-0.793027\pi\)
0.605365 + 0.795948i \(0.293027\pi\)
\(132\) −5.11193e11 4.80386e11i −1.11027 1.04336i
\(133\) −6.60971e11 6.60971e11i −1.37720 1.37720i
\(134\) 1.35654e11 + 3.13632e11i 0.271242 + 0.627110i
\(135\) 8.54716e11i 1.64054i
\(136\) 3.75707e10 1.76548e10i 0.0692445 0.0325386i
\(137\) 5.08070e11i 0.899416i 0.893176 + 0.449708i \(0.148472\pi\)
−0.893176 + 0.449708i \(0.851528\pi\)
\(138\) 1.39695e12 6.04219e11i 2.37600 1.02768i
\(139\) 7.20709e11 + 7.20709e11i 1.17809 + 1.17809i 0.980230 + 0.197860i \(0.0633990\pi\)
0.197860 + 0.980230i \(0.436601\pi\)
\(140\) −9.32201e11 + 2.89617e10i −1.46489 + 0.0455114i
\(141\) 7.71854e11 7.71854e11i 1.16635 1.16635i
\(142\) 2.62801e11 + 1.04105e11i 0.381980 + 0.151316i
\(143\) −4.34885e11 −0.608172
\(144\) 1.27890e12 7.95429e10i 1.72125 0.107055i
\(145\) −6.02490e10 −0.0780595
\(146\) −1.02955e12 4.07839e11i −1.28441 0.508801i
\(147\) 1.37566e11 1.37566e11i 0.165297 0.165297i
\(148\) −4.06166e9 1.30734e11i −0.00470179 0.151338i
\(149\) 3.75941e10 + 3.75941e10i 0.0419367 + 0.0419367i 0.727764 0.685827i \(-0.240560\pi\)
−0.685827 + 0.727764i \(0.740560\pi\)
\(150\) −1.24206e12 + 5.37222e11i −1.33549 + 0.577633i
\(151\) 6.61826e11i 0.686073i 0.939322 + 0.343037i \(0.111456\pi\)
−0.939322 + 0.343037i \(0.888544\pi\)
\(152\) −6.18589e11 + 1.71531e12i −0.618390 + 1.71476i
\(153\) 1.36834e11i 0.131945i
\(154\) 4.20837e11 + 9.72974e11i 0.391516 + 0.905184i
\(155\) −9.59057e11 9.59057e11i −0.861034 0.861034i
\(156\) 8.59436e11 9.14551e11i 0.744781 0.792543i
\(157\) 6.21614e11 6.21614e11i 0.520083 0.520083i −0.397513 0.917596i \(-0.630127\pi\)
0.917596 + 0.397513i \(0.130127\pi\)
\(158\) −4.26100e9 + 1.07564e10i −0.00344269 + 0.00869069i
\(159\) 3.39347e12 2.64825
\(160\) 8.24512e11 + 1.62178e12i 0.621638 + 1.22274i
\(161\) −2.30007e12 −1.67571
\(162\) −1.30538e11 + 3.29529e11i −0.0919187 + 0.232039i
\(163\) −2.56324e11 + 2.56324e11i −0.174485 + 0.174485i −0.788947 0.614462i \(-0.789373\pi\)
0.614462 + 0.788947i \(0.289373\pi\)
\(164\) 5.49469e11 5.84705e11i 0.361661 0.384854i
\(165\) 2.32148e12 + 2.32148e12i 1.47776 + 1.47776i
\(166\) −1.28661e10 2.97464e10i −0.00792231 0.0183164i
\(167\) 5.24193e11i 0.312285i −0.987735 0.156142i \(-0.950094\pi\)
0.987735 0.156142i \(-0.0499059\pi\)
\(168\) −2.87781e12 1.03782e12i −1.65906 0.598303i
\(169\) 1.01413e12i 0.565869i
\(170\) −1.78317e11 + 7.71268e10i −0.0963216 + 0.0416616i
\(171\) −4.25008e12 4.25008e12i −2.22289 2.22289i
\(172\) −7.88275e10 2.53725e12i −0.0399274 1.28516i
\(173\) −8.62237e11 + 8.62237e11i −0.423032 + 0.423032i −0.886246 0.463214i \(-0.846696\pi\)
0.463214 + 0.886246i \(0.346696\pi\)
\(174\) −1.83734e11 7.27835e10i −0.0873311 0.0345949i
\(175\) 2.04503e12 0.941870
\(176\) 1.36865e12 1.55020e12i 0.610906 0.691938i
\(177\) 5.74082e12 2.48382
\(178\) −2.09244e12 8.28890e11i −0.877696 0.347686i
\(179\) −4.27653e11 + 4.27653e11i −0.173940 + 0.173940i −0.788708 0.614768i \(-0.789250\pi\)
0.614768 + 0.788708i \(0.289250\pi\)
\(180\) −5.99411e12 + 1.86226e11i −2.36443 + 0.0734583i
\(181\) −7.91066e11 7.91066e11i −0.302678 0.302678i 0.539383 0.842061i \(-0.318658\pi\)
−0.842061 + 0.539383i \(0.818658\pi\)
\(182\) −1.74070e12 + 7.52899e11i −0.646148 + 0.279476i
\(183\) 1.77510e12i 0.639356i
\(184\) 1.90820e12 + 4.06079e12i 0.667000 + 1.41942i
\(185\) 6.12148e11i 0.207688i
\(186\) −1.76614e12 4.08331e12i −0.581706 1.34490i
\(187\) 1.56149e11 + 1.56149e11i 0.0499356 + 0.0499356i
\(188\) 2.34491e12 + 2.20360e12i 0.728213 + 0.684328i
\(189\) 2.99584e12 2.99584e12i 0.903605 0.903605i
\(190\) 3.14298e12 7.93411e12i 0.920867 2.32463i
\(191\) −9.78732e11 −0.278599 −0.139300 0.990250i \(-0.544485\pi\)
−0.139300 + 0.990250i \(0.544485\pi\)
\(192\) 5.55231e11 + 5.94180e12i 0.153574 + 1.64347i
\(193\) −1.02121e12 −0.274504 −0.137252 0.990536i \(-0.543827\pi\)
−0.137252 + 0.990536i \(0.543827\pi\)
\(194\) 8.99928e11 2.27177e12i 0.235125 0.593547i
\(195\) −4.15326e12 + 4.15326e12i −1.05487 + 1.05487i
\(196\) 4.17929e11 + 3.92743e11i 0.103204 + 0.0969841i
\(197\) 3.26974e12 + 3.26974e12i 0.785144 + 0.785144i 0.980694 0.195550i \(-0.0626492\pi\)
−0.195550 + 0.980694i \(0.562649\pi\)
\(198\) 2.70601e12 + 6.25628e12i 0.631932 + 1.46103i
\(199\) 5.94516e12i 1.35043i −0.737622 0.675214i \(-0.764051\pi\)
0.737622 0.675214i \(-0.235949\pi\)
\(200\) −1.69662e12 3.61052e12i −0.374903 0.797820i
\(201\) 5.24579e12i 1.12780i
\(202\) 4.95172e12 2.14175e12i 1.03591 0.448059i
\(203\) 2.11177e11 + 2.11177e11i 0.0429950 + 0.0429950i
\(204\) −6.36965e11 + 1.97893e10i −0.126226 + 0.00392161i
\(205\) −2.65533e12 + 2.65533e12i −0.512238 + 0.512238i
\(206\) 4.67245e12 + 1.85092e12i 0.877556 + 0.347631i
\(207\) −1.47896e13 −2.70470
\(208\) 2.77338e12 + 2.44860e12i 0.493926 + 0.436083i
\(209\) −9.70001e12 −1.68255
\(210\) 1.33112e13 + 5.27304e12i 2.24912 + 0.890954i
\(211\) 6.50187e12 6.50187e12i 1.07025 1.07025i 0.0729105 0.997338i \(-0.476771\pi\)
0.997338 0.0729105i \(-0.0232288\pi\)
\(212\) 3.10644e11 + 9.99880e12i 0.0498214 + 1.60362i
\(213\) −3.06842e12 3.06842e12i −0.479543 0.479543i
\(214\) −3.69736e12 + 1.59920e12i −0.563139 + 0.243572i
\(215\) 1.18804e13i 1.76368i
\(216\) −7.77461e12 2.80374e12i −1.12508 0.405735i
\(217\) 6.72312e12i 0.948511i
\(218\) −2.32855e12 5.38360e12i −0.320313 0.740564i
\(219\) 1.20208e13 + 1.20208e13i 1.61247 + 1.61247i
\(220\) −6.62770e12 + 7.05273e12i −0.867038 + 0.922640i
\(221\) −2.79359e11 + 2.79359e11i −0.0356455 + 0.0356455i
\(222\) −7.39503e11 + 1.86680e12i −0.0920446 + 0.232357i
\(223\) −6.38459e12 −0.775275 −0.387638 0.921812i \(-0.626709\pi\)
−0.387638 + 0.921812i \(0.626709\pi\)
\(224\) 2.79448e12 8.57443e12i 0.331083 1.01588i
\(225\) 1.31497e13 1.52024
\(226\) −4.11630e12 + 1.03912e13i −0.464420 + 1.17238i
\(227\) 3.98249e12 3.98249e12i 0.438543 0.438543i −0.452978 0.891522i \(-0.649638\pi\)
0.891522 + 0.452978i \(0.149638\pi\)
\(228\) 1.91695e13 2.03989e13i 2.06049 2.19262i
\(229\) −6.19174e12 6.19174e12i −0.649707 0.649707i 0.303215 0.952922i \(-0.401940\pi\)
−0.952922 + 0.303215i \(0.901940\pi\)
\(230\) −8.33617e12 1.92732e13i −0.854011 1.97447i
\(231\) 1.62739e13i 1.62789i
\(232\) 1.97636e11 5.48032e11i 0.0193056 0.0535331i
\(233\) 5.61999e12i 0.536140i 0.963399 + 0.268070i \(0.0863858\pi\)
−0.963399 + 0.268070i \(0.913614\pi\)
\(234\) −1.11928e13 + 4.84119e12i −1.04292 + 0.451092i
\(235\) −1.06490e13 1.06490e13i −0.969247 0.969247i
\(236\) 5.25524e11 + 1.69152e13i 0.0467280 + 1.50405i
\(237\) 1.25590e11 1.25590e11i 0.0109104 0.0109104i
\(238\) 8.95348e11 + 3.54679e11i 0.0760009 + 0.0301066i
\(239\) 1.23308e13 1.02283 0.511414 0.859335i \(-0.329122\pi\)
0.511414 + 0.859335i \(0.329122\pi\)
\(240\) −1.73377e12 2.78758e13i −0.140549 2.25977i
\(241\) 1.52533e13 1.20856 0.604281 0.796771i \(-0.293460\pi\)
0.604281 + 0.796771i \(0.293460\pi\)
\(242\) −1.77681e12 7.03857e11i −0.137612 0.0545130i
\(243\) −7.32243e12 + 7.32243e12i −0.554397 + 0.554397i
\(244\) −5.23031e12 + 1.62496e11i −0.387154 + 0.0120281i
\(245\) −1.89795e12 1.89795e12i −0.137363 0.137363i
\(246\) −1.13054e13 + 4.88988e12i −0.800097 + 0.346063i
\(247\) 1.73538e13i 1.20105i
\(248\) 1.18697e13 5.57769e12i 0.803445 0.377546i
\(249\) 4.97537e11i 0.0329404i
\(250\) −9.96232e11 2.30329e12i −0.0645194 0.149169i
\(251\) 1.60987e13 + 1.60987e13i 1.01997 + 1.01997i 0.999797 + 0.0201706i \(0.00642092\pi\)
0.0201706 + 0.999797i \(0.493579\pi\)
\(252\) 2.16625e13 + 2.03570e13i 1.34278 + 1.26186i
\(253\) −1.68772e13 + 1.68772e13i −1.02362 + 1.02362i
\(254\) 2.83029e12 7.14477e12i 0.167975 0.424036i
\(255\) 2.98252e12 0.173226
\(256\) −1.74566e13 + 2.17990e12i −0.992293 + 0.123913i
\(257\) −2.30607e13 −1.28304 −0.641519 0.767107i \(-0.721696\pi\)
−0.641519 + 0.767107i \(0.721696\pi\)
\(258\) −1.43521e13 + 3.62302e13i −0.781639 + 1.97316i
\(259\) 2.14562e12 2.14562e12i 0.114394 0.114394i
\(260\) −1.26177e13 1.18573e13i −0.658608 0.618918i
\(261\) 1.35788e12 + 1.35788e12i 0.0693967 + 0.0693967i
\(262\) 2.13810e12 + 4.94329e12i 0.106997 + 0.247377i
\(263\) 1.05327e13i 0.516159i 0.966124 + 0.258080i \(0.0830897\pi\)
−0.966124 + 0.258080i \(0.916910\pi\)
\(264\) −2.87317e13 + 1.35013e13i −1.37892 + 0.647968i
\(265\) 4.68184e13i 2.20072i
\(266\) −3.88260e13 + 1.67933e13i −1.78761 + 0.773189i
\(267\) 2.44311e13 + 2.44311e13i 1.10187 + 1.10187i
\(268\) 1.54567e13 4.80209e11i 0.682927 0.0212172i
\(269\) 1.61223e13 1.61223e13i 0.697895 0.697895i −0.266062 0.963956i \(-0.585722\pi\)
0.963956 + 0.266062i \(0.0857224\pi\)
\(270\) 3.59612e13 + 1.42455e13i 1.52522 + 0.604195i
\(271\) 1.25041e13 0.519662 0.259831 0.965654i \(-0.416333\pi\)
0.259831 + 0.965654i \(0.416333\pi\)
\(272\) −1.16618e11 1.87500e12i −0.00474937 0.0763610i
\(273\) 2.91149e13 1.16204
\(274\) 2.13765e13 + 8.46798e12i 0.836196 + 0.331247i
\(275\) 1.50058e13 1.50058e13i 0.575348 0.575348i
\(276\) −2.13891e12 6.88457e13i −0.0803881 2.58748i
\(277\) −1.36829e12 1.36829e12i −0.0504125 0.0504125i 0.681451 0.731864i \(-0.261349\pi\)
−0.731864 + 0.681451i \(0.761349\pi\)
\(278\) 4.23350e13 1.83110e13i 1.52916 0.661403i
\(279\) 4.32301e13i 1.53096i
\(280\) −1.43184e13 + 3.97041e13i −0.497194 + 1.37869i
\(281\) 3.42090e13i 1.16481i −0.812898 0.582406i \(-0.802112\pi\)
0.812898 0.582406i \(-0.197888\pi\)
\(282\) −1.96105e13 4.53394e13i −0.654814 1.51393i
\(283\) 3.26611e13 + 3.26611e13i 1.06956 + 1.06956i 0.997393 + 0.0721666i \(0.0229913\pi\)
0.0721666 + 0.997393i \(0.477009\pi\)
\(284\) 8.76017e12 9.32195e12i 0.281360 0.299403i
\(285\) −9.26375e13 + 9.26375e13i −2.91837 + 2.91837i
\(286\) −7.24820e12 + 1.82973e13i −0.223984 + 0.565424i
\(287\) 1.86142e13 0.564280
\(288\) 1.79687e13 5.51341e13i 0.534390 1.63969i
\(289\) −3.40713e13 −0.994146
\(290\) −1.00417e12 + 2.53491e12i −0.0287486 + 0.0725727i
\(291\) −2.65249e13 + 2.65249e13i −0.745147 + 0.745147i
\(292\) −3.43188e13 + 3.65196e13i −0.946076 + 1.00675i
\(293\) 3.33163e13 + 3.33163e13i 0.901333 + 0.901333i 0.995552 0.0942188i \(-0.0300353\pi\)
−0.0942188 + 0.995552i \(0.530035\pi\)
\(294\) −3.49513e12 8.08075e12i −0.0928012 0.214556i
\(295\) 7.92039e13i 2.06407i
\(296\) −5.56818e12 2.00804e12i −0.142432 0.0513652i
\(297\) 4.39651e13i 1.10395i
\(298\) 2.20831e12 9.55151e11i 0.0544340 0.0235441i
\(299\) −3.01942e13 3.01942e13i −0.730689 0.730689i
\(300\) 1.90174e12 + 6.12120e13i 0.0451840 + 1.45435i
\(301\) 4.16416e13 4.16416e13i 0.971431 0.971431i
\(302\) 2.78456e13 + 1.10306e13i 0.637850 + 0.252675i
\(303\) −8.28222e13 −1.86300
\(304\) 6.18597e13 + 5.46154e13i 1.36648 + 1.20645i
\(305\) 2.44904e13 0.531309
\(306\) 5.75715e12 + 2.28061e12i 0.122670 + 0.0485940i
\(307\) −2.22569e13 + 2.22569e13i −0.465805 + 0.465805i −0.900552 0.434747i \(-0.856838\pi\)
0.434747 + 0.900552i \(0.356838\pi\)
\(308\) 4.79509e13 1.48974e12i 0.985751 0.0306254i
\(309\) −5.45548e13 5.45548e13i −1.10170 1.10170i
\(310\) −5.63358e13 + 2.43667e13i −1.11762 + 0.483401i
\(311\) 3.81764e13i 0.744069i −0.928219 0.372035i \(-0.878660\pi\)
0.928219 0.372035i \(-0.121340\pi\)
\(312\) −2.41545e13 5.14026e13i −0.462539 0.984317i
\(313\) 5.77077e13i 1.08577i 0.839805 + 0.542887i \(0.182669\pi\)
−0.839805 + 0.542887i \(0.817331\pi\)
\(314\) −1.57933e13 3.65142e13i −0.291985 0.675069i
\(315\) −9.83762e13 9.83762e13i −1.78724 1.78724i
\(316\) 3.81547e11 + 3.58554e11i 0.00681191 + 0.00640140i
\(317\) 1.12780e13 1.12780e13i 0.197881 0.197881i −0.601210 0.799091i \(-0.705314\pi\)
0.799091 + 0.601210i \(0.205314\pi\)
\(318\) 5.65587e13 1.42776e14i 0.975327 2.46211i
\(319\) 3.09910e12 0.0525276
\(320\) 8.19768e13 7.66032e12i 1.36573 0.127621i
\(321\) 6.18418e13 1.01276
\(322\) −3.83351e13 + 9.67728e13i −0.617148 + 1.55792i
\(323\) −6.23104e12 + 6.23104e12i −0.0986159 + 0.0986159i
\(324\) 1.16889e13 + 1.09845e13i 0.181876 + 0.170916i
\(325\) 2.68462e13 + 2.68462e13i 0.410700 + 0.410700i
\(326\) 6.51242e12 + 1.50567e13i 0.0979594 + 0.226482i
\(327\) 9.00459e13i 1.33184i
\(328\) −1.54429e13 3.28635e13i −0.224606 0.477978i
\(329\) 7.46508e13i 1.06772i
\(330\) 1.36366e14 5.89818e13i 1.91813 0.829643i
\(331\) 3.48998e13 + 3.48998e13i 0.482802 + 0.482802i 0.906025 0.423223i \(-0.139101\pi\)
−0.423223 + 0.906025i \(0.639101\pi\)
\(332\) −1.46598e12 + 4.55454e10i −0.0199466 + 0.000619705i
\(333\) 1.37965e13 1.37965e13i 0.184640 0.184640i
\(334\) −2.20549e13 8.73670e12i −0.290335 0.115012i
\(335\) −7.23742e13 −0.937211
\(336\) −9.16295e13 + 1.03783e14i −1.16726 + 1.32209i
\(337\) −3.04682e13 −0.381841 −0.190920 0.981606i \(-0.561147\pi\)
−0.190920 + 0.981606i \(0.561147\pi\)
\(338\) 4.26683e13 + 1.69024e13i 0.526094 + 0.208404i
\(339\) 1.21326e14 1.21326e14i 1.47182 1.47182i
\(340\) 2.73025e11 + 8.78796e12i 0.00325889 + 0.104895i
\(341\) 4.93323e13 + 4.93323e13i 0.579405 + 0.579405i
\(342\) −2.49653e14 + 1.07982e14i −2.88532 + 1.24798i
\(343\) 8.06413e13i 0.917148i
\(344\) −1.08066e14 3.89716e13i −1.20953 0.436191i
\(345\) 3.22363e14i 3.55092i
\(346\) 2.19068e13 + 5.06485e13i 0.237499 + 0.549096i
\(347\) 4.49902e13 + 4.49902e13i 0.480071 + 0.480071i 0.905154 0.425083i \(-0.139755\pi\)
−0.425083 + 0.905154i \(0.639755\pi\)
\(348\) −6.12457e12 + 6.51733e12i −0.0643265 + 0.0684516i
\(349\) 1.26485e14 1.26485e14i 1.30767 1.30767i 0.384584 0.923090i \(-0.374345\pi\)
0.923090 0.384584i \(-0.125655\pi\)
\(350\) 3.40844e13 8.60425e13i 0.346882 0.875666i
\(351\) 7.86560e13 0.788030
\(352\) −4.24115e13 8.34217e13i −0.418311 0.822800i
\(353\) −6.13312e13 −0.595554 −0.297777 0.954636i \(-0.596245\pi\)
−0.297777 + 0.954636i \(0.596245\pi\)
\(354\) 9.56819e13 2.41539e14i 0.914770 2.30924i
\(355\) −4.23339e13 + 4.23339e13i −0.398503 + 0.398503i
\(356\) −6.97493e13 + 7.42222e13i −0.646495 + 0.687953i
\(357\) −1.04540e13 1.04540e13i −0.0954125 0.0954125i
\(358\) 1.08654e13 + 2.51207e13i 0.0976534 + 0.225774i
\(359\) 1.56749e14i 1.38734i 0.720291 + 0.693672i \(0.244008\pi\)
−0.720291 + 0.693672i \(0.755992\pi\)
\(360\) −9.20683e13 + 2.55300e14i −0.802503 + 2.22529i
\(361\) 2.70583e14i 2.32280i
\(362\) −4.64679e13 + 2.00986e13i −0.392876 + 0.169929i
\(363\) 2.07458e13 + 2.07458e13i 0.172760 + 0.172760i
\(364\) 2.66523e12 + 8.57867e13i 0.0218614 + 0.703659i
\(365\) 1.65847e14 1.65847e14i 1.33997 1.33997i
\(366\) 7.46855e13 + 2.95855e13i 0.594416 + 0.235469i
\(367\) 2.36073e13 0.185090 0.0925452 0.995708i \(-0.470500\pi\)
0.0925452 + 0.995708i \(0.470500\pi\)
\(368\) 2.02657e14 1.26045e13i 1.56530 0.0973561i
\(369\) 1.19691e14 0.910783
\(370\) 2.57555e13 + 1.02026e13i 0.193090 + 0.0764897i
\(371\) −1.64102e14 + 1.64102e14i −1.21215 + 1.21215i
\(372\) −2.01237e14 + 6.25205e12i −1.46461 + 0.0455026i
\(373\) −1.23900e14 1.23900e14i −0.888533 0.888533i 0.105849 0.994382i \(-0.466244\pi\)
−0.994382 + 0.105849i \(0.966244\pi\)
\(374\) 9.17233e12 3.96727e12i 0.0648165 0.0280348i
\(375\) 3.85247e13i 0.268267i
\(376\) 1.31797e14 6.19324e13i 0.904422 0.424996i
\(377\) 5.54446e12i 0.0374958i
\(378\) −7.61151e13 1.75978e14i −0.507301 1.17288i
\(379\) −1.89125e14 1.89125e14i −1.24232 1.24232i −0.959037 0.283279i \(-0.908578\pi\)
−0.283279 0.959037i \(-0.591422\pi\)
\(380\) −2.81435e14 2.64475e14i −1.82209 1.71228i
\(381\) −8.34212e13 + 8.34212e13i −0.532340 + 0.532340i
\(382\) −1.63125e13 + 4.11791e13i −0.102606 + 0.259017i
\(383\) −1.18647e14 −0.735640 −0.367820 0.929897i \(-0.619896\pi\)
−0.367820 + 0.929897i \(0.619896\pi\)
\(384\) 2.59249e14 + 7.56709e13i 1.58451 + 0.462495i
\(385\) −2.24525e14 −1.35279
\(386\) −1.70204e13 + 4.29661e13i −0.101097 + 0.255209i
\(387\) 2.67758e14 2.67758e14i 1.56795 1.56795i
\(388\) −8.05833e13 7.57270e13i −0.465233 0.437196i
\(389\) 1.64051e14 + 1.64051e14i 0.933807 + 0.933807i 0.997941 0.0641342i \(-0.0204286\pi\)
−0.0641342 + 0.997941i \(0.520429\pi\)
\(390\) 1.05522e14 + 2.43966e14i 0.592224 + 1.36922i
\(391\) 2.16830e13i 0.119991i
\(392\) 2.34898e13 1.10381e13i 0.128176 0.0602311i
\(393\) 8.26813e13i 0.444886i
\(394\) 1.92067e14 8.30742e13i 1.01912 0.440795i
\(395\) −1.73272e12 1.73272e12i −0.00906661 0.00906661i
\(396\) 3.08327e14 9.57914e12i 1.59107 0.0494314i
\(397\) −1.00961e14 + 1.00961e14i −0.513814 + 0.513814i −0.915693 0.401879i \(-0.868357\pi\)
0.401879 + 0.915693i \(0.368357\pi\)
\(398\) −2.50136e14 9.90876e13i −1.25551 0.497350i
\(399\) 6.49402e14 3.21486
\(400\) −1.80186e14 + 1.12069e13i −0.879815 + 0.0547212i
\(401\) 8.85961e13 0.426698 0.213349 0.976976i \(-0.431563\pi\)
0.213349 + 0.976976i \(0.431563\pi\)
\(402\) −2.20711e14 8.74313e13i −1.04853 0.415359i
\(403\) −8.82581e13 + 8.82581e13i −0.413596 + 0.413596i
\(404\) −7.58169e12 2.44034e14i −0.0350484 1.12812i
\(405\) −5.30829e13 5.30829e13i −0.242076 0.242076i
\(406\) 1.24047e13 5.36536e12i 0.0558076 0.0241382i
\(407\) 3.14879e13i 0.139757i
\(408\) −9.78365e12 + 2.71294e13i −0.0428420 + 0.118798i
\(409\) 6.09716e13i 0.263421i 0.991288 + 0.131710i \(0.0420469\pi\)
−0.991288 + 0.131710i \(0.957953\pi\)
\(410\) 6.74638e13 + 1.55976e14i 0.287581 + 0.664886i
\(411\) −2.49589e14 2.49589e14i −1.04977 1.04977i
\(412\) 1.55751e14 1.65739e14i 0.646392 0.687844i
\(413\) −2.77615e14 + 2.77615e14i −1.13689 + 1.13689i
\(414\) −2.46497e14 + 6.22256e14i −0.996116 + 2.51459i
\(415\) 6.86432e12 0.0273737
\(416\) 1.49246e14 7.58765e13i 0.587339 0.298603i
\(417\) −7.08094e14 −2.75006
\(418\) −1.61670e14 + 4.08117e14i −0.619667 + 1.56428i
\(419\) −2.16284e14 + 2.16284e14i −0.818176 + 0.818176i −0.985844 0.167668i \(-0.946376\pi\)
0.167668 + 0.985844i \(0.446376\pi\)
\(420\) 4.43715e14 4.72170e14i 1.65666 1.76290i
\(421\) 3.49912e14 + 3.49912e14i 1.28946 + 1.28946i 0.935115 + 0.354345i \(0.115296\pi\)
0.354345 + 0.935115i \(0.384704\pi\)
\(422\) −1.65193e14 3.81925e14i −0.600859 1.38918i
\(423\) 4.80009e14i 1.72337i
\(424\) 4.25866e14 + 1.53579e14i 1.50925 + 0.544278i
\(425\) 1.92787e13i 0.0674434i
\(426\) −1.80242e14 + 7.79593e13i −0.622447 + 0.269225i
\(427\) −8.58406e13 8.58406e13i −0.292644 0.292644i
\(428\) 5.66111e12 + 1.82216e14i 0.0190529 + 0.613262i
\(429\) 2.13637e14 2.13637e14i 0.709840 0.709840i
\(430\) 4.99855e14 + 1.98010e14i 1.63971 + 0.649547i
\(431\) 4.11853e13 0.133388 0.0666941 0.997773i \(-0.478755\pi\)
0.0666941 + 0.997773i \(0.478755\pi\)
\(432\) −2.47543e14 + 2.80378e14i −0.791573 + 0.896569i
\(433\) 1.87442e14 0.591810 0.295905 0.955217i \(-0.404379\pi\)
0.295905 + 0.955217i \(0.404379\pi\)
\(434\) 2.82868e14 + 1.12054e14i 0.881841 + 0.349328i
\(435\) 2.95972e13 2.95972e13i 0.0911087 0.0911087i
\(436\) −2.65319e14 + 8.24296e12i −0.806478 + 0.0250558i
\(437\) −6.73476e14 6.73476e14i −2.02150 2.02150i
\(438\) 7.06114e14 3.05413e14i 2.09299 0.905273i
\(439\) 2.44174e14i 0.714734i −0.933964 0.357367i \(-0.883675\pi\)
0.933964 0.357367i \(-0.116325\pi\)
\(440\) 1.86272e14 + 3.96401e14i 0.538466 + 1.14589i
\(441\) 8.55511e13i 0.244238i
\(442\) 7.09766e12 + 1.64098e13i 0.0200121 + 0.0462680i
\(443\) 3.95338e14 + 3.95338e14i 1.10090 + 1.10090i 0.994302 + 0.106599i \(0.0339961\pi\)
0.106599 + 0.994302i \(0.466004\pi\)
\(444\) 6.62181e13 + 6.22275e13i 0.182125 + 0.171150i
\(445\) 3.37066e14 3.37066e14i 0.915662 0.915662i
\(446\) −1.06412e14 + 2.68624e14i −0.285527 + 0.720782i
\(447\) −3.69361e13 −0.0978947
\(448\) −3.14184e14 2.60484e14i −0.822537 0.681950i
\(449\) −3.39123e14 −0.877005 −0.438503 0.898730i \(-0.644491\pi\)
−0.438503 + 0.898730i \(0.644491\pi\)
\(450\) 2.19165e14 5.53259e14i 0.559890 1.41338i
\(451\) 1.36586e14 1.36586e14i 0.344694 0.344694i
\(452\) 3.68590e14 + 3.46378e14i 0.918930 + 0.863552i
\(453\) −3.25121e14 3.25121e14i −0.800765 0.800765i
\(454\) −1.01183e14 2.33935e14i −0.246207 0.569230i
\(455\) 4.01687e14i 0.965663i
\(456\) −5.38762e14 1.14652e15i −1.27965 2.72318i
\(457\) 3.62436e14i 0.850535i 0.905068 + 0.425267i \(0.139820\pi\)
−0.905068 + 0.425267i \(0.860180\pi\)
\(458\) −3.63708e14 + 1.57313e14i −0.843320 + 0.364758i
\(459\) −2.82421e13 2.82421e13i −0.0647034 0.0647034i
\(460\) −9.49838e14 + 2.95097e13i −2.15021 + 0.0668031i
\(461\) 4.25739e14 4.25739e14i 0.952333 0.952333i −0.0465818 0.998914i \(-0.514833\pi\)
0.998914 + 0.0465818i \(0.0148328\pi\)
\(462\) −6.84707e14 2.71236e14i −1.51347 0.599539i
\(463\) 1.92004e14 0.419387 0.209693 0.977767i \(-0.432753\pi\)
0.209693 + 0.977767i \(0.432753\pi\)
\(464\) −1.97639e13 1.74493e13i −0.0426602 0.0376643i
\(465\) 9.42271e14 2.00995
\(466\) 2.36455e14 + 9.36681e13i 0.498455 + 0.197455i
\(467\) −5.47493e14 + 5.47493e14i −1.14061 + 1.14061i −0.152266 + 0.988339i \(0.548657\pi\)
−0.988339 + 0.152266i \(0.951343\pi\)
\(468\) 1.71376e13 + 5.51614e14i 0.0352856 + 1.13575i
\(469\) 2.53677e14 + 2.53677e14i 0.516214 + 0.516214i
\(470\) −6.25530e14 + 2.70558e14i −1.25808 + 0.544155i
\(471\) 6.10734e14i 1.21405i
\(472\) 7.20449e14 + 2.59814e14i 1.41554 + 0.510484i
\(473\) 6.11108e14i 1.18681i
\(474\) −3.19087e12 7.37729e12i −0.00612531 0.0141617i
\(475\) 5.98800e14 + 5.98800e14i 1.13623 + 1.13623i
\(476\) 2.98454e13 3.17594e13i 0.0559809 0.0595709i
\(477\) −1.05518e15 + 1.05518e15i −1.95649 + 1.95649i
\(478\) 2.05517e14 5.18804e14i 0.376698 0.950934i
\(479\) −4.71009e14 −0.853461 −0.426730 0.904379i \(-0.640335\pi\)
−0.426730 + 0.904379i \(0.640335\pi\)
\(480\) −1.20174e15 3.91657e14i −2.15270 0.701583i
\(481\) 5.63335e13 0.0997628
\(482\) 2.54225e14 6.41765e14i 0.445103 1.12361i
\(483\) 1.12991e15 1.12991e15i 1.95584 1.95584i
\(484\) −5.92281e13 + 6.30263e13i −0.101363 + 0.107863i
\(485\) 3.65953e14 + 3.65953e14i 0.619222 + 0.619222i
\(486\) 1.86041e14 + 4.30126e14i 0.311249 + 0.719608i
\(487\) 3.48163e14i 0.575934i −0.957640 0.287967i \(-0.907021\pi\)
0.957640 0.287967i \(-0.0929794\pi\)
\(488\) −8.03365e13 + 2.22768e14i −0.131403 + 0.364371i
\(489\) 2.51838e14i 0.407308i
\(490\) −1.11487e14 + 4.82210e13i −0.178298 + 0.0771184i
\(491\) 3.92493e14 + 3.92493e14i 0.620703 + 0.620703i 0.945711 0.325008i \(-0.105367\pi\)
−0.325008 + 0.945711i \(0.605367\pi\)
\(492\) 1.73100e13 + 5.57161e14i 0.0270700 + 0.871310i
\(493\) 1.99079e12 1.99079e12i 0.00307869 0.00307869i
\(494\) −7.30144e14 2.89235e14i −1.11663 0.442337i
\(495\) −1.44371e15 −2.18349
\(496\) −3.68431e13 5.92369e14i −0.0551070 0.886019i
\(497\) 2.96766e14 0.438990
\(498\) 2.09333e13 + 8.29241e12i 0.0306250 + 0.0121316i
\(499\) 8.56521e14 8.56521e14i 1.23932 1.23932i 0.279047 0.960278i \(-0.409982\pi\)
0.960278 0.279047i \(-0.0900185\pi\)
\(500\) −1.13512e14 + 3.52662e12i −0.162446 + 0.00504688i
\(501\) 2.57509e14 + 2.57509e14i 0.364490 + 0.364490i
\(502\) 9.45653e14 4.09020e14i 1.32392 0.572630i
\(503\) 6.57746e14i 0.910823i −0.890281 0.455412i \(-0.849492\pi\)
0.890281 0.455412i \(-0.150508\pi\)
\(504\) 1.21755e15 5.72137e14i 1.66770 0.783668i
\(505\) 1.14267e15i 1.54816i
\(506\) 4.28799e14 + 9.91382e14i 0.574679 + 1.32866i
\(507\) −4.98189e14 4.98189e14i −0.660466 0.660466i
\(508\) −2.53436e14 2.38163e14i −0.332367 0.312337i
\(509\) 6.23390e14 6.23390e14i 0.808746 0.808746i −0.175698 0.984444i \(-0.556218\pi\)
0.984444 + 0.175698i \(0.0562182\pi\)
\(510\) 4.97096e13 1.25486e14i 0.0637975 0.161050i
\(511\) −1.16261e15 −1.47611
\(512\) −1.99231e14 + 7.70800e14i −0.250249 + 0.968181i
\(513\) 1.75440e15 2.18014
\(514\) −3.84351e14 + 9.70252e14i −0.472531 + 1.19285i
\(515\) −7.52672e14 + 7.52672e14i −0.915516 + 0.915516i
\(516\) 1.28514e15 + 1.20769e15i 1.54660 + 1.45340i
\(517\) 5.47765e14 + 5.47765e14i 0.652223 + 0.652223i
\(518\) −5.45137e13 1.26036e14i −0.0642232 0.148484i
\(519\) 8.47145e14i 0.987501i
\(520\) −7.09182e14 + 3.33251e14i −0.817974 + 0.384373i
\(521\) 7.57107e14i 0.864072i −0.901856 0.432036i \(-0.857795\pi\)
0.901856 0.432036i \(-0.142205\pi\)
\(522\) 7.97630e13 3.44996e13i 0.0900770 0.0389607i
\(523\) −1.25634e14 1.25634e14i −0.140394 0.140394i 0.633417 0.773811i \(-0.281652\pi\)
−0.773811 + 0.633417i \(0.781652\pi\)
\(524\) 2.43619e14 7.56879e12i 0.269395 0.00836959i
\(525\) −1.00462e15 + 1.00462e15i −1.09932 + 1.09932i
\(526\) 4.43152e14 + 1.75548e14i 0.479879 + 0.190097i
\(527\) 6.33796e13 0.0679190
\(528\) 8.91821e13 + 1.43388e15i 0.0945782 + 1.52064i
\(529\) −1.39077e15 −1.45966
\(530\) −1.96983e15 7.80319e14i −2.04603 0.810504i
\(531\) −1.78508e15 + 1.78508e15i −1.83501 + 1.83501i
\(532\) 5.94474e13 + 1.91345e15i 0.0604810 + 1.94672i
\(533\) 2.44359e14 + 2.44359e14i 0.246053 + 0.246053i
\(534\) 1.43510e15 6.20719e14i 1.43023 0.618612i
\(535\) 8.53208e14i 0.841607i
\(536\) 2.37411e14 6.58325e14i 0.231790 0.642738i
\(537\) 4.20168e14i 0.406035i
\(538\) −4.09619e14 9.47038e14i −0.391812 0.905868i
\(539\) 9.76271e13 + 9.76271e13i 0.0924341 + 0.0924341i
\(540\) 1.19873e15 1.27560e15i 1.12345 1.19550i
\(541\) −6.24928e14 + 6.24928e14i −0.579756 + 0.579756i −0.934836 0.355080i \(-0.884454\pi\)
0.355080 + 0.934836i \(0.384454\pi\)
\(542\) 2.08405e14 5.26096e14i 0.191387 0.483135i
\(543\) 7.77220e14 0.706554
\(544\) −8.08321e13 2.63439e13i −0.0727428 0.0237075i
\(545\) 1.24233e15 1.10677
\(546\) 4.85257e14 1.22498e15i 0.427969 1.08036i
\(547\) −9.63322e14 + 9.63322e14i −0.841087 + 0.841087i −0.989000 0.147913i \(-0.952744\pi\)
0.147913 + 0.989000i \(0.452744\pi\)
\(548\) 7.12561e14 7.58257e14i 0.615927 0.655426i
\(549\) −5.51960e14 5.51960e14i −0.472346 0.472346i
\(550\) −3.81253e14 8.81455e14i −0.323011 0.746802i
\(551\) 1.23668e14i 0.103735i
\(552\) −2.93226e15 1.05746e15i −2.43521 0.878208i
\(553\) 1.21466e13i 0.00998775i
\(554\) −8.03743e13 + 3.47640e13i −0.0654355 + 0.0283026i
\(555\) −3.00717e14 3.00717e14i −0.242408 0.242408i
\(556\) −6.48202e13 2.08639e15i −0.0517367 1.66527i
\(557\) −2.17103e14 + 2.17103e14i −0.171579 + 0.171579i −0.787673 0.616094i \(-0.788714\pi\)
0.616094 + 0.787673i \(0.288714\pi\)
\(558\) 1.81886e15 + 7.20514e14i 1.42335 + 0.563838i
\(559\) 1.09330e15 0.847181
\(560\) 1.43186e15 + 1.26418e15i 1.09867 + 0.970004i
\(561\) −1.53416e14 −0.116567
\(562\) −1.43931e15 5.70159e14i −1.08294 0.428989i
\(563\) 1.35181e15 1.35181e15i 1.00721 1.00721i 0.00723157 0.999974i \(-0.497698\pi\)
0.999974 0.00723157i \(-0.00230190\pi\)
\(564\) −2.23445e15 + 6.94202e13i −1.64868 + 0.0512213i
\(565\) −1.67388e15 1.67388e15i −1.22309 1.22309i
\(566\) 1.91854e15 8.29818e14i 1.38829 0.600472i
\(567\) 3.72118e14i 0.266670i
\(568\) −2.46205e14 5.23943e14i −0.174736 0.371850i
\(569\) 1.98028e15i 1.39190i −0.718090 0.695951i \(-0.754983\pi\)
0.718090 0.695951i \(-0.245017\pi\)
\(570\) 2.35364e15 + 5.44161e15i 1.63843 + 3.78805i
\(571\) −4.03386e13 4.03386e13i −0.0278114 0.0278114i 0.693064 0.720876i \(-0.256260\pi\)
−0.720876 + 0.693064i \(0.756260\pi\)
\(572\) 6.49033e14 + 6.09920e14i 0.443189 + 0.416481i
\(573\) 4.80801e14 4.80801e14i 0.325173 0.325173i
\(574\) 3.10242e14 7.83173e14i 0.207819 0.524617i
\(575\) 2.08372e15 1.38251
\(576\) −2.02022e15 1.67493e15i −1.32763 1.10071i
\(577\) −1.24036e15 −0.807384 −0.403692 0.914895i \(-0.632273\pi\)
−0.403692 + 0.914895i \(0.632273\pi\)
\(578\) −5.67864e14 + 1.43351e15i −0.366135 + 0.924269i
\(579\) 5.01666e14 5.01666e14i 0.320393 0.320393i
\(580\) 8.99171e13 + 8.44984e13i 0.0568838 + 0.0534557i
\(581\) −2.40599e13 2.40599e13i −0.0150774 0.0150774i
\(582\) 6.73916e14 + 1.55809e15i 0.418340 + 0.967202i
\(583\) 2.40826e15i 1.48090i
\(584\) 9.64533e14 + 2.05259e15i 0.587552 + 1.25035i
\(585\) 2.58287e15i 1.55864i
\(586\) 1.95703e15 8.46466e14i 1.16993 0.506026i
\(587\) −2.42607e13 2.42607e13i −0.0143679 0.0143679i 0.699886 0.714254i \(-0.253234\pi\)
−0.714254 + 0.699886i \(0.753234\pi\)
\(588\) −3.98242e14 + 1.23726e13i −0.233653 + 0.00725916i
\(589\) −1.96858e15 + 1.96858e15i −1.14424 + 1.14424i
\(590\) −3.33242e15 1.32009e15i −1.91899 0.760180i
\(591\) −3.21251e15 −1.83279
\(592\) −1.77291e14 + 2.00807e14i −0.100211 + 0.113504i
\(593\) −1.06516e15 −0.596504 −0.298252 0.954487i \(-0.596404\pi\)
−0.298252 + 0.954487i \(0.596404\pi\)
\(594\) −1.84978e15 7.32764e14i −1.02635 0.406573i
\(595\) −1.44229e14 + 1.44229e14i −0.0792884 + 0.0792884i
\(596\) −3.38119e12 1.08832e14i −0.00184168 0.0592789i
\(597\) 2.92055e15 + 2.92055e15i 1.57618 + 1.57618i
\(598\) −1.77364e15 + 7.67144e14i −0.948436 + 0.410223i
\(599\) 1.54332e14i 0.0817729i 0.999164 + 0.0408865i \(0.0130182\pi\)
−0.999164 + 0.0408865i \(0.986982\pi\)
\(600\) 2.60712e15 + 9.40203e14i 1.36877 + 0.493616i
\(601\) 6.03222e14i 0.313811i 0.987614 + 0.156905i \(0.0501518\pi\)
−0.987614 + 0.156905i \(0.949848\pi\)
\(602\) −1.05799e15 2.44606e15i −0.545381 1.26092i
\(603\) 1.63116e15 + 1.63116e15i 0.833202 + 0.833202i
\(604\) 9.28202e14 9.87726e14i 0.469829 0.499958i
\(605\) 2.86222e14 2.86222e14i 0.143565 0.143565i
\(606\) −1.38039e15 + 3.48465e15i −0.686125 + 1.73205i
\(607\) 3.40313e15 1.67626 0.838128 0.545474i \(-0.183650\pi\)
0.838128 + 0.545474i \(0.183650\pi\)
\(608\) 3.32890e15 1.69241e15i 1.62491 0.826105i
\(609\) −2.07481e14 −0.100365
\(610\) 4.08180e14 1.03041e15i 0.195676 0.493963i
\(611\) −9.79981e14 + 9.79981e14i −0.465577 + 0.465577i
\(612\) 1.91908e14 2.04215e14i 0.0903567 0.0961512i
\(613\) −4.01340e14 4.01340e14i −0.187275 0.187275i 0.607242 0.794517i \(-0.292276\pi\)
−0.794517 + 0.607242i \(0.792276\pi\)
\(614\) 5.65481e14 + 1.30739e15i 0.261512 + 0.604616i
\(615\) 2.60885e15i 1.19574i
\(616\) 7.36515e14 2.04231e15i 0.334570 0.927743i
\(617\) 2.48564e15i 1.11910i 0.828796 + 0.559552i \(0.189027\pi\)
−0.828796 + 0.559552i \(0.810973\pi\)
\(618\) −3.20460e15 + 1.38607e15i −1.43000 + 0.618514i
\(619\) 1.37578e15 + 1.37578e15i 0.608484 + 0.608484i 0.942550 0.334066i \(-0.108421\pi\)
−0.334066 + 0.942550i \(0.608421\pi\)
\(620\) 8.62571e13 + 2.77639e15i 0.0378129 + 1.21710i
\(621\) 3.05252e15 3.05252e15i 1.32634 1.32634i
\(622\) −1.60623e15 6.36284e14i −0.691769 0.274034i
\(623\) −2.36288e15 −1.00869
\(624\) −2.56529e15 + 1.59551e14i −1.08548 + 0.0675127i
\(625\) 2.63321e15 1.10445
\(626\) 2.42799e15 + 9.61811e14i 1.00946 + 0.399881i
\(627\) 4.76512e15 4.76512e15i 1.96382 1.96382i
\(628\) −1.79952e15 + 5.59077e13i −0.735154 + 0.0228399i
\(629\) −2.02270e13 2.02270e13i −0.00819130 0.00819130i
\(630\) −5.77870e15 + 2.49944e15i −2.31984 + 1.00339i
\(631\) 1.74122e14i 0.0692933i −0.999400 0.0346467i \(-0.988969\pi\)
0.999400 0.0346467i \(-0.0110306\pi\)
\(632\) 2.14450e13 1.00772e13i 0.00846022 0.00397553i
\(633\) 6.38807e15i 2.49833i
\(634\) −2.86539e14 6.62478e14i −0.111095 0.256850i
\(635\) 1.15093e15 + 1.15093e15i 0.442378 + 0.442378i
\(636\) −5.06450e15 4.75929e15i −1.92984 1.81354i
\(637\) −1.74660e14 + 1.74660e14i −0.0659822 + 0.0659822i
\(638\) 5.16526e13 1.30391e14i 0.0193454 0.0488354i
\(639\) 1.90823e15 0.708557
\(640\) 1.04400e15 3.57676e15i 0.384337 1.31674i
\(641\) 5.21652e14 0.190398 0.0951988 0.995458i \(-0.469651\pi\)
0.0951988 + 0.995458i \(0.469651\pi\)
\(642\) 1.03071e15 2.60193e15i 0.372989 0.941570i
\(643\) −2.06632e14 + 2.06632e14i −0.0741372 + 0.0741372i −0.743203 0.669066i \(-0.766694\pi\)
0.669066 + 0.743203i \(0.266694\pi\)
\(644\) 3.43268e15 + 3.22581e15i 1.22113 + 1.14754i
\(645\) −5.83623e15 5.83623e15i −2.05851 2.05851i
\(646\) 1.58312e14 + 3.66017e14i 0.0553649 + 0.128004i
\(647\) 4.78314e15i 1.65859i 0.558809 + 0.829297i \(0.311259\pi\)
−0.558809 + 0.829297i \(0.688741\pi\)
\(648\) 6.56978e14 3.08720e14i 0.225885 0.106146i
\(649\) 4.07411e15i 1.38895i
\(650\) 1.57697e15 6.82081e14i 0.533090 0.230575i
\(651\) −3.30272e15 3.30272e15i −1.10707 1.10707i
\(652\) 7.42037e14 2.30537e13i 0.246640 0.00766264i
\(653\) 2.83678e15 2.83678e15i 0.934981 0.934981i −0.0630307 0.998012i \(-0.520077\pi\)
0.998012 + 0.0630307i \(0.0200766\pi\)
\(654\) 3.78858e15 + 1.50079e15i 1.23822 + 0.490504i
\(655\) −1.14072e15 −0.369703
\(656\) −1.64008e15 + 1.02007e14i −0.527102 + 0.0327838i
\(657\) −7.47565e15 −2.38253
\(658\) 3.14085e15 + 1.24420e15i 0.992670 + 0.393231i
\(659\) 4.97751e14 4.97751e14i 0.156006 0.156006i −0.624788 0.780794i \(-0.714815\pi\)
0.780794 + 0.624788i \(0.214815\pi\)
\(660\) −2.08793e14 6.72049e15i −0.0648969 2.08886i
\(661\) 2.20684e15 + 2.20684e15i 0.680242 + 0.680242i 0.960055 0.279813i \(-0.0902724\pi\)
−0.279813 + 0.960055i \(0.590272\pi\)
\(662\) 2.05004e15 8.86698e14i 0.626678 0.271054i
\(663\) 2.74469e14i 0.0832089i
\(664\) −2.25172e13 + 6.24388e13i −0.00677002 + 0.0187728i
\(665\) 8.95955e15i 2.67157i
\(666\) −3.50527e14 8.10417e14i −0.103660 0.239663i
\(667\) 2.15172e14 + 2.15172e14i 0.0631094 + 0.0631094i
\(668\) −7.35174e14 + 7.82320e14i −0.213855 + 0.227569i
\(669\) 3.13642e15 3.13642e15i 0.904879 0.904879i
\(670\) −1.20626e15 + 3.04507e15i −0.345166 + 0.871335i
\(671\) −1.25975e15 −0.357527
\(672\) 2.83939e15 + 5.58496e15i 0.799271 + 1.57213i
\(673\) −3.47072e15 −0.969028 −0.484514 0.874783i \(-0.661004\pi\)
−0.484514 + 0.874783i \(0.661004\pi\)
\(674\) −5.07812e14 + 1.28192e15i −0.140628 + 0.355001i
\(675\) −2.71405e15 + 2.71405e15i −0.745499 + 0.745499i
\(676\) 1.42230e15 1.51351e15i 0.387512 0.412362i
\(677\) −3.88738e15 3.88738e15i −1.05056 1.05056i −0.998652 0.0519033i \(-0.983471\pi\)
−0.0519033 0.998652i \(-0.516529\pi\)
\(678\) −3.08251e15 7.12677e15i −0.826308 1.91042i
\(679\) 2.56538e15i 0.682132i
\(680\) 3.74294e14 + 1.34981e14i 0.0987221 + 0.0356020i
\(681\) 3.91278e15i 1.02371i
\(682\) 2.89782e15 1.25338e15i 0.752068 0.325289i
\(683\) −5.25838e15 5.25838e15i −1.35375 1.35375i −0.881426 0.472321i \(-0.843416\pi\)
−0.472321 0.881426i \(-0.656584\pi\)
\(684\) 3.82250e14 + 1.23036e16i 0.0976201 + 3.14213i
\(685\) −3.44348e15 + 3.44348e15i −0.872367 + 0.872367i
\(686\) −3.39289e15 1.34404e15i −0.852683 0.337777i
\(687\) 6.08336e15 1.51664
\(688\) −3.44081e15 + 3.89721e15i −0.850990 + 0.963867i
\(689\) −4.30850e15 −1.05711
\(690\) 1.35631e16 + 5.37281e15i 3.30132 + 1.30777i
\(691\) −5.14710e15 + 5.14710e15i −1.24289 + 1.24289i −0.284098 + 0.958795i \(0.591694\pi\)
−0.958795 + 0.284098i \(0.908306\pi\)
\(692\) 2.49610e15 7.75492e13i 0.597969 0.0185778i
\(693\) 5.06030e15 + 5.06030e15i 1.20266 + 1.20266i
\(694\) 2.64276e15 1.14306e15i 0.623133 0.269521i
\(695\) 9.76931e15i 2.28532i
\(696\) 1.72132e14 + 3.66309e14i 0.0399494 + 0.0850151i
\(697\) 1.75478e14i 0.0404057i
\(698\) −3.21360e15 7.42984e15i −0.734154 1.69736i
\(699\) −2.76081e15 2.76081e15i −0.625767 0.625767i
\(700\) −3.05206e15 2.86813e15i −0.686363 0.645000i
\(701\) 5.46695e15 5.46695e15i 1.21982 1.21982i 0.252125 0.967695i \(-0.418870\pi\)
0.967695 0.252125i \(-0.0811296\pi\)
\(702\) 1.31095e15 3.30936e15i 0.290224 0.732640i
\(703\) 1.25651e15 0.276001
\(704\) −4.21675e15 + 3.94034e14i −0.919026 + 0.0858783i
\(705\) 1.04626e16 2.26255
\(706\) −1.02220e15 + 2.58044e15i −0.219337 + 0.553692i
\(707\) 4.00512e15 4.00512e15i 0.852725 0.852725i
\(708\) −8.56775e15 8.05142e15i −1.81002 1.70094i
\(709\) 2.91858e15 + 2.91858e15i 0.611811 + 0.611811i 0.943418 0.331607i \(-0.107591\pi\)
−0.331607 + 0.943418i \(0.607591\pi\)
\(710\) 1.07557e15 + 2.48673e15i 0.223728 + 0.517258i
\(711\) 7.81036e13i 0.0161209i
\(712\) 1.96031e15 + 4.17168e15i 0.401500 + 0.854420i
\(713\) 6.85032e15i 1.39225i
\(714\) −6.14074e14 + 2.65603e14i −0.123846 + 0.0535665i
\(715\) −2.94746e15 2.94746e15i −0.589882 0.589882i
\(716\) 1.23802e15 3.84629e13i 0.245870 0.00763871i
\(717\) −6.05748e15 + 6.05748e15i −1.19381 + 1.19381i
\(718\) 6.59503e15 + 2.61252e15i 1.28983 + 0.510946i
\(719\) −3.53754e15 −0.686582 −0.343291 0.939229i \(-0.611542\pi\)
−0.343291 + 0.939229i \(0.611542\pi\)
\(720\) 9.20695e15 + 8.12874e15i 1.77332 + 1.56565i
\(721\) 5.27634e15 1.00853
\(722\) −1.13845e16 4.50980e15i −2.15953 0.855465i
\(723\) −7.49315e15 + 7.49315e15i −1.41060 + 1.41060i
\(724\) 7.11481e13 + 2.29007e15i 0.0132923 + 0.427845i
\(725\) −1.91313e14 1.91313e14i −0.0354721 0.0354721i
\(726\) 1.21863e15 5.27087e14i 0.224243 0.0969909i
\(727\) 6.70485e15i 1.22447i −0.790674 0.612237i \(-0.790270\pi\)
0.790674 0.612237i \(-0.209730\pi\)
\(728\) 3.65380e15 + 1.31766e15i 0.662250 + 0.238826i
\(729\) 8.58171e15i 1.54373i
\(730\) −4.21366e15 9.74198e15i −0.752288 1.73929i
\(731\) −3.92560e14 3.92560e14i −0.0695602 0.0695602i
\(732\) 2.48956e15 2.64921e15i 0.437836 0.465914i
\(733\) 1.66881e15 1.66881e15i 0.291297 0.291297i −0.546295 0.837593i \(-0.683962\pi\)
0.837593 + 0.546295i \(0.183962\pi\)
\(734\) 3.93462e14 9.93253e14i 0.0681671 0.172080i
\(735\) 1.86473e15 0.320653
\(736\) 2.84735e15 8.73665e15i 0.485974 1.49114i
\(737\) 3.72281e15 0.630666
\(738\) 1.99488e15 5.03585e15i 0.335433 0.846765i
\(739\) 5.34409e15 5.34409e15i 0.891928 0.891928i −0.102777 0.994704i \(-0.532773\pi\)
0.994704 + 0.102777i \(0.0327727\pi\)
\(740\) 8.58530e14 9.13586e14i 0.142227 0.151347i
\(741\) 8.52505e15 + 8.52505e15i 1.40183 + 1.40183i
\(742\) 4.16932e15 + 9.63947e15i 0.680525 + 1.57337i
\(743\) 4.45245e15i 0.721374i 0.932687 + 0.360687i \(0.117458\pi\)
−0.932687 + 0.360687i \(0.882542\pi\)
\(744\) −3.09095e15 + 8.57102e15i −0.497097 + 1.37842i
\(745\) 5.09593e14i 0.0813511i
\(746\) −7.27800e15 + 3.14793e15i −1.15332 + 0.498840i
\(747\) −1.54707e14 1.54707e14i −0.0243358 0.0243358i
\(748\) −1.40440e13 4.52038e14i −0.00219296 0.0705856i
\(749\) −2.99055e15 + 2.99055e15i −0.463555 + 0.463555i
\(750\) 1.62088e15 + 6.42089e14i 0.249411 + 0.0988002i
\(751\) 2.33457e15 0.356605 0.178302 0.983976i \(-0.442939\pi\)
0.178302 + 0.983976i \(0.442939\pi\)
\(752\) −4.09091e14 6.57742e15i −0.0620328 0.997372i
\(753\) −1.58170e16 −2.38095
\(754\) 2.33277e14 + 9.24093e13i 0.0348602 + 0.0138093i
\(755\) −4.48557e15 + 4.48557e15i −0.665441 + 0.665441i
\(756\) −8.67269e15 + 2.69444e14i −1.27727 + 0.0396825i
\(757\) −2.83109e15 2.83109e15i −0.413930 0.413930i 0.469175 0.883105i \(-0.344551\pi\)
−0.883105 + 0.469175i \(0.844551\pi\)
\(758\) −1.11093e16 + 4.80508e15i −1.61253 + 0.697461i
\(759\) 1.65818e16i 2.38947i
\(760\) −1.58182e16 + 7.43309e15i −2.26298 + 1.06340i
\(761\) 2.83306e15i 0.402383i −0.979552 0.201192i \(-0.935519\pi\)