Properties

Label 43.8.g.a.24.5
Level 43
Weight 8
Character 43.24
Analytic conductor 13.433
Analytic rank 0
Dimension 300
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4325560958\)
Analytic rank: \(0\)
Dimension: \(300\)
Relative dimension: \(25\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 24.5
Character \(\chi\) \(=\) 43.24
Dual form 43.8.g.a.9.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.86658 + 12.3723i) q^{2} +(-10.7092 + 1.61415i) q^{3} +(-27.2418 - 119.354i) q^{4} +(180.379 - 122.981i) q^{5} +(85.6924 - 148.424i) q^{6} +(797.705 + 1381.66i) q^{7} +(-79.5102 - 38.2901i) q^{8} +(-1977.76 + 610.057i) q^{9} +O(q^{10})\) \(q+(-9.86658 + 12.3723i) q^{2} +(-10.7092 + 1.61415i) q^{3} +(-27.2418 - 119.354i) q^{4} +(180.379 - 122.981i) q^{5} +(85.6924 - 148.424i) q^{6} +(797.705 + 1381.66i) q^{7} +(-79.5102 - 38.2901i) q^{8} +(-1977.76 + 610.057i) q^{9} +(-258.175 + 3445.11i) q^{10} +(-774.777 + 3394.52i) q^{11} +(484.392 + 1234.21i) q^{12} +(-123.816 - 1652.21i) q^{13} +(-24965.0 - 3762.87i) q^{14} +(-1733.21 + 1608.18i) q^{15} +(15376.6 - 7404.97i) q^{16} +(16246.2 + 11076.5i) q^{17} +(11965.9 - 30488.6i) q^{18} +(-22107.6 - 6819.29i) q^{19} +(-19592.1 - 18178.8i) q^{20} +(-10773.0 - 13508.9i) q^{21} +(-34353.6 - 43078.1i) q^{22} +(-54351.5 - 50430.8i) q^{23} +(913.296 + 281.715i) q^{24} +(-11129.8 + 28358.2i) q^{25} +(21663.3 + 14769.8i) q^{26} +(41535.4 - 20002.4i) q^{27} +(143176. - 132848. i) q^{28} +(-192040. - 28945.4i) q^{29} +(-2796.08 - 37311.0i) q^{30} +(-90271.8 - 230009. i) q^{31} +(-57584.2 + 252293. i) q^{32} +(2817.97 - 37603.2i) q^{33} +(-297336. + 91716.1i) q^{34} +(313807. + 151122. i) q^{35} +(126690. + 219434. i) q^{36} +(-168540. + 291920. i) q^{37} +(302497. - 206239. i) q^{38} +(3992.88 + 17494.0i) q^{39} +(-19050.9 + 2871.47i) q^{40} +(-207414. + 260089. i) q^{41} +273429. q^{42} +(323697. + 408704. i) q^{43} +426255. q^{44} +(-281721. + 353267. i) q^{45} +(1.16021e6 - 174873. i) q^{46} +(-105872. - 463855. i) q^{47} +(-152718. + 104121. i) q^{48} +(-860894. + 1.49111e6i) q^{49} +(-241043. - 417499. i) q^{50} +(-191863. - 92396.4i) q^{51} +(-193825. + 59787.0i) q^{52} +(138967. - 1.85439e6i) q^{53} +(-162337. + 711244. i) q^{54} +(277706. + 707584. i) q^{55} +(-10521.6 - 140401. i) q^{56} +(247762. + 37344.1i) q^{57} +(2.25290e6 - 2.09039e6i) q^{58} +(411511. - 198173. i) q^{59} +(239159. + 163056. i) q^{60} +(-454347. + 1.15766e6i) q^{61} +(3.73641e6 + 1.15253e6i) q^{62} +(-2.42056e6 - 2.24595e6i) q^{63} +(-1.19124e6 - 1.49377e6i) q^{64} +(-225523. - 282797. i) q^{65} +(437434. + 405879. i) q^{66} +(-2.01832e6 - 622570. i) q^{67} +(879446. - 2.24079e6i) q^{68} +(663464. + 452342. i) q^{69} +(-4.96593e6 + 2.39147e6i) q^{70} +(-1.14458e6 + 1.06201e6i) q^{71} +(180611. + 27222.7i) q^{72} +(423070. + 5.64548e6i) q^{73} +(-1.94880e6 - 4.96547e6i) q^{74} +(73416.5 - 321659. i) q^{75} +(-211659. + 2.82440e6i) q^{76} +(-5.30813e6 + 1.63734e6i) q^{77} +(-255837. - 123204. i) q^{78} +(2.60854e6 + 4.51812e6i) q^{79} +(1.86295e6 - 3.22672e6i) q^{80} +(3.32741e6 - 2.26859e6i) q^{81} +(-1.17143e6 - 5.13239e6i) q^{82} +(-4.87842e6 + 735304. i) q^{83} +(-1.31887e6 + 1.65380e6i) q^{84} +4.29267e6 q^{85} +(-8.25039e6 - 27634.6i) q^{86} +2.10332e6 q^{87} +(191579. - 240233. i) q^{88} +(1.08804e7 - 1.63996e6i) q^{89} +(-1.59110e6 - 6.97108e6i) q^{90} +(2.18403e6 - 1.48905e6i) q^{91} +(-4.53849e6 + 7.86089e6i) q^{92} +(1.33801e6 + 2.31750e6i) q^{93} +(6.78355e6 + 3.26678e6i) q^{94} +(-4.82640e6 + 1.48875e6i) q^{95} +(209441. - 2.79480e6i) q^{96} +(271421. - 1.18917e6i) q^{97} +(-9.95441e6 - 2.53634e7i) q^{98} +(-538530. - 7.18619e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 300q - 40q^{2} - 12q^{3} - 3028q^{4} + 235q^{5} + 1274q^{6} - 4122q^{7} + 762q^{8} + 8097q^{9} + O(q^{10}) \) \( 300q - 40q^{2} - 12q^{3} - 3028q^{4} + 235q^{5} + 1274q^{6} - 4122q^{7} + 762q^{8} + 8097q^{9} - 1681q^{10} + 4580q^{11} + 9330q^{12} - 20444q^{13} - 45798q^{14} + 50477q^{15} - 74504q^{16} - 25312q^{17} + 2046q^{18} + 4046q^{19} + 140781q^{20} + 100555q^{21} + 95810q^{22} + 1648q^{23} - 292592q^{24} + 419068q^{25} + 393435q^{26} + 274140q^{27} + 233644q^{28} + 605697q^{29} - 1216016q^{30} + 358580q^{31} - 19194q^{32} + 1280291q^{33} + 1137255q^{34} + 652739q^{35} - 8980975q^{36} - 2360047q^{37} - 308490q^{38} + 536339q^{39} + 3057993q^{40} - 1376320q^{41} + 8417790q^{42} + 7173000q^{43} - 3856780q^{44} + 2761486q^{45} - 7073993q^{46} + 1437090q^{47} - 9543469q^{48} - 16053170q^{49} - 3046893q^{50} + 2972901q^{51} + 17415142q^{52} + 3320604q^{53} + 6000486q^{54} + 13427750q^{55} - 5450793q^{56} + 3333100q^{57} - 7876190q^{58} - 7084765q^{59} + 7356443q^{60} + 3354606q^{61} - 719427q^{62} + 14716815q^{63} - 16086234q^{64} - 19914646q^{65} - 8293345q^{66} + 13025470q^{67} - 22191927q^{68} - 33964295q^{69} + 8094727q^{70} + 30843495q^{71} + 93841607q^{72} - 3067637q^{73} + 18179570q^{74} - 41508571q^{75} - 19751872q^{76} - 15169179q^{77} - 69509396q^{78} - 12090149q^{79} - 69662530q^{80} + 3387954q^{81} + 39226888q^{82} + 16408777q^{83} + 98603231q^{84} - 13423424q^{85} + 111906660q^{86} + 49022010q^{87} + 76213954q^{88} - 12540205q^{89} - 92608607q^{90} - 59091937q^{91} - 50489370q^{92} - 52218334q^{93} - 3441600q^{94} - 79947551q^{95} - 23449784q^{96} - 116467587q^{97} + 73909552q^{98} - 20061115q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{20}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.86658 + 12.3723i −0.872091 + 1.09357i 0.122782 + 0.992434i \(0.460818\pi\)
−0.994873 + 0.101134i \(0.967753\pi\)
\(3\) −10.7092 + 1.61415i −0.228998 + 0.0345160i −0.262539 0.964921i \(-0.584560\pi\)
0.0335405 + 0.999437i \(0.489322\pi\)
\(4\) −27.2418 119.354i −0.212826 0.932452i
\(5\) 180.379 122.981i 0.645345 0.439989i −0.195914 0.980621i \(-0.562767\pi\)
0.841259 + 0.540632i \(0.181815\pi\)
\(6\) 85.6924 148.424i 0.161962 0.280526i
\(7\) 797.705 + 1381.66i 0.879020 + 1.52251i 0.852417 + 0.522862i \(0.175136\pi\)
0.0266030 + 0.999646i \(0.491531\pi\)
\(8\) −79.5102 38.2901i −0.0549045 0.0264406i
\(9\) −1977.76 + 610.057i −0.904324 + 0.278947i
\(10\) −258.175 + 3445.11i −0.0816421 + 1.08944i
\(11\) −774.777 + 3394.52i −0.175510 + 0.768960i 0.808158 + 0.588966i \(0.200465\pi\)
−0.983668 + 0.179994i \(0.942392\pi\)
\(12\) 484.392 + 1234.21i 0.0809213 + 0.206184i
\(13\) −123.816 1652.21i −0.0156306 0.208575i −0.999551 0.0299674i \(-0.990460\pi\)
0.983920 0.178608i \(-0.0571594\pi\)
\(14\) −24965.0 3762.87i −2.43155 0.366497i
\(15\) −1733.21 + 1608.18i −0.132596 + 0.123031i
\(16\) 15376.6 7404.97i 0.938512 0.451964i
\(17\) 16246.2 + 11076.5i 0.802012 + 0.546803i 0.893531 0.449001i \(-0.148220\pi\)
−0.0915192 + 0.995803i \(0.529172\pi\)
\(18\) 11965.9 30488.6i 0.483605 1.23221i
\(19\) −22107.6 6819.29i −0.739442 0.228088i −0.0979220 0.995194i \(-0.531220\pi\)
−0.641520 + 0.767107i \(0.721696\pi\)
\(20\) −19592.1 18178.8i −0.547615 0.508112i
\(21\) −10773.0 13508.9i −0.253845 0.318312i
\(22\) −34353.6 43078.1i −0.687849 0.862535i
\(23\) −54351.5 50430.8i −0.931460 0.864268i 0.0595272 0.998227i \(-0.481041\pi\)
−0.990987 + 0.133958i \(0.957231\pi\)
\(24\) 913.296 + 281.715i 0.0134857 + 0.00415978i
\(25\) −11129.8 + 28358.2i −0.142461 + 0.362985i
\(26\) 21663.3 + 14769.8i 0.241723 + 0.164804i
\(27\) 41535.4 20002.4i 0.406111 0.195573i
\(28\) 143176. 132848.i 1.23259 1.14367i
\(29\) −192040. 28945.4i −1.46218 0.220388i −0.630734 0.775999i \(-0.717246\pi\)
−0.831442 + 0.555612i \(0.812484\pi\)
\(30\) −2796.08 37311.0i −0.0189071 0.252298i
\(31\) −90271.8 230009.i −0.544235 1.38669i −0.893246 0.449569i \(-0.851578\pi\)
0.349011 0.937119i \(-0.386518\pi\)
\(32\) −57584.2 + 252293.i −0.310655 + 1.36107i
\(33\) 2817.97 37603.2i 0.0136501 0.182149i
\(34\) −297336. + 91716.1i −1.29739 + 0.400193i
\(35\) 313807. + 151122.i 1.23716 + 0.595784i
\(36\) 126690. + 219434.i 0.452569 + 0.783872i
\(37\) −168540. + 291920.i −0.547011 + 0.947452i 0.451466 + 0.892288i \(0.350901\pi\)
−0.998477 + 0.0551633i \(0.982432\pi\)
\(38\) 302497. 206239.i 0.894290 0.609716i
\(39\) 3992.88 + 17494.0i 0.0107786 + 0.0472239i
\(40\) −19050.9 + 2871.47i −0.0470659 + 0.00709404i
\(41\) −207414. + 260089.i −0.469997 + 0.589358i −0.959170 0.282829i \(-0.908727\pi\)
0.489173 + 0.872187i \(0.337299\pi\)
\(42\) 273429. 0.569471
\(43\) 323697. + 408704.i 0.620868 + 0.783915i
\(44\) 426255. 0.754372
\(45\) −281721. + 353267.i −0.460867 + 0.577909i
\(46\) 1.16021e6 174873.i 1.75745 0.264893i
\(47\) −105872. 463855.i −0.148744 0.651688i −0.993235 0.116119i \(-0.962954\pi\)
0.844492 0.535569i \(-0.179903\pi\)
\(48\) −152718. + 104121.i −0.199318 + 0.135893i
\(49\) −860894. + 1.49111e6i −1.04535 + 1.81061i
\(50\) −241043. 417499.i −0.272709 0.472347i
\(51\) −191863. 92396.4i −0.202533 0.0975347i
\(52\) −193825. + 59787.0i −0.191160 + 0.0589651i
\(53\) 138967. 1.85439e6i 0.128218 1.71094i −0.448320 0.893873i \(-0.647978\pi\)
0.576538 0.817071i \(-0.304403\pi\)
\(54\) −162337. + 711244.i −0.140294 + 0.614668i
\(55\) 277706. + 707584.i 0.225069 + 0.573467i
\(56\) −10521.6 140401.i −0.00800613 0.106834i
\(57\) 247762. + 37344.1i 0.177204 + 0.0267091i
\(58\) 2.25290e6 2.09039e6i 1.51616 1.40679i
\(59\) 411511. 198173.i 0.260855 0.125621i −0.298886 0.954289i \(-0.596615\pi\)
0.559741 + 0.828668i \(0.310901\pi\)
\(60\) 239159. + 163056.i 0.142941 + 0.0974554i
\(61\) −454347. + 1.15766e6i −0.256291 + 0.653018i −0.999878 0.0156207i \(-0.995028\pi\)
0.743587 + 0.668639i \(0.233123\pi\)
\(62\) 3.73641e6 + 1.15253e6i 1.99106 + 0.614160i
\(63\) −2.42056e6 2.24595e6i −1.21962 1.13164i
\(64\) −1.19124e6 1.49377e6i −0.568030 0.712287i
\(65\) −225523. 282797.i −0.101858 0.127726i
\(66\) 437434. + 405879.i 0.187288 + 0.173777i
\(67\) −2.01832e6 622570.i −0.819839 0.252887i −0.143663 0.989627i \(-0.545888\pi\)
−0.676176 + 0.736740i \(0.736364\pi\)
\(68\) 879446. 2.24079e6i 0.339178 0.864212i
\(69\) 663464. + 452342.i 0.243134 + 0.165766i
\(70\) −4.96593e6 + 2.39147e6i −1.73044 + 0.833338i
\(71\) −1.14458e6 + 1.06201e6i −0.379526 + 0.352148i −0.846751 0.531990i \(-0.821444\pi\)
0.467225 + 0.884139i \(0.345254\pi\)
\(72\) 180611. + 27222.7i 0.0570270 + 0.00859543i
\(73\) 423070. + 5.64548e6i 0.127286 + 1.69852i 0.586303 + 0.810092i \(0.300583\pi\)
−0.459016 + 0.888428i \(0.651798\pi\)
\(74\) −1.94880e6 4.96547e6i −0.559059 1.42446i
\(75\) 73416.5 321659.i 0.0200946 0.0880401i
\(76\) −211659. + 2.82440e6i −0.0553082 + 0.738037i
\(77\) −5.30813e6 + 1.63734e6i −1.32502 + 0.408716i
\(78\) −255837. 123204.i −0.0610424 0.0293965i
\(79\) 2.60854e6 + 4.51812e6i 0.595254 + 1.03101i 0.993511 + 0.113736i \(0.0362818\pi\)
−0.398257 + 0.917274i \(0.630385\pi\)
\(80\) 1.86295e6 3.22672e6i 0.406805 0.704607i
\(81\) 3.32741e6 2.26859e6i 0.695678 0.474305i
\(82\) −1.17143e6 5.13239e6i −0.234622 1.02795i
\(83\) −4.87842e6 + 735304.i −0.936497 + 0.141154i −0.599521 0.800359i \(-0.704642\pi\)
−0.336976 + 0.941513i \(0.609404\pi\)
\(84\) −1.31887e6 + 1.65380e6i −0.242786 + 0.304443i
\(85\) 4.29267e6 0.758161
\(86\) −8.25039e6 27634.6i −1.39872 0.00468499i
\(87\) 2.10332e6 0.342443
\(88\) 191579. 240233.i 0.0299681 0.0375788i
\(89\) 1.08804e7 1.63996e6i 1.63599 0.246586i 0.734255 0.678874i \(-0.237532\pi\)
0.901735 + 0.432288i \(0.142294\pi\)
\(90\) −1.59110e6 6.97108e6i −0.230065 1.00798i
\(91\) 2.18403e6 1.48905e6i 0.303818 0.207140i
\(92\) −4.53849e6 + 7.86089e6i −0.607650 + 1.05248i
\(93\) 1.33801e6 + 2.31750e6i 0.172492 + 0.298764i
\(94\) 6.78355e6 + 3.26678e6i 0.842383 + 0.405670i
\(95\) −4.82640e6 + 1.48875e6i −0.577551 + 0.178151i
\(96\) 209441. 2.79480e6i 0.0241609 0.322405i
\(97\) 271421. 1.18917e6i 0.0301955 0.132295i −0.957584 0.288156i \(-0.906958\pi\)
0.987779 + 0.155860i \(0.0498150\pi\)
\(98\) −9.95441e6 2.53634e7i −1.06838 2.72218i
\(99\) −538530. 7.18619e6i −0.0557811 0.744347i
\(100\) 3.68786e6 + 555855.i 0.368786 + 0.0555855i
\(101\) −5.41614e6 + 5.02544e6i −0.523076 + 0.485344i −0.896948 0.442137i \(-0.854221\pi\)
0.373872 + 0.927480i \(0.378030\pi\)
\(102\) 3.03619e6 1.46215e6i 0.283288 0.136424i
\(103\) 2.96944e6 + 2.02453e6i 0.267759 + 0.182555i 0.689755 0.724043i \(-0.257718\pi\)
−0.421996 + 0.906597i \(0.638671\pi\)
\(104\) −53418.6 + 136108.i −0.00465667 + 0.0118650i
\(105\) −3.60456e6 1.11186e6i −0.303871 0.0937318i
\(106\) 2.15720e7 + 2.00158e7i 1.75921 + 1.63231i
\(107\) −144289. 180932.i −0.0113865 0.0142782i 0.776106 0.630603i \(-0.217192\pi\)
−0.787492 + 0.616325i \(0.788621\pi\)
\(108\) −3.51886e6 4.41251e6i −0.268794 0.337057i
\(109\) 2.98537e6 + 2.77002e6i 0.220803 + 0.204876i 0.782816 0.622253i \(-0.213782\pi\)
−0.562013 + 0.827128i \(0.689973\pi\)
\(110\) −1.14944e7 3.54557e6i −0.823406 0.253987i
\(111\) 1.33372e6 3.39827e6i 0.0925625 0.235846i
\(112\) 2.24972e7 + 1.53383e7i 1.51309 + 1.03161i
\(113\) 1.70211e7 8.19691e6i 1.10972 0.534411i 0.213016 0.977049i \(-0.431671\pi\)
0.896701 + 0.442637i \(0.145957\pi\)
\(114\) −2.90660e6 + 2.69693e6i −0.183746 + 0.170491i
\(115\) −1.60059e7 2.41250e6i −0.981381 0.147919i
\(116\) 1.77677e6 + 2.37093e7i 0.105688 + 1.41031i
\(117\) 1.25282e6 + 3.19213e6i 0.0723166 + 0.184260i
\(118\) −1.60835e6 + 7.04662e6i −0.0901140 + 0.394815i
\(119\) −2.34431e6 + 3.12826e7i −0.127526 + 1.70172i
\(120\) 199385. 61502.2i 0.0105332 0.00324905i
\(121\) 6.63486e6 + 3.19518e6i 0.340473 + 0.163963i
\(122\) −9.84003e6 1.70434e7i −0.490611 0.849762i
\(123\) 1.80142e6 3.12015e6i 0.0872863 0.151184i
\(124\) −2.49933e7 + 1.70401e7i −1.17719 + 0.802597i
\(125\) 5.27519e6 + 2.31121e7i 0.241576 + 1.05841i
\(126\) 5.16702e7 7.78804e6i 2.30114 0.346841i
\(127\) −9.16774e6 + 1.14960e7i −0.397145 + 0.498004i −0.939692 0.342021i \(-0.888889\pi\)
0.542547 + 0.840025i \(0.317460\pi\)
\(128\) −2.88902e6 −0.121763
\(129\) −4.12624e6 3.85439e6i −0.169235 0.158086i
\(130\) 5.72400e6 0.228506
\(131\) −1.33980e6 + 1.68005e6i −0.0520702 + 0.0652939i −0.807185 0.590299i \(-0.799010\pi\)
0.755114 + 0.655593i \(0.227581\pi\)
\(132\) −4.56485e6 + 688041.i −0.172750 + 0.0260379i
\(133\) −8.21336e6 3.59851e7i −0.302719 1.32630i
\(134\) 2.76165e7 1.88286e7i 0.991523 0.676009i
\(135\) 5.03222e6 8.71607e6i 0.176032 0.304896i
\(136\) −867620. 1.50276e6i −0.0295763 0.0512276i
\(137\) −1.94095e7 9.34711e6i −0.644899 0.310567i 0.0826951 0.996575i \(-0.473647\pi\)
−0.727594 + 0.686008i \(0.759362\pi\)
\(138\) −1.21426e7 + 3.74551e6i −0.393311 + 0.121320i
\(139\) −2.94593e6 + 3.93107e7i −0.0930401 + 1.24153i 0.733906 + 0.679252i \(0.237695\pi\)
−0.826946 + 0.562282i \(0.809924\pi\)
\(140\) 9.48830e6 4.15710e7i 0.292240 1.28039i
\(141\) 1.88253e6 + 4.79662e6i 0.0565557 + 0.144101i
\(142\) −1.84648e6 2.46395e7i −0.0541171 0.722142i
\(143\) 5.70438e6 + 859797.i 0.163130 + 0.0245878i
\(144\) −2.58937e7 + 2.40258e7i −0.722645 + 0.670516i
\(145\) −3.81998e7 + 1.83961e7i −1.04058 + 0.501115i
\(146\) −7.40218e7 5.04672e7i −1.96845 1.34207i
\(147\) 6.81260e6 1.73582e7i 0.176890 0.450707i
\(148\) 3.94331e7 + 1.21635e7i 0.999872 + 0.308420i
\(149\) 2.24050e7 + 2.07888e7i 0.554873 + 0.514847i 0.907014 0.421100i \(-0.138356\pi\)
−0.352141 + 0.935947i \(0.614546\pi\)
\(150\) 3.25529e6 + 4.08200e6i 0.0787535 + 0.0987538i
\(151\) −1.66115e7 2.08301e7i −0.392634 0.492348i 0.545747 0.837950i \(-0.316246\pi\)
−0.938381 + 0.345602i \(0.887675\pi\)
\(152\) 1.49667e6 + 1.38871e6i 0.0345679 + 0.0320743i
\(153\) −3.88883e7 1.19955e7i −0.877808 0.270768i
\(154\) 3.21154e7 8.18288e7i 0.708584 1.80544i
\(155\) −4.45698e7 3.03872e7i −0.961346 0.655435i
\(156\) 1.97920e6 953133.i 0.0417401 0.0201010i
\(157\) −9.58711e6 + 8.89554e6i −0.197715 + 0.183452i −0.772817 0.634629i \(-0.781153\pi\)
0.575102 + 0.818082i \(0.304962\pi\)
\(158\) −8.16369e7 1.23048e7i −1.64659 0.248184i
\(159\) 1.50504e6 + 2.00833e7i 0.0296932 + 0.396229i
\(160\) 2.06401e7 + 5.25901e7i 0.398375 + 1.01504i
\(161\) 2.63221e7 1.15324e8i 0.497083 2.17786i
\(162\) −4.76248e6 + 6.35509e7i −0.0880097 + 1.17441i
\(163\) 1.63770e7 5.05165e6i 0.296196 0.0913642i −0.143096 0.989709i \(-0.545706\pi\)
0.439291 + 0.898345i \(0.355230\pi\)
\(164\) 3.66930e7 + 1.76704e7i 0.649576 + 0.312819i
\(165\) −4.11616e6 7.12939e6i −0.0713342 0.123555i
\(166\) 3.90360e7 6.76123e7i 0.662349 1.14722i
\(167\) 5.77674e7 3.93852e7i 0.959788 0.654372i 0.0213325 0.999772i \(-0.493209\pi\)
0.938456 + 0.345400i \(0.112257\pi\)
\(168\) 339305. + 1.48659e6i 0.00552088 + 0.0241886i
\(169\) 5.93332e7 8.94304e6i 0.945571 0.142522i
\(170\) −4.23540e7 + 5.31103e7i −0.661186 + 0.829101i
\(171\) 4.78836e7 0.732319
\(172\) 3.99623e7 4.97683e7i 0.598827 0.745767i
\(173\) −2.81489e7 −0.413333 −0.206667 0.978411i \(-0.566262\pi\)
−0.206667 + 0.978411i \(0.566262\pi\)
\(174\) −2.07526e7 + 2.60229e7i −0.298641 + 0.374484i
\(175\) −4.80598e7 + 7.24385e6i −0.677874 + 0.102173i
\(176\) 1.32229e7 + 5.79333e7i 0.182824 + 0.801002i
\(177\) −4.08707e6 + 2.78651e6i −0.0553994 + 0.0377707i
\(178\) −8.70625e7 + 1.50797e8i −1.15707 + 2.00411i
\(179\) −1.96482e7 3.40316e7i −0.256057 0.443503i 0.709125 0.705083i \(-0.249090\pi\)
−0.965182 + 0.261579i \(0.915757\pi\)
\(180\) 4.98384e7 + 2.40009e7i 0.636958 + 0.306743i
\(181\) −8.71407e7 + 2.68793e7i −1.09231 + 0.336933i −0.788022 0.615647i \(-0.788895\pi\)
−0.304288 + 0.952580i \(0.598419\pi\)
\(182\) −3.12598e6 + 4.17133e7i −0.0384358 + 0.512890i
\(183\) 2.99705e6 1.31310e7i 0.0361506 0.158386i
\(184\) 2.39050e6 + 6.09089e6i 0.0282895 + 0.0720806i
\(185\) 5.49932e6 + 7.33834e7i 0.0638570 + 0.852112i
\(186\) −4.18743e7 6.31154e6i −0.477148 0.0719184i
\(187\) −5.01865e7 + 4.65663e7i −0.561231 + 0.520746i
\(188\) −5.24788e7 + 2.52724e7i −0.576012 + 0.277393i
\(189\) 6.07696e7 + 4.14320e7i 0.654742 + 0.446395i
\(190\) 2.92008e7 7.44025e7i 0.308857 0.786955i
\(191\) 7.42271e7 + 2.28960e7i 0.770807 + 0.237762i 0.655121 0.755524i \(-0.272617\pi\)
0.115685 + 0.993286i \(0.463094\pi\)
\(192\) 1.51684e7 + 1.40743e7i 0.154663 + 0.143506i
\(193\) 5.43355e7 + 6.81346e7i 0.544043 + 0.682208i 0.975519 0.219916i \(-0.0705784\pi\)
−0.431476 + 0.902125i \(0.642007\pi\)
\(194\) 1.20348e7 + 1.50912e7i 0.118341 + 0.148394i
\(195\) 2.87165e6 + 2.66450e6i 0.0277339 + 0.0257333i
\(196\) 2.01422e8 + 6.21305e7i 1.91078 + 0.589398i
\(197\) −2.75151e7 + 7.01073e7i −0.256413 + 0.653328i −0.999881 0.0154428i \(-0.995084\pi\)
0.743468 + 0.668771i \(0.233179\pi\)
\(198\) 9.42232e7 + 6.42403e7i 0.862640 + 0.588138i
\(199\) 1.18164e7 5.69048e6i 0.106292 0.0511874i −0.379982 0.924994i \(-0.624070\pi\)
0.486274 + 0.873806i \(0.338356\pi\)
\(200\) 1.97077e6 1.82861e6i 0.0174193 0.0161627i
\(201\) 2.26195e7 + 3.40934e6i 0.196470 + 0.0296131i
\(202\) −8.73751e6 1.16594e8i −0.0745861 0.995283i
\(203\) −1.13199e8 2.88425e8i −0.949741 2.41990i
\(204\) −5.80118e6 + 2.54166e7i −0.0478422 + 0.209610i
\(205\) −5.42733e6 + 7.24227e7i −0.0439995 + 0.587132i
\(206\) −5.43462e7 + 1.67636e7i −0.433146 + 0.133608i
\(207\) 1.38260e8 + 6.65824e7i 1.08343 + 0.521751i
\(208\) −1.41384e7 2.44885e7i −0.108938 0.188686i
\(209\) 4.02767e7 6.97612e7i 0.305170 0.528570i
\(210\) 4.93209e7 3.36264e7i 0.367505 0.250561i
\(211\) −3.04240e7 1.33296e8i −0.222960 0.976853i −0.955236 0.295845i \(-0.904399\pi\)
0.732276 0.681008i \(-0.238458\pi\)
\(212\) −2.25115e8 + 3.39306e7i −1.62266 + 0.244577i
\(213\) 1.05433e7 1.32208e7i 0.0747560 0.0937411i
\(214\) 3.66219e6 0.0255442
\(215\) 1.08651e8 + 3.39133e7i 0.745588 + 0.232721i
\(216\) −4.06838e6 −0.0274684
\(217\) 2.45785e8 3.08205e8i 1.63285 2.04753i
\(218\) −6.37270e7 + 9.60530e6i −0.416606 + 0.0627933i
\(219\) −1.36434e7 5.97756e7i −0.0877744 0.384565i
\(220\) 7.68877e7 5.24211e7i 0.486830 0.331915i
\(221\) 1.62891e7 2.82136e7i 0.101514 0.175827i
\(222\) 2.88852e7 + 5.00306e7i 0.177190 + 0.306902i
\(223\) −1.42358e8 6.85560e7i −0.859637 0.413979i −0.0484913 0.998824i \(-0.515441\pi\)
−0.811146 + 0.584844i \(0.801156\pi\)
\(224\) −3.94519e8 + 1.21693e8i −2.34531 + 0.723432i
\(225\) 4.71186e6 6.28754e7i 0.0275774 0.367995i
\(226\) −6.65251e7 + 2.91465e8i −0.383359 + 1.67961i
\(227\) 1.04118e8 + 2.65288e8i 0.590793 + 1.50532i 0.843148 + 0.537681i \(0.180700\pi\)
−0.252355 + 0.967635i \(0.581205\pi\)
\(228\) −2.29230e6 3.05887e7i −0.0128086 0.170918i
\(229\) 1.65661e8 + 2.49693e7i 0.911581 + 0.137399i 0.588055 0.808821i \(-0.299894\pi\)
0.323525 + 0.946219i \(0.395132\pi\)
\(230\) 1.87772e8 1.74227e8i 1.01761 0.944207i
\(231\) 5.42029e7 2.61027e7i 0.289321 0.139330i
\(232\) 1.41608e7 + 9.65470e6i 0.0744528 + 0.0507611i
\(233\) −8.12472e6 + 2.07015e7i −0.0420788 + 0.107215i −0.950368 0.311127i \(-0.899293\pi\)
0.908290 + 0.418342i \(0.137389\pi\)
\(234\) −5.18551e7 1.59952e7i −0.264567 0.0816081i
\(235\) −7.61423e7 7.06497e7i −0.382726 0.355118i
\(236\) −3.48630e7 4.37168e7i −0.172652 0.216499i
\(237\) −3.52283e7 4.41748e7i −0.171898 0.215554i
\(238\) −3.63907e8 3.37657e8i −1.74973 1.62351i
\(239\) −1.73217e8 5.34304e7i −0.820726 0.253160i −0.144171 0.989553i \(-0.546052\pi\)
−0.676555 + 0.736392i \(0.736528\pi\)
\(240\) −1.47423e7 + 3.75627e7i −0.0688375 + 0.175395i
\(241\) 3.05408e8 + 2.08224e8i 1.40547 + 0.958232i 0.999007 + 0.0445638i \(0.0141898\pi\)
0.406461 + 0.913668i \(0.366763\pi\)
\(242\) −1.04995e8 + 5.05630e7i −0.476228 + 0.229339i
\(243\) −1.05880e8 + 9.82424e7i −0.473361 + 0.439215i
\(244\) 1.50548e8 + 2.26915e7i 0.663454 + 0.0999996i
\(245\) 2.80903e7 + 3.74839e8i 0.122032 + 1.62841i
\(246\) 2.08296e7 + 5.30728e7i 0.0892087 + 0.227300i
\(247\) −8.52962e6 + 3.73707e7i −0.0360156 + 0.157795i
\(248\) −1.62953e6 + 2.17446e7i −0.00678393 + 0.0905253i
\(249\) 5.10571e7 1.57490e7i 0.209584 0.0646481i
\(250\) −3.37998e8 1.62771e8i −1.36812 0.658852i
\(251\) −1.24462e8 2.15574e8i −0.496795 0.860474i 0.503198 0.864171i \(-0.332157\pi\)
−0.999993 + 0.00369680i \(0.998823\pi\)
\(252\) −2.02123e8 + 3.50087e8i −0.795634 + 1.37808i
\(253\) 2.13299e8 1.45425e8i 0.828068 0.564568i
\(254\) −5.17775e7 2.26852e8i −0.198255 0.868610i
\(255\) −4.59711e7 + 6.92903e6i −0.173618 + 0.0261687i
\(256\) 1.80984e8 2.26947e8i 0.674218 0.845443i
\(257\) −4.05462e8 −1.48999 −0.744996 0.667069i \(-0.767549\pi\)
−0.744996 + 0.667069i \(0.767549\pi\)
\(258\) 8.83996e7 1.30214e7i 0.320466 0.0472052i
\(259\) −5.37780e8 −1.92334
\(260\) −2.76093e7 + 3.46210e7i −0.0974202 + 0.122161i
\(261\) 3.97467e8 5.99086e7i 1.38376 0.208568i
\(262\) −7.56689e6 3.31527e7i −0.0259934 0.113884i
\(263\) 1.62122e8 1.10533e8i 0.549536 0.374667i −0.256491 0.966547i \(-0.582566\pi\)
0.806026 + 0.591880i \(0.201614\pi\)
\(264\) −1.66389e6 + 2.88193e6i −0.00556557 + 0.00963985i
\(265\) −2.02987e8 3.51584e8i −0.670051 1.16056i
\(266\) 5.26256e8 + 2.53432e8i 1.71440 + 0.825610i
\(267\) −1.13873e8 + 3.51253e7i −0.366128 + 0.112936i
\(268\) −1.93235e7 + 2.57854e8i −0.0613217 + 0.818281i
\(269\) 4.44010e7 1.94533e8i 0.139078 0.609342i −0.856560 0.516047i \(-0.827403\pi\)
0.995639 0.0932948i \(-0.0297399\pi\)
\(270\) 5.81870e7 + 1.48258e8i 0.179909 + 0.458400i
\(271\) 3.95812e7 + 5.28174e8i 0.120808 + 1.61207i 0.647534 + 0.762036i \(0.275800\pi\)
−0.526726 + 0.850035i \(0.676581\pi\)
\(272\) 3.31832e8 + 5.00157e7i 0.999833 + 0.150701i
\(273\) −2.09857e7 + 1.94718e7i −0.0624242 + 0.0579212i
\(274\) 3.07150e8 1.47916e8i 0.902036 0.434398i
\(275\) −8.76393e7 5.97515e7i −0.254118 0.173254i
\(276\) 3.59149e7 9.15096e7i 0.102824 0.261990i
\(277\) −2.53468e8 7.81847e7i −0.716547 0.221026i −0.0850199 0.996379i \(-0.527095\pi\)
−0.631527 + 0.775354i \(0.717572\pi\)
\(278\) −4.57297e8 4.24310e8i −1.27656 1.18448i
\(279\) 3.18854e8 + 3.99831e8i 0.878977 + 1.10220i
\(280\) −1.91644e7 2.40314e7i −0.0521726 0.0654224i
\(281\) 3.81086e8 + 3.53596e8i 1.02459 + 0.950682i 0.998800 0.0489851i \(-0.0155987\pi\)
0.0257923 + 0.999667i \(0.491789\pi\)
\(282\) −7.79194e7 2.40350e7i −0.206906 0.0638222i
\(283\) −5.35263e7 + 1.36383e8i −0.140383 + 0.357690i −0.983723 0.179690i \(-0.942491\pi\)
0.843340 + 0.537380i \(0.180586\pi\)
\(284\) 1.57936e8 + 1.07679e8i 0.409135 + 0.278943i
\(285\) 4.92837e7 2.37338e7i 0.126109 0.0607310i
\(286\) −6.69204e7 + 6.20931e7i −0.169152 + 0.156950i
\(287\) −5.24812e8 7.91026e7i −1.31044 0.197517i
\(288\) −4.00255e7 5.34103e8i −0.0987332 1.31750i
\(289\) −8.66248e6 2.20716e7i −0.0211106 0.0537888i
\(290\) 1.49300e8 6.54127e8i 0.359474 1.57496i
\(291\) −987196. + 1.31732e7i −0.00234843 + 0.0313376i
\(292\) 6.62285e8 2.04288e8i 1.55670 0.480178i
\(293\) −4.47376e8 2.15445e8i −1.03905 0.500379i −0.165039 0.986287i \(-0.552775\pi\)
−0.874010 + 0.485908i \(0.838489\pi\)
\(294\) 1.47544e8 + 2.55554e8i 0.338615 + 0.586498i
\(295\) 4.98566e7 8.63541e7i 0.113069 0.195842i
\(296\) 2.45783e7 1.67572e7i 0.0550846 0.0375560i
\(297\) 3.57178e7 + 1.56490e8i 0.0791111 + 0.346609i
\(298\) −4.78267e8 + 7.20871e7i −1.04692 + 0.157798i
\(299\) −7.65927e7 + 9.60442e7i −0.165706 + 0.207789i
\(300\) −4.03912e7 −0.0863699
\(301\) −3.06477e8 + 7.73266e8i −0.647762 + 1.63435i
\(302\) 4.21615e8 0.880828
\(303\) 4.98906e7 6.25609e7i 0.103031 0.129197i
\(304\) −3.90436e8 + 5.88487e7i −0.797062 + 0.120138i
\(305\) 6.04145e7 + 2.64693e8i 0.121925 + 0.534187i
\(306\) 5.32107e8 3.62784e8i 1.06163 0.723808i
\(307\) 3.28396e8 5.68798e8i 0.647759 1.12195i −0.335898 0.941898i \(-0.609040\pi\)
0.983657 0.180053i \(-0.0576268\pi\)
\(308\) 3.40026e8 + 5.88942e8i 0.663108 + 1.14854i
\(309\) −3.50682e7 1.68879e7i −0.0676174 0.0325628i
\(310\) 8.15711e8 2.51613e8i 1.55514 0.479698i
\(311\) −4.38733e7 + 5.85449e8i −0.0827064 + 1.10364i 0.789255 + 0.614066i \(0.210467\pi\)
−0.871961 + 0.489575i \(0.837152\pi\)
\(312\) 352371. 1.54384e6i 0.000656839 0.00287780i
\(313\) 2.37961e8 + 6.06314e8i 0.438632 + 1.11762i 0.963802 + 0.266619i \(0.0859065\pi\)
−0.525170 + 0.850997i \(0.675998\pi\)
\(314\) −1.54663e7 2.06383e8i −0.0281924 0.376202i
\(315\) −7.12827e8 1.07441e8i −1.28498 0.193680i
\(316\) 4.68194e8 4.34421e8i 0.834682 0.774472i
\(317\) −2.59536e8 + 1.24986e8i −0.457605 + 0.220371i −0.648462 0.761247i \(-0.724588\pi\)
0.190857 + 0.981618i \(0.438873\pi\)
\(318\) −2.63327e8 1.79533e8i −0.459198 0.313076i
\(319\) 2.47044e8 6.29458e8i 0.426096 1.08567i
\(320\) −3.98581e8 1.22946e8i −0.679973 0.209744i
\(321\) 1.83727e6 + 1.70474e6i 0.00310031 + 0.00287667i
\(322\) 1.16712e9 + 1.46352e9i 1.94814 + 2.44289i
\(323\) −2.83631e8 3.55662e8i −0.468322 0.587258i
\(324\) −3.61409e8 3.35339e8i −0.590325 0.547742i
\(325\) 4.82317e7 + 1.48775e7i 0.0779365 + 0.0240402i
\(326\) −9.90849e7 + 2.52464e8i −0.158397 + 0.403588i
\(327\) −3.64422e7 2.48459e7i −0.0576351 0.0392950i
\(328\) 2.64504e7 1.27378e7i 0.0413879 0.0199314i
\(329\) 5.56438e8 5.16299e8i 0.861452 0.799310i
\(330\) 1.28819e8 + 1.94164e7i 0.197325 + 0.0297420i
\(331\) 6.34074e7 + 8.46112e8i 0.0961040 + 1.28242i 0.811770 + 0.583977i \(0.198504\pi\)
−0.715666 + 0.698442i \(0.753877\pi\)
\(332\) 2.20658e8 + 5.62228e8i 0.330931 + 0.843197i
\(333\) 1.55243e8 6.80165e8i 0.230387 1.00939i
\(334\) −8.26819e7 + 1.10331e9i −0.121422 + 1.62027i
\(335\) −4.40627e8 + 1.35916e8i −0.640346 + 0.197521i
\(336\) −2.65685e8 1.27947e8i −0.382102 0.184011i
\(337\) 4.10787e8 + 7.11504e8i 0.584671 + 1.01268i 0.994916 + 0.100705i \(0.0321099\pi\)
−0.410245 + 0.911975i \(0.634557\pi\)
\(338\) −4.74770e8 + 8.22326e8i −0.668767 + 1.15834i
\(339\) −1.69051e8 + 1.15257e8i −0.235678 + 0.160682i
\(340\) −1.16940e8 5.12347e8i −0.161357 0.706950i
\(341\) 8.50710e8 1.28224e8i 1.16183 0.175117i
\(342\) −4.72447e8 + 5.92430e8i −0.638649 + 0.800840i
\(343\) −1.43307e9 −1.91751
\(344\) −1.00879e7 4.48905e7i −0.0133612 0.0594566i
\(345\) 1.75304e8 0.229840
\(346\) 2.77734e8 3.48267e8i 0.360464 0.452008i
\(347\) −7.34558e8 + 1.10717e8i −0.943785 + 0.142253i −0.602868 0.797841i \(-0.705976\pi\)
−0.340917 + 0.940093i \(0.610737\pi\)
\(348\) −5.72981e7 2.51039e8i −0.0728808 0.319312i
\(349\) −9.58305e8 + 6.53361e8i −1.20674 + 0.822743i −0.988213 0.153087i \(-0.951078\pi\)
−0.218530 + 0.975830i \(0.570126\pi\)
\(350\) 3.84563e8 6.66082e8i 0.479434 0.830405i
\(351\) −3.81909e7 6.61485e7i −0.0471395 0.0816480i
\(352\) −8.11797e8 3.90941e8i −0.992084 0.477762i
\(353\) −3.71656e8 + 1.14641e8i −0.449707 + 0.138716i −0.511332 0.859383i \(-0.670848\pi\)
0.0616254 + 0.998099i \(0.480372\pi\)
\(354\) 5.84977e6 7.80598e7i 0.00700854 0.0935225i
\(355\) −7.58513e7 + 3.32326e8i −0.0899836 + 0.394244i
\(356\) −4.92137e8 1.25395e9i −0.578111 1.47300i
\(357\) −2.53892e7 3.38795e8i −0.0295332 0.394093i
\(358\) 6.14910e8 + 9.26827e7i 0.708306 + 0.106760i
\(359\) 7.63437e8 7.08366e8i 0.870849 0.808030i −0.111756 0.993736i \(-0.535648\pi\)
0.982605 + 0.185706i \(0.0594571\pi\)
\(360\) 3.59264e7 1.73012e7i 0.0405840 0.0195442i
\(361\) −2.96308e8 2.02020e8i −0.331489 0.226005i
\(362\) 5.27221e8 1.34334e9i 0.584135 1.48835i
\(363\) −7.62115e7 2.35081e7i −0.0836271 0.0257956i
\(364\) −2.37220e8 2.20108e8i −0.257808 0.239211i
\(365\) 7.70597e8 + 9.66298e8i 0.829473 + 1.04013i
\(366\) 1.32889e8 + 1.66638e8i 0.141679 + 0.177660i
\(367\) −4.62489e8 4.29127e8i −0.488394 0.453163i 0.397127 0.917764i \(-0.370007\pi\)
−0.885520 + 0.464601i \(0.846198\pi\)
\(368\) −1.20918e9 3.72982e8i −1.26480 0.390140i
\(369\) 2.51546e8 6.40928e8i 0.260630 0.664075i
\(370\) −9.62181e8 6.56004e8i −0.987531 0.673287i
\(371\) 2.67300e9 1.28725e9i 2.71763 1.30874i
\(372\) 2.40153e8 2.22829e8i 0.241873 0.224425i
\(373\) 7.98327e8 + 1.20328e8i 0.796526 + 0.120057i 0.534682 0.845053i \(-0.320431\pi\)
0.261844 + 0.965110i \(0.415669\pi\)
\(374\) −8.09628e7 1.08037e9i −0.0800267 1.06788i
\(375\) −9.37995e7 2.38997e8i −0.0918525 0.234036i
\(376\) −9.34316e6 + 4.09350e7i −0.00906434 + 0.0397135i
\(377\) −2.40462e7 + 3.20875e8i −0.0231128 + 0.308419i
\(378\) −1.11220e9 + 3.43067e8i −1.05916 + 0.326707i
\(379\) 6.02355e8 + 2.90079e8i 0.568349 + 0.273703i 0.695911 0.718128i \(-0.255001\pi\)
−0.127562 + 0.991831i \(0.540715\pi\)
\(380\) 3.09167e8 + 5.35493e8i 0.289035 + 0.500624i
\(381\) 7.96229e7 1.37911e8i 0.0737565 0.127750i
\(382\) −1.01564e9 + 6.92454e8i −0.932223 + 0.635579i
\(383\) 2.81986e7 + 1.23546e8i 0.0256467 + 0.112366i 0.986131 0.165968i \(-0.0530749\pi\)
−0.960484 + 0.278334i \(0.910218\pi\)
\(384\) 3.09391e7 4.66332e6i 0.0278836 0.00420277i
\(385\) −7.56116e8 + 9.48139e8i −0.675268 + 0.846759i
\(386\) −1.37909e9 −1.22050
\(387\) −8.89526e8 6.10843e8i −0.780136 0.535724i
\(388\) −1.49327e8 −0.129786
\(389\) 4.06495e8 5.09728e8i 0.350131 0.439051i −0.575314 0.817933i \(-0.695120\pi\)
0.925445 + 0.378882i \(0.123691\pi\)
\(390\) −6.12994e7 + 9.23940e6i −0.0523275 + 0.00788711i
\(391\) −3.24410e8 1.42133e9i −0.274458 1.20248i
\(392\) 1.25545e8 8.55949e7i 0.105268 0.0717706i
\(393\) 1.16363e7 2.01546e7i 0.00967030 0.0167495i
\(394\) −5.95909e8 1.03214e9i −0.490844 0.850166i
\(395\) 1.02617e9 + 4.94176e8i 0.837777 + 0.403452i
\(396\) −8.43029e8 + 2.60040e8i −0.682197 + 0.210430i
\(397\) −2.64313e7 + 3.52702e8i −0.0212008 + 0.282905i 0.976520 + 0.215427i \(0.0691143\pi\)
−0.997721 + 0.0674781i \(0.978505\pi\)
\(398\) −4.61832e7 + 2.02342e8i −0.0367192 + 0.160877i
\(399\) 1.46044e8 + 3.72114e8i 0.115101 + 0.293272i
\(400\) 3.88538e7 + 5.18468e8i 0.0303545 + 0.405053i
\(401\) 1.18942e9 + 1.79276e8i 0.921149 + 0.138841i 0.592463 0.805598i \(-0.298156\pi\)
0.328687 + 0.944439i \(0.393394\pi\)
\(402\) −2.65359e8 + 2.46217e8i −0.203724 + 0.189028i
\(403\) −3.68846e8 + 1.77627e8i −0.280722 + 0.135189i
\(404\) 7.47351e8 + 5.09535e8i 0.563884 + 0.384450i
\(405\) 3.21203e8 8.18412e8i 0.240263 0.612181i
\(406\) 4.68537e9 + 1.44524e9i 3.47458 + 1.07177i
\(407\) −8.60345e8 7.98284e8i −0.632546 0.586917i
\(408\) 1.17172e7 + 1.46929e7i 0.00854109 + 0.0107102i
\(409\) −1.33803e8 1.67784e8i −0.0967018 0.121260i 0.731126 0.682242i \(-0.238995\pi\)
−0.827828 + 0.560982i \(0.810424\pi\)
\(410\) −8.42486e8 7.81713e8i −0.603697 0.560149i
\(411\) 2.22947e8 + 6.87702e7i 0.158400 + 0.0488600i
\(412\) 1.60743e8 4.09565e8i 0.113238 0.288525i
\(413\) 6.02073e8 + 4.10486e8i 0.420556 + 0.286730i
\(414\) −2.18793e9 + 1.05365e9i −1.51542 + 0.729786i
\(415\) −7.89539e8 + 7.32585e8i −0.542257 + 0.503141i
\(416\) 4.23970e8 + 6.39032e7i 0.288741 + 0.0435207i
\(417\) −3.19048e7 4.25741e8i −0.0215467 0.287521i
\(418\) 4.65714e8 + 1.18662e9i 0.311891 + 0.794684i
\(419\) −1.83418e8 + 8.03605e8i −0.121813 + 0.533696i 0.876791 + 0.480871i \(0.159680\pi\)
−0.998604 + 0.0528244i \(0.983178\pi\)
\(420\) −3.45102e7 + 4.60507e8i −0.0227287 + 0.303294i
\(421\) −2.22505e8 + 6.86336e7i −0.145329 + 0.0448280i −0.366566 0.930392i \(-0.619467\pi\)
0.221237 + 0.975220i \(0.428990\pi\)
\(422\) 1.94936e9 + 9.38763e8i 1.26270 + 0.608082i
\(423\) 4.92367e8 + 8.52804e8i 0.316299 + 0.547845i
\(424\) −8.20541e7 + 1.42122e8i −0.0522781 + 0.0905483i
\(425\) −4.94926e8 + 3.37435e8i −0.312737 + 0.213220i
\(426\) 5.95461e7 + 2.60889e8i 0.0373181 + 0.163501i
\(427\) −1.96193e9 + 2.95713e8i −1.21951 + 0.183812i
\(428\) −1.76643e7 + 2.21503e7i −0.0108904 + 0.0136561i
\(429\) −6.24772e7 −0.0382051
\(430\) −1.49160e9 + 1.00965e9i −0.904716 + 0.612396i
\(431\) −8.50543e8 −0.511712 −0.255856 0.966715i \(-0.582357\pi\)
−0.255856 + 0.966715i \(0.582357\pi\)
\(432\) 4.90555e8 6.15137e8i 0.292749 0.367095i
\(433\) 2.26246e9 3.41011e8i 1.33929 0.201865i 0.559979 0.828507i \(-0.310809\pi\)
0.779307 + 0.626642i \(0.215571\pi\)
\(434\) 1.38814e9 + 6.08185e9i 0.815117 + 3.57126i
\(435\) 3.79396e8 2.58668e8i 0.220994 0.150671i
\(436\) 2.49286e8 4.31776e8i 0.144044 0.249492i
\(437\) 8.57679e8 + 1.48554e9i 0.491631 + 0.851530i
\(438\) 8.74176e8 + 4.20981e8i 0.497095 + 0.239388i
\(439\) −2.11466e9 + 6.52287e8i −1.19293 + 0.367971i −0.826748 0.562572i \(-0.809812\pi\)
−0.366183 + 0.930543i \(0.619336\pi\)
\(440\) 5.01298e6 6.68935e7i 0.00280551 0.0374369i
\(441\) 7.92975e8 3.47425e9i 0.440275 1.92897i
\(442\) 1.88349e8 + 4.79906e8i 0.103749 + 0.264349i
\(443\) 2.24050e8 + 2.98974e9i 0.122442 + 1.63388i 0.633081 + 0.774085i \(0.281790\pi\)
−0.510639 + 0.859795i \(0.670591\pi\)
\(444\) −4.41930e8 6.66102e7i −0.239614 0.0361161i
\(445\) 1.76092e9 1.63390e9i 0.947283 0.878950i
\(446\) 2.25278e9 1.08488e9i 1.20240 0.579043i
\(447\) −2.73496e8 1.86466e8i −0.144835 0.0987471i
\(448\) 1.11363e9 2.83749e9i 0.585153 1.49094i
\(449\) 1.15494e9 + 3.56251e8i 0.602138 + 0.185735i 0.580812 0.814038i \(-0.302735\pi\)
0.0213258 + 0.999773i \(0.493211\pi\)
\(450\) 7.31423e8 + 6.78662e8i 0.378377 + 0.351083i
\(451\) −7.22178e8 9.05583e8i −0.370703 0.464847i
\(452\) −1.44202e9 1.80823e9i −0.734490 0.921021i
\(453\) 2.11518e8 + 1.96260e8i 0.106906 + 0.0991947i
\(454\) −4.30952e9 1.32931e9i −2.16139 0.666700i
\(455\) 2.10830e8 5.37187e8i 0.104928 0.267353i
\(456\) −1.82697e7 1.24561e7i −0.00902307 0.00615182i
\(457\) 2.76153e9 1.32988e9i 1.35345 0.651788i 0.390285 0.920694i \(-0.372377\pi\)
0.963166 + 0.268906i \(0.0866623\pi\)
\(458\) −1.94343e9 + 1.80324e9i −0.945236 + 0.877051i
\(459\) 8.96349e8 + 1.35103e8i 0.432646 + 0.0652109i
\(460\) 1.48087e8 + 1.97609e9i 0.0709358 + 0.946572i
\(461\) −1.28026e8 3.26204e8i −0.0608617 0.155073i 0.897208 0.441608i \(-0.145592\pi\)
−0.958070 + 0.286535i \(0.907497\pi\)
\(462\) −2.11846e8 + 9.28159e8i −0.0999480 + 0.437901i
\(463\) 3.14809e8 4.20083e9i 0.147405 1.96699i −0.0910824 0.995843i \(-0.529033\pi\)
0.238488 0.971145i \(-0.423348\pi\)
\(464\) −3.16726e9 + 9.76972e8i −1.47188 + 0.454014i
\(465\) 5.26356e8 + 2.53480e8i 0.242770 + 0.116912i
\(466\) −1.75961e8 3.04774e8i −0.0805503 0.139517i
\(467\) 1.48387e9 2.57014e9i 0.674196 1.16774i −0.302507 0.953147i \(-0.597823\pi\)
0.976703 0.214595i \(-0.0688432\pi\)
\(468\) 3.46864e8 2.36488e8i 0.156423 0.106647i
\(469\) −7.49841e8 3.28527e9i −0.335633 1.47050i
\(470\) 1.62536e9 2.44984e8i 0.722118 0.108842i
\(471\) 8.83115e7 1.10739e8i 0.0389443 0.0488346i
\(472\) −4.03073e7 −0.0176436
\(473\) −1.63815e9 + 7.82141e8i −0.711768 + 0.339837i
\(474\) 8.94127e8 0.385634
\(475\) 4.39435e8 5.51034e8i 0.188134 0.235913i
\(476\) 3.79756e9 5.72390e8i 1.61391 0.243258i
\(477\) 8.56441e8 + 3.75231e9i 0.361312 + 1.58301i
\(478\) 2.37012e9 1.61592e9i 0.992595 0.676740i
\(479\) −2.14978e9 + 3.72352e9i −0.893756 + 1.54803i −0.0584184 + 0.998292i \(0.518606\pi\)
−0.835337 + 0.549738i \(0.814728\pi\)
\(480\) −3.05927e8 5.29882e8i −0.126262 0.218693i
\(481\) 5.03180e8 + 2.42319e8i 0.206165 + 0.0992840i
\(482\) −5.58954e9 + 1.72415e9i −2.27359 + 0.701309i
\(483\) −9.57369e7 + 1.27752e9i −0.0386602 + 0.515885i
\(484\) 2.00612e8 8.78938e8i 0.0804263 0.352371i
\(485\) −9.72866e7 2.47882e8i −0.0387219 0.0986618i
\(486\) −1.70810e8 2.27930e9i −0.0674972 0.900687i
\(487\) −3.58926e9 5.40994e8i −1.40817 0.212247i −0.599434 0.800424i \(-0.704607\pi\)
−0.808732 + 0.588178i \(0.799846\pi\)
\(488\) 8.04520e7 7.46485e7i 0.0313377 0.0290771i
\(489\) −1.67231e8 + 8.05341e7i −0.0646748 + 0.0311457i
\(490\) −4.91478e9 3.35084e9i −1.88720 1.28667i
\(491\) 1.28973e9 3.28618e9i 0.491715 1.25287i −0.442696 0.896672i \(-0.645978\pi\)
0.934411 0.356197i \(-0.115927\pi\)
\(492\) −4.21475e8 1.30008e8i −0.159549 0.0492144i
\(493\) −2.79932e9 2.59739e9i −1.05217 0.976275i
\(494\) −3.78204e8 4.74252e8i −0.141150 0.176997i
\(495\) −9.80901e8 1.23001e9i −0.363502 0.455817i
\(496\) −3.09128e9 2.86829e9i −1.13750 1.05545i
\(497\) −2.38038e9 7.34250e8i −0.869759 0.268285i
\(498\) −3.08907e8 + 7.87083e8i −0.112079 + 0.285573i
\(499\) 3.44461e9 + 2.34850e9i 1.24105 + 0.846132i 0.992471 0.122480i \(-0.0390847\pi\)
0.248577 + 0.968612i \(0.420037\pi\)
\(500\) 2.61482e9 1.25923e9i 0.935505 0.450516i
\(501\) −5.55069e8 + 5.15029e8i −0.197204 + 0.182978i
\(502\) 3.89515e9 + 5.87100e8i 1.37424 + 0.207133i
\(503\) −1.41479e8 1.88791e9i −0.0495684 0.661445i −0.965549 0.260222i \(-0.916204\pi\)
0.915980 0.401223i \(-0.131415\pi\)
\(504\) 1.06461e8 + 2.71259e8i 0.0370413 + 0.0943796i
\(505\) −3.58928e8 + 1.57257e9i −0.124019 + 0.543362i
\(506\) −3.05292e8 + 4.07384e9i −0.104758 + 1.39790i
\(507\) −6.20975e8 + 1.91546e8i −0.211615 + 0.0652746i
\(508\) 1.62184e9 + 7.81035e8i 0.548888 + 0.264331i
\(509\) 2.65182e9 + 4.59309e9i 0.891318 + 1.54381i 0.838297 + 0.545214i \(0.183552\pi\)
0.0530207 + 0.998593i \(0.483115\pi\)
\(510\) 3.67849e8 6.37134e8i 0.122793 0.212684i
\(511\) −7.46267e9 + 5.08796e9i −2.47412 + 1.68683i
\(512\) 9.39874e8 + 4.11786e9i 0.309474 + 1.35590i
\(513\) −1.05465e9 + 1.58963e8i −0.344904 + 0.0519858i
\(514\) 4.00052e9 5.01650e9i 1.29941 1.62941i
\(515\) 7.84602e8 0.253119
\(516\) −3.47631e8 + 5.97484e8i −0.111390 + 0.191449i
\(517\) 1.65659e9 0.527228
\(518\) 5.30605e9 6.65358e9i 1.67732 2.10330i
\(519\) 3.01452e8 4.54366e7i 0.0946526 0.0142666i
\(520\) 7.10307e6 + 3.11206e7i 0.00221531 + 0.00970591i
\(521\) −1.98714e9 + 1.35481e9i −0.615598 + 0.419708i −0.830571 0.556912i \(-0.811986\pi\)
0.214973 + 0.976620i \(0.431034\pi\)
\(522\) −3.18044e9 + 5.50868e9i −0.978679 + 1.69512i
\(523\) −1.72826e9 2.99343e9i −0.528265 0.914982i −0.999457 0.0329513i \(-0.989509\pi\)
0.471192 0.882031i \(-0.343824\pi\)
\(524\) 2.37019e8 + 1.14142e8i 0.0719654 + 0.0346567i
\(525\) 5.02989e8 1.55152e8i 0.151705 0.0467949i
\(526\) −2.32043e8 + 3.09640e9i −0.0695214 + 0.927698i
\(527\) 1.08111e9 4.73667e9i 0.321762 1.40973i
\(528\) −2.35120e8 5.99075e8i −0.0695137 0.177118i
\(529\) 1.56375e8 + 2.08668e9i 0.0459274 + 0.612858i
\(530\) 6.35270e9 + 9.57515e8i 1.85350 + 0.279370i
\(531\) −6.92971e8 + 6.42983e8i −0.200856 + 0.186367i
\(532\) −4.07121e9 + 1.96059e9i −1.17228 + 0.564543i
\(533\) 4.55403e8 + 3.10489e8i 0.130272 + 0.0888179i
\(534\) 6.88961e8 1.75544e9i 0.195794 0.498876i
\(535\) −4.82779e7 1.48918e7i −0.0136304 0.00420444i
\(536\) 1.36639e8 + 1.26782e8i 0.0383263 + 0.0355617i
\(537\) 2.65348e8 + 3.32736e8i 0.0739446 + 0.0927235i
\(538\) 1.96874e9 + 2.46872e9i 0.545068 + 0.683493i
\(539\) −4.39461e9 4.07760e9i −1.20881 1.12161i
\(540\) −1.17738e9 3.63175e8i −0.321766 0.0992516i
\(541\) 1.57987e9 4.02543e9i 0.428973 1.09301i −0.539079 0.842255i \(-0.681228\pi\)
0.968052 0.250750i \(-0.0806772\pi\)
\(542\) −6.92526e9 4.72156e9i −1.86826 1.27376i
\(543\) 8.89819e8 4.28514e8i 0.238508 0.114859i
\(544\) −3.73004e9 + 3.46097e9i −0.993385 + 0.921726i
\(545\) 8.79159e8 + 1.32512e8i 0.232637 + 0.0350644i
\(546\) −3.38548e7 4.51761e8i −0.00890116 0.118778i
\(547\) 1.06319e9 + 2.70895e9i 0.277749 + 0.707694i 0.999873 + 0.0159301i \(0.00507093\pi\)
−0.722124 + 0.691764i \(0.756834\pi\)
\(548\) −5.86866e8 + 2.57123e9i −0.152338 + 0.667434i
\(549\) 1.92351e8 2.56674e9i 0.0496124 0.662031i
\(550\) 1.60396e9 4.94757e8i 0.411079 0.126801i
\(551\) 4.04816e9 + 1.94949e9i 1.03093 + 0.496468i
\(552\) −3.54319e7 6.13699e7i −0.00896619 0.0155299i
\(553\) −4.16168e9 + 7.20825e9i −1.04648 + 1.81256i
\(554\) 3.46819e9 2.36457e9i 0.866601 0.590838i
\(555\) −1.77345e8 7.77000e8i −0.0440346 0.192928i
\(556\) 4.77213e9 7.19283e8i 1.17747 0.177475i
\(557\) −4.51043e9 + 5.65590e9i −1.10592 + 1.38678i −0.191756 + 0.981443i \(0.561418\pi\)
−0.914166 + 0.405340i \(0.867153\pi\)
\(558\) −8.09283e9 −1.97188
\(559\) 6.35185e8 5.85419e8i 0.153801 0.141751i
\(560\) 5.94434e9 1.43036
\(561\) 4.62292e8 5.79696e8i 0.110547 0.138621i
\(562\) −8.13481e9 + 1.22613e9i −1.93317 + 0.291379i
\(563\) 1.11966e8 + 4.90556e8i 0.0264428 + 0.115854i 0.986427 0.164201i \(-0.0525046\pi\)
−0.959984 + 0.280055i \(0.909647\pi\)
\(564\) 5.21212e8 3.55356e8i 0.122331 0.0834040i
\(565\) 2.06219e9 3.57181e9i 0.481015 0.833143i
\(566\) −1.15925e9 2.00788e9i −0.268732 0.465457i
\(567\) 5.78871e9 + 2.78770e9i 1.33365 + 0.642251i
\(568\) 1.31670e8 4.06149e7i 0.0301487 0.00929964i
\(569\) −4.02392e8 + 5.36955e9i −0.0915706 + 1.22193i 0.742339 + 0.670024i \(0.233716\pi\)
−0.833910 + 0.551901i \(0.813903\pi\)
\(570\) −1.92620e8 + 8.43925e8i −0.0435652 + 0.190872i
\(571\) −9.32666e8 2.37639e9i −0.209652 0.534185i 0.786907 0.617072i \(-0.211681\pi\)
−0.996559 + 0.0828867i \(0.973586\pi\)
\(572\) −5.27772e7 7.04263e8i −0.0117913 0.157343i
\(573\) −8.31870e8 1.25384e8i −0.184720 0.0278421i
\(574\) 6.15678e9 5.71266e9i 1.35882 1.26080i
\(575\) 2.03505e9 9.80027e8i 0.446413 0.214981i
\(576\) 3.26728e9 + 2.22759e9i 0.712373 + 0.485688i
\(577\) 2.24426e9 5.71827e9i 0.486359 1.23922i −0.451520 0.892261i \(-0.649118\pi\)
0.937879 0.346962i \(-0.112787\pi\)
\(578\) 3.58546e8 + 1.10597e8i 0.0772321 + 0.0238229i
\(579\) −6.91869e8 6.41961e8i −0.148132 0.137446i
\(580\) 3.23627e9 + 4.05816e9i 0.688727 + 0.863637i
\(581\) −4.90749e9 6.15379e9i −1.03811 1.30175i
\(582\) −1.53243e8 1.42189e8i −0.0322218 0.0298974i
\(583\) 6.18710e9 + 1.90847e9i 1.29314 + 0.398882i
\(584\) 1.82527e8 4.65072e8i 0.0379213 0.0966219i
\(585\) 6.18553e8 + 4.21722e8i 0.127741 + 0.0870925i
\(586\) 7.07962e9 3.40937e9i 1.45334 0.699893i
\(587\) 1.35589e9 1.25808e9i 0.276689 0.256729i −0.529606 0.848244i \(-0.677660\pi\)
0.806294 + 0.591514i \(0.201470\pi\)
\(588\) −2.25736e9 3.40242e8i −0.457910 0.0690188i
\(589\) 4.27196e8 + 5.70053e9i 0.0861437 + 1.14951i
\(590\) 5.76485e8 + 1.46886e9i 0.115560 + 0.294441i
\(591\) 1.81501e8 7.95206e8i 0.0361678 0.158461i
\(592\) −4.29910e8 + 5.73676e9i −0.0851632 + 1.13642i
\(593\) 7.01683e9 2.16441e9i 1.38181 0.426233i 0.487285 0.873243i \(-0.337987\pi\)
0.894529 + 0.447010i \(0.147511\pi\)
\(594\) −2.28856e9 1.10211e9i −0.448032 0.215761i
\(595\) 3.42429e9 + 5.93104e9i 0.666439 + 1.15431i
\(596\) 1.87087e9 3.24045e9i 0.361979 0.626965i
\(597\) −1.17359e8 + 8.00139e7i −0.0225738 + 0.0153906i
\(598\) −4.32580e8 1.89526e9i −0.0827203 0.362421i
\(599\) −1.69214e9 + 2.55050e8i −0.321694 + 0.0484876i −0.307904 0.951417i \(-0.599628\pi\)
−0.0137899 + 0.999905i \(0.504390\pi\)
\(600\) −1.81537e7 + 2.27640e7i −0.00343112 + 0.00430249i
\(601\) −5.85385e9 −1.09997 −0.549985 0.835174i \(-0.685367\pi\)
−0.549985 + 0.835174i \(0.685367\pi\)
\(602\) −6.54319e9 1.14213e10i −1.22237 2.13368i
\(603\) 4.37155e9 0.811942
\(604\) −2.03363e9 + 2.55009e9i −0.375528 + 0.470897i
\(605\) 1.58974e9 2.39614e8i 0.291864 0.0439915i
\(606\) 2.81772e8 + 1.23452e9i 0.0514332 + 0.225344i
\(607\) −4.05569e9 + 2.76512e9i −0.736046 + 0.501827i −0.872376 0.488836i \(-0.837422\pi\)
0.136330 + 0.990663i \(0.456469\pi\)
\(608\) 2.99350e9 5.18490e9i 0.540154 0.935574i
\(609\) 1.67783e9 + 2.90608e9i 0.301014 + 0.521372i
\(610\) −3.87095e9 1.86415e9i −0.690499 0.332527i
\(611\) −7.53277e8 + 2.32355e8i −0.133601 + 0.0412105i
\(612\) −3.72319e8 + 4.96825e9i −0.0656577 + 0.876141i
\(613\) 5.80416e8 2.54297e9i 0.101772 0.445892i −0.898208 0.439570i \(-0.855131\pi\)
0.999980 0.00632121i \(-0.00201212\pi\)
\(614\) 3.79720e9 + 9.67510e9i 0.662024 + 1.68681i
\(615\) −5.87788e7 7.84349e8i −0.0101896 0.135971i
\(616\) 4.84744e8 + 7.30635e7i 0.0835565 + 0.0125941i
\(617\) −4.70365e9 + 4.36435e9i −0.806190 + 0.748035i −0.971202 0.238257i \(-0.923424\pi\)
0.165012 + 0.986291i \(0.447234\pi\)
\(618\) 5.54945e8 2.67248e8i 0.0945781 0.0455464i
\(619\) −8.81112e9 6.00732e9i −1.49319 1.01804i −0.987901 0.155084i \(-0.950435\pi\)
−0.505285 0.862953i \(-0.668612\pi\)
\(620\) −2.41267e9 + 6.14738e9i −0.406562 + 1.03590i
\(621\) −3.26625e9 1.00750e9i −0.547304 0.168821i
\(622\) −6.81047e9 6.31919e9i −1.13478 1.05292i
\(623\) 1.09452e10 + 1.37249e10i 1.81350 + 2.27405i
\(624\) 1.90939e8 + 2.39430e8i 0.0314593 + 0.0394487i
\(625\) 2.04921e9 + 1.90139e9i 0.335743 + 0.311524i
\(626\) −9.84937e9 3.03813e9i −1.60472 0.494989i
\(627\) −3.18725e8 + 8.12099e8i −0.0516393 + 0.131575i
\(628\) 1.32289e9 + 9.01929e8i 0.213140 + 0.145316i
\(629\) −5.97158e9 + 2.87576e9i −0.956779 + 0.460761i
\(630\) 8.36247e9 7.75924e9i 1.33242 1.23631i
\(631\) 6.94980e9 + 1.04751e9i 1.10121 + 0.165981i 0.674404 0.738363i \(-0.264401\pi\)
0.426806 + 0.904343i \(0.359639\pi\)
\(632\) −3.44061e7 4.59118e8i −0.00542158 0.0723459i
\(633\) 5.40977e8 + 1.37839e9i 0.0847746 + 0.216002i
\(634\) 1.01437e9 4.44425e9i 0.158083 0.692606i
\(635\) −2.39889e8 + 3.20109e9i −0.0371794 + 0.496124i
\(636\) 2.35603e9 7.26738e8i 0.363145 0.112015i
\(637\) 2.57022e9 + 1.23775e9i 0.393987 + 0.189734i
\(638\) 5.35037e9 + 9.26711e9i 0.815664 + 1.41277i
\(639\) 1.61581e9 2.79866e9i 0.244983 0.424324i
\(640\) −5.21120e8 + 3.55293e8i −0.0785792 + 0.0535744i
\(641\) −2.04605e9 8.96434e9i −0.306841 1.34436i −0.859578 0.511004i \(-0.829274\pi\)
0.552737 0.833356i \(-0.313583\pi\)
\(642\) −3.92191e7 + 5.91132e6i −0.00584958 + 0.000881682i
\(643\) −9.04333e8 + 1.13400e9i −0.134150 + 0.168219i −0.844369 0.535762i \(-0.820024\pi\)
0.710219 + 0.703981i \(0.248596\pi\)
\(644\) −1.44815e10 −2.13655
\(645\) −1.21830e9 1.87805e8i −0.178771 0.0275581i
\(646\) 7.19883e9 1.05063
\(647\) 9.02264e8 1.13140e9i 0.130969 0.164230i −0.712023 0.702156i \(-0.752221\pi\)
0.842992 + 0.537926i \(0.180792\pi\)
\(648\) −3.51427e8 + 5.29691e7i −0.0507367 + 0.00764733i
\(649\) 3.53873e8 + 1.55042e9i 0.0508149 + 0.222635i
\(650\) −6.59951e8 + 4.49947e8i −0.0942573 + 0.0642635i
\(651\) −2.13467e9 + 3.69736e9i −0.303248 + 0.525240i
\(652\) −1.04907e9 1.81705e9i −0.148231 0.256744i
\(653\) −2.50593e9 1.20679e9i −0.352186 0.169604i 0.249423 0.968395i \(-0.419759\pi\)
−0.601609 + 0.798791i \(0.705473\pi\)
\(654\) 6.66960e8 2.05730e8i 0.0932347 0.0287591i
\(655\) −3.50579e7 + 4.67815e8i −0.00487463 + 0.0650474i
\(656\) −1.26337e9 + 5.53518e9i −0.174730 + 0.765541i
\(657\) −4.28079e9 1.09073e10i −0.588905 1.50051i
\(658\) 8.97666e8 + 1.19785e10i 0.122836 + 1.63913i
\(659\) −8.55928e9 1.29010e9i −1.16503 0.175601i −0.462081 0.886838i \(-0.652897\pi\)
−0.702952 + 0.711237i \(0.748135\pi\)
\(660\) −7.38789e8 + 6.85496e8i −0.100027 + 0.0928114i
\(661\) 2.54165e9 1.22399e9i 0.342303 0.164844i −0.254832 0.966985i \(-0.582020\pi\)
0.597135 + 0.802141i \(0.296306\pi\)
\(662\) −1.10940e10 7.56374e9i −1.48622 1.01329i
\(663\) −1.28902e8 + 3.28438e8i −0.0171776 + 0.0437679i
\(664\) 4.16039e8 + 1.28331e8i 0.0551501 + 0.0170115i
\(665\) −5.90699e9 5.48088e9i −0.778915 0.722728i
\(666\) 6.88348e9 + 8.63161e9i 0.902918 + 1.13222i
\(667\) 8.97794e9 + 1.12580e10i 1.17148 + 1.46899i
\(668\) −6.27446e9 5.82185e9i −0.814439 0.755689i
\(669\) 1.63520e9 + 5.04392e8i 0.211144 + 0.0651294i
\(670\) 2.66590e9 6.79260e9i 0.342438 0.872517i
\(671\) −3.57767e9 2.43921e9i −0.457163 0.311689i
\(672\) 4.02855e9 1.94005e9i 0.512102 0.246615i
\(673\) −2.41813e9 + 2.24369e9i −0.305792 + 0.283734i −0.818109 0.575063i \(-0.804978\pi\)
0.512317 + 0.858796i \(0.328787\pi\)
\(674\) −1.28560e10 1.93773e9i −1.61732 0.243772i
\(675\) 1.04952e8 + 1.40049e9i 0.0131350 + 0.175274i
\(676\) −2.68373e9 6.83803e9i −0.334137 0.851368i
\(677\) 2.29950e9 1.00748e10i 0.284822 1.24788i −0.606709 0.794924i \(-0.707511\pi\)
0.891531 0.452961i \(-0.149632\pi\)
\(678\) 2.41961e8 3.22874e9i 0.0298154 0.397859i
\(679\) 1.85955e9 5.73597e8i 0.227963 0.0703173i
\(680\) −3.41311e8 1.64367e8i −0.0416265 0.0200463i
\(681\) −1.54324e9 2.67296e9i −0.187248 0.324323i
\(682\) −6.80717e9 + 1.17904e10i −0.821716 + 1.42325i
\(683\) 1.18317e9 8.06670e8i 0.142093 0.0968776i −0.490187 0.871617i \(-0.663071\pi\)
0.632280 + 0.774740i \(0.282119\pi\)
\(684\) −1.30443e9 5.71510e9i −0.155857 0.682853i
\(685\) −4.65058e9 + 7.00962e8i −0.552828 + 0.0833254i
\(686\) 1.41395e10 1.77303e10i 1.67224 2.09692i
\(687\) −1.81440e9 −0.213493
\(688\) 8.00379e9 + 3.88750e9i 0.936993 + 0.455105i
\(689\) −3.08105e9 −0.358865
\(690\) −1.72966e9 + 2.16892e9i −0.200442 + 0.251346i
\(691\) 9.23381e9 1.39177e9i 1.06465 0.160470i 0.406724 0.913551i \(-0.366671\pi\)
0.657928 + 0.753081i \(0.271433\pi\)
\(692\) 7.66826e8 + 3.35968e9i 0.0879681 + 0.385414i
\(693\) 9.49932e9 6.47652e9i 1.08424 0.739223i
\(694\) 5.87776e9 1.01806e10i 0.667503 1.15615i
\(695\) 4.30306e9 + 7.45312e9i 0.486218 + 0.842154i
\(696\) −1.67235e8 8.05363e7i −0.0188016 0.00905439i
\(697\) −6.25057e9 + 1.92805e9i −0.699206 + 0.215676i
\(698\) 1.37161e9 1.83029e10i 0.152664 2.03716i
\(699\) 5.35940e7 2.34811e8i 0.00593534 0.0260044i
\(700\) 2.17381e9 + 5.53879e9i 0.239541 + 0.610340i
\(701\) 3.66688e8 + 4.89311e9i 0.0402053 + 0.536503i 0.980549 + 0.196276i \(0.0628848\pi\)
−0.940343 + 0.340227i \(0.889496\pi\)
\(702\) 1.19522e9 + 1.80151e8i 0.130397 + 0.0196543i
\(703\) 5.71669e9 5.30432e9i 0.620585 0.575819i
\(704\) 5.99359e9 2.88636e9i 0.647415 0.311779i
\(705\) 9.29461e8 + 6.33696e8i 0.0999009 + 0.0681113i
\(706\) 2.24860e9 5.72935e9i 0.240490 0.612758i
\(707\) −1.12640e10 3.47447e9i −1.19873 0.369761i
\(708\) 4.43920e8 + 4.11898e8i 0.0470098 + 0.0436187i
\(709\) −9.05084e9 1.13494e10i −0.953734 1.19594i −0.980543 0.196304i \(-0.937106\pi\)
0.0268096 0.999641i \(-0.491465\pi\)
\(710\) −3.36325e9 4.21738e9i −0.352659 0.442220i
\(711\) −7.91536e9 7.34438e9i −0.825899 0.766323i
\(712\) −9.27899e8 2.86219e8i −0.0963431 0.0297179i
\(713\) −6.69313e9 + 1.70538e10i −0.691537 + 1.76201i
\(714\) 4.44218e9 + 3.02863e9i 0.456723 + 0.311388i
\(715\) 1.13469e9 5.46439e8i 0.116093 0.0559075i
\(716\) −3.52656e9 + 3.27217e9i −0.359050 + 0.333150i
\(717\) 1.94126e9 + 2.92598e8i 0.196683 + 0.0296452i
\(718\) 1.23161e9 + 1.64346e10i 0.124176 + 1.65701i
\(719\) −3.49628e8 8.90838e8i −0.0350797 0.0893815i 0.912261 0.409610i \(-0.134335\pi\)
−0.947340 + 0.320229i \(0.896240\pi\)
\(720\) −1.71598e9 + 7.51818e9i −0.171336 + 0.750670i
\(721\) −4.28485e8 + 5.71774e9i −0.0425758 + 0.568134i
\(722\) 5.42300e9 1.67277e9i 0.536240 0.165408i
\(723\) −3.60678e9 1.73693e9i −0.354924 0.170922i
\(724\) 5.58202e9 + 9.66834e9i 0.546646 + 0.946819i
\(725\) 2.95821e9 5.12376e9i 0.288300 0.499351i
\(726\) 1.04280e9 7.10967e8i 0.101140 0.0689558i
\(727\) −4.78554e8 2.09668e9i −0.0461914 0.202378i 0.946567 0.322508i \(-0.104526\pi\)
−0.992758 + 0.120130i \(0.961669\pi\)
\(728\) −2.30668e8 + 3.47677e7i −0.0221579 + 0.00333976i
\(729\) −4.51603e9 + 5.66292e9i −0.431728 + 0.541370i
\(730\) −1.95585e10 −1.86082
\(731\) 7.31848e8 + 1.02253e10i 0.0692963 + 0.968202i
\(732\) −1.64888e9 −0.155381
\(733\) 5.14125e8 6.44692e8i 0.0482175 0.0604628i −0.757138 0.653255i \(-0.773403\pi\)
0.805356 + 0.592792i \(0.201974\pi\)
\(734\) 9.87247e9 1.48804e9i 0.921488 0.138892i
\(735\) −9.05871e8 3.96888e9i −0.0841513 0.368691i
\(736\) 1.58531e10 1.08085e10i 1.46569 0.999291i
\(737\) 3.67707e9 6.36888e9i 0.338350 0.586039i
\(738\) 5.44786e9 + 9.43597e9i 0.498917 + 0.864150i
\(739\) −6.39110e9 3.07779e9i −0.582532 0.280533i 0.119319 0.992856i \(-0.461929\pi\)
−0.701852 + 0.712323i \(0.747643\pi\)
\(740\) 8.60878e9 2.65546e9i 0.780963 0.240895i
\(741\) 3.10234e7 4.13978e8i 0.00280108 0.0373778i
\(742\) −1.04471e10 + 4.57719e10i −0.938824 + 4.11325i
\(743\) 5.75697e9 + 1.46685e10i 0.514912 + 1.31197i 0.917915 + 0.396776i \(0.129871\pi\)
−0.403003 + 0.915198i \(0.632034\pi\)
\(744\) −1.76481e7 2.35497e8i −0.00157106 0.0209643i
\(745\) 6.59802e9 + 9.94492e8i 0.584611 + 0.0881159i
\(746\) −9.36550e9 + 8.68991e9i −0.825933 + 0.766354i
\(747\) 9.19976e9 4.43037e9i 0.807522 0.388882i
\(748\) 6.92504e9 + 4.72141e9i 0.605015 + 0.412493i
\(749\) 1.34888e8 3.43689e8i 0.0117297 0.0298868i
\(750\) 3.88243e9 + 1.19757e9i 0.336038 + 0.103654i
\(751\) −3.07782e9 2.85580e9i −0.265157 0.246030i 0.536378 0.843978i \(-0.319792\pi\)
−0.8015