Properties

Label 8.18.b.a.5.8
Level $8$
Weight $18$
Character 8.5
Analytic conductor $14.658$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6577669876\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} - 3763915816960 x^{10} + 7317489121656832 x^{9} - 1108241988138827776 x^{8} + 163121042717484777472 x^{7} + 5699397839986467274752 x^{6} + 1127435088957285706235904 x^{5} - 217909345031306501735579648 x^{4} - 78950720850572326734309359616 x^{3} + 13720647095471028734661620662272 x^{2} - 5242030267748791654842336509165568 x + 1286374137827816254118965326485913600\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{120}\cdot 3^{14}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.8
Root \(1.16697 - 180.787i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.18.b.a.5.7

$q$-expansion

\(f(q)\) \(=\) \(q+(18.3339 + 361.574i) q^{2} +13786.7i q^{3} +(-130400. + 13258.2i) q^{4} +96356.3i q^{5} +(-4.98490e6 + 252764. i) q^{6} -1.47728e7 q^{7} +(-7.18455e6 - 4.69061e7i) q^{8} -6.09318e7 q^{9} +O(q^{10})\) \(q+(18.3339 + 361.574i) q^{2} +13786.7i q^{3} +(-130400. + 13258.2i) q^{4} +96356.3i q^{5} +(-4.98490e6 + 252764. i) q^{6} -1.47728e7 q^{7} +(-7.18455e6 - 4.69061e7i) q^{8} -6.09318e7 q^{9} +(-3.48399e7 + 1.76659e6i) q^{10} +6.68721e8i q^{11} +(-1.82786e8 - 1.79778e9i) q^{12} -1.72473e8i q^{13} +(-2.70845e8 - 5.34148e9i) q^{14} -1.32843e9 q^{15} +(1.68283e10 - 3.45772e9i) q^{16} +1.92991e10 q^{17} +(-1.11712e9 - 2.20314e10i) q^{18} -1.11328e11i q^{19} +(-1.27751e9 - 1.25648e10i) q^{20} -2.03668e11i q^{21} +(-2.41792e11 + 1.22603e10i) q^{22} -5.92040e11 q^{23} +(6.46678e11 - 9.90509e10i) q^{24} +7.53655e11 q^{25} +(6.23619e10 - 3.16212e9i) q^{26} +9.40365e11i q^{27} +(1.92638e12 - 1.95861e11i) q^{28} +2.95085e12i q^{29} +(-2.43554e10 - 4.80326e11i) q^{30} -7.53978e12 q^{31} +(1.55875e12 + 6.02129e12i) q^{32} -9.21942e12 q^{33} +(3.53828e11 + 6.97805e12i) q^{34} -1.42346e12i q^{35} +(7.94549e12 - 8.07844e11i) q^{36} -2.20235e13i q^{37} +(4.02534e13 - 2.04108e12i) q^{38} +2.37783e12 q^{39} +(4.51970e12 - 6.92276e11i) q^{40} -8.98214e13 q^{41} +(7.36412e13 - 3.73404e12i) q^{42} -1.45802e13i q^{43} +(-8.86600e12 - 8.72010e13i) q^{44} -5.87116e12i q^{45} +(-1.08544e13 - 2.14066e14i) q^{46} -7.43032e13 q^{47} +(4.76704e13 + 2.32006e14i) q^{48} -1.43935e13 q^{49} +(1.38175e13 + 2.72502e14i) q^{50} +2.66070e14i q^{51} +(2.28668e12 + 2.24905e13i) q^{52} -2.84157e14i q^{53} +(-3.40012e14 + 1.72406e13i) q^{54} -6.44354e13 q^{55} +(1.06136e14 + 6.92937e14i) q^{56} +1.53484e15 q^{57} +(-1.06695e15 + 5.41007e13i) q^{58} +1.09328e15i q^{59} +(1.73227e14 - 1.76125e13i) q^{60} -4.14860e14i q^{61} +(-1.38234e14 - 2.72619e15i) q^{62} +9.00136e14 q^{63} +(-2.14856e15 + 6.73998e14i) q^{64} +1.66189e13 q^{65} +(-1.69028e14 - 3.33351e15i) q^{66} +2.20200e15i q^{67} +(-2.51660e15 + 2.55870e14i) q^{68} -8.16225e15i q^{69} +(5.14685e14 - 2.60976e13i) q^{70} +6.67796e15 q^{71} +(4.37768e14 + 2.85807e15i) q^{72} -1.64289e15 q^{73} +(7.96311e15 - 4.03777e14i) q^{74} +1.03904e16i q^{75} +(1.47601e15 + 1.45172e16i) q^{76} -9.87891e15i q^{77} +(4.35950e13 + 8.59762e14i) q^{78} -1.46317e16 q^{79} +(3.33173e14 + 1.62151e15i) q^{80} -2.08332e16 q^{81} +(-1.64678e15 - 3.24771e16i) q^{82} +3.05535e16i q^{83} +(2.70027e15 + 2.65583e16i) q^{84} +1.85959e15i q^{85} +(5.27183e15 - 2.67313e14i) q^{86} -4.06824e16 q^{87} +(3.13671e16 - 4.80446e15i) q^{88} +4.48498e16 q^{89} +(2.12286e15 - 1.07642e14i) q^{90} +2.54792e15i q^{91} +(7.72018e16 - 7.84936e15i) q^{92} -1.03948e17i q^{93} +(-1.36227e15 - 2.68661e16i) q^{94} +1.07272e16 q^{95} +(-8.30135e16 + 2.14900e16i) q^{96} -3.26514e16 q^{97} +(-2.63889e14 - 5.20431e15i) q^{98} -4.07464e16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 270q^{2} - 27436q^{4} + 5839948q^{6} + 11529600q^{7} + 24334920q^{8} - 602654096q^{9} + O(q^{10}) \) \( 16q + 270q^{2} - 27436q^{4} + 5839948q^{6} + 11529600q^{7} + 24334920q^{8} - 602654096q^{9} + 131002712q^{10} - 2795125400q^{12} + 16363788528q^{14} - 9993282176q^{15} + 26500434192q^{16} - 7489125600q^{17} - 113450563870q^{18} - 209445719856q^{20} + 223126527100q^{22} + 746845345920q^{23} - 1099415493232q^{24} - 1809682431664q^{25} + 2467726531080q^{26} + 3220542267040q^{28} - 1188624268048q^{30} - 318979758592q^{31} + 1455647316000q^{32} + 5633526177600q^{33} - 4461251980292q^{34} - 33088278002484q^{36} + 24076283913900q^{38} - 18457706051456q^{39} + 60626292962592q^{40} + 7482251536032q^{41} - 51630378688160q^{42} + 193654716236040q^{44} - 195097141003568q^{46} - 376698804821760q^{47} - 329350060416480q^{48} + 127691292101520q^{49} + 474997408872102q^{50} - 272251877663120q^{52} + 735354219382520q^{54} + 2209036687713152q^{55} - 162767516076480q^{56} - 190521298294720q^{57} - 623262610679960q^{58} - 1973616194963808q^{60} + 695695648144320q^{62} - 8131096607338880q^{63} + 1111931745501248q^{64} + 2385987975356160q^{65} + 3598826202828312q^{66} + 5981109959771880q^{68} - 10044559836180288q^{70} + 9025926285576576q^{71} - 19918679666289160q^{72} + 11332002046118560q^{73} + 11098735408189464q^{74} + 5959440926938280q^{76} + 4184252259031760q^{78} - 45299671392008448q^{79} + 1337342539452480q^{80} + 20101901999290832q^{81} + 15639739637081420q^{82} + 19796542864700224q^{84} - 14252032276026564q^{86} + 25965768920837760q^{87} - 66964872768837680q^{88} - 69879174608766048q^{89} + 136151511125051240q^{90} + 57336249810701280q^{92} - 192318922166254176q^{94} + 93790444358203776q^{95} - 342799224184788928q^{96} + 95593398602180640q^{97} + 339641261743253790q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 18.3339 + 361.574i 0.0506408 + 0.998717i
\(3\) 13786.7i 1.21319i 0.795011 + 0.606594i \(0.207465\pi\)
−0.795011 + 0.606594i \(0.792535\pi\)
\(4\) −130400. + 13258.2i −0.994871 + 0.101152i
\(5\) 96356.3i 0.110315i 0.998478 + 0.0551575i \(0.0175661\pi\)
−0.998478 + 0.0551575i \(0.982434\pi\)
\(6\) −4.98490e6 + 252764.i −1.21163 + 0.0614369i
\(7\) −1.47728e7 −0.968570 −0.484285 0.874910i \(-0.660920\pi\)
−0.484285 + 0.874910i \(0.660920\pi\)
\(8\) −7.18455e6 4.69061e7i −0.151403 0.988472i
\(9\) −6.09318e7 −0.471827
\(10\) −3.48399e7 + 1.76659e6i −0.110174 + 0.00558645i
\(11\) 6.68721e8i 0.940604i 0.882505 + 0.470302i \(0.155855\pi\)
−0.882505 + 0.470302i \(0.844145\pi\)
\(12\) −1.82786e8 1.79778e9i −0.122716 1.20697i
\(13\) 1.72473e8i 0.0586413i −0.999570 0.0293206i \(-0.990666\pi\)
0.999570 0.0293206i \(-0.00933439\pi\)
\(14\) −2.70845e8 5.34148e9i −0.0490492 0.967327i
\(15\) −1.32843e9 −0.133833
\(16\) 1.68283e10 3.45772e9i 0.979537 0.201266i
\(17\) 1.92991e10 0.670998 0.335499 0.942041i \(-0.391095\pi\)
0.335499 + 0.942041i \(0.391095\pi\)
\(18\) −1.11712e9 2.20314e10i −0.0238937 0.471222i
\(19\) 1.11328e11i 1.50383i −0.659259 0.751916i \(-0.729130\pi\)
0.659259 0.751916i \(-0.270870\pi\)
\(20\) −1.27751e9 1.25648e10i −0.0111586 0.109749i
\(21\) 2.03668e11i 1.17506i
\(22\) −2.41792e11 + 1.22603e10i −0.939397 + 0.0476330i
\(23\) −5.92040e11 −1.57639 −0.788196 0.615424i \(-0.788985\pi\)
−0.788196 + 0.615424i \(0.788985\pi\)
\(24\) 6.46678e11 9.90509e10i 1.19920 0.183680i
\(25\) 7.53655e11 0.987831
\(26\) 6.23619e10 3.16212e9i 0.0585660 0.00296964i
\(27\) 9.40365e11i 0.640774i
\(28\) 1.92638e12 1.95861e11i 0.963602 0.0979725i
\(29\) 2.95085e12i 1.09538i 0.836682 + 0.547689i \(0.184492\pi\)
−0.836682 + 0.547689i \(0.815508\pi\)
\(30\) −2.43554e10 4.80326e11i −0.00677742 0.133661i
\(31\) −7.53978e12 −1.58776 −0.793879 0.608075i \(-0.791942\pi\)
−0.793879 + 0.608075i \(0.791942\pi\)
\(32\) 1.55875e12 + 6.02129e12i 0.250612 + 0.968088i
\(33\) −9.21942e12 −1.14113
\(34\) 3.53828e11 + 6.97805e12i 0.0339799 + 0.670137i
\(35\) 1.42346e12i 0.106848i
\(36\) 7.94549e12 8.07844e11i 0.469407 0.0477261i
\(37\) 2.20235e13i 1.03079i −0.856952 0.515396i \(-0.827645\pi\)
0.856952 0.515396i \(-0.172355\pi\)
\(38\) 4.02534e13 2.04108e12i 1.50190 0.0761553i
\(39\) 2.37783e12 0.0711430
\(40\) 4.51970e12 6.92276e11i 0.109043 0.0167020i
\(41\) −8.98214e13 −1.75678 −0.878389 0.477946i \(-0.841382\pi\)
−0.878389 + 0.477946i \(0.841382\pi\)
\(42\) 7.36412e13 3.73404e12i 1.17355 0.0595059i
\(43\) 1.45802e13i 0.190231i −0.995466 0.0951157i \(-0.969678\pi\)
0.995466 0.0951157i \(-0.0303221\pi\)
\(44\) −8.86600e12 8.72010e13i −0.0951437 0.935780i
\(45\) 5.87116e12i 0.0520496i
\(46\) −1.08544e13 2.14066e14i −0.0798298 1.57437i
\(47\) −7.43032e13 −0.455172 −0.227586 0.973758i \(-0.573083\pi\)
−0.227586 + 0.973758i \(0.573083\pi\)
\(48\) 4.76704e13 + 2.32006e14i 0.244173 + 1.18836i
\(49\) −1.43935e13 −0.0618727
\(50\) 1.38175e13 + 2.72502e14i 0.0500246 + 0.986563i
\(51\) 2.66070e14i 0.814047i
\(52\) 2.28668e12 + 2.24905e13i 0.00593167 + 0.0583405i
\(53\) 2.84157e14i 0.626922i −0.949601 0.313461i \(-0.898512\pi\)
0.949601 0.313461i \(-0.101488\pi\)
\(54\) −3.40012e14 + 1.72406e13i −0.639951 + 0.0324493i
\(55\) −6.44354e13 −0.103763
\(56\) 1.06136e14 + 6.92937e14i 0.146644 + 0.957404i
\(57\) 1.53484e15 1.82443
\(58\) −1.06695e15 + 5.41007e13i −1.09397 + 0.0554709i
\(59\) 1.09328e15i 0.969373i 0.874688 + 0.484687i \(0.161066\pi\)
−0.874688 + 0.484687i \(0.838934\pi\)
\(60\) 1.73227e14 1.76125e13i 0.133147 0.0135374i
\(61\) 4.14860e14i 0.277075i −0.990357 0.138538i \(-0.955760\pi\)
0.990357 0.138538i \(-0.0442402\pi\)
\(62\) −1.38234e14 2.72619e15i −0.0804054 1.58572i
\(63\) 9.00136e14 0.456997
\(64\) −2.14856e15 + 6.73998e14i −0.954154 + 0.299315i
\(65\) 1.66189e13 0.00646902
\(66\) −1.69028e14 3.33351e15i −0.0577878 1.13967i
\(67\) 2.20200e15i 0.662492i 0.943544 + 0.331246i \(0.107469\pi\)
−0.943544 + 0.331246i \(0.892531\pi\)
\(68\) −2.51660e15 + 2.55870e14i −0.667556 + 0.0678726i
\(69\) 8.16225e15i 1.91246i
\(70\) 5.14685e14 2.60976e13i 0.106711 0.00541086i
\(71\) 6.67796e15 1.22729 0.613646 0.789581i \(-0.289702\pi\)
0.613646 + 0.789581i \(0.289702\pi\)
\(72\) 4.37768e14 + 2.85807e15i 0.0714360 + 0.466388i
\(73\) −1.64289e15 −0.238432 −0.119216 0.992868i \(-0.538038\pi\)
−0.119216 + 0.992868i \(0.538038\pi\)
\(74\) 7.96311e15 4.03777e14i 1.02947 0.0522001i
\(75\) 1.03904e16i 1.19842i
\(76\) 1.47601e15 + 1.45172e16i 0.152115 + 1.49612i
\(77\) 9.87891e15i 0.911041i
\(78\) 4.35950e13 + 8.59762e14i 0.00360274 + 0.0710517i
\(79\) −1.46317e16 −1.08509 −0.542543 0.840028i \(-0.682539\pi\)
−0.542543 + 0.840028i \(0.682539\pi\)
\(80\) 3.33173e14 + 1.62151e15i 0.0222027 + 0.108058i
\(81\) −2.08332e16 −1.24921
\(82\) −1.64678e15 3.24771e16i −0.0889647 1.75452i
\(83\) 3.05535e16i 1.48901i 0.667618 + 0.744504i \(0.267314\pi\)
−0.667618 + 0.744504i \(0.732686\pi\)
\(84\) 2.70027e15 + 2.65583e16i 0.118859 + 1.16903i
\(85\) 1.85959e15i 0.0740211i
\(86\) 5.27183e15 2.67313e14i 0.189987 0.00963348i
\(87\) −4.06824e16 −1.32890
\(88\) 3.13671e16 4.80446e15i 0.929761 0.142410i
\(89\) 4.48498e16 1.20766 0.603831 0.797112i \(-0.293640\pi\)
0.603831 + 0.797112i \(0.293640\pi\)
\(90\) 2.12286e15 1.07642e14i 0.0519828 0.00263584i
\(91\) 2.54792e15i 0.0567982i
\(92\) 7.72018e16 7.84936e15i 1.56831 0.159455i
\(93\) 1.03948e17i 1.92625i
\(94\) −1.36227e15 2.68661e16i −0.0230503 0.454588i
\(95\) 1.07272e16 0.165895
\(96\) −8.30135e16 + 2.14900e16i −1.17447 + 0.304040i
\(97\) −3.26514e16 −0.423002 −0.211501 0.977378i \(-0.567835\pi\)
−0.211501 + 0.977378i \(0.567835\pi\)
\(98\) −2.63889e14 5.20431e15i −0.00313328 0.0617933i
\(99\) 4.07464e16i 0.443802i
\(100\) −9.82764e16 + 9.99208e15i −0.982764 + 0.0999208i
\(101\) 4.25294e16i 0.390803i 0.980723 + 0.195402i \(0.0626010\pi\)
−0.980723 + 0.195402i \(0.937399\pi\)
\(102\) −9.62040e16 + 4.87811e15i −0.813002 + 0.0412240i
\(103\) 1.23310e17 0.959140 0.479570 0.877504i \(-0.340793\pi\)
0.479570 + 0.877504i \(0.340793\pi\)
\(104\) −8.09005e15 + 1.23914e15i −0.0579653 + 0.00887847i
\(105\) 1.96247e16 0.129627
\(106\) 1.02744e17 5.20972e15i 0.626117 0.0317478i
\(107\) 6.12850e16i 0.344820i 0.985025 + 0.172410i \(0.0551554\pi\)
−0.985025 + 0.172410i \(0.944845\pi\)
\(108\) −1.24675e16 1.22623e17i −0.0648153 0.637487i
\(109\) 3.63163e17i 1.74573i 0.487962 + 0.872865i \(0.337740\pi\)
−0.487962 + 0.872865i \(0.662260\pi\)
\(110\) −1.18136e15 2.32982e16i −0.00525464 0.103630i
\(111\) 3.03630e17 1.25054
\(112\) −2.48602e17 + 5.10804e16i −0.948750 + 0.194940i
\(113\) 6.33950e16 0.224330 0.112165 0.993690i \(-0.464221\pi\)
0.112165 + 0.993690i \(0.464221\pi\)
\(114\) 2.81397e16 + 5.54959e17i 0.0923907 + 1.82209i
\(115\) 5.70467e16i 0.173900i
\(116\) −3.91228e16 3.84790e17i −0.110799 1.08976i
\(117\) 1.05091e16i 0.0276685i
\(118\) −3.95303e17 + 2.00442e16i −0.968130 + 0.0490899i
\(119\) −2.85102e17 −0.649908
\(120\) 9.54418e15 + 6.23115e16i 0.0202627 + 0.132290i
\(121\) 5.82597e16 0.115264
\(122\) 1.50002e17 7.60601e15i 0.276720 0.0140313i
\(123\) 1.23834e18i 2.13130i
\(124\) 9.83186e17 9.99636e16i 1.57961 0.160604i
\(125\) 1.46133e17i 0.219288i
\(126\) 1.65030e16 + 3.25466e17i 0.0231427 + 0.456411i
\(127\) −8.96529e17 −1.17553 −0.587764 0.809033i \(-0.699991\pi\)
−0.587764 + 0.809033i \(0.699991\pi\)
\(128\) −2.83092e17 7.64508e17i −0.347250 0.937772i
\(129\) 2.01013e17 0.230787
\(130\) 3.04690e14 + 6.00896e15i 0.000327596 + 0.00646072i
\(131\) 7.31204e17i 0.736601i −0.929707 0.368301i \(-0.879940\pi\)
0.929707 0.368301i \(-0.120060\pi\)
\(132\) 1.20221e18 1.22233e17i 1.13528 0.115427i
\(133\) 1.64463e18i 1.45657i
\(134\) −7.96185e17 + 4.03713e16i −0.661642 + 0.0335492i
\(135\) −9.06101e16 −0.0706870
\(136\) −1.38655e17 9.05245e17i −0.101591 0.663262i
\(137\) −1.67484e18 −1.15305 −0.576524 0.817080i \(-0.695591\pi\)
−0.576524 + 0.817080i \(0.695591\pi\)
\(138\) 2.95126e18 1.49646e17i 1.91001 0.0968486i
\(139\) 1.51826e18i 0.924105i 0.886853 + 0.462053i \(0.152887\pi\)
−0.886853 + 0.462053i \(0.847113\pi\)
\(140\) 1.88724e16 + 1.85618e17i 0.0108078 + 0.106300i
\(141\) 1.02439e18i 0.552209i
\(142\) 1.22433e17 + 2.41458e18i 0.0621511 + 1.22572i
\(143\) 1.15336e17 0.0551582
\(144\) −1.02538e18 + 2.10685e17i −0.462172 + 0.0949626i
\(145\) −2.84333e17 −0.120837
\(146\) −3.01206e16 5.94026e17i −0.0120744 0.238126i
\(147\) 1.98438e17i 0.0750632i
\(148\) 2.91990e17 + 2.87185e18i 0.104266 + 1.02550i
\(149\) 9.25567e17i 0.312122i 0.987747 + 0.156061i \(0.0498796\pi\)
−0.987747 + 0.156061i \(0.950120\pi\)
\(150\) −3.75689e18 + 1.90497e17i −1.19689 + 0.0606892i
\(151\) 2.49950e18 0.752574 0.376287 0.926503i \(-0.377201\pi\)
0.376287 + 0.926503i \(0.377201\pi\)
\(152\) −5.22197e18 + 7.99842e17i −1.48650 + 0.227685i
\(153\) −1.17593e18 −0.316595
\(154\) 3.57196e18 1.81119e17i 0.909872 0.0461359i
\(155\) 7.26505e17i 0.175154i
\(156\) −3.10069e17 + 3.15257e16i −0.0707781 + 0.00719623i
\(157\) 5.60339e18i 1.21145i −0.795676 0.605723i \(-0.792884\pi\)
0.795676 0.605723i \(-0.207116\pi\)
\(158\) −2.68257e17 5.29044e18i −0.0549497 1.08369i
\(159\) 3.91757e18 0.760574
\(160\) −5.80189e17 + 1.50195e17i −0.106795 + 0.0276463i
\(161\) 8.74611e18 1.52685
\(162\) −3.81955e17 7.53276e18i −0.0632608 1.24760i
\(163\) 9.07691e18i 1.42673i 0.700790 + 0.713367i \(0.252831\pi\)
−0.700790 + 0.713367i \(0.747169\pi\)
\(164\) 1.17127e19 1.19087e18i 1.74777 0.177701i
\(165\) 8.88349e17i 0.125884i
\(166\) −1.10474e19 + 5.60166e17i −1.48710 + 0.0754046i
\(167\) −3.89443e18 −0.498143 −0.249071 0.968485i \(-0.580125\pi\)
−0.249071 + 0.968485i \(0.580125\pi\)
\(168\) −9.55328e18 + 1.46326e18i −1.16151 + 0.177907i
\(169\) 8.62067e18 0.996561
\(170\) −6.72379e17 + 3.40936e16i −0.0739262 + 0.00374849i
\(171\) 6.78342e18i 0.709548i
\(172\) 1.93307e17 + 1.90126e18i 0.0192422 + 0.189256i
\(173\) 1.88076e19i 1.78214i −0.453868 0.891069i \(-0.649956\pi\)
0.453868 0.891069i \(-0.350044\pi\)
\(174\) −7.45868e17 1.47097e19i −0.0672966 1.32720i
\(175\) −1.11336e19 −0.956783
\(176\) 2.31225e18 + 1.12534e19i 0.189311 + 0.921356i
\(177\) −1.50727e19 −1.17603
\(178\) 8.22273e17 + 1.62165e19i 0.0611570 + 1.20611i
\(179\) 3.45942e18i 0.245331i −0.992448 0.122665i \(-0.960856\pi\)
0.992448 0.122665i \(-0.0391442\pi\)
\(180\) 7.78408e16 + 7.65598e17i 0.00526491 + 0.0517827i
\(181\) 1.78211e19i 1.14992i 0.818182 + 0.574959i \(0.194982\pi\)
−0.818182 + 0.574959i \(0.805018\pi\)
\(182\) −9.21263e17 + 4.67135e16i −0.0567253 + 0.00287631i
\(183\) 5.71953e18 0.336144
\(184\) 4.25354e18 + 2.77703e19i 0.238671 + 1.55822i
\(185\) 2.12210e18 0.113712
\(186\) 3.75851e19 1.90578e18i 1.92378 0.0975469i
\(187\) 1.29057e19i 0.631143i
\(188\) 9.68911e18 9.85123e17i 0.452837 0.0460414i
\(189\) 1.38919e19i 0.620634i
\(190\) 1.96671e17 + 3.87866e18i 0.00840107 + 0.165682i
\(191\) 6.12664e18 0.250287 0.125144 0.992139i \(-0.460061\pi\)
0.125144 + 0.992139i \(0.460061\pi\)
\(192\) −9.29218e18 2.96215e19i −0.363126 1.15757i
\(193\) −3.57527e19 −1.33682 −0.668408 0.743795i \(-0.733024\pi\)
−0.668408 + 0.743795i \(0.733024\pi\)
\(194\) −5.98630e17 1.18059e19i −0.0214212 0.422459i
\(195\) 2.29119e17i 0.00784814i
\(196\) 1.87690e18 1.90831e17i 0.0615553 0.00625853i
\(197\) 1.53763e19i 0.482936i 0.970409 + 0.241468i \(0.0776290\pi\)
−0.970409 + 0.241468i \(0.922371\pi\)
\(198\) 1.47328e19 7.47041e17i 0.443233 0.0224745i
\(199\) −2.52712e19 −0.728407 −0.364204 0.931319i \(-0.618659\pi\)
−0.364204 + 0.931319i \(0.618659\pi\)
\(200\) −5.41467e18 3.53510e19i −0.149561 0.976443i
\(201\) −3.03582e19 −0.803728
\(202\) −1.53775e19 + 7.79732e17i −0.390302 + 0.0197906i
\(203\) 4.35925e19i 1.06095i
\(204\) −3.52760e18 3.46955e19i −0.0823422 0.809871i
\(205\) 8.65485e18i 0.193799i
\(206\) 2.26076e18 + 4.45857e19i 0.0485716 + 0.957909i
\(207\) 3.60741e19 0.743784
\(208\) −5.96365e17 2.90244e18i −0.0118025 0.0574413i
\(209\) 7.44474e19 1.41451
\(210\) 3.59798e17 + 7.09579e18i 0.00656440 + 0.129460i
\(211\) 7.63891e19i 1.33854i −0.743020 0.669269i \(-0.766607\pi\)
0.743020 0.669269i \(-0.233393\pi\)
\(212\) 3.76740e18 + 3.70540e19i 0.0634142 + 0.623706i
\(213\) 9.20667e19i 1.48894i
\(214\) −2.21591e19 + 1.12360e18i −0.344377 + 0.0174620i
\(215\) 1.40490e18 0.0209854
\(216\) 4.41089e19 6.75610e18i 0.633387 0.0970151i
\(217\) 1.11384e20 1.53785
\(218\) −1.31311e20 + 6.65822e18i −1.74349 + 0.0884052i
\(219\) 2.26500e19i 0.289263i
\(220\) 8.40236e18 8.54295e17i 0.103231 0.0104958i
\(221\) 3.32858e18i 0.0393482i
\(222\) 5.56673e18 + 1.09785e20i 0.0633286 + 1.24894i
\(223\) −5.35584e19 −0.586457 −0.293229 0.956042i \(-0.594730\pi\)
−0.293229 + 0.956042i \(0.594730\pi\)
\(224\) −2.30272e19 8.89516e19i −0.242735 0.937660i
\(225\) −4.59216e19 −0.466085
\(226\) 1.16228e18 + 2.29220e19i 0.0113603 + 0.224043i
\(227\) 8.47585e19i 0.797928i 0.916967 + 0.398964i \(0.130630\pi\)
−0.916967 + 0.398964i \(0.869370\pi\)
\(228\) −2.00143e20 + 2.03492e19i −1.81507 + 0.184544i
\(229\) 2.17239e20i 1.89817i 0.315016 + 0.949086i \(0.397990\pi\)
−0.315016 + 0.949086i \(0.602010\pi\)
\(230\) 2.06266e19 1.04589e18i 0.173677 0.00880643i
\(231\) 1.36197e20 1.10526
\(232\) 1.38413e20 2.12005e19i 1.08275 0.165844i
\(233\) −4.79641e19 −0.361736 −0.180868 0.983507i \(-0.557891\pi\)
−0.180868 + 0.983507i \(0.557891\pi\)
\(234\) −3.79982e18 + 1.92673e17i −0.0276330 + 0.00140116i
\(235\) 7.15957e18i 0.0502123i
\(236\) −1.44949e19 1.42564e20i −0.0980538 0.964401i
\(237\) 2.01722e20i 1.31641i
\(238\) −5.22705e18 1.03086e20i −0.0329119 0.649074i
\(239\) −6.27917e18 −0.0381523 −0.0190761 0.999818i \(-0.506072\pi\)
−0.0190761 + 0.999818i \(0.506072\pi\)
\(240\) −2.23552e19 + 4.59334e18i −0.131094 + 0.0269360i
\(241\) 1.50770e19 0.0853436 0.0426718 0.999089i \(-0.486413\pi\)
0.0426718 + 0.999089i \(0.486413\pi\)
\(242\) 1.06813e18 + 2.10652e19i 0.00583705 + 0.115116i
\(243\) 1.65782e20i 0.874749i
\(244\) 5.50027e18 + 5.40976e19i 0.0280266 + 0.275654i
\(245\) 1.38690e18i 0.00682549i
\(246\) 4.47751e20 2.27036e19i 2.12857 0.107931i
\(247\) −1.92011e19 −0.0881866
\(248\) 5.41699e19 + 3.53662e20i 0.240391 + 1.56945i
\(249\) −4.21231e20 −1.80645
\(250\) −5.28380e19 + 2.67920e18i −0.219006 + 0.0111049i
\(251\) 6.51149e18i 0.0260888i 0.999915 + 0.0130444i \(0.00415227\pi\)
−0.999915 + 0.0130444i \(0.995848\pi\)
\(252\) −1.17378e20 + 1.19342e19i −0.454653 + 0.0462261i
\(253\) 3.95909e20i 1.48276i
\(254\) −1.64369e19 3.24162e20i −0.0595297 1.17402i
\(255\) −2.56375e19 −0.0898016
\(256\) 2.71236e20 1.16375e20i 0.918984 0.394294i
\(257\) 2.25404e20 0.738805 0.369402 0.929269i \(-0.379562\pi\)
0.369402 + 0.929269i \(0.379562\pi\)
\(258\) 3.68535e18 + 7.26810e19i 0.0116872 + 0.230491i
\(259\) 3.25349e20i 0.998394i
\(260\) −2.16710e18 + 2.20336e17i −0.00643584 + 0.000654352i
\(261\) 1.79801e20i 0.516829i
\(262\) 2.64384e20 1.34059e19i 0.735656 0.0373021i
\(263\) −4.46257e20 −1.20216 −0.601079 0.799190i \(-0.705262\pi\)
−0.601079 + 0.799190i \(0.705262\pi\)
\(264\) 6.62374e19 + 4.32447e20i 0.172771 + 1.12798i
\(265\) 2.73803e19 0.0691589
\(266\) −5.94657e20 + 3.01526e19i −1.45470 + 0.0737617i
\(267\) 6.18329e20i 1.46512i
\(268\) −2.91944e19 2.87140e20i −0.0670122 0.659094i
\(269\) 4.92825e20i 1.09597i 0.836489 + 0.547984i \(0.184605\pi\)
−0.836489 + 0.547984i \(0.815395\pi\)
\(270\) −1.66124e18 3.27623e19i −0.00357965 0.0705963i
\(271\) −3.92364e20 −0.819313 −0.409657 0.912240i \(-0.634351\pi\)
−0.409657 + 0.912240i \(0.634351\pi\)
\(272\) 3.24771e20 6.67308e19i 0.657267 0.135049i
\(273\) −3.51273e19 −0.0689069
\(274\) −3.07064e19 6.05578e20i −0.0583914 1.15157i
\(275\) 5.03985e20i 0.929158i
\(276\) 1.08216e20 + 1.06436e21i 0.193449 + 1.90265i
\(277\) 7.33443e20i 1.27142i −0.771929 0.635709i \(-0.780708\pi\)
0.771929 0.635709i \(-0.219292\pi\)
\(278\) −5.48965e20 + 2.78358e19i −0.922919 + 0.0467975i
\(279\) 4.59413e20 0.749147
\(280\) −6.67688e19 + 1.02269e19i −0.105616 + 0.0161771i
\(281\) 1.18919e21 1.82493 0.912467 0.409149i \(-0.134174\pi\)
0.912467 + 0.409149i \(0.134174\pi\)
\(282\) 3.70394e20 1.87811e19i 0.551501 0.0279643i
\(283\) 6.56438e20i 0.948438i −0.880407 0.474219i \(-0.842731\pi\)
0.880407 0.474219i \(-0.157269\pi\)
\(284\) −8.70804e20 + 8.85374e19i −1.22100 + 0.124143i
\(285\) 1.47892e20i 0.201262i
\(286\) 2.11457e18 + 4.17027e19i 0.00279326 + 0.0550875i
\(287\) 1.32692e21 1.70156
\(288\) −9.49776e19 3.66888e20i −0.118246 0.456770i
\(289\) −4.54785e20 −0.549762
\(290\) −5.21294e18 1.02807e20i −0.00611927 0.120682i
\(291\) 4.50154e20i 0.513181i
\(292\) 2.14232e20 2.17817e19i 0.237209 0.0241178i
\(293\) 6.98093e20i 0.750825i −0.926858 0.375412i \(-0.877501\pi\)
0.926858 0.375412i \(-0.122499\pi\)
\(294\) 7.17500e19 3.63815e18i 0.0749669 0.00380126i
\(295\) −1.05345e20 −0.106936
\(296\) −1.03303e21 + 1.58229e20i −1.01891 + 0.156065i
\(297\) −6.28842e20 −0.602714
\(298\) −3.34661e20 + 1.69693e19i −0.311722 + 0.0158061i
\(299\) 1.02111e20i 0.0924417i
\(300\) −1.37757e20 1.35490e21i −0.121223 1.19228i
\(301\) 2.15391e20i 0.184252i
\(302\) 4.58257e19 + 9.03755e20i 0.0381110 + 0.751608i
\(303\) −5.86339e20 −0.474118
\(304\) −3.84941e20 1.87346e21i −0.302670 1.47306i
\(305\) 3.99743e19 0.0305656
\(306\) −2.15594e19 4.25185e20i −0.0160326 0.316189i
\(307\) 3.85295e20i 0.278687i −0.990244 0.139344i \(-0.955501\pi\)
0.990244 0.139344i \(-0.0444992\pi\)
\(308\) 1.30976e20 + 1.28821e21i 0.0921533 + 0.906368i
\(309\) 1.70003e21i 1.16362i
\(310\) 2.62686e20 1.33197e19i 0.174929 0.00886993i
\(311\) 2.10525e21 1.36408 0.682041 0.731313i \(-0.261092\pi\)
0.682041 + 0.731313i \(0.261092\pi\)
\(312\) −1.70836e19 1.11535e20i −0.0107713 0.0703228i
\(313\) −2.88772e20 −0.177186 −0.0885928 0.996068i \(-0.528237\pi\)
−0.0885928 + 0.996068i \(0.528237\pi\)
\(314\) 2.02604e21 1.02732e20i 1.20989 0.0613486i
\(315\) 8.67338e19i 0.0504137i
\(316\) 1.90797e21 1.93989e20i 1.07952 0.109758i
\(317\) 2.62929e21i 1.44822i 0.689683 + 0.724111i \(0.257750\pi\)
−0.689683 + 0.724111i \(0.742250\pi\)
\(318\) 7.18246e19 + 1.41649e21i 0.0385161 + 0.759598i
\(319\) −1.97329e21 −1.03032
\(320\) −6.49439e19 2.07028e20i −0.0330190 0.105258i
\(321\) −8.44915e20 −0.418331
\(322\) 1.60351e20 + 3.16237e21i 0.0773208 + 1.52489i
\(323\) 2.14853e21i 1.00907i
\(324\) 2.71665e21 2.76210e20i 1.24280 0.126359i
\(325\) 1.29985e20i 0.0579277i
\(326\) −3.28197e21 + 1.66415e20i −1.42490 + 0.0722510i
\(327\) −5.00681e21 −2.11790
\(328\) 6.45326e20 + 4.21317e21i 0.265982 + 1.73653i
\(329\) 1.09767e21 0.440866
\(330\) 3.21204e20 1.62869e19i 0.125722 0.00637487i
\(331\) 3.08298e21i 1.17607i −0.808836 0.588035i \(-0.799902\pi\)
0.808836 0.588035i \(-0.200098\pi\)
\(332\) −4.05083e20 3.98417e21i −0.150616 1.48137i
\(333\) 1.34193e21i 0.486355i
\(334\) −7.14002e19 1.40812e21i −0.0252264 0.497503i
\(335\) −2.12176e20 −0.0730829
\(336\) −7.04228e20 3.42739e21i −0.236499 1.15101i
\(337\) −1.59524e21 −0.522363 −0.261181 0.965290i \(-0.584112\pi\)
−0.261181 + 0.965290i \(0.584112\pi\)
\(338\) 1.58051e20 + 3.11701e21i 0.0504667 + 0.995283i
\(339\) 8.74005e20i 0.272155i
\(340\) −2.46547e19 2.42490e20i −0.00748737 0.0736415i
\(341\) 5.04201e21i 1.49345i
\(342\) −2.45271e21 + 1.24367e20i −0.708638 + 0.0359321i
\(343\) 3.64925e21 1.02850
\(344\) −6.83902e20 + 1.04752e20i −0.188039 + 0.0288016i
\(345\) 7.86484e20 0.210973
\(346\) 6.80034e21 3.44817e20i 1.77985 0.0902490i
\(347\) 1.54612e21i 0.394859i 0.980317 + 0.197430i \(0.0632594\pi\)
−0.980317 + 0.197430i \(0.936741\pi\)
\(348\) 5.30497e21 5.39373e20i 1.32208 0.134421i
\(349\) 5.41385e21i 1.31671i 0.752708 + 0.658355i \(0.228747\pi\)
−0.752708 + 0.658355i \(0.771253\pi\)
\(350\) −2.04123e20 4.02563e21i −0.0484523 0.955555i
\(351\) 1.62188e20 0.0375758
\(352\) −4.02656e21 + 1.04237e21i −0.910587 + 0.235727i
\(353\) 3.93297e21 0.868232 0.434116 0.900857i \(-0.357061\pi\)
0.434116 + 0.900857i \(0.357061\pi\)
\(354\) −2.76343e20 5.44991e21i −0.0595553 1.17452i
\(355\) 6.43463e20i 0.135389i
\(356\) −5.84840e21 + 5.94626e20i −1.20147 + 0.122157i
\(357\) 3.93061e21i 0.788461i
\(358\) 1.25084e21 6.34247e19i 0.245016 0.0124238i
\(359\) 7.90394e21 1.51196 0.755981 0.654593i \(-0.227160\pi\)
0.755981 + 0.654593i \(0.227160\pi\)
\(360\) −2.75393e20 + 4.21816e19i −0.0514496 + 0.00788047i
\(361\) −6.91355e21 −1.26151
\(362\) −6.44365e21 + 3.26731e20i −1.14844 + 0.0582328i
\(363\) 8.03207e20i 0.139837i
\(364\) −3.37808e19 3.32248e20i −0.00574523 0.0565069i
\(365\) 1.58303e20i 0.0263026i
\(366\) 1.04861e20 + 2.06803e21i 0.0170226 + 0.335713i
\(367\) 5.10700e20 0.0810036 0.0405018 0.999179i \(-0.487104\pi\)
0.0405018 + 0.999179i \(0.487104\pi\)
\(368\) −9.96303e21 + 2.04711e21i −1.54413 + 0.317274i
\(369\) 5.47298e21 0.828896
\(370\) 3.89064e19 + 7.67296e20i 0.00575846 + 0.113566i
\(371\) 4.19781e21i 0.607217i
\(372\) 1.37816e21 + 1.35548e22i 0.194844 + 1.91637i
\(373\) 3.13000e21i 0.432533i −0.976334 0.216266i \(-0.930612\pi\)
0.976334 0.216266i \(-0.0693880\pi\)
\(374\) −4.66637e21 + 2.36612e20i −0.630333 + 0.0319616i
\(375\) −2.01469e21 −0.266037
\(376\) 5.33835e20 + 3.48527e21i 0.0689144 + 0.449925i
\(377\) 5.08943e20 0.0642344
\(378\) 5.02294e21 2.54693e20i 0.619838 0.0314294i
\(379\) 1.31559e22i 1.58741i 0.608305 + 0.793704i \(0.291850\pi\)
−0.608305 + 0.793704i \(0.708150\pi\)
\(380\) −1.39882e21 + 1.42222e20i −0.165044 + 0.0167806i
\(381\) 1.23601e22i 1.42614i
\(382\) 1.12325e20 + 2.21524e21i 0.0126748 + 0.249966i
\(383\) 3.30408e21 0.364637 0.182319 0.983239i \(-0.441640\pi\)
0.182319 + 0.983239i \(0.441640\pi\)
\(384\) 1.05400e22 3.90289e21i 1.13769 0.421280i
\(385\) 9.51895e20 0.100502
\(386\) −6.55488e20 1.29273e22i −0.0676975 1.33510i
\(387\) 8.88400e20i 0.0897564i
\(388\) 4.25774e21 4.32898e20i 0.420833 0.0427874i
\(389\) 7.70023e20i 0.0744615i 0.999307 + 0.0372308i \(0.0118537\pi\)
−0.999307 + 0.0372308i \(0.988146\pi\)
\(390\) −8.28435e19 + 4.20065e18i −0.00783807 + 0.000397436i
\(391\) −1.14258e22 −1.05776
\(392\) 1.03411e20 + 6.75142e20i 0.00936771 + 0.0611594i
\(393\) 1.00809e22 0.893637
\(394\) −5.55969e21 + 2.81909e20i −0.482317 + 0.0244563i
\(395\) 1.40986e21i 0.119701i
\(396\) 5.40222e20 + 5.31331e21i 0.0448914 + 0.441526i
\(397\) 5.29693e21i 0.430829i 0.976523 + 0.215415i \(0.0691103\pi\)
−0.976523 + 0.215415i \(0.930890\pi\)
\(398\) −4.63320e20 9.13740e21i −0.0368871 0.727472i
\(399\) −2.26740e22 −1.76709
\(400\) 1.26827e22 2.60593e21i 0.967616 0.198817i
\(401\) −4.56356e21 −0.340861 −0.170430 0.985370i \(-0.554516\pi\)
−0.170430 + 0.985370i \(0.554516\pi\)
\(402\) −5.56585e20 1.09767e22i −0.0407015 0.802697i
\(403\) 1.30041e21i 0.0931082i
\(404\) −5.63862e20 5.54583e21i −0.0395304 0.388799i
\(405\) 2.00741e21i 0.137806i
\(406\) 1.57619e22 7.99222e20i 1.05959 0.0537274i
\(407\) 1.47275e22 0.969567
\(408\) 1.24803e22 1.91159e21i 0.804662 0.123249i
\(409\) −1.58699e22 −1.00214 −0.501069 0.865407i \(-0.667060\pi\)
−0.501069 + 0.865407i \(0.667060\pi\)
\(410\) 3.12937e21 1.58678e20i 0.193551 0.00981415i
\(411\) 2.30904e22i 1.39887i
\(412\) −1.60796e22 + 1.63486e21i −0.954220 + 0.0970186i
\(413\) 1.61509e22i 0.938906i
\(414\) 6.61380e20 + 1.30434e22i 0.0376659 + 0.742830i
\(415\) −2.94402e21 −0.164260
\(416\) 1.03851e21 2.68843e20i 0.0567699 0.0146962i
\(417\) −2.09318e22 −1.12111
\(418\) 1.36491e21 + 2.69182e22i 0.0716320 + 1.41270i
\(419\) 2.63907e21i 0.135716i 0.997695 + 0.0678581i \(0.0216165\pi\)
−0.997695 + 0.0678581i \(0.978383\pi\)
\(420\) −2.55906e21 + 2.60187e20i −0.128962 + 0.0131120i
\(421\) 1.44643e22i 0.714329i 0.934041 + 0.357165i \(0.116257\pi\)
−0.934041 + 0.357165i \(0.883743\pi\)
\(422\) 2.76203e22 1.40051e21i 1.33682 0.0677847i
\(423\) 4.52743e21 0.214762
\(424\) −1.33287e22 + 2.04154e21i −0.619695 + 0.0949178i
\(425\) 1.45449e22 0.662832
\(426\) −3.32890e22 + 1.68795e21i −1.48703 + 0.0754010i
\(427\) 6.12866e21i 0.268367i
\(428\) −8.12526e20 7.99155e21i −0.0348791 0.343051i
\(429\) 1.59010e21i 0.0669174i
\(430\) 2.57573e19 + 5.07974e20i 0.00106272 + 0.0209585i
\(431\) 1.52835e22 0.618253 0.309127 0.951021i \(-0.399963\pi\)
0.309127 + 0.951021i \(0.399963\pi\)
\(432\) 3.25152e21 + 1.58248e22i 0.128966 + 0.627661i
\(433\) −2.10323e21 −0.0817975 −0.0408988 0.999163i \(-0.513022\pi\)
−0.0408988 + 0.999163i \(0.513022\pi\)
\(434\) 2.04211e21 + 4.02736e22i 0.0778782 + 1.53588i
\(435\) 3.92000e21i 0.146598i
\(436\) −4.81488e21 4.73564e22i −0.176584 1.73678i
\(437\) 6.59107e22i 2.37063i
\(438\) 8.18964e21 4.15263e20i 0.288891 0.0146485i
\(439\) 3.28337e22 1.13598 0.567991 0.823035i \(-0.307721\pi\)
0.567991 + 0.823035i \(0.307721\pi\)
\(440\) 4.62939e20 + 3.02241e21i 0.0157100 + 0.102567i
\(441\) 8.77020e20 0.0291932
\(442\) 1.20353e21 6.10260e19i 0.0392977 0.00199262i
\(443\) 9.12162e21i 0.292173i −0.989272 0.146087i \(-0.953332\pi\)
0.989272 0.146087i \(-0.0466678\pi\)
\(444\) −3.95933e22 + 4.02557e21i −1.24413 + 0.126495i
\(445\) 4.32156e21i 0.133223i
\(446\) −9.81937e20 1.93653e22i −0.0296987 0.585705i
\(447\) −1.27605e22 −0.378663
\(448\) 3.17404e22 9.95687e21i 0.924165 0.289908i
\(449\) 2.31577e22 0.661610 0.330805 0.943699i \(-0.392680\pi\)
0.330805 + 0.943699i \(0.392680\pi\)
\(450\) −8.41923e20 1.66040e22i −0.0236029 0.465487i
\(451\) 6.00654e22i 1.65243i
\(452\) −8.26669e21 + 8.40501e20i −0.223180 + 0.0226914i
\(453\) 3.44598e22i 0.913014i
\(454\) −3.06465e22 + 1.55396e21i −0.796904 + 0.0404077i
\(455\) −2.45508e20 −0.00626570
\(456\) −1.10271e22 7.19935e22i −0.276224 1.80340i
\(457\) 3.81496e22 0.937999 0.468999 0.883198i \(-0.344615\pi\)
0.468999 + 0.883198i \(0.344615\pi\)
\(458\) −7.85479e22 + 3.98284e21i −1.89574 + 0.0961250i
\(459\) 1.81482e22i 0.429958i
\(460\) 7.56335e20 + 7.43888e21i 0.0175903 + 0.173008i
\(461\) 6.60861e22i 1.50887i −0.656373 0.754436i \(-0.727910\pi\)
0.656373 0.754436i \(-0.272090\pi\)
\(462\) 2.49703e21 + 4.92454e22i 0.0559715 + 1.10385i
\(463\) −6.02518e22 −1.32596 −0.662981 0.748636i \(-0.730709\pi\)
−0.662981 + 0.748636i \(0.730709\pi\)
\(464\) 1.02032e22 + 4.96578e22i 0.220462 + 1.07296i
\(465\) 1.00161e22 0.212494
\(466\) −8.79372e20 1.73426e22i −0.0183186 0.361271i
\(467\) 3.05437e21i 0.0624782i 0.999512 + 0.0312391i \(0.00994534\pi\)
−0.999512 + 0.0312391i \(0.990055\pi\)
\(468\) −1.39331e20 1.37039e21i −0.00279872 0.0275266i
\(469\) 3.25298e22i 0.641670i
\(470\) 2.58872e21 1.31263e20i 0.0501479 0.00254279i
\(471\) 7.72520e22 1.46971
\(472\) 5.12817e22 7.85475e21i 0.958199 0.146766i
\(473\) 9.75010e21 0.178933
\(474\) 7.29375e22 3.69836e21i 1.31473 0.0666643i
\(475\) 8.39030e22i 1.48553i
\(476\) 3.71773e22 3.77993e21i 0.646575 0.0657393i
\(477\) 1.73142e22i 0.295799i
\(478\) −1.15122e20 2.27039e21i −0.00193206 0.0381033i
\(479\) −8.21420e22 −1.35430 −0.677148 0.735847i \(-0.736784\pi\)
−0.677148 + 0.735847i \(0.736784\pi\)
\(480\) −2.07069e21 7.99887e21i −0.0335402 0.129562i
\(481\) −3.79846e21 −0.0604469
\(482\) 2.76421e20 + 5.45146e21i 0.00432187 + 0.0852341i
\(483\) 1.20580e23i 1.85235i
\(484\) −7.59705e21 + 7.72416e20i −0.114673 + 0.0116591i
\(485\) 3.14617e21i 0.0466635i
\(486\) 5.99424e22 3.03943e21i 0.873627 0.0442980i
\(487\) 4.20663e22 0.602473 0.301237 0.953549i \(-0.402601\pi\)
0.301237 + 0.953549i \(0.402601\pi\)
\(488\) −1.94594e22 + 2.98058e21i −0.273881 + 0.0419500i
\(489\) −1.25140e23 −1.73090
\(490\) 5.01467e20 2.54274e19i 0.00681673 0.000345648i
\(491\) 8.80209e22i 1.17596i 0.808875 + 0.587980i \(0.200077\pi\)
−0.808875 + 0.587980i \(0.799923\pi\)
\(492\) 1.64181e22 + 1.61479e23i 0.215585 + 2.12037i
\(493\) 5.69487e22i 0.734996i
\(494\) −3.52032e20 6.94263e21i −0.00446584 0.0880735i
\(495\) 3.92617e21 0.0489581
\(496\) −1.26882e23 + 2.60705e22i −1.55527 + 0.319562i
\(497\) −9.86525e22 −1.18872
\(498\) −7.72281e21 1.52306e23i −0.0914800 1.80413i
\(499\) 2.77007e22i 0.322579i −0.986907 0.161290i \(-0.948435\pi\)
0.986907 0.161290i \(-0.0515654\pi\)
\(500\) −1.93746e21 1.90558e22i −0.0221813 0.218163i
\(501\) 5.36912e22i 0.604341i
\(502\) −2.35439e21 + 1.19381e20i −0.0260553 + 0.00132116i
\(503\) −1.28825e23 −1.40176 −0.700878 0.713281i \(-0.747208\pi\)
−0.700878 + 0.713281i \(0.747208\pi\)
\(504\) −6.46707e21 4.22219e22i −0.0691908 0.451729i
\(505\) −4.09798e21 −0.0431115
\(506\) 1.43151e23 7.25858e21i 1.48086 0.0750883i
\(507\) 1.18850e23i 1.20902i
\(508\) 1.16907e23 1.18863e22i 1.16950 0.118907i
\(509\) 1.41955e23i 1.39653i −0.715839 0.698265i \(-0.753956\pi\)
0.715839 0.698265i \(-0.246044\pi\)
\(510\) −4.70036e20 9.26986e21i −0.00454763 0.0896864i
\(511\) 2.42702e22 0.230938
\(512\) 4.70511e22 + 9.59384e22i 0.440327 + 0.897838i
\(513\) 1.04689e23 0.963615
\(514\) 4.13254e21 + 8.15002e22i 0.0374137 + 0.737857i
\(515\) 1.18817e22i 0.105808i
\(516\) −2.62120e22 + 2.66506e21i −0.229603 + 0.0233445i
\(517\) 4.96881e22i 0.428137i
\(518\) −1.17638e23 + 5.96493e21i −0.997112 + 0.0505595i
\(519\) 2.59294e23 2.16207
\(520\) −1.19399e20 7.79527e20i −0.000979429 0.00639444i
\(521\) −1.60040e22 −0.129154 −0.0645772 0.997913i \(-0.520570\pi\)
−0.0645772 + 0.997913i \(0.520570\pi\)
\(522\) 6.50113e22 3.29645e21i 0.516166 0.0261727i
\(523\) 4.32799e22i 0.338082i −0.985609 0.169041i \(-0.945933\pi\)
0.985609 0.169041i \(-0.0540670\pi\)
\(524\) 9.69442e21 + 9.53488e22i 0.0745085 + 0.732823i
\(525\) 1.53496e23i 1.16076i
\(526\) −8.18165e21 1.61355e23i −0.0608783 1.20062i
\(527\) −1.45511e23 −1.06538
\(528\) −1.55147e23 + 3.18782e22i −1.11778 + 0.229671i
\(529\) 2.09461e23 1.48501
\(530\) 5.01989e20 + 9.90001e21i 0.00350227 + 0.0690702i
\(531\) 6.66158e22i 0.457376i
\(532\) −2.18048e22 2.14460e23i −0.147334 1.44909i
\(533\) 1.54918e22i 0.103020i
\(534\) −2.23572e23 + 1.13364e22i −1.46324 + 0.0741950i
\(535\) −5.90519e21 −0.0380388
\(536\) 1.03287e23 1.58204e22i 0.654855 0.100303i
\(537\) 4.76938e22 0.297633
\(538\) −1.78193e23 + 9.03542e21i −1.09456 + 0.0555007i
\(539\) 9.62521e21i 0.0581977i
\(540\) 1.18155e22 1.20132e21i 0.0703244 0.00715011i
\(541\) 2.24293e23i 1.31413i 0.753833 + 0.657066i \(0.228203\pi\)
−0.753833 + 0.657066i \(0.771797\pi\)
\(542\) −7.19358e21 1.41869e23i −0.0414907 0.818262i
\(543\) −2.45693e23 −1.39507
\(544\) 3.00825e22 + 1.16205e23i 0.168160 + 0.649584i
\(545\) −3.49931e22 −0.192580
\(546\) −6.44023e20 1.27011e22i −0.00348950 0.0688185i
\(547\) 7.07789e22i 0.377582i 0.982017 + 0.188791i \(0.0604569\pi\)
−0.982017 + 0.188791i \(0.939543\pi\)
\(548\) 2.18398e23 2.22053e22i 1.14714 0.116633i
\(549\) 2.52781e22i 0.130732i
\(550\) −1.82228e23 + 9.24002e21i −0.927965 + 0.0470533i
\(551\) 3.28512e23 1.64726
\(552\) −3.82859e23 + 5.86421e22i −1.89041 + 0.289552i
\(553\) 2.16152e23 1.05098
\(554\) 2.65194e23 1.34469e22i 1.26979 0.0643857i
\(555\) 2.92566e22i 0.137954i
\(556\) −2.01294e22 1.97981e23i −0.0934748 0.919365i
\(557\) 2.94239e23i 1.34565i 0.739803 + 0.672823i \(0.234919\pi\)
−0.739803 + 0.672823i \(0.765081\pi\)
\(558\) 8.42284e21 + 1.66112e23i 0.0379374 + 0.748186i
\(559\) −2.51470e21 −0.0111554
\(560\) −4.92191e21 2.39544e22i −0.0215048 0.104661i
\(561\) −1.77926e23 −0.765696
\(562\) 2.18025e22 + 4.29980e23i 0.0924162 + 1.82259i
\(563\) 9.39183e22i 0.392129i 0.980591 + 0.196064i \(0.0628162\pi\)
−0.980591 + 0.196064i \(0.937184\pi\)
\(564\) 1.35816e22 + 1.33580e23i 0.0558569 + 0.549377i
\(565\) 6.10850e21i 0.0247470i
\(566\) 2.37351e23 1.20351e22i 0.947221 0.0480297i
\(567\) 3.07766e23 1.20994
\(568\) −4.79781e22 3.13237e23i −0.185816 1.21314i
\(569\) −7.54187e22 −0.287756 −0.143878 0.989595i \(-0.545957\pi\)
−0.143878 + 0.989595i \(0.545957\pi\)
\(570\) −5.34738e22 + 2.71144e21i −0.201004 + 0.0101921i
\(571\) 3.40566e23i 1.26123i −0.776095 0.630616i \(-0.782802\pi\)
0.776095 0.630616i \(-0.217198\pi\)
\(572\) −1.50398e22 + 1.52915e21i −0.0548753 + 0.00557935i
\(573\) 8.44659e22i 0.303646i
\(574\) 2.43276e22 + 4.79779e23i 0.0861685 + 1.69938i
\(575\) −4.46194e23 −1.55721
\(576\) 1.30916e23 4.10679e22i 0.450196 0.141225i
\(577\) −4.78683e23 −1.62201 −0.811006 0.585038i \(-0.801079\pi\)
−0.811006 + 0.585038i \(0.801079\pi\)
\(578\) −8.33801e21 1.64439e23i −0.0278404 0.549057i
\(579\) 4.92910e23i 1.62181i
\(580\) 3.70769e22 3.76973e21i 0.120217 0.0122228i
\(581\) 4.51362e23i 1.44221i
\(582\) 1.62764e23 8.25310e21i 0.512523 0.0259879i
\(583\) 1.90022e23 0.589685
\(584\) 1.18034e22 + 7.70615e22i 0.0360993 + 0.235683i
\(585\) −1.01262e21 −0.00305226
\(586\) 2.52412e23 1.27988e22i 0.749861 0.0380224i
\(587\) 1.81919e22i 0.0532666i −0.999645 0.0266333i \(-0.991521\pi\)
0.999645 0.0266333i \(-0.00847865\pi\)
\(588\) 2.63092e21 + 2.58762e22i 0.00759277 + 0.0746782i
\(589\) 8.39390e23i 2.38772i
\(590\) −1.93139e21 3.80900e22i −0.00541535 0.106799i
\(591\) −2.11988e23 −0.585893
\(592\) −7.61510e22 3.70618e23i −0.207463 1.00970i
\(593\) −9.82089e22 −0.263746 −0.131873 0.991267i \(-0.542099\pi\)
−0.131873 + 0.991267i \(0.542099\pi\)
\(594\) −1.15291e22 2.27373e23i −0.0305220 0.601941i
\(595\) 2.74714e22i 0.0716946i
\(596\) −1.22713e22 1.20694e23i −0.0315717 0.310521i
\(597\) 3.48405e23i 0.883695i
\(598\) −3.69207e22 + 1.87210e21i −0.0923231 + 0.00468132i
\(599\) 2.49917e22 0.0616124 0.0308062 0.999525i \(-0.490193\pi\)
0.0308062 + 0.999525i \(0.490193\pi\)
\(600\) 4.87372e23 7.46502e22i 1.18461 0.181445i
\(601\) −1.67913e23 −0.402394 −0.201197 0.979551i \(-0.564483\pi\)
−0.201197 + 0.979551i \(0.564483\pi\)
\(602\) −7.78800e22 + 3.94897e21i −0.184016 + 0.00933070i
\(603\) 1.34172e23i 0.312582i
\(604\) −3.25934e23 + 3.31388e22i −0.748714 + 0.0761242i
\(605\) 5.61369e21i 0.0127153i
\(606\) −1.07499e22 2.12005e23i −0.0240097 0.473510i
\(607\) −3.57610e23 −0.787600 −0.393800 0.919196i \(-0.628840\pi\)
−0.393800 + 0.919196i \(0.628840\pi\)
\(608\) 6.70339e23 1.73533e23i 1.45584 0.376878i
\(609\) 6.00994e23 1.28713
\(610\) 7.32887e20 + 1.44537e22i 0.00154787 + 0.0305263i
\(611\) 1.28153e22i 0.0266919i
\(612\) 1.53341e23 1.55906e22i 0.314971 0.0320241i
\(613\) 5.01122e23i 1.01515i 0.861608 + 0.507575i \(0.169458\pi\)
−0.861608 + 0.507575i \(0.830542\pi\)
\(614\) 1.39313e23 7.06397e21i 0.278330 0.0141129i
\(615\) 1.19322e23 0.235115
\(616\) −4.63381e23 + 7.09755e22i −0.900538 + 0.137934i
\(617\) −1.62324e23 −0.311141 −0.155571 0.987825i \(-0.549722\pi\)
−0.155571 + 0.987825i \(0.549722\pi\)
\(618\) −6.14688e23 + 3.11683e22i −1.16212 + 0.0589266i
\(619\) 3.38341e23i 0.630934i 0.948937 + 0.315467i \(0.102161\pi\)
−0.948937 + 0.315467i \(0.897839\pi\)
\(620\) 9.63212e21 + 9.47361e22i 0.0177171 + 0.174255i
\(621\) 5.56734e23i 1.01011i
\(622\) 3.85976e22 + 7.61205e23i 0.0690783 + 1.36233i
\(623\) −6.62559e23 −1.16970
\(624\) 4.00149e22 8.22188e21i 0.0696871 0.0143186i
\(625\) 5.60912e23 0.963640
\(626\) −5.29433e21 1.04413e23i −0.00897283 0.176958i
\(627\) 1.02638e24i 1.71607i
\(628\) 7.42906e22 + 7.30681e23i 0.122540 + 1.20523i
\(629\) 4.25033e23i 0.691659i
\(630\) −3.13607e22 + 1.59017e21i −0.0503490 + 0.00255299i
\(631\) 1.07823e24 1.70789 0.853947 0.520359i \(-0.174202\pi\)
0.853947 + 0.520359i \(0.174202\pi\)
\(632\) 1.05122e23 + 6.86316e23i 0.164285 + 1.07258i
\(633\) 1.05315e24 1.62390
\(634\) −9.50684e23 + 4.82053e22i −1.44636 + 0.0733392i
\(635\) 8.63862e22i 0.129678i
\(636\) −5.10851e23 + 5.19398e22i −0.756673 + 0.0769334i
\(637\) 2.48249e21i 0.00362829i
\(638\) −3.61783e22 7.13492e23i −0.0521761 1.02900i
\(639\) −4.06900e23 −0.579069
\(640\) 7.36652e22 2.72777e22i 0.103450 0.0383070i
\(641\) −8.18063e23 −1.13369 −0.566844 0.823825i \(-0.691836\pi\)
−0.566844 + 0.823825i \(0.691836\pi\)
\(642\) −1.54906e22 3.05500e23i −0.0211847 0.417795i
\(643\) 1.03008e24i 1.39020i −0.718913 0.695100i \(-0.755360\pi\)
0.718913 0.695100i \(-0.244640\pi\)
\(644\) −1.14049e24 + 1.15957e23i −1.51901 + 0.154443i
\(645\) 1.93688e22i 0.0254593i
\(646\) 7.76853e23 3.93910e22i 1.00777 0.0511000i
\(647\) 1.16066e24 1.48600 0.742998 0.669293i \(-0.233403\pi\)
0.742998 + 0.669293i \(0.233403\pi\)
\(648\) 1.49677e23 + 9.77206e23i 0.189134 + 1.23481i
\(649\) −7.31102e23 −0.911797
\(650\) 4.69994e22 2.38314e21i 0.0578533 0.00293350i
\(651\) 1.53561e24i 1.86571i
\(652\) −1.20343e23 1.18363e24i −0.144317 1.41942i
\(653\) 1.25728e24i 1.48823i −0.668054 0.744113i \(-0.732872\pi\)
0.668054 0.744113i \(-0.267128\pi\)
\(654\) −9.17946e22 1.81033e24i −0.107252 2.11518i
\(655\) 7.04561e22 0.0812582
\(656\) −1.51154e24 + 3.10577e23i −1.72083 + 0.353579i
\(657\) 1.00104e23 0.112499
\(658\) 2.01246e22 + 3.96889e23i 0.0223258 + 0.440300i
\(659\) 1.29456e24i 1.41774i 0.705338 + 0.708871i \(0.250795\pi\)
−0.705338 + 0.708871i \(0.749205\pi\)
\(660\) 1.17779e22 + 1.15840e23i 0.0127334 + 0.125238i
\(661\) 8.22393e23i 0.877742i 0.898550 + 0.438871i \(0.144622\pi\)
−0.898550 + 0.438871i \(0.855378\pi\)
\(662\) 1.11473e24 5.65232e22i 1.17456 0.0595572i
\(663\) 4.58900e22 0.0477367
\(664\) 1.43314e24 2.19513e23i 1.47184 0.225440i
\(665\) −1.58471e23 −0.160681
\(666\) −4.85207e23 + 2.46029e22i −0.485731 + 0.0246294i
\(667\) 1.74702e24i 1.72675i
\(668\) 5.07832e23 5.16329e22i 0.495588 0.0503880i
\(669\) 7.38391e23i 0.711483i
\(670\) −3.89003e21 7.67174e22i −0.00370098 0.0729891i
\(671\) 2.77425e23 0.260618
\(672\) 1.22635e24 3.17468e23i 1.13756 0.294484i
\(673\) 1.06449e24 0.975016 0.487508 0.873118i \(-0.337906\pi\)
0.487508 + 0.873118i \(0.337906\pi\)
\(674\) −2.92470e22 5.76798e23i −0.0264529 0.521692i
\(675\) 7.08711e23i 0.632976i
\(676\) −1.12413e24 + 1.14294e23i −0.991450 + 0.100804i
\(677\) 1.14609e24i 0.998198i −0.866545 0.499099i \(-0.833664\pi\)
0.866545 0.499099i \(-0.166336\pi\)
\(678\) −3.16018e23 + 1.60240e22i −0.271806 + 0.0137822i
\(679\) 4.82355e23 0.409707
\(680\) 8.72260e22 1.33603e22i 0.0731678 0.0112070i
\(681\) −1.16854e24 −0.968037
\(682\) 1.82306e24 9.24399e22i 1.49154 0.0756297i
\(683\) 1.21554e24i 0.982186i 0.871107 + 0.491093i \(0.163402\pi\)
−0.871107 + 0.491093i \(0.836598\pi\)
\(684\) −8.99357e22 8.84556e23i −0.0717720 0.705909i
\(685\) 1.61381e23i 0.127199i
\(686\) 6.69051e22 + 1.31947e24i 0.0520840 + 1.02718i
\(687\) −2.99500e24 −2.30284
\(688\) −5.04143e22 2.45361e23i −0.0382871 0.186339i
\(689\) −4.90095e22 −0.0367635
\(690\) 1.44194e22 + 2.84372e23i 0.0106839 + 0.210703i
\(691\) 1.76793e24i 1.29390i −0.762531 0.646952i \(-0.776043\pi\)
0.762531 0.646952i \(-0.223957\pi\)
\(692\) 2.49354e23 + 2.45251e24i 0.180266 + 1.77300i
\(693\) 6.01940e23i 0.429854i
\(694\) −5.59037e23 + 2.83465e22i −0.394353 + 0.0199960i
\(695\) −1.46294e23 −0.101943
\(696\) 2.92284e23 + 1.90825e24i 0.201200 + 1.31358i
\(697\) −1.73347e24 −1.17879
\(698\) −1.95751e24 + 9.92571e22i −1.31502 + 0.0666792i
\(699\) 6.61265e23i 0.438854i
\(700\) 1.45182e24 1.47611e23i 0.951875 0.0967802i
\(701\) 1.00329e24i 0.649868i 0.945737 + 0.324934i \(0.105342\pi\)
−0.945737 + 0.324934i \(0.894658\pi\)
\(702\) 2.97354e21 + 5.86430e22i 0.00190287 + 0.0375276i
\(703\) −2.45183e24 −1.55014
\(704\) −4.50717e23 1.43679e24i −0.281537 0.897481i
\(705\) 9.87066e22 0.0609170
\(706\) 7.21069e22 + 1.42206e24i 0.0439680 + 0.867118i
\(707\) 6.28281e23i 0.378520i
\(708\) 1.96548e24 1.99837e23i 1.17000 0.118958i
\(709\) 2.79760e24i 1.64548i 0.568418 + 0.822740i \(0.307556\pi\)
−0.568418 + 0.822740i \(0.692444\pi\)
\(710\) −2.32660e23 + 1.17972e22i −0.135215 + 0.00685620i
\(711\) 8.91536e23 0.511973
\(712\) −3.22225e23 2.10373e24i −0.182844 1.19374i
\(713\) 4.46385e24 2.50293
\(714\) 1.42121e24 7.20636e22i 0.787449 0.0399283i
\(715\) 1.11134e22i 0.00608479i
\(716\) 4.58655e22 + 4.51107e23i 0.0248156 + 0.244072i
\(717\) 8.65688e22i 0.0462859i
\(718\) 1.44910e23 + 2.85786e24i 0.0765670 + 1.51002i
\(719\) 1.18105e24 0.616699 0.308349 0.951273i \(-0.400223\pi\)
0.308349 + 0.951273i \(0.400223\pi\)
\(720\) −2.03008e22 9.88017e22i −0.0104758 0.0509845i
\(721\) −1.82164e24 −0.928994
\(722\) −1.26753e23 2.49976e24i −0.0638838 1.25989i
\(723\) 2.07862e23i 0.103538i
\(724\) −2.36275e23 2.32387e24i −0.116316 1.14402i
\(725\) 2.22392e24i 1.08205i
\(726\) −2.90419e23 + 1.47259e22i −0.139657 + 0.00708145i
\(727\) 2.11470e24 1.00509 0.502547 0.864550i \(-0.332396\pi\)
0.502547 + 0.864550i \(0.332396\pi\)
\(728\) 1.19513e23 1.83057e22i 0.0561434 0.00859942i
\(729\) −4.04830e23 −0.187970
\(730\) 5.72381e22 2.90231e21i 0.0262689 0.00133199i
\(731\) 2.81385e23i 0.127645i
\(732\) −7.45825e23 + 7.58304e22i −0.334420 + 0.0340016i
\(733\) 1.52276e24i 0.674912i −0.941341 0.337456i \(-0.890434\pi\)
0.941341 0.337456i \(-0.109566\pi\)
\(734\) 9.36314e21 + 1.84656e23i 0.00410209 + 0.0808996i
\(735\) 1.91207e22 0.00828061
\(736\) −9.22843e23 3.56484e24i −0.395063 1.52609i
\(737\) −1.47252e24 −0.623143
\(738\) 1.00341e23 + 1.97889e24i 0.0419760 + 0.827832i
\(739\) 2.35464e24i 0.973750i −0.873472 0.486875i \(-0.838137\pi\)
0.873472 0.486875i \(-0.161863\pi\)
\(740\) −2.76721e23 + 2.81351e22i −0.113129 + 0.0115021i
\(741\) 2.64719e23i 0.106987i
\(742\) −1.51782e24 + 7.69623e22i −0.606438 + 0.0307500i
\(743\) 1.71431e24 0.677150 0.338575 0.940939i \(-0.390055\pi\)
0.338575 + 0.940939i \(0.390055\pi\)
\(744\) −4.87581e24 + 7.46822e23i −1.90405 + 0.291640i
\(745\) −8.91841e22 −0.0344318
\(746\) 1.13173e24 5.73852e22i 0.431978 0.0219038i
\(747\) 1.86168e24i 0.702554i
\(748\) −1.71106e23 1.68290e24i −0.0638412 0.627906i
\(749\) 9.05354e23i 0.333982i
\(750\) −3.69372e22 7.28460e23i −0.0134724 0.265696i
\(751\) −3.84431e23 −0.138637 −0.0693184 0.997595i \(-0.522082\pi\)
−0.0693184 + 0.997595i \(0.522082\pi\)
\(752\) −1.25040e24 + 2.56920e23i −0.445858 + 0.0916106i
\(753\) −8.97716e22 −0.0316506
\(754\) 9.33093e21 + 1.84021e23i 0.00325288 + 0.0641520i
\(755\) 2.40843e23i 0.0830203i
\(756\) 1.84181e23 + 1.81150e24i 0.0627782 + 0.617451i
\(757\) 1.62822e24i 0.548781i 0.961618 + 0.274390i \(0.0884760\pi\)
−0.961618 + 0.274390i \(0.911524\pi\)
\(758\) −4.75685e24 + 2.41200e23i −1.58537 + 0.0803876i
\(759\) 5.45827e24 1.79887
\(760\) −7.70698e22 5.03169e23i −0.0251170 0.163983i
\(761\) 2.88866e24 0.930950 0.465475 0.885061i \(-0.345884\pi\)
0.465475 + 0.885061i \(0.345884\pi\)
\(762\) 4.46911e24 2.26610e23i 1.42431 0.0722207i
\(763\) 5.36496e24i 1.69086i
\(764\) −7.98912e23 + 8.12280e22i −0.249004 + 0.0253170i
\(765\) 1.13308e23i 0.0349252i
\(766\) 6.05768e22 + 1.19467e24i 0.0184655 + 0.364169i
\(767\) 1.88562e23 0.0568453