Properties

Label 13.7.f.a.6.6
Level 13
Weight 7
Character 13.6
Analytic conductor 2.991
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 13.f (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.99070308706\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 6.6
Character \(\chi\) = 13.6
Dual form 13.7.f.a.11.6

$q$-expansion

\(f(q)\) \(=\) \(q+(3.63541 + 13.5675i) q^{2} +(-6.58210 + 11.4005i) q^{3} +(-115.436 + 66.6469i) q^{4} +(128.381 - 128.381i) q^{5} +(-178.606 - 47.8572i) q^{6} +(-92.7197 + 346.035i) q^{7} +(-688.234 - 688.234i) q^{8} +(277.852 + 481.253i) q^{9} +O(q^{10})\) \(q+(3.63541 + 13.5675i) q^{2} +(-6.58210 + 11.4005i) q^{3} +(-115.436 + 66.6469i) q^{4} +(128.381 - 128.381i) q^{5} +(-178.606 - 47.8572i) q^{6} +(-92.7197 + 346.035i) q^{7} +(-688.234 - 688.234i) q^{8} +(277.852 + 481.253i) q^{9} +(2208.54 + 1275.10i) q^{10} +(172.402 - 46.1951i) q^{11} -1754.71i q^{12} +(1152.60 - 1870.38i) q^{13} -5031.91 q^{14} +(618.597 + 2308.64i) q^{15} +(2570.22 - 4451.75i) q^{16} +(7243.48 - 4182.03i) q^{17} +(-5519.31 + 5519.31i) q^{18} +(-5546.62 - 1486.21i) q^{19} +(-6263.59 + 23376.0i) q^{20} +(-3334.69 - 3334.69i) q^{21} +(1253.51 + 2171.14i) q^{22} +(-3936.59 - 2272.79i) q^{23} +(12376.3 - 3316.21i) q^{24} -17338.6i q^{25} +(29566.6 + 8838.31i) q^{26} -16912.1 q^{27} +(-12359.0 - 46124.3i) q^{28} +(-6202.97 + 10743.9i) q^{29} +(-29073.6 + 16785.7i) q^{30} +(36960.3 - 36960.3i) q^{31} +(9573.71 + 2565.27i) q^{32} +(-608.122 + 2269.54i) q^{33} +(83072.7 + 83072.7i) q^{34} +(32520.9 + 56327.9i) q^{35} +(-64148.1 - 37035.9i) q^{36} +(-24719.7 + 6623.62i) q^{37} -80656.9i q^{38} +(13736.8 + 25451.3i) q^{39} -176713. q^{40} +(1471.75 + 5492.65i) q^{41} +(33120.5 - 57366.4i) q^{42} +(-59168.2 + 34160.8i) q^{43} +(-16822.7 + 16822.7i) q^{44} +(97455.0 + 26113.0i) q^{45} +(16525.0 - 61672.2i) q^{46} +(-34507.0 - 34507.0i) q^{47} +(33834.9 + 58603.8i) q^{48} +(-9255.96 - 5343.93i) q^{49} +(235241. - 63032.7i) q^{50} +110106. i q^{51} +(-8396.09 + 292726. i) q^{52} -135708. q^{53} +(-61482.4 - 229455. i) q^{54} +(16202.7 - 28063.9i) q^{55} +(301966. - 174340. i) q^{56} +(53452.0 - 53452.0i) q^{57} +(-168318. - 45100.6i) q^{58} +(-40909.6 + 152677. i) q^{59} +(-225272. - 225272. i) q^{60} +(-112703. - 195206. i) q^{61} +(635825. + 367094. i) q^{62} +(-192293. + 51524.7i) q^{63} -189771. i q^{64} +(-92149.9 - 388094. i) q^{65} -33002.8 q^{66} +(7432.96 + 27740.2i) q^{67} +(-557438. + 965511. i) q^{68} +(51822.0 - 29919.5i) q^{69} +(-646003. + 646003. i) q^{70} +(424297. + 113690. i) q^{71} +(139988. - 522442. i) q^{72} +(88665.0 + 88665.0i) q^{73} +(-179732. - 311305. i) q^{74} +(197669. + 114124. i) q^{75} +(739330. - 198103. i) q^{76} +63940.4i q^{77} +(-295372. + 278900. i) q^{78} +262702. q^{79} +(-241554. - 901490. i) q^{80} +(-91236.8 + 158027. i) q^{81} +(-69171.2 + 39936.0i) q^{82} +(-232822. + 232822. i) q^{83} +(607189. + 162696. i) q^{84} +(393034. - 1.46682e6i) q^{85} +(-678577. - 678577. i) q^{86} +(-81657.1 - 141434. i) q^{87} +(-150446. - 86860.2i) q^{88} +(190382. - 51012.8i) q^{89} +1.41715e6i q^{90} +(540348. + 572260. i) q^{91} +605897. q^{92} +(178091. + 664644. i) q^{93} +(342728. - 593622. i) q^{94} +(-902885. + 521281. i) q^{95} +(-92260.5 + 92260.5i) q^{96} +(21803.9 + 5842.34i) q^{97} +(38854.7 - 145008. i) q^{98} +(70133.9 + 70133.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + O(q^{10}) \) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + 4674q^{10} + 228q^{11} - 1552q^{13} - 14616q^{14} + 7486q^{15} - 2138q^{16} + 20898q^{17} - 5630q^{18} - 14036q^{19} - 14634q^{20} - 314q^{21} + 37852q^{22} + 29634q^{23} + 47154q^{24} + 510q^{26} - 107060q^{27} - 40572q^{28} + 1026q^{29} - 247734q^{30} - 118116q^{31} + 180876q^{32} + 306046q^{33} + 101898q^{34} + 104862q^{35} + 105066q^{36} - 31470q^{37} + 28510q^{39} - 275328q^{40} - 357216q^{41} - 25636q^{42} - 480486q^{43} - 797712q^{44} + 464248q^{45} + 1012050q^{46} + 140028q^{47} + 676102q^{48} + 854562q^{49} + 756714q^{50} - 771704q^{52} - 1397076q^{53} - 1271048q^{54} - 205490q^{55} - 1461108q^{56} - 1483394q^{57} + 1133806q^{58} + 1568052q^{59} + 886808q^{60} + 768676q^{61} + 3741966q^{62} + 1336264q^{63} - 946968q^{65} - 5076928q^{66} - 1489892q^{67} - 569052q^{68} - 1475766q^{69} - 2626556q^{70} + 2136948q^{71} + 4787052q^{72} + 326326q^{73} + 2159718q^{74} + 3466008q^{75} + 1522158q^{76} - 1573544q^{78} - 1734344q^{79} - 5214300q^{80} - 773072q^{81} - 3540426q^{82} - 3642132q^{83} + 2952364q^{84} + 3509916q^{85} - 132324q^{86} + 531698q^{87} + 4478052q^{88} + 632754q^{89} - 2946788q^{91} - 1656060q^{92} - 295514q^{93} + 1552210q^{94} - 2753718q^{95} - 3979208q^{96} + 2258214q^{97} + 4984308q^{98} + 4336480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.63541 + 13.5675i 0.454426 + 1.69594i 0.689770 + 0.724028i \(0.257711\pi\)
−0.235345 + 0.971912i \(0.575622\pi\)
\(3\) −6.58210 + 11.4005i −0.243782 + 0.422242i −0.961788 0.273794i \(-0.911721\pi\)
0.718007 + 0.696036i \(0.245055\pi\)
\(4\) −115.436 + 66.6469i −1.80368 + 1.04136i
\(5\) 128.381 128.381i 1.02705 1.02705i 0.0274272 0.999624i \(-0.491269\pi\)
0.999624 0.0274272i \(-0.00873146\pi\)
\(6\) −178.606 47.8572i −0.826878 0.221561i
\(7\) −92.7197 + 346.035i −0.270320 + 1.00885i 0.688593 + 0.725148i \(0.258228\pi\)
−0.958913 + 0.283700i \(0.908438\pi\)
\(8\) −688.234 688.234i −1.34421 1.34421i
\(9\) 277.852 + 481.253i 0.381141 + 0.660156i
\(10\) 2208.54 + 1275.10i 2.20854 + 1.27510i
\(11\) 172.402 46.1951i 0.129528 0.0347071i −0.193472 0.981106i \(-0.561975\pi\)
0.323001 + 0.946399i \(0.395308\pi\)
\(12\) 1754.71i 1.01546i
\(13\) 1152.60 1870.38i 0.524624 0.851334i
\(14\) −5031.91 −1.83378
\(15\) 618.597 + 2308.64i 0.183288 + 0.684040i
\(16\) 2570.22 4451.75i 0.627495 1.08685i
\(17\) 7243.48 4182.03i 1.47435 0.851216i 0.474767 0.880111i \(-0.342532\pi\)
0.999582 + 0.0288953i \(0.00919893\pi\)
\(18\) −5519.31 + 5519.31i −0.946384 + 0.946384i
\(19\) −5546.62 1486.21i −0.808663 0.216681i −0.169279 0.985568i \(-0.554144\pi\)
−0.639384 + 0.768888i \(0.720811\pi\)
\(20\) −6263.59 + 23376.0i −0.782949 + 2.92200i
\(21\) −3334.69 3334.69i −0.360079 0.360079i
\(22\) 1253.51 + 2171.14i 0.117722 + 0.203901i
\(23\) −3936.59 2272.79i −0.323546 0.186799i 0.329426 0.944181i \(-0.393145\pi\)
−0.652972 + 0.757382i \(0.726478\pi\)
\(24\) 12376.3 3316.21i 0.895274 0.239888i
\(25\) 17338.6i 1.10967i
\(26\) 29566.6 + 8838.31i 1.68221 + 0.502863i
\(27\) −16912.1 −0.859224
\(28\) −12359.0 46124.3i −0.562999 2.10114i
\(29\) −6202.97 + 10743.9i −0.254335 + 0.440521i −0.964715 0.263298i \(-0.915190\pi\)
0.710380 + 0.703818i \(0.248523\pi\)
\(30\) −29073.6 + 16785.7i −1.07680 + 0.621691i
\(31\) 36960.3 36960.3i 1.24065 1.24065i 0.280923 0.959730i \(-0.409359\pi\)
0.959730 0.280923i \(-0.0906406\pi\)
\(32\) 9573.71 + 2565.27i 0.292166 + 0.0782857i
\(33\) −608.122 + 2269.54i −0.0169219 + 0.0631533i
\(34\) 83072.7 + 83072.7i 2.11359 + 2.11359i
\(35\) 32520.9 + 56327.9i 0.758505 + 1.31377i
\(36\) −64148.1 37035.9i −1.37492 0.793809i
\(37\) −24719.7 + 6623.62i −0.488020 + 0.130765i −0.494435 0.869215i \(-0.664625\pi\)
0.00641454 + 0.999979i \(0.497958\pi\)
\(38\) 80656.9i 1.46991i
\(39\) 13736.8 + 25451.3i 0.231575 + 0.429058i
\(40\) −176713. −2.76114
\(41\) 1471.75 + 5492.65i 0.0213542 + 0.0796948i 0.975781 0.218751i \(-0.0701983\pi\)
−0.954426 + 0.298446i \(0.903532\pi\)
\(42\) 33120.5 57366.4i 0.447043 0.774301i
\(43\) −59168.2 + 34160.8i −0.744188 + 0.429657i −0.823590 0.567186i \(-0.808032\pi\)
0.0794020 + 0.996843i \(0.474699\pi\)
\(44\) −16822.7 + 16822.7i −0.197486 + 0.197486i
\(45\) 97455.0 + 26113.0i 1.06946 + 0.286562i
\(46\) 16525.0 61672.2i 0.169773 0.633601i
\(47\) −34507.0 34507.0i −0.332364 0.332364i 0.521120 0.853484i \(-0.325515\pi\)
−0.853484 + 0.521120i \(0.825515\pi\)
\(48\) 33834.9 + 58603.8i 0.305943 + 0.529910i
\(49\) −9255.96 5343.93i −0.0786744 0.0454227i
\(50\) 235241. 63032.7i 1.88193 0.504262i
\(51\) 110106.i 0.830043i
\(52\) −8396.09 + 292726.i −0.0597128 + 2.08186i
\(53\) −135708. −0.911544 −0.455772 0.890097i \(-0.650637\pi\)
−0.455772 + 0.890097i \(0.650637\pi\)
\(54\) −61482.4 229455.i −0.390454 1.45719i
\(55\) 16202.7 28063.9i 0.0973865 0.168678i
\(56\) 301966. 174340.i 1.71947 0.992734i
\(57\) 53452.0 53452.0i 0.288629 0.288629i
\(58\) −168318. 45100.6i −0.862673 0.231152i
\(59\) −40909.6 + 152677.i −0.199191 + 0.743391i 0.791951 + 0.610584i \(0.209065\pi\)
−0.991142 + 0.132806i \(0.957601\pi\)
\(60\) −225272. 225272.i −1.04292 1.04292i
\(61\) −112703. 195206.i −0.496528 0.860012i 0.503464 0.864016i \(-0.332059\pi\)
−0.999992 + 0.00400408i \(0.998725\pi\)
\(62\) 635825. + 367094.i 2.66786 + 1.54029i
\(63\) −192293. + 51524.7i −0.769026 + 0.206060i
\(64\) 189771.i 0.723918i
\(65\) −92149.9 388094.i −0.335548 1.41318i
\(66\) −33002.8 −0.114794
\(67\) 7432.96 + 27740.2i 0.0247137 + 0.0922327i 0.977181 0.212408i \(-0.0681304\pi\)
−0.952467 + 0.304640i \(0.901464\pi\)
\(68\) −557438. + 965511.i −1.77284 + 3.07065i
\(69\) 51822.0 29919.5i 0.157749 0.0910765i
\(70\) −646003. + 646003.i −1.88339 + 1.88339i
\(71\) 424297. + 113690.i 1.18548 + 0.317649i 0.797098 0.603849i \(-0.206367\pi\)
0.388383 + 0.921498i \(0.373034\pi\)
\(72\) 139988. 522442.i 0.375054 1.39972i
\(73\) 88665.0 + 88665.0i 0.227921 + 0.227921i 0.811824 0.583903i \(-0.198475\pi\)
−0.583903 + 0.811824i \(0.698475\pi\)
\(74\) −179732. 311305.i −0.443538 0.768230i
\(75\) 197669. + 114124.i 0.468548 + 0.270517i
\(76\) 739330. 198103.i 1.68422 0.451284i
\(77\) 63940.4i 0.140056i
\(78\) −295372. + 278900.i −0.622423 + 0.587713i
\(79\) 262702. 0.532821 0.266411 0.963860i \(-0.414162\pi\)
0.266411 + 0.963860i \(0.414162\pi\)
\(80\) −241554. 901490.i −0.471784 1.76072i
\(81\) −91236.8 + 158027.i −0.171678 + 0.297355i
\(82\) −69171.2 + 39936.0i −0.125454 + 0.0724308i
\(83\) −232822. + 232822.i −0.407184 + 0.407184i −0.880755 0.473572i \(-0.842965\pi\)
0.473572 + 0.880755i \(0.342965\pi\)
\(84\) 607189. + 162696.i 1.02444 + 0.274498i
\(85\) 393034. 1.46682e6i 0.639990 2.38847i
\(86\) −678577. 678577.i −1.06685 1.06685i
\(87\) −81657.1 141434.i −0.124004 0.214782i
\(88\) −150446. 86860.2i −0.220767 0.127460i
\(89\) 190382. 51012.8i 0.270058 0.0723618i −0.121249 0.992622i \(-0.538690\pi\)
0.391307 + 0.920260i \(0.372023\pi\)
\(90\) 1.41715e6i 1.94397i
\(91\) 540348. + 572260.i 0.717050 + 0.759398i
\(92\) 605897. 0.778100
\(93\) 178091. + 664644.i 0.221408 + 0.826305i
\(94\) 342728. 593622.i 0.412635 0.714705i
\(95\) −902885. + 521281.i −1.05308 + 0.607996i
\(96\) −92260.5 + 92260.5i −0.104280 + 0.104280i
\(97\) 21803.9 + 5842.34i 0.0238902 + 0.00640135i 0.270744 0.962651i \(-0.412730\pi\)
−0.246854 + 0.969053i \(0.579397\pi\)
\(98\) 38854.7 145008.i 0.0412825 0.154068i
\(99\) 70133.9 + 70133.9i 0.0722807 + 0.0722807i
\(100\) 1.15556e6 + 2.00149e6i 1.15556 + 2.00149i
\(101\) −919128. 530659.i −0.892096 0.515052i −0.0174687 0.999847i \(-0.505561\pi\)
−0.874628 + 0.484795i \(0.838894\pi\)
\(102\) −1.49387e6 + 400280.i −1.40770 + 0.377193i
\(103\) 1.36264e6i 1.24701i −0.781819 0.623505i \(-0.785708\pi\)
0.781819 0.623505i \(-0.214292\pi\)
\(104\) −2.08052e6 + 494002.i −1.84957 + 0.439166i
\(105\) −856224. −0.739639
\(106\) −493354. 1.84122e6i −0.414229 1.54592i
\(107\) −436768. + 756505.i −0.356533 + 0.617533i −0.987379 0.158375i \(-0.949375\pi\)
0.630846 + 0.775908i \(0.282708\pi\)
\(108\) 1.95226e6 1.12714e6i 1.54977 0.894760i
\(109\) 699676. 699676.i 0.540279 0.540279i −0.383332 0.923611i \(-0.625223\pi\)
0.923611 + 0.383332i \(0.125223\pi\)
\(110\) 439660. + 117807.i 0.330323 + 0.0885098i
\(111\) 87194.7 325415.i 0.0637560 0.237941i
\(112\) 1.30215e6 + 1.30215e6i 0.926844 + 0.926844i
\(113\) −162703. 281810.i −0.112762 0.195309i 0.804121 0.594465i \(-0.202636\pi\)
−0.916883 + 0.399157i \(0.869303\pi\)
\(114\) 919532. + 530892.i 0.620658 + 0.358337i
\(115\) −797168. + 213601.i −0.524151 + 0.140446i
\(116\) 1.65363e6i 1.05941i
\(117\) 1.22038e6 + 35003.4i 0.761969 + 0.0218551i
\(118\) −2.22017e6 −1.35126
\(119\) 775512. + 2.89425e6i 0.460201 + 1.71749i
\(120\) 1.16314e6 2.01462e6i 0.673115 1.16587i
\(121\) −1.50663e6 + 869852.i −0.850452 + 0.491009i
\(122\) 2.23875e6 2.23875e6i 1.23289 1.23289i
\(123\) −72306.3 19374.4i −0.0388563 0.0104115i
\(124\) −1.80325e6 + 6.72983e6i −0.945783 + 3.52971i
\(125\) −219989. 219989.i −0.112634 0.112634i
\(126\) −1.39812e6 2.42162e6i −0.698931 1.21058i
\(127\) 1.49232e6 + 861593.i 0.728537 + 0.420621i 0.817887 0.575379i \(-0.195146\pi\)
−0.0893499 + 0.996000i \(0.528479\pi\)
\(128\) 3.18744e6 854071.i 1.51989 0.407253i
\(129\) 899398.i 0.418970i
\(130\) 4.93048e6 2.66113e6i 2.24419 1.21125i
\(131\) −188031. −0.0836405 −0.0418202 0.999125i \(-0.513316\pi\)
−0.0418202 + 0.999125i \(0.513316\pi\)
\(132\) −81058.9 302516.i −0.0352435 0.131530i
\(133\) 1.02856e6 1.78152e6i 0.437195 0.757244i
\(134\) −349344. + 201694.i −0.145191 + 0.0838258i
\(135\) −2.17120e6 + 2.17120e6i −0.882467 + 0.882467i
\(136\) −7.86342e6 2.10700e6i −3.12604 0.837621i
\(137\) −391825. + 1.46231e6i −0.152381 + 0.568694i 0.846934 + 0.531697i \(0.178446\pi\)
−0.999315 + 0.0369962i \(0.988221\pi\)
\(138\) 594327. + 594327.i 0.226146 + 0.226146i
\(139\) −850478. 1.47307e6i −0.316678 0.548503i 0.663114 0.748518i \(-0.269234\pi\)
−0.979793 + 0.200015i \(0.935901\pi\)
\(140\) −7.50816e6 4.33484e6i −2.73621 1.57975i
\(141\) 620528. 166270.i 0.221362 0.0593139i
\(142\) 6.16996e6i 2.15485i
\(143\) 112308. 375703.i 0.0384064 0.128480i
\(144\) 2.85656e6 0.956656
\(145\) 582965. + 2.17566e6i 0.191222 + 0.713652i
\(146\) −880631. + 1.52530e6i −0.282967 + 0.490113i
\(147\) 121847. 70348.6i 0.0383587 0.0221464i
\(148\) 2.41209e6 2.41209e6i 0.744062 0.744062i
\(149\) 2.52830e6 + 677457.i 0.764311 + 0.204797i 0.619857 0.784715i \(-0.287191\pi\)
0.144454 + 0.989511i \(0.453857\pi\)
\(150\) −829776. + 3.09676e6i −0.245859 + 0.917560i
\(151\) 3.20234e6 + 3.20234e6i 0.930116 + 0.930116i 0.997713 0.0675968i \(-0.0215331\pi\)
−0.0675968 + 0.997713i \(0.521533\pi\)
\(152\) 2.79451e6 + 4.84024e6i 0.795747 + 1.37827i
\(153\) 4.02523e6 + 2.32397e6i 1.12387 + 0.648867i
\(154\) −867513. + 232449.i −0.237527 + 0.0636453i
\(155\) 9.49003e6i 2.54843i
\(156\) −3.28197e6 2.02247e6i −0.864492 0.532732i
\(157\) −6.85806e6 −1.77216 −0.886079 0.463535i \(-0.846581\pi\)
−0.886079 + 0.463535i \(0.846581\pi\)
\(158\) 955027. + 3.56421e6i 0.242128 + 0.903633i
\(159\) 893244. 1.54714e6i 0.222218 0.384892i
\(160\) 1.55842e6 899753.i 0.380473 0.219666i
\(161\) 1.15146e6 1.15146e6i 0.275913 0.275913i
\(162\) −2.47571e6 663365.i −0.582311 0.156030i
\(163\) 1.67160e6 6.23850e6i 0.385985 1.44051i −0.450624 0.892714i \(-0.648799\pi\)
0.836609 0.547801i \(-0.184535\pi\)
\(164\) −535961. 535961.i −0.121507 0.121507i
\(165\) 213295. + 369438.i 0.0474821 + 0.0822413i
\(166\) −4.00523e6 2.31242e6i −0.875594 0.505525i
\(167\) −6.94845e6 + 1.86183e6i −1.49190 + 0.399752i −0.910377 0.413780i \(-0.864208\pi\)
−0.581519 + 0.813533i \(0.697541\pi\)
\(168\) 4.59010e6i 0.968041i
\(169\) −2.16984e6 4.31160e6i −0.449539 0.893260i
\(170\) 2.13300e7 4.34154
\(171\) −825894. 3.08228e6i −0.165172 0.616429i
\(172\) 4.55342e6 7.88675e6i 0.894854 1.54993i
\(173\) −3.34422e6 + 1.93079e6i −0.645887 + 0.372903i −0.786879 0.617108i \(-0.788304\pi\)
0.140992 + 0.990011i \(0.454971\pi\)
\(174\) 1.62206e6 1.62206e6i 0.307906 0.307906i
\(175\) 5.99974e6 + 1.60763e6i 1.11949 + 0.299965i
\(176\) 237463. 886224.i 0.0435570 0.162557i
\(177\) −1.47133e6 1.47133e6i −0.265332 0.265332i
\(178\) 1.38423e6 + 2.39756e6i 0.245442 + 0.425119i
\(179\) −1.03754e6 599021.i −0.180902 0.104444i 0.406814 0.913511i \(-0.366640\pi\)
−0.587717 + 0.809067i \(0.699973\pi\)
\(180\) −1.29901e7 + 3.48070e6i −2.22739 + 0.596828i
\(181\) 9.84528e6i 1.66032i 0.557524 + 0.830161i \(0.311752\pi\)
−0.557524 + 0.830161i \(0.688248\pi\)
\(182\) −5.79977e6 + 9.41158e6i −0.962047 + 1.56116i
\(183\) 2.96728e6 0.484178
\(184\) 1.14508e6 + 4.27350e6i 0.183816 + 0.686010i
\(185\) −2.32320e6 + 4.02390e6i −0.366920 + 0.635523i
\(186\) −8.37014e6 + 4.83250e6i −1.30075 + 0.750988i
\(187\) 1.05560e6 1.05560e6i 0.161427 0.161427i
\(188\) 6.28314e6 + 1.68356e6i 0.945590 + 0.253370i
\(189\) 1.56808e6 5.85217e6i 0.232265 0.866826i
\(190\) −1.03548e7 1.03548e7i −1.50967 1.50967i
\(191\) −4.32966e6 7.49919e6i −0.621375 1.07625i −0.989230 0.146370i \(-0.953241\pi\)
0.367855 0.929883i \(-0.380092\pi\)
\(192\) 2.16349e6 + 1.24909e6i 0.305669 + 0.176478i
\(193\) 1.95142e6 522881.i 0.271443 0.0727329i −0.120530 0.992710i \(-0.538459\pi\)
0.391973 + 0.919977i \(0.371793\pi\)
\(194\) 317064.i 0.0434252i
\(195\) 5.03102e6 + 1.50392e6i 0.678504 + 0.202825i
\(196\) 1.42463e6 0.189205
\(197\) 3.78147e6 + 1.41127e7i 0.494609 + 1.84591i 0.532207 + 0.846615i \(0.321363\pi\)
−0.0375972 + 0.999293i \(0.511970\pi\)
\(198\) −696578. + 1.20651e6i −0.0897375 + 0.155430i
\(199\) 6.10969e6 3.52743e6i 0.775283 0.447610i −0.0594732 0.998230i \(-0.518942\pi\)
0.834756 + 0.550620i \(0.185609\pi\)
\(200\) −1.19330e7 + 1.19330e7i −1.49162 + 1.49162i
\(201\) −365177. 97849.0i −0.0449693 0.0120495i
\(202\) 3.85832e6 1.43994e7i 0.468106 1.74699i
\(203\) −3.14261e6 3.14261e6i −0.375666 0.375666i
\(204\) −7.33823e6 1.27102e7i −0.864372 1.49714i
\(205\) 894099. + 516208.i 0.103782 + 0.0599188i
\(206\) 1.84877e7 4.95376e6i 2.11485 0.566674i
\(207\) 2.52599e6i 0.284788i
\(208\) −5.36404e6 9.93837e6i −0.596076 1.10440i
\(209\) −1.02491e6 −0.112265
\(210\) −3.11272e6 1.16168e7i −0.336111 1.25438i
\(211\) −8.13404e6 + 1.40886e7i −0.865882 + 1.49975i 0.000286127 1.00000i \(0.499909\pi\)
−0.866168 + 0.499752i \(0.833424\pi\)
\(212\) 1.56656e7 9.04452e6i 1.64414 0.949244i
\(213\) −4.08889e6 + 4.08889e6i −0.423123 + 0.423123i
\(214\) −1.18517e7 3.17566e6i −1.20932 0.324036i
\(215\) −3.21049e6 + 1.19817e7i −0.323039 + 1.20560i
\(216\) 1.16395e7 + 1.16395e7i 1.15498 + 1.15498i
\(217\) 9.36259e6 + 1.62165e7i 0.916256 + 1.58700i
\(218\) 1.20365e7 + 6.94927e6i 1.16180 + 0.670764i
\(219\) −1.59443e6 + 427226.i −0.151801 + 0.0406748i
\(220\) 4.31943e6i 0.405657i
\(221\) 526846. 1.83683e7i 0.0488098 1.70173i
\(222\) 4.73206e6 0.432505
\(223\) −792954. 2.95934e6i −0.0715045 0.266858i 0.920913 0.389767i \(-0.127444\pi\)
−0.992418 + 0.122909i \(0.960778\pi\)
\(224\) −1.77534e6 + 3.07498e6i −0.157957 + 0.273589i
\(225\) 8.34424e6 4.81755e6i 0.732553 0.422940i
\(226\) 3.23198e6 3.23198e6i 0.279990 0.279990i
\(227\) −9.95477e6 2.66737e6i −0.851047 0.228037i −0.193173 0.981165i \(-0.561878\pi\)
−0.657875 + 0.753127i \(0.728544\pi\)
\(228\) −2.60787e6 + 9.73269e6i −0.220030 + 0.821161i
\(229\) 4.65694e6 + 4.65694e6i 0.387788 + 0.387788i 0.873898 0.486110i \(-0.161585\pi\)
−0.486110 + 0.873898i \(0.661585\pi\)
\(230\) −5.79606e6 1.00391e7i −0.476375 0.825106i
\(231\) −728955. 420862.i −0.0591377 0.0341432i
\(232\) 1.16634e7 3.12519e6i 0.934030 0.250272i
\(233\) 3.83979e6i 0.303557i −0.988415 0.151778i \(-0.951500\pi\)
0.988415 0.151778i \(-0.0485000\pi\)
\(234\) 3.96166e6 + 1.66848e7i 0.309193 + 1.30218i
\(235\) −8.86012e6 −0.682710
\(236\) −5.45300e6 2.03509e7i −0.414858 1.54827i
\(237\) −1.72913e6 + 2.99494e6i −0.129892 + 0.224979i
\(238\) −3.64485e7 + 2.10436e7i −2.70364 + 1.56095i
\(239\) −222716. + 222716.i −0.0163139 + 0.0163139i −0.715217 0.698903i \(-0.753672\pi\)
0.698903 + 0.715217i \(0.253672\pi\)
\(240\) 1.18674e7 + 3.17986e6i 0.858464 + 0.230025i
\(241\) 2.02661e6 7.56342e6i 0.144784 0.540340i −0.854981 0.518659i \(-0.826432\pi\)
0.999765 0.0216810i \(-0.00690181\pi\)
\(242\) −1.72789e7 1.72789e7i −1.21919 1.21919i
\(243\) −7.36552e6 1.27575e7i −0.513316 0.889089i
\(244\) 2.60198e7 + 1.50225e7i 1.79116 + 1.03413i
\(245\) −1.87435e6 + 502232.i −0.127454 + 0.0341512i
\(246\) 1.05145e6i 0.0706292i
\(247\) −9.17281e6 + 8.66129e6i −0.608712 + 0.574767i
\(248\) −5.08747e7 −3.33539
\(249\) −1.12184e6 4.18676e6i −0.0726662 0.271194i
\(250\) 2.18496e6 3.78445e6i 0.139837 0.242205i
\(251\) 2.09246e7 1.20808e7i 1.32323 0.763968i 0.338989 0.940790i \(-0.389915\pi\)
0.984243 + 0.176822i \(0.0565819\pi\)
\(252\) 1.87635e7 1.87635e7i 1.17250 1.17250i
\(253\) −783669. 209983.i −0.0483917 0.0129665i
\(254\) −6.26448e6 + 2.33794e7i −0.382282 + 1.42670i
\(255\) 1.41356e7 + 1.41356e7i 0.852497 + 0.852497i
\(256\) 1.71026e7 + 2.96226e7i 1.01939 + 1.76564i
\(257\) −2.22130e7 1.28247e7i −1.30860 0.755522i −0.326739 0.945115i \(-0.605950\pi\)
−0.981863 + 0.189593i \(0.939283\pi\)
\(258\) 1.22026e7 3.26968e6i 0.710548 0.190391i
\(259\) 9.16800e6i 0.527686i
\(260\) 3.65027e7 + 3.86585e7i 2.07685 + 2.19950i
\(261\) −6.89402e6 −0.387749
\(262\) −683571. 2.55112e6i −0.0380084 0.141849i
\(263\) 1.04306e7 1.80664e7i 0.573381 0.993125i −0.422835 0.906207i \(-0.638965\pi\)
0.996215 0.0869179i \(-0.0277018\pi\)
\(264\) 1.98051e6 1.14345e6i 0.107638 0.0621447i
\(265\) −1.74224e7 + 1.74224e7i −0.936202 + 0.936202i
\(266\) 2.79101e7 + 7.47848e6i 1.48291 + 0.397346i
\(267\) −671543. + 2.50623e6i −0.0352809 + 0.131670i
\(268\) −2.70683e6 2.70683e6i −0.140623 0.140623i
\(269\) 6.15223e6 + 1.06560e7i 0.316064 + 0.547440i 0.979663 0.200649i \(-0.0643051\pi\)
−0.663599 + 0.748089i \(0.730972\pi\)
\(270\) −3.73510e7 2.15646e7i −1.89763 1.09560i
\(271\) 6.95314e6 1.86309e6i 0.349360 0.0936107i −0.0798717 0.996805i \(-0.525451\pi\)
0.429232 + 0.903194i \(0.358784\pi\)
\(272\) 4.29949e7i 2.13654i
\(273\) −1.00807e7 + 2.39358e6i −0.495453 + 0.117641i
\(274\) −2.12644e7 −1.03372
\(275\) −800956. 2.98921e6i −0.0385133 0.143734i
\(276\) −3.98808e6 + 6.90756e6i −0.189687 + 0.328547i
\(277\) 8.15528e6 4.70845e6i 0.383707 0.221533i −0.295723 0.955274i \(-0.595561\pi\)
0.679430 + 0.733741i \(0.262227\pi\)
\(278\) 1.68941e7 1.68941e7i 0.786322 0.786322i
\(279\) 2.80568e7 + 7.51779e6i 1.29189 + 0.346160i
\(280\) 1.63848e7 6.11488e7i 0.746391 2.78557i
\(281\) 2.53631e7 + 2.53631e7i 1.14310 + 1.14310i 0.987880 + 0.155217i \(0.0496078\pi\)
0.155217 + 0.987880i \(0.450392\pi\)
\(282\) 4.51174e6 + 7.81457e6i 0.201186 + 0.348464i
\(283\) −3.22048e6 1.85935e6i −0.142089 0.0820354i 0.427270 0.904124i \(-0.359475\pi\)
−0.569359 + 0.822089i \(0.692809\pi\)
\(284\) −5.65561e7 + 1.51542e7i −2.46902 + 0.661572i
\(285\) 1.37245e7i 0.592873i
\(286\) 5.50564e6 + 157915.i 0.235348 + 0.00675034i
\(287\) −2.03711e6 −0.0861723
\(288\) 1.42553e6 + 5.32014e6i 0.0596758 + 0.222713i
\(289\) 2.29099e7 3.96811e7i 0.949138 1.64396i
\(290\) −2.73989e7 + 1.58188e7i −1.12341 + 0.648604i
\(291\) −210121. + 210121.i −0.00852690 + 0.00852690i
\(292\) −1.61444e7 4.32587e6i −0.648444 0.173750i
\(293\) −2.11721e6 + 7.90154e6i −0.0841708 + 0.314130i −0.995156 0.0983096i \(-0.968656\pi\)
0.910985 + 0.412439i \(0.135323\pi\)
\(294\) 1.39742e6 + 1.39742e6i 0.0549902 + 0.0549902i
\(295\) 1.43488e7 + 2.48529e7i 0.558921 + 0.968079i
\(296\) 2.15715e7 + 1.24543e7i 0.831775 + 0.480225i
\(297\) −2.91569e6 + 781256.i −0.111294 + 0.0298211i
\(298\) 3.67656e7i 1.38929i
\(299\) −8.78829e6 + 4.74330e6i −0.328769 + 0.177446i
\(300\) −3.04241e7 −1.12682
\(301\) −6.33475e6 2.36416e7i −0.232290 0.866917i
\(302\) −3.18060e7 + 5.50897e7i −1.15475 + 2.00009i
\(303\) 1.20996e7 6.98570e6i 0.434953 0.251120i
\(304\) −2.08723e7 + 2.08723e7i −0.742932 + 0.742932i
\(305\) −3.95298e7 1.05920e7i −1.39324 0.373317i
\(306\) −1.68971e7 + 6.30609e7i −0.589724 + 2.20088i
\(307\) −6.59035e6 6.59035e6i −0.227768 0.227768i 0.583991 0.811760i \(-0.301490\pi\)
−0.811760 + 0.583991i \(0.801490\pi\)
\(308\) −4.26143e6 7.38101e6i −0.145849 0.252618i
\(309\) 1.55348e7 + 8.96905e6i 0.526540 + 0.303998i
\(310\) 1.28756e8 3.45001e7i 4.32198 1.15807i
\(311\) 2.98395e7i 0.991997i 0.868323 + 0.495998i \(0.165198\pi\)
−0.868323 + 0.495998i \(0.834802\pi\)
\(312\) 8.06229e6 2.69706e7i 0.265457 0.888028i
\(313\) 2.98519e7 0.973507 0.486753 0.873540i \(-0.338181\pi\)
0.486753 + 0.873540i \(0.338181\pi\)
\(314\) −2.49318e7 9.30469e7i −0.805314 3.00547i
\(315\) −1.80720e7 + 3.13016e7i −0.578195 + 1.00146i
\(316\) −3.03252e7 + 1.75082e7i −0.961041 + 0.554857i
\(317\) −296518. + 296518.i −0.00930837 + 0.00930837i −0.711746 0.702437i \(-0.752095\pi\)
0.702437 + 0.711746i \(0.252095\pi\)
\(318\) 2.42382e7 + 6.49461e6i 0.753736 + 0.201963i
\(319\) −573093. + 2.13881e6i −0.0176544 + 0.0658872i
\(320\) −2.43630e7 2.43630e7i −0.743501 0.743501i
\(321\) −5.74971e6 9.95878e6i −0.173832 0.301086i
\(322\) 1.98085e7 + 1.14365e7i 0.593314 + 0.342550i
\(323\) −4.63922e7 + 1.24308e7i −1.37669 + 0.368884i
\(324\) 2.43226e7i 0.715113i
\(325\) −3.24297e7 1.99844e7i −0.944698 0.582158i
\(326\) 9.07180e7 2.61843
\(327\) 3.37135e6 + 1.25820e7i 0.0964184 + 0.359838i
\(328\) 2.76732e6 4.79314e6i 0.0784219 0.135831i
\(329\) 1.51401e7 8.74115e6i 0.425149 0.245460i
\(330\) −4.23695e6 + 4.23695e6i −0.117899 + 0.117899i
\(331\) −4.93010e7 1.32102e7i −1.35948 0.364271i −0.495852 0.868407i \(-0.665144\pi\)
−0.863624 + 0.504136i \(0.831811\pi\)
\(332\) 1.13592e7 4.23930e7i 0.310407 1.15846i
\(333\) −1.00560e7 1.00560e7i −0.272329 0.272329i
\(334\) −5.05209e7 8.75047e7i −1.35591 2.34851i
\(335\) 4.51558e6 + 2.60707e6i 0.120110 + 0.0693455i
\(336\) −2.34161e7 + 6.27432e6i −0.617300 + 0.165405i
\(337\) 1.32265e7i 0.345586i −0.984958 0.172793i \(-0.944721\pi\)
0.984958 0.172793i \(-0.0552792\pi\)
\(338\) 5.06094e7 4.51138e7i 1.31063 1.16831i
\(339\) 4.28372e6 0.109957
\(340\) 5.23890e7 + 1.95518e8i 1.33292 + 4.97451i
\(341\) 4.66466e6 8.07943e6i 0.117641 0.203759i
\(342\) 3.88164e7 2.24107e7i 0.970369 0.560243i
\(343\) −2.70948e7 + 2.70948e7i −0.671436 + 0.671436i
\(344\) 6.42322e7 + 1.72110e7i 1.57789 + 0.422795i
\(345\) 2.81188e6 1.04941e7i 0.0684762 0.255557i
\(346\) −3.83536e7 3.83536e7i −0.925929 0.925929i
\(347\) 1.51753e7 + 2.62844e7i 0.363202 + 0.629085i 0.988486 0.151313i \(-0.0483500\pi\)
−0.625284 + 0.780398i \(0.715017\pi\)
\(348\) 1.88523e7 + 1.08844e7i 0.447329 + 0.258266i
\(349\) 2.90453e7 7.78267e6i 0.683282 0.183085i 0.0995515 0.995032i \(-0.468259\pi\)
0.583730 + 0.811948i \(0.301593\pi\)
\(350\) 8.72460e7i 2.03489i
\(351\) −1.94929e7 + 3.16321e7i −0.450769 + 0.731487i
\(352\) 1.76903e6 0.0405609
\(353\) 229504. + 856522.i 0.00521755 + 0.0194722i 0.968486 0.249070i \(-0.0801249\pi\)
−0.963268 + 0.268542i \(0.913458\pi\)
\(354\) 1.46134e7 2.53111e7i 0.329413 0.570560i
\(355\) 6.90675e7 3.98761e7i 1.54379 0.891308i
\(356\) −1.85771e7 + 1.85771e7i −0.411745 + 0.411745i
\(357\) −3.81005e7 1.02090e7i −0.837387 0.224377i
\(358\) 4.35537e6 1.62545e7i 0.0949241 0.354261i
\(359\) 4.71740e7 + 4.71740e7i 1.01957 + 1.01957i 0.999805 + 0.0197704i \(0.00629353\pi\)
0.0197704 + 0.999805i \(0.493706\pi\)
\(360\) −4.91000e7 8.50437e7i −1.05238 1.82278i
\(361\) −1.21868e7 7.03603e6i −0.259040 0.149557i
\(362\) −1.33576e8 + 3.57916e7i −2.81581 + 0.754493i
\(363\) 2.29018e7i 0.478796i
\(364\) −1.00515e8 3.00468e7i −2.08414 0.623009i
\(365\) 2.27659e7 0.468172
\(366\) 1.07873e7 + 4.02586e7i 0.220023 + 0.821137i
\(367\) −4.34550e7 + 7.52663e7i −0.879107 + 1.52266i −0.0267853 + 0.999641i \(0.508527\pi\)
−0.852322 + 0.523017i \(0.824806\pi\)
\(368\) −2.02358e7 + 1.16831e7i −0.406047 + 0.234431i
\(369\) −2.23443e6 + 2.23443e6i −0.0444720 + 0.0444720i
\(370\) −6.30401e7 1.68915e7i −1.24455 0.333475i
\(371\) 1.25828e7 4.69596e7i 0.246408 0.919609i
\(372\) −6.48545e7 6.48545e7i −1.25983 1.25983i
\(373\) 2.61530e7 + 4.52984e7i 0.503959 + 0.872883i 0.999990 + 0.00457763i \(0.00145711\pi\)
−0.496030 + 0.868305i \(0.665210\pi\)
\(374\) 1.81595e7 + 1.04844e7i 0.347127 + 0.200414i
\(375\) 3.95598e6 1.06000e6i 0.0750171 0.0201008i
\(376\) 4.74979e7i 0.893533i
\(377\) 1.29456e7 + 2.39853e7i 0.241600 + 0.447631i
\(378\) 8.51001e7 1.57563
\(379\) −1.50118e7 5.60249e7i −0.275750 1.02911i −0.955337 0.295519i \(-0.904507\pi\)
0.679587 0.733595i \(-0.262159\pi\)
\(380\) 6.94835e7 1.20349e8i 1.26628 2.19327i
\(381\) −1.96452e7 + 1.13422e7i −0.355208 + 0.205079i
\(382\) 8.60054e7 8.60054e7i 1.54289 1.54289i
\(383\) 9.45314e7 + 2.53296e7i 1.68260 + 0.450850i 0.968462 0.249159i \(-0.0801543\pi\)
0.714133 + 0.700010i \(0.246821\pi\)
\(384\) −1.12432e7 + 4.19601e7i −0.198562 + 0.741042i
\(385\) 8.20876e6 + 8.20876e6i 0.143845 + 0.143845i
\(386\) 1.41884e7 + 2.45750e7i 0.246701 + 0.427299i
\(387\) −3.28800e7 1.89833e7i −0.567281 0.327520i
\(388\) −2.90632e6 + 778747.i −0.0497564 + 0.0133322i
\(389\) 4.91172e6i 0.0834420i −0.999129 0.0417210i \(-0.986716\pi\)
0.999129 0.0417210i \(-0.0132841\pi\)
\(390\) −2.11464e6 + 7.37259e7i −0.0356485 + 1.24287i
\(391\) −3.80194e7 −0.636027
\(392\) 2.69239e6 + 1.00481e7i 0.0446972 + 0.166812i
\(393\) 1.23764e6 2.14366e6i 0.0203900 0.0353165i
\(394\) −1.77727e8 + 1.02610e8i −2.90579 + 1.67766i
\(395\) 3.37260e7 3.37260e7i 0.547234 0.547234i
\(396\) −1.27702e7 3.42176e6i −0.205642 0.0551015i
\(397\) −77340.6 + 288639.i −0.00123605 + 0.00461300i −0.966541 0.256512i \(-0.917427\pi\)
0.965305 + 0.261125i \(0.0840934\pi\)
\(398\) 7.00697e7 + 7.00697e7i 1.11143 + 1.11143i
\(399\) 1.35402e7 + 2.34523e7i 0.213160 + 0.369204i
\(400\) −7.71869e7 4.45639e7i −1.20605 0.696311i
\(401\) −5.26672e7 + 1.41121e7i −0.816784 + 0.218857i −0.642940 0.765917i \(-0.722286\pi\)
−0.173844 + 0.984773i \(0.555619\pi\)
\(402\) 5.31027e6i 0.0817408i
\(403\) −2.65294e7 1.11730e8i −0.405334 1.70709i
\(404\) 1.41467e8 2.14541
\(405\) 8.57459e6 + 3.20008e7i 0.129077 + 0.481721i
\(406\) 3.12127e7 5.40621e7i 0.466395 0.807820i
\(407\) −3.95575e6 + 2.28386e6i −0.0586740 + 0.0338755i
\(408\) 7.57788e7 7.57788e7i 1.11575 1.11575i
\(409\) 5.94135e7 + 1.59198e7i 0.868390 + 0.232684i 0.665392 0.746495i \(-0.268265\pi\)
0.202999 + 0.979179i \(0.434931\pi\)
\(410\) −3.75325e6 + 1.40073e7i −0.0544573 + 0.203238i
\(411\) −1.40921e7 1.40921e7i −0.202979 0.202979i
\(412\) 9.08159e7 + 1.57298e8i 1.29858 + 2.24921i
\(413\) −4.90383e7 2.83123e7i −0.696122 0.401906i
\(414\) 3.42715e7 9.18302e6i 0.482983 0.129415i
\(415\) 5.97801e7i 0.836397i
\(416\) 1.58327e7 1.49498e7i 0.219925 0.207661i
\(417\) 2.23917e7 0.308801
\(418\) −3.72595e6 1.39054e7i −0.0510162 0.190395i
\(419\) 2.46953e7 4.27734e7i 0.335716 0.581476i −0.647906 0.761720i \(-0.724355\pi\)
0.983622 + 0.180244i \(0.0576886\pi\)
\(420\) 9.88389e7 5.70647e7i 1.33407 0.770229i
\(421\) 2.55456e7 2.55456e7i 0.342350 0.342350i −0.514900 0.857250i \(-0.672171\pi\)
0.857250 + 0.514900i \(0.172171\pi\)
\(422\) −2.20717e8 5.91411e7i −2.93697 0.786959i
\(423\) 7.01879e6 2.61945e7i 0.0927345 0.346090i
\(424\) 9.33989e7 + 9.33989e7i 1.22530 + 1.22530i
\(425\) −7.25103e7 1.25591e8i −0.944567 1.63604i
\(426\) −7.03409e7 4.06113e7i −0.909870 0.525314i
\(427\) 7.79979e7 2.08995e7i 1.00184 0.268443i
\(428\) 1.16437e8i 1.48511i
\(429\) 3.54399e6 + 3.75329e6i 0.0448870 + 0.0475379i
\(430\) −1.74233e8 −2.19142
\(431\) −1.68152e6 6.27550e6i −0.0210024 0.0783821i 0.954629 0.297797i \(-0.0962518\pi\)
−0.975632 + 0.219415i \(0.929585\pi\)
\(432\) −4.34678e7 + 7.52885e7i −0.539159 + 0.933850i
\(433\) 3.06115e6 1.76736e6i 0.0377070 0.0217701i −0.481028 0.876705i \(-0.659736\pi\)
0.518735 + 0.854935i \(0.326403\pi\)
\(434\) −1.85981e8 + 1.85981e8i −2.27509 + 2.27509i
\(435\) −2.86408e7 7.67428e6i −0.347950 0.0932330i
\(436\) −3.41365e7 + 1.27399e8i −0.411869 + 1.53712i
\(437\) 1.84569e7 + 1.84569e7i 0.221164 + 0.221164i
\(438\) −1.15928e7 2.00793e7i −0.137964 0.238961i
\(439\) −3.27084e7 1.88842e7i −0.386603 0.223206i 0.294084 0.955780i \(-0.404985\pi\)
−0.680687 + 0.732574i \(0.738319\pi\)
\(440\) −3.04657e7 + 8.16327e6i −0.357646 + 0.0958310i
\(441\) 5.93929e6i 0.0692498i
\(442\) 2.51127e8 5.96281e7i 2.90822 0.690533i
\(443\) −1.26822e8 −1.45876 −0.729378 0.684111i \(-0.760190\pi\)
−0.729378 + 0.684111i \(0.760190\pi\)
\(444\) 1.16225e7 + 4.33758e7i 0.132786 + 0.495563i
\(445\) 1.78925e7 3.09906e7i 0.203044 0.351682i
\(446\) 3.72683e7 2.15168e7i 0.420082 0.242535i
\(447\) −2.43649e7 + 2.43649e7i −0.272799 + 0.272799i
\(448\) 6.56673e7 + 1.75955e7i 0.730323 + 0.195689i
\(449\) −4.08346e7 + 1.52397e8i −0.451117 + 1.68359i 0.248144 + 0.968723i \(0.420179\pi\)
−0.699260 + 0.714867i \(0.746487\pi\)
\(450\) 9.56969e7 + 9.56969e7i 1.05017 + 1.05017i
\(451\) 507467. + 878958.i 0.00553194 + 0.00958161i
\(452\) 3.75636e7 + 2.16874e7i 0.406773 + 0.234850i
\(453\) −5.75866e7 + 1.54303e7i −0.619479 + 0.165989i
\(454\) 1.44759e8i 1.54695i
\(455\) 1.42838e8 + 4.09694e6i 1.51639 + 0.0434936i
\(456\) −7.35750e7 −0.775954
\(457\) 1.16416e7 + 4.34469e7i 0.121973 + 0.455208i 0.999714 0.0239272i \(-0.00761699\pi\)
−0.877741 + 0.479135i \(0.840950\pi\)
\(458\) −4.62532e7 + 8.01130e7i −0.481444 + 0.833885i
\(459\) −1.22502e8 + 7.07268e7i −1.26680 + 0.731385i
\(460\) 7.77860e7 7.77860e7i 0.799149 0.799149i
\(461\) 1.04841e8 + 2.80920e7i 1.07011 + 0.286734i 0.750537 0.660829i \(-0.229795\pi\)
0.319570 + 0.947563i \(0.396462\pi\)
\(462\) 3.06001e6 1.14201e7i 0.0310311 0.115810i
\(463\) −8.26572e7 8.26572e7i −0.832795 0.832795i 0.155104 0.987898i \(-0.450429\pi\)
−0.987898 + 0.155104i \(0.950429\pi\)
\(464\) 3.18860e7 + 5.52281e7i 0.319187 + 0.552849i
\(465\) 1.08191e8 + 6.24644e7i 1.07605 + 0.621260i
\(466\) 5.20964e7 1.39592e7i 0.514814 0.137944i
\(467\) 6.08247e7i 0.597213i −0.954376 0.298607i \(-0.903478\pi\)
0.954376 0.298607i \(-0.0965219\pi\)
\(468\) −1.43208e8 + 7.72938e7i −1.39711 + 0.754063i
\(469\) −1.02882e7 −0.0997293
\(470\) −3.22102e7 1.20210e8i −0.310241 1.15784i
\(471\) 4.51405e7 7.81856e7i 0.432019 0.748280i
\(472\) 1.33233e8 7.69220e7i 1.26703 0.731517i
\(473\) −8.62267e6 + 8.62267e6i −0.0814814 + 0.0814814i
\(474\) −4.69200e7 1.25722e7i −0.440578 0.118053i
\(475\) −2.57688e7 + 9.61704e7i −0.240443 + 0.897347i
\(476\) −2.82415e8 2.82415e8i −2.61858 2.61858i
\(477\) −3.77067e7 6.53099e7i −0.347427 0.601761i
\(478\) −3.83137e6 2.21204e6i −0.0350808 0.0202539i
\(479\) 1.47442e8 3.95070e7i 1.34157 0.359474i 0.484556 0.874760i \(-0.338981\pi\)
0.857018 + 0.515287i \(0.172314\pi\)
\(480\) 2.36891e7i 0.214202i
\(481\) −1.61032e7 + 5.38696e7i −0.144703 + 0.484070i
\(482\) 1.09984e8 0.982177
\(483\) 5.54825e6 + 2.07063e7i 0.0492396 + 0.183765i
\(484\) 1.15946e8 2.00824e8i 1.02263 1.77125i
\(485\) 3.54926e6 2.04917e6i 0.0311109 0.0179619i
\(486\) 1.46310e8 1.46310e8i 1.27458 1.27458i
\(487\) −1.33041e8 3.56483e7i −1.15186 0.308640i −0.368149 0.929767i \(-0.620008\pi\)
−0.783710 + 0.621127i \(0.786675\pi\)
\(488\) −5.67820e7 + 2.11913e8i −0.488598 + 1.82347i
\(489\) 6.01196e7 + 6.01196e7i 0.514150 + 0.514150i
\(490\) −1.36281e7 2.36045e7i −0.115837 0.200635i
\(491\) 1.44179e8 + 8.32417e7i 1.21803 + 0.703228i 0.964496 0.264099i \(-0.0850746\pi\)
0.253531 + 0.967327i \(0.418408\pi\)
\(492\) 9.63799e6 2.58249e6i 0.0809266 0.0216842i
\(493\) 1.03764e8i 0.865975i
\(494\) −1.50859e8 9.29650e7i −1.25138 0.771150i
\(495\) 1.80078e7 0.148472
\(496\) −6.95420e7 2.59534e8i −0.569904 2.12691i
\(497\) −7.86813e7 + 1.36280e8i −0.640918 + 1.11010i
\(498\) 5.27256e7 3.04412e7i 0.426908 0.246475i
\(499\) 1.42588e7 1.42588e7i 0.114758 0.114758i −0.647396 0.762154i \(-0.724142\pi\)
0.762154 + 0.647396i \(0.224142\pi\)
\(500\) 4.00562e7 + 1.07330e7i 0.320450 + 0.0858642i
\(501\) 2.45095e7 9.14708e7i 0.194905 0.727394i
\(502\) 2.39976e8 + 2.39976e8i 1.89695 + 1.89695i
\(503\) 6.17833e7 + 1.07012e8i 0.485475 + 0.840867i 0.999861 0.0166916i \(-0.00531335\pi\)
−0.514386 + 0.857559i \(0.671980\pi\)
\(504\) 1.67803e8 + 9.68814e7i 1.31072 + 0.756743i
\(505\) −1.86126e8 + 4.98722e7i −1.44521 + 0.387244i
\(506\) 1.13958e7i 0.0879618i
\(507\) 6.34366e7 + 3.64203e6i 0.486762 + 0.0279460i
\(508\) −2.29690e8 −1.75207
\(509\) 3.07859e7 + 1.14894e8i 0.233452 + 0.871255i 0.978840 + 0.204625i \(0.0655975\pi\)
−0.745388 + 0.666631i \(0.767736\pi\)
\(510\) −1.40396e8 + 2.43173e8i −1.05839 + 1.83318i
\(511\) −3.89021e7 + 2.24602e7i −0.291549 + 0.168326i
\(512\) −1.90394e8 + 1.90394e8i −1.41855 + 1.41855i
\(513\) 9.38050e7 + 2.51350e7i 0.694823 + 0.186177i
\(514\) 9.32458e7 3.47998e8i 0.686657 2.56264i
\(515\) −1.74938e8 1.74938e8i −1.28074 1.28074i
\(516\) 5.99421e7 + 1.03823e8i 0.436298 + 0.755690i
\(517\) −7.54315e6 4.35504e6i −0.0545860 0.0315152i
\(518\) 1.24387e8 3.33294e7i 0.894924 0.239794i
\(519\) 5.08346e7i 0.363628i
\(520\) −2.03679e8 + 3.30520e8i −1.44856 + 2.35065i
\(521\) −8.80817e7 −0.622835 −0.311417 0.950273i \(-0.600804\pi\)
−0.311417 + 0.950273i \(0.600804\pi\)
\(522\) −2.50626e7 9.35348e7i −0.176203 0.657600i
\(523\) −2.38720e7 + 4.13476e7i −0.166872 + 0.289031i −0.937319 0.348474i \(-0.886700\pi\)
0.770446 + 0.637505i \(0.220033\pi\)
\(524\) 2.17056e7 1.25317e7i 0.150861 0.0870997i
\(525\) −5.78187e7 + 5.78187e7i −0.399568 + 0.399568i
\(526\) 2.83036e8 + 7.58391e7i 1.94484 + 0.521118i
\(527\) 1.13152e8 4.22290e8i 0.773093 2.88522i
\(528\) 8.54042e6 + 8.54042e6i 0.0580200 + 0.0580200i
\(529\) −6.36868e7 1.10309e8i −0.430212 0.745149i
\(530\) −2.99716e8 1.73041e8i −2.01318 1.16231i
\(531\) −8.48431e7 + 2.27336e7i −0.566673 + 0.151840i
\(532\) 2.74202e8i 1.82111i
\(533\) 1.19697e7 + 3.57808e6i 0.0790498 + 0.0236303i
\(534\) −3.64447e7 −0.239337
\(535\) 4.10482e7 + 1.53194e8i 0.268061 + 1.00042i
\(536\) 1.39761e7 2.42074e7i 0.0907595 0.157200i
\(537\) 1.36583e7 7.88564e6i 0.0882013 0.0509230i
\(538\) −1.22209e8 + 1.22209e8i −0.784797 + 0.784797i
\(539\) −1.84261e6 493727.i −0.0117671 0.00315297i
\(540\) 1.05930e8 3.95338e8i 0.672728 2.51066i
\(541\) 1.01013e7 + 1.01013e7i 0.0637946 + 0.0637946i 0.738284 0.674490i \(-0.235636\pi\)
−0.674490 + 0.738284i \(0.735636\pi\)
\(542\) 5.05550e7 + 8.75638e7i 0.317516 + 0.549955i
\(543\) −1.12241e8 6.48026e7i −0.701058 0.404756i
\(544\) 8.00750e7 2.14560e7i 0.497393 0.133276i
\(545\) 1.79651e8i 1.10979i
\(546\) −6.91224e7 1.28068e8i −0.424660 0.786800i
\(547\) 1.70550e8 1.04205 0.521025 0.853541i \(-0.325550\pi\)
0.521025 + 0.853541i \(0.325550\pi\)
\(548\) −5.22279e7 1.94917e8i −0.317366 1.18443i
\(549\) 6.26292e7 1.08477e8i 0.378495 0.655572i
\(550\) 3.76444e7 2.17340e7i 0.226262 0.130633i
\(551\) 5.03731e7 5.03731e7i 0.301123 0.301123i
\(552\) −5.62573e7 1.50741e7i −0.334473 0.0896219i
\(553\) −2.43576e7 + 9.09038e7i −0.144032 + 0.537535i
\(554\) 9.35298e7 + 9.35298e7i 0.550073 + 0.550073i
\(555\) −3.05830e7 5.29714e7i −0.178896 0.309858i
\(556\) 1.96351e8 + 1.13363e8i 1.14238 + 0.659551i
\(557\) 1.97060e8 5.28020e7i 1.14033 0.305552i 0.361249 0.932470i \(-0.382351\pi\)
0.779085 + 0.626918i \(0.215684\pi\)
\(558\) 4.07991e8i 2.34827i
\(559\) −4.30353e6 + 1.50041e8i −0.0246371 + 0.858961i
\(560\) 3.34344e8 1.90383
\(561\) 5.08636e6 + 1.89826e7i 0.0288084 + 0.107514i
\(562\) −2.51909e8 + 4.36320e8i −1.41917 + 2.45808i
\(563\) −2.35054e8 + 1.35708e8i −1.31717 + 0.760468i −0.983272 0.182141i \(-0.941697\pi\)
−0.333897 + 0.942609i \(0.608364\pi\)
\(564\) −6.05498e7 + 6.05498e7i −0.337501 + 0.337501i
\(565\) −5.70673e7 1.52911e7i −0.316404 0.0847802i
\(566\) 1.35190e7 5.04535e7i 0.0745580 0.278254i
\(567\) −4.62233e7 4.62233e7i −0.253578 0.253578i
\(568\) −2.13770e8 3.70261e8i −1.16655 2.02052i
\(569\) 4.89066e7 + 2.82362e7i 0.265479 + 0.153274i 0.626831 0.779155i \(-0.284351\pi\)
−0.361352 + 0.932429i \(0.617685\pi\)
\(570\) 1.86207e8 4.98941e7i 1.00548 0.269417i
\(571\) 7.93377e7i 0.426159i −0.977035 0.213079i \(-0.931651\pi\)
0.977035 0.213079i \(-0.0683493\pi\)
\(572\) 1.20750e7 + 5.08546e7i 0.0645207 + 0.271733i
\(573\) 1.13993e8 0.605919
\(574\) −7.40571e6 2.76385e7i −0.0391589 0.146143i
\(575\) −3.94069e7 + 6.82547e7i −0.207285 + 0.359029i
\(576\) 9.13279e7 5.27282e7i 0.477899 0.275915i
\(577\) 2.23051e8 2.23051e8i 1.16112 1.16112i 0.176890 0.984231i \(-0.443396\pi\)
0.984231 0.176890i \(-0.0566036\pi\)
\(578\) 6.21661e8 + 1.66573e8i 3.21936 + 0.862626i
\(579\) −6.88332e6 + 2.56889e7i −0.0354619 + 0.132346i
\(580\) −2.12296e8 2.12296e8i −1.08807 1.08807i
\(581\) −5.89774e7 1.02152e8i −0.300716 0.520856i
\(582\) −3.61470e6 2.08695e6i −0.0183360 0.0105863i
\(583\) −2.33964e7 + 6.26904e6i −0.118071 + 0.0316370i
\(584\) 1.22045e8i 0.612745i
\(585\) 1.61168e8 1.52180e8i 0.805027 0.760135i
\(586\) −1.14901e8 −0.570994
\(587\) 5.07423e6 + 1.89373e7i 0.0250874 + 0.0936275i 0.977334 0.211701i \(-0.0679003\pi\)
−0.952247 + 0.305329i \(0.901234\pi\)
\(588\) −9.37704e6 + 1.62415e7i −0.0461247 + 0.0798903i
\(589\) −2.59936e8 + 1.50074e8i −1.27210 + 0.734445i
\(590\) −2.85028e8 + 2.85028e8i −1.38782 + 1.38782i
\(591\) −1.85782e8 4.97801e7i −0.899997 0.241153i
\(592\) −3.40483e7 + 1.27070e8i −0.164108 + 0.612460i
\(593\) −1.71187e8 1.71187e8i −0.820930 0.820930i 0.165312 0.986241i \(-0.447137\pi\)
−0.986241 + 0.165312i \(0.947137\pi\)
\(594\) −2.11994e7 3.67185e7i −0.101150 0.175196i
\(595\) 4.71129e8 + 2.72007e8i 2.23660 + 1.29130i
\(596\) −3.37007e8 + 9.03008e7i −1.59184 + 0.426533i
\(597\) 9.28717e7i 0.436476i
\(598\) −9.63038e7 1.01991e8i −0.450339 0.476936i
\(599\) 5.55527e7 0.258479 0.129239 0.991613i \(-0.458746\pi\)
0.129239 + 0.991613i \(0.458746\pi\)
\(600\) −5.74983e7 2.14587e8i −0.266196 0.993457i
\(601\) −1.08379e6 + 1.87718e6i −0.00499255 + 0.00864735i −0.868511 0.495670i \(-0.834923\pi\)
0.863518 + 0.504317i \(0.168256\pi\)
\(602\) 2.97729e8 1.71894e8i 1.36468 0.787899i
\(603\) −1.12848e7 + 1.12848e7i −0.0514685 + 0.0514685i
\(604\) −5.83092e8 1.56239e8i −2.64622 0.709052i
\(605\) −8.17502e7 + 3.05096e8i −0.369167 + 1.37775i
\(606\) 1.38766e8 + 1.38766e8i 0.623539 + 0.623539i
\(607\) −3.66232e7 6.34332e7i −0.163753 0.283629i 0.772459 0.635065i \(-0.219027\pi\)
−0.936212 + 0.351436i \(0.885693\pi\)
\(608\) −4.92892e7 2.84571e7i −0.219301 0.126614i
\(609\) 5.65124e7 1.51424e7i 0.250203 0.0670416i
\(610\) 5.74827e8i 2.53249i
\(611\) −1.04314e8 + 2.47685e7i −0.457319 + 0.108587i
\(612\) −6.19541e8 −2.70281
\(613\) −1.09751e8 4.09596e8i −0.476460 1.77817i −0.615771 0.787925i \(-0.711155\pi\)
0.139310 0.990249i \(-0.455511\pi\)
\(614\) 6.54562e7 1.13373e8i 0.282778 0.489786i
\(615\) −1.17701e7 + 6.79547e6i −0.0506005 + 0.0292142i
\(616\) 4.40060e7 4.40060e7i 0.188265 0.188265i
\(617\) 3.30287e8 + 8.85000e7i 1.40616 + 0.376780i 0.880554 0.473946i \(-0.157171\pi\)
0.525609 + 0.850726i \(0.323838\pi\)
\(618\) −6.52123e7 + 2.43376e8i −0.276289 + 1.03113i
\(619\) 2.24219e8 + 2.24219e8i 0.945368 + 0.945368i 0.998583 0.0532152i \(-0.0169469\pi\)
−0.0532152 + 0.998583i \(0.516947\pi\)
\(620\) 6.32481e8 + 1.09549e9i 2.65383 + 4.59656i
\(621\) 6.65760e7 + 3.84376e7i 0.277999 + 0.160503i
\(622\) −4.04848e8 + 1.08479e8i −1.68237 + 0.450789i
\(623\) 7.06088e7i 0.292008i
\(624\) 1.48609e8 + 4.26248e6i 0.611635 + 0.0175432i
\(625\) 2.14430e8 0.878305
\(626\) 1.08524e8 + 4.05016e8i 0.442386 + 1.65101i
\(627\) 6.74604e6 1.16845e7i 0.0273682 0.0474031i
\(628\) 7.91666e8 4.57068e8i 3.19641 1.84545i
\(629\) −1.51356e8 + 1.51356e8i −0.608203 + 0.608203i
\(630\) −4.90384e8 1.31398e8i −1.96117 0.525493i
\(631\) −4.64337e7 + 1.73293e8i −0.184818 + 0.689751i 0.809851 + 0.586636i \(0.199548\pi\)
−0.994669 + 0.103116i \(0.967119\pi\)
\(632\) −1.80800e8 1.80800e8i −0.716222 0.716222i
\(633\) −1.07078e8 1.85465e8i −0.422172 0.731224i
\(634\) −5.10098e6 2.94505e6i −0.0200164 0.0115565i
\(635\) 3.02199e8 8.09739e7i 1.18024 0.316245i
\(636\) 2.38128e8i 0.925633i
\(637\) −2.06636e7 + 1.11528e7i −0.0799443 + 0.0431484i
\(638\) −3.11018e7 −0.119763
\(639\) 6.31779e7 + 2.35783e8i 0.242138 + 0.903671i
\(640\) 2.99561e8 5.18854e8i 1.14273 1.97927i
\(641\) −2.00363e8 + 1.15680e8i −0.760753 + 0.439221i −0.829566 0.558409i \(-0.811412\pi\)
0.0688132 + 0.997630i \(0.478079\pi\)
\(642\) 1.14214e8 1.14214e8i 0.431631 0.431631i
\(643\) −6.58775e7 1.76518e7i −0.247802 0.0663983i 0.132780 0.991146i \(-0.457610\pi\)
−0.380582 + 0.924747i \(0.624276\pi\)
\(644\) −5.61786e7 + 2.09661e8i −0.210336 + 0.784984i
\(645\) −1.15466e8 1.15466e8i −0.430304 0.430304i
\(646\) −3.37309e8 5.84236e8i −1.25121 2.16716i
\(647\) −3.98087e8 2.29835e8i −1.46982 0.848602i −0.470395 0.882456i \(-0.655889\pi\)
−0.999427 + 0.0338536i \(0.989222\pi\)
\(648\) 1.71552e8 4.59671e7i 0.630478 0.168936i
\(649\) 2.82117e7i 0.103204i
\(650\) 1.53244e8 5.12642e8i 0.558010 1.86670i
\(651\) −2.46502e8 −0.893466
\(652\) 2.22814e8 + 8.31554e8i 0.803896 + 3.00018i
\(653\) 9.80912e7 1.69899e8i 0.352282 0.610171i −0.634367 0.773032i \(-0.718739\pi\)
0.986649 + 0.162862i \(0.0520724\pi\)
\(654\) −1.58451e8 + 9.14816e7i −0.566449 + 0.327040i
\(655\) −2.41397e7 + 2.41397e7i −0.0859030 + 0.0859030i
\(656\) 2.82346e7 + 7.56544e6i 0.100016 + 0.0267993i
\(657\) −1.80346e7 + 6.73061e7i −0.0635932 + 0.237333i
\(658\) 1.73636e8 + 1.73636e8i 0.609484 + 0.609484i
\(659\) 1.28039e8 + 2.21770e8i 0.447389 + 0.774900i 0.998215 0.0597198i \(-0.0190207\pi\)
−0.550826 + 0.834620i \(0.685687\pi\)
\(660\) −4.92438e7 2.84309e7i −0.171285 0.0988916i
\(661\) 3.46456e7 9.28327e6i 0.119962 0.0321437i −0.198339 0.980134i \(-0.563555\pi\)
0.318301 + 0.947990i \(0.396888\pi\)
\(662\) 7.16917e8i 2.47112i
\(663\) 2.05940e8 + 1.26908e8i 0.706644 + 0.435461i
\(664\) 3.20473e8 1.09468
\(665\) −9.66660e7 3.60762e8i −0.328707 1.22675i
\(666\) 9.98778e7 1.72993e8i 0.338101 0.585608i
\(667\) 4.88370e7 2.81961e7i 0.164578 0.0950191i
\(668\) 6.78015e8 6.78015e8i 2.27463 2.27463i
\(669\) 3.89574e7 + 1.04386e7i 0.130110 + 0.0348630i
\(670\) −1.89555e7 + 7.07429e7i −0.0630247 + 0.235212i
\(671\) −2.84478e7 2.84478e7i −0.0941631 0.0941631i
\(672\) −2.33710e7 4.04797e7i −0.0770139 0.133392i
\(673\) −4.43212e8 2.55888e8i −1.45401 0.839470i −0.455300 0.890338i \(-0.650468\pi\)
−0.998705 + 0.0508680i \(0.983801\pi\)
\(674\) 1.79451e8 4.80838e7i 0.586094 0.157043i
\(675\) 2.93232e8i 0.953453i
\(676\) 5.37832e8 + 3.53100e8i 1.74103 + 1.14303i
\(677\) −3.49549e8 −1.12653 −0.563263 0.826277i \(-0.690454\pi\)
−0.563263 + 0.826277i \(0.690454\pi\)
\(678\) 1.55731e7 + 5.81195e7i 0.0499672 + 0.186480i
\(679\) −4.04330e6 + 7.00320e6i −0.0129160 + 0.0223711i
\(680\) −1.28002e9 + 7.39018e8i −4.07088 + 2.35033i
\(681\) 9.59328e7 9.59328e7i 0.303757 0.303757i
\(682\) 1.26576e8 + 3.39159e7i 0.399023 + 0.106918i
\(683\) −1.16792e7 + 4.35875e7i −0.0366566 + 0.136804i −0.981829 0.189767i \(-0.939227\pi\)
0.945173 + 0.326571i \(0.105893\pi\)
\(684\) 3.00762e8 + 3.00762e8i 0.939841 + 0.939841i
\(685\) 1.37431e8 + 2.38037e8i 0.427574 + 0.740580i
\(686\) −4.66111e8 2.69109e8i −1.44383 0.833597i
\(687\) −8.37440e7 + 2.24391e7i −0.258276 + 0.0692048i
\(688\) 3.51203e8i 1.07843i
\(689\) −1.56417e8 + 2.53826e8i −0.478218 + 0.776029i
\(690\) 1.52601e8 0.464526
\(691\) −8.90955e7 3.32509e8i −0.270036 1.00779i −0.959095 0.283083i \(-0.908643\pi\)
0.689059 0.724705i \(-0.258024\pi\)
\(692\) 2.57362e8 4.45764e8i 0.776651 1.34520i
\(693\) −3.07715e7 + 1.77660e7i −0.0924591 + 0.0533813i
\(694\) −3.01446e8 + 3.01446e8i −0.901842 + 0.901842i
\(695\) −2.98300e8 7.99293e7i −0.888586 0.238096i
\(696\) −4.11407e7 + 1.53539e8i −0.122024 + 0.455398i
\(697\) 3.36310e7 + 3.36310e7i 0.0993210 + 0.0993210i
\(698\) 2.11183e8 + 3.65780e8i 0.621002 + 1.07561i
\(699\) 4.37757e7 + 2.52739e7i 0.128174 + 0.0740015i
\(700\) −7.99728e8 + 2.14287e8i −2.33157 + 0.624742i
\(701\) 4.19234e8i 1.21703i 0.793541 + 0.608517i \(0.208235\pi\)
−0.793541 + 0.608517i \(0.791765\pi\)
\(702\) −5.00033e8 1.49474e8i −1.44540 0.432072i
\(703\) 1.46955e8 0.422978
\(704\) −8.76648e6 3.27170e7i −0.0251251 0.0937680i
\(705\) 5.83182e7 1.01010e8i 0.166432 0.288269i
\(706\) −1.07865e7 + 6.22761e6i −0.0306526 + 0.0176973i
\(707\) 2.68847e8 2.68847e8i 0.760760 0.760760i
\(708\) 2.67903e8 + 7.17844e7i 0.754880 + 0.202270i
\(709\) 7.17855e7 2.67907e8i 0.201418 0.751702i −0.789094 0.614273i \(-0.789449\pi\)
0.990512 0.137429i \(-0.0438839\pi\)
\(710\) 7.92109e8 + 7.92109e8i 2.21314 + 2.21314i
\(711\) 7.29921e7 + 1.26426e8i 0.203080 + 0.351745i
\(712\) −1.66136e8 9.59189e7i −0.460283 0.265744i
\(713\) −2.29500e8 + 6.14944e7i −0.633162 + 0.169655i
\(714\) 5.54043e8i 1.52212i
\(715\) −3.38149e7 6.26515e7i −0.0925103 0.171401i
\(716\) 1.59692e8 0.435054
\(717\) −1.07314e6 4.00502e6i −0.00291139 0.0108654i
\(718\) −4.68537e8 + 8.11531e8i −1.26582 + 2.19246i
\(719\) 4.35668e8 2.51533e8i 1.17211 0.676718i 0.217934 0.975963i \(-0.430068\pi\)
0.954176 + 0.299245i \(0.0967349\pi\)
\(720\) 3.66729e8 3.66729e8i 0.982535 0.982535i
\(721\) 4.71521e8 + 1.26344e8i 1.25804 + 0.337092i
\(722\) 5.11577e7 1.90923e8i 0.135925 0.507279i
\(723\) 7.28876e7 + 7.28876e7i 0.192859 + 0.192859i
\(724\) −6.56157e8 1.13650e9i −1.72899 2.99470i
\(725\) 1.86283e8 + 1.07551e8i 0.488831 + 0.282227i
\(726\) 3.10721e8 8.32575e7i 0.812009 0.217577i
\(727\) 5.56368e7i 0.144797i 0.997376 + 0.0723984i \(0.0230653\pi\)
−0.997376 + 0.0723984i \(0.976935\pi\)
\(728\) 2.19631e7 7.65735e8i 0.0569246 1.98465i
\(729\) 6.08993e7 0.157192
\(730\) 8.27632e7 + 3.08876e8i 0.212750 + 0.793992i
\(731\) −2.85722e8 + 4.94885e8i −0.731462 + 1.26693i
\(732\) −3.42530e8 + 1.97760e8i −0.873304 + 0.504203i
\(733\) 3.06948e8 3.06948e8i 0.779385 0.779385i −0.200341 0.979726i \(-0.564205\pi\)
0.979726 + 0.200341i \(0.0642050\pi\)
\(734\) −1.17915e9 3.15953e8i −2.98183 0.798978i
\(735\) 6.61148e6 2.46744e7i 0.0166509 0.0621419i
\(736\) −3.18574e7 3.18574e7i −0.0799056 0.0799056i
\(737\) 2.56292e6 + 4.43911e6i 0.00640225 + 0.0110890i
\(738\) −3.84387e7 2.21926e7i −0.0956312 0.0552127i
\(739\) −4.44971e8 + 1.19230e8i −1.10255 + 0.295428i −0.763803 0.645450i \(-0.776670\pi\)
−0.338748 + 0.940877i \(0.610003\pi\)
\(740\) 6.19336e8i 1.52838i
\(741\) −3.83669e7 1.61584e8i −0.0942980 0.397141i
\(742\) 6.82870e8 1.67158
\(743\) 1.03589e8 + 3.86601e8i 0.252551 + 0.942533i 0.969437 + 0.245342i \(0.0789004\pi\)
−0.716885 + 0.697191i \(0.754433\pi\)
\(744\) 3.34862e8 5.79999e8i 0.813107 1.40834i
\(745\) 4.11560e8 2.37614e8i 0.995323 0.574650i
\(746\) −5.19510e8 + 5.19510e8i −1.25134 + 1.25134i
\(747\) −1.76737e8 4.73565e7i −0.423999 0.113610i
\(748\) −5.15018e7 + 1.92207e8i −0.123060 + 0.459267i
\(749\) −2.21280e8 2.21280e8i −0.526619 0.526619i
\(750\) 2.87632e7 + 4.98193e7i 0.0681794 + 0.118090i
\(751\) −5.57597e8 3.21929e8i −1.31644 0.760047i −0.333285 0.942826i \(-0.608157\pi\)
−0.983154 + 0.182780i \(0.941491\pi\)
\(752\) −2.42307e8 + 6.49261e7i −0.569788 + 0.152674i
\(753\) 3.18069e8i 0.744965i
\(754\) −2.78358e8 + 2.62835e8i −0.649367 + 0.613155i
\(755\) 8.22243e8 1.91055
\(756\) 2.09016e8 + 7.80058e8i 0.483742 + 1.80535i
\(757\) 2.10882e8 3.65259e8i 0.486130 0.842002i −0.513743 0.857944i \(-0.671741\pi\)
0.999873 + 0.0159422i \(0.00507477\pi\)
\(758\) 7.05545e8 4.07347e8i 1.62001 0.935312i
\(759\) 7.55211e6 7.55211e6i 0.0172720 0.0172720i
\(760\) 9.80159e8 + 2.62633e8i 2.23283 + 0.598285i
\(761\) −3.35098e6 + 1.25060e7i −0.00760358 + 0.0283769i −0.969623 0.244603i \(-0.921342\pi\)
0.962020 + 0.272980i \(0.0880091\pi\)
\(762\) −2.25304e8 2.25304e8i −0.509218 0.509218i
\(763\) 1.77238e8 + 3.06986e8i 0.399011 + 0.691107i