Properties

Label 29.9.f.a.2.5
Level $29$
Weight $9$
Character 29.2
Analytic conductor $11.814$
Analytic rank $0$
Dimension $228$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 29.f (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.8139796918\)
Analytic rank: \(0\)
Dimension: \(228\)
Relative dimension: \(19\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 2.5
Character \(\chi\) \(=\) 29.2
Dual form 29.9.f.a.15.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-21.4136 - 2.41273i) q^{2} +(91.7346 + 57.6407i) q^{3} +(203.138 + 46.3649i) q^{4} +(-731.114 + 583.044i) q^{5} +(-1825.29 - 1455.62i) q^{6} +(246.757 + 1081.11i) q^{7} +(968.946 + 339.049i) q^{8} +(2246.08 + 4664.03i) q^{9} +O(q^{10})\) \(q+(-21.4136 - 2.41273i) q^{2} +(91.7346 + 57.6407i) q^{3} +(203.138 + 46.3649i) q^{4} +(-731.114 + 583.044i) q^{5} +(-1825.29 - 1455.62i) q^{6} +(246.757 + 1081.11i) q^{7} +(968.946 + 339.049i) q^{8} +(2246.08 + 4664.03i) q^{9} +(17062.5 - 10721.1i) q^{10} +(1725.95 - 603.935i) q^{11} +(15962.3 + 15962.3i) q^{12} +(-2140.33 + 4444.45i) q^{13} +(-2675.52 - 23745.9i) q^{14} +(-100676. + 11343.4i) q^{15} +(-67988.9 - 32741.7i) q^{16} +(-11256.2 + 11256.2i) q^{17} +(-36843.5 - 105293. i) q^{18} +(-124871. - 198730. i) q^{19} +(-175550. + 84540.4i) q^{20} +(-39680.0 + 113399. i) q^{21} +(-38415.8 + 8768.16i) q^{22} +(-242749. + 304398. i) q^{23} +(69342.9 + 86953.2i) q^{24} +(107665. - 471713. i) q^{25} +(56555.5 - 90007.5i) q^{26} +(16792.2 - 149034. i) q^{27} +231056. i q^{28} +(-643056. - 294492. i) q^{29} +2.18319e6 q^{30} +(505726. + 56981.6i) q^{31} +(1.15437e6 + 725339. i) q^{32} +(193140. + 44083.0i) q^{33} +(268195. - 213878. i) q^{34} +(-810745. - 646548. i) q^{35} +(240017. + 1.05158e6i) q^{36} +(-2.15384e6 - 753660. i) q^{37} +(2.19444e6 + 4.55680e6i) q^{38} +(-452524. + 284340. i) q^{39} +(-906091. + 317055. i) q^{40} +(-1.56467e6 - 1.56467e6i) q^{41} +(1.12329e6 - 2.33254e6i) q^{42} +(110419. + 979994. i) q^{43} +(378607. - 42658.8i) q^{44} +(-4.36148e6 - 2.10038e6i) q^{45} +(5.93256e6 - 5.93256e6i) q^{46} +(1.52363e6 + 4.35427e6i) q^{47} +(-4.34968e6 - 6.92247e6i) q^{48} +(4.08599e6 - 1.96771e6i) q^{49} +(-3.44362e6 + 9.84129e6i) q^{50} +(-1.68140e6 + 383770. i) q^{51} +(-640850. + 803600. i) q^{52} +(8.59706e6 + 1.07804e7i) q^{53} +(-719160. + 3.15084e6i) q^{54} +(-909744. + 1.44785e6i) q^{55} +(-127456. + 1.13120e6i) q^{56} -2.54281e7i q^{57} +(1.30596e7 + 7.85765e6i) q^{58} +9.44114e6 q^{59} +(-2.09770e7 - 2.36354e6i) q^{60} +(-1.14038e7 - 7.16550e6i) q^{61} +(-1.06919e7 - 2.44036e6i) q^{62} +(-4.48812e6 + 3.57915e6i) q^{63} +(-7.86551e6 - 6.27253e6i) q^{64} +(-1.02648e6 - 4.49731e6i) q^{65} +(-4.02946e6 - 1.40997e6i) q^{66} +(210114. + 436306. i) q^{67} +(-2.80847e6 + 1.76468e6i) q^{68} +(-3.98142e7 + 1.39316e7i) q^{69} +(1.58010e7 + 1.58010e7i) q^{70} +(3.75374e6 - 7.79473e6i) q^{71} +(594995. + 5.28073e6i) q^{72} +(-3.47680e7 + 3.91741e6i) q^{73} +(4.43029e7 + 2.13352e7i) q^{74} +(3.70665e7 - 3.70665e7i) q^{75} +(-1.61518e7 - 4.61593e7i) q^{76} +(1.07881e6 + 1.71692e6i) q^{77} +(1.03762e7 - 4.99691e6i) q^{78} +(-1.28345e7 + 3.66789e7i) q^{79} +(6.87975e7 - 1.57026e7i) q^{80} +(3.13072e7 - 3.92580e7i) q^{81} +(2.97300e7 + 3.72802e7i) q^{82} +(-2.06941e7 + 9.06670e7i) q^{83} +(-1.33182e7 + 2.11959e7i) q^{84} +(1.66671e6 - 1.47925e7i) q^{85} -2.12516e7i q^{86} +(-4.20157e7 - 6.40813e7i) q^{87} +1.87711e6 q^{88} +(-1.02040e8 - 1.14971e7i) q^{89} +(8.83272e7 + 5.54996e7i) q^{90} +(-5.33310e6 - 1.21725e6i) q^{91} +(-6.34250e7 + 5.05798e7i) q^{92} +(4.31081e7 + 3.43776e7i) q^{93} +(-2.21206e7 - 9.69166e7i) q^{94} +(2.07163e8 + 7.24895e7i) q^{95} +(6.40867e7 + 1.33077e8i) q^{96} +(8.11144e7 - 5.09675e7i) q^{97} +(-9.22431e7 + 3.22773e7i) q^{98} +(6.69339e6 + 6.69339e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 228q - 6q^{2} - 12q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 10q^{7} + 3664q^{8} - 14q^{9} + O(q^{10}) \) \( 228q - 6q^{2} - 12q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 10q^{7} + 3664q^{8} - 14q^{9} - 15884q^{10} + 8376q^{11} - 5036q^{12} - 14q^{13} - 12742q^{14} + 35516q^{15} + 245898q^{16} - 76248q^{17} + 465008q^{18} + 164474q^{19} - 907274q^{20} - 628270q^{21} + 1214962q^{22} + 173408q^{23} + 1858618q^{24} + 43976q^{25} - 4604204q^{26} - 1727586q^{27} + 1079922q^{29} + 8909208q^{30} + 3657848q^{31} + 1160364q^{32} - 4279184q^{33} - 8655374q^{34} - 8269058q^{35} - 3366854q^{36} - 5622890q^{37} + 15536626q^{38} + 16110008q^{39} - 23544696q^{40} - 9561672q^{41} - 14q^{42} + 5181008q^{43} + 51041750q^{44} - 35245194q^{45} - 43159224q^{46} - 12806808q^{47} + 83954488q^{48} + 10429400q^{49} + 80809398q^{50} + 18760882q^{51} - 93050550q^{52} - 30960322q^{53} - 106220916q^{54} - 126174004q^{55} - 40136268q^{56} + 159368354q^{58} + 11188020q^{59} + 255893612q^{60} + 139657128q^{61} + 102501616q^{62} + 9797746q^{63} - 135941792q^{64} - 14207858q^{65} - 447597656q^{66} - 148930894q^{67} - 167094904q^{68} + 66986722q^{69} + 586255934q^{70} - 15272096q^{71} + 41230600q^{72} - 219415072q^{73} - 347464696q^{74} + 391507416q^{75} + 271512490q^{76} + 240416780q^{77} + 141747906q^{78} + 112667220q^{79} - 375642638q^{80} - 358099268q^{81} - 262154910q^{82} - 109463350q^{83} - 694921012q^{84} - 356627386q^{85} + 199703522q^{87} + 251202768q^{88} + 839849154q^{89} + 675826020q^{90} + 533256766q^{91} + 742339570q^{92} + 78998570q^{93} - 209116610q^{94} - 633414122q^{95} - 431412576q^{96} - 402046736q^{97} - 2192087384q^{98} - 1966368188q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{28}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −21.4136 2.41273i −1.33835 0.150796i −0.586402 0.810020i \(-0.699456\pi\)
−0.751946 + 0.659225i \(0.770885\pi\)
\(3\) 91.7346 + 57.6407i 1.13253 + 0.711613i 0.961813 0.273708i \(-0.0882500\pi\)
0.170713 + 0.985321i \(0.445393\pi\)
\(4\) 203.138 + 46.3649i 0.793508 + 0.181113i
\(5\) −731.114 + 583.044i −1.16978 + 0.932871i −0.998628 0.0523732i \(-0.983321\pi\)
−0.171155 + 0.985244i \(0.554750\pi\)
\(6\) −1825.29 1455.62i −1.40841 1.12317i
\(7\) 246.757 + 1081.11i 0.102773 + 0.450277i 0.999963 + 0.00863196i \(0.00274767\pi\)
−0.897190 + 0.441645i \(0.854395\pi\)
\(8\) 968.946 + 339.049i 0.236559 + 0.0827756i
\(9\) 2246.08 + 4664.03i 0.342338 + 0.710872i
\(10\) 17062.5 10721.1i 1.70625 1.07211i
\(11\) 1725.95 603.935i 0.117885 0.0412496i −0.270692 0.962666i \(-0.587253\pi\)
0.388577 + 0.921416i \(0.372967\pi\)
\(12\) 15962.3 + 15962.3i 0.769786 + 0.769786i
\(13\) −2140.33 + 4444.45i −0.0749391 + 0.155613i −0.935073 0.354457i \(-0.884666\pi\)
0.860133 + 0.510069i \(0.170380\pi\)
\(14\) −2675.52 23745.9i −0.0696459 0.618124i
\(15\) −100676. + 11343.4i −1.98865 + 0.224067i
\(16\) −67988.9 32741.7i −1.03743 0.499599i
\(17\) −11256.2 + 11256.2i −0.134771 + 0.134771i −0.771274 0.636503i \(-0.780380\pi\)
0.636503 + 0.771274i \(0.280380\pi\)
\(18\) −36843.5 105293.i −0.350971 1.00302i
\(19\) −124871. 198730.i −0.958177 1.52493i −0.847313 0.531094i \(-0.821781\pi\)
−0.110863 0.993836i \(-0.535362\pi\)
\(20\) −175550. + 84540.4i −1.09719 + 0.528377i
\(21\) −39680.0 + 113399.i −0.204030 + 0.583084i
\(22\) −38415.8 + 8768.16i −0.163991 + 0.0374298i
\(23\) −242749. + 304398.i −0.867455 + 1.08775i 0.127929 + 0.991783i \(0.459167\pi\)
−0.995384 + 0.0959707i \(0.969404\pi\)
\(24\) 69342.9 + 86953.2i 0.209005 + 0.262084i
\(25\) 107665. 471713.i 0.275623 1.20759i
\(26\) 56555.5 90007.5i 0.123760 0.196963i
\(27\) 16792.2 149034.i 0.0315974 0.280435i
\(28\) 231056.i 0.375911i
\(29\) −643056. 294492.i −0.909194 0.416373i
\(30\) 2.18319e6 2.69530
\(31\) 505726. + 56981.6i 0.547606 + 0.0617004i 0.381433 0.924396i \(-0.375431\pi\)
0.166173 + 0.986097i \(0.446859\pi\)
\(32\) 1.15437e6 + 725339.i 1.10089 + 0.691737i
\(33\) 193140. + 44083.0i 0.162861 + 0.0371720i
\(34\) 268195. 213878.i 0.200694 0.160048i
\(35\) −810745. 646548.i −0.540272 0.430852i
\(36\) 240017. + 1.05158e6i 0.142900 + 0.626084i
\(37\) −2.15384e6 753660.i −1.14923 0.402132i −0.312589 0.949889i \(-0.601196\pi\)
−0.836638 + 0.547757i \(0.815482\pi\)
\(38\) 2.19444e6 + 4.55680e6i 1.05242 + 2.18537i
\(39\) −452524. + 284340.i −0.195606 + 0.122908i
\(40\) −906091. + 317055.i −0.353942 + 0.123850i
\(41\) −1.56467e6 1.56467e6i −0.553715 0.553715i 0.373796 0.927511i \(-0.378056\pi\)
−0.927511 + 0.373796i \(0.878056\pi\)
\(42\) 1.12329e6 2.33254e6i 0.360990 0.749603i
\(43\) 110419. + 979994.i 0.0322975 + 0.286649i 0.999471 + 0.0325305i \(0.0103566\pi\)
−0.967173 + 0.254118i \(0.918215\pi\)
\(44\) 378607. 42658.8i 0.101013 0.0113814i
\(45\) −4.36148e6 2.10038e6i −1.06361 0.512209i
\(46\) 5.93256e6 5.93256e6i 1.32498 1.32498i
\(47\) 1.52363e6 + 4.35427e6i 0.312239 + 0.892327i 0.987897 + 0.155112i \(0.0495739\pi\)
−0.675658 + 0.737215i \(0.736140\pi\)
\(48\) −4.34968e6 6.92247e6i −0.819393 1.30406i
\(49\) 4.08599e6 1.96771e6i 0.708782 0.341331i
\(50\) −3.44362e6 + 9.84129e6i −0.550979 + 1.57461i
\(51\) −1.68140e6 + 383770.i −0.248537 + 0.0567270i
\(52\) −640850. + 803600.i −0.0876482 + 0.109907i
\(53\) 8.59706e6 + 1.07804e7i 1.08955 + 1.36625i 0.925038 + 0.379876i \(0.124033\pi\)
0.164511 + 0.986375i \(0.447395\pi\)
\(54\) −719160. + 3.15084e6i −0.0845766 + 0.370554i
\(55\) −909744. + 1.44785e6i −0.0994188 + 0.158224i
\(56\) −127456. + 1.13120e6i −0.0129601 + 0.115024i
\(57\) 2.54281e7i 2.40887i
\(58\) 1.30596e7 + 7.85765e6i 1.15403 + 0.694354i
\(59\) 9.44114e6 0.779142 0.389571 0.920997i \(-0.372623\pi\)
0.389571 + 0.920997i \(0.372623\pi\)
\(60\) −2.09770e7 2.36354e6i −1.61859 0.182372i
\(61\) −1.14038e7 7.16550e6i −0.823628 0.517520i 0.0530531 0.998592i \(-0.483105\pi\)
−0.876681 + 0.481072i \(0.840248\pi\)
\(62\) −1.06919e7 2.44036e6i −0.723583 0.165153i
\(63\) −4.48812e6 + 3.57915e6i −0.284906 + 0.227205i
\(64\) −7.86551e6 6.27253e6i −0.468821 0.373872i
\(65\) −1.02648e6 4.49731e6i −0.0575040 0.251941i
\(66\) −4.02946e6 1.40997e6i −0.212359 0.0743078i
\(67\) 210114. + 436306.i 0.0104269 + 0.0216517i 0.906117 0.423027i \(-0.139032\pi\)
−0.895690 + 0.444678i \(0.853318\pi\)
\(68\) −2.80847e6 + 1.76468e6i −0.131351 + 0.0825333i
\(69\) −3.98142e7 + 1.39316e7i −1.75648 + 0.614617i
\(70\) 1.58010e7 + 1.58010e7i 0.658101 + 0.658101i
\(71\) 3.75374e6 7.79473e6i 0.147717 0.306738i −0.813961 0.580920i \(-0.802693\pi\)
0.961678 + 0.274182i \(0.0884071\pi\)
\(72\) 594995. + 5.28073e6i 0.0221403 + 0.196501i
\(73\) −3.47680e7 + 3.91741e6i −1.22430 + 0.137946i −0.700348 0.713802i \(-0.746972\pi\)
−0.523953 + 0.851747i \(0.675543\pi\)
\(74\) 4.43029e7 + 2.13352e7i 1.47743 + 0.711490i
\(75\) 3.70665e7 3.70665e7i 1.17148 1.17148i
\(76\) −1.61518e7 4.61593e7i −0.484136 1.38358i
\(77\) 1.07881e6 + 1.71692e6i 0.0306890 + 0.0488413i
\(78\) 1.03762e7 4.99691e6i 0.280323 0.134997i
\(79\) −1.28345e7 + 3.66789e7i −0.329511 + 0.941689i 0.653304 + 0.757096i \(0.273382\pi\)
−0.982815 + 0.184593i \(0.940903\pi\)
\(80\) 6.87975e7 1.57026e7i 1.67963 0.383364i
\(81\) 3.13072e7 3.92580e7i 0.727285 0.911986i
\(82\) 2.97300e7 + 3.72802e7i 0.657566 + 0.824561i
\(83\) −2.06941e7 + 9.06670e7i −0.436049 + 1.91046i −0.0230253 + 0.999735i \(0.507330\pi\)
−0.413024 + 0.910720i \(0.635527\pi\)
\(84\) −1.33182e7 + 2.11959e7i −0.267504 + 0.425730i
\(85\) 1.66671e6 1.47925e7i 0.0319290 0.283378i
\(86\) 2.12516e7i 0.388506i
\(87\) −4.20157e7 6.40813e7i −0.733390 1.11855i
\(88\) 1.87711e6 0.0313011
\(89\) −1.02040e8 1.14971e7i −1.62633 0.183244i −0.748812 0.662782i \(-0.769376\pi\)
−0.877521 + 0.479538i \(0.840804\pi\)
\(90\) 8.83272e7 + 5.54996e7i 1.34625 + 0.845902i
\(91\) −5.33310e6 1.21725e6i −0.0777704 0.0177506i
\(92\) −6.34250e7 + 5.05798e7i −0.885339 + 0.706034i
\(93\) 4.31081e7 + 3.43776e7i 0.576271 + 0.459561i
\(94\) −2.21206e7 9.69166e7i −0.283325 1.24133i
\(95\) 2.07163e8 + 7.24895e7i 2.54342 + 0.889981i
\(96\) 6.40867e7 + 1.33077e8i 0.754541 + 1.56682i
\(97\) 8.11144e7 5.09675e7i 0.916243 0.575714i 0.0106884 0.999943i \(-0.496598\pi\)
0.905555 + 0.424229i \(0.139455\pi\)
\(98\) −9.22431e7 + 3.22773e7i −1.00007 + 0.349939i
\(99\) 6.69339e6 + 6.69339e6i 0.0696796 + 0.0696796i
\(100\) 4.37419e7 9.08309e7i 0.437419 0.908309i
\(101\) −2.37782e6 2.11037e7i −0.0228504 0.202803i 0.977100 0.212781i \(-0.0682522\pi\)
−0.999950 + 0.00997872i \(0.996824\pi\)
\(102\) 3.69308e7 4.16110e6i 0.341183 0.0384421i
\(103\) 9.42714e7 + 4.53987e7i 0.837589 + 0.403362i 0.802956 0.596038i \(-0.203259\pi\)
0.0346331 + 0.999400i \(0.488974\pi\)
\(104\) −3.58076e6 + 3.58076e6i −0.0306085 + 0.0306085i
\(105\) −3.71059e7 1.06043e8i −0.305272 0.872416i
\(106\) −1.58084e8 2.51589e8i −1.25217 1.99282i
\(107\) −2.03209e8 + 9.78602e7i −1.55027 + 0.746571i −0.996298 0.0859648i \(-0.972603\pi\)
−0.553972 + 0.832535i \(0.686888\pi\)
\(108\) 1.03211e7 2.94960e7i 0.0758631 0.216804i
\(109\) −8.75303e7 + 1.99782e7i −0.620087 + 0.141531i −0.521012 0.853549i \(-0.674445\pi\)
−0.0990748 + 0.995080i \(0.531588\pi\)
\(110\) 2.29741e7 2.88087e7i 0.156916 0.196767i
\(111\) −1.54140e8 1.93285e8i −1.01537 1.27323i
\(112\) 1.86208e7 8.15830e7i 0.118338 0.518475i
\(113\) −1.29475e8 + 2.06058e8i −0.794095 + 1.26380i 0.166555 + 0.986032i \(0.446736\pi\)
−0.960650 + 0.277763i \(0.910407\pi\)
\(114\) −6.13510e7 + 5.44506e8i −0.363247 + 3.22391i
\(115\) 3.64084e8i 2.08166i
\(116\) −1.16975e8 8.96378e7i −0.646042 0.495062i
\(117\) −2.55364e7 −0.136275
\(118\) −2.02168e8 2.27789e7i −1.04276 0.117491i
\(119\) −1.49468e7 9.39172e6i −0.0745352 0.0468336i
\(120\) −1.01395e8 2.31428e7i −0.488981 0.111607i
\(121\) −1.64978e8 + 1.31566e8i −0.769636 + 0.613764i
\(122\) 2.26908e8 + 1.80953e8i 1.02426 + 0.816821i
\(123\) −5.33456e7 2.33722e8i −0.233066 1.02113i
\(124\) 1.00090e8 + 3.50231e7i 0.423355 + 0.148138i
\(125\) 3.78224e7 + 7.85391e7i 0.154921 + 0.321696i
\(126\) 1.04742e8 6.58138e7i 0.415565 0.261117i
\(127\) 1.95361e8 6.83599e7i 0.750973 0.262777i 0.0724659 0.997371i \(-0.476913\pi\)
0.678507 + 0.734594i \(0.262627\pi\)
\(128\) −9.34956e7 9.34956e7i −0.348298 0.348298i
\(129\) −4.63583e7 + 9.62640e7i −0.167405 + 0.347620i
\(130\) 1.11298e7 + 9.87801e7i 0.0389687 + 0.345857i
\(131\) 3.86813e8 4.35834e7i 1.31346 0.147991i 0.572700 0.819765i \(-0.305896\pi\)
0.740756 + 0.671774i \(0.234467\pi\)
\(132\) 3.71902e7 + 1.79099e7i 0.122499 + 0.0589925i
\(133\) 1.84037e8 1.84037e8i 0.588166 0.588166i
\(134\) −3.44660e6 9.84982e6i −0.0106899 0.0305499i
\(135\) 7.46167e7 + 1.18752e8i 0.224647 + 0.357524i
\(136\) −1.47231e7 + 7.09028e6i −0.0430372 + 0.0207256i
\(137\) −7.13136e7 + 2.03803e8i −0.202437 + 0.578532i −0.999684 0.0251207i \(-0.992003\pi\)
0.797247 + 0.603653i \(0.206289\pi\)
\(138\) 8.86178e8 2.02264e8i 2.44346 0.557703i
\(139\) −1.74155e8 + 2.18383e8i −0.466527 + 0.585006i −0.958317 0.285708i \(-0.907771\pi\)
0.491790 + 0.870714i \(0.336343\pi\)
\(140\) −1.34716e8 1.68929e8i −0.350677 0.439735i
\(141\) −1.11214e8 + 4.87260e8i −0.281373 + 1.23278i
\(142\) −9.91876e7 + 1.57856e8i −0.243952 + 0.388247i
\(143\) −1.00995e6 + 8.96351e6i −0.00241520 + 0.0214355i
\(144\) 3.90643e8i 0.908510i
\(145\) 6.41849e8 1.59622e8i 1.45198 0.361095i
\(146\) 7.53958e8 1.65934
\(147\) 4.88246e8 + 5.50122e7i 1.04561 + 0.117812i
\(148\) −4.02582e8 2.52959e8i −0.839089 0.527234i
\(149\) 1.64110e8 + 3.74571e7i 0.332959 + 0.0759958i 0.385732 0.922611i \(-0.373949\pi\)
−0.0527731 + 0.998607i \(0.516806\pi\)
\(150\) −8.83157e8 + 7.04294e8i −1.74451 + 1.39120i
\(151\) −5.16816e7 4.12147e7i −0.0994096 0.0792765i 0.572524 0.819888i \(-0.305964\pi\)
−0.671933 + 0.740612i \(0.734536\pi\)
\(152\) −5.36135e7 2.34896e8i −0.100438 0.440050i
\(153\) −7.77819e7 2.72171e7i −0.141943 0.0496679i
\(154\) −1.89588e7 3.93683e7i −0.0337076 0.0699945i
\(155\) −4.02966e8 + 2.53200e8i −0.698139 + 0.438670i
\(156\) −1.05108e8 + 3.67789e7i −0.177475 + 0.0621013i
\(157\) −1.36709e8 1.36709e8i −0.225008 0.225008i 0.585595 0.810604i \(-0.300861\pi\)
−0.810604 + 0.585595i \(0.800861\pi\)
\(158\) 3.63328e8 7.54459e8i 0.583003 1.21062i
\(159\) 1.67260e8 + 1.48447e9i 0.261700 + 2.32265i
\(160\) −1.26688e9 + 1.42743e8i −1.93311 + 0.217809i
\(161\) −3.88989e8 1.87327e8i −0.578941 0.278803i
\(162\) −7.65118e8 + 7.65118e8i −1.11088 + 1.11088i
\(163\) −3.18231e8 9.09451e8i −0.450808 1.28833i −0.915305 0.402760i \(-0.868051\pi\)
0.464498 0.885574i \(-0.346235\pi\)
\(164\) −2.45298e8 3.90389e8i −0.339092 0.539662i
\(165\) −1.66910e8 + 8.03797e7i −0.225189 + 0.108445i
\(166\) 6.61890e8 1.89157e9i 0.871673 2.49110i
\(167\) −6.86376e7 + 1.56661e7i −0.0882463 + 0.0201416i −0.266416 0.963858i \(-0.585840\pi\)
0.178170 + 0.984000i \(0.442982\pi\)
\(168\) −7.68955e7 + 9.64239e7i −0.0965304 + 0.121045i
\(169\) 4.93428e8 + 6.18739e8i 0.604890 + 0.758509i
\(170\) −7.13805e7 + 3.12739e8i −0.0854642 + 0.374443i
\(171\) 6.46415e8 1.02876e9i 0.756010 1.20318i
\(172\) −2.30071e7 + 2.04194e8i −0.0262874 + 0.233307i
\(173\) 9.17622e8i 1.02442i −0.858859 0.512212i \(-0.828826\pi\)
0.858859 0.512212i \(-0.171174\pi\)
\(174\) 7.45096e8 + 1.47358e9i 0.812859 + 1.60760i
\(175\) 5.36543e8 0.572074
\(176\) −1.37119e8 1.54496e7i −0.142905 0.0161015i
\(177\) 8.66079e8 + 5.44194e8i 0.882398 + 0.554448i
\(178\) 2.15730e9 + 4.92389e8i 2.14897 + 0.490488i
\(179\) −1.03522e9 + 8.25563e8i −1.00837 + 0.804152i −0.980711 0.195465i \(-0.937378\pi\)
−0.0276643 + 0.999617i \(0.508807\pi\)
\(180\) −7.88598e8 6.28886e8i −0.751218 0.599076i
\(181\) 3.18897e8 + 1.39718e9i 0.297122 + 1.30178i 0.874390 + 0.485224i \(0.161262\pi\)
−0.577268 + 0.816555i \(0.695881\pi\)
\(182\) 1.11264e8 + 3.89329e7i 0.101407 + 0.0354839i
\(183\) −6.33101e8 1.31465e9i −0.564506 1.17221i
\(184\) −3.38417e8 + 2.12642e8i −0.295244 + 0.185514i
\(185\) 2.01412e9 7.04770e8i 1.71948 0.601673i
\(186\) −8.40154e8 8.40154e8i −0.701952 0.701952i
\(187\) −1.26296e7 + 2.62257e7i −0.0103282 + 0.0214467i
\(188\) 1.07621e8 + 9.55161e8i 0.0861519 + 0.764619i
\(189\) 1.65267e8 1.86211e7i 0.129521 0.0145935i
\(190\) −4.26121e9 2.05209e9i −3.26978 1.57464i
\(191\) −3.27414e8 + 3.27414e8i −0.246016 + 0.246016i −0.819333 0.573317i \(-0.805656\pi\)
0.573317 + 0.819333i \(0.305656\pi\)
\(192\) −3.59986e8 1.02878e9i −0.264899 0.757039i
\(193\) −2.20908e7 3.51572e7i −0.0159214 0.0253388i 0.838669 0.544642i \(-0.183334\pi\)
−0.854590 + 0.519303i \(0.826192\pi\)
\(194\) −1.85992e9 + 8.95690e8i −1.31307 + 0.632340i
\(195\) 1.65064e8 4.71726e8i 0.114160 0.326251i
\(196\) 9.21252e8 2.10270e8i 0.624244 0.142480i
\(197\) 1.49913e8 1.87985e8i 0.0995348 0.124813i −0.729569 0.683907i \(-0.760280\pi\)
0.829104 + 0.559094i \(0.188851\pi\)
\(198\) −1.27180e8 1.59479e8i −0.0827481 0.103763i
\(199\) −5.90253e8 + 2.58607e9i −0.376380 + 1.64903i 0.332062 + 0.943258i \(0.392256\pi\)
−0.708442 + 0.705769i \(0.750601\pi\)
\(200\) 2.64256e8 4.20561e8i 0.165160 0.262850i
\(201\) −5.87426e6 + 5.21355e7i −0.00359889 + 0.0319411i
\(202\) 4.57643e8i 0.274866i
\(203\) 1.59701e8 7.67885e8i 0.0940425 0.452181i
\(204\) −3.59351e8 −0.207490
\(205\) 2.05622e9 + 2.31680e8i 1.16427 + 0.131182i
\(206\) −1.90915e9 1.19960e9i −1.06016 0.666143i
\(207\) −1.96496e9 4.48489e8i −1.07022 0.244270i
\(208\) 2.91038e8 2.32095e8i 0.155488 0.123997i
\(209\) −3.35540e8 2.67584e8i −0.175857 0.140241i
\(210\) 5.38718e8 + 2.36028e9i 0.277003 + 1.21363i
\(211\) −2.88675e8 1.01012e8i −0.145640 0.0509616i 0.256475 0.966551i \(-0.417439\pi\)
−0.402115 + 0.915589i \(0.631725\pi\)
\(212\) 1.24656e9 + 2.58851e9i 0.617120 + 1.28146i
\(213\) 7.93642e8 4.98678e8i 0.385573 0.242271i
\(214\) 4.58753e9 1.60525e9i 2.18738 0.765397i
\(215\) −6.52109e8 6.52109e8i −0.305187 0.305187i
\(216\) 6.68007e7 1.38713e8i 0.0306878 0.0637239i
\(217\) 6.31879e7 + 5.60808e8i 0.0284967 + 0.252915i
\(218\) 1.92254e9 2.16618e8i 0.851234 0.0959111i
\(219\) −3.41523e9 1.64469e9i −1.48472 0.715002i
\(220\) −2.51933e8 + 2.51933e8i −0.107546 + 0.107546i
\(221\) −2.59357e7 7.41200e7i −0.0108725 0.0310718i
\(222\) 2.83434e9 + 4.51082e9i 1.16692 + 1.85714i
\(223\) −3.01789e9 + 1.45334e9i −1.22035 + 0.587689i −0.929409 0.369052i \(-0.879682\pi\)
−0.290940 + 0.956741i \(0.593968\pi\)
\(224\) −4.99325e8 + 1.42699e9i −0.198331 + 0.566798i
\(225\) 2.44191e9 5.57350e8i 0.952795 0.217469i
\(226\) 3.26969e9 4.10006e9i 1.25335 1.57165i
\(227\) 3.01448e8 + 3.78004e8i 0.113530 + 0.142362i 0.835349 0.549720i \(-0.185265\pi\)
−0.721820 + 0.692081i \(0.756694\pi\)
\(228\) 1.17897e9 5.16541e9i 0.436278 1.91146i
\(229\) 1.07064e9 1.70391e9i 0.389315 0.619591i −0.593358 0.804939i \(-0.702198\pi\)
0.982673 + 0.185347i \(0.0593411\pi\)
\(230\) −8.78435e8 + 7.79633e9i −0.313905 + 2.78598i
\(231\) 2.19685e8i 0.0771528i
\(232\) −5.23239e8 5.03375e8i −0.180613 0.173756i
\(233\) 2.92256e9 0.991608 0.495804 0.868434i \(-0.334873\pi\)
0.495804 + 0.868434i \(0.334873\pi\)
\(234\) 5.46826e8 + 6.16125e7i 0.182384 + 0.0205497i
\(235\) −3.65268e9 2.29513e9i −1.19768 0.752551i
\(236\) 1.91785e9 + 4.37738e8i 0.618255 + 0.141113i
\(237\) −3.29156e9 + 2.62493e9i −1.04330 + 0.832003i
\(238\) 2.97406e8 + 2.37173e8i 0.0926918 + 0.0739192i
\(239\) −5.34538e8 2.34197e9i −0.163828 0.717776i −0.988382 0.151993i \(-0.951431\pi\)
0.824554 0.565783i \(-0.191426\pi\)
\(240\) 7.21622e9 + 2.52506e9i 2.17503 + 0.761075i
\(241\) −1.40013e9 2.90741e9i −0.415051 0.861862i −0.998754 0.0498950i \(-0.984111\pi\)
0.583704 0.811967i \(-0.301603\pi\)
\(242\) 3.85021e9 2.41925e9i 1.12259 0.705373i
\(243\) 4.20603e9 1.47175e9i 1.20628 0.422095i
\(244\) −1.98432e9 1.98432e9i −0.559826 0.559826i
\(245\) −1.84006e9 + 3.82093e9i −0.510703 + 1.06049i
\(246\) 5.78411e8 + 5.13354e9i 0.157941 + 1.40177i
\(247\) 1.15051e9 1.29632e8i 0.309103 0.0348276i
\(248\) 4.70701e8 + 2.26678e8i 0.124434 + 0.0599242i
\(249\) −7.12448e9 + 7.12448e9i −1.85334 + 1.85334i
\(250\) −6.20420e8 1.77306e9i −0.158827 0.453903i
\(251\) −2.25443e9 3.58790e9i −0.567991 0.903952i −0.999998 0.00208179i \(-0.999337\pi\)
0.432007 0.901870i \(-0.357806\pi\)
\(252\) −1.07765e9 + 5.18971e8i −0.267225 + 0.128689i
\(253\) −2.35136e8 + 6.71980e8i −0.0573901 + 0.164012i
\(254\) −4.34832e9 + 9.92476e8i −1.04469 + 0.238443i
\(255\) 1.00554e9 1.26091e9i 0.237816 0.298211i
\(256\) 3.38226e9 + 4.24122e9i 0.787494 + 0.987487i
\(257\) 5.31442e8 2.32840e9i 0.121821 0.533734i −0.876781 0.480889i \(-0.840314\pi\)
0.998603 0.0528448i \(-0.0168289\pi\)
\(258\) 1.22496e9 1.94951e9i 0.276466 0.439993i
\(259\) 2.83318e8 2.51451e9i 0.0629614 0.558798i
\(260\) 9.61168e8i 0.210332i
\(261\) −7.08321e7 3.66069e9i −0.0152640 0.788861i
\(262\) −8.38820e9 −1.78018
\(263\) −3.99939e9 4.50623e8i −0.835931 0.0941868i −0.316387 0.948630i \(-0.602470\pi\)
−0.519544 + 0.854444i \(0.673898\pi\)
\(264\) 1.72196e8 + 1.08198e8i 0.0354493 + 0.0222743i
\(265\) −1.25709e10 2.86922e9i −2.54907 0.581809i
\(266\) −4.38493e9 + 3.49687e9i −0.875863 + 0.698477i
\(267\) −8.69788e9 6.93633e9i −1.71147 1.36485i
\(268\) 2.24528e7 + 9.83723e7i 0.00435243 + 0.0190693i
\(269\) 7.62086e9 + 2.66665e9i 1.45544 + 0.509281i 0.938060 0.346474i \(-0.112621\pi\)
0.517382 + 0.855755i \(0.326907\pi\)
\(270\) −1.31129e9 2.72293e9i −0.246743 0.512367i
\(271\) 1.67219e8 1.05071e8i 0.0310034 0.0194807i −0.516441 0.856323i \(-0.672744\pi\)
0.547445 + 0.836842i \(0.315601\pi\)
\(272\) 1.13385e9 3.96750e8i 0.207147 0.0724839i
\(273\) −4.19067e8 4.19067e8i −0.0754455 0.0754455i
\(274\) 2.01880e9 4.19208e9i 0.358171 0.743751i
\(275\) −9.90592e7 8.79175e8i −0.0173206 0.153725i
\(276\) −8.73372e9 + 9.84054e8i −1.50509 + 0.169583i
\(277\) 7.47472e9 + 3.59964e9i 1.26963 + 0.611420i 0.942704 0.333631i \(-0.108274\pi\)
0.326923 + 0.945051i \(0.393988\pi\)
\(278\) 4.25618e9 4.25618e9i 0.712591 0.712591i
\(279\) 8.70136e8 + 2.48671e9i 0.143605 + 0.410400i
\(280\) −5.66357e8 9.01352e8i −0.0921422 0.146643i
\(281\) 1.82393e9 8.78359e8i 0.292539 0.140879i −0.281858 0.959456i \(-0.590951\pi\)
0.574397 + 0.818577i \(0.305237\pi\)
\(282\) 3.55712e9 1.01657e10i 0.562473 1.60746i
\(283\) 9.30412e9 2.12360e9i 1.45054 0.331076i 0.576566 0.817050i \(-0.304392\pi\)
0.873973 + 0.485974i \(0.161535\pi\)
\(284\) 1.12393e9 1.40936e9i 0.172769 0.216646i
\(285\) 1.48257e10 + 1.85908e10i 2.24717 + 2.81786i
\(286\) 4.32531e7 1.89504e8i 0.00646477 0.0283240i
\(287\) 1.30549e9 2.07768e9i 0.192418 0.306232i
\(288\) −7.90196e8 + 7.01319e9i −0.114859 + 1.01940i
\(289\) 6.72235e9i 0.963673i
\(290\) −1.41294e10 + 1.86947e9i −1.99771 + 0.264318i
\(291\) 1.03788e10 1.44736
\(292\) −7.24433e9 8.16240e8i −0.996476 0.112276i
\(293\) −1.27677e8 8.02247e7i −0.0173237 0.0108852i 0.523342 0.852123i \(-0.324685\pi\)
−0.540666 + 0.841237i \(0.681828\pi\)
\(294\) −1.03224e10 2.35601e9i −1.38162 0.315347i
\(295\) −6.90255e9 + 5.50460e9i −0.911427 + 0.726839i
\(296\) −1.83142e9 1.46051e9i −0.238573 0.190256i
\(297\) −6.10248e7 2.67367e8i −0.00784297 0.0343623i
\(298\) −3.42381e9 1.19804e9i −0.434155 0.151918i
\(299\) −8.33318e8 1.73040e9i −0.104262 0.216502i
\(300\) 9.24820e9 5.81103e9i 1.14175 0.717411i
\(301\) −1.03224e9 + 3.61196e8i −0.125752 + 0.0440025i
\(302\) 1.00725e9 + 1.00725e9i 0.121090 + 0.121090i
\(303\) 9.98304e8 2.07300e9i 0.118438 0.245940i
\(304\) 1.98303e9 + 1.75999e10i 0.232186 + 2.06071i
\(305\) 1.25153e10 1.41014e9i 1.44625 0.162953i
\(306\) 1.59992e9 + 7.70481e8i 0.182479 + 0.0878772i
\(307\) 7.38884e9 7.38884e9i 0.831807 0.831807i −0.155957 0.987764i \(-0.549846\pi\)
0.987764 + 0.155957i \(0.0498461\pi\)
\(308\) 1.39543e8 + 3.98791e8i 0.0155062 + 0.0443142i
\(309\) 6.03114e9 + 9.59850e9i 0.661554 + 1.05286i
\(310\) 9.23985e9 4.44968e9i 1.00050 0.481816i
\(311\) −3.04845e9 + 8.71197e9i −0.325865 + 0.931268i 0.658104 + 0.752927i \(0.271359\pi\)
−0.983969 + 0.178341i \(0.942927\pi\)
\(312\) −5.34876e8 + 1.22082e8i −0.0564463 + 0.0128835i
\(313\) 3.83088e9 4.80377e9i 0.399136 0.500501i −0.541131 0.840938i \(-0.682004\pi\)
0.940267 + 0.340437i \(0.110575\pi\)
\(314\) 2.59759e9 + 3.25727e9i 0.267209 + 0.335070i
\(315\) 1.19452e9 5.23354e9i 0.121325 0.531561i
\(316\) −4.30779e9 + 6.85580e9i −0.432022 + 0.687559i
\(317\) 3.41064e8 3.02703e9i 0.0337753 0.299764i −0.965456 0.260566i \(-0.916091\pi\)
0.999231 0.0391985i \(-0.0124805\pi\)
\(318\) 3.21914e10i 3.14798i
\(319\) −1.28773e9 1.19915e8i −0.124355 0.0115800i
\(320\) 9.40775e9 0.897193
\(321\) −2.42820e10 2.73592e9i −2.28699 0.257682i
\(322\) 7.87768e9 + 4.94987e9i 0.732782 + 0.460437i
\(323\) 3.64253e9 + 8.31384e8i 0.334652 + 0.0763821i
\(324\) 8.17988e9 6.52324e9i 0.742279 0.591947i
\(325\) 1.86607e9 + 1.48814e9i 0.167260 + 0.133386i
\(326\) 4.62019e9 + 2.02424e10i 0.409063 + 1.79222i
\(327\) −9.18112e9 3.21261e9i −0.802980 0.280975i
\(328\) −9.85579e8 2.04658e9i −0.0851523 0.176820i
\(329\) −4.33150e9 + 2.72166e9i −0.369705 + 0.232301i
\(330\) 3.76807e9 1.31851e9i 0.317734 0.111180i
\(331\) 1.22073e10 + 1.22073e10i 1.01697 + 1.01697i 0.999854 + 0.0171115i \(0.00544702\pi\)
0.0171115 + 0.999854i \(0.494553\pi\)
\(332\) −8.40754e9 + 1.74584e10i −0.692016 + 1.43699i
\(333\) −1.32259e9 1.17383e10i −0.107560 0.954618i
\(334\) 1.50757e9 1.69863e8i 0.121142 0.0136494i
\(335\) −4.08003e8 1.96484e8i −0.0323955 0.0156008i
\(336\) 6.41067e9 6.41067e9i 0.502975 0.502975i
\(337\) 2.56462e9 + 7.32927e9i 0.198840 + 0.568252i 0.999525 0.0308342i \(-0.00981639\pi\)
−0.800685 + 0.599086i \(0.795531\pi\)
\(338\) −9.07320e9 1.44399e10i −0.695174 1.10636i
\(339\) −2.37547e10 + 1.14397e10i −1.79867 + 0.866192i
\(340\) 1.02443e9 2.92764e9i 0.0766593 0.219080i
\(341\) 9.07269e8 2.07078e8i 0.0670994 0.0153150i
\(342\) −1.63242e10 + 2.04699e10i −1.19324 + 1.49627i
\(343\) 7.12134e9 + 8.92988e9i 0.514500 + 0.645162i
\(344\) −2.25276e8 + 9.86999e8i −0.0160872 + 0.0704828i
\(345\) 2.09860e10 3.33991e10i 1.48134 2.35753i
\(346\) −2.21397e9 + 1.96496e10i −0.154479 + 1.37104i
\(347\) 2.82795e10i 1.95053i −0.221028 0.975267i \(-0.570941\pi\)
0.221028 0.975267i \(-0.429059\pi\)
\(348\) −5.56386e9 1.49654e10i −0.379367 1.02040i
\(349\) −1.03125e10 −0.695124 −0.347562 0.937657i \(-0.612990\pi\)
−0.347562 + 0.937657i \(0.612990\pi\)
\(350\) −1.14893e10 1.29453e9i −0.765634 0.0862662i
\(351\) 6.26436e8 + 3.93616e8i 0.0412713 + 0.0259325i
\(352\) 2.43044e9 + 5.54732e8i 0.158312 + 0.0361337i
\(353\) −2.15415e10 + 1.71788e10i −1.38732 + 1.10635i −0.406026 + 0.913861i \(0.633086\pi\)
−0.981298 + 0.192493i \(0.938343\pi\)
\(354\) −1.72329e10 1.37427e10i −1.09735 0.875105i
\(355\) 1.80026e9 + 7.88744e9i 0.113350 + 0.496618i
\(356\) −2.01951e10 7.06657e9i −1.25732 0.439955i
\(357\) −8.29798e8 1.72309e9i −0.0510857 0.106081i
\(358\) 2.41597e10 1.51805e10i 1.47082 0.924177i
\(359\) 1.68278e10 5.88831e9i 1.01309 0.354497i 0.227859 0.973694i \(-0.426828\pi\)
0.785236 + 0.619197i \(0.212542\pi\)
\(360\) −3.51391e9 3.51391e9i −0.209209 0.209209i
\(361\) −1.65322e10 + 3.43295e10i −0.973423 + 2.02133i
\(362\) −3.45770e9 3.06880e10i −0.201351 1.78704i
\(363\) −2.27178e10 + 2.55968e9i −1.30840 + 0.147421i
\(364\) −1.02692e9 4.94538e8i −0.0584966 0.0281705i
\(365\) 2.31354e10 2.31354e10i 1.30348 1.30348i
\(366\) 1.03851e10 + 2.96788e10i 0.578742 + 1.65395i
\(367\) 2.83656e9 + 4.51436e9i 0.156361 + 0.248847i 0.915713 0.401833i \(-0.131627\pi\)
−0.759352 + 0.650680i \(0.774484\pi\)
\(368\) 2.64708e10 1.27477e10i 1.44336 0.695087i
\(369\) 3.78329e9 1.08120e10i 0.204063 0.583178i
\(370\) −4.48298e10 + 1.02321e10i −2.39200 + 0.545957i
\(371\) −9.53343e9 + 1.19545e10i −0.503215 + 0.631012i
\(372\) 7.16298e9 + 8.98209e9i 0.374043 + 0.469035i
\(373\) −2.63206e9 + 1.15318e10i −0.135976 + 0.595748i 0.860320 + 0.509754i \(0.170264\pi\)
−0.996296 + 0.0859936i \(0.972594\pi\)
\(374\) 3.33721e8 5.31114e8i 0.0170568 0.0271457i
\(375\) −1.05742e9 + 9.38487e9i −0.0534715 + 0.474573i
\(376\) 4.73564e9i 0.236934i
\(377\) 2.68521e9 2.22772e9i 0.132927 0.110279i
\(378\) −3.58388e9 −0.175544
\(379\) 1.10992e10 + 1.25058e9i 0.537940 + 0.0606113i 0.376755 0.926313i \(-0.377040\pi\)
0.161185 + 0.986924i \(0.448468\pi\)
\(380\) 3.87217e10 + 2.43305e10i 1.85704 + 1.16685i
\(381\) 2.18617e10 + 4.98980e9i 1.03749 + 0.236801i
\(382\) 7.80106e9 6.22113e9i 0.366353 0.292157i
\(383\) −4.25423e9 3.39264e9i −0.197709 0.157668i 0.519631 0.854391i \(-0.326069\pi\)
−0.717340 + 0.696723i \(0.754641\pi\)
\(384\) −3.18763e9 1.39659e10i −0.146603 0.642310i
\(385\) −1.78978e9 6.26270e8i −0.0814622 0.0285048i
\(386\) 3.88217e8 + 8.06141e8i 0.0174874 + 0.0363130i
\(387\) −4.32272e9 + 2.71614e9i −0.192714 + 0.121090i
\(388\) 1.88405e10 6.59258e9i 0.831315 0.290890i
\(389\) −1.87688e10 1.87688e10i −0.819668 0.819668i 0.166392 0.986060i \(-0.446788\pi\)
−0.986060 + 0.166392i \(0.946788\pi\)
\(390\) −4.67276e9 + 9.70309e9i −0.201983 + 0.419422i
\(391\) −6.93933e8 6.15883e9i −0.0296900 0.263506i
\(392\) 4.62625e9 5.21253e8i 0.195923 0.0220752i
\(393\) 3.79963e10 + 1.82981e10i 1.59284 + 0.767070i
\(394\) −3.66373e9 + 3.66373e9i −0.152033 + 0.152033i
\(395\) −1.20019e10 3.42995e10i −0.493018 1.40896i
\(396\) 1.04934e9 + 1.67002e9i 0.0426714 + 0.0679111i
\(397\) −6.42381e9 + 3.09354e9i −0.258601 + 0.124536i −0.558693 0.829375i \(-0.688697\pi\)
0.300092 + 0.953910i \(0.402983\pi\)
\(398\) 1.88789e10 5.39528e10i 0.752393 2.15022i
\(399\) 2.74906e10 6.27456e9i 1.08466 0.247566i
\(400\) −2.27647e10 + 2.85461e10i −0.889247 + 1.11508i
\(401\) −1.79436e10 2.25006e10i −0.693957 0.870195i 0.302598 0.953118i \(-0.402146\pi\)
−0.996556 + 0.0829230i \(0.973574\pi\)
\(402\) 2.51578e8 1.10223e9i 0.00963314 0.0422056i
\(403\) −1.33567e9 + 2.12571e9i −0.0506384 + 0.0805906i
\(404\) 4.95447e8 4.39721e9i 0.0185982 0.165064i
\(405\) 4.69556e10i 1.74529i
\(406\) −5.27247e9 + 1.60578e10i −0.194048 + 0.590994i
\(407\) −4.17257e9 −0.152064
\(408\) −1.75931e9 1.98226e8i −0.0634894 0.00715353i
\(409\) −4.03209e9 2.53353e9i −0.144091 0.0905383i 0.458057 0.888923i \(-0.348545\pi\)
−0.602148 + 0.798384i \(0.705688\pi\)
\(410\) −4.34720e10 9.92221e9i −1.53842 0.351134i
\(411\) −1.82892e10 + 1.45852e10i −0.640957 + 0.511146i
\(412\) 1.70452e10 + 1.35931e10i 0.591579 + 0.471769i
\(413\) 2.32967e9 + 1.02070e10i 0.0800745 + 0.350829i
\(414\) 4.09947e10 + 1.43447e10i 1.39549 + 0.488302i
\(415\) −3.77331e10 7.83536e10i −1.27213 2.64160i
\(416\) −5.69447e9 + 3.57807e9i −0.190143 + 0.119475i
\(417\) −2.85638e10 + 9.99491e9i −0.944652 + 0.330548i
\(418\) 6.53950e9 + 6.53950e9i 0.214210 + 0.214210i
\(419\) −1.80225e10 + 3.74240e10i −0.584733 + 1.21421i 0.373342 + 0.927694i \(0.378212\pi\)
−0.958075 + 0.286518i \(0.907502\pi\)
\(420\) −2.62097e9 2.32617e10i −0.0842295 0.747557i
\(421\) 1.38732e10 1.56313e9i 0.441618 0.0497584i 0.111644 0.993748i \(-0.464388\pi\)
0.329975 + 0.943990i \(0.392960\pi\)
\(422\) 5.93786e9 + 2.85952e9i 0.187232 + 0.0901661i
\(423\) −1.68863e10 + 1.68863e10i −0.527440 + 0.527440i
\(424\) 4.67502e9 + 1.33604e10i 0.144650 + 0.413387i
\(425\) 4.09781e9 + 6.52162e9i 0.125602 + 0.199894i
\(426\) −1.81979e10 + 8.76363e9i −0.552564 + 0.266101i
\(427\) 4.93274e9 1.40970e10i 0.148381 0.424047i
\(428\) −4.58167e10 + 1.04574e10i −1.36536 + 0.311636i
\(429\) −6.09310e8 + 7.64051e8i −0.0179891 + 0.0225576i
\(430\) 1.23906e10 + 1.55373e10i 0.362426 + 0.454467i
\(431\) 4.58017e9 2.00670e10i 0.132731 0.581532i −0.864193 0.503160i \(-0.832171\pi\)
0.996924 0.0783721i \(-0.0249722\pi\)
\(432\) −6.02132e9 + 9.58288e9i −0.172885 + 0.275145i
\(433\) −8.16114e7 + 7.24321e8i −0.00232166 + 0.0206053i −0.994820 0.101656i \(-0.967586\pi\)
0.992498 + 0.122261i \(0.0390145\pi\)
\(434\) 1.21614e10i 0.342786i
\(435\) 6.80805e10 + 2.23537e10i 1.90137 + 0.624300i
\(436\) −1.87070e10 −0.517677
\(437\) 9.08054e10 + 1.02313e10i 2.48992 + 0.280547i
\(438\) 6.91641e10 + 4.34587e10i 1.87925 + 1.18081i
\(439\) 3.56224e10 + 8.13058e9i 0.959102 + 0.218909i 0.673291 0.739377i \(-0.264880\pi\)
0.285811 + 0.958286i \(0.407737\pi\)
\(440\) −1.37239e9 + 1.09444e9i −0.0366155 + 0.0291999i
\(441\) 1.83549e10 + 1.46375e10i 0.485286 + 0.387003i
\(442\) 3.76544e8 + 1.64975e9i 0.00986568 + 0.0432244i
\(443\) −1.80362e9 6.31112e8i −0.0468305 0.0163867i 0.306762 0.951786i \(-0.400754\pi\)
−0.353593 + 0.935399i \(0.615040\pi\)
\(444\) −2.23500e10 4.64102e10i −0.575103 1.19421i
\(445\) 8.13061e10 5.10880e10i 2.07340 1.30280i
\(446\) 6.81303e10 2.38398e10i 1.72187 0.602509i
\(447\) 1.28955e10 + 1.28955e10i 0.323005 + 0.323005i
\(448\) 4.84045e9 1.00513e10i 0.120164 0.249523i
\(449\) −6.31108e9 5.60124e10i −0.155281 1.37816i −0.793626 0.608406i \(-0.791809\pi\)
0.638345 0.769750i \(-0.279619\pi\)
\(450\) −5.36347e10 + 6.04318e9i −1.30796 + 0.147372i
\(451\) −3.64549e9 1.75558e9i −0.0881150 0.0424339i
\(452\) −3.58552e10 + 3.58552e10i −0.859010 + 0.859010i
\(453\) −2.36535e9 6.75978e9i −0.0561698 0.160524i
\(454\) −5.54306e9 8.82172e9i −0.130475 0.207649i
\(455\) 4.60882e9 2.21949e9i 0.107534 0.0517854i
\(456\) 8.62136e9 2.46384e10i 0.199396 0.569841i
\(457\) −6.07225e10 + 1.38595e10i −1.39215 + 0.317748i −0.851876 0.523744i \(-0.824535\pi\)
−0.540270 + 0.841492i \(0.681678\pi\)
\(458\) −2.70373e10 + 3.39037e10i −0.614470 + 0.770521i
\(459\) 1.48855e9 + 1.86658e9i 0.0335361 + 0.0420530i
\(460\) 1.68807e10 7.39592e10i 0.377016 1.65181i
\(461\) −2.79867e10 + 4.45406e10i −0.619652 + 0.986170i 0.378512 + 0.925596i \(0.376436\pi\)
−0.998164 + 0.0605738i \(0.980707\pi\)
\(462\) 5.30040e8 4.70423e9i 0.0116343 0.103257i
\(463\) 2.02649e10i 0.440981i −0.975389 0.220491i \(-0.929234\pi\)
0.975389 0.220491i \(-0.0707658\pi\)
\(464\) 3.40784e10 + 4.10769e10i 0.735204 + 0.886189i
\(465\) −5.15606e10 −1.10282
\(466\) −6.25825e10 7.05135e9i −1.32712 0.149530i
\(467\) −6.44880e10 4.05205e10i −1.35585 0.851936i −0.359162 0.933275i \(-0.616938\pi\)
−0.996687 + 0.0813389i \(0.974080\pi\)
\(468\) −5.18742e9 1.18399e9i −0.108135 0.0246812i
\(469\) −4.19850e8 + 3.34819e8i −0.00867766 + 0.00692020i
\(470\) 7.26794e10 + 5.79599e10i 1.48943 + 1.18778i
\(471\) −4.66095e9 2.04210e10i −0.0947089 0.414947i
\(472\) 9.14796e9 + 3.20101e9i 0.184313 + 0.0644939i
\(473\) 7.82430e8 + 1.62473e9i 0.0156315 + 0.0324592i
\(474\) 7.68173e10 4.82675e10i 1.52176 0.956184i
\(475\) −1.07188e11 + 3.75067e10i −2.10558 + 0.736774i
\(476\) −2.60083e9 2.60083e9i −0.0506621 0.0506621i
\(477\) −3.09703e10 + 6.43106e10i −0.598236 + 1.24225i
\(478\) 5.79584e9 + 5.14395e10i 0.111021 + 0.985339i
\(479\) −4.76793e10 + 5.37217e9i −0.905708 + 0.102049i −0.552516 0.833502i \(-0.686332\pi\)
−0.353192 + 0.935551i \(0.614904\pi\)
\(480\) −1.24445e11 5.99294e10i −2.34429 1.12895i
\(481\) 7.95953e9 7.95953e9i 0.148699 0.148699i
\(482\) 2.29671e10 + 6.56361e10i 0.425517 + 1.21606i
\(483\) −2.48861e10 3.96060e10i −0.457266 0.727734i
\(484\) −3.96134e10 + 1.90768e10i −0.721873 + 0.347636i
\(485\) −2.95876e10 + 8.45564e10i −0.534739 + 1.52820i
\(486\) −9.36171e10 + 2.13675e10i −1.67807 + 0.383008i
\(487\) 1.80271e10 2.26052e10i 0.320486 0.401877i −0.595326 0.803485i \(-0.702977\pi\)
0.915812 + 0.401607i \(0.131548\pi\)
\(488\) −8.62024e9 1.08094e10i −0.151999 0.190600i
\(489\) 2.32286e10 1.01771e11i 0.406245 1.77987i
\(490\) 4.86212e10 7.73802e10i 0.843415 1.34229i
\(491\) 2.09071e9 1.85556e10i 0.0359723 0.319263i −0.962820 0.270142i \(-0.912929\pi\)
0.998793 0.0491213i \(-0.0156421\pi\)
\(492\) 4.99513e10i 0.852484i
\(493\) 1.05533e10 3.92351e9i 0.178648 0.0664182i
\(494\) −2.49493e10 −0.418939
\(495\) −8.79618e9 9.91091e8i −0.146512 0.0165079i
\(496\) −3.25180e10 2.04324e10i −0.537276 0.337593i
\(497\) 9.35326e9 + 2.13482e9i 0.153298 + 0.0349893i
\(498\) 1.69750e11 1.35371e11i 2.75989 2.20094i
\(499\) −2.94013e10 2.34468e10i −0.474204 0.378165i 0.357026 0.934095i \(-0.383791\pi\)
−0.831229 + 0.555930i \(0.812362\pi\)
\(500\) 4.04172e9 + 1.77079e10i 0.0646674 + 0.283327i
\(501\) −7.19945e9 2.51920e9i −0.114274 0.0399863i
\(502\) 3.96187e10 + 8.22690e10i 0.623857 + 1.29545i
\(503\) −6.48715e10 + 4.07615e10i −1.01340 + 0.636763i −0.932954 0.359996i \(-0.882778\pi\)
−0.0804485 + 0.996759i \(0.525635\pi\)
\(504\) −5.56225e9 + 1.94632e9i −0.0862042 + 0.0301642i
\(505\) 1.40429e10 + 1.40429e10i 0.215919 + 0.215919i
\(506\) 6.65641e9 1.38222e10i 0.101540 0.210850i
\(507\) 9.59988e9 + 8.52013e10i 0.145289 + 1.28948i
\(508\) 4.28548e10 4.82858e9i 0.643495 0.0725045i
\(509\) 8.10824e10 + 3.90472e10i 1.20797 + 0.581727i 0.925937 0.377678i \(-0.123277\pi\)
0.282031 + 0.959405i \(0.408992\pi\)
\(510\) −2.45745e10 + 2.45745e10i −0.363249 + 0.363249i
\(511\) −1.28144e10 3.66215e10i −0.187938 0.537097i
\(512\) −4.41846e10 7.03194e10i −0.642971 1.02328i
\(513\) −3.17145e10 + 1.52729e10i −0.457919 + 0.220522i
\(514\) −1.69979e10 + 4.85771e10i −0.243524 + 0.695951i
\(515\) −9.53926e10 + 2.17727e10i −1.35608 + 0.309517i
\(516\) −1.38804e10 + 1.74055e10i −0.195796 + 0.245520i
\(517\) 5.25940e9 + 6.59508e9i 0.0736163 + 0.0923119i
\(518\) −1.21337e10 + 5.31611e10i −0.168529 + 0.738372i
\(519\) 5.28924e10 8.41777e10i 0.728993 1.16019i
\(520\) 5.30203e8 4.70568e9i 0.00725152 0.0643590i
\(521\) 5.03959e10i 0.683981i −0.939703 0.341991i \(-0.888899\pi\)
0.939703 0.341991i \(-0.111101\pi\)
\(522\) −7.31548e9 + 7.85592e10i −0.0985282 + 1.05807i
\(523\) 1.39207e11 1.86061 0.930305 0.366786i \(-0.119542\pi\)
0.930305 + 0.366786i \(0.119542\pi\)
\(524\) 8.05971e10 + 9.08112e9i 1.06904 + 0.120452i
\(525\) 4.92195e10 + 3.09267e10i 0.647889 + 0.407095i
\(526\) 8.45539e10 + 1.92989e10i 1.10456 + 0.252109i
\(527\) −6.33397e9 + 5.05117e9i −0.0821171 + 0.0654862i
\(528\) −1.16880e10 9.32090e9i −0.150386 0.119928i
\(529\) −1.63051e10 7.14374e10i −0.208210 0.912227i
\(530\) 2.62265e11 + 9.17703e10i 3.32381 + 1.16305i
\(531\) 2.12056e10 + 4.40338e10i 0.266730 + 0.553870i
\(532\) 4.59179e10 2.88521e10i 0.573238 0.360190i
\(533\) 1.03030e10 3.60517e9i 0.127660 0.0446701i
\(534\) 1.69517e11 + 1.69517e11i 2.08472 + 2.08472i
\(535\) 9.15120e10 1.90027e11i 1.11703 2.31953i
\(536\) 5.56600e7 + 4.93996e8i 0.000674348 + 0.00598501i
\(537\) −1.42552e11 + 1.60617e10i −1.71426 + 0.193150i
\(538\) −1.56756e11 7.54896e10i −1.87109 0.901069i
\(539\) 5.86383e9 5.86383e9i 0.0694747 0.0694747i
\(540\) 9.65157e9 + 2.75826e10i 0.113507 + 0.324385i
\(541\) −2.32409e10 3.69877e10i −0.271309 0.431786i 0.683084 0.730340i \(-0.260638\pi\)
−0.954393 + 0.298554i \(0.903496\pi\)
\(542\) −3.83427e9 + 1.84649e9i −0.0444309 + 0.0213968i
\(543\) −5.12804e10 + 1.46551e11i −0.589864 + 1.68573i
\(544\) −2.11585e10 + 4.82928e9i −0.241595 + 0.0551425i
\(545\) 5.23465e10 6.56404e10i 0.593337 0.744021i
\(546\) 7.96263e9 + 9.98482e9i 0.0895954 + 0.112349i
\(547\) 5.37104e9 2.35321e10i 0.0599942 0.262852i −0.936032 0.351916i \(-0.885530\pi\)
0.996026 + 0.0890639i \(0.0283875\pi\)
\(548\) −2.39358e10 + 3.80936e10i −0.265415 + 0.422406i
\(549\) 7.80622e9 6.92821e10i 0.0859313 0.762661i
\(550\) 1.90653e10i 0.208349i
\(551\) 2.17741e10 + 1.64568e11i 0.236230 + 1.78542i
\(552\) −4.33014e10 −0.466386
\(553\) −4.28211e10 4.82477e9i −0.457885 0.0515913i
\(554\) −1.51376e11 9.51156e10i −1.60700 1.00975i
\(555\) 2.25388e11 + 5.14433e10i 2.37552 + 0.542196i
\(556\) −4.55028e10 + 3.62873e10i −0.476145 + 0.379713i
\(557\) 6.15322e9 + 4.90703e9i 0.0639266 + 0.0509797i 0.654932 0.755688i \(-0.272697\pi\)
−0.591005 + 0.806668i \(0.701269\pi\)
\(558\) −1.26330e10 5.53486e10i −0.130307 0.570913i
\(559\) −4.59187e9 1.60676e9i −0.0470265 0.0164553i
\(560\) 3.39526e10 + 7.05032e10i 0.345240 + 0.716897i
\(561\) −2.67024e9 + 1.67783e9i −0.0269587 + 0.0169393i
\(562\) −4.11761e10 + 1.44081e10i −0.412762 + 0.144432i
\(563\) 1.03593e11 + 1.03593e11i 1.03109 + 1.03109i 0.999501 + 0.0315924i \(0.0100579\pi\)
0.0315924 + 0.999501i \(0.489942\pi\)
\(564\) −4.51836e10 + 9.38247e10i −0.446544 + 0.927258i
\(565\) −2.54801e10 2.26142e11i −0.250039 2.21915i
\(566\) −2.04358e11 + 2.30256e10i −1.99125 + 0.224360i
\(567\) 5.01677e10 + 2.41595e10i 0.485391 + 0.233752i
\(568\) 6.27997e9 6.27997e9i 0.0603343 0.0603343i
\(569\) −1.06807e10 3.05238e10i −0.101895 0.291199i 0.881638 0.471925i \(-0.156441\pi\)
−0.983533 + 0.180727i \(0.942155\pi\)
\(570\) −2.72616e11 4.33866e11i −2.58257 4.11014i
\(571\) −1.55543e10 + 7.49054e9i −0.146320 + 0.0704642i −0.505611 0.862761i \(-0.668733\pi\)
0.359291 + 0.933226i \(0.383019\pi\)
\(572\) −6.20751e8 + 1.77400e9i −0.00579874 + 0.0165718i
\(573\) −4.89075e10 + 1.11628e10i −0.453688 + 0.103551i
\(574\) −3.29681e10 + 4.13407e10i −0.303701 + 0.380829i
\(575\) 1.17453e11 + 1.47281e11i 1.07446 + 1.34734i
\(576\) 1.15887e10 5.07736e10i 0.105280 0.461262i
\(577\) −8.16362e10 + 1.29923e11i −0.736511 + 1.17215i 0.242856 + 0.970062i \(0.421916\pi\)
−0.979367 + 0.202088i \(0.935227\pi\)
\(578\) 1.62192e10 1.43950e11i 0.145318 1.28973i
\(579\) 4.49846e9i 0.0400267i
\(580\) 1.37785e11 2.66606e9i 1.21756 0.0235590i
\(581\) −1.03128e11 −0.905047
\(582\) −2.22247e11 2.50412e10i −1.93706 0.218255i
\(583\) 2.13487e10 + 1.34143e10i 0.184798 + 0.116116i
\(584\) −3.50165e10 7.99229e9i −0.301038 0.0687100i
\(585\) 1.86700e10 1.48889e10i 0.159412 0.127127i
\(586\) 2.54046e9 + 2.02595e9i 0.0215438 + 0.0171806i
\(587\) 2.56021e10 + 1.12170e11i 0.215637 + 0.944767i 0.960660 + 0.277728i \(0.0895814\pi\)
−0.745023 + 0.667039i \(0.767561\pi\)
\(588\) 9.66308e10 + 3.38126e10i 0.808362 + 0.282858i
\(589\) −5.18263e10 1.07618e11i −0.430615 0.894180i
\(590\) 1.61089e11 1.01219e11i 1.32941 0.835324i
\(591\) 2.45878e10 8.60365e9i 0.201544 0.0705234i
\(592\) 1.21761e11 + 1.21761e11i 0.991335 + 0.991335i
\(593\) 2.52976e10 5.25311e10i 0.204579 0.424813i −0.773284 0.634060i \(-0.781387\pi\)
0.977863 + 0.209247i \(0.0671014\pi\)
\(594\) 6.61674e8 + 5.87252e9i 0.00531494 + 0.0471714i
\(595\) 1.64036e10 1.84825e9i 0.130880 0.0147466i
\(596\) 3.16004e10 + 1.52179e10i 0.250442 + 0.120606i
\(597\) −2.03209e11 + 2.03209e11i −1.59973 + 1.59973i
\(598\) 1.36693e10 + 3.90646e10i 0.106891 + 0.305477i
\(599\) 8.25461e9 + 1.31371e10i 0.0641193 + 0.102045i 0.877245 0.480043i \(-0.159379\pi\)
−0.813126 + 0.582088i \(0.802236\pi\)
\(600\) 4.84828e10 2.33481e10i 0.374096 0.180155i
\(601\) −1.61029e10 + 4.60196e10i −0.123426 + 0.352732i −0.988973 0.148096i \(-0.952685\pi\)
0.865547 + 0.500828i \(0.166971\pi\)
\(602\) 2.29754e10 5.24398e9i 0.174935 0.0399278i
\(603\) −1.56301e9 + 1.95996e9i −0.0118221 + 0.0148244i
\(604\) −8.58759e9 1.07685e10i −0.0645243 0.0809109i
\(605\) 4.39093e10 1.92379e11i 0.327744 1.43594i
\(606\) −2.63788e10 + 4.19817e10i −0.195598 + 0.311293i
\(607\) −6.02170e9 + 5.34441e10i −0.0443573 + 0.393682i 0.951843 + 0.306587i \(0.0991869\pi\)
−0.996200 + 0.0870949i \(0.972242\pi\)
\(608\) 3.19982e11i 2.34159i
\(609\) 5.89115e10 6.12363e10i 0.428283 0.445184i
\(610\) −2.71400e11 −1.96015
\(611\) −2.26134e10 2.54792e9i −0.162256 0.0182819i
\(612\) −1.45385e10 9.13517e9i −0.103637 0.0651195i
\(613\) −1.85980e11 4.24487e10i −1.31712 0.300623i −0.494478 0.869190i \(-0.664641\pi\)
−0.822637 + 0.568567i \(0.807498\pi\)
\(614\) −1.76049e11 + 1.40394e11i −1.23868 + 0.987814i
\(615\) 1.75272e11 + 1.39775e11i 1.22522 + 0.977078i
\(616\) 4.63192e8 + 2.02938e9i 0.00321690 + 0.0140942i
\(617\) 1.10626e11 + 3.87096e10i 0.763335 + 0.267102i 0.683741 0.729725i \(-0.260352\pi\)
0.0795940 + 0.996827i \(0.474638\pi\)
\(618\) −1.05990e11 2.20090e11i −0.726623 1.50885i
\(619\) −5.58131e10 + 3.50697e10i −0.380166 + 0.238874i −0.708536 0.705675i \(-0.750644\pi\)
0.328369 + 0.944549i \(0.393501\pi\)
\(620\) −9.35973e10 + 3.27511e10i −0.633427 + 0.221646i
\(621\) 4.12895e10 + 4.12895e10i 0.277635 + 0.277635i
\(622\) 8.62978e10 1.79199e11i 0.576552 1.19722i
\(623\) −1.27494e10 1.13154e11i −0.0846323 0.751132i
\(624\) 4.00764e10 4.51552e9i 0.264332 0.0297831i
\(625\) 9.68402e10 + 4.66358e10i 0.634652 + 0.305632i
\(626\) −9.36229e10 + 9.36229e10i −0.609656 + 0.609656i
\(627\) −1.53569e10 4.38875e10i −0.0993650 0.283969i
\(628\) −2.14323e10 3.41093e10i −0.137794 0.219298i
\(629\) 3.27275e10 1.57607e10i 0.209079 0.100687i
\(630\) −3.82061e10 + 1.09187e11i −0.242533 + 0.693119i
\(631\) 1.12550e11 2.56888e10i 0.709951 0.162042i 0.147729 0.989028i \(-0.452804\pi\)
0.562222 + 0.826986i \(0.309947\pi\)
\(632\) −2.48719e10 + 3.11883e10i −0.155898 + 0.195490i
\(633\) −2.06591e10 2.59057e10i −0.128676 0.161354i
\(634\) −1.46068e10 + 6.39966e10i −0.0904062 + 0.396096i
\(635\) −1.02975e11 + 1.63883e11i −0.633338 + 1.00795i
\(636\) −3.48506e10 + 3.09308e11i −0.213001 + 1.89044i
\(637\) 2.23715e10i 0.135874i
\(638\) 2.72857e10 + 5.67475e9i 0.164684 + 0.0342503i
\(639\) 4.47861e10 0.268621
\(640\) 1.22868e11 + 1.38439e10i 0.732351 + 0.0825161i
\(641\) 1.22030e11 + 7.66766e10i 0.722828 + 0.454183i 0.842546 0.538625i \(-0.181056\pi\)
−0.119718 + 0.992808i \(0.538199\pi\)
\(642\) 5.13363e11 + 1.17172e11i 3.02193 + 0.689736i
\(643\) 2.08764e11 1.66483e11i 1.22127 0.973928i 0.221268 0.975213i \(-0.428980\pi\)
0.999999 + 0.00128448i \(0.000408863\pi\)
\(644\) −7.03331e10 5.60888e10i −0.408899 0.326086i
\(645\) −2.22330e10 9.74089e10i −0.128457 0.562808i
\(646\) −7.59936e10 2.65913e10i −0.436362 0.152690i
\(647\) 4.48481e10 + 9.31280e10i 0.255933 + 0.531451i 0.988859 0.148858i \(-0.0475598\pi\)
−0.732925 + 0.680309i \(0.761846\pi\)
\(648\) 4.36454e10 2.74242e10i 0.247536 0.155537i
\(649\) 1.62949e10 5.70184e9i 0.0918488 0.0321393i
\(650\) −3.63686e10 3.63686e10i −0.203739 0.203739i
\(651\) −2.65288e10 + 5.50877e10i −0.147705 + 0.306712i
\(652\) −2.24781e10 1.99499e11i −0.124385 1.10395i
\(653\) 6.68911e10 7.53682e9i 0.367888 0.0414510i 0.0739144 0.997265i \(-0.476451\pi\)
0.293973 + 0.955814i \(0.405022\pi\)
\(654\) 1.88849e11 + 9.09451e10i 1.03230 + 0.497128i
\(655\) −2.57394e11 + 2.57394e11i −1.39840 + 1.39840i
\(656\) 5.51500e10 + 1.57610e11i 0.297804 + 0.851075i
\(657\) −9.63626e10 1.53360e11i −0.517186 0.823097i
\(658\) 9.93195e10 4.78298e10i 0.529823 0.255149i
\(659\) 6.80230e10 1.94398e11i 0.360673 1.03074i −0.610427 0.792073i \(-0.709002\pi\)
0.971100 0.238672i \(-0.0767121\pi\)
\(660\) −3.76326e10 + 8.58939e9i −0.198330 + 0.0452675i
\(661\) 7.95811e10 9.97915e10i 0.416873 0.522742i −0.528412 0.848988i \(-0.677212\pi\)
0.945285 + 0.326246i \(0.105784\pi\)
\(662\) −2.31948e11 2.90854e11i −1.20770 1.51441i
\(663\) 1.89312e9 8.29432e9i 0.00979772 0.0429266i
\(664\) −5.07921e10 + 8.08351e10i −0.261290 + 0.415841i
\(665\) −2.72504e10 + 2.41854e11i −0.139344 + 1.23671i
\(666\) 2.54551e11i 1.29383i
\(667\) 2.45744e11 1.24257e11i 1.24160 0.627795i
\(668\) −1.46693e10 −0.0736720
\(669\) −3.60616e11 4.06317e10i −1.80028 0.202843i
\(670\) 8.26275e9 + 5.19183e9i 0.0410039 + 0.0257645i
\(671\) −2.40099e10 5.48010e9i −0.118441 0.0270333i
\(672\) −1.28058e11 + 1.02123e11i −0.627956 + 0.500778i
\(673\) 2.80135e10 + 2.23400e10i 0.136555 + 0.108899i 0.689385 0.724395i \(-0.257881\pi\)
−0.552830 + 0.833294i \(0.686452\pi\)
\(674\) −3.72342e10 1.63133e11i −0.180427 0.790503i
\(675\) −6.84935e10 2.39669e10i −0.329940 0.115451i
\(676\) 7.15461e10 + 1.48567e11i 0.342609 + 0.711436i
\(677\) −9.35932e10 + 5.88085e10i −0.445543 + 0.279953i −0.736060 0.676917i \(-0.763316\pi\)
0.290517 + 0.956870i \(0.406173\pi\)
\(678\) 5.36274e11 1.87650e11i 2.53786 0.888035i
\(679\) 7.51173e10 + 7.51173e10i 0.353395 + 0.353395i
\(680\) 6.63033e9 1.37680e10i 0.0310099 0.0643926i
\(681\) 5.86482e9 + 5.20517e10i 0.0272688 + 0.242017i
\(682\) −1.99275e10 + 2.24529e9i −0.0921118 + 0.0103785i
\(683\) −2.62168e11 1.26253e11i −1.20475 0.580176i −0.279722 0.960081i \(-0.590242\pi\)
−0.925026 + 0.379905i \(0.875957\pi\)
\(684\) 1.79010e11 1.79010e11i 0.817811 0.817811i
\(685\) −6.66875e10 1.90582e11i −0.302888 0.865605i
\(686\) −1.30948e11 2.08402e11i −0.591292 0.941036i
\(687\) 1.96429e11 9.45953e10i 0.881818 0.424661i
\(688\) 2.45794e10 7.02440e10i 0.109703 0.313513i
\(689\) −6.63134e10 + 1.51356e10i −0.294256 + 0.0671619i
\(690\) −5.29968e11 + 6.64559e11i −2.33805 + 2.93182i
\(691\) −5.72458e10 7.17839e10i −0.251091 0.314858i 0.640272 0.768148i \(-0.278822\pi\)
−0.891363 + 0.453290i \(0.850250\pi\)
\(692\) 4.25455e10 1.86404e11i 0.185536 0.812888i
\(693\) −5.58468e9 + 8.88796e9i −0.0242139 + 0.0385362i
\(694\) −6.82308e10 + 6.05565e11i −0.294132 + 2.61049i
\(695\) 2.61203e11i 1.11954i
\(696\) −1.89843e10 7.63367e10i −0.0809016 0.325309i
\(697\) 3.52245e10 0.149250
\(698\) 2.20827e11 + 2.48813e10i 0.930318 + 0.104822i
\(699\) 2.68100e11 + 1.68458e11i 1.12302 + 0.705641i
\(700\) 1.08992e11 + 2.48768e10i 0.453945 + 0.103610i
\(701\) 2.05854e11 1.64163e11i 0.852486 0.679835i −0.0964383 0.995339i \(-0.530745\pi\)
0.948924 + 0.315504i \(0.102174\pi\)
\(702\) −1.24645e10 9.94013e9i −0.0513248 0.0409302i
\(703\) 1.19176e11 + 5.22142e11i 0.487939 + 2.13780i
\(704\) −1.73637e10 6.07581e9i −0.0706888 0.0247351i
\(705\) −2.02784e11 4.21086e11i −0.820876 1.70457i
\(706\) 5.02729e11 3.15886e11i 2.02356 1.27148i
\(707\) 2.22288e10 7.77819e9i 0.0889689 0.0311316i
\(708\) 1.50702e11 + 1.50702e11i 0.599772 + 0.599772i
\(709\) −1.43384e11 + 2.97740e11i −0.567435 + 1.17829i 0.397936 + 0.917413i \(0.369727\pi\)
−0.965372 + 0.260879i \(0.915988\pi\)
\(710\) −1.95197e10 1.73242e11i −0.0768137 0.681740i
\(711\) −1.99899e11 + 2.25232e10i −0.782225 + 0.0881356i
\(712\) −9.49730e10 4.57366e10i −0.369556 0.177969i
\(713\) −1.40110e11 + 1.40110e11i −0.542138 + 0.542138i
\(714\) 1.36116e10 + 3.88996e10i 0.0523740 + 0.149676i
\(715\) −4.48774e9 7.14220e9i −0.0171713 0.0273280i
\(716\) −2.48570e11 + 1.19705e11i −0.945796 + 0.455471i
\(717\) 8.59568e10 2.45650e11i 0.325240 0.929482i
\(718\) −3.74550e11 + 8.54887e10i −1.40933 + 0.321670i
\(719\) −7.08279e10 + 8.88153e10i −0.265026 + 0.332332i −0.896482 0.443079i \(-0.853886\pi\)
0.631456 + 0.775411i \(0.282457\pi\)
\(720\) 2.27762e11 + 2.85605e11i 0.847523 + 1.06276i
\(721\) −2.58190e10 + 1.13121e11i −0.0955430 + 0.418601i
\(722\) 4.36841e11 6.95228e11i 1.60759 2.55846i
\(723\) 3.91442e10 3.47414e11i 0.143256 1.27144i
\(724\) 2.98605e11i 1.08678i
\(725\) −2.08151e11 + 2.71631e11i −0.753401 + 0.983167i
\(726\) 4.92644e11 1.77332
\(727\) −2.04842e11 2.30801e10i −0.733299 0.0826230i −0.262585 0.964909i \(-0.584575\pi\)
−0.470714 + 0.882286i \(0.656004\pi\)
\(728\) −4.75478e9 2.98763e9i −0.0169280 0.0106366i
\(729\) 1.49485e11 + 3.41189e10i 0.529281 + 0.120805i
\(730\) −5.51230e11 + 4.39591e11i −1.94107 + 1.54795i
\(731\) −1.22740e10 9.78815e9i −0.0429848 0.0342792i
\(732\) −6.76533e10 2.96409e11i −0.235638 1.03240i
\(733\) 6.58819e10 + 2.30531e10i 0.228218 + 0.0798570i 0.441966 0.897032i \(-0.354281\pi\)
−0.213748 + 0.976889i \(0.568567\pi\)
\(734\) −4.98489e10 1.03512e11i −0.171740 0.356622i
\(735\) −3.89039e11 + 2.44449e11i −1.33304 + 0.837605i
\(736\) −5.01014e11 + 1.75313e11i −1.70741 + 0.597450i
\(737\) 6.26147e8 + 6.26147e8i 0.00212230 + 0.00212230i
\(738\) −1.07100e11 + 2.22396e11i −0.361048 + 0.749724i
\(739\) −4.43857e10 3.93934e11i −0.148821 1.32083i −0.816919 0.576752i \(-0.804320\pi\)
0.668098 0.744074i \(-0.267109\pi\)
\(740\) 4.41820e11 4.97812e10i 1.47339 0.166012i
\(741\) 1.13014e11 + 5.44246e10i 0.374851 + 0.180519i
\(742\) 2.32988e11 2.32988e11i 0.768630 0.768630i
\(743\) −2.71919e10 7.77100e10i −0.0892245 0.254989i 0.890621 0.454747i \(-0.150270\pi\)
−0.979845 + 0.199758i \(0.935985\pi\)
\(744\) 3.01137e10 + 4.79258e10i 0.0982818 + 0.156415i
\(745\) −1.41823e11 + 6.82982e10i −0.460384 + 0.221709i
\(746\) 8.41850e10 2.40587e11i 0.271819 0.776813i
\(747\) −4.69355e11 + 1.07127e11i −1.50737 + 0.344046i
\(748\) −3.78151e9 + 4.74187e9i −0.0120798 + 0.0151476i
\(749\) −1.55941e11 1.95544e11i −0.495489 0.621323i
\(750\) 4.52863e10 1.98412e11i 0.143127 0.627080i
\(751\) 2.72292e11 4.33350e11i 0.856002 1.36232i −0.0749540 0.997187i \(-0.523881\pi\)
0.930956 0.365132i \(-0.118976\pi\)
\(752\) 3.89767e10 3.45928e11i 0.121880 1.08172i
\(753\) 4.59081e11i 1.42794i
\(754\) −6.28748e10 + 4.12247e10i −0.194532 + 0.127547i
\(755\) 6.18152e10 0.190242
\(756\) 3.44353e10 + 3.87993e9i 0.105419 + 0.0118778i
\(757\) 1.17601e11 + 7.38935e10i 0.358119 + 0.225021i 0.699059 0.715064i \(-0.253603\pi\)
−0.340940 + 0.940085i \(0.610745\pi\)
\(758\) −2.34656e11 5.35586e10i −0.710811 0.162238i
\(759\) −6.03035e10 + 4.80904e10i −0.181709 + 0.144908i
\(760\) 1.76153e11 + 1.40477e11i 0.528001 + 0.421067i
\(761\) 6.93987e10 + 3.04056e11i 0.206925 + 0.906597i 0.966599 + 0.256293i \(0.0825013\pi\)
−0.759674 + 0.650304i \(0.774642\pi\)
\(762\) −4.56098e11 1.59596e11i −1.35282