Properties

Label 5.10.b.a.4.4
Level 5
Weight 10
Character 5.4
Analytic conductor 2.575
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(2.57517918082\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5}\cdot 3^{2}\cdot 5^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.4
Root \(2.87724i\)
Character \(\chi\) = 5.4
Dual form 5.10.b.a.4.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+41.3193i q^{2}\) \(-37.6407i q^{3}\) \(-1195.29 q^{4}\) \(+(1138.29 + 810.818i) q^{5}\) \(+1555.29 q^{6}\) \(+5315.22i q^{7}\) \(-28233.0i q^{8}\) \(+18266.2 q^{9}\) \(+O(q^{10})\) \(q\)\(+41.3193i q^{2}\) \(-37.6407i q^{3}\) \(-1195.29 q^{4}\) \(+(1138.29 + 810.818i) q^{5}\) \(+1555.29 q^{6}\) \(+5315.22i q^{7}\) \(-28233.0i q^{8}\) \(+18266.2 q^{9}\) \(+(-33502.5 + 47033.3i) q^{10}\) \(+10426.2 q^{11}\) \(+44991.4i q^{12}\) \(-79655.1i q^{13}\) \(-219621. q^{14}\) \(+(30519.7 - 42845.9i) q^{15}\) \(+554581. q^{16}\) \(-313750. i q^{17}\) \(+754746. i q^{18}\) \(+246945. q^{19}\) \(+(-1.36058e6 - 969161. i) q^{20}\) \(+200068. q^{21}\) \(+430806. i q^{22}\) \(+721761. i q^{23}\) \(-1.06271e6 q^{24}\) \(+(638273. + 1.84589e6i) q^{25}\) \(+3.29130e6 q^{26}\) \(-1.42843e6i q^{27}\) \(-6.35321e6i q^{28}\) \(-2.56903e6 q^{29}\) \(+(1.77037e6 + 1.26106e6i) q^{30}\) \(-3.29543e6 q^{31}\) \(+8.45965e6i q^{32}\) \(-392451. i q^{33}\) \(+1.29639e7 q^{34}\) \(+(-4.30967e6 + 6.05025e6i) q^{35}\) \(-2.18333e7 q^{36}\) \(-1.40463e7i q^{37}\) \(+1.02036e7i q^{38}\) \(-2.99827e6 q^{39}\) \(+(2.28918e7 - 3.21373e7i) q^{40}\) \(+1.70412e7 q^{41}\) \(+8.26669e6i q^{42}\) \(+2.92261e7i q^{43}\) \(-1.24624e7 q^{44}\) \(+(2.07922e7 + 1.48105e7i) q^{45}\) \(-2.98227e7 q^{46}\) \(-4.10316e7i q^{47}\) \(-2.08748e7i q^{48}\) \(+1.21021e7 q^{49}\) \(+(-7.62709e7 + 2.63730e7i) q^{50}\) \(-1.18098e7 q^{51}\) \(+9.52108e7i q^{52}\) \(-5.67230e7i q^{53}\) \(+5.90219e7 q^{54}\) \(+(1.18681e7 + 8.45379e6i) q^{55}\) \(+1.50065e8 q^{56}\) \(-9.29518e6i q^{57}\) \(-1.06150e8i q^{58}\) \(-1.60408e8 q^{59}\) \(+(-3.64799e7 + 5.12132e7i) q^{60}\) \(+5.33033e7 q^{61}\) \(-1.36165e8i q^{62}\) \(+9.70887e7i q^{63}\) \(-6.56012e7 q^{64}\) \(+(6.45858e7 - 9.06705e7i) q^{65}\) \(+1.62158e7 q^{66}\) \(+2.80916e8i q^{67}\) \(+3.75022e8i q^{68}\) \(+2.71676e7 q^{69}\) \(+(-2.49992e8 - 1.78073e8i) q^{70}\) \(-8.97228e7 q^{71}\) \(-5.15709e8i q^{72}\) \(-7.60225e7i q^{73}\) \(+5.80383e8 q^{74}\) \(+(6.94805e7 - 2.40250e7i) q^{75}\) \(-2.95170e8 q^{76}\) \(+5.54178e7i q^{77}\) \(-1.23887e8i q^{78}\) \(-4.10672e8 q^{79}\) \(+(6.31273e8 + 4.49665e8i) q^{80}\) \(+3.05766e8 q^{81}\) \(+7.04131e8i q^{82}\) \(-5.21969e8i q^{83}\) \(-2.39139e8 q^{84}\) \(+(2.54394e8 - 3.57138e8i) q^{85}\) \(-1.20760e9 q^{86}\) \(+9.66999e7i q^{87}\) \(-2.94364e8i q^{88}\) \(-2.37312e8 q^{89}\) \(+(-6.11962e8 + 8.59119e8i) q^{90}\) \(+4.23384e8 q^{91}\) \(-8.62712e8i q^{92}\) \(+1.24042e8i q^{93}\) \(+1.69540e9 q^{94}\) \(+(2.81094e8 + 2.00227e8i) q^{95}\) \(+3.18427e8 q^{96}\) \(+6.03778e8i q^{97}\) \(+5.00050e8i q^{98}\) \(+1.90448e8 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut -\mathstrut 1368q^{4} \) \(\mathstrut +\mathstrut 1140q^{5} \) \(\mathstrut +\mathstrut 2808q^{6} \) \(\mathstrut +\mathstrut 11628q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 1368q^{4} \) \(\mathstrut +\mathstrut 1140q^{5} \) \(\mathstrut +\mathstrut 2808q^{6} \) \(\mathstrut +\mathstrut 11628q^{9} \) \(\mathstrut -\mathstrut 69160q^{10} \) \(\mathstrut +\mathstrut 109968q^{11} \) \(\mathstrut -\mathstrut 424536q^{14} \) \(\mathstrut -\mathstrut 396720q^{15} \) \(\mathstrut +\mathstrut 1631264q^{16} \) \(\mathstrut -\mathstrut 636880q^{19} \) \(\mathstrut -\mathstrut 3302280q^{20} \) \(\mathstrut +\mathstrut 3523968q^{21} \) \(\mathstrut -\mathstrut 2435040q^{24} \) \(\mathstrut -\mathstrut 1337900q^{25} \) \(\mathstrut +\mathstrut 6618768q^{26} \) \(\mathstrut -\mathstrut 3531720q^{29} \) \(\mathstrut +\mathstrut 3712680q^{30} \) \(\mathstrut -\mathstrut 10587712q^{31} \) \(\mathstrut +\mathstrut 26434624q^{34} \) \(\mathstrut +\mathstrut 13629840q^{35} \) \(\mathstrut -\mathstrut 56399976q^{36} \) \(\mathstrut +\mathstrut 1686816q^{39} \) \(\mathstrut +\mathstrut 43578400q^{40} \) \(\mathstrut -\mathstrut 16788552q^{41} \) \(\mathstrut +\mathstrut 20638944q^{44} \) \(\mathstrut +\mathstrut 55737180q^{45} \) \(\mathstrut -\mathstrut 61250072q^{46} \) \(\mathstrut -\mathstrut 46921028q^{49} \) \(\mathstrut -\mathstrut 150092400q^{50} \) \(\mathstrut +\mathstrut 84017088q^{51} \) \(\mathstrut +\mathstrut 115855920q^{54} \) \(\mathstrut -\mathstrut 26907120q^{55} \) \(\mathstrut +\mathstrut 315178080q^{56} \) \(\mathstrut -\mathstrut 460829040q^{59} \) \(\mathstrut -\mathstrut 307006560q^{60} \) \(\mathstrut +\mathstrut 360490568q^{61} \) \(\mathstrut +\mathstrut 134995072q^{64} \) \(\mathstrut +\mathstrut 183895680q^{65} \) \(\mathstrut +\mathstrut 18949536q^{66} \) \(\mathstrut -\mathstrut 286524864q^{69} \) \(\mathstrut -\mathstrut 508341960q^{70} \) \(\mathstrut -\mathstrut 47611872q^{71} \) \(\mathstrut +\mathstrut 1176861744q^{74} \) \(\mathstrut +\mathstrut 659239200q^{75} \) \(\mathstrut -\mathstrut 1168489440q^{76} \) \(\mathstrut -\mathstrut 728043520q^{79} \) \(\mathstrut +\mathstrut 965843040q^{80} \) \(\mathstrut -\mathstrut 343387836q^{81} \) \(\mathstrut +\mathstrut 1118898144q^{84} \) \(\mathstrut +\mathstrut 1275419840q^{85} \) \(\mathstrut -\mathstrut 2375904552q^{86} \) \(\mathstrut -\mathstrut 1582700760q^{89} \) \(\mathstrut -\mathstrut 1197088920q^{90} \) \(\mathstrut +\mathstrut 473322528q^{91} \) \(\mathstrut +\mathstrut 3327101704q^{94} \) \(\mathstrut +\mathstrut 1204791600q^{95} \) \(\mathstrut +\mathstrut 399339648q^{96} \) \(\mathstrut -\mathstrut 728787024q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 41.3193i 1.82607i 0.407877 + 0.913037i \(0.366269\pi\)
−0.407877 + 0.913037i \(0.633731\pi\)
\(3\) 37.6407i 0.268294i −0.990961 0.134147i \(-0.957170\pi\)
0.990961 0.134147i \(-0.0428295\pi\)
\(4\) −1195.29 −2.33455
\(5\) 1138.29 + 810.818i 0.814492 + 0.580174i
\(6\) 1555.29 0.489926
\(7\) 5315.22i 0.836719i 0.908281 + 0.418360i \(0.137395\pi\)
−0.908281 + 0.418360i \(0.862605\pi\)
\(8\) 28233.0i 2.43698i
\(9\) 18266.2 0.928018
\(10\) −33502.5 + 47033.3i −1.05944 + 1.48732i
\(11\) 10426.2 0.214714 0.107357 0.994221i \(-0.465761\pi\)
0.107357 + 0.994221i \(0.465761\pi\)
\(12\) 44991.4i 0.626346i
\(13\) 79655.1i 0.773515i −0.922181 0.386758i \(-0.873595\pi\)
0.922181 0.386758i \(-0.126405\pi\)
\(14\) −219621. −1.52791
\(15\) 30519.7 42845.9i 0.155658 0.218524i
\(16\) 554581. 2.11556
\(17\) 313750.i 0.911095i −0.890212 0.455547i \(-0.849444\pi\)
0.890212 0.455547i \(-0.150556\pi\)
\(18\) 754746.i 1.69463i
\(19\) 246945. 0.434719 0.217360 0.976092i \(-0.430256\pi\)
0.217360 + 0.976092i \(0.430256\pi\)
\(20\) −1.36058e6 969161.i −1.90147 1.35444i
\(21\) 200068. 0.224487
\(22\) 430806.i 0.392084i
\(23\) 721761.i 0.537797i 0.963169 + 0.268898i \(0.0866595\pi\)
−0.963169 + 0.268898i \(0.913340\pi\)
\(24\) −1.06271e6 −0.653828
\(25\) 638273. + 1.84589e6i 0.326796 + 0.945095i
\(26\) 3.29130e6 1.41250
\(27\) 1.42843e6i 0.517277i
\(28\) 6.35321e6i 1.95336i
\(29\) −2.56903e6 −0.674493 −0.337247 0.941416i \(-0.609496\pi\)
−0.337247 + 0.941416i \(0.609496\pi\)
\(30\) 1.77037e6 + 1.26106e6i 0.399041 + 0.284242i
\(31\) −3.29543e6 −0.640891 −0.320445 0.947267i \(-0.603833\pi\)
−0.320445 + 0.947267i \(0.603833\pi\)
\(32\) 8.45965e6i 1.42619i
\(33\) 392451.i 0.0576066i
\(34\) 1.29639e7 1.66373
\(35\) −4.30967e6 + 6.05025e6i −0.485443 + 0.681502i
\(36\) −2.18333e7 −2.16650
\(37\) 1.40463e7i 1.23212i −0.787699 0.616060i \(-0.788728\pi\)
0.787699 0.616060i \(-0.211272\pi\)
\(38\) 1.02036e7i 0.793830i
\(39\) −2.99827e6 −0.207530
\(40\) 2.28918e7 3.21373e7i 1.41387 1.98490i
\(41\) 1.70412e7 0.941830 0.470915 0.882178i \(-0.343924\pi\)
0.470915 + 0.882178i \(0.343924\pi\)
\(42\) 8.26669e6i 0.409930i
\(43\) 2.92261e7i 1.30365i 0.758368 + 0.651827i \(0.225997\pi\)
−0.758368 + 0.651827i \(0.774003\pi\)
\(44\) −1.24624e7 −0.501260
\(45\) 2.07922e7 + 1.48105e7i 0.755864 + 0.538412i
\(46\) −2.98227e7 −0.982056
\(47\) 4.10316e7i 1.22653i −0.789878 0.613264i \(-0.789856\pi\)
0.789878 0.613264i \(-0.210144\pi\)
\(48\) 2.08748e7i 0.567593i
\(49\) 1.21021e7 0.299901
\(50\) −7.62709e7 + 2.63730e7i −1.72581 + 0.596753i
\(51\) −1.18098e7 −0.244442
\(52\) 9.52108e7i 1.80581i
\(53\) 5.67230e7i 0.987456i −0.869616 0.493728i \(-0.835634\pi\)
0.869616 0.493728i \(-0.164366\pi\)
\(54\) 5.90219e7 0.944585
\(55\) 1.18681e7 + 8.45379e6i 0.174883 + 0.124572i
\(56\) 1.50065e8 2.03907
\(57\) 9.29518e6i 0.116633i
\(58\) 1.06150e8i 1.23167i
\(59\) −1.60408e8 −1.72342 −0.861710 0.507402i \(-0.830606\pi\)
−0.861710 + 0.507402i \(0.830606\pi\)
\(60\) −3.64799e7 + 5.12132e7i −0.363390 + 0.510154i
\(61\) 5.33033e7 0.492912 0.246456 0.969154i \(-0.420734\pi\)
0.246456 + 0.969154i \(0.420734\pi\)
\(62\) 1.36165e8i 1.17031i
\(63\) 9.70887e7i 0.776491i
\(64\) −6.56012e7 −0.488767
\(65\) 6.45858e7 9.06705e7i 0.448773 0.630022i
\(66\) 1.62158e7 0.105194
\(67\) 2.80916e8i 1.70310i 0.524276 + 0.851548i \(0.324336\pi\)
−0.524276 + 0.851548i \(0.675664\pi\)
\(68\) 3.75022e8i 2.12699i
\(69\) 2.71676e7 0.144288
\(70\) −2.49992e8 1.78073e8i −1.24447 0.886455i
\(71\) −8.97228e7 −0.419025 −0.209513 0.977806i \(-0.567188\pi\)
−0.209513 + 0.977806i \(0.567188\pi\)
\(72\) 5.15709e8i 2.26156i
\(73\) 7.60225e7i 0.313321i −0.987653 0.156660i \(-0.949927\pi\)
0.987653 0.156660i \(-0.0500728\pi\)
\(74\) 5.80383e8 2.24994
\(75\) 6.94805e7 2.40250e7i 0.253564 0.0876775i
\(76\) −2.95170e8 −1.01487
\(77\) 5.54178e7i 0.179656i
\(78\) 1.23887e8i 0.378965i
\(79\) −4.10672e8 −1.18624 −0.593120 0.805114i \(-0.702104\pi\)
−0.593120 + 0.805114i \(0.702104\pi\)
\(80\) 6.31273e8 + 4.49665e8i 1.72311 + 1.22739i
\(81\) 3.05766e8 0.789236
\(82\) 7.04131e8i 1.71985i
\(83\) 5.21969e8i 1.20724i −0.797272 0.603620i \(-0.793724\pi\)
0.797272 0.603620i \(-0.206276\pi\)
\(84\) −2.39139e8 −0.524076
\(85\) 2.54394e8 3.57138e8i 0.528594 0.742080i
\(86\) −1.20760e9 −2.38057
\(87\) 9.66999e7i 0.180963i
\(88\) 2.94364e8i 0.523254i
\(89\) −2.37312e8 −0.400926 −0.200463 0.979701i \(-0.564245\pi\)
−0.200463 + 0.979701i \(0.564245\pi\)
\(90\) −6.11962e8 + 8.59119e8i −0.983180 + 1.38026i
\(91\) 4.23384e8 0.647215
\(92\) 8.62712e8i 1.25551i
\(93\) 1.24042e8i 0.171947i
\(94\) 1.69540e9 2.23973
\(95\) 2.81094e8 + 2.00227e8i 0.354076 + 0.252213i
\(96\) 3.18427e8 0.382639
\(97\) 6.03778e8i 0.692476i 0.938147 + 0.346238i \(0.112541\pi\)
−0.938147 + 0.346238i \(0.887459\pi\)
\(98\) 5.00050e8i 0.547641i
\(99\) 1.90448e8 0.199259
\(100\) −7.62920e8 2.20637e9i −0.762920 2.20637i
\(101\) −2.03606e8 −0.194690 −0.0973451 0.995251i \(-0.531035\pi\)
−0.0973451 + 0.995251i \(0.531035\pi\)
\(102\) 4.87972e8i 0.446369i
\(103\) 9.15893e8i 0.801821i 0.916117 + 0.400910i \(0.131306\pi\)
−0.916117 + 0.400910i \(0.868694\pi\)
\(104\) −2.24890e9 −1.88504
\(105\) 2.27735e8 + 1.62219e8i 0.182843 + 0.130242i
\(106\) 2.34376e9 1.80317
\(107\) 1.66237e9i 1.22603i −0.790072 0.613014i \(-0.789957\pi\)
0.790072 0.613014i \(-0.210043\pi\)
\(108\) 1.70739e9i 1.20761i
\(109\) −1.73161e9 −1.17498 −0.587491 0.809231i \(-0.699884\pi\)
−0.587491 + 0.809231i \(0.699884\pi\)
\(110\) −3.49305e8 + 4.90381e8i −0.227477 + 0.319350i
\(111\) −5.28711e8 −0.330571
\(112\) 2.94772e9i 1.77013i
\(113\) 6.30956e8i 0.364038i 0.983295 + 0.182019i \(0.0582632\pi\)
−0.983295 + 0.182019i \(0.941737\pi\)
\(114\) 3.84070e8 0.212980
\(115\) −5.85217e8 + 8.21571e8i −0.312016 + 0.438031i
\(116\) 3.07073e9 1.57464
\(117\) 1.45500e9i 0.717836i
\(118\) 6.62794e9i 3.14709i
\(119\) 1.66765e9 0.762331
\(120\) −1.20967e9 8.61664e8i −0.532538 0.379334i
\(121\) −2.24924e9 −0.953898
\(122\) 2.20246e9i 0.900094i
\(123\) 6.41442e8i 0.252688i
\(124\) 3.93898e9 1.49619
\(125\) −7.70141e8 + 2.61868e9i −0.282147 + 0.959371i
\(126\) −4.01164e9 −1.41793
\(127\) 2.12104e9i 0.723490i −0.932277 0.361745i \(-0.882181\pi\)
0.932277 0.361745i \(-0.117819\pi\)
\(128\) 1.62074e9i 0.533664i
\(129\) 1.10009e9 0.349763
\(130\) 3.74644e9 + 2.66864e9i 1.15047 + 0.819494i
\(131\) 5.57686e9 1.65451 0.827254 0.561828i \(-0.189902\pi\)
0.827254 + 0.561828i \(0.189902\pi\)
\(132\) 4.69092e8i 0.134485i
\(133\) 1.31257e9i 0.363738i
\(134\) −1.16072e10 −3.10998
\(135\) 1.15820e9 1.62597e9i 0.300111 0.421318i
\(136\) −8.85810e9 −2.22032
\(137\) 2.57317e9i 0.624059i 0.950072 + 0.312029i \(0.101009\pi\)
−0.950072 + 0.312029i \(0.898991\pi\)
\(138\) 1.12255e9i 0.263480i
\(139\) 1.62297e9 0.368761 0.184380 0.982855i \(-0.440972\pi\)
0.184380 + 0.982855i \(0.440972\pi\)
\(140\) 5.15130e9 7.23179e9i 1.13329 1.59100i
\(141\) −1.54446e9 −0.329071
\(142\) 3.70729e9i 0.765171i
\(143\) 8.30504e8i 0.166085i
\(144\) 1.01301e10 1.96328
\(145\) −2.92429e9 2.08301e9i −0.549370 0.391324i
\(146\) 3.14120e9 0.572147
\(147\) 4.55530e8i 0.0804617i
\(148\) 1.67893e10i 2.87644i
\(149\) 5.98422e9 0.994647 0.497324 0.867565i \(-0.334316\pi\)
0.497324 + 0.867565i \(0.334316\pi\)
\(150\) 9.92698e8 + 2.87089e9i 0.160106 + 0.463026i
\(151\) −5.95089e9 −0.931505 −0.465753 0.884915i \(-0.654216\pi\)
−0.465753 + 0.884915i \(0.654216\pi\)
\(152\) 6.97200e9i 1.05940i
\(153\) 5.73101e9i 0.845513i
\(154\) −2.28983e9 −0.328064
\(155\) −3.75114e9 2.67199e9i −0.522001 0.371828i
\(156\) 3.58380e9 0.484488
\(157\) 2.94325e9i 0.386615i 0.981138 + 0.193308i \(0.0619215\pi\)
−0.981138 + 0.193308i \(0.938078\pi\)
\(158\) 1.69687e10i 2.16616i
\(159\) −2.13509e9 −0.264929
\(160\) −6.85923e9 + 9.62951e9i −0.827438 + 1.16162i
\(161\) −3.83632e9 −0.449985
\(162\) 1.26341e10i 1.44120i
\(163\) 2.69823e9i 0.299389i 0.988732 + 0.149694i \(0.0478290\pi\)
−0.988732 + 0.149694i \(0.952171\pi\)
\(164\) −2.03691e10 −2.19875
\(165\) 3.18206e8 4.46722e8i 0.0334219 0.0469202i
\(166\) 2.15674e10 2.20451
\(167\) 1.47132e10i 1.46380i 0.681410 + 0.731902i \(0.261367\pi\)
−0.681410 + 0.731902i \(0.738633\pi\)
\(168\) 5.64853e9i 0.547071i
\(169\) 4.25956e9 0.401675
\(170\) 1.47567e10 + 1.05114e10i 1.35509 + 0.965251i
\(171\) 4.51074e9 0.403427
\(172\) 3.49336e10i 3.04344i
\(173\) 1.56605e8i 0.0132923i −0.999978 0.00664613i \(-0.997884\pi\)
0.999978 0.00664613i \(-0.00211555\pi\)
\(174\) −3.99558e9 −0.330452
\(175\) −9.81130e9 + 3.39256e9i −0.790779 + 0.273436i
\(176\) 5.78220e9 0.454241
\(177\) 6.03785e9i 0.462384i
\(178\) 9.80557e9i 0.732121i
\(179\) 5.35516e9 0.389883 0.194941 0.980815i \(-0.437548\pi\)
0.194941 + 0.980815i \(0.437548\pi\)
\(180\) −2.48526e10 1.77029e10i −1.76460 1.25695i
\(181\) −1.52107e9 −0.105341 −0.0526704 0.998612i \(-0.516773\pi\)
−0.0526704 + 0.998612i \(0.516773\pi\)
\(182\) 1.74940e10i 1.18186i
\(183\) 2.00637e9i 0.132246i
\(184\) 2.03775e10 1.31060
\(185\) 1.13890e10 1.59887e10i 0.714845 1.00355i
\(186\) −5.12534e9 −0.313989
\(187\) 3.27123e9i 0.195625i
\(188\) 4.90445e10i 2.86339i
\(189\) 7.59243e9 0.432815
\(190\) −8.27327e9 + 1.16146e10i −0.460560 + 0.646568i
\(191\) −9.28266e9 −0.504687 −0.252344 0.967638i \(-0.581201\pi\)
−0.252344 + 0.967638i \(0.581201\pi\)
\(192\) 2.46927e9i 0.131134i
\(193\) 6.94351e9i 0.360223i 0.983646 + 0.180111i \(0.0576458\pi\)
−0.983646 + 0.180111i \(0.942354\pi\)
\(194\) −2.49477e10 −1.26451
\(195\) −3.41290e9 2.43105e9i −0.169031 0.120403i
\(196\) −1.44655e10 −0.700132
\(197\) 3.60722e10i 1.70637i −0.521606 0.853187i \(-0.674667\pi\)
0.521606 0.853187i \(-0.325333\pi\)
\(198\) 7.86917e9i 0.363861i
\(199\) −2.25173e10 −1.01784 −0.508918 0.860815i \(-0.669955\pi\)
−0.508918 + 0.860815i \(0.669955\pi\)
\(200\) 5.21150e10 1.80204e10i 2.30318 0.796395i
\(201\) 1.05739e10 0.456931
\(202\) 8.41286e9i 0.355519i
\(203\) 1.36549e10i 0.564362i
\(204\) 1.41161e10 0.570661
\(205\) 1.93978e10 + 1.38173e10i 0.767114 + 0.546426i
\(206\) −3.78441e10 −1.46418
\(207\) 1.31838e10i 0.499085i
\(208\) 4.41753e10i 1.63642i
\(209\) 2.57471e9 0.0933404
\(210\) −6.70278e9 + 9.40988e9i −0.237831 + 0.333885i
\(211\) 3.62300e10 1.25834 0.629169 0.777268i \(-0.283395\pi\)
0.629169 + 0.777268i \(0.283395\pi\)
\(212\) 6.78003e10i 2.30526i
\(213\) 3.37723e9i 0.112422i
\(214\) 6.86879e10 2.23882
\(215\) −2.36970e10 + 3.32677e10i −0.756346 + 1.06182i
\(216\) −4.03289e10 −1.26059
\(217\) 1.75159e10i 0.536246i
\(218\) 7.15490e10i 2.14560i
\(219\) −2.86154e9 −0.0840623
\(220\) −1.41858e10 1.01047e10i −0.408273 0.290818i
\(221\) −2.49918e10 −0.704746
\(222\) 2.18460e10i 0.603647i
\(223\) 4.93834e10i 1.33724i 0.743605 + 0.668619i \(0.233114\pi\)
−0.743605 + 0.668619i \(0.766886\pi\)
\(224\) −4.49649e10 −1.19332
\(225\) 1.16588e10 + 3.37173e10i 0.303272 + 0.877065i
\(226\) −2.60707e10 −0.664760
\(227\) 3.27710e10i 0.819169i −0.912272 0.409585i \(-0.865674\pi\)
0.912272 0.409585i \(-0.134326\pi\)
\(228\) 1.11104e10i 0.272285i
\(229\) −1.35586e10 −0.325803 −0.162902 0.986642i \(-0.552085\pi\)
−0.162902 + 0.986642i \(0.552085\pi\)
\(230\) −3.39468e10 2.41808e10i −0.799877 0.569764i
\(231\) 2.08596e9 0.0482006
\(232\) 7.25313e10i 1.64373i
\(233\) 7.99837e9i 0.177787i −0.996041 0.0888935i \(-0.971667\pi\)
0.996041 0.0888935i \(-0.0283331\pi\)
\(234\) 6.01194e10 1.31082
\(235\) 3.32691e10 4.67057e10i 0.711600 0.998998i
\(236\) 1.91733e11 4.02340
\(237\) 1.54580e10i 0.318262i
\(238\) 6.89062e10i 1.39207i
\(239\) −8.30208e10 −1.64587 −0.822937 0.568133i \(-0.807666\pi\)
−0.822937 + 0.568133i \(0.807666\pi\)
\(240\) 1.69257e10 2.37616e10i 0.329303 0.462300i
\(241\) −6.04789e10 −1.15485 −0.577427 0.816442i \(-0.695943\pi\)
−0.577427 + 0.816442i \(0.695943\pi\)
\(242\) 9.29372e10i 1.74189i
\(243\) 3.96251e10i 0.729024i
\(244\) −6.37128e10 −1.15073
\(245\) 1.37756e10 + 9.81258e9i 0.244267 + 0.173995i
\(246\) 2.65040e10 0.461427
\(247\) 1.96704e10i 0.336262i
\(248\) 9.30398e10i 1.56184i
\(249\) −1.96473e10 −0.323896
\(250\) −1.08202e11 3.18217e10i −1.75188 0.515221i
\(251\) 1.04682e11 1.66471 0.832354 0.554244i \(-0.186993\pi\)
0.832354 + 0.554244i \(0.186993\pi\)
\(252\) 1.16049e11i 1.81275i
\(253\) 7.52525e9i 0.115473i
\(254\) 8.76400e10 1.32115
\(255\) −1.34429e10 9.57557e9i −0.199096 0.141819i
\(256\) −1.00556e11 −1.46328
\(257\) 7.92751e10i 1.13354i 0.823875 + 0.566771i \(0.191808\pi\)
−0.823875 + 0.566771i \(0.808192\pi\)
\(258\) 4.54549e10i 0.638693i
\(259\) 7.46590e10 1.03094
\(260\) −7.71987e10 + 1.08377e11i −1.04768 + 1.47082i
\(261\) −4.69263e10 −0.625942
\(262\) 2.30432e11i 3.02126i
\(263\) 1.04629e8i 0.00134850i −1.00000 0.000674250i \(-0.999785\pi\)
1.00000 0.000674250i \(-0.000214620\pi\)
\(264\) −1.10801e10 −0.140386
\(265\) 4.59920e10 6.45671e10i 0.572897 0.804275i
\(266\) −5.42344e10 −0.664213
\(267\) 8.93258e9i 0.107566i
\(268\) 3.35775e11i 3.97596i
\(269\) 7.38735e9 0.0860208 0.0430104 0.999075i \(-0.486305\pi\)
0.0430104 + 0.999075i \(0.486305\pi\)
\(270\) 6.71839e10 + 4.78560e10i 0.769358 + 0.548024i
\(271\) 1.27706e11 1.43831 0.719153 0.694852i \(-0.244530\pi\)
0.719153 + 0.694852i \(0.244530\pi\)
\(272\) 1.74000e11i 1.92748i
\(273\) 1.59365e10i 0.173644i
\(274\) −1.06322e11 −1.13958
\(275\) 6.65479e9 + 1.92457e10i 0.0701677 + 0.202925i
\(276\) −3.24731e10 −0.336847
\(277\) 3.16563e10i 0.323074i 0.986867 + 0.161537i \(0.0516451\pi\)
−0.986867 + 0.161537i \(0.948355\pi\)
\(278\) 6.70602e10i 0.673385i
\(279\) −6.01949e10 −0.594758
\(280\) 1.70817e11 + 1.21675e11i 1.66081 + 1.18302i
\(281\) −9.50309e10 −0.909257 −0.454628 0.890681i \(-0.650228\pi\)
−0.454628 + 0.890681i \(0.650228\pi\)
\(282\) 6.38159e10i 0.600908i
\(283\) 4.91862e10i 0.455832i −0.973681 0.227916i \(-0.926809\pi\)
0.973681 0.227916i \(-0.0731911\pi\)
\(284\) 1.07245e11 0.978234
\(285\) 7.53670e9 1.05806e10i 0.0676673 0.0949965i
\(286\) 3.43159e10 0.303283
\(287\) 9.05777e10i 0.788048i
\(288\) 1.54525e11i 1.32353i
\(289\) 2.01488e10 0.169906
\(290\) 8.60687e10 1.20830e11i 0.714586 1.00319i
\(291\) 2.27266e10 0.185787
\(292\) 9.08688e10i 0.731462i
\(293\) 3.53889e10i 0.280519i −0.990115 0.140260i \(-0.955206\pi\)
0.990115 0.140260i \(-0.0447937\pi\)
\(294\) 1.88222e10 0.146929
\(295\) −1.82590e11 1.30061e11i −1.40371 0.999883i
\(296\) −3.96568e11 −3.00265
\(297\) 1.48932e10i 0.111067i
\(298\) 2.47264e11i 1.81630i
\(299\) 5.74920e10 0.415994
\(300\) −8.30492e10 + 2.87168e10i −0.591956 + 0.204687i
\(301\) −1.55343e11 −1.09079
\(302\) 2.45887e11i 1.70100i
\(303\) 7.66386e9i 0.0522343i
\(304\) 1.36951e11 0.919675
\(305\) 6.06745e10 + 4.32193e10i 0.401473 + 0.285975i
\(306\) 2.36802e11 1.54397
\(307\) 8.30301e10i 0.533474i −0.963769 0.266737i \(-0.914055\pi\)
0.963769 0.266737i \(-0.0859455\pi\)
\(308\) 6.62402e10i 0.419414i
\(309\) 3.44748e10 0.215124
\(310\) 1.10405e11 1.54995e11i 0.678986 0.953212i
\(311\) 2.13935e10 0.129676 0.0648382 0.997896i \(-0.479347\pi\)
0.0648382 + 0.997896i \(0.479347\pi\)
\(312\) 8.46502e10i 0.505746i
\(313\) 2.56558e11i 1.51090i 0.655204 + 0.755452i \(0.272582\pi\)
−0.655204 + 0.755452i \(0.727418\pi\)
\(314\) −1.21613e11 −0.705988
\(315\) −7.87213e10 + 1.10515e11i −0.450500 + 0.632446i
\(316\) 4.90871e11 2.76933
\(317\) 1.26112e11i 0.701436i 0.936481 + 0.350718i \(0.114062\pi\)
−0.936481 + 0.350718i \(0.885938\pi\)
\(318\) 8.82206e10i 0.483780i
\(319\) −2.67853e10 −0.144823
\(320\) −7.46731e10 5.31907e10i −0.398097 0.283570i
\(321\) −6.25727e10 −0.328936
\(322\) 1.58514e11i 0.821706i
\(323\) 7.74790e10i 0.396071i
\(324\) −3.65478e11 −1.84251
\(325\) 1.47035e11 5.08417e10i 0.731045 0.252781i
\(326\) −1.11489e11 −0.546706
\(327\) 6.51790e10i 0.315241i
\(328\) 4.81124e11i 2.29522i
\(329\) 2.18092e11 1.02626
\(330\) 1.84583e10 + 1.31481e10i 0.0856797 + 0.0610308i
\(331\) 1.71300e11 0.784389 0.392194 0.919882i \(-0.371716\pi\)
0.392194 + 0.919882i \(0.371716\pi\)
\(332\) 6.23904e11i 2.81836i
\(333\) 2.56572e11i 1.14343i
\(334\) −6.07939e11 −2.67301
\(335\) −2.27771e11 + 3.19763e11i −0.988093 + 1.38716i
\(336\) 1.10954e11 0.474916
\(337\) 4.70320e11i 1.98637i −0.116569 0.993183i \(-0.537190\pi\)
0.116569 0.993183i \(-0.462810\pi\)
\(338\) 1.76002e11i 0.733487i
\(339\) 2.37496e10 0.0976693
\(340\) −3.04074e11 + 4.26882e11i −1.23403 + 1.73242i
\(341\) −3.43589e10 −0.137608
\(342\) 1.86381e11i 0.736688i
\(343\) 2.78813e11i 1.08765i
\(344\) 8.25140e11 3.17698
\(345\) 3.09245e10 + 2.20279e10i 0.117521 + 0.0837121i
\(346\) 6.47083e9 0.0242727
\(347\) 2.86642e11i 1.06135i −0.847576 0.530674i \(-0.821939\pi\)
0.847576 0.530674i \(-0.178061\pi\)
\(348\) 1.15584e11i 0.422466i
\(349\) 3.54310e11 1.27841 0.639203 0.769038i \(-0.279264\pi\)
0.639203 + 0.769038i \(0.279264\pi\)
\(350\) −1.40178e11 4.05396e11i −0.499315 1.44402i
\(351\) −1.13782e11 −0.400121
\(352\) 8.82023e10i 0.306223i
\(353\) 2.09491e11i 0.718092i −0.933320 0.359046i \(-0.883102\pi\)
0.933320 0.359046i \(-0.116898\pi\)
\(354\) −2.49480e11 −0.844347
\(355\) −1.02130e11 7.27489e10i −0.341293 0.243108i
\(356\) 2.83656e11 0.935981
\(357\) 6.27715e10i 0.204529i
\(358\) 2.21272e11i 0.711955i
\(359\) −2.88081e11 −0.915355 −0.457678 0.889118i \(-0.651319\pi\)
−0.457678 + 0.889118i \(0.651319\pi\)
\(360\) 4.18146e11 5.87025e11i 1.31210 1.84203i
\(361\) −2.61706e11 −0.811019
\(362\) 6.28498e10i 0.192360i
\(363\) 8.46630e10i 0.255926i
\(364\) −5.06066e11 −1.51095
\(365\) 6.16404e10 8.65355e10i 0.181781 0.255197i
\(366\) 8.29019e10 0.241490
\(367\) 1.33587e10i 0.0384387i −0.999815 0.0192193i \(-0.993882\pi\)
0.999815 0.0192193i \(-0.00611808\pi\)
\(368\) 4.00275e11i 1.13774i
\(369\) 3.11278e11 0.874036
\(370\) 6.60642e11 + 4.70585e11i 1.83256 + 1.30536i
\(371\) 3.01495e11 0.826224
\(372\) 1.48266e11i 0.401419i
\(373\) 4.17763e11i 1.11748i 0.829342 + 0.558741i \(0.188716\pi\)
−0.829342 + 0.558741i \(0.811284\pi\)
\(374\) 1.35165e11 0.357226
\(375\) 9.85687e10 + 2.89886e10i 0.257394 + 0.0756985i
\(376\) −1.15844e12 −2.98903
\(377\) 2.04636e11i 0.521731i
\(378\) 3.13714e11i 0.790353i
\(379\) −2.63110e11 −0.655031 −0.327515 0.944846i \(-0.606211\pi\)
−0.327515 + 0.944846i \(0.606211\pi\)
\(380\) −3.35989e11 2.39329e11i −0.826606 0.588803i
\(381\) −7.98374e10 −0.194108
\(382\) 3.83553e11i 0.921596i
\(383\) 7.84146e10i 0.186210i −0.995656 0.0931049i \(-0.970321\pi\)
0.995656 0.0931049i \(-0.0296792\pi\)
\(384\) 6.10057e10 0.143179
\(385\) −4.49337e10 + 6.30814e10i −0.104232 + 0.146328i
\(386\) −2.86901e11 −0.657793
\(387\) 5.33849e11i 1.20981i
\(388\) 7.21688e11i 1.61662i
\(389\) −1.66007e11 −0.367581 −0.183791 0.982965i \(-0.558837\pi\)
−0.183791 + 0.982965i \(0.558837\pi\)
\(390\) 1.00450e11 1.41019e11i 0.219866 0.308664i
\(391\) 2.26452e11 0.489984
\(392\) 3.41678e11i 0.730852i
\(393\) 2.09917e11i 0.443896i
\(394\) 1.49048e12 3.11596
\(395\) −4.67462e11 3.32980e11i −0.966184 0.688226i
\(396\) −2.27640e11 −0.465179
\(397\) 4.09536e11i 0.827437i 0.910405 + 0.413719i \(0.135770\pi\)
−0.910405 + 0.413719i \(0.864230\pi\)
\(398\) 9.30402e11i 1.85865i
\(399\) 4.94059e10 0.0975889
\(400\) 3.53974e11 + 1.02370e12i 0.691356 + 1.99941i
\(401\) −7.92645e10 −0.153084 −0.0765419 0.997066i \(-0.524388\pi\)
−0.0765419 + 0.997066i \(0.524388\pi\)
\(402\) 4.36905e11i 0.834391i
\(403\) 2.62498e11i 0.495739i
\(404\) 2.43367e11 0.454513
\(405\) 3.48050e11 + 2.47921e11i 0.642826 + 0.457894i
\(406\) 5.64213e11 1.03057
\(407\) 1.46450e11i 0.264554i
\(408\) 3.33425e11i 0.595700i
\(409\) −6.85827e11 −1.21188 −0.605940 0.795510i \(-0.707203\pi\)
−0.605940 + 0.795510i \(0.707203\pi\)
\(410\) −5.70922e11 + 8.01504e11i −0.997814 + 1.40081i
\(411\) 9.68557e10 0.167431
\(412\) 1.09476e12i 1.87189i
\(413\) 8.52601e11i 1.44202i
\(414\) −5.44746e11 −0.911366
\(415\) 4.23222e11 5.94151e11i 0.700410 0.983288i
\(416\) 6.73854e11 1.10318
\(417\) 6.10898e10i 0.0989365i
\(418\) 1.06385e11i 0.170447i
\(419\) −3.31879e11 −0.526037 −0.263018 0.964791i \(-0.584718\pi\)
−0.263018 + 0.964791i \(0.584718\pi\)
\(420\) −2.72209e11 1.93898e11i −0.426856 0.304055i
\(421\) −6.30694e11 −0.978475 −0.489237 0.872151i \(-0.662725\pi\)
−0.489237 + 0.872151i \(0.662725\pi\)
\(422\) 1.49700e12i 2.29782i
\(423\) 7.49490e11i 1.13824i
\(424\) −1.60146e12 −2.40641
\(425\) 5.79148e11 2.00258e11i 0.861071 0.297742i
\(426\) −1.39545e11 −0.205291
\(427\) 2.83319e11i 0.412429i
\(428\) 1.98701e12i 2.86222i
\(429\) −3.12607e10 −0.0445596
\(430\) −1.37460e12 9.79145e11i −1.93896 1.38114i
\(431\) 7.70903e11 1.07610 0.538049 0.842913i \(-0.319161\pi\)
0.538049 + 0.842913i \(0.319161\pi\)
\(432\) 7.92182e11i 1.09433i
\(433\) 1.07829e12i 1.47415i 0.675811 + 0.737075i \(0.263794\pi\)
−0.675811 + 0.737075i \(0.736206\pi\)
\(434\) 7.23746e11 0.979225
\(435\) −7.84060e10 + 1.10072e11i −0.104990 + 0.147393i
\(436\) 2.06977e12 2.74305
\(437\) 1.78235e11i 0.233791i
\(438\) 1.18237e11i 0.153504i
\(439\) 9.56419e11 1.22902 0.614508 0.788910i \(-0.289354\pi\)
0.614508 + 0.788910i \(0.289354\pi\)
\(440\) 2.38676e11 3.35071e11i 0.303579 0.426187i
\(441\) 2.21059e11 0.278313
\(442\) 1.03264e12i 1.28692i
\(443\) 2.06392e11i 0.254611i 0.991864 + 0.127305i \(0.0406328\pi\)
−0.991864 + 0.127305i \(0.959367\pi\)
\(444\) 6.31962e11 0.771734
\(445\) −2.70129e11 1.92417e11i −0.326551 0.232607i
\(446\) −2.04049e12 −2.44190
\(447\) 2.25250e11i 0.266858i
\(448\) 3.48685e11i 0.408961i
\(449\) −1.75939e11 −0.204293 −0.102147 0.994769i \(-0.532571\pi\)
−0.102147 + 0.994769i \(0.532571\pi\)
\(450\) −1.39318e12 + 4.81734e11i −1.60159 + 0.553798i
\(451\) 1.77676e11 0.202224
\(452\) 7.54174e11i 0.849863i
\(453\) 2.23995e11i 0.249918i
\(454\) 1.35408e12 1.49586
\(455\) 4.81933e11 + 3.43288e11i 0.527152 + 0.375497i
\(456\) −2.62431e11 −0.284232
\(457\) 2.98819e11i 0.320469i 0.987079 + 0.160234i \(0.0512250\pi\)
−0.987079 + 0.160234i \(0.948775\pi\)
\(458\) 5.60233e11i 0.594941i
\(459\) −4.48171e11 −0.471288
\(460\) 6.99502e11 9.82014e11i 0.728415 1.02260i
\(461\) 4.39422e11 0.453135 0.226567 0.973995i \(-0.427250\pi\)
0.226567 + 0.973995i \(0.427250\pi\)
\(462\) 8.61906e10i 0.0880179i
\(463\) 1.16254e12i 1.17569i −0.808973 0.587846i \(-0.799976\pi\)
0.808973 0.587846i \(-0.200024\pi\)
\(464\) −1.42473e12 −1.42693
\(465\) −1.00576e11 + 1.41196e11i −0.0997595 + 0.140050i
\(466\) 3.30487e11 0.324652
\(467\) 1.65923e11i 0.161429i 0.996737 + 0.0807144i \(0.0257202\pi\)
−0.996737 + 0.0807144i \(0.974280\pi\)
\(468\) 1.73914e12i 1.67582i
\(469\) −1.49313e12 −1.42501
\(470\) 1.92985e12 + 1.37466e12i 1.82425 + 1.29944i
\(471\) 1.10786e11 0.103727
\(472\) 4.52879e12i 4.19994i
\(473\) 3.04718e11i 0.279913i
\(474\) −6.38712e11 −0.581169
\(475\) 1.57618e11 + 4.55833e11i 0.142064 + 0.410851i
\(476\) −1.99332e12 −1.77970
\(477\) 1.03611e12i 0.916377i
\(478\) 3.43036e12i 3.00549i
\(479\) −1.33180e11 −0.115592 −0.0577960 0.998328i \(-0.518407\pi\)
−0.0577960 + 0.998328i \(0.518407\pi\)
\(480\) 3.62461e11 + 2.58186e11i 0.311656 + 0.221997i
\(481\) −1.11886e12 −0.953064
\(482\) 2.49895e12i 2.10885i
\(483\) 1.44401e11i 0.120728i
\(484\) 2.68849e12 2.22692
\(485\) −4.89554e11 + 6.87273e11i −0.401756 + 0.564016i
\(486\) 1.63728e12 1.33125
\(487\) 1.43276e12i 1.15423i −0.816662 0.577116i \(-0.804178\pi\)
0.816662 0.577116i \(-0.195822\pi\)
\(488\) 1.50491e12i 1.20122i
\(489\) 1.01563e11 0.0803243
\(490\) −4.05449e11 + 5.69200e11i −0.317727 + 0.446049i
\(491\) −1.05688e12 −0.820655 −0.410327 0.911938i \(-0.634586\pi\)
−0.410327 + 0.911938i \(0.634586\pi\)
\(492\) 7.66708e11i 0.589912i
\(493\) 8.06032e11i 0.614527i
\(494\) 8.12769e11 0.614039
\(495\) 2.16784e11 + 1.54418e11i 0.162295 + 0.115605i
\(496\) −1.82758e12 −1.35584
\(497\) 4.76896e11i 0.350607i
\(498\) 8.11813e11i 0.591458i
\(499\) −1.77897e11 −0.128445 −0.0642223 0.997936i \(-0.520457\pi\)
−0.0642223 + 0.997936i \(0.520457\pi\)
\(500\) 9.20541e11 3.13007e12i 0.658685 2.23970i
\(501\) 5.53814e11 0.392730
\(502\) 4.32537e12i 3.03988i
\(503\) 1.58467e12i 1.10378i 0.833917 + 0.551889i \(0.186093\pi\)
−0.833917 + 0.551889i \(0.813907\pi\)
\(504\) 2.74111e12 1.89229
\(505\) −2.31762e11 1.65087e11i −0.158574 0.112954i
\(506\) −3.10939e11 −0.210861
\(507\) 1.60333e11i 0.107767i
\(508\) 2.53525e12i 1.68902i
\(509\) 1.93674e12 1.27891 0.639456 0.768827i \(-0.279159\pi\)
0.639456 + 0.768827i \(0.279159\pi\)
\(510\) 3.95656e11 5.55452e11i 0.258972 0.363564i
\(511\) 4.04076e11 0.262162
\(512\) 3.32508e12i 2.13839i
\(513\) 3.52744e11i 0.224870i
\(514\) −3.27560e12 −2.06993
\(515\) −7.42623e11 + 1.04255e12i −0.465196 + 0.653077i
\(516\) −1.31492e12 −0.816538
\(517\) 4.27805e11i 0.263353i
\(518\) 3.08486e12i 1.88257i
\(519\) −5.89473e9 −0.00356624
\(520\) −2.55990e12 1.82345e12i −1.53535 1.09365i
\(521\) 2.72419e12 1.61982 0.809912 0.586552i \(-0.199515\pi\)
0.809912 + 0.586552i \(0.199515\pi\)
\(522\) 1.93896e12i 1.14302i
\(523\) 4.86784e11i 0.284497i 0.989831 + 0.142249i \(0.0454333\pi\)
−0.989831 + 0.142249i \(0.954567\pi\)
\(524\) −6.66596e12 −3.86253
\(525\) 1.27698e11 + 3.69304e11i 0.0733615 + 0.212162i
\(526\) 4.32320e9 0.00246246
\(527\) 1.03394e12i 0.583912i
\(528\) 2.17646e11i 0.121870i
\(529\) 1.28021e12 0.710775
\(530\) 2.66787e12 + 1.90036e12i 1.46867 + 1.04615i
\(531\) −2.93003e12 −1.59936
\(532\) 1.56889e12i 0.849164i
\(533\) 1.35742e12i 0.728520i
\(534\) −3.69088e11 −0.196424
\(535\) 1.34788e12 1.89225e12i 0.711309 0.998590i
\(536\) 7.93109e12 4.15041
\(537\) 2.01572e11i 0.104603i
\(538\) 3.05240e11i 0.157080i
\(539\) 1.26179e11 0.0643929
\(540\) −1.38438e12 + 1.94350e12i −0.700622 + 0.983586i
\(541\) 1.98233e11 0.0994920 0.0497460 0.998762i \(-0.484159\pi\)
0.0497460 + 0.998762i \(0.484159\pi\)
\(542\) 5.27675e12i 2.62645i
\(543\) 5.72543e10i 0.0282624i
\(544\) 2.65421e12 1.29939
\(545\) −1.97107e12 1.40402e12i −0.957014 0.681694i
\(546\) 6.58485e11 0.317087
\(547\) 4.79532e11i 0.229021i 0.993422 + 0.114510i \(0.0365299\pi\)
−0.993422 + 0.114510i \(0.963470\pi\)
\(548\) 3.07567e12i 1.45689i
\(549\) 9.73647e11 0.457432
\(550\) −7.95219e11 + 2.74972e11i −0.370557 + 0.128131i
\(551\) −6.34408e11 −0.293215
\(552\) 7.67022e11i 0.351627i
\(553\) 2.18281e12i 0.992550i
\(554\) −1.30802e12 −0.589957
\(555\) −6.01825e11 4.28688e11i −0.269248 0.191789i
\(556\) −1.93992e12 −0.860889
\(557\) 1.20856e11i 0.0532011i −0.999646 0.0266006i \(-0.991532\pi\)
0.999646 0.0266006i \(-0.00846822\pi\)
\(558\) 2.48721e12i 1.08607i
\(559\) 2.32801e12 1.00840
\(560\) −2.39007e12 + 3.35536e12i −1.02698 + 1.44176i
\(561\) −1.23131e11 −0.0524851
\(562\) 3.92662e12i 1.66037i
\(563\) 1.01468e12i 0.425637i −0.977092 0.212818i \(-0.931736\pi\)
0.977092 0.212818i \(-0.0682643\pi\)
\(564\) 1.84607e12 0.768231
\(565\) −5.11591e11 + 7.18210e11i −0.211205 + 0.296506i
\(566\) 2.03234e12 0.832382
\(567\) 1.62521e12i 0.660369i
\(568\) 2.53314e12i 1.02116i
\(569\) −1.12630e12 −0.450454 −0.225227 0.974306i \(-0.572312\pi\)
−0.225227 + 0.974306i \(0.572312\pi\)
\(570\) 4.37183e11 + 3.11411e11i 0.173471 + 0.123566i
\(571\) −2.75478e12 −1.08449 −0.542243 0.840221i \(-0.682425\pi\)
−0.542243 + 0.840221i \(0.682425\pi\)
\(572\) 9.92691e11i 0.387732i
\(573\) 3.49405e11i 0.135405i
\(574\) −3.74261e12 −1.43903
\(575\) −1.33229e12 + 4.60680e11i −0.508269 + 0.175750i
\(576\) −1.19828e12 −0.453585
\(577\) 4.14763e12i 1.55779i 0.627155 + 0.778895i \(0.284219\pi\)
−0.627155 + 0.778895i \(0.715781\pi\)
\(578\) 8.32535e11i 0.310261i
\(579\) 2.61358e11 0.0966458
\(580\) 3.49537e12 + 2.48980e12i 1.28253 + 0.913563i
\(581\) 2.77438e12 1.01012
\(582\) 9.39049e11i 0.339262i
\(583\) 5.91408e11i 0.212021i
\(584\) −2.14634e12 −0.763557
\(585\) 1.17974e12 1.65620e12i 0.416470 0.584672i
\(586\) 1.46224e12 0.512248
\(587\) 1.38017e12i 0.479800i 0.970798 + 0.239900i \(0.0771147\pi\)
−0.970798 + 0.239900i \(0.922885\pi\)
\(588\) 5.44490e11i 0.187842i
\(589\) −8.13789e11 −0.278608
\(590\) 5.37405e12 7.54450e12i 1.82586 2.56328i
\(591\) −1.35778e12 −0.457811
\(592\) 7.78980e12i 2.60663i
\(593\) 6.90406e11i 0.229276i 0.993407 + 0.114638i \(0.0365708\pi\)
−0.993407 + 0.114638i \(0.963429\pi\)
\(594\) 6.15377e11 0.202816
\(595\) 1.89827e12 + 1.35216e12i 0.620913 + 0.442285i
\(596\) −7.15286e12 −2.32205
\(597\) 8.47568e11i 0.273080i
\(598\) 2.37553e12i 0.759635i
\(599\) −1.24239e12 −0.394309 −0.197155 0.980372i \(-0.563170\pi\)
−0.197155 + 0.980372i \(0.563170\pi\)
\(600\) −6.78299e11 1.96164e12i −0.213668 0.617930i
\(601\) 2.01140e12 0.628873 0.314437 0.949278i \(-0.398184\pi\)
0.314437 + 0.949278i \(0.398184\pi\)
\(602\) 6.41867e12i 1.99187i
\(603\) 5.13126e12i 1.58050i
\(604\) 7.11302e12 2.17464
\(605\) −2.56028e12 1.82373e12i −0.776943 0.553427i
\(606\) −3.16666e11 −0.0953837
\(607\) 2.73579e12i 0.817963i −0.912543 0.408981i \(-0.865884\pi\)
0.912543 0.408981i \(-0.134116\pi\)
\(608\) 2.08907e12i 0.619992i
\(609\) −5.13981e11 −0.151415
\(610\) −1.78579e12 + 2.50703e12i −0.522211 + 0.733120i
\(611\) −3.26838e12 −0.948738
\(612\) 6.85021e12i 1.97389i
\(613\) 1.63707e12i 0.468269i −0.972204 0.234135i \(-0.924774\pi\)
0.972204 0.234135i \(-0.0752257\pi\)
\(614\) 3.43075e12 0.974162
\(615\) 5.20093e11 7.30146e11i 0.146603 0.205812i
\(616\) 1.56461e12 0.437817
\(617\) 1.22267e12i 0.339646i −0.985475 0.169823i \(-0.945680\pi\)
0.985475 0.169823i \(-0.0543197\pi\)
\(618\) 1.42448e12i 0.392832i
\(619\) 5.78784e12 1.58456 0.792280 0.610158i \(-0.208894\pi\)
0.792280 + 0.610158i \(0.208894\pi\)
\(620\) 4.48370e12 + 3.19380e12i 1.21863 + 0.868050i
\(621\) 1.03099e12 0.278190
\(622\) 8.83967e11i 0.236799i
\(623\) 1.26136e12i 0.335463i
\(624\) −1.66279e12 −0.439042
\(625\) −2.99991e12 + 2.35636e12i −0.786409 + 0.617706i
\(626\) −1.06008e13 −2.75902
\(627\) 9.69138e10i 0.0250427i
\(628\) 3.51803e12i 0.902571i
\(629\) −4.40702e12 −1.12258
\(630\) −4.56640e12 3.25271e12i −1.15489 0.822646i
\(631\) 2.00341e12 0.503081 0.251540 0.967847i \(-0.419063\pi\)
0.251540 + 0.967847i \(0.419063\pi\)
\(632\) 1.15945e13i 2.89084i
\(633\) 1.36372e12i 0.337605i
\(634\) −5.21084e12 −1.28087
\(635\) 1.71978e12 2.41435e12i 0.419750 0.589277i
\(636\) 2.55205e12 0.618489
\(637\) 9.63992e11i 0.231978i
\(638\) 1.10675e12i 0.264458i
\(639\) −1.63889e12 −0.388863
\(640\) −1.31412e12 + 1.84487e12i −0.309618 + 0.434666i
\(641\) 2.75478e12 0.644505 0.322253 0.946654i \(-0.395560\pi\)
0.322253 + 0.946654i \(0.395560\pi\)
\(642\) 2.58546e12i 0.600662i
\(643\) 7.38857e12i 1.70455i −0.523091 0.852277i \(-0.675221\pi\)
0.523091 0.852277i \(-0.324779\pi\)
\(644\) 4.58550e12 1.05051
\(645\) 1.25222e12 + 8.91972e11i 0.284879 + 0.202924i
\(646\) 3.20138e12 0.723254
\(647\) 4.12045e12i 0.924432i −0.886767 0.462216i \(-0.847054\pi\)
0.886767 0.462216i \(-0.152946\pi\)
\(648\) 8.63269e12i 1.92335i
\(649\) −1.67245e12 −0.370043
\(650\) 2.10075e12 + 6.07537e12i 0.461598 + 1.33494i
\(651\) −6.59311e11 −0.143872
\(652\) 3.22517e12i 0.698937i
\(653\) 6.51407e12i 1.40198i 0.713170 + 0.700992i \(0.247259\pi\)
−0.713170 + 0.700992i \(0.752741\pi\)
\(654\) −2.69315e12 −0.575654
\(655\) 6.34807e12 + 4.52182e12i 1.34758 + 0.959903i
\(656\) 9.45073e12 1.99250
\(657\) 1.38864e12i 0.290767i
\(658\) 9.01141e12i 1.87403i
\(659\) 1.74145e12 0.359688 0.179844 0.983695i \(-0.442441\pi\)
0.179844 + 0.983695i \(0.442441\pi\)
\(660\) −3.80348e11 + 5.33961e11i −0.0780250 + 0.109537i
\(661\) −1.39849e12 −0.284939 −0.142469 0.989799i \(-0.545504\pi\)
−0.142469 + 0.989799i \(0.545504\pi\)
\(662\) 7.07800e12i 1.43235i
\(663\) 9.40708e11i 0.189079i
\(664\) −1.47368e13 −2.94202
\(665\) −1.06425e12 + 1.49408e12i −0.211031 + 0.296262i
\(666\) 1.06014e13 2.08799
\(667\) 1.85422e12i 0.362740i
\(668\) 1.75865e13i 3.41732i
\(669\) 1.85882e12 0.358774
\(670\) −1.32124e13 9.41137e12i −2.53306 1.80433i
\(671\) 5.55753e11 0.105835
\(672\) 1.69251e12i 0.320161i
\(673\) 7.23077e12i 1.35868i 0.733824 + 0.679340i \(0.237734\pi\)
−0.733824 + 0.679340i \(0.762266\pi\)
\(674\) 1.94333e13 3.62725
\(675\) 2.63673e12 9.11730e11i 0.488876 0.169044i
\(676\) −5.09140e12 −0.937728
\(677\) 1.09854e12i 0.200986i −0.994938 0.100493i \(-0.967958\pi\)
0.994938 0.100493i \(-0.0320419\pi\)
\(678\) 9.81319e11i 0.178351i
\(679\) −3.20921e12 −0.579408
\(680\) −1.00831e13 7.18231e12i −1.80843 1.28817i
\(681\) −1.23352e12 −0.219779
\(682\) 1.41969e12i 0.251283i
\(683\) 1.51781e12i 0.266885i 0.991057 + 0.133442i \(0.0426031\pi\)
−0.991057 + 0.133442i \(0.957397\pi\)
\(684\) −5.39163e12 −0.941820
\(685\) −2.08637e12 + 2.92900e12i −0.362063 + 0.508291i
\(686\) −1.15204e13 −1.98613
\(687\) 5.10355e11i 0.0874112i
\(688\) 1.62082e13i 2.75796i
\(689\) −4.51828e12 −0.763812
\(690\) −9.10180e11 + 1.27778e12i −0.152864 + 0.214603i
\(691\) 1.51489e12 0.252772 0.126386 0.991981i \(-0.459662\pi\)
0.126386 + 0.991981i \(0.459662\pi\)
\(692\) 1.87188e11i 0.0310314i
\(693\) 1.01227e12i 0.166724i
\(694\) 1.18439e13 1.93810
\(695\) 1.84741e12 + 1.31594e12i 0.300353 + 0.213946i
\(696\) 2.73013e12 0.441003
\(697\) 5.34668e12i 0.858097i
\(698\) 1.46398e13i 2.33446i
\(699\) −3.01064e11 −0.0476993
\(700\) 1.17273e13 4.05509e12i 1.84611 0.638350i
\(701\) 7.62368e12 1.19243 0.596216 0.802824i \(-0.296670\pi\)
0.596216 + 0.802824i \(0.296670\pi\)
\(702\) 4.70140e12i 0.730651i
\(703\) 3.46866e12i 0.535627i
\(704\) −6.83975e11 −0.104945
\(705\) −1.75804e12 1.25227e12i −0.268026 0.190918i
\(706\) 8.65605e12 1.31129
\(707\) 1.08221e12i 0.162901i
\(708\) 7.21697e12i 1.07946i
\(709\) −1.00657e13 −1.49602 −0.748010 0.663687i \(-0.768991\pi\)
−0.748010 + 0.663687i \(0.768991\pi\)
\(710\) 3.00594e12 4.21996e12i 0.443933 0.623226i
\(711\) −7.50140e12 −1.10085
\(712\) 6.70002e12i 0.977049i
\(713\) 2.37851e12i 0.344669i
\(714\) 2.59367e12 0.373485
\(715\) 6.73388e11 9.45353e11i 0.0963580 0.135275i
\(716\) −6.40096e12 −0.910199
\(717\) 3.12496e12i 0.441579i
\(718\) 1.19033e13i 1.67151i
\(719\) −8.94464e12 −1.24820 −0.624098 0.781346i \(-0.714534\pi\)
−0.624098 + 0.781346i \(0.714534\pi\)
\(720\) 1.15310e13 + 8.21366e12i 1.59908 + 1.13904i
\(721\) −4.86817e12 −0.670899
\(722\) 1.08135e13i 1.48098i
\(723\) 2.27647e12i 0.309841i
\(724\) 1.81812e12 0.245923
\(725\) −1.63974e12 4.74214e12i −0.220422 0.637460i
\(726\) −3.49822e12 −0.467339
\(727\) 1.22168e13i 1.62201i 0.585038 + 0.811006i \(0.301079\pi\)
−0.585038 + 0.811006i \(0.698921\pi\)
\(728\) 1.19534e13i 1.57725i
\(729\) 4.52688e12 0.593642
\(730\) 3.57559e12 + 2.54694e12i 0.466009 + 0.331945i
\(731\) 9.16968e12 1.18775
\(732\) 2.39819e12i 0.308734i
\(733\) 1.44452e13i 1.84823i −0.382118 0.924114i \(-0.624805\pi\)
0.382118 0.924114i \(-0.375195\pi\)
\(734\) 5.51974e11 0.0701919
\(735\) 3.69352e11 5.18524e11i 0.0466818 0.0655354i
\(736\) −6.10584e12 −0.767000
\(737\) 2.92889e12i 0.365679i
\(738\) 1.28618e13i 1.59605i
\(739\) 1.11591e13 1.37635 0.688175 0.725545i \(-0.258412\pi\)
0.688175 + 0.725545i \(0.258412\pi\)
\(740\) −1.36131e13 + 1.91111e13i −1.66884 + 2.34284i
\(741\) −7.40409e11 −0.0902172
\(742\) 1.24576e13i 1.50875i
\(743\) 9.35882e12i 1.12660i 0.826251 + 0.563302i \(0.190469\pi\)
−0.826251 + 0.563302i \(0.809531\pi\)
\(744\) 3.50208e12 0.419033
\(745\) 6.81176e12 + 4.85211e12i 0.810133 + 0.577069i
\(746\) −1.72617e13 −2.04061
\(747\) 9.53439e12i 1.12034i
\(748\) 3.91007e12i 0.456696i
\(749\) 8.83585e12 1.02584
\(750\) −1.19779e12 + 4.07279e12i −0.138231 + 0.470020i
\(751\) −1.28609e13 −1.47533 −0.737667 0.675165i \(-0.764072\pi\)
−0.737667 + 0.675165i \(0.764072\pi\)
\(752\) 2.27553e13i 2.59480i
\(753\) 3.94028e12i 0.446632i
\(754\) −8.45543e12 −0.952719
\(755\) −6.77382e12 4.82509e12i −0.758704 0.540435i
\(756\) −9.07514e12 −1.01043
\(757\) 1.42250e13i 1.57442i 0.616684 + 0.787211i \(0.288476\pi\)
−0.616684 + 0.787211i \(0.711524\pi\)
\(758\) 1.08716e13i 1.19613i
\(759\) 2.83256e11 0.0309807
\(760\) 5.65302e12 7.93614e12i 0.614638 0.862875i
\(761\) 1.65722e13 1.79122 0.895610 0.444841i \(-0.146740\pi\)
0.895610 + 0.444841i \(0.146740\pi\)
\(762\) 3.29883e12i 0.354456i
\(763\) 9.20389e12i 0.983130i
\(764\) 1.10954e13 1.17822
\(765\) 4.64681e12 6.52354e12i 0.490545 0.688664i
\(766\) 3.24004e12 0.340033
\(767\) 1.27773e13i 1.33309i
\(768\) 3.78498e12i 0.392589i
\(769\) −2.81269e12 −0.290037 −0.145019 0.989429i \(-0.546324\pi\)
−0.145019 + 0.989429i \(0.546324\pi\)
\(770\) −2.60648e12 1.85663e12i −0.267206 0.190334i
\(771\) 2.98397e12 0.304123
\(772\) 8.29949e12i 0.840957i
\(773\) 8.57982e12i 0.864311i 0.901799 + 0.432156i \(0.142247\pi\)
−0.901799 + 0.432156i \(0.857753\pi\)
\(774\) −2.20583e13 −2.20921
\(775\) −2.10338e12 6.08299e12i −0.209440 0.605703i
\(776\) 1.70465e13 1.68755
\(777\) 2.81021e12i 0.276595i
\(778\) 6.85930e12i 0.671230i
\(779\) 4.20824e12 0.409432
\(780\) 4.07940e12 + 2.90581e12i 0.394612 + 0.281087i
\(781\) −9.35472e11 −0.0899707
\(782\) 9.35687e12i