Properties

Label 25.8.e.a.4.2
Level $25$
Weight $8$
Character 25.4
Analytic conductor $7.810$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,8,Mod(4,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.4");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 25.e (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.80962563710\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 4.2
Character \(\chi\) \(=\) 25.4
Dual form 25.8.e.a.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-17.4863 - 5.68165i) q^{2} +(-14.4903 + 19.9442i) q^{3} +(169.936 + 123.466i) q^{4} +(110.554 - 256.716i) q^{5} +(366.698 - 266.422i) q^{6} -1022.55i q^{7} +(-886.753 - 1220.51i) q^{8} +(488.018 + 1501.97i) q^{9} +O(q^{10})\) \(q+(-17.4863 - 5.68165i) q^{2} +(-14.4903 + 19.9442i) q^{3} +(169.936 + 123.466i) q^{4} +(110.554 - 256.716i) q^{5} +(366.698 - 266.422i) q^{6} -1022.55i q^{7} +(-886.753 - 1220.51i) q^{8} +(488.018 + 1501.97i) q^{9} +(-3391.75 + 3860.88i) q^{10} +(-98.7198 + 303.828i) q^{11} +(-4924.85 + 1600.18i) q^{12} +(-7560.04 + 2456.41i) q^{13} +(-5809.76 + 17880.6i) q^{14} +(3518.03 + 5924.79i) q^{15} +(263.079 + 809.674i) q^{16} +(-9287.44 - 12783.1i) q^{17} -29036.6i q^{18} +(-38825.3 + 28208.2i) q^{19} +(50482.7 - 29975.6i) q^{20} +(20393.9 + 14817.0i) q^{21} +(3452.49 - 4751.95i) q^{22} +(9156.62 + 2975.17i) q^{23} +37191.4 q^{24} +(-53680.7 - 56761.7i) q^{25} +146154. q^{26} +(-88303.0 - 28691.4i) q^{27} +(126250. - 173768. i) q^{28} +(106851. + 77631.9i) q^{29} +(-27854.8 - 123591. i) q^{30} +(-104477. + 75906.9i) q^{31} +177452. i q^{32} +(-4629.13 - 6371.45i) q^{33} +(89774.3 + 276297. i) q^{34} +(-262504. - 113047. i) q^{35} +(-102509. + 315492. i) q^{36} +(-533404. + 173313. i) q^{37} +(839181. - 272667. i) q^{38} +(60556.3 - 186373. i) q^{39} +(-411358. + 92711.3i) q^{40} +(20960.8 + 64510.7i) q^{41} +(-272429. - 374967. i) q^{42} -440061. i q^{43} +(-54288.5 + 39442.9i) q^{44} +(439530. + 40766.0i) q^{45} +(-143212. - 104049. i) q^{46} +(257611. - 354571. i) q^{47} +(-19960.4 - 6485.53i) q^{48} -222062. q^{49} +(616178. + 1.29755e6i) q^{50} +389526. q^{51} +(-1.58801e6 - 515974. i) q^{52} +(-1.21580e6 + 1.67340e6i) q^{53} +(1.38108e6 + 1.00341e6i) q^{54} +(67083.6 + 58932.3i) q^{55} +(-1.24803e6 + 906748. i) q^{56} -1.18309e6i q^{57} +(-1.42736e6 - 1.96459e6i) q^{58} +(56873.2 + 175038. i) q^{59} +(-133669. + 1.44119e6i) q^{60} +(251837. - 775075. i) q^{61} +(2.25819e6 - 733731. i) q^{62} +(1.53583e6 - 499022. i) q^{63} +(1.04190e6 - 3.20663e6i) q^{64} +(-205193. + 2.21234e6i) q^{65} +(44746.1 + 137714. i) q^{66} +(370061. + 509345. i) q^{67} -3.31899e6i q^{68} +(-192020. + 139510. i) q^{69} +(3.94794e6 + 3.46822e6i) q^{70} +(-3.89707e6 - 2.83139e6i) q^{71} +(1.40041e6 - 1.92750e6i) q^{72} +(3.01937e6 + 981052. i) q^{73} +1.03120e7 q^{74} +(1.90992e6 - 248125. i) q^{75} -1.00806e7 q^{76} +(310679. + 100946. i) q^{77} +(-2.11781e6 + 2.91492e6i) q^{78} +(-6.74288e6 - 4.89899e6i) q^{79} +(236940. + 21976.0i) q^{80} +(-942451. + 684731. i) q^{81} -1.24715e6i q^{82} +(-39823.3 - 54812.1i) q^{83} +(1.63626e6 + 5.03590e6i) q^{84} +(-4.30837e6 + 971015. i) q^{85} +(-2.50027e6 + 7.69504e6i) q^{86} +(-3.09661e6 + 1.00615e6i) q^{87} +(458366. - 148932. i) q^{88} +(1.89980e6 - 5.84698e6i) q^{89} +(-7.45415e6 - 3.21010e6i) q^{90} +(2.51179e6 + 7.73050e6i) q^{91} +(1.18871e6 + 1.63612e6i) q^{92} -3.18362e6i q^{93} +(-6.51921e6 + 4.73648e6i) q^{94} +(2.94921e6 + 1.30856e7i) q^{95} +(-3.53914e6 - 2.57134e6i) q^{96} +(-6.28592e6 + 8.65183e6i) q^{97} +(3.88305e6 + 1.26168e6i) q^{98} -504517. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 5 q^{2} - 5 q^{3} + 893 q^{4} - 510 q^{5} + 173 q^{6} - 2510 q^{8} + 6587 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 5 q^{2} - 5 q^{3} + 893 q^{4} - 510 q^{5} + 173 q^{6} - 2510 q^{8} + 6587 q^{9} - 5805 q^{10} - 472 q^{11} + 16635 q^{12} - 5 q^{13} - 19409 q^{14} + 375 q^{15} - 42071 q^{16} + 31910 q^{17} - 48685 q^{19} - 171405 q^{20} + 2268 q^{21} + 197230 q^{22} + 356525 q^{23} + 544720 q^{24} + 170220 q^{25} - 708942 q^{26} - 319805 q^{27} - 565125 q^{28} - 332885 q^{29} + 66235 q^{30} - 39057 q^{31} - 161110 q^{33} + 1156301 q^{34} + 337515 q^{35} + 1920669 q^{36} - 1480960 q^{37} - 2136945 q^{38} + 1307509 q^{39} - 282470 q^{40} + 1955408 q^{41} - 684355 q^{42} - 3558164 q^{44} - 1351725 q^{45} - 2982527 q^{46} + 1018980 q^{47} + 8967210 q^{48} - 3298162 q^{49} + 8550165 q^{50} - 3922092 q^{51} + 8058740 q^{52} + 316580 q^{53} - 6933535 q^{54} - 2889990 q^{55} + 480880 q^{56} - 12912030 q^{58} - 3625740 q^{59} - 10459240 q^{60} + 656223 q^{61} + 15439920 q^{62} + 16010850 q^{63} + 572908 q^{64} - 9903445 q^{65} + 8105266 q^{66} - 25482280 q^{67} - 9378031 q^{69} + 16449030 q^{70} + 2533578 q^{71} + 8757215 q^{72} + 8477055 q^{73} + 20547876 q^{74} + 28650170 q^{75} - 22436480 q^{76} + 20387770 q^{77} - 23613305 q^{78} - 5343505 q^{79} - 44517070 q^{80} + 7686054 q^{81} - 20224125 q^{83} + 10924626 q^{84} + 2795615 q^{85} + 27540603 q^{86} - 3545560 q^{87} + 36319550 q^{88} - 17844415 q^{89} - 67695745 q^{90} + 9123478 q^{91} - 88054710 q^{92} - 15200999 q^{94} + 42119295 q^{95} - 8739232 q^{96} + 41971560 q^{97} + 60378980 q^{98} + 57867624 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −17.4863 5.68165i −1.54559 0.502192i −0.592676 0.805441i \(-0.701928\pi\)
−0.952911 + 0.303250i \(0.901928\pi\)
\(3\) −14.4903 + 19.9442i −0.309851 + 0.426474i −0.935335 0.353764i \(-0.884902\pi\)
0.625484 + 0.780237i \(0.284902\pi\)
\(4\) 169.936 + 123.466i 1.32763 + 0.964576i
\(5\) 110.554 256.716i 0.395529 0.918453i
\(6\) 366.698 266.422i 0.693074 0.503547i
\(7\) 1022.55i 1.12678i −0.826190 0.563392i \(-0.809496\pi\)
0.826190 0.563392i \(-0.190504\pi\)
\(8\) −886.753 1220.51i −0.612333 0.842804i
\(9\) 488.018 + 1501.97i 0.223145 + 0.686770i
\(10\) −3391.75 + 3860.88i −1.07256 + 1.22092i
\(11\) −98.7198 + 303.828i −0.0223630 + 0.0688262i −0.961615 0.274402i \(-0.911520\pi\)
0.939252 + 0.343228i \(0.111520\pi\)
\(12\) −4924.85 + 1600.18i −0.822733 + 0.267322i
\(13\) −7560.04 + 2456.41i −0.954382 + 0.310098i −0.744495 0.667628i \(-0.767310\pi\)
−0.209887 + 0.977726i \(0.567310\pi\)
\(14\) −5809.76 + 17880.6i −0.565862 + 1.74154i
\(15\) 3518.03 + 5924.79i 0.269141 + 0.453267i
\(16\) 263.079 + 809.674i 0.0160571 + 0.0494186i
\(17\) −9287.44 12783.1i −0.458485 0.631050i 0.515709 0.856764i \(-0.327529\pi\)
−0.974194 + 0.225714i \(0.927529\pi\)
\(18\) 29036.6i 1.17352i
\(19\) −38825.3 + 28208.2i −1.29861 + 0.943493i −0.999941 0.0108654i \(-0.996541\pi\)
−0.298665 + 0.954358i \(0.596541\pi\)
\(20\) 50482.7 29975.6i 1.41103 0.837844i
\(21\) 20393.9 + 14817.0i 0.480544 + 0.349135i
\(22\) 3452.49 4751.95i 0.0691279 0.0951464i
\(23\) 9156.62 + 2975.17i 0.156923 + 0.0509875i 0.386425 0.922321i \(-0.373710\pi\)
−0.229502 + 0.973308i \(0.573710\pi\)
\(24\) 37191.4 0.549166
\(25\) −53680.7 56761.7i −0.687114 0.726550i
\(26\) 146154. 1.63081
\(27\) −88303.0 28691.4i −0.863381 0.280529i
\(28\) 126250. 173768.i 1.08687 1.49595i
\(29\) 106851. + 77631.9i 0.813554 + 0.591082i 0.914859 0.403774i \(-0.132302\pi\)
−0.101305 + 0.994855i \(0.532302\pi\)
\(30\) −27854.8 123591.i −0.188354 0.835723i
\(31\) −104477. + 75906.9i −0.629875 + 0.457631i −0.856357 0.516385i \(-0.827278\pi\)
0.226482 + 0.974015i \(0.427278\pi\)
\(32\) 177452.i 0.957319i
\(33\) −4629.13 6371.45i −0.0224234 0.0308631i
\(34\) 89774.3 + 276297.i 0.391720 + 1.20559i
\(35\) −262504. 113047.i −1.03490 0.445676i
\(36\) −102509. + 315492.i −0.366189 + 1.12701i
\(37\) −533404. + 173313.i −1.73121 + 0.562505i −0.993624 0.112747i \(-0.964035\pi\)
−0.737588 + 0.675251i \(0.764035\pi\)
\(38\) 839181. 272667.i 2.48092 0.806101i
\(39\) 60556.3 186373.i 0.163468 0.503103i
\(40\) −411358. + 92711.3i −1.01627 + 0.229046i
\(41\) 20960.8 + 64510.7i 0.0474968 + 0.146180i 0.971992 0.235013i \(-0.0755133\pi\)
−0.924495 + 0.381193i \(0.875513\pi\)
\(42\) −272429. 374967.i −0.567389 0.780944i
\(43\) 440061.i 0.844059i −0.906582 0.422030i \(-0.861318\pi\)
0.906582 0.422030i \(-0.138682\pi\)
\(44\) −54288.5 + 39442.9i −0.0960778 + 0.0698046i
\(45\) 439530. + 40766.0i 0.719026 + 0.0666891i
\(46\) −143212. 104049.i −0.216933 0.157611i
\(47\) 257611. 354571.i 0.361927 0.498150i −0.588757 0.808310i \(-0.700383\pi\)
0.950684 + 0.310160i \(0.100383\pi\)
\(48\) −19960.4 6485.53i −0.0260510 0.00846449i
\(49\) −222062. −0.269642
\(50\) 616178. + 1.29755e6i 0.697126 + 1.46801i
\(51\) 389526. 0.411188
\(52\) −1.58801e6 515974.i −1.56617 0.508881i
\(53\) −1.21580e6 + 1.67340e6i −1.12175 + 1.54396i −0.318887 + 0.947793i \(0.603309\pi\)
−0.802863 + 0.596163i \(0.796691\pi\)
\(54\) 1.38108e6 + 1.00341e6i 1.19355 + 0.867165i
\(55\) 67083.6 + 58932.3i 0.0543685 + 0.0477621i
\(56\) −1.24803e6 + 906748.i −0.949659 + 0.689967i
\(57\) 1.18309e6i 0.846164i
\(58\) −1.42736e6 1.96459e6i −0.960582 1.32213i
\(59\) 56873.2 + 175038.i 0.0360517 + 0.110956i 0.967463 0.253013i \(-0.0814215\pi\)
−0.931411 + 0.363969i \(0.881422\pi\)
\(60\) −133669. + 1.44119e6i −0.0798918 + 0.861376i
\(61\) 251837. 775075.i 0.142058 0.437209i −0.854563 0.519348i \(-0.826175\pi\)
0.996621 + 0.0821386i \(0.0261750\pi\)
\(62\) 2.25819e6 733731.i 1.20334 0.390990i
\(63\) 1.53583e6 499022.i 0.773841 0.251436i
\(64\) 1.04190e6 3.20663e6i 0.496815 1.52904i
\(65\) −205193. + 2.21234e6i −0.0926757 + 0.999208i
\(66\) 44746.1 + 137714.i 0.0191581 + 0.0589625i
\(67\) 370061. + 509345.i 0.150318 + 0.206895i 0.877535 0.479513i \(-0.159187\pi\)
−0.727217 + 0.686408i \(0.759187\pi\)
\(68\) 3.31899e6i 1.28004i
\(69\) −192020. + 139510.i −0.0703678 + 0.0511252i
\(70\) 3.94794e6 + 3.46822e6i 1.37571 + 1.20855i
\(71\) −3.89707e6 2.83139e6i −1.29221 0.938849i −0.292367 0.956306i \(-0.594443\pi\)
−0.999848 + 0.0174577i \(0.994443\pi\)
\(72\) 1.40041e6 1.92750e6i 0.442173 0.608599i
\(73\) 3.01937e6 + 981052.i 0.908419 + 0.295163i 0.725707 0.688003i \(-0.241513\pi\)
0.182711 + 0.983167i \(0.441513\pi\)
\(74\) 1.03120e7 2.95822
\(75\) 1.90992e6 248125.i 0.522757 0.0679134i
\(76\) −1.00806e7 −2.63413
\(77\) 310679. + 100946.i 0.0775523 + 0.0251983i
\(78\) −2.11781e6 + 2.91492e6i −0.505308 + 0.695497i
\(79\) −6.74288e6 4.89899e6i −1.53869 1.11792i −0.951151 0.308725i \(-0.900098\pi\)
−0.587537 0.809197i \(-0.699902\pi\)
\(80\) 236940. + 21976.0i 0.0517397 + 0.00479881i
\(81\) −942451. + 684731.i −0.197043 + 0.143160i
\(82\) 1.24715e6i 0.249787i
\(83\) −39823.3 54812.1i −0.00764477 0.0105221i 0.805178 0.593034i \(-0.202070\pi\)
−0.812822 + 0.582512i \(0.802070\pi\)
\(84\) 1.63626e6 + 5.03590e6i 0.301214 + 0.927042i
\(85\) −4.30837e6 + 971015.i −0.760934 + 0.171498i
\(86\) −2.50027e6 + 7.69504e6i −0.423879 + 1.30457i
\(87\) −3.09661e6 + 1.00615e6i −0.504162 + 0.163812i
\(88\) 458366. 148932.i 0.0717006 0.0232969i
\(89\) 1.89980e6 5.84698e6i 0.285656 0.879157i −0.700546 0.713607i \(-0.747060\pi\)
0.986201 0.165550i \(-0.0529399\pi\)
\(90\) −7.45415e6 3.21010e6i −1.07783 0.464163i
\(91\) 2.51179e6 + 7.73050e6i 0.349413 + 1.07538i
\(92\) 1.18871e6 + 1.63612e6i 0.159154 + 0.219057i
\(93\) 3.18362e6i 0.410422i
\(94\) −6.51921e6 + 4.73648e6i −0.809557 + 0.588177i
\(95\) 2.94921e6 + 1.30856e7i 0.352918 + 1.56589i
\(96\) −3.53914e6 2.57134e6i −0.408271 0.296627i
\(97\) −6.28592e6 + 8.65183e6i −0.699307 + 0.962514i 0.300654 + 0.953733i \(0.402795\pi\)
−0.999961 + 0.00878043i \(0.997205\pi\)
\(98\) 3.88305e6 + 1.26168e6i 0.416756 + 0.135412i
\(99\) −504517. −0.0522579
\(100\) −2.11416e6 1.62736e7i −0.211416 1.62736i
\(101\) 9.30291e6 0.898451 0.449225 0.893419i \(-0.351700\pi\)
0.449225 + 0.893419i \(0.351700\pi\)
\(102\) −6.81138e6 2.21315e6i −0.635527 0.206495i
\(103\) −3.37848e6 + 4.65008e6i −0.304643 + 0.419305i −0.933701 0.358053i \(-0.883441\pi\)
0.629058 + 0.777358i \(0.283441\pi\)
\(104\) 9.70196e6 + 7.04888e6i 0.845751 + 0.614474i
\(105\) 6.05839e6 3.59735e6i 0.510734 0.303264i
\(106\) 3.07675e7 2.23539e7i 2.50912 1.82299i
\(107\) 1.27436e7i 1.00566i −0.864386 0.502829i \(-0.832293\pi\)
0.864386 0.502829i \(-0.167707\pi\)
\(108\) −1.14635e7 1.57781e7i −0.875654 1.20523i
\(109\) −452809. 1.39360e6i −0.0334906 0.103073i 0.932914 0.360100i \(-0.117257\pi\)
−0.966404 + 0.257026i \(0.917257\pi\)
\(110\) −838213. 1.41165e6i −0.0600454 0.101124i
\(111\) 4.27259e6 1.31497e7i 0.296525 0.912609i
\(112\) 827931. 269011.i 0.0556841 0.0180929i
\(113\) 2.79323e7 9.07576e6i 1.82109 0.591709i 0.821320 0.570468i \(-0.193238\pi\)
0.999774 0.0212414i \(-0.00676186\pi\)
\(114\) −6.72188e6 + 2.06878e7i −0.424936 + 1.30782i
\(115\) 1.77607e6 2.02173e6i 0.108897 0.123960i
\(116\) 8.57299e6 + 2.63849e7i 0.509952 + 1.56947i
\(117\) −7.37887e6 1.01561e7i −0.425931 0.586244i
\(118\) 3.38390e6i 0.189596i
\(119\) −1.30713e7 + 9.49686e6i −0.711057 + 0.516613i
\(120\) 4.11165e6 9.54762e6i 0.217211 0.504383i
\(121\) 1.56829e7 + 1.13943e7i 0.804780 + 0.584707i
\(122\) −8.80740e6 + 1.21224e7i −0.439125 + 0.604404i
\(123\) −1.59034e6 516734.i −0.0770590 0.0250380i
\(124\) −2.71263e7 −1.27766
\(125\) −2.05062e7 + 7.50546e6i −0.939076 + 0.343710i
\(126\) −2.96913e7 −1.32231
\(127\) 1.29664e7 + 4.21305e6i 0.561704 + 0.182509i 0.576088 0.817388i \(-0.304579\pi\)
−0.0143840 + 0.999897i \(0.504579\pi\)
\(128\) −2.30870e7 + 3.17765e7i −0.973043 + 1.33928i
\(129\) 8.77666e6 + 6.37661e6i 0.359969 + 0.261533i
\(130\) 1.61578e7 3.75199e7i 0.645032 1.49782i
\(131\) 3.40064e7 2.47071e7i 1.32163 0.960223i 0.321723 0.946834i \(-0.395738\pi\)
0.999910 0.0133893i \(-0.00426208\pi\)
\(132\) 1.65428e6i 0.0626037i
\(133\) 2.88443e7 + 3.97008e7i 1.06311 + 1.46325i
\(134\) −3.57708e6 1.10091e7i −0.128429 0.395263i
\(135\) −1.71278e7 + 1.94968e7i −0.599145 + 0.682018i
\(136\) −7.36621e6 + 2.26709e7i −0.251106 + 0.772826i
\(137\) −1.19167e7 + 3.87197e6i −0.395945 + 0.128650i −0.500220 0.865898i \(-0.666748\pi\)
0.104276 + 0.994548i \(0.466748\pi\)
\(138\) 4.15037e6 1.34854e6i 0.134434 0.0436803i
\(139\) 1.59189e7 4.89935e7i 0.502762 1.54734i −0.301739 0.953391i \(-0.597567\pi\)
0.804501 0.593952i \(-0.202433\pi\)
\(140\) −3.06515e7 5.16210e7i −0.944070 1.58993i
\(141\) 3.33877e6 + 1.02757e7i 0.100304 + 0.308705i
\(142\) 5.20585e7 + 7.16524e7i 1.52575 + 2.10001i
\(143\) 2.53945e6i 0.0726212i
\(144\) −1.08772e6 + 790271.i −0.0303561 + 0.0220550i
\(145\) 3.17421e7 1.88479e7i 0.864665 0.513422i
\(146\) −4.72236e7 3.43100e7i −1.25581 0.912401i
\(147\) 3.21775e6 4.42885e6i 0.0835491 0.114995i
\(148\) −1.12043e8 3.64049e7i −2.84098 0.923090i
\(149\) −4.56427e7 −1.13037 −0.565184 0.824965i \(-0.691195\pi\)
−0.565184 + 0.824965i \(0.691195\pi\)
\(150\) −3.48072e7 6.51270e6i −0.842073 0.157558i
\(151\) −2.15140e7 −0.508512 −0.254256 0.967137i \(-0.581831\pi\)
−0.254256 + 0.967137i \(0.581831\pi\)
\(152\) 6.88570e7 + 2.23730e7i 1.59036 + 0.516739i
\(153\) 1.46673e7 2.01878e7i 0.331078 0.455689i
\(154\) −4.85910e6 3.53034e6i −0.107209 0.0778922i
\(155\) 7.93617e6 + 3.52126e7i 0.171179 + 0.759517i
\(156\) 3.33014e7 2.41949e7i 0.702306 0.510255i
\(157\) 5.54897e7i 1.14436i 0.820127 + 0.572181i \(0.193903\pi\)
−0.820127 + 0.572181i \(0.806097\pi\)
\(158\) 9.00738e7 + 1.23976e8i 1.81677 + 2.50056i
\(159\) −1.57574e7 4.84963e7i −0.310881 0.956794i
\(160\) 4.55548e7 + 1.96180e7i 0.879253 + 0.378647i
\(161\) 3.04225e6 9.36309e6i 0.0574519 0.176819i
\(162\) 2.03704e7 6.61875e6i 0.376441 0.122313i
\(163\) −7.40445e7 + 2.40585e7i −1.33917 + 0.435123i −0.889036 0.457837i \(-0.848624\pi\)
−0.450136 + 0.892960i \(0.648624\pi\)
\(164\) −4.40287e6 + 1.35506e7i −0.0779440 + 0.239887i
\(165\) −2.14742e6 + 483982.i −0.0372154 + 0.00838756i
\(166\) 384940. + 1.18472e6i 0.00653153 + 0.0201020i
\(167\) −3.75879e7 5.17353e7i −0.624511 0.859566i 0.373160 0.927767i \(-0.378274\pi\)
−0.997672 + 0.0682009i \(0.978274\pi\)
\(168\) 3.80301e7i 0.618792i
\(169\) 355630. 258381.i 0.00566755 0.00411772i
\(170\) 8.08546e7 + 7.49919e6i 1.26221 + 0.117069i
\(171\) −6.13153e7 4.45482e7i −0.937740 0.681308i
\(172\) 5.43324e7 7.47822e7i 0.814160 1.12059i
\(173\) −5.19992e7 1.68956e7i −0.763546 0.248091i −0.0987459 0.995113i \(-0.531483\pi\)
−0.664800 + 0.747022i \(0.731483\pi\)
\(174\) 5.98650e7 0.861491
\(175\) −5.80416e7 + 5.48912e7i −0.818665 + 0.774229i
\(176\) −271973. −0.00376038
\(177\) −4.31509e6 1.40206e6i −0.0584903 0.0190047i
\(178\) −6.64410e7 + 9.14482e7i −0.883011 + 1.21536i
\(179\) −2.56917e7 1.86661e7i −0.334816 0.243258i 0.407655 0.913136i \(-0.366347\pi\)
−0.742472 + 0.669878i \(0.766347\pi\)
\(180\) 6.96588e7 + 6.11945e7i 0.890271 + 0.782094i
\(181\) 9.08646e7 6.60170e7i 1.13899 0.827524i 0.152011 0.988379i \(-0.451425\pi\)
0.986978 + 0.160855i \(0.0514251\pi\)
\(182\) 1.49449e8i 1.83757i
\(183\) 1.18090e7 + 1.62538e7i 0.142441 + 0.196054i
\(184\) −4.48844e6 1.38140e7i −0.0531169 0.163477i
\(185\) −1.44775e7 + 1.56093e8i −0.168110 + 1.81252i
\(186\) −1.80882e7 + 5.56698e7i −0.206111 + 0.634344i
\(187\) 4.80071e6 1.55985e6i 0.0536859 0.0174436i
\(188\) 8.75547e7 2.84482e7i 0.961008 0.312250i
\(189\) −2.93383e7 + 9.02941e7i −0.316096 + 0.972844i
\(190\) 2.27769e7 2.45575e8i 0.240911 2.59745i
\(191\) 2.99679e7 + 9.22318e7i 0.311200 + 0.957776i 0.977290 + 0.211905i \(0.0679667\pi\)
−0.666090 + 0.745871i \(0.732033\pi\)
\(192\) 4.88562e7 + 6.72448e7i 0.498156 + 0.685653i
\(193\) 1.09650e8i 1.09789i −0.835858 0.548946i \(-0.815029\pi\)
0.835858 0.548946i \(-0.184971\pi\)
\(194\) 1.59074e8 1.15574e8i 1.56421 1.13646i
\(195\) −4.11501e7 3.61500e7i −0.397420 0.349130i
\(196\) −3.77364e7 2.74171e7i −0.357984 0.260091i
\(197\) 9.14089e6 1.25814e7i 0.0851837 0.117245i −0.764298 0.644863i \(-0.776915\pi\)
0.849482 + 0.527617i \(0.176915\pi\)
\(198\) 8.82214e6 + 2.86649e6i 0.0807692 + 0.0262435i
\(199\) −8.15977e7 −0.733993 −0.366997 0.930222i \(-0.619614\pi\)
−0.366997 + 0.930222i \(0.619614\pi\)
\(200\) −2.16767e7 + 1.15852e8i −0.191597 + 1.02399i
\(201\) −1.55208e7 −0.134812
\(202\) −1.62674e8 5.28559e7i −1.38863 0.451194i
\(203\) 7.93824e7 1.09261e8i 0.666021 0.916700i
\(204\) 6.61945e7 + 4.80931e7i 0.545904 + 0.396623i
\(205\) 1.88782e7 + 1.75094e6i 0.153046 + 0.0141949i
\(206\) 8.54974e7 6.21175e7i 0.681424 0.495084i
\(207\) 1.52049e7i 0.119148i
\(208\) −3.97778e6 5.47494e6i −0.0306492 0.0421850i
\(209\) −4.73764e6 1.45809e7i −0.0358963 0.110477i
\(210\) −1.26378e8 + 2.84828e7i −0.941680 + 0.212234i
\(211\) −2.87908e7 + 8.86091e7i −0.210992 + 0.649366i 0.788422 + 0.615135i \(0.210898\pi\)
−0.999414 + 0.0342315i \(0.989102\pi\)
\(212\) −4.13216e8 + 1.34262e8i −2.97853 + 0.967782i
\(213\) 1.12940e8 3.66963e7i 0.800788 0.260192i
\(214\) −7.24048e7 + 2.22839e8i −0.505033 + 1.55433i
\(215\) −1.12970e8 4.86503e7i −0.775229 0.333850i
\(216\) 4.32848e7 + 1.33217e8i 0.292245 + 0.899439i
\(217\) 7.76185e7 + 1.06833e8i 0.515651 + 0.709733i
\(218\) 2.69417e7i 0.176128i
\(219\) −6.33179e7 + 4.60031e7i −0.407354 + 0.295960i
\(220\) 4.12381e6 + 1.82972e7i 0.0261107 + 0.115853i
\(221\) 1.01614e8 + 7.38268e7i 0.633257 + 0.460088i
\(222\) −1.49424e8 + 2.05664e8i −0.916609 + 1.26160i
\(223\) −4.42681e7 1.43836e7i −0.267315 0.0868560i 0.172293 0.985046i \(-0.444883\pi\)
−0.439608 + 0.898190i \(0.644883\pi\)
\(224\) 1.81454e8 1.07869
\(225\) 5.90570e7 1.08327e8i 0.345647 0.634015i
\(226\) −5.39999e8 −3.11181
\(227\) −2.02902e7 6.59270e6i −0.115132 0.0374087i 0.250884 0.968017i \(-0.419279\pi\)
−0.366016 + 0.930608i \(0.619279\pi\)
\(228\) 1.46071e8 2.01049e8i 0.816190 1.12339i
\(229\) 7.73537e7 + 5.62007e7i 0.425654 + 0.309256i 0.779909 0.625893i \(-0.215265\pi\)
−0.354255 + 0.935149i \(0.615265\pi\)
\(230\) −4.25437e7 + 2.52616e7i −0.230562 + 0.136903i
\(231\) −6.51512e6 + 4.73351e6i −0.0347761 + 0.0252663i
\(232\) 1.99253e8i 1.04761i
\(233\) −1.93361e7 2.66138e7i −0.100144 0.137836i 0.756004 0.654566i \(-0.227149\pi\)
−0.856148 + 0.516731i \(0.827149\pi\)
\(234\) 7.13256e7 + 2.19518e8i 0.363907 + 1.11999i
\(235\) −6.25440e7 1.05332e8i −0.314375 0.529446i
\(236\) −1.19464e7 + 3.67671e7i −0.0591621 + 0.182082i
\(237\) 1.95413e8 6.34935e7i 0.953529 0.309820i
\(238\) 2.82527e8 9.17985e7i 1.35844 0.441384i
\(239\) 9.58475e7 2.94988e8i 0.454138 1.39769i −0.418006 0.908444i \(-0.637271\pi\)
0.872144 0.489249i \(-0.162729\pi\)
\(240\) −3.87163e6 + 4.40715e6i −0.0180782 + 0.0205787i
\(241\) 8.36868e7 + 2.57562e8i 0.385121 + 1.18528i 0.936392 + 0.350955i \(0.114143\pi\)
−0.551271 + 0.834326i \(0.685857\pi\)
\(242\) −2.09498e8 2.88349e8i −0.950223 1.30787i
\(243\) 2.31775e8i 1.03620i
\(244\) 1.38491e8 1.00620e8i 0.610321 0.443424i
\(245\) −2.45498e7 + 5.70068e7i −0.106651 + 0.247654i
\(246\) 2.48734e7 + 1.80716e7i 0.106527 + 0.0773967i
\(247\) 2.24230e8 3.08626e8i 0.946792 1.30315i
\(248\) 1.85290e8 + 6.02045e7i 0.771386 + 0.250639i
\(249\) 1.67024e6 0.00685615
\(250\) 4.01222e8 1.47337e7i 1.62403 0.0596379i
\(251\) 1.08362e8 0.432531 0.216265 0.976335i \(-0.430612\pi\)
0.216265 + 0.976335i \(0.430612\pi\)
\(252\) 3.22605e8 + 1.04821e8i 1.26990 + 0.412616i
\(253\) −1.80788e6 + 2.48833e6i −0.00701856 + 0.00966021i
\(254\) −2.02798e8 1.47341e8i −0.776507 0.564166i
\(255\) 4.30636e7 9.99974e7i 0.162637 0.377657i
\(256\) 2.35101e8 1.70811e8i 0.875818 0.636319i
\(257\) 2.61066e8i 0.959365i −0.877442 0.479683i \(-0.840752\pi\)
0.877442 0.479683i \(-0.159248\pi\)
\(258\) −1.17242e8 1.61369e8i −0.425024 0.584995i
\(259\) 1.77221e8 + 5.45431e8i 0.633821 + 1.95070i
\(260\) −3.08018e8 + 3.50623e8i −1.08685 + 1.23718i
\(261\) −6.44552e7 + 1.98373e8i −0.224396 + 0.690621i
\(262\) −7.35024e8 + 2.38824e8i −2.52492 + 0.820395i
\(263\) −3.23474e8 + 1.05103e8i −1.09646 + 0.356262i −0.800740 0.599011i \(-0.795560\pi\)
−0.295723 + 0.955274i \(0.595560\pi\)
\(264\) −3.67153e6 + 1.12998e7i −0.0122810 + 0.0377970i
\(265\) 2.95177e8 + 4.97115e8i 0.974367 + 1.64095i
\(266\) −2.78815e8 8.58104e8i −0.908301 2.79546i
\(267\) 8.90847e7 + 1.22615e8i 0.286427 + 0.394233i
\(268\) 1.32246e8i 0.419673i
\(269\) −2.38178e8 + 1.73047e8i −0.746051 + 0.542038i −0.894600 0.446867i \(-0.852540\pi\)
0.148549 + 0.988905i \(0.452540\pi\)
\(270\) 4.10276e8 2.43614e8i 1.26853 0.753232i
\(271\) 1.48620e7 + 1.07978e7i 0.0453611 + 0.0329568i 0.610235 0.792221i \(-0.291075\pi\)
−0.564874 + 0.825177i \(0.691075\pi\)
\(272\) 7.90679e6 1.08828e7i 0.0238237 0.0327905i
\(273\) −1.90575e8 6.19217e7i −0.566888 0.184193i
\(274\) 2.30379e8 0.676574
\(275\) 2.25452e7 1.07062e7i 0.0653716 0.0310436i
\(276\) −4.98558e7 −0.142736
\(277\) 5.45001e8 + 1.77082e8i 1.54070 + 0.500604i 0.951569 0.307434i \(-0.0994704\pi\)
0.589130 + 0.808038i \(0.299470\pi\)
\(278\) −5.56728e8 + 7.66270e8i −1.55413 + 2.13907i
\(279\) −1.64996e8 1.19877e8i −0.454840 0.330461i
\(280\) 9.48018e7 + 4.20633e8i 0.258085 + 1.14512i
\(281\) −1.37189e7 + 9.96734e6i −0.0368847 + 0.0267983i −0.606075 0.795408i \(-0.707257\pi\)
0.569190 + 0.822206i \(0.307257\pi\)
\(282\) 1.98653e8i 0.527502i
\(283\) −2.80705e8 3.86358e8i −0.736204 1.01330i −0.998828 0.0483992i \(-0.984588\pi\)
0.262624 0.964898i \(-0.415412\pi\)
\(284\) −3.12674e8 9.62311e8i −0.809985 2.49288i
\(285\) −3.03717e8 1.30795e8i −0.777162 0.334682i
\(286\) −1.44283e7 + 4.44056e7i −0.0364698 + 0.112242i
\(287\) 6.59654e7 2.14334e7i 0.164714 0.0535187i
\(288\) −2.66527e8 + 8.65999e7i −0.657458 + 0.213621i
\(289\) 4.96514e7 1.52811e8i 0.121001 0.372403i
\(290\) −6.62140e8 + 1.49232e8i −1.59425 + 0.359310i
\(291\) −8.14689e7 2.50735e8i −0.193806 0.596472i
\(292\) 3.91973e8 + 5.39505e8i 0.921333 + 1.26811i
\(293\) 3.56340e8i 0.827615i 0.910364 + 0.413807i \(0.135801\pi\)
−0.910364 + 0.413807i \(0.864199\pi\)
\(294\) −8.14298e7 + 5.91622e7i −0.186882 + 0.135778i
\(295\) 5.12224e7 + 4.75083e6i 0.116167 + 0.0107744i
\(296\) 6.84528e8 + 4.97339e8i 1.53416 + 1.11463i
\(297\) 1.74345e7 2.39965e7i 0.0386156 0.0531497i
\(298\) 7.98124e8 + 2.59326e8i 1.74708 + 0.567661i
\(299\) −7.65326e7 −0.165576
\(300\) 3.55199e8 + 1.93644e8i 0.759534 + 0.414076i
\(301\) −4.49983e8 −0.951073
\(302\) 3.76200e8 + 1.22235e8i 0.785950 + 0.255371i
\(303\) −1.34802e8 + 1.85539e8i −0.278386 + 0.383165i
\(304\) −3.30536e7 2.40149e7i −0.0674779 0.0490256i
\(305\) −1.71132e8 1.50338e8i −0.345368 0.303402i
\(306\) −3.71177e8 + 2.69676e8i −0.740552 + 0.538043i
\(307\) 4.29682e8i 0.847546i −0.905769 0.423773i \(-0.860706\pi\)
0.905769 0.423773i \(-0.139294\pi\)
\(308\) 4.03322e7 + 5.55126e7i 0.0786547 + 0.108259i
\(309\) −4.37869e7 1.34762e8i −0.0844286 0.259845i
\(310\) 6.12914e7 6.60830e8i 0.116851 1.25986i
\(311\) −1.40942e8 + 4.33775e8i −0.265692 + 0.817717i 0.725841 + 0.687863i \(0.241451\pi\)
−0.991533 + 0.129854i \(0.958549\pi\)
\(312\) −2.81169e8 + 9.13573e7i −0.524114 + 0.170295i
\(313\) 4.30361e7 1.39833e7i 0.0793283 0.0257753i −0.269084 0.963117i \(-0.586721\pi\)
0.348412 + 0.937341i \(0.386721\pi\)
\(314\) 3.15273e8 9.70311e8i 0.574689 1.76871i
\(315\) 4.16852e7 4.49441e8i 0.0751442 0.810187i
\(316\) −5.41001e8 1.66503e9i −0.964480 2.96836i
\(317\) 1.92798e8 + 2.65364e8i 0.339935 + 0.467881i 0.944423 0.328734i \(-0.106622\pi\)
−0.604487 + 0.796615i \(0.706622\pi\)
\(318\) 9.37549e8i 1.63493i
\(319\) −3.41351e7 + 2.48006e7i −0.0588754 + 0.0427755i
\(320\) −7.08005e8 6.21975e8i −1.20785 1.06108i
\(321\) 2.54161e8 + 1.84659e8i 0.428886 + 0.311604i
\(322\) −1.06396e8 + 1.46441e8i −0.177594 + 0.244437i
\(323\) 7.21176e8 + 2.34324e8i 1.19078 + 0.386909i
\(324\) −2.44697e8 −0.399688
\(325\) 5.45258e8 + 2.97259e8i 0.881070 + 0.480334i
\(326\) 1.43146e9 2.28832
\(327\) 3.43556e7 + 1.11628e7i 0.0543352 + 0.0176546i
\(328\) 6.01490e7 8.27880e7i 0.0941174 0.129542i
\(329\) −3.62566e8 2.63419e8i −0.561308 0.407814i
\(330\) 4.03003e7 + 3.73782e6i 0.0617318 + 0.00572557i
\(331\) −7.27376e8 + 5.28470e8i −1.10246 + 0.800981i −0.981459 0.191672i \(-0.938609\pi\)
−0.120997 + 0.992653i \(0.538609\pi\)
\(332\) 1.42314e7i 0.0213434i
\(333\) −5.20621e8 7.16574e8i −0.772622 1.06342i
\(334\) 3.63332e8 + 1.11822e9i 0.533570 + 1.64216i
\(335\) 1.71668e8 3.86904e7i 0.249479 0.0562272i
\(336\) −6.63177e6 + 2.04105e7i −0.00953766 + 0.0293539i
\(337\) 1.63192e8 5.30243e7i 0.232270 0.0754692i −0.190569 0.981674i \(-0.561033\pi\)
0.422840 + 0.906205i \(0.361033\pi\)
\(338\) −7.68669e6 + 2.49756e6i −0.0108276 + 0.00351809i
\(339\) −2.23739e8 + 6.88598e8i −0.311920 + 0.959991i
\(340\) −8.52035e8 3.66926e8i −1.17566 0.506294i
\(341\) −1.27487e7 3.92365e7i −0.0174111 0.0535859i
\(342\) 8.19071e8 + 1.12736e9i 1.10721 + 1.52395i
\(343\) 6.15043e8i 0.822955i
\(344\) −5.37099e8 + 3.90225e8i −0.711377 + 0.516845i
\(345\) 1.45860e7 + 6.47178e7i 0.0191236 + 0.0848510i
\(346\) 8.13279e8 + 5.90882e8i 1.05554 + 0.766892i
\(347\) −1.44027e8 + 1.98236e8i −0.185050 + 0.254700i −0.891456 0.453107i \(-0.850315\pi\)
0.706406 + 0.707807i \(0.250315\pi\)
\(348\) −6.50452e8 2.11345e8i −0.827347 0.268821i
\(349\) −3.78867e8 −0.477087 −0.238543 0.971132i \(-0.576670\pi\)
−0.238543 + 0.971132i \(0.576670\pi\)
\(350\) 1.32681e9 6.30072e8i 1.65413 0.785511i
\(351\) 7.38052e8 0.910987
\(352\) −5.39150e7 1.75181e7i −0.0658886 0.0214085i
\(353\) 5.38107e8 7.40641e8i 0.651115 0.896182i −0.348032 0.937483i \(-0.613150\pi\)
0.999147 + 0.0413003i \(0.0131500\pi\)
\(354\) 6.74891e7 + 4.90337e7i 0.0808579 + 0.0587467i
\(355\) −1.15770e9 + 6.87419e8i −1.37340 + 0.815497i
\(356\) 1.04475e9 7.59053e8i 1.22726 0.891655i
\(357\) 3.98309e8i 0.463321i
\(358\) 3.43199e8 + 4.72372e8i 0.395325 + 0.544119i
\(359\) 725385. + 2.23251e6i 0.000827443 + 0.00254661i 0.951469 0.307743i \(-0.0995738\pi\)
−0.950642 + 0.310290i \(0.899574\pi\)
\(360\) −3.39999e8 5.72601e8i −0.384078 0.646834i
\(361\) 4.35479e8 1.34027e9i 0.487183 1.49939i
\(362\) −1.96397e9 + 6.38133e8i −2.17598 + 0.707020i
\(363\) −4.54500e8 + 1.47676e8i −0.498724 + 0.162045i
\(364\) −5.27609e8 + 1.62381e9i −0.573399 + 1.76474i
\(365\) 5.85654e8 6.66660e8i 0.630400 0.717595i
\(366\) −1.14149e8 3.51313e8i −0.121699 0.374551i
\(367\) 3.21777e7 + 4.42888e7i 0.0339800 + 0.0467695i 0.825669 0.564155i \(-0.190798\pi\)
−0.791689 + 0.610924i \(0.790798\pi\)
\(368\) 8.19659e6i 0.00857365i
\(369\) −8.66636e7 + 6.29648e7i −0.0897935 + 0.0652388i
\(370\) 1.14003e9 2.64724e9i 1.17006 2.71699i
\(371\) 1.71114e9 + 1.24321e9i 1.73971 + 1.26397i
\(372\) 3.93068e8 5.41012e8i 0.395884 0.544887i
\(373\) −7.78487e8 2.52946e8i −0.776731 0.252375i −0.106287 0.994335i \(-0.533896\pi\)
−0.670444 + 0.741960i \(0.733896\pi\)
\(374\) −9.28093e7 −0.0917362
\(375\) 1.47451e8 5.17737e8i 0.144390 0.506990i
\(376\) −6.61194e8 −0.641463
\(377\) −9.98495e8 3.24431e8i −0.959734 0.311837i
\(378\) 1.02604e9 1.41222e9i 0.977108 1.34487i
\(379\) 5.80232e8 + 4.21563e8i 0.547475 + 0.397764i 0.826854 0.562417i \(-0.190128\pi\)
−0.279379 + 0.960181i \(0.590128\pi\)
\(380\) −1.11445e9 + 2.58784e9i −1.04188 + 2.41933i
\(381\) −2.71913e8 + 1.97557e8i −0.251880 + 0.183001i
\(382\) 1.78306e9i 1.63661i
\(383\) 4.60000e8 + 6.33135e8i 0.418371 + 0.575839i 0.965235 0.261383i \(-0.0841785\pi\)
−0.546864 + 0.837222i \(0.684178\pi\)
\(384\) −2.99219e8 9.20902e8i −0.269668 0.829954i
\(385\) 6.02611e7 6.85962e7i 0.0538176 0.0612615i
\(386\) −6.22995e8 + 1.91738e9i −0.551352 + 1.69689i
\(387\) 6.60956e8 2.14758e8i 0.579674 0.188348i
\(388\) −2.13641e9 + 6.94162e8i −1.85684 + 0.603323i
\(389\) 3.74137e7 1.15148e8i 0.0322260 0.0991816i −0.933650 0.358187i \(-0.883395\pi\)
0.965876 + 0.259006i \(0.0833949\pi\)
\(390\) 5.14173e8 + 8.65930e8i 0.438918 + 0.739191i
\(391\) −4.70098e7 1.44681e8i −0.0397713 0.122404i
\(392\) 1.96914e8 + 2.71029e8i 0.165111 + 0.227256i
\(393\) 1.03624e9i 0.861168i
\(394\) −2.31323e8 + 1.68066e8i −0.190538 + 0.138434i
\(395\) −2.00310e9 + 1.18940e9i −1.63536 + 0.971043i
\(396\) −8.57356e7 6.22905e7i −0.0693790 0.0504068i
\(397\) −7.81407e8 + 1.07551e9i −0.626774 + 0.862680i −0.997824 0.0659329i \(-0.978998\pi\)
0.371050 + 0.928613i \(0.378998\pi\)
\(398\) 1.42684e9 + 4.63609e8i 1.13445 + 0.368605i
\(399\) −1.20976e9 −0.953444
\(400\) 3.18362e7 5.83967e7i 0.0248720 0.0456225i
\(401\) −7.65251e8 −0.592651 −0.296325 0.955087i \(-0.595761\pi\)
−0.296325 + 0.955087i \(0.595761\pi\)
\(402\) 2.71401e8 + 8.81836e7i 0.208363 + 0.0677013i
\(403\) 6.03391e8 8.30496e8i 0.459231 0.632077i
\(404\) 1.58090e9 + 1.14859e9i 1.19281 + 0.866624i
\(405\) 7.15896e7 + 3.17641e8i 0.0535497 + 0.237599i
\(406\) −2.00889e9 + 1.45954e9i −1.48975 + 1.08237i
\(407\) 1.79173e8i 0.131732i
\(408\) −3.45413e8 4.75421e8i −0.251784 0.346551i
\(409\) −3.67978e8 1.13252e9i −0.265944 0.818491i −0.991474 0.130301i \(-0.958406\pi\)
0.725531 0.688190i \(-0.241594\pi\)
\(410\) −3.20162e8 1.37877e8i −0.229417 0.0987979i
\(411\) 9.54534e7 2.93775e8i 0.0678180 0.208722i
\(412\) −1.14825e9 + 3.73090e8i −0.808904 + 0.262829i
\(413\) 1.78984e8 5.81556e7i 0.125023 0.0406224i
\(414\) 8.63887e7 2.65877e8i 0.0598351 0.184153i
\(415\) −1.84737e7 + 4.16359e6i −0.0126878 + 0.00285956i
\(416\) −4.35895e8 1.34155e9i −0.296862 0.913648i
\(417\) 7.46465e8 + 1.02742e9i 0.504119 + 0.693861i
\(418\) 2.81885e8i 0.188779i
\(419\) 1.51623e9 1.10161e9i 1.00697 0.731607i 0.0433986 0.999058i \(-0.486181\pi\)
0.963571 + 0.267451i \(0.0861814\pi\)
\(420\) 1.47369e9 + 1.36683e8i 0.970584 + 0.0900209i
\(421\) −1.38677e9 1.00755e9i −0.905768 0.658079i 0.0341731 0.999416i \(-0.489120\pi\)
−0.939941 + 0.341337i \(0.889120\pi\)
\(422\) 1.00689e9 1.38587e9i 0.652212 0.897693i
\(423\) 6.58271e8 + 2.13885e8i 0.422877 + 0.137401i
\(424\) 3.12052e9 1.98814
\(425\) −2.27032e8 + 1.21338e9i −0.143458 + 0.766715i
\(426\) −2.18339e9 −1.36835
\(427\) −7.92551e8 2.57515e8i −0.492640 0.160068i
\(428\) 1.57340e9 2.16560e9i 0.970033 1.33514i
\(429\) 5.06473e7 + 3.67974e7i 0.0309710 + 0.0225018i
\(430\) 1.69902e9 + 1.49257e9i 1.03053 + 0.905308i
\(431\) 1.16008e9 8.42851e8i 0.697942 0.507084i −0.181319 0.983424i \(-0.558037\pi\)
0.879261 + 0.476340i \(0.158037\pi\)
\(432\) 7.90448e7i 0.0471715i
\(433\) 5.28990e8 + 7.28093e8i 0.313141 + 0.431002i 0.936358 0.351048i \(-0.114174\pi\)
−0.623216 + 0.782049i \(0.714174\pi\)
\(434\) −7.50276e8 2.30911e9i −0.440562 1.35591i
\(435\) −8.40477e7 + 9.06183e8i −0.0489568 + 0.527841i
\(436\) 9.51137e7 2.92730e8i 0.0549592 0.169147i
\(437\) −4.39433e8 + 1.42780e8i −0.251888 + 0.0818434i
\(438\) 1.36857e9 4.44676e8i 0.778230 0.252862i
\(439\) 6.41251e8 1.97357e9i 0.361745 1.11334i −0.590250 0.807221i \(-0.700971\pi\)
0.951994 0.306115i \(-0.0990293\pi\)
\(440\) 1.24409e7 1.34135e8i 0.00696252 0.0750683i
\(441\) −1.08370e8 3.33530e8i −0.0601694 0.185182i
\(442\) −1.35739e9 1.86829e9i −0.747701 1.02912i
\(443\) 2.76277e9i 1.50984i 0.655814 + 0.754922i \(0.272325\pi\)
−0.655814 + 0.754922i \(0.727675\pi\)
\(444\) 2.34960e9 1.70709e9i 1.27395 0.925582i
\(445\) −1.29098e9 1.13411e9i −0.694480 0.610094i
\(446\) 6.92363e8 + 5.03031e8i 0.369540 + 0.268487i
\(447\) 6.61377e8 9.10308e8i 0.350246 0.482072i
\(448\) −3.27893e9 1.06539e9i −1.72290 0.559803i
\(449\) −6.46933e8 −0.337285 −0.168642 0.985677i \(-0.553938\pi\)
−0.168642 + 0.985677i \(0.553938\pi\)
\(450\) −1.64817e9 + 1.55871e9i −0.852624 + 0.806344i
\(451\) −2.16694e7 −0.0111232
\(452\) 5.86725e9 + 1.90639e9i 2.98848 + 0.971016i
\(453\) 3.11744e8 4.29079e8i 0.157563 0.216867i
\(454\) 3.17344e8 + 2.30564e8i 0.159160 + 0.115637i
\(455\) 2.26223e9 + 2.09820e8i 1.12589 + 0.104425i
\(456\) −1.44397e9 + 1.04911e9i −0.713150 + 0.518134i
\(457\) 1.27008e8i 0.0622480i −0.999516 0.0311240i \(-0.990091\pi\)
0.999516 0.0311240i \(-0.00990868\pi\)
\(458\) −1.03332e9 1.42224e9i −0.502580 0.691742i
\(459\) 4.53345e8 + 1.39525e9i 0.218819 + 0.673455i
\(460\) 5.51433e8 1.24281e8i 0.264144 0.0595323i
\(461\) −4.68245e8 + 1.44111e9i −0.222597 + 0.685085i 0.775929 + 0.630820i \(0.217281\pi\)
−0.998527 + 0.0542645i \(0.982719\pi\)
\(462\) 1.40820e8 4.57551e7i 0.0664380 0.0215870i
\(463\) −6.00587e8 + 1.95143e8i −0.281218 + 0.0913732i −0.446230 0.894918i \(-0.647234\pi\)
0.165012 + 0.986292i \(0.447234\pi\)
\(464\) −3.47463e7 + 1.06938e8i −0.0161471 + 0.0496957i
\(465\) −8.17285e8 3.51961e8i −0.376954 0.162334i
\(466\) 1.86906e8 + 5.75239e8i 0.0855606 + 0.263328i
\(467\) −2.23062e8 3.07019e8i −0.101348 0.139494i 0.755331 0.655344i \(-0.227476\pi\)
−0.856679 + 0.515850i \(0.827476\pi\)
\(468\) 2.63693e9i 1.18916i
\(469\) 5.20830e8 3.78405e8i 0.233126 0.169376i
\(470\) 4.95206e8 + 2.19722e9i 0.220010 + 0.976182i
\(471\) −1.10670e9 8.04063e8i −0.488041 0.354582i
\(472\) 1.63203e8 2.24629e8i 0.0714382 0.0983263i
\(473\) 1.33703e8 + 4.34427e7i 0.0580934 + 0.0188757i
\(474\) −3.77780e9 −1.62935
\(475\) 3.68532e9 + 6.89552e8i 1.57778 + 0.295216i
\(476\) −3.39382e9 −1.44233
\(477\) −3.10672e9 1.00944e9i −1.31066 0.425858i
\(478\) −3.35204e9 + 4.61369e9i −1.40382 + 1.93219i
\(479\) 2.02579e9 + 1.47182e9i 0.842210 + 0.611901i 0.922987 0.384831i \(-0.125740\pi\)
−0.0807771 + 0.996732i \(0.525740\pi\)
\(480\) −1.05137e9 + 6.24282e8i −0.433921 + 0.257654i
\(481\) 3.60683e9 2.62051e9i 1.47781 1.07369i
\(482\) 4.97928e9i 2.02536i
\(483\) 1.42656e8 + 1.96349e8i 0.0576070 + 0.0792893i
\(484\) 1.25828e9 + 3.87260e9i 0.504452 + 1.55254i
\(485\) 1.52613e9 + 2.57019e9i 0.607428 + 1.02298i
\(486\) −1.31687e9 + 4.05290e9i −0.520373 + 1.60154i
\(487\) −1.29561e9 + 4.20968e8i −0.508302 + 0.165157i −0.551930 0.833891i \(-0.686108\pi\)
0.0436280 + 0.999048i \(0.486108\pi\)
\(488\) −1.16930e9 + 3.79930e8i −0.455468 + 0.147991i
\(489\) 5.93100e8 1.82537e9i 0.229375 0.705945i
\(490\) 7.53178e8 8.57356e8i 0.289209 0.329211i
\(491\) −2.91980e8 8.98621e8i −0.111319 0.342603i 0.879843 0.475265i \(-0.157648\pi\)
−0.991161 + 0.132661i \(0.957648\pi\)
\(492\) −2.06458e8 2.84165e8i −0.0781544 0.107570i
\(493\) 2.08689e9i 0.784395i
\(494\) −5.67446e9 + 4.12274e9i −2.11778 + 1.53866i
\(495\) −5.57762e7 + 1.29517e8i −0.0206695 + 0.0479965i
\(496\) −8.89455e7 6.46227e7i −0.0327294 0.0237793i
\(497\) −2.89523e9 + 3.98495e9i −1.05788 + 1.45605i
\(498\) −2.92063e7 9.48970e6i −0.0105968 0.00344310i
\(499\) −7.84007e8 −0.282467 −0.141234 0.989976i \(-0.545107\pi\)
−0.141234 + 0.989976i \(0.545107\pi\)
\(500\) −4.41141e9 1.25637e9i −1.57828 0.449492i
\(501\) 1.57648e9 0.560088
\(502\) −1.89484e9 6.15672e8i −0.668514 0.217213i
\(503\) −3.70041e8 + 5.09318e8i −0.129647 + 0.178443i −0.868905 0.494978i \(-0.835176\pi\)
0.739259 + 0.673422i \(0.235176\pi\)
\(504\) −1.97097e9 1.43199e9i −0.685760 0.498234i
\(505\) 1.02847e9 2.38820e9i 0.355363 0.825185i
\(506\) 4.57510e7 3.32401e7i 0.0156991 0.0114060i
\(507\) 1.08368e7i 0.00369294i
\(508\) 1.68330e9 + 2.31686e9i 0.569689 + 0.784109i
\(509\) 7.64194e8 + 2.35195e9i 0.256857 + 0.790524i 0.993458 + 0.114197i \(0.0364295\pi\)
−0.736601 + 0.676327i \(0.763570\pi\)
\(510\) −1.32117e9 + 1.50391e9i −0.441026 + 0.502027i
\(511\) 1.00317e9 3.08745e9i 0.332585 1.02359i
\(512\) −3.00031e8 + 9.74859e7i −0.0987918 + 0.0320994i
\(513\) 4.23773e9 1.37692e9i 1.38587 0.450296i
\(514\) −1.48328e9 + 4.56508e9i −0.481785 + 1.48278i
\(515\) 8.20245e8 + 1.38139e9i 0.264617 + 0.445648i
\(516\) 7.04177e8 + 2.16723e9i 0.225636 + 0.694435i
\(517\) 8.22973e7 + 1.13273e8i 0.0261920 + 0.0360502i
\(518\) 1.05445e10i 3.33328i
\(519\) 1.09045e9 7.92260e8i 0.342390 0.248761i
\(520\) 2.88215e9 1.71136e9i 0.898885 0.533741i
\(521\) −1.33615e9 9.70767e8i −0.413925 0.300734i 0.361264 0.932464i \(-0.382345\pi\)
−0.775189 + 0.631729i \(0.782345\pi\)
\(522\) 2.25417e9 3.10260e9i 0.693648 0.954725i
\(523\) 3.43665e9 + 1.11663e9i 1.05046 + 0.341315i 0.782849 0.622212i \(-0.213766\pi\)
0.267611 + 0.963527i \(0.413766\pi\)
\(524\) 8.82939e9 2.68084
\(525\) −2.53719e8 1.95298e9i −0.0765237 0.589035i
\(526\) 6.25353e9 1.87359
\(527\) 1.94065e9 + 6.30554e8i 0.577576 + 0.187666i
\(528\) 3.94097e6 5.42428e6i 0.00116516 0.00160370i
\(529\) −2.67957e9 1.94682e9i −0.786992 0.571783i
\(530\) −2.33713e9 1.03698e10i −0.681896 3.02556i
\(531\) −2.35145e8 + 1.70843e8i −0.0681562 + 0.0495184i
\(532\) 1.03079e10i 2.96810i
\(533\) −3.16929e8 4.36215e8i −0.0906602 0.124783i
\(534\) −8.61110e8 2.65022e9i −0.244717 0.753162i
\(535\) −3.27149e9 1.40886e9i −0.923649 0.397767i
\(536\) 2.93509e8 9.03327e8i 0.0823273 0.253378i
\(537\) 7.44560e8 2.41922e8i 0.207487 0.0674165i
\(538\) 5.14805e9 1.67270e9i 1.42529 0.463106i
\(539\) 2.19219e7 6.74688e7i 0.00603001 0.0185585i
\(540\) −5.31781e9 + 1.19852e9i −1.45330 + 0.327542i
\(541\) 1.56118e9 + 4.80483e9i 0.423900 + 1.30463i 0.904044 + 0.427440i \(0.140585\pi\)
−0.480143 + 0.877190i \(0.659415\pi\)
\(542\) −1.98531e8 2.73255e8i −0.0535589 0.0737175i
\(543\) 2.76883e9i 0.742158i
\(544\) 2.26838e9 1.64808e9i 0.604116 0.438916i
\(545\) −4.07819e8 3.78249e7i −0.107915 0.0100090i
\(546\) 2.98064e9 + 2.16557e9i 0.783675 + 0.569373i
\(547\) −2.33063e9 + 3.20783e9i −0.608860 + 0.838023i −0.996483 0.0837945i \(-0.973296\pi\)
0.387624 + 0.921818i \(0.373296\pi\)
\(548\) −2.50313e9 8.13318e8i −0.649759 0.211119i
\(549\) 1.28704e9 0.331961
\(550\) −4.55061e8 + 5.91187e7i −0.116627 + 0.0151515i
\(551\) −6.33839e9 −1.61417
\(552\) 3.40548e8 + 1.10651e8i 0.0861771 + 0.0280006i
\(553\) −5.00945e9 + 6.89492e9i −1.25966 + 1.73377i
\(554\) −8.52394e9 6.19301e9i −2.12989 1.54745i
\(555\) −2.90338e9 2.55059e9i −0.720905 0.633307i
\(556\) 8.75422e9 6.36031e9i 2.16001 1.56934i
\(557\) 1.52549e9i 0.374038i −0.982356 0.187019i \(-0.940117\pi\)
0.982356 0.187019i \(-0.0598825\pi\)
\(558\) 2.20408e9 + 3.03365e9i 0.537041 + 0.739173i
\(559\) 1.08097e9 + 3.32688e9i 0.261741 + 0.805555i
\(560\) 2.24715e7 2.42283e8i 0.00540723 0.0582995i
\(561\) −3.84539e7 + 1.18349e8i −0.00919540 + 0.0283005i
\(562\) 2.96523e8 9.63463e7i 0.0704664 0.0228959i
\(563\) 2.82310e9 9.17280e8i 0.666725 0.216632i 0.0439506 0.999034i \(-0.486006\pi\)
0.622774 + 0.782402i \(0.286006\pi\)
\(564\) −7.01317e8 + 2.15843e9i −0.164603 + 0.506596i
\(565\) 7.58133e8 8.17402e9i 0.176838 1.90663i
\(566\) 2.71335e9 + 8.35084e9i 0.628997 + 1.93585i
\(567\) 7.00170e8 + 9.63702e8i 0.161311 + 0.222025i
\(568\) 7.26717e9i 1.66397i
\(569\) −3.69771e9 + 2.68655e9i −0.841473 + 0.611366i −0.922782 0.385323i \(-0.874090\pi\)
0.0813087 + 0.996689i \(0.474090\pi\)
\(570\) 4.56776e9 + 4.01273e9i 1.03310 + 0.907565i
\(571\) −4.16842e9 3.02854e9i −0.937013 0.680779i 0.0106871 0.999943i \(-0.496598\pi\)
−0.947700 + 0.319163i \(0.896598\pi\)
\(572\) 3.13535e8 4.31544e8i 0.0700487 0.0964138i
\(573\) −2.27373e9 7.38781e8i −0.504892 0.164049i
\(574\) −1.27527e9 −0.281456
\(575\) −3.22659e8 6.79455e8i −0.0707793 0.149047i
\(576\) 5.32470e9 1.16096
\(577\) −6.24522e9 2.02920e9i −1.35342 0.439753i −0.459579 0.888137i \(-0.652000\pi\)
−0.893841 + 0.448384i \(0.852000\pi\)
\(578\) −1.73644e9 + 2.39000e9i −0.374035 + 0.514815i
\(579\) 2.18689e9 + 1.58887e9i 0.468222 + 0.340183i
\(580\) 7.72120e9 + 7.16135e8i 1.64319 + 0.152404i
\(581\) −5.60481e7 + 4.07213e7i −0.0118562 + 0.00861401i
\(582\) 4.84732e9i 1.01923i
\(583\) −3.88404e8 5.34592e8i −0.0811790 0.111733i
\(584\) −1.48005e9 4.55512e9i −0.307490 0.946358i
\(585\) −3.42300e9 + 7.71471e8i −0.706906 + 0.159321i
\(586\) 2.02460e9 6.23108e9i 0.415621 1.27915i
\(587\) 5.13875e9 1.66968e9i 1.04863 0.340722i 0.266502 0.963834i \(-0.414132\pi\)
0.782132 + 0.623112i \(0.214132\pi\)
\(588\) 1.09362e9 3.55340e8i 0.221844 0.0720814i
\(589\) 1.91515e9 5.89422e9i 0.386188 1.18856i
\(590\) −8.68699e8 3.74102e8i −0.174135 0.0749909i
\(591\) 1.18471e8 + 3.64615e8i 0.0236078 + 0.0726572i
\(592\) −2.80655e8 3.86288e8i −0.0555964 0.0765218i
\(593\) 1.05787e8i 0.0208324i −0.999946 0.0104162i \(-0.996684\pi\)
0.999946 0.0104162i \(-0.00331564\pi\)
\(594\) −4.41205e8 + 3.20555e8i −0.0863751 + 0.0627552i
\(595\) 9.92910e8 + 4.40552e9i 0.193242 + 0.857409i
\(596\) −7.75635e9 5.63532e9i −1.50071 1.09033i
\(597\) 1.18238e9 1.62740e9i 0.227429 0.313029i
\(598\) 1.33827e9 + 4.34832e8i 0.255912 + 0.0831509i
\(599\) −8.45951e9 −1.60824 −0.804121 0.594465i \(-0.797364\pi\)
−0.804121 + 0.594465i \(0.797364\pi\)
\(600\) −1.99646e9 2.11105e9i −0.377339 0.398997i
\(601\) −1.01316e9 −0.190379 −0.0951894 0.995459i \(-0.530346\pi\)
−0.0951894 + 0.995459i \(0.530346\pi\)
\(602\) 7.86855e9 + 2.55665e9i 1.46997 + 0.477621i
\(603\) −5.84422e8 + 8.04388e8i −0.108547 + 0.149402i
\(604\) −3.65600e9 2.65624e9i −0.675114 0.490499i
\(605\) 4.65889e9 2.76636e9i 0.855340 0.507884i
\(606\) 3.41136e9 2.47850e9i 0.622692 0.452412i
\(607\) 3.34168e9i 0.606464i −0.952917 0.303232i \(-0.901934\pi\)
0.952917 0.303232i \(-0.0980656\pi\)
\(608\) −5.00562e9 6.88964e9i −0.903223 1.24318i
\(609\) 1.02884e9 + 3.16644e9i 0.184581 + 0.568081i
\(610\) 2.13830e9 + 3.60117e9i 0.381430 + 0.642376i
\(611\) −1.07658e9 + 3.31336e9i −0.190942 + 0.587658i
\(612\) 4.98500e9 1.61973e9i 0.879094 0.285635i
\(613\) −7.17341e9 + 2.33078e9i −1.25781 + 0.408686i −0.860713 0.509091i \(-0.829982\pi\)
−0.397095 + 0.917778i \(0.629982\pi\)
\(614\) −2.44130e9 + 7.51356e9i −0.425630 + 1.30996i
\(615\) −3.08472e8 + 3.51139e8i −0.0534753 + 0.0608718i
\(616\) −1.52290e8 4.68701e8i −0.0262506 0.0807911i
\(617\) 9.80170e7 + 1.34909e8i 0.0167998 + 0.0231229i 0.817334 0.576164i \(-0.195451\pi\)
−0.800534 + 0.599287i \(0.795451\pi\)
\(618\) 2.60528e9i 0.444012i
\(619\) 2.68571e9 1.95128e9i 0.455136 0.330676i −0.336484 0.941689i \(-0.609238\pi\)
0.791620 + 0.611013i \(0.209238\pi\)
\(620\) −2.99891e9 + 6.96374e9i −0.505351 + 1.17347i
\(621\) −7.23196e8 5.25433e8i −0.121181 0.0880433i
\(622\) 4.92912e9 6.78435e9i 0.821302 1.13042i
\(623\) −5.97882e9 1.94264e9i −0.990621 0.321872i
\(624\) 1.66832e8 0.0274875
\(625\) −3.40271e8 + 6.09402e9i −0.0557500 + 0.998445i
\(626\) −8.31992e8 −0.135553
\(627\) 3.59455e8 + 1.16794e8i 0.0582382 + 0.0189228i
\(628\) −6.85108e9 + 9.42971e9i −1.10383 + 1.51929i
\(629\) 7.16943e9 + 5.20890e9i 1.14870 + 0.834581i
\(630\) −3.28249e9 + 7.62222e9i −0.523011 + 1.21448i
\(631\) −4.52710e9 + 3.28913e9i −0.717327 + 0.521169i −0.885529 0.464584i \(-0.846204\pi\)
0.168202 + 0.985753i \(0.446204\pi\)
\(632\) 1.25740e10i 1.98135i
\(633\) −1.35005e9 1.85818e9i −0.211561 0.291189i
\(634\) −1.86363e9 5.73566e9i −0.290434 0.893863i
\(635\) 2.51504e9 2.86291e9i 0.389796 0.443711i
\(636\) 3.30988e9 1.01868e10i 0.510167 1.57013i
\(637\) 1.67880e9 5.45475e8i 0.257342 0.0836155i
\(638\) 7.37806e8 2.39728e8i 0.112479 0.0365465i
\(639\) 2.35081e9 7.23504e9i 0.356422 1.09695i
\(640\) 5.60517e9 + 9.43979e9i 0.845198 + 1.42342i
\(641\) 1.45255e9 + 4.47049e9i 0.217835 + 0.670428i 0.998940 + 0.0460282i \(0.0146564\pi\)
−0.781105 + 0.624400i \(0.785344\pi\)
\(642\) −3.39518e9 4.67307e9i −0.506396 0.696994i
\(643\) 1.86444e9i 0.276573i 0.990392 + 0.138286i \(0.0441594\pi\)
−0.990392 + 0.138286i \(0.955841\pi\)
\(644\) 1.67301e9 1.21551e9i 0.246830 0.179332i
\(645\) 2.60727e9 1.54815e9i 0.382584 0.227171i
\(646\) −1.12794e10 8.19494e9i −1.64616 1.19600i
\(647\) −7.03636e7 + 9.68472e7i −0.0102137 + 0.0140580i −0.814093 0.580734i \(-0.802766\pi\)
0.803880 + 0.594792i \(0.202766\pi\)
\(648\) 1.67144e9 + 5.43085e8i 0.241312 + 0.0784071i
\(649\) −5.87959e7 −0.00844288
\(650\) −7.84564e9 8.29593e9i −1.12055 1.18486i
\(651\) −3.25541e9 −0.462458
\(652\) −1.55532e10 5.05355e9i −2.19763 0.714053i
\(653\) 1.07999e9 1.48647e9i 0.151783 0.208911i −0.726354 0.687321i \(-0.758787\pi\)
0.878137 + 0.478410i \(0.158787\pi\)
\(654\) −5.37331e8 3.90394e8i −0.0751138 0.0545733i
\(655\) −2.58316e9 1.14614e10i −0.359176 1.59366i
\(656\) −4.67183e7 + 3.39429e7i −0.00646136 + 0.00469445i
\(657\) 5.01376e9i 0.689739i
\(658\) 4.84328e9 + 6.66621e9i 0.662749 + 0.912196i
\(659\) 2.15022e9 + 6.61771e9i 0.292674 + 0.900759i 0.983993 + 0.178209i \(0.0570302\pi\)
−0.691318 + 0.722550i \(0.742970\pi\)
\(660\) −4.24679e8 1.82887e8i −0.0574986 0.0247616i
\(661\) −6.61552e7 + 2.03605e8i −0.00890962 + 0.0274210i −0.955412 0.295274i \(-0.904589\pi\)
0.946503 + 0.322695i \(0.104589\pi\)
\(662\) 1.57217e10 5.10830e9i 2.10619 0.684342i
\(663\) −2.94483e9 + 9.56834e8i −0.392431 + 0.127508i
\(664\) −3.15853e7 + 9.72097e7i −0.00418694 + 0.0128861i
\(665\) 1.33806e10 3.01571e9i 1.76442 0.397662i
\(666\) 5.03243e9 + 1.54882e10i 0.660113 + 2.03162i
\(667\) 7.47428e8 + 1.02875e9i 0.0975279 + 0.134236i
\(668\) 1.34325e10i 1.74357i
\(669\) 9.28327e8 6.74469e8i 0.119870 0.0870904i
\(670\) −3.22167e9 2.98807e8i −0.413828 0.0383822i
\(671\) 2.10628e8 + 1.53030e8i 0.0269146 + 0.0195546i
\(672\) −2.62932e9 + 3.61895e9i −0.334234 + 0.460034i
\(673\) −1.74978e9 5.68539e8i −0.221275 0.0718965i 0.196282 0.980548i \(-0.437113\pi\)
−0.417556 + 0.908651i \(0.637113\pi\)
\(674\) −3.15489e9 −0.396894
\(675\) 3.11160e9 + 6.55241e9i 0.389422 + 0.820045i
\(676\) 9.23356e7 0.0114962
\(677\) 1.53350e10 + 4.98265e9i 1.89943 + 0.617163i 0.966112 + 0.258121i \(0.0831035\pi\)
0.933321 + 0.359042i \(0.116897\pi\)
\(678\) 7.82475e9 1.07698e10i 0.964199 1.32711i
\(679\) 8.84691e9 + 6.42766e9i 1.08455 + 0.787968i
\(680\) 5.00560e9 + 4.39737e9i 0.610485 + 0.536305i
\(681\) 4.25498e8 3.09142e8i 0.0516277 0.0375097i
\(682\) 7.58536e8i 0.0915653i
\(683\) 9.27789e9 + 1.27699e10i 1.11423 + 1.53361i 0.815026 + 0.579425i \(0.196723\pi\)
0.299209 + 0.954188i \(0.403277\pi\)
\(684\) −4.91950e9 1.51407e10i −0.587794 1.80904i
\(685\) −3.23441e8 + 3.48727e9i −0.0384484 + 0.414541i
\(686\) −3.49446e9 + 1.07548e10i −0.413281 + 1.27195i
\(687\) −2.24176e9 + 7.28391e8i −0.263779 + 0.0857070i
\(688\) 3.56306e8 1.15771e8i 0.0417122 0.0135531i
\(689\) 5.08093e9 1.56375e10i 0.591801 1.82138i
\(690\) 1.12648e8 1.21455e9i 0.0130543 0.140748i
\(691\) −2.71163e9 8.34553e9i −0.312649 0.962234i −0.976711 0.214557i \(-0.931169\pi\)
0.664063 0.747677i \(-0.268831\pi\)
\(692\) −6.75051e9 9.29128e9i −0.774400 1.06587i
\(693\) 5.15893e8i 0.0588834i
\(694\) 3.64480e9 2.64810e9i 0.413919 0.300730i
\(695\) −1.08175e10 9.50305e9i −1.22231 1.07378i
\(696\) 3.97395e9 + 2.88724e9i 0.446776 + 0.324602i
\(697\) 6.29973e8 8.67083e8i 0.0704705 0.0969943i
\(698\) 6.62498e9 + 2.15259e9i 0.737379 + 0.239589i
\(699\) 8.10978e8 0.0898129
\(700\) −1.66405e10 + 2.16184e9i −1.83368 + 0.238221i
\(701\) −4.79206e9 −0.525423 −0.262711 0.964874i \(-0.584617\pi\)
−0.262711 + 0.964874i \(0.584617\pi\)
\(702\) −1.29058e10 4.19335e9i −1.40801 0.457490i
\(703\) 1.58207e10 2.17753e10i 1.71744 2.36386i
\(704\) 8.71408e8 + 6.33115e8i 0.0941276 + 0.0683877i
\(705\) 3.00704e9 + 2.78900e8i 0.323204 + 0.0299769i
\(706\) −1.36176e10 + 9.89375e9i −1.45641 + 1.05814i
\(707\) 9.51268e9i 1.01236i
\(708\) −5.60184e8 7.71027e8i −0.0593218 0.0816494i
\(709\) 4.34950e9 + 1.33864e10i 0.458329 + 1.41059i 0.867182 + 0.497992i \(0.165929\pi\)
−0.408853 + 0.912600i \(0.634071\pi\)
\(710\) 2.41496e10 5.44279e9i 2.53224 0.570713i
\(711\) 4.06746e9 1.25184e10i 0.424405 1.30618i
\(712\) −8.82096e9 + 2.86610e9i −0.915874 + 0.297585i
\(713\) −1.18249e9 + 3.84215e8i −0.122176 + 0.0396973i
\(714\) −2.26305e9 + 6.96496e9i −0.232676 + 0.716102i
\(715\) −6.51916e8 2.80746e8i −0.0666992 0.0287238i
\(716\) −2.06132e9 6.34408e9i −0.209869 0.645912i
\(717\) 4.49444e9 + 6.18607e9i 0.455364 + 0.626755i
\(718\) 4.31597e7i 0.00435154i
\(719\) −1.18125e10 + 8.58230e9i −1.18520 + 0.861098i −0.992749 0.120209i \(-0.961644\pi\)
−0.192451 + 0.981307i \(0.561644\pi\)
\(720\) 8.26240e7 + 3.66601e8i 0.00824978 + 0.0366041i
\(721\) 4.75493e9 + 3.45466e9i 0.472467 + 0.343267i
\(722\) −1.52298e10 + 2.09621e10i −1.50597 + 2.07278i
\(723\) −6.34951e9 2.06308e9i −0.624822 0.203017i
\(724\) 2.35920e10 2.31036
\(725\) −1.32933e9 1.02324e10i −0.129554 0.997228i
\(726\) 8.78657e9 0.852199
\(727\) −1.49764e10 4.86613e9i −1.44556 0.469692i −0.521937 0.852984i \(-0.674790\pi\)
−0.923627 + 0.383292i \(0.874790\pi\)
\(728\) 7.20783e9 9.92072e9i 0.692380 0.952979i
\(729\) 2.56143e9 + 1.86099e9i 0.244871 + 0.177909i
\(730\) −1.40287e10 + 8.32995e9i −1.33471 + 0.792524i
\(731\) −5.62532e9 + 4.08704e9i −0.532644 + 0.386988i
\(732\) 4.22011e9i 0.397681i
\(733\) 3.68838e9 + 5.07662e9i 0.345917 + 0.476114i 0.946158 0.323706i \(-0.104929\pi\)
−0.600241 + 0.799819i \(0.704929\pi\)
\(734\) −3.11036e8 9.57271e8i −0.0290318 0.0893508i
\(735\) −7.81221e8 1.31567e9i −0.0725719 0.122220i
\(736\) −5.27950e8 + 1.62486e9i −0.0488113 + 0.150226i
\(737\) −1.91286e8 + 6.21525e7i −0.0176014 + 0.00571903i
\(738\) 1.87317e9 6.08631e8i 0.171546 0.0557387i
\(739\) −5.58101e9 + 1.71766e10i −0.508695 + 1.56560i 0.285773 + 0.958297i \(0.407750\pi\)
−0.794468 + 0.607305i \(0.792250\pi\)
\(740\) −2.17325e10 + 2.47384e10i −1.97151 + 2.24420i
\(741\) 2.90614e9 + 8.94418e9i 0.262393 + 0.807563i
\(742\) −2.28580e10 3.14613e10i −2.05411 2.82724i
\(743\) 6.60453e9i 0.590719i −0.955386 0.295359i \(-0.904561\pi\)
0.955386 0.295359i \(-0.0954394\pi\)
\(744\) −3.88565e9 + 2.82309e9i −0.345906 + 0.251315i
\(745\) −5.04598e9 + 1.17172e10i −0.447093 + 1.03819i
\(746\) 1.21757e10 + 8.84618e9i 1.07376 + 0.780135i
\(747\) 6.28914e7 8.65626e7i 0.00552038 0.00759816i
\(748\) 1.00840e9 + 3.27650e8i 0.0881004 + 0.0286256i
\(749\) −1.30310e10 −1.13316
\(750\) −5.51998e9 + 8.21554e9i −0.477774 + 0.711086i
\(751\) 1.77504e10 1.52921 0.764606 0.644498i \(-0.222933\pi\)
0.764606 + 0.644498i \(0.222933\pi\)
\(752\) 3.54859e8 + 1.15301e8i 0.0304294 + 0.00988710i
\(753\) −1.57019e9 + 2.16118e9i −0.134020 + 0.184463i
\(754\) 1.56167e10 + 1.13462e10i 1.32675 + 0.963941i
\(755\) −2.37845e9 + 5.52297e9i −0.201131 + 0.467045i
\(756\) −1.61339e10 + 1.17219e10i −1.35804 + 0.986673i
\(757\) 4.47588e9i 0.375010i 0.982264 + 0.187505i \(0.0600401\pi\)
−0.982264 + 0.187505i \(0.939960\pi\)
\(758\) −7.75095e9 1.06683e10i −0.646417 0.889716i
\(759\) −2.34311e7 7.21134e7i −0.00194512 0.00598646i
\(760\) 1.33559e10 1.52032e10i 1.10363 1.25629i
\(761\) −3.55234e9 + 1.09330e10i −0.292192 + 0.899274i 0.691959 + 0.721937i \(0.256748\pi\)
−0.984150 + 0.177337i \(0.943252\pi\)
\(762\) 5.87721e9 1.90962e9i 0.481204 0.156353i
\(763\) −1.42503e9 + 4.63019e8i −0.116141 + 0.0377366i
\(764\) −6.29484e9 + 1.93735e10i −0.510691 + 1.57174i
\(765\) −3.56100e9 5.99715e9i −0.287578 0.484318i
\(766\) −4.44645e9 1.36848e10i −0.357448 1.10011i
\(767\) −8.59927e8 1.18359e9i −0.0688141 0.0947145i
\(768\) 7.16400e9i 0.570678i
\(769\) 1.39011e10 1.00997e10i 1.10231 0.800878i 0.120878 0.992667i \(-0.461429\pi\)
0.981436 + 0.191789i \(0.0614290\pi\)
\(770\) −1.44348e9 + 8.57113e8i −0.113945 + 0.0676582i
\(771\) 5.20675e9 + 3.78292e9i 0.409144 + 0.297260i
\(772\) 1.35381e10 1.86336e10i 1.05900 1.45759i
\(773\) −1.63763e10 5.32099e9i −1.27523 0.414347i −0.408331 0.912834i \(-0.633889\pi\)
−0.866897 + 0.498487i \(0.833889\pi\)
\(774\) −1.27779e10 −0.990524
\(775\) 9.91700e9 + 1.85555e9i 0.765287 + 0.143191i
\(776\) 1.61337e10 1.23942
\(777\) −1.34462e10 4.36893e9i −1.02831 0.334119i
\(778\) −1.30846e9 + 1.80093e9i −0.0996163 + 0.137110i
\(779\) −2.63355e9 1.91338e9i −0.199600 0.145018i
\(780\) −2.52961e9 1.12238e10i −0.190863 0.846856i
\(781\) 1.24498e9 9.04527e8i 0.0935152 0.0679427i
\(782\) 2.79704e9i 0.209158i
\(783\) −7.20792e9 9.92085e9i −0.536591 0.738554i
\(784\) −5.84199e7 1.79798e8i −0.00432967 0.0133254i
\(785\) 1.42451e10 + 6.13460e9i 1.05104 + 0.452629i
\(786\) 5.88757e9 1.81201e10i 0.432472 1.33101i
\(787\) 1.06931e10 3.47441e9i 0.781977 0.254080i 0.109293 0.994010i \(-0.465141\pi\)
0.672684 + 0.739930i \(0.265141\pi\)
\(788\) 3.10673e9 1.00944e9i 0.226184 0.0734917i
\(789\) 2.59104e9 7.97440e9i 0.187804 0.578001i
\(790\) 4.17846e10 9.41734e9i 3.01523 0.679569i
\(791\) −9.28040e9 2.85621e10i −0.666729 2.05198i
\(792\) 4.47382e8 + 6.15768e8i 0.0319993 + 0.0440432i
\(793\) 6.47821e9i 0.461316i
\(794\) 1.97746e10 1.43671e10i 1.40196 1.01859i
\(795\) −1.41918e10 1.31628e9i −1.00173 0.0929099i
\(796\) −1.38664e10 1.00745e10i −0.974468 0.707992i
\(797\) −1.13669e10 + 1.56452e10i −0.795314 + 1.09466i 0.198112 + 0.980179i \(0.436519\pi\)
−0.993426 + 0.114476i \(0.963481\pi\)
\(798\) 2.11543e10 + 6.87345e9i 1.47363 + 0.478812i
\(799\) −6.92504e9 −0.480296
\(800\) 1.00725e10 9.52577e9i 0.695540 0.657787i
\(801\) 9.70910e9 0.667521
\(802\) 1.33814e10 + 4.34789e9i 0.915993 + 0.297624i
\(803\) −5.96143e8 + 8.20520e8i −0.0406299 + 0.0559223i
\(804\) −2.63754e9 1.91628e9i −0.178979 0.130036i
\(805\) −2.06732e9 1.81612e9i −0.139676 0.122704i
\(806\) −1.52697e10 + 1.10941e10i −1.02721 + 0.746308i
\(807\) 7.25777e9i 0.486123i
\(808\) −8.24939e9 1.13543e10i −0.550151 0.757218i
\(809\) −3.96809e9 1.22125e10i −0.263488 0.810934i −0.992038 0.125941i \(-0.959805\pi\)
0.728549 0.684993i \(-0.240195\pi\)
\(810\) 5.52889e8 5.96113e9i 0.0365545 0.394122i
\(811\) −3.71060e9 + 1.14200e10i −0.244270 + 0.751787i 0.751485 + 0.659750i \(0.229338\pi\)
−0.995756 + 0.0920368i \(0.970662\pi\)
\(812\) 2.69799e10 8.76629e9i 1.76845 0.574606i
\(813\) −4.30709e8 + 1.39946e8i −0.0281104 + 0.00913362i
\(814\) −1.01800e9 + 3.13307e9i −0.0661547 + 0.203603i
\(815\) −2.00970e9 + 2.16681e10i −0.130041 + 1.40207i
\(816\) 1.02476e8 + 3.15389e8i 0.00660248 + 0.0203203i
\(817\) 1.24133e10 + 1.70855e10i 0.796364 + 1.09610i
\(818\) 2.18943e10i 1.39860i
\(819\) −1.03851e10 + 7.54525e9i −0.660570 + 0.479932i
\(820\) 2.99191e9 + 2.62836e9i 0.189496 + 0.166470i
\(821\) 7.72272e9 + 5.61089e9i 0.487045 + 0.353859i 0.804047 0.594566i \(-0.202676\pi\)
−0.317002 + 0.948425i \(0.602676\pi\)
\(822\) −3.33826e9 + 4.59472e9i −0.209637 + 0.288541i
\(823\) 2.36304e10 + 7.67797e9i 1.47765 + 0.480117i 0.933409 0.358813i \(-0.116819\pi\)
0.544239 + 0.838930i \(0.316819\pi\)
\(824\) 8.67136e9 0.539935
\(825\) −1.13159e8 + 6.04782e8i −0.00701620 + 0.0374982i
\(826\) −3.46020e9 −0.213634
\(827\) −3.88985e9 1.26389e9i −0.239146 0.0777033i 0.186992 0.982361i \(-0.440126\pi\)
−0.426138 + 0.904658i \(0.640126\pi\)
\(828\) −1.87728e9 + 2.58386e9i −0.114927 + 0.158184i
\(829\) −2.17511e10 1.58031e10i −1.32599 0.963389i −0.999837 0.0180720i \(-0.994247\pi\)
−0.326154 0.945317i \(-0.605753\pi\)
\(830\) 3.46694e8 + 3.21556e7i 0.0210462 + 0.00195201i
\(831\) −1.14290e10 + 8.30364e9i −0.690882 + 0.501955i
\(832\) 2.68015e10i 1.61335i
\(833\) 2.06239e9 + 2.83864e9i 0.123627 + 0.170158i
\(834\) −7.21548e9 2.22070e10i −0.430709 1.32559i
\(835\) −1.74367e10 + 3.92987e9i −1.03648 + 0.233601i
\(836\) 9.95152e8 3.06276e9i 0.0589071 0.181297i
\(837\) 1.14035e10 3.70522e9i 0.672201 0.218411i
\(838\) −3.27723e10 + 1.06484e10i −1.92377 + 0.625070i
\(839\) 9.19449e9 2.82977e10i 0.537478 1.65419i −0.200755 0.979641i \(-0.564340\pi\)
0.738233 0.674545i \(-0.235660\pi\)
\(840\) −9.76291e9 4.20436e9i −0.568331 0.244750i
\(841\) 5.99566e7 + 1.84527e8i 0.00347577 + 0.0106973i
\(842\) 1.85250e10 + 2.54974e10i 1.06946 + 1.47199i
\(843\) 4.18042e8i 0.0240338i
\(844\) −1.58328e10 + 1.15032e10i −0.906481 + 0.658597i
\(845\) −2.70140e7 1.19861e8i −0.00154025 0.00683406i
\(846\) −1.02955e10 7.48013e9i −0.584591 0.424730i
\(847\) 1.16512e10 1.60365e10i 0.658838 0.906813i
\(848\) −1.67476e9 5.44163e8i −0.0943122 0.0306439i
\(849\) 1.17731e10 0.660258
\(850\) 1.08639e10 1.99276e10i 0.606765 1.11298i
\(851\) −5.39981e9 −0.300348
\(852\) 2.37233e10 + 7.70815e9i 1.31412 + 0.426984i
\(853\) 4.05490e9 5.58109e9i 0.223696 0.307891i −0.682387 0.730991i \(-0.739058\pi\)
0.906083 + 0.423100i \(0.139058\pi\)
\(854\) 1.23957e10 + 9.00600e9i 0.681033 + 0.494799i
\(855\) −1.82148e10 + 1.08156e10i −0.996653 + 0.591793i
\(856\) −1.55537e10 + 1.13005e10i −0.847572 + 0.615797i
\(857\) 1.39676e10i 0.758033i −0.925390 0.379016i \(-0.876262\pi\)
0.925390 0.379016i \(-0.123738\pi\)
\(858\) −6.76565e8 9.31211e8i −0.0365682 0.0503318i
\(859\) 3.60021e9 + 1.10803e10i 0.193799 + 0.596452i 0.999989 + 0.00479460i \(0.00152617\pi\)
−0.806189 + 0.591657i \(0.798474\pi\)
\(860\) −1.31911e10 2.22154e10i −0.707190 1.19100i
\(861\) −5.28386e8 + 1.62620e9i −0.0282124 + 0.0868288i
\(862\) −2.50744e10 + 8.14717e9i −1.33338 + 0.433243i
\(863\) 4.07855e9 1.32520e9i 0.216007 0.0701850i −0.199014 0.979997i \(-0.563774\pi\)
0.415022 + 0.909812i \(0.363774\pi\)
\(864\) 5.09135e9 1.56696e10i 0.268556 0.826531i
\(865\) −1.00861e10 + 1.14811e10i −0.529865 + 0.603154i
\(866\) −5.11333e9 1.57372e10i −0.267541 0.823408i
\(867\) 2.32823e9 + 3.20454e9i 0.121328 + 0.166993i
\(868\) 2.77379e10i 1.43964i
\(869\) 2.15411e9 1.56505e9i 0.111352 0.0809020i
\(870\) 6.61830e9 1.53683e10i 0.340745 0.791239i
\(871\) −4.04883e9 2.94165e9i −0.207619 0.150844i
\(872\) −1.29938e9 + 1.78844e9i −0.0663633 + 0.0913412i
\(873\) −1.60624e10 5.21899e9i −0.817072 0.265483i
\(874\) 8.49530e9 0.430416
\(875\) 7.67470e9 + 2.09686e10i 0.387287 + 1.05814i
\(876\) −1.64398e10 −0.826290
\(877\) −8.32916e9 2.70631e9i −0.416968 0.135481i 0.0930167 0.995665i \(-0.470349\pi\)
−0.509985 + 0.860183i \(0.670349\pi\)
\(878\) −2.24262e10 + 3.08671e10i −1.11822 + 1.53909i
\(879\) −7.10692e9 5.16348e9i −0.352956 0.256437i
\(880\) −3.00676e7 + 6.98197e7i −0.00148734 + 0.00345373i
\(881\) 1.50828e10 1.09583e10i 0.743131 0.539916i −0.150559 0.988601i \(-0.548107\pi\)
0.893690 + 0.448685i \(0.148107\pi\)
\(882\) 6.44793e9i 0.316432i
\(883\) −7.47778e9 1.02923e10i −0.365519 0.503094i 0.586157 0.810198i \(-0.300640\pi\)
−0.951676 + 0.307103i \(0.900640\pi\)
\(884\) 8.15277e9 + 2.50917e10i 0.396938 + 1.22165i
\(885\) −8.36980e8 + 9.52749e8i −0.0405895 + 0.0462037i
\(886\) 1.56971e10 4.83107e10i 0.758231 2.33360i
\(887\) 2.12907e10 6.91777e9i 1.02437 0.332838i 0.251808 0.967777i \(-0.418975\pi\)
0.772562 + 0.634939i \(0.218975\pi\)
\(888\) −1.98381e10 + 6.44578e9i −0.950723 + 0.308908i
\(889\) 4.30804e9 1.32588e10i 0.205648 0.632919i
\(890\) 1.61309e10 + 2.71664e10i 0.766995 + 1.29171i
\(891\) −1.15002e8 3.53940e8i −0.00544670 0.0167632i
\(892\) −5.74686e9 7.90988e9i −0.271115 0.373158i
\(893\) 2.10331e10i 0.988376i
\(894\) −1.67371e10 + 1.21602e10i −0.783428 + 0.569194i
\(895\) −7.63218e9 + 4.53184e9i −0.355851 + 0.211297i
\(896\) 3.24930e10 + 2.36075e10i 1.50908 + 1.09641i
\(897\) 1.10898e9 1.52638e9i 0.0513039 0.0706138i
\(898\) 1.13125e10 + 3.67565e9i 0.521303 + 0.169382i
\(899\) −1.70563e10 −0.782934
\(900\) 2.34106e10 1.11172e10i 1.07044 0.508332i
\(901\) 3.26829e10 1.48862
\(902\) 3.78919e8 + 1.23118e8i 0.0171919 + 0.00558598i
\(903\) 6.52040e9 8.97456e9i 0.294691 0.405607i
\(904\) −3.58461e10 2.60437e10i −1.61381 1.17250i
\(905\) −6.90217e9 3.06248e10i −0.309539 1.37342i
\(906\) −7.88914e9 + 5.73179e9i −0.352436 + 0.256060i
\(907\) 3.60249e10i 1.60316i 0.597886 + 0.801581i \(0.296008\pi\)
−0.597886 + 0.801581i \(0.703992\pi\)
\(908\) −2.63407e9 3.62549e9i −0.116769 0.160718i
\(909\) 4.53999e9 + 1.39727e10i 0.200485 + 0.617029i
\(910\) −3.83659e10 1.65222e10i −1.68772 0.726812i
\(911\) 7.53830e9 2.32005e10i 0.330338 1.01668i −0.638635 0.769510i \(-0.720500\pi\)
0.968973 0.247167i \(-0.0794995\pi\)
\(912\) 9.57914e8 3.11245e8i 0.0418162 0.0135869i
\(913\) 2.05848e7 6.68842e6i 0.000895158 0.000290854i
\(914\) −7.21617e8 + 2.22091e9i −0.0312604 + 0.0962098i
\(915\) 5.47813e9 1.23465e9i 0.236406 0.0532808i
\(916\) 6.20631e9 + 1.91011e10i 0.266808 + 0.821152i
\(917\) −2.52642e10 3.47732e10i −1.08196 1.48920i
\(918\) 2.69736e10i 1.15077i
\(919\) −1.64816e10 + 1.19746e10i −0.700478 + 0.508927i −0.880088 0.474811i \(-0.842516\pi\)
0.179610 + 0.983738i \(0.442516\pi\)
\(920\) −4.04248e9 3.74937e8i −0.171155 0.0158745i
\(921\) 8.56967e9 + 6.22623e9i 0.361456 + 0.262613i
\(922\) 1.63758e10 2.25393e10i 0.688087 0.947071i
\(923\) 3.64171e10 + 1.18326e10i 1.52440 + 0.495308i
\(924\) −1.69158e9 −0.0705409
\(925\) 3.84711e10 + 2.09733e10i 1.59823 + 0.871307i
\(926\) 1.16108e10 0.480533
\(927\) −8.63302e9 2.80504e9i −0.355946 0.115654i
\(928\) −1.37760e10 + 1.89610e10i −0.565854 + 0.778831i
\(929\) −3.53109e10 2.56549e10i −1.44496 1.04982i −0.986978 0.160857i \(-0.948574\pi\)
−0.457977 0.888964i \(-0.651426\pi\)
\(930\) 1.22916e10 + 1.07980e10i 0.501092 + 0.440204i
\(931\) 8.62163e9 6.26398e9i 0.350159 0.254406i
\(932\) 6.91000e9i 0.279590i
\(933\) −6.60900e9 9.09651e9i −0.266410 0.366682i
\(934\) 2.15617e9 + 6.63600e9i 0.0865901 + 0.266497i
\(935\) 1.30300e8 1.40486e9i 0.00521319 0.0562074i
\(936\) −5.85245e9 + 1.80120e10i −0.233277 + 0.717953i
\(937\) −2.39264e10 + 7.77416e9i −0.950143 + 0.308720i −0.742774 0.669542i \(-0.766490\pi\)
−0.207370 + 0.978263i \(0.566490\pi\)
\(938\) −1.12574e10 + 3.65774e9i −0.445376 + 0.144711i
\(939\) −3.44721e8 + 1.06094e9i −0.0135875 + 0.0418179i
\(940\) 2.37639e9 2.56217e10i 0.0933191 1.00614i
\(941\) 9.31046e9 + 2.86546e10i 0.364257 + 1.12107i 0.950445 + 0.310892i \(0.100628\pi\)
−0.586189 + 0.810175i \(0.699372\pi\)
\(942\) 1.47837e10 + 2.03480e10i 0.576241 + 0.793128i
\(943\) 6.53062e8i 0.0253609i
\(944\) −1.26761e8 + 9.20975e7i −0.00490439 + 0.00356324i
\(945\) 1.99364e10 + 1.75140e10i 0.768487 + 0.675108i
\(946\) −2.09115e9 1.51931e9i −0.0803092 0.0583480i
\(947\) −7.00568e9 + 9.64250e9i −0.268056 + 0.368948i −0.921732 0.387827i \(-0.873226\pi\)
0.653676 + 0.756774i \(0.273226\pi\)
\(948\) 4.10470e10 + 1.33370e10i 1.56477 + 0.508426i
\(949\) −2.52364e10 −0.958508
\(950\) −6.05249e10 3.29964e10i −2.29035 1.24863i
\(951\) −8.08619e9 −0.304868
\(952\) 2.31820e10 + 7.53230e9i 0.870808 + 0.282943i
\(953\) 6.88486e9 9.47619e9i 0.257674 0.354657i −0.660507 0.750820i \(-0.729658\pi\)
0.918180 + 0.396163i \(0.129658\pi\)
\(954\) 4.85899e10 + 3.53026e10i 1.81187 + 1.31640i
\(955\) 2.69904e10 + 2.50334e9i 1.00276 + 0.0930053i
\(956\) 5.27089e10 3.82952e10i 1.95111 1.41756i
\(957\) 1.04017e9i 0.0383629i
\(958\) −2.70612e10 3.72466e10i −0.994417 1.36870i
\(959\) 3.95928e9 + 1.21854e10i 0.144961 + 0.446144i
\(960\) 2.26640e10 5.10798e9i 0.826775 0.186337i
\(961\) −3.34831e9 + 1.03050e10i −0.121701 + 0.374556i
\(962\) −7.79589e10 + 2.53304e10i −2.82327 + 0.917338i
\(963\) 1.91405e10 6.21912e9i 0.690655 0.224407i
\(964\) −1.75786e10 + 5.41015e10i −0.631998 + 1.94509i
\(965\) −2.81490e10 1.21223e10i −1.00836 0.434248i
\(966\) −1.37894e9 4.24395e9i −0.0492183 0.151478i
\(967\) −1.36802e9 1.88292e9i −0.0486520 0.0669638i 0.783998 0.620764i \(-0.213177\pi\)
−0.832650 + 0.553800i \(0.813177\pi\)
\(968\) 2.92451e10i 1.03631i
\(969\) −1.51235e10 + 1.09878e10i −0.533972 + 0.387953i
\(970\) −1.20834e10 5.36140e10i −0.425099 1.88615i
\(971\) 8.72472e9 + 6.33888e9i 0.305833 + 0.222201i 0.730106 0.683334i \(-0.239471\pi\)
−0.424274 + 0.905534i \(0.639471\pi\)
\(972\) 2.86163e10 3.93870e10i 0.999498 1.37569i
\(973\) −5.00982e10 1.62779e10i −1.74352 0.566504i
\(974\) 2.50472e10 0.868565
\(975\) −1.38296e10 + 6.56736e9i −0.477851 + 0.226921i
\(976\) 6.93811e8 0.0238873
\(977\) 9.33617e9 + 3.03350e9i 0.320286 + 0.104067i 0.464748 0.885443i \(-0.346145\pi\)
−0.144462 + 0.989510i \(0.546145\pi\)
\(978\) −2.07423e10 + 2.85493e10i −0.709039 + 0.975909i
\(979\) 1.58893e9 + 1.15443e9i 0.0541210 + 0.0393212i
\(980\) −1.12103e10 + 6.65645e9i −0.380474 + 0.225918i
\(981\) 1.87216e9 1.36021e9i 0.0633144 0.0460006i
\(982\) 1.73725e10i 0.585426i
\(983\) 2.13492e10 + 2.93846e10i 0.716876 + 0.986696i 0.999622 + 0.0275006i \(0.00875481\pi\)
−0.282746 + 0.959195i \(0.591245\pi\)
\(984\) 7.79563e8 + 2.39925e9i 0.0260836 + 0.0802772i
\(985\) −2.21927e9 3.73752e9i −0.0739918 0.124611i
\(986\) −1.18570e10 + 3.64920e10i −0.393917 + 1.21235i
\(987\) 1.05074e10 3.41405e9i 0.347844 0.113021i
\(988\) 7.62095e10 2.47620e10i 2.51397 0.816838i
\(989\) 1.30925e9 4.02947e9i 0.0430365 0.132453i
\(990\) 1.71119e9 1.94788e9i 0.0560500 0.0638027i
\(991\) −6.01077e9 1.84992e10i −0.196188 0.603804i −0.999961 0.00886768i \(-0.997177\pi\)
0.803773 0.594936i \(-0.202823\pi\)
\(992\) −1.34698e10 1.85397e10i −0.438099 0.602991i
\(993\) 2.21646e10i 0.718353i
\(994\) 7.32681e10 5.32324e10i 2.36626 1.71919i
\(995\) −9.02093e9 + 2.09474e10i −0.290316 + 0.674139i
\(996\) 2.83833e8 + 2.06217e8i 0.00910240 + 0.00661328i
\(997\) −3.04870e10 + 4.19618e10i −0.974277 + 1.34098i −0.0344200 + 0.999407i \(0.510958\pi\)
−0.939857 + 0.341569i \(0.889042\pi\)
\(998\) 1.37094e10 + 4.45445e9i 0.436577 + 0.141853i
\(999\) 5.20738e10 1.65249
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 25.8.e.a.4.2 64
25.12 odd 20 625.8.a.g.1.59 64
25.13 odd 20 625.8.a.g.1.6 64
25.19 even 10 inner 25.8.e.a.19.2 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.8.e.a.4.2 64 1.1 even 1 trivial
25.8.e.a.19.2 yes 64 25.19 even 10 inner
625.8.a.g.1.6 64 25.13 odd 20
625.8.a.g.1.59 64 25.12 odd 20