Properties

Label 17.10.c.a.13.2
Level $17$
Weight $10$
Character 17.13
Analytic conductor $8.756$
Analytic rank $0$
Dimension $24$
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] = [17,10,Mod(4,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.c (of order \(4\), degree \(2\), 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: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 17.13
Dual form 17.10.c.a.4.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-35.4517i q^{2} +(137.825 + 137.825i) q^{3} -744.825 q^{4} +(178.043 + 178.043i) q^{5} +(4886.12 - 4886.12i) q^{6} +(7491.11 - 7491.11i) q^{7} +8254.04i q^{8} +18308.3i q^{9} +O(q^{10})\) \(q-35.4517i q^{2} +(137.825 + 137.825i) q^{3} -744.825 q^{4} +(178.043 + 178.043i) q^{5} +(4886.12 - 4886.12i) q^{6} +(7491.11 - 7491.11i) q^{7} +8254.04i q^{8} +18308.3i q^{9} +(6311.91 - 6311.91i) q^{10} +(27737.0 - 27737.0i) q^{11} +(-102655. - 102655. i) q^{12} -20877.3 q^{13} +(-265573. - 265573. i) q^{14} +49077.3i q^{15} -88730.4 q^{16} +(286460. - 191125. i) q^{17} +649060. q^{18} +888282. i q^{19} +(-132610. - 132610. i) q^{20} +2.06492e6 q^{21} +(-983326. - 983326. i) q^{22} +(-839804. + 839804. i) q^{23} +(-1.13761e6 + 1.13761e6i) q^{24} -1.88973e6i q^{25} +740136. i q^{26} +(189472. - 189472. i) q^{27} +(-5.57957e6 + 5.57957e6i) q^{28} +(1.43731e6 + 1.43731e6i) q^{29} +1.73987e6 q^{30} +(710945. + 710945. i) q^{31} +7.37171e6i q^{32} +7.64570e6 q^{33} +(-6.77571e6 - 1.01555e7i) q^{34} +2.66747e6 q^{35} -1.36365e7i q^{36} +(-8.16382e6 - 8.16382e6i) q^{37} +3.14911e7 q^{38} +(-2.87741e6 - 2.87741e6i) q^{39} +(-1.46957e6 + 1.46957e6i) q^{40} +(-1.89573e7 + 1.89573e7i) q^{41} -7.32050e7i q^{42} +3.58732e7i q^{43} +(-2.06592e7 + 2.06592e7i) q^{44} +(-3.25965e6 + 3.25965e6i) q^{45} +(2.97725e7 + 2.97725e7i) q^{46} -1.67650e7 q^{47} +(-1.22292e7 - 1.22292e7i) q^{48} -7.18799e7i q^{49} -6.69941e7 q^{50} +(6.58229e7 + 1.31395e7i) q^{51} +1.55499e7 q^{52} +8.53149e7i q^{53} +(-6.71710e6 - 6.71710e6i) q^{54} +9.87674e6 q^{55} +(6.18319e7 + 6.18319e7i) q^{56} +(-1.22427e8 + 1.22427e8i) q^{57} +(5.09551e7 - 5.09551e7i) q^{58} -495397. i q^{59} -3.65540e7i q^{60} +(5.17968e7 - 5.17968e7i) q^{61} +(2.52042e7 - 2.52042e7i) q^{62} +(1.37149e8 + 1.37149e8i) q^{63} +2.15910e8 q^{64} +(-3.71705e6 - 3.71705e6i) q^{65} -2.71053e8i q^{66} -2.90055e8 q^{67} +(-2.13362e8 + 1.42355e8i) q^{68} -2.31491e8 q^{69} -9.45665e7i q^{70} +(2.15692e8 + 2.15692e8i) q^{71} -1.51117e8 q^{72} +(-7.17563e7 - 7.17563e7i) q^{73} +(-2.89421e8 + 2.89421e8i) q^{74} +(2.60451e8 - 2.60451e8i) q^{75} -6.61614e8i q^{76} -4.15563e8i q^{77} +(-1.02009e8 + 1.02009e8i) q^{78} +(2.24060e8 - 2.24060e8i) q^{79} +(-1.57978e7 - 1.57978e7i) q^{80} +4.12589e8 q^{81} +(6.72069e8 + 6.72069e8i) q^{82} +4.86233e7i q^{83} -1.53800e9 q^{84} +(8.50304e7 + 1.69736e7i) q^{85} +1.27177e9 q^{86} +3.96193e8i q^{87} +(2.28943e8 + 2.28943e8i) q^{88} +6.13841e7 q^{89} +(1.15560e8 + 1.15560e8i) q^{90} +(-1.56394e8 + 1.56394e8i) q^{91} +(6.25506e8 - 6.25506e8i) q^{92} +1.95971e8i q^{93} +5.94346e8i q^{94} +(-1.58152e8 + 1.58152e8i) q^{95} +(-1.01600e9 + 1.01600e9i) q^{96} +(-8.46864e8 - 8.46864e8i) q^{97} -2.54827e9 q^{98} +(5.07817e8 + 5.07817e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7} + 21946 q^{10} + 18132 q^{11} - 95142 q^{12} + 244832 q^{13} - 341100 q^{14} - 279932 q^{16} - 98022 q^{17} + 888764 q^{18} + 1364262 q^{20} - 775748 q^{21} - 4573190 q^{22} - 377526 q^{23} - 307054 q^{24} + 3996108 q^{27} - 1024780 q^{28} + 2160042 q^{29} + 39084792 q^{30} - 585086 q^{31} - 30349992 q^{33} + 4441318 q^{34} - 25532364 q^{35} + 1515390 q^{37} + 13171392 q^{38} - 25687084 q^{39} - 63240118 q^{40} - 72707928 q^{41} - 3606450 q^{44} + 156729418 q^{45} + 118549536 q^{46} + 153365328 q^{47} + 26098270 q^{48} - 236105676 q^{50} + 256903592 q^{51} - 209898380 q^{52} - 187411976 q^{54} + 255767540 q^{55} - 107638596 q^{56} - 443390988 q^{57} - 281433730 q^{58} + 52149382 q^{61} + 176928228 q^{62} + 620111642 q^{63} + 1006108924 q^{64} - 489714396 q^{65} - 26076868 q^{67} - 308011950 q^{68} - 751973532 q^{69} + 149240178 q^{71} + 1171736028 q^{72} - 175256556 q^{73} - 37609818 q^{74} - 233543476 q^{75} - 1202722924 q^{78} - 469987182 q^{79} + 481103586 q^{80} + 347156560 q^{81} - 984422080 q^{82} - 935672904 q^{84} - 725828294 q^{85} + 690159588 q^{86} + 992281114 q^{88} - 191594460 q^{89} + 914946474 q^{90} + 926854816 q^{91} + 3064830552 q^{92} + 1213246572 q^{95} + 3594247550 q^{96} - 2200567348 q^{97} - 4413444720 q^{98} - 1224966600 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 35.4517i 1.56676i −0.621543 0.783380i \(-0.713494\pi\)
0.621543 0.783380i \(-0.286506\pi\)
\(3\) 137.825 + 137.825i 0.982384 + 0.982384i 0.999848 0.0174636i \(-0.00555910\pi\)
−0.0174636 + 0.999848i \(0.505559\pi\)
\(4\) −744.825 −1.45474
\(5\) 178.043 + 178.043i 0.127397 + 0.127397i 0.767930 0.640533i \(-0.221287\pi\)
−0.640533 + 0.767930i \(0.721287\pi\)
\(6\) 4886.12 4886.12i 1.53916 1.53916i
\(7\) 7491.11 7491.11i 1.17925 1.17925i 0.199312 0.979936i \(-0.436129\pi\)
0.979936 0.199312i \(-0.0638707\pi\)
\(8\) 8254.04i 0.712462i
\(9\) 18308.3i 0.930156i
\(10\) 6311.91 6311.91i 0.199600 0.199600i
\(11\) 27737.0 27737.0i 0.571206 0.571206i −0.361259 0.932465i \(-0.617653\pi\)
0.932465 + 0.361259i \(0.117653\pi\)
\(12\) −102655. 102655.i −1.42911 1.42911i
\(13\) −20877.3 −0.202735 −0.101368 0.994849i \(-0.532322\pi\)
−0.101368 + 0.994849i \(0.532322\pi\)
\(14\) −265573. 265573.i −1.84760 1.84760i
\(15\) 49077.3i 0.250305i
\(16\) −88730.4 −0.338479
\(17\) 286460. 191125.i 0.831847 0.555005i
\(18\) 649060. 1.45733
\(19\) 888282.i 1.56372i 0.623453 + 0.781861i \(0.285729\pi\)
−0.623453 + 0.781861i \(0.714271\pi\)
\(20\) −132610. 132610.i −0.185329 0.185329i
\(21\) 2.06492e6 2.31695
\(22\) −983326. 983326.i −0.894943 0.894943i
\(23\) −839804. + 839804.i −0.625752 + 0.625752i −0.946996 0.321244i \(-0.895899\pi\)
0.321244 + 0.946996i \(0.395899\pi\)
\(24\) −1.13761e6 + 1.13761e6i −0.699911 + 0.699911i
\(25\) 1.88973e6i 0.967540i
\(26\) 740136.i 0.317637i
\(27\) 189472. 189472.i 0.0686132 0.0686132i
\(28\) −5.57957e6 + 5.57957e6i −1.71549 + 1.71549i
\(29\) 1.43731e6 + 1.43731e6i 0.377363 + 0.377363i 0.870150 0.492787i \(-0.164022\pi\)
−0.492787 + 0.870150i \(0.664022\pi\)
\(30\) 1.73987e6 0.392168
\(31\) 710945. + 710945.i 0.138264 + 0.138264i 0.772851 0.634587i \(-0.218830\pi\)
−0.634587 + 0.772851i \(0.718830\pi\)
\(32\) 7.37171e6i 1.24278i
\(33\) 7.64570e6 1.12229
\(34\) −6.77571e6 1.01555e7i −0.869560 1.30330i
\(35\) 2.66747e6 0.300465
\(36\) 1.36365e7i 1.35313i
\(37\) −8.16382e6 8.16382e6i −0.716120 0.716120i 0.251689 0.967808i \(-0.419014\pi\)
−0.967808 + 0.251689i \(0.919014\pi\)
\(38\) 3.14911e7 2.44998
\(39\) −2.87741e6 2.87741e6i −0.199164 0.199164i
\(40\) −1.46957e6 + 1.46957e6i −0.0907654 + 0.0907654i
\(41\) −1.89573e7 + 1.89573e7i −1.04773 + 1.04773i −0.0489266 + 0.998802i \(0.515580\pi\)
−0.998802 + 0.0489266i \(0.984420\pi\)
\(42\) 7.32050e7i 3.63010i
\(43\) 3.58732e7i 1.60016i 0.599896 + 0.800078i \(0.295209\pi\)
−0.599896 + 0.800078i \(0.704791\pi\)
\(44\) −2.06592e7 + 2.06592e7i −0.830954 + 0.830954i
\(45\) −3.25965e6 + 3.25965e6i −0.118499 + 0.118499i
\(46\) 2.97725e7 + 2.97725e7i 0.980403 + 0.980403i
\(47\) −1.67650e7 −0.501143 −0.250572 0.968098i \(-0.580619\pi\)
−0.250572 + 0.968098i \(0.580619\pi\)
\(48\) −1.22292e7 1.22292e7i −0.332517 0.332517i
\(49\) 7.18799e7i 1.78125i
\(50\) −6.69941e7 −1.51590
\(51\) 6.58229e7 + 1.31395e7i 1.36242 + 0.271964i
\(52\) 1.55499e7 0.294926
\(53\) 8.53149e7i 1.48519i 0.669738 + 0.742597i \(0.266406\pi\)
−0.669738 + 0.742597i \(0.733594\pi\)
\(54\) −6.71710e6 6.71710e6i −0.107500 0.107500i
\(55\) 9.87674e6 0.145540
\(56\) 6.18319e7 + 6.18319e7i 0.840169 + 0.840169i
\(57\) −1.22427e8 + 1.22427e8i −1.53618 + 1.53618i
\(58\) 5.09551e7 5.09551e7i 0.591237 0.591237i
\(59\) 495397.i 0.00532255i −0.999996 0.00266127i \(-0.999153\pi\)
0.999996 0.00266127i \(-0.000847111\pi\)
\(60\) 3.65540e7i 0.364128i
\(61\) 5.17968e7 5.17968e7i 0.478981 0.478981i −0.425825 0.904806i \(-0.640016\pi\)
0.904806 + 0.425825i \(0.140016\pi\)
\(62\) 2.52042e7 2.52042e7i 0.216626 0.216626i
\(63\) 1.37149e8 + 1.37149e8i 1.09689 + 1.09689i
\(64\) 2.15910e8 1.60865
\(65\) −3.71705e6 3.71705e6i −0.0258278 0.0258278i
\(66\) 2.71053e8i 1.75836i
\(67\) −2.90055e8 −1.75851 −0.879254 0.476353i \(-0.841958\pi\)
−0.879254 + 0.476353i \(0.841958\pi\)
\(68\) −2.13362e8 + 1.42355e8i −1.21012 + 0.807386i
\(69\) −2.31491e8 −1.22946
\(70\) 9.45665e7i 0.470756i
\(71\) 2.15692e8 + 2.15692e8i 1.00733 + 1.00733i 0.999973 + 0.00735485i \(0.00234114\pi\)
0.00735485 + 0.999973i \(0.497659\pi\)
\(72\) −1.51117e8 −0.662701
\(73\) −7.17563e7 7.17563e7i −0.295738 0.295738i 0.543604 0.839342i \(-0.317059\pi\)
−0.839342 + 0.543604i \(0.817059\pi\)
\(74\) −2.89421e8 + 2.89421e8i −1.12199 + 1.12199i
\(75\) 2.60451e8 2.60451e8i 0.950496 0.950496i
\(76\) 6.61614e8i 2.27480i
\(77\) 4.15563e8i 1.34719i
\(78\) −1.02009e8 + 1.02009e8i −0.312042 + 0.312042i
\(79\) 2.24060e8 2.24060e8i 0.647205 0.647205i −0.305112 0.952316i \(-0.598694\pi\)
0.952316 + 0.305112i \(0.0986939\pi\)
\(80\) −1.57978e7 1.57978e7i −0.0431212 0.0431212i
\(81\) 4.12589e8 1.06497
\(82\) 6.72069e8 + 6.72069e8i 1.64154 + 1.64154i
\(83\) 4.86233e7i 0.112459i 0.998418 + 0.0562293i \(0.0179078\pi\)
−0.998418 + 0.0562293i \(0.982092\pi\)
\(84\) −1.53800e9 −3.37055
\(85\) 8.50304e7 + 1.69736e7i 0.176681 + 0.0352687i
\(86\) 1.27177e9 2.50706
\(87\) 3.96193e8i 0.741431i
\(88\) 2.28943e8 + 2.28943e8i 0.406963 + 0.406963i
\(89\) 6.13841e7 0.103705 0.0518526 0.998655i \(-0.483487\pi\)
0.0518526 + 0.998655i \(0.483487\pi\)
\(90\) 1.15560e8 + 1.15560e8i 0.185659 + 0.185659i
\(91\) −1.56394e8 + 1.56394e8i −0.239075 + 0.239075i
\(92\) 6.25506e8 6.25506e8i 0.910304 0.910304i
\(93\) 1.95971e8i 0.271656i
\(94\) 5.94346e8i 0.785171i
\(95\) −1.58152e8 + 1.58152e8i −0.199213 + 0.199213i
\(96\) −1.01600e9 + 1.01600e9i −1.22088 + 1.22088i
\(97\) −8.46864e8 8.46864e8i −0.971272 0.971272i 0.0283265 0.999599i \(-0.490982\pi\)
−0.999599 + 0.0283265i \(0.990982\pi\)
\(98\) −2.54827e9 −2.79079
\(99\) 5.07817e8 + 5.07817e8i 0.531311 + 0.531311i
\(100\) 1.40752e9i 1.40752i
\(101\) −6.82815e8 −0.652916 −0.326458 0.945212i \(-0.605855\pi\)
−0.326458 + 0.945212i \(0.605855\pi\)
\(102\) 4.65817e8 2.33354e9i 0.426103 2.13459i
\(103\) −1.41375e8 −0.123767 −0.0618836 0.998083i \(-0.519711\pi\)
−0.0618836 + 0.998083i \(0.519711\pi\)
\(104\) 1.72322e8i 0.144441i
\(105\) 3.67644e8 + 3.67644e8i 0.295172 + 0.295172i
\(106\) 3.02456e9 2.32694
\(107\) −4.87536e7 4.87536e7i −0.0359567 0.0359567i 0.688900 0.724857i \(-0.258094\pi\)
−0.724857 + 0.688900i \(0.758094\pi\)
\(108\) −1.41123e8 + 1.41123e8i −0.0998141 + 0.0998141i
\(109\) 1.63837e9 1.63837e9i 1.11172 1.11172i 0.118797 0.992919i \(-0.462096\pi\)
0.992919 0.118797i \(-0.0379038\pi\)
\(110\) 3.50148e8i 0.228026i
\(111\) 2.25035e9i 1.40701i
\(112\) −6.64689e8 + 6.64689e8i −0.399151 + 0.399151i
\(113\) −1.27796e9 + 1.27796e9i −0.737335 + 0.737335i −0.972061 0.234727i \(-0.924581\pi\)
0.234727 + 0.972061i \(0.424581\pi\)
\(114\) 4.34025e9 + 4.34025e9i 2.40682 + 2.40682i
\(115\) −2.99041e8 −0.159438
\(116\) −1.07054e9 1.07054e9i −0.548963 0.548963i
\(117\) 3.82227e8i 0.188575i
\(118\) −1.75627e7 −0.00833916
\(119\) 7.14163e8 3.57764e9i 0.326464 1.63544i
\(120\) −4.05086e8 −0.178333
\(121\) 8.19261e8i 0.347447i
\(122\) −1.83628e9 1.83628e9i −0.750448 0.750448i
\(123\) −5.22556e9 −2.05854
\(124\) −5.29529e8 5.29529e8i −0.201137 0.201137i
\(125\) 6.84191e8 6.84191e8i 0.250658 0.250658i
\(126\) 4.86218e9 4.86218e9i 1.71856 1.71856i
\(127\) 1.52729e9i 0.520962i −0.965479 0.260481i \(-0.916119\pi\)
0.965479 0.260481i \(-0.0838811\pi\)
\(128\) 3.88006e9i 1.27760i
\(129\) −4.94421e9 + 4.94421e9i −1.57197 + 1.57197i
\(130\) −1.31776e8 + 1.31776e8i −0.0404660 + 0.0404660i
\(131\) −2.35621e9 2.35621e9i −0.699027 0.699027i 0.265174 0.964201i \(-0.414571\pi\)
−0.964201 + 0.265174i \(0.914571\pi\)
\(132\) −5.69470e9 −1.63263
\(133\) 6.65422e9 + 6.65422e9i 1.84402 + 1.84402i
\(134\) 1.02830e10i 2.75516i
\(135\) 6.74681e7 0.0174822
\(136\) 1.57755e9 + 2.36445e9i 0.395420 + 0.592659i
\(137\) 3.58940e8 0.0870521 0.0435261 0.999052i \(-0.486141\pi\)
0.0435261 + 0.999052i \(0.486141\pi\)
\(138\) 8.20676e9i 1.92627i
\(139\) 2.71208e9 + 2.71208e9i 0.616221 + 0.616221i 0.944560 0.328339i \(-0.106489\pi\)
−0.328339 + 0.944560i \(0.606489\pi\)
\(140\) −1.98680e9 −0.437097
\(141\) −2.31062e9 2.31062e9i −0.492315 0.492315i
\(142\) 7.64664e9 7.64664e9i 1.57824 1.57824i
\(143\) −5.79074e8 + 5.79074e8i −0.115804 + 0.115804i
\(144\) 1.62450e9i 0.314839i
\(145\) 5.11804e8i 0.0961497i
\(146\) −2.54389e9 + 2.54389e9i −0.463351 + 0.463351i
\(147\) 9.90683e9 9.90683e9i 1.74987 1.74987i
\(148\) 6.08061e9 + 6.08061e9i 1.04176 + 1.04176i
\(149\) 9.74736e9 1.62013 0.810063 0.586342i \(-0.199433\pi\)
0.810063 + 0.586342i \(0.199433\pi\)
\(150\) −9.23343e9 9.23343e9i −1.48920 1.48920i
\(151\) 1.70584e9i 0.267019i −0.991048 0.133509i \(-0.957375\pi\)
0.991048 0.133509i \(-0.0426247\pi\)
\(152\) −7.33191e9 −1.11409
\(153\) 3.49917e9 + 5.24458e9i 0.516242 + 0.773748i
\(154\) −1.47324e10 −2.11072
\(155\) 2.53157e8i 0.0352287i
\(156\) 2.14316e9 + 2.14316e9i 0.289731 + 0.289731i
\(157\) 5.43318e9 0.713683 0.356842 0.934165i \(-0.383854\pi\)
0.356842 + 0.934165i \(0.383854\pi\)
\(158\) −7.94330e9 7.94330e9i −1.01401 1.01401i
\(159\) −1.17585e10 + 1.17585e10i −1.45903 + 1.45903i
\(160\) −1.31248e9 + 1.31248e9i −0.158326 + 0.158326i
\(161\) 1.25821e10i 1.47583i
\(162\) 1.46270e10i 1.66854i
\(163\) 5.40333e9 5.40333e9i 0.599539 0.599539i −0.340651 0.940190i \(-0.610647\pi\)
0.940190 + 0.340651i \(0.110647\pi\)
\(164\) 1.41199e10 1.41199e10i 1.52417 1.52417i
\(165\) 1.36126e9 + 1.36126e9i 0.142976 + 0.142976i
\(166\) 1.72378e9 0.176196
\(167\) 3.33317e9 + 3.33317e9i 0.331614 + 0.331614i 0.853199 0.521585i \(-0.174659\pi\)
−0.521585 + 0.853199i \(0.674659\pi\)
\(168\) 1.70439e10i 1.65074i
\(169\) −1.01686e10 −0.958898
\(170\) 6.01744e8 3.01447e9i 0.0552576 0.276816i
\(171\) −1.62629e10 −1.45451
\(172\) 2.67193e10i 2.32780i
\(173\) 2.19655e9 + 2.19655e9i 0.186437 + 0.186437i 0.794154 0.607717i \(-0.207914\pi\)
−0.607717 + 0.794154i \(0.707914\pi\)
\(174\) 1.40457e10 1.16164
\(175\) −1.41562e10 1.41562e10i −1.14097 1.14097i
\(176\) −2.46112e9 + 2.46112e9i −0.193342 + 0.193342i
\(177\) 6.82780e7 6.82780e7i 0.00522879 0.00522879i
\(178\) 2.17617e9i 0.162481i
\(179\) 1.41139e10i 1.02756i 0.857922 + 0.513780i \(0.171755\pi\)
−0.857922 + 0.513780i \(0.828245\pi\)
\(180\) 2.42787e9 2.42787e9i 0.172385 0.172385i
\(181\) −5.83032e9 + 5.83032e9i −0.403774 + 0.403774i −0.879561 0.475787i \(-0.842163\pi\)
0.475787 + 0.879561i \(0.342163\pi\)
\(182\) 5.54444e9 + 5.54444e9i 0.374573 + 0.374573i
\(183\) 1.42777e10 0.941086
\(184\) −6.93177e9 6.93177e9i −0.445825 0.445825i
\(185\) 2.90701e9i 0.182463i
\(186\) 6.94752e9 0.425620
\(187\) 2.64430e9 1.32468e10i 0.158133 0.792179i
\(188\) 1.24870e10 0.729031
\(189\) 2.83871e9i 0.161824i
\(190\) 5.60676e9 + 5.60676e9i 0.312119 + 0.312119i
\(191\) 7.61281e9 0.413899 0.206950 0.978352i \(-0.433646\pi\)
0.206950 + 0.978352i \(0.433646\pi\)
\(192\) 2.97577e10 + 2.97577e10i 1.58032 + 1.58032i
\(193\) 9.45202e9 9.45202e9i 0.490362 0.490362i −0.418058 0.908420i \(-0.637289\pi\)
0.908420 + 0.418058i \(0.137289\pi\)
\(194\) −3.00228e10 + 3.00228e10i −1.52175 + 1.52175i
\(195\) 1.02460e9i 0.0507457i
\(196\) 5.35380e10i 2.59125i
\(197\) −2.57548e10 + 2.57548e10i −1.21831 + 1.21831i −0.250093 + 0.968222i \(0.580461\pi\)
−0.968222 + 0.250093i \(0.919539\pi\)
\(198\) 1.80030e10 1.80030e10i 0.832437 0.832437i
\(199\) −1.14612e10 1.14612e10i −0.518075 0.518075i 0.398913 0.916989i \(-0.369387\pi\)
−0.916989 + 0.398913i \(0.869387\pi\)
\(200\) 1.55979e10 0.689335
\(201\) −3.99768e10 3.99768e10i −1.72753 1.72753i
\(202\) 2.42070e10i 1.02296i
\(203\) 2.15341e10 0.890009
\(204\) −4.90265e10 9.78660e9i −1.98196 0.395636i
\(205\) −6.75041e9 −0.266955
\(206\) 5.01199e9i 0.193913i
\(207\) −1.53753e10 1.53753e10i −0.582048 0.582048i
\(208\) 1.85245e9 0.0686217
\(209\) 2.46383e10 + 2.46383e10i 0.893208 + 0.893208i
\(210\) 1.30336e10 1.30336e10i 0.462464 0.462464i
\(211\) 1.70125e10 1.70125e10i 0.590876 0.590876i −0.346992 0.937868i \(-0.612797\pi\)
0.937868 + 0.346992i \(0.112797\pi\)
\(212\) 6.35446e10i 2.16057i
\(213\) 5.94553e10i 1.97917i
\(214\) −1.72840e9 + 1.72840e9i −0.0563355 + 0.0563355i
\(215\) −6.38696e9 + 6.38696e9i −0.203855 + 0.203855i
\(216\) 1.56391e9 + 1.56391e9i 0.0488843 + 0.0488843i
\(217\) 1.06515e10 0.326094
\(218\) −5.80832e10 5.80832e10i −1.74179 1.74179i
\(219\) 1.97796e10i 0.581057i
\(220\) −7.35644e9 −0.211722
\(221\) −5.98050e9 + 3.99017e9i −0.168645 + 0.112519i
\(222\) −7.97788e10 −2.20444
\(223\) 1.28505e10i 0.347974i −0.984748 0.173987i \(-0.944335\pi\)
0.984748 0.173987i \(-0.0556651\pi\)
\(224\) 5.52223e10 + 5.52223e10i 1.46554 + 1.46554i
\(225\) 3.45976e10 0.899964
\(226\) 4.53059e10 + 4.53059e10i 1.15523 + 1.15523i
\(227\) 1.28875e10 1.28875e10i 0.322144 0.322144i −0.527445 0.849589i \(-0.676850\pi\)
0.849589 + 0.527445i \(0.176850\pi\)
\(228\) 9.11867e10 9.11867e10i 2.23473 2.23473i
\(229\) 3.34994e10i 0.804965i 0.915428 + 0.402482i \(0.131853\pi\)
−0.915428 + 0.402482i \(0.868147\pi\)
\(230\) 1.06015e10i 0.249801i
\(231\) 5.72748e10 5.72748e10i 1.32346 1.32346i
\(232\) −1.18636e10 + 1.18636e10i −0.268857 + 0.268857i
\(233\) −3.74162e10 3.74162e10i −0.831683 0.831683i 0.156064 0.987747i \(-0.450119\pi\)
−0.987747 + 0.156064i \(0.950119\pi\)
\(234\) −1.35506e10 −0.295452
\(235\) −2.98487e9 2.98487e9i −0.0638441 0.0638441i
\(236\) 3.68984e8i 0.00774290i
\(237\) 6.17619e10 1.27161
\(238\) −1.26834e11 2.53183e10i −2.56235 0.511491i
\(239\) 3.33753e10 0.661659 0.330829 0.943691i \(-0.392672\pi\)
0.330829 + 0.943691i \(0.392672\pi\)
\(240\) 4.35465e9i 0.0847232i
\(241\) −5.92853e10 5.92853e10i −1.13206 1.13206i −0.989834 0.142228i \(-0.954573\pi\)
−0.142228 0.989834i \(-0.545427\pi\)
\(242\) 2.90442e10 0.544365
\(243\) 5.31356e10 + 5.31356e10i 0.977592 + 0.977592i
\(244\) −3.85795e10 + 3.85795e10i −0.696791 + 0.696791i
\(245\) 1.27977e10 1.27977e10i 0.226926 0.226926i
\(246\) 1.85255e11i 3.22524i
\(247\) 1.85449e10i 0.317021i
\(248\) −5.86816e9 + 5.86816e9i −0.0985076 + 0.0985076i
\(249\) −6.70149e9 + 6.70149e9i −0.110478 + 0.110478i
\(250\) −2.42558e10 2.42558e10i −0.392721 0.392721i
\(251\) −5.60110e10 −0.890721 −0.445360 0.895351i \(-0.646924\pi\)
−0.445360 + 0.895351i \(0.646924\pi\)
\(252\) −1.02152e11 1.02152e11i −1.59568 1.59568i
\(253\) 4.65873e10i 0.714867i
\(254\) −5.41452e10 −0.816222
\(255\) 9.37990e9 + 1.40587e10i 0.138921 + 0.208216i
\(256\) −2.70091e10 −0.393034
\(257\) 5.71990e10i 0.817880i −0.912561 0.408940i \(-0.865899\pi\)
0.912561 0.408940i \(-0.134101\pi\)
\(258\) 1.75281e11 + 1.75281e11i 2.46290 + 2.46290i
\(259\) −1.22312e11 −1.68897
\(260\) 2.76855e9 + 2.76855e9i 0.0375727 + 0.0375727i
\(261\) −2.63146e10 + 2.63146e10i −0.351007 + 0.351007i
\(262\) −8.35318e10 + 8.35318e10i −1.09521 + 1.09521i
\(263\) 7.34514e10i 0.946671i −0.880882 0.473335i \(-0.843050\pi\)
0.880882 0.473335i \(-0.156950\pi\)
\(264\) 6.31079e10i 0.799587i
\(265\) −1.51897e10 + 1.51897e10i −0.189209 + 0.189209i
\(266\) 2.35903e11 2.35903e11i 2.88913 2.88913i
\(267\) 8.46024e9 + 8.46024e9i 0.101878 + 0.101878i
\(268\) 2.16040e11 2.55816
\(269\) 8.83230e10 + 8.83230e10i 1.02846 + 1.02846i 0.999583 + 0.0288794i \(0.00919386\pi\)
0.0288794 + 0.999583i \(0.490806\pi\)
\(270\) 2.39186e9i 0.0273904i
\(271\) −1.21335e11 −1.36655 −0.683274 0.730162i \(-0.739444\pi\)
−0.683274 + 0.730162i \(0.739444\pi\)
\(272\) −2.54177e10 + 1.69586e10i −0.281563 + 0.187858i
\(273\) −4.31099e10 −0.469727
\(274\) 1.27250e10i 0.136390i
\(275\) −5.24154e10 5.24154e10i −0.552665 0.552665i
\(276\) 1.72420e11 1.78854
\(277\) 6.44252e10 + 6.44252e10i 0.657501 + 0.657501i 0.954788 0.297287i \(-0.0960817\pi\)
−0.297287 + 0.954788i \(0.596082\pi\)
\(278\) 9.61481e10 9.61481e10i 0.965470 0.965470i
\(279\) −1.30162e10 + 1.30162e10i −0.128607 + 0.128607i
\(280\) 2.20174e10i 0.214070i
\(281\) 1.42723e11i 1.36558i 0.730616 + 0.682788i \(0.239233\pi\)
−0.730616 + 0.682788i \(0.760767\pi\)
\(282\) −8.19156e10 + 8.19156e10i −0.771340 + 0.771340i
\(283\) 6.69221e10 6.69221e10i 0.620198 0.620198i −0.325384 0.945582i \(-0.605494\pi\)
0.945582 + 0.325384i \(0.105494\pi\)
\(284\) −1.60653e11 1.60653e11i −1.46540 1.46540i
\(285\) −4.35945e10 −0.391408
\(286\) 2.05292e10 + 2.05292e10i 0.181436 + 0.181436i
\(287\) 2.84022e11i 2.47106i
\(288\) −1.34963e11 −1.15598
\(289\) 4.55304e10 1.09499e11i 0.383938 0.923359i
\(290\) 1.81443e10 0.150643
\(291\) 2.33438e11i 1.90832i
\(292\) 5.34459e10 + 5.34459e10i 0.430221 + 0.430221i
\(293\) −7.89311e10 −0.625668 −0.312834 0.949808i \(-0.601278\pi\)
−0.312834 + 0.949808i \(0.601278\pi\)
\(294\) −3.51214e11 3.51214e11i −2.74163 2.74163i
\(295\) 8.82018e7 8.82018e7i 0.000678076 0.000678076i
\(296\) 6.73845e10 6.73845e10i 0.510208 0.510208i
\(297\) 1.05108e10i 0.0783846i
\(298\) 3.45561e11i 2.53835i
\(299\) 1.75328e10 1.75328e10i 0.126862 0.126862i
\(300\) −1.93990e11 + 1.93990e11i −1.38272 + 1.38272i
\(301\) 2.68730e11 + 2.68730e11i 1.88698 + 1.88698i
\(302\) −6.04750e10 −0.418355
\(303\) −9.41088e10 9.41088e10i −0.641414 0.641414i
\(304\) 7.88175e10i 0.529288i
\(305\) 1.84440e10 0.122041
\(306\) 1.85929e11 1.24052e11i 1.21228 0.808827i
\(307\) −1.58427e11 −1.01790 −0.508952 0.860795i \(-0.669967\pi\)
−0.508952 + 0.860795i \(0.669967\pi\)
\(308\) 3.09521e11i 1.95980i
\(309\) −1.94850e10 1.94850e10i −0.121587 0.121587i
\(310\) 8.97484e9 0.0551949
\(311\) 2.39841e10 + 2.39841e10i 0.145379 + 0.145379i 0.776050 0.630671i \(-0.217220\pi\)
−0.630671 + 0.776050i \(0.717220\pi\)
\(312\) 2.37502e10 2.37502e10i 0.141897 0.141897i
\(313\) −1.06428e10 + 1.06428e10i −0.0626766 + 0.0626766i −0.737750 0.675074i \(-0.764112\pi\)
0.675074 + 0.737750i \(0.264112\pi\)
\(314\) 1.92616e11i 1.11817i
\(315\) 4.88368e10i 0.279479i
\(316\) −1.66885e11 + 1.66885e11i −0.941512 + 0.941512i
\(317\) −6.29985e10 + 6.29985e10i −0.350399 + 0.350399i −0.860258 0.509859i \(-0.829698\pi\)
0.509859 + 0.860258i \(0.329698\pi\)
\(318\) 4.16859e11 + 4.16859e11i 2.28595 + 2.28595i
\(319\) 7.97334e10 0.431104
\(320\) 3.84412e10 + 3.84412e10i 0.204938 + 0.204938i
\(321\) 1.34389e10i 0.0706465i
\(322\) 4.46058e11 2.31228
\(323\) 1.69773e11 + 2.54457e11i 0.867874 + 1.30078i
\(324\) −3.07307e11 −1.54924
\(325\) 3.94524e10i 0.196154i
\(326\) −1.91557e11 1.91557e11i −0.939333 0.939333i
\(327\) 4.51617e11 2.18426
\(328\) −1.56474e11 1.56474e11i −0.746467 0.746467i
\(329\) −1.25588e11 + 1.25588e11i −0.590972 + 0.590972i
\(330\) 4.82590e10 4.82590e10i 0.224009 0.224009i
\(331\) 1.07644e11i 0.492905i −0.969155 0.246453i \(-0.920735\pi\)
0.969155 0.246453i \(-0.0792649\pi\)
\(332\) 3.62158e10i 0.163598i
\(333\) 1.49465e11 1.49465e11i 0.666103 0.666103i
\(334\) 1.18167e11 1.18167e11i 0.519560 0.519560i
\(335\) −5.16422e10 5.16422e10i −0.224028 0.224028i
\(336\) −1.83221e11 −0.784239
\(337\) 1.68618e10 + 1.68618e10i 0.0712146 + 0.0712146i 0.741817 0.670602i \(-0.233964\pi\)
−0.670602 + 0.741817i \(0.733964\pi\)
\(338\) 3.60496e11i 1.50236i
\(339\) −3.52269e11 −1.44869
\(340\) −6.33327e10 1.26424e10i −0.257024 0.0513066i
\(341\) 3.94390e10 0.157954
\(342\) 5.76548e11i 2.27886i
\(343\) −2.36167e11 2.36167e11i −0.921290 0.921290i
\(344\) −2.96099e11 −1.14005
\(345\) −4.12153e10 4.12153e10i −0.156629 0.156629i
\(346\) 7.78714e10 7.78714e10i 0.292103 0.292103i
\(347\) 1.71997e11 1.71997e11i 0.636853 0.636853i −0.312925 0.949778i \(-0.601309\pi\)
0.949778 + 0.312925i \(0.101309\pi\)
\(348\) 2.95095e11i 1.07859i
\(349\) 1.16043e11i 0.418703i −0.977840 0.209351i \(-0.932865\pi\)
0.977840 0.209351i \(-0.0671352\pi\)
\(350\) −5.01860e11 + 5.01860e11i −1.78763 + 1.78763i
\(351\) −3.95566e9 + 3.95566e9i −0.0139103 + 0.0139103i
\(352\) 2.04469e11 + 2.04469e11i 0.709882 + 0.709882i
\(353\) −1.46033e11 −0.500570 −0.250285 0.968172i \(-0.580524\pi\)
−0.250285 + 0.968172i \(0.580524\pi\)
\(354\) −2.42057e9 2.42057e9i −0.00819225 0.00819225i
\(355\) 7.68046e10i 0.256661i
\(356\) −4.57204e10 −0.150864
\(357\) 5.91516e11 3.94658e11i 1.92735 1.28592i
\(358\) 5.00360e11 1.60994
\(359\) 3.10843e10i 0.0987680i −0.998780 0.0493840i \(-0.984274\pi\)
0.998780 0.0493840i \(-0.0157258\pi\)
\(360\) −2.69053e10 2.69053e10i −0.0844260 0.0844260i
\(361\) −4.66356e11 −1.44523
\(362\) 2.06695e11 + 2.06695e11i 0.632617 + 0.632617i
\(363\) −1.12914e11 + 1.12914e11i −0.341326 + 0.341326i
\(364\) 1.16486e11 1.16486e11i 0.347791 0.347791i
\(365\) 2.55514e10i 0.0753522i
\(366\) 5.06170e11i 1.47446i
\(367\) −8.70676e10 + 8.70676e10i −0.250530 + 0.250530i −0.821188 0.570658i \(-0.806688\pi\)
0.570658 + 0.821188i \(0.306688\pi\)
\(368\) 7.45161e10 7.45161e10i 0.211804 0.211804i
\(369\) −3.47075e11 3.47075e11i −0.974552 0.974552i
\(370\) −1.03059e11 −0.285875
\(371\) 6.39103e11 + 6.39103e11i 1.75141 + 1.75141i
\(372\) 1.45964e11i 0.395188i
\(373\) −2.86421e11 −0.766153 −0.383077 0.923717i \(-0.625135\pi\)
−0.383077 + 0.923717i \(0.625135\pi\)
\(374\) −4.69621e11 9.37450e10i −1.24115 0.247757i
\(375\) 1.88597e11 0.492486
\(376\) 1.38379e11i 0.357045i
\(377\) −3.00071e10 3.00071e10i −0.0765048 0.0765048i
\(378\) −1.00637e11 −0.253539
\(379\) 1.10915e11 + 1.10915e11i 0.276129 + 0.276129i 0.831562 0.555432i \(-0.187447\pi\)
−0.555432 + 0.831562i \(0.687447\pi\)
\(380\) 1.17795e11 1.17795e11i 0.289803 0.289803i
\(381\) 2.10499e11 2.10499e11i 0.511784 0.511784i
\(382\) 2.69887e11i 0.648481i
\(383\) 5.08058e11i 1.20648i −0.797561 0.603238i \(-0.793877\pi\)
0.797561 0.603238i \(-0.206123\pi\)
\(384\) 5.34768e11 5.34768e11i 1.25509 1.25509i
\(385\) 7.39878e10 7.39878e10i 0.171627 0.171627i
\(386\) −3.35090e11 3.35090e11i −0.768279 0.768279i
\(387\) −6.56777e11 −1.48840
\(388\) 6.30765e11 + 6.30765e11i 1.41294 + 1.41294i
\(389\) 6.40697e11i 1.41866i −0.704875 0.709332i \(-0.748997\pi\)
0.704875 0.709332i \(-0.251003\pi\)
\(390\) −3.63239e10 −0.0795063
\(391\) −8.00624e10 + 4.01077e11i −0.173234 + 0.867826i
\(392\) 5.93300e11 1.26907
\(393\) 6.49489e11i 1.37343i
\(394\) 9.13051e11 + 9.13051e11i 1.90881 + 1.90881i
\(395\) 7.97843e10 0.164904
\(396\) −3.78235e11 3.78235e11i −0.772918 0.772918i
\(397\) −3.16257e8 + 3.16257e8i −0.000638974 + 0.000638974i −0.707426 0.706787i \(-0.750144\pi\)
0.706787 + 0.707426i \(0.250144\pi\)
\(398\) −4.06321e11 + 4.06321e11i −0.811700 + 0.811700i
\(399\) 1.83423e12i 3.62306i
\(400\) 1.67676e11i 0.327492i
\(401\) 1.18020e11 1.18020e11i 0.227932 0.227932i −0.583896 0.811828i \(-0.698472\pi\)
0.811828 + 0.583896i \(0.198472\pi\)
\(402\) −1.41725e12 + 1.41725e12i −2.70662 + 2.70662i
\(403\) −1.48426e10 1.48426e10i −0.0280309 0.0280309i
\(404\) 5.08578e11 0.949820
\(405\) 7.34585e10 + 7.34585e10i 0.135673 + 0.135673i
\(406\) 7.63421e11i 1.39443i
\(407\) −4.52880e11 −0.818104
\(408\) −1.08454e11 + 5.43305e11i −0.193764 + 0.970673i
\(409\) −7.90370e11 −1.39661 −0.698306 0.715800i \(-0.746062\pi\)
−0.698306 + 0.715800i \(0.746062\pi\)
\(410\) 2.39314e11i 0.418254i
\(411\) 4.94708e10 + 4.94708e10i 0.0855186 + 0.0855186i
\(412\) 1.05300e11 0.180049
\(413\) −3.71108e9 3.71108e9i −0.00627661 0.00627661i
\(414\) −5.45083e11 + 5.45083e11i −0.911929 + 0.911929i
\(415\) −8.65701e9 + 8.65701e9i −0.0143269 + 0.0143269i
\(416\) 1.53901e11i 0.251955i
\(417\) 7.47584e11i 1.21073i
\(418\) 8.73470e11 8.73470e11i 1.39944 1.39944i
\(419\) 6.57921e11 6.57921e11i 1.04282 1.04282i 0.0437823 0.999041i \(-0.486059\pi\)
0.999041 0.0437823i \(-0.0139408\pi\)
\(420\) −2.73830e11 2.73830e11i −0.429397 0.429397i
\(421\) 5.05324e11 0.783973 0.391986 0.919971i \(-0.371788\pi\)
0.391986 + 0.919971i \(0.371788\pi\)
\(422\) −6.03122e11 6.03122e11i −0.925761 0.925761i
\(423\) 3.06937e11i 0.466142i
\(424\) −7.04192e11 −1.05814
\(425\) −3.61174e11 5.41330e11i −0.536990 0.804845i
\(426\) 2.10779e12 3.10088
\(427\) 7.76031e11i 1.12967i
\(428\) 3.63129e10 + 3.63129e10i 0.0523075 + 0.0523075i
\(429\) −1.59621e11 −0.227527
\(430\) 2.26429e11 + 2.26429e11i 0.319392 + 0.319392i
\(431\) −4.23744e11 + 4.23744e11i −0.591502 + 0.591502i −0.938037 0.346535i \(-0.887358\pi\)
0.346535 + 0.938037i \(0.387358\pi\)
\(432\) −1.68119e10 + 1.68119e10i −0.0232242 + 0.0232242i
\(433\) 1.27100e11i 0.173760i 0.996219 + 0.0868801i \(0.0276897\pi\)
−0.996219 + 0.0868801i \(0.972310\pi\)
\(434\) 3.77615e11i 0.510911i
\(435\) −7.05393e10 + 7.05393e10i −0.0944559 + 0.0944559i
\(436\) −1.22030e12 + 1.22030e12i −1.61725 + 1.61725i
\(437\) −7.45982e11 7.45982e11i −0.978502 0.978502i
\(438\) −7.01220e11 −0.910377
\(439\) 2.83275e11 + 2.83275e11i 0.364013 + 0.364013i 0.865288 0.501275i \(-0.167135\pi\)
−0.501275 + 0.865288i \(0.667135\pi\)
\(440\) 8.15230e10i 0.103692i
\(441\) 1.31600e12 1.65684
\(442\) 1.41458e11 + 2.12019e11i 0.176290 + 0.264226i
\(443\) 7.13038e11 0.879622 0.439811 0.898090i \(-0.355045\pi\)
0.439811 + 0.898090i \(0.355045\pi\)
\(444\) 1.67612e12i 2.04683i
\(445\) 1.09290e10 + 1.09290e10i 0.0132117 + 0.0132117i
\(446\) −4.55571e11 −0.545192
\(447\) 1.34343e12 + 1.34343e12i 1.59159 + 1.59159i
\(448\) 1.61741e12 1.61741e12i 1.89700 1.89700i
\(449\) −1.43681e11 + 1.43681e11i −0.166836 + 0.166836i −0.785587 0.618751i \(-0.787639\pi\)
0.618751 + 0.785587i \(0.287639\pi\)
\(450\) 1.22655e12i 1.41003i
\(451\) 1.05164e12i 1.19694i
\(452\) 9.51857e11 9.51857e11i 1.07263 1.07263i
\(453\) 2.35107e11 2.35107e11i 0.262315 0.262315i
\(454\) −4.56882e11 4.56882e11i −0.504723 0.504723i
\(455\) −5.56896e10 −0.0609148
\(456\) −1.01052e12 1.01052e12i −1.09447 1.09447i
\(457\) 1.60912e12i 1.72570i −0.505457 0.862852i \(-0.668676\pi\)
0.505457 0.862852i \(-0.331324\pi\)
\(458\) 1.18761e12 1.26119
\(459\) 1.80632e10 9.04888e10i 0.0189950 0.0951563i
\(460\) 2.22733e11 0.231940
\(461\) 4.13437e10i 0.0426339i 0.999773 + 0.0213170i \(0.00678591\pi\)
−0.999773 + 0.0213170i \(0.993214\pi\)
\(462\) −2.03049e12 2.03049e12i −2.07354 2.07354i
\(463\) −6.72372e11 −0.679978 −0.339989 0.940429i \(-0.610423\pi\)
−0.339989 + 0.940429i \(0.610423\pi\)
\(464\) −1.27533e11 1.27533e11i −0.127730 0.127730i
\(465\) −3.48912e10 + 3.48912e10i −0.0346081 + 0.0346081i
\(466\) −1.32647e12 + 1.32647e12i −1.30305 + 1.30305i
\(467\) 1.62022e12i 1.57633i −0.615463 0.788166i \(-0.711031\pi\)
0.615463 0.788166i \(-0.288969\pi\)
\(468\) 2.84692e11i 0.274327i
\(469\) −2.17284e12 + 2.17284e12i −2.07372 + 2.07372i
\(470\) −1.05819e11 + 1.05819e11i −0.100028 + 0.100028i
\(471\) 7.48826e11 + 7.48826e11i 0.701111 + 0.701111i
\(472\) 4.08903e9 0.00379211
\(473\) 9.95017e11 + 9.95017e11i 0.914019 + 0.914019i
\(474\) 2.18956e12i 1.99230i
\(475\) 1.67861e12 1.51296
\(476\) −5.31926e11 + 2.66471e12i −0.474920 + 2.37914i
\(477\) −1.56197e12 −1.38146
\(478\) 1.18321e12i 1.03666i
\(479\) −1.42190e12 1.42190e12i −1.23412 1.23412i −0.962365 0.271759i \(-0.912395\pi\)
−0.271759 0.962365i \(-0.587605\pi\)
\(480\) −3.61784e11 −0.311074
\(481\) 1.70438e11 + 1.70438e11i 0.145183 + 0.145183i
\(482\) −2.10177e12 + 2.10177e12i −1.77367 + 1.77367i
\(483\) −1.73413e12 + 1.73413e12i −1.44984 + 1.44984i
\(484\) 6.10206e11i 0.505443i
\(485\) 3.01556e11i 0.247474i
\(486\) 1.88375e12 1.88375e12i 1.53165 1.53165i
\(487\) 4.08238e11 4.08238e11i 0.328877 0.328877i −0.523283 0.852159i \(-0.675293\pi\)
0.852159 + 0.523283i \(0.175293\pi\)
\(488\) 4.27532e11 + 4.27532e11i 0.341256 + 0.341256i
\(489\) 1.48942e12 1.17795
\(490\) −4.53700e11 4.53700e11i −0.355538 0.355538i
\(491\) 1.26185e12i 0.979812i 0.871775 + 0.489906i \(0.162969\pi\)
−0.871775 + 0.489906i \(0.837031\pi\)
\(492\) 3.89213e12 2.99464
\(493\) 6.86437e11 + 1.37025e11i 0.523347 + 0.104470i
\(494\) −6.57449e11 −0.496696
\(495\) 1.80826e11i 0.135375i
\(496\) −6.30824e10 6.30824e10i −0.0467994 0.0467994i
\(497\) 3.23154e12 2.37578
\(498\) 2.37579e11 + 2.37579e11i 0.173092 + 0.173092i
\(499\) −8.84504e11 + 8.84504e11i −0.638627 + 0.638627i −0.950217 0.311590i \(-0.899139\pi\)
0.311590 + 0.950217i \(0.399139\pi\)
\(500\) −5.09602e11 + 5.09602e11i −0.364642 + 0.364642i
\(501\) 9.18786e11i 0.651545i
\(502\) 1.98569e12i 1.39555i
\(503\) 1.01707e12 1.01707e12i 0.708425 0.708425i −0.257779 0.966204i \(-0.582991\pi\)
0.966204 + 0.257779i \(0.0829906\pi\)
\(504\) −1.13204e12 + 1.13204e12i −0.781489 + 0.781489i
\(505\) −1.21570e11 1.21570e11i −0.0831794 0.0831794i
\(506\) 1.65160e12 1.12003
\(507\) −1.40149e12 1.40149e12i −0.942006 0.942006i
\(508\) 1.13757e12i 0.757862i
\(509\) 8.60532e11 0.568247 0.284124 0.958788i \(-0.408297\pi\)
0.284124 + 0.958788i \(0.408297\pi\)
\(510\) 4.98404e11 3.32533e11i 0.326224 0.217655i
\(511\) −1.07507e12 −0.697497
\(512\) 1.02908e12i 0.661808i
\(513\) 1.68304e11 + 1.68304e11i 0.107292 + 0.107292i
\(514\) −2.02780e12 −1.28142
\(515\) −2.51708e10 2.51708e10i −0.0157676 0.0157676i
\(516\) 3.68257e12 3.68257e12i 2.28680 2.28680i
\(517\) −4.65010e11 + 4.65010e11i −0.286256 + 0.286256i
\(518\) 4.33618e12i 2.64620i
\(519\) 6.05477e11i 0.366306i
\(520\) 3.06806e10 3.06806e10i 0.0184013 0.0184013i
\(521\) −3.77471e11 + 3.77471e11i −0.224447 + 0.224447i −0.810368 0.585921i \(-0.800733\pi\)
0.585921 + 0.810368i \(0.300733\pi\)
\(522\) 9.32900e11 + 9.32900e11i 0.549943 + 0.549943i
\(523\) −2.80630e12 −1.64013 −0.820063 0.572274i \(-0.806062\pi\)
−0.820063 + 0.572274i \(0.806062\pi\)
\(524\) 1.75497e12 + 1.75497e12i 1.01690 + 1.01690i
\(525\) 3.90213e12i 2.24174i
\(526\) −2.60398e12 −1.48321
\(527\) 3.39536e11 + 6.77777e10i 0.191751 + 0.0382771i
\(528\) −6.78405e11 −0.379871
\(529\) 3.90613e11i 0.216868i
\(530\) 5.38500e11 + 5.38500e11i 0.296445 + 0.296445i
\(531\) 9.06987e9 0.00495080
\(532\) −4.95623e12 4.95623e12i −2.68256 2.68256i
\(533\) 3.95777e11 3.95777e11i 0.212412 0.212412i
\(534\) 2.99930e11 2.99930e11i 0.159619 0.159619i
\(535\) 1.73604e10i 0.00916154i
\(536\) 2.39413e12i 1.25287i
\(537\) −1.94524e12 + 1.94524e12i −1.00946 + 1.00946i
\(538\) 3.13120e12 3.13120e12i 1.61135 1.61135i
\(539\) −1.99374e12 1.99374e12i −1.01746 1.01746i
\(540\) −5.02519e10 −0.0254320
\(541\) −1.28357e12 1.28357e12i −0.644216 0.644216i 0.307373 0.951589i \(-0.400550\pi\)
−0.951589 + 0.307373i \(0.900550\pi\)
\(542\) 4.30154e12i 2.14105i
\(543\) −1.60712e12 −0.793323
\(544\) 1.40892e12 + 2.11170e12i 0.689748 + 1.03380i
\(545\) 5.83400e11 0.283258
\(546\) 1.52832e12i 0.735949i
\(547\) 1.09744e12 + 1.09744e12i 0.524127 + 0.524127i 0.918815 0.394688i \(-0.129147\pi\)
−0.394688 + 0.918815i \(0.629147\pi\)
\(548\) −2.67347e11 −0.126638
\(549\) 9.48309e11 + 9.48309e11i 0.445527 + 0.445527i
\(550\) −1.85822e12 + 1.85822e12i −0.865893 + 0.865893i
\(551\) −1.27674e12 + 1.27674e12i −0.590091 + 0.590091i
\(552\) 1.91074e12i 0.875942i
\(553\) 3.35691e12i 1.52643i
\(554\) 2.28398e12 2.28398e12i 1.03015 1.03015i
\(555\) 4.00658e11 4.00658e11i 0.179248 0.179248i
\(556\) −2.02003e12 2.02003e12i −0.896439 0.896439i
\(557\) −1.71558e12 −0.755202 −0.377601 0.925968i \(-0.623251\pi\)
−0.377601 + 0.925968i \(0.623251\pi\)
\(558\) 4.61445e11 + 4.61445e11i 0.201496 + 0.201496i
\(559\) 7.48936e11i 0.324408i
\(560\) −2.36686e11 −0.101701
\(561\) 2.19018e12 1.46128e12i 0.933571 0.622876i
\(562\) 5.05978e12 2.13953
\(563\) 1.79733e12i 0.753945i −0.926224 0.376972i \(-0.876965\pi\)
0.926224 0.376972i \(-0.123035\pi\)
\(564\) 1.72101e12 + 1.72101e12i 0.716189 + 0.716189i
\(565\) −4.55063e11 −0.187868
\(566\) −2.37250e12 2.37250e12i −0.971701 0.971701i
\(567\) 3.09075e12 3.09075e12i 1.25586 1.25586i
\(568\) −1.78033e12 + 1.78033e12i −0.717683 + 0.717683i
\(569\) 3.85698e12i 1.54256i 0.636497 + 0.771279i \(0.280383\pi\)
−0.636497 + 0.771279i \(0.719617\pi\)
\(570\) 1.54550e12i 0.613242i
\(571\) 2.46389e12 2.46389e12i 0.969970 0.969970i −0.0295917 0.999562i \(-0.509421\pi\)
0.999562 + 0.0295917i \(0.00942070\pi\)
\(572\) 4.31309e11 4.31309e11i 0.168464 0.168464i
\(573\) 1.04923e12 + 1.04923e12i 0.406608 + 0.406608i
\(574\) 1.00691e13 3.87156
\(575\) 1.58700e12 + 1.58700e12i 0.605440 + 0.605440i
\(576\) 3.95294e12i 1.49630i
\(577\) −1.43479e12 −0.538885 −0.269442 0.963017i \(-0.586839\pi\)
−0.269442 + 0.963017i \(0.586839\pi\)
\(578\) −3.88193e12 1.61413e12i −1.44668 0.601538i
\(579\) 2.60544e12 0.963447
\(580\) 3.81205e11i 0.139872i
\(581\) 3.64243e11 + 3.64243e11i 0.132617 + 0.132617i
\(582\) −8.27576e12 −2.98989
\(583\) 2.36638e12 + 2.36638e12i 0.848352 + 0.848352i
\(584\) 5.92280e11 5.92280e11i 0.210702 0.210702i
\(585\) 6.80527e10 6.80527e10i 0.0240239 0.0240239i
\(586\) 2.79824e12i 0.980271i
\(587\) 4.09270e12i 1.42278i −0.702797 0.711391i \(-0.748066\pi\)
0.702797 0.711391i \(-0.251934\pi\)
\(588\) −7.37885e12 + 7.37885e12i −2.54560 + 2.54560i
\(589\) −6.31519e11 + 6.31519e11i −0.216206 + 0.216206i
\(590\) −3.12691e9 3.12691e9i −0.00106238 0.00106238i
\(591\) −7.09928e12 −2.39371
\(592\) 7.24378e11 + 7.24378e11i 0.242392 + 0.242392i
\(593\) 2.09962e12i 0.697258i 0.937261 + 0.348629i \(0.113353\pi\)
−0.937261 + 0.348629i \(0.886647\pi\)
\(594\) −3.72625e11 −0.122810
\(595\) 7.64123e11 5.09821e11i 0.249941 0.166760i
\(596\) −7.26008e12 −2.35686
\(597\) 3.15928e12i 1.01790i
\(598\) −6.21569e11 6.21569e11i −0.198762 0.198762i
\(599\) 5.11389e12 1.62304 0.811522 0.584322i \(-0.198639\pi\)
0.811522 + 0.584322i \(0.198639\pi\)
\(600\) 2.14977e12 + 2.14977e12i 0.677192 + 0.677192i
\(601\) −2.66709e12 + 2.66709e12i −0.833879 + 0.833879i −0.988045 0.154166i \(-0.950731\pi\)
0.154166 + 0.988045i \(0.450731\pi\)
\(602\) 9.52695e12 9.52695e12i 2.95645 2.95645i
\(603\) 5.31041e12i 1.63569i
\(604\) 1.27055e12i 0.388442i
\(605\) −1.45863e11 + 1.45863e11i −0.0442636 + 0.0442636i
\(606\) −3.33632e12 + 3.33632e12i −1.00494 + 1.00494i
\(607\) 4.44942e12 + 4.44942e12i 1.33031 + 1.33031i 0.905086 + 0.425228i \(0.139806\pi\)
0.425228 + 0.905086i \(0.360194\pi\)
\(608\) −6.54816e12 −1.94336
\(609\) 2.96793e12 + 2.96793e12i 0.874331 + 0.874331i
\(610\) 6.53873e11i 0.191209i
\(611\) 3.50007e11 0.101599
\(612\) −2.60627e12 3.90629e12i −0.750996 1.12560i
\(613\) −3.31541e12 −0.948342 −0.474171 0.880433i \(-0.657252\pi\)
−0.474171 + 0.880433i \(0.657252\pi\)
\(614\) 5.61652e12i 1.59481i
\(615\) −9.30373e11 9.30373e11i −0.262252 0.262252i
\(616\) 3.43007e12 0.959820
\(617\) 1.13051e12 + 1.13051e12i 0.314046 + 0.314046i 0.846475 0.532429i \(-0.178721\pi\)
−0.532429 + 0.846475i \(0.678721\pi\)
\(618\) −6.90776e11 + 6.90776e11i −0.190497 + 0.190497i
\(619\) 3.89551e12 3.89551e12i 1.06649 1.06649i 0.0688618 0.997626i \(-0.478063\pi\)
0.997626 0.0688618i \(-0.0219367\pi\)
\(620\) 1.88557e11i 0.0512485i
\(621\) 3.18238e11i 0.0858697i
\(622\) 8.50276e11 8.50276e11i 0.227774 0.227774i
\(623\) 4.59835e11 4.59835e11i 0.122294 0.122294i
\(624\) 2.55313e11 + 2.55313e11i 0.0674128 + 0.0674128i
\(625\) −3.44724e12 −0.903674
\(626\) 3.77305e11 + 3.77305e11i 0.0981992 + 0.0981992i
\(627\) 6.79153e12i 1.75495i
\(628\) −4.04677e12 −1.03822
\(629\) −3.89891e12 7.78295e11i −0.993152 0.198251i
\(630\) 1.73135e12 0.437877
\(631\) 3.91651e12i 0.983482i 0.870741 + 0.491741i \(0.163639\pi\)
−0.870741 + 0.491741i \(0.836361\pi\)
\(632\) 1.84940e12 + 1.84940e12i 0.461109 + 0.461109i
\(633\) 4.68948e12 1.16093
\(634\) 2.23341e12 + 2.23341e12i 0.548992 + 0.548992i
\(635\) 2.71923e11 2.71923e11i 0.0663689 0.0663689i
\(636\) 8.75802e12 8.75802e12i 2.12250 2.12250i
\(637\) 1.50066e12i 0.361122i
\(638\) 2.82669e12i 0.675437i
\(639\) −3.94894e12 + 3.94894e12i −0.936972 + 0.936972i
\(640\) 6.90816e11 6.90816e11i 0.162762 0.162762i
\(641\) −8.33887e11 8.33887e11i −0.195095 0.195095i 0.602799 0.797893i \(-0.294052\pi\)
−0.797893 + 0.602799i \(0.794052\pi\)
\(642\) −4.76432e11 −0.110686
\(643\) −5.78323e12 5.78323e12i −1.33420 1.33420i −0.901573 0.432627i \(-0.857587\pi\)
−0.432627 0.901573i \(-0.642413\pi\)
\(644\) 9.37148e12i 2.14695i
\(645\) −1.76056e12 −0.400527
\(646\) 9.02093e12 6.01874e12i 2.03800 1.35975i
\(647\) 4.11649e11 0.0923544 0.0461772 0.998933i \(-0.485296\pi\)
0.0461772 + 0.998933i \(0.485296\pi\)
\(648\) 3.40553e12i 0.758747i
\(649\) −1.37409e10 1.37409e10i −0.00304027 0.00304027i
\(650\) 1.39865e12 0.307327
\(651\) 1.46804e12 + 1.46804e12i 0.320350 + 0.320350i
\(652\) −4.02453e12 + 4.02453e12i −0.872171 + 0.872171i
\(653\) −1.15152e12 + 1.15152e12i −0.247835 + 0.247835i −0.820082 0.572246i \(-0.806072\pi\)
0.572246 + 0.820082i \(0.306072\pi\)
\(654\) 1.60106e13i 3.42222i
\(655\) 8.39012e11i 0.178108i
\(656\) 1.68209e12 1.68209e12i 0.354635 0.354635i
\(657\) 1.31373e12 1.31373e12i 0.275083 0.275083i
\(658\) 4.45232e12 + 4.45232e12i 0.925912 + 0.925912i
\(659\) −1.03788e12 −0.214369 −0.107184 0.994239i \(-0.534184\pi\)
−0.107184 + 0.994239i \(0.534184\pi\)
\(660\) −1.01390e12 1.01390e12i −0.207992 0.207992i
\(661\) 3.57716e12i 0.728840i −0.931235 0.364420i \(-0.881267\pi\)
0.931235 0.364420i \(-0.118733\pi\)
\(662\) −3.81616e12 −0.772264
\(663\) −1.37420e12 2.74317e11i −0.276211 0.0551367i
\(664\) −4.01339e11 −0.0801225
\(665\) 2.36947e12i 0.469844i
\(666\) −5.29881e12 5.29881e12i −1.04362 1.04362i
\(667\) −2.41412e12 −0.472271
\(668\) −2.48263e12 2.48263e12i −0.482411 0.482411i
\(669\) 1.77111e12 1.77111e12i 0.341844 0.341844i
\(670\) −1.83080e12 + 1.83080e12i −0.350999 + 0.350999i
\(671\) 2.87338e12i 0.547194i
\(672\) 1.52220e13i 2.87945i
\(673\) −1.86013e12 + 1.86013e12i −0.349524 + 0.349524i −0.859932 0.510408i \(-0.829494\pi\)
0.510408 + 0.859932i \(0.329494\pi\)
\(674\) 5.97779e11 5.97779e11i 0.111576 0.111576i
\(675\) −3.58050e11 3.58050e11i −0.0663860 0.0663860i
\(676\) 7.57385e12 1.39494
\(677\) 1.25400e12 + 1.25400e12i 0.229430 + 0.229430i 0.812454 0.583025i \(-0.198131\pi\)
−0.583025 + 0.812454i \(0.698131\pi\)
\(678\) 1.24886e13i 2.26975i
\(679\) −1.26879e13 −2.29074
\(680\) −1.40101e11 + 7.01844e11i −0.0251276 + 0.125878i
\(681\) 3.55242e12 0.632939
\(682\) 1.39818e12i 0.247476i
\(683\) 3.50606e12 + 3.50606e12i 0.616490 + 0.616490i 0.944629 0.328139i \(-0.106421\pi\)
−0.328139 + 0.944629i \(0.606421\pi\)
\(684\) 1.21130e13 2.11592
\(685\) 6.39066e10 + 6.39066e10i 0.0110902 + 0.0110902i
\(686\) −8.37254e12 + 8.37254e12i −1.44344 + 1.44344i
\(687\) −4.61704e12 + 4.61704e12i −0.790784 + 0.790784i
\(688\) 3.18304e12i 0.541620i
\(689\) 1.78114e12i 0.301101i
\(690\) −1.46115e12 + 1.46115e12i −0.245400 + 0.245400i
\(691\) −7.68434e10 + 7.68434e10i −0.0128220 + 0.0128220i −0.713489 0.700667i \(-0.752886\pi\)
0.700667 + 0.713489i \(0.252886\pi\)
\(692\) −1.63604e12 1.63604e12i −0.271217 0.271217i
\(693\) 7.60823e12 1.25310
\(694\) −6.09760e12 6.09760e12i −0.997795 0.997795i
\(695\) 9.65733e11i 0.157009i
\(696\) −3.27020e12 −0.528241
\(697\) −1.80729e12 + 9.05371e12i −0.290055 + 1.45305i
\(698\) −4.11394e12 −0.656007
\(699\) 1.03137e13i 1.63406i
\(700\) 1.05439e13 + 1.05439e13i 1.65981 + 1.65981i
\(701\) −8.17857e12 −1.27922 −0.639611 0.768698i \(-0.720905\pi\)
−0.639611 + 0.768698i \(0.720905\pi\)
\(702\) 1.40235e11 + 1.40235e11i 0.0217941 + 0.0217941i
\(703\) 7.25177e12 7.25177e12i 1.11981 1.11981i
\(704\) 5.98870e12 5.98870e12i 0.918874 0.918874i
\(705\) 8.22778e11i 0.125439i
\(706\) 5.17712e12i 0.784273i
\(707\) −5.11505e12 + 5.11505e12i −0.769950 + 0.769950i
\(708\) −5.08551e10 + 5.08551e10i −0.00760650 + 0.00760650i
\(709\) 6.78334e12 + 6.78334e12i 1.00817 + 1.00817i 0.999966 + 0.00820759i \(0.00261259\pi\)
0.00820759 + 0.999966i \(0.497387\pi\)
\(710\) 2.72285e12 0.402126
\(711\) 4.10214e12 + 4.10214e12i 0.602001 + 0.602001i
\(712\) 5.06666e11i 0.0738860i
\(713\) −1.19411e12 −0.173038
\(714\) −1.39913e13 2.09703e13i −2.01473 3.01969i
\(715\) −2.06200e11 −0.0295060
\(716\) 1.05123e13i 1.49483i
\(717\) 4.59993e12 + 4.59993e12i 0.650003 + 0.650003i
\(718\) −1.10199e12 −0.154746
\(719\) 2.10444e12 + 2.10444e12i 0.293668 + 0.293668i 0.838527 0.544859i \(-0.183417\pi\)
−0.544859 + 0.838527i \(0.683417\pi\)
\(720\) 2.89230e11 2.89230e11i 0.0401095 0.0401095i
\(721\) −1.05906e12 + 1.05906e12i −0.145952 + 0.145952i
\(722\) 1.65331e13i 2.26432i
\(723\) 1.63420e13i 2.22424i
\(724\) 4.34256e12 4.34256e12i 0.587385 0.587385i
\(725\) 2.71612e12 2.71612e12i 0.365114 0.365114i
\(726\) 4.00301e12 + 4.00301e12i 0.534776 + 0.534776i
\(727\) 1.39200e13 1.84814 0.924071 0.382220i \(-0.124840\pi\)
0.924071 + 0.382220i \(0.124840\pi\)
\(728\) −1.29088e12 1.29088e12i −0.170332 0.170332i
\(729\) 6.52580e12i 0.855775i
\(730\) −9.05840e11 −0.118059
\(731\) 6.85627e12 + 1.02762e13i 0.888095 + 1.33108i
\(732\) −1.06344e13 −1.36903
\(733\) 2.97939e12i 0.381206i 0.981667 + 0.190603i \(0.0610443\pi\)
−0.981667 + 0.190603i \(0.938956\pi\)
\(734\) 3.08670e12 + 3.08670e12i 0.392520 + 0.392520i
\(735\) 3.52767e12 0.445857
\(736\) −6.19079e12 6.19079e12i −0.777671 0.777671i
\(737\) −8.04528e12 + 8.04528e12i −1.00447 + 1.00447i
\(738\) −1.23044e13 + 1.23044e13i −1.52689 + 1.52689i
\(739\) 1.74914e12i 0.215737i −0.994165 0.107868i \(-0.965598\pi\)
0.994165 0.107868i \(-0.0344025\pi\)
\(740\) 2.16522e12i 0.265435i
\(741\) 2.55595e12 2.55595e12i 0.311437 0.311437i
\(742\) 2.26573e13 2.26573e13i 2.74404 2.74404i
\(743\) −3.63529e12 3.63529e12i −0.437612 0.437612i 0.453595 0.891208i \(-0.350141\pi\)
−0.891208 + 0.453595i \(0.850141\pi\)
\(744\) −1.61756e12 −0.193545
\(745\) 1.73545e12 + 1.73545e12i 0.206399 + 0.206399i
\(746\) 1.01541e13i 1.20038i
\(747\) −8.90208e11 −0.104604
\(748\) −1.96954e12 + 9.86653e12i −0.230042 + 1.15241i
\(749\) −7.30437e11 −0.0848037
\(750\) 6.68608e12i 0.771607i
\(751\) −6.61319e12 6.61319e12i −0.758632 0.758632i 0.217441 0.976073i \(-0.430229\pi\)
−0.976073 + 0.217441i \(0.930229\pi\)
\(752\) 1.48756e12 0.169627
\(753\) −7.71969e12 7.71969e12i −0.875030 0.875030i
\(754\) −1.06380e12 + 1.06380e12i −0.119865 + 0.119865i
\(755\) 3.03712e11 3.03712e11i 0.0340174 0.0340174i
\(756\) 2.11434e12i 0.235411i
\(757\) 4.90172e12i 0.542521i −0.962506 0.271261i \(-0.912560\pi\)
0.962506 0.271261i \(-0.0874405\pi\)
\(758\) 3.93212e12 3.93212e12i 0.432628 0.432628i
\(759\) −6.42088e12 + 6.42088e12i −0.702274 + 0.702274i
\(760\) −1.30539e12 1.30539e12i −0.141932 0.141932i
\(761\) 9.45949e12 1.02244 0.511219 0.859451i \(-0.329194\pi\)
0.511219 + 0.859451i \(0.329194\pi\)
\(762\) −7.46254e12 7.46254e12i −0.801843 0.801843i
\(763\) 2.45465e13i 2.62198i
\(764\) −5.67021e12 −0.602114
\(765\) −3.10758e11 + 1.55676e12i −0.0328054 + 0.164341i
\(766\) −1.80115e13 −1.89026
\(767\) 1.03426e10i 0.00107907i
\(768\) −3.72251e12 3.72251e12i −0.386110 0.386110i
\(769\) 1.62983e13 1.68064 0.840318 0.542093i \(-0.182368\pi\)
0.840318 + 0.542093i \(0.182368\pi\)
\(770\) −2.62300e12 2.62300e12i −0.268899 0.268899i
\(771\) 7.88344e12 7.88344e12i 0.803472 0.803472i
\(772\) −7.04010e12 + 7.04010e12i −0.713347 + 0.713347i
\(773\) 1.21072e13i 1.21965i 0.792535 + 0.609827i \(0.208761\pi\)
−0.792535 + 0.609827i \(0.791239\pi\)
\(774\) 2.32839e13i 2.33196i
\(775\) 1.34349e12 1.34349e12i 0.133776 0.133776i
\(776\) 6.99005e12 6.99005e12i 0.691994 0.691994i
\(777\) −1.68576e13 1.68576e13i −1.65921 1.65921i
\(778\) −2.27138e13 −2.22270
\(779\) −1.68394e13 1.68394e13i −1.63836 1.63836i
\(780\) 7.63148e11i 0.0738216i
\(781\) 1.19653e13 1.15078
\(782\) 1.42189e13 + 2.83835e12i 1.35967 + 0.271416i
\(783\) 5.44659e11 0.0517842
\(784\) 6.37793e12i 0.602917i
\(785\) 9.67337e11 + 9.67337e11i 0.0909210 + 0.0909210i
\(786\) −2.30255e13 −2.15183
\(787\) 3.37207e12 + 3.37207e12i 0.313336 + 0.313336i 0.846201 0.532864i \(-0.178884\pi\)
−0.532864 + 0.846201i \(0.678884\pi\)
\(788\) 1.91828e13 1.91828e13i 1.77233 1.77233i
\(789\) 1.01234e13 1.01234e13i 0.929994 0.929994i
\(790\) 2.82849e12i 0.258364i
\(791\) 1.91467e13i 1.73900i
\(792\) −4.19154e12 + 4.19154e12i −0.378539 + 0.378539i
\(793\) −1.08138e12 + 1.08138e12i −0.0971063 + 0.0971063i
\(794\) 1.12119e10 + 1.12119e10i 0.00100112 + 0.00100112i
\(795\) −4.18702e12 −0.371752
\(796\) 8.53662e12 + 8.53662e12i 0.753663 + 0.753663i
\(797\) 8.30651e12i 0.729216i 0.931161 + 0.364608i \(0.118797\pi\)
−0.931161 + 0.364608i \(0.881203\pi\)
\(798\) 6.50266e13 5.67647
\(799\) −4.80248e12 + 3.20420e12i −0.416874 + 0.278137i
\(800\) 1.39305e13 1.20244
\(801\) 1.12384e12i 0.0964621i
\(802\) −4.18401e12 4.18401e12i −0.357115 0.357115i
\(803\) −3.98062e12 −0.337855
\(804\) 2.97757e13 + 2.97757e13i 2.51310 + 2.51310i
\(805\) −2.24015e12 + 2.24015e12i −0.188017 + 0.188017i
\(806\) −5.26196e11 + 5.26196e11i −0.0439177 + 0.0439177i
\(807\) 2.43462e13i 2.02069i
\(808\) 5.63599e12i 0.465178i
\(809\) 5.44748e12 5.44748e12i 0.447124 0.447124i −0.447274 0.894397i \(-0.647605\pi\)
0.894397 + 0.447274i \(0.147605\pi\)
\(810\) 2.60423e12 2.60423e12i 0.212567 0.212567i
\(811\) −9.61807e12 9.61807e12i −0.780718 0.780718i 0.199234 0.979952i \(-0.436155\pi\)
−0.979952 + 0.199234i \(0.936155\pi\)
\(812\) −1.60391e13 −1.29473
\(813\) −1.67230e13 1.67230e13i −1.34247 1.34247i
\(814\) 1.60554e13i 1.28177i
\(815\) 1.92405e12 0.152759
\(816\) −5.84049e12 1.16587e12i −0.461152 0.0920543i
\(817\) −3.18655e13 −2.50220
\(818\) 2.80200e13i 2.18815i
\(819\) −2.86331e12 2.86331e12i −0.222377 0.222377i
\(820\) 5.02787e12 0.388349
\(821\) 8.40128e12 + 8.40128e12i 0.645359 + 0.645359i 0.951868 0.306509i \(-0.0991609\pi\)
−0.306509 + 0.951868i \(0.599161\pi\)
\(822\) 1.75382e12 1.75382e12i 0.133987 0.133987i
\(823\) −5.70064e12 + 5.70064e12i −0.433136 + 0.433136i −0.889694 0.456558i \(-0.849082\pi\)
0.456558 + 0.889694i \(0.349082\pi\)
\(824\) 1.16692e12i 0.0881794i
\(825\) 1.44483e13i 1.08586i
\(826\) −1.31564e11 + 1.31564e11i −0.00983393 + 0.00983393i
\(827\) −2.57189e12 + 2.57189e12i −0.191195 + 0.191195i −0.796213 0.605017i \(-0.793166\pi\)
0.605017 + 0.796213i \(0.293166\pi\)
\(828\) 1.14519e13 + 1.14519e13i 0.846725 + 0.846725i
\(829\) 1.25002e13 0.919223 0.459612 0.888120i \(-0.347989\pi\)
0.459612 + 0.888120i \(0.347989\pi\)
\(830\) 3.06906e11 + 3.06906e11i 0.0224468 + 0.0224468i
\(831\) 1.77588e13i 1.29184i
\(832\) −4.50762e12 −0.326131
\(833\) −1.37380e13 2.05907e13i −0.988604 1.48173i
\(834\) 2.65031e13 1.89693
\(835\) 1.18689e12i 0.0844932i
\(836\) −1.83512e13 1.83512e13i −1.29938 1.29938i
\(837\) 2.69408e11 0.0189734
\(838\) −2.33244e13 2.33244e13i −1.63385 1.63385i
\(839\) 7.22630e12 7.22630e12i 0.503486 0.503486i −0.409034 0.912519i \(-0.634134\pi\)
0.912519 + 0.409034i \(0.134134\pi\)
\(840\) −3.03454e12 + 3.03454e12i −0.210299 + 0.210299i
\(841\) 1.03754e13i 0.715194i
\(842\) 1.79146e13i 1.22830i
\(843\) −1.96708e13 + 1.96708e13i −1.34152 + 1.34152i
\(844\) −1.26713e13 + 1.26713e13i −0.859569 + 0.859569i
\(845\) −1.81045e12 1.81045e12i −0.122161 0.122161i
\(846\) −1.08815e13 −0.730332
\(847\) 6.13718e12 + 6.13718e12i 0.409726 + 0.409726i
\(848\) 7.57002e12i 0.502708i
\(849\) 1.84470e13 1.21855
\(850\) −1.91911e13 + 1.28042e13i −1.26100 + 0.841334i
\(851\) 1.37120e13 0.896227
\(852\) 4.42838e13i 2.87916i
\(853\) 3.04023e12 + 3.04023e12i 0.196624 + 0.196624i 0.798551 0.601927i \(-0.205600\pi\)
−0.601927 + 0.798551i \(0.705600\pi\)
\(854\) −2.75116e13 −1.76993
\(855\) −2.89549e12 2.89549e12i −0.185299 0.185299i
\(856\) 4.02414e11 4.02414e11i 0.0256178 0.0256178i
\(857\) 7.28572e12 7.28572e12i 0.461380 0.461380i −0.437727 0.899108i \(-0.644217\pi\)
0.899108 + 0.437727i \(0.144217\pi\)
\(858\) 5.65885e12i 0.356480i
\(859\) 2.08459e13i 1.30633i 0.757218 + 0.653163i \(0.226558\pi\)
−0.757218 + 0.653163i \(0.773442\pi\)
\(860\) 4.75716e12 4.75716e12i 0.296555 0.296555i
\(861\) −3.91453e13 + 3.91453e13i −2.42753 + 2.42753i
\(862\) 1.50225e13 + 1.50225e13i 0.926741 + 0.926741i
\(863\) 2.55853e13 1.57015 0.785076 0.619400i \(-0.212624\pi\)
0.785076 + 0.619400i \(0.212624\pi\)
\(864\) 1.39673e12 + 1.39673e12i 0.0852709 + 0.0852709i
\(865\) 7.82158e11i 0.0475031i
\(866\) 4.50592e12 0.272240
\(867\) 2.13669e13 8.81648e12i 1.28427 0.529919i
\(868\) −7.93352e12 −0.474381
\(869\) 1.24295e13i 0.739375i
\(870\) 2.50074e12 + 2.50074e12i 0.147990 + 0.147990i
\(871\) 6.05557e12 0.356511
\(872\) 1.35232e13 + 1.35232e13i 0.792055 + 0.792055i
\(873\) 1.55046e13 1.55046e13i 0.903435 0.903435i
\(874\) −2.64463e13 + 2.64463e13i −1.53308 + 1.53308i
\(875\) 1.02507e13i 0.591177i
\(876\) 1.47323e13i 0.845284i
\(877\) 1.31732e13 1.31732e13i 0.751955 0.751955i −0.222889 0.974844i \(-0.571549\pi\)
0.974844 + 0.222889i \(0.0715488\pi\)
\(878\) 1.00426e13 1.00426e13i 0.570322 0.570322i
\(879\) −1.08787e13 1.08787e13i −0.614646 0.614646i
\(880\) −8.76367e11 −0.0492622
\(881\) 7.53673e12 + 7.53673e12i 0.421494 + 0.421494i 0.885718 0.464224i \(-0.153667\pi\)
−0.464224 + 0.885718i \(0.653667\pi\)
\(882\) 4.66544e13i 2.59587i
\(883\) 7.80893e12 0.432283 0.216142 0.976362i \(-0.430653\pi\)
0.216142 + 0.976362i \(0.430653\pi\)
\(884\) 4.45443e12 2.97198e12i 0.245333 0.163686i
\(885\) 2.43128e10 0.00133226
\(886\) 2.52784e13i 1.37816i
\(887\) 1.17336e13 + 1.17336e13i 0.636465 + 0.636465i 0.949682 0.313217i \(-0.101407\pi\)
−0.313217 + 0.949682i \(0.601407\pi\)
\(888\) 1.85745e13 1.00244
\(889\) −1.14411e13 1.14411e13i −0.614343 0.614343i
\(890\) 3.87451e11 3.87451e11i 0.0206996 0.0206996i
\(891\) 1.14440e13 1.14440e13i 0.608315 0.608315i
\(892\) 9.57134e12i 0.506210i
\(893\) 1.48920e13i 0.783649i
\(894\) 4.76268e13 4.76268e13i 2.49363 2.49363i
\(895\) −2.51287e12 + 2.51287e12i −0.130908 + 0.130908i
\(896\) −2.90660e13 2.90660e13i −1.50660 1.50660i
\(897\) 4.83291e12 0.249254
\(898\) 5.09373e12 + 5.09373e12i 0.261392 + 0.261392i
\(899\) 2.04369e12i 0.104351i
\(900\) −2.57692e13 −1.30921
\(901\) 1.63058e13 + 2.44393e13i 0.824291 + 1.23545i
\(902\) 3.72824e13 1.87532
\(903\) 7.40753e13i 3.70748i
\(904\) −1.05483e13 1.05483e13i −0.525323 0.525323i
\(905\) −2.07609e12 −0.102879
\(906\) −8.33494e12 8.33494e12i −0.410985 0.410985i
\(907\) −2.28101e13 + 2.28101e13i −1.11916 + 1.11916i −0.127299 + 0.991864i \(0.540631\pi\)
−0.991864 + 0.127299i \(0.959369\pi\)
\(908\) −9.59889e12 + 9.59889e12i −0.468635 + 0.468635i
\(909\) 1.25012e13i 0.607314i
\(910\) 1.97429e12i 0.0954389i
\(911\) −2.25384e13 + 2.25384e13i −1.08415 + 1.08415i −0.0880334 + 0.996118i \(0.528058\pi\)
−0.996118 + 0.0880334i \(0.971942\pi\)
\(912\) 1.08630e13 1.08630e13i 0.519964 0.519964i
\(913\) 1.34867e12 + 1.34867e12i 0.0642371 + 0.0642371i
\(914\) −5.70462e13 −2.70376
\(915\) 2.54204e12 + 2.54204e12i 0.119891 + 0.119891i
\(916\) 2.49512e13i 1.17101i
\(917\) −3.53013e13 −1.64865
\(918\) −3.20798e12 6.40373e11i −0.149087 0.0297605i
\(919\) 2.75490e13 1.27405 0.637023 0.770845i \(-0.280166\pi\)
0.637023 + 0.770845i \(0.280166\pi\)
\(920\) 2.46830e12i 0.113593i
\(921\) −2.18352e13 2.18352e13i −0.999973 0.999973i
\(922\) 1.46571e12 0.0667971
\(923\) −4.50306e12 4.50306e12i −0.204221 0.204221i
\(924\) −4.26597e13 + 4.26597e13i −1.92528 + 1.92528i
\(925\) −1.54274e13 + 1.54274e13i −0.692874 + 0.692874i
\(926\) 2.38367e13i 1.06536i
\(927\) 2.58833e12i 0.115123i
\(928\) −1.05954e13 + 1.05954e13i −0.468978 + 0.468978i
\(929\) −2.47616e13 + 2.47616e13i −1.09071 + 1.09071i −0.0952519 + 0.995453i \(0.530366\pi\)
−0.995453 + 0.0952519i \(0.969634\pi\)
\(930\) 1.23695e12 + 1.23695e12i 0.0542226 + 0.0542226i
\(931\) 6.38496e13 2.78538
\(932\) 2.78685e13 + 2.78685e13i 1.20988 + 1.20988i
\(933\) 6.61119e12i 0.285635i
\(934\) −5.74395e13 −2.46973
\(935\) 2.82929e12 1.88769e12i 0.121067 0.0807754i
\(936\) 3.15492e12 0.134353
\(937\) 3.69015e13i 1.56392i −0.623326 0.781962i \(-0.714219\pi\)
0.623326 0.781962i \(-0.285781\pi\)
\(938\) 7.70308e13 + 7.70308e13i 3.24902 + 3.24902i
\(939\) −2.93367e12 −0.123145
\(940\) 2.22321e12 + 2.22321e12i 0.0928763 + 0.0928763i
\(941\) 2.56997e13 2.56997e13i 1.06850 1.06850i 0.0710264 0.997474i \(-0.477373\pi\)
0.997474 0.0710264i \(-0.0226275\pi\)
\(942\) 2.65472e13 2.65472e13i 1.09847 1.09847i
\(943\) 3.18408e13i 1.31124i
\(944\) 4.39568e10i 0.00180157i
\(945\) 5.05411e11 5.05411e11i 0.0206159 0.0206159i
\(946\) 3.52751e13 3.52751e13i 1.43205 1.43205i
\(947\) −1.97657e13 1.97657e13i −0.798616 0.798616i 0.184261 0.982877i \(-0.441011\pi\)
−0.982877 + 0.184261i \(0.941011\pi\)
\(948\) −4.60018e13 −1.84985
\(949\) 1.49808e12 + 1.49808e12i 0.0599565 + 0.0599565i
\(950\) 5.95096e13i 2.37045i
\(951\) −1.73655e13 −0.688454
\(952\) 2.95300e13 + 5.89473e12i 1.16519 + 0.232593i
\(953\) 3.85787e12 0.151506 0.0757529 0.997127i \(-0.475864\pi\)
0.0757529 + 0.997127i \(0.475864\pi\)
\(954\) 5.53744e13i 2.16442i
\(955\) 1.35540e12 + 1.35540e12i 0.0527295 + 0.0527295i
\(956\) −2.48587e13 −0.962539
\(957\) 1.09892e13 + 1.09892e13i 0.423510 + 0.423510i
\(958\) −5.04088e13 + 5.04088e13i −1.93358 + 1.93358i
\(959\) 2.68886e12 2.68886e12i 0.102656 0.102656i
\(960\) 1.05963e13i 0.402655i
\(961\) 2.54287e13i 0.961766i
\(962\) 6.04234e12 6.04234e12i 0.227466 0.227466i
\(963\) 8.92594e11 8.92594e11i 0.0334453 0.0334453i
\(964\) 4.41572e13 + 4.41572e13i 1.64685 + 1.64685i
\(965\) 3.36572e12 0.124941
\(966\) 6.14778e13 + 6.14778e13i 2.27154 + 2.27154i
\(967\) 1.57206e13i 0.578164i 0.957304 + 0.289082i \(0.0933500\pi\)
−0.957304 + 0.289082i \(0.906650\pi\)
\(968\) −6.76221e12 −0.247542
\(969\) −1.16715e13 + 5.84693e13i −0.425277 + 2.13045i
\(970\) −1.06907e13 −0.387732
\(971\) 2.52084e13i 0.910036i −0.890482 0.455018i \(-0.849633\pi\)
0.890482 0.455018i \(-0.150367\pi\)
\(972\) −3.95767e13 3.95767e13i −1.42214 1.42214i
\(973\) 4.06331e13 1.45335
\(974\) −1.44727e13 1.44727e13i −0.515271 0.515271i
\(975\) −5.43751e12 + 5.43751e12i −0.192699 + 0.192699i
\(976\) −4.59594e12 + 4.59594e12i −0.162125 + 0.162125i
\(977\) 3.60657e13i 1.26639i −0.773991 0.633197i \(-0.781742\pi\)
0.773991 0.633197i \(-0.218258\pi\)
\(978\) 5.28027e13i 1.84557i
\(979\) 1.70261e12 1.70261e12i 0.0592371 0.0592371i
\(980\) −9.53203e12 + 9.53203e12i −0.330117 + 0.330117i
\(981\) 2.99958e13 + 2.99958e13i 1.03407 + 1.03407i
\(982\) 4.47349e13 1.53513
\(983\) 1.57108e13 + 1.57108e13i 0.536670 + 0.536670i 0.922549 0.385879i \(-0.126102\pi\)
−0.385879 + 0.922549i \(0.626102\pi\)
\(984\) 4.31320e13i 1.46663i
\(985\) −9.17088e12 −0.310419
\(986\) 4.85779e12 2.43354e13i 0.163679 0.819958i
\(987\) −3.46183e13 −1.16112
\(988\) 1.38127e13i 0.461182i
\(989\) −3.01265e13 3.01265e13i −1.00130 1.00130i
\(990\) 6.41060e12 0.212100
\(991\) −7.41356e12 7.41356e12i −0.244172 0.244172i 0.574402 0.818574i \(-0.305235\pi\)
−0.818574 + 0.574402i \(0.805235\pi\)
\(992\) −5.24088e12 + 5.24088e12i −0.171831 + 0.171831i
\(993\) 1.48360e13 1.48360e13i 0.484222 0.484222i
\(994\) 1.14564e14i 3.72227i
\(995\) 4.08118e12i 0.132002i
\(996\) 4.99143e12 4.99143e12i 0.160716 0.160716i
\(997\) −1.63998e13 + 1.63998e13i −0.525667 + 0.525667i −0.919277 0.393611i \(-0.871226\pi\)
0.393611 + 0.919277i \(0.371226\pi\)
\(998\) 3.13572e13 + 3.13572e13i 1.00058 + 1.00058i
\(999\) −3.09363e12 −0.0982705
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 17.10.c.a.13.2 yes 24
17.2 even 8 289.10.a.f.1.22 24
17.4 even 4 inner 17.10.c.a.4.11 24
17.15 even 8 289.10.a.f.1.21 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.c.a.4.11 24 17.4 even 4 inner
17.10.c.a.13.2 yes 24 1.1 even 1 trivial
289.10.a.f.1.21 24 17.15 even 8
289.10.a.f.1.22 24 17.2 even 8