Properties

Label 15.10.e.a.2.13
Level $15$
Weight $10$
Character 15.2
Analytic conductor $7.726$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,10,Mod(2,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 15.e (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: \(7.72553754246\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2.13
Character \(\chi\) \(=\) 15.2
Dual form 15.10.e.a.8.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(20.3831 - 20.3831i) q^{2} +(65.1534 + 124.250i) q^{3} -318.940i q^{4} +(840.534 + 1116.52i) q^{5} +(3860.62 + 1204.57i) q^{6} +(1024.24 + 1024.24i) q^{7} +(3935.17 + 3935.17i) q^{8} +(-11193.1 + 16190.6i) q^{9} +O(q^{10})\) \(q+(20.3831 - 20.3831i) q^{2} +(65.1534 + 124.250i) q^{3} -318.940i q^{4} +(840.534 + 1116.52i) q^{5} +(3860.62 + 1204.57i) q^{6} +(1024.24 + 1024.24i) q^{7} +(3935.17 + 3935.17i) q^{8} +(-11193.1 + 16190.6i) q^{9} +(39890.9 + 5625.54i) q^{10} -82348.4i q^{11} +(39628.2 - 20780.0i) q^{12} +(46183.3 - 46183.3i) q^{13} +41754.1 q^{14} +(-83964.4 + 177182. i) q^{15} +323719. q^{16} +(-283339. + 283339. i) q^{17} +(101865. + 558163. i) q^{18} -448101. i q^{19} +(356104. - 268080. i) q^{20} +(-60528.7 + 193994. i) q^{21} +(-1.67851e6 - 1.67851e6i) q^{22} +(-577002. - 577002. i) q^{23} +(-232554. + 745333. i) q^{24} +(-540130. + 1.87695e6i) q^{25} -1.88271e6i q^{26} +(-2.74095e6 - 335864. i) q^{27} +(326669. - 326669. i) q^{28} -3.17522e6 q^{29} +(1.90005e6 + 5.32296e6i) q^{30} +4.84504e6 q^{31} +(4.58358e6 - 4.58358e6i) q^{32} +(1.02318e7 - 5.36528e6i) q^{33} +1.15507e7i q^{34} +(-282680. + 2.00449e6i) q^{35} +(5.16382e6 + 3.56991e6i) q^{36} +(-2.00195e6 - 2.00195e6i) q^{37} +(-9.13367e6 - 9.13367e6i) q^{38} +(8.74726e6 + 2.72927e6i) q^{39} +(-1.08607e6 + 7.70135e6i) q^{40} -2.19158e7i q^{41} +(2.72042e6 + 5.18795e6i) q^{42} +(5.07147e6 - 5.07147e6i) q^{43} -2.62642e7 q^{44} +(-2.74854e7 + 1.11142e6i) q^{45} -2.35222e7 q^{46} +(1.80519e7 - 1.80519e7i) q^{47} +(2.10914e7 + 4.02220e7i) q^{48} -3.82555e7i q^{49} +(2.72486e7 + 4.92676e7i) q^{50} +(-5.36654e7 - 1.67443e7i) q^{51} +(-1.47297e7 - 1.47297e7i) q^{52} +(2.88144e7 + 2.88144e7i) q^{53} +(-6.27149e7 + 4.90230e7i) q^{54} +(9.19440e7 - 6.92166e7i) q^{55} +8.06107e6i q^{56} +(5.56765e7 - 2.91953e7i) q^{57} +(-6.47207e7 + 6.47207e7i) q^{58} -1.79216e8 q^{59} +(5.65102e7 + 2.67796e7i) q^{60} -2.05711e7 q^{61} +(9.87569e7 - 9.87569e7i) q^{62} +(-2.80473e7 + 5.11866e6i) q^{63} -2.11108e7i q^{64} +(9.03834e7 + 1.27462e7i) q^{65} +(9.91942e7 - 3.17916e8i) q^{66} +(1.55434e8 + 1.55434e8i) q^{67} +(9.03681e7 + 9.03681e7i) q^{68} +(3.40988e7 - 1.09286e8i) q^{69} +(3.50958e7 + 4.66195e7i) q^{70} +3.49681e8i q^{71} +(-1.07759e8 + 1.96662e7i) q^{72} +(5.01248e7 - 5.01248e7i) q^{73} -8.16117e7 q^{74} +(-2.68403e8 + 5.51788e7i) q^{75} -1.42917e8 q^{76} +(8.43441e7 - 8.43441e7i) q^{77} +(2.33927e8 - 1.22665e8i) q^{78} +5.64363e8i q^{79} +(2.72096e8 + 3.61440e8i) q^{80} +(-1.36851e8 - 3.62445e8i) q^{81} +(-4.46710e8 - 4.46710e8i) q^{82} +(-2.73321e8 - 2.73321e8i) q^{83} +(6.18722e7 + 1.93050e7i) q^{84} +(-5.54512e8 - 7.81990e7i) q^{85} -2.06744e8i q^{86} +(-2.06876e8 - 3.94520e8i) q^{87} +(3.24055e8 - 3.24055e8i) q^{88} -2.28966e8 q^{89} +(-5.37582e8 + 5.82890e8i) q^{90} +9.46051e7 q^{91} +(-1.84029e8 + 1.84029e8i) q^{92} +(3.15671e8 + 6.01996e8i) q^{93} -7.35907e8i q^{94} +(5.00316e8 - 3.76644e8i) q^{95} +(8.68144e8 + 2.70873e8i) q^{96} +(7.06282e8 + 7.06282e8i) q^{97} +(-7.79765e8 - 7.79765e8i) q^{98} +(1.33327e9 + 9.21731e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 150 q^{3} - 4548 q^{6} - 9760 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 150 q^{3} - 4548 q^{6} - 9760 q^{7} - 39820 q^{10} + 191940 q^{12} + 114260 q^{13} - 40230 q^{15} - 1494724 q^{16} + 994800 q^{18} + 592212 q^{21} + 308260 q^{22} + 5808020 q^{25} + 4786830 q^{27} - 12953300 q^{28} - 17343060 q^{30} + 16124104 q^{31} + 19638120 q^{33} - 48943956 q^{36} - 35578660 q^{37} + 144132840 q^{40} + 46648260 q^{42} - 118721020 q^{43} - 129688380 q^{45} + 3145024 q^{46} + 275395140 q^{48} - 64226868 q^{51} - 157103680 q^{52} + 144539740 q^{55} + 48163500 q^{57} - 209634300 q^{58} - 140815620 q^{60} + 63607744 q^{61} + 89858580 q^{63} + 358931400 q^{66} + 153311540 q^{67} + 420519420 q^{70} - 1534046760 q^{72} + 628070360 q^{73} + 138090210 q^{75} - 2457023472 q^{76} - 403337880 q^{78} + 2250542952 q^{81} + 4138031440 q^{82} + 108907340 q^{85} - 2878139760 q^{87} - 595851300 q^{88} + 693868920 q^{90} - 4369040216 q^{91} - 293672640 q^{93} + 7291125636 q^{96} + 3987642200 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.3831 20.3831i 0.900813 0.900813i −0.0946933 0.995506i \(-0.530187\pi\)
0.995506 + 0.0946933i \(0.0301870\pi\)
\(3\) 65.1534 + 124.250i 0.464399 + 0.885626i
\(4\) 318.940i 0.622929i
\(5\) 840.534 + 1116.52i 0.601437 + 0.798920i
\(6\) 3860.62 + 1204.57i 1.21612 + 0.379447i
\(7\) 1024.24 + 1024.24i 0.161235 + 0.161235i 0.783114 0.621879i \(-0.213630\pi\)
−0.621879 + 0.783114i \(0.713630\pi\)
\(8\) 3935.17 + 3935.17i 0.339671 + 0.339671i
\(9\) −11193.1 + 16190.6i −0.568667 + 0.822568i
\(10\) 39890.9 + 5625.54i 1.26146 + 0.177895i
\(11\) 82348.4i 1.69585i −0.530115 0.847926i \(-0.677851\pi\)
0.530115 0.847926i \(-0.322149\pi\)
\(12\) 39628.2 20780.0i 0.551682 0.289288i
\(13\) 46183.3 46183.3i 0.448476 0.448476i −0.446371 0.894848i \(-0.647284\pi\)
0.894848 + 0.446371i \(0.147284\pi\)
\(14\) 41754.1 0.290485
\(15\) −83964.4 + 177182.i −0.428237 + 0.903666i
\(16\) 323719. 1.23489
\(17\) −283339. + 283339.i −0.822785 + 0.822785i −0.986507 0.163721i \(-0.947650\pi\)
0.163721 + 0.986507i \(0.447650\pi\)
\(18\) 101865. + 558163.i 0.228718 + 1.25324i
\(19\) 448101.i 0.788832i −0.918932 0.394416i \(-0.870947\pi\)
0.918932 0.394416i \(-0.129053\pi\)
\(20\) 356104. 268080.i 0.497670 0.374653i
\(21\) −60528.7 + 193994.i −0.0679164 + 0.217671i
\(22\) −1.67851e6 1.67851e6i −1.52765 1.52765i
\(23\) −577002. 577002.i −0.429934 0.429934i 0.458672 0.888606i \(-0.348325\pi\)
−0.888606 + 0.458672i \(0.848325\pi\)
\(24\) −232554. + 745333.i −0.143078 + 0.458564i
\(25\) −540130. + 1.87695e6i −0.276547 + 0.961000i
\(26\) 1.88271e6i 0.807987i
\(27\) −2.74095e6 335864.i −0.992576 0.121626i
\(28\) 326669. 326669.i 0.100438 0.100438i
\(29\) −3.17522e6 −0.833647 −0.416823 0.908987i \(-0.636857\pi\)
−0.416823 + 0.908987i \(0.636857\pi\)
\(30\) 1.90005e6 + 5.32296e6i 0.428273 + 1.19980i
\(31\) 4.84504e6 0.942259 0.471129 0.882064i \(-0.343846\pi\)
0.471129 + 0.882064i \(0.343846\pi\)
\(32\) 4.58358e6 4.58358e6i 0.772733 0.772733i
\(33\) 1.02318e7 5.36528e6i 1.50189 0.787552i
\(34\) 1.15507e7i 1.48235i
\(35\) −282680. + 2.00449e6i −0.0318411 + 0.225786i
\(36\) 5.16382e6 + 3.56991e6i 0.512401 + 0.354239i
\(37\) −2.00195e6 2.00195e6i −0.175608 0.175608i 0.613830 0.789438i \(-0.289628\pi\)
−0.789438 + 0.613830i \(0.789628\pi\)
\(38\) −9.13367e6 9.13367e6i −0.710590 0.710590i
\(39\) 8.74726e6 + 2.72927e6i 0.605454 + 0.188910i
\(40\) −1.08607e6 + 7.70135e6i −0.0670792 + 0.475660i
\(41\) 2.19158e7i 1.21124i −0.795755 0.605618i \(-0.792926\pi\)
0.795755 0.605618i \(-0.207074\pi\)
\(42\) 2.72042e6 + 5.18795e6i 0.134901 + 0.257261i
\(43\) 5.07147e6 5.07147e6i 0.226217 0.226217i −0.584893 0.811110i \(-0.698864\pi\)
0.811110 + 0.584893i \(0.198864\pi\)
\(44\) −2.62642e7 −1.05640
\(45\) −2.74854e7 + 1.11142e6i −0.999183 + 0.0404037i
\(46\) −2.35222e7 −0.774581
\(47\) 1.80519e7 1.80519e7i 0.539614 0.539614i −0.383802 0.923416i \(-0.625385\pi\)
0.923416 + 0.383802i \(0.125385\pi\)
\(48\) 2.10914e7 + 4.02220e7i 0.573481 + 1.09365i
\(49\) 3.82555e7i 0.948007i
\(50\) 2.72486e7 + 4.92676e7i 0.616565 + 1.11480i
\(51\) −5.36654e7 1.67443e7i −1.11078 0.346579i
\(52\) −1.47297e7 1.47297e7i −0.279369 0.279369i
\(53\) 2.88144e7 + 2.88144e7i 0.501612 + 0.501612i 0.911939 0.410327i \(-0.134585\pi\)
−0.410327 + 0.911939i \(0.634585\pi\)
\(54\) −6.27149e7 + 4.90230e7i −1.00369 + 0.784563i
\(55\) 9.19440e7 6.92166e7i 1.35485 1.01995i
\(56\) 8.06107e6i 0.109533i
\(57\) 5.56765e7 2.91953e7i 0.698610 0.366333i
\(58\) −6.47207e7 + 6.47207e7i −0.750960 + 0.750960i
\(59\) −1.79216e8 −1.92550 −0.962750 0.270393i \(-0.912846\pi\)
−0.962750 + 0.270393i \(0.912846\pi\)
\(60\) 5.65102e7 + 2.67796e7i 0.562920 + 0.266761i
\(61\) −2.05711e7 −0.190227 −0.0951136 0.995466i \(-0.530321\pi\)
−0.0951136 + 0.995466i \(0.530321\pi\)
\(62\) 9.87569e7 9.87569e7i 0.848799 0.848799i
\(63\) −2.80473e7 + 5.11866e6i −0.224315 + 0.0409377i
\(64\) 2.11108e7i 0.157288i
\(65\) 9.03834e7 + 1.27462e7i 0.628027 + 0.0885665i
\(66\) 9.91942e7 3.17916e8i 0.643485 2.06236i
\(67\) 1.55434e8 + 1.55434e8i 0.942341 + 0.942341i 0.998426 0.0560850i \(-0.0178618\pi\)
−0.0560850 + 0.998426i \(0.517862\pi\)
\(68\) 9.03681e7 + 9.03681e7i 0.512537 + 0.512537i
\(69\) 3.40988e7 1.09286e8i 0.181100 0.580422i
\(70\) 3.50958e7 + 4.66195e7i 0.174708 + 0.232074i
\(71\) 3.49681e8i 1.63309i 0.577284 + 0.816543i \(0.304112\pi\)
−0.577284 + 0.816543i \(0.695888\pi\)
\(72\) −1.07759e8 + 1.96662e7i −0.472562 + 0.0862429i
\(73\) 5.01248e7 5.01248e7i 0.206585 0.206585i −0.596229 0.802814i \(-0.703335\pi\)
0.802814 + 0.596229i \(0.203335\pi\)
\(74\) −8.16117e7 −0.316381
\(75\) −2.68403e8 + 5.51788e7i −0.979515 + 0.201371i
\(76\) −1.42917e8 −0.491386
\(77\) 8.43441e7 8.43441e7i 0.273430 0.273430i
\(78\) 2.33927e8 1.22665e8i 0.715574 0.375228i
\(79\) 5.64363e8i 1.63018i 0.579331 + 0.815092i \(0.303314\pi\)
−0.579331 + 0.815092i \(0.696686\pi\)
\(80\) 2.72096e8 + 3.61440e8i 0.742708 + 0.986577i
\(81\) −1.36851e8 3.62445e8i −0.353236 0.935534i
\(82\) −4.46710e8 4.46710e8i −1.09110 1.09110i
\(83\) −2.73321e8 2.73321e8i −0.632152 0.632152i 0.316455 0.948607i \(-0.397507\pi\)
−0.948607 + 0.316455i \(0.897507\pi\)
\(84\) 6.18722e7 + 1.93050e7i 0.135593 + 0.0423071i
\(85\) −5.54512e8 7.81990e7i −1.15219 0.162486i
\(86\) 2.06744e8i 0.407559i
\(87\) −2.06876e8 3.94520e8i −0.387145 0.738299i
\(88\) 3.24055e8 3.24055e8i 0.576031 0.576031i
\(89\) −2.28966e8 −0.386826 −0.193413 0.981117i \(-0.561956\pi\)
−0.193413 + 0.981117i \(0.561956\pi\)
\(90\) −5.37582e8 + 5.82890e8i −0.863681 + 0.936474i
\(91\) 9.46051e7 0.144620
\(92\) −1.84029e8 + 1.84029e8i −0.267818 + 0.267818i
\(93\) 3.15671e8 + 6.01996e8i 0.437584 + 0.834489i
\(94\) 7.35907e8i 0.972183i
\(95\) 5.00316e8 3.76644e8i 0.630214 0.474433i
\(96\) 8.68144e8 + 2.70873e8i 1.04321 + 0.325496i
\(97\) 7.06282e8 + 7.06282e8i 0.810037 + 0.810037i 0.984639 0.174602i \(-0.0558638\pi\)
−0.174602 + 0.984639i \(0.555864\pi\)
\(98\) −7.79765e8 7.79765e8i −0.853977 0.853977i
\(99\) 1.33327e9 + 9.21731e8i 1.39495 + 0.964374i
\(100\) 5.98635e8 + 1.72269e8i 0.598635 + 0.172269i
\(101\) 1.11479e9i 1.06598i 0.846122 + 0.532990i \(0.178932\pi\)
−0.846122 + 0.532990i \(0.821068\pi\)
\(102\) −1.43517e9 + 7.52564e8i −1.31281 + 0.688403i
\(103\) 2.48271e8 2.48271e8i 0.217349 0.217349i −0.590031 0.807380i \(-0.700885\pi\)
0.807380 + 0.590031i \(0.200885\pi\)
\(104\) 3.63478e8 0.304669
\(105\) −2.67475e8 + 9.54764e7i −0.214749 + 0.0766556i
\(106\) 1.17465e9 0.903717
\(107\) 3.67462e8 3.67462e8i 0.271010 0.271010i −0.558497 0.829507i \(-0.688622\pi\)
0.829507 + 0.558497i \(0.188622\pi\)
\(108\) −1.07120e8 + 8.74197e8i −0.0757643 + 0.618304i
\(109\) 6.88571e8i 0.467229i −0.972329 0.233614i \(-0.924945\pi\)
0.972329 0.233614i \(-0.0750553\pi\)
\(110\) 4.63254e8 3.28495e9i 0.301684 2.13925i
\(111\) 1.18308e8 3.79176e8i 0.0739709 0.237076i
\(112\) 3.31564e8 + 3.31564e8i 0.199107 + 0.199107i
\(113\) −1.10051e9 1.10051e9i −0.634951 0.634951i 0.314354 0.949306i \(-0.398212\pi\)
−0.949306 + 0.314354i \(0.898212\pi\)
\(114\) 5.39768e8 1.72995e9i 0.299319 0.959314i
\(115\) 1.59247e8 1.12923e9i 0.0849047 0.602062i
\(116\) 1.01270e9i 0.519303i
\(117\) 2.30803e8 + 1.26467e9i 0.113869 + 0.623936i
\(118\) −3.65298e9 + 3.65298e9i −1.73452 + 1.73452i
\(119\) −5.80412e8 −0.265323
\(120\) −1.02765e9 + 3.66825e8i −0.452409 + 0.161489i
\(121\) −4.42331e9 −1.87591
\(122\) −4.19302e8 + 4.19302e8i −0.171359 + 0.171359i
\(123\) 2.72303e9 1.42789e9i 1.07270 0.562497i
\(124\) 1.54528e9i 0.586960i
\(125\) −2.54966e9 + 9.74575e8i −0.934088 + 0.357043i
\(126\) −4.67357e8 + 6.76025e8i −0.165189 + 0.238943i
\(127\) 1.77889e9 + 1.77889e9i 0.606782 + 0.606782i 0.942104 0.335322i \(-0.108845\pi\)
−0.335322 + 0.942104i \(0.608845\pi\)
\(128\) 1.91649e9 + 1.91649e9i 0.631046 + 0.631046i
\(129\) 9.60553e8 + 2.99706e8i 0.305399 + 0.0952887i
\(130\) 2.10210e9 1.58249e9i 0.645517 0.485953i
\(131\) 1.76491e9i 0.523604i 0.965122 + 0.261802i \(0.0843167\pi\)
−0.965122 + 0.261802i \(0.915683\pi\)
\(132\) −1.71120e9 3.26332e9i −0.490589 0.935571i
\(133\) 4.58960e8 4.58960e8i 0.127187 0.127187i
\(134\) 6.33643e9 1.69775
\(135\) −1.92886e9 3.34264e9i −0.499803 0.866139i
\(136\) −2.22997e9 −0.558952
\(137\) −2.64774e9 + 2.64774e9i −0.642144 + 0.642144i −0.951082 0.308938i \(-0.900026\pi\)
0.308938 + 0.951082i \(0.400026\pi\)
\(138\) −1.53255e9 2.92263e9i −0.359715 0.685989i
\(139\) 6.49613e8i 0.147601i −0.997273 0.0738003i \(-0.976487\pi\)
0.997273 0.0738003i \(-0.0235127\pi\)
\(140\) 6.39311e8 + 9.01577e7i 0.140649 + 0.0198347i
\(141\) 3.41909e9 + 1.06680e9i 0.728492 + 0.227300i
\(142\) 7.12757e9 + 7.12757e9i 1.47111 + 1.47111i
\(143\) −3.80312e9 3.80312e9i −0.760550 0.760550i
\(144\) −3.62340e9 + 5.24120e9i −0.702240 + 1.01578i
\(145\) −2.66888e9 3.54521e9i −0.501386 0.666017i
\(146\) 2.04339e9i 0.372190i
\(147\) 4.75324e9 2.49248e9i 0.839579 0.440254i
\(148\) −6.38500e8 + 6.38500e8i −0.109391 + 0.109391i
\(149\) −8.65549e8 −0.143865 −0.0719323 0.997410i \(-0.522917\pi\)
−0.0719323 + 0.997410i \(0.522917\pi\)
\(150\) −4.34616e9 + 6.59559e9i −0.700963 + 1.06376i
\(151\) 8.86598e9 1.38781 0.693906 0.720066i \(-0.255888\pi\)
0.693906 + 0.720066i \(0.255888\pi\)
\(152\) 1.76335e9 1.76335e9i 0.267943 0.267943i
\(153\) −1.41600e9 7.75887e9i −0.208906 1.14469i
\(154\) 3.43838e9i 0.492619i
\(155\) 4.07242e9 + 5.40961e9i 0.566709 + 0.752789i
\(156\) 8.70471e8 2.78985e9i 0.117678 0.377155i
\(157\) −9.86785e9 9.86785e9i −1.29621 1.29621i −0.930879 0.365328i \(-0.880957\pi\)
−0.365328 0.930879i \(-0.619043\pi\)
\(158\) 1.15035e10 + 1.15035e10i 1.46849 + 1.46849i
\(159\) −1.70283e9 + 5.45754e9i −0.211292 + 0.677188i
\(160\) 8.97033e9 + 1.26503e9i 1.08210 + 0.152602i
\(161\) 1.18197e9i 0.138641i
\(162\) −1.01772e10 4.59830e9i −1.16094 0.524541i
\(163\) 2.65413e9 2.65413e9i 0.294495 0.294495i −0.544358 0.838853i \(-0.683227\pi\)
0.838853 + 0.544358i \(0.183227\pi\)
\(164\) −6.98980e9 −0.754514
\(165\) 1.45906e10 + 6.91433e9i 1.53248 + 0.726227i
\(166\) −1.11422e10 −1.13890
\(167\) −1.73810e8 + 1.73810e8i −0.0172922 + 0.0172922i −0.715700 0.698408i \(-0.753892\pi\)
0.698408 + 0.715700i \(0.253892\pi\)
\(168\) −1.00159e9 + 5.25206e8i −0.0970056 + 0.0508672i
\(169\) 6.33871e9i 0.597738i
\(170\) −1.28966e10 + 9.70871e9i −1.18428 + 0.891541i
\(171\) 7.25502e9 + 5.01562e9i 0.648868 + 0.448582i
\(172\) −1.61749e9 1.61749e9i −0.140917 0.140917i
\(173\) 6.59575e9 + 6.59575e9i 0.559831 + 0.559831i 0.929259 0.369428i \(-0.120447\pi\)
−0.369428 + 0.929259i \(0.620447\pi\)
\(174\) −1.22583e10 3.82476e9i −1.01382 0.316324i
\(175\) −2.47566e9 + 1.36922e9i −0.199536 + 0.110358i
\(176\) 2.66577e10i 2.09419i
\(177\) −1.16766e10 2.22676e10i −0.894201 1.70527i
\(178\) −4.66703e9 + 4.66703e9i −0.348458 + 0.348458i
\(179\) −1.20765e10 −0.879229 −0.439615 0.898187i \(-0.644885\pi\)
−0.439615 + 0.898187i \(0.644885\pi\)
\(180\) 3.54476e8 + 8.76617e9i 0.0251687 + 0.622420i
\(181\) −1.34269e10 −0.929869 −0.464934 0.885345i \(-0.653922\pi\)
−0.464934 + 0.885345i \(0.653922\pi\)
\(182\) 1.92834e9 1.92834e9i 0.130276 0.130276i
\(183\) −1.34028e9 2.55595e9i −0.0883414 0.168470i
\(184\) 4.54120e9i 0.292072i
\(185\) 5.52519e8 3.91793e9i 0.0346797 0.245914i
\(186\) 1.87049e10 + 5.83618e9i 1.14590 + 0.357537i
\(187\) 2.33325e10 + 2.33325e10i 1.39532 + 1.39532i
\(188\) −5.75747e9 5.75747e9i −0.336141 0.336141i
\(189\) −2.46337e9 3.15138e9i −0.140427 0.179648i
\(190\) 2.52081e9 1.78751e10i 0.140329 0.995080i
\(191\) 1.10522e10i 0.600897i −0.953798 0.300448i \(-0.902864\pi\)
0.953798 0.300448i \(-0.0971363\pi\)
\(192\) 2.62302e9 1.37544e9i 0.139298 0.0730444i
\(193\) −1.47391e10 + 1.47391e10i −0.764649 + 0.764649i −0.977159 0.212510i \(-0.931836\pi\)
0.212510 + 0.977159i \(0.431836\pi\)
\(194\) 2.87924e10 1.45938
\(195\) 4.30508e9 + 1.20606e10i 0.213219 + 0.597327i
\(196\) −1.22012e10 −0.590541
\(197\) 2.65779e9 2.65779e9i 0.125726 0.125726i −0.641444 0.767170i \(-0.721664\pi\)
0.767170 + 0.641444i \(0.221664\pi\)
\(198\) 4.59639e10 8.38844e9i 2.12531 0.387871i
\(199\) 6.95237e9i 0.314263i 0.987578 + 0.157132i \(0.0502247\pi\)
−0.987578 + 0.157132i \(0.949775\pi\)
\(200\) −9.51163e9 + 5.26062e9i −0.420359 + 0.232489i
\(201\) −9.18557e9 + 2.94396e10i −0.396939 + 1.27218i
\(202\) 2.27230e10 + 2.27230e10i 0.960248 + 0.960248i
\(203\) −3.25217e9 3.25217e9i −0.134413 0.134413i
\(204\) −5.34043e9 + 1.71160e10i −0.215894 + 0.691937i
\(205\) 2.44695e10 1.84209e10i 0.967681 0.728483i
\(206\) 1.01210e10i 0.391582i
\(207\) 1.58004e10 2.88359e9i 0.598140 0.109161i
\(208\) 1.49504e10 1.49504e10i 0.553818 0.553818i
\(209\) −3.69004e10 −1.33774
\(210\) −3.50586e9 + 7.39806e9i −0.124396 + 0.262501i
\(211\) 3.15506e8 0.0109581 0.00547907 0.999985i \(-0.498256\pi\)
0.00547907 + 0.999985i \(0.498256\pi\)
\(212\) 9.19004e9 9.19004e9i 0.312468 0.312468i
\(213\) −4.34478e10 + 2.27829e10i −1.44630 + 0.758404i
\(214\) 1.49800e10i 0.488259i
\(215\) 9.92516e9 + 1.39968e9i 0.316785 + 0.0446740i
\(216\) −9.46440e9 1.21078e10i −0.295836 0.378462i
\(217\) 4.96247e9 + 4.96247e9i 0.151925 + 0.151925i
\(218\) −1.40352e10 1.40352e10i −0.420886 0.420886i
\(219\) 9.49380e9 + 2.96220e9i 0.278896 + 0.0870193i
\(220\) −2.20759e10 2.93246e10i −0.635355 0.843975i
\(221\) 2.61711e10i 0.738000i
\(222\) −5.31728e9 1.01402e10i −0.146927 0.280195i
\(223\) −1.62449e10 + 1.62449e10i −0.439892 + 0.439892i −0.891976 0.452083i \(-0.850681\pi\)
0.452083 + 0.891976i \(0.350681\pi\)
\(224\) 9.38932e9 0.249183
\(225\) −2.43433e10 2.97539e10i −0.633225 0.773967i
\(226\) −4.48635e10 −1.14395
\(227\) 1.08873e10 1.08873e10i 0.272146 0.272146i −0.557818 0.829964i \(-0.688361\pi\)
0.829964 + 0.557818i \(0.188361\pi\)
\(228\) −9.31153e9 1.77574e10i −0.228199 0.435184i
\(229\) 4.83302e10i 1.16134i −0.814139 0.580670i \(-0.802791\pi\)
0.814139 0.580670i \(-0.197209\pi\)
\(230\) −1.97712e10 2.62631e10i −0.465862 0.618828i
\(231\) 1.59751e10 + 4.98444e9i 0.369138 + 0.115176i
\(232\) −1.24950e10 1.24950e10i −0.283165 0.283165i
\(233\) 1.83510e10 + 1.83510e10i 0.407904 + 0.407904i 0.881007 0.473103i \(-0.156866\pi\)
−0.473103 + 0.881007i \(0.656866\pi\)
\(234\) 3.04823e10 + 2.10733e10i 0.664624 + 0.459475i
\(235\) 3.53287e10 + 4.98217e9i 0.755652 + 0.106565i
\(236\) 5.71592e10i 1.19945i
\(237\) −7.01221e10 + 3.67702e10i −1.44373 + 0.757056i
\(238\) −1.18306e10 + 1.18306e10i −0.239007 + 0.239007i
\(239\) 4.50658e10 0.893422 0.446711 0.894678i \(-0.352595\pi\)
0.446711 + 0.894678i \(0.352595\pi\)
\(240\) −2.71808e10 + 5.73570e10i −0.528825 + 1.11593i
\(241\) 4.13402e10 0.789397 0.394698 0.918811i \(-0.370849\pi\)
0.394698 + 0.918811i \(0.370849\pi\)
\(242\) −9.01606e10 + 9.01606e10i −1.68985 + 1.68985i
\(243\) 3.61174e10 4.06183e10i 0.664490 0.747297i
\(244\) 6.56093e9i 0.118498i
\(245\) 4.27132e10 3.21550e10i 0.757382 0.570166i
\(246\) 2.63990e10 8.46084e10i 0.459600 1.47301i
\(247\) −2.06948e10 2.06948e10i −0.353772 0.353772i
\(248\) 1.90661e10 + 1.90661e10i 0.320058 + 0.320058i
\(249\) 1.61523e10 5.17679e10i 0.266279 0.853421i
\(250\) −3.21052e10 + 7.18348e10i −0.519810 + 1.16307i
\(251\) 7.04408e10i 1.12019i 0.828428 + 0.560096i \(0.189236\pi\)
−0.828428 + 0.560096i \(0.810764\pi\)
\(252\) 1.63254e9 + 8.94540e9i 0.0255013 + 0.139732i
\(253\) −4.75152e10 + 4.75152e10i −0.729105 + 0.729105i
\(254\) 7.25185e10 1.09319
\(255\) −2.64121e10 7.39929e10i −0.391176 1.09587i
\(256\) 8.89366e10 1.29420
\(257\) 7.47241e10 7.47241e10i 1.06847 1.06847i 0.0709916 0.997477i \(-0.477384\pi\)
0.997477 0.0709916i \(-0.0226164\pi\)
\(258\) 2.56879e10 1.34701e10i 0.360945 0.189270i
\(259\) 4.10093e9i 0.0566283i
\(260\) 4.06525e9 2.88268e10i 0.0551706 0.391216i
\(261\) 3.55404e10 5.14087e10i 0.474067 0.685731i
\(262\) 3.59744e10 + 3.59744e10i 0.471669 + 0.471669i
\(263\) −8.97191e10 8.97191e10i −1.15634 1.15634i −0.985257 0.171079i \(-0.945275\pi\)
−0.171079 0.985257i \(-0.554725\pi\)
\(264\) 6.13770e10 + 1.91505e10i 0.777657 + 0.242640i
\(265\) −7.95250e9 + 5.63914e10i −0.0990598 + 0.702436i
\(266\) 1.87101e10i 0.229144i
\(267\) −1.49179e10 2.84490e10i −0.179642 0.342583i
\(268\) 4.95739e10 4.95739e10i 0.587011 0.587011i
\(269\) −1.26755e11 −1.47598 −0.737988 0.674814i \(-0.764224\pi\)
−0.737988 + 0.674814i \(0.764224\pi\)
\(270\) −1.07449e11 2.88172e10i −1.23046 0.330001i
\(271\) 2.28677e10 0.257550 0.128775 0.991674i \(-0.458896\pi\)
0.128775 + 0.991674i \(0.458896\pi\)
\(272\) −9.17222e10 + 9.17222e10i −1.01605 + 1.01605i
\(273\) 6.16384e9 + 1.17547e10i 0.0671614 + 0.128079i
\(274\) 1.07938e11i 1.15690i
\(275\) 1.54564e11 + 4.44789e10i 1.62971 + 0.468982i
\(276\) −3.48557e10 1.08755e10i −0.361562 0.112812i
\(277\) −6.91666e10 6.91666e10i −0.705891 0.705891i 0.259778 0.965668i \(-0.416351\pi\)
−0.965668 + 0.259778i \(0.916351\pi\)
\(278\) −1.32411e10 1.32411e10i −0.132961 0.132961i
\(279\) −5.42309e10 + 7.84442e10i −0.535831 + 0.775072i
\(280\) −9.00039e9 + 6.77560e9i −0.0875084 + 0.0658775i
\(281\) 1.08754e11i 1.04056i 0.853995 + 0.520282i \(0.174173\pi\)
−0.853995 + 0.520282i \(0.825827\pi\)
\(282\) 9.14364e10 4.79469e10i 0.860990 0.451481i
\(283\) 8.44004e10 8.44004e10i 0.782178 0.782178i −0.198020 0.980198i \(-0.563451\pi\)
0.980198 + 0.198020i \(0.0634512\pi\)
\(284\) 1.11527e11 1.01730
\(285\) 7.93952e10 + 3.76245e10i 0.712841 + 0.337807i
\(286\) −1.55038e11 −1.37023
\(287\) 2.24469e10 2.24469e10i 0.195293 0.195293i
\(288\) 2.29066e10 + 1.25515e11i 0.196198 + 1.07505i
\(289\) 4.19744e10i 0.353952i
\(290\) −1.26662e11 1.78623e10i −1.05161 0.148302i
\(291\) −4.17387e10 + 1.33772e11i −0.341209 + 1.09357i
\(292\) −1.59868e10 1.59868e10i −0.128688 0.128688i
\(293\) −3.26512e10 3.26512e10i −0.258818 0.258818i 0.565755 0.824573i \(-0.308585\pi\)
−0.824573 + 0.565755i \(0.808585\pi\)
\(294\) 4.60813e10 1.47690e11i 0.359718 1.15289i
\(295\) −1.50637e11 2.00099e11i −1.15807 1.53832i
\(296\) 1.57560e10i 0.119298i
\(297\) −2.76578e10 + 2.25713e11i −0.206260 + 1.68326i
\(298\) −1.76426e10 + 1.76426e10i −0.129595 + 0.129595i
\(299\) −5.32957e10 −0.385631
\(300\) 1.75987e10 + 8.56042e10i 0.125440 + 0.610168i
\(301\) 1.03888e10 0.0729481
\(302\) 1.80716e11 1.80716e11i 1.25016 1.25016i
\(303\) −1.38513e11 + 7.26327e10i −0.944059 + 0.495040i
\(304\) 1.45059e11i 0.974119i
\(305\) −1.72907e10 2.29681e10i −0.114410 0.151976i
\(306\) −1.87012e11 1.29287e11i −1.21934 0.842964i
\(307\) 7.53263e10 + 7.53263e10i 0.483976 + 0.483976i 0.906399 0.422423i \(-0.138820\pi\)
−0.422423 + 0.906399i \(0.638820\pi\)
\(308\) −2.69007e10 2.69007e10i −0.170328 0.170328i
\(309\) 4.70233e10 + 1.46719e10i 0.293427 + 0.0915533i
\(310\) 1.93273e11 + 2.72560e10i 1.18862 + 0.167623i
\(311\) 1.40125e11i 0.849365i −0.905342 0.424683i \(-0.860386\pi\)
0.905342 0.424683i \(-0.139614\pi\)
\(312\) 2.36818e10 + 4.51621e10i 0.141488 + 0.269822i
\(313\) −2.82281e10 + 2.82281e10i −0.166239 + 0.166239i −0.785324 0.619085i \(-0.787504\pi\)
0.619085 + 0.785324i \(0.287504\pi\)
\(314\) −4.02274e11 −2.33528
\(315\) −2.92898e10 2.70131e10i −0.167618 0.154589i
\(316\) 1.79998e11 1.01549
\(317\) 1.23329e11 1.23329e11i 0.685962 0.685962i −0.275375 0.961337i \(-0.588802\pi\)
0.961337 + 0.275375i \(0.0888020\pi\)
\(318\) 7.65325e10 + 1.45950e11i 0.419685 + 0.800355i
\(319\) 2.61474e11i 1.41374i
\(320\) 2.35708e10 1.77444e10i 0.125660 0.0945988i
\(321\) 6.95986e10 + 2.17157e10i 0.365871 + 0.114157i
\(322\) −2.40922e10 2.40922e10i −0.124889 0.124889i
\(323\) 1.26965e11 + 1.26965e11i 0.649039 + 0.649039i
\(324\) −1.15598e11 + 4.36472e10i −0.582771 + 0.220041i
\(325\) 6.17389e10 + 1.11629e11i 0.306961 + 0.555011i
\(326\) 1.08199e11i 0.530571i
\(327\) 8.55548e10 4.48627e10i 0.413790 0.216981i
\(328\) 8.62421e10 8.62421e10i 0.411422 0.411422i
\(329\) 3.69788e10 0.174009
\(330\) 4.38337e11 1.56466e11i 2.03468 0.726287i
\(331\) −1.92628e11 −0.882052 −0.441026 0.897494i \(-0.645385\pi\)
−0.441026 + 0.897494i \(0.645385\pi\)
\(332\) −8.71729e10 + 8.71729e10i −0.393786 + 0.393786i
\(333\) 5.48207e10 1.00048e10i 0.244312 0.0445872i
\(334\) 7.08556e9i 0.0311541i
\(335\) −4.28982e10 + 3.04193e11i −0.186096 + 1.31961i
\(336\) −1.95943e10 + 6.27993e10i −0.0838691 + 0.268799i
\(337\) −5.09282e10 5.09282e10i −0.215092 0.215092i 0.591335 0.806426i \(-0.298601\pi\)
−0.806426 + 0.591335i \(0.798601\pi\)
\(338\) 1.29202e11 + 1.29202e11i 0.538450 + 0.538450i
\(339\) 6.50362e10 2.08440e11i 0.267458 0.857200i
\(340\) −2.49408e10 + 1.76856e11i −0.101217 + 0.717735i
\(341\) 3.98982e11i 1.59793i
\(342\) 2.50113e11 4.56459e10i 0.988598 0.180420i
\(343\) 8.05142e10 8.05142e10i 0.314086 0.314086i
\(344\) 3.99141e10 0.153679
\(345\) 1.50682e11 5.37865e10i 0.572631 0.204403i
\(346\) 2.68883e11 1.00861
\(347\) −1.56116e9 + 1.56116e9i −0.00578048 + 0.00578048i −0.709991 0.704211i \(-0.751301\pi\)
0.704211 + 0.709991i \(0.251301\pi\)
\(348\) −1.25828e11 + 6.59810e10i −0.459908 + 0.241164i
\(349\) 2.50276e11i 0.903037i 0.892262 + 0.451518i \(0.149117\pi\)
−0.892262 + 0.451518i \(0.850883\pi\)
\(350\) −2.25527e10 + 7.83706e10i −0.0803326 + 0.279156i
\(351\) −1.42097e11 + 1.11075e11i −0.499693 + 0.390601i
\(352\) −3.77450e11 3.77450e11i −1.31044 1.31044i
\(353\) 1.25732e11 + 1.25732e11i 0.430981 + 0.430981i 0.888962 0.457981i \(-0.151427\pi\)
−0.457981 + 0.888962i \(0.651427\pi\)
\(354\) −6.91886e11 2.15878e11i −2.34164 0.730624i
\(355\) −3.90427e11 + 2.93919e11i −1.30471 + 0.982199i
\(356\) 7.30263e10i 0.240965i
\(357\) −3.78158e10 7.21161e10i −0.123216 0.234977i
\(358\) −2.46156e11 + 2.46156e11i −0.792021 + 0.792021i
\(359\) −8.80376e10 −0.279733 −0.139866 0.990170i \(-0.544667\pi\)
−0.139866 + 0.990170i \(0.544667\pi\)
\(360\) −1.12533e11 1.03786e11i −0.353117 0.325669i
\(361\) 1.21893e11 0.377744
\(362\) −2.73681e11 + 2.73681e11i −0.837638 + 0.837638i
\(363\) −2.88194e11 5.49595e11i −0.871173 1.66136i
\(364\) 3.01733e10i 0.0900879i
\(365\) 9.80972e10 + 1.38340e10i 0.289293 + 0.0407971i
\(366\) −7.94172e10 2.47793e10i −0.231339 0.0721811i
\(367\) −1.89632e11 1.89632e11i −0.545649 0.545649i 0.379530 0.925179i \(-0.376086\pi\)
−0.925179 + 0.379530i \(0.876086\pi\)
\(368\) −1.86786e11 1.86786e11i −0.530921 0.530921i
\(369\) 3.54829e11 + 2.45304e11i 0.996325 + 0.688790i
\(370\) −6.85974e10 9.11215e10i −0.190283 0.252763i
\(371\) 5.90254e10i 0.161754i
\(372\) 1.92000e11 1.00680e11i 0.519827 0.272584i
\(373\) 4.61071e11 4.61071e11i 1.23333 1.23333i 0.270648 0.962678i \(-0.412762\pi\)
0.962678 0.270648i \(-0.0872381\pi\)
\(374\) 9.51177e11 2.51385
\(375\) −2.87210e11 2.53299e11i −0.749996 0.661442i
\(376\) 1.42075e11 0.366582
\(377\) −1.46642e11 + 1.46642e11i −0.373871 + 0.373871i
\(378\) −1.14446e11 1.40237e10i −0.288328 0.0353305i
\(379\) 4.62185e10i 0.115064i 0.998344 + 0.0575320i \(0.0183231\pi\)
−0.998344 + 0.0575320i \(0.981677\pi\)
\(380\) −1.20127e11 1.59570e11i −0.295538 0.392578i
\(381\) −1.05126e11 + 3.36928e11i −0.255593 + 0.819171i
\(382\) −2.25279e11 2.25279e11i −0.541296 0.541296i
\(383\) 2.07140e11 + 2.07140e11i 0.491893 + 0.491893i 0.908902 0.417009i \(-0.136922\pi\)
−0.417009 + 0.908902i \(0.636922\pi\)
\(384\) −1.13258e11 + 3.62989e11i −0.265813 + 0.851928i
\(385\) 1.65066e11 + 2.32782e10i 0.382900 + 0.0539978i
\(386\) 6.00855e11i 1.37761i
\(387\) 2.53449e10 + 1.38875e11i 0.0574369 + 0.314721i
\(388\) 2.25261e11 2.25261e11i 0.504596 0.504596i
\(389\) −2.20485e11 −0.488209 −0.244104 0.969749i \(-0.578494\pi\)
−0.244104 + 0.969749i \(0.578494\pi\)
\(390\) 3.33582e11 + 1.58081e11i 0.730150 + 0.346010i
\(391\) 3.26975e11 0.707487
\(392\) 1.50542e11 1.50542e11i 0.322010 0.322010i
\(393\) −2.19290e11 + 1.14990e11i −0.463717 + 0.243161i
\(394\) 1.08348e11i 0.226510i
\(395\) −6.30125e11 + 4.74366e11i −1.30239 + 0.980453i
\(396\) 2.93976e11 4.25233e11i 0.600737 0.868957i
\(397\) 4.28620e11 + 4.28620e11i 0.865995 + 0.865995i 0.992026 0.126031i \(-0.0402239\pi\)
−0.126031 + 0.992026i \(0.540224\pi\)
\(398\) 1.41711e11 + 1.41711e11i 0.283093 + 0.283093i
\(399\) 8.69286e10 + 2.71229e10i 0.171706 + 0.0535746i
\(400\) −1.74850e11 + 6.07605e11i −0.341504 + 1.18673i
\(401\) 4.37345e11i 0.844645i −0.906446 0.422323i \(-0.861215\pi\)
0.906446 0.422323i \(-0.138785\pi\)
\(402\) 4.12840e11 + 7.87300e11i 0.788432 + 1.50357i
\(403\) 2.23760e11 2.23760e11i 0.422581 0.422581i
\(404\) 3.55552e11 0.664029
\(405\) 2.89651e11 4.57445e11i 0.534967 0.844873i
\(406\) −1.32578e11 −0.242162
\(407\) −1.64857e11 + 1.64857e11i −0.297806 + 0.297806i
\(408\) −1.45290e11 2.77074e11i −0.259577 0.495023i
\(409\) 3.62658e11i 0.640829i −0.947278 0.320414i \(-0.896178\pi\)
0.947278 0.320414i \(-0.103822\pi\)
\(410\) 1.23288e11 8.74239e11i 0.215473 1.52793i
\(411\) −5.01490e11 1.56472e11i −0.866911 0.270488i
\(412\) −7.91834e10 7.91834e10i −0.135393 0.135393i
\(413\) −1.83560e11 1.83560e11i −0.310457 0.310457i
\(414\) 2.63285e11 3.80838e11i 0.440478 0.637146i
\(415\) 7.54341e10 5.34905e11i 0.124839 0.885239i
\(416\) 4.23369e11i 0.693105i
\(417\) 8.07143e10 4.23245e10i 0.130719 0.0685456i
\(418\) −7.52143e11 + 7.52143e11i −1.20506 + 1.20506i
\(419\) 9.88666e10 0.156706 0.0783531 0.996926i \(-0.475034\pi\)
0.0783531 + 0.996926i \(0.475034\pi\)
\(420\) 3.04512e10 + 8.53084e10i 0.0477510 + 0.133773i
\(421\) 3.49968e11 0.542949 0.271475 0.962446i \(-0.412489\pi\)
0.271475 + 0.962446i \(0.412489\pi\)
\(422\) 6.43099e9 6.43099e9i 0.00987124 0.00987124i
\(423\) 9.02152e10 + 4.94328e11i 0.137009 + 0.750730i
\(424\) 2.26779e11i 0.340766i
\(425\) −3.78775e11 6.84855e11i −0.563159 1.01824i
\(426\) −4.21214e11 + 1.34999e12i −0.619669 + 1.98603i
\(427\) −2.10696e10 2.10696e10i −0.0306712 0.0306712i
\(428\) −1.17198e11 1.17198e11i −0.168820 0.168820i
\(429\) 2.24751e11 7.20323e11i 0.320364 1.02676i
\(430\) 2.30835e11 1.73776e11i 0.325607 0.245121i
\(431\) 3.02202e11i 0.421841i 0.977503 + 0.210921i \(0.0676462\pi\)
−0.977503 + 0.210921i \(0.932354\pi\)
\(432\) −8.87296e11 1.08725e11i −1.22572 0.150194i
\(433\) −7.76050e11 + 7.76050e11i −1.06095 + 1.06095i −0.0629306 + 0.998018i \(0.520045\pi\)
−0.998018 + 0.0629306i \(0.979955\pi\)
\(434\) 2.02301e11 0.273712
\(435\) 2.66605e11 5.62590e11i 0.356999 0.753339i
\(436\) −2.19612e11 −0.291050
\(437\) −2.58555e11 + 2.58555e11i −0.339146 + 0.339146i
\(438\) 2.53892e11 1.33134e11i 0.329621 0.172845i
\(439\) 3.93238e11i 0.505318i −0.967555 0.252659i \(-0.918695\pi\)
0.967555 0.252659i \(-0.0813050\pi\)
\(440\) 6.34194e11 + 8.94361e10i 0.806650 + 0.113756i
\(441\) 6.19380e11 + 4.28196e11i 0.779800 + 0.539100i
\(442\) 5.33447e11 + 5.33447e11i 0.664800 + 0.664800i
\(443\) 2.73298e10 + 2.73298e10i 0.0337148 + 0.0337148i 0.723763 0.690048i \(-0.242411\pi\)
−0.690048 + 0.723763i \(0.742411\pi\)
\(444\) −1.20934e11 3.77331e10i −0.147681 0.0460786i
\(445\) −1.92454e11 2.55646e11i −0.232652 0.309043i
\(446\) 6.62244e11i 0.792521i
\(447\) −5.63935e10 1.07544e11i −0.0668106 0.127410i
\(448\) 2.16224e10 2.16224e10i 0.0253603 0.0253603i
\(449\) −1.92379e11 −0.223382 −0.111691 0.993743i \(-0.535627\pi\)
−0.111691 + 0.993743i \(0.535627\pi\)
\(450\) −1.10267e12 1.10285e11i −1.26762 0.126782i
\(451\) −1.80473e12 −2.05408
\(452\) −3.50996e11 + 3.50996e11i −0.395529 + 0.395529i
\(453\) 5.77649e11 + 1.10160e12i 0.644499 + 1.22908i
\(454\) 4.43832e11i 0.490306i
\(455\) 7.95188e10 + 1.05629e11i 0.0869798 + 0.115540i
\(456\) 3.33984e11 + 1.04208e11i 0.361730 + 0.112865i
\(457\) 6.72795e11 + 6.72795e11i 0.721539 + 0.721539i 0.968919 0.247380i \(-0.0795696\pi\)
−0.247380 + 0.968919i \(0.579570\pi\)
\(458\) −9.85119e11 9.85119e11i −1.04615 1.04615i
\(459\) 8.71781e11 6.81455e11i 0.916749 0.716605i
\(460\) −3.60155e11 5.07903e10i −0.375042 0.0528896i
\(461\) 2.96575e11i 0.305830i −0.988239 0.152915i \(-0.951134\pi\)
0.988239 0.152915i \(-0.0488661\pi\)
\(462\) 4.27219e11 2.24022e11i 0.436276 0.228772i
\(463\) 2.47116e11 2.47116e11i 0.249911 0.249911i −0.571023 0.820934i \(-0.693453\pi\)
0.820934 + 0.571023i \(0.193453\pi\)
\(464\) −1.02788e12 −1.02946
\(465\) −4.06811e11 + 8.58453e11i −0.403510 + 0.851487i
\(466\) 7.48100e11 0.734891
\(467\) 9.82524e11 9.82524e11i 0.955911 0.955911i −0.0431575 0.999068i \(-0.513742\pi\)
0.999068 + 0.0431575i \(0.0137417\pi\)
\(468\) 4.03352e11 7.36121e10i 0.388668 0.0709321i
\(469\) 3.18401e11i 0.303876i
\(470\) 8.21659e11 6.18555e11i 0.776696 0.584707i
\(471\) 5.83155e11 1.86900e12i 0.545997 1.74991i
\(472\) −7.05246e11 7.05246e11i −0.654036 0.654036i
\(473\) −4.17627e11 4.17627e11i −0.383631 0.383631i
\(474\) −6.79814e11 + 2.17879e12i −0.618568 + 1.98250i
\(475\) 8.41064e11 + 2.42033e11i 0.758068 + 0.218149i
\(476\) 1.85116e11i 0.165277i
\(477\) −7.89043e11 + 1.44001e11i −0.697860 + 0.127360i
\(478\) 9.18579e11 9.18579e11i 0.804806 0.804806i
\(479\) −5.76293e10 −0.0500188 −0.0250094 0.999687i \(-0.507962\pi\)
−0.0250094 + 0.999687i \(0.507962\pi\)
\(480\) 4.27268e11 + 1.19698e12i 0.367380 + 1.02921i
\(481\) −1.84913e11 −0.157512
\(482\) 8.42639e11 8.42639e11i 0.711099 0.711099i
\(483\) 1.46860e11 7.70095e10i 0.122784 0.0643846i
\(484\) 1.41077e12i 1.16856i
\(485\) −1.94927e11 + 1.38223e12i −0.159969 + 1.13434i
\(486\) −9.17405e10 1.56411e12i −0.0745929 1.27176i
\(487\) −2.33381e11 2.33381e11i −0.188012 0.188012i 0.606824 0.794836i \(-0.292443\pi\)
−0.794836 + 0.606824i \(0.792443\pi\)
\(488\) −8.09506e10 8.09506e10i −0.0646146 0.0646146i
\(489\) 5.02702e11 + 1.56850e11i 0.397576 + 0.124049i
\(490\) 2.15208e11 1.52605e12i 0.168646 1.19587i
\(491\) 1.81080e11i 0.140606i 0.997526 + 0.0703031i \(0.0223966\pi\)
−0.997526 + 0.0703031i \(0.977603\pi\)
\(492\) −4.55409e11 8.68482e11i −0.350396 0.668217i
\(493\) 8.99663e11 8.99663e11i 0.685913 0.685913i
\(494\) −8.43645e11 −0.637366
\(495\) 9.15236e10 + 2.26338e12i 0.0685188 + 1.69447i
\(496\) 1.56843e12 1.16358
\(497\) −3.58155e11 + 3.58155e11i −0.263310 + 0.263310i
\(498\) −7.25955e11 1.38442e12i −0.528905 1.00864i
\(499\) 1.03433e12i 0.746808i 0.927669 + 0.373404i \(0.121809\pi\)
−0.927669 + 0.373404i \(0.878191\pi\)
\(500\) 3.10830e11 + 8.13189e11i 0.222412 + 0.581870i
\(501\) −3.29202e10 1.02715e10i −0.0233449 0.00728394i
\(502\) 1.43580e12 + 1.43580e12i 1.00908 + 1.00908i
\(503\) 1.98943e12 + 1.98943e12i 1.38571 + 1.38571i 0.834098 + 0.551617i \(0.185989\pi\)
0.551617 + 0.834098i \(0.314011\pi\)
\(504\) −1.30514e11 9.02281e10i −0.0900987 0.0622880i
\(505\) −1.24470e12 + 9.37023e11i −0.851632 + 0.641120i
\(506\) 1.93701e12i 1.31357i
\(507\) −7.87584e11 + 4.12989e11i −0.529372 + 0.277589i
\(508\) 5.67359e11 5.67359e11i 0.377982 0.377982i
\(509\) −2.16622e10 −0.0143045 −0.00715224 0.999974i \(-0.502277\pi\)
−0.00715224 + 0.999974i \(0.502277\pi\)
\(510\) −2.04656e12 9.69844e11i −1.33955 0.634799i
\(511\) 1.02679e11 0.0666175
\(512\) 8.31559e11 8.31559e11i 0.534784 0.534784i
\(513\) −1.50501e11 + 1.22822e12i −0.0959424 + 0.782975i
\(514\) 3.04621e12i 1.92498i
\(515\) 4.85881e11 + 6.85205e10i 0.304367 + 0.0429228i
\(516\) 9.55880e10 3.06358e11i 0.0593581 0.190242i
\(517\) −1.48655e12 1.48655e12i −0.915105 0.915105i
\(518\) −8.35896e10 8.35896e10i −0.0510115 0.0510115i
\(519\) −3.89785e11 + 1.24926e12i −0.235816 + 0.755786i
\(520\) 3.05515e11 + 4.05832e11i 0.183239 + 0.243406i
\(521\) 2.17277e12i 1.29194i −0.763361 0.645972i \(-0.776452\pi\)
0.763361 0.645972i \(-0.223548\pi\)
\(522\) −3.23444e11 1.77229e12i −0.190670 1.04476i
\(523\) −1.78674e12 + 1.78674e12i −1.04425 + 1.04425i −0.0452735 + 0.998975i \(0.514416\pi\)
−0.998975 + 0.0452735i \(0.985584\pi\)
\(524\) 5.62901e11 0.326168
\(525\) −3.31424e11 2.18391e11i −0.190400 0.125464i
\(526\) −3.65750e12 −2.08329
\(527\) −1.37279e12 + 1.37279e12i −0.775277 + 0.775277i
\(528\) 3.31222e12 1.73684e12i 1.85467 0.972539i
\(529\) 1.13529e12i 0.630313i
\(530\) 9.87334e11 + 1.31153e12i 0.543529 + 0.721998i
\(531\) 2.00598e12 2.90162e12i 1.09497 1.58385i
\(532\) −1.46381e11 1.46381e11i −0.0792285 0.0792285i
\(533\) −1.01214e12 1.01214e12i −0.543211 0.543211i
\(534\) −8.83951e11 2.75805e11i −0.470427 0.146780i
\(535\) 7.19145e11 + 1.01416e11i 0.379511 + 0.0535199i
\(536\) 1.22331e12i 0.640171i
\(537\) −7.86825e11 1.50050e12i −0.408313 0.778668i
\(538\) −2.58365e12 + 2.58365e12i −1.32958 + 1.32958i
\(539\) −3.15028e12 −1.60768
\(540\) −1.06610e12 + 6.15189e11i −0.539543 + 0.311341i
\(541\) −1.30087e12 −0.652897 −0.326449 0.945215i \(-0.605852\pi\)
−0.326449 + 0.945215i \(0.605852\pi\)
\(542\) 4.66114e11 4.66114e11i 0.232004 0.232004i
\(543\) −8.74807e11 1.66829e12i −0.431830 0.823516i
\(544\) 2.59741e12i 1.27159i
\(545\) 7.68806e11 5.78767e11i 0.373278 0.281009i
\(546\) 3.65234e11 + 1.13958e11i 0.175875 + 0.0548755i
\(547\) 9.16679e11 + 9.16679e11i 0.437798 + 0.437798i 0.891270 0.453472i \(-0.149815\pi\)
−0.453472 + 0.891270i \(0.649815\pi\)
\(548\) 8.44468e11 + 8.44468e11i 0.400010 + 0.400010i
\(549\) 2.30253e11 3.33058e11i 0.108176 0.156475i
\(550\) 4.05711e12 2.24388e12i 1.89053 1.04560i
\(551\) 1.42282e12i 0.657607i
\(552\) 5.64243e11 2.95875e11i 0.258667 0.135638i
\(553\) −5.78041e11 + 5.78041e11i −0.262842 + 0.262842i
\(554\) −2.81966e12 −1.27175
\(555\) 5.22801e11 1.86616e11i 0.233893 0.0834892i
\(556\) −2.07187e11 −0.0919446
\(557\) 1.35194e12 1.35194e12i 0.595125 0.595125i −0.343886 0.939011i \(-0.611743\pi\)
0.939011 + 0.343886i \(0.111743\pi\)
\(558\) 4.93542e11 + 2.70433e12i 0.215511 + 1.18088i
\(559\) 4.68434e11i 0.202906i
\(560\) −9.15086e10 + 6.48890e11i −0.0393202 + 0.278821i
\(561\) −1.37887e12 + 4.41926e12i −0.587747 + 1.88372i
\(562\) 2.21675e12 + 2.21675e12i 0.937353 + 0.937353i
\(563\) 8.58856e11 + 8.58856e11i 0.360274 + 0.360274i 0.863914 0.503640i \(-0.168006\pi\)
−0.503640 + 0.863914i \(0.668006\pi\)
\(564\) 3.40246e11 1.09048e12i 0.141592 0.453799i
\(565\) 3.03730e11 2.15376e12i 0.125392 0.889159i
\(566\) 3.44068e12i 1.40919i
\(567\) 2.31061e11 5.11397e11i 0.0938866 0.207795i
\(568\) −1.37605e12 + 1.37605e12i −0.554712 + 0.554712i
\(569\) 4.55908e12 1.82336 0.911679 0.410903i \(-0.134787\pi\)
0.911679 + 0.410903i \(0.134787\pi\)
\(570\) 2.38522e12 8.51415e11i 0.946438 0.337835i
\(571\) 4.00706e12 1.57748 0.788738 0.614729i \(-0.210735\pi\)
0.788738 + 0.614729i \(0.210735\pi\)
\(572\) −1.21296e12 + 1.21296e12i −0.473768 + 0.473768i
\(573\) 1.37324e12 7.20091e11i 0.532170 0.279056i
\(574\) 9.15073e11i 0.351846i
\(575\) 1.39466e12 7.71350e11i 0.532064 0.294270i
\(576\) 3.41797e11 + 2.36295e11i 0.129380 + 0.0894444i
\(577\) 1.96117e12 + 1.96117e12i 0.736588 + 0.736588i 0.971916 0.235328i \(-0.0756164\pi\)
−0.235328 + 0.971916i \(0.575616\pi\)
\(578\) −8.55567e11 8.55567e11i −0.318844 0.318844i
\(579\) −2.79163e12 8.71026e11i −1.03230 0.322090i
\(580\) −1.13071e12 + 8.51210e11i −0.414881 + 0.312328i
\(581\) 5.59890e11i 0.203850i
\(582\) 1.87592e12 + 3.57745e12i 0.677737 + 1.29247i
\(583\) 2.37282e12 2.37282e12i 0.850659 0.850659i
\(584\) 3.94499e11 0.140342
\(585\) −1.21804e12 + 1.32069e12i −0.429990 + 0.466230i
\(586\) −1.33106e12 −0.466294
\(587\) 1.22469e12 1.22469e12i 0.425749 0.425749i −0.461428 0.887177i \(-0.652663\pi\)
0.887177 + 0.461428i \(0.152663\pi\)
\(588\) −7.94949e11 1.51600e12i −0.274247 0.522998i
\(589\) 2.17107e12i 0.743284i
\(590\) −7.14910e12 1.00819e12i −2.42894 0.342537i
\(591\) 5.03395e11 + 1.57066e11i 0.169733 + 0.0529589i
\(592\) −6.48068e11 6.48068e11i −0.216857 0.216857i
\(593\) −3.60622e11 3.60622e11i −0.119759 0.119759i 0.644688 0.764446i \(-0.276987\pi\)
−0.764446 + 0.644688i \(0.776987\pi\)
\(594\) 4.03696e12 + 5.16447e12i 1.33050 + 1.70211i
\(595\) −4.87856e11 6.48044e11i −0.159575 0.211972i
\(596\) 2.76058e11i 0.0896173i
\(597\) −8.63831e11 + 4.52970e11i −0.278320 + 0.145944i
\(598\) −1.08633e12 + 1.08633e12i −0.347381 + 0.347381i
\(599\) 3.56745e12 1.13224 0.566118 0.824324i \(-0.308445\pi\)
0.566118 + 0.824324i \(0.308445\pi\)
\(600\) −1.27335e12 8.39071e11i −0.401112 0.264313i
\(601\) −5.62010e12 −1.75715 −0.878575 0.477604i \(-0.841505\pi\)
−0.878575 + 0.477604i \(0.841505\pi\)
\(602\) 2.11755e11 2.11755e11i 0.0657126 0.0657126i
\(603\) −4.25634e12 + 7.76785e11i −1.31102 + 0.239262i
\(604\) 2.82771e12i 0.864508i
\(605\) −3.71794e12 4.93873e12i −1.12824 1.49871i
\(606\) −1.34285e12 + 4.30380e12i −0.404482 + 1.29636i
\(607\) 2.36872e12 + 2.36872e12i 0.708214 + 0.708214i 0.966160 0.257945i \(-0.0830454\pi\)
−0.257945 + 0.966160i \(0.583045\pi\)
\(608\) −2.05390e12 2.05390e12i −0.609556 0.609556i
\(609\) 1.92192e11 6.15971e11i 0.0566183 0.181461i
\(610\) −8.20598e11 1.15723e11i −0.239964 0.0338405i
\(611\) 1.66739e12i 0.484008i
\(612\) −2.47461e12 + 4.51618e11i −0.713059 + 0.130134i
\(613\) 3.72266e12 3.72266e12i 1.06483 1.06483i 0.0670840 0.997747i \(-0.478630\pi\)
0.997747 0.0670840i \(-0.0213696\pi\)
\(614\) 3.07076e12 0.871944
\(615\) 3.88307e12 + 1.84014e12i 1.09455 + 0.518697i
\(616\) 6.63816e11 0.185752
\(617\) −4.38107e12 + 4.38107e12i −1.21702 + 1.21702i −0.248346 + 0.968671i \(0.579887\pi\)
−0.968671 + 0.248346i \(0.920113\pi\)
\(618\) 1.25754e12 6.59421e11i 0.346795 0.181850i
\(619\) 1.48562e12i 0.406724i 0.979104 + 0.203362i \(0.0651868\pi\)
−0.979104 + 0.203362i \(0.934813\pi\)
\(620\) 1.72534e12 1.29886e12i 0.468934 0.353020i
\(621\) 1.38774e12 + 1.77533e12i 0.374451 + 0.479034i
\(622\) −2.85618e12 2.85618e12i −0.765120 0.765120i
\(623\) −2.34515e11 2.34515e11i −0.0623698 0.0623698i
\(624\) 2.83165e12 + 8.83515e11i 0.747669 + 0.233283i
\(625\) −3.23122e12 2.02760e12i −0.847044 0.531523i
\(626\) 1.15075e12i 0.299500i
\(627\) −2.40418e12 4.58487e12i −0.621246 1.18474i
\(628\) −3.14725e12 + 3.14725e12i −0.807444 + 0.807444i
\(629\) 1.13446e12 0.288976
\(630\) −1.14763e12 + 4.64063e10i −0.290247 + 0.0117367i
\(631\) 2.44337e12 0.613560 0.306780 0.951781i \(-0.400748\pi\)
0.306780 + 0.951781i \(0.400748\pi\)
\(632\) −2.22086e12 + 2.22086e12i −0.553726 + 0.553726i
\(633\) 2.05563e10 + 3.92016e10i 0.00508895 + 0.00970481i
\(634\) 5.02767e12i 1.23585i
\(635\) −4.90958e11 + 3.48139e12i −0.119829 + 0.849711i
\(636\) 1.74062e12 + 5.43099e11i 0.421840 + 0.131620i
\(637\) −1.76676e12 1.76676e12i −0.425159 0.425159i
\(638\) 5.32964e12 + 5.32964e12i 1.27352 + 1.27352i
\(639\) −5.66154e12 3.91400e12i −1.34332 0.928682i
\(640\) −5.28933e11 + 3.75068e12i −0.124621 + 0.883690i
\(641\) 2.32307e12i 0.543503i 0.962367 + 0.271752i \(0.0876029\pi\)
−0.962367 + 0.271752i \(0.912397\pi\)
\(642\) 1.86127e12 9.76000e11i 0.432415 0.226747i
\(643\) 1.90280e12 1.90280e12i 0.438980 0.438980i −0.452689 0.891669i \(-0.649535\pi\)
0.891669 + 0.452689i \(0.149535\pi\)
\(644\) −3.76978e11 −0.0863633
\(645\) 4.72748e11 + 1.32439e12i 0.107550 + 0.301299i
\(646\) 5.17585e12 1.16933
\(647\) 1.99698e12 1.99698e12i 0.448026 0.448026i −0.446672 0.894698i \(-0.647391\pi\)
0.894698 + 0.446672i \(0.147391\pi\)
\(648\) 8.87750e11 1.96481e12i 0.197789 0.437758i
\(649\) 1.47582e13i 3.26536i
\(650\) 3.53377e12 + 1.01691e12i 0.776476 + 0.223446i
\(651\) −2.93264e11 + 9.39907e11i −0.0639948 + 0.205102i
\(652\) −8.46508e11 8.46508e11i −0.183450 0.183450i
\(653\) −5.98379e12 5.98379e12i −1.28786 1.28786i −0.936087 0.351769i \(-0.885580\pi\)
−0.351769 0.936087i \(-0.614420\pi\)
\(654\) 8.29430e11 2.65831e12i 0.177288 0.568206i
\(655\) −1.97057e12 + 1.48347e12i −0.418317 + 0.314915i
\(656\) 7.09454e12i 1.49574i
\(657\) 2.50501e11 + 1.37260e12i 0.0524523 + 0.287409i
\(658\) 7.53742e11 7.53742e11i 0.156750 0.156750i
\(659\) 3.54936e12 0.733103 0.366552 0.930398i \(-0.380538\pi\)
0.366552 + 0.930398i \(0.380538\pi\)
\(660\) 2.20525e12 4.65353e12i 0.452388 0.954629i
\(661\) 7.97007e11 0.162389 0.0811943 0.996698i \(-0.474127\pi\)
0.0811943 + 0.996698i \(0.474127\pi\)
\(662\) −3.92636e12 + 3.92636e12i −0.794564 + 0.794564i
\(663\) −3.25175e12 + 1.70513e12i −0.653592 + 0.342726i
\(664\) 2.15113e12i 0.429447i
\(665\) 8.98213e11 + 1.26669e11i 0.178107 + 0.0251173i
\(666\) 9.13485e11 1.32134e12i 0.179915 0.260245i
\(667\) 1.83211e12 + 1.83211e12i 0.358413 + 0.358413i
\(668\) 5.54348e10 + 5.54348e10i 0.0107718 + 0.0107718i
\(669\) −3.07685e12 9.60019e11i −0.593866 0.185294i
\(670\) 5.32598e12 + 7.07478e12i 1.02109 + 1.35636i
\(671\) 1.69399e12i 0.322597i
\(672\) 6.11746e11 + 1.16662e12i 0.115720 + 0.220683i
\(673\) −1.71719e11 + 1.71719e11i −0.0322663 + 0.0322663i −0.723056 0.690790i \(-0.757263\pi\)
0.690790 + 0.723056i \(0.257263\pi\)
\(674\) −2.07615e12 −0.387515
\(675\) 2.11087e12 4.96322e12i 0.391376 0.920231i
\(676\) 2.02167e12 0.372348
\(677\) 3.13073e11 3.13073e11i 0.0572792 0.0572792i −0.677887 0.735166i \(-0.737104\pi\)
0.735166 + 0.677887i \(0.237104\pi\)
\(678\) −2.92301e12 5.57428e12i −0.531247 1.01311i
\(679\) 1.44680e12i 0.261212i
\(680\) −1.87437e12 2.48982e12i −0.336175 0.446558i
\(681\) 2.06208e12 + 6.43398e11i 0.367404 + 0.114635i
\(682\) −8.13247e12 8.13247e12i −1.43944 1.43944i
\(683\) 6.65471e12 + 6.65471e12i 1.17014 + 1.17014i 0.982177 + 0.187958i \(0.0601869\pi\)
0.187958 + 0.982177i \(0.439813\pi\)
\(684\) 1.59968e12 2.31391e12i 0.279435 0.404198i
\(685\) −5.18178e12 7.30752e11i −0.899231 0.126813i
\(686\) 3.28225e12i 0.565866i
\(687\) 6.00503e12 3.14888e12i 1.02851 0.539325i
\(688\) 1.64173e12 1.64173e12i 0.279353 0.279353i
\(689\) 2.66148e12 0.449922
\(690\) 1.97502e12 4.16769e12i 0.331705 0.699963i
\(691\) −3.74698e12 −0.625216 −0.312608 0.949882i \(-0.601203\pi\)
−0.312608 + 0.949882i \(0.601203\pi\)
\(692\) 2.10365e12 2.10365e12i 0.348735 0.348735i
\(693\) 4.21513e11 + 2.30965e12i 0.0694243 + 0.380406i
\(694\) 6.36423e10i 0.0104143i
\(695\) 7.25309e11 5.46022e11i 0.117921 0.0887725i
\(696\) 7.38410e11 2.36659e12i 0.119277 0.382281i
\(697\) 6.20959e12 + 6.20959e12i 0.996588 + 0.996588i
\(698\) 5.10140e12 + 5.10140e12i 0.813467 + 0.813467i
\(699\) −1.08448e12 + 3.47574e12i −0.171820 + 0.550681i
\(700\) 4.36699e11 + 7.89587e11i 0.0687450 + 0.124296i
\(701\) 9.55991e12i 1.49528i 0.664104 + 0.747640i \(0.268813\pi\)
−0.664104 + 0.747640i \(0.731187\pi\)
\(702\) −6.32335e11 + 5.16042e12i −0.0982722 + 0.801988i
\(703\) −8.97074e11 + 8.97074e11i −0.138525 + 0.138525i
\(704\) −1.73844e12 −0.266737
\(705\) 1.68275e12 + 4.71419e12i 0.256548 + 0.718714i
\(706\) 5.12559e12 0.776467
\(707\) −1.14181e12 + 1.14181e12i −0.171873 + 0.171873i
\(708\) −7.10202e12 + 3.72412e12i −1.06226 + 0.557023i
\(709\) 1.13119e13i 1.68124i −0.541629 0.840618i \(-0.682192\pi\)
0.541629 0.840618i \(-0.317808\pi\)
\(710\) −1.96714e12 + 1.39491e13i −0.290518 + 2.06007i
\(711\) −9.13738e12 6.31695e12i −1.34094 0.927032i
\(712\) −9.01019e11 9.01019e11i −0.131393 0.131393i
\(713\) −2.79560e12 2.79560e12i −0.405109 0.405109i
\(714\) −2.24075e12 6.99146e11i −0.322665 0.100676i
\(715\) 1.04963e12 7.44292e12i 0.150196 1.06504i
\(716\) 3.85167e12i 0.547697i
\(717\) 2.93619e12 + 5.59942e12i 0.414904 + 0.791237i
\(718\) −1.79448e12 + 1.79448e12i −0.251987 + 0.251987i
\(719\) −1.17904e13 −1.64531 −0.822654 0.568543i \(-0.807507\pi\)
−0.822654 + 0.568543i \(0.807507\pi\)
\(720\) −8.89752e12 + 3.59787e11i −1.23388 + 0.0498941i
\(721\) 5.08575e11 0.0700885
\(722\) 2.48456e12 2.48456e12i 0.340277 0.340277i
\(723\) 2.69345e12 + 5.13651e12i 0.366595 + 0.699110i
\(724\) 4.28236e12i 0.579242i
\(725\) 1.71503e12 5.95973e12i 0.230542 0.801135i
\(726\) −1.70767e13 5.32817e12i −2.28134 0.711809i
\(727\) −6.72393e12 6.72393e12i −0.892726 0.892726i 0.102053 0.994779i \(-0.467459\pi\)
−0.994779 + 0.102053i \(0.967459\pi\)
\(728\) 3.72287e11 + 3.72287e11i 0.0491231 + 0.0491231i
\(729\) 7.39999e12 + 1.84117e12i 0.970414 + 0.241446i
\(730\) 2.28150e12 1.71754e12i 0.297350 0.223849i
\(731\) 2.87389e12i 0.372256i
\(732\) −8.15195e11 + 4.27467e11i −0.104945 + 0.0550304i
\(733\) 2.05455e12 2.05455e12i 0.262875 0.262875i −0.563346 0.826221i \(-0.690486\pi\)
0.826221 + 0.563346i \(0.190486\pi\)
\(734\) −7.73056e12 −0.983057
\(735\) 6.77817e12 + 3.21210e12i 0.856682 + 0.405972i
\(736\) −5.28947e12 −0.664449
\(737\) 1.27997e13 1.27997e13i 1.59807 1.59807i
\(738\) 1.22326e13 2.23245e12i 1.51797 0.277031i
\(739\) 2.38731e12i 0.294448i 0.989103 + 0.147224i \(0.0470339\pi\)
−0.989103 + 0.147224i \(0.952966\pi\)
\(740\) −1.24958e12 1.76220e11i −0.153187 0.0216030i
\(741\) 1.22299e12 3.91965e12i 0.149018 0.477602i
\(742\) 1.20312e12 + 1.20312e12i 0.145711 + 0.145711i
\(743\) −5.20539e12 5.20539e12i −0.626619 0.626619i 0.320596 0.947216i \(-0.396117\pi\)
−0.947216 + 0.320596i \(0.896117\pi\)
\(744\) −1.12674e12 + 3.61117e12i −0.134817 + 0.432086i
\(745\) −7.27524e11 9.66407e11i −0.0865255 0.114936i
\(746\) 1.87961e13i 2.22199i
\(747\) 7.48453e12 1.36593e12i 0.879472 0.160504i
\(748\) 7.44167e12 7.44167e12i 0.869186 0.869186i
\(749\) 7.52736e11 0.0873925
\(750\) −1.10172e13 + 6.91221e11i −1.27144 + 0.0797703i
\(751\) −1.52194e13 −1.74589 −0.872946 0.487817i \(-0.837793\pi\)
−0.872946 + 0.487817i \(0.837793\pi\)
\(752\) 5.84374e12 5.84374e12i 0.666363 0.666363i
\(753\) −8.75226e12 + 4.58946e12i −0.992071 + 0.520216i
\(754\) 5.97802e12i 0.673576i
\(755\) 7.45216e12 + 9.89909e12i 0.834681 + 1.10875i
\(756\) −1.00510e12 + 7.85667e11i −0.111908 + 0.0874763i
\(757\) −2.62754e10 2.62754e10i −0.00290816 0.00290816i 0.705651 0.708559i \(-0.250655\pi\)
−0.708559 + 0.705651i \(0.750655\pi\)
\(758\) 9.42075e11 + 9.42075e11i 0.103651 + 0.103651i
\(759\) −8.99953e12 2.80798e12i −0.984310 0.307119i
\(760\) 3.45098e12 + 4.86669e11i 0.375216 + 0.0529142i
\(761\) 9.67608e12i 1.04585i 0.852379 + 0.522924i \(0.175159\pi\)
−0.852379 + 0.522924i \(0.824841\pi\)
\(762\) 4.72483e12 + 9.01042e12i 0.507678 + 0.968161i
\(763\) 7.05258e11 7.05258e11i 0.0753335 0.0753335i
\(764\) −3.52499e12 −0.374316
\(765\) 7.47277e12 8.10259e12i 0.788870 0.855357i
\(766\) 8.44432e12 0.886207
\(767\) −8.27680e12 + 8.27680e12i −0.863541 + 0.863541i
\(768\) 5.79452e12 + 1.10504e13i 0.601024 + 1.14617i
\(769\) 8.66863e12i 0.893886i 0.894562 + 0.446943i \(0.147487\pi\)
−0.894562 + 0.446943i \(0.852513\pi\)
\(770\) 3.83904e12 2.89008e12i 0.393563 0.296279i
\(771\) 1.41530e13 + 4.41593e12i 1.44246 + 0.450067i
\(772\) 4.70087e12 + 4.70087e12i 0.476322 + 0.476322i
\(773\) −8.83371e12 8.83371e12i −0.889888 0.889888i 0.104624 0.994512i \(-0.466636\pi\)
−0.994512 + 0.104624i \(0.966636\pi\)
\(774\) 3.34731e12 + 2.31410e12i 0.335245 + 0.231765i
\(775\) −2.61696e12 + 9.09393e12i −0.260579 + 0.905511i
\(776\) 5.55867e12i 0.550292i
\(777\) 5.09540e11 2.67190e11i 0.0501515 0.0262981i
\(778\) −4.49416e12 + 4.49416e12i −0.439785 + 0.439785i
\(779\) −9.82046e12 −0.955462
\(780\) 3.84660e12 1.37306e12i 0.372092 0.132820i
\(781\) 2.87956e13 2.76947
\(782\) 6.66475e12 6.66475e12i 0.637314 0.637314i
\(783\) 8.70310e12 + 1.06644e12i 0.827458 + 0.101393i
\(784\) 1.23840e13i 1.17068i
\(785\) 2.72344e12 1.93120e13i 0.255979 1.81515i
\(786\) −2.12596e12 + 6.81366e12i −0.198680 + 0.636765i
\(787\) −1.07137e13 1.07137e13i −0.995525 0.995525i 0.00446477 0.999990i \(-0.498579\pi\)
−0.999990 + 0.00446477i \(0.998579\pi\)
\(788\) −8.47676e11 8.47676e11i −0.0783180 0.0783180i
\(789\) 5.30208e12 1.69931e13i 0.487080 1.56108i
\(790\) −3.17485e12 + 2.25129e13i −0.290002 + 2.05641i
\(791\) 2.25436e12i 0.204752i
\(792\) 1.61948e12 + 8.87380e12i 0.146255 + 0.801395i
\(793\) −9.50040e11 + 9.50040e11i −0.0853124 + 0.0853124i
\(794\) 1.74732e13 1.56020
\(795\) −7.52476e12 + 2.68599e12i −0.668098 + 0.238481i
\(796\) 2.21738e12 0.195764
\(797\) −1.12446e13 + 1.12446e13i −0.987147 + 0.987147i −0.999918 0.0127714i \(-0.995935\pi\)
0.0127714 + 0.999918i \(0.495935\pi\)
\(798\) 2.32472e12 1.21902e12i 0.202935 0.106414i
\(799\) 1.02296e13i 0.887973i
\(800\) 6.12743e12 + 1.10789e13i 0.528900 + 0.956294i
\(801\) 2.56283e12 3.70710e12i 0.219975 0.318191i
\(802\) −8.91443e12 8.91443e12i −0.760868 0.760868i
\(803\) −4.12769e12 4.12769e12i −0.350338 0.350338i
\(804\) 9.38946e12 + 2.92964e12i 0.792480 + 0.247265i
\(805\) 1.31970e12 9.93487e11i 0.110763 0.0833837i
\(806\) 9.12183e12i 0.761333i
\(807\) −8.25851e12 1.57493e13i −0.685442 1.30716i
\(808\) −4.38690e12 + 4.38690e12i −0.362082 + 0.362082i
\(809\) −1.50241e13 −1.23316 −0.616582 0.787290i \(-0.711483\pi\)
−0.616582 + 0.787290i \(0.711483\pi\)
\(810\) −3.42016e12 1.52281e13i −0.279167 1.24298i
\(811\) −4.11791e12 −0.334259 −0.167129 0.985935i \(-0.553450\pi\)
−0.167129 + 0.985935i \(0.553450\pi\)
\(812\) −1.03724e12 + 1.03724e12i −0.0837296 + 0.0837296i
\(813\) 1.48991e12 + 2.84131e12i 0.119606 + 0.228093i
\(814\) 6.72059e12i 0.536535i
\(815\) 5.19429e12 + 7.32517e11i 0.412399 + 0.0581578i
\(816\) −1.73725e13 5.42046e12i −1.37169 0.427987i
\(817\) −2.27253e12 2.27253e12i −0.178447 0.178447i
\(818\) −7.39208e12 7.39208e12i −0.577267 0.577267i
\(819\) −1.05892e12 + 1.53171e12i −0.0822405 + 0.118960i
\(820\) −5.87516e12 7.80429e12i −0.453793 0.602797i
\(821\) 2.90851e11i 0.0223422i 0.999938 + 0.0111711i \(0.00355594\pi\)
−0.999938 + 0.0111711i \(0.996444\pi\)
\(822\) −1.34113e13 + 7.03254e12i −1.02458 + 0.537265i
\(823\) 5.85316e12 5.85316e12i 0.444724 0.444724i −0.448872 0.893596i \(-0.648174\pi\)
0.893596 + 0.448872i \(0.148174\pi\)
\(824\) 1.95397e12 0.147654
\(825\) 4.54389e12 + 2.21025e13i 0.341495 + 1.66111i
\(826\) −7.48302e12 −0.559328
\(827\) −2.49386e11 + 2.49386e11i −0.0185394 + 0.0185394i −0.716316 0.697776i \(-0.754173\pi\)
0.697776 + 0.716316i \(0.254173\pi\)
\(828\) −9.19692e11 5.03938e12i −0.0679995 0.372598i
\(829\) 6.93314e12i 0.509841i −0.966962 0.254920i \(-0.917951\pi\)
0.966962 0.254920i \(-0.0820493\pi\)
\(830\) −9.36543e12 1.24406e13i −0.684978 0.909892i
\(831\) 4.08750e12 1.31004e13i 0.297340 0.952970i
\(832\) −9.74967e11 9.74967e11i −0.0705399 0.0705399i
\(833\) 1.08393e13 + 1.08393e13i 0.780006 + 0.780006i
\(834\) 7.82503e11 2.50791e12i 0.0560065 0.179500i
\(835\) −3.40156e11 4.79699e10i −0.0242153 0.00341492i
\(836\) 1.17690e13i 0.833318i
\(837\) −1.32800e13 1.62727e12i −0.935263 0.114603i
\(838\) 2.01520e12 2.01520e12i 0.141163 0.141163i
\(839\) 4.80824e12 0.335009 0.167505 0.985871i \(-0.446429\pi\)
0.167505 + 0.985871i \(0.446429\pi\)
\(840\) −1.42827e12 6.76843e11i −0.0989816 0.0469063i
\(841\) −4.42515e12 −0.305033
\(842\) 7.13343e12 7.13343e12i 0.489096 0.489096i
\(843\) −1.35127e13 + 7.08572e12i −0.921550 + 0.483237i
\(844\) 1.00627e11i 0.00682614i
\(845\) −7.07733e12 + 5.32790e12i −0.477545 + 0.359502i
\(846\) 1.19148e13 + 8.23706e12i 0.799686 + 0.552848i
\(847\) −4.53051e12 4.53051e12i −0.302462 0.302462i
\(848\) 9.32775e12 + 9.32775e12i 0.619434 + 0.619434i
\(849\) 1.59857e13 + 4.98776e12i 1.05596 + 0.329474i
\(850\) −2.16800e13 6.23886e12i −1.42454 0.409940i
\(851\) 2.31026e12i 0.151000i
\(852\) 7.26637e12 + 1.38572e13i 0.472432 + 0.900944i
\(853\) 1.15224e13 1.15224e13i 0.745201 0.745201i −0.228373 0.973574i \(-0.573340\pi\)
0.973574 + 0.228373i \(0.0733405\pi\)
\(854\) −8.58927e11 −0.0552581
\(855\) 4.98028e11 + 1.23162e13i 0.0318718 + 0.788188i
\(856\) 2.89205e12 0.184109
\(857\) −1.69219e13 + 1.69219e13i −1.07161 + 1.07161i −0.0743768 + 0.997230i \(0.523697\pi\)
−0.997230 + 0.0743768i \(0.976303\pi\)
\(858\) −1.01013e13 1.92635e13i −0.636332 1.21351i
\(859\) 2.07492e13i 1.30027i −0.759820 0.650133i \(-0.774713\pi\)
0.759820 0.650133i \(-0.225287\pi\)
\(860\) 4.46413e11 3.16553e12i 0.0278288 0.197334i
\(861\) 4.25151e12 + 1.32653e12i 0.263651 + 0.0822628i
\(862\) 6.15980e12 + 6.15980e12i 0.380000 + 0.380000i
\(863\) 4.66294e12 + 4.66294e12i 0.286161 + 0.286161i 0.835560 0.549399i \(-0.185143\pi\)
−0.549399 + 0.835560i \(0.685143\pi\)
\(864\) −1.41028e13 + 1.10239e13i −0.860981 + 0.673012i
\(865\) −1.82037e12 + 1.29083e13i −0.110557 + 0.783963i
\(866\) 3.16366e13i 1.91143i
\(867\) 5.21531e12 2.73477e12i 0.313469 0.164375i
\(868\) 1.58273e12 1.58273e12i 0.0946383 0.0946383i
\(869\) 4.64744e13 2.76455
\(870\) −6.03308e12 1.69015e13i −0.357028 1.00021i
\(871\) 1.43569e13 0.845235
\(872\) 2.70964e12 2.70964e12i 0.158704 0.158704i
\(873\) −1.93406e13 + 3.52967e12i −1.12695 + 0.205670i
\(874\) 1.05403e13i 0.611014i
\(875\) −3.60965e12 1.61326e12i −0.208175 0.0930398i
\(876\) 9.44762e11 3.02795e12i 0.0542068 0.173732i
\(877\) 2.08823e13 + 2.08823e13i 1.19201 + 1.19201i 0.976501 + 0.215512i \(0.0691419\pi\)
0.215512 + 0.976501i \(0.430858\pi\)
\(878\) −8.01539e12 8.01539e12i −0.455197 0.455197i
\(879\) 1.92957e12 6.18425e12i 0.109021 0.349411i
\(880\) 2.97640e13 2.24067e13i 1.67309 1.25952i
\(881\) 8.03323e12i 0.449261i −0.974444 0.224630i \(-0.927883\pi\)
0.974444 0.224630i \(-0.0721174\pi\)
\(882\) 2.13528e13 3.89691e12i 1.18808 0.216826i
\(883\) 2.03835e12 2.03835e12i 0.112838 0.112838i −0.648433 0.761271i \(-0.724575\pi\)
0.761271 + 0.648433i \(0.224575\pi\)
\(884\) 8.34699e12 0.459721
\(885\) 1.50478e13 3.17538e13i 0.824571 1.74001i
\(886\) 1.11413e12 0.0607414
\(887\) 1.29315e13 1.29315e13i 0.701445 0.701445i −0.263276 0.964721i \(-0.584803\pi\)
0.964721 + 0.263276i \(0.0848029\pi\)
\(888\) 1.95768e12 1.02656e12i 0.105653 0.0554019i
\(889\) 3.64400e12i 0.195669i
\(890\) −9.13365e12 1.28806e12i −0.487966 0.0688145i
\(891\) −2.98468e13 + 1.12695e13i −1.58653 + 0.599037i
\(892\) 5.18115e12 + 5.18115e12i 0.274022 + 0.274022i
\(893\) −8.08908e12 8.08908e12i −0.425665 0.425665i
\(894\) −3.34156e12 1.04261e12i −0.174957 0.0545889i
\(895\) −1.01507e13 1.34837e13i −0.528801 0.702434i
\(896\) 3.92587e12i 0.203493i
\(897\) −3.47240e12 6.62198e12i −0.179087 0.341525i
\(898\) −3.92127e12 + 3.92127e12i −0.201225 + 0.201225i
\(899\) −1.53841e13 −0.785511
\(900\) −9.48970e12 + 7.76404e12i −0.482127 + 0.394454i
\(901\) −1.63285e13 −0.825438
\(902\) −3.67859e13 + 3.67859e13i −1.85034 + 1.85034i
\(903\) 6.76863e11 + 1.29080e12i 0.0338771 + 0.0646047i
\(904\) 8.66137e12i 0.431349i
\(905\) −1.12858e13 1.49914e13i −0.559258 0.742891i
\(906\) 3.42282e13 + 1.06797e13i 1.68775 + 0.526600i
\(907\) 2.57581e13 + 2.57581e13i 1.26381 + 1.26381i 0.949233 + 0.314573i \(0.101861\pi\)
0.314573 + 0.949233i \(0.398139\pi\)
\(908\) −3.47238e12 3.47238e12i −0.169528 0.169528i
\(909\) −1.80492e13 1.24780e13i −0.876841 0.606187i
\(910\) 3.77388e12 + 5.32205e11i 0.182432 + 0.0257272i
\(911\) 2.17283e13i 1.04519i −0.852583 0.522593i \(-0.824965\pi\)
0.852583 0.522593i \(-0.175035\pi\)
\(912\) 1.80235e13 9.45106e12i 0.862705 0.452380i
\(913\) −2.25075e13 + 2.25075e13i −1.07204 + 1.07204i
\(914\) 2.74272e13 1.29994
\(915\) 1.72724e12 3.64482e12i 0.0814624 0.171902i
\(916\) −1.54144e13 −0.723432
\(917\) −1.80769e12 + 1.80769e12i −0.0844231 + 0.0844231i
\(918\) 3.87944e12 3.16597e13i 0.180292 1.47135i
\(919\) 2.50024e13i 1.15628i 0.815938 + 0.578139i \(0.196221\pi\)
−0.815938 + 0.578139i \(0.803779\pi\)
\(920\) 5.07036e12 3.81703e12i 0.233342 0.175663i
\(921\) −4.45152e12 + 1.42670e13i −0.203864 + 0.653380i
\(922\) −6.04510e12 6.04510e12i −0.275496 0.275496i
\(923\) 1.61494e13 + 1.61494e13i 0.732401 + 0.732401i
\(924\) 1.58973e12 5.09508e12i 0.0717465 0.229946i
\(925\) 4.83888e12 2.67625e12i 0.217324 0.120196i
\(926\) 1.00740e13i 0.450247i
\(927\) 1.24074e12 + 6.79857e12i 0.0551853 + 0.302384i
\(928\) −1.45538e13 + 1.45538e13i −0.644187 + 0.644187i
\(929\) 1.27155e13 0.560097 0.280048 0.959986i \(-0.409650\pi\)
0.280048 + 0.959986i \(0.409650\pi\)
\(930\) 9.20585e12 + 2.57900e13i 0.403544 + 1.13052i
\(931\) −1.71423e13 −0.747818
\(932\) 5.85286e12 5.85286e12i 0.254095 0.254095i
\(933\) 1.74105e13 9.12964e12i 0.752220 0.394445i
\(934\) 4.00537e13i 1.72219i
\(935\) −6.43956e12 + 4.56631e13i −0.275552 + 1.95395i
\(936\) −4.06843e12 + 5.88492e12i −0.173255 + 0.250611i
\(937\) −3.51292e12 3.51292e12i −0.148881 0.148881i 0.628737 0.777618i \(-0.283572\pi\)
−0.777618 + 0.628737i \(0.783572\pi\)
\(938\) 6.48999e12 + 6.48999e12i 0.273736 + 0.273736i
\(939\) −5.34649e12 1.66818e12i −0.224426 0.0700241i
\(940\) 1.58901e12 1.12677e13i 0.0663821 0.470718i
\(941\) 4.01656e12i 0.166994i 0.996508 + 0.0834971i \(0.0266089\pi\)
−0.996508 + 0.0834971i \(0.973391\pi\)
\(942\) −2.62096e13 4.99825e13i −1.08450 2.06818i
\(943\) −1.26454e13 + 1.26454e13i −0.520752 + 0.520752i
\(944\) −5.80157e13 −2.37778
\(945\) 1.44804e12 5.39926e12i 0.0590662 0.220237i
\(946\) −1.70250e13 −0.691159
\(947\) 2.64335e13 2.64335e13i 1.06802 1.06802i 0.0705084 0.997511i \(-0.477538\pi\)
0.997511 0.0705084i \(-0.0224622\pi\)
\(948\) 1.17275e13 + 2.23647e13i 0.471592 + 0.899343i
\(949\) 4.62985e12i 0.185297i
\(950\) 2.20769e13 1.22101e13i 0.879389 0.486366i
\(951\) 2.33590e13 + 7.28834e12i 0.926066 + 0.288946i
\(952\) −2.28402e12 2.28402e12i −0.0901225 0.0901225i
\(953\) 3.23595e13 + 3.23595e13i 1.27082 + 1.27082i 0.945660 + 0.325158i \(0.105418\pi\)
0.325158 + 0.945660i \(0.394582\pi\)
\(954\) −1.31479e13 + 1.90183e13i −0.513914 + 0.743369i
\(955\) 1.23401e13 9.28978e12i 0.480069 0.361402i
\(956\) 1.43733e13i 0.556538i
\(957\) −3.24881e13 + 1.70359e13i −1.25205 + 0.656541i
\(958\) −1.17466e12 + 1.17466e12i −0.0450576 + 0.0450576i
\(959\) −5.42381e12 −0.207072
\(960\) 3.74045e12 + 1.77256e12i 0.142136 + 0.0673566i
\(961\) −2.96516e12 −0.112148
\(962\) −3.76910e12 + 3.76910e12i −0.141889 + 0.141889i
\(963\) 1.83641e12 + 1.00625e13i 0.0688099 + 0.377039i
\(964\) 1.31850e13i 0.491738i
\(965\) −2.88452e13 4.06785e12i −1.07078 0.151005i
\(966\) 1.42377e12 4.56315e12i 0.0526067 0.168604i
\(967\) −3.64300e12 3.64300e12i −0.133980 0.133980i 0.636936 0.770916i \(-0.280201\pi\)
−0.770916 + 0.636936i \(0.780201\pi\)
\(968\) −1.74064e13 1.74064e13i −0.637193 0.637193i
\(969\) −7.50315e12 + 2.40475e13i −0.273393 + 0.876219i
\(970\) 2.42010e13 + 3.21474e13i 0.877728 + 1.16593i
\(971\) 4.47547e13i 1.61567i −0.589410 0.807834i \(-0.700640\pi\)
0.589410 0.807834i \(-0.299360\pi\)
\(972\) −1.29548e13 1.15193e13i −0.465513 0.413930i
\(973\) 6.65356e11 6.65356e11i 0.0237983 0.0237983i
\(974\) −9.51405e12 −0.338727
\(975\) −9.84737e12 + 1.49440e13i −0.348979 + 0.529599i
\(976\) −6.65924e12 −0.234909
\(977\) −1.39173e13 + 1.39173e13i −0.488685 + 0.488685i −0.907891 0.419206i \(-0.862309\pi\)
0.419206 + 0.907891i \(0.362309\pi\)
\(978\) 1.34437e13 7.04952e12i 0.469887 0.246397i
\(979\) 1.88550e13i 0.656000i
\(980\) −1.02555e13 1.36229e13i −0.355173 0.471795i
\(981\) 1.11484e13 + 7.70722e12i 0.384327 + 0.265697i
\(982\) 3.69097e12 + 3.69097e12i 0.126660 + 0.126660i
\(983\) −2.41768e13 2.41768e13i −0.825863 0.825863i 0.161079 0.986942i \(-0.448503\pi\)
−0.986942 + 0.161079i \(0.948503\pi\)
\(984\) 1.63345e13 + 5.09660e12i 0.555430 + 0.173302i
\(985\) 5.20146e12 + 7.33527e11i 0.176061 + 0.0248287i
\(986\) 3.66758e13i 1.23576i
\(987\) 2.40930e12 + 4.59462e12i 0.0808096 + 0.154107i
\(988\) −6.60037e12 + 6.60037e12i −0.220375 + 0.220375i
\(989\) −5.85250e12 −0.194517
\(990\) 4.80001e13 + 4.42690e13i 1.58812 + 1.46468i
\(991\) 1.21293e13 0.399487 0.199743 0.979848i \(-0.435989\pi\)
0.199743 + 0.979848i \(0.435989\pi\)
\(992\) 2.22076e13 2.22076e13i 0.728115 0.728115i
\(993\) −1.25504e13 2.39340e13i −0.409624 0.781168i
\(994\) 1.46006e13i 0.474387i
\(995\) −7.76249e12 + 5.84370e12i −0.251071 + 0.189010i
\(996\) −1.65108e13 5.15161e12i −0.531621 0.165873i
\(997\) −2.35103e13 2.35103e13i −0.753582 0.753582i 0.221564 0.975146i \(-0.428884\pi\)
−0.975146 + 0.221564i \(0.928884\pi\)
\(998\) 2.10829e13 + 2.10829e13i 0.672734 + 0.672734i
\(999\) 4.81485e12 + 6.15962e12i 0.152946 + 0.195663i
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 15.10.e.a.2.13 yes 32
3.2 odd 2 inner 15.10.e.a.2.4 32
5.2 odd 4 75.10.e.f.68.13 32
5.3 odd 4 inner 15.10.e.a.8.4 yes 32
5.4 even 2 75.10.e.f.32.4 32
15.2 even 4 75.10.e.f.68.4 32
15.8 even 4 inner 15.10.e.a.8.13 yes 32
15.14 odd 2 75.10.e.f.32.13 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.10.e.a.2.4 32 3.2 odd 2 inner
15.10.e.a.2.13 yes 32 1.1 even 1 trivial
15.10.e.a.8.4 yes 32 5.3 odd 4 inner
15.10.e.a.8.13 yes 32 15.8 even 4 inner
75.10.e.f.32.4 32 5.4 even 2
75.10.e.f.32.13 32 15.14 odd 2
75.10.e.f.68.4 32 15.2 even 4
75.10.e.f.68.13 32 5.2 odd 4