Properties

Label 12.11.d.a.7.10
Level $12$
Weight $11$
Character 12.7
Analytic conductor $7.624$
Analytic rank $0$
Dimension $10$
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] = [12,11,Mod(7,12)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(12, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.7");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\), degree \(1\), 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: \(7.62428703208\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2 x^{9} + 198 x^{8} - 1066 x^{7} + 30608 x^{6} - 147714 x^{5} + 2092829 x^{4} - 9587938 x^{3} + 101463432 x^{2} - 344403128 x + 1648684816 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{39}\cdot 3^{18} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 7.10
Root \(3.29676 + 5.71016i\) of defining polynomial
Character \(\chi\) \(=\) 12.7
Dual form 12.11.d.a.7.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(31.4354 + 5.98464i) q^{2} +140.296i q^{3} +(952.368 + 376.259i) q^{4} +581.119 q^{5} +(-839.621 + 4410.26i) q^{6} +18141.8i q^{7} +(27686.3 + 17527.4i) q^{8} -19683.0 q^{9} +O(q^{10})\) \(q+(31.4354 + 5.98464i) q^{2} +140.296i q^{3} +(952.368 + 376.259i) q^{4} +581.119 q^{5} +(-839.621 + 4410.26i) q^{6} +18141.8i q^{7} +(27686.3 + 17527.4i) q^{8} -19683.0 q^{9} +(18267.7 + 3477.79i) q^{10} +3142.03i q^{11} +(-52787.7 + 133614. i) q^{12} +277162. q^{13} +(-108572. + 570295. i) q^{14} +81528.8i q^{15} +(765434. + 716674. i) q^{16} -405267. q^{17} +(-618743. - 117796. i) q^{18} -4.64051e6i q^{19} +(553440. + 218651. i) q^{20} -2.54522e6 q^{21} +(-18803.9 + 98771.0i) q^{22} -1.16775e7i q^{23} +(-2.45903e6 + 3.88428e6i) q^{24} -9.42793e6 q^{25} +(8.71269e6 + 1.65871e6i) q^{26} -2.76145e6i q^{27} +(-6.82602e6 + 1.72777e7i) q^{28} +3.05985e7 q^{29} +(-487920. + 2.56289e6i) q^{30} +2.15851e7i q^{31} +(1.97727e7 + 2.71098e7i) q^{32} -440815. q^{33} +(-1.27397e7 - 2.42538e6i) q^{34} +1.05426e7i q^{35} +(-1.87455e7 - 7.40590e6i) q^{36} -8.42940e7 q^{37} +(2.77717e7 - 1.45876e8i) q^{38} +3.88847e7i q^{39} +(1.60890e7 + 1.01855e7i) q^{40} +1.25396e8 q^{41} +(-8.00101e7 - 1.52322e7i) q^{42} +9.50638e7i q^{43} +(-1.18222e6 + 2.99237e6i) q^{44} -1.14382e7 q^{45} +(6.98854e7 - 3.67086e8i) q^{46} +4.66101e7i q^{47} +(-1.00547e8 + 1.07387e8i) q^{48} -4.66498e7 q^{49} +(-2.96371e8 - 5.64227e7i) q^{50} -5.68574e7i q^{51} +(2.63960e8 + 1.04285e8i) q^{52} -6.20248e7 q^{53} +(1.65263e7 - 8.68072e7i) q^{54} +1.82590e6i q^{55} +(-3.17979e8 + 5.02279e8i) q^{56} +6.51045e8 q^{57} +(9.61877e8 + 1.83121e8i) q^{58} +9.07127e7i q^{59} +(-3.06759e7 + 7.76454e7i) q^{60} -1.27440e9 q^{61} +(-1.29179e8 + 6.78535e8i) q^{62} -3.57085e8i q^{63} +(4.59320e8 + 9.70539e8i) q^{64} +1.61064e8 q^{65} +(-1.38572e7 - 2.63812e6i) q^{66} -9.02217e8i q^{67} +(-3.85963e8 - 1.52485e8i) q^{68} +1.63830e9 q^{69} +(-6.30934e7 + 3.31409e8i) q^{70} -2.49217e9i q^{71} +(-5.44949e8 - 3.44992e8i) q^{72} -2.26517e9 q^{73} +(-2.64981e9 - 5.04469e8i) q^{74} -1.32270e9i q^{75} +(1.74603e9 - 4.41947e9i) q^{76} -5.70021e7 q^{77} +(-2.32711e8 + 1.22236e9i) q^{78} +2.04203e9i q^{79} +(4.44809e8 + 4.16473e8i) q^{80} +3.87420e8 q^{81} +(3.94187e9 + 7.50449e8i) q^{82} +6.44397e9i q^{83} +(-2.42399e9 - 9.57664e8i) q^{84} -2.35508e8 q^{85} +(-5.68922e8 + 2.98837e9i) q^{86} +4.29286e9i q^{87} +(-5.50717e7 + 8.69912e7i) q^{88} +7.08476e9 q^{89} +(-3.59563e8 - 6.84533e7i) q^{90} +5.02821e9i q^{91} +(4.39375e9 - 1.11212e10i) q^{92} -3.02830e9 q^{93} +(-2.78945e8 + 1.46521e9i) q^{94} -2.69669e9i q^{95} +(-3.80340e9 + 2.77403e9i) q^{96} -4.17526e9 q^{97} +(-1.46646e9 - 2.79182e8i) q^{98} -6.18446e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 22 q^{2} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 20176 q^{8} - 196830 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 22 q^{2} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 20176 q^{8} - 196830 q^{9} - 369196 q^{10} + 310068 q^{12} - 285100 q^{13} - 2495544 q^{14} + 3590128 q^{16} + 2264420 q^{17} - 433026 q^{18} + 1194248 q^{20} + 3555576 q^{21} - 2139528 q^{22} - 6858432 q^{24} + 23043438 q^{25} + 29599340 q^{26} - 41542224 q^{28} - 46672708 q^{29} + 19963908 q^{30} - 83717408 q^{32} + 22665096 q^{33} + 37514588 q^{34} + 12675852 q^{36} - 194467900 q^{37} - 218769048 q^{38} + 340155488 q^{40} + 276227780 q^{41} - 15919416 q^{42} + 532887504 q^{44} - 61332228 q^{45} - 70057824 q^{46} + 27126576 q^{48} + 653625226 q^{49} + 20815602 q^{50} - 959132296 q^{52} - 1522721956 q^{53} - 47829690 q^{54} - 632703744 q^{56} + 844537752 q^{57} + 1851304388 q^{58} - 1708229736 q^{60} - 3488124604 q^{61} - 806085192 q^{62} - 877634432 q^{64} + 6725245912 q^{65} + 1244885112 q^{66} + 3081993176 q^{68} - 1698239520 q^{69} + 598086768 q^{70} - 397124208 q^{72} + 3090518708 q^{73} - 9824720260 q^{74} + 2750616432 q^{76} - 4577505312 q^{77} + 4510566972 q^{78} + 16715013152 q^{80} + 3874204890 q^{81} + 830592764 q^{82} - 10263359664 q^{84} - 3285444680 q^{85} - 15186172488 q^{86} - 12375555840 q^{88} - 13670065996 q^{89} + 7266884868 q^{90} + 12601016256 q^{92} + 3947087880 q^{93} + 38474881584 q^{94} - 27853204320 q^{96} - 18805077484 q^{97} - 31671844202 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.4354 + 5.98464i 0.982356 + 0.187020i
\(3\) 140.296i 0.577350i
\(4\) 952.368 + 376.259i 0.930047 + 0.367440i
\(5\) 581.119 0.185958 0.0929791 0.995668i \(-0.470361\pi\)
0.0929791 + 0.995668i \(0.470361\pi\)
\(6\) −839.621 + 4410.26i −0.107976 + 0.567164i
\(7\) 18141.8i 1.07942i 0.841851 + 0.539710i \(0.181466\pi\)
−0.841851 + 0.539710i \(0.818534\pi\)
\(8\) 27686.3 + 17527.4i 0.844919 + 0.534895i
\(9\) −19683.0 −0.333333
\(10\) 18267.7 + 3477.79i 0.182677 + 0.0347779i
\(11\) 3142.03i 0.0195095i 0.999952 + 0.00975477i \(0.00310509\pi\)
−0.999952 + 0.00975477i \(0.996895\pi\)
\(12\) −52787.7 + 133614.i −0.212142 + 0.536963i
\(13\) 277162. 0.746477 0.373239 0.927735i \(-0.378247\pi\)
0.373239 + 0.927735i \(0.378247\pi\)
\(14\) −108572. + 570295.i −0.201873 + 1.06037i
\(15\) 81528.8i 0.107363i
\(16\) 765434. + 716674.i 0.729975 + 0.683474i
\(17\) −405267. −0.285428 −0.142714 0.989764i \(-0.545583\pi\)
−0.142714 + 0.989764i \(0.545583\pi\)
\(18\) −618743. 117796.i −0.327452 0.0623400i
\(19\) 4.64051e6i 1.87412i −0.349169 0.937060i \(-0.613536\pi\)
0.349169 0.937060i \(-0.386464\pi\)
\(20\) 553440. + 218651.i 0.172950 + 0.0683285i
\(21\) −2.54522e6 −0.623203
\(22\) −18803.9 + 98771.0i −0.00364867 + 0.0191653i
\(23\) 1.16775e7i 1.81430i −0.420806 0.907151i \(-0.638253\pi\)
0.420806 0.907151i \(-0.361747\pi\)
\(24\) −2.45903e6 + 3.88428e6i −0.308822 + 0.487814i
\(25\) −9.42793e6 −0.965420
\(26\) 8.71269e6 + 1.65871e6i 0.733306 + 0.139606i
\(27\) 2.76145e6i 0.192450i
\(28\) −6.82602e6 + 1.72777e7i −0.396622 + 1.00391i
\(29\) 3.05985e7 1.49180 0.745900 0.666058i \(-0.232020\pi\)
0.745900 + 0.666058i \(0.232020\pi\)
\(30\) −487920. + 2.56289e6i −0.0200790 + 0.105469i
\(31\) 2.15851e7i 0.753955i 0.926223 + 0.376977i \(0.123037\pi\)
−0.926223 + 0.376977i \(0.876963\pi\)
\(32\) 1.97727e7 + 2.71098e7i 0.589272 + 0.807934i
\(33\) −440815. −0.0112638
\(34\) −1.27397e7 2.42538e6i −0.280392 0.0533807i
\(35\) 1.05426e7i 0.200727i
\(36\) −1.87455e7 7.40590e6i −0.310016 0.122480i
\(37\) −8.42940e7 −1.21559 −0.607796 0.794093i \(-0.707946\pi\)
−0.607796 + 0.794093i \(0.707946\pi\)
\(38\) 2.77717e7 1.45876e8i 0.350498 1.84105i
\(39\) 3.88847e7i 0.430979i
\(40\) 1.60890e7 + 1.01855e7i 0.157120 + 0.0994680i
\(41\) 1.25396e8 1.08234 0.541170 0.840913i \(-0.317981\pi\)
0.541170 + 0.840913i \(0.317981\pi\)
\(42\) −8.00101e7 1.52322e7i −0.612207 0.116551i
\(43\) 9.50638e7i 0.646655i 0.946287 + 0.323328i \(0.104802\pi\)
−0.946287 + 0.323328i \(0.895198\pi\)
\(44\) −1.18222e6 + 2.99237e6i −0.00716859 + 0.0181448i
\(45\) −1.14382e7 −0.0619861
\(46\) 6.98854e7 3.67086e8i 0.339311 1.78229i
\(47\) 4.66101e7i 0.203232i 0.994824 + 0.101616i \(0.0324012\pi\)
−0.994824 + 0.101616i \(0.967599\pi\)
\(48\) −1.00547e8 + 1.07387e8i −0.394604 + 0.421451i
\(49\) −4.66498e7 −0.165147
\(50\) −2.96371e8 5.64227e7i −0.948386 0.180553i
\(51\) 5.68574e7i 0.164792i
\(52\) 2.63960e8 + 1.04285e8i 0.694259 + 0.274286i
\(53\) −6.20248e7 −0.148315 −0.0741577 0.997247i \(-0.523627\pi\)
−0.0741577 + 0.997247i \(0.523627\pi\)
\(54\) 1.65263e7 8.68072e7i 0.0359920 0.189055i
\(55\) 1.82590e6i 0.00362796i
\(56\) −3.17979e8 + 5.02279e8i −0.577376 + 0.912022i
\(57\) 6.51045e8 1.08202
\(58\) 9.61877e8 + 1.83121e8i 1.46548 + 0.278996i
\(59\) 9.07127e7i 0.126884i 0.997986 + 0.0634422i \(0.0202079\pi\)
−0.997986 + 0.0634422i \(0.979792\pi\)
\(60\) −3.06759e7 + 7.76454e7i −0.0394495 + 0.0998526i
\(61\) −1.27440e9 −1.50889 −0.754446 0.656362i \(-0.772094\pi\)
−0.754446 + 0.656362i \(0.772094\pi\)
\(62\) −1.29179e8 + 6.78535e8i −0.141005 + 0.740652i
\(63\) 3.57085e8i 0.359807i
\(64\) 4.59320e8 + 9.70539e8i 0.427775 + 0.903885i
\(65\) 1.61064e8 0.138814
\(66\) −1.38572e7 2.63812e6i −0.0110651 0.00210656i
\(67\) 9.02217e8i 0.668247i −0.942529 0.334124i \(-0.891560\pi\)
0.942529 0.334124i \(-0.108440\pi\)
\(68\) −3.85963e8 1.52485e8i −0.265461 0.104878i
\(69\) 1.63830e9 1.04749
\(70\) −6.30934e7 + 3.31409e8i −0.0375399 + 0.197185i
\(71\) 2.49217e9i 1.38129i −0.723192 0.690647i \(-0.757326\pi\)
0.723192 0.690647i \(-0.242674\pi\)
\(72\) −5.44949e8 3.44992e8i −0.281640 0.178298i
\(73\) −2.26517e9 −1.09267 −0.546333 0.837568i \(-0.683977\pi\)
−0.546333 + 0.837568i \(0.683977\pi\)
\(74\) −2.64981e9 5.04469e8i −1.19414 0.227340i
\(75\) 1.32270e9i 0.557385i
\(76\) 1.74603e9 4.41947e9i 0.688627 1.74302i
\(77\) −5.70021e7 −0.0210590
\(78\) −2.32711e8 + 1.22236e9i −0.0806016 + 0.423375i
\(79\) 2.04203e9i 0.663631i 0.943344 + 0.331815i \(0.107661\pi\)
−0.943344 + 0.331815i \(0.892339\pi\)
\(80\) 4.44809e8 + 4.16473e8i 0.135745 + 0.127098i
\(81\) 3.87420e8 0.111111
\(82\) 3.94187e9 + 7.50449e8i 1.06324 + 0.202419i
\(83\) 6.44397e9i 1.63592i 0.575273 + 0.817962i \(0.304896\pi\)
−0.575273 + 0.817962i \(0.695104\pi\)
\(84\) −2.42399e9 9.57664e8i −0.579608 0.228990i
\(85\) −2.35508e8 −0.0530777
\(86\) −5.68922e8 + 2.98837e9i −0.120937 + 0.635246i
\(87\) 4.29286e9i 0.861291i
\(88\) −5.50717e7 + 8.69912e7i −0.0104356 + 0.0164840i
\(89\) 7.08476e9 1.26875 0.634374 0.773026i \(-0.281258\pi\)
0.634374 + 0.773026i \(0.281258\pi\)
\(90\) −3.59563e8 6.84533e7i −0.0608924 0.0115926i
\(91\) 5.02821e9i 0.805762i
\(92\) 4.39375e9 1.11212e10i 0.666648 1.68739i
\(93\) −3.02830e9 −0.435296
\(94\) −2.78945e8 + 1.46521e9i −0.0380084 + 0.199646i
\(95\) 2.69669e9i 0.348508i
\(96\) −3.80340e9 + 2.77403e9i −0.466461 + 0.340217i
\(97\) −4.17526e9 −0.486211 −0.243106 0.970000i \(-0.578166\pi\)
−0.243106 + 0.970000i \(0.578166\pi\)
\(98\) −1.46646e9 2.79182e8i −0.162233 0.0308857i
\(99\) 6.18446e7i 0.00650318i
\(100\) −8.97886e9 3.54734e9i −0.897886 0.354734i
\(101\) 5.10423e9 0.485650 0.242825 0.970070i \(-0.421926\pi\)
0.242825 + 0.970070i \(0.421926\pi\)
\(102\) 3.40271e8 1.78733e9i 0.0308194 0.161884i
\(103\) 5.36716e9i 0.462976i −0.972838 0.231488i \(-0.925641\pi\)
0.972838 0.231488i \(-0.0743594\pi\)
\(104\) 7.67358e9 + 4.85793e9i 0.630713 + 0.399287i
\(105\) −1.47908e9 −0.115890
\(106\) −1.94977e9 3.71196e8i −0.145698 0.0277379i
\(107\) 1.25180e10i 0.892517i −0.894904 0.446259i \(-0.852756\pi\)
0.894904 0.446259i \(-0.147244\pi\)
\(108\) 1.03902e9 2.62992e9i 0.0707139 0.178988i
\(109\) 1.78943e9 0.116301 0.0581503 0.998308i \(-0.481480\pi\)
0.0581503 + 0.998308i \(0.481480\pi\)
\(110\) −1.09273e7 + 5.73977e7i −0.000678501 + 0.00356395i
\(111\) 1.18261e10i 0.701822i
\(112\) −1.30018e10 + 1.38864e10i −0.737755 + 0.787949i
\(113\) −2.08033e10 −1.12912 −0.564559 0.825393i \(-0.690954\pi\)
−0.564559 + 0.825393i \(0.690954\pi\)
\(114\) 2.04659e10 + 3.89627e9i 1.06293 + 0.202360i
\(115\) 6.78600e9i 0.337384i
\(116\) 2.91411e10 + 1.15130e10i 1.38744 + 0.548148i
\(117\) −5.45537e9 −0.248826
\(118\) −5.42883e8 + 2.85159e9i −0.0237299 + 0.124646i
\(119\) 7.35227e9i 0.308097i
\(120\) −1.42899e9 + 2.25723e9i −0.0574279 + 0.0907130i
\(121\) 2.59276e10 0.999619
\(122\) −4.00614e10 7.62685e9i −1.48227 0.282193i
\(123\) 1.75926e10i 0.624890i
\(124\) −8.12158e9 + 2.05569e10i −0.277033 + 0.701213i
\(125\) −1.11537e10 −0.365486
\(126\) 2.13703e9 1.12251e10i 0.0672910 0.353458i
\(127\) 3.45877e10i 1.04689i −0.852058 0.523447i \(-0.824646\pi\)
0.852058 0.523447i \(-0.175354\pi\)
\(128\) 8.63059e9 + 3.32581e10i 0.251183 + 0.967940i
\(129\) −1.33371e10 −0.373346
\(130\) 5.06311e9 + 9.63910e8i 0.136364 + 0.0259609i
\(131\) 5.54439e10i 1.43713i 0.695457 + 0.718567i \(0.255202\pi\)
−0.695457 + 0.718567i \(0.744798\pi\)
\(132\) −4.19818e8 1.65861e8i −0.0104759 0.00413879i
\(133\) 8.41871e10 2.02296
\(134\) 5.39944e9 2.83616e10i 0.124976 0.656457i
\(135\) 1.60473e9i 0.0357877i
\(136\) −1.12203e10 7.10329e9i −0.241163 0.152674i
\(137\) −5.51790e10 −1.14333 −0.571664 0.820488i \(-0.693702\pi\)
−0.571664 + 0.820488i \(0.693702\pi\)
\(138\) 5.15007e10 + 9.80465e9i 1.02901 + 0.195901i
\(139\) 5.84773e10i 1.12697i 0.826125 + 0.563487i \(0.190540\pi\)
−0.826125 + 0.563487i \(0.809460\pi\)
\(140\) −3.96673e9 + 1.00404e10i −0.0737552 + 0.186685i
\(141\) −6.53922e9 −0.117336
\(142\) 1.49147e10 7.83424e10i 0.258330 1.35692i
\(143\) 8.70851e8i 0.0145634i
\(144\) −1.50660e10 1.41063e10i −0.243325 0.227825i
\(145\) 1.77814e10 0.277412
\(146\) −7.12066e10 1.35562e10i −1.07339 0.204350i
\(147\) 6.54479e9i 0.0953474i
\(148\) −8.02789e10 3.17164e10i −1.13056 0.446658i
\(149\) −5.65933e10 −0.770608 −0.385304 0.922790i \(-0.625903\pi\)
−0.385304 + 0.922790i \(0.625903\pi\)
\(150\) 7.91589e9 4.15796e10i 0.104242 0.547551i
\(151\) 4.52959e10i 0.576998i −0.957480 0.288499i \(-0.906844\pi\)
0.957480 0.288499i \(-0.0931562\pi\)
\(152\) 8.13361e10 1.28478e11i 1.00246 1.58348i
\(153\) 7.97687e9 0.0951427
\(154\) −1.79188e9 3.41137e8i −0.0206874 0.00393845i
\(155\) 1.25435e10i 0.140204i
\(156\) −1.46307e10 + 3.70326e10i −0.158359 + 0.400831i
\(157\) −8.52098e10 −0.893288 −0.446644 0.894712i \(-0.647381\pi\)
−0.446644 + 0.894712i \(0.647381\pi\)
\(158\) −1.22208e10 + 6.41920e10i −0.124112 + 0.651922i
\(159\) 8.70184e9i 0.0856299i
\(160\) 1.14903e10 + 1.57540e10i 0.109580 + 0.150242i
\(161\) 2.11850e11 1.95839
\(162\) 1.21787e10 + 2.31857e9i 0.109151 + 0.0207800i
\(163\) 1.31501e11i 1.14285i 0.820653 + 0.571426i \(0.193610\pi\)
−0.820653 + 0.571426i \(0.806390\pi\)
\(164\) 1.19423e11 + 4.71813e10i 1.00663 + 0.397696i
\(165\) −2.56166e8 −0.00209460
\(166\) −3.85648e10 + 2.02569e11i −0.305950 + 1.60706i
\(167\) 8.75191e10i 0.673784i −0.941543 0.336892i \(-0.890624\pi\)
0.941543 0.336892i \(-0.109376\pi\)
\(168\) −7.04679e10 4.46112e10i −0.526556 0.333348i
\(169\) −6.10399e10 −0.442772
\(170\) −7.40330e9 1.40943e9i −0.0521412 0.00992658i
\(171\) 9.13391e10i 0.624706i
\(172\) −3.57686e10 + 9.05357e10i −0.237607 + 0.601420i
\(173\) 7.79794e10 0.503210 0.251605 0.967830i \(-0.419042\pi\)
0.251605 + 0.967830i \(0.419042\pi\)
\(174\) −2.56912e10 + 1.34948e11i −0.161079 + 0.846095i
\(175\) 1.71040e11i 1.04209i
\(176\) −2.25181e9 + 2.40502e9i −0.0133343 + 0.0142415i
\(177\) −1.27266e10 −0.0732567
\(178\) 2.22712e11 + 4.23997e10i 1.24636 + 0.237281i
\(179\) 4.15281e10i 0.225984i −0.993596 0.112992i \(-0.963957\pi\)
0.993596 0.112992i \(-0.0360434\pi\)
\(180\) −1.08934e10 4.30371e9i −0.0576500 0.0227762i
\(181\) −2.42696e11 −1.24931 −0.624654 0.780901i \(-0.714760\pi\)
−0.624654 + 0.780901i \(0.714760\pi\)
\(182\) −3.00920e10 + 1.58064e11i −0.150694 + 0.791545i
\(183\) 1.78794e11i 0.871159i
\(184\) 2.04676e11 3.23306e11i 0.970460 1.53294i
\(185\) −4.89848e10 −0.226049
\(186\) −9.51959e10 1.81233e10i −0.427616 0.0814090i
\(187\) 1.27336e9i 0.00556857i
\(188\) −1.75375e10 + 4.43900e10i −0.0746755 + 0.189015i
\(189\) 5.00977e10 0.207734
\(190\) 1.61387e10 8.47714e10i 0.0651779 0.342359i
\(191\) 3.31770e11i 1.30518i −0.757711 0.652590i \(-0.773682\pi\)
0.757711 0.652590i \(-0.226318\pi\)
\(192\) −1.36163e11 + 6.44409e10i −0.521858 + 0.246976i
\(193\) −8.15179e10 −0.304415 −0.152208 0.988349i \(-0.548638\pi\)
−0.152208 + 0.988349i \(0.548638\pi\)
\(194\) −1.31251e11 2.49874e10i −0.477633 0.0909312i
\(195\) 2.25967e10i 0.0801440i
\(196\) −4.44278e10 1.75524e10i −0.153594 0.0606815i
\(197\) 1.09584e11 0.369333 0.184666 0.982801i \(-0.440880\pi\)
0.184666 + 0.982801i \(0.440880\pi\)
\(198\) 3.70118e8 1.94411e9i 0.00121622 0.00638844i
\(199\) 5.96022e10i 0.190984i −0.995430 0.0954920i \(-0.969558\pi\)
0.995430 0.0954920i \(-0.0304424\pi\)
\(200\) −2.61024e11 1.65247e11i −0.815701 0.516398i
\(201\) 1.26578e11 0.385813
\(202\) 1.60454e11 + 3.05470e10i 0.477082 + 0.0908263i
\(203\) 5.55113e11i 1.61028i
\(204\) 2.13931e10 5.41492e10i 0.0605512 0.153264i
\(205\) 7.28699e10 0.201270
\(206\) 3.21205e10 1.68719e11i 0.0865857 0.454807i
\(207\) 2.29848e11i 0.604767i
\(208\) 2.12149e11 + 1.98635e11i 0.544910 + 0.510197i
\(209\) 1.45806e10 0.0365632
\(210\) −4.64954e10 8.85175e9i −0.113845 0.0216737i
\(211\) 4.78144e11i 1.14326i 0.820510 + 0.571632i \(0.193689\pi\)
−0.820510 + 0.571632i \(0.806311\pi\)
\(212\) −5.90705e10 2.33374e10i −0.137940 0.0544970i
\(213\) 3.49642e11 0.797491
\(214\) 7.49158e10 3.93509e11i 0.166919 0.876770i
\(215\) 5.52434e10i 0.120251i
\(216\) 4.84011e10 7.64543e10i 0.102941 0.162605i
\(217\) −3.91592e11 −0.813833
\(218\) 5.62514e10 + 1.07091e10i 0.114249 + 0.0217505i
\(219\) 3.17795e11i 0.630851i
\(220\) −6.87009e8 + 1.73892e9i −0.00133306 + 0.00337417i
\(221\) −1.12324e11 −0.213065
\(222\) 7.07750e10 3.71759e11i 0.131255 0.689440i
\(223\) 1.98948e11i 0.360758i 0.983597 + 0.180379i \(0.0577324\pi\)
−0.983597 + 0.180379i \(0.942268\pi\)
\(224\) −4.91820e11 + 3.58712e11i −0.872100 + 0.636072i
\(225\) 1.85570e11 0.321807
\(226\) −6.53959e11 1.24500e11i −1.10920 0.211168i
\(227\) 7.86470e11i 1.30483i 0.757863 + 0.652413i \(0.226243\pi\)
−0.757863 + 0.652413i \(0.773757\pi\)
\(228\) 6.20034e11 + 2.44961e11i 1.00633 + 0.397579i
\(229\) 2.14353e11 0.340370 0.170185 0.985412i \(-0.445563\pi\)
0.170185 + 0.985412i \(0.445563\pi\)
\(230\) 4.06118e10 2.13321e11i 0.0630976 0.331431i
\(231\) 7.99718e9i 0.0121584i
\(232\) 8.47160e11 + 5.36314e11i 1.26045 + 0.797956i
\(233\) −4.85585e11 −0.707107 −0.353554 0.935414i \(-0.615027\pi\)
−0.353554 + 0.935414i \(0.615027\pi\)
\(234\) −1.71492e11 3.26484e10i −0.244435 0.0465354i
\(235\) 2.70861e10i 0.0377926i
\(236\) −3.41315e10 + 8.63919e10i −0.0466225 + 0.118008i
\(237\) −2.86489e11 −0.383147
\(238\) 4.40007e10 2.31122e11i 0.0576202 0.302661i
\(239\) 1.23745e12i 1.58685i −0.608666 0.793426i \(-0.708295\pi\)
0.608666 0.793426i \(-0.291705\pi\)
\(240\) −5.84296e10 + 6.24049e10i −0.0733798 + 0.0783723i
\(241\) 1.00244e12 1.23303 0.616516 0.787342i \(-0.288543\pi\)
0.616516 + 0.787342i \(0.288543\pi\)
\(242\) 8.15043e11 + 1.55167e11i 0.981982 + 0.186949i
\(243\) 5.43536e10i 0.0641500i
\(244\) −1.21370e12 4.79506e11i −1.40334 0.554428i
\(245\) −2.71091e10 −0.0307104
\(246\) −1.05285e11 + 5.53029e11i −0.116867 + 0.613864i
\(247\) 1.28617e12i 1.39899i
\(248\) −3.78331e11 + 5.97611e11i −0.403286 + 0.637030i
\(249\) −9.04064e11 −0.944501
\(250\) −3.50622e11 6.67511e10i −0.359037 0.0683531i
\(251\) 9.10834e11i 0.914262i −0.889399 0.457131i \(-0.848877\pi\)
0.889399 0.457131i \(-0.151123\pi\)
\(252\) 1.34356e11 3.40077e11i 0.132207 0.334637i
\(253\) 3.66910e10 0.0353962
\(254\) 2.06995e11 1.08728e12i 0.195790 1.02842i
\(255\) 3.30409e10i 0.0306444i
\(256\) 7.22682e10 + 1.09713e12i 0.0657275 + 0.997838i
\(257\) 3.40622e11 0.303814 0.151907 0.988395i \(-0.451459\pi\)
0.151907 + 0.988395i \(0.451459\pi\)
\(258\) −4.19256e11 7.98176e10i −0.366759 0.0698232i
\(259\) 1.52924e12i 1.31213i
\(260\) 1.53392e11 + 6.06018e10i 0.129103 + 0.0510057i
\(261\) −6.02271e11 −0.497267
\(262\) −3.31812e11 + 1.74290e12i −0.268773 + 1.41178i
\(263\) 8.19806e11i 0.651527i 0.945451 + 0.325764i \(0.105621\pi\)
−0.945451 + 0.325764i \(0.894379\pi\)
\(264\) −1.22045e10 7.72635e9i −0.00951703 0.00602497i
\(265\) −3.60438e10 −0.0275805
\(266\) 2.64646e12 + 5.03830e11i 1.98727 + 0.378334i
\(267\) 9.93965e11i 0.732512i
\(268\) 3.39467e11 8.59243e11i 0.245541 0.621501i
\(269\) −1.13267e12 −0.804156 −0.402078 0.915605i \(-0.631712\pi\)
−0.402078 + 0.915605i \(0.631712\pi\)
\(270\) 9.60373e9 5.04454e10i 0.00669301 0.0351562i
\(271\) 1.56800e12i 1.07275i 0.843980 + 0.536375i \(0.180207\pi\)
−0.843980 + 0.536375i \(0.819793\pi\)
\(272\) −3.10205e11 2.90444e11i −0.208355 0.195082i
\(273\) −7.05439e11 −0.465207
\(274\) −1.73457e12 3.30226e11i −1.12316 0.213825i
\(275\) 2.96228e10i 0.0188349i
\(276\) 1.56027e12 + 6.16426e11i 0.974213 + 0.384889i
\(277\) 2.90739e12 1.78281 0.891405 0.453208i \(-0.149720\pi\)
0.891405 + 0.453208i \(0.149720\pi\)
\(278\) −3.49966e11 + 1.83826e12i −0.210766 + 1.10709i
\(279\) 4.24859e11i 0.251318i
\(280\) −1.84784e11 + 2.91884e11i −0.107368 + 0.169598i
\(281\) 1.81823e12 1.03781 0.518905 0.854832i \(-0.326340\pi\)
0.518905 + 0.854832i \(0.326340\pi\)
\(282\) −2.05563e11 3.91349e10i −0.115266 0.0219441i
\(283\) 2.28784e12i 1.26036i 0.776450 + 0.630179i \(0.217019\pi\)
−0.776450 + 0.630179i \(0.782981\pi\)
\(284\) 9.37702e11 2.37347e12i 0.507543 1.28467i
\(285\) 3.78335e11 0.201211
\(286\) −5.21173e9 + 2.73755e10i −0.00272365 + 0.0143065i
\(287\) 2.27491e12i 1.16830i
\(288\) −3.89186e11 5.33602e11i −0.196424 0.269311i
\(289\) −1.85175e12 −0.918531
\(290\) 5.58965e11 + 1.06415e11i 0.272518 + 0.0518817i
\(291\) 5.85773e11i 0.280714i
\(292\) −2.15728e12 8.52292e11i −1.01623 0.401489i
\(293\) −3.64665e10 −0.0168871 −0.00844357 0.999964i \(-0.502688\pi\)
−0.00844357 + 0.999964i \(0.502688\pi\)
\(294\) 3.91682e10 2.05738e11i 0.0178319 0.0936651i
\(295\) 5.27149e10i 0.0235952i
\(296\) −2.33379e12 1.47746e12i −1.02708 0.650214i
\(297\) 8.67656e9 0.00375461
\(298\) −1.77903e12 3.38690e11i −0.757011 0.144119i
\(299\) 3.23655e12i 1.35433i
\(300\) 4.97678e11 1.25970e12i 0.204806 0.518395i
\(301\) −1.72463e12 −0.698012
\(302\) 2.71080e11 1.42390e12i 0.107910 0.566818i
\(303\) 7.16104e11i 0.280390i
\(304\) 3.32573e12 3.55200e12i 1.28091 1.36806i
\(305\) −7.40581e11 −0.280591
\(306\) 2.50756e11 + 4.77387e10i 0.0934640 + 0.0177936i
\(307\) 1.45894e12i 0.534992i −0.963559 0.267496i \(-0.913804\pi\)
0.963559 0.267496i \(-0.0861961\pi\)
\(308\) −5.42870e10 2.14476e10i −0.0195858 0.00773792i
\(309\) 7.52991e11 0.267299
\(310\) −7.50683e10 + 3.94310e11i −0.0262209 + 0.137730i
\(311\) 2.53238e12i 0.870415i 0.900330 + 0.435207i \(0.143325\pi\)
−0.900330 + 0.435207i \(0.856675\pi\)
\(312\) −6.81549e11 + 1.07657e12i −0.230528 + 0.364142i
\(313\) 3.44067e12 1.14531 0.572653 0.819798i \(-0.305914\pi\)
0.572653 + 0.819798i \(0.305914\pi\)
\(314\) −2.67860e12 5.09950e11i −0.877527 0.167063i
\(315\) 2.07509e11i 0.0669090i
\(316\) −7.68331e11 + 1.94476e12i −0.243845 + 0.617208i
\(317\) −2.61867e12 −0.818060 −0.409030 0.912521i \(-0.634133\pi\)
−0.409030 + 0.912521i \(0.634133\pi\)
\(318\) 5.20774e10 2.73546e11i 0.0160145 0.0841191i
\(319\) 9.61416e10i 0.0291043i
\(320\) 2.66920e11 + 5.63999e11i 0.0795484 + 0.168085i
\(321\) 1.75623e12 0.515295
\(322\) 6.65960e12 + 1.26785e12i 1.92384 + 0.366258i
\(323\) 1.88064e12i 0.534926i
\(324\) 3.68967e11 + 1.45770e11i 0.103339 + 0.0408267i
\(325\) −2.61306e12 −0.720664
\(326\) −7.86985e11 + 4.13378e12i −0.213736 + 1.12269i
\(327\) 2.51050e11i 0.0671461i
\(328\) 3.47175e12 + 2.19787e12i 0.914490 + 0.578938i
\(329\) −8.45592e11 −0.219372
\(330\) −8.05268e9 1.53306e9i −0.00205765 0.000391733i
\(331\) 4.64858e12i 1.16999i −0.811038 0.584993i \(-0.801097\pi\)
0.811038 0.584993i \(-0.198903\pi\)
\(332\) −2.42460e12 + 6.13703e12i −0.601104 + 1.52149i
\(333\) 1.65916e12 0.405197
\(334\) 5.23770e11 2.75120e12i 0.126011 0.661896i
\(335\) 5.24296e11i 0.124266i
\(336\) −1.94820e12 1.82410e12i −0.454923 0.425943i
\(337\) −1.43141e12 −0.329316 −0.164658 0.986351i \(-0.552652\pi\)
−0.164658 + 0.986351i \(0.552652\pi\)
\(338\) −1.91881e12 3.65301e11i −0.434960 0.0828072i
\(339\) 2.91862e12i 0.651897i
\(340\) −2.24291e11 8.86121e10i −0.0493647 0.0195029i
\(341\) −6.78210e10 −0.0147093
\(342\) −5.46631e11 + 2.87128e12i −0.116833 + 0.613684i
\(343\) 4.27830e12i 0.901157i
\(344\) −1.66622e12 + 2.63196e12i −0.345892 + 0.546371i
\(345\) 9.52050e11 0.194789
\(346\) 2.45131e12 + 4.66679e11i 0.494332 + 0.0941104i
\(347\) 6.99656e12i 1.39071i −0.718666 0.695356i \(-0.755247\pi\)
0.718666 0.695356i \(-0.244753\pi\)
\(348\) −1.61523e12 + 4.08838e12i −0.316473 + 0.801041i
\(349\) 8.06897e11 0.155844 0.0779222 0.996959i \(-0.475171\pi\)
0.0779222 + 0.996959i \(0.475171\pi\)
\(350\) 1.02361e12 5.37670e12i 0.194892 1.02371i
\(351\) 7.65368e11i 0.143660i
\(352\) −8.51798e10 + 6.21265e10i −0.0157624 + 0.0114964i
\(353\) 8.82163e12 1.60944 0.804721 0.593653i \(-0.202315\pi\)
0.804721 + 0.593653i \(0.202315\pi\)
\(354\) −4.00067e11 7.61644e10i −0.0719642 0.0137005i
\(355\) 1.44825e12i 0.256863i
\(356\) 6.74730e12 + 2.66570e12i 1.17999 + 0.466189i
\(357\) 1.03150e12 0.177880
\(358\) 2.48531e11 1.30545e12i 0.0422635 0.221997i
\(359\) 9.24360e11i 0.155013i −0.996992 0.0775066i \(-0.975304\pi\)
0.996992 0.0775066i \(-0.0246959\pi\)
\(360\) −3.16681e11 2.00482e11i −0.0523732 0.0331560i
\(361\) −1.54032e13 −2.51232
\(362\) −7.62924e12 1.45245e12i −1.22727 0.233646i
\(363\) 3.63753e12i 0.577131i
\(364\) −1.89191e12 + 4.78871e12i −0.296069 + 0.749397i
\(365\) −1.31634e12 −0.203190
\(366\) 1.07002e12 5.62046e12i 0.162924 0.855788i
\(367\) 3.72669e12i 0.559748i 0.960037 + 0.279874i \(0.0902927\pi\)
−0.960037 + 0.279874i \(0.909707\pi\)
\(368\) 8.36894e12 8.93834e12i 1.24003 1.32440i
\(369\) −2.46817e12 −0.360780
\(370\) −1.53986e12 2.93157e11i −0.222061 0.0422757i
\(371\) 1.12524e12i 0.160094i
\(372\) −2.88406e12 1.13943e12i −0.404846 0.159945i
\(373\) −1.67319e12 −0.231740 −0.115870 0.993264i \(-0.536966\pi\)
−0.115870 + 0.993264i \(0.536966\pi\)
\(374\) 7.62061e9 4.00286e10i 0.00104143 0.00547032i
\(375\) 1.56483e12i 0.211013i
\(376\) −8.16956e11 + 1.29046e12i −0.108707 + 0.171714i
\(377\) 8.48074e12 1.11359
\(378\) 1.57484e12 + 2.99816e11i 0.204069 + 0.0388505i
\(379\) 4.67608e11i 0.0597979i −0.999553 0.0298989i \(-0.990481\pi\)
0.999553 0.0298989i \(-0.00951855\pi\)
\(380\) 1.01465e12 2.56824e12i 0.128056 0.324129i
\(381\) 4.85252e12 0.604425
\(382\) 1.98552e12 1.04293e13i 0.244095 1.28215i
\(383\) 9.26004e12i 1.12362i 0.827267 + 0.561810i \(0.189895\pi\)
−0.827267 + 0.561810i \(0.810105\pi\)
\(384\) −4.66599e12 + 1.21084e12i −0.558840 + 0.145021i
\(385\) −3.31250e10 −0.00391609
\(386\) −2.56255e12 4.87855e11i −0.299044 0.0569317i
\(387\) 1.87114e12i 0.215552i
\(388\) −3.97639e12 1.57098e12i −0.452199 0.178654i
\(389\) 2.57559e12 0.289153 0.144577 0.989494i \(-0.453818\pi\)
0.144577 + 0.989494i \(0.453818\pi\)
\(390\) −1.35233e11 + 7.10335e11i −0.0149885 + 0.0787300i
\(391\) 4.73249e12i 0.517852i
\(392\) −1.29156e12 8.17651e11i −0.139535 0.0883360i
\(393\) −7.77857e12 −0.829730
\(394\) 3.44483e12 + 6.55823e11i 0.362816 + 0.0690726i
\(395\) 1.18666e12i 0.123408i
\(396\) 2.32696e10 5.88988e10i 0.00238953 0.00604827i
\(397\) 1.20101e13 1.21785 0.608923 0.793229i \(-0.291602\pi\)
0.608923 + 0.793229i \(0.291602\pi\)
\(398\) 3.56697e11 1.87362e12i 0.0357178 0.187614i
\(399\) 1.18111e13i 1.16796i
\(400\) −7.21646e12 6.75675e12i −0.704732 0.659839i
\(401\) −8.93905e12 −0.862124 −0.431062 0.902322i \(-0.641861\pi\)
−0.431062 + 0.902322i \(0.641861\pi\)
\(402\) 3.97902e12 + 7.57521e11i 0.379005 + 0.0721547i
\(403\) 5.98256e12i 0.562810i
\(404\) 4.86111e12 + 1.92051e12i 0.451678 + 0.178448i
\(405\) 2.25138e11 0.0206620
\(406\) −3.32215e12 + 1.74502e13i −0.301154 + 1.58187i
\(407\) 2.64854e11i 0.0237157i
\(408\) 9.96563e11 1.57417e12i 0.0881463 0.139236i
\(409\) 1.11240e13 0.971955 0.485978 0.873971i \(-0.338464\pi\)
0.485978 + 0.873971i \(0.338464\pi\)
\(410\) 2.29070e12 + 4.36100e11i 0.197719 + 0.0376415i
\(411\) 7.74140e12i 0.660101i
\(412\) 2.01944e12 5.11151e12i 0.170116 0.430589i
\(413\) −1.64569e12 −0.136962
\(414\) −1.37555e12 + 7.22535e12i −0.113104 + 0.594097i
\(415\) 3.74472e12i 0.304213i
\(416\) 5.48024e12 + 7.51379e12i 0.439878 + 0.603105i
\(417\) −8.20414e12 −0.650658
\(418\) 4.58347e11 + 8.72597e10i 0.0359181 + 0.00683805i
\(419\) 9.31086e12i 0.720974i 0.932764 + 0.360487i \(0.117390\pi\)
−0.932764 + 0.360487i \(0.882610\pi\)
\(420\) −1.40863e12 5.56517e11i −0.107783 0.0425826i
\(421\) 8.00485e12 0.605261 0.302630 0.953108i \(-0.402135\pi\)
0.302630 + 0.953108i \(0.402135\pi\)
\(422\) −2.86152e12 + 1.50306e13i −0.213813 + 1.12309i
\(423\) 9.17427e11i 0.0677439i
\(424\) −1.71724e12 1.08714e12i −0.125314 0.0793331i
\(425\) 3.82083e12 0.275558
\(426\) 1.09911e13 + 2.09248e12i 0.783420 + 0.149147i
\(427\) 2.31200e13i 1.62873i
\(428\) 4.71002e12 1.19218e13i 0.327947 0.830083i
\(429\) −1.22177e11 −0.00840820
\(430\) −3.30612e11 + 1.73660e12i −0.0224893 + 0.118129i
\(431\) 2.49720e13i 1.67906i −0.543313 0.839530i \(-0.682830\pi\)
0.543313 0.839530i \(-0.317170\pi\)
\(432\) 1.97906e12 2.11371e12i 0.131535 0.140484i
\(433\) 2.14688e12 0.141049 0.0705243 0.997510i \(-0.477533\pi\)
0.0705243 + 0.997510i \(0.477533\pi\)
\(434\) −1.23099e13 2.34354e12i −0.799474 0.152203i
\(435\) 2.49466e12i 0.160164i
\(436\) 1.70419e12 + 6.73288e11i 0.108165 + 0.0427335i
\(437\) −5.41893e13 −3.40022
\(438\) 1.90189e12 9.99002e12i 0.117982 0.619720i
\(439\) 2.89742e13i 1.77700i −0.458872 0.888502i \(-0.651746\pi\)
0.458872 0.888502i \(-0.348254\pi\)
\(440\) −3.20032e10 + 5.05523e10i −0.00194058 + 0.00306533i
\(441\) 9.18209e11 0.0550489
\(442\) −3.53096e12 6.72221e11i −0.209306 0.0398475i
\(443\) 3.44524e12i 0.201930i 0.994890 + 0.100965i \(0.0321930\pi\)
−0.994890 + 0.100965i \(0.967807\pi\)
\(444\) 4.44968e12 1.12628e13i 0.257878 0.652728i
\(445\) 4.11709e12 0.235934
\(446\) −1.19063e12 + 6.25402e12i −0.0674689 + 0.354393i
\(447\) 7.93982e12i 0.444911i
\(448\) −1.76073e13 + 8.33290e12i −0.975671 + 0.461749i
\(449\) 1.60801e13 0.881163 0.440582 0.897713i \(-0.354772\pi\)
0.440582 + 0.897713i \(0.354772\pi\)
\(450\) 5.83346e12 + 1.11057e12i 0.316129 + 0.0601842i
\(451\) 3.93998e11i 0.0211160i
\(452\) −1.98124e13 7.82742e12i −1.05013 0.414884i
\(453\) 6.35484e12 0.333130
\(454\) −4.70674e12 + 2.47230e13i −0.244029 + 1.28180i
\(455\) 2.92199e12i 0.149838i
\(456\) 1.80250e13 + 1.14111e13i 0.914222 + 0.578768i
\(457\) 1.01711e13 0.510256 0.255128 0.966907i \(-0.417882\pi\)
0.255128 + 0.966907i \(0.417882\pi\)
\(458\) 6.73826e12 + 1.28282e12i 0.334365 + 0.0636560i
\(459\) 1.11912e12i 0.0549306i
\(460\) 2.55329e12 6.46277e12i 0.123969 0.313783i
\(461\) 9.47340e12 0.454989 0.227495 0.973779i \(-0.426947\pi\)
0.227495 + 0.973779i \(0.426947\pi\)
\(462\) 4.78602e10 2.51394e11i 0.00227387 0.0119439i
\(463\) 2.15026e13i 1.01062i 0.862939 + 0.505308i \(0.168621\pi\)
−0.862939 + 0.505308i \(0.831379\pi\)
\(464\) 2.34212e13 + 2.19292e13i 1.08898 + 1.01961i
\(465\) −1.75981e12 −0.0809468
\(466\) −1.52645e13 2.90605e12i −0.694631 0.132243i
\(467\) 3.94717e12i 0.177706i 0.996045 + 0.0888529i \(0.0283201\pi\)
−0.996045 + 0.0888529i \(0.971680\pi\)
\(468\) −5.19553e12 2.05263e12i −0.231420 0.0914286i
\(469\) 1.63679e13 0.721319
\(470\) −1.62100e11 + 8.51461e11i −0.00706796 + 0.0371258i
\(471\) 1.19546e13i 0.515740i
\(472\) −1.58996e12 + 2.51150e12i −0.0678698 + 0.107207i
\(473\) −2.98693e11 −0.0126159
\(474\) −9.00589e12 1.71453e12i −0.376387 0.0716562i
\(475\) 4.37503e13i 1.80931i
\(476\) 2.76636e12 7.00207e12i 0.113207 0.286544i
\(477\) 1.22083e12 0.0494384
\(478\) 7.40566e12 3.88996e13i 0.296773 1.55885i
\(479\) 2.30004e13i 0.912132i 0.889946 + 0.456066i \(0.150742\pi\)
−0.889946 + 0.456066i \(0.849258\pi\)
\(480\) −2.21023e12 + 1.61204e12i −0.0867423 + 0.0632661i
\(481\) −2.33631e13 −0.907412
\(482\) 3.15122e13 + 5.99926e12i 1.21128 + 0.230602i
\(483\) 2.97218e13i 1.13068i
\(484\) 2.46926e13 + 9.75547e12i 0.929693 + 0.367300i
\(485\) −2.42633e12 −0.0904150
\(486\) −3.25287e11 + 1.70863e12i −0.0119973 + 0.0630182i
\(487\) 2.30674e13i 0.842081i −0.907042 0.421041i \(-0.861665\pi\)
0.907042 0.421041i \(-0.138335\pi\)
\(488\) −3.52835e13 2.23370e13i −1.27489 0.807098i
\(489\) −1.84490e13 −0.659826
\(490\) −8.52186e11 1.62238e11i −0.0301685 0.00574345i
\(491\) 2.98502e12i 0.104602i −0.998631 0.0523010i \(-0.983344\pi\)
0.998631 0.0523010i \(-0.0166555\pi\)
\(492\) −6.61935e12 + 1.67546e13i −0.229610 + 0.581177i
\(493\) −1.24006e13 −0.425801
\(494\) 7.69726e12 4.04313e13i 0.261639 1.37430i
\(495\) 3.59391e10i 0.00120932i
\(496\) −1.54695e13 + 1.65220e13i −0.515308 + 0.550368i
\(497\) 4.52125e13 1.49100
\(498\) −2.84196e13 5.41049e12i −0.927836 0.176640i
\(499\) 3.07334e13i 0.993364i 0.867933 + 0.496682i \(0.165448\pi\)
−0.867933 + 0.496682i \(0.834552\pi\)
\(500\) −1.06225e13 4.19670e12i −0.339919 0.134294i
\(501\) 1.22786e13 0.389009
\(502\) 5.45101e12 2.86324e13i 0.170985 0.898130i
\(503\) 4.69700e12i 0.145875i −0.997337 0.0729375i \(-0.976763\pi\)
0.997337 0.0729375i \(-0.0232374\pi\)
\(504\) 6.25878e12 9.88637e12i 0.192459 0.304007i
\(505\) 2.96617e12 0.0903106
\(506\) 1.15340e12 + 2.19582e11i 0.0347717 + 0.00661980i
\(507\) 8.56366e12i 0.255634i
\(508\) 1.30139e13 3.29402e13i 0.384671 0.973662i
\(509\) −3.25728e13 −0.953379 −0.476690 0.879072i \(-0.658163\pi\)
−0.476690 + 0.879072i \(0.658163\pi\)
\(510\) 1.97738e11 1.03865e12i 0.00573111 0.0301037i
\(511\) 4.10943e13i 1.17944i
\(512\) −4.29417e12 + 3.49213e13i −0.122048 + 0.992524i
\(513\) −1.28145e13 −0.360674
\(514\) 1.07076e13 + 2.03850e12i 0.298453 + 0.0568192i
\(515\) 3.11896e12i 0.0860941i
\(516\) −1.27018e13 5.01819e12i −0.347230 0.137183i
\(517\) −1.46451e11 −0.00396496
\(518\) 9.15197e12 4.80724e13i 0.245395 1.28898i
\(519\) 1.09402e13i 0.290529i
\(520\) 4.45927e12 + 2.82304e12i 0.117286 + 0.0742506i
\(521\) 5.30729e13 1.38256 0.691281 0.722586i \(-0.257047\pi\)
0.691281 + 0.722586i \(0.257047\pi\)
\(522\) −1.89326e13 3.60437e12i −0.488493 0.0929988i
\(523\) 1.20881e13i 0.308924i −0.987999 0.154462i \(-0.950636\pi\)
0.987999 0.154462i \(-0.0493644\pi\)
\(524\) −2.08613e13 + 5.28030e13i −0.528061 + 1.33660i
\(525\) 2.39962e13 0.601653
\(526\) −4.90624e12 + 2.57709e13i −0.121849 + 0.640032i
\(527\) 8.74772e12i 0.215200i
\(528\) −3.37415e11 3.15921e11i −0.00822233 0.00769854i
\(529\) −9.49367e13 −2.29169
\(530\) −1.13305e12 2.15709e11i −0.0270938 0.00515809i
\(531\) 1.78550e12i 0.0422948i
\(532\) 8.01772e13 + 3.16762e13i 1.88145 + 0.743318i
\(533\) 3.47549e13 0.807942
\(534\) −5.94852e12 + 3.12457e13i −0.136994 + 0.719587i
\(535\) 7.27446e12i 0.165971i
\(536\) 1.58135e13 2.49791e13i 0.357442 0.564615i
\(537\) 5.82624e12 0.130472
\(538\) −3.56058e13 6.77859e12i −0.789968 0.150393i
\(539\) 1.46575e11i 0.00322194i
\(540\) 6.03794e11 1.52829e12i 0.0131498 0.0332842i
\(541\) −1.20532e12 −0.0260085 −0.0130042 0.999915i \(-0.504139\pi\)
−0.0130042 + 0.999915i \(0.504139\pi\)
\(542\) −9.38388e12 + 4.92905e13i −0.200626 + 1.05382i
\(543\) 3.40493e13i 0.721289i
\(544\) −8.01322e12 1.09867e13i −0.168195 0.230607i
\(545\) 1.03987e12 0.0216270
\(546\) −2.21758e13 4.22180e12i −0.456999 0.0870030i
\(547\) 6.28676e13i 1.28378i 0.766797 + 0.641890i \(0.221849\pi\)
−0.766797 + 0.641890i \(0.778151\pi\)
\(548\) −5.25508e13 2.07616e13i −1.06335 0.420105i
\(549\) 2.50841e13 0.502964
\(550\) 1.77282e11 9.31206e11i 0.00352250 0.0185026i
\(551\) 1.41993e14i 2.79581i
\(552\) 4.53586e13 + 2.87152e13i 0.885042 + 0.560295i
\(553\) −3.70461e13 −0.716336
\(554\) 9.13951e13 + 1.73997e13i 1.75135 + 0.333421i
\(555\) 6.87238e12i 0.130510i
\(556\) −2.20026e13 + 5.56919e13i −0.414095 + 1.04814i
\(557\) −7.32140e13 −1.36558 −0.682791 0.730614i \(-0.739234\pi\)
−0.682791 + 0.730614i \(0.739234\pi\)
\(558\) 2.54263e12 1.33556e13i 0.0470015 0.246884i
\(559\) 2.63480e13i 0.482713i
\(560\) −7.55557e12 + 8.06963e12i −0.137192 + 0.146526i
\(561\) 1.78648e11 0.00321502
\(562\) 5.71569e13 + 1.08815e13i 1.01950 + 0.194091i
\(563\) 7.76911e13i 1.37350i 0.726893 + 0.686751i \(0.240964\pi\)
−0.726893 + 0.686751i \(0.759036\pi\)
\(564\) −6.22775e12 2.46044e12i −0.109128 0.0431139i
\(565\) −1.20892e13 −0.209969
\(566\) −1.36919e13 + 7.19193e13i −0.235712 + 1.23812i
\(567\) 7.02851e12i 0.119936i
\(568\) 4.36814e13 6.89990e13i 0.738847 1.16708i
\(569\) 8.43027e13 1.41345 0.706725 0.707489i \(-0.250172\pi\)
0.706725 + 0.707489i \(0.250172\pi\)
\(570\) 1.18931e13 + 2.26420e12i 0.197661 + 0.0376305i
\(571\) 9.41889e13i 1.55174i −0.630892 0.775870i \(-0.717311\pi\)
0.630892 0.775870i \(-0.282689\pi\)
\(572\) −3.27665e11 + 8.29371e11i −0.00535119 + 0.0135447i
\(573\) 4.65461e13 0.753546
\(574\) −1.36145e13 + 7.15126e13i −0.218495 + 1.14769i
\(575\) 1.10094e14i 1.75156i
\(576\) −9.04080e12 1.91031e13i −0.142592 0.301295i
\(577\) 5.21382e13 0.815224 0.407612 0.913155i \(-0.366362\pi\)
0.407612 + 0.913155i \(0.366362\pi\)
\(578\) −5.82106e13 1.10821e13i −0.902324 0.171784i
\(579\) 1.14366e13i 0.175754i
\(580\) 1.69344e13 + 6.69041e12i 0.258007 + 0.101933i
\(581\) −1.16905e14 −1.76585
\(582\) 3.50564e12 1.84140e13i 0.0524992 0.275761i
\(583\) 1.94884e11i 0.00289357i
\(584\) −6.27143e13 3.97027e13i −0.923214 0.584461i
\(585\) −3.17022e12 −0.0462712
\(586\) −1.14634e12 2.18239e11i −0.0165892 0.00315823i
\(587\) 6.27357e12i 0.0900169i 0.998987 + 0.0450084i \(0.0143315\pi\)
−0.998987 + 0.0450084i \(0.985669\pi\)
\(588\) 2.46254e12 6.23305e12i 0.0350345 0.0886776i
\(589\) 1.00166e14 1.41300
\(590\) −3.15480e11 + 1.65711e12i −0.00441277 + 0.0231789i
\(591\) 1.53743e13i 0.213234i
\(592\) −6.45215e13 6.04113e13i −0.887352 0.830825i
\(593\) −2.50022e13 −0.340961 −0.170480 0.985361i \(-0.554532\pi\)
−0.170480 + 0.985361i \(0.554532\pi\)
\(594\) 2.72751e11 + 5.19261e10i 0.00368837 + 0.000702188i
\(595\) 4.27255e12i 0.0572931i
\(596\) −5.38976e13 2.12937e13i −0.716702 0.283152i
\(597\) 8.36195e12 0.110265
\(598\) 1.93696e13 1.01742e14i 0.253288 1.33044i
\(599\) 6.23083e13i 0.808001i −0.914759 0.404000i \(-0.867619\pi\)
0.914759 0.404000i \(-0.132381\pi\)
\(600\) 2.31836e13 3.66207e13i 0.298142 0.470945i
\(601\) −6.66674e13 −0.850239 −0.425120 0.905137i \(-0.639768\pi\)
−0.425120 + 0.905137i \(0.639768\pi\)
\(602\) −5.42144e13 1.03213e13i −0.685696 0.130542i
\(603\) 1.77583e13i 0.222749i
\(604\) 1.70430e13 4.31384e13i 0.212012 0.536635i
\(605\) 1.50670e13 0.185887
\(606\) −4.28562e12 + 2.25110e13i −0.0524386 + 0.275443i
\(607\) 5.40578e11i 0.00656016i −0.999995 0.00328008i \(-0.998956\pi\)
0.999995 0.00328008i \(-0.00104408\pi\)
\(608\) 1.25803e14 9.17553e13i 1.51417 1.10437i
\(609\) −7.78801e13 −0.929695
\(610\) −2.32805e13 4.43211e12i −0.275640 0.0524761i
\(611\) 1.29185e13i 0.151708i
\(612\) 7.59692e12 + 3.00137e12i 0.0884872 + 0.0349593i
\(613\) 1.04416e14 1.20633 0.603163 0.797618i \(-0.293907\pi\)
0.603163 + 0.797618i \(0.293907\pi\)
\(614\) 8.73125e12 4.58625e13i 0.100054 0.525552i
\(615\) 1.02234e13i 0.116203i
\(616\) −1.57818e12 9.99101e11i −0.0177931 0.0112643i
\(617\) −8.83409e13 −0.987952 −0.493976 0.869476i \(-0.664457\pi\)
−0.493976 + 0.869476i \(0.664457\pi\)
\(618\) 2.36706e13 + 4.50638e12i 0.262583 + 0.0499903i
\(619\) 5.36101e13i 0.589921i 0.955509 + 0.294960i \(0.0953065\pi\)
−0.955509 + 0.294960i \(0.904694\pi\)
\(620\) −4.71961e12 + 1.19460e13i −0.0515166 + 0.130396i
\(621\) −3.22467e13 −0.349162
\(622\) −1.51554e13 + 7.96063e13i −0.162785 + 0.855057i
\(623\) 1.28530e14i 1.36951i
\(624\) −2.78677e13 + 2.97637e13i −0.294563 + 0.314604i
\(625\) 8.55879e13 0.897454
\(626\) 1.08159e14 + 2.05912e13i 1.12510 + 0.214195i
\(627\) 2.04560e12i 0.0211098i
\(628\) −8.11511e13 3.20610e13i −0.830800 0.328230i
\(629\) 3.41616e13 0.346964
\(630\) 1.24187e12 6.52313e12i 0.0125133 0.0657284i
\(631\) 1.20585e13i 0.120544i 0.998182 + 0.0602720i \(0.0191968\pi\)
−0.998182 + 0.0602720i \(0.980803\pi\)
\(632\) −3.57915e13 + 5.65362e13i −0.354972 + 0.560714i
\(633\) −6.70817e13 −0.660063
\(634\) −8.23191e13 1.56718e13i −0.803626 0.152994i
\(635\) 2.00996e13i 0.194679i
\(636\) 3.27414e12 8.28736e12i 0.0314639 0.0796398i
\(637\) −1.29295e13 −0.123278
\(638\) −5.75373e11 + 3.02225e12i −0.00544309 + 0.0285908i
\(639\) 4.90534e13i 0.460432i
\(640\) 5.01540e12 + 1.93270e13i 0.0467096 + 0.179996i
\(641\) 1.89650e14 1.75252 0.876261 0.481837i \(-0.160030\pi\)
0.876261 + 0.481837i \(0.160030\pi\)
\(642\) 5.52078e13 + 1.05104e13i 0.506203 + 0.0963705i
\(643\) 1.11907e14i 1.01813i 0.860729 + 0.509064i \(0.170008\pi\)
−0.860729 + 0.509064i \(0.829992\pi\)
\(644\) 2.01760e14 + 7.97106e13i 1.82140 + 0.719592i
\(645\) −7.75043e12 −0.0694268
\(646\) −1.12550e13 + 5.91188e13i −0.100042 + 0.525488i
\(647\) 7.82465e13i 0.690150i −0.938575 0.345075i \(-0.887854\pi\)
0.938575 0.345075i \(-0.112146\pi\)
\(648\) 1.07262e13 + 6.79048e12i 0.0938799 + 0.0594327i
\(649\) −2.85022e11 −0.00247546
\(650\) −8.21426e13 1.56382e13i −0.707948 0.134778i
\(651\) 5.49389e13i 0.469867i
\(652\) −4.94783e13 + 1.25237e14i −0.419930 + 1.06291i
\(653\) −1.20791e14 −1.01735 −0.508674 0.860959i \(-0.669864\pi\)
−0.508674 + 0.860959i \(0.669864\pi\)
\(654\) −1.50244e12 + 7.89185e12i −0.0125577 + 0.0659614i
\(655\) 3.22195e13i 0.267247i
\(656\) 9.59823e13 + 8.98680e13i 0.790082 + 0.739751i
\(657\) 4.45854e13 0.364222
\(658\) −2.65815e13 5.06056e12i −0.215502 0.0410270i
\(659\) 7.03328e13i 0.565889i −0.959136 0.282944i \(-0.908689\pi\)
0.959136 0.282944i \(-0.0913112\pi\)
\(660\) −2.43964e11 9.63848e10i −0.00194808 0.000769642i
\(661\) −1.51959e13 −0.120425 −0.0602127 0.998186i \(-0.519178\pi\)
−0.0602127 + 0.998186i \(0.519178\pi\)
\(662\) 2.78201e13 1.46130e14i 0.218811 1.14934i
\(663\) 1.57587e13i 0.123013i
\(664\) −1.12946e14 + 1.78410e14i −0.875047 + 1.38222i
\(665\) 4.89228e13 0.376186
\(666\) 5.21563e13 + 9.92946e12i 0.398048 + 0.0757800i
\(667\) 3.57313e14i 2.70658i
\(668\) 3.29298e13 8.33504e13i 0.247575 0.626651i
\(669\) −2.79117e13 −0.208284
\(670\) 3.13772e12 1.64815e13i 0.0232402 0.122074i
\(671\) 4.00422e12i 0.0294378i
\(672\) −5.03260e13 6.90005e13i −0.367236 0.503507i
\(673\) −3.29058e11 −0.00238340 −0.00119170 0.999999i \(-0.500379\pi\)
−0.00119170 + 0.999999i \(0.500379\pi\)
\(674\) −4.49968e13 8.56645e12i −0.323506 0.0615887i
\(675\) 2.60347e13i 0.185795i
\(676\) −5.81324e13 2.29668e13i −0.411799 0.162692i
\(677\) −4.89695e13 −0.344336 −0.172168 0.985068i \(-0.555077\pi\)
−0.172168 + 0.985068i \(0.555077\pi\)
\(678\) 1.74669e13 9.17479e13i 0.121918 0.640395i
\(679\) 7.57468e13i 0.524826i
\(680\) −6.52036e12 4.12786e12i −0.0448463 0.0283910i
\(681\) −1.10339e14 −0.753342
\(682\) −2.13198e12 4.05884e11i −0.0144498 0.00275093i
\(683\) 2.08049e14i 1.39979i −0.714247 0.699893i \(-0.753231\pi\)
0.714247 0.699893i \(-0.246769\pi\)
\(684\) −3.43671e13 + 8.69884e13i −0.229542 + 0.581006i
\(685\) −3.20656e13 −0.212611
\(686\) −2.56041e13 + 1.34490e14i −0.168534 + 0.885257i
\(687\) 3.00729e13i 0.196513i
\(688\) −6.81297e13 + 7.27651e13i −0.441972 + 0.472042i
\(689\) −1.71909e13 −0.110714
\(690\) 2.99281e13 + 5.69767e12i 0.191352 + 0.0364294i
\(691\) 7.10583e13i 0.451050i −0.974237 0.225525i \(-0.927590\pi\)
0.974237 0.225525i \(-0.0724097\pi\)
\(692\) 7.42651e13 + 2.93405e13i 0.468009 + 0.184900i
\(693\) 1.12197e12 0.00701966
\(694\) 4.18719e13 2.19939e14i 0.260091 1.36617i
\(695\) 3.39823e13i 0.209570i
\(696\) −7.52427e13 + 1.18853e14i −0.460700 + 0.727721i
\(697\) −5.08188e13 −0.308930
\(698\) 2.53651e13 + 4.82899e12i 0.153095 + 0.0291460i
\(699\) 6.81256e13i 0.408249i
\(700\) 6.43552e13 1.62893e14i 0.382907 0.969195i
\(701\) −8.56643e13 −0.506069 −0.253034 0.967457i \(-0.581429\pi\)
−0.253034 + 0.967457i \(0.581429\pi\)
\(702\) 4.58045e12 2.40596e13i 0.0268672 0.141125i
\(703\) 3.91167e14i 2.27816i
\(704\) −3.04947e12 + 1.44320e12i −0.0176344 + 0.00834571i
\(705\) −3.80007e12 −0.0218196
\(706\) 2.77312e14 + 5.27943e13i 1.58105 + 0.300998i
\(707\) 9.26000e13i 0.524220i
\(708\) −1.21205e13 4.78851e12i −0.0681322 0.0269175i
\(709\) 7.70651e13 0.430156 0.215078 0.976597i \(-0.430999\pi\)
0.215078 + 0.976597i \(0.430999\pi\)
\(710\) 8.66725e12 4.55263e13i 0.0480385 0.252331i
\(711\) 4.01932e13i 0.221210i
\(712\) 1.96151e14 + 1.24178e14i 1.07199 + 0.678646i
\(713\) 2.52059e14 1.36790
\(714\) 3.24255e13 + 6.17313e12i 0.174741 + 0.0332670i
\(715\) 5.06068e11i 0.00270819i
\(716\) 1.56253e13 3.95501e13i 0.0830356 0.210176i
\(717\) 1.73609e14 0.916170
\(718\) 5.53196e12 2.90576e13i 0.0289906 0.152278i
\(719\) 1.84786e14i 0.961664i 0.876813 + 0.480832i \(0.159665\pi\)
−0.876813 + 0.480832i \(0.840335\pi\)
\(720\) −8.75517e12 8.19744e12i −0.0452483 0.0423658i
\(721\) 9.73699e13 0.499745
\(722\) −4.84206e14 9.21827e13i −2.46800 0.469855i
\(723\) 1.40639e14i 0.711892i
\(724\) −2.31136e14 9.13165e13i −1.16192 0.459046i
\(725\) −2.88481e14 −1.44021
\(726\) −2.17693e13 + 1.14347e14i −0.107935 + 0.566948i
\(727\) 1.03169e14i 0.508015i −0.967202 0.254008i \(-0.918251\pi\)
0.967202 0.254008i \(-0.0817489\pi\)
\(728\) −8.81317e13 + 1.39213e14i −0.430998 + 0.680803i
\(729\) −7.62560e12 −0.0370370
\(730\) −4.13796e13 7.87780e12i −0.199605 0.0380006i
\(731\) 3.85262e13i 0.184573i
\(732\) 6.72728e13 1.70278e14i 0.320099 0.810219i
\(733\) −4.49715e13 −0.212528 −0.106264 0.994338i \(-0.533889\pi\)
−0.106264 + 0.994338i \(0.533889\pi\)
\(734\) −2.23029e13 + 1.17150e14i −0.104684 + 0.549872i
\(735\) 3.80330e12i 0.0177306i
\(736\) 3.16574e14 2.30895e14i 1.46584 1.06912i
\(737\) 2.83480e12 0.0130372
\(738\) −7.75878e13 1.47711e13i −0.354415 0.0674731i
\(739\) 1.52473e14i 0.691782i 0.938275 + 0.345891i \(0.112423\pi\)
−0.938275 + 0.345891i \(0.887577\pi\)
\(740\) −4.66516e13 1.84310e13i −0.210236 0.0830596i
\(741\) 1.80445e14 0.807706
\(742\) 6.73417e12 3.53724e13i 0.0299409 0.157270i
\(743\) 4.33975e14i 1.91655i 0.285844 + 0.958276i \(0.407726\pi\)
−0.285844 + 0.958276i \(0.592274\pi\)
\(744\) −8.38425e13 5.30784e13i −0.367790 0.232837i
\(745\) −3.28874e13 −0.143301
\(746\) −5.25973e13 1.00134e13i −0.227651 0.0433400i
\(747\) 1.26837e14i 0.545308i
\(748\) 4.79114e11 1.21271e12i 0.00204612 0.00517903i
\(749\) 2.27099e14 0.963401
\(750\) 9.36492e12 4.91909e13i 0.0394637 0.207290i
\(751\) 9.28346e13i 0.388607i 0.980942 + 0.194303i \(0.0622446\pi\)
−0.980942 + 0.194303i \(0.937755\pi\)
\(752\) −3.34043e13 + 3.56770e13i −0.138903 + 0.148354i
\(753\) 1.27786e14 0.527849
\(754\) 2.66596e14 + 5.07542e13i 1.09395 + 0.208264i
\(755\) 2.63223e13i 0.107298i
\(756\) 4.77114e13 + 1.88497e13i 0.193203 + 0.0763300i
\(757\) −1.57105e14 −0.631990 −0.315995 0.948761i \(-0.602338\pi\)
−0.315995 + 0.948761i \(0.602338\pi\)
\(758\) 2.79846e12 1.46994e13i 0.0111834 0.0587428i
\(759\) 5.14760e12i 0.0204360i
\(760\) 4.72660e13 7.46613e13i 0.186415 0.294461i
\(761\) −3.45476e14 −1.35361 −0.676806 0.736161i \(-0.736636\pi\)
−0.676806 + 0.736161i \(0.736636\pi\)
\(762\) 1.52541e14 + 2.90406e13i 0.593761 + 0.113040i
\(763\) 3.24634e13i 0.125537i
\(764\) 1.24831e14 3.15967e14i 0.479576 1.21388i
\(765\) 4.63551e12 0.0176926
\(766\) −5.54180e13 + 2.91093e14i −0.210139 + 1.10379i
\(767\) 2.51421e13i 0.0947163i
\(768\) −1.53924e14 + 1.01389e13i −0.576102 + 0.0379478i
\(769\) −4.95927e14 −1.84411 −0.922053 0.387064i \(-0.873489\pi\)
−0.922053 + 0.387064i \(0.873489\pi\)
\(770\) −1.04130e12 1.98241e11i −0.00384700 0.000732387i
\(771\) 4.77880e13i 0.175407i
\(772\) −7.76351e13 3.06718e13i −0.283121 0.111854i
\(773\) 5.38678e14 1.95179 0.975893 0.218251i \(-0.0700352\pi\)
0.975893 + 0.218251i \(0.0700352\pi\)
\(774\) 1.11981e13 5.88200e13i 0.0403125 0.211749i
\(775\) 2.03503e14i 0.727882i
\(776\) −1.15598e14 7.31816e13i −0.410809 0.260072i
\(777\) 2.14547e14 0.757561
\(778\) 8.09645e13 + 1.54139e13i 0.284051 + 0.0540774i
\(779\) 5.81900e14i 2.02844i
\(780\) −8.50219e12 + 2.15203e13i −0.0294481 + 0.0745377i
\(781\) 7.83048e12 0.0269484
\(782\) −2.83222e13 + 1.48768e14i −0.0968487 + 0.508715i
\(783\) 8.44963e13i 0.287097i
\(784\) −3.57074e13 3.34327e13i −0.120553 0.112873i
\(785\) −4.95171e13 −0.166114
\(786\) −2.44522e14 4.65519e13i −0.815091 0.155176i
\(787\) 9.70514e13i 0.321461i 0.986998 + 0.160730i \(0.0513850\pi\)
−0.986998 + 0.160730i \(0.948615\pi\)
\(788\) 1.04365e14 + 4.12321e13i 0.343497 + 0.135708i
\(789\) −1.15016e14 −0.376159
\(790\) −7.10174e12 + 3.73032e13i −0.0230797 + 0.121230i
\(791\) 3.77409e14i 1.21879i
\(792\) 1.08398e12 1.71225e12i 0.00347852 0.00549466i
\(793\) −3.53216e14 −1.12635
\(794\) 3.77541e14 + 7.18758e13i 1.19636 + 0.227762i
\(795\) 5.05681e12i 0.0159236i
\(796\) 2.24259e13 5.67632e13i 0.0701752 0.177624i
\(797\) −1.94845e14 −0.605896 −0.302948 0.953007i \(-0.597971\pi\)
−0.302948 + 0.953007i \(0.597971\pi\)
\(798\) −7.06853e13 + 3.71288e14i −0.218431 + 1.14735i
\(799\) 1.88895e13i 0.0580080i
\(800\) −1.86416e14 2.55589e14i −0.568895 0.779996i
\(801\) −1.39449e14 −0.422916
\(802\) −2.81003e14 5.34970e13i −0.846913 0.161234i
\(803\) 7.11725e12i 0.0213174i
\(804\) 1.20548e14 + 4.76259e13i 0.358824 + 0.141763i
\(805\) 1.23110e14 0.364179
\(806\) −3.58034e13 + 1.88064e14i −0.105257 + 0.552880i
\(807\) 1.58909e14i 0.464280i
\(808\) 1.41317e14 + 8.94641e13i 0.410335 + 0.259772i
\(809\) 3.48567e14 1.00587 0.502937 0.864323i \(-0.332253\pi\)
0.502937 + 0.864323i \(0.332253\pi\)
\(810\) 7.07729e12 + 1.34737e12i 0.0202975 + 0.00386421i
\(811\) 2.49629e14i 0.711527i −0.934576 0.355764i \(-0.884221\pi\)
0.934576 0.355764i \(-0.115779\pi\)
\(812\) −2.08866e14 + 5.28672e14i −0.591681 + 1.49763i
\(813\) −2.19984e14 −0.619352
\(814\) 1.58506e12 8.32580e12i 0.00443530 0.0232972i
\(815\) 7.64176e13i 0.212523i
\(816\) 4.07482e13 4.35206e13i 0.112631 0.120294i
\(817\) 4.41144e14 1.21191
\(818\) 3.49689e14 + 6.65734e13i 0.954806 + 0.181775i
\(819\) 9.89703e13i 0.268587i
\(820\) 6.93990e13 + 2.74180e13i 0.187191 + 0.0739547i
\(821\) 1.10644e14 0.296628 0.148314 0.988940i \(-0.452615\pi\)
0.148314 + 0.988940i \(0.452615\pi\)
\(822\) 4.63295e13 2.43354e14i 0.123452 0.648455i
\(823\) 7.95142e13i 0.210594i −0.994441 0.105297i \(-0.966421\pi\)
0.994441 0.105297i \(-0.0335793\pi\)
\(824\) 9.40725e13 1.48597e14i 0.247643 0.391177i
\(825\) 4.15597e12 0.0108743
\(826\) −5.17330e13 9.84888e12i −0.134545 0.0256145i
\(827\) 4.26755e14i 1.10319i 0.834112 + 0.551595i \(0.185981\pi\)
−0.834112 + 0.551595i \(0.814019\pi\)
\(828\) −8.64822e13 + 2.18900e14i −0.222216 + 0.562462i
\(829\) −2.10345e14 −0.537230 −0.268615 0.963248i \(-0.586566\pi\)
−0.268615 + 0.963248i \(0.586566\pi\)
\(830\) −2.24108e13 + 1.17717e14i −0.0568940 + 0.298846i
\(831\) 4.07896e14i 1.02931i
\(832\) 1.27306e14 + 2.68996e14i 0.319325 + 0.674729i
\(833\) 1.89056e13 0.0471375
\(834\) −2.57900e14 4.90988e13i −0.639178 0.121686i
\(835\) 5.08590e13i 0.125296i
\(836\) 1.38861e13 + 5.48609e12i 0.0340055 + 0.0134348i
\(837\) 5.96061e13 0.145099
\(838\) −5.57221e13 + 2.92691e14i −0.134837 + 0.708253i
\(839\) 5.23755e14i 1.25985i −0.776657 0.629924i \(-0.783086\pi\)
0.776657 0.629924i \(-0.216914\pi\)
\(840\) −4.09502e13 2.59245e13i −0.0979174 0.0619888i
\(841\) 5.15563e14 1.22547
\(842\) 2.51636e14 + 4.79061e13i 0.594582 + 0.113196i
\(843\) 2.55091e14i 0.599180i
\(844\) −1.79906e14 + 4.55369e14i −0.420081 + 1.06329i
\(845\) −3.54714e13 −0.0823371
\(846\) 5.49047e12 2.88397e13i 0.0126695 0.0665486i
\(847\) 4.70373e14i 1.07901i
\(848\) −4.74759e13 4.44516e13i −0.108267 0.101370i
\(849\) −3.20976e14 −0.727668
\(850\) 1.20109e14 + 2.28663e13i 0.270696 + 0.0515348i
\(851\) 9.84340e14i 2.20545i
\(852\) 3.32988e14 + 1.31556e14i 0.741704 + 0.293030i
\(853\) −2.01871e13 −0.0447022 −0.0223511 0.999750i \(-0.507115\pi\)
−0.0223511 + 0.999750i \(0.507115\pi\)
\(854\) 1.38365e14 7.26786e14i 0.304604 1.59999i
\(855\) 5.30789e13i 0.116169i
\(856\) 2.19409e14 3.46578e14i 0.477403 0.754105i
\(857\) −3.39453e14 −0.734304 −0.367152 0.930161i \(-0.619667\pi\)
−0.367152 + 0.930161i \(0.619667\pi\)
\(858\) −3.84068e12 7.31185e11i −0.00825985 0.00157250i
\(859\) 2.59695e14i 0.555262i −0.960688 0.277631i \(-0.910451\pi\)
0.960688 0.277631i \(-0.0895493\pi\)
\(860\) −2.07858e13 + 5.26120e13i −0.0441850 + 0.111839i
\(861\) −3.19161e14 −0.674518
\(862\) 1.49448e14 7.85003e14i 0.314018 1.64943i
\(863\) 3.06623e14i 0.640547i −0.947325 0.320274i \(-0.896225\pi\)
0.947325 0.320274i \(-0.103775\pi\)
\(864\) 7.48623e13 5.46013e13i 0.155487 0.113406i
\(865\) 4.53154e13 0.0935761
\(866\) 6.74881e13 + 1.28483e13i 0.138560 + 0.0263789i
\(867\) 2.59794e14i 0.530314i
\(868\) −3.72940e14 1.47340e14i −0.756903 0.299035i
\(869\) −6.41612e12 −0.0129471
\(870\) −1.49296e13 + 7.84207e13i −0.0299539 + 0.157338i
\(871\) 2.50060e14i 0.498831i
\(872\) 4.95426e13 + 3.13641e13i 0.0982645 + 0.0622085i
\(873\) 8.21817e13 0.162070
\(874\) −1.70346e15 3.24304e14i −3.34022 0.635908i
\(875\) 2.02349e14i 0.394513i
\(876\) 1.19573e14 3.02658e14i 0.231800 0.586721i
\(877\) 2.51052e14 0.483912 0.241956 0.970287i \(-0.422211\pi\)
0.241956 + 0.970287i \(0.422211\pi\)
\(878\) 1.73400e14 9.10815e14i 0.332335 1.74565i
\(879\) 5.11611e12i 0.00974980i
\(880\) −1.30857e12 + 1.39760e12i −0.00247961 + 0.00264832i
\(881\) −4.49257e14 −0.846478 −0.423239 0.906018i \(-0.639107\pi\)
−0.423239 + 0.906018i \(0.639107\pi\)
\(882\) 2.88642e13 + 5.49515e12i 0.0540776 + 0.0102952i
\(883\) 5.14061e14i 0.957660i 0.877908 + 0.478830i \(0.158939\pi\)
−0.877908 + 0.478830i \(0.841061\pi\)
\(884\) −1.06974e14 4.22631e13i −0.198161 0.0782888i
\(885\) −7.39570e12 −0.0136227
\(886\) −2.06185e13 + 1.08302e14i −0.0377649 + 0.198367i
\(887\) 2.84864e14i 0.518824i −0.965767 0.259412i \(-0.916471\pi\)
0.965767 0.259412i \(-0.0835287\pi\)
\(888\) 2.07281e14 3.27421e14i 0.375401 0.592983i
\(889\) 6.27483e14 1.13004
\(890\) 1.29422e14 + 2.46393e13i 0.231771 + 0.0441244i
\(891\) 1.21729e12i 0.00216773i
\(892\) −7.48561e13 + 1.89472e14i −0.132557 + 0.335522i
\(893\) 2.16295e14 0.380880
\(894\) 4.75169e13 2.49591e14i 0.0832072 0.437061i
\(895\) 2.41328e13i 0.0420235i
\(896\) −6.03363e14 + 1.56575e14i −1.04481 + 0.271132i
\(897\) 4.54075e14 0.781925
\(898\) 5.05483e14 + 9.62334e13i 0.865616 + 0.164795i
\(899\) 6.60472e14i 1.12475i
\(900\) 1.76731e14 + 6.98223e13i 0.299295 + 0.118245i
\(901\) 2.51366e13 0.0423333
\(902\) −2.35793e12 + 1.23855e13i −0.00394911 + 0.0207434i
\(903\) 2.41959e14i 0.402997i
\(904\) −5.75966e14 3.64628e14i −0.954013 0.603959i
\(905\) −1.41035e14 −0.232319
\(906\) 1.99767e14 + 3.80314e13i 0.327252 + 0.0623020i
\(907\) 6.52723e14i 1.06339i 0.846936 + 0.531695i \(0.178445\pi\)
−0.846936 + 0.531695i \(0.821555\pi\)
\(908\) −2.95916e14 + 7.49009e14i −0.479446 + 1.21355i
\(909\) −1.00467e14 −0.161883
\(910\) −1.74871e13 + 9.18540e13i −0.0280227 + 0.147194i
\(911\) 7.55207e14i 1.20358i 0.798655 + 0.601789i \(0.205545\pi\)
−0.798655 + 0.601789i \(0.794455\pi\)
\(912\) 4.98332e14 + 4.66587e14i 0.789850 + 0.739534i
\(913\) −2.02472e13 −0.0319161
\(914\) 3.19734e14 + 6.08706e13i 0.501253 + 0.0954281i
\(915\) 1.03901e14i 0.161999i
\(916\) 2.04143e14 + 8.06521e13i 0.316560 + 0.125066i
\(917\) −1.00585e15 −1.55127
\(918\) −6.69755e12 + 3.51801e13i −0.0102731 + 0.0539614i
\(919\) 6.42521e14i 0.980189i −0.871669 0.490094i \(-0.836962\pi\)
0.871669 0.490094i \(-0.163038\pi\)
\(920\) 1.18941e14 1.87879e14i 0.180465 0.285062i
\(921\) 2.04684e14 0.308878
\(922\) 2.97800e14 + 5.66948e13i 0.446961 + 0.0850921i
\(923\) 6.90735e14i 1.03110i
\(924\) 3.00901e12 7.61626e12i 0.00446749 0.0113079i
\(925\) 7.94717e14 1.17356
\(926\) −1.28685e14 + 6.75943e14i −0.189005 + 0.992784i
\(927\) 1.05642e14i 0.154325i
\(928\) 6.05016e14 + 8.29520e14i 0.879077 + 1.20528i
\(929\) −5.50071e14 −0.794951 −0.397476 0.917613i \(-0.630114\pi\)
−0.397476 + 0.917613i \(0.630114\pi\)
\(930\) −5.53202e13 1.05318e13i −0.0795186 0.0151387i
\(931\) 2.16479e14i 0.309504i
\(932\) −4.62455e14 1.82706e14i −0.657643 0.259820i
\(933\) −3.55283e14 −0.502534
\(934\) −2.36224e13 + 1.24081e14i −0.0332345 + 0.174570i
\(935\) 7.39975e11i 0.00103552i
\(936\) −1.51039e14 9.56187e13i −0.210238 0.133096i
\(937\) −1.18951e14 −0.164691 −0.0823456 0.996604i \(-0.526241\pi\)
−0.0823456 + 0.996604i \(0.526241\pi\)
\(938\) 5.14530e14 + 9.79557e13i 0.708592 + 0.134901i
\(939\) 4.82713e14i 0.661243i
\(940\) −1.01914e13 + 2.57959e13i −0.0138865 + 0.0351489i
\(941\) 1.25811e15 1.70518 0.852588 0.522584i \(-0.175032\pi\)
0.852588 + 0.522584i \(0.175032\pi\)
\(942\) 7.15440e13 3.75798e14i 0.0964536 0.506640i
\(943\) 1.46431e15i 1.96369i
\(944\) −6.50115e13 + 6.94347e13i −0.0867222 + 0.0926225i
\(945\) 2.91127e13 0.0386299
\(946\) −9.38954e12 1.78757e12i −0.0123934 0.00235943i
\(947\) 5.61155e14i 0.736772i 0.929673 + 0.368386i \(0.120089\pi\)
−0.929673 + 0.368386i \(0.879911\pi\)
\(948\) −2.72843e14 1.07794e14i −0.356345 0.140784i
\(949\) −6.27820e14 −0.815650
\(950\) −2.61830e14 + 1.37531e15i −0.338377 + 1.77739i
\(951\) 3.67390e14i 0.472307i
\(952\) 1.28866e14 2.03557e14i 0.164799 0.260317i
\(953\) −4.49938e14 −0.572385 −0.286192 0.958172i \(-0.592390\pi\)
−0.286192 + 0.958172i \(0.592390\pi\)
\(954\) 3.83774e13 + 7.30625e12i 0.0485662 + 0.00924598i
\(955\) 1.92798e14i 0.242709i
\(956\) 4.65600e14 1.17850e15i 0.583074 1.47585i
\(957\) −1.34883e13 −0.0168034
\(958\) −1.37649e14 + 7.23026e14i −0.170587 + 0.896038i
\(959\) 1.00105e15i 1.23413i
\(960\) −7.91269e13 + 3.74478e13i −0.0970438 + 0.0459273i
\(961\) 3.53713e14 0.431553
\(962\) −7.34427e14 1.39819e14i −0.891401 0.169704i
\(963\) 2.46392e14i 0.297506i
\(964\) 9.54695e14 + 3.77178e14i 1.14678 + 0.453066i
\(965\) −4.73716e13 −0.0566085
\(966\) −1.77874e14 + 9.34316e14i −0.211459 + 1.11073i
\(967\) 2.27748e13i 0.0269353i 0.999909 + 0.0134677i \(0.00428702\pi\)
−0.999909 + 0.0134677i \(0.995713\pi\)
\(968\) 7.17838e14 + 4.54443e14i 0.844597 + 0.534691i
\(969\) −2.63847e14 −0.308840
\(970\) −7.62725e13 1.45207e13i −0.0888197 0.0169094i
\(971\) 5.54217e14i 0.642072i −0.947067 0.321036i \(-0.895969\pi\)
0.947067 0.321036i \(-0.104031\pi\)
\(972\) −2.04510e13 + 5.17646e13i −0.0235713 + 0.0596625i
\(973\) −1.06088e15 −1.21648
\(974\) 1.38050e14 7.25133e14i 0.157486 0.827224i
\(975\) 3.66602e14i 0.416075i
\(976\) −9.75473e14 9.13332e14i −1.10145 1.03129i
\(977\) 2.31981e14 0.260604 0.130302 0.991474i \(-0.458405\pi\)
0.130302 + 0.991474i \(0.458405\pi\)
\(978\) −5.79953e14 1.10411e14i −0.648184 0.123401i
\(979\) 2.22605e13i 0.0247527i
\(980\) −2.58179e13 1.02000e13i −0.0285621 0.0112842i
\(981\) −3.52213e13 −0.0387668
\(982\) 1.78643e13 9.38353e13i 0.0195627 0.102756i
\(983\) 6.70127e14i 0.730112i −0.930986 0.365056i \(-0.881050\pi\)
0.930986 0.365056i \(-0.118950\pi\)
\(984\) −3.08352e14 + 4.87073e14i −0.334250 + 0.527981i
\(985\) 6.36817e13 0.0686805
\(986\) −3.89817e14 7.42129e13i −0.418289 0.0796334i
\(987\) 1.18633e14i 0.126655i
\(988\) 4.83933e14 1.22491e15i 0.514044 1.30112i
\(989\) 1.11010e15 1.17323
\(990\) 2.15083e11 1.12976e12i 0.000226167 0.00118798i
\(991\) 1.09249e15i 1.14300i 0.820601 + 0.571501i \(0.193639\pi\)
−0.820601 + 0.571501i \(0.806361\pi\)
\(992\) −5.85167e14 + 4.26795e14i −0.609146 + 0.444285i
\(993\) 6.52178e14 0.675492
\(994\) 1.42127e15 + 2.70580e14i 1.46469 + 0.278846i
\(995\) 3.46360e13i 0.0355150i
\(996\) −8.61002e14 3.40162e14i −0.878430 0.347048i
\(997\) −6.70174e14 −0.680317 −0.340159 0.940368i \(-0.610481\pi\)
−0.340159 + 0.940368i \(0.610481\pi\)
\(998\) −1.83928e14 + 9.66118e14i −0.185779 + 0.975837i
\(999\) 2.32773e14i 0.233941i
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 12.11.d.a.7.10 yes 10
3.2 odd 2 36.11.d.e.19.1 10
4.3 odd 2 inner 12.11.d.a.7.9 10
8.3 odd 2 192.11.g.e.127.8 10
8.5 even 2 192.11.g.e.127.3 10
12.11 even 2 36.11.d.e.19.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.11.d.a.7.9 10 4.3 odd 2 inner
12.11.d.a.7.10 yes 10 1.1 even 1 trivial
36.11.d.e.19.1 10 3.2 odd 2
36.11.d.e.19.2 10 12.11 even 2
192.11.g.e.127.3 10 8.5 even 2
192.11.g.e.127.8 10 8.3 odd 2