Properties

Label 12.8.b.a.11.2
Level $12$
Weight $8$
Character 12.11
Analytic conductor $3.749$
Analytic rank $0$
Dimension $4$
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] = [12,8,Mod(11,12)]
 
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, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.11");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 12.b (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: \(3.74862030581\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{3}, \sqrt{-5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.2
Root \(-0.866025 + 1.11803i\) of defining polynomial
Character \(\chi\) \(=\) 12.11
Dual form 12.8.b.a.11.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.3923 + 4.47214i) q^{2} +(-31.1769 + 34.8569i) q^{3} +(88.0000 - 92.9516i) q^{4} -205.718i q^{5} +(168.115 - 501.670i) q^{6} -999.230i q^{7} +(-498.831 + 1359.53i) q^{8} +(-243.000 - 2173.46i) q^{9} +O(q^{10})\) \(q+(-10.3923 + 4.47214i) q^{2} +(-31.1769 + 34.8569i) q^{3} +(88.0000 - 92.9516i) q^{4} -205.718i q^{5} +(168.115 - 501.670i) q^{6} -999.230i q^{7} +(-498.831 + 1359.53i) q^{8} +(-243.000 - 2173.46i) q^{9} +(920.000 + 2137.89i) q^{10} +1974.54 q^{11} +(496.432 + 5965.35i) q^{12} -12730.0 q^{13} +(4468.69 + 10384.3i) q^{14} +(7170.69 + 6413.66i) q^{15} +(-896.000 - 16359.5i) q^{16} -18854.5i q^{17} +(12245.3 + 21500.5i) q^{18} -23911.8i q^{19} +(-19121.8 - 18103.2i) q^{20} +(34830.0 + 31152.9i) q^{21} +(-20520.0 + 8830.40i) q^{22} -72372.0 q^{23} +(-31836.9 - 59773.6i) q^{24} +35805.0 q^{25} +(132294. - 56930.3i) q^{26} +(83335.9 + 59291.5i) q^{27} +(-92880.0 - 87932.2i) q^{28} +106106. i q^{29} +(-103203. - 34584.4i) q^{30} +90372.2i q^{31} +(82473.3 + 166006. i) q^{32} +(-61560.0 + 68826.2i) q^{33} +(84320.0 + 195942. i) q^{34} -205560. q^{35} +(-223410. - 168677. i) q^{36} +43310.0 q^{37} +(106937. + 248499. i) q^{38} +(396882. - 443728. i) q^{39} +(279680. + 102619. i) q^{40} -785790. i q^{41} +(-501284. - 167986. i) q^{42} +70805.9i q^{43} +(173759. - 183536. i) q^{44} +(-447120. + 49989.5i) q^{45} +(752112. - 323657. i) q^{46} -563762. q^{47} +(598175. + 478806. i) q^{48} -174917. q^{49} +(-372096. + 160125. i) q^{50} +(657209. + 587826. i) q^{51} +(-1.12024e6 + 1.18327e6i) q^{52} +348943. i q^{53} +(-1.13121e6 - 243486. i) q^{54} -406198. i q^{55} +(1.35848e6 + 498446. i) q^{56} +(833490. + 745496. i) q^{57} +(-474520. - 1.10268e6i) q^{58} +758119. q^{59} +(1.22718e6 - 102125. i) q^{60} +314198. q^{61} +(-404157. - 939175. i) q^{62} +(-2.17178e6 + 242813. i) q^{63} +(-1.59949e6 - 1.35635e6i) q^{64} +2.61879e6i q^{65} +(331950. - 990567. i) q^{66} +811351. i q^{67} +(-1.75256e6 - 1.65920e6i) q^{68} +(2.25634e6 - 2.52266e6i) q^{69} +(2.13624e6 - 919291. i) q^{70} -265004. q^{71} +(3.07610e6 + 753822. i) q^{72} -259270. q^{73} +(-450091. + 193688. i) q^{74} +(-1.11629e6 + 1.24805e6i) q^{75} +(-2.22264e6 - 2.10424e6i) q^{76} -1.97302e6i q^{77} +(-2.14011e6 + 6.38626e6i) q^{78} -5.23482e6i q^{79} +(-3.36544e6 + 184324. i) q^{80} +(-4.66487e6 + 1.05630e6i) q^{81} +(3.51416e6 + 8.16617e6i) q^{82} +1.01017e7 q^{83} +(5.96075e6 - 496049. i) q^{84} -3.87872e6 q^{85} +(-316654. - 735836. i) q^{86} +(-3.69852e6 - 3.30805e6i) q^{87} +(-984960. + 2.68444e6i) q^{88} -3.88455e6i q^{89} +(4.42305e6 - 2.51909e6i) q^{90} +1.27202e7i q^{91} +(-6.36874e6 + 6.72709e6i) q^{92} +(-3.15009e6 - 2.81753e6i) q^{93} +(5.85878e6 - 2.52122e6i) q^{94} -4.91909e6 q^{95} +(-8.35770e6 - 2.30078e6i) q^{96} +7.24301e6 q^{97} +(1.81779e6 - 782253. i) q^{98} +(-479813. - 4.29158e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 352 q^{4} + 1296 q^{6} - 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 352 q^{4} + 1296 q^{6} - 972 q^{9} + 3680 q^{10} + 12960 q^{12} - 50920 q^{13} - 3584 q^{16} + 38880 q^{18} + 139320 q^{21} - 82080 q^{22} + 62208 q^{24} + 143220 q^{25} - 371520 q^{28} - 298080 q^{30} - 246240 q^{33} + 337280 q^{34} - 85536 q^{36} + 173240 q^{37} + 1118720 q^{40} - 557280 q^{42} - 1788480 q^{45} + 3008448 q^{46} + 2280960 q^{48} - 699668 q^{49} - 4480960 q^{52} - 3464208 q^{54} + 3333960 q^{57} - 1898080 q^{58} + 2384640 q^{60} + 1256792 q^{61} - 6397952 q^{64} - 1231200 q^{66} + 9025344 q^{69} + 8544960 q^{70} + 11819520 q^{72} - 1037080 q^{73} - 8890560 q^{76} - 16498080 q^{78} - 18659484 q^{81} + 14056640 q^{82} + 12260160 q^{84} - 15514880 q^{85} - 3939840 q^{88} - 894240 q^{90} - 12600360 q^{93} + 23435136 q^{94} - 10285056 q^{96} + 28972040 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.3923 + 4.47214i −0.918559 + 0.395285i
\(3\) −31.1769 + 34.8569i −0.666667 + 0.745356i
\(4\) 88.0000 92.9516i 0.687500 0.726184i
\(5\) 205.718i 0.736000i −0.929826 0.368000i \(-0.880043\pi\)
0.929826 0.368000i \(-0.119957\pi\)
\(6\) 168.115 501.670i 0.317745 0.948176i
\(7\) 999.230i 1.10109i −0.834806 0.550544i \(-0.814420\pi\)
0.834806 0.550544i \(-0.185580\pi\)
\(8\) −498.831 + 1359.53i −0.344459 + 0.938801i
\(9\) −243.000 2173.46i −0.111111 0.993808i
\(10\) 920.000 + 2137.89i 0.290930 + 0.676059i
\(11\) 1974.54 0.447292 0.223646 0.974670i \(-0.428204\pi\)
0.223646 + 0.974670i \(0.428204\pi\)
\(12\) 496.432 + 5965.35i 0.0829325 + 0.996555i
\(13\) −12730.0 −1.60704 −0.803520 0.595278i \(-0.797042\pi\)
−0.803520 + 0.595278i \(0.797042\pi\)
\(14\) 4468.69 + 10384.3i 0.435243 + 1.01141i
\(15\) 7170.69 + 6413.66i 0.548582 + 0.490667i
\(16\) −896.000 16359.5i −0.0546875 0.998504i
\(17\) 18854.5i 0.930774i −0.885107 0.465387i \(-0.845915\pi\)
0.885107 0.465387i \(-0.154085\pi\)
\(18\) 12245.3 + 21500.5i 0.494899 + 0.868950i
\(19\) 23911.8i 0.799788i −0.916561 0.399894i \(-0.869047\pi\)
0.916561 0.399894i \(-0.130953\pi\)
\(20\) −19121.8 18103.2i −0.534472 0.506000i
\(21\) 34830.0 + 31152.9i 0.820703 + 0.734059i
\(22\) −20520.0 + 8830.40i −0.410864 + 0.176808i
\(23\) −72372.0 −1.24029 −0.620145 0.784487i \(-0.712926\pi\)
−0.620145 + 0.784487i \(0.712926\pi\)
\(24\) −31836.9 59773.6i −0.470101 0.882612i
\(25\) 35805.0 0.458304
\(26\) 132294. 56930.3i 1.47616 0.635238i
\(27\) 83335.9 + 59291.5i 0.814815 + 0.579721i
\(28\) −92880.0 87932.2i −0.799593 0.756998i
\(29\) 106106.i 0.807879i 0.914786 + 0.403940i \(0.132359\pi\)
−0.914786 + 0.403940i \(0.867641\pi\)
\(30\) −103203. 34584.4i −0.697858 0.233860i
\(31\) 90372.2i 0.544840i 0.962178 + 0.272420i \(0.0878240\pi\)
−0.962178 + 0.272420i \(0.912176\pi\)
\(32\) 82473.3 + 166006.i 0.444927 + 0.895567i
\(33\) −61560.0 + 68826.2i −0.298195 + 0.333392i
\(34\) 84320.0 + 195942.i 0.367921 + 0.854971i
\(35\) −205560. −0.810401
\(36\) −223410. 168677.i −0.798077 0.602556i
\(37\) 43310.0 0.140567 0.0702833 0.997527i \(-0.477610\pi\)
0.0702833 + 0.997527i \(0.477610\pi\)
\(38\) 106937. + 248499.i 0.316144 + 0.734652i
\(39\) 396882. 443728.i 1.07136 1.19782i
\(40\) 279680. + 102619.i 0.690958 + 0.253522i
\(41\) 785790.i 1.78059i −0.455388 0.890293i \(-0.650499\pi\)
0.455388 0.890293i \(-0.349501\pi\)
\(42\) −501284. 167986.i −1.04403 0.349865i
\(43\) 70805.9i 0.135809i 0.997692 + 0.0679047i \(0.0216314\pi\)
−0.997692 + 0.0679047i \(0.978369\pi\)
\(44\) 173759. 183536.i 0.307513 0.324816i
\(45\) −447120. + 49989.5i −0.731443 + 0.0817778i
\(46\) 752112. 323657.i 1.13928 0.490268i
\(47\) −563762. −0.792051 −0.396025 0.918240i \(-0.629611\pi\)
−0.396025 + 0.918240i \(0.629611\pi\)
\(48\) 598175. + 478806.i 0.780699 + 0.624907i
\(49\) −174917. −0.212396
\(50\) −372096. + 160125.i −0.420979 + 0.181161i
\(51\) 657209. + 587826.i 0.693758 + 0.620516i
\(52\) −1.12024e6 + 1.18327e6i −1.10484 + 1.16701i
\(53\) 348943.i 0.321950i 0.986958 + 0.160975i \(0.0514639\pi\)
−0.986958 + 0.160975i \(0.948536\pi\)
\(54\) −1.13121e6 243486.i −0.977610 0.210424i
\(55\) 406198.i 0.329207i
\(56\) 1.35848e6 + 498446.i 1.03370 + 0.379280i
\(57\) 833490. + 745496.i 0.596126 + 0.533192i
\(58\) −474520. 1.10268e6i −0.319342 0.742085i
\(59\) 758119. 0.480568 0.240284 0.970703i \(-0.422759\pi\)
0.240284 + 0.970703i \(0.422759\pi\)
\(60\) 1.22718e6 102125.i 0.733465 0.0610384i
\(61\) 314198. 0.177235 0.0886174 0.996066i \(-0.471755\pi\)
0.0886174 + 0.996066i \(0.471755\pi\)
\(62\) −404157. 939175.i −0.215367 0.500467i
\(63\) −2.17178e6 + 242813.i −1.09427 + 0.122343i
\(64\) −1.59949e6 1.35635e6i −0.762695 0.646758i
\(65\) 2.61879e6i 1.18278i
\(66\) 331950. 990567.i 0.142125 0.424112i
\(67\) 811351.i 0.329570i 0.986330 + 0.164785i \(0.0526930\pi\)
−0.986330 + 0.164785i \(0.947307\pi\)
\(68\) −1.75256e6 1.65920e6i −0.675914 0.639907i
\(69\) 2.25634e6 2.52266e6i 0.826860 0.924458i
\(70\) 2.13624e6 919291.i 0.744401 0.320339i
\(71\) −265004. −0.0878715 −0.0439357 0.999034i \(-0.513990\pi\)
−0.0439357 + 0.999034i \(0.513990\pi\)
\(72\) 3.07610e6 + 753822.i 0.971261 + 0.238015i
\(73\) −259270. −0.0780050 −0.0390025 0.999239i \(-0.512418\pi\)
−0.0390025 + 0.999239i \(0.512418\pi\)
\(74\) −450091. + 193688.i −0.129119 + 0.0555638i
\(75\) −1.11629e6 + 1.24805e6i −0.305536 + 0.341600i
\(76\) −2.22264e6 2.10424e6i −0.580793 0.549854i
\(77\) 1.97302e6i 0.492508i
\(78\) −2.14011e6 + 6.38626e6i −0.510628 + 1.52376i
\(79\) 5.23482e6i 1.19456i −0.802033 0.597279i \(-0.796248\pi\)
0.802033 0.597279i \(-0.203752\pi\)
\(80\) −3.36544e6 + 184324.i −0.734899 + 0.0402500i
\(81\) −4.66487e6 + 1.05630e6i −0.975309 + 0.220846i
\(82\) 3.51416e6 + 8.16617e6i 0.703839 + 1.63557i
\(83\) 1.01017e7 1.93919 0.969594 0.244718i \(-0.0786955\pi\)
0.969594 + 0.244718i \(0.0786955\pi\)
\(84\) 5.96075e6 496049.i 1.09730 0.0913161i
\(85\) −3.87872e6 −0.685050
\(86\) −316654. 735836.i −0.0536834 0.124749i
\(87\) −3.69852e6 3.30805e6i −0.602158 0.538586i
\(88\) −984960. + 2.68444e6i −0.154074 + 0.419918i
\(89\) 3.88455e6i 0.584085i −0.956405 0.292042i \(-0.905665\pi\)
0.956405 0.292042i \(-0.0943348\pi\)
\(90\) 4.42305e6 2.51909e6i 0.639547 0.364246i
\(91\) 1.27202e7i 1.76949i
\(92\) −6.36874e6 + 6.72709e6i −0.852699 + 0.900679i
\(93\) −3.15009e6 2.81753e6i −0.406100 0.363227i
\(94\) 5.85878e6 2.52122e6i 0.727545 0.313086i
\(95\) −4.91909e6 −0.588644
\(96\) −8.35770e6 2.30078e6i −0.964134 0.265416i
\(97\) 7.24301e6 0.805783 0.402891 0.915248i \(-0.368005\pi\)
0.402891 + 0.915248i \(0.368005\pi\)
\(98\) 1.81779e6 782253.i 0.195098 0.0839568i
\(99\) −479813. 4.29158e6i −0.0496991 0.444522i
\(100\) 3.15084e6 3.32813e6i 0.315084 0.332813i
\(101\) 1.12157e7i 1.08318i 0.840642 + 0.541591i \(0.182178\pi\)
−0.840642 + 0.541591i \(0.817822\pi\)
\(102\) −9.45876e6 3.16974e6i −0.882538 0.295749i
\(103\) 1.15817e7i 1.04434i −0.852843 0.522168i \(-0.825123\pi\)
0.852843 0.522168i \(-0.174877\pi\)
\(104\) 6.35011e6 1.73068e7i 0.553560 1.50869i
\(105\) 6.40872e6 7.16517e6i 0.540267 0.604037i
\(106\) −1.56052e6 3.62632e6i −0.127262 0.295730i
\(107\) −218675. −0.0172566 −0.00862831 0.999963i \(-0.502747\pi\)
−0.00862831 + 0.999963i \(0.502747\pi\)
\(108\) 1.28448e7 2.52855e6i 0.981170 0.193147i
\(109\) 9.80701e6 0.725344 0.362672 0.931917i \(-0.381865\pi\)
0.362672 + 0.931917i \(0.381865\pi\)
\(110\) 1.81657e6 + 4.22134e6i 0.130130 + 0.302396i
\(111\) −1.35027e6 + 1.50965e6i −0.0937111 + 0.104772i
\(112\) −1.63469e7 + 895310.i −1.09944 + 0.0602158i
\(113\) 5.41533e6i 0.353061i 0.984295 + 0.176531i \(0.0564875\pi\)
−0.984295 + 0.176531i \(0.943513\pi\)
\(114\) −1.19958e7 4.01994e6i −0.758340 0.254128i
\(115\) 1.48882e7i 0.912853i
\(116\) 9.86271e6 + 9.33732e6i 0.586669 + 0.555417i
\(117\) 3.09339e6 + 2.76681e7i 0.178560 + 1.59709i
\(118\) −7.87860e6 + 3.39041e6i −0.441430 + 0.189961i
\(119\) −1.88400e7 −1.02486
\(120\) −1.22965e7 + 6.54943e6i −0.649603 + 0.345995i
\(121\) −1.55884e7 −0.799930
\(122\) −3.26524e6 + 1.40514e6i −0.162801 + 0.0700582i
\(123\) 2.73902e7 + 2.44985e7i 1.32717 + 1.18706i
\(124\) 8.40024e6 + 7.95275e6i 0.395654 + 0.374577i
\(125\) 2.34375e7i 1.07331i
\(126\) 2.14839e7 1.22359e7i 0.956791 0.544928i
\(127\) 1.65498e7i 0.716936i −0.933542 0.358468i \(-0.883299\pi\)
0.933542 0.358468i \(-0.116701\pi\)
\(128\) 2.26881e7 + 6.94247e6i 0.956234 + 0.292603i
\(129\) −2.46807e6 2.20751e6i −0.101226 0.0905396i
\(130\) −1.17116e7 2.72153e7i −0.467535 1.08645i
\(131\) −2.54476e6 −0.0989004 −0.0494502 0.998777i \(-0.515747\pi\)
−0.0494502 + 0.998777i \(0.515747\pi\)
\(132\) 980223. + 1.17788e7i 0.0370951 + 0.445751i
\(133\) −2.38934e7 −0.880637
\(134\) −3.62847e6 8.43181e6i −0.130274 0.302729i
\(135\) 1.21973e7 1.71437e7i 0.426675 0.599704i
\(136\) 2.56333e7 + 9.40521e6i 0.873812 + 0.320614i
\(137\) 2.54632e7i 0.846040i −0.906120 0.423020i \(-0.860970\pi\)
0.906120 0.423020i \(-0.139030\pi\)
\(138\) −1.21669e7 + 3.63069e7i −0.394095 + 1.17601i
\(139\) 3.98426e7i 1.25833i −0.777270 0.629167i \(-0.783396\pi\)
0.777270 0.629167i \(-0.216604\pi\)
\(140\) −1.80893e7 + 1.91071e7i −0.557151 + 0.588501i
\(141\) 1.75764e7 1.96510e7i 0.528034 0.590360i
\(142\) 2.75400e6 1.18513e6i 0.0807151 0.0347342i
\(143\) −2.51359e7 −0.718816
\(144\) −3.53389e7 + 5.92277e6i −0.986244 + 0.165294i
\(145\) 2.18279e7 0.594599
\(146\) 2.69441e6 1.15949e6i 0.0716521 0.0308342i
\(147\) 5.45337e6 6.09706e6i 0.141597 0.158310i
\(148\) 3.81128e6 4.02573e6i 0.0966395 0.102077i
\(149\) 2.47666e6i 0.0613359i −0.999530 0.0306679i \(-0.990237\pi\)
0.999530 0.0306679i \(-0.00976344\pi\)
\(150\) 6.01937e6 1.79623e7i 0.145624 0.434553i
\(151\) 5.67175e7i 1.34060i 0.742092 + 0.670298i \(0.233834\pi\)
−0.742092 + 0.670298i \(0.766166\pi\)
\(152\) 3.25088e7 + 1.19279e7i 0.750842 + 0.275494i
\(153\) −4.09795e7 + 4.58165e6i −0.925011 + 0.103419i
\(154\) 8.82360e6 + 2.05042e7i 0.194681 + 0.452397i
\(155\) 1.85912e7 0.401002
\(156\) −6.31957e6 7.59389e7i −0.133276 1.60150i
\(157\) −2.54237e7 −0.524312 −0.262156 0.965026i \(-0.584434\pi\)
−0.262156 + 0.965026i \(0.584434\pi\)
\(158\) 2.34108e7 + 5.44019e7i 0.472191 + 1.09727i
\(159\) −1.21630e7 1.08790e7i −0.239968 0.214634i
\(160\) 3.41504e7 1.69663e7i 0.659137 0.327466i
\(161\) 7.23163e7i 1.36567i
\(162\) 4.37548e7 3.18393e7i 0.808581 0.588385i
\(163\) 4.04251e7i 0.731130i 0.930786 + 0.365565i \(0.119124\pi\)
−0.930786 + 0.365565i \(0.880876\pi\)
\(164\) −7.30404e7 6.91495e7i −1.29303 1.22415i
\(165\) 1.41588e7 + 1.26640e7i 0.245376 + 0.219471i
\(166\) −1.04980e8 + 4.51761e7i −1.78126 + 0.766532i
\(167\) 5.30738e7 0.881805 0.440902 0.897555i \(-0.354658\pi\)
0.440902 + 0.897555i \(0.354658\pi\)
\(168\) −5.97276e7 + 3.18124e7i −0.971834 + 0.517623i
\(169\) 9.93044e7 1.58258
\(170\) 4.03088e7 1.73462e7i 0.629258 0.270790i
\(171\) −5.19713e7 + 5.81057e6i −0.794835 + 0.0888653i
\(172\) 6.58152e6 + 6.23092e6i 0.0986226 + 0.0933689i
\(173\) 7.80723e6i 0.114640i 0.998356 + 0.0573199i \(0.0182555\pi\)
−0.998356 + 0.0573199i \(0.981744\pi\)
\(174\) 5.32302e7 + 1.78380e7i 0.766012 + 0.256699i
\(175\) 3.57774e7i 0.504633i
\(176\) −1.76919e6 3.23024e7i −0.0244613 0.446623i
\(177\) −2.36358e7 + 2.64256e7i −0.320379 + 0.358194i
\(178\) 1.73722e7 + 4.03694e7i 0.230880 + 0.536516i
\(179\) −7.52215e7 −0.980294 −0.490147 0.871640i \(-0.663057\pi\)
−0.490147 + 0.871640i \(0.663057\pi\)
\(180\) −3.47000e7 + 4.59596e7i −0.443481 + 0.587384i
\(181\) 3.63087e7 0.455130 0.227565 0.973763i \(-0.426924\pi\)
0.227565 + 0.973763i \(0.426924\pi\)
\(182\) −5.68864e7 1.32192e8i −0.699454 1.62538i
\(183\) −9.79572e6 + 1.09520e7i −0.118157 + 0.132103i
\(184\) 3.61014e7 9.83919e7i 0.427230 1.16439i
\(185\) 8.90966e6i 0.103457i
\(186\) 4.53371e7 + 1.51930e7i 0.516604 + 0.173120i
\(187\) 3.72290e7i 0.416328i
\(188\) −4.96110e7 + 5.24026e7i −0.544535 + 0.575175i
\(189\) 5.92458e7 8.32717e7i 0.638324 0.897183i
\(190\) 5.11207e7 2.19989e7i 0.540704 0.232682i
\(191\) 1.29538e8 1.34518 0.672590 0.740015i \(-0.265182\pi\)
0.672590 + 0.740015i \(0.265182\pi\)
\(192\) 9.71452e7 1.34663e7i 0.990528 0.137308i
\(193\) −1.19989e8 −1.20141 −0.600703 0.799472i \(-0.705112\pi\)
−0.600703 + 0.799472i \(0.705112\pi\)
\(194\) −7.52716e7 + 3.23917e7i −0.740159 + 0.318514i
\(195\) −9.12829e7 8.16459e7i −0.881593 0.788521i
\(196\) −1.53927e7 + 1.62588e7i −0.146022 + 0.154238i
\(197\) 3.80955e7i 0.355011i −0.984120 0.177506i \(-0.943197\pi\)
0.984120 0.177506i \(-0.0568028\pi\)
\(198\) 2.41789e7 + 4.24536e7i 0.221364 + 0.388675i
\(199\) 1.00917e8i 0.907775i 0.891059 + 0.453888i \(0.149963\pi\)
−0.891059 + 0.453888i \(0.850037\pi\)
\(200\) −1.78606e7 + 4.86779e7i −0.157867 + 0.430256i
\(201\) −2.82812e7 2.52954e7i −0.245647 0.219713i
\(202\) −5.01581e7 1.16557e8i −0.428165 0.994966i
\(203\) 1.06024e8 0.889547
\(204\) 1.12474e8 9.35998e6i 0.927568 0.0771915i
\(205\) −1.61651e8 −1.31051
\(206\) 5.17947e7 + 1.20360e8i 0.412810 + 0.959284i
\(207\) 1.75864e7 + 1.57298e8i 0.137810 + 1.23261i
\(208\) 1.14061e7 + 2.08256e8i 0.0878850 + 1.60464i
\(209\) 4.72148e7i 0.357739i
\(210\) −3.45578e7 + 1.03123e8i −0.257501 + 0.768403i
\(211\) 2.02240e8i 1.48210i −0.671448 0.741052i \(-0.734327\pi\)
0.671448 0.741052i \(-0.265673\pi\)
\(212\) 3.24348e7 + 3.07070e7i 0.233795 + 0.221341i
\(213\) 8.26200e6 9.23720e6i 0.0585810 0.0654955i
\(214\) 2.27254e6 977944.i 0.0158512 0.00682128i
\(215\) 1.45661e7 0.0999557
\(216\) −1.22179e8 + 8.37212e7i −0.824914 + 0.565259i
\(217\) 9.03026e7 0.599917
\(218\) −1.01917e8 + 4.38583e7i −0.666271 + 0.286717i
\(219\) 8.08324e6 9.03734e6i 0.0520033 0.0581415i
\(220\) −3.77568e7 3.57455e7i −0.239065 0.226330i
\(221\) 2.40018e8i 1.49579i
\(222\) 7.28108e6 2.17273e7i 0.0446643 0.133282i
\(223\) 4.63341e7i 0.279791i −0.990166 0.139896i \(-0.955323\pi\)
0.990166 0.139896i \(-0.0446767\pi\)
\(224\) 1.65878e8 8.24098e7i 0.986098 0.489904i
\(225\) −8.70062e6 7.78207e7i −0.0509227 0.455466i
\(226\) −2.42181e7 5.62777e7i −0.139560 0.324308i
\(227\) −1.52540e8 −0.865554 −0.432777 0.901501i \(-0.642466\pi\)
−0.432777 + 0.901501i \(0.642466\pi\)
\(228\) 1.42642e8 1.18706e7i 0.797032 0.0663284i
\(229\) −4.39128e7 −0.241639 −0.120819 0.992675i \(-0.538552\pi\)
−0.120819 + 0.992675i \(0.538552\pi\)
\(230\) −6.65823e7 1.54723e8i −0.360837 0.838509i
\(231\) 6.87732e7 + 6.15126e7i 0.367094 + 0.328339i
\(232\) −1.44254e8 5.29289e7i −0.758438 0.278282i
\(233\) 2.42578e8i 1.25634i −0.778077 0.628168i \(-0.783805\pi\)
0.778077 0.628168i \(-0.216195\pi\)
\(234\) −1.55883e8 2.73701e8i −0.795323 1.39644i
\(235\) 1.15976e8i 0.582949i
\(236\) 6.67144e7 7.04683e7i 0.330391 0.348981i
\(237\) 1.82470e8 + 1.63206e8i 0.890371 + 0.796372i
\(238\) 1.95791e8 8.42550e7i 0.941398 0.405113i
\(239\) −1.34211e8 −0.635909 −0.317954 0.948106i \(-0.602996\pi\)
−0.317954 + 0.948106i \(0.602996\pi\)
\(240\) 9.84992e7 1.23055e8i 0.459932 0.574594i
\(241\) 4.19220e8 1.92922 0.964612 0.263674i \(-0.0849343\pi\)
0.964612 + 0.263674i \(0.0849343\pi\)
\(242\) 1.61999e8 6.97133e7i 0.734783 0.316200i
\(243\) 1.08617e8 1.95535e8i 0.485597 0.874183i
\(244\) 2.76494e7 2.92052e7i 0.121849 0.128705i
\(245\) 3.59836e7i 0.156323i
\(246\) −3.94208e8 1.32103e8i −1.68831 0.565772i
\(247\) 3.04397e8i 1.28529i
\(248\) −1.22864e8 4.50804e7i −0.511496 0.187675i
\(249\) −3.14939e8 + 3.52113e8i −1.29279 + 1.44539i
\(250\) 1.04816e8 + 2.43569e8i 0.424264 + 0.985900i
\(251\) −4.44551e8 −1.77445 −0.887225 0.461337i \(-0.847370\pi\)
−0.887225 + 0.461337i \(0.847370\pi\)
\(252\) −1.68547e8 + 2.23238e8i −0.663467 + 0.878753i
\(253\) −1.42901e8 −0.554772
\(254\) 7.40131e7 + 1.71991e8i 0.283394 + 0.658548i
\(255\) 1.20927e8 1.35200e8i 0.456700 0.510606i
\(256\) −2.66830e8 + 2.93162e7i −0.994019 + 0.109211i
\(257\) 3.24979e7i 0.119423i 0.998216 + 0.0597117i \(0.0190181\pi\)
−0.998216 + 0.0597117i \(0.980982\pi\)
\(258\) 3.55212e7 + 1.19036e7i 0.128771 + 0.0431527i
\(259\) 4.32766e7i 0.154776i
\(260\) 2.43421e8 + 2.30454e8i 0.858917 + 0.813162i
\(261\) 2.30617e8 2.57837e7i 0.802877 0.0897644i
\(262\) 2.64460e7 1.13805e7i 0.0908458 0.0390938i
\(263\) 4.26351e8 1.44518 0.722590 0.691277i \(-0.242952\pi\)
0.722590 + 0.691277i \(0.242952\pi\)
\(264\) −6.28632e7 1.18025e8i −0.210273 0.394785i
\(265\) 7.17839e7 0.236955
\(266\) 2.48307e8 1.06854e8i 0.808917 0.348102i
\(267\) 1.35403e8 + 1.21108e8i 0.435351 + 0.389390i
\(268\) 7.54164e7 + 7.13989e7i 0.239328 + 0.226579i
\(269\) 3.00361e8i 0.940829i −0.882445 0.470415i \(-0.844104\pi\)
0.882445 0.470415i \(-0.155896\pi\)
\(270\) −5.00895e7 + 2.32711e8i −0.154872 + 0.719521i
\(271\) 1.68618e8i 0.514648i −0.966325 0.257324i \(-0.917159\pi\)
0.966325 0.257324i \(-0.0828408\pi\)
\(272\) −3.08450e8 + 1.68937e7i −0.929381 + 0.0509017i
\(273\) −4.43386e8 3.96576e8i −1.31890 1.17966i
\(274\) 1.13875e8 + 2.64621e8i 0.334426 + 0.777137i
\(275\) 7.06983e7 0.204996
\(276\) −3.59277e7 4.31724e8i −0.102860 1.23602i
\(277\) −4.20256e8 −1.18805 −0.594026 0.804446i \(-0.702462\pi\)
−0.594026 + 0.804446i \(0.702462\pi\)
\(278\) 1.78182e8 + 4.14057e8i 0.497400 + 1.15585i
\(279\) 1.96420e8 2.19604e7i 0.541466 0.0605378i
\(280\) 1.02540e8 2.79465e8i 0.279150 0.760805i
\(281\) 5.09954e8i 1.37107i 0.728041 + 0.685533i \(0.240431\pi\)
−0.728041 + 0.685533i \(0.759569\pi\)
\(282\) −9.47770e7 + 2.82823e8i −0.251670 + 0.751004i
\(283\) 1.54638e7i 0.0405567i 0.999794 + 0.0202784i \(0.00645525\pi\)
−0.999794 + 0.0202784i \(0.993545\pi\)
\(284\) −2.33203e7 + 2.46325e7i −0.0604116 + 0.0638109i
\(285\) 1.53362e8 1.71464e8i 0.392429 0.438749i
\(286\) 2.61220e8 1.12411e8i 0.660275 0.284137i
\(287\) −7.85185e8 −1.96058
\(288\) 3.40765e8 2.19592e8i 0.840585 0.541679i
\(289\) 5.48456e7 0.133659
\(290\) −2.26842e8 + 9.76174e7i −0.546174 + 0.235036i
\(291\) −2.25815e8 + 2.52469e8i −0.537189 + 0.600595i
\(292\) −2.28158e7 + 2.40996e7i −0.0536284 + 0.0566460i
\(293\) 7.93186e8i 1.84221i −0.389318 0.921104i \(-0.627289\pi\)
0.389318 0.921104i \(-0.372711\pi\)
\(294\) −2.94062e7 + 8.77507e7i −0.0674876 + 0.201389i
\(295\) 1.55959e8i 0.353698i
\(296\) −2.16044e7 + 5.88812e7i −0.0484195 + 0.131964i
\(297\) 1.64550e8 + 1.17073e8i 0.364460 + 0.259305i
\(298\) 1.10760e7 + 2.57382e7i 0.0242451 + 0.0563406i
\(299\) 9.21296e8 1.99320
\(300\) 1.77747e7 + 2.13589e8i 0.0380083 + 0.456725i
\(301\) 7.07513e7 0.149538
\(302\) −2.53648e8 5.89426e8i −0.529917 1.23142i
\(303\) −3.90944e8 3.49671e8i −0.807356 0.722121i
\(304\) −3.91185e8 + 2.14250e7i −0.798591 + 0.0437384i
\(305\) 6.46363e7i 0.130445i
\(306\) 4.05382e8 2.30880e8i 0.808797 0.460639i
\(307\) 5.07669e8i 1.00137i −0.865628 0.500687i \(-0.833081\pi\)
0.865628 0.500687i \(-0.166919\pi\)
\(308\) −1.83395e8 1.73625e8i −0.357652 0.338599i
\(309\) 4.03700e8 + 3.61080e8i 0.778402 + 0.696224i
\(310\) −1.93206e8 + 8.31424e7i −0.368344 + 0.158510i
\(311\) 2.79184e8 0.526296 0.263148 0.964756i \(-0.415239\pi\)
0.263148 + 0.964756i \(0.415239\pi\)
\(312\) 4.05284e8 + 7.60918e8i 0.755472 + 1.41839i
\(313\) −6.92840e7 −0.127711 −0.0638554 0.997959i \(-0.520340\pi\)
−0.0638554 + 0.997959i \(0.520340\pi\)
\(314\) 2.64211e8 1.13698e8i 0.481611 0.207253i
\(315\) 4.99510e7 + 4.46776e8i 0.0900446 + 0.805383i
\(316\) −4.86585e8 4.60665e8i −0.867470 0.821259i
\(317\) 8.97465e8i 1.58238i 0.611572 + 0.791189i \(0.290537\pi\)
−0.611572 + 0.791189i \(0.709463\pi\)
\(318\) 1.75054e8 + 5.86627e7i 0.305266 + 0.102298i
\(319\) 2.09510e8i 0.361358i
\(320\) −2.79026e8 + 3.29044e8i −0.476014 + 0.561344i
\(321\) 6.81761e6 7.62232e6i 0.0115044 0.0128623i
\(322\) −3.23408e8 7.51533e8i −0.539828 1.25445i
\(323\) −4.50846e8 −0.744422
\(324\) −3.12324e8 + 5.26562e8i −0.510150 + 0.860086i
\(325\) −4.55798e8 −0.736513
\(326\) −1.80787e8 4.20110e8i −0.289004 0.671585i
\(327\) −3.05752e8 + 3.41842e8i −0.483563 + 0.540640i
\(328\) 1.06830e9 + 3.91976e8i 1.67162 + 0.613340i
\(329\) 5.63327e8i 0.872118i
\(330\) −2.03778e8 6.82882e7i −0.312146 0.104604i
\(331\) 1.19136e9i 1.80570i 0.429957 + 0.902849i \(0.358529\pi\)
−0.429957 + 0.902849i \(0.641471\pi\)
\(332\) 8.88947e8 9.38967e8i 1.33319 1.40821i
\(333\) −1.05243e7 9.41325e7i −0.0156185 0.139696i
\(334\) −5.51559e8 + 2.37353e8i −0.809989 + 0.348564i
\(335\) 1.66910e8 0.242563
\(336\) 4.78438e8 5.97714e8i 0.688078 0.859619i
\(337\) 1.15595e9 1.64526 0.822630 0.568577i \(-0.192506\pi\)
0.822630 + 0.568577i \(0.192506\pi\)
\(338\) −1.03200e9 + 4.44103e8i −1.45369 + 0.625569i
\(339\) −1.88761e8 1.68833e8i −0.263156 0.235374i
\(340\) −3.41327e8 + 3.60533e8i −0.470972 + 0.497473i
\(341\) 1.78443e8i 0.243702i
\(342\) 5.14116e8 2.92808e8i 0.694976 0.395814i
\(343\) 6.48126e8i 0.867222i
\(344\) −9.62627e7 3.53201e7i −0.127498 0.0467808i
\(345\) −5.18957e8 4.64170e8i −0.680401 0.608569i
\(346\) −3.49150e7 8.11351e7i −0.0453154 0.105303i
\(347\) 1.31673e9 1.69178 0.845892 0.533355i \(-0.179069\pi\)
0.845892 + 0.533355i \(0.179069\pi\)
\(348\) −6.32958e8 + 5.26743e7i −0.805096 + 0.0669995i
\(349\) −2.79115e8 −0.351474 −0.175737 0.984437i \(-0.556231\pi\)
−0.175737 + 0.984437i \(0.556231\pi\)
\(350\) 1.60001e8 + 3.71810e8i 0.199474 + 0.463535i
\(351\) −1.06087e9 7.54781e8i −1.30944 0.931635i
\(352\) 1.62847e8 + 3.27785e8i 0.199012 + 0.400580i
\(353\) 6.39614e8i 0.773938i −0.922093 0.386969i \(-0.873522\pi\)
0.922093 0.386969i \(-0.126478\pi\)
\(354\) 1.27451e8 3.80326e8i 0.152698 0.455664i
\(355\) 5.45161e7i 0.0646734i
\(356\) −3.61075e8 3.41840e8i −0.424153 0.401558i
\(357\) 5.87373e8 6.56703e8i 0.683243 0.763889i
\(358\) 7.81725e8 3.36401e8i 0.900457 0.387495i
\(359\) −7.06233e8 −0.805596 −0.402798 0.915289i \(-0.631962\pi\)
−0.402798 + 0.915289i \(0.631962\pi\)
\(360\) 1.55075e8 6.32809e8i 0.175179 0.714848i
\(361\) 3.22098e8 0.360340
\(362\) −3.77331e8 + 1.62377e8i −0.418064 + 0.179906i
\(363\) 4.85997e8 5.43362e8i 0.533287 0.596233i
\(364\) 1.18236e9 + 1.11938e9i 1.28498 + 1.21653i
\(365\) 5.33366e7i 0.0574117i
\(366\) 5.28215e7 1.57624e8i 0.0563154 0.168050i
\(367\) 1.52201e9i 1.60726i −0.595126 0.803632i \(-0.702898\pi\)
0.595126 0.803632i \(-0.297102\pi\)
\(368\) 6.48453e7 + 1.18397e9i 0.0678284 + 1.23843i
\(369\) −1.70788e9 + 1.90947e8i −1.76956 + 0.197843i
\(370\) 3.98452e7 + 9.25919e7i 0.0408950 + 0.0950313i
\(371\) 3.48674e8 0.354496
\(372\) −5.39101e8 + 4.48636e7i −0.542963 + 0.0451850i
\(373\) −4.19200e8 −0.418254 −0.209127 0.977888i \(-0.567062\pi\)
−0.209127 + 0.977888i \(0.567062\pi\)
\(374\) 1.66493e8 + 3.86895e8i 0.164568 + 0.382422i
\(375\) 8.16957e8 + 7.30708e8i 0.799999 + 0.715541i
\(376\) 2.81222e8 7.66451e8i 0.272829 0.743578i
\(377\) 1.35073e9i 1.29829i
\(378\) −2.43298e8 + 1.13034e9i −0.231696 + 1.07644i
\(379\) 1.84045e9i 1.73655i 0.496082 + 0.868275i \(0.334771\pi\)
−0.496082 + 0.868275i \(0.665229\pi\)
\(380\) −4.32880e8 + 4.57238e8i −0.404693 + 0.427464i
\(381\) 5.76875e8 + 5.15972e8i 0.534372 + 0.477957i
\(382\) −1.34620e9 + 5.79312e8i −1.23563 + 0.531729i
\(383\) −1.87842e8 −0.170843 −0.0854216 0.996345i \(-0.527224\pi\)
−0.0854216 + 0.996345i \(0.527224\pi\)
\(384\) −9.49339e8 + 5.74392e8i −0.855583 + 0.517666i
\(385\) −4.05886e8 −0.362486
\(386\) 1.24696e9 5.36606e8i 1.10356 0.474897i
\(387\) 1.53894e8 1.72058e7i 0.134968 0.0150899i
\(388\) 6.37385e8 6.73249e8i 0.553976 0.585147i
\(389\) 3.22401e8i 0.277698i 0.990314 + 0.138849i \(0.0443403\pi\)
−0.990314 + 0.138849i \(0.955660\pi\)
\(390\) 1.31377e9 + 4.40260e8i 1.12149 + 0.375822i
\(391\) 1.36454e9i 1.15443i
\(392\) 8.72540e7 2.37805e8i 0.0731617 0.199397i
\(393\) 7.93379e7 8.87024e7i 0.0659336 0.0737160i
\(394\) 1.70368e8 + 3.95900e8i 0.140330 + 0.326099i
\(395\) −1.07690e9 −0.879195
\(396\) −4.41132e8 3.33059e8i −0.356973 0.269518i
\(397\) −1.34603e9 −1.07966 −0.539832 0.841773i \(-0.681512\pi\)
−0.539832 + 0.841773i \(0.681512\pi\)
\(398\) −4.51314e8 1.04876e9i −0.358830 0.833845i
\(399\) 7.44922e8 8.32848e8i 0.587091 0.656388i
\(400\) −3.20813e7 5.85751e8i −0.0250635 0.457618i
\(401\) 8.73134e8i 0.676201i 0.941110 + 0.338100i \(0.109784\pi\)
−0.941110 + 0.338100i \(0.890216\pi\)
\(402\) 4.07031e8 + 1.36401e8i 0.312490 + 0.104719i
\(403\) 1.15044e9i 0.875579i
\(404\) 1.04252e9 + 9.86981e8i 0.786590 + 0.744688i
\(405\) 2.17300e8 + 9.59649e8i 0.162543 + 0.717827i
\(406\) −1.10184e9 + 4.74154e8i −0.817101 + 0.351624i
\(407\) 8.55172e7 0.0628743
\(408\) −1.12700e9 + 6.00270e8i −0.821513 + 0.437558i
\(409\) 1.61913e9 1.17017 0.585086 0.810971i \(-0.301061\pi\)
0.585086 + 0.810971i \(0.301061\pi\)
\(410\) 1.67993e9 7.22927e8i 1.20378 0.518025i
\(411\) 8.87566e8 + 7.93863e8i 0.630601 + 0.564026i
\(412\) −1.07653e9 1.01919e9i −0.758381 0.717981i
\(413\) 7.57535e8i 0.529148i
\(414\) −8.86219e8 1.55604e9i −0.613818 1.07775i
\(415\) 2.07810e9i 1.42724i
\(416\) −1.04989e9 2.11325e9i −0.715015 1.43921i
\(417\) 1.38879e9 + 1.24217e9i 0.937907 + 0.838889i
\(418\) 2.11151e8 + 4.90670e8i 0.141409 + 0.328604i
\(419\) −1.83155e9 −1.21638 −0.608192 0.793790i \(-0.708105\pi\)
−0.608192 + 0.793790i \(0.708105\pi\)
\(420\) −1.02046e8 1.22624e9i −0.0672086 0.807609i
\(421\) 1.29973e9 0.848918 0.424459 0.905447i \(-0.360464\pi\)
0.424459 + 0.905447i \(0.360464\pi\)
\(422\) 9.04445e8 + 2.10174e9i 0.585853 + 1.36140i
\(423\) 1.36994e8 + 1.22531e9i 0.0880057 + 0.787147i
\(424\) −4.74398e8 1.74063e8i −0.302247 0.110899i
\(425\) 6.75086e8i 0.426578i
\(426\) −4.45512e7 + 1.32945e8i −0.0279207 + 0.0833176i
\(427\) 3.13956e8i 0.195151i
\(428\) −1.92434e7 + 2.03262e7i −0.0118639 + 0.0125315i
\(429\) 7.83659e8 8.76157e8i 0.479211 0.535774i
\(430\) −1.51375e8 + 6.51414e7i −0.0918152 + 0.0395110i
\(431\) −2.25303e9 −1.35549 −0.677746 0.735296i \(-0.737043\pi\)
−0.677746 + 0.735296i \(0.737043\pi\)
\(432\) 8.95309e8 1.41646e9i 0.534294 0.845299i
\(433\) −3.38794e8 −0.200552 −0.100276 0.994960i \(-0.531973\pi\)
−0.100276 + 0.994960i \(0.531973\pi\)
\(434\) −9.38452e8 + 4.03845e8i −0.551059 + 0.237138i
\(435\) −6.80527e8 + 7.60853e8i −0.396399 + 0.443188i
\(436\) 8.63017e8 9.11578e8i 0.498674 0.526734i
\(437\) 1.73054e9i 0.991968i
\(438\) −4.35873e7 + 1.30068e8i −0.0247857 + 0.0739625i
\(439\) 1.72596e9i 0.973657i 0.873498 + 0.486828i \(0.161846\pi\)
−0.873498 + 0.486828i \(0.838154\pi\)
\(440\) 5.52239e8 + 2.02624e8i 0.309060 + 0.113398i
\(441\) 4.25048e7 + 3.80175e8i 0.0235995 + 0.211081i
\(442\) −1.07339e9 2.49434e9i −0.591263 1.37397i
\(443\) 1.73582e9 0.948616 0.474308 0.880359i \(-0.342698\pi\)
0.474308 + 0.880359i \(0.342698\pi\)
\(444\) 2.15004e7 + 2.58359e8i 0.0116575 + 0.140082i
\(445\) −7.99123e8 −0.429886
\(446\) 2.07212e8 + 4.81518e8i 0.110597 + 0.257005i
\(447\) 8.63286e7 + 7.72146e7i 0.0457170 + 0.0408906i
\(448\) −1.35530e9 + 1.59826e9i −0.712138 + 0.839795i
\(449\) 9.57315e8i 0.499106i 0.968361 + 0.249553i \(0.0802836\pi\)
−0.968361 + 0.249553i \(0.919716\pi\)
\(450\) 4.38444e8 + 7.69826e8i 0.226814 + 0.398243i
\(451\) 1.55157e9i 0.796442i
\(452\) 5.03363e8 + 4.76549e8i 0.256388 + 0.242730i
\(453\) −1.97699e9 1.76828e9i −0.999221 0.893730i
\(454\) 1.58525e9 6.82181e8i 0.795062 0.342140i
\(455\) 2.61678e9 1.30235
\(456\) −1.42929e9 + 7.61278e8i −0.705902 + 0.375981i
\(457\) −2.22751e9 −1.09172 −0.545862 0.837875i \(-0.683798\pi\)
−0.545862 + 0.837875i \(0.683798\pi\)
\(458\) 4.56355e8 1.96384e8i 0.221959 0.0955162i
\(459\) 1.11791e9 1.57126e9i 0.539590 0.758409i
\(460\) 1.38389e9 + 1.31017e9i 0.662900 + 0.627587i
\(461\) 2.47517e9i 1.17666i −0.808620 0.588331i \(-0.799785\pi\)
0.808620 0.588331i \(-0.200215\pi\)
\(462\) −9.89804e8 3.31695e8i −0.466984 0.156492i
\(463\) 2.48039e9i 1.16141i 0.814113 + 0.580706i \(0.197223\pi\)
−0.814113 + 0.580706i \(0.802777\pi\)
\(464\) 1.73584e9 9.50709e7i 0.806670 0.0441809i
\(465\) −5.79617e8 + 6.48031e8i −0.267335 + 0.298889i
\(466\) 1.08484e9 + 2.52095e9i 0.496611 + 1.15402i
\(467\) −1.07555e9 −0.488677 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(468\) 2.84401e9 + 2.14726e9i 1.28254 + 0.968331i
\(469\) 8.10726e8 0.362885
\(470\) −5.18661e8 1.20526e9i −0.230431 0.535473i
\(471\) 7.92632e8 8.86190e8i 0.349541 0.390799i
\(472\) −3.78173e8 + 1.03068e9i −0.165536 + 0.451158i
\(473\) 1.39809e8i 0.0607464i
\(474\) −2.62616e9 8.80055e8i −1.13265 0.379564i
\(475\) 8.56162e8i 0.366546i
\(476\) −1.65792e9 + 1.75121e9i −0.704595 + 0.744241i
\(477\) 7.58413e8 8.47931e7i 0.319957 0.0357723i
\(478\) 1.39476e9 6.00209e8i 0.584119 0.251365i
\(479\) 3.09105e8 0.128508 0.0642541 0.997934i \(-0.479533\pi\)
0.0642541 + 0.997934i \(0.479533\pi\)
\(480\) −4.73313e8 + 1.71933e9i −0.195346 + 0.709603i
\(481\) −5.51336e8 −0.225896
\(482\) −4.35666e9 + 1.87481e9i −1.77211 + 0.762593i
\(483\) −2.52072e9 2.25460e9i −1.01791 0.910446i
\(484\) −1.37178e9 + 1.44896e9i −0.549952 + 0.580897i
\(485\) 1.49002e9i 0.593056i
\(486\) −2.54322e8 + 2.51781e9i −0.100498 + 0.994937i
\(487\) 2.10568e9i 0.826115i 0.910705 + 0.413058i \(0.135539\pi\)
−0.910705 + 0.413058i \(0.864461\pi\)
\(488\) −1.56732e8 + 4.27161e8i −0.0610502 + 0.166388i
\(489\) −1.40909e9 1.26033e9i −0.544952 0.487420i
\(490\) −1.60924e8 3.73953e8i −0.0617922 0.143592i
\(491\) 5.94413e8 0.226622 0.113311 0.993560i \(-0.463854\pi\)
0.113311 + 0.993560i \(0.463854\pi\)
\(492\) 4.68751e9 3.90091e8i 1.77445 0.147669i
\(493\) 2.00058e9 0.751953
\(494\) −1.36131e9 3.16339e9i −0.508056 1.18061i
\(495\) −8.82855e8 + 9.87062e7i −0.327168 + 0.0365785i
\(496\) 1.47844e9 8.09735e7i 0.544025 0.0297959i
\(497\) 2.64800e8i 0.0967542i
\(498\) 1.69825e9 5.06771e9i 0.616167 1.83869i
\(499\) 3.39922e9i 1.22469i −0.790590 0.612346i \(-0.790226\pi\)
0.790590 0.612346i \(-0.209774\pi\)
\(500\) −2.17855e9 2.06250e9i −0.779422 0.737902i
\(501\) −1.65468e9 + 1.84999e9i −0.587870 + 0.657259i
\(502\) 4.61991e9 1.98809e9i 1.62994 0.701413i
\(503\) 4.02401e9 1.40985 0.704923 0.709284i \(-0.250982\pi\)
0.704923 + 0.709284i \(0.250982\pi\)
\(504\) 7.53241e8 3.07373e9i 0.262076 1.06944i
\(505\) 2.30727e9 0.797222
\(506\) 1.48507e9 6.39074e8i 0.509590 0.219293i
\(507\) −3.09600e9 + 3.46144e9i −1.05505 + 1.17958i
\(508\) −1.53833e9 1.45638e9i −0.520628 0.492893i
\(509\) 1.18155e9i 0.397136i −0.980087 0.198568i \(-0.936371\pi\)
0.980087 0.198568i \(-0.0636291\pi\)
\(510\) −6.52073e8 + 1.94584e9i −0.217671 + 0.649548i
\(511\) 2.59070e8i 0.0858904i
\(512\) 2.64187e9 1.49796e9i 0.869895 0.493237i
\(513\) 1.41777e9 1.99271e9i 0.463654 0.651679i
\(514\) −1.45335e8 3.37728e8i −0.0472062 0.109697i
\(515\) −2.38256e9 −0.768631
\(516\) −4.22382e8 + 3.51503e7i −0.135342 + 0.0112630i
\(517\) −1.11317e9 −0.354278
\(518\) 1.93539e8 + 4.49744e8i 0.0611807 + 0.142171i
\(519\) −2.72135e8 2.43405e8i −0.0854475 0.0764266i
\(520\) −3.56033e9 1.30633e9i −1.11040 0.407420i
\(521\) 3.54418e9i 1.09795i 0.835838 + 0.548976i \(0.184982\pi\)
−0.835838 + 0.548976i \(0.815018\pi\)
\(522\) −2.28133e9 + 1.29930e9i −0.702007 + 0.399819i
\(523\) 2.88980e9i 0.883307i 0.897186 + 0.441654i \(0.145608\pi\)
−0.897186 + 0.441654i \(0.854392\pi\)
\(524\) −2.23939e8 + 2.36540e8i −0.0679940 + 0.0718199i
\(525\) 1.24709e9 + 1.11543e9i 0.376131 + 0.336422i
\(526\) −4.43077e9 + 1.90670e9i −1.32748 + 0.571257i
\(527\) 1.70392e9 0.507123
\(528\) 1.18112e9 + 9.45421e8i 0.349200 + 0.279516i
\(529\) 1.83288e9 0.538319
\(530\) −7.46000e8 + 3.21027e8i −0.217657 + 0.0936648i
\(531\) −1.84223e8 1.64774e9i −0.0533965 0.477593i
\(532\) −2.10262e9 + 2.22093e9i −0.605438 + 0.639505i
\(533\) 1.00031e10i 2.86147i
\(534\) −1.94876e9 6.53053e8i −0.553815 0.185590i
\(535\) 4.49854e7i 0.0127009i
\(536\) −1.10306e9 4.04727e8i −0.309400 0.113523i
\(537\) 2.34517e9 2.62198e9i 0.653529 0.730668i
\(538\) 1.34326e9 + 3.12145e9i 0.371895 + 0.864207i
\(539\) −3.45380e8 −0.0950029
\(540\) −5.20169e8 2.64241e9i −0.142156 0.722141i
\(541\) −4.59048e8 −0.124643 −0.0623215 0.998056i \(-0.519850\pi\)
−0.0623215 + 0.998056i \(0.519850\pi\)
\(542\) 7.54081e8 + 1.75233e9i 0.203433 + 0.472735i
\(543\) −1.13199e9 + 1.26561e9i −0.303420 + 0.339234i
\(544\) 3.12996e9 1.55500e9i 0.833571 0.414126i
\(545\) 2.01748e9i 0.533853i
\(546\) 6.38135e9 + 2.13846e9i 1.67779 + 0.562247i
\(547\) 6.87269e7i 0.0179544i −0.999960 0.00897720i \(-0.997142\pi\)
0.999960 0.00897720i \(-0.00285757\pi\)
\(548\) −2.36684e9 2.24076e9i −0.614381 0.581652i
\(549\) −7.63501e7 6.82896e8i −0.0196928 0.176137i
\(550\) −7.34719e8 + 3.16173e8i −0.188301 + 0.0810317i
\(551\) 2.53718e9 0.646132
\(552\) 2.30410e9 + 4.32594e9i 0.583062 + 1.09470i
\(553\) −5.23079e9 −1.31531
\(554\) 4.36743e9 1.87944e9i 1.09129 0.469619i
\(555\) 3.10563e8 + 2.77776e8i 0.0771123 + 0.0689713i
\(556\) −3.70343e9 3.50615e9i −0.913783 0.865105i
\(557\) 1.71176e9i 0.419710i −0.977732 0.209855i \(-0.932701\pi\)
0.977732 0.209855i \(-0.0672992\pi\)
\(558\) −1.94305e9 + 1.10664e9i −0.473439 + 0.269641i
\(559\) 9.01359e8i 0.218251i
\(560\) 1.84182e8 + 3.36285e9i 0.0443188 + 0.809188i
\(561\) 1.29768e9 + 1.16068e9i 0.310312 + 0.277552i
\(562\) −2.28058e9 5.29959e9i −0.541962 1.25940i
\(563\) −1.29253e9 −0.305255 −0.152627 0.988284i \(-0.548773\pi\)
−0.152627 + 0.988284i \(0.548773\pi\)
\(564\) −2.79869e8 3.36303e9i −0.0656868 0.789322i
\(565\) 1.11403e9 0.259853
\(566\) −6.91561e7 1.60704e8i −0.0160315 0.0372537i
\(567\) 1.05549e9 + 4.66128e9i 0.243171 + 1.07390i
\(568\) 1.32192e8 3.60280e8i 0.0302682 0.0824938i
\(569\) 5.52303e9i 1.25685i −0.777869 0.628426i \(-0.783699\pi\)
0.777869 0.628426i \(-0.216301\pi\)
\(570\) −8.26976e8 + 2.46776e9i −0.187038 + 0.558138i
\(571\) 6.19314e9i 1.39215i −0.717971 0.696073i \(-0.754929\pi\)
0.717971 0.696073i \(-0.245071\pi\)
\(572\) −2.21196e9 + 2.33642e9i −0.494186 + 0.521993i
\(573\) −4.03860e9 + 4.51529e9i −0.896787 + 1.00264i
\(574\) 8.15988e9 3.51145e9i 1.80091 0.774988i
\(575\) −2.59128e9 −0.568430
\(576\) −2.55929e9 + 3.80601e9i −0.558009 + 0.829835i
\(577\) −2.63098e9 −0.570167 −0.285083 0.958503i \(-0.592021\pi\)
−0.285083 + 0.958503i \(0.592021\pi\)
\(578\) −5.69972e8 + 2.45277e8i −0.122774 + 0.0528335i
\(579\) 3.74088e9 4.18243e9i 0.800937 0.895475i
\(580\) 1.92086e9 2.02894e9i 0.408787 0.431789i
\(581\) 1.00939e10i 2.13522i
\(582\) 1.21766e9 3.63360e9i 0.256033 0.764024i
\(583\) 6.89001e8i 0.144006i
\(584\) 1.29332e8 3.52485e8i 0.0268696 0.0732312i
\(585\) 5.69184e9 6.36367e8i 1.17546 0.131420i
\(586\) 3.54724e9 + 8.24303e9i 0.728196 + 1.69218i
\(587\) −6.81888e8 −0.139149 −0.0695744 0.997577i \(-0.522164\pi\)
−0.0695744 + 0.997577i \(0.522164\pi\)
\(588\) −8.68343e7 1.04344e9i −0.0176145 0.211664i
\(589\) 2.16096e9 0.435756
\(590\) 6.97469e8 + 1.62077e9i 0.139812 + 0.324893i
\(591\) 1.32789e9 + 1.18770e9i 0.264610 + 0.236674i
\(592\) −3.88058e7 7.08529e8i −0.00768724 0.140356i
\(593\) 8.90525e8i 0.175370i −0.996148 0.0876849i \(-0.972053\pi\)
0.996148 0.0876849i \(-0.0279468\pi\)
\(594\) −2.23362e9 4.80772e8i −0.437277 0.0941211i
\(595\) 3.87573e9i 0.754300i
\(596\) −2.30210e8 2.17946e8i −0.0445411 0.0421684i
\(597\) −3.51765e9 3.14628e9i −0.676616 0.605183i
\(598\) −9.57439e9 + 4.12016e9i −1.83087 + 0.787880i
\(599\) −8.68984e9 −1.65203 −0.826015 0.563648i \(-0.809398\pi\)
−0.826015 + 0.563648i \(0.809398\pi\)
\(600\) −1.13992e9 2.14019e9i −0.215449 0.404505i
\(601\) −6.48769e9 −1.21907 −0.609536 0.792758i \(-0.708644\pi\)
−0.609536 + 0.792758i \(0.708644\pi\)
\(602\) −7.35269e8 + 3.16410e8i −0.137360 + 0.0591101i
\(603\) 1.76344e9 1.97158e8i 0.327529 0.0366188i
\(604\) 5.27198e9 + 4.99114e9i 0.973520 + 0.921660i
\(605\) 3.20681e9i 0.588748i
\(606\) 5.62658e9 + 1.88553e9i 1.02705 + 0.344175i
\(607\) 7.67054e9i 1.39209i −0.718001 0.696043i \(-0.754942\pi\)
0.718001 0.696043i \(-0.245058\pi\)
\(608\) 3.96949e9 1.97209e9i 0.716263 0.355847i
\(609\) −3.30551e9 + 3.69567e9i −0.593031 + 0.663029i
\(610\) 2.89062e8 + 6.71720e8i 0.0515628 + 0.119821i
\(611\) 7.17669e9 1.27286
\(612\) −3.18033e9 + 4.21230e9i −0.560843 + 0.742829i
\(613\) 1.01986e10 1.78825 0.894123 0.447821i \(-0.147800\pi\)
0.894123 + 0.447821i \(0.147800\pi\)
\(614\) 2.27036e9 + 5.27585e9i 0.395828 + 0.919821i
\(615\) 5.03979e9 5.63466e9i 0.873674 0.976798i
\(616\) 2.68237e9 + 9.84201e8i 0.462367 + 0.169649i
\(617\) 7.66633e9i 1.31398i 0.753898 + 0.656991i \(0.228171\pi\)
−0.753898 + 0.656991i \(0.771829\pi\)
\(618\) −5.81017e9 1.94705e9i −0.990215 0.331832i
\(619\) 7.72256e9i 1.30871i 0.756187 + 0.654356i \(0.227060\pi\)
−0.756187 + 0.654356i \(0.772940\pi\)
\(620\) 1.63603e9 1.72808e9i 0.275689 0.291202i
\(621\) −6.03119e9 4.29105e9i −1.01061 0.719023i
\(622\) −2.90137e9 + 1.24855e9i −0.483434 + 0.208037i
\(623\) −3.88156e9 −0.643129
\(624\) −7.61476e9 6.09521e9i −1.25461 1.00425i
\(625\) −2.02425e9 −0.331653
\(626\) 7.20020e8 3.09847e8i 0.117310 0.0504821i
\(627\) 1.64576e9 + 1.47201e9i 0.266643 + 0.238492i
\(628\) −2.23728e9 + 2.36317e9i −0.360465 + 0.380747i
\(629\) 8.16589e8i 0.130836i
\(630\) −2.51715e9 4.41964e9i −0.401067 0.704198i
\(631\) 3.86511e9i 0.612433i 0.951962 + 0.306217i \(0.0990632\pi\)
−0.951962 + 0.306217i \(0.900937\pi\)
\(632\) 7.11690e9 + 2.61129e9i 1.12145 + 0.411477i
\(633\) 7.04945e9 + 6.30522e9i 1.10470 + 0.988069i
\(634\) −4.01358e9 9.32673e9i −0.625489 1.45351i
\(635\) −3.40460e9 −0.527665
\(636\) −2.08157e9 + 1.73226e8i −0.320841 + 0.0267002i
\(637\) 2.22669e9 0.341328
\(638\) −9.36958e8 2.17729e9i −0.142839 0.331928i
\(639\) 6.43959e7 + 5.75975e8i 0.00976350 + 0.0873274i
\(640\) 1.42819e9 4.66737e9i 0.215356 0.703788i
\(641\) 3.14005e9i 0.470905i −0.971886 0.235453i \(-0.924343\pi\)
0.971886 0.235453i \(-0.0756573\pi\)
\(642\) −3.67626e7 + 1.09703e8i −0.00548320 + 0.0163623i
\(643\) 7.73104e9i 1.14683i 0.819265 + 0.573416i \(0.194382\pi\)
−0.819265 + 0.573416i \(0.805618\pi\)
\(644\) 6.72191e9 + 6.36383e9i 0.991727 + 0.938897i
\(645\) −4.54125e8 + 5.07727e8i −0.0666371 + 0.0745026i
\(646\) 4.68533e9 2.01624e9i 0.683795 0.294259i
\(647\) 2.19275e9 0.318290 0.159145 0.987255i \(-0.449126\pi\)
0.159145 + 0.987255i \(0.449126\pi\)
\(648\) 8.90909e8 6.86894e9i 0.128624 0.991693i
\(649\) 1.49693e9 0.214954
\(650\) 4.73679e9 2.03839e9i 0.676530 0.291132i
\(651\) −2.81536e9 + 3.14766e9i −0.399945 + 0.447152i
\(652\) 3.75758e9 + 3.55741e9i 0.530935 + 0.502652i
\(653\) 6.45493e9i 0.907184i 0.891209 + 0.453592i \(0.149858\pi\)
−0.891209 + 0.453592i \(0.850142\pi\)
\(654\) 1.64871e9 4.91989e9i 0.230474 0.687754i
\(655\) 5.23504e8i 0.0727907i
\(656\) −1.28551e10 + 7.04068e8i −1.77792 + 0.0973758i
\(657\) 6.30026e7 + 5.63512e8i 0.00866722 + 0.0775220i
\(658\) −2.51928e9 5.85427e9i −0.344735 0.801092i
\(659\) −7.43719e9 −1.01230 −0.506151 0.862445i \(-0.668932\pi\)
−0.506151 + 0.862445i \(0.668932\pi\)
\(660\) 2.42311e9 2.01650e8i 0.328073 0.0273020i
\(661\) 2.66092e9 0.358365 0.179183 0.983816i \(-0.442655\pi\)
0.179183 + 0.983816i \(0.442655\pi\)
\(662\) −5.32793e9 1.23810e10i −0.713765 1.65864i
\(663\) −8.36628e9 7.48302e9i −1.11490 0.997194i
\(664\) −5.03902e9 + 1.37335e10i −0.667972 + 1.82051i
\(665\) 4.91530e9i 0.648149i
\(666\) 5.30345e8 + 9.31187e8i 0.0695663 + 0.122145i
\(667\) 7.67910e9i 1.00200i
\(668\) 4.67049e9 4.93329e9i 0.606241 0.640353i
\(669\) 1.61506e9 + 1.44455e9i 0.208544 + 0.186527i
\(670\) −1.73458e9 + 7.46443e8i −0.222809 + 0.0958815i
\(671\) 6.20396e8 0.0792757
\(672\) −2.29901e9 + 8.35126e9i −0.292246 + 1.06160i
\(673\) 9.42499e9 1.19187 0.595934 0.803033i \(-0.296782\pi\)
0.595934 + 0.803033i \(0.296782\pi\)
\(674\) −1.20130e10 + 5.16957e9i −1.51127 + 0.650346i
\(675\) 2.98384e9 + 2.12293e9i 0.373433 + 0.265689i
\(676\) 8.73879e9 9.23050e9i 1.08802 1.14924i
\(677\) 1.08473e10i 1.34357i −0.740746 0.671785i \(-0.765528\pi\)
0.740746 0.671785i \(-0.234472\pi\)
\(678\) 2.71671e9 + 9.10400e8i 0.334764 + 0.112183i
\(679\) 7.23743e9i 0.887238i
\(680\) 1.93482e9 5.27323e9i 0.235972 0.643126i
\(681\) 4.75574e9 5.31707e9i 0.577036 0.645146i
\(682\) −7.98023e8 1.85444e9i −0.0963319 0.223855i
\(683\) 1.18751e10 1.42615 0.713075 0.701088i \(-0.247302\pi\)
0.713075 + 0.701088i \(0.247302\pi\)
\(684\) −4.03337e9 + 5.34214e9i −0.481917 + 0.638292i
\(685\) −5.23824e9 −0.622685
\(686\) 2.89851e9 + 6.73553e9i 0.342800 + 0.796594i
\(687\) 1.36907e9 1.53066e9i 0.161093 0.180107i
\(688\) 1.15835e9 6.34421e7i 0.135606 0.00742708i
\(689\) 4.44204e9i 0.517387i
\(690\) 7.46899e9 + 2.50294e9i 0.865546 + 0.290054i
\(691\) 9.50025e8i 0.109537i −0.998499 0.0547686i \(-0.982558\pi\)
0.998499 0.0547686i \(-0.0174421\pi\)
\(692\) 7.25695e8 + 6.87036e8i 0.0832497 + 0.0788149i
\(693\) −4.28827e9 + 4.79443e8i −0.489458 + 0.0547231i
\(694\) −1.36839e10 + 5.88861e9i −1.55400 + 0.668736i
\(695\) −8.19635e9 −0.926134
\(696\) 6.34233e9 3.37808e9i 0.713044 0.379785i
\(697\) −1.48157e10 −1.65732
\(698\) 2.90064e9 1.24824e9i 0.322850 0.138932i
\(699\) 8.45551e9 + 7.56284e9i 0.936418 + 0.837558i
\(700\) −3.32557e9 3.14841e9i −0.366457 0.346935i
\(701\) 7.66122e9i 0.840011i 0.907522 + 0.420006i \(0.137972\pi\)
−0.907522 + 0.420006i \(0.862028\pi\)
\(702\) 1.44003e10 + 3.09958e9i 1.57106 + 0.338160i
\(703\) 1.03562e9i 0.112423i
\(704\) −3.15825e9 2.67816e9i −0.341147 0.289290i
\(705\) −4.04256e9 3.61578e9i −0.434505 0.388633i
\(706\) 2.86044e9 + 6.64706e9i 0.305926 + 0.710908i
\(707\) 1.12071e10 1.19268
\(708\) 3.76354e8 + 4.52244e9i 0.0398548 + 0.478913i
\(709\) −6.07576e9 −0.640234 −0.320117 0.947378i \(-0.603722\pi\)
−0.320117 + 0.947378i \(0.603722\pi\)
\(710\) −2.43803e8 5.66548e8i −0.0255644 0.0594063i
\(711\) −1.13777e10 + 1.27206e9i −1.18716 + 0.132729i
\(712\) 5.28116e9 + 1.93773e9i 0.548339 + 0.201194i
\(713\) 6.54042e9i 0.675759i
\(714\) −3.16729e9 + 9.45147e9i −0.325645 + 0.971753i
\(715\) 5.17091e9i 0.529049i
\(716\) −6.61949e9 + 6.99196e9i −0.673952 + 0.711874i
\(717\) 4.18428e9 4.67817e9i 0.423939 0.473978i
\(718\) 7.33938e9 3.15837e9i 0.739987 0.318440i
\(719\) 1.50425e10 1.50928 0.754639 0.656140i \(-0.227812\pi\)
0.754639 + 0.656140i \(0.227812\pi\)
\(720\) 1.21842e9 + 7.26986e9i 0.121656 + 0.725876i
\(721\) −1.15727e10 −1.14991
\(722\) −3.34734e9 + 1.44046e9i −0.330993 + 0.142437i
\(723\) −1.30700e10 + 1.46127e10i −1.28615 + 1.43796i
\(724\) 3.19517e9 3.37495e9i 0.312902 0.330508i
\(725\) 3.79912e9i 0.370254i
\(726\) −2.62065e9 + 7.82022e9i −0.254173 + 0.758475i
\(727\) 9.39530e9i 0.906860i −0.891292 0.453430i \(-0.850200\pi\)
0.891292 0.453430i \(-0.149800\pi\)
\(728\) −1.72935e10 6.34522e9i −1.66120 0.609519i
\(729\) 3.42939e9 + 9.88222e9i 0.327846 + 0.944731i
\(730\) −2.38528e8 5.54290e8i −0.0226939 0.0527360i
\(731\) 1.33501e9 0.126408
\(732\) 1.55978e8 + 1.87430e9i 0.0146985 + 0.176624i
\(733\) 7.71856e9 0.723890 0.361945 0.932200i \(-0.382113\pi\)
0.361945 + 0.932200i \(0.382113\pi\)
\(734\) 6.80665e9 + 1.58172e10i 0.635327 + 1.47637i
\(735\) −1.25428e9 1.12186e9i −0.116516 0.104215i
\(736\) −5.96876e9 1.20142e10i −0.551838 1.11076i
\(737\) 1.60204e9i 0.147414i
\(738\) 1.68949e10 9.62226e9i 1.54724 0.881211i
\(739\) 3.96381e8i 0.0361291i 0.999837 + 0.0180646i \(0.00575044\pi\)
−0.999837 + 0.0180646i \(0.994250\pi\)
\(740\) −8.28167e8 7.84050e8i −0.0751289 0.0711267i
\(741\) −1.06103e10 9.49017e9i −0.957999 0.856860i
\(742\) −3.62353e9 + 1.55932e9i −0.325625 + 0.140127i
\(743\) −4.86457e9 −0.435094 −0.217547 0.976050i \(-0.569806\pi\)
−0.217547 + 0.976050i \(0.569806\pi\)
\(744\) 5.40187e9 2.87717e9i 0.480882 0.256130i
\(745\) −5.09494e8 −0.0451432
\(746\) 4.35645e9 1.87472e9i 0.384191 0.165329i
\(747\) −2.45471e9 2.19556e10i −0.215465 1.92718i
\(748\) −3.46049e9 3.27615e9i −0.302331 0.286225i
\(749\) 2.18506e8i 0.0190011i
\(750\) −1.17579e10 3.94020e9i −1.01769 0.341039i
\(751\) 8.71438e9i 0.750753i 0.926872 + 0.375376i \(0.122487\pi\)
−0.926872 + 0.375376i \(0.877513\pi\)
\(752\) 5.05131e8 + 9.22285e9i 0.0433153 + 0.790866i
\(753\) 1.38597e10 1.54957e10i 1.18297 1.32260i
\(754\) 6.04064e9 + 1.40372e10i 0.513196 + 1.19256i
\(755\) 1.16678e10 0.986678
\(756\) −2.52660e9 1.28349e10i −0.212672 1.08035i
\(757\) 1.67972e10 1.40735 0.703673 0.710524i \(-0.251542\pi\)
0.703673 + 0.710524i \(0.251542\pi\)
\(758\) −8.23076e9 1.91266e10i −0.686432 1.59512i
\(759\) 4.45522e9 4.98109e9i 0.369848 0.413502i
\(760\) 2.45379e9 6.68765e9i 0.202764 0.552619i
\(761\) 4.88336e8i 0.0401673i 0.999798 + 0.0200836i \(0.00639325\pi\)
−0.999798 + 0.0200836i \(0.993607\pi\)
\(762\) −8.30256e9 2.78228e9i −0.679782 0.227803i
\(763\) 9.79946e9i 0.798668i
\(764\) 1.13993e10 1.20408e10i 0.924811 0.976849i
\(765\) 9.42529e8 + 8.43024e9i 0.0761167 + 0.680808i
\(766\) 1.95211e9 8.40056e8i 0.156930 0.0675317i
\(767\) −9.65085e9 −0.772292
\(768\) 7.29706e9 1.02148e10i 0.581278 0.813705i
\(769\) 9.73330e9 0.771824 0.385912 0.922536i \(-0.373887\pi\)
0.385912 + 0.922536i \(0.373887\pi\)
\(770\) 4.21809e9 1.81518e9i 0.332965 0.143285i
\(771\) −1.13277e9 1.01318e9i −0.0890129 0.0796156i
\(772\) −1.05590e10 + 1.11531e10i −0.825966 + 0.872442i
\(773\) 2.10035e10i 1.63555i 0.575540 + 0.817774i \(0.304792\pi\)
−0.575540 + 0.817774i \(0.695208\pi\)
\(774\) −1.52236e9 + 8.67041e8i −0.118012 + 0.0672119i
\(775\) 3.23578e9i 0.249702i
\(776\) −3.61304e9 + 9.84708e9i −0.277560 + 0.756470i
\(777\) 1.50849e9 + 1.34923e9i 0.115363 + 0.103184i
\(778\) −1.44182e9 3.35049e9i −0.109770 0.255082i
\(779\) −1.87897e10 −1.42409
\(780\) −1.56220e10 + 1.30005e9i −1.17871 + 0.0980911i
\(781\) −5.23260e8 −0.0393042
\(782\) −6.10241e9 1.41807e10i −0.456329 1.06041i
\(783\) −6.29118e9 + 8.84243e9i −0.468345 + 0.658272i
\(784\) 1.56726e8 + 2.86155e9i 0.0116154 + 0.212078i
\(785\) 5.23012e9i 0.385894i
\(786\) −4.27814e8 + 1.27663e9i −0.0314251 + 0.0937750i
\(787\) 2.27878e10i 1.66644i 0.552939 + 0.833222i \(0.313506\pi\)
−0.552939 + 0.833222i \(0.686494\pi\)
\(788\) −3.54104e9 3.35240e9i −0.257804 0.244070i
\(789\) −1.32923e10 + 1.48612e10i −0.963453 + 1.07717i
\(790\) 1.11915e10 4.81604e9i 0.807592 0.347532i
\(791\) 5.41116e9 0.388752
\(792\) 6.07387e9 + 1.48845e9i 0.434437 + 0.106462i
\(793\) −3.99974e9 −0.284823
\(794\) 1.39884e10 6.01964e9i 0.991734 0.426775i
\(795\) −2.23800e9 + 2.50216e9i −0.157970 + 0.176616i
\(796\) 9.38039e9 + 8.88069e9i 0.659212 + 0.624095i
\(797\) 1.22577e10i 0.857638i −0.903391 0.428819i \(-0.858930\pi\)
0.903391 0.428819i \(-0.141070\pi\)
\(798\) −4.01685e9 + 1.19866e10i −0.279818 + 0.834999i
\(799\) 1.06295e10i 0.737221i
\(800\) 2.95296e9 + 5.94383e9i 0.203912 + 0.410442i
\(801\) −8.44291e9 + 9.43946e8i −0.580468 + 0.0648983i
\(802\) −3.90477e9 9.07387e9i −0.267292 0.621130i
\(803\) −5.11938e8 −0.0348910
\(804\) −4.83999e9 + 4.02780e8i −0.328434 + 0.0273320i
\(805\) 1.48768e10 1.00513
\(806\) 5.14492e9 + 1.19557e10i 0.346103 + 0.804271i
\(807\) 1.04696e10 + 9.36434e9i 0.701253 + 0.627220i
\(808\) −1.52481e10 5.59473e9i −1.01689 0.373112i
\(809\) 3.89938e9i 0.258926i −0.991584 0.129463i \(-0.958675\pi\)
0.991584 0.129463i \(-0.0413253\pi\)
\(810\) −6.54993e9 9.00117e9i −0.433051 0.595116i
\(811\) 9.83894e9i 0.647702i −0.946108 0.323851i \(-0.895022\pi\)
0.946108 0.323851i \(-0.104978\pi\)
\(812\) 9.33013e9 9.85512e9i 0.611563 0.645975i
\(813\) 5.87748e9 + 5.25698e9i 0.383596 + 0.343099i
\(814\) −8.88721e8 + 3.82445e8i −0.0577537 + 0.0248533i
\(815\) 8.31618e9 0.538111
\(816\) 9.02767e9 1.12783e10i 0.581648 0.726654i
\(817\) 1.69310e9 0.108619
\(818\) −1.68265e10 + 7.24097e9i −1.07487 + 0.462551i
\(819\) 2.76468e10 3.09101e9i 1.75854 0.196610i
\(820\) −1.42253e10 + 1.50258e10i −0.900977 + 0.951673i
\(821\) 1.76060e10i 1.11035i −0.831733 0.555176i \(-0.812651\pi\)
0.831733 0.555176i \(-0.187349\pi\)
\(822\) −1.27741e10 4.28075e9i −0.802195 0.268824i
\(823\) 1.59689e10i 0.998564i −0.866439 0.499282i \(-0.833597\pi\)
0.866439 0.499282i \(-0.166403\pi\)
\(824\) 1.57456e10 + 5.77728e9i 0.980424 + 0.359731i
\(825\) −2.20416e9 + 2.46432e9i −0.136664 + 0.152795i
\(826\) 3.38780e9 + 7.87253e9i 0.209164 + 0.486054i
\(827\) −1.38691e10 −0.852666 −0.426333 0.904566i \(-0.640195\pi\)
−0.426333 + 0.904566i \(0.640195\pi\)
\(828\) 1.61687e10 + 1.22075e10i 0.989847 + 0.747344i
\(829\) −3.03083e10 −1.84766 −0.923828 0.382808i \(-0.874957\pi\)
−0.923828 + 0.382808i \(0.874957\pi\)
\(830\) 9.29354e9 + 2.15962e10i 0.564167 + 1.31101i
\(831\) 1.31023e10 1.46488e10i 0.792034 0.885521i
\(832\) 2.03615e10 + 1.72663e10i 1.22568 + 1.03937i
\(833\) 3.29798e9i 0.197692i
\(834\) −1.99879e10 6.69816e9i −1.19312 0.399829i
\(835\) 1.09182e10i 0.649008i
\(836\) −4.38869e9 4.15490e9i −0.259784 0.245945i
\(837\) −5.35830e9 + 7.53125e9i −0.315855 + 0.443944i
\(838\) 1.90341e10 8.19096e9i 1.11732 0.480818i
\(839\) −1.76156e10 −1.02975 −0.514873 0.857266i \(-0.672161\pi\)
−0.514873 + 0.857266i \(0.672161\pi\)
\(840\) 6.54439e9 + 1.22870e10i 0.380971 + 0.715270i
\(841\) 5.99141e9 0.347331
\(842\) −1.35072e10 + 5.81257e9i −0.779781 + 0.335564i
\(843\) −1.77754e10 1.58988e10i −1.02193 0.914044i
\(844\) −1.87985e10 1.77971e10i −1.07628 1.01895i
\(845\) 2.04287e10i 1.16478i
\(846\) −6.90345e9 1.21212e10i −0.391985 0.688253i
\(847\) 1.55764e10i 0.880794i
\(848\) 5.70852e9 3.12653e8i 0.321468 0.0176067i
\(849\) −5.39019e8 4.82113e8i −0.0302292 0.0270378i
\(850\) 3.01908e9 + 7.01570e9i 0.168620 + 0.391837i
\(851\) −3.13443e9 −0.174343
\(852\) −1.31556e8 1.58084e9i −0.00728740 0.0875688i
\(853\) −7.77452e9 −0.428896 −0.214448 0.976735i \(-0.568795\pi\)
−0.214448 + 0.976735i \(0.568795\pi\)
\(854\) 1.40405e9 + 3.26273e9i 0.0771403 + 0.179258i
\(855\) 1.19534e9 + 1.06914e10i 0.0654049 + 0.584999i
\(856\) 1.09082e8 2.97295e8i 0.00594421 0.0162005i
\(857\) 3.40944e9i 0.185033i −0.995711 0.0925166i \(-0.970509\pi\)
0.995711 0.0925166i \(-0.0294911\pi\)
\(858\) −4.22573e9 + 1.26099e10i −0.228400 + 0.681564i
\(859\) 1.01843e9i 0.0548221i 0.999624 + 0.0274111i \(0.00872631\pi\)
−0.999624 + 0.0274111i \(0.991274\pi\)
\(860\) 1.28181e9 1.35394e9i 0.0687195 0.0725863i
\(861\) 2.44796e10 2.73691e10i 1.30706 1.46133i
\(862\) 2.34142e10 1.00759e10i 1.24510 0.535805i
\(863\) 2.23663e10 1.18456 0.592278 0.805734i \(-0.298229\pi\)
0.592278 + 0.805734i \(0.298229\pi\)
\(864\) −2.96974e9 + 1.87242e10i −0.156646 + 0.987655i
\(865\) 1.60609e9 0.0843749
\(866\) 3.52085e9 1.51513e9i 0.184219 0.0792752i
\(867\) −1.70992e9 + 1.91174e9i −0.0891062 + 0.0996237i
\(868\) 7.94663e9 8.39377e9i 0.412443 0.435650i
\(869\) 1.03364e10i 0.534316i
\(870\) 3.66961e9 1.09504e10i 0.188931 0.563785i
\(871\) 1.03285e10i 0.529631i
\(872\) −4.89204e9 + 1.33329e10i −0.249852 + 0.680954i
\(873\) −1.76005e9 1.57424e10i −0.0895314 0.800793i
\(874\) −7.73923e9 1.79844e10i −0.392110 0.911181i
\(875\) −2.34194e10 −1.18181
\(876\) −1.28710e8 1.54664e9i −0.00646915 0.0777363i
\(877\) −7.42860e9 −0.371885 −0.185942 0.982561i \(-0.559534\pi\)
−0.185942 + 0.982561i \(0.559534\pi\)
\(878\) −7.71874e9 1.79367e10i −0.384872 0.894361i
\(879\) 2.76480e10 + 2.47291e10i 1.37310 + 1.22814i
\(880\) −6.64520e9 + 3.63954e8i −0.328714 + 0.0180035i
\(881\) 2.83256e10i 1.39561i 0.716288 + 0.697804i \(0.245840\pi\)
−0.716288 + 0.697804i \(0.754160\pi\)
\(882\) −2.14192e9 3.76080e9i −0.105114 0.184561i
\(883\) 2.16342e10i 1.05750i −0.848779 0.528748i \(-0.822662\pi\)
0.848779 0.528748i \(-0.177338\pi\)
\(884\) 2.23101e10 + 2.11216e10i 1.08622 + 1.02836i
\(885\) 5.43623e9 + 4.86232e9i 0.263631 + 0.235799i
\(886\) −1.80391e10 + 7.76280e9i −0.871359 + 0.374973i
\(887\) −2.48940e9 −0.119774 −0.0598869 0.998205i \(-0.519074\pi\)
−0.0598869 + 0.998205i \(0.519074\pi\)
\(888\) −1.37886e9 2.58879e9i −0.0660806 0.124066i
\(889\) −1.65371e10 −0.789410
\(890\) 8.30473e9 3.57379e9i 0.394876 0.169927i
\(891\) −9.21096e9 + 2.08571e9i −0.436248 + 0.0987827i
\(892\) −4.30683e9 4.07740e9i −0.203180 0.192356i
\(893\) 1.34806e10i 0.633472i
\(894\) −1.24247e9 4.16365e8i −0.0581572 0.0194891i
\(895\) 1.54744e10i 0.721496i
\(896\) 6.93712e9 2.26707e10i 0.322182 1.05290i
\(897\) −2.87232e10 + 3.21135e10i −1.32880 + 1.48564i
\(898\) −4.28124e9 9.94871e9i −0.197289 0.458458i
\(899\) −9.58902e9 −0.440165
\(900\) −7.99921e9 6.03948e9i −0.365762 0.276154i
\(901\) 6.57915e9 0.299663
\(902\) 6.93884e9 + 1.61244e10i 0.314821 + 0.731579i
\(903\) −2.20581e9 + 2.46617e9i −0.0996921 + 0.111459i
\(904\) −7.36230e9 2.70133e9i −0.331454 0.121615i
\(905\) 7.46936e9i 0.334976i
\(906\) 2.84535e10 + 9.53509e9i 1.27112 + 0.425967i
\(907\) 6.03196e8i 0.0268431i −0.999910 0.0134216i \(-0.995728\pi\)
0.999910 0.0134216i \(-0.00427234\pi\)
\(908\) −1.34235e10 + 1.41789e10i −0.595068 + 0.628552i
\(909\) 2.43768e10 2.72541e9i 1.07647 0.120354i
\(910\) −2.71943e10 + 1.17026e10i −1.19628 + 0.514798i
\(911\) 2.68931e10 1.17849 0.589246 0.807954i \(-0.299425\pi\)
0.589246 + 0.807954i \(0.299425\pi\)
\(912\) 1.14491e10 1.43034e10i 0.499793 0.624393i
\(913\) 1.99461e10 0.867383
\(914\) 2.31490e10 9.96172e9i 1.00281 0.431542i
\(915\) 2.25302e9 + 2.01516e9i 0.0972278 + 0.0869632i
\(916\) −3.86433e9 + 4.08176e9i −0.166127 + 0.175474i
\(917\) 2.54280e9i 0.108898i
\(918\) −4.59081e9 + 2.13285e10i −0.195857 + 0.909934i
\(919\) 1.44011e10i 0.612056i −0.952022 0.306028i \(-0.901000\pi\)
0.952022 0.306028i \(-0.0990002\pi\)
\(920\) −2.02410e10 7.42671e9i −0.856988 0.314441i
\(921\) 1.76957e10 + 1.58276e10i 0.746380 + 0.667583i
\(922\) 1.10693e10 + 2.57227e10i 0.465117 + 1.08083i
\(923\) 3.37350e9 0.141213
\(924\) 1.17697e10 9.79468e8i 0.490811 0.0408449i
\(925\) 1.55071e9 0.0644222
\(926\) −1.10926e10 2.57770e10i −0.459088 1.06682i
\(927\) −2.51722e10 + 2.81434e9i −1.03787 + 0.116037i
\(928\) −1.76142e10 + 8.75091e9i −0.723510 + 0.359447i
\(929\) 8.33324e9i 0.341003i 0.985357 + 0.170502i \(0.0545388\pi\)
−0.985357 + 0.170502i \(0.945461\pi\)
\(930\) 3.12547e9 9.32666e9i 0.127416 0.380221i
\(931\) 4.18258e9i 0.169871i
\(932\) −2.25480e10 2.13469e10i −0.912332 0.863732i
\(933\) −8.70411e9 + 9.73149e9i −0.350864 + 0.392278i
\(934\) 1.11775e10 4.81001e9i 0.448879 0.193167i
\(935\) −7.65868e9 −0.306417
\(936\) −3.91587e10 9.59615e9i −1.56086 0.382500i
\(937\) 2.24458e10 0.891346 0.445673 0.895196i \(-0.352964\pi\)
0.445673 + 0.895196i \(0.352964\pi\)
\(938\) −8.42531e9 + 3.62568e9i −0.333331 + 0.143443i
\(939\) 2.16006e9 2.41502e9i 0.0851405 0.0951900i
\(940\) 1.07802e10 + 1.02059e10i 0.423329 + 0.400778i
\(941\) 2.64833e10i 1.03612i 0.855345 + 0.518059i \(0.173345\pi\)
−0.855345 + 0.518059i \(0.826655\pi\)
\(942\) −4.27411e9 + 1.27543e10i −0.166597 + 0.497140i
\(943\) 5.68692e10i 2.20844i
\(944\) −6.79274e8 1.24024e10i −0.0262811 0.479849i
\(945\) −1.71305e10 1.21879e10i −0.660327 0.469807i
\(946\) −6.25244e8 1.45294e9i −0.0240121 0.0557992i
\(947\) 2.26400e10 0.866266 0.433133 0.901330i \(-0.357408\pi\)
0.433133 + 0.901330i \(0.357408\pi\)
\(948\) 3.12275e10 2.59873e9i 1.19044 0.0990678i
\(949\) 3.30051e9 0.125357
\(950\) 3.82887e9 + 8.89750e9i 0.144890 + 0.336694i
\(951\) −3.12828e10 2.79802e10i −1.17943 1.05492i
\(952\) 9.39797e9 2.56135e10i 0.353024 0.962144i
\(953\) 4.67746e10i 1.75059i −0.483586 0.875297i \(-0.660666\pi\)
0.483586 0.875297i \(-0.339334\pi\)
\(954\) −7.50245e9 + 4.27292e9i −0.279759 + 0.159333i
\(955\) 2.66483e10i 0.990052i
\(956\) −1.18106e10 + 1.24751e10i −0.437187 + 0.461787i
\(957\) −7.30286e9 6.53188e9i −0.269340 0.240905i
\(958\) −3.21231e9 + 1.38236e9i −0.118042 + 0.0507974i
\(959\) −2.54436e10 −0.931564
\(960\) −2.77027e9 1.99845e10i −0.101058 0.729029i
\(961\) 1.93455e10 0.703149
\(962\) 5.72965e9 2.46565e9i 0.207499 0.0892933i
\(963\) 5.31380e7 + 4.75281e8i 0.00191740 + 0.0171498i
\(964\) 3.68914e10 3.89672e10i 1.32634 1.40097i
\(965\) 2.46839e10i 0.884235i
\(966\) 3.62789e10 + 1.21575e10i 1.29489 + 0.433934i
\(967\) 1.66727e10i 0.592942i 0.955042 + 0.296471i \(0.0958098\pi\)
−0.955042 + 0.296471i \(0.904190\pi\)
\(968\) 7.77596e9 2.11928e10i 0.275543 0.750975i
\(969\) 1.40560e10 1.57151e10i 0.496281 0.554859i
\(970\) 6.66357e9 + 1.54847e10i 0.234426 + 0.544757i
\(971\) 1.55445e9 0.0544889 0.0272445 0.999629i \(-0.491327\pi\)
0.0272445 + 0.999629i \(0.491327\pi\)
\(972\) −8.61699e9 2.73032e10i −0.300970 0.953634i
\(973\) −3.98119e10 −1.38554
\(974\) −9.41688e9 2.18829e10i −0.326551 0.758836i
\(975\) 1.42104e10 1.58877e10i 0.491009 0.548964i
\(976\) −2.81521e8 5.14012e9i −0.00969253 0.176970i
\(977\) 7.71063e9i 0.264520i −0.991215 0.132260i \(-0.957777\pi\)
0.991215 0.132260i \(-0.0422234\pi\)
\(978\) 2.02801e10 + 6.79608e9i 0.693240 + 0.232313i
\(979\) 7.67019e9i 0.261256i
\(980\) 3.34474e9 + 3.16656e9i 0.113519 + 0.107472i
\(981\) −2.38310e9 2.13151e10i −0.0805938 0.720853i
\(982\) −6.17732e9 + 2.65829e9i −0.208166 + 0.0895804i
\(983\) 5.24036e10 1.75964 0.879820 0.475307i \(-0.157663\pi\)
0.879820 + 0.475307i \(0.157663\pi\)
\(984\) −4.69695e10 + 2.50171e10i −1.57157 + 0.837056i
\(985\) −7.83694e9 −0.261288
\(986\) −2.07906e10 + 8.94685e9i −0.690713 + 0.297236i
\(987\) −1.96358e10 1.75628e10i −0.650038 0.581412i
\(988\) 2.82942e10 + 2.67870e10i 0.933358 + 0.883637i
\(989\) 5.12436e9i 0.168443i
\(990\) 8.73347e9 4.97403e9i 0.286064 0.162924i
\(991\) 6.02219e9i 0.196561i −0.995159 0.0982803i \(-0.968666\pi\)
0.995159 0.0982803i \(-0.0313342\pi\)
\(992\) −1.50023e10 + 7.45330e9i −0.487941 + 0.242414i
\(993\) −4.15271e10 3.71430e10i −1.34589 1.20380i
\(994\) −1.18422e9 2.75188e9i −0.0382455 0.0888744i
\(995\) 2.07605e10 0.668122
\(996\) 5.01479e9 + 6.02600e10i 0.160822 + 1.93251i
\(997\) 9.88566e9 0.315917 0.157958 0.987446i \(-0.449509\pi\)
0.157958 + 0.987446i \(0.449509\pi\)
\(998\) 1.52018e10 + 3.53257e10i 0.484102 + 1.12495i
\(999\) 3.60928e9 + 2.56791e9i 0.114536 + 0.0814895i
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 12.8.b.a.11.2 yes 4
3.2 odd 2 inner 12.8.b.a.11.3 yes 4
4.3 odd 2 inner 12.8.b.a.11.4 yes 4
8.3 odd 2 192.8.c.b.191.2 4
8.5 even 2 192.8.c.b.191.3 4
12.11 even 2 inner 12.8.b.a.11.1 4
24.5 odd 2 192.8.c.b.191.1 4
24.11 even 2 192.8.c.b.191.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.8.b.a.11.1 4 12.11 even 2 inner
12.8.b.a.11.2 yes 4 1.1 even 1 trivial
12.8.b.a.11.3 yes 4 3.2 odd 2 inner
12.8.b.a.11.4 yes 4 4.3 odd 2 inner
192.8.c.b.191.1 4 24.5 odd 2
192.8.c.b.191.2 4 8.3 odd 2
192.8.c.b.191.3 4 8.5 even 2
192.8.c.b.191.4 4 24.11 even 2