Properties

Label 12.15.d.a.7.5
Level $12$
Weight $15$
Character 12.7
Analytic conductor $14.919$
Analytic rank $0$
Dimension $14$
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] = [12,15,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, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.7");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 15 \)
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: \(14.9194761782\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - x^{13} + 9158 x^{12} + 65217 x^{11} + 61148515 x^{10} + 439019974 x^{9} + 189458968156 x^{8} + 1788546506656 x^{7} + 430738312102192 x^{6} + \cdots + 89\!\cdots\!84 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{81}\cdot 3^{41} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 7.5
Root \(-33.2709 + 57.6269i\) of defining polynomial
Character \(\chi\) \(=\) 12.7
Dual form 12.15.d.a.7.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-47.8547 - 118.718i) q^{2} +1262.67i q^{3} +(-11803.8 + 11362.4i) q^{4} -132280. q^{5} +(149901. - 60424.5i) q^{6} -304975. i q^{7} +(1.91379e6 + 857581. i) q^{8} -1.59432e6 q^{9} +O(q^{10})\) \(q+(-47.8547 - 118.718i) q^{2} +1262.67i q^{3} +(-11803.8 + 11362.4i) q^{4} -132280. q^{5} +(149901. - 60424.5i) q^{6} -304975. i q^{7} +(1.91379e6 + 857581. i) q^{8} -1.59432e6 q^{9} +(6.33024e6 + 1.57040e7i) q^{10} +4.87590e6i q^{11} +(-1.43469e7 - 1.49043e7i) q^{12} +9.89669e7 q^{13} +(-3.62060e7 + 1.45945e7i) q^{14} -1.67026e8i q^{15} +(1.02262e7 - 2.68241e8i) q^{16} +4.23677e7 q^{17} +(7.62959e7 + 1.89275e8i) q^{18} -1.40872e9i q^{19} +(1.56142e9 - 1.50303e9i) q^{20} +3.85082e8 q^{21} +(5.78856e8 - 2.33335e8i) q^{22} +4.23629e9i q^{23} +(-1.08284e9 + 2.41648e9i) q^{24} +1.13946e10 q^{25} +(-4.73603e9 - 1.17491e10i) q^{26} -2.01310e9i q^{27} +(3.46526e9 + 3.59988e9i) q^{28} -5.57826e9 q^{29} +(-1.98289e10 + 7.99298e9i) q^{30} +9.56870e8i q^{31} +(-3.23343e10 + 1.16226e10i) q^{32} -6.15663e9 q^{33} +(-2.02750e9 - 5.02980e9i) q^{34} +4.03423e10i q^{35} +(1.88191e10 - 1.81154e10i) q^{36} +1.19922e11 q^{37} +(-1.67240e11 + 6.74138e10i) q^{38} +1.24962e11i q^{39} +(-2.53157e11 - 1.13441e11i) q^{40} +2.10357e11 q^{41} +(-1.84280e10 - 4.57161e10i) q^{42} +3.76222e11i q^{43} +(-5.54020e10 - 5.75544e10i) q^{44} +2.10898e11 q^{45} +(5.02923e11 - 2.02726e11i) q^{46} -8.87229e11i q^{47} +(3.38698e11 + 1.29122e10i) q^{48} +5.85213e11 q^{49} +(-5.45285e11 - 1.35274e12i) q^{50} +5.34962e10i q^{51} +(-1.16819e12 + 1.12450e12i) q^{52} -1.43248e11 q^{53} +(-2.38990e11 + 9.63362e10i) q^{54} -6.44986e11i q^{55} +(2.61541e11 - 5.83660e11i) q^{56} +1.77874e12 q^{57} +(2.66946e11 + 6.62239e11i) q^{58} +2.40999e12i q^{59} +(1.89782e12 + 1.97155e12i) q^{60} -2.37831e12 q^{61} +(1.13598e11 - 4.57908e10i) q^{62} +4.86229e11i q^{63} +(2.92715e12 + 3.28247e12i) q^{64} -1.30914e13 q^{65} +(2.94624e11 + 7.30901e11i) q^{66} +1.58948e12i q^{67} +(-5.00102e11 + 4.81400e11i) q^{68} -5.34901e12 q^{69} +(4.78935e12 - 1.93057e12i) q^{70} -1.62907e13i q^{71} +(-3.05120e12 - 1.36726e12i) q^{72} +8.92687e12 q^{73} +(-5.73882e12 - 1.42368e13i) q^{74} +1.43875e13i q^{75} +(1.60064e13 + 1.66283e13i) q^{76} +1.48703e12 q^{77} +(1.48352e13 - 5.98003e12i) q^{78} -1.91983e13i q^{79} +(-1.35272e12 + 3.54830e13i) q^{80} +2.54187e12 q^{81} +(-1.00666e13 - 2.49732e13i) q^{82} +4.14129e11i q^{83} +(-4.54545e12 + 4.37546e12i) q^{84} -5.60442e12 q^{85} +(4.46642e13 - 1.80040e13i) q^{86} -7.04347e12i q^{87} +(-4.18148e12 + 9.33146e12i) q^{88} +3.16654e13 q^{89} +(-1.00925e13 - 2.50373e13i) q^{90} -3.01825e13i q^{91} +(-4.81345e13 - 5.00045e13i) q^{92} -1.20821e12 q^{93} +(-1.05330e14 + 4.24581e13i) q^{94} +1.86346e14i q^{95} +(-1.46754e13 - 4.08274e13i) q^{96} +6.43443e13 q^{97} +(-2.80052e13 - 6.94752e13i) q^{98} -7.77376e12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9} + 586324 q^{10} + 621108 q^{12} + 109934140 q^{13} - 200755992 q^{14} + 380631536 q^{16} - 291483380 q^{17} - 290166786 q^{18} + 5316726088 q^{20} - 1117661976 q^{21} - 9373833288 q^{22} + 2880331488 q^{24} + 12506859258 q^{25} - 45510637748 q^{26} + 83579713776 q^{28} - 12126204812 q^{29} - 44941179132 q^{30} + 67974212192 q^{32} - 34345330344 q^{33} - 57269346212 q^{34} - 14839958484 q^{36} + 119365701580 q^{37} + 102957884712 q^{38} - 491601579872 q^{40} + 189318893932 q^{41} + 240539889384 q^{42} - 997611383472 q^{44} + 25706864052 q^{45} + 1368039641184 q^{46} - 465649986384 q^{48} - 769149171250 q^{49} + 2170057449522 q^{50} - 2399333559176 q^{52} + 1251391890964 q^{53} - 90656394426 q^{54} + 2319191796096 q^{56} + 1805052294792 q^{57} - 5157502168892 q^{58} + 2354207329944 q^{60} - 7882441676660 q^{61} - 9161379391272 q^{62} + 17520900128384 q^{64} + 5858206778312 q^{65} - 6614704234440 q^{66} + 18747786717976 q^{68} - 13777261381728 q^{69} - 8213486211792 q^{70} - 6939794663568 q^{72} + 39185062250428 q^{73} - 7698562888484 q^{74} - 9224963770896 q^{76} - 41289727781472 q^{77} + 10470873014172 q^{78} - 57127847610848 q^{80} + 35586121596606 q^{81} + 107070799921084 q^{82} - 28102976768880 q^{84} - 188880254078680 q^{85} + 102443851819896 q^{86} - 83262676567680 q^{88} + 223721333984572 q^{89} - 934789838652 q^{90} - 79895035003584 q^{92} + 12688158423960 q^{93} - 52692266305296 q^{94} - 2264434006752 q^{96} + 282902280361756 q^{97} - 228639957171082 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −47.8547 118.718i −0.373865 0.927483i
\(3\) 1262.67i 0.577350i
\(4\) −11803.8 + 11362.4i −0.720450 + 0.693507i
\(5\) −132280. −1.69319 −0.846595 0.532238i \(-0.821351\pi\)
−0.846595 + 0.532238i \(0.821351\pi\)
\(6\) 149901. 60424.5i 0.535483 0.215851i
\(7\) 304975.i 0.370321i −0.982708 0.185161i \(-0.940719\pi\)
0.982708 0.185161i \(-0.0592805\pi\)
\(8\) 1.91379e6 + 857581.i 0.912567 + 0.408927i
\(9\) −1.59432e6 −0.333333
\(10\) 6.33024e6 + 1.57040e7i 0.633024 + 1.57040i
\(11\) 4.87590e6i 0.250211i 0.992143 + 0.125105i \(0.0399269\pi\)
−0.992143 + 0.125105i \(0.960073\pi\)
\(12\) −1.43469e7 1.49043e7i −0.400397 0.415952i
\(13\) 9.89669e7 1.57720 0.788599 0.614907i \(-0.210807\pi\)
0.788599 + 0.614907i \(0.210807\pi\)
\(14\) −3.62060e7 + 1.45945e7i −0.343467 + 0.138450i
\(15\) 1.67026e8i 0.977563i
\(16\) 1.02262e7 2.68241e8i 0.0380955 0.999274i
\(17\) 4.23677e7 0.103251 0.0516253 0.998667i \(-0.483560\pi\)
0.0516253 + 0.998667i \(0.483560\pi\)
\(18\) 7.62959e7 + 1.89275e8i 0.124622 + 0.309161i
\(19\) 1.40872e9i 1.57597i −0.615693 0.787986i \(-0.711124\pi\)
0.615693 0.787986i \(-0.288876\pi\)
\(20\) 1.56142e9 1.50303e9i 1.21986 1.17424i
\(21\) 3.85082e8 0.213805
\(22\) 5.78856e8 2.33335e8i 0.232066 0.0935451i
\(23\) 4.23629e9i 1.24420i 0.782937 + 0.622101i \(0.213721\pi\)
−0.782937 + 0.622101i \(0.786279\pi\)
\(24\) −1.08284e9 + 2.41648e9i −0.236094 + 0.526871i
\(25\) 1.13946e10 1.86689
\(26\) −4.73603e9 1.17491e10i −0.589660 1.46283i
\(27\) 2.01310e9i 0.192450i
\(28\) 3.46526e9 + 3.59988e9i 0.256820 + 0.266798i
\(29\) −5.57826e9 −0.323380 −0.161690 0.986842i \(-0.551694\pi\)
−0.161690 + 0.986842i \(0.551694\pi\)
\(30\) −1.98289e10 + 7.99298e9i −0.906673 + 0.365477i
\(31\) 9.56870e8i 0.0347793i 0.999849 + 0.0173897i \(0.00553558\pi\)
−0.999849 + 0.0173897i \(0.994464\pi\)
\(32\) −3.23343e10 + 1.16226e10i −0.941052 + 0.338261i
\(33\) −6.15663e9 −0.144459
\(34\) −2.02750e9 5.02980e9i −0.0386018 0.0957632i
\(35\) 4.03423e10i 0.627024i
\(36\) 1.88191e10 1.81154e10i 0.240150 0.231169i
\(37\) 1.19922e11 1.26324 0.631620 0.775278i \(-0.282390\pi\)
0.631620 + 0.775278i \(0.282390\pi\)
\(38\) −1.67240e11 + 6.74138e10i −1.46169 + 0.589201i
\(39\) 1.24962e11i 0.910596i
\(40\) −2.53157e11 1.13441e11i −1.54515 0.692390i
\(41\) 2.10357e11 1.08012 0.540059 0.841627i \(-0.318402\pi\)
0.540059 + 0.841627i \(0.318402\pi\)
\(42\) −1.84280e10 4.57161e10i −0.0799343 0.198301i
\(43\) 3.76222e11i 1.38409i 0.721854 + 0.692046i \(0.243290\pi\)
−0.721854 + 0.692046i \(0.756710\pi\)
\(44\) −5.54020e10 5.75544e10i −0.173523 0.180264i
\(45\) 2.10898e11 0.564396
\(46\) 5.02923e11 2.02726e11i 1.15398 0.465164i
\(47\) 8.87229e11i 1.75126i −0.482982 0.875630i \(-0.660446\pi\)
0.482982 0.875630i \(-0.339554\pi\)
\(48\) 3.38698e11 + 1.29122e10i 0.576931 + 0.0219944i
\(49\) 5.85213e11 0.862862
\(50\) −5.45285e11 1.35274e12i −0.697965 1.73151i
\(51\) 5.34962e10i 0.0596118i
\(52\) −1.16819e12 + 1.12450e12i −1.13629 + 1.09380i
\(53\) −1.43248e11 −0.121943 −0.0609717 0.998139i \(-0.519420\pi\)
−0.0609717 + 0.998139i \(0.519420\pi\)
\(54\) −2.38990e11 + 9.63362e10i −0.178494 + 0.0719504i
\(55\) 6.44986e11i 0.423654i
\(56\) 2.61541e11 5.83660e11i 0.151434 0.337943i
\(57\) 1.77874e12 0.909888
\(58\) 2.66946e11 + 6.62239e11i 0.120900 + 0.299929i
\(59\) 2.40999e12i 0.968391i 0.874960 + 0.484195i \(0.160888\pi\)
−0.874960 + 0.484195i \(0.839112\pi\)
\(60\) 1.89782e12 + 1.97155e12i 0.677947 + 0.704285i
\(61\) −2.37831e12 −0.756764 −0.378382 0.925650i \(-0.623519\pi\)
−0.378382 + 0.925650i \(0.623519\pi\)
\(62\) 1.13598e11 4.57908e10i 0.0322572 0.0130028i
\(63\) 4.86229e11i 0.123440i
\(64\) 2.92715e12 + 3.28247e12i 0.665558 + 0.746346i
\(65\) −1.30914e13 −2.67050
\(66\) 2.94624e11 + 7.30901e11i 0.0540083 + 0.133983i
\(67\) 1.58948e12i 0.262259i 0.991365 + 0.131129i \(0.0418604\pi\)
−0.991365 + 0.131129i \(0.958140\pi\)
\(68\) −5.00102e11 + 4.81400e11i −0.0743869 + 0.0716050i
\(69\) −5.34901e12 −0.718340
\(70\) 4.78935e12 1.93057e12i 0.581554 0.234422i
\(71\) 1.62907e13i 1.79115i −0.444913 0.895574i \(-0.646766\pi\)
0.444913 0.895574i \(-0.353234\pi\)
\(72\) −3.05120e12 1.36726e12i −0.304189 0.136309i
\(73\) 8.92687e12 0.808052 0.404026 0.914747i \(-0.367610\pi\)
0.404026 + 0.914747i \(0.367610\pi\)
\(74\) −5.73882e12 1.42368e13i −0.472281 1.17163i
\(75\) 1.43875e13i 1.07785i
\(76\) 1.60064e13 + 1.66283e13i 1.09295 + 1.13541i
\(77\) 1.48703e12 0.0926583
\(78\) 1.48352e13 5.98003e12i 0.844563 0.340440i
\(79\) 1.91983e13i 0.999706i −0.866110 0.499853i \(-0.833387\pi\)
0.866110 0.499853i \(-0.166613\pi\)
\(80\) −1.35272e12 + 3.54830e13i −0.0645028 + 1.69196i
\(81\) 2.54187e12 0.111111
\(82\) −1.00666e13 2.49732e13i −0.403818 1.00179i
\(83\) 4.14129e11i 0.0152612i 0.999971 + 0.00763061i \(0.00242892\pi\)
−0.999971 + 0.00763061i \(0.997571\pi\)
\(84\) −4.54545e12 + 4.37546e12i −0.154036 + 0.148275i
\(85\) −5.60442e12 −0.174823
\(86\) 4.46642e13 1.80040e13i 1.28372 0.517464i
\(87\) 7.04347e12i 0.186703i
\(88\) −4.18148e12 + 9.33146e12i −0.102318 + 0.228334i
\(89\) 3.16654e13 0.715904 0.357952 0.933740i \(-0.383475\pi\)
0.357952 + 0.933740i \(0.383475\pi\)
\(90\) −1.00925e13 2.50373e13i −0.211008 0.523468i
\(91\) 3.01825e13i 0.584070i
\(92\) −4.81345e13 5.00045e13i −0.862863 0.896384i
\(93\) −1.20821e12 −0.0200799
\(94\) −1.05330e14 + 4.24581e13i −1.62426 + 0.654735i
\(95\) 1.86346e14i 2.66842i
\(96\) −1.46754e13 4.08274e13i −0.195295 0.543317i
\(97\) 6.43443e13 0.796358 0.398179 0.917308i \(-0.369642\pi\)
0.398179 + 0.917308i \(0.369642\pi\)
\(98\) −2.80052e13 6.94752e13i −0.322594 0.800290i
\(99\) 7.77376e12i 0.0834036i
\(100\) −1.34500e14 + 1.29470e14i −1.34500 + 1.29470i
\(101\) 4.71110e13 0.439413 0.219706 0.975566i \(-0.429490\pi\)
0.219706 + 0.975566i \(0.429490\pi\)
\(102\) 6.35096e12 2.56005e12i 0.0552889 0.0222868i
\(103\) 6.34102e13i 0.515583i −0.966201 0.257791i \(-0.917005\pi\)
0.966201 0.257791i \(-0.0829948\pi\)
\(104\) 1.89402e14 + 8.48722e13i 1.43930 + 0.644959i
\(105\) −5.09388e13 −0.362012
\(106\) 6.85510e12 + 1.70061e13i 0.0455904 + 0.113100i
\(107\) 5.12243e13i 0.318999i 0.987198 + 0.159500i \(0.0509881\pi\)
−0.987198 + 0.159500i \(0.949012\pi\)
\(108\) 2.28736e13 + 2.37623e13i 0.133466 + 0.138651i
\(109\) −2.78956e13 −0.152598 −0.0762992 0.997085i \(-0.524310\pi\)
−0.0762992 + 0.997085i \(0.524310\pi\)
\(110\) −7.65713e13 + 3.08656e13i −0.392932 + 0.158389i
\(111\) 1.51421e14i 0.729332i
\(112\) −8.18068e13 3.11873e12i −0.370052 0.0141076i
\(113\) 1.90871e14 0.811319 0.405659 0.914024i \(-0.367042\pi\)
0.405659 + 0.914024i \(0.367042\pi\)
\(114\) −8.51210e13 2.11168e14i −0.340175 0.843906i
\(115\) 5.60378e14i 2.10667i
\(116\) 6.58449e13 6.33825e13i 0.232979 0.224266i
\(117\) −1.57785e14 −0.525733
\(118\) 2.86108e14 1.15329e14i 0.898166 0.362048i
\(119\) 1.29211e13i 0.0382359i
\(120\) 1.43238e14 3.19653e14i 0.399752 0.892092i
\(121\) 3.55975e14 0.937395
\(122\) 1.13814e14 + 2.82348e14i 0.282928 + 0.701886i
\(123\) 2.65611e14i 0.623606i
\(124\) −1.08724e13 1.12948e13i −0.0241197 0.0250568i
\(125\) −6.99905e14 −1.46781
\(126\) 5.77241e13 2.32684e13i 0.114489 0.0461501i
\(127\) 4.50531e14i 0.845471i −0.906253 0.422735i \(-0.861070\pi\)
0.906253 0.422735i \(-0.138930\pi\)
\(128\) 2.49609e14 5.04587e14i 0.443395 0.896327i
\(129\) −4.75042e14 −0.799106
\(130\) 6.26485e14 + 1.55418e15i 0.998405 + 2.47684i
\(131\) 1.94922e14i 0.294417i 0.989105 + 0.147208i \(0.0470288\pi\)
−0.989105 + 0.147208i \(0.952971\pi\)
\(132\) 7.26719e13 6.99542e13i 0.104076 0.100184i
\(133\) −4.29624e14 −0.583616
\(134\) 1.88699e14 7.60640e13i 0.243241 0.0980495i
\(135\) 2.66293e14i 0.325854i
\(136\) 8.10830e13 + 3.63338e13i 0.0942231 + 0.0422219i
\(137\) −1.14701e15 −1.26626 −0.633131 0.774044i \(-0.718231\pi\)
−0.633131 + 0.774044i \(0.718231\pi\)
\(138\) 2.55976e14 + 6.35023e14i 0.268562 + 0.666248i
\(139\) 2.30780e14i 0.230194i −0.993354 0.115097i \(-0.963282\pi\)
0.993354 0.115097i \(-0.0367179\pi\)
\(140\) −4.58386e14 4.76194e14i −0.434846 0.451739i
\(141\) 1.12027e15 1.01109
\(142\) −1.93400e15 + 7.79587e14i −1.66126 + 0.669648i
\(143\) 4.82553e14i 0.394632i
\(144\) −1.63038e13 + 4.27662e14i −0.0126985 + 0.333091i
\(145\) 7.37894e14 0.547543
\(146\) −4.27193e14 1.05978e15i −0.302103 0.749455i
\(147\) 7.38928e14i 0.498174i
\(148\) −1.41554e15 + 1.36260e15i −0.910101 + 0.876066i
\(149\) 3.10081e14 0.190183 0.0950913 0.995469i \(-0.469686\pi\)
0.0950913 + 0.995469i \(0.469686\pi\)
\(150\) 1.70806e15 6.88512e14i 0.999687 0.402970i
\(151\) 1.66702e15i 0.931328i −0.884961 0.465664i \(-0.845815\pi\)
0.884961 0.465664i \(-0.154185\pi\)
\(152\) 1.20809e15 2.69599e15i 0.644457 1.43818i
\(153\) −6.75478e13 −0.0344169
\(154\) −7.11614e13 1.76537e14i −0.0346417 0.0859390i
\(155\) 1.26575e14i 0.0588880i
\(156\) −1.41987e15 1.47503e15i −0.631505 0.656039i
\(157\) 9.32853e14 0.396749 0.198374 0.980126i \(-0.436434\pi\)
0.198374 + 0.980126i \(0.436434\pi\)
\(158\) −2.27918e15 + 9.18728e14i −0.927211 + 0.373755i
\(159\) 1.80874e14i 0.0704040i
\(160\) 4.27720e15 1.53744e15i 1.59338 0.572740i
\(161\) 1.29196e15 0.460754
\(162\) −1.21640e14 3.01765e14i −0.0415406 0.103054i
\(163\) 4.90106e15i 1.60316i 0.597887 + 0.801580i \(0.296007\pi\)
−0.597887 + 0.801580i \(0.703993\pi\)
\(164\) −2.48303e15 + 2.39017e15i −0.778170 + 0.749069i
\(165\) 8.14401e14 0.244597
\(166\) 4.91645e13 1.98181e13i 0.0141545 0.00570564i
\(167\) 2.90593e15i 0.802177i −0.916039 0.401088i \(-0.868632\pi\)
0.916039 0.401088i \(-0.131368\pi\)
\(168\) 7.36967e14 + 3.30239e14i 0.195112 + 0.0874306i
\(169\) 5.85707e15 1.48756
\(170\) 2.68198e14 + 6.65344e14i 0.0653602 + 0.162145i
\(171\) 2.24595e15i 0.525324i
\(172\) −4.27479e15 4.44086e15i −0.959877 0.997168i
\(173\) 7.13782e15 1.53902 0.769508 0.638638i \(-0.220502\pi\)
0.769508 + 0.638638i \(0.220502\pi\)
\(174\) −8.36186e14 + 3.37064e14i −0.173164 + 0.0698019i
\(175\) 3.47507e15i 0.691349i
\(176\) 1.30791e15 + 4.98618e13i 0.250029 + 0.00953189i
\(177\) −3.04301e15 −0.559101
\(178\) −1.51534e15 3.75925e15i −0.267652 0.663989i
\(179\) 7.67927e14i 0.130421i 0.997872 + 0.0652107i \(0.0207719\pi\)
−0.997872 + 0.0652107i \(0.979228\pi\)
\(180\) −2.48940e15 + 2.39631e15i −0.406619 + 0.391413i
\(181\) −1.13752e16 −1.78735 −0.893676 0.448713i \(-0.851882\pi\)
−0.893676 + 0.448713i \(0.851882\pi\)
\(182\) −3.58320e15 + 1.44437e15i −0.541715 + 0.218364i
\(183\) 3.00301e15i 0.436918i
\(184\) −3.63296e15 + 8.10738e15i −0.508787 + 1.13542i
\(185\) −1.58633e16 −2.13890
\(186\) 5.78184e13 + 1.43436e14i 0.00750716 + 0.0186237i
\(187\) 2.06581e14i 0.0258344i
\(188\) 1.00811e16 + 1.04727e16i 1.21451 + 1.26170i
\(189\) −6.13945e14 −0.0712684
\(190\) 2.21226e16 8.91752e15i 2.47491 0.997629i
\(191\) 1.00557e16i 1.08437i 0.840259 + 0.542185i \(0.182403\pi\)
−0.840259 + 0.542185i \(0.817597\pi\)
\(192\) −4.14465e15 + 3.69602e15i −0.430903 + 0.384260i
\(193\) −1.56620e14 −0.0157017 −0.00785085 0.999969i \(-0.502499\pi\)
−0.00785085 + 0.999969i \(0.502499\pi\)
\(194\) −3.07918e15 7.63882e15i −0.297730 0.738608i
\(195\) 1.65300e16i 1.54181i
\(196\) −6.90777e15 + 6.64944e15i −0.621649 + 0.598401i
\(197\) 1.34099e16 1.16456 0.582281 0.812988i \(-0.302161\pi\)
0.582281 + 0.812988i \(0.302161\pi\)
\(198\) −9.22884e14 + 3.72011e14i −0.0773554 + 0.0311817i
\(199\) 1.95305e16i 1.58031i 0.612908 + 0.790154i \(0.290000\pi\)
−0.612908 + 0.790154i \(0.710000\pi\)
\(200\) 2.18069e16 + 9.77179e15i 1.70366 + 0.763421i
\(201\) −2.00698e15 −0.151415
\(202\) −2.25448e15 5.59291e15i −0.164281 0.407548i
\(203\) 1.70123e15i 0.119754i
\(204\) −6.07847e14 6.31461e14i −0.0413412 0.0429473i
\(205\) −2.78262e16 −1.82884
\(206\) −7.52792e15 + 3.03448e15i −0.478194 + 0.192759i
\(207\) 6.75401e15i 0.414734i
\(208\) 1.01205e15 2.65469e16i 0.0600841 1.57605i
\(209\) 6.86876e15 0.394325
\(210\) 2.43766e15 + 6.04734e15i 0.135344 + 0.335760i
\(211\) 1.59797e16i 0.858204i −0.903256 0.429102i \(-0.858830\pi\)
0.903256 0.429102i \(-0.141170\pi\)
\(212\) 1.69088e15 1.62765e15i 0.0878540 0.0845686i
\(213\) 2.05697e16 1.03412
\(214\) 6.08124e15 2.45133e15i 0.295867 0.119263i
\(215\) 4.97668e16i 2.34353i
\(216\) 1.72639e15 3.85265e15i 0.0786980 0.175624i
\(217\) 2.91822e14 0.0128795
\(218\) 1.33494e15 + 3.31170e15i 0.0570512 + 0.141532i
\(219\) 1.12717e16i 0.466529i
\(220\) 7.32860e15 + 7.61331e15i 0.293807 + 0.305221i
\(221\) 4.19300e15 0.162847
\(222\) 1.79764e16 7.24621e15i 0.676443 0.272672i
\(223\) 3.22714e16i 1.17675i 0.808589 + 0.588374i \(0.200232\pi\)
−0.808589 + 0.588374i \(0.799768\pi\)
\(224\) 3.54459e15 + 9.86117e15i 0.125265 + 0.348492i
\(225\) −1.81667e16 −0.622296
\(226\) −9.13409e15 2.26598e16i −0.303324 0.752484i
\(227\) 1.07194e16i 0.345137i −0.984998 0.172568i \(-0.944793\pi\)
0.984998 0.172568i \(-0.0552066\pi\)
\(228\) −2.09959e16 + 2.02108e16i −0.655528 + 0.631014i
\(229\) 2.34325e16 0.709529 0.354764 0.934956i \(-0.384561\pi\)
0.354764 + 0.934956i \(0.384561\pi\)
\(230\) −6.65268e16 + 2.68167e16i −1.95390 + 0.787610i
\(231\) 1.87762e15i 0.0534963i
\(232\) −1.06756e16 4.78381e15i −0.295106 0.132239i
\(233\) 2.07306e16 0.556060 0.278030 0.960572i \(-0.410319\pi\)
0.278030 + 0.960572i \(0.410319\pi\)
\(234\) 7.55077e15 + 1.87319e16i 0.196553 + 0.487608i
\(235\) 1.17363e17i 2.96522i
\(236\) −2.73833e16 2.84471e16i −0.671586 0.697677i
\(237\) 2.42410e16 0.577181
\(238\) −1.53397e15 + 6.18337e14i −0.0354631 + 0.0142951i
\(239\) 2.50399e16i 0.562144i 0.959687 + 0.281072i \(0.0906900\pi\)
−0.959687 + 0.281072i \(0.909310\pi\)
\(240\) −4.48031e16 1.70803e15i −0.976854 0.0372407i
\(241\) 6.25474e16 1.32462 0.662308 0.749231i \(-0.269577\pi\)
0.662308 + 0.749231i \(0.269577\pi\)
\(242\) −1.70351e16 4.22606e16i −0.350459 0.869418i
\(243\) 3.20953e15i 0.0641500i
\(244\) 2.80733e16 2.70234e16i 0.545210 0.524821i
\(245\) −7.74122e16 −1.46099
\(246\) 3.15328e16 1.27107e16i 0.578384 0.233145i
\(247\) 1.39416e17i 2.48562i
\(248\) −8.20594e14 + 1.83125e15i −0.0142222 + 0.0317385i
\(249\) −5.22907e14 −0.00881107
\(250\) 3.34938e16 + 8.30912e16i 0.548762 + 1.36137i
\(251\) 8.02535e16i 1.27864i 0.768941 + 0.639320i \(0.220784\pi\)
−0.768941 + 0.639320i \(0.779216\pi\)
\(252\) −5.52474e15 5.73938e15i −0.0856068 0.0889326i
\(253\) −2.06557e16 −0.311312
\(254\) −5.34861e16 + 2.15600e16i −0.784160 + 0.316092i
\(255\) 7.07650e15i 0.100934i
\(256\) −7.18484e16 5.48615e15i −0.997097 0.0761356i
\(257\) −2.11552e16 −0.285683 −0.142842 0.989746i \(-0.545624\pi\)
−0.142842 + 0.989746i \(0.545624\pi\)
\(258\) 2.27330e16 + 5.63960e16i 0.298758 + 0.741157i
\(259\) 3.65732e16i 0.467805i
\(260\) 1.54529e17 1.48750e17i 1.92396 1.85201i
\(261\) 8.89355e15 0.107793
\(262\) 2.31408e16 9.32796e15i 0.273067 0.110072i
\(263\) 1.33110e17i 1.52940i −0.644388 0.764699i \(-0.722888\pi\)
0.644388 0.764699i \(-0.277112\pi\)
\(264\) −1.17825e16 5.27981e15i −0.131829 0.0590732i
\(265\) 1.89489e16 0.206473
\(266\) 2.05596e16 + 5.10040e16i 0.218194 + 0.541294i
\(267\) 3.99828e16i 0.413328i
\(268\) −1.80603e16 1.87619e16i −0.181878 0.188944i
\(269\) 9.41135e16 0.923391 0.461696 0.887038i \(-0.347241\pi\)
0.461696 + 0.887038i \(0.347241\pi\)
\(270\) 3.16137e16 1.27434e16i 0.302224 0.121826i
\(271\) 3.83327e16i 0.357096i −0.983931 0.178548i \(-0.942860\pi\)
0.983931 0.178548i \(-0.0571399\pi\)
\(272\) 4.33260e14 1.13647e16i 0.00393338 0.103176i
\(273\) 3.81104e16 0.337213
\(274\) 5.48899e16 + 1.36171e17i 0.473412 + 1.17444i
\(275\) 5.55589e16i 0.467116i
\(276\) 6.31389e16 6.07777e16i 0.517528 0.498174i
\(277\) −8.30340e16 −0.663586 −0.331793 0.943352i \(-0.607654\pi\)
−0.331793 + 0.943352i \(0.607654\pi\)
\(278\) −2.73977e16 + 1.10439e16i −0.213501 + 0.0860616i
\(279\) 1.52556e15i 0.0115931i
\(280\) −3.45968e16 + 7.72067e16i −0.256407 + 0.572201i
\(281\) −8.26427e16 −0.597393 −0.298697 0.954348i \(-0.596552\pi\)
−0.298697 + 0.954348i \(0.596552\pi\)
\(282\) −5.36104e16 1.32996e17i −0.378012 0.937770i
\(283\) 4.46688e16i 0.307255i 0.988129 + 0.153628i \(0.0490956\pi\)
−0.988129 + 0.153628i \(0.950904\pi\)
\(284\) 1.85102e17 + 1.92293e17i 1.24217 + 1.29043i
\(285\) −2.35292e17 −1.54061
\(286\) 5.72876e16 2.30924e16i 0.366015 0.147539i
\(287\) 6.41539e16i 0.399990i
\(288\) 5.15513e16 1.85301e16i 0.313684 0.112754i
\(289\) −1.66583e17 −0.989339
\(290\) −3.53117e16 8.76012e16i −0.204707 0.507837i
\(291\) 8.12454e16i 0.459777i
\(292\) −1.05371e17 + 1.01431e17i −0.582161 + 0.560390i
\(293\) −1.25777e17 −0.678463 −0.339232 0.940703i \(-0.610167\pi\)
−0.339232 + 0.940703i \(0.610167\pi\)
\(294\) 8.77239e16 3.53612e16i 0.462048 0.186250i
\(295\) 3.18794e17i 1.63967i
\(296\) 2.29505e17 + 1.02843e17i 1.15279 + 0.516572i
\(297\) 9.81565e15 0.0481531
\(298\) −1.48388e16 3.68121e16i −0.0711026 0.176391i
\(299\) 4.19252e17i 1.96235i
\(300\) −1.63477e17 1.69828e17i −0.747496 0.776536i
\(301\) 1.14738e17 0.512558
\(302\) −1.97905e17 + 7.97749e16i −0.863791 + 0.348191i
\(303\) 5.94854e16i 0.253695i
\(304\) −3.77875e17 1.44058e16i −1.57483 0.0600374i
\(305\) 3.14604e17 1.28134
\(306\) 3.23248e15 + 8.01913e15i 0.0128673 + 0.0319211i
\(307\) 2.18013e17i 0.848229i −0.905609 0.424114i \(-0.860585\pi\)
0.905609 0.424114i \(-0.139415\pi\)
\(308\) −1.75527e16 + 1.68963e16i −0.0667557 + 0.0642592i
\(309\) 8.00658e16 0.297672
\(310\) −1.50267e16 + 6.05722e15i −0.0546176 + 0.0220162i
\(311\) 2.54095e17i 0.902971i 0.892278 + 0.451486i \(0.149106\pi\)
−0.892278 + 0.451486i \(0.850894\pi\)
\(312\) −1.07165e17 + 2.39151e17i −0.372367 + 0.830980i
\(313\) 7.43667e16 0.252678 0.126339 0.991987i \(-0.459677\pi\)
0.126339 + 0.991987i \(0.459677\pi\)
\(314\) −4.46415e16 1.10746e17i −0.148331 0.367978i
\(315\) 6.43186e16i 0.209008i
\(316\) 2.18139e17 + 2.26613e17i 0.693304 + 0.720238i
\(317\) 1.10543e17 0.343651 0.171826 0.985127i \(-0.445033\pi\)
0.171826 + 0.985127i \(0.445033\pi\)
\(318\) −2.14730e16 + 8.65570e15i −0.0652985 + 0.0263216i
\(319\) 2.71990e16i 0.0809130i
\(320\) −3.87205e17 4.34206e17i −1.12692 1.26371i
\(321\) −6.46792e16 −0.184174
\(322\) −6.18266e16 1.53379e17i −0.172260 0.427342i
\(323\) 5.96841e16i 0.162720i
\(324\) −3.00038e16 + 2.88818e16i −0.0800500 + 0.0770564i
\(325\) 1.12769e18 2.94446
\(326\) 5.81844e17 2.34539e17i 1.48690 0.599366i
\(327\) 3.52228e16i 0.0881027i
\(328\) 4.02581e17 + 1.80399e17i 0.985680 + 0.441689i
\(329\) −2.70583e17 −0.648529
\(330\) −3.89730e16 9.66839e16i −0.0914462 0.226859i
\(331\) 1.45361e17i 0.333927i 0.985963 + 0.166964i \(0.0533962\pi\)
−0.985963 + 0.166964i \(0.946604\pi\)
\(332\) −4.70551e15 4.88832e15i −0.0105838 0.0109949i
\(333\) −1.91194e17 −0.421080
\(334\) −3.44986e17 + 1.39063e17i −0.744005 + 0.299906i
\(335\) 2.10256e17i 0.444054i
\(336\) 3.93791e15 1.03295e17i 0.00814500 0.213650i
\(337\) −4.26108e17 −0.863198 −0.431599 0.902066i \(-0.642050\pi\)
−0.431599 + 0.902066i \(0.642050\pi\)
\(338\) −2.80289e17 6.95338e17i −0.556145 1.37968i
\(339\) 2.41006e17i 0.468415i
\(340\) 6.61537e16 6.36798e16i 0.125951 0.121241i
\(341\) −4.66560e15 −0.00870216
\(342\) 2.66634e17 1.07479e17i 0.487229 0.196400i
\(343\) 3.85317e17i 0.689857i
\(344\) −3.22641e17 + 7.20010e17i −0.565992 + 1.26308i
\(345\) 7.07570e17 1.21629
\(346\) −3.41579e17 8.47387e17i −0.575384 1.42741i
\(347\) 1.97652e17i 0.326284i −0.986603 0.163142i \(-0.947837\pi\)
0.986603 0.163142i \(-0.0521628\pi\)
\(348\) 8.00309e16 + 8.31401e16i 0.129480 + 0.134510i
\(349\) −5.44653e17 −0.863658 −0.431829 0.901955i \(-0.642132\pi\)
−0.431829 + 0.901955i \(0.642132\pi\)
\(350\) −4.12553e17 + 1.66299e17i −0.641214 + 0.258471i
\(351\) 1.99230e17i 0.303532i
\(352\) −5.66704e16 1.57659e17i −0.0846365 0.235461i
\(353\) 4.38699e17 0.642308 0.321154 0.947027i \(-0.395929\pi\)
0.321154 + 0.947027i \(0.395929\pi\)
\(354\) 1.45622e17 + 3.61259e17i 0.209028 + 0.518556i
\(355\) 2.15494e18i 3.03275i
\(356\) −3.73774e17 + 3.59796e17i −0.515773 + 0.496485i
\(357\) 1.63150e16 0.0220755
\(358\) 9.11666e16 3.67489e16i 0.120964 0.0487600i
\(359\) 1.24662e18i 1.62208i −0.584992 0.811039i \(-0.698902\pi\)
0.584992 0.811039i \(-0.301098\pi\)
\(360\) 4.03614e17 + 1.80862e17i 0.515050 + 0.230797i
\(361\) −1.18548e18 −1.48369
\(362\) 5.44358e17 + 1.35044e18i 0.668228 + 1.65774i
\(363\) 4.49478e17i 0.541205i
\(364\) 3.42946e17 + 3.56269e17i 0.405057 + 0.420793i
\(365\) −1.18085e18 −1.36819
\(366\) −3.56511e17 + 1.43708e17i −0.405234 + 0.163348i
\(367\) 2.63416e17i 0.293751i −0.989155 0.146875i \(-0.953078\pi\)
0.989155 0.146875i \(-0.0469216\pi\)
\(368\) 1.13634e18 + 4.33210e16i 1.24330 + 0.0473984i
\(369\) −3.35378e17 −0.360039
\(370\) 7.59134e17 + 1.88326e18i 0.799662 + 1.98380i
\(371\) 4.36872e16i 0.0451582i
\(372\) 1.42615e16 1.37282e16i 0.0144665 0.0139255i
\(373\) −1.50232e17 −0.149555 −0.0747776 0.997200i \(-0.523825\pi\)
−0.0747776 + 0.997200i \(0.523825\pi\)
\(374\) 2.45248e16 9.88587e15i 0.0239610 0.00965859i
\(375\) 8.83746e17i 0.847439i
\(376\) 7.60871e17 1.69797e18i 0.716137 1.59814i
\(377\) −5.52063e17 −0.510034
\(378\) 2.93802e16 + 7.28862e16i 0.0266448 + 0.0661002i
\(379\) 1.59400e17i 0.141910i 0.997480 + 0.0709549i \(0.0226046\pi\)
−0.997480 + 0.0709549i \(0.977395\pi\)
\(380\) −2.11734e18 2.19960e18i −1.85057 1.92246i
\(381\) 5.68870e17 0.488133
\(382\) 1.19379e18 4.81212e17i 1.00574 0.405408i
\(383\) 1.69592e18i 1.40286i −0.712738 0.701431i \(-0.752545\pi\)
0.712738 0.701431i \(-0.247455\pi\)
\(384\) 6.37124e17 + 3.15172e17i 0.517494 + 0.255994i
\(385\) −1.96705e17 −0.156888
\(386\) 7.49502e15 + 1.85936e16i 0.00587032 + 0.0145631i
\(387\) 5.99819e17i 0.461364i
\(388\) −7.59511e17 + 7.31108e17i −0.573736 + 0.552280i
\(389\) −1.15846e17 −0.0859474 −0.0429737 0.999076i \(-0.513683\pi\)
−0.0429737 + 0.999076i \(0.513683\pi\)
\(390\) −1.96241e18 + 7.91040e17i −1.43000 + 0.576430i
\(391\) 1.79482e17i 0.128465i
\(392\) 1.11998e18 + 5.01868e17i 0.787420 + 0.352847i
\(393\) −2.46122e17 −0.169982
\(394\) −6.41728e17 1.59200e18i −0.435389 1.08011i
\(395\) 2.53955e18i 1.69269i
\(396\) 8.83287e16 + 9.17602e16i 0.0578410 + 0.0600881i
\(397\) 1.68846e18 1.08632 0.543159 0.839630i \(-0.317228\pi\)
0.543159 + 0.839630i \(0.317228\pi\)
\(398\) 2.31862e18 9.34627e17i 1.46571 0.590822i
\(399\) 5.42471e17i 0.336951i
\(400\) 1.16523e17 3.05649e18i 0.0711200 1.86553i
\(401\) 2.33261e18 1.39904 0.699521 0.714612i \(-0.253397\pi\)
0.699521 + 0.714612i \(0.253397\pi\)
\(402\) 9.60433e16 + 2.38264e17i 0.0566089 + 0.140435i
\(403\) 9.46985e16i 0.0548539i
\(404\) −5.56091e17 + 5.35295e17i −0.316575 + 0.304736i
\(405\) −3.36239e17 −0.188132
\(406\) 2.01967e17 8.14120e16i 0.111070 0.0447720i
\(407\) 5.84726e17i 0.316076i
\(408\) −4.58774e16 + 1.02381e17i −0.0243768 + 0.0543998i
\(409\) 4.78215e17 0.249782 0.124891 0.992170i \(-0.460142\pi\)
0.124891 + 0.992170i \(0.460142\pi\)
\(410\) 1.33161e18 + 3.30346e18i 0.683741 + 1.69622i
\(411\) 1.44829e18i 0.731077i
\(412\) 7.20494e17 + 7.48484e17i 0.357561 + 0.371452i
\(413\) 7.34987e17 0.358616
\(414\) −8.01822e17 + 3.23211e17i −0.384659 + 0.155055i
\(415\) 5.47812e16i 0.0258401i
\(416\) −3.20003e18 + 1.15025e18i −1.48423 + 0.533505i
\(417\) 2.91398e17 0.132903
\(418\) −3.28703e17 8.15444e17i −0.147424 0.365730i
\(419\) 8.14966e17i 0.359452i 0.983717 + 0.179726i \(0.0575212\pi\)
−0.983717 + 0.179726i \(0.942479\pi\)
\(420\) 6.01274e17 5.78788e17i 0.260812 0.251058i
\(421\) −3.50746e18 −1.49630 −0.748149 0.663531i \(-0.769057\pi\)
−0.748149 + 0.663531i \(0.769057\pi\)
\(422\) −1.89707e18 + 7.64703e17i −0.795970 + 0.320853i
\(423\) 1.41453e18i 0.583754i
\(424\) −2.74147e17 1.22847e17i −0.111281 0.0498659i
\(425\) 4.82763e17 0.192757
\(426\) −9.84358e17 2.44199e18i −0.386621 0.959128i
\(427\) 7.25327e17i 0.280246i
\(428\) −5.82033e17 6.04644e17i −0.221228 0.229823i
\(429\) −6.09302e17 −0.227841
\(430\) −5.90820e18 + 2.38158e18i −2.17358 + 0.876164i
\(431\) 2.91458e16i 0.0105496i −0.999986 0.00527478i \(-0.998321\pi\)
0.999986 0.00527478i \(-0.00167902\pi\)
\(432\) −5.39994e17 2.05863e16i −0.192310 0.00733147i
\(433\) 4.42405e18 1.55026 0.775131 0.631800i \(-0.217684\pi\)
0.775131 + 0.631800i \(0.217684\pi\)
\(434\) −1.39651e16 3.46445e16i −0.00481521 0.0119455i
\(435\) 9.31713e17i 0.316124i
\(436\) 3.29275e17 3.16961e17i 0.109939 0.105828i
\(437\) 5.96773e18 1.96083
\(438\) 1.33815e18 5.39402e17i 0.432698 0.174419i
\(439\) 2.81162e18i 0.894756i 0.894345 + 0.447378i \(0.147642\pi\)
−0.894345 + 0.447378i \(0.852358\pi\)
\(440\) 5.53128e17 1.23437e18i 0.173243 0.386613i
\(441\) −9.33019e17 −0.287621
\(442\) −2.00655e17 4.97784e17i −0.0608827 0.151038i
\(443\) 4.60447e18i 1.37516i −0.726108 0.687580i \(-0.758673\pi\)
0.726108 0.687580i \(-0.241327\pi\)
\(444\) −1.72051e18 1.78735e18i −0.505797 0.525447i
\(445\) −4.18871e18 −1.21216
\(446\) 3.83119e18 1.54434e18i 1.09141 0.439945i
\(447\) 3.91528e17i 0.109802i
\(448\) 1.00107e18 8.92710e17i 0.276388 0.246470i
\(449\) −5.52679e18 −1.50227 −0.751135 0.660148i \(-0.770493\pi\)
−0.751135 + 0.660148i \(0.770493\pi\)
\(450\) 8.69360e17 + 2.15671e18i 0.232655 + 0.577169i
\(451\) 1.02568e18i 0.270257i
\(452\) −2.25302e18 + 2.16876e18i −0.584514 + 0.562655i
\(453\) 2.10489e18 0.537703
\(454\) −1.27259e18 + 5.12976e17i −0.320109 + 0.129035i
\(455\) 3.99255e18i 0.988941i
\(456\) 3.40413e18 + 1.52541e18i 0.830334 + 0.372077i
\(457\) −1.05705e18 −0.253912 −0.126956 0.991908i \(-0.540521\pi\)
−0.126956 + 0.991908i \(0.540521\pi\)
\(458\) −1.12136e18 2.78185e18i −0.265268 0.658076i
\(459\) 8.52903e16i 0.0198706i
\(460\) 6.36725e18 + 6.61461e18i 1.46099 + 1.51775i
\(461\) −2.91154e18 −0.657986 −0.328993 0.944332i \(-0.606709\pi\)
−0.328993 + 0.944332i \(0.606709\pi\)
\(462\) 2.22907e17 8.98530e16i 0.0496169 0.0200004i
\(463\) 7.77165e18i 1.70391i −0.523616 0.851954i \(-0.675417\pi\)
0.523616 0.851954i \(-0.324583\pi\)
\(464\) −5.70442e16 + 1.49632e18i −0.0123193 + 0.323145i
\(465\) 1.59822e17 0.0339990
\(466\) −9.92060e17 2.46110e18i −0.207891 0.515736i
\(467\) 1.86591e18i 0.385187i 0.981279 + 0.192594i \(0.0616899\pi\)
−0.981279 + 0.192594i \(0.938310\pi\)
\(468\) 1.86247e18 1.79282e18i 0.378764 0.364600i
\(469\) 4.84751e17 0.0971201
\(470\) 1.39331e19 5.61638e18i 2.75019 1.10859i
\(471\) 1.17788e18i 0.229063i
\(472\) −2.06676e18 + 4.61222e18i −0.396001 + 0.883722i
\(473\) −1.83442e18 −0.346314
\(474\) −1.16005e18 2.87784e18i −0.215788 0.535325i
\(475\) 1.60517e19i 2.94217i
\(476\) 1.46815e17 + 1.52519e17i 0.0265169 + 0.0275470i
\(477\) 2.28384e17 0.0406478
\(478\) 2.97269e18 1.19828e18i 0.521379 0.210166i
\(479\) 3.73123e18i 0.644916i 0.946584 + 0.322458i \(0.104509\pi\)
−0.946584 + 0.322458i \(0.895491\pi\)
\(480\) 1.94127e18 + 5.40067e18i 0.330671 + 0.919938i
\(481\) 1.18683e19 1.99238
\(482\) −2.99319e18 7.42550e18i −0.495228 1.22856i
\(483\) 1.63132e18i 0.266017i
\(484\) −4.20188e18 + 4.04474e18i −0.675346 + 0.650090i
\(485\) −8.51150e18 −1.34838
\(486\) 3.81028e17 1.53591e17i 0.0594981 0.0239835i
\(487\) 7.72609e18i 1.18921i 0.804019 + 0.594603i \(0.202691\pi\)
−0.804019 + 0.594603i \(0.797309\pi\)
\(488\) −4.55160e18 2.03960e18i −0.690598 0.309461i
\(489\) −6.18840e18 −0.925585
\(490\) 3.70454e18 + 9.19021e18i 0.546213 + 1.35504i
\(491\) 6.80565e18i 0.989234i −0.869111 0.494617i \(-0.835308\pi\)
0.869111 0.494617i \(-0.164692\pi\)
\(492\) −3.01798e18 3.13523e18i −0.432475 0.449277i
\(493\) −2.36338e17 −0.0333891
\(494\) −1.65512e19 + 6.67173e18i −2.30537 + 0.929287i
\(495\) 1.02832e18i 0.141218i
\(496\) 2.56672e17 + 9.78512e15i 0.0347541 + 0.00132493i
\(497\) −4.96826e18 −0.663300
\(498\) 2.50236e16 + 6.20784e16i 0.00329415 + 0.00817212i
\(499\) 9.27270e17i 0.120366i 0.998187 + 0.0601828i \(0.0191684\pi\)
−0.998187 + 0.0601828i \(0.980832\pi\)
\(500\) 8.26157e18 7.95262e18i 1.05748 1.01793i
\(501\) 3.66922e18 0.463137
\(502\) 9.52752e18 3.84051e18i 1.18592 0.478039i
\(503\) 4.08155e18i 0.501013i −0.968115 0.250507i \(-0.919403\pi\)
0.968115 0.250507i \(-0.0805972\pi\)
\(504\) −4.16981e17 + 9.30542e17i −0.0504781 + 0.112648i
\(505\) −6.23186e18 −0.744009
\(506\) 9.88474e17 + 2.45220e18i 0.116389 + 0.288737i
\(507\) 7.39552e18i 0.858841i
\(508\) 5.11912e18 + 5.31800e18i 0.586340 + 0.609119i
\(509\) −4.70789e18 −0.531865 −0.265932 0.963992i \(-0.585680\pi\)
−0.265932 + 0.963992i \(0.585680\pi\)
\(510\) −8.40107e17 + 3.38644e17i −0.0936146 + 0.0377357i
\(511\) 2.72248e18i 0.299239i
\(512\) 2.78699e18 + 8.79223e18i 0.302166 + 0.953255i
\(513\) −2.83588e18 −0.303296
\(514\) 1.01238e18 + 2.51150e18i 0.106807 + 0.264966i
\(515\) 8.38793e18i 0.872979i
\(516\) 5.60732e18 5.39763e18i 0.575715 0.554185i
\(517\) 4.32604e18 0.438184
\(518\) −4.34189e18 + 1.75020e18i −0.433881 + 0.174896i
\(519\) 9.01268e18i 0.888551i
\(520\) −2.50542e19 1.12269e19i −2.43701 1.09204i
\(521\) 1.67781e19 1.61019 0.805097 0.593143i \(-0.202113\pi\)
0.805097 + 0.593143i \(0.202113\pi\)
\(522\) −4.25598e17 1.05582e18i −0.0403001 0.0999764i
\(523\) 1.42496e19i 1.33134i 0.746244 + 0.665672i \(0.231855\pi\)
−0.746244 + 0.665672i \(0.768145\pi\)
\(524\) −2.21479e18 2.30083e18i −0.204180 0.212113i
\(525\) 4.38785e18 0.399150
\(526\) −1.58025e19 + 6.36994e18i −1.41849 + 0.571788i
\(527\) 4.05404e16i 0.00359099i
\(528\) −6.29587e16 + 1.65146e18i −0.00550324 + 0.144354i
\(529\) −6.35330e18 −0.548037
\(530\) −9.06796e17 2.24958e18i −0.0771931 0.191500i
\(531\) 3.84230e18i 0.322797i
\(532\) 5.07122e18 4.88157e18i 0.420466 0.404742i
\(533\) 2.08184e19 1.70356
\(534\) 4.74667e18 1.91337e18i 0.383354 0.154529i
\(535\) 6.77597e18i 0.540126i
\(536\) −1.36310e18 + 3.04193e18i −0.107245 + 0.239329i
\(537\) −9.69635e17 −0.0752988
\(538\) −4.50378e18 1.11729e19i −0.345224 0.856430i
\(539\) 2.85344e18i 0.215897i
\(540\) −3.02573e18 3.14328e18i −0.225982 0.234762i
\(541\) 1.95653e19 1.44246 0.721232 0.692693i \(-0.243576\pi\)
0.721232 + 0.692693i \(0.243576\pi\)
\(542\) −4.55078e18 + 1.83440e18i −0.331200 + 0.133506i
\(543\) 1.43631e19i 1.03193i
\(544\) −1.36993e18 + 4.92421e17i −0.0971642 + 0.0349256i
\(545\) 3.69004e18 0.258378
\(546\) −1.82376e18 4.52438e18i −0.126072 0.312759i
\(547\) 2.64078e19i 1.80227i −0.433536 0.901136i \(-0.642734\pi\)
0.433536 0.901136i \(-0.357266\pi\)
\(548\) 1.35392e19 1.30328e19i 0.912279 0.878162i
\(549\) 3.79180e18 0.252255
\(550\) 6.59583e18 2.65875e18i 0.433242 0.174638i
\(551\) 7.85819e18i 0.509637i
\(552\) −1.02369e19 4.58721e18i −0.655534 0.293748i
\(553\) −5.85500e18 −0.370212
\(554\) 3.97357e18 + 9.85761e18i 0.248092 + 0.615465i
\(555\) 2.00300e19i 1.23490i
\(556\) 2.62222e18 + 2.72409e18i 0.159641 + 0.165843i
\(557\) −5.68683e18 −0.341888 −0.170944 0.985281i \(-0.554682\pi\)
−0.170944 + 0.985281i \(0.554682\pi\)
\(558\) −1.81111e17 + 7.30053e16i −0.0107524 + 0.00433426i
\(559\) 3.72335e19i 2.18299i
\(560\) 1.08214e19 + 4.12547e17i 0.626569 + 0.0238868i
\(561\) −2.60842e17 −0.0149155
\(562\) 3.95484e18 + 9.81116e18i 0.223344 + 0.554072i
\(563\) 2.24264e19i 1.25084i −0.780289 0.625419i \(-0.784928\pi\)
0.780289 0.625419i \(-0.215072\pi\)
\(564\) −1.32235e19 + 1.27290e19i −0.728440 + 0.701199i
\(565\) −2.52485e19 −1.37372
\(566\) 5.30299e18 2.13761e18i 0.284974 0.114872i
\(567\) 7.75207e17i 0.0411468i
\(568\) 1.39706e19 3.11770e19i 0.732448 1.63454i
\(569\) −1.89410e18 −0.0980881 −0.0490441 0.998797i \(-0.515617\pi\)
−0.0490441 + 0.998797i \(0.515617\pi\)
\(570\) 1.12598e19 + 2.79334e19i 0.575981 + 1.42889i
\(571\) 6.41743e17i 0.0324271i 0.999869 + 0.0162136i \(0.00516116\pi\)
−0.999869 + 0.0162136i \(0.994839\pi\)
\(572\) −5.48297e18 5.69598e18i −0.273680 0.284313i
\(573\) −1.26970e19 −0.626062
\(574\) −7.61621e18 + 3.07007e18i −0.370984 + 0.149543i
\(575\) 4.82708e19i 2.32279i
\(576\) −4.66683e18 5.23331e18i −0.221853 0.248782i
\(577\) −1.69503e18 −0.0796060 −0.0398030 0.999208i \(-0.512673\pi\)
−0.0398030 + 0.999208i \(0.512673\pi\)
\(578\) 7.97178e18 + 1.97763e19i 0.369880 + 0.917595i
\(579\) 1.97759e17i 0.00906538i
\(580\) −8.70999e18 + 8.38427e18i −0.394477 + 0.379725i
\(581\) 1.26299e17 0.00565156
\(582\) 9.64527e18 3.88798e18i 0.426436 0.171895i
\(583\) 6.98464e17i 0.0305115i
\(584\) 1.70842e19 + 7.65552e18i 0.737402 + 0.330434i
\(585\) 2.08719e19 0.890165
\(586\) 6.01900e18 + 1.49319e19i 0.253654 + 0.629263i
\(587\) 2.21997e19i 0.924444i −0.886764 0.462222i \(-0.847052\pi\)
0.886764 0.462222i \(-0.152948\pi\)
\(588\) −8.39601e18 8.72219e18i −0.345487 0.358909i
\(589\) 1.34796e18 0.0548113
\(590\) −3.78465e19 + 1.52558e19i −1.52077 + 0.613015i
\(591\) 1.69322e19i 0.672360i
\(592\) 1.22634e18 3.21679e19i 0.0481237 1.26232i
\(593\) −7.48231e18 −0.290170 −0.145085 0.989419i \(-0.546346\pi\)
−0.145085 + 0.989419i \(0.546346\pi\)
\(594\) −4.69725e17 1.16529e18i −0.0180028 0.0446612i
\(595\) 1.70921e18i 0.0647406i
\(596\) −3.66014e18 + 3.52327e18i −0.137017 + 0.131893i
\(597\) −2.46605e19 −0.912392
\(598\) 4.97727e19 2.00632e19i 1.82005 0.733655i
\(599\) 1.41980e19i 0.513144i −0.966525 0.256572i \(-0.917407\pi\)
0.966525 0.256572i \(-0.0825931\pi\)
\(600\) −1.23385e19 + 2.75348e19i −0.440761 + 0.983610i
\(601\) −5.45515e19 −1.92613 −0.963064 0.269271i \(-0.913217\pi\)
−0.963064 + 0.269271i \(0.913217\pi\)
\(602\) −5.49078e18 1.36215e19i −0.191628 0.475389i
\(603\) 2.53414e18i 0.0874196i
\(604\) 1.89414e19 + 1.96773e19i 0.645883 + 0.670975i
\(605\) −4.70886e19 −1.58719
\(606\) 7.06198e18 2.84666e18i 0.235298 0.0948477i
\(607\) 4.27195e19i 1.40704i 0.710678 + 0.703518i \(0.248388\pi\)
−0.710678 + 0.703518i \(0.751612\pi\)
\(608\) 1.63729e19 + 4.55499e19i 0.533090 + 1.48307i
\(609\) −2.14809e18 −0.0691402
\(610\) −1.50553e19 3.73491e19i −0.479050 1.18843i
\(611\) 8.78063e19i 2.76209i
\(612\) 7.97324e17 7.67507e17i 0.0247956 0.0238683i
\(613\) 2.26370e19 0.695979 0.347989 0.937498i \(-0.386864\pi\)
0.347989 + 0.937498i \(0.386864\pi\)
\(614\) −2.58820e19 + 1.04329e19i −0.786718 + 0.317123i
\(615\) 3.51351e19i 1.05588i
\(616\) 2.84587e18 + 1.27525e18i 0.0845570 + 0.0378905i
\(617\) 2.57332e19 0.755959 0.377980 0.925814i \(-0.376619\pi\)
0.377980 + 0.925814i \(0.376619\pi\)
\(618\) −3.83153e18 9.50524e18i −0.111289 0.276086i
\(619\) 5.78179e18i 0.166046i 0.996548 + 0.0830229i \(0.0264575\pi\)
−0.996548 + 0.0830229i \(0.973543\pi\)
\(620\) 1.43820e18 + 1.49407e18i 0.0408392 + 0.0424258i
\(621\) 8.52805e18 0.239447
\(622\) 3.01656e19 1.21597e19i 0.837490 0.337589i
\(623\) 9.65717e18i 0.265115i
\(624\) 3.35199e19 + 1.27788e18i 0.909935 + 0.0346896i
\(625\) 2.30367e19 0.618386
\(626\) −3.55880e18 8.82865e18i −0.0944677 0.234355i
\(627\) 8.67294e18i 0.227664i
\(628\) −1.10113e19 + 1.05995e19i −0.285838 + 0.275148i
\(629\) 5.08081e18 0.130430
\(630\) −7.63577e18 + 3.07795e18i −0.193851 + 0.0781408i
\(631\) 1.55480e19i 0.390363i 0.980767 + 0.195181i \(0.0625296\pi\)
−0.980767 + 0.195181i \(0.937470\pi\)
\(632\) 1.64641e19 3.67415e19i 0.408807 0.912299i
\(633\) 2.01770e19 0.495484
\(634\) −5.29002e18 1.31235e19i −0.128479 0.318731i
\(635\) 5.95964e19i 1.43154i
\(636\) 2.05517e18 + 2.13501e18i 0.0488257 + 0.0507225i
\(637\) 5.79167e19 1.36091
\(638\) −3.22901e18 + 1.30160e18i −0.0750455 + 0.0302506i
\(639\) 2.59726e19i 0.597049i
\(640\) −3.30184e19 + 6.67470e19i −0.750751 + 1.51765i
\(641\) 5.09427e19 1.14571 0.572857 0.819655i \(-0.305835\pi\)
0.572857 + 0.819655i \(0.305835\pi\)
\(642\) 3.09521e18 + 7.67857e18i 0.0688564 + 0.170819i
\(643\) 9.83096e18i 0.216331i 0.994133 + 0.108166i \(0.0344977\pi\)
−0.994133 + 0.108166i \(0.965502\pi\)
\(644\) −1.52501e19 + 1.46798e19i −0.331950 + 0.319536i
\(645\) 6.28388e19 1.35304
\(646\) −7.08557e18 + 2.85617e18i −0.150920 + 0.0608354i
\(647\) 3.59831e19i 0.758174i −0.925361 0.379087i \(-0.876238\pi\)
0.925361 0.379087i \(-0.123762\pi\)
\(648\) 4.86460e18 + 2.17986e18i 0.101396 + 0.0454363i
\(649\) −1.17509e19 −0.242302
\(650\) −5.39652e19 1.33877e20i −1.10083 2.73093i
\(651\) 3.68473e17i 0.00743600i
\(652\) −5.56880e19 5.78514e19i −1.11180 1.15500i
\(653\) −5.18011e19 −1.02317 −0.511584 0.859233i \(-0.670941\pi\)
−0.511584 + 0.859233i \(0.670941\pi\)
\(654\) −4.18157e18 + 1.68558e18i −0.0817138 + 0.0329385i
\(655\) 2.57844e19i 0.498504i
\(656\) 2.15115e18 5.64264e19i 0.0411476 1.07933i
\(657\) −1.42323e19 −0.269351
\(658\) 1.29487e19 + 3.21230e19i 0.242462 + 0.601500i
\(659\) 6.80634e19i 1.26100i 0.776188 + 0.630501i \(0.217151\pi\)
−0.776188 + 0.630501i \(0.782849\pi\)
\(660\) −9.61307e18 + 9.25357e18i −0.176220 + 0.169630i
\(661\) −4.72630e19 −0.857257 −0.428628 0.903481i \(-0.641003\pi\)
−0.428628 + 0.903481i \(0.641003\pi\)
\(662\) 1.72569e19 6.95621e18i 0.309712 0.124844i
\(663\) 5.29436e18i 0.0940196i
\(664\) −3.55150e17 + 7.92558e17i −0.00624072 + 0.0139269i
\(665\) 5.68309e19 0.988172
\(666\) 9.14954e18 + 2.26981e19i 0.157427 + 0.390544i
\(667\) 2.36311e19i 0.402349i
\(668\) 3.30184e19 + 3.43012e19i 0.556315 + 0.577928i
\(669\) −4.07479e19 −0.679396
\(670\) −2.49612e19 + 1.00618e19i −0.411853 + 0.166016i
\(671\) 1.15964e19i 0.189350i
\(672\) −1.24514e19 + 4.47564e18i −0.201202 + 0.0723219i
\(673\) −3.15023e19 −0.503775 −0.251888 0.967756i \(-0.581051\pi\)
−0.251888 + 0.967756i \(0.581051\pi\)
\(674\) 2.03913e19 + 5.05866e19i 0.322720 + 0.800602i
\(675\) 2.29384e19i 0.359283i
\(676\) −6.91359e19 + 6.65505e19i −1.07171 + 1.03163i
\(677\) −7.30326e19 −1.12046 −0.560230 0.828337i \(-0.689287\pi\)
−0.560230 + 0.828337i \(0.689287\pi\)
\(678\) 2.86118e19 1.15333e19i 0.434447 0.175124i
\(679\) 1.96234e19i 0.294908i
\(680\) −1.07257e19 4.80625e18i −0.159538 0.0714897i
\(681\) 1.35351e19 0.199265
\(682\) 2.23271e17 + 5.53890e17i 0.00325344 + 0.00807111i
\(683\) 7.11794e19i 1.02662i 0.858204 + 0.513309i \(0.171581\pi\)
−0.858204 + 0.513309i \(0.828419\pi\)
\(684\) −2.55194e19 2.65109e19i −0.364316 0.378470i
\(685\) 1.51727e20 2.14402
\(686\) −4.57440e19 + 1.84392e19i −0.639831 + 0.257914i
\(687\) 2.95874e19i 0.409647i
\(688\) 1.00918e20 + 3.84731e18i 1.38309 + 0.0527276i
\(689\) −1.41768e19 −0.192329
\(690\) −3.38606e19 8.40011e19i −0.454727 1.12808i
\(691\) 4.10966e19i 0.546336i 0.961966 + 0.273168i \(0.0880715\pi\)
−0.961966 + 0.273168i \(0.911929\pi\)
\(692\) −8.42537e19 + 8.11029e19i −1.10878 + 1.06732i
\(693\) −2.37081e18 −0.0308861
\(694\) −2.34648e19 + 9.45860e18i −0.302623 + 0.121986i
\(695\) 3.05277e19i 0.389762i
\(696\) 6.04035e18 1.34797e19i 0.0763480 0.170379i
\(697\) 8.91237e18 0.111523
\(698\) 2.60642e19 + 6.46600e19i 0.322892 + 0.801029i
\(699\) 2.61759e19i 0.321041i
\(700\) 3.94852e19 + 4.10192e19i 0.479455 + 0.498082i
\(701\) 7.27378e19 0.874448 0.437224 0.899353i \(-0.355962\pi\)
0.437224 + 0.899353i \(0.355962\pi\)
\(702\) −2.36521e19 + 9.53409e18i −0.281521 + 0.113480i
\(703\) 1.68936e20i 1.99083i
\(704\) −1.60050e19 + 1.42725e19i −0.186744 + 0.166530i
\(705\) −1.48190e20 −1.71197
\(706\) −2.09938e19 5.20814e19i −0.240137 0.595730i
\(707\) 1.43677e19i 0.162724i
\(708\) 3.59192e19 3.45759e19i 0.402804 0.387740i
\(709\) −6.27906e19 −0.697222 −0.348611 0.937268i \(-0.613347\pi\)
−0.348611 + 0.937268i \(0.613347\pi\)
\(710\) 2.55830e20 1.03124e20i 2.81283 1.13384i
\(711\) 3.06082e19i 0.333235i
\(712\) 6.06010e19 + 2.71557e19i 0.653311 + 0.292752i
\(713\) −4.05358e18 −0.0432725
\(714\) −7.80752e17 1.93689e18i −0.00825326 0.0204747i
\(715\) 6.38322e19i 0.668187i
\(716\) −8.72551e18 9.06449e18i −0.0904482 0.0939620i
\(717\) −3.16170e19 −0.324554
\(718\) −1.47996e20 + 5.96565e19i −1.50445 + 0.606439i
\(719\) 3.98180e19i 0.400846i −0.979709 0.200423i \(-0.935768\pi\)
0.979709 0.200423i \(-0.0642317\pi\)
\(720\) 2.15668e18 5.65713e19i 0.0215009 0.563987i
\(721\) −1.93386e19 −0.190931
\(722\) 5.67307e19 + 1.40737e20i 0.554699 + 1.37610i
\(723\) 7.89765e19i 0.764768i
\(724\) 1.34271e20 1.29250e20i 1.28770 1.23954i
\(725\) −6.35620e19 −0.603714
\(726\) 5.33610e19 2.15096e19i 0.501958 0.202338i
\(727\) 1.08316e20i 1.00914i −0.863371 0.504569i \(-0.831651\pi\)
0.863371 0.504569i \(-0.168349\pi\)
\(728\) 2.58839e19 5.77630e19i 0.238842 0.533003i
\(729\) −4.05256e18 −0.0370370
\(730\) 5.65093e19 + 1.40188e20i 0.511517 + 1.26897i
\(731\) 1.59397e19i 0.142908i
\(732\) 3.41215e19 + 3.54471e19i 0.303006 + 0.314777i
\(733\) −8.71515e19 −0.766562 −0.383281 0.923632i \(-0.625206\pi\)
−0.383281 + 0.923632i \(0.625206\pi\)
\(734\) −3.12721e19 + 1.26057e19i −0.272449 + 0.109823i
\(735\) 9.77457e19i 0.843502i
\(736\) −4.92365e19 1.36977e20i −0.420865 1.17086i
\(737\) −7.75012e18 −0.0656200
\(738\) 1.60494e19 + 3.98153e19i 0.134606 + 0.333930i
\(739\) 7.02462e19i 0.583596i −0.956480 0.291798i \(-0.905747\pi\)
0.956480 0.291798i \(-0.0942534\pi\)
\(740\) 1.87248e20 1.80245e20i 1.54097 1.48335i
\(741\) 1.76036e20 1.43507
\(742\) 5.18645e18 2.09064e18i 0.0418835 0.0168831i
\(743\) 7.37552e19i 0.590026i −0.955493 0.295013i \(-0.904676\pi\)
0.955493 0.295013i \(-0.0953240\pi\)
\(744\) −2.31226e18 1.03614e18i −0.0183242 0.00821119i
\(745\) −4.10176e19 −0.322015
\(746\) 7.18933e18 + 1.78353e19i 0.0559135 + 0.138710i
\(747\) 6.60256e17i 0.00508708i
\(748\) −2.34726e18 2.43845e18i −0.0179163 0.0186124i
\(749\) 1.56222e19 0.118132
\(750\) −1.04916e20 + 4.22914e19i −0.785985 + 0.316828i
\(751\) 1.45768e20i 1.08189i 0.841059 + 0.540943i \(0.181932\pi\)
−0.841059 + 0.540943i \(0.818068\pi\)
\(752\) −2.37991e20 9.07296e18i −1.74999 0.0667151i
\(753\) −1.01333e20 −0.738223
\(754\) 2.64188e19 + 6.55397e19i 0.190684 + 0.473048i
\(755\) 2.20514e20i 1.57692i
\(756\) 7.24691e18 6.97590e18i 0.0513453 0.0494251i
\(757\) −1.18561e19 −0.0832285 −0.0416143 0.999134i \(-0.513250\pi\)
−0.0416143 + 0.999134i \(0.513250\pi\)
\(758\) 1.89236e19 7.62802e18i 0.131619 0.0530552i
\(759\) 2.60812e19i 0.179736i
\(760\) −1.59807e20 + 3.56627e20i −1.09119 + 2.43511i
\(761\) 1.04958e20 0.710103 0.355051 0.934847i \(-0.384463\pi\)
0.355051 + 0.934847i \(0.384463\pi\)
\(762\) −2.72231e19 6.75350e19i −0.182496 0.452735i
\(763\) 8.50747e18i 0.0565104i
\(764\) −1.14257e20 1.18696e20i −0.752019 0.781235i
\(765\) 8.93525e18 0.0582743
\(766\) −2.01336e20 + 8.11580e19i −1.30113 + 0.524481i
\(767\) 2.38509e20i 1.52735i
\(768\) 6.92717e18 9.07205e19i 0.0439569 0.575674i
\(769\) 2.55140e20 1.60433 0.802165 0.597102i \(-0.203681\pi\)
0.802165 + 0.597102i \(0.203681\pi\)
\(770\) 9.41326e18 + 2.33524e19i 0.0586550 + 0.145511i
\(771\) 2.67119e19i 0.164939i
\(772\) 1.84872e18 1.77959e18i 0.0113123 0.0108892i
\(773\) −1.49521e20 −0.906662 −0.453331 0.891342i \(-0.649764\pi\)
−0.453331 + 0.891342i \(0.649764\pi\)
\(774\) −7.12092e19 + 2.87042e19i −0.427907 + 0.172488i
\(775\) 1.09031e19i 0.0649292i
\(776\) 1.23142e20 + 5.51805e19i 0.726730 + 0.325652i
\(777\) 4.61797e19 0.270087
\(778\) 5.54376e18 + 1.37529e19i 0.0321327 + 0.0797147i
\(779\) 2.96334e20i 1.70224i
\(780\) 1.87821e20 + 1.95118e20i 1.06926 + 1.11080i
\(781\) 7.94318e19 0.448164
\(782\) 2.13077e19 8.58906e18i 0.119149 0.0480284i
\(783\) 1.12296e19i 0.0622344i
\(784\) 5.98449e18 1.56978e20i 0.0328711 0.862236i
\(785\) −1.23398e20 −0.671771
\(786\) 1.17781e19 + 2.92190e19i 0.0635502 + 0.157655i
\(787\) 2.26036e20i 1.20880i 0.796681 + 0.604400i \(0.206587\pi\)
−0.796681 + 0.604400i \(0.793413\pi\)
\(788\) −1.58289e20 + 1.52369e20i −0.839008 + 0.807632i
\(789\) 1.68073e20 0.882998
\(790\) 3.01490e20 1.21530e20i 1.56994 0.632838i
\(791\) 5.82111e19i 0.300449i
\(792\) 6.66663e18 1.48774e19i 0.0341059 0.0761114i
\(793\) −2.35374e20 −1.19357
\(794\) −8.08008e19 2.00450e20i −0.406137 1.00754i
\(795\) 2.39261e19i 0.119207i
\(796\) −2.21914e20 2.30535e20i −1.09596 1.13853i
\(797\) 2.13241e20 1.04391 0.521954 0.852974i \(-0.325203\pi\)
0.521954 + 0.852974i \(0.325203\pi\)
\(798\) −6.44010e19 + 2.59598e19i −0.312516 + 0.125974i
\(799\) 3.75899e19i 0.180819i
\(800\) −3.68436e20 + 1.32434e20i −1.75684 + 0.631496i
\(801\) −5.04849e19 −0.238635
\(802\) −1.11626e20 2.76922e20i −0.523053 1.29759i
\(803\) 4.35265e19i 0.202183i
\(804\) 2.36900e19 2.28041e19i 0.109087 0.105008i
\(805\) −1.70902e20 −0.780144
\(806\) 1.12424e19 4.53177e18i 0.0508761 0.0205080i
\(807\) 1.18834e20i 0.533120i
\(808\) 9.01606e19 + 4.04015e19i 0.400994 + 0.179688i
\(809\) 1.21626e20 0.536274 0.268137 0.963381i \(-0.413592\pi\)
0.268137 + 0.963381i \(0.413592\pi\)
\(810\) 1.60906e19 + 3.99176e19i 0.0703360 + 0.174489i
\(811\) 4.05480e20i 1.75721i 0.477548 + 0.878605i \(0.341526\pi\)
−0.477548 + 0.878605i \(0.658474\pi\)
\(812\) −1.93301e19 2.00811e19i −0.0830505 0.0862770i
\(813\) 4.84014e19 0.206169
\(814\) 6.94174e19 2.79819e19i 0.293155 0.118170i
\(815\) 6.48315e20i 2.71445i
\(816\) 1.43499e19 + 5.47062e17i 0.0595685 + 0.00227094i
\(817\) 5.29990e20 2.18129
\(818\) −2.28849e19 5.67727e19i −0.0933846 0.231668i
\(819\) 4.81206e19i 0.194690i
\(820\) 3.28456e20 3.16173e20i 1.31759 1.26832i
\(821\) 7.86083e19 0.312656 0.156328 0.987705i \(-0.450034\pi\)
0.156328 + 0.987705i \(0.450034\pi\)
\(822\) −1.71938e20 + 6.93076e19i −0.678062 + 0.273324i
\(823\) 1.32288e20i 0.517276i −0.965974 0.258638i \(-0.916726\pi\)
0.965974 0.258638i \(-0.0832737\pi\)
\(824\) 5.43794e19 1.21354e20i 0.210836 0.470504i
\(825\) −7.01522e19 −0.269689
\(826\) −3.51726e19 8.72561e19i −0.134074 0.332610i
\(827\) 5.83599e19i 0.220585i −0.993899 0.110292i \(-0.964821\pi\)
0.993899 0.110292i \(-0.0351788\pi\)
\(828\) 7.67419e19 + 7.97233e19i 0.287621 + 0.298795i
\(829\) 2.77327e20 1.03065 0.515324 0.856995i \(-0.327671\pi\)
0.515324 + 0.856995i \(0.327671\pi\)
\(830\) −6.50351e18 + 2.62154e18i −0.0239663 + 0.00966073i
\(831\) 1.04844e20i 0.383122i
\(832\) 2.89691e20 + 3.24855e20i 1.04972 + 1.17714i
\(833\) 2.47941e19 0.0890911
\(834\) −1.39448e19 3.45941e19i −0.0496877 0.123265i
\(835\) 3.84398e20i 1.35824i
\(836\) −8.10778e19 + 7.80458e19i −0.284091 + 0.273467i
\(837\) 1.92627e18 0.00669329
\(838\) 9.67510e19 3.90000e19i 0.333386 0.134387i
\(839\) 1.79936e20i 0.614870i −0.951569 0.307435i \(-0.900529\pi\)
0.951569 0.307435i \(-0.0994707\pi\)
\(840\) −9.74862e19 4.36842e19i −0.330361 0.148037i
\(841\) −2.66441e20 −0.895426
\(842\) 1.67849e20 + 4.16398e20i 0.559414 + 1.38779i
\(843\) 1.04350e20i 0.344905i
\(844\) 1.81568e20 + 1.88622e20i 0.595171 + 0.618293i
\(845\) −7.74775e20 −2.51871
\(846\) 1.67930e20 6.76920e19i 0.541421 0.218245i
\(847\) 1.08564e20i 0.347137i
\(848\) −1.46488e18 + 3.84250e19i −0.00464549 + 0.121855i
\(849\) −5.64018e19 −0.177394
\(850\) −2.31025e19 5.73125e19i −0.0720653 0.178779i
\(851\) 5.08023e20i 1.57172i
\(852\) −2.42802e20 + 2.33722e20i −0.745031 + 0.717169i
\(853\) −5.09296e20 −1.54998 −0.774991 0.631972i \(-0.782246\pi\)
−0.774991 + 0.631972i \(0.782246\pi\)
\(854\) 8.61093e19 3.47104e19i 0.259923 0.104774i
\(855\) 2.97095e20i 0.889473i
\(856\) −4.39290e19 + 9.80327e19i −0.130447 + 0.291108i
\(857\) 3.36054e20 0.989790 0.494895 0.868953i \(-0.335206\pi\)
0.494895 + 0.868953i \(0.335206\pi\)
\(858\) 2.91580e19 + 7.23350e19i 0.0851818 + 0.211319i
\(859\) 4.59208e20i 1.33063i −0.746563 0.665315i \(-0.768297\pi\)
0.746563 0.665315i \(-0.231703\pi\)
\(860\) 5.65471e20 + 5.87439e20i 1.62525 + 1.68839i
\(861\) 8.10049e19 0.230935
\(862\) −3.46012e18 + 1.39476e18i −0.00978454 + 0.00394412i
\(863\) 9.50106e19i 0.266499i 0.991082 + 0.133250i \(0.0425412\pi\)
−0.991082 + 0.133250i \(0.957459\pi\)
\(864\) 2.33973e19 + 6.50921e19i 0.0650983 + 0.181106i
\(865\) −9.44194e20 −2.60584
\(866\) −2.11712e20 5.25214e20i −0.579589 1.43784i
\(867\) 2.10338e20i 0.571195i
\(868\) −3.44462e18 + 3.31581e18i −0.00927905 + 0.00893205i
\(869\) 9.36088e19 0.250137
\(870\) 1.10611e20 4.45869e19i 0.293200 0.118188i
\(871\) 1.57305e20i 0.413634i
\(872\) −5.33863e19 2.39227e19i −0.139256 0.0624016i
\(873\) −1.02586e20 −0.265453
\(874\) −2.85584e20 7.08476e20i −0.733085 1.81863i
\(875\) 2.13454e20i 0.543560i
\(876\) −1.28073e20 1.33049e20i −0.323541 0.336111i
\(877\) 3.67289e20 0.920473 0.460236 0.887796i \(-0.347765\pi\)
0.460236 + 0.887796i \(0.347765\pi\)
\(878\) 3.33789e20 1.34549e20i 0.829871 0.334518i
\(879\) 1.58814e20i 0.391711i
\(880\) −1.73011e20 6.59574e18i −0.423346 0.0161393i
\(881\) 4.65384e20 1.12974 0.564872 0.825179i \(-0.308926\pi\)
0.564872 + 0.825179i \(0.308926\pi\)
\(882\) 4.46494e19 + 1.10766e20i 0.107531 + 0.266763i
\(883\) 4.03179e20i 0.963325i 0.876357 + 0.481662i \(0.159967\pi\)
−0.876357 + 0.481662i \(0.840033\pi\)
\(884\) −4.94936e19 + 4.76427e19i −0.117323 + 0.112935i
\(885\) 4.02530e20 0.946663
\(886\) −5.46632e20 + 2.20346e20i −1.27544 + 0.514125i
\(887\) 1.37724e20i 0.318820i 0.987212 + 0.159410i \(0.0509592\pi\)
−0.987212 + 0.159410i \(0.949041\pi\)
\(888\) −1.29856e20 + 2.89788e20i −0.298243 + 0.665564i
\(889\) −1.37401e20 −0.313096
\(890\) 2.00450e20 + 4.97275e20i 0.453185 + 1.12426i
\(891\) 1.23939e19i 0.0278012i
\(892\) −3.66681e20 3.80926e20i −0.816083 0.847788i
\(893\) −1.24985e21 −2.75994
\(894\) 4.64814e19 1.87365e19i 0.101839 0.0410511i
\(895\) 1.01582e20i 0.220828i
\(896\) −1.53887e20 7.61246e19i −0.331929 0.164198i
\(897\) −5.29375e20 −1.13296
\(898\) 2.64483e20 + 6.56128e20i 0.561647 + 1.39333i
\(899\) 5.33767e18i 0.0112469i
\(900\) 2.14436e20 2.06417e20i 0.448333 0.431567i
\(901\) −6.06910e18 −0.0125907
\(902\) 1.21767e20 4.90837e19i 0.250659 0.101040i
\(903\) 1.44876e20i 0.295926i
\(904\) 3.65288e20 + 1.63688e20i 0.740383 + 0.331770i
\(905\) 1.50472e21 3.02632
\(906\) −1.00729e20 2.49888e20i −0.201028 0.498710i
\(907\) 4.42250e19i 0.0875824i −0.999041 0.0437912i \(-0.986056\pi\)
0.999041 0.0437912i \(-0.0139436\pi\)
\(908\) 1.21799e20 + 1.26531e20i 0.239355 + 0.248654i
\(909\) −7.51101e19 −0.146471
\(910\) 4.73987e20 1.91062e20i 0.917226 0.369731i
\(911\) 5.50033e20i 1.05623i 0.849172 + 0.528117i \(0.177102\pi\)
−0.849172 + 0.528117i \(0.822898\pi\)
\(912\) 1.81897e19 4.77130e20i 0.0346626 0.909227i
\(913\) −2.01925e18 −0.00381852
\(914\) 5.05849e19 + 1.25491e20i 0.0949288 + 0.235499i
\(915\) 3.97240e20i 0.739784i
\(916\) −2.76594e20 + 2.66250e20i −0.511180 + 0.492063i
\(917\) 5.94466e19 0.109029
\(918\) −1.01255e19 + 4.08154e18i −0.0184296 + 0.00742892i
\(919\) 6.55183e19i 0.118346i −0.998248 0.0591730i \(-0.981154\pi\)
0.998248 0.0591730i \(-0.0188464\pi\)
\(920\) 4.80570e20 1.07245e21i 0.861473 1.92248i
\(921\) 2.75277e20 0.489725
\(922\) 1.39331e20 + 3.45652e20i 0.245998 + 0.610270i
\(923\) 1.61224e21i 2.82500i
\(924\) −2.13343e19 2.21631e19i −0.0371001 0.0385414i
\(925\) 1.36646e21 2.35833
\(926\) −9.22633e20 + 3.71910e20i −1.58035 + 0.637032i
\(927\) 1.01096e20i 0.171861i
\(928\) 1.80369e20 6.48336e19i 0.304317 0.109387i
\(929\) 3.92793e20 0.657739 0.328869 0.944375i \(-0.393332\pi\)
0.328869 + 0.944375i \(0.393332\pi\)
\(930\) −7.64824e18 1.89737e19i −0.0127110 0.0315335i
\(931\) 8.24400e20i 1.35985i
\(932\) −2.44701e20 + 2.35550e20i −0.400613 + 0.385631i
\(933\) −3.20837e20 −0.521331
\(934\) 2.21516e20 8.92925e19i 0.357255 0.144008i
\(935\) 2.73266e19i 0.0437425i
\(936\) −3.01968e20 1.35314e20i −0.479767 0.214986i
\(937\) −4.24903e20 −0.670059 −0.335029 0.942208i \(-0.608746\pi\)
−0.335029 + 0.942208i \(0.608746\pi\)
\(938\) −2.31976e19 5.75486e19i −0.0363098 0.0900772i
\(939\) 9.39002e19i 0.145884i
\(940\) −1.33353e21 1.38534e21i −2.05640 2.13629i
\(941\) 1.27519e20 0.195186 0.0975931 0.995226i \(-0.468886\pi\)
0.0975931 + 0.995226i \(0.468886\pi\)
\(942\) 1.39836e20 5.63672e19i 0.212452 0.0856387i
\(943\) 8.91135e20i 1.34388i
\(944\) 6.46456e20 + 2.46449e19i 0.967688 + 0.0368913i
\(945\) 8.12129e19 0.120671
\(946\) 8.77857e19 + 2.17778e20i 0.129475 + 0.321201i
\(947\) 9.03455e20i 1.32269i 0.750083 + 0.661343i \(0.230013\pi\)
−0.750083 + 0.661343i \(0.769987\pi\)
\(948\) −2.86137e20 + 2.75436e20i −0.415830 + 0.400279i
\(949\) 8.83465e20 1.27446
\(950\) −1.90563e21 + 7.68152e20i −2.72881 + 1.09997i
\(951\) 1.39579e20i 0.198407i
\(952\) 1.10809e19 2.47283e19i 0.0156357 0.0348928i
\(953\) −6.56931e20 −0.920173 −0.460087 0.887874i \(-0.652182\pi\)
−0.460087 + 0.887874i \(0.652182\pi\)
\(954\) −1.09293e19 2.71132e19i −0.0151968 0.0377001i
\(955\) 1.33017e21i 1.83604i
\(956\) −2.84514e20 2.95567e20i −0.389851 0.404997i
\(957\) 3.43433e19 0.0467152
\(958\) 4.42963e20 1.78557e20i 0.598149 0.241112i
\(959\) 3.49810e20i 0.468924i
\(960\) 5.48256e20 4.88910e20i 0.729601 0.650625i
\(961\) 7.56028e20 0.998790
\(962\) −5.67953e20 1.40898e21i −0.744882 1.84790i
\(963\) 8.16681e19i 0.106333i
\(964\) −7.38300e20 + 7.10690e20i −0.954320 + 0.918631i
\(965\) 2.07178e19 0.0265859
\(966\) 1.93667e20 7.80663e19i 0.246726 0.0994543i
\(967\) 5.87530e20i 0.743096i −0.928414 0.371548i \(-0.878827\pi\)
0.928414 0.371548i \(-0.121173\pi\)
\(968\) 6.81263e20 + 3.05278e20i 0.855436 + 0.383326i
\(969\) 7.53611e19 0.0939465
\(970\) 4.07315e20 + 1.01047e21i 0.504114 + 1.25060i
\(971\) 1.24174e21i 1.52580i 0.646516 + 0.762900i \(0.276225\pi\)
−0.646516 + 0.762900i \(0.723775\pi\)
\(972\) −3.64680e19 3.78847e19i −0.0444885 0.0462169i
\(973\) −7.03822e19 −0.0852458
\(974\) 9.17225e20 3.69730e20i 1.10297 0.444603i
\(975\) 1.42389e21i 1.69998i
\(976\) −2.43210e19 + 6.37960e20i −0.0288293 + 0.756214i
\(977\) −1.06987e21 −1.25912 −0.629560 0.776952i \(-0.716765\pi\)
−0.629560 + 0.776952i \(0.716765\pi\)
\(978\) 2.96144e20 + 7.34674e20i 0.346044 + 0.858465i
\(979\) 1.54397e20i 0.179127i
\(980\) 9.13762e20 8.79590e20i 1.05257 1.01321i
\(981\) 4.44746e19 0.0508661
\(982\) −8.07952e20 + 3.25683e20i −0.917498 + 0.369840i
\(983\) 9.78571e20i 1.10336i 0.834055 + 0.551681i \(0.186013\pi\)
−0.834055 + 0.551681i \(0.813987\pi\)
\(984\) −2.27783e20 + 5.08324e20i −0.255009 + 0.569083i
\(985\) −1.77387e21 −1.97182
\(986\) 1.13099e19 + 2.80575e19i 0.0124830 + 0.0309679i
\(987\) 3.41656e20i 0.374428i
\(988\) 1.58411e21 + 1.64565e21i 1.72380 + 1.79077i
\(989\) −1.59378e21 −1.72209
\(990\) 1.22079e20 4.92098e19i 0.130977 0.0527965i
\(991\) 4.07431e20i 0.434049i 0.976166 + 0.217024i \(0.0696351\pi\)
−0.976166 + 0.217024i \(0.930365\pi\)
\(992\) −1.11213e19 3.09397e19i −0.0117645 0.0327292i
\(993\) −1.83542e20 −0.192793
\(994\) 2.37755e20 + 5.89822e20i 0.247985 + 0.615199i
\(995\) 2.58350e21i 2.67576i
\(996\) 6.17231e18 5.94149e18i 0.00634793 0.00611054i
\(997\) 9.14631e20 0.934071 0.467036 0.884238i \(-0.345322\pi\)
0.467036 + 0.884238i \(0.345322\pi\)
\(998\) 1.10083e20 4.43743e19i 0.111637 0.0450005i
\(999\) 2.41414e20i 0.243111i
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 12.15.d.a.7.5 14
3.2 odd 2 36.15.d.e.19.10 14
4.3 odd 2 inner 12.15.d.a.7.6 yes 14
12.11 even 2 36.15.d.e.19.9 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.15.d.a.7.5 14 1.1 even 1 trivial
12.15.d.a.7.6 yes 14 4.3 odd 2 inner
36.15.d.e.19.9 14 12.11 even 2
36.15.d.e.19.10 14 3.2 odd 2