Properties

Label 12.15.d.a.7.7
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 7.7
Root \(37.1678 + 64.3766i\) of defining polynomial
Character \(\chi\) \(=\) 12.7
Dual form 12.15.d.a.7.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(26.2042 - 125.289i) q^{2} -1262.67i q^{3} +(-15010.7 - 6566.21i) q^{4} -40325.1 q^{5} +(-158198. - 33087.2i) q^{6} +421333. i q^{7} +(-1.21602e6 + 1.70861e6i) q^{8} -1.59432e6 q^{9} +O(q^{10})\) \(q+(26.2042 - 125.289i) q^{2} -1262.67i q^{3} +(-15010.7 - 6566.21i) q^{4} -40325.1 q^{5} +(-158198. - 33087.2i) q^{6} +421333. i q^{7} +(-1.21602e6 + 1.70861e6i) q^{8} -1.59432e6 q^{9} +(-1.05669e6 + 5.05229e6i) q^{10} -1.42281e6i q^{11} +(-8.29092e6 + 1.89535e7i) q^{12} -2.76240e7 q^{13} +(5.27883e7 + 1.10407e7i) q^{14} +5.09171e7i q^{15} +(1.82205e8 + 1.97126e8i) q^{16} +3.56692e8 q^{17} +(-4.17780e7 + 1.99751e8i) q^{18} +3.85490e8i q^{19} +(6.05307e8 + 2.64783e8i) q^{20} +5.32002e8 q^{21} +(-1.78262e8 - 3.72836e7i) q^{22} +6.03923e9i q^{23} +(2.15740e9 + 1.53542e9i) q^{24} -4.47740e9 q^{25} +(-7.23866e8 + 3.46098e9i) q^{26} +2.01310e9i q^{27} +(2.76656e9 - 6.32449e9i) q^{28} -1.53493e10 q^{29} +(6.37935e9 + 1.33424e9i) q^{30} -3.72252e10i q^{31} +(2.94723e10 - 1.76628e10i) q^{32} -1.79653e9 q^{33} +(9.34685e9 - 4.46896e10i) q^{34} -1.69903e10i q^{35} +(2.39319e10 + 1.04687e10i) q^{36} -1.69904e11 q^{37} +(4.82976e10 + 1.01015e10i) q^{38} +3.48799e10i q^{39} +(4.90360e10 - 6.88999e10i) q^{40} -3.36802e11 q^{41} +(1.39407e10 - 6.66540e10i) q^{42} +2.13791e11i q^{43} +(-9.34245e9 + 2.13573e10i) q^{44} +6.42912e10 q^{45} +(7.56649e11 + 1.58253e11i) q^{46} +4.76171e11i q^{47} +(2.48905e11 - 2.30064e11i) q^{48} +5.00702e11 q^{49} +(-1.17327e11 + 5.60969e11i) q^{50} -4.50383e11i q^{51} +(4.14655e11 + 1.81385e11i) q^{52} -1.64539e12 q^{53} +(2.52219e11 + 5.27516e10i) q^{54} +5.73748e10i q^{55} +(-7.19893e11 - 5.12347e11i) q^{56} +4.86745e11 q^{57} +(-4.02216e11 + 1.92310e12i) q^{58} +9.85223e10i q^{59} +(3.34332e11 - 7.64300e11i) q^{60} +2.21058e12 q^{61} +(-4.66390e12 - 9.75457e11i) q^{62} -6.71740e11i q^{63} +(-1.44065e12 - 4.15540e12i) q^{64} +1.11394e12 q^{65} +(-4.70767e10 + 2.25085e11i) q^{66} -9.25057e12i q^{67} +(-5.35419e12 - 2.34211e12i) q^{68} +7.62552e12 q^{69} +(-2.12869e12 - 4.45217e11i) q^{70} +4.91016e12i q^{71} +(1.93872e12 - 2.72408e12i) q^{72} +8.74284e12 q^{73} +(-4.45221e12 + 2.12871e13i) q^{74} +5.65346e12i q^{75} +(2.53121e12 - 5.78646e12i) q^{76} +5.99475e11 q^{77} +(4.37006e12 + 9.14000e11i) q^{78} -5.31538e12i q^{79} +(-7.34745e12 - 7.94914e12i) q^{80} +2.54187e12 q^{81} +(-8.82564e12 + 4.21976e13i) q^{82} +1.43700e13i q^{83} +(-7.98571e12 - 3.49323e12i) q^{84} -1.43836e13 q^{85} +(2.67857e13 + 5.60223e12i) q^{86} +1.93810e13i q^{87} +(2.43102e12 + 1.73016e12i) q^{88} +1.13769e13 q^{89} +(1.68470e12 - 8.05498e12i) q^{90} -1.16389e13i q^{91} +(3.96548e13 - 9.06529e13i) q^{92} -4.70029e13 q^{93} +(5.96590e13 + 1.24777e13i) q^{94} -1.55449e13i q^{95} +(-2.23022e13 - 3.72137e13i) q^{96} -8.88449e13 q^{97} +(1.31205e13 - 6.27325e13i) q^{98} +2.26841e12i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26.2042 125.289i 0.204721 0.978820i
\(3\) 1262.67i 0.577350i
\(4\) −15010.7 6566.21i −0.916179 0.400769i
\(5\) −40325.1 −0.516161 −0.258081 0.966123i \(-0.583090\pi\)
−0.258081 + 0.966123i \(0.583090\pi\)
\(6\) −158198. 33087.2i −0.565122 0.118195i
\(7\) 421333.i 0.511610i 0.966728 + 0.255805i \(0.0823404\pi\)
−0.966728 + 0.255805i \(0.917660\pi\)
\(8\) −1.21602e6 + 1.70861e6i −0.579842 + 0.814729i
\(9\) −1.59432e6 −0.333333
\(10\) −1.05669e6 + 5.05229e6i −0.105669 + 0.505229i
\(11\) 1.42281e6i 0.0730125i −0.999333 0.0365063i \(-0.988377\pi\)
0.999333 0.0365063i \(-0.0116229\pi\)
\(12\) −8.29092e6 + 1.89535e7i −0.231384 + 0.528956i
\(13\) −2.76240e7 −0.440234 −0.220117 0.975474i \(-0.570644\pi\)
−0.220117 + 0.975474i \(0.570644\pi\)
\(14\) 5.27883e7 + 1.10407e7i 0.500774 + 0.104737i
\(15\) 5.09171e7i 0.298006i
\(16\) 1.82205e8 + 1.97126e8i 0.678768 + 0.734353i
\(17\) 3.56692e8 0.869263 0.434632 0.900608i \(-0.356879\pi\)
0.434632 + 0.900608i \(0.356879\pi\)
\(18\) −4.17780e7 + 1.99751e8i −0.0682402 + 0.326273i
\(19\) 3.85490e8i 0.431259i 0.976475 + 0.215629i \(0.0691803\pi\)
−0.976475 + 0.215629i \(0.930820\pi\)
\(20\) 6.05307e8 + 2.64783e8i 0.472896 + 0.206862i
\(21\) 5.32002e8 0.295378
\(22\) −1.78262e8 3.72836e7i −0.0714661 0.0149472i
\(23\) 6.03923e9i 1.77373i 0.462033 + 0.886863i \(0.347120\pi\)
−0.462033 + 0.886863i \(0.652880\pi\)
\(24\) 2.15740e9 + 1.53542e9i 0.470384 + 0.334772i
\(25\) −4.47740e9 −0.733578
\(26\) −7.23866e8 + 3.46098e9i −0.0901249 + 0.430910i
\(27\) 2.01310e9i 0.192450i
\(28\) 2.76656e9 6.32449e9i 0.205037 0.468726i
\(29\) −1.53493e10 −0.889820 −0.444910 0.895575i \(-0.646764\pi\)
−0.444910 + 0.895575i \(0.646764\pi\)
\(30\) 6.37935e9 + 1.33424e9i 0.291694 + 0.0610079i
\(31\) 3.72252e10i 1.35302i −0.736433 0.676511i \(-0.763491\pi\)
0.736433 0.676511i \(-0.236509\pi\)
\(32\) 2.94723e10 1.76628e10i 0.857757 0.514055i
\(33\) −1.79653e9 −0.0421538
\(34\) 9.34685e9 4.46896e10i 0.177956 0.850853i
\(35\) 1.69903e10i 0.264073i
\(36\) 2.39319e10 + 1.04687e10i 0.305393 + 0.133590i
\(37\) −1.69904e11 −1.78975 −0.894874 0.446319i \(-0.852735\pi\)
−0.894874 + 0.446319i \(0.852735\pi\)
\(38\) 4.82976e10 + 1.01015e10i 0.422125 + 0.0882875i
\(39\) 3.48799e10i 0.254169i
\(40\) 4.90360e10 6.88999e10i 0.299292 0.420531i
\(41\) −3.36802e11 −1.72937 −0.864685 0.502315i \(-0.832482\pi\)
−0.864685 + 0.502315i \(0.832482\pi\)
\(42\) 1.39407e10 6.66540e10i 0.0604700 0.289122i
\(43\) 2.13791e11i 0.786521i 0.919427 + 0.393261i \(0.128653\pi\)
−0.919427 + 0.393261i \(0.871347\pi\)
\(44\) −9.34245e9 + 2.13573e10i −0.0292612 + 0.0668925i
\(45\) 6.42912e10 0.172054
\(46\) 7.56649e11 + 1.58253e11i 1.73616 + 0.363118i
\(47\) 4.76171e11i 0.939892i 0.882695 + 0.469946i \(0.155727\pi\)
−0.882695 + 0.469946i \(0.844273\pi\)
\(48\) 2.48905e11 2.30064e11i 0.423979 0.391887i
\(49\) 5.00702e11 0.738256
\(50\) −1.17327e11 + 5.60969e11i −0.150178 + 0.718041i
\(51\) 4.50383e11i 0.501869i
\(52\) 4.14655e11 + 1.81385e11i 0.403333 + 0.176432i
\(53\) −1.64539e12 −1.40067 −0.700337 0.713812i \(-0.746967\pi\)
−0.700337 + 0.713812i \(0.746967\pi\)
\(54\) 2.52219e11 + 5.27516e10i 0.188374 + 0.0393985i
\(55\) 5.73748e10i 0.0376862i
\(56\) −7.19893e11 5.12347e11i −0.416823 0.296653i
\(57\) 4.86745e11 0.248987
\(58\) −4.02216e11 + 1.92310e12i −0.182164 + 0.870974i
\(59\) 9.85223e10i 0.0395886i 0.999804 + 0.0197943i \(0.00630114\pi\)
−0.999804 + 0.0197943i \(0.993699\pi\)
\(60\) 3.34332e11 7.64300e11i 0.119432 0.273027i
\(61\) 2.21058e12 0.703392 0.351696 0.936114i \(-0.385605\pi\)
0.351696 + 0.936114i \(0.385605\pi\)
\(62\) −4.66390e12 9.75457e11i −1.32436 0.276991i
\(63\) 6.71740e11i 0.170537i
\(64\) −1.44065e12 4.15540e12i −0.327567 0.944828i
\(65\) 1.11394e12 0.227231
\(66\) −4.70767e10 + 2.25085e11i −0.00862975 + 0.0412610i
\(67\) 9.25057e12i 1.52632i −0.646211 0.763159i \(-0.723648\pi\)
0.646211 0.763159i \(-0.276352\pi\)
\(68\) −5.35419e12 2.34211e12i −0.796401 0.348374i
\(69\) 7.62552e12 1.02406
\(70\) −2.12869e12 4.45217e11i −0.258480 0.0540612i
\(71\) 4.91016e12i 0.539867i 0.962879 + 0.269934i \(0.0870018\pi\)
−0.962879 + 0.269934i \(0.912998\pi\)
\(72\) 1.93872e12 2.72408e12i 0.193281 0.271576i
\(73\) 8.74284e12 0.791394 0.395697 0.918381i \(-0.370503\pi\)
0.395697 + 0.918381i \(0.370503\pi\)
\(74\) −4.45221e12 + 2.12871e13i −0.366398 + 1.75184i
\(75\) 5.65346e12i 0.423531i
\(76\) 2.53121e12 5.78646e12i 0.172835 0.395110i
\(77\) 5.99475e11 0.0373539
\(78\) 4.37006e12 + 9.14000e11i 0.248786 + 0.0520336i
\(79\) 5.31538e12i 0.276787i −0.990377 0.138393i \(-0.955806\pi\)
0.990377 0.138393i \(-0.0441938\pi\)
\(80\) −7.34745e12 7.94914e12i −0.350353 0.379044i
\(81\) 2.54187e12 0.111111
\(82\) −8.82564e12 + 4.21976e13i −0.354038 + 1.69274i
\(83\) 1.43700e13i 0.529555i 0.964310 + 0.264777i \(0.0852984\pi\)
−0.964310 + 0.264777i \(0.914702\pi\)
\(84\) −7.98571e12 3.49323e12i −0.270619 0.118378i
\(85\) −1.43836e13 −0.448680
\(86\) 2.67857e13 + 5.60223e12i 0.769863 + 0.161017i
\(87\) 1.93810e13i 0.513738i
\(88\) 2.43102e12 + 1.73016e12i 0.0594854 + 0.0423357i
\(89\) 1.13769e13 0.257214 0.128607 0.991696i \(-0.458949\pi\)
0.128607 + 0.991696i \(0.458949\pi\)
\(90\) 1.68470e12 8.05498e12i 0.0352229 0.168410i
\(91\) 1.16389e13i 0.225228i
\(92\) 3.96548e13 9.06529e13i 0.710855 1.62505i
\(93\) −4.70029e13 −0.781167
\(94\) 5.96590e13 + 1.24777e13i 0.919986 + 0.192415i
\(95\) 1.55449e13i 0.222599i
\(96\) −2.23022e13 3.72137e13i −0.296790 0.495227i
\(97\) −8.88449e13 −1.09959 −0.549795 0.835300i \(-0.685294\pi\)
−0.549795 + 0.835300i \(0.685294\pi\)
\(98\) 1.31205e13 6.27325e13i 0.151136 0.722620i
\(99\) 2.26841e12i 0.0243375i
\(100\) 6.72089e13 + 2.93996e13i 0.672089 + 0.293996i
\(101\) −5.95274e13 −0.555223 −0.277611 0.960693i \(-0.589543\pi\)
−0.277611 + 0.960693i \(0.589543\pi\)
\(102\) −5.64280e13 1.18019e13i −0.491240 0.102743i
\(103\) 1.33826e14i 1.08813i −0.839044 0.544063i \(-0.816885\pi\)
0.839044 0.544063i \(-0.183115\pi\)
\(104\) 3.35912e13 4.71987e13i 0.255266 0.358671i
\(105\) −2.14530e13 −0.152463
\(106\) −4.31161e13 + 2.06149e14i −0.286747 + 1.37101i
\(107\) 8.37947e13i 0.521831i 0.965362 + 0.260916i \(0.0840244\pi\)
−0.965362 + 0.260916i \(0.915976\pi\)
\(108\) 1.32184e13 3.02179e13i 0.0771281 0.176319i
\(109\) −2.00753e14 −1.09819 −0.549095 0.835760i \(-0.685028\pi\)
−0.549095 + 0.835760i \(0.685028\pi\)
\(110\) 7.18844e12 + 1.50346e12i 0.0368880 + 0.00771515i
\(111\) 2.14532e14i 1.03331i
\(112\) −8.30558e13 + 7.67690e13i −0.375702 + 0.347264i
\(113\) 3.27875e14 1.39367 0.696833 0.717233i \(-0.254592\pi\)
0.696833 + 0.717233i \(0.254592\pi\)
\(114\) 1.27548e13 6.09837e13i 0.0509728 0.243714i
\(115\) 2.43532e14i 0.915528i
\(116\) 2.30403e14 + 1.00787e14i 0.815234 + 0.356613i
\(117\) 4.40416e13 0.146745
\(118\) 1.23438e13 + 2.58170e12i 0.0387502 + 0.00810461i
\(119\) 1.50286e14i 0.444723i
\(120\) −8.69974e13 6.19160e13i −0.242794 0.172796i
\(121\) 3.77725e14 0.994669
\(122\) 5.79266e13 2.76962e14i 0.143999 0.688495i
\(123\) 4.25268e14i 0.998452i
\(124\) −2.44428e14 + 5.58775e14i −0.542250 + 1.23961i
\(125\) 4.26676e14 0.894805
\(126\) −8.41617e13 1.76024e13i −0.166925 0.0349123i
\(127\) 6.21176e14i 1.16570i −0.812578 0.582852i \(-0.801937\pi\)
0.812578 0.582852i \(-0.198063\pi\)
\(128\) −5.58377e14 + 7.16090e13i −0.991877 + 0.127203i
\(129\) 2.69947e14 0.454098
\(130\) 2.91899e13 1.39564e14i 0.0465189 0.222419i
\(131\) 5.33781e14i 0.806240i 0.915147 + 0.403120i \(0.132074\pi\)
−0.915147 + 0.403120i \(0.867926\pi\)
\(132\) 2.69671e13 + 1.17964e13i 0.0386204 + 0.0168940i
\(133\) −1.62419e14 −0.220636
\(134\) −1.15899e15 2.42404e14i −1.49399 0.312469i
\(135\) 8.11783e13i 0.0993352i
\(136\) −4.33744e14 + 6.09448e14i −0.504035 + 0.708214i
\(137\) −7.49540e14 −0.827467 −0.413734 0.910398i \(-0.635775\pi\)
−0.413734 + 0.910398i \(0.635775\pi\)
\(138\) 1.99821e14 9.55394e14i 0.209646 1.00237i
\(139\) 1.89011e15i 1.88531i −0.333765 0.942656i \(-0.608319\pi\)
0.333765 0.942656i \(-0.391681\pi\)
\(140\) −1.11562e14 + 2.55035e14i −0.105832 + 0.241938i
\(141\) 6.01245e14 0.542647
\(142\) 6.15189e14 + 1.28667e14i 0.528433 + 0.110522i
\(143\) 3.93036e13i 0.0321426i
\(144\) −2.90494e14 3.14283e14i −0.226256 0.244784i
\(145\) 6.18961e14 0.459290
\(146\) 2.29100e14 1.09538e15i 0.162015 0.774633i
\(147\) 6.32219e14i 0.426232i
\(148\) 2.55038e15 + 1.11563e15i 1.63973 + 0.717276i
\(149\) −1.16262e15 −0.713071 −0.356536 0.934282i \(-0.616042\pi\)
−0.356536 + 0.934282i \(0.616042\pi\)
\(150\) 7.08317e14 + 1.48145e14i 0.414561 + 0.0867056i
\(151\) 1.08753e15i 0.607581i 0.952739 + 0.303791i \(0.0982523\pi\)
−0.952739 + 0.303791i \(0.901748\pi\)
\(152\) −6.58652e14 4.68762e14i −0.351359 0.250062i
\(153\) −5.68683e14 −0.289754
\(154\) 1.57088e13 7.51076e13i 0.00764711 0.0365628i
\(155\) 1.50111e15i 0.698377i
\(156\) 2.29028e14 5.23570e14i 0.101863 0.232864i
\(157\) −3.10158e14 −0.131912 −0.0659562 0.997823i \(-0.521010\pi\)
−0.0659562 + 0.997823i \(0.521010\pi\)
\(158\) −6.65959e14 1.39286e14i −0.270924 0.0566639i
\(159\) 2.07757e15i 0.808679i
\(160\) −1.18847e15 + 7.12253e14i −0.442741 + 0.265335i
\(161\) −2.54452e15 −0.907455
\(162\) 6.66077e13 3.18468e14i 0.0227467 0.108758i
\(163\) 1.56606e15i 0.512266i 0.966642 + 0.256133i \(0.0824486\pi\)
−0.966642 + 0.256133i \(0.917551\pi\)
\(164\) 5.05563e15 + 2.21151e15i 1.58441 + 0.693078i
\(165\) 7.24452e13 0.0217581
\(166\) 1.80041e15 + 3.76555e14i 0.518339 + 0.108411i
\(167\) 1.49948e15i 0.413928i 0.978349 + 0.206964i \(0.0663582\pi\)
−0.978349 + 0.206964i \(0.933642\pi\)
\(168\) −6.46923e14 + 9.08984e14i −0.171273 + 0.240653i
\(169\) −3.17429e15 −0.806194
\(170\) −3.76912e14 + 1.80211e15i −0.0918540 + 0.439177i
\(171\) 6.14595e14i 0.143753i
\(172\) 1.40380e15 3.20915e15i 0.315214 0.720594i
\(173\) 1.19192e15 0.256994 0.128497 0.991710i \(-0.458985\pi\)
0.128497 + 0.991710i \(0.458985\pi\)
\(174\) 2.42823e15 + 5.07864e14i 0.502857 + 0.105173i
\(175\) 1.88648e15i 0.375305i
\(176\) 2.80473e14 2.59243e14i 0.0536170 0.0495585i
\(177\) 1.24401e14 0.0228565
\(178\) 2.98123e14 1.42540e15i 0.0526569 0.251766i
\(179\) 6.42994e15i 1.09203i −0.837774 0.546016i \(-0.816144\pi\)
0.837774 0.546016i \(-0.183856\pi\)
\(180\) −9.65054e14 4.22149e14i −0.157632 0.0689539i
\(181\) −1.60145e15 −0.251631 −0.125816 0.992054i \(-0.540155\pi\)
−0.125816 + 0.992054i \(0.540155\pi\)
\(182\) −1.45823e15 3.04988e14i −0.220457 0.0461088i
\(183\) 2.79122e15i 0.406104i
\(184\) −1.03187e16 7.34380e15i −1.44511 1.02848i
\(185\) 6.85140e15 0.923798
\(186\) −1.23168e15 + 5.88895e15i −0.159921 + 0.764622i
\(187\) 5.07504e14i 0.0634671i
\(188\) 3.12664e15 7.14765e15i 0.376680 0.861109i
\(189\) −8.48183e14 −0.0984593
\(190\) −1.94761e15 4.07342e14i −0.217884 0.0455706i
\(191\) 4.83572e15i 0.521468i −0.965411 0.260734i \(-0.916035\pi\)
0.965411 0.260734i \(-0.0839645\pi\)
\(192\) −5.24688e15 + 1.81906e15i −0.545497 + 0.189121i
\(193\) 5.13392e15 0.514692 0.257346 0.966319i \(-0.417152\pi\)
0.257346 + 0.966319i \(0.417152\pi\)
\(194\) −2.32811e15 + 1.11313e16i −0.225109 + 1.07630i
\(195\) 1.40653e15i 0.131192i
\(196\) −7.51587e15 3.28771e15i −0.676374 0.295870i
\(197\) 1.29818e16 1.12738 0.563692 0.825985i \(-0.309380\pi\)
0.563692 + 0.825985i \(0.309380\pi\)
\(198\) 2.84207e14 + 5.94421e13i 0.0238220 + 0.00498239i
\(199\) 2.28758e16i 1.85100i 0.378753 + 0.925498i \(0.376353\pi\)
−0.378753 + 0.925498i \(0.623647\pi\)
\(200\) 5.44460e15 7.65014e15i 0.425359 0.597667i
\(201\) −1.16804e16 −0.881220
\(202\) −1.55987e15 + 7.45813e15i −0.113666 + 0.543464i
\(203\) 6.46715e15i 0.455240i
\(204\) −2.95731e15 + 6.76055e15i −0.201134 + 0.459802i
\(205\) 1.35816e16 0.892633
\(206\) −1.67669e16 3.50680e15i −1.06508 0.222762i
\(207\) 9.62848e15i 0.591242i
\(208\) −5.03324e15 5.44542e15i −0.298816 0.323287i
\(209\) 5.48478e14 0.0314873
\(210\) −5.62160e14 + 2.68783e15i −0.0312122 + 0.149234i
\(211\) 2.20180e16i 1.18250i 0.806488 + 0.591250i \(0.201366\pi\)
−0.806488 + 0.591250i \(0.798634\pi\)
\(212\) 2.46984e16 + 1.08040e16i 1.28327 + 0.561347i
\(213\) 6.19989e15 0.311693
\(214\) 1.04986e16 + 2.19578e15i 0.510779 + 0.106830i
\(215\) 8.62114e15i 0.405972i
\(216\) −3.43960e15 2.44796e15i −0.156795 0.111591i
\(217\) 1.56842e16 0.692219
\(218\) −5.26059e15 + 2.51522e16i −0.224822 + 1.07493i
\(219\) 1.10393e16i 0.456911i
\(220\) 3.76735e14 8.61235e14i 0.0151035 0.0345273i
\(221\) −9.85327e15 −0.382679
\(222\) 2.68785e16 + 5.62165e15i 1.01143 + 0.211540i
\(223\) 1.34954e16i 0.492097i 0.969258 + 0.246048i \(0.0791322\pi\)
−0.969258 + 0.246048i \(0.920868\pi\)
\(224\) 7.44190e15 + 1.24176e16i 0.262995 + 0.438837i
\(225\) 7.13843e15 0.244526
\(226\) 8.59171e15 4.10791e16i 0.285312 1.36415i
\(227\) 1.75395e16i 0.564724i −0.959308 0.282362i \(-0.908882\pi\)
0.959308 0.282362i \(-0.0911179\pi\)
\(228\) −7.30636e15 3.19607e15i −0.228117 0.0997865i
\(229\) −4.49532e16 −1.36117 −0.680585 0.732669i \(-0.738275\pi\)
−0.680585 + 0.732669i \(0.738275\pi\)
\(230\) −3.05119e16 6.38158e15i −0.896138 0.187427i
\(231\) 7.56936e14i 0.0215663i
\(232\) 1.86650e16 2.62259e16i 0.515955 0.724962i
\(233\) −7.20644e16 −1.93299 −0.966494 0.256690i \(-0.917368\pi\)
−0.966494 + 0.256690i \(0.917368\pi\)
\(234\) 1.15408e15 5.51793e15i 0.0300416 0.143637i
\(235\) 1.92016e16i 0.485136i
\(236\) 6.46918e14 1.47889e15i 0.0158659 0.0362703i
\(237\) −6.71155e15 −0.159803
\(238\) 1.88292e16 + 3.93813e15i 0.435304 + 0.0910440i
\(239\) 6.29661e16i 1.41358i 0.707421 + 0.706792i \(0.249858\pi\)
−0.707421 + 0.706792i \(0.750142\pi\)
\(240\) −1.00371e16 + 9.27736e15i −0.218841 + 0.202277i
\(241\) −8.13249e15 −0.172228 −0.0861141 0.996285i \(-0.527445\pi\)
−0.0861141 + 0.996285i \(0.527445\pi\)
\(242\) 9.89801e15 4.73249e16i 0.203629 0.973603i
\(243\) 3.20953e15i 0.0641500i
\(244\) −3.31823e16 1.45151e16i −0.644433 0.281898i
\(245\) −2.01908e16 −0.381059
\(246\) 5.32814e16 + 1.11438e16i 0.977305 + 0.204404i
\(247\) 1.06488e16i 0.189854i
\(248\) 6.36033e16 + 4.52664e16i 1.10235 + 0.784539i
\(249\) 1.81445e16 0.305738
\(250\) 1.11807e16 5.34579e16i 0.183185 0.875854i
\(251\) 6.32148e16i 1.00717i −0.863946 0.503585i \(-0.832014\pi\)
0.863946 0.503585i \(-0.167986\pi\)
\(252\) −4.41078e15 + 1.00833e16i −0.0683458 + 0.156242i
\(253\) 8.59266e15 0.129504
\(254\) −7.78265e16 1.62774e16i −1.14102 0.238644i
\(255\) 1.81617e16i 0.259045i
\(256\) −5.66003e15 + 7.18350e16i −0.0785486 + 0.996910i
\(257\) 6.39849e16 0.864063 0.432032 0.901858i \(-0.357797\pi\)
0.432032 + 0.901858i \(0.357797\pi\)
\(258\) 7.07374e15 3.38213e16i 0.0929633 0.444481i
\(259\) 7.15861e16i 0.915652i
\(260\) −1.67210e16 7.31436e15i −0.208185 0.0910674i
\(261\) 2.44717e16 0.296607
\(262\) 6.68769e16 + 1.39873e16i 0.789164 + 0.165054i
\(263\) 1.32846e17i 1.52636i 0.646187 + 0.763180i \(0.276363\pi\)
−0.646187 + 0.763180i \(0.723637\pi\)
\(264\) 2.18461e15 3.06957e15i 0.0244425 0.0343439i
\(265\) 6.63504e16 0.722973
\(266\) −4.25608e15 + 2.03494e16i −0.0451687 + 0.215963i
\(267\) 1.43652e16i 0.148502i
\(268\) −6.07411e16 + 1.38857e17i −0.611701 + 1.39838i
\(269\) −5.81633e16 −0.570668 −0.285334 0.958428i \(-0.592104\pi\)
−0.285334 + 0.958428i \(0.592104\pi\)
\(270\) −1.01707e16 2.12721e15i −0.0972314 0.0203360i
\(271\) 7.87355e16i 0.733476i 0.930324 + 0.366738i \(0.119525\pi\)
−0.930324 + 0.366738i \(0.880475\pi\)
\(272\) 6.49912e16 + 7.03135e16i 0.590028 + 0.638346i
\(273\) −1.46960e16 −0.130035
\(274\) −1.96411e16 + 9.39091e16i −0.169400 + 0.809942i
\(275\) 6.37048e15i 0.0535604i
\(276\) −1.14464e17 5.00707e16i −0.938223 0.410412i
\(277\) 4.58065e16 0.366074 0.183037 0.983106i \(-0.441407\pi\)
0.183037 + 0.983106i \(0.441407\pi\)
\(278\) −2.36810e17 4.95289e16i −1.84538 0.385962i
\(279\) 5.93489e16i 0.451007i
\(280\) 2.90298e16 + 2.06605e16i 0.215148 + 0.153121i
\(281\) 2.01962e17 1.45991 0.729954 0.683496i \(-0.239541\pi\)
0.729954 + 0.683496i \(0.239541\pi\)
\(282\) 1.57552e16 7.53293e16i 0.111091 0.531154i
\(283\) 1.73138e17i 1.19093i −0.803381 0.595465i \(-0.796968\pi\)
0.803381 0.595465i \(-0.203032\pi\)
\(284\) 3.22411e16 7.37048e16i 0.216362 0.494615i
\(285\) −1.96280e16 −0.128518
\(286\) 4.92431e15 + 1.02992e15i 0.0314618 + 0.00658024i
\(287\) 1.41906e17i 0.884762i
\(288\) −4.69884e16 + 2.81602e16i −0.285919 + 0.171352i
\(289\) −4.11484e16 −0.244382
\(290\) 1.62194e16 7.75490e16i 0.0940262 0.449563i
\(291\) 1.12181e17i 0.634848i
\(292\) −1.31236e17 5.74073e16i −0.725058 0.317166i
\(293\) 2.01914e17 1.08916 0.544582 0.838707i \(-0.316688\pi\)
0.544582 + 0.838707i \(0.316688\pi\)
\(294\) −7.92101e16 1.65668e16i −0.417205 0.0872585i
\(295\) 3.97292e15i 0.0204341i
\(296\) 2.06606e17 2.90300e17i 1.03777 1.45816i
\(297\) 2.86425e15 0.0140513
\(298\) −3.04655e16 + 1.45663e17i −0.145980 + 0.697969i
\(299\) 1.66828e17i 0.780853i
\(300\) 3.71218e16 8.48623e16i 0.169738 0.388030i
\(301\) −9.00771e16 −0.402392
\(302\) 1.36256e17 + 2.84980e16i 0.594713 + 0.124384i
\(303\) 7.51632e16i 0.320558i
\(304\) −7.59902e16 + 7.02383e16i −0.316696 + 0.292724i
\(305\) −8.91419e16 −0.363064
\(306\) −1.49019e16 + 7.12497e16i −0.0593187 + 0.283618i
\(307\) 4.51709e17i 1.75748i −0.477301 0.878740i \(-0.658385\pi\)
0.477301 0.878740i \(-0.341615\pi\)
\(308\) −8.99853e15 3.93628e15i −0.0342229 0.0149703i
\(309\) −1.68977e17 −0.628230
\(310\) 1.88072e17 + 3.93354e16i 0.683586 + 0.142972i
\(311\) 4.92127e17i 1.74886i 0.485152 + 0.874430i \(0.338764\pi\)
−0.485152 + 0.874430i \(0.661236\pi\)
\(312\) −5.95961e16 4.24145e16i −0.207079 0.147378i
\(313\) −5.06792e17 −1.72194 −0.860972 0.508652i \(-0.830144\pi\)
−0.860972 + 0.508652i \(0.830144\pi\)
\(314\) −8.12746e15 + 3.88594e16i −0.0270052 + 0.129119i
\(315\) 2.70880e16i 0.0880243i
\(316\) −3.49019e16 + 7.97875e16i −0.110928 + 0.253586i
\(317\) −1.35753e17 −0.422022 −0.211011 0.977484i \(-0.567676\pi\)
−0.211011 + 0.977484i \(0.567676\pi\)
\(318\) 2.60297e17 + 5.44412e16i 0.791552 + 0.165553i
\(319\) 2.18391e16i 0.0649680i
\(320\) 5.80944e16 + 1.67567e17i 0.169077 + 0.487683i
\(321\) 1.05805e17 0.301279
\(322\) −6.66773e16 + 3.18801e17i −0.185775 + 0.888236i
\(323\) 1.37501e17i 0.374877i
\(324\) −3.81551e16 1.66904e16i −0.101798 0.0445299i
\(325\) 1.23684e17 0.322946
\(326\) 1.96210e17 + 4.10375e16i 0.501417 + 0.104871i
\(327\) 2.53484e17i 0.634040i
\(328\) 4.09557e17 5.75464e17i 1.00276 1.40897i
\(329\) −2.00626e17 −0.480858
\(330\) 1.89837e15 9.07659e15i 0.00445434 0.0212973i
\(331\) 1.13631e17i 0.261036i 0.991446 + 0.130518i \(0.0416640\pi\)
−0.991446 + 0.130518i \(0.958336\pi\)
\(332\) 9.43565e16 2.15704e17i 0.212229 0.485167i
\(333\) 2.70882e17 0.596583
\(334\) 1.87868e17 + 3.92926e16i 0.405161 + 0.0847395i
\(335\) 3.73030e17i 0.787825i
\(336\) 9.69336e16 + 1.04872e17i 0.200493 + 0.216912i
\(337\) 1.63714e17 0.331647 0.165824 0.986155i \(-0.446972\pi\)
0.165824 + 0.986155i \(0.446972\pi\)
\(338\) −8.31799e16 + 3.97704e17i −0.165045 + 0.789120i
\(339\) 4.13996e17i 0.804634i
\(340\) 2.15908e17 + 9.44460e16i 0.411071 + 0.179817i
\(341\) −5.29642e16 −0.0987875
\(342\) −7.70020e16 1.61050e16i −0.140708 0.0294292i
\(343\) 4.96719e17i 0.889308i
\(344\) −3.65286e17 2.59974e17i −0.640802 0.456058i
\(345\) −3.07500e17 −0.528580
\(346\) 3.12333e16 1.49334e17i 0.0526120 0.251551i
\(347\) 6.87073e17i 1.13422i −0.823643 0.567109i \(-0.808062\pi\)
0.823643 0.567109i \(-0.191938\pi\)
\(348\) 1.27260e17 2.90922e17i 0.205890 0.470676i
\(349\) 3.05107e16 0.0483810 0.0241905 0.999707i \(-0.492299\pi\)
0.0241905 + 0.999707i \(0.492299\pi\)
\(350\) −2.36355e17 4.94337e16i −0.367357 0.0768328i
\(351\) 5.56098e16i 0.0847230i
\(352\) −2.51307e16 4.19334e16i −0.0375324 0.0626270i
\(353\) −3.83405e17 −0.561352 −0.280676 0.959803i \(-0.590559\pi\)
−0.280676 + 0.959803i \(0.590559\pi\)
\(354\) 3.25983e15 1.55860e16i 0.00467920 0.0223724i
\(355\) 1.98003e17i 0.278659i
\(356\) −1.70775e17 7.47031e16i −0.235654 0.103083i
\(357\) 1.89761e17 0.256761
\(358\) −8.05601e17 1.68492e17i −1.06890 0.223562i
\(359\) 6.14785e17i 0.799948i −0.916526 0.399974i \(-0.869019\pi\)
0.916526 0.399974i \(-0.130981\pi\)
\(360\) −7.81792e16 + 1.09849e17i −0.0997640 + 0.140177i
\(361\) 6.50404e17 0.814016
\(362\) −4.19649e16 + 2.00645e17i −0.0515141 + 0.246302i
\(363\) 4.76941e17i 0.574273i
\(364\) −7.64234e16 + 1.74708e17i −0.0902644 + 0.206349i
\(365\) −3.52556e17 −0.408487
\(366\) −3.49710e17 7.31419e16i −0.397503 0.0831378i
\(367\) 1.08652e18i 1.21165i 0.795599 + 0.605824i \(0.207156\pi\)
−0.795599 + 0.605824i \(0.792844\pi\)
\(368\) −1.19049e18 + 1.10038e18i −1.30254 + 1.20395i
\(369\) 5.36971e17 0.576457
\(370\) 1.79536e17 8.58405e17i 0.189121 0.904233i
\(371\) 6.93255e17i 0.716598i
\(372\) 7.05545e17 + 3.08631e17i 0.715689 + 0.313068i
\(373\) 1.51836e18 1.51152 0.755760 0.654848i \(-0.227268\pi\)
0.755760 + 0.654848i \(0.227268\pi\)
\(374\) −6.35847e16 1.32988e16i −0.0621229 0.0129930i
\(375\) 5.38749e17i 0.516616i
\(376\) −8.13591e17 5.79032e17i −0.765757 0.544989i
\(377\) 4.24009e17 0.391728
\(378\) −2.22260e16 + 1.06268e17i −0.0201567 + 0.0963740i
\(379\) 8.49805e17i 0.756563i −0.925691 0.378281i \(-0.876515\pi\)
0.925691 0.378281i \(-0.123485\pi\)
\(380\) −1.02071e17 + 2.33340e17i −0.0892108 + 0.203940i
\(381\) −7.84337e17 −0.673020
\(382\) −6.05863e17 1.26716e17i −0.510423 0.106755i
\(383\) 1.02544e18i 0.848244i 0.905605 + 0.424122i \(0.139417\pi\)
−0.905605 + 0.424122i \(0.860583\pi\)
\(384\) 9.04181e16 + 7.05043e17i 0.0734407 + 0.572660i
\(385\) −2.41739e16 −0.0192806
\(386\) 1.34530e17 6.43223e17i 0.105368 0.503791i
\(387\) 3.40852e17i 0.262174i
\(388\) 1.33362e18 + 5.83374e17i 1.00742 + 0.440682i
\(389\) 6.00365e17 0.445419 0.222709 0.974885i \(-0.428510\pi\)
0.222709 + 0.974885i \(0.428510\pi\)
\(390\) −1.76223e17 3.68571e16i −0.128414 0.0268577i
\(391\) 2.15415e18i 1.54183i
\(392\) −6.08862e17 + 8.55505e17i −0.428072 + 0.601478i
\(393\) 6.73987e17 0.465483
\(394\) 3.40179e17 1.62648e18i 0.230799 1.10351i
\(395\) 2.14343e17i 0.142866i
\(396\) 1.48949e16 3.40504e16i 0.00975373 0.0222975i
\(397\) −6.36458e17 −0.409483 −0.204742 0.978816i \(-0.565635\pi\)
−0.204742 + 0.978816i \(0.565635\pi\)
\(398\) 2.86609e18 + 5.99444e17i 1.81179 + 0.378937i
\(399\) 2.05081e17i 0.127384i
\(400\) −8.15807e17 8.82614e17i −0.497929 0.538705i
\(401\) 1.25198e18 0.750907 0.375454 0.926841i \(-0.377487\pi\)
0.375454 + 0.926841i \(0.377487\pi\)
\(402\) −3.06075e17 + 1.46342e18i −0.180404 + 0.862556i
\(403\) 1.02831e18i 0.595645i
\(404\) 8.93547e17 + 3.90869e17i 0.508684 + 0.222516i
\(405\) −1.02501e17 −0.0573512
\(406\) −8.10263e17 1.69467e17i −0.445599 0.0931971i
\(407\) 2.41741e17i 0.130674i
\(408\) 7.69529e17 + 5.47673e17i 0.408887 + 0.291005i
\(409\) −2.66842e18 −1.39377 −0.696885 0.717183i \(-0.745431\pi\)
−0.696885 + 0.717183i \(0.745431\pi\)
\(410\) 3.55895e17 1.70162e18i 0.182740 0.873728i
\(411\) 9.46418e17i 0.477738i
\(412\) −8.78728e17 + 2.00882e18i −0.436088 + 0.996919i
\(413\) −4.15107e16 −0.0202539
\(414\) −1.20634e18 2.52307e17i −0.578720 0.121039i
\(415\) 5.79472e17i 0.273335i
\(416\) −8.14143e17 + 4.87917e17i −0.377614 + 0.226304i
\(417\) −2.38658e18 −1.08849
\(418\) 1.43724e16 6.87183e16i 0.00644609 0.0308204i
\(419\) 3.95429e18i 1.74410i −0.489420 0.872048i \(-0.662791\pi\)
0.489420 0.872048i \(-0.337209\pi\)
\(420\) 3.22024e17 + 1.40865e17i 0.139683 + 0.0611023i
\(421\) −2.93875e18 −1.25368 −0.626842 0.779146i \(-0.715653\pi\)
−0.626842 + 0.779146i \(0.715653\pi\)
\(422\) 2.75862e18 + 5.76966e17i 1.15746 + 0.242082i
\(423\) 7.59171e17i 0.313297i
\(424\) 2.00082e18 2.81133e18i 0.812170 1.14117i
\(425\) −1.59706e18 −0.637672
\(426\) 1.62463e17 7.76778e17i 0.0638099 0.305091i
\(427\) 9.31390e17i 0.359862i
\(428\) 5.50213e17 1.25781e18i 0.209134 0.478091i
\(429\) 4.96273e16 0.0185575
\(430\) −1.08013e18 2.25910e17i −0.397373 0.0831107i
\(431\) 6.89902e16i 0.0249716i 0.999922 + 0.0124858i \(0.00397446\pi\)
−0.999922 + 0.0124858i \(0.996026\pi\)
\(432\) −3.96834e17 + 3.66797e17i −0.141326 + 0.130629i
\(433\) 4.13265e18 1.44815 0.724076 0.689721i \(-0.242267\pi\)
0.724076 + 0.689721i \(0.242267\pi\)
\(434\) 4.10992e17 1.96505e18i 0.141711 0.677558i
\(435\) 7.81540e17i 0.265171i
\(436\) 3.01345e18 + 1.31819e18i 1.00614 + 0.440121i
\(437\) −2.32806e18 −0.764934
\(438\) −1.38310e18 2.89276e17i −0.447234 0.0935392i
\(439\) 1.68057e18i 0.534815i −0.963584 0.267408i \(-0.913833\pi\)
0.963584 0.267408i \(-0.0861670\pi\)
\(440\) −9.80312e16 6.97688e16i −0.0307041 0.0218521i
\(441\) −7.98281e17 −0.246085
\(442\) −2.58197e17 + 1.23451e18i −0.0783422 + 0.374574i
\(443\) 8.49726e17i 0.253777i 0.991917 + 0.126889i \(0.0404991\pi\)
−0.991917 + 0.126889i \(0.959501\pi\)
\(444\) 1.40866e18 3.22027e18i 0.414120 0.946698i
\(445\) −4.58775e17 −0.132764
\(446\) 1.69082e18 + 3.53636e17i 0.481674 + 0.100742i
\(447\) 1.46800e18i 0.411692i
\(448\) 1.75080e18 6.06994e17i 0.483383 0.167586i
\(449\) 2.54692e18 0.692294 0.346147 0.938180i \(-0.387490\pi\)
0.346147 + 0.938180i \(0.387490\pi\)
\(450\) 1.87057e17 8.94367e17i 0.0500595 0.239347i
\(451\) 4.79205e17i 0.126266i
\(452\) −4.92162e18 2.15289e18i −1.27685 0.558539i
\(453\) 1.37319e18 0.350787
\(454\) −2.19751e18 4.59609e17i −0.552763 0.115611i
\(455\) 4.69339e17i 0.116254i
\(456\) −5.91890e17 + 8.31657e17i −0.144373 + 0.202857i
\(457\) −1.34598e18 −0.323316 −0.161658 0.986847i \(-0.551684\pi\)
−0.161658 + 0.986847i \(0.551684\pi\)
\(458\) −1.17797e18 + 5.63215e18i −0.278660 + 1.33234i
\(459\) 7.18056e17i 0.167290i
\(460\) −1.59908e18 + 3.65558e18i −0.366916 + 0.838788i
\(461\) 1.46325e18 0.330683 0.165341 0.986236i \(-0.447127\pi\)
0.165341 + 0.986236i \(0.447127\pi\)
\(462\) −9.48358e16 1.98349e16i −0.0211095 0.00441506i
\(463\) 1.76338e18i 0.386615i −0.981138 0.193308i \(-0.938078\pi\)
0.981138 0.193308i \(-0.0619216\pi\)
\(464\) −2.79672e18 3.02575e18i −0.603981 0.653442i
\(465\) 1.89540e18 0.403208
\(466\) −1.88839e18 + 9.02887e18i −0.395722 + 1.89205i
\(467\) 8.72993e18i 1.80216i 0.433656 + 0.901078i \(0.357223\pi\)
−0.433656 + 0.901078i \(0.642777\pi\)
\(468\) −6.61094e17 2.89186e17i −0.134444 0.0588107i
\(469\) 3.89757e18 0.780879
\(470\) −2.40575e18 5.03164e17i −0.474861 0.0993173i
\(471\) 3.91626e17i 0.0761597i
\(472\) −1.68336e17 1.19805e17i −0.0322540 0.0229552i
\(473\) 3.04184e17 0.0574259
\(474\) −1.75871e17 + 8.40883e17i −0.0327149 + 0.156418i
\(475\) 1.72599e18i 0.316362i
\(476\) 9.86809e17 2.25590e18i 0.178232 0.407446i
\(477\) 2.62328e18 0.466891
\(478\) 7.88896e18 + 1.64998e18i 1.38365 + 0.289390i
\(479\) 1.82595e18i 0.315603i −0.987471 0.157801i \(-0.949559\pi\)
0.987471 0.157801i \(-0.0504406\pi\)
\(480\) 8.99337e17 + 1.50064e18i 0.153191 + 0.255617i
\(481\) 4.69343e18 0.787907
\(482\) −2.13106e17 + 1.01891e18i −0.0352587 + 0.168581i
\(483\) 3.21288e18i 0.523920i
\(484\) −5.66991e18 2.48022e18i −0.911295 0.398633i
\(485\) 3.58268e18 0.567565
\(486\) −4.02118e17 8.41032e16i −0.0627914 0.0131328i
\(487\) 1.22367e19i 1.88349i −0.336329 0.941745i \(-0.609185\pi\)
0.336329 0.941745i \(-0.390815\pi\)
\(488\) −2.68810e18 + 3.77702e18i −0.407856 + 0.573074i
\(489\) 1.97741e18 0.295757
\(490\) −5.29086e17 + 2.52969e18i −0.0780106 + 0.372988i
\(491\) 2.33384e17i 0.0339235i 0.999856 + 0.0169617i \(0.00539935\pi\)
−0.999856 + 0.0169617i \(0.994601\pi\)
\(492\) 2.79240e18 6.38356e18i 0.400149 0.914761i
\(493\) −5.47497e18 −0.773488
\(494\) −1.33417e18 2.79043e17i −0.185833 0.0388671i
\(495\) 9.14740e16i 0.0125621i
\(496\) 7.33806e18 6.78262e18i 0.993595 0.918387i
\(497\) −2.06881e18 −0.276201
\(498\) 4.75463e17 2.27331e18i 0.0625910 0.299263i
\(499\) 1.34709e19i 1.74860i −0.485382 0.874302i \(-0.661320\pi\)
0.485382 0.874302i \(-0.338680\pi\)
\(500\) −6.40470e18 2.80165e18i −0.819802 0.358611i
\(501\) 1.89334e18 0.238981
\(502\) −7.92012e18 1.65650e18i −0.985839 0.206188i
\(503\) 5.59052e18i 0.686240i 0.939292 + 0.343120i \(0.111484\pi\)
−0.939292 + 0.343120i \(0.888516\pi\)
\(504\) 1.14774e18 + 8.16847e17i 0.138941 + 0.0988843i
\(505\) 2.40045e18 0.286584
\(506\) 2.25164e17 1.07657e18i 0.0265122 0.126761i
\(507\) 4.00807e18i 0.465457i
\(508\) −4.07877e18 + 9.32427e18i −0.467179 + 1.06799i
\(509\) −1.05635e19 −1.19339 −0.596697 0.802466i \(-0.703521\pi\)
−0.596697 + 0.802466i \(0.703521\pi\)
\(510\) 2.27546e18 + 4.75914e17i 0.253559 + 0.0530319i
\(511\) 3.68364e18i 0.404885i
\(512\) 8.85181e18 + 2.59152e18i 0.959716 + 0.280973i
\(513\) −7.76028e17 −0.0829958
\(514\) 1.67668e18 8.01661e18i 0.176892 0.845763i
\(515\) 5.39654e18i 0.561649i
\(516\) −4.05208e18 1.77252e18i −0.416035 0.181989i
\(517\) 6.77500e17 0.0686239
\(518\) −8.96896e18 1.87586e18i −0.896259 0.187453i
\(519\) 1.50499e18i 0.148376i
\(520\) −1.35457e18 + 1.90329e18i −0.131758 + 0.185132i
\(521\) −8.20022e18 −0.786976 −0.393488 0.919330i \(-0.628732\pi\)
−0.393488 + 0.919330i \(0.628732\pi\)
\(522\) 6.41263e17 3.06604e18i 0.0607215 0.290325i
\(523\) 1.36598e19i 1.27624i 0.769936 + 0.638121i \(0.220288\pi\)
−0.769936 + 0.638121i \(0.779712\pi\)
\(524\) 3.50492e18 8.01242e18i 0.323116 0.738660i
\(525\) −2.38199e18 −0.216683
\(526\) 1.66441e19 + 3.48112e18i 1.49403 + 0.312477i
\(527\) 1.32779e19i 1.17613i
\(528\) −3.27337e17 3.54143e17i −0.0286126 0.0309558i
\(529\) −2.48794e19 −2.14610
\(530\) 1.73866e18 8.31297e18i 0.148008 0.707661i
\(531\) 1.57076e17i 0.0131962i
\(532\) 2.43803e18 + 1.06648e18i 0.202142 + 0.0884242i
\(533\) 9.30382e18 0.761326
\(534\) −1.79980e18 3.76430e17i −0.145357 0.0304015i
\(535\) 3.37903e18i 0.269349i
\(536\) 1.58056e19 + 1.12488e19i 1.24353 + 0.885023i
\(537\) −8.11886e18 −0.630485
\(538\) −1.52413e18 + 7.28722e18i −0.116827 + 0.558581i
\(539\) 7.12402e17i 0.0539019i
\(540\) −5.33033e17 + 1.21854e18i −0.0398105 + 0.0910089i
\(541\) 1.34807e19 0.993876 0.496938 0.867786i \(-0.334458\pi\)
0.496938 + 0.867786i \(0.334458\pi\)
\(542\) 9.86470e18 + 2.06320e18i 0.717941 + 0.150158i
\(543\) 2.02210e18i 0.145279i
\(544\) 1.05125e19 6.30018e18i 0.745617 0.446849i
\(545\) 8.09540e18 0.566843
\(546\) −3.85098e17 + 1.84125e18i −0.0266209 + 0.127281i
\(547\) 2.44729e19i 1.67022i 0.550080 + 0.835112i \(0.314597\pi\)
−0.550080 + 0.835112i \(0.685403\pi\)
\(548\) 1.12511e19 + 4.92163e18i 0.758108 + 0.331623i
\(549\) −3.52438e18 −0.234464
\(550\) 7.98152e17 + 1.66934e17i 0.0524260 + 0.0109649i
\(551\) 5.91699e18i 0.383742i
\(552\) −9.27276e18 + 1.30290e19i −0.593794 + 0.834332i
\(553\) 2.23954e18 0.141607
\(554\) 1.20032e18 5.73905e18i 0.0749428 0.358320i
\(555\) 8.65102e18i 0.533355i
\(556\) −1.24108e19 + 2.83718e19i −0.755576 + 1.72728i
\(557\) 3.42126e18 0.205683 0.102842 0.994698i \(-0.467206\pi\)
0.102842 + 0.994698i \(0.467206\pi\)
\(558\) 7.43577e18 + 1.55519e18i 0.441455 + 0.0923304i
\(559\) 5.90577e18i 0.346253i
\(560\) 3.34923e18 3.09572e18i 0.193923 0.179244i
\(561\) −6.40808e17 −0.0366427
\(562\) 5.29226e18 2.53036e19i 0.298873 1.42899i
\(563\) 1.43757e19i 0.801808i 0.916120 + 0.400904i \(0.131304\pi\)
−0.916120 + 0.400904i \(0.868696\pi\)
\(564\) −9.02509e18 3.94790e18i −0.497162 0.217476i
\(565\) −1.32216e19 −0.719356
\(566\) −2.16922e19 4.53694e18i −1.16571 0.243808i
\(567\) 1.07097e18i 0.0568455i
\(568\) −8.38955e18 5.97084e18i −0.439846 0.313038i
\(569\) 8.31630e18 0.430670 0.215335 0.976540i \(-0.430916\pi\)
0.215335 + 0.976540i \(0.430916\pi\)
\(570\) −5.14337e17 + 2.45917e18i −0.0263102 + 0.125796i
\(571\) 1.44832e19i 0.731834i 0.930647 + 0.365917i \(0.119245\pi\)
−0.930647 + 0.365917i \(0.880755\pi\)
\(572\) 2.58076e17 5.89974e17i 0.0128818 0.0294483i
\(573\) −6.10589e18 −0.301070
\(574\) −1.77792e19 3.71853e18i −0.866023 0.181129i
\(575\) 2.70401e19i 1.30117i
\(576\) 2.29687e18 + 6.62505e18i 0.109189 + 0.314943i
\(577\) 1.78526e19 0.838435 0.419218 0.907886i \(-0.362304\pi\)
0.419218 + 0.907886i \(0.362304\pi\)
\(578\) −1.07826e18 + 5.15545e18i −0.0500299 + 0.239206i
\(579\) 6.48242e18i 0.297158i
\(580\) −9.29102e18 4.06423e18i −0.420792 0.184070i
\(581\) −6.05456e18 −0.270925
\(582\) 1.40551e19 + 2.93963e18i 0.621402 + 0.129967i
\(583\) 2.34107e18i 0.102267i
\(584\) −1.06314e19 + 1.49381e19i −0.458883 + 0.644771i
\(585\) −1.77598e18 −0.0757438
\(586\) 5.29101e18 2.52976e19i 0.222974 1.06610i
\(587\) 8.73511e18i 0.363749i 0.983322 + 0.181874i \(0.0582165\pi\)
−0.983322 + 0.181874i \(0.941784\pi\)
\(588\) −4.15128e18 + 9.49003e18i −0.170821 + 0.390505i
\(589\) 1.43499e19 0.583502
\(590\) −4.97763e17 1.04107e17i −0.0200013 0.00418328i
\(591\) 1.63917e19i 0.650896i
\(592\) −3.09574e19 3.34926e19i −1.21482 1.31431i
\(593\) 2.36193e19 0.915974 0.457987 0.888959i \(-0.348571\pi\)
0.457987 + 0.888959i \(0.348571\pi\)
\(594\) 7.50554e16 3.58859e17i 0.00287658 0.0137537i
\(595\) 6.06030e18i 0.229549i
\(596\) 1.74517e19 + 7.63399e18i 0.653301 + 0.285777i
\(597\) 2.88845e19 1.06867
\(598\) −2.09017e19 4.37159e18i −0.764315 0.159857i
\(599\) 2.83926e19i 1.02616i −0.858340 0.513082i \(-0.828504\pi\)
0.858340 0.513082i \(-0.171496\pi\)
\(600\) −9.65956e18 6.87470e18i −0.345063 0.245581i
\(601\) −1.27318e19 −0.449542 −0.224771 0.974412i \(-0.572163\pi\)
−0.224771 + 0.974412i \(0.572163\pi\)
\(602\) −2.36040e18 + 1.12857e19i −0.0823779 + 0.393869i
\(603\) 1.47484e19i 0.508772i
\(604\) 7.14097e18 1.63246e19i 0.243500 0.556653i
\(605\) −1.52318e19 −0.513409
\(606\) 9.41712e18 + 1.96959e18i 0.313769 + 0.0656248i
\(607\) 5.47340e18i 0.180275i −0.995929 0.0901377i \(-0.971269\pi\)
0.995929 0.0901377i \(-0.0287307\pi\)
\(608\) 6.80882e18 + 1.13613e19i 0.221690 + 0.369915i
\(609\) −8.16585e18 −0.262833
\(610\) −2.33590e18 + 1.11685e19i −0.0743266 + 0.355374i
\(611\) 1.31537e19i 0.413772i
\(612\) 8.53631e18 + 3.73409e18i 0.265467 + 0.116125i
\(613\) 2.99704e19 0.921445 0.460722 0.887544i \(-0.347590\pi\)
0.460722 + 0.887544i \(0.347590\pi\)
\(614\) −5.65942e19 1.18367e19i −1.72026 0.359792i
\(615\) 1.71490e19i 0.515362i
\(616\) −7.28972e17 + 1.02427e18i −0.0216594 + 0.0304333i
\(617\) 3.07296e19 0.902736 0.451368 0.892338i \(-0.350936\pi\)
0.451368 + 0.892338i \(0.350936\pi\)
\(618\) −4.42792e18 + 2.11710e19i −0.128612 + 0.614925i
\(619\) 2.87760e19i 0.826411i 0.910638 + 0.413205i \(0.135591\pi\)
−0.910638 + 0.413205i \(0.864409\pi\)
\(620\) 9.85658e18 2.25326e19i 0.279888 0.639838i
\(621\) −1.21575e19 −0.341354
\(622\) 6.16582e19 + 1.28958e19i 1.71182 + 0.358027i
\(623\) 4.79346e18i 0.131593i
\(624\) −6.87574e18 + 6.35530e18i −0.186650 + 0.172522i
\(625\) 1.01221e19 0.271714
\(626\) −1.32801e19 + 6.34954e19i −0.352517 + 1.68547i
\(627\) 6.92544e17i 0.0181792i
\(628\) 4.65568e18 + 2.03656e18i 0.120855 + 0.0528665i
\(629\) −6.06035e19 −1.55576
\(630\) 3.39383e18 + 7.09820e17i 0.0861600 + 0.0180204i
\(631\) 3.32565e19i 0.834969i 0.908684 + 0.417485i \(0.137088\pi\)
−0.908684 + 0.417485i \(0.862912\pi\)
\(632\) 9.08192e18 + 6.46360e18i 0.225506 + 0.160492i
\(633\) 2.78014e19 0.682717
\(634\) −3.55731e18 + 1.70084e19i −0.0863966 + 0.413084i
\(635\) 2.50490e19i 0.601691i
\(636\) 1.36418e19 3.11858e19i 0.324094 0.740895i
\(637\) −1.38314e19 −0.325005
\(638\) 2.73620e18 + 5.72276e17i 0.0635920 + 0.0133003i
\(639\) 7.82838e18i 0.179956i
\(640\) 2.25166e19 2.88764e18i 0.511968 0.0656573i
\(641\) −5.79342e19 −1.30295 −0.651477 0.758668i \(-0.725850\pi\)
−0.651477 + 0.758668i \(0.725850\pi\)
\(642\) 2.77253e18 1.32562e19i 0.0616781 0.294898i
\(643\) 4.06293e19i 0.894052i 0.894521 + 0.447026i \(0.147517\pi\)
−0.894521 + 0.447026i \(0.852483\pi\)
\(644\) 3.81950e19 + 1.67079e19i 0.831391 + 0.363680i
\(645\) −1.08856e19 −0.234388
\(646\) 1.72274e19 + 3.60312e18i 0.366937 + 0.0767451i
\(647\) 4.19383e19i 0.883651i 0.897101 + 0.441825i \(0.145669\pi\)
−0.897101 + 0.441825i \(0.854331\pi\)
\(648\) −3.09095e18 + 4.34306e18i −0.0644269 + 0.0905254i
\(649\) 1.40178e17 0.00289047
\(650\) 3.24104e18 1.54962e19i 0.0661136 0.316106i
\(651\) 1.98039e19i 0.399653i
\(652\) 1.02831e19 2.35077e19i 0.205301 0.469328i
\(653\) −2.43906e19 −0.481760 −0.240880 0.970555i \(-0.577436\pi\)
−0.240880 + 0.970555i \(0.577436\pi\)
\(654\) 3.17588e19 + 6.64236e18i 0.620612 + 0.129801i
\(655\) 2.15248e19i 0.416150i
\(656\) −6.13671e19 6.63926e19i −1.17384 1.26997i
\(657\) −1.39389e19 −0.263798
\(658\) −5.25726e18 + 2.51363e19i −0.0984415 + 0.470674i
\(659\) 2.47690e19i 0.458891i 0.973321 + 0.229446i \(0.0736913\pi\)
−0.973321 + 0.229446i \(0.926309\pi\)
\(660\) −1.08745e18 4.75690e17i −0.0199344 0.00872000i
\(661\) −1.08965e19 −0.197642 −0.0988208 0.995105i \(-0.531507\pi\)
−0.0988208 + 0.995105i \(0.531507\pi\)
\(662\) 1.42367e19 + 2.97761e18i 0.255507 + 0.0534394i
\(663\) 1.24414e19i 0.220940i
\(664\) −2.45528e19 1.74742e19i −0.431443 0.307058i
\(665\) 6.54958e18 0.113884
\(666\) 7.09826e18 3.39385e19i 0.122133 0.583947i
\(667\) 9.26978e19i 1.57830i
\(668\) 9.84587e18 2.25082e19i 0.165890 0.379232i
\(669\) 1.70401e19 0.284112
\(670\) 4.67366e19 + 9.77496e18i 0.771140 + 0.161284i
\(671\) 3.14523e18i 0.0513565i
\(672\) 1.56793e19 9.39663e18i 0.253363 0.151840i
\(673\) −3.49979e19 −0.559675 −0.279838 0.960047i \(-0.590281\pi\)
−0.279838 + 0.960047i \(0.590281\pi\)
\(674\) 4.29000e18 2.05116e19i 0.0678950 0.324623i
\(675\) 9.01344e18i 0.141177i
\(676\) 4.76483e19 + 2.08430e19i 0.738618 + 0.323098i
\(677\) 2.72380e18 0.0417882 0.0208941 0.999782i \(-0.493349\pi\)
0.0208941 + 0.999782i \(0.493349\pi\)
\(678\) −5.18691e19 1.08484e19i −0.787592 0.164725i
\(679\) 3.74333e19i 0.562561i
\(680\) 1.74908e19 2.45760e19i 0.260163 0.365552i
\(681\) −2.21465e19 −0.326043
\(682\) −1.38789e18 + 6.63584e18i −0.0202238 + 0.0966952i
\(683\) 1.07215e20i 1.54636i −0.634188 0.773179i \(-0.718665\pi\)
0.634188 0.773179i \(-0.281335\pi\)
\(684\) −4.03556e18 + 9.22549e18i −0.0576117 + 0.131703i
\(685\) 3.02253e19 0.427106
\(686\) 6.22335e19 + 1.30162e19i 0.870473 + 0.182060i
\(687\) 5.67609e19i 0.785872i
\(688\) −4.21439e19 + 3.89539e19i −0.577584 + 0.533865i
\(689\) 4.54522e19 0.616624
\(690\) −8.05780e18 + 3.85263e19i −0.108211 + 0.517385i
\(691\) 3.15507e19i 0.419434i −0.977762 0.209717i \(-0.932746\pi\)
0.977762 0.209717i \(-0.0672542\pi\)
\(692\) −1.78915e19 7.82638e18i −0.235453 0.102995i
\(693\) −9.55757e17 −0.0124513
\(694\) −8.60827e19 1.80042e19i −1.11020 0.232198i
\(695\) 7.62188e19i 0.973125i
\(696\) −3.31146e19 2.35676e19i −0.418557 0.297887i
\(697\) −1.20135e20 −1.50328
\(698\) 7.99510e17 3.82266e18i 0.00990458 0.0473563i
\(699\) 9.09931e19i 1.11601i
\(700\) −1.23870e19 + 2.83173e19i −0.150411 + 0.343847i
\(701\) 1.08018e19 0.129859 0.0649295 0.997890i \(-0.479318\pi\)
0.0649295 + 0.997890i \(0.479318\pi\)
\(702\) −6.96729e18 1.45721e18i −0.0829286 0.0173445i
\(703\) 6.54963e19i 0.771844i
\(704\) −5.91233e18 + 2.04977e18i −0.0689843 + 0.0239165i
\(705\) −2.42452e19 −0.280093
\(706\) −1.00468e19 + 4.80365e19i −0.114920 + 0.549463i
\(707\) 2.50808e19i 0.284057i
\(708\) −1.86734e18 8.16841e17i −0.0209407 0.00916019i
\(709\) −2.65544e19 −0.294857 −0.147429 0.989073i \(-0.547100\pi\)
−0.147429 + 0.989073i \(0.547100\pi\)
\(710\) −2.48075e19 5.18851e18i −0.272757 0.0570471i
\(711\) 8.47444e18i 0.0922622i
\(712\) −1.38345e19 + 1.94387e19i −0.149143 + 0.209559i
\(713\) 2.24811e20 2.39989
\(714\) 4.97254e18 2.37750e19i 0.0525643 0.251323i
\(715\) 1.58492e18i 0.0165907i
\(716\) −4.22203e19 + 9.65177e19i −0.437653 + 1.00050i
\(717\) 7.95051e19 0.816133
\(718\) −7.70258e19 1.61100e19i −0.783006 0.163766i
\(719\) 7.59497e19i 0.764581i 0.924042 + 0.382291i \(0.124865\pi\)
−0.924042 + 0.382291i \(0.875135\pi\)
\(720\) 1.17142e19 + 1.26735e19i 0.116784 + 0.126348i
\(721\) 5.63852e19 0.556696
\(722\) 1.70433e19 8.14885e19i 0.166646 0.796776i
\(723\) 1.02686e19i 0.0994360i
\(724\) 2.40389e19 + 1.05155e19i 0.230539 + 0.100846i
\(725\) 6.87249e19 0.652752
\(726\) −5.97554e19 1.24979e19i −0.562110 0.117565i
\(727\) 2.39540e19i 0.223171i 0.993755 + 0.111586i \(0.0355929\pi\)
−0.993755 + 0.111586i \(0.964407\pi\)
\(728\) 1.98863e19 + 1.41531e19i 0.183500 + 0.130596i
\(729\) −4.05256e18 −0.0370370
\(730\) −9.23846e18 + 4.41714e19i −0.0836256 + 0.399835i
\(731\) 7.62576e19i 0.683694i
\(732\) −1.83278e19 + 4.18982e19i −0.162754 + 0.372064i
\(733\) 1.74351e20 1.53355 0.766774 0.641918i \(-0.221861\pi\)
0.766774 + 0.641918i \(0.221861\pi\)
\(734\) 1.36129e20 + 2.84715e19i 1.18599 + 0.248049i
\(735\) 2.54943e19i 0.220004i
\(736\) 1.06670e20 + 1.77990e20i 0.911792 + 1.52143i
\(737\) −1.31618e19 −0.111440
\(738\) 1.40709e19 6.72766e19i 0.118013 0.564247i
\(739\) 1.29448e20i 1.07544i −0.843124 0.537719i \(-0.819286\pi\)
0.843124 0.537719i \(-0.180714\pi\)
\(740\) −1.02844e20 4.49877e19i −0.846364 0.370230i
\(741\) −1.34458e19 −0.109613
\(742\) −8.68573e19 1.81662e19i −0.701421 0.146702i
\(743\) 4.21533e19i 0.337217i −0.985683 0.168609i \(-0.946073\pi\)
0.985683 0.168609i \(-0.0539274\pi\)
\(744\) 5.71563e19 8.03096e19i 0.452954 0.636440i
\(745\) 4.68826e19 0.368060
\(746\) 3.97876e19 1.90234e20i 0.309439 1.47951i
\(747\) 2.29105e19i 0.176518i
\(748\) −3.33238e18 + 7.61799e18i −0.0254357 + 0.0581472i
\(749\) −3.53054e19 −0.266974
\(750\) −6.74994e19 1.41175e19i −0.505674 0.105762i
\(751\) 9.37893e19i 0.696103i 0.937475 + 0.348052i \(0.113157\pi\)
−0.937475 + 0.348052i \(0.886843\pi\)
\(752\) −9.38659e19 + 8.67609e19i −0.690213 + 0.637968i
\(753\) −7.98192e19 −0.581490
\(754\) 1.11108e19 5.31236e19i 0.0801949 0.383432i
\(755\) 4.38549e19i 0.313610i
\(756\) 1.27318e19 + 5.56934e18i 0.0902064 + 0.0394595i
\(757\) −1.92048e20 −1.34815 −0.674075 0.738663i \(-0.735457\pi\)
−0.674075 + 0.738663i \(0.735457\pi\)
\(758\) −1.06471e20 2.22685e19i −0.740539 0.154884i
\(759\) 1.08496e19i 0.0747693i
\(760\) 2.65602e19 + 1.89029e19i 0.181358 + 0.129072i
\(761\) −1.72126e20 −1.16454 −0.582269 0.812996i \(-0.697835\pi\)
−0.582269 + 0.812996i \(0.697835\pi\)
\(762\) −2.05530e19 + 9.82688e19i −0.137781 + 0.658766i
\(763\) 8.45840e19i 0.561845i
\(764\) −3.17523e19 + 7.25874e19i −0.208988 + 0.477758i
\(765\) 2.29322e19 0.149560
\(766\) 1.28477e20 + 2.68710e19i 0.830278 + 0.173653i
\(767\) 2.72158e18i 0.0174282i
\(768\) 9.07035e19 + 7.14672e18i 0.575566 + 0.0453501i
\(769\) −2.90260e19 −0.182517 −0.0912585 0.995827i \(-0.529089\pi\)
−0.0912585 + 0.995827i \(0.529089\pi\)
\(770\) −6.33458e17 + 3.02872e18i −0.00394714 + 0.0188723i
\(771\) 8.07915e19i 0.498867i
\(772\) −7.70636e19 3.37104e19i −0.471550 0.206273i
\(773\) −1.24192e20 −0.753072 −0.376536 0.926402i \(-0.622885\pi\)
−0.376536 + 0.926402i \(0.622885\pi\)
\(774\) −4.27050e19 8.93177e18i −0.256621 0.0536724i
\(775\) 1.66672e20i 0.992546i
\(776\) 1.08037e20 1.51801e20i 0.637588 0.895867i
\(777\) −9.03893e19 −0.528652
\(778\) 1.57321e19 7.52192e19i 0.0911863 0.435985i
\(779\) 1.29834e20i 0.745805i
\(780\) −9.23559e18 + 2.11130e19i −0.0525778 + 0.120195i
\(781\) 6.98621e18 0.0394171
\(782\) 2.69891e20 + 5.64477e19i 1.50918 + 0.315645i
\(783\) 3.08996e19i 0.171246i
\(784\) 9.12306e19 + 9.87016e19i 0.501104 + 0.542140i
\(785\) 1.25072e19 0.0680881
\(786\) 1.76613e19 8.44432e19i 0.0952939 0.455624i
\(787\) 1.78948e20i 0.956982i −0.878092 0.478491i \(-0.841184\pi\)
0.878092 0.478491i \(-0.158816\pi\)
\(788\) −1.94866e20 8.52413e19i −1.03289 0.451821i
\(789\) 1.67739e20 0.881244
\(790\) 2.68549e19 + 5.61670e18i 0.139841 + 0.0292477i
\(791\) 1.38144e20i 0.713013i
\(792\) −3.87584e18 2.75843e18i −0.0198285 0.0141119i
\(793\) −6.10651e19 −0.309657
\(794\) −1.66779e19 + 7.97412e19i −0.0838297 + 0.400811i
\(795\) 8.37783e19i 0.417409i
\(796\) 1.50207e20 3.43382e20i 0.741822 1.69584i
\(797\) −2.76149e20 −1.35187 −0.675936 0.736961i \(-0.736260\pi\)
−0.675936 + 0.736961i \(0.736260\pi\)
\(798\) 2.56944e19 + 5.37400e18i 0.124686 + 0.0260782i
\(799\) 1.69847e20i 0.817014i
\(800\) −1.31959e20 + 7.90834e19i −0.629232 + 0.377099i
\(801\) −1.81385e19 −0.0857379
\(802\) 3.28071e19 1.56859e20i 0.153726 0.735003i
\(803\) 1.24394e19i 0.0577817i
\(804\) 1.75330e20 + 7.66957e19i 0.807355 + 0.353166i
\(805\) 1.02608e20 0.468393
\(806\) 1.28836e20 + 2.69460e19i 0.583030 + 0.121941i
\(807\) 7.34408e19i 0.329475i
\(808\) 7.23863e19 1.01709e20i 0.321942 0.452356i
\(809\) 1.62231e20 0.715308 0.357654 0.933854i \(-0.383577\pi\)
0.357654 + 0.933854i \(0.383577\pi\)
\(810\) −2.68596e18 + 1.28422e19i −0.0117410 + 0.0561366i
\(811\) 3.71751e20i 1.61104i 0.592568 + 0.805521i \(0.298114\pi\)
−0.592568 + 0.805521i \(0.701886\pi\)
\(812\) −4.24647e19 + 9.70763e19i −0.182446 + 0.417082i
\(813\) 9.94166e19 0.423472
\(814\) 3.02875e19 + 6.33463e18i 0.127906 + 0.0267517i
\(815\) 6.31516e19i 0.264412i
\(816\) 8.87823e19 8.20622e19i 0.368549 0.340653i
\(817\) −8.24143e19 −0.339194
\(818\) −6.99239e19 + 3.34324e20i −0.285334 + 1.36425i
\(819\) 1.85562e19i 0.0750759i
\(820\) −2.03869e20 8.91794e19i −0.817812 0.357740i
\(821\) −3.82848e20 −1.52274 −0.761368 0.648320i \(-0.775472\pi\)
−0.761368 + 0.648320i \(0.775472\pi\)
\(822\) 1.18576e20 + 2.48002e19i 0.467620 + 0.0978029i
\(823\) 2.71424e19i 0.106133i −0.998591 0.0530663i \(-0.983101\pi\)
0.998591 0.0530663i \(-0.0168995\pi\)
\(824\) 2.28656e20 + 1.62735e20i 0.886528 + 0.630942i
\(825\) 8.04379e18 0.0309231
\(826\) −1.08776e18 + 5.20083e18i −0.00414640 + 0.0198250i
\(827\) 2.43731e20i 0.921240i 0.887597 + 0.460620i \(0.152373\pi\)
−0.887597 + 0.460620i \(0.847627\pi\)
\(828\) −6.32226e19 + 1.44530e20i −0.236952 + 0.541683i
\(829\) 1.75101e20 0.650740 0.325370 0.945587i \(-0.394511\pi\)
0.325370 + 0.945587i \(0.394511\pi\)
\(830\) −7.26015e19 1.51846e19i −0.267546 0.0559574i
\(831\) 5.78382e19i 0.211353i
\(832\) 3.97966e19 + 1.14789e20i 0.144206 + 0.415945i
\(833\) 1.78597e20 0.641738
\(834\) −6.25384e19 + 2.99012e20i −0.222835 + 1.06543i
\(835\) 6.04665e19i 0.213653i
\(836\) −8.23302e18 3.60142e18i −0.0288480 0.0126191i
\(837\) 7.49378e19 0.260389
\(838\) −4.95429e20 1.03619e20i −1.70716 0.357052i
\(839\) 3.16749e20i 1.08238i 0.840899 + 0.541192i \(0.182027\pi\)
−0.840899 + 0.541192i \(0.817973\pi\)
\(840\) 2.60872e19 3.66549e19i 0.0884042 0.124216i
\(841\) −6.19578e19 −0.208221
\(842\) −7.70078e19 + 3.68193e20i −0.256655 + 1.22713i
\(843\) 2.55011e20i 0.842879i
\(844\) 1.44575e20 3.30506e20i 0.473910 1.08338i
\(845\) 1.28004e20 0.416126
\(846\) −9.51157e19 1.98935e19i −0.306662 0.0641384i
\(847\) 1.59148e20i 0.508882i
\(848\) −2.99798e20 3.24349e20i −0.950732 1.02859i
\(849\) −2.18615e20 −0.687584
\(850\) −4.18496e19 + 2.00093e20i −0.130545 + 0.624167i
\(851\) 1.02609e21i 3.17452i
\(852\) −9.30645e19 4.07097e19i −0.285566 0.124917i
\(853\) 5.23738e20 1.59394 0.796968 0.604021i \(-0.206436\pi\)
0.796968 + 0.604021i \(0.206436\pi\)
\(854\) 1.16693e20 + 2.44064e19i 0.352241 + 0.0736712i
\(855\) 2.47836e19i 0.0741996i
\(856\) −1.43172e20 1.01896e20i −0.425151 0.302580i
\(857\) 5.14937e20 1.51666 0.758330 0.651871i \(-0.226016\pi\)
0.758330 + 0.651871i \(0.226016\pi\)
\(858\) 1.30045e18 6.21776e18i 0.00379911 0.0181645i
\(859\) 1.34780e19i 0.0390546i 0.999809 + 0.0195273i \(0.00621612\pi\)
−0.999809 + 0.0195273i \(0.993784\pi\)
\(860\) −5.66082e19 + 1.29409e20i −0.162701 + 0.371943i
\(861\) −1.79179e20 −0.510818
\(862\) 8.64372e18 + 1.80784e18i 0.0244427 + 0.00511220i
\(863\) 1.69934e20i 0.476655i −0.971185 0.238327i \(-0.923401\pi\)
0.971185 0.238327i \(-0.0765991\pi\)
\(864\) 3.55569e19 + 5.93306e19i 0.0989299 + 0.165076i
\(865\) −4.80642e19 −0.132650
\(866\) 1.08293e20 5.17776e20i 0.296466 1.41748i
\(867\) 5.19567e19i 0.141094i
\(868\) −2.35430e20 1.02985e20i −0.634196 0.277420i
\(869\) −7.56277e18 −0.0202089
\(870\) −9.79184e19 2.04797e19i −0.259555 0.0542860i
\(871\) 2.55538e20i 0.671936i
\(872\) 2.44120e20 3.43009e20i 0.636777 0.894727i
\(873\) 1.41648e20 0.366530
\(874\) −6.10050e19 + 2.91680e20i −0.156598 + 0.748733i
\(875\) 1.79773e20i 0.457791i
\(876\) −7.24862e19 + 1.65707e20i −0.183116 + 0.418613i
\(877\) −2.95602e20 −0.740815 −0.370408 0.928869i \(-0.620782\pi\)
−0.370408 + 0.928869i \(0.620782\pi\)
\(878\) −2.10556e20 4.40379e19i −0.523488 0.109488i
\(879\) 2.54950e20i 0.628829i
\(880\) −1.13101e19 + 1.04540e19i −0.0276750 + 0.0255802i
\(881\) 3.77738e20 0.916980 0.458490 0.888700i \(-0.348391\pi\)
0.458490 + 0.888700i \(0.348391\pi\)
\(882\) −2.09183e19 + 1.00016e20i −0.0503787 + 0.240873i
\(883\) 9.48860e19i 0.226713i −0.993554 0.113357i \(-0.963840\pi\)
0.993554 0.113357i \(-0.0361603\pi\)
\(884\) 1.47904e20 + 6.46986e19i 0.350602 + 0.153366i
\(885\) −5.01647e18 −0.0117976
\(886\) 1.06461e20 + 2.22664e19i 0.248403 + 0.0519535i
\(887\) 5.81775e20i 1.34676i −0.739297 0.673379i \(-0.764842\pi\)
0.739297 0.673379i \(-0.235158\pi\)
\(888\) −3.66552e20 2.60875e20i −0.841869 0.599157i
\(889\) 2.61722e20 0.596386
\(890\) −1.20218e19 + 5.74794e19i −0.0271795 + 0.129952i
\(891\) 3.61659e18i 0.00811250i
\(892\) 8.86133e19 2.02574e20i 0.197217 0.450849i
\(893\) −1.83559e20 −0.405337
\(894\) 1.83924e20 + 3.84677e19i 0.402972 + 0.0842818i
\(895\) 2.59288e20i 0.563665i
\(896\) −3.01712e19 2.35262e20i −0.0650783 0.507454i
\(897\) −2.10647e20 −0.450826
\(898\) 6.67401e19 3.19101e20i 0.141727 0.677632i
\(899\) 5.71379e20i 1.20395i
\(900\) −1.07153e20 4.68724e19i −0.224030 0.0979985i
\(901\) −5.86897e20 −1.21755
\(902\) 6.00391e19 + 1.25572e19i 0.123591 + 0.0258492i
\(903\) 1.13737e20i 0.232321i
\(904\) −3.98701e20 + 5.60210e20i −0.808106 + 1.13546i
\(905\) 6.45788e19 0.129882
\(906\) 3.59834e19 1.72046e20i 0.0718134 0.343358i
\(907\) 1.49722e20i 0.296506i −0.988949 0.148253i \(-0.952635\pi\)
0.988949 0.148253i \(-0.0473650\pi\)
\(908\) −1.15168e20 + 2.63280e20i −0.226324 + 0.517388i
\(909\) 9.49059e19 0.185074
\(910\) 5.88030e19 + 1.22987e19i 0.113792 + 0.0237995i
\(911\) 3.99678e20i 0.767506i 0.923436 + 0.383753i \(0.125369\pi\)
−0.923436 + 0.383753i \(0.874631\pi\)
\(912\) 8.86875e19 + 9.59502e19i 0.169005 + 0.182845i
\(913\) 2.04458e19 0.0386641
\(914\) −3.52705e19 + 1.68637e20i −0.0661894 + 0.316468i
\(915\) 1.12556e20i 0.209615i
\(916\) 6.74779e20 + 2.95172e20i 1.24708 + 0.545516i
\(917\) −2.24899e20 −0.412480
\(918\) 8.99645e19 + 1.88161e19i 0.163747 + 0.0342477i
\(919\) 2.96913e20i 0.536315i 0.963375 + 0.268158i \(0.0864148\pi\)
−0.963375 + 0.268158i \(0.913585\pi\)
\(920\) 4.16102e20 + 2.96139e20i 0.745907 + 0.530862i
\(921\) −5.70357e20 −1.01468
\(922\) 3.83433e19 1.83329e20i 0.0676975 0.323679i
\(923\) 1.35638e20i 0.237668i
\(924\) −4.97020e18 + 1.13621e19i −0.00864311 + 0.0197586i
\(925\) 7.60729e20 1.31292
\(926\) −2.20932e20 4.62080e19i −0.378427 0.0791481i
\(927\) 2.13362e20i 0.362709i
\(928\) −4.52379e20 + 2.71111e20i −0.763250 + 0.457416i
\(929\) 1.18672e20 0.198719 0.0993595 0.995052i \(-0.468321\pi\)
0.0993595 + 0.995052i \(0.468321\pi\)
\(930\) 4.96674e19 2.37472e20i 0.0825450 0.394668i
\(931\) 1.93016e20i 0.318379i
\(932\) 1.08173e21 + 4.73189e20i 1.77096 + 0.774682i
\(933\) 6.21392e20 1.00970
\(934\) 1.09376e21 + 2.28761e20i 1.76399 + 0.368939i
\(935\) 2.04652e19i 0.0327592i
\(936\) −5.35553e19 + 7.52499e19i −0.0850886 + 0.119557i
\(937\) −1.25633e21 −1.98119 −0.990597 0.136816i \(-0.956313\pi\)
−0.990597 + 0.136816i \(0.956313\pi\)
\(938\) 1.02133e20 4.88322e20i 0.159862 0.764340i
\(939\) 6.39908e20i 0.994165i
\(940\) −1.26082e20 + 2.88230e20i −0.194428 + 0.444471i
\(941\) −1.12598e21 −1.72346 −0.861731 0.507365i \(-0.830620\pi\)
−0.861731 + 0.507365i \(0.830620\pi\)
\(942\) 4.90664e19 + 1.02623e19i 0.0745467 + 0.0155915i
\(943\) 2.03402e21i 3.06743i
\(944\) −1.94214e19 + 1.79513e19i −0.0290720 + 0.0268715i
\(945\) 3.42030e19 0.0508209
\(946\) 7.97090e18 3.81109e19i 0.0117563 0.0562096i
\(947\) 5.36078e20i 0.784835i 0.919787 + 0.392417i \(0.128361\pi\)
−0.919787 + 0.392417i \(0.871639\pi\)
\(948\) 1.00745e20 + 4.40694e19i 0.146408 + 0.0640441i
\(949\) −2.41512e20 −0.348398
\(950\) −2.16248e20 4.52283e19i −0.309661 0.0647658i
\(951\) 1.71411e20i 0.243655i
\(952\) −2.56780e20 1.82750e20i −0.362329 0.257869i
\(953\) 7.55090e20 1.05767 0.528833 0.848726i \(-0.322630\pi\)
0.528833 + 0.848726i \(0.322630\pi\)
\(954\) 6.87410e19 3.28668e20i 0.0955823 0.457003i
\(955\) 1.95001e20i 0.269161i
\(956\) 4.13449e20 9.45164e20i 0.566521 1.29510i
\(957\) 2.75754e19 0.0375093
\(958\) −2.28772e20 4.78477e19i −0.308919 0.0646104i
\(959\) 3.15806e20i 0.423340i
\(960\) 2.11581e20 7.33538e19i 0.281564 0.0976167i
\(961\) −6.28768e20 −0.830667
\(962\) 1.22988e20 5.88035e20i 0.161301 0.771219i
\(963\) 1.33596e20i 0.173944i
\(964\) 1.22074e20 + 5.33996e19i 0.157792 + 0.0690238i
\(965\) −2.07026e20 −0.265664
\(966\) 4.02539e20 + 8.41911e19i 0.512823 + 0.107257i
\(967\) 5.17850e20i 0.654966i −0.944857 0.327483i \(-0.893800\pi\)
0.944857 0.327483i \(-0.106200\pi\)
\(968\) −4.59320e20 + 6.45386e20i −0.576751 + 0.810386i
\(969\) 1.73618e20 0.216435
\(970\) 9.38814e19 4.48870e20i 0.116192 0.555544i
\(971\) 7.83883e20i 0.963201i 0.876391 + 0.481600i \(0.159944\pi\)
−0.876391 + 0.481600i \(0.840056\pi\)
\(972\) −2.10744e19 + 4.81771e19i −0.0257094 + 0.0587729i
\(973\) 7.96365e20 0.964544
\(974\) −1.53313e21 3.20655e20i −1.84360 0.385589i
\(975\) 1.56171e20i 0.186453i
\(976\) 4.02780e20 + 4.35764e20i 0.477440 + 0.516538i
\(977\) 1.40271e20 0.165084 0.0825420 0.996588i \(-0.473696\pi\)
0.0825420 + 0.996588i \(0.473696\pi\)
\(978\) 5.18166e19 2.47748e20i 0.0605476 0.289493i
\(979\) 1.61871e19i 0.0187798i
\(980\) 3.03078e20 + 1.32577e20i 0.349118 + 0.152717i
\(981\) 3.20066e20 0.366063
\(982\) 2.92404e19 + 6.11565e18i 0.0332050 + 0.00694483i
\(983\) 1.18991e21i 1.34165i 0.741615 + 0.670826i \(0.234060\pi\)
−0.741615 + 0.670826i \(0.765940\pi\)
\(984\) −7.26618e20 5.17133e20i −0.813468 0.578944i
\(985\) −5.23493e20 −0.581912
\(986\) −1.43467e20 + 6.85954e20i −0.158349 + 0.757105i
\(987\) 2.53324e20i 0.277623i
\(988\) −6.99220e19 + 1.59845e20i −0.0760879 + 0.173941i
\(989\) −1.29113e21 −1.39507
\(990\) −1.14607e19 2.39701e18i −0.0122960 0.00257172i
\(991\) 1.35364e21i 1.44208i −0.692895 0.721039i \(-0.743665\pi\)
0.692895 0.721039i \(-0.256335\pi\)
\(992\) −6.57500e20 1.09711e21i −0.695527 1.16056i
\(993\) 1.43478e20 0.150709
\(994\) −5.42116e19 + 2.59199e20i −0.0565441 + 0.270352i
\(995\) 9.22470e20i 0.955412i
\(996\) −2.72362e20 1.19141e20i −0.280111 0.122531i
\(997\) 1.79645e21 1.83463 0.917315 0.398162i \(-0.130352\pi\)
0.917315 + 0.398162i \(0.130352\pi\)
\(998\) −1.68775e21 3.52994e20i −1.71157 0.357975i
\(999\) 3.42033e20i 0.344437i
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.7.7 14
3.2 odd 2 36.15.d.e.19.8 14
4.3 odd 2 inner 12.15.d.a.7.8 yes 14
12.11 even 2 36.15.d.e.19.7 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.15.d.a.7.7 14 1.1 even 1 trivial
12.15.d.a.7.8 yes 14 4.3 odd 2 inner
36.15.d.e.19.7 14 12.11 even 2
36.15.d.e.19.8 14 3.2 odd 2