Properties

Label 14.10.c.a.9.3
Level $14$
Weight $10$
Character 14.9
Analytic conductor $7.211$
Analytic rank $0$
Dimension $6$
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] = [14,10,Mod(9,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.9");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.21050170629\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 1116x^{4} - 3085x^{3} + 1245325x^{2} - 2341500x + 4410000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.3
Root \(-16.9063 + 29.2826i\) of defining polynomial
Character \(\chi\) \(=\) 14.9
Dual form 14.10.c.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.00000 + 13.8564i) q^{2} +(11.9224 + 20.6501i) q^{3} +(-128.000 - 221.703i) q^{4} +(-541.184 + 937.358i) q^{5} -381.515 q^{6} +(-5624.74 - 2952.27i) q^{7} +4096.00 q^{8} +(9557.22 - 16553.6i) q^{9} +O(q^{10})\) \(q+(-8.00000 + 13.8564i) q^{2} +(11.9224 + 20.6501i) q^{3} +(-128.000 - 221.703i) q^{4} +(-541.184 + 937.358i) q^{5} -381.515 q^{6} +(-5624.74 - 2952.27i) q^{7} +4096.00 q^{8} +(9557.22 - 16553.6i) q^{9} +(-8658.94 - 14997.7i) q^{10} +(-37454.4 - 64872.9i) q^{11} +(3052.12 - 5286.43i) q^{12} -50060.6 q^{13} +(85905.8 - 54320.5i) q^{14} -25808.7 q^{15} +(-32768.0 + 56755.8i) q^{16} +(-59482.6 - 103027. i) q^{17} +(152915. + 264857. i) q^{18} +(-402181. + 696599. i) q^{19} +277086. q^{20} +(-6095.40 - 151350. i) q^{21} +1.19854e6 q^{22} +(-134394. + 232777. i) q^{23} +(48834.0 + 84582.9i) q^{24} +(390803. + 676891. i) q^{25} +(400485. - 693660. i) q^{26} +925113. q^{27} +(65441.0 + 1.62491e6i) q^{28} -5.29735e6 q^{29} +(206470. - 357616. i) q^{30} +(-2.73293e6 - 4.73357e6i) q^{31} +(-524288. - 908093. i) q^{32} +(893089. - 1.54688e6i) q^{33} +1.90344e6 q^{34} +(5.81135e6 - 3.67467e6i) q^{35} -4.89329e6 q^{36} +(-1.55446e6 + 2.69240e6i) q^{37} +(-6.43490e6 - 1.11456e7i) q^{38} +(-596840. - 1.03376e6i) q^{39} +(-2.21669e6 + 3.83942e6i) q^{40} +2.07841e7 q^{41} +(2.14592e6 + 1.12634e6i) q^{42} +4.76437e6 q^{43} +(-9.58832e6 + 1.66075e7i) q^{44} +(1.03444e7 + 1.79171e7i) q^{45} +(-2.15031e6 - 3.72444e6i) q^{46} +(-1.50766e7 + 2.61135e7i) q^{47} -1.56269e6 q^{48} +(2.29218e7 + 3.32115e7i) q^{49} -1.25057e7 q^{50} +(1.41835e6 - 2.45665e6i) q^{51} +(6.40775e6 + 1.10986e7i) q^{52} +(-2.85871e7 - 4.95142e7i) q^{53} +(-7.40091e6 + 1.28187e7i) q^{54} +8.10788e7 q^{55} +(-2.30389e7 - 1.20925e7i) q^{56} -1.91798e7 q^{57} +(4.23788e7 - 7.34023e7i) q^{58} +(-9.18379e7 - 1.59068e8i) q^{59} +(3.30352e6 + 5.72186e6i) q^{60} +(-2.65083e7 + 4.59138e7i) q^{61} +8.74537e7 q^{62} +(-1.02628e8 + 6.48941e7i) q^{63} +1.67772e7 q^{64} +(2.70920e7 - 4.69247e7i) q^{65} +(1.42894e7 + 2.47500e7i) q^{66} +(-8.67433e7 - 1.50244e8i) q^{67} +(-1.52275e7 + 2.63749e7i) q^{68} -6.40918e6 q^{69} +(4.42695e6 + 1.09922e8i) q^{70} -1.68342e8 q^{71} +(3.91464e7 - 6.78035e7i) q^{72} +(2.32340e8 + 4.02424e8i) q^{73} +(-2.48714e7 - 4.30785e7i) q^{74} +(-9.31858e6 + 1.61403e7i) q^{75} +2.05917e8 q^{76} +(1.91489e7 + 4.75469e8i) q^{77} +1.90989e7 q^{78} +(2.06864e8 - 3.58299e8i) q^{79} +(-3.54670e7 - 6.14307e7i) q^{80} +(-1.77085e8 - 3.06720e8i) q^{81} +(-1.66272e8 + 2.87992e8i) q^{82} +3.50584e8 q^{83} +(-3.27744e7 + 2.07241e7i) q^{84} +1.28764e8 q^{85} +(-3.81150e7 + 6.60171e7i) q^{86} +(-6.31569e7 - 1.09391e8i) q^{87} +(-1.53413e8 - 2.65719e8i) q^{88} +(-2.58736e8 + 4.48144e8i) q^{89} -3.31021e8 q^{90} +(2.81578e8 + 1.47792e8i) q^{91} +6.88098e7 q^{92} +(6.51659e7 - 1.12871e8i) q^{93} +(-2.41226e8 - 4.17815e8i) q^{94} +(-4.35308e8 - 7.53976e8i) q^{95} +(1.25015e7 - 2.16532e7i) q^{96} +1.32529e9 q^{97} +(-6.43567e8 + 5.19218e7i) q^{98} -1.43184e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 48 q^{2} - 233 q^{3} - 768 q^{4} - 733 q^{5} + 7456 q^{6} + 5012 q^{7} + 24576 q^{8} - 15058 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 48 q^{2} - 233 q^{3} - 768 q^{4} - 733 q^{5} + 7456 q^{6} + 5012 q^{7} + 24576 q^{8} - 15058 q^{9} - 11728 q^{10} + 7339 q^{11} - 59648 q^{12} + 197036 q^{13} - 142576 q^{14} + 738238 q^{15} - 196608 q^{16} - 306665 q^{17} - 240928 q^{18} - 377991 q^{19} + 375296 q^{20} - 1585927 q^{21} - 234848 q^{22} - 2267255 q^{23} - 954368 q^{24} - 142612 q^{25} - 1576288 q^{26} + 21348358 q^{27} + 998144 q^{28} - 13085956 q^{29} - 5905904 q^{30} - 6654517 q^{31} - 3145728 q^{32} + 3747977 q^{33} + 9813280 q^{34} + 22864807 q^{35} + 7709696 q^{36} - 22287969 q^{37} - 6047856 q^{38} + 3151974 q^{39} - 3002368 q^{40} + 68096196 q^{41} + 58323776 q^{42} - 125648280 q^{43} + 1878784 q^{44} - 86300638 q^{45} - 36276080 q^{46} - 52703019 q^{47} + 30539776 q^{48} + 57596070 q^{49} + 4563584 q^{50} + 97736333 q^{51} - 25220608 q^{52} - 12091125 q^{53} - 170786864 q^{54} + 377435398 q^{55} + 20529152 q^{56} - 158517670 q^{57} + 104687648 q^{58} - 12949897 q^{59} - 94494464 q^{60} - 160252153 q^{61} + 212944544 q^{62} - 356021666 q^{63} + 100663296 q^{64} + 334191270 q^{65} + 59967632 q^{66} - 480890225 q^{67} - 78506240 q^{68} + 1131233162 q^{69} - 349171760 q^{70} - 74421440 q^{71} - 61677568 q^{72} + 251382283 q^{73} - 356607504 q^{74} + 16322324 q^{75} + 193531392 q^{76} - 527045155 q^{77} - 100863168 q^{78} + 286494785 q^{79} - 48037888 q^{80} - 2165894587 q^{81} - 544769568 q^{82} + 2295182344 q^{83} - 527183104 q^{84} - 2389185074 q^{85} + 1005186240 q^{86} + 1412199358 q^{87} + 30060544 q^{88} - 901243845 q^{89} + 2761620416 q^{90} + 1026798920 q^{91} + 1160834560 q^{92} + 710456889 q^{93} - 843248304 q^{94} - 887366177 q^{95} - 244318208 q^{96} + 629707876 q^{97} - 2185885296 q^{98} - 1256218868 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.00000 + 13.8564i −0.353553 + 0.612372i
\(3\) 11.9224 + 20.6501i 0.0849799 + 0.147190i 0.905383 0.424597i \(-0.139584\pi\)
−0.820403 + 0.571786i \(0.806251\pi\)
\(4\) −128.000 221.703i −0.250000 0.433013i
\(5\) −541.184 + 937.358i −0.387239 + 0.670718i −0.992077 0.125630i \(-0.959905\pi\)
0.604838 + 0.796349i \(0.293238\pi\)
\(6\) −381.515 −0.120180
\(7\) −5624.74 2952.27i −0.885444 0.464745i
\(8\) 4096.00 0.353553
\(9\) 9557.22 16553.6i 0.485557 0.841009i
\(10\) −8658.94 14997.7i −0.273820 0.474270i
\(11\) −37454.4 64872.9i −0.771322 1.33597i −0.936839 0.349762i \(-0.886263\pi\)
0.165517 0.986207i \(-0.447071\pi\)
\(12\) 3052.12 5286.43i 0.0424900 0.0735948i
\(13\) −50060.6 −0.486128 −0.243064 0.970010i \(-0.578153\pi\)
−0.243064 + 0.970010i \(0.578153\pi\)
\(14\) 85905.8 54320.5i 0.597649 0.377910i
\(15\) −25808.7 −0.131630
\(16\) −32768.0 + 56755.8i −0.125000 + 0.216506i
\(17\) −59482.6 103027.i −0.172731 0.299179i 0.766643 0.642074i \(-0.221926\pi\)
−0.939374 + 0.342895i \(0.888592\pi\)
\(18\) 152915. + 264857.i 0.343341 + 0.594683i
\(19\) −402181. + 696599.i −0.707996 + 1.22629i 0.257603 + 0.966251i \(0.417067\pi\)
−0.965599 + 0.260034i \(0.916266\pi\)
\(20\) 277086. 0.387239
\(21\) −6095.40 151350.i −0.00683936 0.169822i
\(22\) 1.19854e6 1.09081
\(23\) −134394. + 232777.i −0.100139 + 0.173447i −0.911742 0.410763i \(-0.865262\pi\)
0.811603 + 0.584210i \(0.198596\pi\)
\(24\) 48834.0 + 84582.9i 0.0300449 + 0.0520394i
\(25\) 390803. + 676891.i 0.200091 + 0.346568i
\(26\) 400485. 693660.i 0.171872 0.297691i
\(27\) 925113. 0.335010
\(28\) 65441.0 + 1.62491e6i 0.0201205 + 0.499595i
\(29\) −5.29735e6 −1.39081 −0.695405 0.718618i \(-0.744775\pi\)
−0.695405 + 0.718618i \(0.744775\pi\)
\(30\) 206470. 357616.i 0.0465383 0.0806068i
\(31\) −2.73293e6 4.73357e6i −0.531497 0.920579i −0.999324 0.0367596i \(-0.988296\pi\)
0.467827 0.883820i \(-0.345037\pi\)
\(32\) −524288. 908093.i −0.0883883 0.153093i
\(33\) 893089. 1.54688e6i 0.131094 0.227061i
\(34\) 1.90344e6 0.244278
\(35\) 5.81135e6 3.67467e6i 0.654592 0.413916i
\(36\) −4.89329e6 −0.485557
\(37\) −1.55446e6 + 2.69240e6i −0.136355 + 0.236174i −0.926114 0.377243i \(-0.876872\pi\)
0.789759 + 0.613417i \(0.210206\pi\)
\(38\) −6.43490e6 1.11456e7i −0.500629 0.867115i
\(39\) −596840. 1.03376e6i −0.0413111 0.0715530i
\(40\) −2.21669e6 + 3.83942e6i −0.136910 + 0.237135i
\(41\) 2.07841e7 1.14869 0.574345 0.818613i \(-0.305257\pi\)
0.574345 + 0.818613i \(0.305257\pi\)
\(42\) 2.14592e6 + 1.12634e6i 0.106412 + 0.0558530i
\(43\) 4.76437e6 0.212519 0.106259 0.994338i \(-0.466113\pi\)
0.106259 + 0.994338i \(0.466113\pi\)
\(44\) −9.58832e6 + 1.66075e7i −0.385661 + 0.667984i
\(45\) 1.03444e7 + 1.79171e7i 0.376054 + 0.651344i
\(46\) −2.15031e6 3.72444e6i −0.0708093 0.122645i
\(47\) −1.50766e7 + 2.61135e7i −0.450675 + 0.780592i −0.998428 0.0560482i \(-0.982150\pi\)
0.547753 + 0.836640i \(0.315483\pi\)
\(48\) −1.56269e6 −0.0424900
\(49\) 2.29218e7 + 3.32115e7i 0.568024 + 0.823012i
\(50\) −1.25057e7 −0.282972
\(51\) 1.41835e6 2.45665e6i 0.0293573 0.0508483i
\(52\) 6.40775e6 + 1.10986e7i 0.121532 + 0.210500i
\(53\) −2.85871e7 4.95142e7i −0.497655 0.861963i 0.502342 0.864669i \(-0.332472\pi\)
−0.999996 + 0.00270617i \(0.999139\pi\)
\(54\) −7.40091e6 + 1.28187e7i −0.118444 + 0.205151i
\(55\) 8.10788e7 1.19475
\(56\) −2.30389e7 1.20925e7i −0.313052 0.164312i
\(57\) −1.91798e7 −0.240662
\(58\) 4.23788e7 7.34023e7i 0.491726 0.851694i
\(59\) −9.18379e7 1.59068e8i −0.986706 1.70902i −0.634097 0.773254i \(-0.718628\pi\)
−0.352609 0.935771i \(-0.614705\pi\)
\(60\) 3.30352e6 + 5.72186e6i 0.0329076 + 0.0569976i
\(61\) −2.65083e7 + 4.59138e7i −0.245131 + 0.424579i −0.962168 0.272455i \(-0.912164\pi\)
0.717038 + 0.697035i \(0.245498\pi\)
\(62\) 8.74537e7 0.751650
\(63\) −1.02628e8 + 6.48941e7i −0.820789 + 0.519007i
\(64\) 1.67772e7 0.125000
\(65\) 2.70920e7 4.69247e7i 0.188248 0.326055i
\(66\) 1.42894e7 + 2.47500e7i 0.0926973 + 0.160556i
\(67\) −8.67433e7 1.50244e8i −0.525896 0.910878i −0.999545 0.0301643i \(-0.990397\pi\)
0.473649 0.880713i \(-0.342936\pi\)
\(68\) −1.52275e7 + 2.63749e7i −0.0863654 + 0.149589i
\(69\) −6.40918e6 −0.0340394
\(70\) 4.42695e6 + 1.09922e8i 0.0220376 + 0.547196i
\(71\) −1.68342e8 −0.786195 −0.393097 0.919497i \(-0.628596\pi\)
−0.393097 + 0.919497i \(0.628596\pi\)
\(72\) 3.91464e7 6.78035e7i 0.171670 0.297342i
\(73\) 2.32340e8 + 4.02424e8i 0.957570 + 1.65856i 0.728375 + 0.685179i \(0.240276\pi\)
0.229195 + 0.973381i \(0.426391\pi\)
\(74\) −2.48714e7 4.30785e7i −0.0964177 0.167000i
\(75\) −9.31858e6 + 1.61403e7i −0.0340075 + 0.0589026i
\(76\) 2.05917e8 0.707996
\(77\) 1.91489e7 + 4.75469e8i 0.0620776 + 1.54139i
\(78\) 1.90989e7 0.0584228
\(79\) 2.06864e8 3.58299e8i 0.597535 1.03496i −0.395649 0.918402i \(-0.629480\pi\)
0.993184 0.116559i \(-0.0371863\pi\)
\(80\) −3.54670e7 6.14307e7i −0.0968099 0.167680i
\(81\) −1.77085e8 3.06720e8i −0.457088 0.791699i
\(82\) −1.66272e8 + 2.87992e8i −0.406123 + 0.703426i
\(83\) 3.50584e8 0.810850 0.405425 0.914128i \(-0.367124\pi\)
0.405425 + 0.914128i \(0.367124\pi\)
\(84\) −3.27744e7 + 2.07241e7i −0.0718253 + 0.0454171i
\(85\) 1.28764e8 0.267553
\(86\) −3.81150e7 + 6.60171e7i −0.0751368 + 0.130141i
\(87\) −6.31569e7 1.09391e8i −0.118191 0.204713i
\(88\) −1.53413e8 2.65719e8i −0.272703 0.472336i
\(89\) −2.58736e8 + 4.48144e8i −0.437122 + 0.757117i −0.997466 0.0711428i \(-0.977335\pi\)
0.560345 + 0.828260i \(0.310669\pi\)
\(90\) −3.31021e8 −0.531820
\(91\) 2.81578e8 + 1.47792e8i 0.430439 + 0.225926i
\(92\) 6.88098e7 0.100139
\(93\) 6.51659e7 1.12871e8i 0.0903331 0.156462i
\(94\) −2.41226e8 4.17815e8i −0.318675 0.551962i
\(95\) −4.35308e8 7.53976e8i −0.548328 0.949732i
\(96\) 1.25015e7 2.16532e7i 0.0150225 0.0260197i
\(97\) 1.32529e9 1.51998 0.759990 0.649935i \(-0.225204\pi\)
0.759990 + 0.649935i \(0.225204\pi\)
\(98\) −6.43567e8 + 5.19218e7i −0.704817 + 0.0568633i
\(99\) −1.43184e9 −1.49808
\(100\) 1.00046e8 1.73284e8i 0.100046 0.173284i
\(101\) −3.16581e7 5.48335e7i −0.0302718 0.0524324i 0.850493 0.525987i \(-0.176304\pi\)
−0.880764 + 0.473555i \(0.842971\pi\)
\(102\) 2.26935e7 + 3.93063e7i 0.0207588 + 0.0359552i
\(103\) 5.64570e8 9.77863e8i 0.494254 0.856073i −0.505724 0.862695i \(-0.668775\pi\)
0.999978 + 0.00662253i \(0.00210803\pi\)
\(104\) −2.05048e8 −0.171872
\(105\) 1.45167e8 + 7.61943e7i 0.116551 + 0.0611746i
\(106\) 9.14786e8 0.703790
\(107\) −9.23383e7 + 1.59935e8i −0.0681012 + 0.117955i −0.898065 0.439862i \(-0.855027\pi\)
0.829964 + 0.557817i \(0.188361\pi\)
\(108\) −1.18414e8 2.05100e8i −0.0837525 0.145064i
\(109\) 6.03407e8 + 1.04513e9i 0.409441 + 0.709172i 0.994827 0.101582i \(-0.0323905\pi\)
−0.585386 + 0.810754i \(0.699057\pi\)
\(110\) −6.48630e8 + 1.12346e9i −0.422406 + 0.731629i
\(111\) −7.41313e7 −0.0463498
\(112\) 3.51870e8 2.22497e8i 0.211301 0.133611i
\(113\) 3.17054e8 0.182928 0.0914639 0.995808i \(-0.470845\pi\)
0.0914639 + 0.995808i \(0.470845\pi\)
\(114\) 1.53438e8 2.65763e8i 0.0850868 0.147375i
\(115\) −1.45464e8 2.51951e8i −0.0775559 0.134331i
\(116\) 6.78061e8 + 1.17444e9i 0.347703 + 0.602238i
\(117\) −4.78440e8 + 8.28682e8i −0.236043 + 0.408838i
\(118\) 2.93881e9 1.39541
\(119\) 3.04110e7 + 7.55108e8i 0.0139017 + 0.345182i
\(120\) −1.05713e8 −0.0465383
\(121\) −1.62669e9 + 2.81751e9i −0.689875 + 1.19490i
\(122\) −4.24133e8 7.34620e8i −0.173334 0.300223i
\(123\) 2.47795e8 + 4.29193e8i 0.0976156 + 0.169075i
\(124\) −6.99630e8 + 1.21179e9i −0.265748 + 0.460290i
\(125\) −2.95998e9 −1.08441
\(126\) −7.81793e7 1.94120e9i −0.0276327 0.686125i
\(127\) −1.91107e9 −0.651868 −0.325934 0.945392i \(-0.605679\pi\)
−0.325934 + 0.945392i \(0.605679\pi\)
\(128\) −1.34218e8 + 2.32472e8i −0.0441942 + 0.0765466i
\(129\) 5.68025e7 + 9.83848e7i 0.0180598 + 0.0312806i
\(130\) 4.33471e8 + 7.50795e8i 0.133111 + 0.230556i
\(131\) 3.02645e9 5.24197e9i 0.897869 1.55516i 0.0676566 0.997709i \(-0.478448\pi\)
0.830213 0.557447i \(-0.188219\pi\)
\(132\) −4.57261e8 −0.131094
\(133\) 4.31871e9 2.73084e9i 1.19680 0.756770i
\(134\) 2.77579e9 0.743729
\(135\) −5.00656e8 + 8.67162e8i −0.129729 + 0.224698i
\(136\) −2.43641e8 4.21998e8i −0.0610696 0.105776i
\(137\) −2.49781e9 4.32634e9i −0.605783 1.04925i −0.991927 0.126809i \(-0.959527\pi\)
0.386144 0.922438i \(-0.373807\pi\)
\(138\) 5.12734e7 8.88082e7i 0.0120347 0.0208448i
\(139\) −5.39864e9 −1.22664 −0.613321 0.789834i \(-0.710167\pi\)
−0.613321 + 0.789834i \(0.710167\pi\)
\(140\) −1.55854e9 8.18033e8i −0.342879 0.179968i
\(141\) −7.18995e8 −0.153193
\(142\) 1.34674e9 2.33262e9i 0.277962 0.481444i
\(143\) 1.87499e9 + 3.24758e9i 0.374961 + 0.649452i
\(144\) 6.26342e8 + 1.08486e9i 0.121389 + 0.210252i
\(145\) 2.86684e9 4.96551e9i 0.538577 0.932842i
\(146\) −7.43487e9 −1.35421
\(147\) −4.12540e8 + 8.69297e8i −0.0728682 + 0.153547i
\(148\) 7.95883e8 0.136355
\(149\) −3.12472e8 + 5.41218e8i −0.0519366 + 0.0899568i −0.890825 0.454347i \(-0.849873\pi\)
0.838888 + 0.544304i \(0.183206\pi\)
\(150\) −1.49097e8 2.58244e8i −0.0240469 0.0416505i
\(151\) 5.50838e9 + 9.54079e9i 0.862238 + 1.49344i 0.869763 + 0.493469i \(0.164271\pi\)
−0.00752500 + 0.999972i \(0.502395\pi\)
\(152\) −1.64734e9 + 2.85327e9i −0.250314 + 0.433557i
\(153\) −2.27395e9 −0.335483
\(154\) −6.74148e9 3.53842e9i −0.965855 0.506951i
\(155\) 5.91606e9 0.823266
\(156\) −1.52791e8 + 2.64642e8i −0.0206556 + 0.0357765i
\(157\) 3.40159e9 + 5.89172e9i 0.446821 + 0.773916i 0.998177 0.0603538i \(-0.0192229\pi\)
−0.551356 + 0.834270i \(0.685890\pi\)
\(158\) 3.30982e9 + 5.73278e9i 0.422521 + 0.731828i
\(159\) 6.81650e8 1.18065e9i 0.0845813 0.146499i
\(160\) 1.13494e9 0.136910
\(161\) 1.44315e9 9.12545e8i 0.169276 0.107038i
\(162\) 5.66672e9 0.646420
\(163\) −1.03329e9 + 1.78972e9i −0.114651 + 0.198582i −0.917640 0.397412i \(-0.869908\pi\)
0.802989 + 0.595994i \(0.203242\pi\)
\(164\) −2.66036e9 4.60788e9i −0.287173 0.497397i
\(165\) 9.66650e8 + 1.67429e9i 0.101529 + 0.175854i
\(166\) −2.80467e9 + 4.85783e9i −0.286679 + 0.496542i
\(167\) −6.75774e8 −0.0672322 −0.0336161 0.999435i \(-0.510702\pi\)
−0.0336161 + 0.999435i \(0.510702\pi\)
\(168\) −2.49668e7 6.19928e8i −0.00241808 0.0600412i
\(169\) −8.09844e9 −0.763679
\(170\) −1.03011e9 + 1.78421e9i −0.0945942 + 0.163842i
\(171\) 7.68747e9 + 1.33151e10i 0.687545 + 1.19086i
\(172\) −6.09839e8 1.05627e9i −0.0531297 0.0920234i
\(173\) 9.72079e9 1.68369e10i 0.825076 1.42907i −0.0767850 0.997048i \(-0.524466\pi\)
0.901861 0.432026i \(-0.142201\pi\)
\(174\) 2.02102e9 0.167147
\(175\) −1.99801e8 4.96109e9i −0.0161037 0.399858i
\(176\) 4.90922e9 0.385661
\(177\) 2.18985e9 3.79293e9i 0.167700 0.290466i
\(178\) −4.13978e9 7.17031e9i −0.309092 0.535362i
\(179\) −2.04825e9 3.54767e9i −0.149123 0.258288i 0.781781 0.623553i \(-0.214312\pi\)
−0.930903 + 0.365265i \(0.880978\pi\)
\(180\) 2.64817e9 4.58677e9i 0.188027 0.325672i
\(181\) −2.41926e10 −1.67544 −0.837720 0.546101i \(-0.816112\pi\)
−0.837720 + 0.546101i \(0.816112\pi\)
\(182\) −4.30049e9 + 2.71932e9i −0.290534 + 0.183712i
\(183\) −1.26417e9 −0.0833248
\(184\) −5.50478e8 + 9.53457e8i −0.0354046 + 0.0613226i
\(185\) −1.68250e9 2.91417e9i −0.105604 0.182912i
\(186\) 1.04265e9 + 1.80593e9i 0.0638752 + 0.110635i
\(187\) −4.45577e9 + 7.71762e9i −0.266462 + 0.461526i
\(188\) 7.71922e9 0.450675
\(189\) −5.20352e9 2.73118e9i −0.296633 0.155694i
\(190\) 1.39299e10 0.775453
\(191\) −2.90999e9 + 5.04025e9i −0.158213 + 0.274033i −0.934224 0.356686i \(-0.883907\pi\)
0.776011 + 0.630719i \(0.217240\pi\)
\(192\) 2.00024e8 + 3.46452e8i 0.0106225 + 0.0183987i
\(193\) −1.19292e10 2.06619e10i −0.618874 1.07192i −0.989692 0.143215i \(-0.954256\pi\)
0.370818 0.928706i \(-0.379077\pi\)
\(194\) −1.06023e10 + 1.83637e10i −0.537394 + 0.930794i
\(195\) 1.29200e9 0.0639892
\(196\) 4.42908e9 9.33289e9i 0.214369 0.451715i
\(197\) −1.13267e10 −0.535802 −0.267901 0.963446i \(-0.586330\pi\)
−0.267901 + 0.963446i \(0.586330\pi\)
\(198\) 1.14547e10 1.98401e10i 0.529652 0.917384i
\(199\) −8.76433e9 1.51803e10i −0.396168 0.686184i 0.597081 0.802181i \(-0.296327\pi\)
−0.993250 + 0.115997i \(0.962994\pi\)
\(200\) 1.60073e9 + 2.77254e9i 0.0707429 + 0.122530i
\(201\) 2.06837e9 3.58252e9i 0.0893811 0.154813i
\(202\) 1.01306e9 0.0428108
\(203\) 2.97962e10 + 1.56392e10i 1.23149 + 0.646372i
\(204\) −7.26193e8 −0.0293573
\(205\) −1.12480e10 + 1.94821e10i −0.444818 + 0.770448i
\(206\) 9.03311e9 + 1.56458e10i 0.349490 + 0.605335i
\(207\) 2.56887e9 + 4.44941e9i 0.0972468 + 0.168436i
\(208\) 1.64039e9 2.84123e9i 0.0607660 0.105250i
\(209\) 6.02538e10 2.18437
\(210\) −2.21712e9 + 1.40194e9i −0.0786687 + 0.0497444i
\(211\) −3.12620e10 −1.08579 −0.542895 0.839801i \(-0.682672\pi\)
−0.542895 + 0.839801i \(0.682672\pi\)
\(212\) −7.31829e9 + 1.26756e10i −0.248827 + 0.430981i
\(213\) −2.00703e9 3.47628e9i −0.0668108 0.115720i
\(214\) −1.47741e9 2.55895e9i −0.0481548 0.0834066i
\(215\) −2.57840e9 + 4.46592e9i −0.0822957 + 0.142540i
\(216\) 3.78926e9 0.118444
\(217\) 1.39723e9 + 3.46935e10i 0.0427759 + 1.06213i
\(218\) −1.93090e10 −0.579037
\(219\) −5.54007e9 + 9.59568e9i −0.162748 + 0.281889i
\(220\) −1.03781e10 1.79754e10i −0.298686 0.517340i
\(221\) 2.97773e9 + 5.15759e9i 0.0839693 + 0.145439i
\(222\) 5.93050e8 1.02719e9i 0.0163871 0.0283834i
\(223\) 2.74321e10 0.742825 0.371413 0.928468i \(-0.378873\pi\)
0.371413 + 0.928468i \(0.378873\pi\)
\(224\) 2.68046e8 + 6.65563e9i 0.00711368 + 0.176634i
\(225\) 1.49400e10 0.388622
\(226\) −2.53643e9 + 4.39323e9i −0.0646748 + 0.112020i
\(227\) −5.78305e9 1.00165e10i −0.144557 0.250381i 0.784650 0.619939i \(-0.212843\pi\)
−0.929208 + 0.369558i \(0.879509\pi\)
\(228\) 2.45501e9 + 4.25221e9i 0.0601654 + 0.104210i
\(229\) −2.11891e10 + 3.67007e10i −0.509159 + 0.881890i 0.490785 + 0.871281i \(0.336710\pi\)
−0.999944 + 0.0106087i \(0.996623\pi\)
\(230\) 4.65484e9 0.109681
\(231\) −9.59019e9 + 6.06413e9i −0.221602 + 0.140125i
\(232\) −2.16980e10 −0.491726
\(233\) 4.26184e10 7.38173e10i 0.947318 1.64080i 0.196276 0.980549i \(-0.437115\pi\)
0.751042 0.660254i \(-0.229552\pi\)
\(234\) −7.65504e9 1.32589e10i −0.166908 0.289092i
\(235\) −1.63184e10 2.82643e10i −0.349038 0.604552i
\(236\) −2.35105e10 + 4.07214e10i −0.493353 + 0.854512i
\(237\) 9.86522e9 0.203114
\(238\) −1.07064e10 5.61948e9i −0.216295 0.113527i
\(239\) 1.81331e10 0.359486 0.179743 0.983714i \(-0.442473\pi\)
0.179743 + 0.983714i \(0.442473\pi\)
\(240\) 8.45700e8 1.46480e9i 0.0164538 0.0284988i
\(241\) −1.24598e10 2.15810e10i −0.237921 0.412092i 0.722196 0.691688i \(-0.243133\pi\)
−0.960118 + 0.279596i \(0.909799\pi\)
\(242\) −2.60270e10 4.50801e10i −0.487815 0.844921i
\(243\) 1.33270e10 2.30831e10i 0.245192 0.424684i
\(244\) 1.35723e10 0.245131
\(245\) −4.35360e10 + 3.51240e9i −0.771971 + 0.0622812i
\(246\) −7.92943e9 −0.138049
\(247\) 2.01334e10 3.48721e10i 0.344177 0.596132i
\(248\) −1.11941e10 1.93887e10i −0.187912 0.325474i
\(249\) 4.17979e9 + 7.23960e9i 0.0689060 + 0.119349i
\(250\) 2.36799e10 4.10147e10i 0.383397 0.664064i
\(251\) −3.47730e9 −0.0552981 −0.0276491 0.999618i \(-0.508802\pi\)
−0.0276491 + 0.999618i \(0.508802\pi\)
\(252\) 2.75235e10 + 1.44463e10i 0.429934 + 0.225660i
\(253\) 2.01346e10 0.308959
\(254\) 1.52886e10 2.64806e10i 0.230470 0.399186i
\(255\) 1.53517e9 + 2.65899e9i 0.0227366 + 0.0393810i
\(256\) −2.14748e9 3.71955e9i −0.0312500 0.0541266i
\(257\) −3.77069e10 + 6.53102e10i −0.539164 + 0.933860i 0.459785 + 0.888030i \(0.347927\pi\)
−0.998949 + 0.0458298i \(0.985407\pi\)
\(258\) −1.81768e9 −0.0255405
\(259\) 1.66921e10 1.05549e10i 0.230496 0.145749i
\(260\) −1.38711e10 −0.188248
\(261\) −5.06279e10 + 8.76901e10i −0.675317 + 1.16968i
\(262\) 4.84233e10 + 8.38715e10i 0.634890 + 1.09966i
\(263\) −5.88025e10 1.01849e11i −0.757870 1.31267i −0.943935 0.330132i \(-0.892907\pi\)
0.186064 0.982538i \(-0.440427\pi\)
\(264\) 3.65809e9 6.33600e9i 0.0463486 0.0802782i
\(265\) 6.18834e10 0.770846
\(266\) 3.28990e9 + 8.16886e10i 0.0402916 + 1.00045i
\(267\) −1.23390e10 −0.148586
\(268\) −2.22063e10 + 3.84624e10i −0.262948 + 0.455439i
\(269\) 3.71283e10 + 6.43082e10i 0.432335 + 0.748826i 0.997074 0.0764436i \(-0.0243565\pi\)
−0.564739 + 0.825270i \(0.691023\pi\)
\(270\) −8.01050e9 1.38746e10i −0.0917324 0.158885i
\(271\) −4.01996e10 + 6.96277e10i −0.452751 + 0.784188i −0.998556 0.0537244i \(-0.982891\pi\)
0.545805 + 0.837913i \(0.316224\pi\)
\(272\) 7.79651e9 0.0863654
\(273\) 3.05139e8 + 7.57665e9i 0.00332480 + 0.0825553i
\(274\) 7.99300e10 0.856707
\(275\) 2.92746e10 5.07051e10i 0.308669 0.534631i
\(276\) 8.20375e8 + 1.42093e9i 0.00850984 + 0.0147395i
\(277\) 6.52889e10 + 1.13084e11i 0.666316 + 1.15409i 0.978927 + 0.204212i \(0.0654631\pi\)
−0.312611 + 0.949881i \(0.601204\pi\)
\(278\) 4.31891e10 7.48058e10i 0.433683 0.751162i
\(279\) −1.04477e11 −1.03229
\(280\) 2.38033e10 1.50515e10i 0.231433 0.146341i
\(281\) −6.23328e10 −0.596401 −0.298200 0.954503i \(-0.596386\pi\)
−0.298200 + 0.954503i \(0.596386\pi\)
\(282\) 5.75196e9 9.96268e9i 0.0541620 0.0938113i
\(283\) −3.39157e8 5.87437e8i −0.00314312 0.00544405i 0.864450 0.502720i \(-0.167667\pi\)
−0.867593 + 0.497276i \(0.834334\pi\)
\(284\) 2.15478e10 + 3.73219e10i 0.196549 + 0.340432i
\(285\) 1.03798e10 1.79783e10i 0.0931938 0.161416i
\(286\) −5.99996e10 −0.530275
\(287\) −1.16905e11 6.13601e10i −1.01710 0.533848i
\(288\) −2.00429e10 −0.171670
\(289\) 5.22176e10 9.04435e10i 0.440328 0.762671i
\(290\) 4.58694e10 + 7.94482e10i 0.380831 + 0.659619i
\(291\) 1.58006e10 + 2.73674e10i 0.129168 + 0.223725i
\(292\) 5.94789e10 1.03021e11i 0.478785 0.829280i
\(293\) 5.67165e9 0.0449578 0.0224789 0.999747i \(-0.492844\pi\)
0.0224789 + 0.999747i \(0.492844\pi\)
\(294\) −8.74502e9 1.26707e10i −0.0682649 0.0989094i
\(295\) 1.98805e11 1.52837
\(296\) −6.36707e9 + 1.10281e10i −0.0482089 + 0.0835002i
\(297\) −3.46496e10 6.00148e10i −0.258401 0.447563i
\(298\) −4.99956e9 8.65949e9i −0.0367247 0.0636091i
\(299\) 6.72785e9 1.16530e10i 0.0486806 0.0843173i
\(300\) 4.77111e9 0.0340075
\(301\) −2.67983e10 1.40657e10i −0.188174 0.0987671i
\(302\) −1.76268e11 −1.21939
\(303\) 7.54878e8 1.30749e9i 0.00514500 0.00891139i
\(304\) −2.63574e10 4.56523e10i −0.176999 0.306571i
\(305\) −2.86917e10 4.96956e10i −0.189849 0.328828i
\(306\) 1.81916e10 3.15088e10i 0.118611 0.205440i
\(307\) −1.81171e11 −1.16403 −0.582017 0.813176i \(-0.697736\pi\)
−0.582017 + 0.813176i \(0.697736\pi\)
\(308\) 1.02962e11 6.51053e10i 0.651924 0.412229i
\(309\) 2.69240e10 0.168007
\(310\) −4.73285e10 + 8.19754e10i −0.291069 + 0.504146i
\(311\) −5.19032e10 8.98990e10i −0.314610 0.544920i 0.664745 0.747071i \(-0.268540\pi\)
−0.979354 + 0.202150i \(0.935207\pi\)
\(312\) −2.44466e9 4.23427e9i −0.0146057 0.0252978i
\(313\) 7.44320e10 1.28920e11i 0.438339 0.759226i −0.559222 0.829018i \(-0.688900\pi\)
0.997562 + 0.0697919i \(0.0222335\pi\)
\(314\) −1.08851e11 −0.631900
\(315\) −5.28867e9 1.31318e11i −0.0302656 0.751498i
\(316\) −1.05914e11 −0.597535
\(317\) −9.88493e10 + 1.71212e11i −0.549803 + 0.952286i 0.448485 + 0.893790i \(0.351964\pi\)
−0.998288 + 0.0584960i \(0.981370\pi\)
\(318\) 1.09064e10 + 1.88904e10i 0.0598080 + 0.103590i
\(319\) 1.98409e11 + 3.43655e11i 1.07276 + 1.85808i
\(320\) −9.07955e9 + 1.57263e10i −0.0484049 + 0.0838398i
\(321\) −4.40356e9 −0.0231489
\(322\) 1.09936e9 + 2.72973e10i 0.00569887 + 0.141504i
\(323\) 9.56912e10 0.489171
\(324\) −4.53338e10 + 7.85204e10i −0.228544 + 0.395850i
\(325\) −1.95638e10 3.38855e10i −0.0972699 0.168476i
\(326\) −1.65327e10 2.86354e10i −0.0810707 0.140419i
\(327\) −1.43881e10 + 2.49208e10i −0.0695885 + 0.120531i
\(328\) 8.51315e10 0.406123
\(329\) 1.61896e11 1.02371e11i 0.761824 0.481722i
\(330\) −3.09328e10 −0.143584
\(331\) −2.78940e10 + 4.83139e10i −0.127728 + 0.221231i −0.922796 0.385289i \(-0.874102\pi\)
0.795068 + 0.606520i \(0.207435\pi\)
\(332\) −4.48747e10 7.77253e10i −0.202713 0.351108i
\(333\) 2.97126e10 + 5.14638e10i 0.132416 + 0.229352i
\(334\) 5.40619e9 9.36380e9i 0.0237702 0.0411712i
\(335\) 1.87776e11 0.814590
\(336\) 8.78971e9 + 4.61347e9i 0.0376225 + 0.0197470i
\(337\) 4.01748e11 1.69676 0.848378 0.529391i \(-0.177580\pi\)
0.848378 + 0.529391i \(0.177580\pi\)
\(338\) 6.47875e10 1.12215e11i 0.270001 0.467656i
\(339\) 3.78003e9 + 6.54720e9i 0.0155452 + 0.0269251i
\(340\) −1.64818e10 2.85473e10i −0.0668882 0.115854i
\(341\) −2.04720e11 + 3.54586e11i −0.819910 + 1.42013i
\(342\) −2.45999e11 −0.972335
\(343\) −3.08798e10 2.54477e11i −0.120462 0.992718i
\(344\) 1.95149e10 0.0751368
\(345\) 3.46854e9 6.00769e9i 0.0131814 0.0228308i
\(346\) 1.55533e11 + 2.69390e11i 0.583417 + 1.01051i
\(347\) 1.68936e11 + 2.92606e11i 0.625518 + 1.08343i 0.988440 + 0.151610i \(0.0484456\pi\)
−0.362923 + 0.931819i \(0.618221\pi\)
\(348\) −1.61682e10 + 2.80041e10i −0.0590955 + 0.102356i
\(349\) −3.59959e11 −1.29879 −0.649395 0.760451i \(-0.724978\pi\)
−0.649395 + 0.760451i \(0.724978\pi\)
\(350\) 7.03413e10 + 3.69202e10i 0.250556 + 0.131510i
\(351\) −4.63117e10 −0.162858
\(352\) −3.92738e10 + 6.80242e10i −0.136352 + 0.236168i
\(353\) −9.51732e10 1.64845e11i −0.326233 0.565053i 0.655528 0.755171i \(-0.272446\pi\)
−0.981761 + 0.190118i \(0.939113\pi\)
\(354\) 3.50375e10 + 6.06868e10i 0.118582 + 0.205390i
\(355\) 9.11040e10 1.57797e11i 0.304446 0.527315i
\(356\) 1.32473e11 0.437122
\(357\) −1.52305e10 + 9.63066e9i −0.0496258 + 0.0313797i
\(358\) 6.55439e10 0.210891
\(359\) −1.96349e11 + 3.40086e11i −0.623884 + 1.08060i 0.364872 + 0.931058i \(0.381113\pi\)
−0.988756 + 0.149540i \(0.952221\pi\)
\(360\) 4.23707e10 + 7.33883e10i 0.132955 + 0.230285i
\(361\) −1.62156e11 2.80862e11i −0.502517 0.870385i
\(362\) 1.93541e11 3.35222e11i 0.592357 1.02599i
\(363\) −7.75758e10 −0.234502
\(364\) −3.27602e9 8.13439e10i −0.00978115 0.242867i
\(365\) −5.02954e11 −1.48324
\(366\) 1.01133e10 1.75168e10i 0.0294598 0.0510258i
\(367\) 1.62237e10 + 2.81002e10i 0.0466823 + 0.0808561i 0.888422 0.459027i \(-0.151802\pi\)
−0.841740 + 0.539883i \(0.818468\pi\)
\(368\) −8.80765e9 1.52553e10i −0.0250349 0.0433616i
\(369\) 1.98638e11 3.44051e11i 0.557754 0.966059i
\(370\) 5.38399e10 0.149347
\(371\) 1.46154e10 + 3.62901e11i 0.0400523 + 0.994503i
\(372\) −3.33649e10 −0.0903331
\(373\) 2.19500e11 3.80185e11i 0.587143 1.01696i −0.407461 0.913223i \(-0.633586\pi\)
0.994604 0.103740i \(-0.0330809\pi\)
\(374\) −7.12923e10 1.23482e11i −0.188417 0.326348i
\(375\) −3.52900e10 6.11240e10i −0.0921532 0.159614i
\(376\) −6.17538e10 + 1.06961e11i −0.159338 + 0.275981i
\(377\) 2.65189e11 0.676112
\(378\) 7.94726e10 5.02526e10i 0.200219 0.126604i
\(379\) −3.56933e11 −0.888607 −0.444304 0.895876i \(-0.646549\pi\)
−0.444304 + 0.895876i \(0.646549\pi\)
\(380\) −1.11439e11 + 1.93018e11i −0.274164 + 0.474866i
\(381\) −2.27845e10 3.94638e10i −0.0553957 0.0959482i
\(382\) −4.65599e10 8.06441e10i −0.111873 0.193770i
\(383\) 7.62364e10 1.32045e11i 0.181037 0.313566i −0.761197 0.648521i \(-0.775388\pi\)
0.942234 + 0.334955i \(0.108721\pi\)
\(384\) −6.40076e9 −0.0150225
\(385\) −4.56047e11 2.39367e11i −1.05788 0.555252i
\(386\) 3.81733e11 0.875220
\(387\) 4.55341e10 7.88674e10i 0.103190 0.178730i
\(388\) −1.69637e11 2.93820e11i −0.379995 0.658171i
\(389\) −2.78559e11 4.82478e11i −0.616800 1.06833i −0.990066 0.140604i \(-0.955096\pi\)
0.373266 0.927724i \(-0.378238\pi\)
\(390\) −1.03360e10 + 1.79025e10i −0.0226236 + 0.0391852i
\(391\) 3.19765e10 0.0691887
\(392\) 9.38877e10 + 1.36034e11i 0.200827 + 0.290979i
\(393\) 1.44330e11 0.305203
\(394\) 9.06133e10 1.56947e11i 0.189435 0.328110i
\(395\) 2.23903e11 + 3.87811e11i 0.462778 + 0.801555i
\(396\) 1.83275e11 + 3.17442e11i 0.374521 + 0.648689i
\(397\) −4.32956e11 + 7.49901e11i −0.874755 + 1.51512i −0.0177309 + 0.999843i \(0.505644\pi\)
−0.857024 + 0.515277i \(0.827689\pi\)
\(398\) 2.80458e11 0.560267
\(399\) 1.07881e11 + 5.66239e10i 0.213093 + 0.111846i
\(400\) −5.12233e10 −0.100046
\(401\) 3.38246e11 5.85858e11i 0.653254 1.13147i −0.329074 0.944304i \(-0.606737\pi\)
0.982328 0.187166i \(-0.0599301\pi\)
\(402\) 3.30939e10 + 5.73203e10i 0.0632020 + 0.109469i
\(403\) 1.36812e11 + 2.36965e11i 0.258376 + 0.447520i
\(404\) −8.10448e9 + 1.40374e10i −0.0151359 + 0.0262162i
\(405\) 3.83342e11 0.708010
\(406\) −4.55073e11 + 2.87755e11i −0.831216 + 0.525600i
\(407\) 2.32885e11 0.420695
\(408\) 5.80954e9 1.00624e10i 0.0103794 0.0179776i
\(409\) 1.39521e11 + 2.41658e11i 0.246539 + 0.427018i 0.962563 0.271058i \(-0.0873734\pi\)
−0.716024 + 0.698075i \(0.754040\pi\)
\(410\) −1.79968e11 3.11713e11i −0.314534 0.544789i
\(411\) 5.95596e10 1.03160e11i 0.102959 0.178330i
\(412\) −2.89060e11 −0.494254
\(413\) 4.69528e10 + 1.16585e12i 0.0794121 + 1.97181i
\(414\) −8.22038e10 −0.137528
\(415\) −1.89730e11 + 3.28623e11i −0.313993 + 0.543852i
\(416\) 2.62462e10 + 4.54597e10i 0.0429681 + 0.0744229i
\(417\) −6.43645e10 1.11483e11i −0.104240 0.180549i
\(418\) −4.82031e11 + 8.34902e11i −0.772292 + 1.33765i
\(419\) −9.62344e10 −0.152534 −0.0762671 0.997087i \(-0.524300\pi\)
−0.0762671 + 0.997087i \(0.524300\pi\)
\(420\) −1.68895e9 4.19369e10i −0.00264847 0.0657619i
\(421\) 4.35437e10 0.0675547 0.0337774 0.999429i \(-0.489246\pi\)
0.0337774 + 0.999429i \(0.489246\pi\)
\(422\) 2.50096e11 4.33179e11i 0.383884 0.664907i
\(423\) 2.88181e11 + 4.99144e11i 0.437657 + 0.758043i
\(424\) −1.17093e11 2.02810e11i −0.175947 0.304750i
\(425\) 4.64920e10 8.05265e10i 0.0691238 0.119726i
\(426\) 6.42251e10 0.0944847
\(427\) 2.84652e11 1.79993e11i 0.414371 0.262018i
\(428\) 4.72772e10 0.0681012
\(429\) −4.47085e10 + 7.74375e10i −0.0637284 + 0.110381i
\(430\) −4.12544e10 7.14547e10i −0.0581918 0.100791i
\(431\) −3.88074e11 6.72163e11i −0.541709 0.938268i −0.998806 0.0488511i \(-0.984444\pi\)
0.457097 0.889417i \(-0.348889\pi\)
\(432\) −3.03141e10 + 5.25056e10i −0.0418763 + 0.0725318i
\(433\) 5.97634e11 0.817033 0.408517 0.912751i \(-0.366046\pi\)
0.408517 + 0.912751i \(0.366046\pi\)
\(434\) −4.91904e11 2.58187e11i −0.665544 0.349326i
\(435\) 1.36718e11 0.183073
\(436\) 1.54472e11 2.67554e11i 0.204720 0.354586i
\(437\) −1.08102e11 1.87238e11i −0.141797 0.245599i
\(438\) −8.86411e10 1.53531e11i −0.115080 0.199325i
\(439\) 1.59917e11 2.76984e11i 0.205496 0.355930i −0.744795 0.667294i \(-0.767453\pi\)
0.950291 + 0.311364i \(0.100786\pi\)
\(440\) 3.32099e11 0.422406
\(441\) 7.68838e11 6.20284e10i 0.967969 0.0780939i
\(442\) −9.52875e10 −0.118751
\(443\) 2.21049e11 3.82869e11i 0.272692 0.472317i −0.696858 0.717209i \(-0.745419\pi\)
0.969550 + 0.244892i \(0.0787526\pi\)
\(444\) 9.48880e9 + 1.64351e10i 0.0115875 + 0.0200701i
\(445\) −2.80048e11 4.85057e11i −0.338541 0.586371i
\(446\) −2.19457e11 + 3.80110e11i −0.262628 + 0.454886i
\(447\) −1.49016e10 −0.0176543
\(448\) −9.43675e10 4.95309e10i −0.110681 0.0580932i
\(449\) −7.93959e11 −0.921913 −0.460956 0.887423i \(-0.652494\pi\)
−0.460956 + 0.887423i \(0.652494\pi\)
\(450\) −1.19520e11 + 2.07014e11i −0.137399 + 0.237982i
\(451\) −7.78454e11 1.34832e12i −0.886010 1.53461i
\(452\) −4.05829e10 7.02916e10i −0.0457320 0.0792101i
\(453\) −1.31346e11 + 2.27497e11i −0.146546 + 0.253825i
\(454\) 1.85058e11 0.204435
\(455\) −2.90920e11 + 1.83956e11i −0.318216 + 0.201216i
\(456\) −7.85604e10 −0.0850868
\(457\) −4.85797e10 + 8.41426e10i −0.0520993 + 0.0902387i −0.890899 0.454202i \(-0.849925\pi\)
0.838800 + 0.544440i \(0.183258\pi\)
\(458\) −3.39026e11 5.87211e11i −0.360030 0.623590i
\(459\) −5.50282e10 9.53116e10i −0.0578666 0.100228i
\(460\) −3.72387e10 + 6.44994e10i −0.0387779 + 0.0671654i
\(461\) 8.96191e11 0.924158 0.462079 0.886839i \(-0.347104\pi\)
0.462079 + 0.886839i \(0.347104\pi\)
\(462\) −7.30558e9 1.81399e11i −0.00746047 0.185244i
\(463\) −6.89366e11 −0.697164 −0.348582 0.937278i \(-0.613337\pi\)
−0.348582 + 0.937278i \(0.613337\pi\)
\(464\) 1.73584e11 3.00656e11i 0.173851 0.301119i
\(465\) 7.05334e10 + 1.22167e11i 0.0699611 + 0.121176i
\(466\) 6.81895e11 + 1.18108e12i 0.669855 + 1.16022i
\(467\) 1.87790e11 3.25262e11i 0.182703 0.316451i −0.760097 0.649810i \(-0.774849\pi\)
0.942800 + 0.333358i \(0.108182\pi\)
\(468\) 2.44961e11 0.236043
\(469\) 4.43482e10 + 1.10117e12i 0.0423251 + 1.05094i
\(470\) 5.22190e11 0.493615
\(471\) −8.11098e10 + 1.40486e11i −0.0759416 + 0.131535i
\(472\) −3.76168e11 6.51542e11i −0.348853 0.604231i
\(473\) −1.78447e11 3.09079e11i −0.163920 0.283919i
\(474\) −7.89218e10 + 1.36697e11i −0.0718116 + 0.124381i
\(475\) −6.28695e11 −0.566655
\(476\) 1.63517e11 1.03396e11i 0.145993 0.0923151i
\(477\) −1.09285e12 −0.966558
\(478\) −1.45065e11 + 2.51260e11i −0.127098 + 0.220139i
\(479\) 5.90992e11 + 1.02363e12i 0.512946 + 0.888448i 0.999887 + 0.0150137i \(0.00477920\pi\)
−0.486941 + 0.873435i \(0.661887\pi\)
\(480\) 1.35312e10 + 2.34367e10i 0.0116346 + 0.0201517i
\(481\) 7.78172e10 1.34783e11i 0.0662861 0.114811i
\(482\) 3.98713e11 0.336472
\(483\) 3.60500e10 + 1.89216e10i 0.0301400 + 0.0158196i
\(484\) 8.32865e11 0.689875
\(485\) −7.17225e11 + 1.24227e12i −0.588596 + 1.01948i
\(486\) 2.13233e11 + 3.69330e11i 0.173377 + 0.300297i
\(487\) 1.39234e11 + 2.41160e11i 0.112167 + 0.194278i 0.916644 0.399706i \(-0.130888\pi\)
−0.804477 + 0.593984i \(0.797554\pi\)
\(488\) −1.08578e11 + 1.88063e11i −0.0866669 + 0.150111i
\(489\) −4.92771e10 −0.0389722
\(490\) 2.99618e11 6.31351e11i 0.234794 0.494753i
\(491\) 7.96998e10 0.0618857 0.0309429 0.999521i \(-0.490149\pi\)
0.0309429 + 0.999521i \(0.490149\pi\)
\(492\) 6.34355e10 1.09873e11i 0.0488078 0.0845376i
\(493\) 3.15100e11 + 5.45770e11i 0.240236 + 0.416101i
\(494\) 3.22135e11 + 5.57954e11i 0.243370 + 0.421529i
\(495\) 7.74888e11 1.34214e12i 0.580117 1.00479i
\(496\) 3.58210e11 0.265748
\(497\) 9.46880e11 + 4.96991e11i 0.696132 + 0.365380i
\(498\) −1.33753e11 −0.0974478
\(499\) −1.59936e11 + 2.77017e11i −0.115477 + 0.200011i −0.917970 0.396649i \(-0.870173\pi\)
0.802494 + 0.596661i \(0.203506\pi\)
\(500\) 3.78878e11 + 6.56236e11i 0.271103 + 0.469564i
\(501\) −8.05682e9 1.39548e10i −0.00571339 0.00989588i
\(502\) 2.78184e10 4.81829e10i 0.0195508 0.0338631i
\(503\) −1.67487e12 −1.16661 −0.583306 0.812253i \(-0.698241\pi\)
−0.583306 + 0.812253i \(0.698241\pi\)
\(504\) −4.20362e11 + 2.65806e11i −0.290193 + 0.183497i
\(505\) 6.85314e10 0.0468898
\(506\) −1.61077e11 + 2.78993e11i −0.109233 + 0.189198i
\(507\) −9.65524e10 1.67234e11i −0.0648974 0.112406i
\(508\) 2.44617e11 + 4.23689e11i 0.162967 + 0.282267i
\(509\) 3.12305e11 5.40927e11i 0.206228 0.357198i −0.744295 0.667851i \(-0.767214\pi\)
0.950523 + 0.310653i \(0.100548\pi\)
\(510\) −4.91255e10 −0.0321544
\(511\) −1.18786e11 2.94946e12i −0.0770672 1.91359i
\(512\) 6.87195e10 0.0441942
\(513\) −3.72063e11 + 6.44433e11i −0.237186 + 0.410818i
\(514\) −6.03310e11 1.04496e12i −0.381247 0.660339i
\(515\) 6.11072e11 + 1.05841e12i 0.382789 + 0.663010i
\(516\) 1.45414e10 2.51865e10i 0.00902992 0.0156403i
\(517\) 2.25874e12 1.39046
\(518\) 1.27157e10 + 3.15732e11i 0.00775989 + 0.192679i
\(519\) 4.63579e11 0.280460
\(520\) 1.10969e11 1.92203e11i 0.0665557 0.115278i
\(521\) −3.21473e11 5.56808e11i −0.191150 0.331082i 0.754481 0.656321i \(-0.227888\pi\)
−0.945632 + 0.325239i \(0.894555\pi\)
\(522\) −8.10047e11 1.40304e12i −0.477521 0.827091i
\(523\) −8.08666e11 + 1.40065e12i −0.472619 + 0.818601i −0.999509 0.0313330i \(-0.990025\pi\)
0.526890 + 0.849934i \(0.323358\pi\)
\(524\) −1.54954e12 −0.897869
\(525\) 1.00065e11 6.32738e10i 0.0574864 0.0363502i
\(526\) 1.88168e12 1.07179
\(527\) −3.25123e11 + 5.63130e11i −0.183612 + 0.318025i
\(528\) 5.85295e10 + 1.01376e11i 0.0327734 + 0.0567653i
\(529\) 8.64453e11 + 1.49728e12i 0.479944 + 0.831288i
\(530\) −4.95067e11 + 8.57481e11i −0.272535 + 0.472045i
\(531\) −3.51086e12 −1.91641
\(532\) −1.15823e12 6.07922e11i −0.626891 0.329038i
\(533\) −1.04046e12 −0.558411
\(534\) 9.87118e10 1.70974e11i 0.0525332 0.0909901i
\(535\) −9.99439e10 1.73108e11i −0.0527430 0.0913535i
\(536\) −3.55301e11 6.15399e11i −0.185932 0.322044i
\(537\) 4.88398e10 8.45930e10i 0.0253448 0.0438986i
\(538\) −1.18811e12 −0.611414
\(539\) 1.29600e12 2.73092e12i 0.661389 1.39367i
\(540\) 2.56336e11 0.129729
\(541\) 1.21728e12 2.10840e12i 0.610948 1.05819i −0.380132 0.924932i \(-0.624122\pi\)
0.991081 0.133262i \(-0.0425451\pi\)
\(542\) −6.43193e11 1.11404e12i −0.320143 0.554505i
\(543\) −2.88432e11 4.99580e11i −0.142379 0.246607i
\(544\) −6.23720e10 + 1.08032e11i −0.0305348 + 0.0528878i
\(545\) −1.30622e12 −0.634206
\(546\) −1.07426e11 5.63850e10i −0.0517301 0.0271517i
\(547\) 3.63462e12 1.73587 0.867934 0.496680i \(-0.165448\pi\)
0.867934 + 0.496680i \(0.165448\pi\)
\(548\) −6.39440e11 + 1.10754e12i −0.302891 + 0.524623i
\(549\) 5.06692e11 + 8.77616e11i 0.238050 + 0.412315i
\(550\) 4.68393e11 + 8.11281e11i 0.218262 + 0.378041i
\(551\) 2.13050e12 3.69013e12i 0.984688 1.70553i
\(552\) −2.62520e10 −0.0120347
\(553\) −2.22135e12 + 1.40462e12i −1.01008 + 0.638699i
\(554\) −2.08924e12 −0.942313
\(555\) 4.01186e10 6.94875e10i 0.0179485 0.0310877i
\(556\) 6.91026e11 + 1.19689e12i 0.306660 + 0.531152i
\(557\) 2.22234e10 + 3.84921e10i 0.00978278 + 0.0169443i 0.870875 0.491504i \(-0.163553\pi\)
−0.861093 + 0.508448i \(0.830219\pi\)
\(558\) 8.35814e11 1.44767e12i 0.364969 0.632144i
\(559\) −2.38507e11 −0.103311
\(560\) 1.81328e10 + 4.50240e11i 0.00779146 + 0.193463i
\(561\) −2.12493e11 −0.0905757
\(562\) 4.98662e11 8.63708e11i 0.210859 0.365219i
\(563\) 1.93179e12 + 3.34596e12i 0.810349 + 1.40357i 0.912620 + 0.408810i \(0.134056\pi\)
−0.102270 + 0.994757i \(0.532611\pi\)
\(564\) 9.20313e10 + 1.59403e11i 0.0382983 + 0.0663346i
\(565\) −1.71584e11 + 2.97193e11i −0.0708369 + 0.122693i
\(566\) 1.08530e10 0.00444505
\(567\) 9.05362e10 + 2.24803e12i 0.0367874 + 0.913435i
\(568\) −6.89529e11 −0.277962
\(569\) 1.03247e12 1.78828e12i 0.412925 0.715206i −0.582284 0.812986i \(-0.697841\pi\)
0.995208 + 0.0977795i \(0.0311740\pi\)
\(570\) 1.66077e11 + 2.87653e11i 0.0658979 + 0.114139i
\(571\) 1.55084e12 + 2.68613e12i 0.610527 + 1.05746i 0.991152 + 0.132734i \(0.0423755\pi\)
−0.380625 + 0.924729i \(0.624291\pi\)
\(572\) 4.79997e11 8.31379e11i 0.187481 0.324726i
\(573\) −1.38776e11 −0.0537796
\(574\) 1.78547e12 1.12900e12i 0.686514 0.434101i
\(575\) −2.10087e11 −0.0801480
\(576\) 1.60343e11 2.77723e11i 0.0606946 0.105126i
\(577\) −1.04111e11 1.80326e11i −0.0391027 0.0677279i 0.845812 0.533482i \(-0.179117\pi\)
−0.884914 + 0.465754i \(0.845783\pi\)
\(578\) 8.35481e11 + 1.44710e12i 0.311359 + 0.539290i
\(579\) 2.84447e11 4.92677e11i 0.105184 0.182184i
\(580\) −1.46782e12 −0.538577
\(581\) −1.97194e12 1.03502e12i −0.717963 0.376839i
\(582\) −5.05618e11 −0.182671
\(583\) −2.14142e12 + 3.70905e12i −0.767704 + 1.32970i
\(584\) 9.51663e11 + 1.64833e12i 0.338552 + 0.586389i
\(585\) −5.17848e11 8.96938e11i −0.182810 0.316637i
\(586\) −4.53732e10 + 7.85887e10i −0.0158950 + 0.0275309i
\(587\) −2.56958e12 −0.893286 −0.446643 0.894712i \(-0.647381\pi\)
−0.446643 + 0.894712i \(0.647381\pi\)
\(588\) 2.45531e11 1.98089e10i 0.0847047 0.00683382i
\(589\) 4.39653e12 1.50519
\(590\) −1.59044e12 + 2.75472e12i −0.540359 + 0.935929i
\(591\) −1.35041e11 2.33897e11i −0.0455324 0.0788644i
\(592\) −1.01873e11 1.76449e11i −0.0340888 0.0590435i
\(593\) −1.01774e12 + 1.76278e12i −0.337980 + 0.585399i −0.984053 0.177877i \(-0.943077\pi\)
0.646073 + 0.763276i \(0.276410\pi\)
\(594\) 1.10879e12 0.365434
\(595\) −7.24265e11 3.80146e11i −0.236903 0.124344i
\(596\) 1.59986e11 0.0519366
\(597\) 2.08983e11 3.61969e11i 0.0673327 0.116624i
\(598\) 1.07646e11 + 1.86448e11i 0.0344224 + 0.0596213i
\(599\) 1.40874e12 + 2.44002e12i 0.447107 + 0.774412i 0.998196 0.0600345i \(-0.0191211\pi\)
−0.551090 + 0.834446i \(0.685788\pi\)
\(600\) −3.81689e10 + 6.61105e10i −0.0120235 + 0.0208252i
\(601\) 2.84630e12 0.889908 0.444954 0.895553i \(-0.353220\pi\)
0.444954 + 0.895553i \(0.353220\pi\)
\(602\) 4.09287e11 2.58803e11i 0.127012 0.0803129i
\(603\) −3.31610e12 −1.02141
\(604\) 1.41014e12 2.44244e12i 0.431119 0.746720i
\(605\) −1.76067e12 3.04958e12i −0.534293 0.925423i
\(606\) 1.20781e10 + 2.09198e10i 0.00363806 + 0.00630131i
\(607\) −1.51972e12 + 2.63223e12i −0.454375 + 0.787000i −0.998652 0.0519053i \(-0.983471\pi\)
0.544277 + 0.838905i \(0.316804\pi\)
\(608\) 8.43436e11 0.250314
\(609\) 3.22895e10 + 8.01752e11i 0.00951225 + 0.236190i
\(610\) 9.18136e11 0.268487
\(611\) 7.54744e11 1.30725e12i 0.219086 0.379468i
\(612\) 2.91066e11 + 5.04141e11i 0.0838706 + 0.145268i
\(613\) −2.85482e12 4.94469e12i −0.816594 1.41438i −0.908178 0.418584i \(-0.862526\pi\)
0.0915841 0.995797i \(-0.470807\pi\)
\(614\) 1.44937e12 2.51038e12i 0.411548 0.712823i
\(615\) −5.36410e11 −0.151202
\(616\) 7.84337e10 + 1.94752e12i 0.0219477 + 0.544965i
\(617\) −2.92315e12 −0.812023 −0.406011 0.913868i \(-0.633081\pi\)
−0.406011 + 0.913868i \(0.633081\pi\)
\(618\) −2.15392e11 + 3.73070e11i −0.0593993 + 0.102883i
\(619\) −2.88780e12 5.00181e12i −0.790604 1.36937i −0.925593 0.378519i \(-0.876433\pi\)
0.134989 0.990847i \(-0.456900\pi\)
\(620\) −7.57256e11 1.31161e12i −0.205817 0.356485i
\(621\) −1.24330e11 + 2.15346e11i −0.0335477 + 0.0581064i
\(622\) 1.66090e12 0.444925
\(623\) 2.77837e12 1.75684e12i 0.738913 0.467235i
\(624\) 7.82290e10 0.0206556
\(625\) 8.38607e11 1.45251e12i 0.219836 0.380767i
\(626\) 1.19091e12 + 2.06272e12i 0.309953 + 0.536854i
\(627\) 7.18368e11 + 1.24425e12i 0.185628 + 0.321517i
\(628\) 8.70806e11 1.50828e12i 0.223410 0.386958i
\(629\) 3.69853e11 0.0942110
\(630\) 1.86191e12 + 9.77265e11i 0.470897 + 0.247161i
\(631\) 2.44150e12 0.613090 0.306545 0.951856i \(-0.400827\pi\)
0.306545 + 0.951856i \(0.400827\pi\)
\(632\) 8.47315e11 1.46759e12i 0.211260 0.365914i
\(633\) −3.72716e11 6.45564e11i −0.0922703 0.159817i
\(634\) −1.58159e12 2.73939e12i −0.388769 0.673368i
\(635\) 1.03424e12 1.79136e12i 0.252429 0.437220i
\(636\) −3.49005e11 −0.0845813
\(637\) −1.14748e12 1.66259e12i −0.276132 0.400089i
\(638\) −6.34909e12 −1.51711
\(639\) −1.60888e12 + 2.78666e12i −0.381742 + 0.661197i
\(640\) −1.45273e11 2.51620e11i −0.0342275 0.0592837i
\(641\) −3.95349e12 6.84764e12i −0.924952 1.60206i −0.791639 0.610989i \(-0.790772\pi\)
−0.133313 0.991074i \(-0.542562\pi\)
\(642\) 3.52285e10 6.10175e10i 0.00818439 0.0141758i
\(643\) 1.32729e12 0.306208 0.153104 0.988210i \(-0.451073\pi\)
0.153104 + 0.988210i \(0.451073\pi\)
\(644\) −3.87037e11 2.03145e11i −0.0886679 0.0465393i
\(645\) −1.22962e11 −0.0279739
\(646\) −7.65530e11 + 1.32594e12i −0.172948 + 0.299555i
\(647\) 1.61610e12 + 2.79917e12i 0.362576 + 0.628000i 0.988384 0.151977i \(-0.0485641\pi\)
−0.625808 + 0.779977i \(0.715231\pi\)
\(648\) −7.25341e11 1.25633e12i −0.161605 0.279908i
\(649\) −6.87946e12 + 1.19156e13i −1.52214 + 2.63642i
\(650\) 6.26042e11 0.137560
\(651\) −6.99766e11 + 4.42481e11i −0.152700 + 0.0965561i
\(652\) 5.29046e11 0.114651
\(653\) 9.19644e11 1.59287e12i 0.197929 0.342824i −0.749927 0.661520i \(-0.769912\pi\)
0.947857 + 0.318696i \(0.103245\pi\)
\(654\) −2.30209e11 3.98734e11i −0.0492065 0.0852281i
\(655\) 3.27573e12 + 5.67374e12i 0.695381 + 1.20444i
\(656\) −6.81052e11 + 1.17962e12i −0.143586 + 0.248699i
\(657\) 8.88208e12 1.85982
\(658\) 1.23329e11 + 3.06227e12i 0.0256476 + 0.636834i
\(659\) 5.84606e12 1.20748 0.603738 0.797182i \(-0.293677\pi\)
0.603738 + 0.797182i \(0.293677\pi\)
\(660\) 2.47462e11 4.28618e11i 0.0507647 0.0879270i
\(661\) −2.82594e12 4.89468e12i −0.575780 0.997280i −0.995956 0.0898379i \(-0.971365\pi\)
0.420176 0.907443i \(-0.361968\pi\)
\(662\) −4.46304e11 7.73022e11i −0.0903171 0.156434i
\(663\) −7.10032e10 + 1.22981e11i −0.0142714 + 0.0247188i
\(664\) 1.43599e12 0.286679
\(665\) 2.22555e11 + 5.52606e12i 0.0441306 + 1.09577i
\(666\) −9.50804e11 −0.187265
\(667\) 7.11933e11 1.23310e12i 0.139275 0.241231i
\(668\) 8.64991e10 + 1.49821e11i 0.0168081 + 0.0291124i
\(669\) 3.27055e11 + 5.66476e11i 0.0631252 + 0.109336i
\(670\) −1.50221e12 + 2.60190e12i −0.288001 + 0.498832i
\(671\) 3.97141e12 0.756299
\(672\) −1.34244e11 + 8.48860e10i −0.0253941 + 0.0160574i
\(673\) −1.86409e12 −0.350267 −0.175133 0.984545i \(-0.556036\pi\)
−0.175133 + 0.984545i \(0.556036\pi\)
\(674\) −3.21398e12 + 5.56678e12i −0.599894 + 1.03905i
\(675\) 3.61537e11 + 6.26201e11i 0.0670326 + 0.116104i
\(676\) 1.03660e12 + 1.79544e12i 0.190920 + 0.330683i
\(677\) 1.14713e12 1.98689e12i 0.209877 0.363517i −0.741799 0.670622i \(-0.766027\pi\)
0.951675 + 0.307106i \(0.0993604\pi\)
\(678\) −1.20961e11 −0.0219842
\(679\) −7.45441e12 3.91261e12i −1.34586 0.706403i
\(680\) 5.27418e11 0.0945942
\(681\) 1.37895e11 2.38841e11i 0.0245690 0.0425547i
\(682\) −3.27553e12 5.67338e12i −0.579764 1.00418i
\(683\) 2.46771e12 + 4.27420e12i 0.433911 + 0.751556i 0.997206 0.0746998i \(-0.0237999\pi\)
−0.563295 + 0.826256i \(0.690467\pi\)
\(684\) 1.96799e12 3.40866e12i 0.343772 0.595431i
\(685\) 5.40710e12 0.938332
\(686\) 3.77318e12 + 1.60794e12i 0.650503 + 0.277211i
\(687\) −1.01050e12 −0.173073
\(688\) −1.56119e11 + 2.70406e11i −0.0265649 + 0.0460117i
\(689\) 1.43108e12 + 2.47871e12i 0.241924 + 0.419024i
\(690\) 5.54967e10 + 9.61230e10i 0.00932065 + 0.0161438i
\(691\) −3.95992e12 + 6.85879e12i −0.660747 + 1.14445i 0.319672 + 0.947528i \(0.396427\pi\)
−0.980420 + 0.196920i \(0.936906\pi\)
\(692\) −4.97704e12 −0.825076
\(693\) 8.05372e12 + 4.22717e12i 1.32647 + 0.696227i
\(694\) −5.40595e12 −0.884616
\(695\) 2.92166e12 5.06046e12i 0.475004 0.822731i
\(696\) −2.58691e11 4.48065e11i −0.0417868 0.0723769i
\(697\) −1.23629e12 2.14132e12i −0.198414 0.343664i
\(698\) 2.87968e12 4.98774e12i 0.459192 0.795344i
\(699\) 2.03245e12 0.322012
\(700\) −1.07431e12 + 6.79316e11i −0.169118 + 0.106938i
\(701\) −1.24405e12 −0.194584 −0.0972919 0.995256i \(-0.531018\pi\)
−0.0972919 + 0.995256i \(0.531018\pi\)
\(702\) 3.70494e11 6.41714e11i 0.0575790 0.0997297i
\(703\) −1.25035e12 2.16567e12i −0.193078 0.334421i
\(704\) −6.28380e11 1.08839e12i −0.0964152 0.166996i
\(705\) 3.89108e11 6.73955e11i 0.0593225 0.102750i
\(706\) 3.04554e12 0.461364
\(707\) 1.61855e10 + 4.01887e11i 0.00243634 + 0.0604946i
\(708\) −1.12120e12 −0.167700
\(709\) 3.64164e12 6.30751e12i 0.541239 0.937454i −0.457594 0.889161i \(-0.651289\pi\)
0.998833 0.0482926i \(-0.0153780\pi\)
\(710\) 1.45766e12 + 2.52475e12i 0.215276 + 0.372868i
\(711\) −3.95409e12 6.84868e12i −0.580274 1.00506i
\(712\) −1.05978e12 + 1.83560e12i −0.154546 + 0.267681i
\(713\) 1.46916e12 0.212895
\(714\) −1.16022e10 2.88085e11i −0.00167071 0.0414839i
\(715\) −4.05885e12 −0.580799
\(716\) −5.24351e11 + 9.08202e11i −0.0745613 + 0.129144i
\(717\) 2.16190e11 + 3.74451e11i 0.0305491 + 0.0529126i
\(718\) −3.14158e12 5.44138e12i −0.441152 0.764098i
\(719\) 1.97345e12 3.41811e12i 0.275388 0.476986i −0.694845 0.719160i \(-0.744527\pi\)
0.970233 + 0.242174i \(0.0778603\pi\)
\(720\) −1.35586e12 −0.188027
\(721\) −6.06247e12 + 3.83346e12i −0.835490 + 0.528303i
\(722\) 5.18899e12 0.710666
\(723\) 2.97100e11 5.14592e11i 0.0404371 0.0700391i
\(724\) 3.09665e12 + 5.36356e12i 0.418860 + 0.725486i
\(725\) −2.07022e12 3.58573e12i −0.278289 0.482010i
\(726\) 6.20607e11 1.07492e12i 0.0829090 0.143603i
\(727\) −1.29298e13 −1.71667 −0.858335 0.513089i \(-0.828501\pi\)
−0.858335 + 0.513089i \(0.828501\pi\)
\(728\) 1.15334e12 + 6.05358e11i 0.152183 + 0.0798768i
\(729\) −6.33557e12 −0.830830
\(730\) 4.02363e12 6.96913e12i 0.524403 0.908292i
\(731\) −2.83397e11 4.90858e11i −0.0367086 0.0635811i
\(732\) 1.61813e11 + 2.80269e11i 0.0208312 + 0.0360807i
\(733\) 3.52694e11 6.10884e11i 0.0451263 0.0781611i −0.842580 0.538571i \(-0.818964\pi\)
0.887706 + 0.460410i \(0.152298\pi\)
\(734\) −5.19158e11 −0.0660187
\(735\) −5.91583e11 8.57147e11i −0.0747691 0.108333i
\(736\) 2.81845e11 0.0354046
\(737\) −6.49784e12 + 1.12546e13i −0.811269 + 1.40516i
\(738\) 3.17820e12 + 5.50481e12i 0.394392 + 0.683107i
\(739\) −1.24236e12 2.15182e12i −0.153231 0.265403i 0.779183 0.626797i \(-0.215634\pi\)
−0.932413 + 0.361394i \(0.882301\pi\)
\(740\) −4.30719e11 + 7.46027e11i −0.0528021 + 0.0914560i
\(741\) 9.60152e11 0.116992
\(742\) −5.14543e12 2.70069e12i −0.623167 0.327083i
\(743\) 7.27764e12 0.876074 0.438037 0.898957i \(-0.355674\pi\)
0.438037 + 0.898957i \(0.355674\pi\)
\(744\) 2.66919e11 4.62318e11i 0.0319376 0.0553175i
\(745\) −3.38210e11 5.85797e11i −0.0402238 0.0696697i
\(746\) 3.51200e12 + 6.08295e12i 0.415173 + 0.719101i
\(747\) 3.35061e12 5.80342e12i 0.393714 0.681932i
\(748\) 2.28135e12 0.266462
\(749\) 9.91549e11 6.26983e11i 0.115119 0.0727927i
\(750\) 1.12928e12 0.130324
\(751\) 2.75196e12 4.76654e12i 0.315691 0.546794i −0.663893 0.747828i \(-0.731097\pi\)
0.979584 + 0.201034i \(0.0644302\pi\)
\(752\) −9.88061e11 1.71137e12i −0.112669 0.195148i
\(753\) −4.14576e10 7.18067e10i −0.00469923 0.00813931i
\(754\) −2.12151e12 + 3.67456e12i −0.239042 + 0.414032i
\(755\) −1.19242e13 −1.33557
\(756\) 6.05404e10 + 1.50323e12i 0.00674058 + 0.167369i
\(757\) 1.41842e13 1.56991 0.784955 0.619553i \(-0.212686\pi\)
0.784955 + 0.619553i \(0.212686\pi\)
\(758\) 2.85546e12 4.94580e12i 0.314170 0.544159i
\(759\) 2.40052e11 + 4.15782e11i 0.0262553 + 0.0454755i
\(760\) −1.78302e12 3.08828e12i −0.193863 0.335781i
\(761\) −5.00695e12 + 8.67229e12i −0.541180 + 0.937352i 0.457656 + 0.889129i \(0.348689\pi\)
−0.998837 + 0.0482227i \(0.984644\pi\)
\(762\) 7.29102e11 0.0783414
\(763\) −3.08497e11 7.66001e12i −0.0329526 0.818218i
\(764\) 1.48992e12 0.158213
\(765\) 1.23063e12 2.13151e12i 0.129912 0.225014i
\(766\) 1.21978e12 + 2.11273e12i 0.128013 + 0.221724i
\(767\) 4.59746e12 + 7.96303e12i 0.479665 + 0.830805i
\(768\) 5.12061e10 8.86916e10i 0.00531124 0.00919935i
\(769\) 1.39641e12 0.143994 0.0719968 0.997405i \(-0.477063\pi\)
0.0719968 + 0.997405i \(0.477063\pi\)
\(770\) 6.96514e12 4.40424e12i 0.714038 0.451506i
\(771\) −1.79822e12 −0.183273
\(772\) −3.05387e12 + 5.28945e12i −0.309437 + 0.535960i
\(773\) 3.71378e12 + 6.43246e12i 0.374118 + 0.647992i 0.990195 0.139695i \(-0.0446121\pi\)
−0.616077 + 0.787686i \(0.711279\pi\)
\(774\) 7.28546e11 + 1.26188e12i 0.0729663 + 0.126381i
\(775\) 2.13607e12 3.69979e12i 0.212696 0.368400i
\(776\) 5.42838e12 0.537394
\(777\) 4.16969e11 + 2.18856e11i 0.0410402 + 0.0215409i
\(778\) 8.91389e12 0.872286
\(779\) −8.35896e12 + 1.44781e13i −0.813268 + 1.40862i
\(780\) −1.65376e11 2.86440e11i −0.0159973 0.0277081i
\(781\) 6.30515e12 + 1.09208e13i 0.606409 + 1.05033i
\(782\) −2.55812e11 + 4.43079e11i −0.0244619 + 0.0423692i
\(783\) −4.90065e12 −0.465935
\(784\) −2.63605e12 + 2.12672e11i −0.249190 + 0.0201042i
\(785\) −7.36353e12 −0.692106
\(786\) −1.15464e12 + 1.99989e12i −0.107906 + 0.186898i
\(787\) 2.15657e12 + 3.73529e12i 0.200391 + 0.347087i 0.948654 0.316314i \(-0.102445\pi\)
−0.748264 + 0.663402i \(0.769112\pi\)
\(788\) 1.44981e12 + 2.51115e12i 0.133950 + 0.232009i
\(789\) 1.40213e12 2.42856e12i 0.128808 0.223101i
\(790\) −7.16489e12 −0.654467
\(791\) −1.78335e12 9.36029e11i −0.161972 0.0850149i
\(792\) −5.86481e12 −0.529652
\(793\) 1.32702e12 2.29847e12i 0.119165 0.206400i
\(794\) −6.92729e12 1.19984e13i −0.618545 1.07135i
\(795\) 7.37796e11 + 1.27790e12i 0.0655064 + 0.113460i
\(796\) −2.24367e12 + 3.88615e12i −0.198084 + 0.343092i
\(797\) −6.97760e12 −0.612553 −0.306276 0.951943i \(-0.599083\pi\)
−0.306276 + 0.951943i \(0.599083\pi\)
\(798\) −1.64766e12 + 1.04186e12i −0.143831 + 0.0909484i
\(799\) 3.58718e12 0.311382
\(800\) 4.09787e11 7.09771e11i 0.0353715 0.0612652i
\(801\) 4.94560e12 + 8.56602e12i 0.424495 + 0.735246i
\(802\) 5.41193e12 + 9.37373e12i 0.461921 + 0.800070i
\(803\) 1.74043e13 3.01451e13i 1.47719 2.55857i
\(804\) −1.05900e12 −0.0893811
\(805\) 7.43696e10 + 1.84661e12i 0.00624186 + 0.154986i
\(806\) −4.37798e12 −0.365398
\(807\) −8.85314e11 + 1.53341e12i −0.0734796 + 0.127270i
\(808\) −1.29672e11 2.24598e11i −0.0107027 0.0185376i
\(809\) −1.14195e11 1.97791e11i −0.00937296 0.0162344i 0.861301 0.508095i \(-0.169650\pi\)
−0.870674 + 0.491861i \(0.836317\pi\)
\(810\) −3.06674e12 + 5.31175e12i −0.250319 + 0.433566i
\(811\) −1.24712e12 −0.101231 −0.0506156 0.998718i \(-0.516118\pi\)
−0.0506156 + 0.998718i \(0.516118\pi\)
\(812\) −3.46664e11 8.60772e12i −0.0279838 0.694842i
\(813\) −1.91709e12 −0.153899
\(814\) −1.86308e12 + 3.22695e12i −0.148738 + 0.257622i
\(815\) −1.11840e12 1.93713e12i −0.0887950 0.153798i
\(816\) 9.29527e10 + 1.60999e11i 0.00733933 + 0.0127121i
\(817\) −1.91614e12 + 3.31885e12i −0.150463 + 0.260609i
\(818\) −4.46468e12 −0.348658
\(819\) 5.13759e12 3.24864e12i 0.399008 0.252304i
\(820\) 5.75897e12 0.444818
\(821\) 2.13203e11 3.69278e11i 0.0163775 0.0283667i −0.857720 0.514116i \(-0.828120\pi\)
0.874098 + 0.485750i \(0.161453\pi\)
\(822\) 9.52953e11 + 1.65056e12i 0.0728029 + 0.126098i
\(823\) 5.10619e11 + 8.84418e11i 0.0387970 + 0.0671983i 0.884772 0.466024i \(-0.154314\pi\)
−0.845975 + 0.533223i \(0.820981\pi\)
\(824\) 2.31248e12 4.00533e12i 0.174745 0.302667i
\(825\) 1.39609e12 0.104923
\(826\) −1.65301e13 8.67617e12i −1.23556 0.648511i
\(827\) −5.09034e12 −0.378418 −0.189209 0.981937i \(-0.560592\pi\)
−0.189209 + 0.981937i \(0.560592\pi\)
\(828\) 6.57630e11 1.13905e12i 0.0486234 0.0842182i
\(829\) −6.45038e12 1.11724e13i −0.474340 0.821582i 0.525228 0.850962i \(-0.323980\pi\)
−0.999568 + 0.0293800i \(0.990647\pi\)
\(830\) −3.03568e12 5.25796e12i −0.222027 0.384562i
\(831\) −1.55679e12 + 2.69645e12i −0.113247 + 0.196149i
\(832\) −8.39877e11 −0.0607660
\(833\) 2.05823e12 4.33707e12i 0.148112 0.312100i
\(834\) 2.05966e12 0.147418
\(835\) 3.65718e11 6.33442e11i 0.0260350 0.0450939i
\(836\) −7.71249e12 1.33584e13i −0.546093 0.945861i
\(837\) −2.52827e12 4.37909e12i −0.178057 0.308403i
\(838\) 7.69875e11 1.33346e12i 0.0539290 0.0934078i
\(839\) −6.08459e12 −0.423938 −0.211969 0.977276i \(-0.567988\pi\)
−0.211969 + 0.977276i \(0.567988\pi\)
\(840\) 5.94606e11 + 3.12092e11i 0.0412071 + 0.0216285i
\(841\) 1.35548e13 0.934353
\(842\) −3.48349e11 + 6.03359e11i −0.0238842 + 0.0413687i
\(843\) −7.43153e11 1.28718e12i −0.0506821 0.0877839i
\(844\) 4.00153e12 + 6.93086e12i 0.271447 + 0.470161i
\(845\) 4.38274e12 7.59113e12i 0.295727 0.512214i
\(846\) −9.22179e12 −0.618940
\(847\) 1.74677e13 1.10453e13i 1.16617 0.737400i
\(848\) 3.74696e12 0.248827
\(849\) 8.08709e9 1.40073e10i 0.000534205 0.000925270i
\(850\) 7.43872e11 + 1.28842e12i 0.0488779 + 0.0846591i
\(851\) −4.17821e11 7.23686e11i −0.0273091 0.0473007i
\(852\) −5.13801e11 + 8.89929e11i −0.0334054 + 0.0578598i
\(853\) 1.69683e13 1.09741 0.548703 0.836017i \(-0.315122\pi\)
0.548703 + 0.836017i \(0.315122\pi\)
\(854\) 2.16842e11 + 5.38420e12i 0.0139503 + 0.346387i
\(855\) −1.66413e13 −1.06498
\(856\) −3.78218e11 + 6.55092e11i −0.0240774 + 0.0417033i
\(857\) 2.35529e12 + 4.07948e12i 0.149152 + 0.258339i 0.930914 0.365237i \(-0.119012\pi\)
−0.781762 + 0.623577i \(0.785679\pi\)
\(858\) −7.15337e11 1.23900e12i −0.0450628 0.0780510i
\(859\) −4.02258e12 + 6.96732e12i −0.252079 + 0.436613i −0.964098 0.265547i \(-0.914447\pi\)
0.712019 + 0.702160i \(0.247781\pi\)
\(860\) 1.32014e12 0.0822957
\(861\) −1.26687e11 3.14566e12i −0.00785630 0.195073i
\(862\) 1.24184e13 0.766093
\(863\) −8.78137e12 + 1.52098e13i −0.538907 + 0.933414i 0.460056 + 0.887890i \(0.347829\pi\)
−0.998963 + 0.0455244i \(0.985504\pi\)
\(864\) −4.85026e11 8.40089e11i −0.0296110 0.0512877i
\(865\) 1.05215e13 + 1.82237e13i 0.639004 + 1.10679i
\(866\) −4.78107e12 + 8.28106e12i −0.288865 + 0.500329i
\(867\) 2.49023e12 0.149676
\(868\) 7.51278e12 4.75053e12i 0.449223 0.284056i
\(869\) −3.09919e13 −1.84357
\(870\) −1.09374e12 + 1.89442e12i −0.0647260 + 0.112109i
\(871\) 4.34242e12 + 7.52129e12i 0.255653 + 0.442803i
\(872\) 2.47155e12 + 4.28086e12i 0.144759 + 0.250730i
\(873\) 1.26661e13 2.19383e13i 0.738037 1.27832i
\(874\) 3.45925e12 0.200531
\(875\) 1.66491e13 + 8.73867e12i 0.960186 + 0.503975i
\(876\) 2.83652e12 0.162748
\(877\) −4.21010e12 + 7.29210e12i −0.240322 + 0.416250i −0.960806 0.277221i \(-0.910586\pi\)
0.720484 + 0.693472i \(0.243920\pi\)
\(878\) 2.55867e12 + 4.43174e12i 0.145308 + 0.251680i
\(879\) 6.76194e10 + 1.17120e11i 0.00382051 + 0.00661732i
\(880\) −2.65679e12 + 4.60170e12i −0.149343 + 0.258670i
\(881\) −3.03091e13 −1.69504 −0.847522 0.530760i \(-0.821907\pi\)
−0.847522 + 0.530760i \(0.821907\pi\)
\(882\) −5.29121e12 + 1.11496e13i −0.294406 + 0.620368i
\(883\) −2.44649e12 −0.135432 −0.0677159 0.997705i \(-0.521571\pi\)
−0.0677159 + 0.997705i \(0.521571\pi\)
\(884\) 7.62300e11 1.32034e12i 0.0419847 0.0727196i
\(885\) 2.37022e12 + 4.10534e12i 0.129880 + 0.224959i
\(886\) 3.53679e12 + 6.12590e12i 0.192822 + 0.333978i
\(887\) −1.02686e13 + 1.77858e13i −0.557001 + 0.964753i 0.440744 + 0.897633i \(0.354715\pi\)
−0.997745 + 0.0671207i \(0.978619\pi\)
\(888\) −3.03642e11 −0.0163871
\(889\) 1.07493e13 + 5.64200e12i 0.577193 + 0.302953i
\(890\) 8.96152e12 0.478770
\(891\) −1.32652e13 + 2.29761e13i −0.705123 + 1.22131i
\(892\) −3.51131e12 6.08176e12i −0.185706 0.321653i
\(893\) −1.21271e13 2.10047e13i −0.638152 1.10531i
\(894\) 1.19213e11 2.06483e11i 0.00624173 0.0108110i
\(895\) 4.43391e12 0.230985
\(896\) 1.44126e12 9.11347e11i 0.0747061 0.0472387i
\(897\) 3.20847e11 0.0165475
\(898\) 6.35167e12 1.10014e13i 0.325945 0.564554i
\(899\) 1.44773e13 + 2.50754e13i 0.739211 + 1.28035i
\(900\) −1.91231e12 3.31223e12i −0.0971556 0.168278i
\(901\) −3.40087e12 + 5.89047e12i −0.171921 + 0.297775i
\(902\) 2.49105e13 1.25301
\(903\) −2.90407e10 7.21085e11i −0.00145349 0.0360904i
\(904\) 1.29865e12 0.0646748
\(905\) 1.30926e13 2.26771e13i 0.648796 1.12375i
\(906\) −2.10153e12 3.63996e12i −0.103624 0.179481i
\(907\) −6.75232e12 1.16954e13i −0.331299 0.573827i 0.651468 0.758676i \(-0.274154\pi\)
−0.982767 + 0.184849i \(0.940820\pi\)
\(908\) −1.48046e12 + 2.56423e12i −0.0722787 + 0.125190i
\(909\) −1.21025e12 −0.0587948
\(910\) −2.21616e11 5.50275e12i −0.0107131 0.266007i
\(911\) 2.83771e13 1.36501 0.682504 0.730882i \(-0.260891\pi\)
0.682504 + 0.730882i \(0.260891\pi\)
\(912\) 6.28484e11 1.08857e12i 0.0300827 0.0521048i
\(913\) −1.31309e13 2.27434e13i −0.625426 1.08327i
\(914\) −7.77276e11 1.34628e12i −0.0368398 0.0638084i
\(915\) 6.84146e11 1.18498e12i 0.0322667 0.0558875i
\(916\) 1.08488e13 0.509159
\(917\) −3.24987e13 + 2.05498e13i −1.51776 + 0.959723i
\(918\) 1.76090e12 0.0818357
\(919\) 1.30106e13 2.25350e13i 0.601696 1.04217i −0.390868 0.920447i \(-0.627825\pi\)
0.992564 0.121722i \(-0.0388415\pi\)
\(920\) −5.95820e11 1.03199e12i −0.0274201 0.0474931i
\(921\) −2.15998e12 3.74120e12i −0.0989196 0.171334i
\(922\) −7.16953e12 + 1.24180e13i −0.326739 + 0.565929i
\(923\) 8.42730e12 0.382191
\(924\) 2.57198e12 + 1.34996e12i 0.116076 + 0.0609252i
\(925\) −2.42995e12 −0.109134
\(926\) 5.51493e12 9.55213e12i 0.246485 0.426924i
\(927\) −1.07914e13 1.86913e13i −0.479977 0.831344i
\(928\) 2.77734e12 + 4.81049e12i 0.122931 + 0.212923i
\(929\) 8.52205e12 1.47606e13i 0.375382 0.650181i −0.615002 0.788525i \(-0.710845\pi\)
0.990384 + 0.138345i \(0.0441782\pi\)
\(930\) −2.25707e12 −0.0989399
\(931\) −3.23538e13 + 2.61025e12i −1.41141 + 0.113870i
\(932\) −2.18206e13 −0.947318
\(933\) 1.23762e12 2.14361e12i 0.0534710 0.0926145i
\(934\) 3.00464e12 + 5.20419e12i 0.129191 + 0.223765i
\(935\) −4.82278e12 8.35330e12i −0.206369 0.357442i
\(936\) −1.95969e12 + 3.39428e12i −0.0834538 + 0.144546i
\(937\) 1.17078e13 0.496188 0.248094 0.968736i \(-0.420196\pi\)
0.248094 + 0.968736i \(0.420196\pi\)
\(938\) −1.56131e13 8.19487e12i −0.658530 0.345644i
\(939\) 3.54962e12 0.149000
\(940\) −4.17752e12 + 7.23567e12i −0.174519 + 0.302276i
\(941\) 7.99721e12 + 1.38516e13i 0.332495 + 0.575898i 0.983000 0.183603i \(-0.0587762\pi\)
−0.650505 + 0.759502i \(0.725443\pi\)
\(942\) −1.29776e12 2.24778e12i −0.0536988 0.0930090i
\(943\) −2.79325e12 + 4.83806e12i −0.115029 + 0.199236i
\(944\) 1.20374e13 0.493353
\(945\) 5.37616e12 3.39949e12i 0.219295 0.138666i
\(946\) 5.71029e12 0.231819
\(947\) 1.35192e13 2.34159e13i 0.546231 0.946099i −0.452298 0.891867i \(-0.649396\pi\)
0.998528 0.0542323i \(-0.0172712\pi\)
\(948\) −1.26275e12 2.18715e12i −0.0507784 0.0879509i
\(949\) −1.16311e13 2.01456e13i −0.465502 0.806273i
\(950\) 5.02956e12 8.71145e12i 0.200343 0.347004i
\(951\) −4.71407e12 −0.186889
\(952\) 1.24563e11 + 3.09292e12i 0.00491500 + 0.122040i
\(953\) −3.10710e13 −1.22022 −0.610108 0.792318i \(-0.708874\pi\)
−0.610108 + 0.792318i \(0.708874\pi\)
\(954\) 8.74280e12 1.51430e13i 0.341730 0.591894i
\(955\) −3.14968e12 5.45541e12i −0.122532 0.212233i
\(956\) −2.32104e12 4.02016e12i −0.0898716 0.155662i
\(957\) −4.73101e12 + 8.19434e12i −0.182326 + 0.315799i
\(958\) −1.89117e13 −0.725415
\(959\) 1.27703e12 + 3.17087e13i 0.0487547 + 1.21058i
\(960\) −4.32999e11 −0.0164538
\(961\) −1.71799e12 + 2.97564e12i −0.0649777 + 0.112545i
\(962\) 1.24507e12 + 2.15653e12i 0.0468714 + 0.0811836i
\(963\) 1.76499e12 + 3.05706e12i 0.0661340 + 0.114547i
\(964\) −3.18970e12 + 5.52473e12i −0.118961 + 0.206046i
\(965\) 2.58235e13 0.958610
\(966\) −5.50585e11 + 3.48150e11i −0.0203436 + 0.0128638i
\(967\) −1.42603e13 −0.524457 −0.262228 0.965006i \(-0.584457\pi\)
−0.262228 + 0.965006i \(0.584457\pi\)
\(968\) −6.66292e12 + 1.15405e13i −0.243908 + 0.422460i
\(969\) 1.14086e12 + 1.97604e12i 0.0415697 + 0.0720009i
\(970\) −1.14756e13 1.98763e13i −0.416200 0.720880i
\(971\) −1.29280e13 + 2.23920e13i −0.466709 + 0.808364i −0.999277 0.0380235i \(-0.987894\pi\)
0.532568 + 0.846387i \(0.321227\pi\)
\(972\) −6.82345e12 −0.245192
\(973\) 3.03660e13 + 1.59382e13i 1.08612 + 0.570076i
\(974\) −4.45548e12 −0.158628
\(975\) 4.66494e11 8.07991e11i 0.0165320 0.0286342i
\(976\) −1.73725e12 3.00900e12i −0.0612827 0.106145i
\(977\) −5.41303e12 9.37565e12i −0.190071 0.329212i 0.755203 0.655491i \(-0.227538\pi\)
−0.945273 + 0.326279i \(0.894205\pi\)
\(978\) 3.94217e11 6.82804e11i 0.0137788 0.0238655i
\(979\) 3.87632e13 1.34865
\(980\) 6.35131e12 + 9.20245e12i 0.219961 + 0.318703i
\(981\) 2.30676e13 0.795227
\(982\) −6.37598e11 + 1.10435e12i −0.0218799 + 0.0378971i
\(983\) 1.38301e13 + 2.39545e13i 0.472428 + 0.818269i 0.999502 0.0315503i \(-0.0100444\pi\)
−0.527074 + 0.849819i \(0.676711\pi\)
\(984\) 1.01497e12 + 1.75798e12i 0.0345123 + 0.0597771i
\(985\) 6.12981e12 1.06171e13i 0.207484 0.359372i
\(986\) −1.00832e13 −0.339745
\(987\) 4.04416e12 + 2.12267e12i 0.135644 + 0.0711958i
\(988\) −1.03083e13 −0.344177
\(989\) −6.40303e11 + 1.10904e12i −0.0212815 + 0.0368607i
\(990\) 1.23982e13 + 2.14743e13i 0.410204 + 0.710495i
\(991\) 1.35483e13 + 2.34663e13i 0.446223 + 0.772881i 0.998137 0.0610206i \(-0.0194355\pi\)
−0.551914 + 0.833901i \(0.686102\pi\)
\(992\) −2.86568e12 + 4.96351e12i −0.0939562 + 0.162737i
\(993\) −1.33025e12 −0.0434172
\(994\) −1.44616e13 + 9.14443e12i −0.469869 + 0.297110i
\(995\) 1.89724e13 0.613648
\(996\) 1.07002e12 1.85334e12i 0.0344530 0.0596743i
\(997\) −1.56566e13 2.71180e13i −0.501845 0.869221i −0.999998 0.00213142i \(-0.999322\pi\)
0.498153 0.867089i \(-0.334012\pi\)
\(998\) −2.55898e12 4.43228e12i −0.0816543 0.141429i
\(999\) −1.43805e12 + 2.49078e12i −0.0456804 + 0.0791207i
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 14.10.c.a.9.3 6
3.2 odd 2 126.10.g.f.37.2 6
4.3 odd 2 112.10.i.b.65.1 6
7.2 even 3 98.10.a.j.1.1 3
7.3 odd 6 98.10.c.k.67.1 6
7.4 even 3 inner 14.10.c.a.11.3 yes 6
7.5 odd 6 98.10.a.i.1.3 3
7.6 odd 2 98.10.c.k.79.1 6
21.11 odd 6 126.10.g.f.109.2 6
28.11 odd 6 112.10.i.b.81.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.10.c.a.9.3 6 1.1 even 1 trivial
14.10.c.a.11.3 yes 6 7.4 even 3 inner
98.10.a.i.1.3 3 7.5 odd 6
98.10.a.j.1.1 3 7.2 even 3
98.10.c.k.67.1 6 7.3 odd 6
98.10.c.k.79.1 6 7.6 odd 2
112.10.i.b.65.1 6 4.3 odd 2
112.10.i.b.81.1 6 28.11 odd 6
126.10.g.f.37.2 6 3.2 odd 2
126.10.g.f.109.2 6 21.11 odd 6