Properties

Label 7.18.c.a.2.3
Level $7$
Weight $18$
Character 7.2
Analytic conductor $12.826$
Analytic rank $0$
Dimension $20$
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] = [7,18,Mod(2,7)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 18, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7.2");
 
S:= CuspForms(chi, 18);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 7.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: \(12.8255461141\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 5 x^{19} + 231900 x^{18} + 2573595 x^{17} + 36222331443 x^{16} + 522056283042 x^{15} + \cdots + 54\!\cdots\!25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{50}\cdot 3^{18}\cdot 7^{19} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2.3
Root \(-94.3198 + 163.367i\) of defining polynomial
Character \(\chi\) \(=\) 7.2
Dual form 7.18.c.a.4.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-175.640 + 304.217i) q^{2} +(-3368.41 - 5834.25i) q^{3} +(3837.49 + 6646.72i) q^{4} +(-348474. + 603575. i) q^{5} +2.36650e6 q^{6} +(-1.46022e7 - 4.40528e6i) q^{7} -4.87389e7 q^{8} +(4.18777e7 - 7.25344e7i) q^{9} +O(q^{10})\) \(q+(-175.640 + 304.217i) q^{2} +(-3368.41 - 5834.25i) q^{3} +(3837.49 + 6646.72i) q^{4} +(-348474. + 603575. i) q^{5} +2.36650e6 q^{6} +(-1.46022e7 - 4.40528e6i) q^{7} -4.87389e7 q^{8} +(4.18777e7 - 7.25344e7i) q^{9} +(-1.22412e8 - 2.12023e8i) q^{10} +(1.70437e8 + 2.95205e8i) q^{11} +(2.58524e7 - 4.47777e7i) q^{12} +4.02063e9 q^{13} +(3.90488e9 - 3.66849e9i) q^{14} +4.69521e9 q^{15} +(8.05750e9 - 1.39560e10i) q^{16} +(-1.58479e10 - 2.74494e10i) q^{17} +(1.47108e10 + 2.54798e10i) q^{18} +(4.66364e10 - 8.07766e10i) q^{19} -5.34905e9 q^{20} +(2.34846e10 + 1.00032e11i) q^{21} -1.19742e11 q^{22} +(1.87988e11 - 3.25605e11i) q^{23} +(1.64173e11 + 2.84355e11i) q^{24} +(1.38602e11 + 2.40065e11i) q^{25} +(-7.06182e11 + 1.22314e12i) q^{26} -1.43424e12 q^{27} +(-2.67550e10 - 1.13962e11i) q^{28} -1.93368e12 q^{29} +(-8.24664e11 + 1.42836e12i) q^{30} +(-3.98024e11 - 6.89398e11i) q^{31} +(-3.63724e11 - 6.29988e11i) q^{32} +(1.14820e12 - 1.98874e12i) q^{33} +1.11341e13 q^{34} +(7.74740e12 - 7.27838e12i) q^{35} +6.42821e11 q^{36} +(5.12219e12 - 8.87189e12i) q^{37} +(1.63824e13 + 2.83751e13i) q^{38} +(-1.35431e13 - 2.34574e13i) q^{39} +(1.69842e13 - 2.94176e13i) q^{40} +5.03264e12 q^{41} +(-3.45561e13 - 1.04251e13i) q^{42} -1.11062e14 q^{43} +(-1.30810e12 + 2.26569e12i) q^{44} +(2.91866e13 + 5.05527e13i) q^{45} +(6.60363e13 + 1.14378e14i) q^{46} +(-1.57543e13 + 2.72872e13i) q^{47} -1.08564e14 q^{48} +(1.93817e14 + 1.28654e14i) q^{49} -9.73757e13 q^{50} +(-1.06764e14 + 1.84921e14i) q^{51} +(1.54291e13 + 2.67240e13i) q^{52} +(-2.86591e14 - 4.96390e14i) q^{53} +(2.51909e14 - 4.36319e14i) q^{54} -2.37571e14 q^{55} +(7.11695e14 + 2.14709e14i) q^{56} -6.28362e14 q^{57} +(3.39631e14 - 5.88258e14i) q^{58} +(4.66053e14 + 8.07228e14i) q^{59} +(1.80178e13 + 3.12077e13i) q^{60} +(1.22189e15 - 2.11638e15i) q^{61} +2.79635e14 q^{62} +(-9.31041e14 + 8.74678e14i) q^{63} +2.36776e15 q^{64} +(-1.40109e15 + 2.42675e15i) q^{65} +(4.03339e14 + 6.98604e14i) q^{66} +(-1.65088e15 - 2.85941e15i) q^{67} +(1.21632e14 - 2.10673e14i) q^{68} -2.53288e15 q^{69} +(8.53456e14 + 3.63526e15i) q^{70} -9.31042e15 q^{71} +(-2.04108e15 + 3.53525e15i) q^{72} +(4.87732e14 + 8.44776e14i) q^{73} +(1.79932e15 + 3.11651e15i) q^{74} +(9.33733e14 - 1.61727e15i) q^{75} +7.15866e14 q^{76} +(-1.18829e15 - 5.06147e15i) q^{77} +9.51484e15 q^{78} +(1.02667e16 - 1.77825e16i) q^{79} +(5.61565e15 + 9.72660e15i) q^{80} +(-5.77000e14 - 9.99393e14i) q^{81} +(-8.83930e14 + 1.53101e15i) q^{82} -9.40532e15 q^{83} +(-5.74761e14 + 5.39966e14i) q^{84} +2.20903e16 q^{85} +(1.95068e16 - 3.37868e16i) q^{86} +(6.51342e15 + 1.12816e16i) q^{87} +(-8.30691e15 - 1.43880e16i) q^{88} +(-2.00272e16 + 3.46881e16i) q^{89} -2.05053e16 q^{90} +(-5.87101e16 - 1.77120e16i) q^{91} +2.88561e15 q^{92} +(-2.68141e15 + 4.64434e15i) q^{93} +(-5.53414e15 - 9.58542e15i) q^{94} +(3.25031e16 + 5.62971e16i) q^{95} +(-2.45034e15 + 4.24411e15i) q^{96} +5.62891e16 q^{97} +(-7.31806e16 + 3.63659e16i) q^{98} +2.85501e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9} + 222553738 q^{10} - 148256184 q^{11} + 2808533140 q^{12} + 3578734040 q^{13} + 25683984606 q^{14} - 26900793736 q^{15} - 50209759472 q^{16} + 15259176570 q^{17} + 81764237020 q^{18} - 71656970872 q^{19} - 180641544216 q^{20} - 669146889614 q^{21} + 1499692748380 q^{22} - 316306503180 q^{23} + 694489934496 q^{24} + 591325905568 q^{25} + 4488505674324 q^{26} - 11473086373360 q^{27} + 2858273469380 q^{28} + 284876854680 q^{29} - 9357829097258 q^{30} - 1607821082076 q^{31} + 18893460602400 q^{32} + 9589772011550 q^{33} - 32628298247940 q^{34} - 103506510744 q^{35} + 76724663114416 q^{36} + 5528585266950 q^{37} - 15690283928010 q^{38} + 28451541414128 q^{39} - 91022360866896 q^{40} - 66727631114424 q^{41} - 74393390286880 q^{42} - 93028396916240 q^{43} + 162849953080692 q^{44} + 8592264491540 q^{45} - 563088234018354 q^{46} + 162460135616460 q^{47} + 16\!\cdots\!20 q^{48}+ \cdots + 92\!\cdots\!80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −175.640 + 304.217i −0.485140 + 0.840288i −0.999854 0.0170743i \(-0.994565\pi\)
0.514714 + 0.857362i \(0.327898\pi\)
\(3\) −3368.41 5834.25i −0.296411 0.513398i 0.678901 0.734229i \(-0.262456\pi\)
−0.975312 + 0.220831i \(0.929123\pi\)
\(4\) 3837.49 + 6646.72i 0.0292777 + 0.0507105i
\(5\) −348474. + 603575.i −0.398956 + 0.691012i −0.993597 0.112979i \(-0.963961\pi\)
0.594641 + 0.803991i \(0.297294\pi\)
\(6\) 2.36650e6 0.575203
\(7\) −1.46022e7 4.40528e6i −0.957381 0.288829i
\(8\) −4.87389e7 −1.02710
\(9\) 4.18777e7 7.25344e7i 0.324281 0.561672i
\(10\) −1.22412e8 2.12023e8i −0.387100 0.670476i
\(11\) 1.70437e8 + 2.95205e8i 0.239732 + 0.415228i 0.960637 0.277806i \(-0.0896071\pi\)
−0.720905 + 0.693034i \(0.756274\pi\)
\(12\) 2.58524e7 4.47777e7i 0.0173564 0.0300622i
\(13\) 4.02063e9 1.36702 0.683512 0.729940i \(-0.260452\pi\)
0.683512 + 0.729940i \(0.260452\pi\)
\(14\) 3.90488e9 3.66849e9i 0.707163 0.664353i
\(15\) 4.69521e9 0.473020
\(16\) 8.05750e9 1.39560e10i 0.469008 0.812346i
\(17\) −1.58479e10 2.74494e10i −0.551006 0.954370i −0.998202 0.0599342i \(-0.980911\pi\)
0.447197 0.894436i \(-0.352422\pi\)
\(18\) 1.47108e10 + 2.54798e10i 0.314644 + 0.544979i
\(19\) 4.66364e10 8.07766e10i 0.629969 1.09114i −0.357588 0.933880i \(-0.616401\pi\)
0.987557 0.157260i \(-0.0502659\pi\)
\(20\) −5.34905e9 −0.0467221
\(21\) 2.34846e10 + 1.00032e11i 0.135494 + 0.577130i
\(22\) −1.19742e11 −0.465215
\(23\) 1.87988e11 3.25605e11i 0.500546 0.866971i −0.499454 0.866340i \(-0.666466\pi\)
1.00000 0.000630533i \(-0.000200705\pi\)
\(24\) 1.64173e11 + 2.84355e11i 0.304442 + 0.527309i
\(25\) 1.38602e11 + 2.40065e11i 0.181668 + 0.314658i
\(26\) −7.06182e11 + 1.22314e12i −0.663198 + 1.14869i
\(27\) −1.43424e12 −0.977303
\(28\) −2.67550e10 1.13962e11i −0.0133833 0.0570055i
\(29\) −1.93368e12 −0.717797 −0.358898 0.933377i \(-0.616848\pi\)
−0.358898 + 0.933377i \(0.616848\pi\)
\(30\) −8.24664e11 + 1.42836e12i −0.229481 + 0.397473i
\(31\) −3.98024e11 6.89398e11i −0.0838175 0.145176i 0.821069 0.570829i \(-0.193378\pi\)
−0.904887 + 0.425652i \(0.860045\pi\)
\(32\) −3.63724e11 6.29988e11i −0.0584786 0.101288i
\(33\) 1.14820e12 1.98874e12i 0.142118 0.246156i
\(34\) 1.11341e13 1.06926
\(35\) 7.74740e12 7.27838e12i 0.581537 0.546332i
\(36\) 6.42821e11 0.0379768
\(37\) 5.12219e12 8.87189e12i 0.239740 0.415242i −0.720899 0.693040i \(-0.756271\pi\)
0.960640 + 0.277797i \(0.0896044\pi\)
\(38\) 1.63824e13 + 2.83751e13i 0.611247 + 1.05871i
\(39\) −1.35431e13 2.34574e13i −0.405200 0.701828i
\(40\) 1.69842e13 2.94176e13i 0.409766 0.709736i
\(41\) 5.03264e12 0.0984312 0.0492156 0.998788i \(-0.484328\pi\)
0.0492156 + 0.998788i \(0.484328\pi\)
\(42\) −3.45561e13 1.04251e13i −0.550688 0.166135i
\(43\) −1.11062e14 −1.44905 −0.724524 0.689250i \(-0.757940\pi\)
−0.724524 + 0.689250i \(0.757940\pi\)
\(44\) −1.30810e12 + 2.26569e12i −0.0140376 + 0.0243138i
\(45\) 2.91866e13 + 5.05527e13i 0.258748 + 0.448165i
\(46\) 6.60363e13 + 1.14378e14i 0.485670 + 0.841205i
\(47\) −1.57543e13 + 2.72872e13i −0.0965087 + 0.167158i −0.910237 0.414087i \(-0.864101\pi\)
0.813729 + 0.581245i \(0.197434\pi\)
\(48\) −1.08564e14 −0.556076
\(49\) 1.93817e14 + 1.28654e14i 0.833156 + 0.553038i
\(50\) −9.73757e13 −0.352538
\(51\) −1.06764e14 + 1.84921e14i −0.326648 + 0.565771i
\(52\) 1.54291e13 + 2.67240e13i 0.0400233 + 0.0693224i
\(53\) −2.86591e14 4.96390e14i −0.632292 1.09516i −0.987082 0.160216i \(-0.948781\pi\)
0.354790 0.934946i \(-0.384552\pi\)
\(54\) 2.51909e14 4.36319e14i 0.474129 0.821216i
\(55\) −2.37571e14 −0.382570
\(56\) 7.11695e14 + 2.14709e14i 0.983322 + 0.296655i
\(57\) −6.28362e14 −0.746919
\(58\) 3.39631e14 5.88258e14i 0.348232 0.603156i
\(59\) 4.66053e14 + 8.07228e14i 0.413232 + 0.715738i 0.995241 0.0974439i \(-0.0310667\pi\)
−0.582009 + 0.813182i \(0.697733\pi\)
\(60\) 1.80178e13 + 3.12077e13i 0.0138489 + 0.0239870i
\(61\) 1.22189e15 2.11638e15i 0.816075 1.41348i −0.0924778 0.995715i \(-0.529479\pi\)
0.908553 0.417769i \(-0.137188\pi\)
\(62\) 2.79635e14 0.162653
\(63\) −9.31041e14 + 8.74678e14i −0.472688 + 0.444072i
\(64\) 2.36776e15 1.05150
\(65\) −1.40109e15 + 2.42675e15i −0.545382 + 0.944630i
\(66\) 4.03339e14 + 6.98604e14i 0.137895 + 0.238840i
\(67\) −1.65088e15 2.85941e15i −0.496684 0.860282i 0.503309 0.864107i \(-0.332116\pi\)
−0.999993 + 0.00382490i \(0.998782\pi\)
\(68\) 1.21632e14 2.10673e14i 0.0322644 0.0558835i
\(69\) −2.53288e15 −0.593469
\(70\) 8.53456e14 + 3.63526e15i 0.176949 + 0.753706i
\(71\) −9.31042e15 −1.71109 −0.855546 0.517727i \(-0.826778\pi\)
−0.855546 + 0.517727i \(0.826778\pi\)
\(72\) −2.04108e15 + 3.53525e15i −0.333068 + 0.576891i
\(73\) 4.87732e14 + 8.44776e14i 0.0707842 + 0.122602i 0.899245 0.437445i \(-0.144116\pi\)
−0.828461 + 0.560047i \(0.810783\pi\)
\(74\) 1.79932e15 + 3.11651e15i 0.232615 + 0.402902i
\(75\) 9.33733e14 1.61727e15i 0.107697 0.186536i
\(76\) 7.15866e14 0.0737762
\(77\) −1.18829e15 5.06147e15i −0.109585 0.466773i
\(78\) 9.51484e15 0.786316
\(79\) 1.02667e16 1.77825e16i 0.761382 1.31875i −0.180756 0.983528i \(-0.557854\pi\)
0.942138 0.335225i \(-0.108812\pi\)
\(80\) 5.61565e15 + 9.72660e15i 0.374227 + 0.648181i
\(81\) −5.77000e14 9.99393e14i −0.0345982 0.0599258i
\(82\) −8.83930e14 + 1.53101e15i −0.0477530 + 0.0827105i
\(83\) −9.40532e15 −0.458363 −0.229182 0.973384i \(-0.573605\pi\)
−0.229182 + 0.973384i \(0.573605\pi\)
\(84\) −5.74761e14 + 5.39966e14i −0.0252996 + 0.0237680i
\(85\) 2.20903e16 0.879309
\(86\) 1.95068e16 3.37868e16i 0.702992 1.21762i
\(87\) 6.51342e15 + 1.12816e16i 0.212763 + 0.368516i
\(88\) −8.30691e15 1.43880e16i −0.246228 0.426479i
\(89\) −2.00272e16 + 3.46881e16i −0.539268 + 0.934040i 0.459676 + 0.888087i \(0.347966\pi\)
−0.998944 + 0.0459527i \(0.985368\pi\)
\(90\) −2.05053e16 −0.502117
\(91\) −5.87101e16 1.77120e16i −1.30876 0.394836i
\(92\) 2.88561e15 0.0586193
\(93\) −2.68141e15 + 4.64434e15i −0.0496888 + 0.0860636i
\(94\) −5.53414e15 9.58542e15i −0.0936405 0.162190i
\(95\) 3.25031e16 + 5.62971e16i 0.502660 + 0.870633i
\(96\) −2.45034e15 + 4.24411e15i −0.0346674 + 0.0600456i
\(97\) 5.62891e16 0.729230 0.364615 0.931158i \(-0.381201\pi\)
0.364615 + 0.931158i \(0.381201\pi\)
\(98\) −7.31806e16 + 3.63659e16i −0.868909 + 0.431790i
\(99\) 2.85501e16 0.310962
\(100\) −1.06376e15 + 1.84249e15i −0.0106376 + 0.0184249i
\(101\) 7.15769e16 + 1.23975e17i 0.657720 + 1.13921i 0.981204 + 0.192971i \(0.0618125\pi\)
−0.323484 + 0.946234i \(0.604854\pi\)
\(102\) −3.75041e16 6.49590e16i −0.316940 0.548957i
\(103\) −1.57859e16 + 2.73420e16i −0.122787 + 0.212674i −0.920866 0.389880i \(-0.872517\pi\)
0.798079 + 0.602553i \(0.205850\pi\)
\(104\) −1.95961e17 −1.40406
\(105\) −6.85603e16 2.06837e16i −0.452860 0.136622i
\(106\) 2.01347e17 1.22700
\(107\) 1.34478e17 2.32923e17i 0.756641 1.31054i −0.187913 0.982186i \(-0.560172\pi\)
0.944554 0.328355i \(-0.106494\pi\)
\(108\) −5.50387e15 9.53298e15i −0.0286132 0.0495595i
\(109\) −8.70915e16 1.50847e17i −0.418649 0.725122i 0.577154 0.816635i \(-0.304163\pi\)
−0.995804 + 0.0915129i \(0.970830\pi\)
\(110\) 4.17269e16 7.22731e16i 0.185600 0.321469i
\(111\) −6.90145e16 −0.284246
\(112\) −1.79137e17 + 1.68293e17i −0.683648 + 0.642261i
\(113\) 3.92028e17 1.38724 0.693618 0.720343i \(-0.256016\pi\)
0.693618 + 0.720343i \(0.256016\pi\)
\(114\) 1.10365e17 1.91158e17i 0.362360 0.627627i
\(115\) 1.31018e17 + 2.26930e17i 0.399392 + 0.691767i
\(116\) −7.42047e15 1.28526e16i −0.0210154 0.0363998i
\(117\) 1.68375e17 2.91634e17i 0.443300 0.767818i
\(118\) −3.27430e17 −0.801901
\(119\) 1.10492e17 + 4.70636e17i 0.251873 + 1.07284i
\(120\) −2.28839e17 −0.485836
\(121\) 1.94626e17 3.37102e17i 0.385057 0.666939i
\(122\) 4.29226e17 + 7.43442e17i 0.791822 + 1.37148i
\(123\) −1.69520e16 2.93617e16i −0.0291761 0.0505344i
\(124\) 3.05482e15 5.29111e15i 0.00490797 0.00850085i
\(125\) −7.24925e17 −1.08782
\(126\) −1.02564e17 4.36866e17i −0.143828 0.612631i
\(127\) −1.26889e18 −1.66376 −0.831882 0.554952i \(-0.812737\pi\)
−0.831882 + 0.554952i \(0.812737\pi\)
\(128\) −3.68199e17 + 6.37739e17i −0.451645 + 0.782272i
\(129\) 3.74101e17 + 6.47962e17i 0.429513 + 0.743939i
\(130\) −4.92172e17 8.52467e17i −0.529174 0.916556i
\(131\) 3.32147e17 5.75295e17i 0.334598 0.579541i −0.648809 0.760951i \(-0.724733\pi\)
0.983408 + 0.181410i \(0.0580660\pi\)
\(132\) 1.76248e16 0.0166436
\(133\) −1.03684e18 + 9.74069e17i −0.918273 + 0.862682i
\(134\) 1.15984e18 0.963846
\(135\) 4.99795e17 8.65670e17i 0.389901 0.675329i
\(136\) 7.72410e17 + 1.33785e18i 0.565936 + 0.980229i
\(137\) 1.60985e17 + 2.78834e17i 0.110831 + 0.191964i 0.916105 0.400937i \(-0.131316\pi\)
−0.805275 + 0.592902i \(0.797982\pi\)
\(138\) 4.44874e17 7.70545e17i 0.287916 0.498685i
\(139\) 3.70885e17 0.225743 0.112871 0.993610i \(-0.463995\pi\)
0.112871 + 0.993610i \(0.463995\pi\)
\(140\) 7.81079e16 + 2.35641e16i 0.0447308 + 0.0134947i
\(141\) 2.12267e17 0.114425
\(142\) 1.63528e18 2.83239e18i 0.830120 1.43781i
\(143\) 6.85264e17 + 1.18691e18i 0.327719 + 0.567626i
\(144\) −6.74860e17 1.16889e18i −0.304181 0.526857i
\(145\) 6.73837e17 1.16712e18i 0.286370 0.496007i
\(146\) −3.42660e17 −0.137361
\(147\) 9.77410e16 1.56414e18i 0.0369726 0.591667i
\(148\) 7.86253e16 0.0280762
\(149\) −1.28190e18 + 2.22031e18i −0.432284 + 0.748739i −0.997070 0.0764994i \(-0.975626\pi\)
0.564785 + 0.825238i \(0.308959\pi\)
\(150\) 3.28001e17 + 5.68114e17i 0.104496 + 0.180992i
\(151\) −6.68975e17 1.15870e18i −0.201422 0.348872i 0.747565 0.664188i \(-0.231223\pi\)
−0.948987 + 0.315316i \(0.897889\pi\)
\(152\) −2.27301e18 + 3.93697e18i −0.647039 + 1.12070i
\(153\) −2.65470e18 −0.714724
\(154\) 1.74849e18 + 5.27497e17i 0.445387 + 0.134367i
\(155\) 5.54804e17 0.133758
\(156\) 1.03943e17 1.80035e17i 0.0237267 0.0410958i
\(157\) −4.42552e18 7.66522e18i −0.956791 1.65721i −0.730215 0.683218i \(-0.760580\pi\)
−0.226577 0.973993i \(-0.572753\pi\)
\(158\) 3.60649e18 + 6.24663e18i 0.738754 + 1.27956i
\(159\) −1.93071e18 + 3.34409e18i −0.374836 + 0.649236i
\(160\) 5.06993e17 0.0933216
\(161\) −4.17942e18 + 3.92641e18i −0.729619 + 0.685449i
\(162\) 4.05376e17 0.0671399
\(163\) −1.44458e17 + 2.50209e17i −0.0227064 + 0.0393286i −0.877155 0.480207i \(-0.840562\pi\)
0.854449 + 0.519535i \(0.173895\pi\)
\(164\) 1.93127e16 + 3.34505e16i 0.00288184 + 0.00499149i
\(165\) 8.00237e17 + 1.38605e18i 0.113398 + 0.196411i
\(166\) 1.65195e18 2.86125e18i 0.222370 0.385157i
\(167\) 7.79591e18 0.997188 0.498594 0.866836i \(-0.333850\pi\)
0.498594 + 0.866836i \(0.333850\pi\)
\(168\) −1.14461e18 4.87543e18i −0.139165 0.592768i
\(169\) 7.51507e18 0.868753
\(170\) −3.87994e18 + 6.72025e18i −0.426588 + 0.738872i
\(171\) −3.90606e18 6.76549e18i −0.408575 0.707672i
\(172\) −4.26198e17 7.38197e17i −0.0424248 0.0734819i
\(173\) −3.48194e18 + 6.03090e18i −0.329936 + 0.571466i −0.982499 0.186269i \(-0.940360\pi\)
0.652563 + 0.757734i \(0.273694\pi\)
\(174\) −4.57606e18 −0.412879
\(175\) −9.66333e17 4.11605e18i −0.0830431 0.353718i
\(176\) 5.49318e18 0.449745
\(177\) 3.13971e18 5.43815e18i 0.244973 0.424305i
\(178\) −7.03513e18 1.21852e19i −0.523241 0.906281i
\(179\) −6.33193e17 1.09672e18i −0.0449040 0.0777761i 0.842700 0.538384i \(-0.180965\pi\)
−0.887604 + 0.460608i \(0.847632\pi\)
\(180\) −2.24006e17 + 3.87990e17i −0.0151511 + 0.0262425i
\(181\) 2.50270e19 1.61488 0.807440 0.589949i \(-0.200852\pi\)
0.807440 + 0.589949i \(0.200852\pi\)
\(182\) 1.57001e19 1.47496e19i 0.966709 0.908186i
\(183\) −1.64634e19 −0.967574
\(184\) −9.16234e18 + 1.58696e19i −0.514109 + 0.890462i
\(185\) 3.56990e18 + 6.18325e18i 0.191292 + 0.331327i
\(186\) −9.41924e17 1.63146e18i −0.0482121 0.0835058i
\(187\) 5.40214e18 9.35678e18i 0.264187 0.457586i
\(188\) −2.41827e17 −0.0113022
\(189\) 2.09430e19 + 6.31823e18i 0.935651 + 0.282273i
\(190\) −2.28354e19 −0.975443
\(191\) −1.00934e19 + 1.74824e19i −0.412340 + 0.714195i −0.995145 0.0984176i \(-0.968622\pi\)
0.582805 + 0.812612i \(0.301955\pi\)
\(192\) −7.97558e18 1.38141e19i −0.311675 0.539837i
\(193\) 1.57182e19 + 2.72247e19i 0.587714 + 1.01795i 0.994531 + 0.104440i \(0.0333052\pi\)
−0.406817 + 0.913509i \(0.633361\pi\)
\(194\) −9.88659e18 + 1.71241e19i −0.353779 + 0.612763i
\(195\) 1.88777e19 0.646629
\(196\) −1.11352e17 + 1.78196e18i −0.00365193 + 0.0584414i
\(197\) −3.19025e19 −1.00199 −0.500993 0.865451i \(-0.667032\pi\)
−0.500993 + 0.865451i \(0.667032\pi\)
\(198\) −5.01452e18 + 8.68540e18i −0.150860 + 0.261298i
\(199\) −8.94836e18 1.54990e19i −0.257924 0.446738i 0.707761 0.706451i \(-0.249705\pi\)
−0.965686 + 0.259714i \(0.916372\pi\)
\(200\) −6.75529e18 1.17005e19i −0.186590 0.323184i
\(201\) −1.11217e19 + 1.92633e19i −0.294445 + 0.509993i
\(202\) −5.02869e19 −1.27635
\(203\) 2.82360e19 + 8.51841e18i 0.687205 + 0.207320i
\(204\) −1.63883e18 −0.0382540
\(205\) −1.75374e18 + 3.03757e18i −0.0392697 + 0.0680172i
\(206\) −5.54526e18 9.60467e18i −0.119138 0.206353i
\(207\) −1.57450e19 2.72712e19i −0.324635 0.562285i
\(208\) 3.23962e19 5.61119e19i 0.641145 1.11050i
\(209\) 3.17943e19 0.604095
\(210\) 1.83342e19 1.72243e19i 0.334502 0.314252i
\(211\) −5.36032e19 −0.939269 −0.469635 0.882861i \(-0.655614\pi\)
−0.469635 + 0.882861i \(0.655614\pi\)
\(212\) 2.19958e18 3.80978e18i 0.0370241 0.0641277i
\(213\) 3.13613e19 + 5.43193e19i 0.507186 + 0.878472i
\(214\) 4.72394e19 + 8.18210e19i 0.734154 + 1.27159i
\(215\) 3.87021e19 6.70341e19i 0.578107 1.00131i
\(216\) 6.99032e19 1.00378
\(217\) 2.77503e18 + 1.18201e19i 0.0383142 + 0.163198i
\(218\) 6.11869e19 0.812415
\(219\) 3.28576e18 5.69110e18i 0.0419624 0.0726810i
\(220\) −9.11676e17 1.57907e18i −0.0112008 0.0194003i
\(221\) −6.37186e19 1.10364e20i −0.753238 1.30465i
\(222\) 1.21217e19 2.09954e19i 0.137899 0.238849i
\(223\) 5.03091e18 0.0550878 0.0275439 0.999621i \(-0.491231\pi\)
0.0275439 + 0.999621i \(0.491231\pi\)
\(224\) 2.53589e18 + 1.08015e19i 0.0267314 + 0.113861i
\(225\) 2.32173e19 0.235646
\(226\) −6.88557e19 + 1.19261e20i −0.673004 + 1.16568i
\(227\) −9.90843e19 1.71619e20i −0.932792 1.61564i −0.778524 0.627615i \(-0.784031\pi\)
−0.154268 0.988029i \(-0.549302\pi\)
\(228\) −2.41133e18 4.17654e18i −0.0218681 0.0378766i
\(229\) −8.69399e19 + 1.50584e20i −0.759657 + 1.31576i 0.183368 + 0.983044i \(0.441300\pi\)
−0.943026 + 0.332720i \(0.892033\pi\)
\(230\) −9.20477e19 −0.775044
\(231\) −2.55272e19 + 2.39819e19i −0.207158 + 0.194617i
\(232\) 9.42455e19 0.737246
\(233\) 2.48459e19 4.30343e19i 0.187383 0.324556i −0.756994 0.653422i \(-0.773333\pi\)
0.944377 + 0.328865i \(0.106666\pi\)
\(234\) 5.91466e19 + 1.02445e20i 0.430126 + 0.744999i
\(235\) −1.09799e19 1.90177e19i −0.0770055 0.133377i
\(236\) −3.57695e18 + 6.19545e18i −0.0241969 + 0.0419103i
\(237\) −1.38330e20 −0.902727
\(238\) −1.62582e20 4.90488e19i −1.02369 0.308833i
\(239\) 6.11461e19 0.371524 0.185762 0.982595i \(-0.440525\pi\)
0.185762 + 0.982595i \(0.440525\pi\)
\(240\) 3.78316e19 6.55263e19i 0.221850 0.384255i
\(241\) 1.17227e20 + 2.03043e20i 0.663562 + 1.14932i 0.979673 + 0.200601i \(0.0642895\pi\)
−0.316111 + 0.948722i \(0.602377\pi\)
\(242\) 6.83681e19 + 1.18417e20i 0.373614 + 0.647118i
\(243\) −9.64960e19 + 1.67136e20i −0.509162 + 0.881895i
\(244\) 1.87560e19 0.0955712
\(245\) −1.45192e20 + 7.21509e19i −0.714549 + 0.355083i
\(246\) 1.19097e19 0.0566180
\(247\) 1.87508e20 3.24773e20i 0.861183 1.49161i
\(248\) 1.93993e19 + 3.36005e19i 0.0860886 + 0.149110i
\(249\) 3.16809e19 + 5.48730e19i 0.135864 + 0.235323i
\(250\) 1.27326e20 2.20534e20i 0.527747 0.914084i
\(251\) 2.79234e19 0.111877 0.0559385 0.998434i \(-0.482185\pi\)
0.0559385 + 0.998434i \(0.482185\pi\)
\(252\) −9.38660e18 2.83181e18i −0.0363583 0.0109688i
\(253\) 1.28161e20 0.479987
\(254\) 2.22867e20 3.86017e20i 0.807159 1.39804i
\(255\) −7.44092e19 1.28881e20i −0.260637 0.451436i
\(256\) 2.58331e19 + 4.47443e19i 0.0875260 + 0.151600i
\(257\) −5.58059e19 + 9.66586e19i −0.182915 + 0.316817i −0.942872 0.333156i \(-0.891887\pi\)
0.759957 + 0.649973i \(0.225220\pi\)
\(258\) −2.62828e20 −0.833497
\(259\) −1.13878e20 + 1.06984e20i −0.349457 + 0.328301i
\(260\) −2.15066e19 −0.0638702
\(261\) −8.09782e19 + 1.40258e20i −0.232768 + 0.403166i
\(262\) 1.16676e20 + 2.02089e20i 0.324654 + 0.562318i
\(263\) −3.01084e20 5.21492e20i −0.811079 1.40483i −0.912109 0.409947i \(-0.865547\pi\)
0.101030 0.994883i \(-0.467786\pi\)
\(264\) −5.59621e19 + 9.69292e19i −0.145969 + 0.252826i
\(265\) 3.99478e20 1.00903
\(266\) −1.14218e20 4.86508e20i −0.279410 1.19014i
\(267\) 2.69839e20 0.639379
\(268\) 1.26705e19 2.19459e19i 0.0290835 0.0503741i
\(269\) 3.18153e20 + 5.51058e20i 0.707526 + 1.22547i 0.965772 + 0.259392i \(0.0835220\pi\)
−0.258246 + 0.966079i \(0.583145\pi\)
\(270\) 1.75567e20 + 3.04092e20i 0.378314 + 0.655258i
\(271\) 1.47154e20 2.54878e20i 0.307279 0.532223i −0.670487 0.741921i \(-0.733915\pi\)
0.977766 + 0.209698i \(0.0672481\pi\)
\(272\) −5.10778e20 −1.03370
\(273\) 9.44230e19 + 4.02191e20i 0.185223 + 0.788950i
\(274\) −1.13101e20 −0.215074
\(275\) −4.72457e19 + 8.18319e19i −0.0871032 + 0.150867i
\(276\) −9.71990e18 1.68354e19i −0.0173754 0.0300951i
\(277\) −1.31262e20 2.27352e20i −0.227541 0.394113i 0.729538 0.683941i \(-0.239735\pi\)
−0.957079 + 0.289828i \(0.906402\pi\)
\(278\) −6.51421e19 + 1.12829e20i −0.109517 + 0.189689i
\(279\) −6.66734e19 −0.108722
\(280\) −3.77600e20 + 3.54741e20i −0.597294 + 0.561135i
\(281\) −2.25835e20 −0.346567 −0.173284 0.984872i \(-0.555438\pi\)
−0.173284 + 0.984872i \(0.555438\pi\)
\(282\) −3.72825e19 + 6.45752e19i −0.0555121 + 0.0961498i
\(283\) 2.17831e20 + 3.77295e20i 0.314728 + 0.545125i 0.979380 0.202028i \(-0.0647534\pi\)
−0.664652 + 0.747153i \(0.731420\pi\)
\(284\) −3.57286e19 6.18838e19i −0.0500968 0.0867703i
\(285\) 2.18968e20 3.79263e20i 0.297988 0.516130i
\(286\) −4.81438e20 −0.635959
\(287\) −7.34875e19 2.21702e19i −0.0942362 0.0284298i
\(288\) −6.09277e19 −0.0758541
\(289\) −8.86922e19 + 1.53619e20i −0.107215 + 0.185701i
\(290\) 2.36705e20 + 4.09985e20i 0.277859 + 0.481266i
\(291\) −1.89604e20 3.28405e20i −0.216151 0.374385i
\(292\) −3.74333e18 + 6.48363e18i −0.00414480 + 0.00717900i
\(293\) 5.17283e19 0.0556357 0.0278179 0.999613i \(-0.491144\pi\)
0.0278179 + 0.999613i \(0.491144\pi\)
\(294\) 4.58670e20 + 3.04459e20i 0.479234 + 0.318109i
\(295\) −6.49630e20 −0.659445
\(296\) −2.49650e20 + 4.32406e20i −0.246236 + 0.426494i
\(297\) −2.44447e20 4.23395e20i −0.234291 0.405804i
\(298\) −4.50303e20 7.79948e20i −0.419437 0.726487i
\(299\) 7.55831e20 1.30914e21i 0.684258 1.18517i
\(300\) 1.43328e19 0.0126124
\(301\) 1.62175e21 + 4.89258e20i 1.38729 + 0.418527i
\(302\) 4.69994e20 0.390871
\(303\) 4.82200e20 8.35195e20i 0.389911 0.675345i
\(304\) −7.51545e20 1.30171e21i −0.590921 1.02351i
\(305\) 8.51597e20 + 1.47501e21i 0.651157 + 1.12784i
\(306\) 4.66270e20 8.07604e20i 0.346741 0.600573i
\(307\) 2.14791e20 0.155360 0.0776801 0.996978i \(-0.475249\pi\)
0.0776801 + 0.996978i \(0.475249\pi\)
\(308\) 2.90821e19 2.73215e19i 0.0204619 0.0192231i
\(309\) 2.12693e20 0.145582
\(310\) −9.74455e19 + 1.68781e20i −0.0648914 + 0.112395i
\(311\) −4.34823e20 7.53136e20i −0.281741 0.487989i 0.690073 0.723740i \(-0.257578\pi\)
−0.971814 + 0.235751i \(0.924245\pi\)
\(312\) 6.60077e20 + 1.14329e21i 0.416180 + 0.720844i
\(313\) −9.75522e20 + 1.68965e21i −0.598564 + 1.03674i 0.394470 + 0.918909i \(0.370928\pi\)
−0.993033 + 0.117834i \(0.962405\pi\)
\(314\) 3.10919e21 1.85671
\(315\) −2.03490e20 8.66755e20i −0.118278 0.503798i
\(316\) 1.57594e20 0.0891660
\(317\) −1.33346e21 + 2.30962e21i −0.734473 + 1.27214i 0.220481 + 0.975391i \(0.429237\pi\)
−0.954954 + 0.296754i \(0.904096\pi\)
\(318\) −6.78219e20 1.17471e21i −0.363697 0.629941i
\(319\) −3.29571e20 5.70833e20i −0.172079 0.298049i
\(320\) −8.25103e20 + 1.42912e21i −0.419501 + 0.726598i
\(321\) −1.81191e21 −0.897106
\(322\) −4.60407e20 1.96108e21i −0.222007 0.945629i
\(323\) −2.95636e21 −1.38847
\(324\) 4.42846e18 7.67032e18i 0.00202591 0.00350898i
\(325\) 5.57266e20 + 9.65213e20i 0.248344 + 0.430145i
\(326\) −5.07452e19 8.78933e19i −0.0220316 0.0381598i
\(327\) −5.86719e20 + 1.01623e21i −0.248184 + 0.429868i
\(328\) −2.45285e20 −0.101098
\(329\) 3.50255e20 3.29051e20i 0.140676 0.132159i
\(330\) −5.62213e20 −0.220056
\(331\) −1.31789e20 + 2.28266e20i −0.0502739 + 0.0870769i −0.890067 0.455829i \(-0.849343\pi\)
0.839793 + 0.542906i \(0.182676\pi\)
\(332\) −3.60928e19 6.25145e19i −0.0134198 0.0232438i
\(333\) −4.29011e20 7.43070e20i −0.155487 0.269311i
\(334\) −1.36927e21 + 2.37165e21i −0.483776 + 0.837925i
\(335\) 2.30116e21 0.792620
\(336\) 1.58527e21 + 4.78254e20i 0.532376 + 0.160611i
\(337\) 1.38343e21 0.453006 0.226503 0.974010i \(-0.427271\pi\)
0.226503 + 0.974010i \(0.427271\pi\)
\(338\) −1.31994e21 + 2.28621e21i −0.421467 + 0.730002i
\(339\) −1.32051e21 2.28719e21i −0.411192 0.712205i
\(340\) 8.47713e19 + 1.46828e20i 0.0257441 + 0.0445901i
\(341\) 1.35676e20 2.34998e20i 0.0401875 0.0696067i
\(342\) 2.74423e21 0.792864
\(343\) −2.26341e21 2.73244e21i −0.637914 0.770107i
\(344\) 5.41303e21 1.48831
\(345\) 8.82644e20 1.52878e21i 0.236768 0.410094i
\(346\) −1.22313e21 2.11853e21i −0.320130 0.554482i
\(347\) 3.41199e21 + 5.90973e21i 0.871378 + 1.50927i 0.860571 + 0.509330i \(0.170107\pi\)
0.0108067 + 0.999942i \(0.496560\pi\)
\(348\) −4.99903e19 + 8.65858e19i −0.0124584 + 0.0215786i
\(349\) 2.58265e21 0.628130 0.314065 0.949402i \(-0.398309\pi\)
0.314065 + 0.949402i \(0.398309\pi\)
\(350\) 1.42190e21 + 4.28967e20i 0.337513 + 0.101823i
\(351\) −5.76655e21 −1.33600
\(352\) 1.23984e20 2.14746e20i 0.0280384 0.0485639i
\(353\) −3.10974e21 5.38623e21i −0.686498 1.18905i −0.972964 0.230958i \(-0.925814\pi\)
0.286466 0.958090i \(-0.407519\pi\)
\(354\) 1.10292e21 + 1.91031e21i 0.237692 + 0.411695i
\(355\) 3.24444e21 5.61953e21i 0.682651 1.18239i
\(356\) −3.07416e20 −0.0631541
\(357\) 2.37363e21 2.22993e21i 0.476137 0.447313i
\(358\) 4.44855e20 0.0871390
\(359\) −3.08443e20 + 5.34240e20i −0.0590028 + 0.102196i −0.894018 0.448031i \(-0.852125\pi\)
0.835015 + 0.550227i \(0.185459\pi\)
\(360\) −1.42252e21 2.46388e21i −0.265759 0.460308i
\(361\) −1.60972e21 2.78811e21i −0.293723 0.508743i
\(362\) −4.39573e21 + 7.61362e21i −0.783444 + 1.35696i
\(363\) −2.62232e21 −0.456540
\(364\) −1.07572e20 4.58199e20i −0.0182952 0.0779278i
\(365\) −6.79847e20 −0.112959
\(366\) 2.89162e21 5.00843e21i 0.469409 0.813040i
\(367\) 3.31072e21 + 5.73434e21i 0.525123 + 0.909540i 0.999572 + 0.0292569i \(0.00931409\pi\)
−0.474449 + 0.880283i \(0.657353\pi\)
\(368\) −3.02943e21 5.24712e21i −0.469520 0.813233i
\(369\) 2.10756e20 3.65039e20i 0.0319194 0.0552860i
\(370\) −2.50806e21 −0.371213
\(371\) 1.99812e21 + 8.51090e21i 0.289030 + 1.23111i
\(372\) −4.11595e19 −0.00581910
\(373\) −3.62546e21 + 6.27948e21i −0.501000 + 0.867758i 0.498999 + 0.866603i \(0.333701\pi\)
−0.999999 + 0.00115565i \(0.999632\pi\)
\(374\) 1.89766e21 + 3.28684e21i 0.256336 + 0.443987i
\(375\) 2.44184e21 + 4.22940e21i 0.322442 + 0.558486i
\(376\) 7.67846e20 1.32995e21i 0.0991237 0.171687i
\(377\) −7.77462e21 −0.981245
\(378\) −5.60053e21 + 5.26149e21i −0.691113 + 0.649274i
\(379\) 1.02143e22 1.23246 0.616232 0.787564i \(-0.288658\pi\)
0.616232 + 0.787564i \(0.288658\pi\)
\(380\) −2.49461e20 + 4.32079e20i −0.0294335 + 0.0509803i
\(381\) 4.27413e21 + 7.40302e21i 0.493158 + 0.854174i
\(382\) −3.54562e21 6.14119e21i −0.400086 0.692969i
\(383\) 7.96976e21 1.38040e22i 0.879541 1.52341i 0.0276948 0.999616i \(-0.491183\pi\)
0.851846 0.523793i \(-0.175483\pi\)
\(384\) 4.96097e21 0.535490
\(385\) 3.46906e21 + 1.04657e21i 0.366265 + 0.110497i
\(386\) −1.10430e22 −1.14049
\(387\) −4.65102e21 + 8.05580e21i −0.469899 + 0.813889i
\(388\) 2.16008e20 + 3.74138e20i 0.0213502 + 0.0369796i
\(389\) −3.91270e21 6.77699e21i −0.378360 0.655338i 0.612464 0.790498i \(-0.290178\pi\)
−0.990824 + 0.135160i \(0.956845\pi\)
\(390\) −3.31567e21 + 5.74291e21i −0.313706 + 0.543354i
\(391\) −1.19169e22 −1.10321
\(392\) −9.44645e21 6.27043e21i −0.855731 0.568023i
\(393\) −4.47522e21 −0.396714
\(394\) 5.60334e21 9.70527e21i 0.486104 0.841956i
\(395\) 7.15539e21 + 1.23935e22i 0.607516 + 1.05225i
\(396\) 1.09560e20 + 1.89764e20i 0.00910426 + 0.0157690i
\(397\) 7.30746e21 1.26569e22i 0.594357 1.02946i −0.399281 0.916829i \(-0.630740\pi\)
0.993637 0.112627i \(-0.0359265\pi\)
\(398\) 6.28674e21 0.500518
\(399\) 9.17546e21 + 2.76811e21i 0.715086 + 0.215732i
\(400\) 4.46713e21 0.340815
\(401\) 4.81226e21 8.33508e21i 0.359436 0.622562i −0.628430 0.777866i \(-0.716302\pi\)
0.987867 + 0.155304i \(0.0496357\pi\)
\(402\) −3.90681e21 6.76680e21i −0.285694 0.494837i
\(403\) −1.60031e21 2.77181e21i −0.114580 0.198459i
\(404\) −5.49351e20 + 9.51503e20i −0.0385131 + 0.0667066i
\(405\) 8.04278e20 0.0552126
\(406\) −7.55079e21 + 7.09368e21i −0.507600 + 0.476870i
\(407\) 3.49204e21 0.229894
\(408\) 5.20358e21 9.01287e21i 0.335499 0.581101i
\(409\) 1.34445e22 + 2.32866e22i 0.848978 + 1.47047i 0.882121 + 0.471023i \(0.156115\pi\)
−0.0331424 + 0.999451i \(0.510551\pi\)
\(410\) −6.16053e20 1.06704e21i −0.0381027 0.0659958i
\(411\) 1.08452e21 1.87845e21i 0.0657028 0.113801i
\(412\) −2.42313e20 −0.0143797
\(413\) −3.24933e21 1.38404e22i −0.188894 0.804587i
\(414\) 1.10618e22 0.629975
\(415\) 3.27751e21 5.67681e21i 0.182867 0.316735i
\(416\) −1.46240e21 2.53295e21i −0.0799416 0.138463i
\(417\) −1.24929e21 2.16384e21i −0.0669125 0.115896i
\(418\) −5.58433e21 + 9.67235e21i −0.293071 + 0.507614i
\(419\) 4.17261e21 0.214580 0.107290 0.994228i \(-0.465783\pi\)
0.107290 + 0.994228i \(0.465783\pi\)
\(420\) −1.25620e20 5.35075e20i −0.00633055 0.0269647i
\(421\) −1.26695e22 −0.625695 −0.312847 0.949803i \(-0.601283\pi\)
−0.312847 + 0.949803i \(0.601283\pi\)
\(422\) 9.41485e21 1.63070e22i 0.455677 0.789256i
\(423\) 1.31951e21 + 2.28545e21i 0.0625919 + 0.108412i
\(424\) 1.39681e22 + 2.41935e22i 0.649425 + 1.12484i
\(425\) 4.39309e21 7.60906e21i 0.200200 0.346757i
\(426\) −2.20331e22 −0.984226
\(427\) −2.71656e22 + 2.55211e22i −1.18955 + 1.11754i
\(428\) 2.06423e21 0.0886108
\(429\) 4.61650e21 7.99601e21i 0.194279 0.336501i
\(430\) 1.35953e22 + 2.35477e22i 0.560926 + 0.971552i
\(431\) −6.87532e21 1.19084e22i −0.278123 0.481723i 0.692796 0.721134i \(-0.256379\pi\)
−0.970918 + 0.239411i \(0.923046\pi\)
\(432\) −1.15564e22 + 2.00162e22i −0.458363 + 0.793908i
\(433\) −4.44706e22 −1.72952 −0.864760 0.502185i \(-0.832530\pi\)
−0.864760 + 0.502185i \(0.832530\pi\)
\(434\) −4.08328e21 1.23187e21i −0.155721 0.0469789i
\(435\) −9.07903e21 −0.339532
\(436\) 6.68425e20 1.15775e21i 0.0245142 0.0424598i
\(437\) −1.75342e22 3.03701e22i −0.630657 1.09233i
\(438\) 1.15422e21 + 1.99916e21i 0.0407153 + 0.0705210i
\(439\) −1.16435e22 + 2.01671e22i −0.402842 + 0.697743i −0.994068 0.108763i \(-0.965311\pi\)
0.591225 + 0.806506i \(0.298644\pi\)
\(440\) 1.15790e22 0.392936
\(441\) 1.74484e22 8.67071e21i 0.580803 0.288620i
\(442\) 4.47660e22 1.46170
\(443\) −1.95032e22 + 3.37804e22i −0.624702 + 1.08202i 0.363896 + 0.931440i \(0.381446\pi\)
−0.988598 + 0.150577i \(0.951887\pi\)
\(444\) −2.64842e20 4.58720e20i −0.00832208 0.0144143i
\(445\) −1.39579e22 2.41758e22i −0.430289 0.745282i
\(446\) −8.83627e20 + 1.53049e21i −0.0267253 + 0.0462896i
\(447\) 1.72718e22 0.512535
\(448\) −3.45745e22 1.04307e22i −1.00668 0.303703i
\(449\) 2.68781e22 0.767901 0.383950 0.923354i \(-0.374563\pi\)
0.383950 + 0.923354i \(0.374563\pi\)
\(450\) −4.07787e21 + 7.06309e21i −0.114321 + 0.198010i
\(451\) 8.57747e20 + 1.48566e21i 0.0235971 + 0.0408714i
\(452\) 1.50440e21 + 2.60570e21i 0.0406151 + 0.0703474i
\(453\) −4.50676e21 + 7.80594e21i −0.119407 + 0.206819i
\(454\) 6.96125e22 1.81014
\(455\) 3.11494e22 2.92637e22i 0.794975 0.746849i
\(456\) 3.06257e22 0.767157
\(457\) 2.86655e22 4.96502e22i 0.704810 1.22077i −0.261950 0.965082i \(-0.584365\pi\)
0.966760 0.255686i \(-0.0823012\pi\)
\(458\) −3.05402e22 5.28971e22i −0.737081 1.27666i
\(459\) 2.27297e22 + 3.93690e22i 0.538500 + 0.932709i
\(460\) −1.00556e21 + 1.74168e21i −0.0233865 + 0.0405067i
\(461\) 3.52330e21 0.0804436 0.0402218 0.999191i \(-0.487194\pi\)
0.0402218 + 0.999191i \(0.487194\pi\)
\(462\) −2.81209e21 1.19780e22i −0.0630336 0.268489i
\(463\) −5.80448e22 −1.27739 −0.638697 0.769458i \(-0.720526\pi\)
−0.638697 + 0.769458i \(0.720526\pi\)
\(464\) −1.55806e22 + 2.69864e22i −0.336652 + 0.583099i
\(465\) −1.86881e21 3.23687e21i −0.0396473 0.0686712i
\(466\) 8.72784e21 + 1.51171e22i 0.181814 + 0.314911i
\(467\) 1.65098e22 2.85958e22i 0.337713 0.584936i −0.646289 0.763092i \(-0.723680\pi\)
0.984002 + 0.178157i \(0.0570134\pi\)
\(468\) 2.58455e21 0.0519152
\(469\) 1.15100e22 + 4.90263e22i 0.227042 + 0.967074i
\(470\) 7.71402e21 0.149434
\(471\) −2.98139e22 + 5.16392e22i −0.567206 + 0.982430i
\(472\) −2.27149e22 3.93434e22i −0.424428 0.735132i
\(473\) −1.89290e22 3.27860e22i −0.347383 0.601685i
\(474\) 2.42963e22 4.20824e22i 0.437949 0.758551i
\(475\) 2.58555e22 0.457781
\(476\) −2.70417e21 + 2.54047e21i −0.0470300 + 0.0441829i
\(477\) −4.80072e22 −0.820162
\(478\) −1.07397e22 + 1.86017e22i −0.180241 + 0.312187i
\(479\) 2.55756e22 + 4.42983e22i 0.421672 + 0.730357i 0.996103 0.0881959i \(-0.0281101\pi\)
−0.574431 + 0.818553i \(0.694777\pi\)
\(480\) −1.70776e21 2.95792e21i −0.0276615 0.0479111i
\(481\) 2.05944e22 3.56706e22i 0.327731 0.567646i
\(482\) −8.23586e22 −1.28768
\(483\) 3.69856e22 + 1.11581e22i 0.568176 + 0.171411i
\(484\) 2.98750e21 0.0450943
\(485\) −1.96153e22 + 3.39746e22i −0.290931 + 0.503907i
\(486\) −3.38970e22 5.87114e22i −0.494030 0.855686i
\(487\) −9.91124e21 1.71668e22i −0.141949 0.245863i 0.786282 0.617868i \(-0.212004\pi\)
−0.928230 + 0.372006i \(0.878670\pi\)
\(488\) −5.95538e22 + 1.03150e23i −0.838188 + 1.45178i
\(489\) 1.94638e21 0.0269217
\(490\) 3.55202e21 5.68425e22i 0.0482846 0.772692i
\(491\) −7.24176e22 −0.967501 −0.483751 0.875206i \(-0.660726\pi\)
−0.483751 + 0.875206i \(0.660726\pi\)
\(492\) 1.30106e20 2.25350e20i 0.00170842 0.00295906i
\(493\) 3.06448e22 + 5.30783e22i 0.395510 + 0.685044i
\(494\) 6.58676e22 + 1.14086e23i 0.835589 + 1.44728i
\(495\) −9.94895e21 + 1.72321e22i −0.124060 + 0.214879i
\(496\) −1.28283e22 −0.157244
\(497\) 1.35953e23 + 4.10150e22i 1.63817 + 0.494213i
\(498\) −2.22577e22 −0.263652
\(499\) 1.24514e22 2.15665e22i 0.144999 0.251145i −0.784374 0.620288i \(-0.787016\pi\)
0.929372 + 0.369143i \(0.120349\pi\)
\(500\) −2.78189e21 4.81837e21i −0.0318489 0.0551640i
\(501\) −2.62598e22 4.54833e22i −0.295577 0.511955i
\(502\) −4.90445e21 + 8.49475e21i −0.0542761 + 0.0940089i
\(503\) 1.33942e23 1.45743 0.728715 0.684817i \(-0.240118\pi\)
0.728715 + 0.684817i \(0.240118\pi\)
\(504\) 4.53779e22 4.26308e22i 0.485496 0.456105i
\(505\) −9.97707e22 −1.04961
\(506\) −2.25101e22 + 3.89886e22i −0.232861 + 0.403328i
\(507\) −2.53138e22 4.38448e22i −0.257508 0.446016i
\(508\) −4.86934e21 8.43395e21i −0.0487112 0.0843702i
\(509\) 4.22115e22 7.31125e22i 0.415269 0.719267i −0.580187 0.814483i \(-0.697021\pi\)
0.995457 + 0.0952155i \(0.0303540\pi\)
\(510\) 5.22768e22 0.505781
\(511\) −3.40047e21 1.44842e22i −0.0323565 0.137821i
\(512\) −1.14670e23 −1.07314
\(513\) −6.68877e22 + 1.15853e23i −0.615671 + 1.06637i
\(514\) −1.96034e22 3.39541e22i −0.177478 0.307402i
\(515\) −1.10020e22 1.90559e22i −0.0979734 0.169695i
\(516\) −2.87122e21 + 4.97309e21i −0.0251503 + 0.0435616i
\(517\) −1.07404e22 −0.0925448
\(518\) −1.25449e22 5.34344e22i −0.106332 0.452916i
\(519\) 4.69144e22 0.391186
\(520\) 6.82874e22 1.18277e23i 0.560160 0.970226i
\(521\) −2.36147e22 4.09019e22i −0.190573 0.330083i 0.754867 0.655878i \(-0.227701\pi\)
−0.945440 + 0.325795i \(0.894368\pi\)
\(522\) −2.84459e22 4.92698e22i −0.225850 0.391185i
\(523\) 1.02112e23 1.76864e23i 0.797652 1.38157i −0.123490 0.992346i \(-0.539409\pi\)
0.921142 0.389228i \(-0.127258\pi\)
\(524\) 5.09843e21 0.0391851
\(525\) −2.07591e22 + 1.95024e22i −0.156984 + 0.147480i
\(526\) 2.11529e23 1.57395
\(527\) −1.26157e22 + 2.18510e22i −0.0923679 + 0.159986i
\(528\) −1.85033e22 3.20486e22i −0.133309 0.230898i
\(529\) −1.54099e20 2.66907e20i −0.00109251 0.00189229i
\(530\) −7.01642e22 + 1.21528e23i −0.489520 + 0.847874i
\(531\) 7.80691e22 0.536013
\(532\) −1.04532e22 3.15359e21i −0.0706319 0.0213087i
\(533\) 2.02344e22 0.134558
\(534\) −4.73944e22 + 8.20894e22i −0.310189 + 0.537263i
\(535\) 9.37243e22 + 1.62335e23i 0.603733 + 1.04570i
\(536\) 8.04622e22 + 1.39365e23i 0.510142 + 0.883592i
\(537\) −4.26570e21 + 7.38841e21i −0.0266201 + 0.0461073i
\(538\) −2.23521e23 −1.37300
\(539\) −4.94557e21 + 7.91433e22i −0.0299028 + 0.478530i
\(540\) 7.67182e21 0.0456616
\(541\) 5.28973e22 9.16208e22i 0.309925 0.536806i −0.668421 0.743784i \(-0.733029\pi\)
0.978346 + 0.206977i \(0.0663627\pi\)
\(542\) 5.16922e22 + 8.95334e22i 0.298147 + 0.516406i
\(543\) −8.43010e22 1.46014e23i −0.478668 0.829077i
\(544\) −1.15285e22 + 1.99680e22i −0.0644441 + 0.111620i
\(545\) 1.21396e23 0.668091
\(546\) −1.38937e23 4.19155e22i −0.752804 0.227111i
\(547\) −2.21065e22 −0.117931 −0.0589655 0.998260i \(-0.518780\pi\)
−0.0589655 + 0.998260i \(0.518780\pi\)
\(548\) −1.23555e21 + 2.14004e21i −0.00648973 + 0.0112405i
\(549\) −1.02340e23 1.77259e23i −0.529276 0.916733i
\(550\) −1.65964e22 2.87458e22i −0.0845145 0.146383i
\(551\) −9.01799e22 + 1.56196e23i −0.452190 + 0.783216i
\(552\) 1.23450e23 0.609549
\(553\) −2.28254e23 + 2.14436e23i −1.10983 + 1.04264i
\(554\) 9.22189e22 0.441557
\(555\) 2.40497e22 4.16554e22i 0.113402 0.196418i
\(556\) 1.42327e21 + 2.46517e21i 0.00660922 + 0.0114475i
\(557\) 1.49386e23 + 2.58743e23i 0.683187 + 1.18331i 0.974003 + 0.226535i \(0.0727399\pi\)
−0.290816 + 0.956779i \(0.593927\pi\)
\(558\) 1.17105e22 2.02832e22i 0.0527453 0.0913576i
\(559\) −4.46539e23 −1.98088
\(560\) −3.91524e22 1.66768e23i −0.171065 0.728643i
\(561\) −7.27864e22 −0.313232
\(562\) 3.96656e22 6.87028e22i 0.168134 0.291216i
\(563\) −1.10240e23 1.90942e23i −0.460276 0.797222i 0.538698 0.842499i \(-0.318916\pi\)
−0.998974 + 0.0452767i \(0.985583\pi\)
\(564\) 8.14572e20 + 1.41088e21i 0.00335009 + 0.00580253i
\(565\) −1.36612e23 + 2.36618e23i −0.553447 + 0.958598i
\(566\) −1.53039e23 −0.610749
\(567\) 4.02286e21 + 1.71352e22i 0.0158153 + 0.0673648i
\(568\) 4.53780e23 1.75746
\(569\) 8.59154e22 1.48810e23i 0.327806 0.567776i −0.654270 0.756261i \(-0.727024\pi\)
0.982076 + 0.188484i \(0.0603575\pi\)
\(570\) 7.69188e22 + 1.33227e23i 0.289132 + 0.500791i
\(571\) −1.35596e23 2.34859e23i −0.502158 0.869763i −0.999997 0.00249343i \(-0.999206\pi\)
0.497839 0.867269i \(-0.334127\pi\)
\(572\) −5.25938e21 + 9.10952e21i −0.0191897 + 0.0332376i
\(573\) 1.35995e23 0.488889
\(574\) 1.96519e22 1.84622e22i 0.0696069 0.0653931i
\(575\) 1.04222e23 0.363732
\(576\) 9.91565e22 1.71744e23i 0.340981 0.590596i
\(577\) 1.91479e23 + 3.31652e23i 0.648824 + 1.12380i 0.983404 + 0.181429i \(0.0580723\pi\)
−0.334580 + 0.942367i \(0.608594\pi\)
\(578\) −3.11557e22 5.39633e22i −0.104028 0.180182i
\(579\) 1.05891e23 1.83408e23i 0.348409 0.603463i
\(580\) 1.03434e22 0.0335370
\(581\) 1.37338e23 + 4.14331e22i 0.438828 + 0.132388i
\(582\) 1.33208e23 0.419455
\(583\) 9.76914e22 1.69207e23i 0.303161 0.525091i
\(584\) −2.37715e22 4.11735e22i −0.0727022 0.125924i
\(585\) 1.17349e23 + 2.03254e23i 0.353715 + 0.612652i
\(586\) −9.08554e21 + 1.57366e22i −0.0269911 + 0.0467500i
\(587\) −5.78587e22 −0.169412 −0.0847061 0.996406i \(-0.526995\pi\)
−0.0847061 + 0.996406i \(0.526995\pi\)
\(588\) 1.07715e22 5.35270e21i 0.0310862 0.0154478i
\(589\) −7.42496e22 −0.211210
\(590\) 1.14101e23 1.97628e23i 0.319923 0.554124i
\(591\) 1.07461e23 + 1.86127e23i 0.296999 + 0.514418i
\(592\) −8.25440e22 1.42970e23i −0.224880 0.389504i
\(593\) 2.89830e23 5.02001e23i 0.778357 1.34815i −0.154531 0.987988i \(-0.549387\pi\)
0.932888 0.360167i \(-0.117280\pi\)
\(594\) 1.71738e23 0.454656
\(595\) −3.22567e23 9.73141e22i −0.841833 0.253970i
\(596\) −1.96770e22 −0.0506252
\(597\) −6.02834e22 + 1.04414e23i −0.152903 + 0.264836i
\(598\) 2.65508e23 + 4.59873e23i 0.663922 + 1.14995i
\(599\) −3.66750e23 6.35229e23i −0.904153 1.56604i −0.822051 0.569414i \(-0.807170\pi\)
−0.0821020 0.996624i \(-0.526163\pi\)
\(600\) −4.55091e22 + 7.88241e22i −0.110615 + 0.191590i
\(601\) −3.70541e23 −0.887979 −0.443990 0.896032i \(-0.646437\pi\)
−0.443990 + 0.896032i \(0.646437\pi\)
\(602\) −4.33683e23 + 4.07429e23i −1.02471 + 0.962679i
\(603\) −2.76541e23 −0.644261
\(604\) 5.13436e21 8.89298e21i 0.0117943 0.0204284i
\(605\) 1.35644e23 + 2.34943e23i 0.307242 + 0.532159i
\(606\) 1.69387e23 + 2.93387e23i 0.378323 + 0.655274i
\(607\) 5.73587e22 9.93482e22i 0.126327 0.218804i −0.795924 0.605397i \(-0.793015\pi\)
0.922251 + 0.386592i \(0.126348\pi\)
\(608\) −6.78511e22 −0.147359
\(609\) −4.54117e22 1.93429e23i −0.0972570 0.414262i
\(610\) −5.98296e23 −1.26361
\(611\) −6.33421e22 + 1.09712e23i −0.131930 + 0.228509i
\(612\) −1.01874e22 1.76450e22i −0.0209255 0.0362440i
\(613\) 2.07779e23 + 3.59884e23i 0.420908 + 0.729035i 0.996029 0.0890343i \(-0.0283781\pi\)
−0.575120 + 0.818069i \(0.695045\pi\)
\(614\) −3.77258e22 + 6.53430e22i −0.0753715 + 0.130547i
\(615\) 2.36293e22 0.0465599
\(616\) 5.79159e22 + 2.46691e23i 0.112554 + 0.479420i
\(617\) −1.53976e23 −0.295141 −0.147571 0.989052i \(-0.547145\pi\)
−0.147571 + 0.989052i \(0.547145\pi\)
\(618\) −3.73574e22 + 6.47049e22i −0.0706276 + 0.122331i
\(619\) 2.04273e23 + 3.53812e23i 0.380927 + 0.659784i 0.991195 0.132411i \(-0.0422717\pi\)
−0.610268 + 0.792195i \(0.708938\pi\)
\(620\) 2.12905e21 + 3.68763e21i 0.00391613 + 0.00678293i
\(621\) −2.69620e23 + 4.66995e23i −0.489185 + 0.847294i
\(622\) 3.05489e23 0.546735
\(623\) 4.45252e23 4.18297e23i 0.786062 0.738476i
\(624\) −4.36495e23 −0.760169
\(625\) 1.46873e23 2.54391e23i 0.252326 0.437041i
\(626\) −3.42681e23 5.93540e23i −0.580775 1.00593i
\(627\) −1.07096e23 1.85496e23i −0.179060 0.310142i
\(628\) 3.39657e22 5.88304e22i 0.0560253 0.0970386i
\(629\) −3.24704e23 −0.528393
\(630\) 2.99422e23 + 9.03316e22i 0.480717 + 0.145026i
\(631\) 9.38758e23 1.48698 0.743489 0.668749i \(-0.233170\pi\)
0.743489 + 0.668749i \(0.233170\pi\)
\(632\) −5.00390e23 + 8.66701e23i −0.782012 + 1.35449i
\(633\) 1.80558e23 + 3.12735e23i 0.278409 + 0.482219i
\(634\) −4.68416e23 8.11321e23i −0.712645 1.23434i
\(635\) 4.42175e23 7.65869e23i 0.663769 1.14968i
\(636\) −2.96363e22 −0.0438974
\(637\) 7.79269e23 + 5.17269e23i 1.13894 + 0.756016i
\(638\) 2.31542e23 0.333930
\(639\) −3.89899e23 + 6.75326e23i −0.554875 + 0.961072i
\(640\) −2.56615e23 4.44471e23i −0.360373 0.624185i
\(641\) 3.68348e23 + 6.37997e23i 0.510463 + 0.884148i 0.999926 + 0.0121244i \(0.00385940\pi\)
−0.489463 + 0.872024i \(0.662807\pi\)
\(642\) 3.18243e23 5.51213e23i 0.435222 0.753827i
\(643\) 3.74387e23 0.505275 0.252638 0.967561i \(-0.418702\pi\)
0.252638 + 0.967561i \(0.418702\pi\)
\(644\) −4.21362e22 1.27119e22i −0.0561210 0.0169309i
\(645\) −5.21458e23 −0.685428
\(646\) 5.19253e23 8.99373e23i 0.673601 1.16671i
\(647\) −2.66734e23 4.61997e23i −0.341501 0.591498i 0.643210 0.765690i \(-0.277602\pi\)
−0.984712 + 0.174192i \(0.944269\pi\)
\(648\) 2.81224e22 + 4.87093e22i 0.0355356 + 0.0615495i
\(649\) −1.58865e23 + 2.75163e23i −0.198130 + 0.343171i
\(650\) −3.91512e23 −0.481927
\(651\) 5.96142e22 5.60052e22i 0.0724287 0.0680440i
\(652\) −2.21743e21 −0.00265916
\(653\) 2.80024e23 4.85016e23i 0.331462 0.574109i −0.651337 0.758789i \(-0.725791\pi\)
0.982799 + 0.184680i \(0.0591248\pi\)
\(654\) −2.06102e23 3.56980e23i −0.240809 0.417093i
\(655\) 2.31489e23 + 4.00950e23i 0.266980 + 0.462423i
\(656\) 4.05505e22 7.02354e22i 0.0461650 0.0799602i
\(657\) 8.17004e22 0.0918160
\(658\) 3.85842e22 + 1.64348e23i 0.0428045 + 0.182324i
\(659\) −2.69931e23 −0.295615 −0.147807 0.989016i \(-0.547222\pi\)
−0.147807 + 0.989016i \(0.547222\pi\)
\(660\) −6.14180e21 + 1.06379e22i −0.00664006 + 0.0115009i
\(661\) −3.87591e23 6.71328e23i −0.413677 0.716510i 0.581611 0.813467i \(-0.302422\pi\)
−0.995289 + 0.0969569i \(0.969089\pi\)
\(662\) −4.62948e22 8.01850e22i −0.0487798 0.0844890i
\(663\) −4.29261e23 + 7.43501e23i −0.446535 + 0.773422i
\(664\) 4.58405e23 0.470783
\(665\) −2.26613e23 9.65247e23i −0.229774 0.978711i
\(666\) 3.01406e23 0.301731
\(667\) −3.63509e23 + 6.29616e23i −0.359290 + 0.622309i
\(668\) 2.99167e22 + 5.18173e22i 0.0291954 + 0.0505679i
\(669\) −1.69462e22 2.93516e22i −0.0163286 0.0282820i
\(670\) −4.04174e23 + 7.00050e23i −0.384532 + 0.666029i
\(671\) 8.33024e23 0.782557
\(672\) 5.44768e22 5.11789e22i 0.0505328 0.0474736i
\(673\) 1.04442e24 0.956635 0.478318 0.878187i \(-0.341247\pi\)
0.478318 + 0.878187i \(0.341247\pi\)
\(674\) −2.42986e23 + 4.20864e23i −0.219772 + 0.380656i
\(675\) −1.98788e23 3.44310e23i −0.177545 0.307516i
\(676\) 2.88390e22 + 4.99506e22i 0.0254351 + 0.0440548i
\(677\) −1.13538e23 + 1.96653e23i −0.0988864 + 0.171276i −0.911224 0.411911i \(-0.864861\pi\)
0.812338 + 0.583187i \(0.198195\pi\)
\(678\) 9.27736e23 0.797943
\(679\) −8.21944e23 2.47969e23i −0.698150 0.210622i
\(680\) −1.07666e24 −0.903134
\(681\) −6.67512e23 + 1.15617e24i −0.552979 + 0.957788i
\(682\) 4.76601e22 + 8.25498e22i 0.0389931 + 0.0675381i
\(683\) 6.98898e23 + 1.21053e24i 0.564726 + 0.978134i 0.997075 + 0.0764275i \(0.0243514\pi\)
−0.432349 + 0.901706i \(0.642315\pi\)
\(684\) 2.99789e22 5.19249e22i 0.0239243 0.0414380i
\(685\) −2.24396e23 −0.176866
\(686\) 1.22880e24 2.08640e23i 0.956590 0.162421i
\(687\) 1.17140e24 0.900682
\(688\) −8.94880e23 + 1.54998e24i −0.679615 + 1.17713i
\(689\) −1.15228e24 1.99580e24i −0.864358 1.49711i
\(690\) 3.10054e23 + 5.37030e23i 0.229731 + 0.397907i
\(691\) −5.58627e23 + 9.67570e23i −0.408845 + 0.708140i −0.994761 0.102232i \(-0.967402\pi\)
0.585916 + 0.810372i \(0.300735\pi\)
\(692\) −5.34476e22 −0.0386390
\(693\) −4.16893e23 1.25771e23i −0.297709 0.0898149i
\(694\) −2.39712e24 −1.69096
\(695\) −1.29244e23 + 2.23857e23i −0.0900614 + 0.155991i
\(696\) −3.17457e23 5.49852e23i −0.218528 0.378501i
\(697\) −7.97568e22 1.38143e23i −0.0542362 0.0939398i
\(698\) −4.53615e23 + 7.85685e23i −0.304731 + 0.527810i
\(699\) −3.34764e23 −0.222169
\(700\) 2.36500e22 2.22182e22i 0.0155059 0.0145672i
\(701\) 6.20491e23 0.401913 0.200957 0.979600i \(-0.435595\pi\)
0.200957 + 0.979600i \(0.435595\pi\)
\(702\) 1.01283e24 1.75428e24i 0.648146 1.12262i
\(703\) −4.77761e23 8.27506e23i −0.302058 0.523180i
\(704\) 4.03554e23 + 6.98976e23i 0.252077 + 0.436611i
\(705\) −7.39696e22 + 1.28119e23i −0.0456505 + 0.0790690i
\(706\) 2.18477e24 1.33219
\(707\) −4.99036e23 2.12562e24i −0.300654 1.28062i
\(708\) 4.81944e22 0.0286889
\(709\) 4.01310e23 6.95090e23i 0.236041 0.408835i −0.723534 0.690289i \(-0.757483\pi\)
0.959575 + 0.281454i \(0.0908167\pi\)
\(710\) 1.13970e24 + 1.97402e24i 0.662363 + 1.14725i
\(711\) −8.59897e23 1.48938e24i −0.493804 0.855294i
\(712\) 9.76103e23 1.69066e24i 0.553880 0.959348i
\(713\) −2.99295e23 −0.167818
\(714\) 2.61479e23 + 1.11376e24i 0.144878 + 0.617102i
\(715\) −9.55187e23 −0.522982
\(716\) 4.85974e21 8.41731e21i 0.00262937 0.00455421i
\(717\) −2.05965e23 3.56742e23i −0.110124 0.190740i
\(718\) −1.08350e23 1.87667e23i −0.0572493 0.0991587i
\(719\) −7.93157e23 + 1.37379e24i −0.414156 + 0.717339i −0.995339 0.0964335i \(-0.969256\pi\)
0.581184 + 0.813772i \(0.302590\pi\)
\(720\) 9.40684e23 0.485420
\(721\) 3.50958e23 3.29712e23i 0.178980 0.168145i
\(722\) 1.13092e24 0.569988
\(723\) 7.89734e23 1.36786e24i 0.393374 0.681344i
\(724\) 9.60407e22 + 1.66347e23i 0.0472800 + 0.0818913i
\(725\) −2.68011e23 4.64209e23i −0.130401 0.225861i
\(726\) 4.60583e23 7.97753e23i 0.221486 0.383625i
\(727\) −8.99415e23 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(728\) 2.86146e24 + 8.63265e23i 1.34422 + 0.405534i
\(729\) 1.15112e24 0.534488
\(730\) 1.19408e23 2.06821e23i 0.0548011 0.0949183i
\(731\) 1.76010e24 + 3.04858e24i 0.798434 + 1.38293i
\(732\) −6.31779e22 1.09427e23i −0.0283283 0.0490661i
\(733\) 4.79871e23 8.31161e23i 0.212687 0.368385i −0.739868 0.672753i \(-0.765112\pi\)
0.952555 + 0.304368i \(0.0984452\pi\)
\(734\) −2.32598e24 −1.01903
\(735\) 9.10013e23 + 6.04055e23i 0.394099 + 0.261598i
\(736\) −2.73503e23 −0.117085
\(737\) 5.62742e23 9.74698e23i 0.238142 0.412474i
\(738\) 7.40340e22 + 1.28231e23i 0.0309708 + 0.0536430i
\(739\) 1.41321e24 + 2.44776e24i 0.584427 + 1.01226i 0.994947 + 0.100405i \(0.0320138\pi\)
−0.410520 + 0.911852i \(0.634653\pi\)
\(740\) −2.73989e22 + 4.74562e22i −0.0112012 + 0.0194010i
\(741\) −2.52641e24 −1.02106
\(742\) −2.94011e24 8.86990e23i −1.17471 0.354393i
\(743\) 5.12221e23 0.202326 0.101163 0.994870i \(-0.467744\pi\)
0.101163 + 0.994870i \(0.467744\pi\)
\(744\) 1.30689e23 2.26360e23i 0.0510352 0.0883955i
\(745\) −8.93415e23 1.54744e24i −0.344925 0.597428i
\(746\) −1.27355e24 2.20585e24i −0.486111 0.841969i
\(747\) −3.93874e23 + 6.82209e23i −0.148639 + 0.257450i
\(748\) 8.29225e22 0.0309392
\(749\) −2.98977e24 + 2.80877e24i −1.10292 + 1.03615i
\(750\) −1.71554e24 −0.625719
\(751\) −1.27581e24 + 2.20977e24i −0.460094 + 0.796906i −0.998965 0.0454821i \(-0.985518\pi\)
0.538871 + 0.842388i \(0.318851\pi\)
\(752\) 2.53880e23 + 4.39733e23i 0.0905267 + 0.156797i
\(753\) −9.40573e22 1.62912e23i −0.0331616 0.0574375i
\(754\) 1.36553e24 2.36517e24i 0.476042 0.824528i
\(755\) 9.32481e23 0.321433
\(756\) 3.83731e22 + 1.63449e23i 0.0130795 + 0.0557116i
\(757\) −2.71960e24 −0.916620 −0.458310 0.888792i \(-0.651545\pi\)
−0.458310 + 0.888792i \(0.651545\pi\)
\(758\) −1.79403e24 + 3.10735e24i −0.597918 + 1.03563i
\(759\) −4.31697e23 7.47721e23i −0.142273 0.246425i
\(760\) −1.58417e24 2.74386e24i −0.516280 0.894224i
\(761\) 1.52735e24 2.64545e24i 0.492231 0.852569i −0.507729 0.861517i \(-0.669515\pi\)
0.999960 + 0.00894781i \(0.00284821\pi\)
\(762\) −3.00283e24 −0.957003
\(763\) 6.07204e23 + 2.58636e24i 0.191371 + 0.815136i
\(764\) −1.54934e23 −0.0482895
\(765\) 9.25093e23 1.60231e24i 0.285143 0.493883i
\(766\) 2.79961e24 + 4.84907e24i 0.853401 + 1.47813i
\(767\) 1.87383e24 + 3.24557e24i 0.564897 + 0.978431i
\(768\) 1.74033e23 3.01434e23i 0.0518873 0.0898715i
\(769\) 2.84393e24 0.838582 0.419291 0.907852i \(-0.362279\pi\)
0.419291 + 0.907852i \(0.362279\pi\)
\(770\) −9.27688e23 + 8.71527e23i −0.270540 + 0.254162i
\(771\) 7.51908e23 0.216871
\(772\) −1.20637e23 + 2.08949e23i −0.0344138 + 0.0596065i
\(773\) 1.68100e24 + 2.91158e24i 0.474288 + 0.821490i 0.999567 0.0294399i \(-0.00937237\pi\)
−0.525279 + 0.850930i \(0.676039\pi\)
\(774\) −1.63381e24 2.82983e24i −0.455934 0.789701i
\(775\) 1.10333e23 1.91103e23i 0.0304539 0.0527477i
\(776\) −2.74347e24 −0.748989
\(777\) 1.00776e24 + 3.04028e23i 0.272132 + 0.0820985i
\(778\) 2.74890e24 0.734230
\(779\) 2.34704e23 4.06520e23i 0.0620087 0.107402i
\(780\) 7.24429e22 + 1.25475e23i 0.0189318 + 0.0327908i
\(781\) −1.58684e24 2.74849e24i −0.410203 0.710493i
\(782\) 2.09308e24 3.62531e24i 0.535214 0.927018i
\(783\) 2.77336e24 0.701505
\(784\) 3.35717e24 1.66829e24i 0.840015 0.417431i
\(785\) 6.16871e24 1.52687
\(786\) 7.86026e23 1.36144e24i 0.192462 0.333354i
\(787\) −5.70589e23 9.88289e23i −0.138210 0.239386i 0.788609 0.614894i \(-0.210801\pi\)
−0.926819 + 0.375509i \(0.877468\pi\)
\(788\) −1.22425e23 2.12047e23i −0.0293358 0.0508112i
\(789\) −2.02834e24 + 3.51320e24i −0.480825 + 0.832813i
\(790\) −5.02708e24 −1.17892
\(791\) −5.72447e24 1.72699e24i −1.32811 0.400674i
\(792\) −1.39150e24 −0.319388
\(793\) 4.91279e24 8.50920e24i 1.11559 1.93227i
\(794\) 2.56696e24 + 4.44610e24i 0.576693 + 0.998861i
\(795\) −1.34561e24 2.33066e24i −0.299087 0.518033i
\(796\) 6.86784e22 1.18954e23i 0.0151029 0.0261589i
\(797\) −2.54880e23 −0.0554549 −0.0277274 0.999616i \(-0.508827\pi\)
−0.0277274 + 0.999616i \(0.508827\pi\)
\(798\) −2.45368e24 + 2.30514e24i −0.528194 + 0.496218i
\(799\) 9.98689e23 0.212707
\(800\) 1.00825e23 1.74635e23i 0.0212474 0.0368015i
\(801\) 1.67739e24 + 2.90532e24i 0.349749 + 0.605783i
\(802\) 1.69045e24 + 2.92794e24i 0.348754 + 0.604060i
\(803\) −1.66255e23 + 2.87962e23i −0.0339385 + 0.0587832i
\(804\) −1.70717e23 −0.0344827
\(805\) −9.13460e23 3.89084e24i −0.182568 0.777640i
\(806\) 1.12431e24 0.222350
\(807\) 2.14334e24 3.71238e24i 0.419436 0.726485i
\(808\) −3.48858e24 6.04240e24i −0.675542 1.17007i
\(809\) −1.20865e23 2.09344e23i −0.0231600 0.0401143i 0.854213 0.519923i \(-0.174039\pi\)
−0.877373 + 0.479809i \(0.840706\pi\)
\(810\) −1.41263e23 + 2.44675e23i −0.0267859 + 0.0463945i
\(811\) 4.36045e24 0.818189 0.409095 0.912492i \(-0.365845\pi\)
0.409095 + 0.912492i \(0.365845\pi\)
\(812\) 5.17357e22 + 2.20366e23i 0.00960647 + 0.0409183i
\(813\) −1.98270e24 −0.364324
\(814\) −6.13341e23 + 1.06234e24i −0.111531 + 0.193177i
\(815\) −1.00680e23 1.74383e23i −0.0181177 0.0313808i
\(816\) 1.72051e24 + 2.98001e24i 0.306401 + 0.530702i
\(817\) −5.17952e24 + 8.97120e24i −0.912856 + 1.58111i
\(818\) −9.44555e24 −1.64749
\(819\) −3.74338e24 + 3.51676e24i −0.646175 + 0.607057i
\(820\) −2.69199e22 −0.00459891
\(821\) −1.96791e24 + 3.40852e24i −0.332727 + 0.576300i −0.983046 0.183362i \(-0.941302\pi\)
0.650319 + 0.759662i \(0.274635\pi\)
\(822\) 3.80971e23 + 6.59861e23i 0.0637501 + 0.110418i
\(823\) 1.90951e24 + 3.30737e24i 0.316245 + 0.547753i 0.979701 0.200462i \(-0.0642445\pi\)
−0.663456 + 0.748215i \(0.730911\pi\)
\(824\) 7.69388e23 1.33262e24i 0.126114 0.218436i
\(825\) 6.36570e23 0.103273
\(826\) 4.78119e24 + 1.44242e24i 0.767725 + 0.231612i
\(827\) 2.81100e23 0.0446749 0.0223375 0.999750i \(-0.492889\pi\)
0.0223375 + 0.999750i \(0.492889\pi\)
\(828\) 1.20843e23 2.09306e23i 0.0190092 0.0329248i
\(829\) −3.69730e24 6.40391e24i −0.575666 0.997083i −0.995969 0.0896994i \(-0.971409\pi\)
0.420303 0.907384i \(-0.361924\pi\)
\(830\) 1.15132e24 + 1.99415e24i 0.177432 + 0.307322i
\(831\) −8.84285e23 + 1.53163e24i −0.134891 + 0.233638i
\(832\) 9.51990e24 1.43742
\(833\) 4.59859e23 7.35906e24i 0.0687293 1.09987i
\(834\) 8.77700e23 0.129848
\(835\) −2.71667e24 + 4.70542e24i −0.397834 + 0.689069i
\(836\) 1.22010e23 + 2.11328e23i 0.0176865 + 0.0306339i
\(837\) 5.70861e23 + 9.88761e23i 0.0819151 + 0.141881i
\(838\) −7.32876e23 + 1.26938e24i −0.104101 + 0.180309i
\(839\) 4.36851e23 0.0614266 0.0307133 0.999528i \(-0.490222\pi\)
0.0307133 + 0.999528i \(0.490222\pi\)
\(840\) 3.34156e24 + 1.00810e24i 0.465130 + 0.140324i
\(841\) −3.51803e24 −0.484767
\(842\) 2.22527e24 3.85428e24i 0.303550 0.525764i
\(843\) 7.60704e23 + 1.31758e24i 0.102726 + 0.177927i
\(844\) −2.05702e23 3.56286e23i −0.0274996 0.0476308i
\(845\) −2.61881e24 + 4.53591e24i −0.346594 + 0.600319i
\(846\) −9.27030e23 −0.121463
\(847\) −4.32700e24 + 4.06505e24i −0.561277 + 0.527299i
\(848\) −9.23683e24 −1.18620
\(849\) 1.46749e24 2.54176e24i 0.186578 0.323162i
\(850\) 1.54320e24 + 2.67290e24i 0.194250 + 0.336451i
\(851\) −1.92582e24 3.33562e24i −0.240002 0.415696i
\(852\) −2.40697e23 + 4.16899e23i −0.0296985 + 0.0514393i
\(853\) 4.47276e24 0.546398 0.273199 0.961958i \(-0.411918\pi\)
0.273199 + 0.961958i \(0.411918\pi\)
\(854\) −2.99257e24 1.27467e25i −0.361954 1.54173i
\(855\) 5.44463e24 0.652014
\(856\) −6.55432e24 + 1.13524e25i −0.777143 + 1.34605i
\(857\) −3.67024e24 6.35704e24i −0.430881 0.746308i 0.566068 0.824358i \(-0.308464\pi\)
−0.996949 + 0.0780503i \(0.975131\pi\)
\(858\) 1.62168e24 + 2.80883e24i 0.188505 + 0.326500i
\(859\) −2.38320e23 + 4.12782e23i −0.0274295 + 0.0475093i −0.879414 0.476057i \(-0.842066\pi\)
0.851985 + 0.523567i \(0.175399\pi\)
\(860\) 5.94076e23 0.0677025
\(861\) 1.18189e23 + 5.03423e23i 0.0133368 + 0.0568076i
\(862\) 4.83032e24 0.539714
\(863\) 1.26362e24 2.18865e24i 0.139806 0.242150i −0.787617 0.616165i \(-0.788686\pi\)
0.927423 + 0.374014i \(0.122019\pi\)
\(864\) 5.21667e23 + 9.03553e23i 0.0571513 + 0.0989890i
\(865\) −2.42673e24 4.20322e24i −0.263260 0.455979i
\(866\) 7.81080e24 1.35287e25i 0.839060 1.45330i
\(867\) 1.19501e24 0.127118
\(868\) −6.79159e22 + 6.38044e22i −0.00715408 + 0.00672099i
\(869\) 6.99933e24 0.730110
\(870\) 1.59464e24 2.76199e24i 0.164721 0.285305i
\(871\) −6.63759e24 1.14966e25i −0.678978 1.17603i
\(872\) 4.24475e24 + 7.35211e24i 0.429993 + 0.744770i
\(873\) 2.35726e24 4.08289e24i 0.236476 0.409588i
\(874\) 1.23188e25 1.22383
\(875\) 1.05855e25 + 3.19350e24i 1.04146 + 0.314194i
\(876\) 5.04362e22 0.00491425
\(877\) −8.12881e24 + 1.40795e25i −0.784387 + 1.35860i 0.144977 + 0.989435i \(0.453689\pi\)
−0.929364 + 0.369163i \(0.879644\pi\)
\(878\) −4.09012e24 7.08429e24i −0.390870 0.677007i
\(879\) −1.74242e23 3.01796e23i −0.0164910 0.0285633i
\(880\) −1.91423e24 + 3.31554e24i −0.179428 + 0.310779i
\(881\) −1.08647e25 −1.00861 −0.504304 0.863526i \(-0.668251\pi\)
−0.504304 + 0.863526i \(0.668251\pi\)
\(882\) −4.26863e23 + 6.83103e24i −0.0392469 + 0.628063i
\(883\) −8.32880e24 −0.758432 −0.379216 0.925308i \(-0.623806\pi\)
−0.379216 + 0.925308i \(0.623806\pi\)
\(884\) 4.89039e23 8.47040e23i 0.0441061 0.0763940i
\(885\) 2.18822e24 + 3.79010e24i 0.195467 + 0.338558i
\(886\) −6.85105e24 1.18664e25i −0.606137 1.04986i
\(887\) 5.18561e24 8.98174e24i 0.454411 0.787063i −0.544243 0.838928i \(-0.683183\pi\)
0.998654 + 0.0518644i \(0.0165164\pi\)
\(888\) 3.36369e24 0.291948
\(889\) 1.85286e25 + 5.58981e24i 1.59286 + 0.480543i
\(890\) 9.80624e24 0.835002
\(891\) 1.96684e23 3.40667e23i 0.0165886 0.0287323i
\(892\) 1.93061e22 + 3.34391e22i 0.00161284 + 0.00279353i
\(893\) 1.46944e24 + 2.54515e24i 0.121595 + 0.210609i
\(894\) −3.03361e24 + 5.25437e24i −0.248651 + 0.430677i
\(895\) 8.82605e23 0.0716590
\(896\) 8.18592e24 7.69036e24i 0.658339 0.618484i
\(897\) −1.01838e25 −0.811286
\(898\) −4.72086e24 + 8.17677e24i −0.372540 + 0.645257i
\(899\) 7.69651e23 + 1.33307e24i 0.0601640 + 0.104207i
\(900\) 8.90960e22 + 1.54319e23i 0.00689917 + 0.0119497i
\(901\) −9.08374e24 + 1.57335e25i −0.696793 + 1.20688i
\(902\) −6.02617e23 −0.0457916
\(903\) −2.60824e24 1.11097e25i −0.196337 0.836289i
\(904\) −1.91070e25 −1.42482
\(905\) −8.72125e24 + 1.51056e25i −0.644267 + 1.11590i
\(906\) −1.58313e24 2.74206e24i −0.115858 0.200672i
\(907\) −1.13495e24 1.96579e24i −0.0822839 0.142520i 0.821947 0.569564i \(-0.192888\pi\)
−0.904231 + 0.427045i \(0.859555\pi\)
\(908\) 7.60469e23 1.31717e24i 0.0546200 0.0946046i
\(909\) 1.19899e25 0.853146
\(910\) 3.43143e24 + 1.46160e25i 0.241893 + 1.03033i
\(911\) −1.33907e25 −0.935186 −0.467593 0.883944i \(-0.654879\pi\)
−0.467593 + 0.883944i \(0.654879\pi\)
\(912\) −5.06302e24 + 8.76941e24i −0.350311 + 0.606756i
\(913\) −1.60301e24 2.77650e24i −0.109884 0.190325i
\(914\) 1.00696e25 + 1.74411e25i 0.683864 + 1.18449i
\(915\) 5.73705e24 9.93686e24i 0.386020 0.668606i
\(916\) −1.33452e24 −0.0889640
\(917\) −7.38440e24 + 6.93737e24i −0.487726 + 0.458200i
\(918\) −1.59689e25 −1.04499
\(919\) 6.74207e24 1.16776e25i 0.437131 0.757132i −0.560336 0.828265i \(-0.689328\pi\)
0.997467 + 0.0711329i \(0.0226614\pi\)
\(920\) −6.38567e24 1.10603e25i −0.410214 0.710511i
\(921\) −7.23504e23 1.25315e24i −0.0460505 0.0797617i
\(922\) −6.18831e23 + 1.07185e24i −0.0390264 + 0.0675958i
\(923\) −3.74338e25 −2.33910
\(924\) −2.57361e23 7.76424e22i −0.0159342 0.00480714i
\(925\) 2.83977e24 0.174212
\(926\) 1.01950e25 1.76582e25i 0.619715 1.07338i
\(927\) 1.32216e24 + 2.29004e24i 0.0796352 + 0.137932i
\(928\) 7.03325e23 + 1.21820e24i 0.0419757 + 0.0727041i
\(929\) 1.46979e25 2.54575e25i 0.869203 1.50550i 0.00639141 0.999980i \(-0.497966\pi\)
0.862812 0.505525i \(-0.168701\pi\)
\(930\) 1.31294e24 0.0769381
\(931\) 1.94312e25 9.65598e24i 1.12830 0.560692i
\(932\) 3.81383e23 0.0219445
\(933\) −2.92932e24 + 5.07374e24i −0.167022 + 0.289290i
\(934\) 5.79954e24 + 1.00451e25i 0.327676 + 0.567552i
\(935\) 3.76501e24 + 6.52119e24i 0.210798 + 0.365113i
\(936\) −8.20642e24 + 1.42139e25i −0.455312 + 0.788623i
\(937\) 3.06390e25 1.68456 0.842282 0.539038i \(-0.181212\pi\)
0.842282 + 0.539038i \(0.181212\pi\)
\(938\) −1.69362e25 5.10942e24i −0.922767 0.278386i
\(939\) 1.31438e25 0.709683
\(940\) 8.42704e22 1.45961e23i 0.00450909 0.00780996i
\(941\) 1.26260e25 + 2.18689e25i 0.669505 + 1.15962i 0.978043 + 0.208405i \(0.0668272\pi\)
−0.308537 + 0.951212i \(0.599839\pi\)
\(942\) −1.04730e25 1.81398e25i −0.550349 0.953233i
\(943\) 9.46076e23 1.63865e24i 0.0492694 0.0853370i
\(944\) 1.50209e25 0.775236
\(945\) −1.11116e25 + 1.04389e25i −0.568338 + 0.533932i
\(946\) 1.32987e25 0.674118
\(947\) 1.20821e24 2.09267e24i 0.0606968 0.105130i −0.834080 0.551643i \(-0.814001\pi\)
0.894777 + 0.446513i \(0.147334\pi\)
\(948\) −5.30841e23 9.19443e23i −0.0264298 0.0457777i
\(949\) 1.96099e24 + 3.39653e24i 0.0967637 + 0.167600i
\(950\) −4.54125e24 + 7.86568e24i −0.222088 + 0.384668i
\(951\) 1.79665e25 0.870823
\(952\) −5.38526e24 2.29383e25i −0.258698 1.10191i
\(953\) 2.80905e25 1.33743 0.668713 0.743521i \(-0.266846\pi\)
0.668713 + 0.743521i \(0.266846\pi\)
\(954\) 8.43196e24 1.46046e25i 0.397894 0.689172i
\(955\) −7.03461e24 1.21843e25i −0.329012 0.569865i
\(956\) 2.34647e23 + 4.06421e23i 0.0108774 + 0.0188401i
\(957\) −2.22026e24 + 3.84559e24i −0.102012 + 0.176690i
\(958\) −1.79684e25 −0.818280
\(959\) −1.12239e24 4.78077e24i −0.0506623 0.215794i
\(960\) 1.11171e25 0.497379
\(961\) 1.09582e25 1.89802e25i 0.485949 0.841689i
\(962\) 7.23440e24 + 1.25303e25i 0.317991 + 0.550776i
\(963\) −1.12633e25 1.95086e25i −0.490729 0.849968i
\(964\) −8.99711e23 + 1.55835e24i −0.0388551 + 0.0672991i
\(965\) −2.19095e25 −0.937888
\(966\) −9.89061e24 + 9.29185e24i −0.419679 + 0.394273i
\(967\) −1.59698e25 −0.671699 −0.335850 0.941916i \(-0.609023\pi\)
−0.335850 + 0.941916i \(0.609023\pi\)
\(968\) −9.48586e24 + 1.64300e25i −0.395491 + 0.685010i
\(969\) 9.95822e24 + 1.72481e25i 0.411557 + 0.712837i
\(970\) −6.89044e24 1.19346e25i −0.282284 0.488931i
\(971\) −1.35692e25 + 2.35025e25i −0.551049 + 0.954444i 0.447151 + 0.894459i \(0.352439\pi\)
−0.998199 + 0.0599856i \(0.980895\pi\)
\(972\) −1.48121e24 −0.0596284
\(973\) −5.41573e24 1.63385e24i −0.216122 0.0652009i
\(974\) 6.96322e24 0.275460
\(975\) 3.75420e24 6.50246e24i 0.147224 0.254999i
\(976\) −1.96908e25 3.41055e25i −0.765492 1.32587i
\(977\) 1.08715e25 + 1.88300e25i 0.418973 + 0.725683i 0.995836 0.0911580i \(-0.0290568\pi\)
−0.576863 + 0.816841i \(0.695723\pi\)
\(978\) −3.41861e23 + 5.92121e23i −0.0130608 + 0.0226219i
\(979\) −1.36535e25 −0.517119
\(980\) −1.03674e24 6.88175e23i −0.0389268 0.0258391i
\(981\) −1.45888e25 −0.543041
\(982\) 1.27194e25 2.20306e25i 0.469374 0.812979i
\(983\) 1.40092e25 + 2.42646e25i 0.512517 + 0.887706i 0.999895 + 0.0145143i \(0.00462020\pi\)
−0.487378 + 0.873191i \(0.662046\pi\)
\(984\) 8.26221e23 + 1.43106e24i 0.0299666 + 0.0519037i
\(985\) 1.11172e25 1.92555e25i 0.399748 0.692385i
\(986\) −2.15297e25 −0.767512
\(987\) −3.09957e24 9.35097e23i −0.109548 0.0330492i
\(988\) 2.87824e24 0.100854
\(989\) −2.08783e25 + 3.61623e25i −0.725315 + 1.25628i
\(990\) −3.49486e24 6.05327e24i −0.120373 0.208493i
\(991\) 1.27277e25 + 2.20451e25i 0.434635 + 0.752810i 0.997266 0.0738981i \(-0.0235440\pi\)
−0.562631 + 0.826708i \(0.690211\pi\)
\(992\) −2.89541e23 + 5.01501e23i −0.00980306 + 0.0169794i
\(993\) 1.77568e24 0.0596068
\(994\) −3.63561e25 + 3.41552e25i −1.21002 + 1.13677i
\(995\) 1.24731e25 0.411602
\(996\) −2.43150e23 + 4.21149e23i −0.00795556 + 0.0137794i
\(997\) 1.05853e25 + 1.83342e25i 0.343394 + 0.594776i 0.985061 0.172208i \(-0.0550900\pi\)
−0.641666 + 0.766984i \(0.721757\pi\)
\(998\) 4.37392e24 + 7.57586e24i 0.140689 + 0.243681i
\(999\) −7.34644e24 + 1.27244e25i −0.234299 + 0.405818i
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 7.18.c.a.2.3 20
7.2 even 3 49.18.a.f.1.8 10
7.4 even 3 inner 7.18.c.a.4.3 yes 20
7.5 odd 6 49.18.a.g.1.8 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.18.c.a.2.3 20 1.1 even 1 trivial
7.18.c.a.4.3 yes 20 7.4 even 3 inner
49.18.a.f.1.8 10 7.2 even 3
49.18.a.g.1.8 10 7.5 odd 6